Finite Group Databasebeta

← #14926737

Subgroups — #14926737

Order 2816.

2756 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623235C212yesmaximal, complemented
2#13076973C211yesmaximal, characteristic, complemented
3#13076960C211yesmaximal, characteristic, complemented
4#13076949C211yesmaximal, characteristic, complemented
5#13074756C212yesmaximal, complemented
6#13074748C212yesmaximal, complemented
7#13073692C212yesmaximal, complemented
8#13073675C212yesmaximal, complemented
9#13073205C211yesmaximal, characteristic, complemented
10#13072977C211yesmaximal, characteristic, complemented
11#13072746C212yesmaximal, complemented
12#13072384C211yesmaximal, characteristic, complemented
13#13072320C211yesmaximal, characteristic, complemented
14#13072252C211yesmaximal, characteristic, complemented
15#13072202C211yesmaximal, characteristic, complemented
16#13072157C212yesmaximal, complemented
17#13072054C211yesmaximal, characteristic, complemented
18#13071970C211yesmaximal, characteristic, complemented
19#13071269C212yesmaximal, complemented
20#13071124C211yesmaximal, characteristic, complemented
21D11×#390C211yesmaximal, characteristic, complemented
22C42×D44C211yesmaximal, characteristic, complemented
23C11×#2860C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C2×C11×#126C2212yescomplemented
26C2×#66993C2211yescharacteristic
27C2×#66991C2211yescharacteristic
28#10623235—216no—
29C2×#66951C2212yescomplemented
30C2×#66949C2212yes—
31C2×#66948C2211yescharacteristic
32C2×#66948C2212yes—
33C2×#66948C2211yescharacteristic
34C2×#66948C2212yescomplemented
35C2×#66948C2211yescharacteristic, complemented
36C2×#66947C2212yescomplemented
37C2×#66946C2212yes—
38C2×#66946C2211yescharacteristic, complemented
39C2×C4⋊C4×D11C2211yescharacteristic
40C2×#66938C2212yescomplemented
41C2×#66937C2212yescomplemented
42C2×#66937C2212yescomplemented
43C2×#66936C2212yescomplemented
44C2×#66935C2212yes—
45C2×#66935C2212yes—
46C2×#66935C2212yes—
47C2×C22⋊C4×D11C2212yes—
48C2×C22⋊C4×D11C2212yes—
49C2×#66928C2212yescomplemented
50C2×#66928C2212yescomplemented
51C2×#66927C2211yescharacteristic
52C2×C4×D44C2211yescharacteristic
53C2×C4×D44C2211yescharacteristic
54C2×C4×D44C2211yescharacteristic
55C2×C42×D11C2211yescharacteristic
56C2×C42×D11C2211yescharacteristic, complemented
57C2×#66922C2211yescharacteristic, complemented
58C11×#390C2211yescharacteristic
59C11×#390C2211yescharacteristic
60C11×#390C2211yescharacteristic
61C11×#389C2211yescharacteristic, complemented
62C11×#389C2211yescharacteristic, complemented
63C11×#389C2211yescharacteristic, complemented
64C11×#388C2212yescomplemented
65C11×#388C2212yescomplemented
66C11×#388C2212yescomplemented
67C43×C11C2211yescharacteristic, complemented
68#10622834C2211yescharacteristic
69#10622607C2212yescomplemented
70#10622607C2212yescomplemented
71#10622604C2212yescomplemented
72#10622603C2212yescomplemented
73#10622603C2212yescomplemented
