Finite Group Databasebeta

← #14925902

Subgroups — #14925902

Order 2816.

3206 conjugacy classes of subgroups.

The subgroup lattice has 1198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623359C211yesmaximal, characteristic, complemented
2C2×C4×D4×D11C211yesmaximal, characteristic, complemented
3#13074231C212yesmaximal, complemented
4#13074221C212yesmaximal, complemented
5#13074090C211yesmaximal, characteristic, complemented
6#13073992C211yesmaximal, characteristic, complemented
7#13073797C211yesmaximal, characteristic, complemented
8#13073793C211yesmaximal, characteristic, complemented
9#13073770C211yesmaximal, characteristic, complemented
10#13073579C211yesmaximal, characteristic, complemented
11#13073571C211yesmaximal, characteristic, complemented
12#13073541C211yesmaximal, characteristic, complemented
13#13072007C212yesmaximal, complemented
14#13071983C212yesmaximal, complemented
15#13071876C211yesmaximal, characteristic, complemented
16#13071875C211yesmaximal, characteristic, complemented
17#13071829C211yesmaximal, characteristic, complemented
18C4×#66936C212yesmaximal, complemented
19C4×#66937C212yesmaximal, complemented
20C4×#66991C212yesmaximal, complemented
21C4×#66990C212yesmaximal, complemented
22C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2388C211yesmaximal, characteristic, complemented
24C22×C11×#41C2211yescharacteristic, complemented
25C22×D4×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2212yescomplemented
30#10623359—28no—
31C2×#66999C2211yescharacteristic
32C2×#66999C2211yescharacteristic, complemented
33C2×#66991C2212yes—
34C2×#66991C2211yescharacteristic
35C2×#66991C2211yescharacteristic, complemented
36C2×#66990C2212yes—
37C2×#66990C2212yes—
38C2×#66988C2212yescomplemented
39C2×D4×Dic11C2211yescharacteristic
40C2×C4×C22⋊D11C2211yescharacteristic
41C2×C4×C22⋊D11C2212yes—
42C2×C4×C22⋊D11C2211yescharacteristic
43C2×C4×C22⋊D11C2212yescomplemented
44C2×C4×C22⋊D11C2212yescomplemented
45C2×#66979C2211yescharacteristic, complemented
46C4×D4×D11—28no—
47C2×#66946C2211yescharacteristic
48C2×C4⋊C4×D11C2211yescharacteristic
49C2×#66937C2212yes—
50C2×#66936C2212yes—
51C2×(C22⋊D11)⋊C4C2211yescharacteristic
52C2×(C22⋊D11)⋊C4C2211yescharacteristic
53C2×C22⋊C4×D11C2212yes—
54C2×C22⋊C4×D11C2211yescharacteristic
55C2×C22⋊C4×D11C2211yescharacteristic
56C2×C4×D44C2211yescharacteristic
57C2×C42×D11C2211yescharacteristic
58C2×C42×D11C2212yescomplemented
59C11×#395C2211yescharacteristic, complemented
60C11×#394C2212yescomplemented
61C11×#394C2211yescharacteristic, complemented
62C11×#393C2211yescharacteristic, complemented
63C11×#392C2212yes—
64C11×#392C2211yescharacteristic, complemented
65C4×C11×C22⋊C4C2211yescharacteristic, complemented
66C4×C11×C22⋊C4C2212yescomplemented
67#10622844C2211yescharacteristic, complemented
68#10622842C2211yescharacteristic, complemented
69#10622836C2212yes—
70#10622836C2211yescharacteristic, complemented
71#10622835C2212yes—
72#10622835C2212yescomplemented
73#10622835C2211yescharacteristic, complemented
74#10622834C2212yescomplemented
75#10622833C2212yescomplemented
76C4×C22⋊Dic11C2212yescomplemented
77C4×C22⋊Dic11C2211yescharacteristic, complemented
78C4×C22⋊Dic11C2212yescomplemented
79#10622602C2212yes—
80#10622602C2212yescomplemented
81#10622600C2212yescomplemented
82#10622599C2211yescharacteristic, complemented
83#10622596C2211yescharacteristic, complemented
84#10622586C2212yescomplemented
85#10622574C2212yes—
86#10622570C2212yescomplemented
87#10622569C2212yes—
88#10622569C2212yes—
89#10622569C2212yes—
