Finite Group Databasebeta

← #14577659

Subgroups — #14577659

Order 2432.

1252 conjugacy classes of subgroups.

The subgroup lattice has 1096 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927256C211yesmaximal, characteristic, complemented
2#11927248C211yesmaximal, characteristic, complemented
3#11927245C211yesmaximal, characteristic, complemented
4#11927245C211yesmaximal, characteristic, complemented
5#11927239C211yesmaximal, characteristic, complemented
6#11927237C211yesmaximal, characteristic, complemented
7#11927212C211yesmaximal, characteristic, complemented
8#11927187C211yesmaximal, characteristic, complemented
9#11927186C211yesmaximal, characteristic, complemented
10#11927185C211yesmaximal, characteristic, complemented
11#11927183C211yesmaximal, characteristic, complemented
12#11927181C211yesmaximal, characteristic, complemented
13#11927181C211yesmaximal, characteristic, complemented
14#11927178C211yesmaximal, characteristic, complemented
15#11927176C211yesmaximal, characteristic, complemented
16#11927176C211yesmaximal, characteristic, complemented
17#11927146C211yesmaximal, characteristic, complemented
18#11927144C211yesmaximal, characteristic, complemented
19#11927133C211yesmaximal, characteristic, complemented
20#11927128C211yesmaximal, characteristic, complemented
21#11927127C211yesmaximal, characteristic, complemented
22#11927093C211yesmaximal, characteristic, complemented
23#11927077C211yesmaximal, characteristic, complemented
24#11927053C211yesmaximal, characteristic, complemented
25#11927052C211yesmaximal, characteristic, complemented
26C2×#10597330C211yesmaximal, characteristic, complemented
27#121×D19C211yesmaximal, characteristic, complemented
28#11927017C211yesmaximal, characteristic, complemented
29#11927016C211yesmaximal, characteristic, complemented
30C4×D4×D19C211yesmaximal, characteristic, complemented
31C19×#538C211yesmaximal, characteristic, complemented
32C22×C22⋊D19C2211yescharacteristic
33C22×C22⋊D19C2211yescharacteristic, complemented
34C22×C22⋊D19C2211yescharacteristic, complemented
35C2×#64545C2211yescharacteristic, complemented
36C2×#64543C2211yescharacteristic, complemented
37C2×#64543C2211yescharacteristic, complemented
38C2×D4×D19C2211yescharacteristic
39C2×D4×D19C2211yescharacteristic
40C2×D4×D19C2211yescharacteristic, complemented
41C2×D4×D19C2211yescharacteristic, complemented
42C2×D4×D19C2211yescharacteristic, complemented
43C2×#64541C2211yescharacteristic, complemented
44C22×D76C2211yescharacteristic, complemented
45C22×C4×D19C2211yescharacteristic, complemented
46C22×C4×D19C2211yescharacteristic, complemented
47C19×#126C2211yescharacteristic, complemented
48C19×#126C2211yescharacteristic, complemented
49C19×#124C2211yescharacteristic, complemented
50C19×#124C2211yescharacteristic, complemented
51C19×#123C2211yescharacteristic, complemented
52C19×#123C2211yescharacteristic, complemented
53C19×C22⋊Q8C2211yescharacteristic, complemented
54C19×#121C2211yescharacteristic, complemented
55C19×#121C2211yescharacteristic, complemented
56C19×#121C2211yescharacteristic, complemented
57C19×#120C2211yescharacteristic, complemented
58C19×#120C2211yescharacteristic, complemented
59C4×D4×C19C2211yescharacteristic, complemented
60C4×D4×C19C2211yescharacteristic, complemented
61C2×C22⋊C4×C19C2211yescharacteristic, complemented
62C2×C22⋊Dic19C2211yescharacteristic, complemented
63#10597393C2211yescharacteristic, complemented
64#10597392C2211yescharacteristic, complemented
65#10597390C2211yescharacteristic, complemented
66#10597386C2211yescharacteristic, complemented
67#10597386C2211yescharacteristic, complemented
68#10597386C2211yescharacteristic, complemented
69#10597385C2211yescharacteristic, complemented
70#10597385C2211yescharacteristic, complemented
71#10597385C2211yescharacteristic, complemented
72#10597385C2211yescharacteristic, complemented
73#10597385C2211yescharacteristic, complemented
74#10597385C2211yescharacteristic, complemented
75#10597385C2211yescharacteristic, complemented
76#10597385C2211yescharacteristic, complemented
77#10597385C2211yescharacteristic, complemented
78#10597384C2211yescharacteristic, complemented
79#10597384C2211yescharacteristic, complemented
80#10597383C2211yescharacteristic, complemented
81#10597383C2211yescharacteristic, complemented
82#10597383C2211yescharacteristic, complemented
83#10597383C2211yescharacteristic, complemented
