Finite Group Databasebeta

← #14578146

Subgroups — #14578146

Order 2432.

1160 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927290C211yesmaximal, characteristic, complemented
2#11927289C211yesmaximal, characteristic, complemented
3#11927287C211yesmaximal, characteristic, complemented
4#11927286C211yesmaximal, characteristic, complemented
5#11927278C211yesmaximal, characteristic, complemented
6#11927277C211yesmaximal, characteristic, complemented
7#11927204C211yesmaximal, characteristic, complemented
8#11927202C211yesmaximal, characteristic, complemented
9#11927191C211yesmaximal, characteristic, complemented
10#11927190C211yesmaximal, characteristic, complemented
11#11927186C211yesmaximal, characteristic, complemented
12#11927184C211yesmaximal, characteristic, complemented
13#11927184C211yesmaximal, characteristic, complemented
14#11927183C211yesmaximal, characteristic, complemented
15#11927178C211yesmaximal, characteristic, complemented
16#11927176C211yesmaximal, characteristic, complemented
17#11927162C211yesmaximal, characteristic, complemented
18#11927160C211yesmaximal, characteristic, complemented
19#11927133C211yesmaximal, characteristic, complemented
20#11927133C211yesmaximal, characteristic, complemented
21#11927128C211yesmaximal, characteristic, complemented
22#11927127C211yesmaximal, characteristic, complemented
23#11927126C211yesmaximal, characteristic, complemented
24#11927110C211yesmaximal, characteristic, complemented
25#11927109C211yesmaximal, characteristic, complemented
26#11927105C211yesmaximal, characteristic, complemented
27#11927104C211yesmaximal, characteristic, complemented
28#11927091C211yesmaximal, characteristic, complemented
29#11927077C211yesmaximal, characteristic, complemented
30#124×D19C211yesmaximal, characteristic, complemented
31C19×#538C211yesmaximal, characteristic, complemented
32C22×C22⋊D19C2211yescharacteristic, complemented
33C22×C22⋊D19C2211yescharacteristic, complemented
34C2×Q8×D19C2211yescharacteristic, complemented
35C2×#64543C2211yescharacteristic, complemented
36C2×D4×D19C2211yescharacteristic
37C2×D4×D19C2211yescharacteristic, complemented
38C2×D4×D19C2211yescharacteristic, complemented
39C2×D4×D19C2211yescharacteristic, complemented
40C2×#64541C2211yescharacteristic, complemented
41C2×#64541C2211yescharacteristic, complemented
42C2×#64541C2211yescharacteristic, complemented
43C22×D76C2211yescharacteristic, complemented
44C19×#126C2211yescharacteristic, complemented
45C19×#126C2211yescharacteristic, complemented
46C19×#124C2211yescharacteristic, complemented
47C19×#124C2211yescharacteristic, complemented
48C19×#123C2211yescharacteristic, complemented
49C19×#123C2211yescharacteristic, complemented
50C19×C22⋊Q8C2211yescharacteristic, complemented
51C19×#121C2211yescharacteristic, complemented
52C19×#121C2211yescharacteristic, complemented
53C19×#121C2211yescharacteristic, complemented
54C19×#120C2211yescharacteristic, complemented
55C19×#120C2211yescharacteristic, complemented
56C4×D4×C19C2211yescharacteristic, complemented
57C4×D4×C19C2211yescharacteristic, complemented
58C2×C22⋊C4×C19C2211yescharacteristic, complemented
59#10597399C2211yescharacteristic, complemented
60#10597399C2211yescharacteristic, complemented
61#10597393C2211yescharacteristic, complemented
62#10597393C2211yescharacteristic, complemented
63#10597392C2211yescharacteristic, complemented
64#10597386C2211yescharacteristic
65#10597386C2211yescharacteristic
66#10597386C2211yescharacteristic, complemented
67#10597385C2211yescharacteristic
68#10597385C2211yescharacteristic, complemented
69#10597385C2211yescharacteristic, complemented
70#10597385C2211yescharacteristic, complemented
71#10597384C2211yescharacteristic, complemented
72#10597384C2211yescharacteristic, complemented
73#10597384C2211yescharacteristic, complemented
74#10597383C2211yescharacteristic, complemented