90#10622569C2212yescomplemented
91#10622569C2212yescomplemented
92#10622569C2212yescomplemented
93#10622568C2212yes—
94#10622566C2211yescharacteristic, complemented
95#10622566C2212yescomplemented
96#10622565C2212yescomplemented
97#10622564C2212yescomplemented
98#10622564C2212yescomplemented
99#10622562C2211yescharacteristic, complemented
100#10622559C2212yescomplemented
101#10622558C2212yescomplemented
102#10622557C2212yescomplemented
103#10622557C2212yescomplemented
104C22⋊C4×Dic11C2212yescomplemented
105C4×(C2×D11)⋊C4C2212yes—
106C4×(C2×D11)⋊C4C2212yescomplemented
107C4×C4⋊Dic11C2212yescomplemented
108C4×Dic11⋊C4C2212yescomplemented
109#10622290C2211yescharacteristic, complemented
110#10622287C2211yescharacteristic, complemented
111#10622282C2212yescomplemented
112#10622281C2212yes—
113#10622280C2212yescomplemented
114#10622279C2211yescharacteristic
115#10622279C2211yescharacteristic
116#10622278C2212yes—
117#10622277C2212yes—
118D11×#95C2211yescharacteristic, complemented
119D11×#95C2211yescharacteristic, complemented
120#10622274C2211yescharacteristic, complemented
121#10622272C2211yescharacteristic, complemented
122#10622267C2212yescomplemented
123#10622265C2212yescomplemented
124#10622260C2212yescomplemented
125C24×D11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C2×C11×#41—24no—
128C2×C11×#41—44no—
129C22×Q8×C11C2311yescharacteristic
130C22×D4×C11C2311yescharacteristic
131C22×D4×C11C2312yes—
132C22×D4×C11C2312yes—
133C22×D4×C11C2311yescharacteristic
134C23×C4×C11C2312yes—
135C23×C4×C11C2311yescharacteristic
136C23×C4×C11C2311yescharacteristic
137C22×C22⋊D11C2311yescharacteristic
138C22×C22⋊D11C2312yes—
139C22×C22⋊D11C2312yes—
140C22×C22⋊D11C2312yes—
141C22×C22⋊D11C2311yescharacteristic
142C23×Dic11C2311yescharacteristic
143C23×Dic11C2311yescharacteristic
144C2×D4×D11—24no—
145C2×D4×D11—24no—
146C2×D4×D11—24no—
147C22×D44C2311yescharacteristic
148C22×C4×D11—24no—
149C22×C4×D11—44no—
150C22×C4×D11—44no—
151C22×C4×D11D418yescomplemented
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2311yescharacteristic
154C22×C4×D11C2311yescharacteristic
155C22×C4×D11C2312yes—
156C22×C4×D11C2312yes—
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2311yescharacteristic
159C22×C4×D11C2311yescharacteristic
160C22×C4×D11C2311yescharacteristic
161C22×C4×D11C2311yescharacteristic
162C22×C4×D11C2311yescharacteristic
163C4×D4×C11—24no—
164C4×D4×C11—44no—
165C2×C11×C4⋊C4C2311yescharacteristic
166C2×C11×C4⋊C4C2312yes—
167C2×C11×C22⋊C4C2311yescharacteristic
168C2×C11×C22⋊C4C2311yescharacteristic
169C2×C11×C22⋊C4C2312yes—
170C2×C11×C22⋊C4C2312yes—
171C2×C11×C22⋊C4C2312yes—
172C2×C11×C22⋊C4C2312yes—
173C2×C11×C22⋊C4C2312yes—
174C2×C42×C11C2311yescharacteristic
175C2×C42×C11C2312yes—
176C2×C22⋊Dic11C2311yescharacteristic
177C2×C22⋊Dic11C2311yescharacteristic
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2312yes—
182C2×C22⋊Dic11C2312yes—
183C2×C22⋊Dic11C2312yes—
184C2×C22⋊Dic11C2312yes—
185C2×C22⋊Dic11C2312yes—
186C2×C22⋊Dic11C2312yes—
187#66999—24no—
188#66999—24no—
189#66991—28no—
190#66991—24no—
191#66991—24no—
192#66990—28no—
193#66990—28no—
194#66988—28no—
195D4×Dic11—24no—
196C4×C22⋊D11—24no—
197C4×C22⋊D11—24no—
198C4×C22⋊D11—28no—
199C4×C22⋊D11—28no—
200C4×C22⋊D11—44no—
201C2×(C2×D11)⋊C4C2311yescharacteristic
202C2×(C2×D11)⋊C4C2311yescharacteristic
203C2×(C2×D11)⋊C4C2311yescharacteristic
204C2×(C2×D11)⋊C4C2311yescharacteristic
205C2×(C2×D11)⋊C4C2312yes—
206C2×(C2×D11)⋊C4C2312yes—
207C2×(C2×D11)⋊C4C2312yes—
208C2×(C2×D11)⋊C4C2312yes—
209C2×(C2×D11)⋊C4C2312yes—
210C2×(C2×D11)⋊C4C2312yes—
