Finite Group Databasebeta

← #23777424

Subgroups — #23777424

Order 10112.

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#19099275C211yesmaximal, characteristic, complemented
2#19099267C211yesmaximal, characteristic, complemented
3#19099264C211yesmaximal, characteristic, complemented
4#19099264C211yesmaximal, characteristic, complemented
5#19099258C211yesmaximal, characteristic, complemented
6#19099256C211yesmaximal, characteristic, complemented
7#19099231C211yesmaximal, characteristic, complemented
8#19099206C211yesmaximal, characteristic, complemented
9#19099205C211yesmaximal, characteristic, complemented
10#19099204C211yesmaximal, characteristic, complemented
11#19099202C211yesmaximal, characteristic, complemented
12#19099200C211yesmaximal, characteristic, complemented
13#19099200C211yesmaximal, characteristic, complemented
14#19099197C211yesmaximal, characteristic, complemented
15#19099195C211yesmaximal, characteristic, complemented
16#19099195C211yesmaximal, characteristic, complemented
17#19099165C211yesmaximal, characteristic, complemented
18#19099163C211yesmaximal, characteristic, complemented
19#19099152C211yesmaximal, characteristic, complemented
20#19099147C211yesmaximal, characteristic, complemented
21#19099146C211yesmaximal, characteristic, complemented
22#19099112C211yesmaximal, characteristic, complemented
23#19099096C211yesmaximal, characteristic, complemented
24#19099072C211yesmaximal, characteristic, complemented
25#19099071C211yesmaximal, characteristic, complemented
26C2×#14579134C211yesmaximal, characteristic, complemented
27#121×D79C211yesmaximal, characteristic, complemented
28#19099036C211yesmaximal, characteristic, complemented
29#19099035C211yesmaximal, characteristic, complemented
30C4×D4×D79C211yesmaximal, characteristic, complemented
31#538×C79C211yesmaximal, characteristic, complemented
32C2×#11929625C2211yescharacteristic, complemented
33C2×#11929624C2211yescharacteristic, complemented
34C2×#11929623C2211yescharacteristic, complemented
35C2×#11929623C2211yescharacteristic, complemented
36C22×D316C2211yescharacteristic, complemented
37C22×C22⋊D79C2211yescharacteristic
38C22×C22⋊D79C2211yescharacteristic, complemented
39C22×C22⋊D79C2211yescharacteristic, complemented
40C2×D4×D79C2211yescharacteristic
41C2×D4×D79C2211yescharacteristic
42C2×D4×D79C2211yescharacteristic, complemented
43C2×D4×D79C2211yescharacteristic, complemented
44C2×D4×D79C2211yescharacteristic, complemented
45C22×C4×D79C2211yescharacteristic, complemented
46C22×C4×D79C2211yescharacteristic, complemented
47#14579159C2211yescharacteristic, complemented
48#14579157C2211yescharacteristic, complemented
49#14579157C2211yescharacteristic, complemented
50#14579157C2211yescharacteristic, complemented
51#14579156C2211yescharacteristic, complemented
52#14579156C2211yescharacteristic, complemented
53#14579155C2211yescharacteristic, complemented
54#14579154C2211yescharacteristic, complemented
55#14579151C2211yescharacteristic, complemented
56#14579151C2211yescharacteristic, complemented
57#14579151C2211yescharacteristic, complemented
58#14579150C2211yescharacteristic, complemented
59#14579149C2211yescharacteristic, complemented
60#14579147C2211yescharacteristic, complemented
61#14579147C2211yescharacteristic, complemented
62#14579147C2211yescharacteristic, complemented
63#14579146C2211yescharacteristic, complemented
64#14579146C2211yescharacteristic, complemented
65#14579146C2211yescharacteristic, complemented
66#14579146C2211yescharacteristic, complemented
67#14579145C2211yescharacteristic, complemented
68#14579145C2211yescharacteristic, complemented
69#14579144C2211yescharacteristic, complemented
70#14579143C2211yescharacteristic, complemented
71#14579143C2211yescharacteristic, complemented
72#14579143C2211yescharacteristic, complemented
73#14579143C2211yescharacteristic, complemented
74#14579142C2211yescharacteristic, complemented
75#14579139C2211yescharacteristic, complemented
76#14579139C2211yescharacteristic, complemented
77#14579139C2211yescharacteristic, complemented
78#14579138C2211yescharacteristic, complemented
79#14579138C2211yescharacteristic, complemented
80#14579137C2211yescharacteristic, complemented
81#14579136C2211yescharacteristic, complemented
82#14579136C2211yescharacteristic, complemented
83#14579136C2211yescharacteristic, complemented
