Finite Group Databasebeta

← #14927066

Subgroups — #14927066

Order 2816.

2176 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076988C211yesmaximal, characteristic, complemented
2#13076983C211yesmaximal, characteristic, complemented
3#13076947C211yesmaximal, characteristic, complemented
4#13076917C211yesmaximal, characteristic, complemented
5#13074643C212yesmaximal, complemented
6#13074598C212yesmaximal, complemented
7#13074107C212yesmaximal, complemented
8#13073676C212yesmaximal, complemented
9#13073213C211yesmaximal, characteristic, complemented
10#13072968C211yesmaximal, characteristic, complemented
11#13072862C212yesmaximal, complemented
12#13072414C211yesmaximal, characteristic, complemented
13#13072340C211yesmaximal, characteristic, complemented
14#13072267C211yesmaximal, characteristic, complemented
15#13072182C211yesmaximal, characteristic, complemented
16#13072072C212yesmaximal, complemented
17#13072067C211yesmaximal, characteristic, complemented
18#13071972C211yesmaximal, characteristic
19#13071270C212yesmaximal, complemented
20#13071211C212yesmaximal, complemented
21C4×#66977C211yesmaximal, characteristic, complemented
22C2×#10622552C211yesmaximal, characteristic, complemented
23C42×D4×C11C211yesmaximal, characteristic, complemented
24C23×D44C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C22×C42×C11C2211yescharacteristic
29C22×C42×C11C2211yescharacteristic, complemented
30C2×#66990C2212yes—
31C2×#66983C2211yescharacteristic
32C2×#66983C2211yescharacteristic
33C2×#66982C2212yescomplemented
34C22×(C2×D11)⋊C4C2212yes—
35C22×(C2×D11)⋊C4C2212yes—
36C22×C4⋊Dic11C2211yescharacteristic
37C2×#66977C2211yescharacteristic
38C2×#66977C2211yescharacteristic, complemented
39C2×#66929C2212yescomplemented
40C2×#66928C2211yescharacteristic
41C2×#66928C2211yescharacteristic
42C2×#66923C2211yescharacteristic, complemented
43C2×C4×Dic22C2211yescharacteristic, complemented
44C4×C11×C4⋊C4C2211yescharacteristic, complemented
45C4×C11×C4⋊C4C2211yescharacteristic, complemented
46C4×C11×C4⋊C4C2211yescharacteristic, complemented
47C4×C11×C22⋊C4C2211yescharacteristic
48C4×C11×C22⋊C4C2211yescharacteristic
49C4×C11×C22⋊C4C2211yescharacteristic
50C4×C11×C22⋊C4C2211yescharacteristic, complemented
51C4×C11×C22⋊C4C2211yescharacteristic, complemented
52C4×C11×C22⋊C4C2211yescharacteristic, complemented
53C43×C11C2211yescharacteristic, complemented
54#10622833C2212yes—
55#10622826C2212yescomplemented
56#10622826C2212yescomplemented
57#10622826C2212yescomplemented
58#10622825C2211yescharacteristic
59#10622825C2211yescharacteristic, complemented
60#10622823C2212yes—
61C4×C22⋊Dic11C2212yes—
62#10622606C2212yescomplemented
63#10622605C2212yescomplemented
64#10622604C2212yes—
65#10622603C2212yescomplemented
66#10622603C2212yescomplemented
67#10622597C2212yescomplemented
68#10622573C2212yes—
69#10622572C2212yescomplemented
70#10622572C2212yescomplemented
71#10622570C2212yescomplemented
72#10622570C2212yescomplemented
73#10622568C2212yes—
74#10622568C2212yes—
75#10622568C2212yes—
76#10622561C2212yescomplemented
77#10622559C2212yes—
78#10622555C2212yes—
79#10622555C2212yes—
80#10622553C2212yescomplemented
81#10622553C2212yescomplemented
82#10622553C2212yescomplemented
83#10622553C2212yescomplemented
84#10622553C2212yescomplemented
85#10622553C2212yescomplemented