74#10622601C2211yescharacteristic
75#10622601C2211yescharacteristic
76#10622600C2211yescharacteristic
77#10622600C2211yescharacteristic, complemented
78#10622592C2212yescomplemented
79#10622589C2211yescharacteristic, complemented
80C4⋊C4×Dic11C2211yescharacteristic, complemented
81#10622586C2211yescharacteristic, complemented
82#10622574C2212yes—
83#10622574C2212yescomplemented
84#10622574C2212yescomplemented
85#10622573C2212yes—
86#10622573C2212yes—
87#10622573C2212yes—
88#10622572C2212yescomplemented
89#10622570C2212yes—
90#10622570C2212yes—
91#10622570C2212yescomplemented
92#10622570C2212yescomplemented
93#10622569C2212yescomplemented
94#10622568C2212yes—
95#10622564C2212yescomplemented
96#10622560C2212yescomplemented
97#10622552C2211yescharacteristic
98#10622552C2211yescharacteristic
99#10622552C2211yescharacteristic, complemented
100#10622552C2212yescomplemented
101#10622552C2211yescharacteristic, complemented
102#10622552C2212yescomplemented
103C4×(C2×D11)⋊C4C2211yescharacteristic
104C4×(C2×D11)⋊C4C2211yescharacteristic
105C4×(C2×D11)⋊C4C2211yescharacteristic
106C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
107C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
108C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
109C4×C4⋊Dic11C2211yescharacteristic, complemented
110C4×C4⋊Dic11C2211yescharacteristic, complemented
111C4×C4⋊Dic11C2211yescharacteristic, complemented
112#10622288C2212yescomplemented
113#10622285C2212yescomplemented
114#10622284C2212yescomplemented
115#10622282C2212yescomplemented
116#10622282C2212yescomplemented
117#10622281C2212yes—
118#10622279C2212yescomplemented
119#10622278C2212yes—
120#10622278C2212yes—
121#10622278C2212yescomplemented
122#10622278C2212yescomplemented
123#10622270C2212yescomplemented
124C24×D11C2312yes—
125C22×D4×C11C2311yescharacteristic
126C22×C22⋊D11C2312yes—
127C22×C22⋊D11C2312yes—
128C22×C22⋊D11C2312yes—
129C22×C22⋊D11C2312yes—
130C2×D4×D11—24no—
131C2×D4×D11—42no—
132C2×D4×D11—42no—
133C22×D44C2311yescharacteristic
134C22×D44C2311yescharacteristic
135C22×D44C2312yes—
136C22×D44C2311yescharacteristic
137C22×D44C2312yes—
138C22×D44C2312yes—
139C22×D44C2312yes—
140C22×D44C2312yes—
141C22×C4×D11C2311yescharacteristic
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2312yes—
146C22×C4×D11C2312yes—
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×Dic22C2312yes—
150C11×#126—28no—
151C2×C11×C4⋊C4C2311yescharacteristic
152C2×C11×C4⋊C4C2312yes—
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2312yes—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2311yescharacteristic
165C2×C42×C11C2311yescharacteristic
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2311yescharacteristic
169C2×C42×C11C2311yescharacteristic
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173#66993—42no—
174#66991—42no—
175C2×(C2×D11)⋊C4C2311yescharacteristic
176C2×(C2×D11)⋊C4C2311yescharacteristic