211C2×(C2×D11)⋊C4C2312yes—
212#66979—24no—
213C2×C4⋊Dic11C2311yescharacteristic
214C2×C4⋊Dic11C2312yes—
215C2×C4⋊Dic11C2311yescharacteristic
216C2×C4⋊Dic11C2312yes—
217C2×C4⋊Dic11C2311yescharacteristic
218C2×Dic11⋊C4C2311yescharacteristic
219C2×Dic11⋊C4C2311yescharacteristic
220C2×Dic11⋊C4C2312yes—
221C2×Dic11⋊C4C2312yes—
222C2×Dic11⋊C4C2312yes—
223C2×Dic11⋊C4C2312yes—
224C2×Dic11⋊C4C2312yes—
225C2×C4×Dic11C2311yescharacteristic
226C2×C4×Dic11C2311yescharacteristic
227C2×C4×Dic11C2311yescharacteristic
228C2×C4×Dic11C2312yes—
229C2×C4×Dic11C2312yes—
230C2×C4×Dic11C2312yes—
231C2×C4×Dic11C2312yes—
232#66946—24no—
233C4⋊C4×D11—24no—
234#66937—28no—
235#66936—28no—
236(C22⋊D11)⋊C4—24no—
237(C22⋊D11)⋊C4—24no—
238C22⋊C4×D11—24no—
239C22⋊C4×D11—24no—
240C22⋊C4×D11—28no—
241C4×D44—24no—
242C42×D11—24no—
243C42×D11—44no—
244C11×#95C2312yes—
245C11×#95C2312yes—
246C11×#95C2311yescharacteristic
247C11×#95C2311yescharacteristic
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2311yescharacteristic
257C11⋊#95C2311yescharacteristic
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262#34957—111nomaximal, Sylow
263C24×C11C2412yes—
264C24×C11C2411yescharacteristic
265C24×C11C2411yescharacteristic
266C23×D11—22no—
267C23×D11—22no—
268C23×D11—24no—
269C23×D11—22no—
270C23×D11—22no—
271C23×D11—22no—
272C23×D11—24no—
273C23×D11—42no—
274C23×D11—42no—
275C23×D11C2×D414yes—
276C23×D11C2411yescharacteristic
277C23×D11C2411yescharacteristic
278C23×D11C2411yescharacteristic
279C11×#41—416no—
280C2×Q8×C11—22no—
281C2×Q8×C11—42no—
282C2×D4×C11—22no—
283C2×D4×C11—22no—
284C2×D4×C11—24no—
285C2×D4×C11—24no—
286C2×D4×C11—22no—
287C2×D4×C11—22no—
288C2×D4×C11—24no—
289C2×D4×C11—42no—
290C2×D4×C11—42no—
291C2×D4×C11—42no—
292C2×D4×C11—42no—
293C22×C4×C11—24no—
294C22×C4×C11—24no—
295C22×C4×C11—22no—
296C22×C4×C11—24no—
297C22×C4×C11—24no—
298C22×C4×C11—24no—
299C22×C4×C11C2×D414yes—
300C22×C4×C11C2412yes—
301C22×C4×C11C2411yescharacteristic
302C22×C4×C11C2411yescharacteristic
303C22×C4×C11C2412yes—
304C22×C4×C11C2411yescharacteristic
305C22×C4×C11C2411yescharacteristic
306C22×C4×C11C2412yes—
307C22×C4×C11C2411yescharacteristic
308C2×C22⋊D11—22no—
309C2×C22⋊D11—24no—
310C2×C22⋊D11—22no—
311C2×C22⋊D11—22no—
312C2×C22⋊D11—24no—
313C2×C22⋊D11—24no—
314C2×C22⋊D11—22no—
315C2×C22⋊D11—22no—
316C2×C22⋊D11—24no—
317C2×C22⋊D11—24no—
318C2×C22⋊D11—24no—
319C2×C22⋊D11—24no—
320C2×C22⋊D11—24no—
321C2×C22⋊D11—42no—
322C2×C22⋊D11#4114yescomplemented
323C22×Dic11—22no—
324C22×Dic11—42no—
325C22×Dic11—42no—
326C22×Dic11C2×D414yes—
327C22×Dic11C2412yes—
328C22×Dic11C2411yescharacteristic
329C22×Dic11C2412yes—
330C22×Dic11C2412yes—
331C22×Dic11C2411yescharacteristic
332C22×Dic11C2411yescharacteristic
333C22×Dic11C2411yescharacteristic
334C22×Dic11C2412yes—
335C22×Dic11C2411yescharacteristic
336D4×D11—232no—
337C2×D44—22no—
338C2×D44—22no—
339C2×D44#4114yescomplemented
340C2×C4×D11—22no—
341C2×C4×D11—22no—
342C2×C4×D11—24no—
343C2×C4×D11—22no—
344C2×C4×D11—22no—
345C2×C4×D11—22no—
346C2×C4×D11—24no—
347C2×C4×D11—24no—
348C2×C4×D11—24no—
349C2×C4×D11—22no—
350C2×C4×D11—22no—
351C2×C4×D11—24no—
352C2×C4×D11—24no—
353C2×C4×D11—24no—
354C2×C4×D11—24no—
355C2×C4×D11—42no—
356C2×C4×D11—42no—
357C2×C4×D11—42no—
358C2×C4×D11—42no—
359C2×C4×D11—42no—
360C2×C4×D11—42no—
361C2×C4×D11—416no—
362C2×C4×D11—416no—
363C2×C4×D11C2×D414yes—
364C2×C4×D11C2×D414yes—
365C2×C4×D11C2×D414yes—
366C2×C4×D11C2×D414yes—
367C11×C4⋊C4—22no—
368C11×C4⋊C4—42no—
369C11×C22⋊C4—22no—
370C11×C22⋊C4—22no—
371C11×C22⋊C4—24no—
372C11×C22⋊C4—24no—