84#14579136C2211yescharacteristic, complemented
85#14579135C2211yescharacteristic, complemented
86#14579134C2211yescharacteristic
87#14579134C2211yescharacteristic, complemented
88#14579134C2211yescharacteristic, complemented
89#14579134C2211yescharacteristic, complemented
90#14579134C2211yescharacteristic, complemented
91#14579134C2211yescharacteristic, complemented
92#14579134C2211yescharacteristic, complemented
93#14579134C2211yescharacteristic, complemented
94#14579134C2211yescharacteristic, complemented
95#14579134C2211yescharacteristic, complemented
96#14579134C2211yescharacteristic, complemented
97#14579134C2211yescharacteristic, complemented
98#14579134C2211yescharacteristic, complemented
99#14579134C2211yescharacteristic, complemented
100#14579134C2211yescharacteristic, complemented
101#14579134C2211yescharacteristic, complemented
102#14579133C2211yescharacteristic, complemented
103#14579133C2211yescharacteristic, complemented
104#14579133C2211yescharacteristic, complemented
105#14579133C2211yescharacteristic, complemented
106#14579133C2211yescharacteristic, complemented
107#14579133C2211yescharacteristic, complemented
108#14579133C2211yescharacteristic, complemented
109#14579133C2211yescharacteristic, complemented
110#14579133C2211yescharacteristic, complemented
111#14579132C2211yescharacteristic, complemented
112#14579132C2211yescharacteristic, complemented
113#14579131C2211yescharacteristic, complemented
114#14579131C2211yescharacteristic, complemented
115#14579131C2211yescharacteristic, complemented
116#14579131C2211yescharacteristic, complemented
117#14579131C2211yescharacteristic, complemented
118#14579131C2211yescharacteristic, complemented
119#14579129C2211yescharacteristic, complemented
120#14579129C2211yescharacteristic, complemented
121#14579129C2211yescharacteristic, complemented
122#14579129C2211yescharacteristic, complemented
123#14579126C2211yescharacteristic, complemented
124C4×D316C2211yescharacteristic, complemented
125C4×D316C2211yescharacteristic, complemented
126C4×D316C2211yescharacteristic, complemented
127D4×Dic79C2211yescharacteristic, complemented
128D4×Dic79C2211yescharacteristic, complemented
129#14579123C2211yescharacteristic, complemented
130#14579123C2211yescharacteristic, complemented
131#14579123C2211yescharacteristic, complemented
132#14579123C2211yescharacteristic, complemented
133C4×C22⋊D79C2211yescharacteristic
134C4×C22⋊D79C2211yescharacteristic
135C4×C22⋊D79C2211yescharacteristic, complemented
136C4×C22⋊D79C2211yescharacteristic, complemented
137C4×C22⋊D79C2211yescharacteristic, complemented
138C4×C22⋊D79C2211yescharacteristic, complemented
139C4×C22⋊D79C2211yescharacteristic, complemented
140(C22⋊D79)⋊C4C2211yescharacteristic
141(C22⋊D79)⋊C4C2211yescharacteristic
142(C22⋊D79)⋊C4C2211yescharacteristic, complemented
143(C22⋊D79)⋊C4C2211yescharacteristic, complemented
144(C22⋊D79)⋊C4C2211yescharacteristic, complemented
145(C22⋊D79)⋊C4C2211yescharacteristic, complemented
146(C22⋊D79)⋊C4C2211yescharacteristic, complemented
147(C22⋊D79)⋊C4C2211yescharacteristic, complemented
148(C22⋊D79)⋊C4C2211yescharacteristic, complemented
149(C22⋊D79)⋊C4C2211yescharacteristic, complemented
150(C22⋊D79)⋊C4C2211yescharacteristic, complemented
151(C22⋊D79)⋊C4C2211yescharacteristic, complemented
152(C22⋊D79)⋊C4C2211yescharacteristic, complemented
153#14579119C2211yescharacteristic, complemented
154#14579118C2211yescharacteristic, complemented
155#14579118C2211yescharacteristic, complemented
156#14579117C2211yescharacteristic, complemented
157#14579117C2211yescharacteristic, complemented
158#14579117C2211yescharacteristic, complemented
159C2×Dic79⋊C4C2211yescharacteristic, complemented
160C4⋊C4×D79C2211yescharacteristic, complemented
161C4⋊C4×D79C2211yescharacteristic, complemented
162C2×C22⋊Dic79C2211yescharacteristic, complemented
163C2×(C2×D79)⋊C4C2211yescharacteristic, complemented
164C2×(C2×D79)⋊C4C2211yescharacteristic, complemented
165C22⋊C4×D79C2211yescharacteristic, complemented
166C22⋊C4×D79C2211yescharacteristic, complemented
167C22⋊C4×D79C2211yescharacteristic, complemented
168C22⋊C4×D79C2211yescharacteristic, complemented
169C22⋊C4×D79C2211yescharacteristic, complemented
170C22⋊C4×D79C2211yescharacteristic, complemented
171C42×D79C2211yescharacteristic, complemented