177C2×(C2×D11)⋊C4C2311yescharacteristic
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)⋊C4C2311yescharacteristic
197C2×(C2×D11)⋊C4C2311yescharacteristic
198C2×(C2×D11)⋊C4C2311yescharacteristic
199C2×C4⋊Dic11C2311yescharacteristic
200C2×C4⋊Dic11C2311yescharacteristic
201C2×C4⋊Dic11C2311yescharacteristic
202C2×C4⋊Dic11C2311yescharacteristic
203C2×C4⋊Dic11C2312yes—
204C2×C4⋊Dic11C2311yescharacteristic
205C2×Dic11⋊C4C2312yes—
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2312yes—
209C2×C4×Dic11C2311yescharacteristic
210C2×C4×Dic11C2311yescharacteristic
211C2×C4×Dic11C2312yes—
212C2×C4×Dic11C2311yescharacteristic
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2311yescharacteristic
216#66951—28no—
217#66949—28no—
218#66948—28no—
219#66948—24no—
220#66948—28no—
221#66948—42no—
222#66948—42no—
223#66947—28no—
224#66946—28no—
225#66946—42no—
226C4⋊C4×D11—42no—
227#66938—28no—
228#66937—28no—
229#66937—44no—
230#66936—28no—
231#66935—28no—
232#66935—28no—
233#66935—28no—
234C22⋊C4×D11—28no—
235C22⋊C4×D11—44no—
236#66928—28no—
237#66928—44no—
238#66927—42no—
239C4×D44—24no—
240C4×D44—24no—
241C4×D44D418yescomplemented
242C42×D11—42no—
243C42×D11—42no—
244#66922—42no—
245C11×#95C2312yes—
246C11×#95C2312yes—
247C11×#95C2312yes—
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2311yescharacteristic
253C11⋊#95C2312yes—
254C11⋊#95C2311yescharacteristic
255C11⋊#95C2311yescharacteristic
256C11⋊#95C2311yescharacteristic
257C11⋊#95C2311yescharacteristic
258#35007—111nomaximal, Sylow
259C24×C11C2412yes—
260C23×D11—24no—
261C23×D11—24no—
262C23×D11—24no—
263C23×D11—42no—
264C23×D11—42no—
265C23×D11—42no—
266C23×D11—42no—
267C23×D11C2412yes—
268C23×D11C2412yes—
269C23×D11C2411yescharacteristic
270C23×D11C2411yescharacteristic
271C2×D4×C11—22no—
272C2×D4×C11—22no—
273C2×D4×C11—22no—
274C22×C4×C11C2412yes—
275C22×C4×C11C2412yes—
276C22×C4×C11C2411yescharacteristic
277C22×C4×C11C2412yes—
278C22×C4×C11C2411yescharacteristic
279C22×C4×C11C2411yescharacteristic
280C22×C4×C11C2411yescharacteristic
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2411yescharacteristic
283C22×C4×C11C2411yescharacteristic
284C2×C22⋊D11—24no—
285C2×C22⋊D11—24no—
286C2×C22⋊D11—24no—
287C2×C22⋊D11—24no—
288C2×C22⋊D11—42no—
289C2×C22⋊D11—42no—
290C2×C22⋊D11—42no—
291C2×C22⋊D11—42no—
292C2×C22⋊D11—42no—
293C2×C22⋊D11—42no—
294C2×C22⋊D11—42no—
295C2×C22⋊D11—42no—
296C22×Dic11C2411yescharacteristic
297C22×Dic11C2411yescharacteristic
298C22×Dic11C2412yes—
299C22×Dic11C2412yes—
300C22×Dic11C2411yescharacteristic
301C22×Dic11C2411yescharacteristic
302C22×Dic11C2411yescharacteristic
303C22×Dic11C2411yescharacteristic
304D4×D11—416no—
305C2×D44—24no—
306C2×D44—24no—
307C2×D44—24no—
308C2×D44—22no—
309C2×D44—22no—
310C2×D44—24no—
311C2×D44—24no—
312C2×D44—24no—
313C2×D44—22no—
314C2×D44—22no—
315C2×D44—24no—
316C2×D44—22no—
317C2×D44—22no—
318C2×D44—22no—
319C2×D44—22no—
320C2×D44—42no—