86#10622553C2212yescomplemented
87#10622553C2212yescomplemented
88#10622553C2212yescomplemented
89#10622553C2212yescomplemented
90#10622553C2212yescomplemented
91#10622552C2212yes—
92#10622552C2211yescharacteristic
93#10622552C2211yescharacteristic
94#10622552C2211yescharacteristic
95#10622552C2211yescharacteristic
96#10622552C2211yescharacteristic
97#10622552C2211yescharacteristic
98#10622552C2212yes—
99#10622552C2211yescharacteristic
100#10622552C2211yescharacteristic
101#10622549C2211yescharacteristic, complemented
102C4×C4⋊Dic11C2211yescharacteristic, complemented
103#10622546C2212yescomplemented
104C4×Dic11⋊C4C2212yescomplemented
105#10622542C2211yescharacteristic, complemented
106#10622542C2211yescharacteristic, complemented
107#10622541C2211yescharacteristic, complemented
108#10622541C2211yescharacteristic, complemented
109#10622541C2211yescharacteristic, complemented
110#10622541C2211yescharacteristic, complemented
111#10622289C2212yescomplemented
112#10622288C2212yescomplemented
113#10622288C2212yescomplemented
114#10622288C2212yescomplemented
115#10622285C2212yes—
116#10622285C2212yes—
117#10622282C2212yescomplemented
118#10622282C2212yescomplemented
119#10622282C2212yescomplemented
120#10622282C2212yescomplemented
121#10622273C2212yescomplemented
122#10622270C2212yescomplemented
123C24×D11C2312yes—
124C22×D4×C11C2311yescharacteristic
125C23×C4×C11C2311yescharacteristic
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C23×Dic11C2312yes—
134C22×D44—24no—
135C22×D44—42no—
136C22×D44—42no—
137C22×D44C2311yescharacteristic
138C22×D44C2311yescharacteristic
139C22×D44C2312yes—
140C22×Dic22C2311yescharacteristic
141C4×D4×C11—24no—
142C4×D4×C11—24no—
143C4×D4×C11—24no—
144C2×C11×C4⋊C4C2311yescharacteristic
145C2×C11×C4⋊C4C2311yescharacteristic
146C2×C11×C4⋊C4C2311yescharacteristic
147C2×C11×C22⋊C4C2311yescharacteristic
148C2×C11×C22⋊C4C2311yescharacteristic
149C2×C11×C22⋊C4C2311yescharacteristic
150C2×C11×C22⋊C4C2311yescharacteristic
151C2×C11×C22⋊C4C2311yescharacteristic
152C2×C11×C22⋊C4C2311yescharacteristic
153C2×C42×C11—42no—
154C2×C42×C11—42no—
155C2×C42×C11C2311yescharacteristic
156C2×C42×C11C2311yescharacteristic
157C2×C42×C11C2311yescharacteristic
158C2×C42×C11C2311yescharacteristic
159C2×C42×C11C2311yescharacteristic
160C2×C42×C11C2311yescharacteristic
161C2×C42×C11C2311yescharacteristic
162C2×C42×C11C2311yescharacteristic
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2311yescharacteristic
165C2×C42×C11C2311yescharacteristic
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C22⋊Dic11C2312yes—
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172#66990—28no—
173#66983—42no—
174#66983—42no—
175#66982—44no—
176C2×(C2×D11)⋊C4—28no—
177C2×(C2×D11)⋊C4—44no—
178C2×(C2×D11)⋊C4C2312yes—
179C2×(C2×D11)⋊C4C2312yes—
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×C4⋊Dic11—42no—
201C2×C4⋊Dic11C2311yescharacteristic
202C2×C4⋊Dic11C2311yescharacteristic
203C2×C4⋊Dic11C2311yescharacteristic
204C2×C4⋊Dic11C2311yescharacteristic
205C2×C4⋊Dic11C2311yescharacteristic
206C2×C4⋊Dic11C2312yes—
207#66977—24no—
208#66977—42no—
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2312yes—
215C2×Dic11⋊C4C2312yes—
216C2×Dic11⋊C4C2312yes—
217C2×Dic11⋊C4C2312yes—
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2312yes—