84#10597381C2211yescharacteristic, complemented
85D4×Dic19C2211yescharacteristic, complemented
86D4×Dic19C2211yescharacteristic, complemented
87#10597376C2211yescharacteristic, complemented
88#10597375C2211yescharacteristic, complemented
89C4×C22⋊D19C2211yescharacteristic
90C4×C22⋊D19C2211yescharacteristic
91C4×C22⋊D19C2211yescharacteristic, complemented
92C4×C22⋊D19C2211yescharacteristic, complemented
93C4×C22⋊D19C2211yescharacteristic, complemented
94C4×C22⋊D19C2211yescharacteristic, complemented
95C4×C22⋊D19C2211yescharacteristic, complemented
96C2×(C2×D19)⋊C4C2211yescharacteristic, complemented
97C2×(C2×D19)⋊C4C2211yescharacteristic, complemented
98C2×Dic19⋊C4C2211yescharacteristic, complemented
99#10597344C2211yescharacteristic, complemented
100#10597344C2211yescharacteristic, complemented
101#10597342C2211yescharacteristic, complemented
102#10597342C2211yescharacteristic, complemented
103#10597342C2211yescharacteristic, complemented
104#10597341C2211yescharacteristic, complemented
105#10597341C2211yescharacteristic, complemented
106#10597341C2211yescharacteristic, complemented
107#10597341C2211yescharacteristic, complemented
108#10597340C2211yescharacteristic, complemented
109#10597340C2211yescharacteristic, complemented
110#10597340C2211yescharacteristic, complemented
111#10597340C2211yescharacteristic, complemented
112#10597339C2211yescharacteristic, complemented
113#10597339C2211yescharacteristic, complemented
114#10597339C2211yescharacteristic, complemented
115#10597339C2211yescharacteristic, complemented
116#10597338C2211yescharacteristic, complemented
117C4⋊C4×D19C2211yescharacteristic, complemented
118C4⋊C4×D19C2211yescharacteristic, complemented
119#10597335C2211yescharacteristic, complemented
120#10597335C2211yescharacteristic, complemented
121#10597335C2211yescharacteristic, complemented
122#10597333C2211yescharacteristic, complemented
123#10597332C2211yescharacteristic, complemented
124#10597332C2211yescharacteristic, complemented
125#10597331C2211yescharacteristic, complemented
126#10597331C2211yescharacteristic, complemented
127#10597331C2211yescharacteristic, complemented
128#10597330C2211yescharacteristic
129#10597330C2211yescharacteristic, complemented
130#10597330C2211yescharacteristic, complemented
131#10597330C2211yescharacteristic, complemented
132#10597330C2211yescharacteristic, complemented
133#10597330C2211yescharacteristic, complemented
134#10597330C2211yescharacteristic, complemented
135#10597330C2211yescharacteristic, complemented
136#10597330C2211yescharacteristic, complemented
137#10597330C2211yescharacteristic, complemented
138#10597330C2211yescharacteristic, complemented
139#10597330C2211yescharacteristic, complemented
140#10597330C2211yescharacteristic, complemented
141#10597330C2211yescharacteristic, complemented
142#10597330C2211yescharacteristic, complemented
143#10597330C2211yescharacteristic, complemented
144#10597329C2211yescharacteristic, complemented
145#10597329C2211yescharacteristic, complemented
146#10597329C2211yescharacteristic, complemented
147#10597329C2211yescharacteristic, complemented
148#10597328C2211yescharacteristic, complemented
149#10597328C2211yescharacteristic, complemented
150#10597328C2211yescharacteristic, complemented
151#10597328C2211yescharacteristic, complemented
152#10597328C2211yescharacteristic, complemented
153#10597328C2211yescharacteristic, complemented
154(C22⋊D19)⋊C4C2211yescharacteristic
155(C22⋊D19)⋊C4C2211yescharacteristic
156(C22⋊D19)⋊C4C2211yescharacteristic, complemented
157(C22⋊D19)⋊C4C2211yescharacteristic, complemented
158(C22⋊D19)⋊C4C2211yescharacteristic, complemented
159(C22⋊D19)⋊C4C2211yescharacteristic, complemented
160(C22⋊D19)⋊C4C2211yescharacteristic, complemented
161(C22⋊D19)⋊C4C2211yescharacteristic, complemented
162(C22⋊D19)⋊C4C2211yescharacteristic, complemented
163(C22⋊D19)⋊C4C2211yescharacteristic, complemented
164(C22⋊D19)⋊C4C2211yescharacteristic, complemented
165(C22⋊D19)⋊C4C2211yescharacteristic, complemented
166(C22⋊D19)⋊C4C2211yescharacteristic, complemented
167C22⋊C4×D19C2211yescharacteristic, complemented
168C22⋊C4×D19C2211yescharacteristic, complemented
169C22⋊C4×D19C2211yescharacteristic, complemented
170C22⋊C4×D19C2211yescharacteristic, complemented
171C22⋊C4×D19C2211yescharacteristic, complemented
172C22⋊C4×D19C2211yescharacteristic, complemented