321C2×D44—42no—
322C2×D44—42no—
323C2×D44—42no—
324C2×D44—42no—
325C2×D44—42no—
326C2×D44—42no—
327C2×D44—42no—
328C2×D44C2×D414yes—
329C2×C4×D11—22no—
330C2×C4×D11—24no—
331C2×C4×D11—24no—
332C2×C4×D11—22no—
333C2×C4×D11—22no—
334C2×C4×D11—22no—
335C2×C4×D11—22no—
336C2×C4×D11—22no—
337C2×C4×D11—22no—
338C2×C4×D11—22no—
339C2×C4×D11—22no—
340C2×C4×D11—41no—
341C2×C4×D11—41no—
342C2×C4×D11—41no—
343C2×C4×D11—41no—
344C2×C4×D11—41no—
345C2×C4×D11—41no—
346C2×C4×D11—42no—
347C2×C4×D11—42no—
348C2×C4×D11—42no—
349C2×C4×D11—42no—
350C2×C4×D11C2×D414yes—
351C2×C4×D11C2×D414yescomplemented
352C2×C4×D11#4114yes—
353C2×Dic22—24no—
354C2×Dic22—42no—
355C2×Dic22—42no—
356C11×C4⋊C4—24no—
357C11×C4⋊C4—24no—
358C11×C4⋊C4—24no—
359C11×C4⋊C4—22no—
360C11×C4⋊C4—22no—
361C11×C4⋊C4—22no—
362C11×C22⋊C4—24no—
363C11×C22⋊C4—24no—
364C11×C22⋊C4—24no—
365C11×C22⋊C4—24no—
366C11×C22⋊C4—24no—
367C11×C22⋊C4—42no—
368C42×C11—22no—
369C42×C11—22no—
370C42×C11—22no—
371C42×C11—22no—
372C42×C11—22no—
373C42×C11—41no—
374C42×C11C2×D414yescomplemented
375C22⋊Dic11—24no—
376C22⋊Dic11—42no—
377C22⋊Dic11—42no—
378(C2×D11)⋊C4—24no—
379(C2×D11)⋊C4—24no—
380(C2×D11)⋊C4—22no—
381(C2×D11)⋊C4—24no—
382(C2×D11)⋊C4—24no—
383(C2×D11)⋊C4—24no—
384(C2×D11)⋊C4—24no—
385(C2×D11)⋊C4—22no—
386(C2×D11)⋊C4—24no—
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4—24no—
389(C2×D11)⋊C4—24no—
390(C2×D11)⋊C4—22no—
391(C2×D11)⋊C4—24no—
392(C2×D11)⋊C4—24no—
393(C2×D11)⋊C4—42no—
394(C2×D11)⋊C4—42no—
395(C2×D11)⋊C4—42no—
396(C2×D11)⋊C4—42no—
397(C2×D11)⋊C4—42no—
398(C2×D11)⋊C4—42no—
399(C2×D11)⋊C4C2×D414yes—
400(C2×D11)⋊C4C2×D414yescomplemented
401(C2×D11)⋊C4#4114yes—
402C4⋊Dic11—22no—
403C4⋊Dic11—22no—
404C4⋊Dic11—22no—
405C4⋊Dic11—22no—
406C4⋊Dic11—42no—
407C4⋊Dic11C2×D414yescomplemented
408Dic11⋊C4—24no—
409Dic11⋊C4—24no—
410Dic11⋊C4—42no—
411Dic11⋊C4—42no—
412C4×Dic11—24no—
413C4×Dic11—22no—
414C4×Dic11—22no—
415C4×Dic11—41no—
416C4×Dic11—41no—
417C4×Dic11—41no—
418C4×Dic11—41no—
419C2×#538—112no—
420#2860D1111yescharacteristic, complemented
421#2858—111no—
422#2856—111no—
423#2854—111no—
424#2662—112no—
425#2661—112no—
426#2555—112no—
427#2554—112no—
428#2512—111no—
429#2491—111no—
430#2472—112no—
431#2445—111no—
432#2440—111no—
433#2433—111no—
434#2428—111no—
435#2424—112no—
436#2416—111no—
437#2408—111no—
438#2321—112no—
439C4×#121—111no—
440C2×#390—111no—
441C42×D4—111no—
442C23×C11—22no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—22no—
446C23×C11—22no—
447C23×C11—22no—
448C23×C11—22no—
449C23×C11C2511yescharacteristic
450C22×D11—21no—
451C22×D11—21no—
452C22×D11—21no—
453C22×D11—21no—
454C22×D11—21no—
455C22×D11—21no—
456C22×D11—21no—
457C22×D11—21no—
458C22×D11—21no—
459C22×D11—21no—
460C22×D11—22no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—22no—
473C22×D11—22no—
474C22×D11—48no—
475C22×D11—48no—
476C22×D11—48no—
477C22×D11—84no—
478C22×D11—84no—
479C22×D11—84no—