172#126×C79C2211yescharacteristic, complemented
173#126×C79C2211yescharacteristic, complemented
174#124×C79C2211yescharacteristic, complemented
175#124×C79C2211yescharacteristic, complemented
176#123×C79C2211yescharacteristic, complemented
177#123×C79C2211yescharacteristic, complemented
178C22⋊Q8×C79C2211yescharacteristic, complemented
179#121×C79C2211yescharacteristic, complemented
180#121×C79C2211yescharacteristic, complemented
181#121×C79C2211yescharacteristic, complemented
182#120×C79C2211yescharacteristic, complemented
183#120×C79C2211yescharacteristic, complemented
184C4×D4×C79C2211yescharacteristic, complemented
185C4×D4×C79C2211yescharacteristic, complemented
186C2×C22⋊C4×C79C2211yescharacteristic, complemented
187C23×D79C2311yescharacteristic
188C23×D79C2311yescharacteristic
189C23×D79C2311yescharacteristic
190C23×D79C2311yescharacteristic
191C23×D79C2311yescharacteristic
192#11929625—42no—
193#11929624—42no—
194#11929623—42no—
195#11929623—42no—
196C2×Dic158C2311yescharacteristic
197C2×Dic158C2311yescharacteristic
198C2×D316—42no—
199C2×D316C2311yescharacteristic
200C2×D316C2311yescharacteristic
201C2×D316C2311yescharacteristic
202C2×D316C2311yescharacteristic
203C2×D316C2311yescharacteristic
204C2×D316C2311yescharacteristic
205C2×D316C2311yescharacteristic
206C2×D316C2311yescharacteristic
207C2×D316C2311yescharacteristic
208C2×D316C2311yescharacteristic
209C2×C22⋊D79—24no—
210C2×C22⋊D79—42no—
211C2×C22⋊D79—42no—
212C2×C22⋊D79C2311yescharacteristic
213C2×C22⋊D79C2311yescharacteristic
214C2×C22⋊D79C2311yescharacteristic
215C2×C22⋊D79C2311yescharacteristic
216C2×C22⋊D79C2311yescharacteristic
217C2×C22⋊D79C2311yescharacteristic
218C2×C22⋊D79C2311yescharacteristic
219C2×C22⋊D79C2311yescharacteristic
220C2×C22⋊D79C2311yescharacteristic
221C2×C22⋊D79C2311yescharacteristic
222C2×C22⋊D79C2311yescharacteristic
223C2×C22⋊D79C2311yescharacteristic
224C2×C22⋊D79C2311yescharacteristic
225C2×C22⋊D79C2311yescharacteristic
226C2×C22⋊D79C2311yescharacteristic
227C2×C22⋊D79C2311yescharacteristic
228C2×C22⋊D79C2311yescharacteristic
229C2×C22⋊D79C2311yescharacteristic
230C2×C22⋊D79C2311yescharacteristic
231C2×C22⋊D79C2311yescharacteristic
232D4×D79—24no—
233D4×D79—24no—
234D4×D79—42no—
235D4×D79—42no—
236D4×D79—42no—
237C22×Dic79C2311yescharacteristic
238C22×Dic79C2311yescharacteristic
239C22×Dic79C2311yescharacteristic
240C22×Dic79C2311yescharacteristic
241C22×Dic79C2311yescharacteristic
242C22×Dic79C2311yescharacteristic
243C22×Dic79C2311yescharacteristic
244C2×C4×D79—42no—
245C2×C4×D79—42no—
246C2×C4×D79C2311yescharacteristic
247C2×C4×D79C2311yescharacteristic
248C2×C4×D79C2311yescharacteristic
249C2×C4×D79C2311yescharacteristic
250C2×C4×D79C2311yescharacteristic
251C2×C4×D79C2311yescharacteristic
252C2×C4×D79C2311yescharacteristic
253C2×C4×D79C2311yescharacteristic
254C2×C4×D79C2311yescharacteristic
255C2×C4×D79C2311yescharacteristic
256C2×C4×D79C2311yescharacteristic
257C2×C4×D79C2311yescharacteristic
258C2×C4×D79C2311yescharacteristic
259C2×C4×D79C2311yescharacteristic
260C2×C4×D79C2311yescharacteristic
261C2×C4×D79C2311yescharacteristic
262C4⋊Dic79C2311yescharacteristic
263C4⋊Dic79C2311yescharacteristic
264C4⋊Dic79C2311yescharacteristic
265C4⋊Dic79C2311yescharacteristic
266Dic79⋊C4C2311yescharacteristic
267Dic79⋊C4C2311yescharacteristic
268Dic79⋊C4C2311yescharacteristic
269Dic79⋊C4C2311yescharacteristic
270Dic79⋊C4C2311yescharacteristic
271Dic79⋊C4C2311yescharacteristic
272Dic79⋊C4C2311yescharacteristic
273Dic79⋊C4C2311yescharacteristic
274Dic79⋊C4C2311yescharacteristic
275Dic79⋊C4C2311yescharacteristic
276Dic79⋊C4C2311yescharacteristic
277Dic79⋊C4C2311yescharacteristic
278Dic79⋊C4C2311yescharacteristic
279Dic79⋊C4C2311yescharacteristic
280Dic79⋊C4C2311yescharacteristic
281Dic79⋊C4C2311yescharacteristic
282C22⋊Dic79C2311yescharacteristic
283C22⋊Dic79C2311yescharacteristic
284C22⋊Dic79C2311yescharacteristic
285C22⋊Dic79C2311yescharacteristic
286C22⋊Dic79C2311yescharacteristic
287C22⋊Dic79C2311yescharacteristic
288C22⋊Dic79C2311yescharacteristic
289C22⋊Dic79C2311yescharacteristic
290(C2×D79)⋊C4C2311yescharacteristic
291(C2×D79)⋊C4C2311yescharacteristic
292(C2×D79)⋊C4C2311yescharacteristic
293(C2×D79)⋊C4C2311yescharacteristic
294(C2×D79)⋊C4C2311yescharacteristic
295(C2×D79)⋊C4C2311yescharacteristic
296(C2×D79)⋊C4C2311yescharacteristic