75#10597383C2211yescharacteristic, complemented
76#10597383C2211yescharacteristic, complemented
77#10597383C2211yescharacteristic, complemented
78#10597383C2211yescharacteristic, complemented
79#10597383C2211yescharacteristic, complemented
80#10597383C2211yescharacteristic, complemented
81#10597383C2211yescharacteristic, complemented
82#10597382C2211yescharacteristic, complemented
83#10597382C2211yescharacteristic, complemented
84#10597382C2211yescharacteristic, complemented
85#10597381C2211yescharacteristic, complemented
86#10597381C2211yescharacteristic, complemented
87#10597376C2211yescharacteristic, complemented
88#10597376C2211yescharacteristic, complemented
89#10597375C2211yescharacteristic, complemented
90#10597375C2211yescharacteristic, complemented
91#10597375C2211yescharacteristic, complemented
92C4×C22⋊D19C2211yescharacteristic, complemented
93C4×C22⋊D19C2211yescharacteristic, complemented
94C4×C22⋊D19C2211yescharacteristic, complemented
95C4×C22⋊D19C2211yescharacteristic, complemented
96C4×C22⋊D19C2211yescharacteristic, complemented
97C2×(C2×D19)⋊C4C2211yescharacteristic, complemented
98#10597370C2211yescharacteristic, complemented
99#10597344C2211yescharacteristic, complemented
100#10597344C2211yescharacteristic, complemented
101#10597343C2211yescharacteristic, complemented
102#10597342C2211yescharacteristic, complemented
103#10597342C2211yescharacteristic, complemented
104#10597342C2211yescharacteristic, complemented
105#10597342C2211yescharacteristic, complemented
106#10597341C2211yescharacteristic, complemented
107#10597341C2211yescharacteristic, complemented
108#10597341C2211yescharacteristic, complemented
109#10597341C2211yescharacteristic, complemented
110#10597340C2211yescharacteristic, complemented
111#10597340C2211yescharacteristic, complemented
112#10597340C2211yescharacteristic, complemented
113#10597340C2211yescharacteristic, complemented
114#10597340C2211yescharacteristic, complemented
115#10597339C2211yescharacteristic, complemented
116#10597339C2211yescharacteristic, complemented
117#10597339C2211yescharacteristic, complemented
118#10597338C2211yescharacteristic, complemented
119#10597335C2211yescharacteristic, complemented
120#10597334C2211yescharacteristic, complemented
121#10597333C2211yescharacteristic, complemented
122#10597333C2211yescharacteristic, complemented
123#10597332C2211yescharacteristic, complemented
124#10597331C2211yescharacteristic, complemented
125#10597331C2211yescharacteristic, complemented
126#10597331C2211yescharacteristic, complemented
127#10597331C2211yescharacteristic, complemented
128#10597331C2211yescharacteristic, complemented
129#10597331C2211yescharacteristic, complemented
130#10597331C2211yescharacteristic, complemented
131#10597331C2211yescharacteristic, complemented
132#10597331C2211yescharacteristic, complemented
133#10597331C2211yescharacteristic, complemented
134#10597331C2211yescharacteristic, complemented
135#10597331C2211yescharacteristic, complemented
136#10597331C2211yescharacteristic, complemented
137#10597331C2211yescharacteristic, complemented
138#10597331C2211yescharacteristic, complemented
139#10597330C2211yescharacteristic
140#10597330C2211yescharacteristic
141#10597330C2211yescharacteristic, complemented
142#10597330C2211yescharacteristic, complemented
143#10597330C2211yescharacteristic, complemented
144#10597330C2211yescharacteristic, complemented
145#10597330C2211yescharacteristic, complemented
146#10597330C2211yescharacteristic, complemented
147#10597330C2211yescharacteristic, complemented
148#10597330C2211yescharacteristic, complemented
149#10597330C2211yescharacteristic, complemented
150#10597329C2211yescharacteristic, complemented
151#10597329C2211yescharacteristic, complemented
152#10597329C2211yescharacteristic, complemented
153#10597329C2211yescharacteristic, complemented
154#10597329C2211yescharacteristic, complemented