480C22×D11—84no—
481C22×D11C22×D412yes—
482C22×D11C22×D412yes—
483C22×D11C2×#4112yes—
484C22×D11C2×#4112yes—
485D4×C11—44no—
486C2×C4×C11—21no—
487C2×C4×C11—21no—
488C2×C4×C11—21no—
489C2×C4×C11—21no—
490C2×C4×C11—21no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—21no—
495C2×C4×C11—21no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—21no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—21no—
505C2×C4×C11—22no—
506C2×C4×C11—21no—
507C2×C4×C11—22no—
508C2×C4×C11C22×D412yes—
509C2×C4×C11C22×D412yes—
510C2×C4×C11C22×D412yes—
511C2×C4×C11C2×#4112yes—
512C2×C4×C11C2×#4112yes—
513C2×C4×C11H(5,𝔽2)12yes—
514C2×C4×C11H(5,𝔽2)12yes—
515C2×C4×C11H(5,𝔽2)12yes—
516C22⋊D11—48no—
517C22⋊D11—84no—
518C22⋊D11—84no—
519C22⋊D11—84no—
520C2×Dic11—21no—
521C2×Dic11—21no—
522C2×Dic11—21no—
523C2×Dic11—21no—
524C2×Dic11—21no—
525C2×Dic11—21no—
526C2×Dic11—21no—
527C2×Dic11—21no—
528C2×Dic11—22no—
529C2×Dic11—22no—
530C2×Dic11—21no—
531C2×Dic11—21no—
532C2×Dic11—21no—
533C2×Dic11—21no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—21no—
539C2×Dic11—21no—
540C2×Dic11C22×D412yes—
541C2×Dic11C22×D412yes—
542C2×Dic11C2×#4112yes—
543C2×Dic11C2×#4112yes—
544D44—28no—
545D44—48no—
546D44—44no—
547D44—44no—
548D44—84no—
549D44—84no—
550D44—84no—
551D44—84no—
552C4×D11—28no—
553C4×D11—44no—
554C4×D11—44no—
555C4×D11—44no—
556C4×D11—44no—
557C4×D11—44no—
558C4×D11—84no—
559C4×D11—84no—
560Dic22—84no—
561C23×D4—111no—
562#538—2216no—
563C2×C4⋊Q8—111no—
564C2×#127—111no—
565C2×#127—111no—
566C2×#126—112no—
567C2×#126C2×D1112yescomplemented
568C2×#124—112no—
569C2×#124—112no—
570C2×#124—112no—
571C2×#123—112no—
572C2×#123—112no—
573C2×C22⋊Q8—112no—
574C2×#121—111no—
575C2×#121—112no—
576C2×#121—111no—
577C2×#121—112no—
578C2×#121—111no—
579C2×#121—111no—
580C2×#121—112no—
581C2×#121—112no—
582C2×#120—112no—
583C2×#120—112no—
584C2×#120—112no—
585C2×C4×D4—112no—
586C2×C4×D4—111no—
587C2×C4×D4—111no—
588C2×C4×D4—111no—
589C2×C4×D4—111no—
590C22×C4⋊C4—111no—
591C22×C22⋊C4—112no—
592C22×C22⋊C4—112no—
593C22×C42—111no—
594C22×C42—111no—
595#398—112no—
596#397—112no—
597#396—112no—
598#396—112no—
599#395—112no—
600#394—112no—
601#394—112no—
602#394—112no—
603#394—112no—
604#394—112no—
605#394—112no—
606#393—112no—
607#392—112no—
608#392—112no—
609#392—112no—
610#392—112no—
611#390—111no—
612#390—111no—
613#390—111no—
614#390—112no—
615#390—112no—
616#390—112no—
617#390—112no—
618#390—112no—
619#390—111no—
620#390—111no—
621#390—111no—
622#390—111no—
623#390—112no—
624#390C2×D1111yescharacteristic
625#390C2×D1111yescharacteristic
626#390C2×D1111yescharacteristic
627#389—111no—
628#389C2×D1111yescharacteristic, complemented
629#389C2×D1111yescharacteristic, complemented
630#389C2×D1111yescharacteristic, complemented
631#388—112no—
632#388—112no—
633#388—112no—
634#388—112no—
635#388—112no—
636#388C2×D1112yescomplemented
637#388C2×D1112yescomplemented
638#388C2×D1112yescomplemented