297(C2×D79)⋊C4C2311yescharacteristic
298(C2×D79)⋊C4C2311yescharacteristic
299(C2×D79)⋊C4C2311yescharacteristic
300(C2×D79)⋊C4C2311yescharacteristic
301(C2×D79)⋊C4C2311yescharacteristic
302(C2×D79)⋊C4C2311yescharacteristic
303(C2×D79)⋊C4C2311yescharacteristic
304(C2×D79)⋊C4C2311yescharacteristic
305(C2×D79)⋊C4C2311yescharacteristic
306(C2×D79)⋊C4C2311yescharacteristic
307(C2×D79)⋊C4C2311yescharacteristic
308(C2×D79)⋊C4C2311yescharacteristic
309(C2×D79)⋊C4C2311yescharacteristic
310(C2×D79)⋊C4C2311yescharacteristic
311(C2×D79)⋊C4C2311yescharacteristic
312(C2×D79)⋊C4C2311yescharacteristic
313(C2×D79)⋊C4C2311yescharacteristic
314C4×Dic79C2311yescharacteristic
315C4×Dic79C2311yescharacteristic
316C4×Dic79C2311yescharacteristic
317C4×Dic79C2311yescharacteristic
318C4×Dic79C2311yescharacteristic
319C4×Dic79C2311yescharacteristic
320C4×Dic79C2311yescharacteristic
321C4×Dic79C2311yescharacteristic
322C24×C79C2311yescharacteristic
323C2×Q8×C79C2311yescharacteristic
324C2×D4×C79C2311yescharacteristic
325C2×D4×C79C2311yescharacteristic
326C2×D4×C79C2311yescharacteristic
327C2×D4×C79C2311yescharacteristic
328C2×D4×C79C2311yescharacteristic
329C2×D4×C79C2311yescharacteristic
330C2×D4×C79C2311yescharacteristic
331C22×C4×C79C2311yescharacteristic
332C22×C4×C79C2311yescharacteristic
333C22×C4×C79C2311yescharacteristic
334C22×C4×C79C2311yescharacteristic
335C4⋊C4×C79C2311yescharacteristic
336C4⋊C4×C79C2311yescharacteristic
337C4⋊C4×C79C2311yescharacteristic
338C4⋊C4×C79C2311yescharacteristic
339C4⋊C4×C79C2311yescharacteristic
340C4⋊C4×C79C2311yescharacteristic
341C22⋊C4×C79C2311yescharacteristic
342C22⋊C4×C79C2311yescharacteristic
343C22⋊C4×C79C2311yescharacteristic
344C22⋊C4×C79C2311yescharacteristic
345C22⋊C4×C79C2311yescharacteristic
346C22⋊C4×C79C2311yescharacteristic
347C22⋊C4×C79C2311yescharacteristic
348C22⋊C4×C79C2311yescharacteristic
349C22⋊C4×C79C2311yescharacteristic
350C22⋊C4×C79C2311yescharacteristic
351C22⋊C4×C79C2311yescharacteristic
352C22⋊C4×C79C2311yescharacteristic
353C22⋊C4×C79C2311yescharacteristic
354C22⋊C4×C79C2311yescharacteristic
355C42×C79C2311yescharacteristic
356C42×C79C2311yescharacteristic
357C23×C79—22no—
358C23×C79—41no—
359C23×C79—41no—
360C23×C79C2411yescharacteristic
361C23×C79C2411yescharacteristic
362C23×C79C2411yescharacteristic
363C23×C79C2411yescharacteristic
364C23×C79C2411yescharacteristic
365C22×D79—22no—
366C22×D79—22no—
367C22×D79—22no—
368C22×D79—22no—
369C22×D79—22no—
370C22×D79—22no—
371C22×D79—22no—
372C22×D79—41no—
373C22×D79—41no—
374C22×D79—41no—
375C22×D79—41no—
376C22×D79—41no—
377C22×D79—41no—
378C22×D79—41no—
379C22×D79—41no—
380C22×D79C2411yescharacteristic
381C22×D79C2411yescharacteristic
382C22×D79C2411yescharacteristic
383C22×D79C2411yescharacteristic
384C22×D79C2411yescharacteristic
385C22×D79C2411yescharacteristic
386Q8×C79—41no—
387D4×C79—22no—
388D4×C79—22no—
389D4×C79—41no—
390D4×C79—41no—
391D4×C79—41no—
392D4×C79—41no—
393D4×C79—41no—
394C2×C4×C79—41no—
395C2×C4×C79—41no—
396C2×C4×C79—41no—
397C2×C4×C79—41no—
398C2×C4×C79C2411yescharacteristic
399C2×C4×C79C2411yescharacteristic
400C2×C4×C79C2411yescharacteristic
401C2×C4×C79C2411yescharacteristic
402C2×C4×C79C2411yescharacteristic
403C2×C4×C79C2411yescharacteristic
404C2×C4×C79C2411yescharacteristic
405C2×C4×C79C2411yescharacteristic
406C2×C4×C79C2411yescharacteristic
407C2×C4×C79C2411yescharacteristic
408C22⋊D79—22no—
409C22⋊D79—22no—
410C22⋊D79—22no—
411C22⋊D79—22no—
412C22⋊D79—22no—
413C22⋊D79—22no—
414C22⋊D79—22no—
415C22⋊D79—22no—
416C22⋊D79—22no—
417C22⋊D79—22no—
418C22⋊D79—22no—
419C22⋊D79—41no—
420C22⋊D79—41no—
421C22⋊D79—41no—
422C22⋊D79—41no—
423C22⋊D79—41no—
424C22⋊D79—41no—
425C22⋊D79—41no—
426C22⋊D79—41no—
427C22⋊D79#4114yescomplemented
428C2×Dic79—22no—
429C2×Dic79—22no—
430C2×Dic79—22no—
431C2×Dic79—41no—
432C2×Dic79—41no—
433C2×Dic79—41no—
434C2×Dic79—41no—
435C2×Dic79C2411yescharacteristic
436C2×Dic79C2411yescharacteristic
437C2×Dic79C2411yescharacteristic
438C2×Dic79C2411yescharacteristic
439C2×Dic79C2411yescharacteristic
440C2×Dic79C2411yescharacteristic
441C2×Dic79C2411yescharacteristic
442C2×Dic79C2411yescharacteristic
443C2×Dic79C2411yescharacteristic
444C2×Dic79C2411yescharacteristic
445D316—22no—
446D316—22no—
447D316—22no—
448D316—22no—
449D316—22no—
450D316—41no—
451D316—41no—
452D316—41no—
453D316—41no—