373C11×C22⋊C4—24no—
374C11×C22⋊C4—42no—
375C11×C22⋊C4—42no—
376C42×C11—22no—
377C42×C11—24no—
378C22⋊Dic11—22no—
379C22⋊Dic11—24no—
380C22⋊Dic11—24no—
381C22⋊Dic11—24no—
382C22⋊Dic11—24no—
383C22⋊Dic11—24no—
384C22⋊Dic11—24no—
385C22⋊Dic11—22no—
386C22⋊Dic11—24no—
387C22⋊Dic11—24no—
388C22⋊Dic11—42no—
389(C2×D11)⋊C4—22no—
390(C2×D11)⋊C4—22no—
391(C2×D11)⋊C4—22no—
392(C2×D11)⋊C4—24no—
393(C2×D11)⋊C4—24no—
394(C2×D11)⋊C4—24no—
395(C2×D11)⋊C4—24no—
396(C2×D11)⋊C4—22no—
397(C2×D11)⋊C4—24no—
398(C2×D11)⋊C4—42no—
399(C2×D11)⋊C4#4118yescomplemented
400C4⋊Dic11—22no—
401C4⋊Dic11—24no—
402C4⋊Dic11—22no—
403C4⋊Dic11—22no—
404C4⋊Dic11—24no—
405Dic11⋊C4—22no—
406Dic11⋊C4—24no—
407Dic11⋊C4—24no—
408Dic11⋊C4—24no—
409Dic11⋊C4—22no—
410Dic11⋊C4—24no—
411Dic11⋊C4—42no—
412C4×Dic11—22no—
413C4×Dic11—22no—
414C4×Dic11—22no—
415C4×Dic11—24no—
416C4×Dic11—24no—
417C4×Dic11—42no—
418C4×Dic11—42no—
419C2×#525—111no—
420C22×C4×D4—111no—
421#2602—112no—
422#2602—112no—
423#2591—111no—
424#2583—111no—
425#2564—111no—
426#2564—111no—
427#2561—111no—
428#2543—111no—
429#2543—111no—
430#2539—111no—
431#2412—112no—
432#2410—112no—
433#2395—111no—
434#2395—111no—
435#2388—111no—
436#2388D1111yescharacteristic, complemented
437C4×#123—112no—
438C4×#121—112no—
439C4×#121—112no—
440C4×#120—112no—
441C2×C4×C22⋊C4—111no—
442C23×C11—21no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—21no—
446C23×C11—21no—
447C23×C11—21no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11—22no—
451C23×C11—22no—
452C23×C11—22no—
453C23×C11—22no—
454C23×C11—22no—
455C23×C11—22no—
456C23×C11—22no—
457C23×C11C22×D412yes—
458C23×C11C2×#4112yes—
459C23×C11C2511yescharacteristic
460C22×D11—22no—
461C22×D11—21no—
462C22×D11—21no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—28no—
466C22×D11—21no—
467C22×D11—22no—
468C22×D11—21no—
469C22×D11—22no—
470C22×D11—28no—
471C22×D11—28no—
472C22×D11—44no—
473C22×D11—48no—
474C22×D11—48no—
475C22×D11—48no—
476C22×D11—48no—
477C22×D11—44no—
478C22×D11—44no—
479C22×D11C22×D412yes—
480C22×D11C22×D412yes—
481C22×D11C2×#4112yes—
482C22×D11C2×#4112yes—
483C22×D11C2×#4112yes—
484C22×D11C2×#4114yes—
485Q8×C11—44no—
486D4×C11—28no—
487D4×C11—48no—
488D4×C11—44no—
489D4×C11—48no—
490C2×C4×C11—21no—
491C2×C4×C11—22no—
492C2×C4×C11—21no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—28no—
496C2×C4×C11—21no—
497C2×C4×C11—22no—
498C2×C4×C11—21no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—22no—
506C2×C4×C11—44no—
507C2×C4×C11—48no—
508C2×C4×C11C22×D412yes—
509C2×C4×C11C22×D412yes—
510C2×C4×C11C2×#4112yes—
511C2×C4×C11C2×#4114yes—
512C2×C4×C11H(5,𝔽2)14yes—
513C22⋊D11—28no—
514C22⋊D11—28no—
515C22⋊D11—48no—
516C22⋊D11—48no—
517C22⋊D11—48no—
518C2×Dic11—21no—
519C2×Dic11—22no—
520C2×Dic11—21no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—21no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—21no—
528C2×Dic11—22no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—22no—
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—44no—
538C2×Dic11—44no—
539C2×Dic11C22×D412yes—
540C2×Dic11C22×D412yes—
541C2×Dic11C2×#4114yes—
542C2×Dic11C2×#4112yes—
543D44—28no—
544C4×D11—28no—
545C4×D11—28no—
546C4×D11—28no—
547C4×D11—44no—
548C4×D11—44no—
549C4×D11—48no—
550C4×D11—44no—
551C4×D11—48no—
552C4×D11—44no—
553C4×D11—44no—
554C4×D11—44no—
555C22×#41C2×D1111yescharacteristic, complemented
556C23×D4—111no—
557C24×C4—111no—
558C24×C4—111no—
559#525—228no—
560C2×#123—112no—
561C2×#123—112no—
562C2×C22⋊Q8—111no—
563C2×C22⋊Q8—111no—
564C2×#121—111no—
565C2×#121—112no—
566C2×#121—111no—
567C2×#121—112no—