155#10597328C2211yescharacteristic, complemented
156#10597328C2211yescharacteristic, complemented
157#10597328C2211yescharacteristic, complemented
158#10597328C2211yescharacteristic, complemented
159#10597328C2211yescharacteristic, complemented
160#10597328C2211yescharacteristic, complemented
161#10597328C2211yescharacteristic, complemented
162#10597328C2211yescharacteristic, complemented
163(C22⋊D19)⋊C4C2211yescharacteristic, complemented
164(C22⋊D19)⋊C4C2211yescharacteristic, complemented
165(C22⋊D19)⋊C4C2211yescharacteristic, complemented
166(C22⋊D19)⋊C4C2211yescharacteristic, complemented
167(C22⋊D19)⋊C4C2211yescharacteristic, complemented
168C22⋊C4×D19C2211yescharacteristic, complemented
169C22⋊C4×D19C2211yescharacteristic, complemented
170C22⋊C4×D19C2211yescharacteristic, complemented
171C22⋊C4×D19C2211yescharacteristic, complemented
172C22⋊C4×D19C2211yescharacteristic, complemented
173C22⋊C4×D19C2211yescharacteristic, complemented
174#10597325C2211yescharacteristic, complemented
175#10597324C2211yescharacteristic, complemented
176#10597324C2211yescharacteristic, complemented
177#10597324C2211yescharacteristic, complemented
178#10597323C2211yescharacteristic, complemented
179#10597322C2211yescharacteristic, complemented
180#10597321C2211yescharacteristic, complemented
181#10597321C2211yescharacteristic, complemented
182#10597321C2211yescharacteristic, complemented
183C4×D76C2211yescharacteristic, complemented
184C4×D76C2211yescharacteristic, complemented
185C42×D19C2211yescharacteristic, complemented
186C4×Dic38C2211yescharacteristic, 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—42no—
206C2×C22⋊D19—42no—
207C2×C22⋊D19C2311yescharacteristic
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
227C22×Dic19C2311yescharacteristic
228C22×Dic19C2311yescharacteristic
229C22×Dic19C2311yescharacteristic
230Q8×D19—42no—
231#64543—42no—
232D4×D19—42no—
233D4×D19—42no—
234D4×D19—42no—
235D4×D19—42no—
236#64541—42no—
237#64541—42no—
238#64541—42no—
239C2×D76—42no—
240C2×D76C2311yescharacteristic
241C2×D76C2311yescharacteristic
242C2×D76C2311yescharacteristic
243C2×D76C2311yescharacteristic
244C2×D76C2311yescharacteristic
245C2×D76C2311yescharacteristic
246C2×D76C2311yescharacteristic
247C2×D76C2311yescharacteristic
248C2×D76C2311yescharacteristic
249C2×D76C2311yescharacteristic
250C2×C4×D19C2311yescharacteristic
251C2×C4×D19C2311yescharacteristic
252C2×C4×D19C2311yescharacteristic
253C2×C4×D19C2311yescharacteristic
254C2×C4×D19C2311yescharacteristic
255C2×C4×D19C2311yescharacteristic
256C2×C4×D19C2311yescharacteristic
257C2×C4×D19C2311yescharacteristic
258C2×C4×D19C2311yescharacteristic
259C2×C4×D19C2311yescharacteristic
260C2×C4×D19C2311yescharacteristic
261C2×C4×D19C2311yescharacteristic
262C2×Dic38C2311yescharacteristic
263C2×Dic38C2311yescharacteristic
264C2×Dic38C2311yescharacteristic
265C2×Dic38C2311yescharacteristic
266C2×Dic38C2311yescharacteristic
267C2×Dic38C2311yescharacteristic
268C4⋊C4×C19C2311yescharacteristic
269C4⋊C4×C19C2311yescharacteristic
270C4⋊C4×C19C2311yescharacteristic
271C4⋊C4×C19C2311yescharacteristic
272C4⋊C4×C19C2311yescharacteristic
273C4⋊C4×C19C2311yescharacteristic
274C22⋊C4×C19C2311yescharacteristic
275C22⋊C4×C19C2311yescharacteristic
276C22⋊C4×C19C2311yescharacteristic
277C22⋊C4×C19C2311yescharacteristic
278C22⋊C4×C19C2311yescharacteristic
279C22⋊C4×C19C2311yescharacteristic
280C22⋊C4×C19C2311yescharacteristic
281C22⋊C4×C19C2311yescharacteristic
282C22⋊C4×C19C2311yescharacteristic
283C22⋊C4×C19C2311yescharacteristic
284C22⋊C4×C19C2311yescharacteristic
285C22⋊C4×C19C2311yescharacteristic
286C22⋊C4×C19C2311yescharacteristic
287C22⋊C4×C19C2311yescharacteristic
288C42×C19C2311yescharacteristic
289C42×C19C2311yescharacteristic
290C22⋊Dic19C2311yescharacteristic
291C22⋊Dic19C2311yescharacteristic
292C22⋊Dic19C2311yescharacteristic