454D316—41no—
455C4×D79—22no—
456C4×D79—22no—
457C4×D79—22no—
458C4×D79—22no—
459C4×D79—22no—
460C4×D79—22no—
461C4×D79—41no—
462C4×D79—41no—
463C4×D79—41no—
464C4×D79—41no—
465C4×D79—41no—
466C4×D79—41no—
467C4×D79—41no—
468C4×D79—41no—
469C4×D79—41no—
470C4×D79—41no—
471Dic158—22no—
472Dic158—41no—
473C22×C79—21no—
474C22×C79—21no—
475C22×C79—21no—
476C22×C79—21no—
477C22×C79—21no—
478C22×C79—21no—
479C22×C79—21no—
480C22×C79—21no—
481C22×C79—21no—
482C22×C79—21no—
483C22×C79—21no—
484C22×C79—21no—
485C22×C79—21no—
486C22×C79—21no—
487C22×C79—82no—
488C22×C79C2×#4112yes—
489C22×C79C2511yescharacteristic
490C2×D79—21no—
491C2×D79—21no—
492C2×D79—21no—
493C2×D79—21no—
494C2×D79—21no—
495C2×D79—21no—
496C2×D79—21no—
497C2×D79—21no—
498C2×D79—21no—
499C2×D79—21no—
500C2×D79—21no—
501C2×D79—21no—
502C2×D79—21no—
503C2×D79—21no—
504C2×D79—21no—
505C2×D79—21no—
506C2×D79—44no—
507C2×D79—44no—
508C2×D79—82no—
509C2×D79—82no—
510C2×D79—82no—
511C2×D79C2×#4112yes—
512C2×D79H(5,𝔽2)12yes—
513C4×C79—21no—
514C4×C79—21no—
515C4×C79—21no—
516C4×C79—21no—
517C4×C79—21no—
518C4×C79—21no—
519C4×C79—21no—
520C4×C79—21no—
521C4×C79—21no—
522C4×C79—21no—
523Dic79—21no—
524Dic79—21no—
525Dic79—21no—
526Dic79—21no—
527Dic79—21no—
528Dic79—21no—
529Dic79—21no—
530Dic79—21no—
531Dic79C2×#4112yes—
532Dic79H(5,𝔽2)12yes—
533C2×C79—22no—
534C2×C79—41no—
535C2×C79—41no—
536C2×C79—41no—
537C2×C79—41no—
538C2×C79C22×#4111yescharacteristic
539C2×C79C2×H(5,𝔽2)11yescharacteristic
540C2×C79C2×H(5,𝔽2)11yescharacteristic
541D79—22no—
542D79—22no—
543D79—41no—
544D79—41no—
545D79—41no—
546D79—41no—
547#3519—791nomaximal, Sylow
548C79#351911yescharacteristic, complemented, Sylow
549#555—791no—
550#554—791no—
551#553—791no—
552#553—791no—
553#553—791no—
554#553—791no—
555#550—791no—
556#546—791no—
557#546—791no—
558#546—791no—
559#546—791no—
560#546—791no—
561#546—791no—
562D42—791no—
563D42—791no—
564D42—791no—
565#540—791no—
566#540—791no—
567#538—791no—
568#538—791no—
569#538—791no—
570#538D7911yescharacteristic, complemented
571#532—791no—
572#529—791no—
573#525—791no—
574#525—791no—
575C2×#121—791no—
576C2×#121—791no—
577#518—791no—
578#518—791no—
579C2×C4×D4—791no—
580C2×#41—791no—
581C2×#41—791no—
582C2×#41—791no—
583C2×#41—791no—
584C22×D4—791no—
585C22×D4—791no—
586C22×D4—791no—
587C22×D4—791no—
588C22×D4—791no—
589C22×D4—791no—
590C22×D4—791no—
591C22×D4—791no—
592C22×D4—791no—
593C23×C4—791no—
594C23×C4—791no—
595C4⋊Q8—791no—
596#127—791no—
597#127—791no—
598#127—791no—
599#126—791no—
600#126—791no—
601#126—791no—
602#126—791no—
603#126C2×D7911yescharacteristic, complemented
604#126C2×D7911yescharacteristic, complemented
605#125—791no—
606#125—791no—
607#125—791no—
608#124—791no—
609#124—791no—
610#124—791no—
611#124—791no—
612#124—791no—
613#124C2×D7911yescharacteristic, complemented
614#124C2×D7911yescharacteristic, complemented
615#123—791no—
616#123—791no—
617#123—791no—
618#123—791no—
619#123—791no—
620#123—791no—
621#123—791no—
622#123—791no—
623#123—791no—
624#123—791no—
625#123—791no—
626#123—791no—
627#123C2×D7911yescharacteristic, complemented
628#123C2×D7911yescharacteristic, complemented
629C22⋊Q8—791no—
630C22⋊Q8—791no—
631C22⋊Q8—791no—
632C22⋊Q8—791no—
633C22⋊Q8—791no—
634C22⋊Q8—791no—
635C22⋊Q8C2×D7911yescharacteristic, complemented
636#121—791no—
637#121—791no—
638#121—791no—
639#121—791no—
640#121—791no—
641#121—791no—
642#121—791no—
643#121—791no—
644#121—791no—
645#121—791no—
646#121—791no—
647#121—791no—
648#121—791no—
649#121—791no—
650#121—791no—
651#121—791no—
652#121—791no—
653#121—791no—
654#121—791no—
655#121—791no—
656#121—791no—
657#121—791no—
658#121—791no—
659#121—791no—
660#121—791no—
661#121—791no—
662#121—791no—
663#121—791no—
664#121—791no—
665#121—791no—
666#121—791no—
667#121—791no—
668#121C2×D7911yescharacteristic, complemented
669#121C2×D7911yescharacteristic, complemented
670#121C2×D7911yescharacteristic, complemented
671#120—791no—
672#120—791no—
673#120—791no—
674#120—791no—
675#120—791no—
676#120—791no—
677#120—791no—
678#120—791no—
679#120—791no—
680#120—791no—
681#120C2×D7911yescharacteristic, complemented
682#120C2×D7911yescharacteristic, complemented
683C4×Q8—791no—
684C4×D4—791no—
685C4×D4—791no—
686C4×D4—791no—
687C4×D4—791no—
688C4×D4—791no—
689C4×D4—791no—
690C4×D4—791no—
691C4×D4—791no—
692C4×D4—791no—