173#10597325C2211yescharacteristic, complemented
174#10597324C2211yescharacteristic, complemented
175#10597324C2211yescharacteristic, complemented
176#10597323C2211yescharacteristic, complemented
177#10597323C2211yescharacteristic, complemented
178#10597323C2211yescharacteristic, complemented
179#10597322C2211yescharacteristic, complemented
180#10597321C2211yescharacteristic, complemented
181C4×D76C2211yescharacteristic, complemented
182C4×D76C2211yescharacteristic, complemented
183C4×D76C2211yescharacteristic, complemented
184#10597318C2211yescharacteristic, complemented
185#10597318C2211yescharacteristic, complemented
186C42×D19C2211yescharacteristic, complemented
187C24×C19C2311yescharacteristic
188C23×D19C2311yescharacteristic
189C23×D19C2311yescharacteristic
190C23×D19C2311yescharacteristic
191C23×D19C2311yescharacteristic
192C23×D19C2311yescharacteristic
193C2×Q8×C19C2311yescharacteristic
194C2×D4×C19C2311yescharacteristic
195C2×D4×C19C2311yescharacteristic
196C2×D4×C19C2311yescharacteristic
197C2×D4×C19C2311yescharacteristic
198C2×D4×C19C2311yescharacteristic
199C2×D4×C19C2311yescharacteristic
200C2×D4×C19C2311yescharacteristic
201C22×C4×C19C2311yescharacteristic
202C22×C4×C19C2311yescharacteristic
203C22×C4×C19C2311yescharacteristic
204C22×C4×C19C2311yescharacteristic
205C2×C22⋊D19—24no—
206C2×C22⋊D19—42no—
207C2×C22⋊D19—42no—
208C2×C22⋊D19C2311yescharacteristic
209C2×C22⋊D19C2311yescharacteristic
210C2×C22⋊D19C2311yescharacteristic
211C2×C22⋊D19C2311yescharacteristic
212C2×C22⋊D19C2311yescharacteristic
213C2×C22⋊D19C2311yescharacteristic
214C2×C22⋊D19C2311yescharacteristic
215C2×C22⋊D19C2311yescharacteristic
216C2×C22⋊D19C2311yescharacteristic
217C2×C22⋊D19C2311yescharacteristic
218C2×C22⋊D19C2311yescharacteristic
219C2×C22⋊D19C2311yescharacteristic
220C2×C22⋊D19C2311yescharacteristic
221C2×C22⋊D19C2311yescharacteristic
222C2×C22⋊D19C2311yescharacteristic
223C2×C22⋊D19C2311yescharacteristic
224C2×C22⋊D19C2311yescharacteristic
225C2×C22⋊D19C2311yescharacteristic
226C2×C22⋊D19C2311yescharacteristic
227C2×C22⋊D19C2311yescharacteristic
228C22×Dic19C2311yescharacteristic
229C22×Dic19C2311yescharacteristic
230C22×Dic19C2311yescharacteristic
231C22×Dic19C2311yescharacteristic
232C22×Dic19C2311yescharacteristic
233C22×Dic19C2311yescharacteristic
234C22×Dic19C2311yescharacteristic
235#64545—42no—
236#64543—42no—
237#64543—42no—
238D4×D19—24no—
239D4×D19—24no—
240D4×D19—42no—
241D4×D19—42no—
242D4×D19—42no—
243#64541—42no—
244C2×D76—42no—
245C2×D76C2311yescharacteristic
246C2×D76C2311yescharacteristic
247C2×D76C2311yescharacteristic
248C2×D76C2311yescharacteristic
249C2×D76C2311yescharacteristic
250C2×D76C2311yescharacteristic
251C2×D76C2311yescharacteristic
252C2×D76C2311yescharacteristic
253C2×D76C2311yescharacteristic
254C2×D76C2311yescharacteristic
255C2×C4×D19—42no—
256C2×C4×D19—42no—
257C2×C4×D19C2311yescharacteristic
258C2×C4×D19C2311yescharacteristic
259C2×C4×D19C2311yescharacteristic
260C2×C4×D19C2311yescharacteristic
261C2×C4×D19C2311yescharacteristic
262C2×C4×D19C2311yescharacteristic
263C2×C4×D19C2311yescharacteristic
264C2×C4×D19C2311yescharacteristic
265C2×C4×D19C2311yescharacteristic
266C2×C4×D19C2311yescharacteristic
267C2×C4×D19C2311yescharacteristic
268C2×C4×D19C2311yescharacteristic
269C2×C4×D19C2311yescharacteristic
270C2×C4×D19C2311yescharacteristic
271C2×C4×D19C2311yescharacteristic
272C2×C4×D19C2311yescharacteristic
273C2×Dic38C2311yescharacteristic
274C2×Dic38C2311yescharacteristic
275C4⋊C4×C19C2311yescharacteristic
276C4⋊C4×C19C2311yescharacteristic
277C4⋊C4×C19C2311yescharacteristic
278C4⋊C4×C19C2311yescharacteristic
279C4⋊C4×C19C2311yescharacteristic
280C4⋊C4×C19C2311yescharacteristic
281C22⋊C4×C19C2311yescharacteristic
282C22⋊C4×C19C2311yescharacteristic
283C22⋊C4×C19C2311yescharacteristic
284C22⋊C4×C19C2311yescharacteristic
285C22⋊C4×C19C2311yescharacteristic
286C22⋊C4×C19C2311yescharacteristic
287C22⋊C4×C19C2311yescharacteristic
288C22⋊C4×C19C2311yescharacteristic
289C22⋊C4×C19C2311yescharacteristic
290C22⋊C4×C19C2311yescharacteristic
291C22⋊C4×C19C2311yescharacteristic
292C22⋊C4×C19C2311yescharacteristic
293C22⋊C4×C19C2311yescharacteristic
294C22⋊C4×C19C2311yescharacteristic
295C42×C19C2311yescharacteristic
296C42×C19C2311yescharacteristic
297C22⋊Dic19C2311yescharacteristic
298C22⋊Dic19C2311yescharacteristic
299C22⋊Dic19C2311yescharacteristic