293C22⋊Dic19C2311yescharacteristic
294C22⋊Dic19C2311yescharacteristic
295C22⋊Dic19C2311yescharacteristic
296C22⋊Dic19C2311yescharacteristic
297C22⋊Dic19C2311yescharacteristic
298C22⋊Dic19C2311yescharacteristic
299C22⋊Dic19C2311yescharacteristic
300C22⋊Dic19C2311yescharacteristic
301C22⋊Dic19C2311yescharacteristic
302(C2×D19)⋊C4C2311yescharacteristic
303(C2×D19)⋊C4C2311yescharacteristic
304(C2×D19)⋊C4C2311yescharacteristic
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
329(C2×D19)⋊C4C2311yescharacteristic
330C4⋊Dic19C2311yescharacteristic
331C4⋊Dic19C2311yescharacteristic
332C4⋊Dic19C2311yescharacteristic
333C4⋊Dic19C2311yescharacteristic
334Dic19⋊C4C2311yescharacteristic
335Dic19⋊C4C2311yescharacteristic
336Dic19⋊C4C2311yescharacteristic
337Dic19⋊C4C2311yescharacteristic
338Dic19⋊C4C2311yescharacteristic
339Dic19⋊C4C2311yescharacteristic
340Dic19⋊C4C2311yescharacteristic
341Dic19⋊C4C2311yescharacteristic
342Dic19⋊C4C2311yescharacteristic
343Dic19⋊C4C2311yescharacteristic
344Dic19⋊C4C2311yescharacteristic
345Dic19⋊C4C2311yescharacteristic
346C4×Dic19C2311yescharacteristic
347C4×Dic19C2311yescharacteristic
348C4×Dic19C2311yescharacteristic
349C4×Dic19C2311yescharacteristic
350C4×Dic19C2311yescharacteristic
351C4×Dic19C2311yescharacteristic
352C4×Dic19C2311yescharacteristic
353C4×Dic19C2311yescharacteristic
354C23×C19—41no—
355C23×C19—41no—
356C23×C19—41no—
357C23×C19C2411yescharacteristic
358C23×C19C2411yescharacteristic
359C23×C19C2411yescharacteristic
360C23×C19C2411yescharacteristic
361C23×C19C2411yescharacteristic
362C22×D19—22no—
363C22×D19—22no—
364C22×D19—41no—
365C22×D19—41no—
366C22×D19—41no—
367C22×D19—41no—
368C22×D19—41no—
369C22×D19—41no—
370C22×D19—41no—
371C22×D19—41no—
372C22×D19—41no—
373C22×D19—41no—
374C22×D19—41no—
375C22×D19—41no—
376C22×D19—41no—
377C22×D19C2411yescharacteristic
378C22×D19C2411yescharacteristic
379C22×D19C2411yescharacteristic
380C22×D19C2411yescharacteristic
381C22×D19C2411yescharacteristic
382C22×D19C2411yescharacteristic
383Q8×C19—41no—
384D4×C19—41no—
385D4×C19—41no—
386D4×C19—41no—
387D4×C19—41no—
388D4×C19—41no—
389D4×C19—41no—
390D4×C19—41no—
391C2×C4×C19—41no—
392C2×C4×C19—41no—
393C2×C4×C19—41no—
394C2×C4×C19—41no—
395C2×C4×C19C2411yescharacteristic
396C2×C4×C19C2411yescharacteristic
397C2×C4×C19C2411yescharacteristic
398C2×C4×C19C2411yescharacteristic
399C2×C4×C19C2411yescharacteristic
400C2×C4×C19C2411yescharacteristic
401C2×C4×C19C2411yescharacteristic
402C2×C4×C19C2411yescharacteristic
403C2×C4×C19C2411yescharacteristic
404C2×C4×C19C2411yescharacteristic
405C22⋊D19—22no—
406C22⋊D19—22no—
407C22⋊D19—22no—
408C22⋊D19—22no—
409C22⋊D19—22no—
410C22⋊D19—22no—
411C22⋊D19—22no—
412C22⋊D19—41no—
413C22⋊D19—41no—
414C22⋊D19—41no—
415C22⋊D19—41no—
416C22⋊D19—41no—
417C22⋊D19—41no—
418C22⋊D19—41no—
419C22⋊D19—41no—
420C22⋊D19—41no—
421C22⋊D19—41no—
422C22⋊D19—41no—
423C22⋊D19—41no—
424C22⋊D19—41no—
425C2×Dic19—22no—
426C2×Dic19—41no—
427C2×Dic19—41no—
428C2×Dic19C2411yescharacteristic
429C2×Dic19C2411yescharacteristic
430C2×Dic19C2411yescharacteristic
431C2×Dic19C2411yescharacteristic
432C2×Dic19C2411yescharacteristic
433C2×Dic19C2411yescharacteristic
434C2×Dic19C2411yescharacteristic
435C2×Dic19C2411yescharacteristic
436C2×Dic19C2411yescharacteristic
437C2×Dic19C2411yescharacteristic
438D76—22no—
439D76—22no—
440D76—22no—
441D76—41no—
442D76—41no—
443D76—41no—
444D76—41no—
445D76—41no—
446D76—41no—
447D76—41no—
448C4×D19—22no—
449C4×D19—22no—
450C4×D19—22no—
451C4×D19—41no—
452C4×D19—41no—
453C4×D19—41no—
454C4×D19—41no—
455C4×D19—41no—
456C4×D19—41no—
457C4×D19—41no—
458C4×D19—41no—
459C4×D19—41no—
460Dic38—22no—
461Dic38—22no—
462Dic38—41no—
463Dic38—41no—
464Dic38—41no—
465Dic38—41no—
466#3558—191nomaximal, Sylow
467C22×C19—21no—
468C22×C19—21no—
469C22×C19—21no—
470C22×C19—21no—
471C22×C19—21no—
472C22×C19—21no—
473C22×C19—21no—