693C4×D4—791no—
694C4×D4—791no—
695C4×D4—791no—
696C4×D4—791no—
697C4×D4—791no—
698C4×D4—791no—
699C4×D4—791no—
700C4×D4—791no—
701C4×D4—791no—
702C4×D4—791no—
703C4×D4—791no—
704C4×D4—791no—
705C4×D4—791no—
706C4×D4—791no—
707C4×D4—791no—
708C4×D4—791no—
709C4×D4—791no—
710C4×D4—791no—
711C4×D4—791no—
712C4×D4—791no—
713C4×D4C2×D7911yescharacteristic, complemented
714C4×D4C2×D7911yescharacteristic, complemented
715#117—791no—
716#117—791no—
717#117—791no—
718#117—791no—
719#117—791no—
720#117—791no—
721C2×C4⋊C4—791no—
722C2×C4⋊C4—791no—
723C2×C4⋊C4—791no—
724C2×C22⋊C4—791no—
725C2×C22⋊C4—791no—
726C2×C22⋊C4—791no—
727C2×C22⋊C4—791no—
728C2×C22⋊C4—791no—
729C2×C22⋊C4—791no—
730C2×C22⋊C4—791no—
731C2×C22⋊C4—791no—
732C2×C22⋊C4—791no—
733C2×C22⋊C4C2×D7911yescharacteristic, complemented
734C2×C42—791no—
735C24—791no—
736C24—791no—
737C24—791no—
738C24—791no—
739C24—791no—
740C24C22×D7911yescharacteristic
741#41—3162no—
742#41—3162no—
743#41—3162no—
744#41—3162no—
745C2×Q8—791no—
746C2×Q8—791no—
747C2×Q8C22×D7911yescharacteristic
748C2×D4—3162no—
749C2×D4—3162no—
750C2×D4—3162no—
751C2×D4—3162no—
752C2×D4—3162no—
753C2×D4—3162no—
754C2×D4—791no—
755C2×D4—791no—
756C2×D4—791no—
757C2×D4—791no—
758C2×D4—791no—
759C2×D4—791no—
760C2×D4—791no—
761C2×D4—791no—
762C2×D4—791no—
763C2×D4—791no—
764C2×D4—791no—
765C2×D4—791no—
766C2×D4—791no—
767C2×D4—791no—
768C2×D4—791no—
769C2×D4—791no—
770C2×D4—791no—
771C2×D4—791no—
772C2×D4—791no—
773C2×D4—791no—
774C2×D4—791no—
775C2×D4—791no—
776C2×D4—791no—
777C2×D4—791no—
778C2×D4—791no—
779C2×D4—791no—
780C2×D4—791no—
781C2×D4—791no—
782C2×D4—791no—
783C2×D4—791no—
784C2×D4—1584no—
785C2×D4—1584no—
786C2×D4—1584no—
787C2×D4C22×D7911yescharacteristic
788C2×D4C22×D7911yescharacteristic
789C2×D4C22×D7911yescharacteristic
790C2×D4C22×D7911yescharacteristic
791C2×D4C22×D7911yescharacteristic
792C2×D4C22×D7911yescharacteristic
793C2×D4C22×D7911yescharacteristic
794C22×C4—3162no—
795C22×C4—3162no—
796C22×C4—791no—
797C22×C4—791no—
798C22×C4—791no—
799C22×C4—791no—
800C22×C4—791no—
801C22×C4—791no—
802C22×C4—791no—
803C22×C4—791no—
804C22×C4—791no—
805C22×C4—791no—
806C22×C4—791no—
807C22×C4—791no—
808C22×C4—791no—
809C22×C4—791no—
810C22×C4—791no—
811C22×C4—791no—
812C22×C4—791no—
813C22×C4—791no—
814C22×C4—791no—
815C22×C4—791no—
816C22×C4—791no—
817C22×C4—791no—
818C22×C4—791no—
819C22×C4C22×D7911yescharacteristic
820C22×C4C22×D7911yescharacteristic
821C22×C4C22×D7911yescharacteristic
822C22×C4C22×D7911yescharacteristic
823C4⋊C4—791no—
824C4⋊C4—791no—
825C4⋊C4—791no—
826C4⋊C4—791no—
827C4⋊C4—791no—
828C4⋊C4—791no—
829C4⋊C4—791no—
830C4⋊C4—791no—
831C4⋊C4—791no—
832C4⋊C4—791no—
833C4⋊C4—791no—
834C4⋊C4—791no—
835C4⋊C4—791no—
836C4⋊C4—791no—
837C4⋊C4—791no—
838C4⋊C4—791no—
839C4⋊C4—791no—
840C4⋊C4—791no—
841C4⋊C4—791no—
842C4⋊C4—791no—
843C4⋊C4C22×D7911yescharacteristic
844C4⋊C4C22×D7911yescharacteristic
845C4⋊C4C22×D7911yescharacteristic
846C4⋊C4C22×D7911yescharacteristic
847C4⋊C4C22×D7911yescharacteristic
848C4⋊C4C22×D7911yescharacteristic
849C22⋊C4—791no—
850C22⋊C4—791no—
851C22⋊C4—791no—
852C22⋊C4—791no—
853C22⋊C4—791no—
854C22⋊C4—791no—
855C22⋊C4—791no—
856C22⋊C4—791no—
857C22⋊C4—791no—
858C22⋊C4—791no—
859C22⋊C4—791no—
860C22⋊C4—791no—
861C22⋊C4—791no—
862C22⋊C4—791no—
863C22⋊C4—791no—
864C22⋊C4—791no—
865C22⋊C4—791no—
866C22⋊C4—791no—
867C22⋊C4—791no—
868C22⋊C4—791no—
869C22⋊C4—791no—
870C22⋊C4—791no—
871C22⋊C4—791no—
872C22⋊C4—791no—
873C22⋊C4—791no—
874C22⋊C4—791no—
875C22⋊C4—791no—
876C22⋊C4—791no—
877C22⋊C4—791no—
878C22⋊C4—791no—
879C22⋊C4—791no—
880C22⋊C4—791no—
881C22⋊C4C22×D7911yescharacteristic
882C22⋊C4C22×D7911yescharacteristic
883C22⋊C4C22×D7911yescharacteristic
884C22⋊C4C22×D7911yescharacteristic
885C22⋊C4C22×D7911yescharacteristic
886C22⋊C4C22×D7911yescharacteristic
887C22⋊C4C22×D7911yescharacteristic
888C22⋊C4C22×D7911yescharacteristic
889C22⋊C4C22×D7911yescharacteristic
890C22⋊C4C22×D7911yescharacteristic
891C22⋊C4C22×D7911yescharacteristic
892C22⋊C4C22×D7911yescharacteristic
893C22⋊C4C22×D7911yescharacteristic
894C22⋊C4C22×D7911yescharacteristic
895C42—791no—
896C42—791no—
897C42—791no—
898C42—791no—
899C42—791no—
900C42—791no—
901C42—791no—
902C42—791no—
903C42C22×D7911yescharacteristic
904C42C22×D7911yescharacteristic
905C23—22no—
906C23—41no—
907C23—41no—
908C23—3161no—
909C23—3161no—