300C22⋊Dic19C2311yescharacteristic
301C22⋊Dic19C2311yescharacteristic
302C22⋊Dic19C2311yescharacteristic
303C22⋊Dic19C2311yescharacteristic
304C22⋊Dic19C2311yescharacteristic
305(C2×D19)⋊C4C2311yescharacteristic
306(C2×D19)⋊C4C2311yescharacteristic
307(C2×D19)⋊C4C2311yescharacteristic
308(C2×D19)⋊C4C2311yescharacteristic
309(C2×D19)⋊C4C2311yescharacteristic
310(C2×D19)⋊C4C2311yescharacteristic
311(C2×D19)⋊C4C2311yescharacteristic
312(C2×D19)⋊C4C2311yescharacteristic
313(C2×D19)⋊C4C2311yescharacteristic
314(C2×D19)⋊C4C2311yescharacteristic
315(C2×D19)⋊C4C2311yescharacteristic
316(C2×D19)⋊C4C2311yescharacteristic
317(C2×D19)⋊C4C2311yescharacteristic
318(C2×D19)⋊C4C2311yescharacteristic
319(C2×D19)⋊C4C2311yescharacteristic
320(C2×D19)⋊C4C2311yescharacteristic
321(C2×D19)⋊C4C2311yescharacteristic
322(C2×D19)⋊C4C2311yescharacteristic
323(C2×D19)⋊C4C2311yescharacteristic
324(C2×D19)⋊C4C2311yescharacteristic
325(C2×D19)⋊C4C2311yescharacteristic
326(C2×D19)⋊C4C2311yescharacteristic
327(C2×D19)⋊C4C2311yescharacteristic
328(C2×D19)⋊C4C2311yescharacteristic
329C4⋊Dic19C2311yescharacteristic
330C4⋊Dic19C2311yescharacteristic
331C4⋊Dic19C2311yescharacteristic
332C4⋊Dic19C2311yescharacteristic
333Dic19⋊C4C2311yescharacteristic
334Dic19⋊C4C2311yescharacteristic
335Dic19⋊C4C2311yescharacteristic
336Dic19⋊C4C2311yescharacteristic
337Dic19⋊C4C2311yescharacteristic
338Dic19⋊C4C2311yescharacteristic
339Dic19⋊C4C2311yescharacteristic
340Dic19⋊C4C2311yescharacteristic
341Dic19⋊C4C2311yescharacteristic
342Dic19⋊C4C2311yescharacteristic
343Dic19⋊C4C2311yescharacteristic
344Dic19⋊C4C2311yescharacteristic
345Dic19⋊C4C2311yescharacteristic
346Dic19⋊C4C2311yescharacteristic
347Dic19⋊C4C2311yescharacteristic
348Dic19⋊C4C2311yescharacteristic
349C4×Dic19C2311yescharacteristic
350C4×Dic19C2311yescharacteristic
351C4×Dic19C2311yescharacteristic
352C4×Dic19C2311yescharacteristic
353C4×Dic19C2311yescharacteristic
354C4×Dic19C2311yescharacteristic
355C4×Dic19C2311yescharacteristic
356C4×Dic19C2311yescharacteristic
357C23×C19—22no—
358C23×C19—41no—
359C23×C19—41no—
360C23×C19C2411yescharacteristic
361C23×C19C2411yescharacteristic
362C23×C19C2411yescharacteristic
363C23×C19C2411yescharacteristic
364C23×C19C2411yescharacteristic
365C22×D19—22no—
366C22×D19—22no—
367C22×D19—22no—
368C22×D19—22no—
369C22×D19—22no—
370C22×D19—22no—
371C22×D19—22no—
372C22×D19—41no—
373C22×D19—41no—
374C22×D19—41no—
375C22×D19—41no—
376C22×D19—41no—
377C22×D19—41no—
378C22×D19—41no—
379C22×D19—41no—
380C22×D19C2411yescharacteristic
381C22×D19C2411yescharacteristic
382C22×D19C2411yescharacteristic
383C22×D19C2411yescharacteristic
384C22×D19C2411yescharacteristic
385C22×D19C2411yescharacteristic
386Q8×C19—41no—
387D4×C19—22no—
388D4×C19—22no—
389D4×C19—41no—
390D4×C19—41no—
391D4×C19—41no—
392D4×C19—41no—
393D4×C19—41no—
394C2×C4×C19—41no—
395C2×C4×C19—41no—
396C2×C4×C19—41no—
397C2×C4×C19—41no—
398C2×C4×C19C2411yescharacteristic
399C2×C4×C19C2411yescharacteristic
400C2×C4×C19C2411yescharacteristic
401C2×C4×C19C2411yescharacteristic
402C2×C4×C19C2411yescharacteristic
403C2×C4×C19C2411yescharacteristic
404C2×C4×C19C2411yescharacteristic
405C2×C4×C19C2411yescharacteristic
406C2×C4×C19C2411yescharacteristic
407C2×C4×C19C2411yescharacteristic
408C22⋊D19—22no—
409C22⋊D19—22no—
410C22⋊D19—22no—
411C22⋊D19—22no—
412C22⋊D19—22no—
413C22⋊D19—22no—
414C22⋊D19—22no—
415C22⋊D19—22no—
416C22⋊D19—22no—
417C22⋊D19—22no—
418C22⋊D19—22no—
419C22⋊D19—41no—
420C22⋊D19—41no—
421C22⋊D19—41no—
422C22⋊D19—41no—
423C22⋊D19—41no—
424C22⋊D19—41no—
425C22⋊D19—41no—
426C22⋊D19—41no—
427C22⋊D19#4114yescomplemented
428C2×Dic19—22no—
429C2×Dic19—22no—
430C2×Dic19—22no—
431C2×Dic19—41no—
432C2×Dic19—41no—
433C2×Dic19—41no—
434C2×Dic19—41no—
435C2×Dic19C2411yescharacteristic
436C2×Dic19C2411yescharacteristic
437C2×Dic19C2411yescharacteristic
438C2×Dic19C2411yescharacteristic
439C2×Dic19C2411yescharacteristic
440C2×Dic19C2411yescharacteristic
441C2×Dic19C2411yescharacteristic
442C2×Dic19C2411yescharacteristic
443C2×Dic19C2411yescharacteristic
444C2×Dic19C2411yescharacteristic
445D76—22no—
446D76—22no—
447D76—22no—
448D76—22no—
449D76—22no—
450D76—41no—
451D76—41no—
452D76—41no—
453D76—41no—
454D76—41no—
455C4×D19—22no—
456C4×D19—22no—
457C4×D19—22no—
458C4×D19—22no—
459C4×D19—22no—
460C4×D19—22no—
461C4×D19—41no—
462C4×D19—41no—
463C4×D19—41no—
464C4×D19—41no—