568C2×#120—112no—
569C2×#120—112no—
570C2×C4×D4—111no—
571C2×C4×D4—111no—
572C2×C4×D4—111no—
573C2×C4×D4—112no—
574C2×C4×D4—112no—
575C2×C4×D4—112no—
576C2×C4×D4—111no—
577C2×C4×D4—111no—
578C2×C4×D4—111no—
579C2×C4×D4—111no—
580C2×C4×D4—228no—
581C2×C4×D4C2×D1111yescharacteristic
582C2×C4×D4C2×D1112yescomplemented
583C2×#117—111no—
584C22×C4⋊C4—111no—
585C22×C22⋊C4—111no—
586C22×C22⋊C4—111no—
587C22×C22⋊C4—112no—
588C22×C42—111no—
589C22×C42—112no—
590#400—111no—
591#400—111no—
592#399—111no—
593#399—111no—
594#398—111no—
595#398—111no—
596#397—111no—
597#397—112no—
598#397—112no—
599#397—111no—
600#395—111no—
601#395C2×D1111yescharacteristic, complemented
602#394—111no—
603#394—112no—
604#394—112no—
605#394—112no—
606#394C2×D1111yescharacteristic, complemented
607#394C2×D1112yescomplemented
608#393—111no—
609#393C2×D1111yescharacteristic, complemented
610#392—112no—
611#392—111no—
612#392C2×D1112yes—
613#392C2×D1111yescharacteristic, complemented
614#390—112no—
615#390—112no—
616#389—112no—
617#389—112no—
618#388—112no—
619#388—112no—
620#388—112no—
621#388—112no—
622#388—112no—
623#388—112no—
624#387—112no—
625#387—112no—
626#386—112no—
627#386—112no—
628#386—112no—
629#386—112no—
630#386—112no—
631#386—112no—
632#386—112no—
633#386—112no—
634#385—112no—
635#385—112no—
636#385—112no—
637#385—112no—
638#381—112no—
639#380—112no—
640#380—112no—
641#379—112no—
642C4×C4⋊C4—112no—
643C4×C4⋊C4—112no—
644C4×C22⋊C4—111no—
645C4×C22⋊C4—112no—
646C4×C22⋊C4—112no—
647C4×C22⋊C4—112no—
648C4×C22⋊C4—112no—
649C4×C22⋊C4—112no—
650C4×C22⋊C4—111no—
651C4×C22⋊C4—111no—
652C4×C22⋊C4C2×D1111yescharacteristic, complemented
653C4×C22⋊C4C2×D1112yescomplemented
654C2×#95—111no—
655C2×#95—111no—
656C22×C11—22no—
657C22×C11—22no—
658C22×C11—22no—
659C22×C11—22no—
660C22×C11—24no—
661C22×C11—41no—
662C22×C11—41no—
663C22×C11—42no—
664C22×C11—42no—
665C22×C11—42no—
666C22×C11—42no—
667C22×C11—42no—
668C22×C11—42no—
669C22×C11—42no—
670C22×C11—42no—
671C22×C11—42no—
672C22×C11—42no—
673C22×C11C23×D411yescharacteristic
674C22×C11C22×#4111yescharacteristic
675C22×C11C22×#4111yescharacteristic
676C22×C11C22×#4112yes—
677C22×C11C2×H(5,𝔽2)12yes—
678C2×D11—22no—
679C2×D11—22no—
680C2×D11—22no—
681C2×D11—22no—
682C2×D11—24no—
683C2×D11—24no—
684C2×D11—24no—
685C2×D11—24no—
686C2×D11—22no—
687C2×D11—24no—
688C2×D11—416no—
689C2×D11—416no—
690C2×D11—41no—
691C2×D11—41no—
692C2×D11—42no—
693C2×D11#52514yes—
694C2×D11#53214yes—
695C4×C11—22no—
696C4×C11—22no—
697C4×C11—24no—
698C4×C11—41no—
699C4×C11—42no—
700C4×C11—41no—
701C4×C11—42no—
702C4×C11#53414yes—
703Dic11—22no—
704Dic11—22no—
705Dic11—22no—
706Dic11—24no—
707Dic11—42no—
708Dic11—41no—
709Dic11—42no—
710Dic11—41no—
711Dic11—42no—
712C25—111no—
713C25—111no—
714C2×#41—24no—
715C2×#41—44no—
716C22×Q8C22×D1111yescharacteristic
717C22×D4—111no—
718C22×D4—111no—
719C22×D4—112no—
720C22×D4—112no—
721C22×D4—112no—
722C22×D4—111no—
723C22×D4—224no—
724C22×D4—224no—
725C22×D4—224no—
726C22×D4C22×D1111yescharacteristic
727C22×D4C22×D1112yes—
728C22×D4C22×D1112yes—
729C22×D4C22×D1111yescharacteristic
730C23×C4—111no—
731C23×C4—111no—
732C23×C4—111no—
733C23×C4—118no—
734C23×C4—111no—
735C23×C4—111no—
736C23×C4—111no—
737C23×C4—111no—
738C23×C4—111no—
739C23×C4—111no—
740C23×C4—112no—
741C23×C4—112no—
742C23×C4—111no—
743C23×C4—111no—
744C23×C4—224no—
745C23×C4—444no—
746C23×C4—444no—
747C23×C4C22×D1112yes—
748C23×C4C22×D1111yescharacteristic
749C23×C4C22×D1111yescharacteristic
750#123—228no—
751#123—228no—
752C22⋊Q8—224no—
753C22⋊Q8—224no—
754#121—228no—