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—82no—
483C22×C19C2511yescharacteristic
484C2×D19—21no—
485C2×D19—21no—
486C2×D19—21no—
487C2×D19—21no—
488C2×D19—21no—
489C2×D19—21no—
490C2×D19—21no—
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—82no—
502C2×D19—82no—
503C2×D19—82no—
504C2×D19—82no—
505C2×D19—82no—
506C2×D19H(5,𝔽2)12yes—
507C4×C19—21no—
508C4×C19—21no—
509C4×C19—21no—
510C4×C19—21no—
511C4×C19—21no—
512C4×C19—21no—
513C4×C19—21no—
514C4×C19—21no—
515C4×C19—21no—
516C4×C19—21no—
517Dic19—21no—
518Dic19—21no—
519Dic19—21no—
520Dic19—21no—
521Dic19—21no—
522Dic19—21no—
523Dic19—21no—
524Dic19—21no—
525Dic19—21no—
526Dic19H(5,𝔽2)12yes—
527#562—191no—
528#562—191no—
529H(3,𝔽4)—191no—
530H(3,𝔽4)—191no—
531#559—191no—
532#559—191no—
533#548—191no—
534#548—191no—
535#546—191no—
536#546—191no—
537#546—191no—
538#546—191no—
539#546—191no—
540#546—191no—
541D42—191no—
542D42—191no—
543#542—191no—
544#542—191no—
545#538—191no—
546#538—191no—
547#538—191no—
548#538—191no—
549#538—191no—
550#538D1911yescharacteristic, complemented
551#535—191no—
552#535—191no—
553#534—191no—
554#534—191no—
555#532—191no—
556#529—191no—
557C2×#124—191no—
558C2×C19—41no—
559C2×C19—41no—
560C2×C19—41no—
561C2×C19—41no—
562C2×C19—41no—
563C2×C19C2×H(5,𝔽2)11yescharacteristic
564C2×C19C2×H(5,𝔽2)11yescharacteristic
565C2×C19#58511yescharacteristic
566D19—22no—
567D19—41no—
568D19—41no—
569D19—41no—
570D19—41no—
571D19—41no—
572C2×#41—191no—
573C2×#41—191no—
574C2×#41—191no—
575C2×#41—191no—
576C22×Q8—191no—
577C22×D4—191no—
578C22×D4—191no—
579C22×D4—191no—
580C22×D4—191no—
581C22×D4—191no—
582C22×D4—191no—
583C22×D4—191no—
584C4⋊Q8—191no—
585#127—191no—
586#127—191no—
587#127—191no—
588#126—191no—
589#126—191no—
590#126—191no—
591#126—191no—
592#126C2×D1911yescharacteristic, complemented
593#126C2×D1911yescharacteristic, complemented
594#125—191no—
595#124—191no—
596#124—191no—
597#124—191no—
598#124—191no—
599#124—191no—
600#124—191no—
601#124—191no—
602#124—191no—
603#124—191no—
604#124—191no—
605#124—191no—
606#124—191no—
607#124—191no—
608#124—191no—
609#124—191no—
610#124—191no—
611#124—191no—
612#124—191no—
613#124—191no—
614#124—191no—
615#124—191no—
616#124—191no—
617#124—191no—
618#124C2×D1911yescharacteristic, complemented
619#124C2×D1911yescharacteristic, complemented
620#123—191no—
621#123—191no—
622#123—191no—
623#123—191no—
624#123—191no—
625#123—191no—
626#123—191no—
627#123—191no—
628#123—191no—
629#123—191no—
630#123—191no—
631#123—191no—
632#123—191no—
633#123—191no—
634#123—191no—
635#123—191no—
636#123C2×D1911yescharacteristic, complemented
637#123C2×D1911yescharacteristic, complemented
638C22⋊Q8—191no—
639C22⋊Q8—191no—
640C22⋊Q8—191no—
641C22⋊Q8—191no—
642C22⋊Q8—191no—
643C22⋊Q8—191no—
644C22⋊Q8—191no—
645C22⋊Q8—191no—
646C22⋊Q8—191no—
647C22⋊Q8—191no—
648C22⋊Q8C2×D1911yescharacteristic, complemented
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#121—191no—
668#121—191no—
669#121—191no—
670#121—191no—
671#121—191no—
672#121—191no—
673#121C2×D1911yescharacteristic, complemented
674#121C2×D1911yescharacteristic, complemented
675#121C2×D1911yescharacteristic, complemented
676#120—191no—
677#120—191no—
678#120—191no—
679#120—191no—
680#120—191no—
681#120—191no—
682#120—191no—
683#120—191no—
684#120—191no—
685#120—191no—
686#120—191no—
687#120—191no—
688#120—191no—
689#120—191no—
690#120—191no—
691#120—191no—
692#120—191no—
693#120—191no—
694#120C2×D1911yescharacteristic, complemented
695#120C2×D1911yescharacteristic, complemented
696C4×Q8—191no—
697C4×Q8—191no—
698C4×Q8—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×D4—191no—
713C4×D4—191no—
714C4×D4C2×D1911yescharacteristic, complemented
715C4×D4C2×D1911yescharacteristic, complemented
716#117—191no—
717#117—191no—
718C2×C22⋊C4—191no—
719C2×C22⋊C4—191no—
720C2×C22⋊C4—191no—
721C2×C22⋊C4—191no—
722C2×C22⋊C4—191no—
723C2×C22⋊C4—191no—