465C4×D19—41no—
466C4×D19—41no—
467C4×D19—41no—
468C4×D19—41no—
469C4×D19—41no—
470C4×D19—41no—
471Dic38—22no—
472Dic38—41no—
473#3519—191nomaximal, Sylow
474C22×C19—21no—
475C22×C19—21no—
476C22×C19—21no—
477C22×C19—21no—
478C22×C19—21no—
479C22×C19—21no—
480C22×C19—21no—
481C22×C19—21no—
482C22×C19—21no—
483C22×C19—21no—
484C22×C19—21no—
485C22×C19—21no—
486C22×C19—21no—
487C22×C19—21no—
488C22×C19—82no—
489C22×C19C2×#4112yes—
490C22×C19C2511yescharacteristic
491C2×D19—21no—
492C2×D19—21no—
493C2×D19—21no—
494C2×D19—21no—
495C2×D19—21no—
496C2×D19—21no—
497C2×D19—21no—
498C2×D19—21no—
499C2×D19—21no—
500C2×D19—21no—
501C2×D19—21no—
502C2×D19—21no—
503C2×D19—21no—
504C2×D19—21no—
505C2×D19—21no—
506C2×D19—21no—
507C2×D19—44no—
508C2×D19—44no—
509C2×D19—82no—
510C2×D19—82no—
511C2×D19—82no—
512C2×D19C2×#4112yes—
513C2×D19H(5,𝔽2)12yes—
514C4×C19—21no—
515C4×C19—21no—
516C4×C19—21no—
517C4×C19—21no—
518C4×C19—21no—
519C4×C19—21no—
520C4×C19—21no—
521C4×C19—21no—
522C4×C19—21no—
523C4×C19—21no—
524Dic19—21no—
525Dic19—21no—
526Dic19—21no—
527Dic19—21no—
528Dic19—21no—
529Dic19—21no—
530Dic19—21no—
531Dic19—21no—
532Dic19C2×#4112yes—
533Dic19H(5,𝔽2)12yes—
534#555—191no—
535#554—191no—
536#553—191no—
537#553—191no—
538#553—191no—
539#553—191no—
540#550—191no—
541#546—191no—
542#546—191no—
543#546—191no—
544#546—191no—
545#546—191no—
546#546—191no—
547D42—191no—
548D42—191no—
549D42—191no—
550#540—191no—
551#540—191no—
552#538—191no—
553#538—191no—
554#538—191no—
555#538D1911yescharacteristic, complemented
556#532—191no—
557#529—191no—
558#525—191no—
559#525—191no—
560C2×#121—191no—
561C2×#121—191no—
562#518—191no—
563#518—191no—
564C2×C4×D4—191no—
565C2×C19—22no—
566C2×C19—41no—
567C2×C19—41no—
568C2×C19—41no—
569C2×C19—41no—
570C2×C19C22×#4111yescharacteristic
571C2×C19C2×H(5,𝔽2)11yescharacteristic
572C2×C19C2×H(5,𝔽2)11yescharacteristic
573D19—22no—
574D19—22no—
575D19—41no—
576D19—41no—
577D19—41no—
578D19—41no—
579C2×#41—191no—
580C2×#41—191no—
581C2×#41—191no—
582C2×#41—191no—
583C22×D4—191no—
584C22×D4—191no—
585C22×D4—191no—
586C22×D4—191no—
587C22×D4—191no—
588C22×D4—191no—
589C22×D4—191no—
590C22×D4—191no—
591C22×D4—191no—
592C23×C4—191no—
593C23×C4—191no—
594C4⋊Q8—191no—
595#127—191no—
596#127—191no—
597#127—191no—
598#126—191no—
599#126—191no—
600#126—191no—
601#126—191no—
602#126C2×D1911yescharacteristic, complemented
603#126C2×D1911yescharacteristic, complemented
604#125—191no—
605#125—191no—
606#125—191no—
607#124—191no—
608#124—191no—
609#124—191no—
610#124—191no—
611#124—191no—
612#124C2×D1911yescharacteristic, complemented
613#124C2×D1911yescharacteristic, complemented
614#123—191no—
615#123—191no—
616#123—191no—
617#123—191no—
618#123—191no—
619#123—191no—
620#123—191no—
621#123—191no—
622#123—191no—
623#123—191no—
624#123—191no—
625#123—191no—
626#123C2×D1911yescharacteristic, complemented
627#123C2×D1911yescharacteristic, complemented
628C22⋊Q8—191no—
629C22⋊Q8—191no—
630C22⋊Q8—191no—
631C22⋊Q8—191no—
632C22⋊Q8—191no—
633C22⋊Q8—191no—
634C22⋊Q8C2×D1911yescharacteristic, complemented
635#121—191no—
636#121—191no—
637#121—191no—
638#121—191no—
639#121—191no—
640#121—191no—
641#121—191no—
642#121—191no—
643#121—191no—
644#121—191no—
645#121—191no—
646#121—191no—
647#121—191no—
648#121—191no—
649#121—191no—
650#121—191no—
651#121—191no—
652#121—191no—
653#121—191no—
654#121—191no—
655#121—191no—
656#121—191no—
657#121—191no—
658#121—191no—
659#121—191no—
660#121—191no—
661#121—191no—
662#121—191no—
663#121—191no—
664#121—191no—
665#121—191no—
666#121—191no—
667#121C2×D1911yescharacteristic, complemented
668#121C2×D1911yescharacteristic, complemented
669#121C2×D1911yescharacteristic, complemented
670#120—191no—
671#120—191no—
672#120—191no—
673#120—191no—
674#120—191no—
675#120—191no—
676#120—191no—
677#120—191no—
678#120—191no—
679#120—191no—
680#120C2×D1911yescharacteristic, complemented
681#120C2×D1911yescharacteristic, complemented
682C4×Q8—191no—
683C4×D4—191no—
684C4×D4—191no—
685C4×D4—191no—
686C4×D4—191no—
687C4×D4—191no—
688C4×D4—191no—
689C4×D4—191no—
690C4×D4—191no—
691C4×D4—191no—
692C4×D4—191no—
693C4×D4—191no—
694C4×D4—191no—
695C4×D4—191no—
696C4×D4—191no—
697C4×D4—191no—
698C4×D4—191no—
699C4×D4—191no—
700C4×D4—191no—
701C4×D4—191no—
702C4×D4—191no—
703C4×D4—191no—
704C4×D4—191no—
705C4×D4—191no—
706C4×D4—191no—
707C4×D4—191no—
708C4×D4—191no—
709C4×D4—191no—