220#66929—44no—
221#66928—42no—
222#66928—42no—
223#66923—42no—
224C4×Dic22—42no—
225C11×#95C2311yescharacteristic
226C11×#95C2311yescharacteristic
227C11×#95C2311yescharacteristic
228C11×#95C2311yescharacteristic
229C11×#95C2311yescharacteristic
230C11×#95C2311yescharacteristic
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244#35025—111nomaximal, Sylow
245C24×C11C2411yescharacteristic
246C24×C11C2411yescharacteristic
247C23×D11—24no—
248C23×D11—24no—
249C23×D11—24no—
250C23×D11—42no—
251C23×D11—42no—
252C23×D11—42no—
253C23×D11—42no—
254C23×D11C2412yes—
255C23×D11C2412yes—
256C2×D4×C11—22no—
257C2×D4×C11—22no—
258C2×D4×C11#4114yes—
259C22×C4×C11—22no—
260C22×C4×C11—22no—
261C22×C4×C11—22no—
262C22×C4×C11—22no—
263C22×C4×C11—22no—
264C22×C4×C11—22no—
265C22×C4×C11—22no—
266C22×C4×C11—22no—
267C22×C4×C11—22no—
268C22×C4×C11—22no—
269C22×C4×C11—41no—
270C22×C4×C11—41no—
271C22×C4×C11—41no—
272C22×C4×C11—41no—
273C22×C4×C11—41no—
274C22×C4×C11—41no—
275C22×C4×C11#4114yes—
276C22×C4×C11#4114yes—
277C22×C4×C11C2411yescharacteristic
278C22×C4×C11C2411yescharacteristic
279C22×C4×C11C2411yescharacteristic
280C22×C4×C11C2411yescharacteristic
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2411yescharacteristic
283C22×C4×C11C2411yescharacteristic
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2411yescharacteristic
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C2×C22⋊D11—24no—
291C2×C22⋊D11—24no—
292C2×C22⋊D11—42no—
293C2×C22⋊D11—42no—
294C2×C22⋊D11—42no—
295C2×C22⋊D11—42no—
296C22×Dic11—24no—
297C22×Dic11—42no—
298C22×Dic11—42no—
299C22×Dic11C2412yes—
300C22×Dic11C2412yes—
301C22×Dic11C2412yes—
302C22×Dic11C2412yes—
303C22×Dic11C2412yes—
304C22×Dic11C2412yes—
305C2×D44—24no—
306C2×D44—22no—
307C2×D44—22no—
308C2×D44—22no—
309C2×D44—22no—
310C2×D44—22no—
311C2×D44—22no—
312C2×D44—42no—
313C2×D44—42no—
314C2×D44—416no—
315C2×Dic22—22no—
316C2×Dic22—22no—
317C2×Dic22—22no—
318C11×C4⋊C4—22no—
319C11×C4⋊C4—22no—
320C11×C4⋊C4—22no—
321C11×C22⋊C4—22no—
322C11×C22⋊C4—22no—
323C11×C22⋊C4—22no—
324C11×C22⋊C4—22no—
325C11×C22⋊C4—22no—
326C11×C22⋊C4—22no—
327C42×C11—22no—
328C42×C11—22no—
329C42×C11—22no—
330C42×C11—22no—
331C42×C11—22no—
332C42×C11—22no—
333C42×C11—22no—
334C42×C11—22no—
335C42×C11—41no—
336C42×C11—41no—
337C42×C11—41no—
338C42×C11—41no—
339C42×C11—41no—
340C22⋊Dic11—24no—
341C22⋊Dic11—24no—
342C22⋊Dic11—42no—
343C22⋊Dic11—42no—
344(C2×D11)⋊C4—24no—
345(C2×D11)⋊C4—24no—
346(C2×D11)⋊C4—24no—
347(C2×D11)⋊C4—24no—
348(C2×D11)⋊C4—24no—
349(C2×D11)⋊C4—24no—
350(C2×D11)⋊C4—24no—
351(C2×D11)⋊C4—24no—
352(C2×D11)⋊C4—42no—
353(C2×D11)⋊C4—42no—
354(C2×D11)⋊C4—42no—
355(C2×D11)⋊C4—42no—
356(C2×D11)⋊C4—42no—
357(C2×D11)⋊C4—42no—
358(C2×D11)⋊C4—42no—
359(C2×D11)⋊C4—42no—
360(C2×D11)⋊C4—42no—
361(C2×D11)⋊C4—42no—
362(C2×D11)⋊C4—42no—
363(C2×D11)⋊C4—42no—
364(C2×D11)⋊C4—42no—
365(C2×D11)⋊C4—42no—
366C4⋊Dic11—22no—
367C4⋊Dic11—22no—
368C4⋊Dic11—22no—
369C4⋊Dic11—22no—
370C4⋊Dic11—22no—
371C4⋊Dic11—42no—
372Dic11⋊C4—24no—
373Dic11⋊C4—24no—
374Dic11⋊C4—42no—
375Dic11⋊C4—42no—
376Dic11⋊C4—42no—
377Dic11⋊C4—42no—
378Dic11⋊C4—42no—
379Dic11⋊C4—42no—
380Dic11⋊C4—42no—
381C4×Dic11—42no—
382C4×Dic11—42no—
383#2861—111no—
384#2860—111no—
385#2854—111no—
386#2850—111no—
387#2651—112no—
388#2648—112no—
389#2593—112no—
390#2554—112no—