724C2×C22⋊C4—191no—
725C2×C22⋊C4C2×D1911yescharacteristic, complemented
726C2×C42—191no—
727C19#355811yescharacteristic, complemented, Sylow
728C24—191no—
729C24—191no—
730C24—191no—
731C24—191no—
732C24—191no—
733C24C22×D1911yescharacteristic
734#41—762no—
735#41—762no—
736#41—762no—
737#41—762no—
738C2×Q8—191no—
739C2×Q8—191no—
740C2×Q8—191no—
741C2×Q8—191no—
742C2×Q8—191no—
743C2×Q8—191no—
744C2×Q8—762no—
745C2×Q8C22×D1911yescharacteristic
746C2×D4—191no—
747C2×D4—191no—
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—762no—
777C2×D4—762no—
778C2×D4—762no—
779C2×D4—762no—
780C2×D4—762no—
781C2×D4—762no—
782C2×D4—762no—
783C2×D4C22×D1911yescharacteristic
784C2×D4C22×D1911yescharacteristic
785C2×D4C22×D1911yescharacteristic
786C2×D4C22×D1911yescharacteristic
787C2×D4C22×D1911yescharacteristic
788C2×D4C22×D1911yescharacteristic
789C2×D4C22×D1911yescharacteristic
790C22×C4—191no—
791C22×C4—191no—
792C22×C4—191no—
793C22×C4—191no—
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×C4C22×D1911yescharacteristic
806C22×C4C22×D1911yescharacteristic
807C22×C4C22×D1911yescharacteristic
808C22×C4C22×D1911yescharacteristic
809C4⋊C4—191no—
810C4⋊C4—191no—
811C4⋊C4—191no—
812C4⋊C4—191no—
813C4⋊C4—191no—
814C4⋊C4—191no—
815C4⋊C4—191no—
816C4⋊C4—191no—
817C4⋊C4—191no—
818C4⋊C4—191no—
819C4⋊C4—191no—
820C4⋊C4—191no—
821C4⋊C4—191no—
822C4⋊C4—191no—
823C4⋊C4—191no—
824C4⋊C4—191no—
825C4⋊C4C22×D1911yescharacteristic
826C4⋊C4C22×D1911yescharacteristic
827C4⋊C4C22×D1911yescharacteristic
828C4⋊C4C22×D1911yescharacteristic
829C4⋊C4C22×D1911yescharacteristic
830C4⋊C4C22×D1911yescharacteristic
831C22⋊C4—191no—
832C22⋊C4—191no—
833C22⋊C4—191no—
834C22⋊C4—191no—
835C22⋊C4—191no—
836C22⋊C4—191no—
837C22⋊C4—191no—
838C22⋊C4—191no—
839C22⋊C4—191no—
840C22⋊C4—191no—
841C22⋊C4—191no—
842C22⋊C4—191no—
843C22⋊C4—191no—
844C22⋊C4—191no—
845C22⋊C4—191no—
846C22⋊C4—191no—
847C22⋊C4—191no—
848C22⋊C4—191no—
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⋊C4C22×D1911yescharacteristic
872C22⋊C4C22×D1911yescharacteristic
873C22⋊C4C22×D1911yescharacteristic
874C22⋊C4C22×D1911yescharacteristic
875C22⋊C4C22×D1911yescharacteristic
876C22⋊C4C22×D1911yescharacteristic
877C22⋊C4C22×D1911yescharacteristic
878C22⋊C4C22×D1911yescharacteristic
879C22⋊C4C22×D1911yescharacteristic
880C22⋊C4C22×D1911yescharacteristic
881C22⋊C4C22×D1911yescharacteristic
882C22⋊C4C22×D1911yescharacteristic
883C22⋊C4C22×D1911yescharacteristic
884C22⋊C4C22×D1911yescharacteristic
885C42—191no—
886C42—191no—
887C42—191no—
888C42—191no—
889C42—191no—
890C42—191no—
891C42—191no—
892C42—191no—
893C42C22×D1911yescharacteristic
894C42C22×D1911yescharacteristic
895C23—41no—
896C23—41no—
897C23—41no—
898C23—191no—
899C23—191no—
900C23—191no—
901C23—191no—
902C23—191no—
903C23—191no—
904C23—382no—
905C23—382no—
906C23—761no—
907C23—761no—
908C23—761no—
909C23—761no—
910C23—761no—
911C23—761no—
912C23—761no—
913C23—761no—
914C23—761no—
915C23—761no—
916C23—761no—
917C23—761no—
918C23—761no—
919C23C23×D1911yescharacteristic
920C23C23×D1911yescharacteristic
921C23C23×D1911yescharacteristic
922C23C23×D1911yescharacteristic
923C23C23×D1911yescharacteristic
924Q8—41no—
925Q8—382no—
926Q8—382no—
927Q8—761no—
928Q8—761no—
929Q8—761no—
930Q8—761no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—382no—
939D4—382no—
940D4—382no—
941D4—382no—
942D4—382no—
943D4—382no—
944D4—382no—
945D4—382no—
946D4—382no—
947D4—382no—
948D4—761no—
949D4—761no—
950D4—761no—
951D4—761no—
952D4—761no—
953D4—761no—
954D4—761no—
955D4—761no—
956D4—761no—
957D4—761no—
958D4—761no—
959D4—761no—
960D4—761no—
961D4—761no—
962D4—761no—
963D4—761no—
964D4—761no—
965D4—761no—
966D4—761no—
967D4—761no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—191no—
973C2×C4—191no—
974C2×C4—191no—
975C2×C4—191no—
976C2×C4—191no—
977C2×C4—191no—
978C2×C4—191no—
979C2×C4—191no—
980C2×C4—191no—