639#386—112no—
640#386—112no—
641#386—112no—
642#386—112no—
643#386—112no—
644#385—112no—
645#384—111no—
646#380—111no—
647#380—111no—
648#379—112no—
649C4×C4⋊C4—111no—
650C4×C4⋊C4—111no—
651C4×C4⋊C4—111no—
652C4×C4⋊C4—111no—
653C4×C22⋊C4—111no—
654C4×C22⋊C4—111no—
655C4×C22⋊C4—111no—
656C4×C22⋊C4—111no—
657C4×C22⋊C4—111no—
658C4×C22⋊C4—111no—
659C4×C22⋊C4—112no—
660C43C2×D1111yescharacteristic, complemented
661C22×C11—42no—
662C22×C11—42no—
663C22×C11—42no—
664C22×C11—42no—
665C22×C11—42no—
666C22×C11—42no—
667C22×C11—42no—
668C22×C11C23×D411yescharacteristic
669C22×C11C22×#4111yescharacteristic
670C22×C11C22×#4111yescharacteristic
671C22×C11C2×H(5,𝔽2)11yescharacteristic
672C22×C11C2×H(5,𝔽2)11yescharacteristic
673C22×C11C2×H(5,𝔽2)11yescharacteristic
674C22×C11#58511yescharacteristic
675C2×D11—22no—
676C2×D11—22no—
677C2×D11—22no—
678C2×D11—22no—
679C2×D11—22no—
680C2×D11—22no—
681C2×D11—22no—
682C2×D11—22no—
683C2×D11—22no—
684C2×D11—41no—
685C2×D11—41no—
686C2×D11—41no—
687C2×D11—41no—
688C2×D11—42no—
689C2×D11—42no—
690C2×D11—42no—
691C2×D11—42no—
692C2×D11—42no—
693C2×D11—42no—
694C2×D11—42no—
695C2×D11—42no—
696C2×D11—42no—
697C2×D11—42no—
698C2×D11—42no—
699C2×D11—42no—
700C2×D11—42no—
701C2×D11—42no—
702C2×D11—816no—
703C2×D11#53214yes—
704C4×C11—22no—
705C4×C11—22no—
706C4×C11—22no—
707C4×C11—22no—
708C4×C11—22no—
709C4×C11—42no—
710C4×C11—41no—
711C4×C11—42no—
712C4×C11—42no—
713C4×C11#53814yescomplemented
714Dic11—22no—
715Dic11—22no—
716Dic11—22no—
717Dic11—22no—
718Dic11—41no—
719Dic11—42no—
720Dic11—42no—
721Dic11—41no—
722C25—112no—
723C22×Q8—112no—
724C22×D4—112no—
725C22×D4—112no—
726C22×D4—112no—
727C22×D4—112no—
728C22×D4—111no—
729C22×D4—112no—
730C22×D4—111no—
731C22×D4—111no—
732C22×D4—112no—
733C22×D4—112no—
734C22×D4—112no—
735C22×D4—112no—
736C22×D4—224no—
737C22×D4—442no—
738C22×D4—442no—
739C22×D4C22×D1111yescharacteristic
740C23×C4—111no—
741C23×C4—111no—
742C23×C4—111no—
743C23×C4—111no—
744C23×C4—111no—
745C23×C4—111no—
746C23×C4—112no—
747C23×C4—112no—
748C4⋊Q8—442no—
749#127—442no—
750#127—442no—
751#126—28no—
752#126—228no—
753#124—228no—
754#124—228no—
755#124—444no—
756#123—228no—
757#123—228no—
758C22⋊Q8—228no—
759#121—228no—
760#121—228no—
761#121—224no—
762#121—228no—
763#121—444no—
764#121—442no—
765#121—442no—
766#121—442no—
767#120—228no—
768#120—228no—
769#120—228no—
770C4×D4—118no—
771C4×D4—224no—
772C4×D4—224no—
773C4×D4—228no—
774C4×D4—442no—
775C2×C4⋊C4—111no—
776C2×C4⋊C4—111no—
777C2×C4⋊C4—111no—
778C2×C4⋊C4—111no—
779C2×C4⋊C4—112no—
780C2×C4⋊C4—111no—
781C2×C4⋊C4—112no—
782C2×C4⋊C4—112no—
783C2×C4⋊C4—112no—
784C2×C4⋊C4—112no—
785C2×C4⋊C4—442no—
786C2×C4⋊C4C22×D1111yescharacteristic
787C2×C4⋊C4C22×D1111yescharacteristic
788C2×C4⋊C4C22×D1112yes—
789C2×C4⋊C4C22×D1112yes—
790C2×C4⋊C4C22×D1112yes—
791C2×C4⋊C4C22×D1111yescharacteristic
792C2×C22⋊C4—111no—
793C2×C22⋊C4—111no—