391#2513—111no—
392#2490—111no—
393#2480—112no—
394#2448—111no—
395#2442—111no—
396#2435—111no—
397#2426—111no—
398#2418—112no—
399#2417—111no—
400#2408—111no—
401#2321—112no—
402#2312—112no—
403C4×C22⋊Q8—111no—
404C2×#390—111no—
405C42×D4D1111yescharacteristic, complemented
406C23×C11—21no—
407C23×C11—21no—
408C23×C11—21no—
409C23×C11—21no—
410C23×C11—21no—
411C23×C11—21no—
412C23×C11—21no—
413C23×C11—21no—
414C23×C11—21no—
415C23×C11—21no—
416C23×C11C2×#4112yes—
417C23×C11C2×#4112yes—
418C23×C11C2×#4112yes—
419C23×C11C2×#4112yes—
420C23×C11C2511yescharacteristic
421C22×D11—22no—
422C22×D11—22no—
423C22×D11—22no—
424C22×D11—22no—
425C22×D11—22no—
426C22×D11—22no—
427C22×D11—22no—
428C22×D11—22no—
429C22×D11—22no—
430C22×D11—22no—
431C22×D11—22no—
432C22×D11—22no—
433C22×D11—22no—
434C22×D11—22no—
435C22×D11—48no—
436C22×D11—48no—
437C22×D11—48no—
438C22×D11—84no—
439C22×D11—84no—
440C22×D11—84no—
441C22×D11—84no—
442D4×C11—28no—
443C2×C4×C11—21no—
444C2×C4×C11—21no—
445C2×C4×C11—21no—
446C2×C4×C11—21no—
447C2×C4×C11—21no—
448C2×C4×C11—21no—
449C2×C4×C11—21no—
450C2×C4×C11—21no—
451C2×C4×C11—21no—
452C2×C4×C11—21no—
453C2×C4×C11—28no—
454C2×C4×C11—21no—
455C2×C4×C11—21no—
456C2×C4×C11—21no—
457C2×C4×C11—21no—
458C2×C4×C11—21no—
459C2×C4×C11—21no—
460C2×C4×C11—21no—
461C2×C4×C11—21no—
462C2×C4×C11—21no—
463C2×C4×C11—21no—
464C2×C4×C11—21no—
465C2×C4×C11—21no—
466C2×C4×C11—21no—
467C2×C4×C11—21no—
468C2×C4×C11—21no—
469C2×C4×C11—21no—
470C2×C4×C11—21no—
471C2×C4×C11—21no—
472C2×C4×C11—21no—
473C2×C4×C11—21no—
474C2×C4×C11—21no—
475C2×C4×C11—44no—
476C2×C4×C11—44no—
477C2×C4×C11—44no—
478C2×C4×C11—44no—
479C2×C4×C11—44no—
480C2×C4×C11C2×#4112yes—
481C2×C4×C11C2×#4112yes—
482C2×C4×C11C2×#4112yes—
483C2×C4×C11C2×#4112yes—
484C2×C4×C11C2×#4112yes—
485C2×C4×C11H(5,𝔽2)12yes—
486C2×C4×C11H(5,𝔽2)12yes—
487C2×C4×C11H(5,𝔽2)12yes—
488C22⋊D11—84no—
489C22⋊D11—84no—
490C2×Dic11—22no—
491C2×Dic11—22no—
492C2×Dic11—22no—
493C2×Dic11—22no—
494C2×Dic11—22no—
495C2×Dic11—22no—
496C2×Dic11—22no—
497C2×Dic11—22no—
498C2×Dic11—22no—
499C2×Dic11—22no—
500C2×Dic11—22no—
501C2×Dic11—22no—
502C2×Dic11—22no—
503C2×Dic11—22no—
504C2×Dic11—22no—
505C2×Dic11—22no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—84no—
509D44—48no—
510D44—44no—
511D44—44no—
512Dic22—44no—
513C23×D4—111no—
514C2×#126—112no—
515C2×#125—111no—
516C2×#124—111no—
517C2×#124—111no—
518C2×#123—112no—
519C2×C22⋊Q8—111no—
520C2×C22⋊Q8—111no—
521C2×#121—111no—
522C2×#121—111no—
523C2×#120—112no—
524C2×C4×Q8—111no—
525C2×C4×D4C2×D1111yescharacteristic
526C2×C4×D4C2×D1111yescharacteristic
527C2×C4×D4C2×D1111yescharacteristic
528C22×C4⋊C4—111no—
529C22×C22⋊C4—112no—
530C22×C22⋊C4—112no—
531C22×C42C2×D1111yescharacteristic
532C22×C42C2×D1111yescharacteristic, complemented
533#400—112no—
534#399—112no—
535#398—112no—
536#398—112no—
537#397—112no—
538#397—112no—
539#397—112no—
540#397—112no—
541#396—112no—
542#396—112no—
543#394—112no—
544#394—112no—
545#394—112no—
546#394—112no—
547#394—112no—
548#392—112no—
549#391—111no—
550#391—111no—
551#390—112no—
552#390—112no—
553#390—112no—
554#390—111no—
555#390—111no—
556#390—111no—
557#390—111no—
558#390—111no—
559#390—111no—
560#390—112no—
561#390—111no—
562#390—111no—
563#389—111no—
564#389—111no—
565#389—111no—
566#389—111no—
567#388—112no—
568#388—112no—