755#121—224no—
756#121—224no—
757#121—228no—
758#120—228no—
759#120—228no—
760C4×D4—24no—
761C4×D4—44no—
762C4×D4—224no—
763C4×D4—224no—
764C4×D4—224no—
765C4×D4—224no—
766C4×D4—224no—
767C4×D4—228no—
768C4×D4—228no—
769C4×D4—224no—
770C4×D4—224no—
771C4×D4—444no—
772#117—224no—
773C2×C4⋊C4—111no—
774C2×C4⋊C4—111no—
775C2×C4⋊C4—111no—
776C2×C4⋊C4—111no—
777C2×C4⋊C4—111no—
778C2×C4⋊C4—112no—
779C2×C4⋊C4—112no—
780C2×C4⋊C4—112no—
781C2×C4⋊C4—112no—
782C2×C4⋊C4—112no—
783C2×C4⋊C4—112no—
784C2×C4⋊C4—112no—
785C2×C4⋊C4—224no—
786C2×C4⋊C4C22×D1111yescharacteristic
787C2×C4⋊C4C22×D1112yes—
788C2×C22⋊C4—112no—
789C2×C22⋊C4—111no—
790C2×C22⋊C4—111no—
791C2×C22⋊C4—112no—
792C2×C22⋊C4—112no—
793C2×C22⋊C4—112no—
794C2×C22⋊C4—112no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—112no—
797C2×C22⋊C4—112no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—111no—
800C2×C22⋊C4—111no—
801C2×C22⋊C4—111no—
802C2×C22⋊C4—111no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—112no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—228no—
811C2×C22⋊C4—224no—
812C2×C22⋊C4—224no—
813C2×C22⋊C4C22×D1111yescharacteristic
814C2×C22⋊C4C22×D1111yescharacteristic
815C2×C22⋊C4C22×D1112yes—
816C2×C22⋊C4C22×D1112yes—
817C2×C22⋊C4C22×D1112yes—
818C2×C22⋊C4C22×D1112yes—
819C2×C22⋊C4C22×D1112yes—
820C2×C42—111no—
821C2×C42—111no—
822C2×C42—112no—
823C2×C42—111no—
824C2×C42—112no—
825C2×C42—112no—
826C2×C42—112no—
827C2×C42—224no—
828C2×C42—444no—
829C2×C42C22×D1111yescharacteristic
830C2×C42C22×D1112yes—
831#95—112no—
832#95—112no—
833#95—111no—
834#95—111no—
835#95—112no—
836#95—112no—
837#95—112no—
838#95—112no—
839#95—112no—
840#95—112no—
841#95—112no—
842#95—112no—
843#95—112no—
844#95—112no—
845#95C22×D1111yescharacteristic
846#95C22×D1111yescharacteristic
847#95C22×D1112yes—
848#95C22×D1112yes—
849C2×C11—42no—
850C2×C11—42no—
851C2×C11—82no—
852C2×C11C2×#52511yescharacteristic
853C2×C11C2×#53211yescharacteristic
854C2×C11C2×#53411yescharacteristic
855C2×C11#348112yes—
856C2×C11#348112yes—
857D11—24no—
858D11—24no—
859D11—42no—
860C24—111no—
861C24—111no—
862C24—111no—
863C24—114no—
864C24—222no—
865C24—224no—
866C24—222no—
867C24—222no—
868C24—222no—
869C24—224no—
870C24—222no—
871C24—442no—
872C24—442no—
873C24C23×D1112yes—
874C24C23×D1111yescharacteristic
875C24C23×D1111yescharacteristic
876#41—416no—
877C2×Q8—22no—
878C2×Q8—42no—
879C2×D4—22no—
880C2×D4—22no—
881C2×D4—24no—
882C2×D4—24no—
883C2×D4—22no—
884C2×D4—22no—
885C2×D4—24no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—114no—
891C2×D4—114no—
892C2×D4—222no—
893C2×D4—222no—
894C2×D4—222no—
895C2×D4—224no—
896C2×D4—2232no—
897C2×D4—222no—
898C2×D4—222no—
899C2×D4—222no—
900C2×D4—222no—
901C2×D4—224no—
902C2×D4—224no—
903C2×D4—224no—
904C2×D4—224no—
905C2×D4—224no—
906C2×D4—224no—
907C2×D4—224no—
908C2×D4—442no—
909C22×C4—24no—
910C22×C4—22no—
911C22×C4—24no—
912C22×C4—24no—
913C22×C4—24no—
914C22×C4—24no—
915C22×C4—112no—
916C22×C4—111no—
917C22×C4—111no—
918C22×C4—111no—
919C22×C4—114no—
920C22×C4—114no—
921C22×C4—114no—
922C22×C4—114no—
923C22×C4—114no—
924C22×C4—112no—
925C22×C4—111no—
926C22×C4—112no—
927C22×C4—112no—
928C22×C4—111no—
929C22×C4—222no—
930C22×C4—224no—
931C22×C4—222no—
932C22×C4—222no—
933C22×C4—222no—
934C22×C4—222no—
935C22×C4—224no—
936C22×C4—224no—
937C22×C4—224no—
938C22×C4—222no—
939C22×C4—224no—
940C22×C4—224no—
941C22×C4—222no—
942C22×C4—222no—
943C22×C4—224no—
944C22×C4—224no—
945C22×C4—4416no—
946C22×C4—442no—
947C22×C4—442no—
948C22×C4—442no—
949C22×C4—442no—
950C22×C4—442no—
951C22×C4—442no—