981C2×C4—191no—
982C2×C4—382no—
983C2×C4—382no—
984C2×C4—382no—
985C2×C4—382no—
986C2×C4—761no—
987C2×C4—761no—
988C2×C4—761no—
989C2×C4—761no—
990C2×C4—761no—
991C2×C4—761no—
992C2×C4—761no—
993C2×C4—761no—
994C2×C4—761no—
995C2×C4—761no—
996C2×C4—761no—
997C2×C4C23×D1911yescharacteristic
998C2×C4C23×D1911yescharacteristic
999C2×C4C23×D1911yescharacteristic
1000C2×C4C23×D1911yescharacteristic
1001C2×C4C23×D1911yescharacteristic
1002C2×C4C23×D1911yescharacteristic
1003C2×C4C23×D1911yescharacteristic
1004C2×C4C23×D1911yescharacteristic
1005C2×C4C23×D1911yescharacteristic
1006C2×C4C23×D1911yescharacteristic
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—21no—
1017C22—21no—
1018C22—21no—
1019C22—21no—
1020C22—21no—
1021C22—21no—
1022C22—82no—
1023C22—192no—
1024C22—381no—
1025C22—381no—
1026C22—381no—
1027C22—381no—
1028C22—381no—
1029C22—381no—
1030C22—381no—
1031C22—381no—
1032C22—381no—
1033C22—381no—
1034C22—381no—
1035C22—381no—
1036C22—381no—
1037C22—381no—
1038C22—381no—
1039C22—381no—
1040C22—381no—
1041C22—1522no—
1042C22—1522no—
1043C22—1522no—
1044C22—1522no—
1045C22—1522no—
1046C22C24×D1911yescharacteristic
1047C4—21no—
1048C4—21no—
1049C4—21no—
1050C4—21no—
1051C4—21no—
1052C4—21no—
1053C4—21no—
1054C4—21no—
1055C4—21no—
1056C4—21no—
1057C4—192no—
1058C4—381no—
1059C4—381no—
1060C4—381no—
1061C4—381no—
1062C4—381no—
1063C4—381no—
1064C4—381no—
1065C4—381no—
1066C4—381no—
1067C2—41no—
1068C2—41no—
1069C2—41no—
1070C2—41no—
1071C2—41no—
1072C2—382no—
1073C2—761no—
1074C2—761no—
1075C2—761no—
1076C2—761no—
1077C2—761no—
1078C2H(5,𝔽2)×D1911yescharacteristic
1079C2H(5,𝔽2)×D1911yescharacteristic
1080C2#1192738011yescharacteristic
subgroupG/H
center, FrattiniC22C24×D19
commutator, socle, cosocleC22×C19C25
FittingC19×#538C2
hypercenter#538D19
hypocenterC19#3558
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ #538

Complements

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

NH ≅ G/Ntype
1. #11927290C2semidirect
2. #11927289C2semidirect
3. #11927287C2semidirect
4. #11927286C2semidirect
5. #11927278C2semidirect
6. #11927277C2semidirect
7. #11927204C2semidirect
8. #11927202C2semidirect
9. #11927191C2semidirect
10. #11927190C2semidirect
11. #11927186C2semidirect
12. #11927184C2semidirect
13. #11927184C2semidirect
14. #11927183C2semidirect
15. #11927178C2semidirect
16. #11927176C2semidirect
17. #11927162C2semidirect
18. #11927160C2semidirect
19. #11927133C2semidirect
20. #11927133C2semidirect
21. #11927128C2semidirect
22. #11927127C2semidirect
23. #11927126C2semidirect
24. #11927110C2semidirect
25. #11927109C2semidirect
26. #11927105C2semidirect
27. #11927104C2semidirect
28. #11927091C2semidirect
29. #11927077C2semidirect
30. #124×D19C2semidirect
31. C19×#538C2semidirect
32. C22×C22⋊D19C22semidirect
33. C22×C22⋊D19C22semidirect
34. C2×Q8×D19C22semidirect
35. C2×#64543C22semidirect
37. C2×D4×D19C22semidirect
38. C2×D4×D19C22semidirect
39. C2×D4×D19C22semidirect
40. C2×#64541C22semidirect
41. C2×#64541C22semidirect
42. C2×#64541C22semidirect
43. C22×D76C22semidirect
44. C19×#126C22semidirect
45. C19×#126C22semidirect
46. C19×#124C22semidirect
47. C19×#124C22semidirect
48. C19×#123C22semidirect
49. C19×#123C22semidirect
50. C19×C22⋊Q8C22semidirect
51. C19×#121C22semidirect
52. C19×#121C22semidirect
53. C19×#121C22semidirect
54. C19×#120C22semidirect
55. C19×#120C22semidirect
56. C4×D4×C19C22semidirect
57. C4×D4×C19C22semidirect
58. C2×C22⋊C4×C19C22semidirect
59. #10597399C22semidirect
60. #10597399C22semidirect
61. #10597393C22semidirect
62. #10597393C22semidirect
63. #10597392C22semidirect
66. #10597386C22semidirect
68. #10597385C22semidirect
69. #10597385C22semidirect
70. #10597385C22semidirect
71. #10597384C22semidirect
72. #10597384C22semidirect
73. #10597384C22semidirect
74. #10597383C22semidirect
75. #10597383C22semidirect
76. #10597383C22semidirect
77. #10597383C22semidirect