569#388—112no—
570#388—112no—
571#388—112no—
572#388—112no—
573#388—112no—
574#388—112no—
575#388—112no—
576#388—112no—
577#388—112no—
578#388—112no—
579#388—112no—
580#388—112no—
581#388—112no—
582#388—112no—
583#388—112no—
584#387—112no—
585#386—112no—
586#386—112no—
587#386—112no—
588#386—112no—
589#385—112no—
590#385—112no—
591#382—111no—
592#380—111no—
593#380—111no—
594#380—112no—
595#380—112no—
596#379—112no—
597#379—112no—
598#379—112no—
599C4×C4⋊C4—112no—
600C4×C4⋊C4—111no—
601C4×C4⋊C4C2×D1111yescharacteristic, complemented
602C4×C4⋊C4C2×D1111yescharacteristic, complemented
603C4×C4⋊C4C2×D1111yescharacteristic, complemented
604C4×C22⋊C4—112no—
605C4×C22⋊C4C2×D1111yescharacteristic
606C4×C22⋊C4C2×D1111yescharacteristic
607C4×C22⋊C4C2×D1111yescharacteristic
608C4×C22⋊C4C2×D1111yescharacteristic, complemented
609C4×C22⋊C4C2×D1111yescharacteristic, complemented
610C4×C22⋊C4C2×D1111yescharacteristic, complemented
611C43C2×D1111yescharacteristic, complemented
612C22×C11—22no—
613C22×C11—22no—
614C22×C11—22no—
615C22×C11—22no—
616C22×C11—22no—
617C22×C11—22no—
618C22×C11—22no—
619C22×C11—22no—
620C22×C11—22no—
621C22×C11—41no—
622C22×C11—41no—
623C22×C11—41no—
624C22×C11—41no—
625C22×C11#52914yes—
626C22×C11C22×#4111yescharacteristic
627C22×C11C22×#4111yescharacteristic
628C22×C11C22×#4111yescharacteristic
629C22×C11C2×H(5,𝔽2)11yescharacteristic
630C22×C11C2×H(5,𝔽2)11yescharacteristic
631C22×C11C2×H(5,𝔽2)11yescharacteristic
632C22×C11#58511yescharacteristic
633C2×D11—42no—
634C2×D11—42no—
635C2×D11—42no—
636C2×D11—42no—
637C2×D11—42no—
638C2×D11—42no—
639C2×D11—42no—
640C2×D11—42no—
641C2×D11—42no—
642C2×D11—42no—
643C2×D11—42no—
644C2×D11—42no—
645C2×D11—42no—
646C2×D11—42no—
647C2×D11—816no—
648C4×C11—22no—
649C4×C11—22no—
650C4×C11—22no—
651C4×C11—22no—
652C4×C11—22no—
653C4×C11—41no—
654C4×C11—41no—
655C4×C11—41no—
656C4×C11—41no—
657C4×C11—41no—
658C4×C11—41no—
659C4×C11—41no—
660C4×C11#53814yes—
661Dic11—42no—
662Dic11—42no—
663Dic11—42no—
664Dic11—42no—
665Dic11—42no—
666Dic11—42no—
667C25—112no—
668C22×Q8—111no—
669C22×D4—112no—
670C22×D4—112no—
671C22×D4—111no—
672C22×D4—111no—
673C22×D4—112no—
674C22×D4—224no—
675C22×D4—442no—
676C22×D4—442no—
677C22×D4C22×D1111yescharacteristic
678C23×C4—112no—
679C23×C4C22×D1111yescharacteristic
680C23×C4C22×D1111yescharacteristic
681C23×C4C22×D1111yescharacteristic
682C23×C4C22×D1111yescharacteristic
683C23×C4C22×D1111yescharacteristic
684C23×C4C22×D1111yescharacteristic
685#126—444no—
686#125—442no—
687#124—442no—
688#124—442no—
689#123—444no—
690C22⋊Q8—224no—
691C22⋊Q8—442no—
692#121—442no—
693#121—442no—
694#120—228no—
695C4×Q8—442no—
696C4×D4—24no—
697C4×D4—24no—
698C4×D4—24no—
699C2×C4⋊C4—111no—
700C2×C4⋊C4—111no—
701C2×C4⋊C4—111no—
702C2×C4⋊C4—111no—
703C2×C4⋊C4—111no—
704C2×C4⋊C4—112no—
705C2×C4⋊C4—112no—
706C2×C4⋊C4—112no—
707C2×C4⋊C4—112no—
708C2×C4⋊C4—112no—
709C2×C4⋊C4—112no—
710C2×C4⋊C4—112no—
711C2×C4⋊C4—112no—
712C2×C4⋊C4—112no—
713C2×C4⋊C4—112no—
714C2×C4⋊C4—442no—
715C2×C4⋊C4C22×D1111yescharacteristic
716C2×C4⋊C4C22×D1111yescharacteristic
717C2×C4⋊C4C22×D1111yescharacteristic
718C2×C22⋊C4—112no—
719C2×C22⋊C4—112no—
720C2×C22⋊C4—112no—
721C2×C22⋊C4—112no—
722C2×C22⋊C4—112no—
723C2×C22⋊C4—112no—
724C2×C22⋊C4—112no—
725C2×C22⋊C4—112no—
726C2×C22⋊C4—112no—
727C2×C22⋊C4—112no—