952C22×C4—4416no—
953C22×C4—442no—
954C22×C4—442no—
955C22×C4D4×D1114yes—
956C22×C4C23×D1112yes—
957C22×C4C23×D1111yescharacteristic
958C22×C4C23×D1111yescharacteristic
959C22×C4C23×D1112yes—
960C22×C4C23×D1111yescharacteristic
961C22×C4C23×D1112yes—
962C22×C4C23×D1111yescharacteristic
963C22×C4C23×D1111yescharacteristic
964C4⋊C4—22no—
965C4⋊C4—42no—
966C4⋊C4—222no—
967C4⋊C4—222no—
968C4⋊C4—224no—
969C4⋊C4—224no—
970C4⋊C4—224no—
971C4⋊C4—224no—
972C4⋊C4—222no—
973C4⋊C4—222no—
974C4⋊C4—222no—
975C4⋊C4—224no—
976C4⋊C4—224no—
977C4⋊C4—442no—
978C22⋊C4—22no—
979C22⋊C4—22no—
980C22⋊C4—24no—
981C22⋊C4—24no—
982C22⋊C4—24no—
983C22⋊C4—42no—
984C22⋊C4—42no—
985C22⋊C4—118no—
986C22⋊C4—222no—
987C22⋊C4—222no—
988C22⋊C4—222no—
989C22⋊C4—224no—
990C22⋊C4—224no—
991C22⋊C4—224no—
992C22⋊C4—224no—
993C22⋊C4—222no—
994C22⋊C4—224no—
995C22⋊C4—224no—
996C22⋊C4—224no—
997C22⋊C4—224no—
998C22⋊C4—224no—
999C22⋊C4—224no—
1000C22⋊C4—222no—
1001C22⋊C4—224no—
1002C22⋊C4—224no—
1003C22⋊C4—222no—
1004C22⋊C4—224no—
1005C22⋊C4—442no—
1006C22⋊C4—442no—
1007C42—22no—
1008C42—24no—
1009C42—222no—
1010C42—222no—
1011C42—222no—
1012C42—224no—
1013C42—224no—
1014C42—442no—
1015C42—442no—
1016C11#3495711yescharacteristic, complemented, Sylow
1017C23—21no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—112no—
1033C23—112no—
1034C23—114no—
1035C23—112no—
1036C23—112no—
1037C23—112no—
1038C23—228no—
1039C23—228no—
1040C23—228no—
1041C23—222no—
1042C23—222no—
1043C23—222no—
1044C23—221no—
1045C23—221no—
1046C23—221no—
1047C23—222no—
1048C23—222no—
1049C23—221no—
1050C23—444no—
1051C23—448no—
1052C23—444no—
1053C23—448no—
1054C23—448no—
1055C23—448no—
1056C23—444no—
1057C23C2×D4×D1112yes—
1058C23#41×D1112yes—
1059C23C24×D1111yescharacteristic
1060Q8—44no—
1061D4—28no—
1062D4—48no—
1063D4—44no—
1064D4—48no—
1065D4—228no—
1066D4—228no—
1067D4—228no—
1068D4—448no—
1069D4—448no—
1070D4—448no—
1071C2×C4—21no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—21no—
1076C2×C4—28no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—44no—
1088C2×C4—48no—
1089C2×C4—112no—
1090C2×C4—112no—
1091C2×C4—114no—
1092C2×C4—112no—
1093C2×C4—228no—
1094C2×C4—221no—
1095C2×C4—222no—
1096C2×C4—222no—
1097C2×C4—222no—
1098C2×C4—222no—
1099C2×C4—221no—
1100C2×C4—228no—
1101C2×C4—228no—
1102C2×C4—221no—
1103C2×C4—222no—
1104C2×C4—222no—
1105C2×C4—221no—
1106C2×C4—222no—
1107C2×C4—222no—
1108C2×C4—222no—
1109C2×C4—222no—
1110C2×C4—222no—
1111C2×C4—222no—
1112C2×C4—222no—
1113C2×C4—222no—
1114C2×C4—222no—
1115C2×C4—444no—
1116C2×C4—444no—
1117C2×C4—448no—
1118C2×C4—448no—
1119C2×C4—444no—
1120C2×C4—444no—
1121C2×C4—444no—
1122C2×C4—444no—
1123C2×C4—444no—
1124C2×C4—444no—
1125C2×C4C2×D4×D1112yes—
1126C2×C4C2×D4×D1112yes—
1127C2×C4#6703714yes—
1128C2×C4#41×D1114yes—
1129C2×C4#41×D1112yes—
1130C22—22no—
1131C22—22no—
1132C22—24no—
1133C22—22no—
1134C22—22no—
1135C22—41no—
1136C22—41no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—114no—
1148C22—114no—
1149C22—222no—
1150C22—222no—
1151C22—222no—
1152C22—224no—
1153C22—224no—
1154C22—224no—
1155C22—224no—
1156C22—222no—
1157C22—224no—
1158C22—222no—
1159C22—4416no—
1160C22—4416no—
1161C22—441no—
1162C22—441no—
1163C22—442no—
1164C22C22×D4×D1111yescharacteristic
1165C22C2×#6703712yes—
1166C22C2×#41×D1112yes—
1167C22C2×#41×D1111yescharacteristic
1168C22C2×#41×D1111yescharacteristic
1169C4—22no—
1170C4—24no—
1171C4—22no—
1172C4—41no—
1173C4—41no—
1174C4—42no—
1175C4—42no—
1176C4—222no—
1177C4—222no—
1178C4—224no—
1179C4—222no—
1180C4—441no—
1181C4—442no—
1182C4—441no—
1183C4—442no—
1184C4—442no—