78. #10597383C22semidirect
79. #10597383C22semidirect
80. #10597383C22semidirect
81. #10597383C22semidirect
82. #10597382C22semidirect
83. #10597382C22semidirect
84. #10597382C22semidirect
85. #10597381C22semidirect
86. #10597381C22semidirect
87. #10597376C22semidirect
88. #10597376C22semidirect
89. #10597375C22semidirect
90. #10597375C22semidirect
91. #10597375C22semidirect
92. C4×C22⋊D19C22semidirect
93. C4×C22⋊D19C22semidirect
94. C4×C22⋊D19C22semidirect
95. C4×C22⋊D19C22semidirect
96. C4×C22⋊D19C22semidirect
97. C2×(C2×D19)⋊C4C22semidirect
98. #10597370C22semidirect
99. #10597344C22semidirect
100. #10597344C22semidirect
101. #10597343C22semidirect
102. #10597342C22semidirect
103. #10597342C22semidirect
104. #10597342C22semidirect
105. #10597342C22semidirect
106. #10597341C22semidirect
107. #10597341C22semidirect
108. #10597341C22semidirect
109. #10597341C22semidirect
110. #10597340C22semidirect
111. #10597340C22semidirect
112. #10597340C22semidirect
113. #10597340C22semidirect
114. #10597340C22semidirect
115. #10597339C22semidirect
116. #10597339C22semidirect
117. #10597339C22semidirect
118. #10597338C22semidirect
119. #10597335C22semidirect
120. #10597334C22semidirect
121. #10597333C22semidirect
122. #10597333C22semidirect
123. #10597332C22semidirect
124. #10597331C22semidirect
125. #10597331C22semidirect
126. #10597331C22semidirect
127. #10597331C22semidirect
128. #10597331C22semidirect
129. #10597331C22semidirect
130. #10597331C22semidirect
131. #10597331C22semidirect
132. #10597331C22semidirect
133. #10597331C22semidirect
134. #10597331C22semidirect
135. #10597331C22semidirect
136. #10597331C22semidirect
137. #10597331C22semidirect
138. #10597331C22semidirect
141. #10597330C22semidirect
142. #10597330C22semidirect
143. #10597330C22semidirect
144. #10597330C22semidirect
145. #10597330C22semidirect
146. #10597330C22semidirect
147. #10597330C22semidirect
148. #10597330C22semidirect
149. #10597330C22semidirect
150. #10597329C22semidirect
151. #10597329C22semidirect
152. #10597329C22semidirect
153. #10597329C22semidirect
154. #10597329C22semidirect
155. #10597328C22semidirect
156. #10597328C22semidirect
157. #10597328C22semidirect
158. #10597328C22semidirect
159. #10597328C22semidirect
160. #10597328C22semidirect
161. #10597328C22semidirect
162. #10597328C22semidirect
163. (C22⋊D19)⋊C4C22semidirect
164. (C22⋊D19)⋊C4C22semidirect
165. (C22⋊D19)⋊C4C22semidirect
166. (C22⋊D19)⋊C4C22semidirect
167. (C22⋊D19)⋊C4C22semidirect
168. C22⋊C4×D19C22semidirect
169. C22⋊C4×D19C22semidirect
170. C22⋊C4×D19C22semidirect
171. C22⋊C4×D19C22semidirect
172. C22⋊C4×D19C22semidirect
173. C22⋊C4×D19C22semidirect
174. #10597325C22semidirect
175. #10597324C22semidirect
176. #10597324C22semidirect
177. #10597324C22semidirect
178. #10597323C22semidirect
179. #10597322C22semidirect
180. #10597321C22semidirect
181. #10597321C22semidirect
182. #10597321C22semidirect
183. C4×D76C22semidirect
184. C4×D76C22semidirect
185. C42×D19C22semidirect
186. C4×Dic38C22semidirect
550. #538D19semidirect
592. #126C2×D19semidirect
593. #126C2×D19semidirect
618. #124C2×D19semidirect
619. #124C2×D19semidirect
636. #123C2×D19semidirect
637. #123C2×D19semidirect
648. C22⋊Q8C2×D19semidirect
673. #121C2×D19semidirect
674. #121C2×D19semidirect
675. #121C2×D19semidirect
694. #120C2×D19semidirect
695. #120C2×D19semidirect
714. C4×D4C2×D19semidirect
715. C4×D4C2×D19semidirect
725. C2×C22⋊C4C2×D19semidirect
727. C19#3558semidirect

Maximal subgroups

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

subgroupindex
#119272902
#119272892
#119272872
#119272862
#119272782
#119272772
#119272042
#119272022
#119271912
#119271902
#119271862
#119271842
#119271832
#119271782
#119271762
#119271622
#119271602
#119271332
#119271282
#119271272
#119271262
#119271102
#119271092
#119271052
#119271042
#119270912
#119270772
#124×D192
C19×#5382
#355819