728C2×C22⋊C4—112no—
729C2×C22⋊C4—112no—
730C2×C22⋊C4—112no—
731C2×C22⋊C4—112no—
732C2×C22⋊C4—112no—
733C2×C22⋊C4—112no—
734C2×C22⋊C4—112no—
735C2×C22⋊C4—112no—
736C2×C22⋊C4—112no—
737C2×C22⋊C4—112no—
738C2×C22⋊C4—112no—
739C2×C22⋊C4—112no—
740C2×C22⋊C4—112no—
741C2×C22⋊C4—112no—
742C2×C22⋊C4—112no—
743C2×C22⋊C4—112no—
744C2×C22⋊C4—228no—
745C2×C22⋊C4—444no—
746C2×C22⋊C4C22×D1111yescharacteristic
747C2×C22⋊C4C22×D1111yescharacteristic
748C2×C22⋊C4C22×D1111yescharacteristic
749C2×C22⋊C4C22×D1111yescharacteristic
750C2×C22⋊C4C22×D1111yescharacteristic
751C2×C22⋊C4C22×D1111yescharacteristic
752C2×C42—42no—
753C2×C42—42no—
754C2×C42—112no—
755C2×C42—112no—
756C2×C42C22×D1111yescharacteristic
757C2×C42C22×D1111yescharacteristic
758C2×C42C22×D1111yescharacteristic
759C2×C42C22×D1111yescharacteristic
760C2×C42C22×D1111yescharacteristic
761C2×C42C22×D1111yescharacteristic
762C2×C42C22×D1111yescharacteristic
763C2×C42C22×D1111yescharacteristic
764C2×C42C22×D1111yescharacteristic
765C2×C42C22×D1111yescharacteristic
766C2×C42C22×D1111yescharacteristic
767C2×C42C22×D1111yescharacteristic
768C2×C42C22×D1111yescharacteristic
769#95—112no—
770#95—112no—
771#95—112no—
772#95—112no—
773#95—112no—
774#95—112no—
775#95—112no—
776#95—112no—
777#95—112no—
778#95—112no—
779#95—112no—
780#95—112no—
781#95—112no—
782#95C22×D1111yescharacteristic
783#95C22×D1111yescharacteristic
784#95C22×D1111yescharacteristic
785#95C22×D1111yescharacteristic
786#95C22×D1111yescharacteristic
787#95C22×D1111yescharacteristic
788C2×C11—24no—
789C2×C11—42no—
790C2×C11C2×#52911yescharacteristic
791C2×C11C2×#53811yescharacteristic
792C2×C11#346011yescharacteristic
793C2×C11#350511yescharacteristic
794C2×C11#350811yescharacteristic
795C2×C11#351411yescharacteristic
796C2×C11#351911yescharacteristic
797D11—82no—
798D11—82no—
799C24—112no—
800C24—112no—
801C24—224no—
802C24—224no—
803C24—224no—
804C24—442no—
805C24—442no—
806C24—442no—
807C24—442no—
808C24C23×D1111yescharacteristic
809C24C23×D1111yescharacteristic
810C2×Q8—222no—
811C2×Q8—222no—
812C2×Q8—222no—
813C2×D4—22no—
814C2×D4—22no—
815C2×D4—224no—
816C2×D4—224no—
817C2×D4—224no—
818C2×D4—222no—
819C2×D4—222no—
820C2×D4—222no—
821C2×D4—222no—
822C2×D4—222no—
823C2×D4—222no—
824C2×D4—442no—
825C2×D4—442no—
826C2×D4—4416no—
827C2×D4—442no—
828C2×D4—442no—
829C2×D4—442no—
830C2×D4—442no—
831C2×D4#433914yes—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—41no—
843C22×C4—41no—
844C22×C4—41no—
845C22×C4—41no—
846C22×C4—41no—
847C22×C4—41no—
848C22×C4—112no—
849C22×C4—112no—
850C22×C4—112no—
851C22×C4—112no—
852C22×C4—112no—
853C22×C4—112no—
854C22×C4—224no—
855C22×C4—442no—
856C22×C4—442no—
857C22×C4#433914yes—
858C22×C4#433914yes—
859C22×C4C23×D1111yescharacteristic
860C22×C4C23×D1111yescharacteristic
861C22×C4C23×D1111yescharacteristic
862C22×C4C23×D1111yescharacteristic
863C22×C4C23×D1111yescharacteristic
864C22×C4C23×D1111yescharacteristic
865C22×C4C23×D1111yescharacteristic
866C22×C4C23×D1111yescharacteristic
867C22×C4C23×D1111yescharacteristic
868C22×C4C23×D1111yescharacteristic
869C22×C4C23×D1111yescharacteristic
870C22×C4C23×D1111yescharacteristic
871C22×C4C23×D1111yescharacteristic
872C4⋊C4—22no—
873C4⋊C4—22no—
874C4⋊C4—22no—
875C4⋊C4—224no—
876C4⋊C4—222no—
877C4⋊C4—222no—
878C4⋊C4—222no—
879C4⋊C4—222no—