910C23—3161no—
911C23—3161no—
912C23—3161no—
913C23—3161no—
914C23—3161no—
915C23—3161no—
916C23—791no—
917C23—791no—
918C23—791no—
919C23—791no—
920C23—791no—
921C23—791no—
922C23—1582no—
923C23—1582no—
924C23—1582no—
925C23—1582no—
926C23—1582no—
927C23—1582no—
928C23—1582no—
929C23C23×D7911yescharacteristic
930C23C23×D7911yescharacteristic
931C23C23×D7911yescharacteristic
932C23C23×D7911yescharacteristic
933C23C23×D7911yescharacteristic
934Q8—41no—
935Q8—3161no—
936Q8—1582no—
937D4—22no—
938D4—22no—
939D4—41no—
940D4—41no—
941D4—41no—
942D4—41no—
943D4—41no—
944D4—3161no—
945D4—3161no—
946D4—3161no—
947D4—3161no—
948D4—3161no—
949D4—3161no—
950D4—3161no—
951D4—3161no—
952D4—3161no—
953D4—3161no—
954D4—3161no—
955D4—3161no—
956D4—3161no—
957D4—794no—
958D4—1582no—
959D4—1582no—
960D4—1582no—
961D4—1582no—
962D4—1582no—
963D4—1582no—
964D4—1582no—
965D4—1582no—
966D4—1582no—
967D4—1582no—
968D4—1582no—
969D4—1582no—
970D4—1582no—
971D4—1582no—
972D4—1582no—
973D4—1582no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—3161no—
979C2×C4—3161no—
980C2×C4—3161no—
981C2×C4—3161no—
982C2×C4—3161no—
983C2×C4—3161no—
984C2×C4—3161no—
985C2×C4—3161no—
986C2×C4—3161no—
987C2×C4—3161no—
988C2×C4—3161no—
989C2×C4—3161no—
990C2×C4—3161no—
991C2×C4—3161no—
992C2×C4—791no—
993C2×C4—791no—
994C2×C4—791no—
995C2×C4—791no—
996C2×C4—791no—
997C2×C4—791no—
998C2×C4—791no—
999C2×C4—791no—
1000C2×C4—791no—
1001C2×C4—791no—
1002C2×C4—1582no—
1003C2×C4—1582no—
1004C2×C4—1582no—
1005C2×C4—1582no—
1006C2×C4—1582no—
1007C2×C4—1582no—
1008C2×C4—1582no—
1009C2×C4—1582no—
1010C2×C4—1582no—
1011C2×C4C23×D7911yescharacteristic
1012C2×C4C23×D7911yescharacteristic
1013C2×C4C23×D7911yescharacteristic
1014C2×C4C23×D7911yescharacteristic
1015C2×C4C23×D7911yescharacteristic
1016C2×C4C23×D7911yescharacteristic
1017C2×C4C23×D7911yescharacteristic
1018C2×C4C23×D7911yescharacteristic
1019C2×C4C23×D7911yescharacteristic
1020C2×C4C23×D7911yescharacteristic
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—3164no—
1037C22—3164no—
1038C22—792no—
1039C22—792no—
1040C22—6322no—
1041C22—6322no—
1042C22—6322no—
1043C22—1581no—
1044C22—1581no—
1045C22—1581no—
1046C22—1581no—
1047C22—1581no—
1048C22—1581no—
1049C22—1581no—
1050C22—1581no—
1051C22—1581no—
1052C22—1581no—
1053C22—1581no—
1054C22—1581no—
1055C22—1581no—
1056C22—1581no—
1057C22—1581no—
1058C22—1581no—
1059C22#41×D7912yes—
1060C22C24×D7911yescharacteristic
1061C4—21no—
1062C4—21no—
1063C4—21no—
1064C4—21no—
1065C4—21no—
1066C4—21no—
1067C4—21no—
1068C4—21no—
1069C4—21no—
1070C4—21no—
1071C4—792no—
1072C4—792no—
1073C4—1581no—
1074C4—1581no—
1075C4—1581no—
1076C4—1581no—
1077C4—1581no—
1078C4—1581no—
1079C4—1581no—
1080C4—1581no—
1081C2—22no—
1082C2—41no—
1083C2—41no—
1084C2—41no—
1085C2—41no—
1086C2—3161no—
1087C2—3161no—
1088C2—3161no—
1089C2—3161no—
1090C2—1582no—
1091C2—1582no—
1092C2C2×#41×D7911yescharacteristic
1093C2H(5,𝔽2)×D7911yescharacteristic
1094C2H(5,𝔽2)×D7911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D79
commutator, socle, cosocleC22×C79C25
Fitting#538×C79C2
hypercenter#538D79
hypocenterC79#3519
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #538

Complements

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

NH ≅ G/Ntype
1. #19099275C2semidirect
2. #19099267C2semidirect
3. #19099264C2semidirect
4. #19099264C2semidirect
5. #19099258C2semidirect
6. #19099256C2semidirect
7. #19099231C2semidirect
8. #19099206C2semidirect
9. #19099205C2semidirect
10. #19099204C2semidirect
11. #19099202C2semidirect
12. #19099200C2semidirect
13. #19099200C2semidirect
14. #19099197C2semidirect
15. #19099195C2semidirect
16. #19099195C2semidirect
17. #19099165C2semidirect
18. #19099163C2semidirect
19. #19099152C2semidirect
20. #19099147C2semidirect
21. #19099146C2semidirect
22. #19099112C2semidirect
23. #19099096C2semidirect
24. #19099072C2semidirect
25. #19099071C2semidirect
26. C2×#14579134C2semidirect
27. #121×D79C2semidirect
28. #19099036C2semidirect
29. #19099035C2semidirect
30. C4×D4×D79C2semidirect
31. #538×C79C2semidirect
32. C2×#11929625C22semidirect
33. C2×#11929624C22semidirect
34. C2×#11929623C22semidirect
35. C2×#11929623C22semidirect
36. C22×D316C22semidirect
38. C22×C22⋊D79C22semidirect
39. C22×C22⋊D79C22semidirect
42. C2×D4×D79C22semidirect
43. C2×D4×D79C22semidirect
44. C2×D4×D79C22semidirect