1185C4#1062312014yes—
1186C2—42no—
1187C2—42no—
1188C2—82no—
1189C2—224no—
1190C2—224no—
1191C2—442no—
1192C2D11×#52511yescharacteristic
1193C2D11×#53211yescharacteristic
1194C2C2×#1062312011yescharacteristic
1195C2#1308221812yes—
1196C2#1308222412yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2388C2
hypercenter#2388D11
hypocenterC11#34957
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2388

Complements

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

NH ≅ G/Ntype
1. C2×#10623359C2semidirect
2. C2×C4×D4×D11C2semidirect
3. #13074231C2semidirect
4. #13074221C2semidirect
5. #13074090C2semidirect
6. #13073992C2semidirect
7. #13073797C2semidirect
8. #13073793C2semidirect
9. #13073770C2semidirect
10. #13073579C2semidirect
11. #13073571C2semidirect
12. #13073541C2semidirect
13. #13072007C2semidirect
14. #13071983C2semidirect
15. #13071876C2semidirect
16. #13071875C2semidirect
17. #13071829C2semidirect
18. C4×#66936C2semidirect
19. C4×#66937C2semidirect
20. C4×#66991C2semidirect
21. C4×#66990C2semidirect
22. C4×C22⋊C4×D11C2semidirect
23. C11×#2388C2semidirect
24. C22×C11×#41C22semidirect
29. C2×C4×D4×C11C22semidirect
32. C2×#66999C22semidirect
35. C2×#66991C22semidirect
38. C2×#66988C22semidirect
43. C2×C4×C22⋊D11C22semidirect
44. C2×C4×C22⋊D11C22semidirect
45. C2×#66979C22semidirect
58. C2×C42×D11C22semidirect
59. C11×#395C22semidirect
60. C11×#394C22semidirect
61. C11×#394C22semidirect
62. C11×#393C22semidirect
64. C11×#392C22semidirect
65. C4×C11×C22⋊C4C22semidirect
66. C4×C11×C22⋊C4C22semidirect
67. #10622844C22semidirect
68. #10622842C22semidirect
70. #10622836C22semidirect
72. #10622835C22semidirect
73. #10622835C22semidirect
74. #10622834C22semidirect
75. #10622833C22semidirect
76. C4×C22⋊Dic11C22semidirect
77. C4×C22⋊Dic11C22semidirect
78. C4×C22⋊Dic11C22semidirect
80. #10622602C22semidirect
81. #10622600C22semidirect
82. #10622599C22semidirect
83. #10622596C22semidirect
84. #10622586C22semidirect
86. #10622570C22semidirect
90. #10622569C22semidirect
91. #10622569C22semidirect
92. #10622569C22semidirect
94. #10622566C22semidirect
95. #10622566C22semidirect
96. #10622565C22semidirect
97. #10622564C22semidirect
98. #10622564C22semidirect
99. #10622562C22semidirect
100. #10622559C22semidirect
101. #10622558C22semidirect
102. #10622557C22semidirect
103. #10622557C22semidirect
104. C22⋊C4×Dic11C22semidirect
106. C4×(C2×D11)⋊C4C22semidirect
107. C4×C4⋊Dic11C22semidirect
108. C4×Dic11⋊C4C22semidirect
109. #10622290C22semidirect
110. #10622287C22semidirect
111. #10622282C22semidirect
113. #10622280C22semidirect
118. D11×#95C22semidirect
119. D11×#95C22semidirect
120. #10622274C22semidirect
121. #10622272C22semidirect
122. #10622267C22semidirect
123. #10622265C22semidirect
124. #10622260C22semidirect
151. C22×C4×D11D4semidirect
322. C2×C22⋊D11#41semidirect
339. C2×D44#41semidirect
399. (C2×D11)⋊C4#41semidirect
436. #2388D11semidirect
555. C22×#41C2×D11semidirect
582. C2×C4×D4C2×D11semidirect
601. #395C2×D11semidirect
606. #394C2×D11semidirect
607. #394C2×D11semidirect
609. #393C2×D11semidirect
613. #392C2×D11semidirect
652. C4×C22⋊C4C2×D11semidirect
653. C4×C22⋊C4C2×D11semidirect
1016. C11#34957semidirect

Maximal subgroups

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

subgroupindex
C2×#106233592
C2×C4×D4×D112
#130742312
#130742212
#130740902
#130739922
#130737972
#130737932
#130737702
#130735792
#130735712
#130735412
#130720072
#130719832
#130718762
#130718752
#130718292
C4×#669362
C4×#669372
C4×#669912
C4×#669902
C4×C22⋊C4×D112
C11×#23882
#3495711