794C2×C22⋊C4—111no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—112no—
797C2×C22⋊C4—112no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—111no—
802C2×C22⋊C4—111no—
803C2×C22⋊C4—111no—
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—112no—
811C2×C22⋊C4—112no—
812C2×C22⋊C4—112no—
813C2×C22⋊C4—112no—
814C2×C22⋊C4—112no—
815C2×C22⋊C4—112no—
816C2×C22⋊C4—112no—
817C2×C22⋊C4—112no—
818C2×C22⋊C4—112no—
819C2×C22⋊C4—228no—
820C2×C22⋊C4—444no—
821C2×C22⋊C4C22×D1112yes—
822C2×C22⋊C4C22×D1112yes—
823C2×C22⋊C4C22×D1112yes—
824C2×C22⋊C4C22×D1112yes—
825C2×C22⋊C4C22×D1112yes—
826C2×C22⋊C4C22×D1112yes—
827C2×C42—112no—
828C2×C42—111no—
829C2×C42—111no—
830C2×C42—111no—
831C2×C42—111no—
832C2×C42—111no—
833C2×C42—111no—
834C2×C42—442no—
835C2×C42—442no—
836C2×C42C22×D1111yescharacteristic
837C2×C42C22×D1111yescharacteristic
838C2×C42C22×D1111yescharacteristic
839C2×C42C22×D1111yescharacteristic
840C2×C42C22×D1111yescharacteristic
841C2×C42C22×D1111yescharacteristic
842C2×C42C22×D1111yescharacteristic
843#95—111no—
844#95—111no—
845#95—111no—
846#95—111no—
847#95—111no—
848#95—111no—
849#95—112no—
850#95—112no—
851#95—112no—
852#95—112no—
853#95C22×D1112yes—
854#95C22×D1112yes—
855#95C22×D1112yes—
856C2×C11—82no—
857C2×C11C2×#53211yescharacteristic
858C2×C11C2×#53811yescharacteristic
859C2×C11#346011yescharacteristic
860C2×C11#349611yescharacteristic
861C2×C11#349811yescharacteristic
862C2×C11#351411yescharacteristic
863C2×C11#351911yescharacteristic
864D11—24no—
865D11—42no—
866D11—82no—
867D11—82no—
868C24—111no—
869C24—111no—
870C24—112no—
871C24—112no—
872C24—224no—
873C24—224no—
874C24—224no—
875C24—442no—
876C24—442no—
877C24—442no—
878C24—442no—
879C24C23×D1112yes—
880C2×Q8—224no—
881C2×Q8—442no—
882C2×Q8—442no—
883C2×D4—22no—
884C2×D4—22no—
885C2×D4—22no—
886C2×D4—114no—
887C2×D4—222no—
888C2×D4—222no—
889C2×D4—224no—
890C2×D4—224no—
891C2×D4—224no—
892C2×D4—224no—
893C2×D4—224no—
894C2×D4—224no—
895C2×D4—224no—
896C2×D4—224no—
897C2×D4—224no—
898C2×D4—224no—
899C2×D4—222no—
900C2×D4—222no—
901C2×D4—224no—
902C2×D4—222no—
903C2×D4—222no—
904C2×D4—222no—
905C2×D4—222no—
906C2×D4—442no—
907C2×D4—442no—
908C2×D4—442no—
909C2×D4—442no—
910C2×D4—442no—
911C2×D4—442no—
912C2×D4—442no—
913C2×D4—442no—
914C2×D4—4416no—
915C2×D4—442no—
916C2×D4—442no—
917C2×D4—442no—
918C2×D4—442no—
919C2×D4—442no—
920C2×D4—442no—
921C2×D4—442no—
922C2×D4—442no—
923C22×C4—111no—
924C22×C4—111no—
925C22×C4—111no—
926C22×C4—111no—
927C22×C4—114no—
928C22×C4—114no—
929C22×C4—114no—
930C22×C4—111no—
931C22×C4—111no—
932C22×C4—112no—
933C22×C4—112no—
934C22×C4—222no—
935C22×C4—224no—
936C22×C4—222no—
937C22×C4—224no—
938C22×C4—222no—
939C22×C4—222no—
940C22×C4—222no—
941C22×C4—222no—
942C22×C4—222no—
943C22×C4—222no—
944C22×C4—222no—
945C22×C4—441no—
946C22×C4—441no—
947C22×C4—441no—
948C22×C4—441no—
949C22×C4—441no—
950C22×C4—441no—
951C22×C4—442no—
952C22×C4—442no—
953C22×C4—442no—
954C22×C4—442no—