880C4⋊C4—222no—
881C4⋊C4—224no—
882C4⋊C4—442no—
883C4⋊C4—442no—
884C4⋊C4—442no—
885C4⋊C4—442no—
886C4⋊C4—442no—
887C4⋊C4—442no—
888C4⋊C4—442no—
889C4⋊C4—442no—
890C22⋊C4—22no—
891C22⋊C4—22no—
892C22⋊C4—22no—
893C22⋊C4—22no—
894C22⋊C4—22no—
895C22⋊C4—22no—
896C22⋊C4—224no—
897C22⋊C4—224no—
898C22⋊C4—224no—
899C22⋊C4—224no—
900C22⋊C4—224no—
901C22⋊C4—224no—
902C22⋊C4—224no—
903C22⋊C4—224no—
904C22⋊C4—224no—
905C22⋊C4—224no—
906C22⋊C4—442no—
907C22⋊C4—442no—
908C22⋊C4—442no—
909C22⋊C4—442no—
910C22⋊C4—442no—
911C22⋊C4—442no—
912C22⋊C4—442no—
913C22⋊C4—442no—
914C22⋊C4—442no—
915C22⋊C4—442no—
916C22⋊C4—442no—
917C22⋊C4—442no—
918C22⋊C4—442no—
919C22⋊C4—442no—
920C22⋊C4—442no—
921C22⋊C4—442no—
922C42—22no—
923C42—22no—
924C42—22no—
925C42—22no—
926C42—22no—
927C42—22no—
928C42—22no—
929C42—22no—
930C42—41no—
931C42—41no—
932C42—41no—
933C42—41no—
934C42—41no—
935C42—442no—
936C42—442no—
937C11#3502511yescharacteristic, complemented, Sylow
938C23—21no—
939C23—21no—
940C23—21no—
941C23—21no—
942C23—21no—
943C23—21no—
944C23—21no—
945C23—21no—
946C23—21no—
947C23—21no—
948C23—222no—
949C23—222no—
950C23—222no—
951C23—222no—
952C23—222no—
953C23—222no—
954C23—222no—
955C23—222no—
956C23—222no—
957C23—222no—
958C23—222no—
959C23—222no—
960C23—222no—
961C23—222no—
962C23—448no—
963C23—448no—
964C23—448no—
965C23—884no—
966C23—884no—
967C23—884no—
968C23—884no—
969C23C2×#433912yes—
970C23C2×#433912yes—
971C23C2×#433912yes—
972C23C2×#433912yes—
973C23C24×D1111yescharacteristic
974Q8—444no—
975D4—28no—
976D4—448no—
977D4—444no—
978D4—444no—
979D4—884no—
980D4—884no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—28no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—44no—
1014C2×C4—44no—
1015C2×C4—44no—
1016C2×C4—44no—
1017C2×C4—44no—
1018C2×C4—222no—
1019C2×C4—222no—
1020C2×C4—222no—
1021C2×C4—222no—
1022C2×C4—222no—
1023C2×C4—222no—
1024C2×C4—222no—
1025C2×C4—222no—
1026C2×C4—222no—
1027C2×C4—222no—
1028C2×C4—222no—
1029C2×C4—222no—
1030C2×C4—222no—
1031C2×C4—222no—
1032C2×C4—222no—
1033C2×C4—222no—
1034C2×C4—222no—
1035C2×C4—222no—
1036C2×C4—884no—
1037C2×C4C2×#433912yes—
1038C2×C4C2×#433912yes—
1039C2×C4C2×#433912yes—
1040C2×C4C2×#433912yes—
1041C2×C4C2×#433912yes—
1042C2×C4#6703712yes—
1043C2×C4#6704212yes—
1044C2×C4#6704212yes—
1045C22—22no—
1046C22—22no—
1047C22—22no—
1048C22—22no—
1049C22—22no—
1050C22—22no—
1051C22—22no—
1052C22—22no—
1053C22—22no—
1054C22—41no—
1055C22—41no—
1056C22—41no—
1057C22—41no—
1058C22—442no—
1059C22—442no—
1060C22—442no—
1061C22—442no—
1062C22—442no—
1063C22—442no—
1064C22—442no—
1065C22—442no—
1066C22—442no—
1067C22—442no—
1068C22—442no—
1069C22—442no—
1070C22—442no—
1071C22—442no—
1072C22—8816no—
1073C22#1062301014yes—
1074C22C22×#433911yescharacteristic
1075C22C22×#433911yescharacteristic
1076C22C22×#433911yescharacteristic
1077C22C2×#6703711yescharacteristic
1078C22C2×#6704211yescharacteristic
1079C22C2×#6704211yescharacteristic
1080C22#1062345311yescharacteristic
1081C4—22no—
1082C4—22no—
1083C4—22no—
1084C4—22no—
1085C4—22no—
1086C4—41no—
1087C4—41no—
1088C4—41no—
1089C4—41no—
1090C4—41no—
1091C4—41no—
1092C4—41no—
1093C4—442no—
1094C4—442no—
1095C4—442no—
1096C4—442no—
1097C4—442no—
1098C4—442no—
1099C4#1062309114yes—
1100C2—24no—
1101C2—42no—
1102C2—882no—
1103C2—882no—
1104C2C2×#1062301011yescharacteristic