45. C22×C4×D79C22semidirect
46. C22×C4×D79C22semidirect
47. #14579159C22semidirect
48. #14579157C22semidirect
49. #14579157C22semidirect
50. #14579157C22semidirect
51. #14579156C22semidirect
52. #14579156C22semidirect
53. #14579155C22semidirect
54. #14579154C22semidirect
55. #14579151C22semidirect
56. #14579151C22semidirect
57. #14579151C22semidirect
58. #14579150C22semidirect
59. #14579149C22semidirect
60. #14579147C22semidirect
61. #14579147C22semidirect
62. #14579147C22semidirect
63. #14579146C22semidirect
64. #14579146C22semidirect
65. #14579146C22semidirect
66. #14579146C22semidirect
67. #14579145C22semidirect
68. #14579145C22semidirect
69. #14579144C22semidirect
70. #14579143C22semidirect
71. #14579143C22semidirect
72. #14579143C22semidirect
73. #14579143C22semidirect
74. #14579142C22semidirect
75. #14579139C22semidirect
76. #14579139C22semidirect
77. #14579139C22semidirect
78. #14579138C22semidirect
79. #14579138C22semidirect
80. #14579137C22semidirect
81. #14579136C22semidirect
82. #14579136C22semidirect
83. #14579136C22semidirect
84. #14579136C22semidirect
85. #14579135C22semidirect
87. #14579134C22semidirect
88. #14579134C22semidirect
89. #14579134C22semidirect
90. #14579134C22semidirect
91. #14579134C22semidirect
92. #14579134C22semidirect
93. #14579134C22semidirect
94. #14579134C22semidirect
95. #14579134C22semidirect
96. #14579134C22semidirect
97. #14579134C22semidirect
98. #14579134C22semidirect
99. #14579134C22semidirect
100. #14579134C22semidirect
101. #14579134C22semidirect
102. #14579133C22semidirect
103. #14579133C22semidirect
104. #14579133C22semidirect
105. #14579133C22semidirect
106. #14579133C22semidirect
107. #14579133C22semidirect
108. #14579133C22semidirect
109. #14579133C22semidirect
110. #14579133C22semidirect
111. #14579132C22semidirect
112. #14579132C22semidirect
113. #14579131C22semidirect
114. #14579131C22semidirect
115. #14579131C22semidirect
116. #14579131C22semidirect
117. #14579131C22semidirect
118. #14579131C22semidirect
119. #14579129C22semidirect
120. #14579129C22semidirect
121. #14579129C22semidirect
122. #14579129C22semidirect
123. #14579126C22semidirect
124. C4×D316C22semidirect
125. C4×D316C22semidirect
126. C4×D316C22semidirect
127. D4×Dic79C22semidirect
128. D4×Dic79C22semidirect
129. #14579123C22semidirect
130. #14579123C22semidirect
131. #14579123C22semidirect
132. #14579123C22semidirect
135. C4×C22⋊D79C22semidirect
136. C4×C22⋊D79C22semidirect
137. C4×C22⋊D79C22semidirect
138. C4×C22⋊D79C22semidirect
139. C4×C22⋊D79C22semidirect
142. (C22⋊D79)⋊C4C22semidirect
143. (C22⋊D79)⋊C4C22semidirect
144. (C22⋊D79)⋊C4C22semidirect
145. (C22⋊D79)⋊C4C22semidirect
146. (C22⋊D79)⋊C4C22semidirect
147. (C22⋊D79)⋊C4C22semidirect
148. (C22⋊D79)⋊C4C22semidirect
149. (C22⋊D79)⋊C4C22semidirect
150. (C22⋊D79)⋊C4C22semidirect
151. (C22⋊D79)⋊C4C22semidirect
152. (C22⋊D79)⋊C4C22semidirect
153. #14579119C22semidirect
154. #14579118C22semidirect
155. #14579118C22semidirect
156. #14579117C22semidirect
157. #14579117C22semidirect
158. #14579117C22semidirect
159. C2×Dic79⋊C4C22semidirect
160. C4⋊C4×D79C22semidirect
161. C4⋊C4×D79C22semidirect
162. C2×C22⋊Dic79C22semidirect
163. C2×(C2×D79)⋊C4C22semidirect
164. C2×(C2×D79)⋊C4C22semidirect
165. C22⋊C4×D79C22semidirect
166. C22⋊C4×D79C22semidirect
167. C22⋊C4×D79C22semidirect
168. C22⋊C4×D79C22semidirect
169. C22⋊C4×D79C22semidirect
170. C22⋊C4×D79C22semidirect
171. C42×D79C22semidirect
172. #126×C79C22semidirect
173. #126×C79C22semidirect
174. #124×C79C22semidirect
175. #124×C79C22semidirect
176. #123×C79C22semidirect
177. #123×C79C22semidirect
178. C22⋊Q8×C79C22semidirect
179. #121×C79C22semidirect
180. #121×C79C22semidirect
181. #121×C79C22semidirect
182. #120×C79C22semidirect
183. #120×C79C22semidirect
184. C4×D4×C79C22semidirect
185. C4×D4×C79C22semidirect
186. C2×C22⋊C4×C79C22semidirect
427. C22⋊D79#41semidirect
548. C79#3519semidirect
570. #538D79semidirect
603. #126C2×D79semidirect
604. #126C2×D79semidirect
613. #124C2×D79semidirect
614. #124C2×D79semidirect
627. #123C2×D79semidirect
628. #123C2×D79semidirect
635. C22⋊Q8C2×D79semidirect
668. #121C2×D79semidirect
669. #121C2×D79semidirect
670. #121C2×D79semidirect
681. #120C2×D79semidirect
682. #120C2×D79semidirect
713. C4×D4C2×D79semidirect
714. C4×D4C2×D79semidirect
733. C2×C22⋊C4C2×D79semidirect