710C4×D4—191no—
711C4×D4—191no—
712C4×D4C2×D1911yescharacteristic, complemented
713C4×D4C2×D1911yescharacteristic, complemented
714#117—191no—
715#117—191no—
716#117—191no—
717#117—191no—
718#117—191no—
719#117—191no—
720C2×C4⋊C4—191no—
721C2×C4⋊C4—191no—
722C2×C4⋊C4—191no—
723C2×C22⋊C4—191no—
724C2×C22⋊C4—191no—
725C2×C22⋊C4—191no—
726C2×C22⋊C4—191no—
727C2×C22⋊C4—191no—
728C2×C22⋊C4—191no—
729C2×C22⋊C4—191no—
730C2×C22⋊C4—191no—
731C2×C22⋊C4—191no—
732C2×C22⋊C4C2×D1911yescharacteristic, complemented
733C2×C42—191no—
734C19#351911yescharacteristic, complemented, Sylow
735C24—191no—
736C24—191no—
737C24—191no—
738C24—191no—
739C24—191no—
740C24C22×D1911yescharacteristic
741#41—762no—
742#41—762no—
743#41—762no—
744#41—762no—
745C2×Q8—191no—
746C2×Q8—191no—
747C2×Q8C22×D1911yescharacteristic
748C2×D4—191no—
749C2×D4—191no—
750C2×D4—191no—
751C2×D4—191no—
752C2×D4—191no—
753C2×D4—191no—
754C2×D4—191no—
755C2×D4—191no—
756C2×D4—191no—
757C2×D4—191no—
758C2×D4—191no—
759C2×D4—191no—
760C2×D4—191no—
761C2×D4—191no—
762C2×D4—191no—
763C2×D4—191no—
764C2×D4—191no—
765C2×D4—191no—
766C2×D4—191no—
767C2×D4—191no—
768C2×D4—191no—
769C2×D4—191no—
770C2×D4—191no—
771C2×D4—191no—
772C2×D4—191no—
773C2×D4—191no—
774C2×D4—191no—
775C2×D4—191no—
776C2×D4—191no—
777C2×D4—191no—
778C2×D4—384no—
779C2×D4—384no—
780C2×D4—384no—
781C2×D4—762no—
782C2×D4—762no—
783C2×D4—762no—
784C2×D4—762no—
785C2×D4—762no—
786C2×D4—762no—
787C2×D4C22×D1911yescharacteristic
788C2×D4C22×D1911yescharacteristic
789C2×D4C22×D1911yescharacteristic
790C2×D4C22×D1911yescharacteristic
791C2×D4C22×D1911yescharacteristic
792C2×D4C22×D1911yescharacteristic
793C2×D4C22×D1911yescharacteristic
794C22×C4—191no—
795C22×C4—191no—
796C22×C4—191no—
797C22×C4—191no—
798C22×C4—191no—
799C22×C4—191no—
800C22×C4—191no—
801C22×C4—191no—
802C22×C4—191no—
803C22×C4—191no—
804C22×C4—191no—
805C22×C4—191no—
806C22×C4—191no—
807C22×C4—191no—
808C22×C4—191no—
809C22×C4—191no—
810C22×C4—191no—
811C22×C4—191no—
812C22×C4—191no—
813C22×C4—191no—
814C22×C4—191no—
815C22×C4—191no—
816C22×C4—191no—
817C22×C4—762no—
818C22×C4—762no—
819C22×C4C22×D1911yescharacteristic
820C22×C4C22×D1911yescharacteristic
821C22×C4C22×D1911yescharacteristic
822C22×C4C22×D1911yescharacteristic
823C4⋊C4—191no—
824C4⋊C4—191no—
825C4⋊C4—191no—
826C4⋊C4—191no—
827C4⋊C4—191no—
828C4⋊C4—191no—
829C4⋊C4—191no—
830C4⋊C4—191no—
831C4⋊C4—191no—
832C4⋊C4—191no—
833C4⋊C4—191no—
834C4⋊C4—191no—
835C4⋊C4—191no—
836C4⋊C4—191no—
837C4⋊C4—191no—
838C4⋊C4—191no—
839C4⋊C4—191no—
840C4⋊C4—191no—
841C4⋊C4—191no—
842C4⋊C4—191no—
843C4⋊C4C22×D1911yescharacteristic
844C4⋊C4C22×D1911yescharacteristic
845C4⋊C4C22×D1911yescharacteristic
846C4⋊C4C22×D1911yescharacteristic
847C4⋊C4C22×D1911yescharacteristic
848C4⋊C4C22×D1911yescharacteristic
849C22⋊C4—191no—
850C22⋊C4—191no—
851C22⋊C4—191no—
852C22⋊C4—191no—
853C22⋊C4—191no—
854C22⋊C4—191no—
855C22⋊C4—191no—
856C22⋊C4—191no—
857C22⋊C4—191no—
858C22⋊C4—191no—
859C22⋊C4—191no—
860C22⋊C4—191no—
861C22⋊C4—191no—
862C22⋊C4—191no—
863C22⋊C4—191no—
864C22⋊C4—191no—
865C22⋊C4—191no—
866C22⋊C4—191no—
867C22⋊C4—191no—
868C22⋊C4—191no—
869C22⋊C4—191no—
870C22⋊C4—191no—
871C22⋊C4—191no—
872C22⋊C4—191no—
873C22⋊C4—191no—
874C22⋊C4—191no—
875C22⋊C4—191no—
876C22⋊C4—191no—
877C22⋊C4—191no—
878C22⋊C4—191no—
879C22⋊C4—191no—
880C22⋊C4—191no—
881C22⋊C4C22×D1911yescharacteristic
882C22⋊C4C22×D1911yescharacteristic
883C22⋊C4C22×D1911yescharacteristic
884C22⋊C4C22×D1911yescharacteristic
885C22⋊C4C22×D1911yescharacteristic
886C22⋊C4C22×D1911yescharacteristic
887C22⋊C4C22×D1911yescharacteristic
888C22⋊C4C22×D1911yescharacteristic
889C22⋊C4C22×D1911yescharacteristic
890C22⋊C4C22×D1911yescharacteristic
891C22⋊C4C22×D1911yescharacteristic
892C22⋊C4C22×D1911yescharacteristic
893C22⋊C4C22×D1911yescharacteristic
894C22⋊C4C22×D1911yescharacteristic
895C42—191no—
896C42—191no—
897C42—191no—
898C42—191no—
899C42—191no—
900C42—191no—
901C42—191no—
902C42—191no—
903C42C22×D1911yescharacteristic
904C42C22×D1911yescharacteristic
905C23—22no—
906C23—41no—
907C23—41no—
908C23—191no—
909C23—191no—
910C23—191no—
911C23—191no—
912C23—191no—
913C23—191no—
914C23—382no—
915C23—382no—
916C23—382no—
917C23—382no—
918C23—382no—
919C23—382no—
920C23—382no—
921C23—761no—
922C23—761no—
923C23—761no—
924C23—761no—
925C23—761no—
926C23—761no—
927C23—761no—
928C23—761no—
929C23C23×D1911yescharacteristic