1105C2C2×#1062309111yescharacteristic
1106C2#1308203211yescharacteristic
1107C2#1308245511yescharacteristic
1108C2#1308249211yescharacteristic
1109C2#1308257711yescharacteristic
1110C2#1308264811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC42×D4×C11C2
prime radical#13071972C2
hypercenterC42×D4D11
hypocenterC11#35025
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C42×D4

Complements

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

NH ≅ G/Ntype
1. #13076988C2semidirect
2. #13076983C2semidirect
3. #13076947C2semidirect
4. #13076917C2semidirect
5. #13074643C2semidirect
6. #13074598C2semidirect
7. #13074107C2semidirect
8. #13073676C2semidirect
9. #13073213C2semidirect
10. #13072968C2semidirect
11. #13072862C2semidirect
12. #13072414C2semidirect
13. #13072340C2semidirect
14. #13072267C2semidirect
15. #13072182C2semidirect
16. #13072072C2semidirect
17. #13072067C2semidirect
19. #13071270C2semidirect
20. #13071211C2semidirect
21. C4×#66977C2semidirect
22. C2×#10622552C2semidirect
23. C42×D4×C11C2semidirect
29. C22×C42×C11C22semidirect
33. C2×#66982C22semidirect
38. C2×#66977C22semidirect
39. C2×#66929C22semidirect
42. C2×#66923C22semidirect
43. C2×C4×Dic22C22semidirect
44. C4×C11×C4⋊C4C22semidirect
45. C4×C11×C4⋊C4C22semidirect
46. C4×C11×C4⋊C4C22semidirect
50. C4×C11×C22⋊C4C22semidirect
51. C4×C11×C22⋊C4C22semidirect
52. C4×C11×C22⋊C4C22semidirect
53. C43×C11C22semidirect
55. #10622826C22semidirect
56. #10622826C22semidirect
57. #10622826C22semidirect
59. #10622825C22semidirect
62. #10622606C22semidirect
63. #10622605C22semidirect
65. #10622603C22semidirect
66. #10622603C22semidirect
67. #10622597C22semidirect
69. #10622572C22semidirect
70. #10622572C22semidirect
71. #10622570C22semidirect
72. #10622570C22semidirect
76. #10622561C22semidirect
80. #10622553C22semidirect
81. #10622553C22semidirect
82. #10622553C22semidirect
83. #10622553C22semidirect
84. #10622553C22semidirect
85. #10622553C22semidirect
86. #10622553C22semidirect
87. #10622553C22semidirect
88. #10622553C22semidirect
89. #10622553C22semidirect
90. #10622553C22semidirect
101. #10622549C22semidirect
102. C4×C4⋊Dic11C22semidirect
103. #10622546C22semidirect
104. C4×Dic11⋊C4C22semidirect
105. #10622542C22semidirect
106. #10622542C22semidirect
107. #10622541C22semidirect
108. #10622541C22semidirect
109. #10622541C22semidirect
110. #10622541C22semidirect
111. #10622289C22semidirect
112. #10622288C22semidirect
113. #10622288C22semidirect
114. #10622288C22semidirect
117. #10622282C22semidirect
118. #10622282C22semidirect
119. #10622282C22semidirect
120. #10622282C22semidirect
121. #10622273C22semidirect
122. #10622270C22semidirect
405. C42×D4D11semidirect
532. C22×C42C2×D11semidirect
601. C4×C4⋊C4C2×D11semidirect
602. C4×C4⋊C4C2×D11semidirect
603. C4×C4⋊C4C2×D11semidirect
608. C4×C22⋊C4C2×D11semidirect
609. C4×C22⋊C4C2×D11semidirect
610. C4×C22⋊C4C2×D11semidirect
611. C43C2×D11semidirect
937. C11#35025semidirect

Maximal subgroups

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

subgroupindex
#130769882
#130769832
#130769472
#130769172
#130746432
#130745982
#130741072
#130736762
#130732132
#130729682
#130728622
#130724142
#130723402
#130722672
#130721822
#130720722
#130720672
#130719722
#130712702
#130712112
C4×#669772
C2×#106225522
C42×D4×C112
#3502511