930C23C23×D1911yescharacteristic
931C23C23×D1911yescharacteristic
932C23C23×D1911yescharacteristic
933C23C23×D1911yescharacteristic
934Q8—41no—
935Q8—382no—
936Q8—761no—
937D4—22no—
938D4—22no—
939D4—41no—
940D4—41no—
941D4—41no—
942D4—41no—
943D4—41no—
944D4—194no—
945D4—382no—
946D4—382no—
947D4—382no—
948D4—382no—
949D4—382no—
950D4—382no—
951D4—382no—
952D4—382no—
953D4—382no—
954D4—382no—
955D4—382no—
956D4—382no—
957D4—382no—
958D4—382no—
959D4—382no—
960D4—382no—
961D4—761no—
962D4—761no—
963D4—761no—
964D4—761no—
965D4—761no—
966D4—761no—
967D4—761no—
968D4—761no—
969D4—761no—
970D4—761no—
971D4—761no—
972D4—761no—
973D4—761no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—191no—
979C2×C4—191no—
980C2×C4—191no—
981C2×C4—191no—
982C2×C4—191no—
983C2×C4—191no—
984C2×C4—191no—
985C2×C4—191no—
986C2×C4—191no—
987C2×C4—191no—
988C2×C4—382no—
989C2×C4—382no—
990C2×C4—382no—
991C2×C4—382no—
992C2×C4—382no—
993C2×C4—382no—
994C2×C4—382no—
995C2×C4—382no—
996C2×C4—382no—
997C2×C4—761no—
998C2×C4—761no—
999C2×C4—761no—
1000C2×C4—761no—
1001C2×C4—761no—
1002C2×C4—761no—
1003C2×C4—761no—
1004C2×C4—761no—
1005C2×C4—761no—
1006C2×C4—761no—
1007C2×C4—761no—
1008C2×C4—761no—
1009C2×C4—761no—
1010C2×C4—761no—
1011C2×C4C23×D1911yescharacteristic
1012C2×C4C23×D1911yescharacteristic
1013C2×C4C23×D1911yescharacteristic
1014C2×C4C23×D1911yescharacteristic
1015C2×C4C23×D1911yescharacteristic
1016C2×C4C23×D1911yescharacteristic
1017C2×C4C23×D1911yescharacteristic
1018C2×C4C23×D1911yescharacteristic
1019C2×C4C23×D1911yescharacteristic
1020C2×C4C23×D1911yescharacteristic
1021C22—21no—
1022C22—21no—
1023C22—21no—
1024C22—21no—
1025C22—21no—
1026C22—21no—
1027C22—21no—
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—21no—
1032C22—21no—
1033C22—21no—
1034C22—21no—
1035C22—82no—
1036C22—192no—
1037C22—192no—
1038C22—381no—
1039C22—381no—
1040C22—381no—
1041C22—381no—
1042C22—381no—
1043C22—381no—
1044C22—381no—
1045C22—381no—
1046C22—381no—
1047C22—381no—
1048C22—381no—
1049C22—381no—
1050C22—381no—
1051C22—381no—
1052C22—381no—
1053C22—381no—
1054C22—764no—
1055C22—764no—
1056C22—1522no—
1057C22—1522no—
1058C22—1522no—
1059C22#41×D1912yes—
1060C22C24×D1911yescharacteristic
1061C4—21no—
1062C4—21no—
1063C4—21no—
1064C4—21no—
1065C4—21no—
1066C4—21no—
1067C4—21no—
1068C4—21no—
1069C4—21no—
1070C4—21no—
1071C4—192no—
1072C4—192no—
1073C4—381no—
1074C4—381no—
1075C4—381no—
1076C4—381no—
1077C4—381no—
1078C4—381no—
1079C4—381no—
1080C4—381no—
1081C2—22no—
1082C2—41no—
1083C2—41no—
1084C2—41no—
1085C2—41no—
1086C2—382no—
1087C2—382no—
1088C2—761no—
1089C2—761no—
1090C2—761no—
1091C2—761no—
1092C2C2×#41×D1911yescharacteristic
1093C2H(5,𝔽2)×D1911yescharacteristic
1094C2H(5,𝔽2)×D1911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D19
commutator, socle, cosocleC22×C19C25
FittingC19×#538C2
hypercenter#538D19
hypocenterC19#3519
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ #538

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #11927256C2semidirect
2. #11927248C2semidirect
3. #11927245C2semidirect
4. #11927245C2semidirect
5. #11927239C2semidirect
6. #11927237C2semidirect
7. #11927212C2semidirect
8. #11927187C2semidirect
9. #11927186C2semidirect
10. #11927185C2semidirect
11. #11927183C2semidirect
12. #11927181C2semidirect
13. #11927181C2semidirect
14. #11927178C2semidirect
15. #11927176C2semidirect
16. #11927176C2semidirect
17. #11927146C2semidirect
18. #11927144C2semidirect
19. #11927133C2semidirect
20. #11927128C2semidirect
21. #11927127C2semidirect
22. #11927093C2semidirect
23. #11927077C2semidirect
24. #11927053C2semidirect
25. #11927052C2semidirect
26. C2×#10597330C2semidirect
27. #121×D19C2semidirect
28. #11927017C2semidirect
29. #11927016C2semidirect
30. C4×D4×D19C2semidirect
31. C19×#538C2semidirect
33. C22×C22⋊D19C22semidirect
34. C22×C22⋊D19C22semidirect
35. C2×#64545C22semidirect
36. C2×#64543C22semidirect
37. C2×#64543C22semidirect
40. C2×D4×D19C22semidirect
41. C2×D4×D19C22semidirect
42. C2×D4×D19C22semidirect
43. C2×#64541C22semidirect
44. C22×D76C22semidirect
45. C22×C4×D19C22semidirect
46. C22×C4×D19C22semidirect
47. C19×#126C22semidirect
48. C19×#126C22semidirect
49. C19×#124C22semidirect
50. C19×#124C22semidirect
51. C19×#123C22semidirect
52. C19×#123C22semidirect
53. C19×C22⋊Q8C22semidirect
54. C19×#121C22semidirect
55. C19×#121C22semidirect
56. C19×#121C22semidirect
57. C19×#120C22semidirect
58. C19×#120C22semidirect
59. C4×D4×C19C22semidirect
60. C4×D4×C19C22semidirect
61. C2×C22⋊C4×C19C22semidirect
62. C2×C22⋊Dic19C22semidirect
63. #10597393C22semidirect
64. #10597392C22semidirect
65. #10597390C22semidirect
66. #10597386C22semidirect
67. #10597386C22semidirect
68. #10597386C22semidirect
69. #10597385C22semidirect
70. #10597385C22semidirect
71. #10597385C22semidirect
72. #10597385C22semidirect
73. #10597385C22semidirect
74. #10597385C22semidirect
75. #10597385C22semidirect
76. #10597385C22semidirect
77. #10597385C22semidirect
78. #10597384C22semidirect
79. #10597384C22semidirect
80. #10597383C22semidirect
81. #10597383C22semidirect
82. #10597383C22semidirect
83. #10597383C22semidirect
84. #10597381C22semidirect
85. D4×Dic19C22semidirect
86. D4×Dic19C22semidirect
87. #10597376C22semidirect
88. #10597375C22semidirect
91. C4×C22⋊D19C22semidirect
92. C4×C22⋊D19C22semidirect
93. C4×C22⋊D19C22semidirect
94. C4×C22⋊D19C22semidirect
95. C4×C22⋊D19C22semidirect
96. C2×(C2×D19)⋊C4C22semidirect
97. C2×(C2×D19)⋊C4C22semidirect
98. C2×Dic19⋊C4C22semidirect
99. #10597344C22semidirect
100. #10597344C22semidirect
101. #10597342C22semidirect
102. #10597342C22semidirect
103. #10597342C22semidirect
104. #10597341C22semidirect
105. #10597341C22semidirect
106. #10597341C22semidirect
107. #10597341C22semidirect
108. #10597340C22semidirect
109. #10597340C22semidirect
110. #10597340C22semidirect
111. #10597340C22semidirect
112. #10597339C22semidirect
113. #10597339C22semidirect
114. #10597339C22semidirect
115. #10597339C22semidirect
116. #10597338C22semidirect
117. C4⋊C4×D19C22semidirect
118. C4⋊C4×D19C22semidirect
119. #10597335C22semidirect
120. #10597335C22semidirect
121. #10597335C22semidirect
122. #10597333C22semidirect
123. #10597332C22semidirect
124. #10597332C22semidirect
125. #10597331C22semidirect
126. #10597331C22semidirect
127. #10597331C22semidirect
129. #10597330C22semidirect
130. #10597330C22semidirect
131. #10597330C22semidirect
132. #10597330C22semidirect
133. #10597330C22semidirect
134. #10597330C22semidirect
135. #10597330C22semidirect
136. #10597330C22semidirect
137. #10597330C22semidirect
138. #10597330C22semidirect
139. #10597330C22semidirect
140. #10597330C22semidirect
141. #10597330C22semidirect
142. #10597330C22semidirect
143. #10597330C22semidirect
144. #10597329C22semidirect
145. #10597329C22semidirect
146. #10597329C22semidirect
147. #10597329C22semidirect
148. #10597328C22semidirect
149. #10597328C22semidirect
150. #10597328C22semidirect
151. #10597328C22semidirect
152. #10597328C22semidirect
153. #10597328C22semidirect
156. (C22⋊D19)⋊C4C22semidirect
157. (C22⋊D19)⋊C4C22semidirect
158. (C22⋊D19)⋊C4C22semidirect
159. (C22⋊D19)⋊C4C22semidirect
160. (C22⋊D19)⋊C4C22semidirect
161. (C22⋊D19)⋊C4C22semidirect
162. (C22⋊D19)⋊C4C22semidirect
163. (C22⋊D19)⋊C4C22semidirect
164. (C22⋊D19)⋊C4C22semidirect
165. (C22⋊D19)⋊C4C22semidirect
166. (C22⋊D19)⋊C4C22semidirect
167. C22⋊C4×D19C22semidirect
168. C22⋊C4×D19C22semidirect
169. C22⋊C4×D19C22semidirect
170. C22⋊C4×D19C22semidirect
171. C22⋊C4×D19C22semidirect
172. C22⋊C4×D19C22semidirect
173. #10597325C22semidirect
174. #10597324C22semidirect
175. #10597324C22semidirect
176. #10597323C22semidirect
177. #10597323C22semidirect
178. #10597323C22semidirect
179. #10597322C22semidirect
180. #10597321C22semidirect
181. C4×D76C22semidirect
182. C4×D76C22semidirect
183. C4×D76C22semidirect
184. #10597318C22semidirect
185. #10597318C22semidirect
186. C42×D19C22semidirect
427. C22⋊D19#41semidirect
555. #538D19semidirect
602. #126C2×D19semidirect
603. #126C2×D19semidirect
612. #124C2×D19semidirect
613. #124C2×D19semidirect
626. #123C2×D19semidirect
627. #123C2×D19semidirect
634. C22⋊Q8C2×D19semidirect
667. #121C2×D19semidirect
668. #121C2×D19semidirect
669. #121C2×D19semidirect
680. #120C2×D19semidirect
681. #120C2×D19semidirect
712. C4×D4C2×D19semidirect
713. C4×D4C2×D19semidirect
732. C2×C22⋊C4C2×D19semidirect
734. C19#3519semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#119272562
#119272482
#119272452
#119272392
#119272372
#119272122
#119271872
#119271862
#119271852
#119271832
#119271812
#119271782
#119271762
#119271462
#119271442
#119271332
#119271282
#119271272
#119270932
#119270772
#119270532
#119270522
C2×#105973302
#121×D192
#119270172
#119270162
C4×D4×D192
C19×#5382
#351919