955C22×C4C23×D1112yes—
956C22×C4C23×D1111yescharacteristic
957C22×C4C23×D1112yes—
958C22×C4C23×D1112yes—
959C22×C4C23×D1111yescharacteristic
960C22×C4C23×D1111yescharacteristic
961C22×C4C23×D1111yescharacteristic
962C22×C4C23×D1111yescharacteristic
963C22×C4C23×D1111yescharacteristic
964C22×C4C23×D1111yescharacteristic
965C4⋊C4—24no—
966C4⋊C4—24no—
967C4⋊C4—24no—
968C4⋊C4—22no—
969C4⋊C4—22no—
970C4⋊C4—22no—
971C4⋊C4—114no—
972C4⋊C4—222no—
973C4⋊C4—222no—
974C4⋊C4—224no—
975C4⋊C4—224no—
976C4⋊C4—222no—
977C4⋊C4—222no—
978C4⋊C4—442no—
979C4⋊C4—442no—
980C4⋊C4—442no—
981C22⋊C4—24no—
982C22⋊C4—24no—
983C22⋊C4—24no—
984C22⋊C4—24no—
985C22⋊C4—24no—
986C22⋊C4—42no—
987C22⋊C4—114no—
988C22⋊C4—114no—
989C22⋊C4—114no—
990C22⋊C4—224no—
991C22⋊C4—222no—
992C22⋊C4—224no—
993C22⋊C4—224no—
994C22⋊C4—224no—
995C22⋊C4—224no—
996C22⋊C4—222no—
997C22⋊C4—224no—
998C22⋊C4—224no—
999C22⋊C4—224no—
1000C22⋊C4—224no—
1001C22⋊C4—224no—
1002C22⋊C4—224no—
1003C22⋊C4—222no—
1004C22⋊C4—224no—
1005C22⋊C4—224no—
1006C22⋊C4—442no—
1007C22⋊C4—442no—
1008C22⋊C4—442no—
1009C22⋊C4—442no—
1010C22⋊C4—442no—
1011C22⋊C4—442no—
1012C22⋊C4—442no—
1013C22⋊C4—442no—
1014C42—22no—
1015C42—22no—
1016C42—22no—
1017C42—22no—
1018C42—22no—
1019C42—41no—
1020C42—224no—
1021C42—222no—
1022C42—222no—
1023C42—441no—
1024C42—441no—
1025C42—441no—
1026C42—441no—
1027C42D4×D1114yescomplemented
1028C11#3500711yescharacteristic, complemented, Sylow
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—112no—
1037C23—112no—
1038C23—112no—
1039C23—112no—
1040C23—221no—
1041C23—221no—
1042C23—221no—
1043C23—221no—
1044C23—221no—
1045C23—221no—
1046C23—221no—
1047C23—221no—
1048C23—221no—
1049C23—221no—
1050C23—222no—
1051C23—222no—
1052C23—222no—
1053C23—222no—
1054C23—222no—
1055C23—222no—
1056C23—222no—
1057C23—222no—
1058C23—222no—
1059C23—222no—
1060C23—222no—
1061C23—222no—
1062C23—222no—
1063C23—222no—
1064C23—448no—
1065C23—448no—
1066C23—448no—
1067C23—884no—
1068C23—884no—
1069C23—884no—
1070C23—884no—
1071C23C24×D1111yescharacteristic
1072Q8—884no—
1073D4—44no—
1074D4—228no—
1075D4—448no—
1076D4—448no—
1077D4—444no—
1078D4—444no—
1079D4—884no—
1080D4—884no—
1081D4—884no—
1082D4—884no—
1083D4—884no—
1084D4—884no—
1085D4—884no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—21no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—21no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—21no—
1107C2×C4—22no—
1108C2×C4—112no—
1109C2×C4—112no—
1110C2×C4—112no—
1111C2×C4—112no—
1112C2×C4—221no—
1113C2×C4—221no—
1114C2×C4—221no—
1115C2×C4—221no—
1116C2×C4—221no—
1117C2×C4—221no—
1118C2×C4—221no—
1119C2×C4—221no—
1120C2×C4—228no—
1121C2×C4—222no—
1122C2×C4—222no—
1123C2×C4—221no—
1124C2×C4—221no—
1125C2×C4—221no—
1126C2×C4—221no—
1127C2×C4—222no—
1128C2×C4—222no—
1129C2×C4—221no—
1130C2×C4—221no—
1131C2×C4—222no—
1132C2×C4—222no—
1133C2×C4—444no—
1134C2×C4—444no—
1135C2×C4—444no—
1136C2×C4—444no—
1137C2×C4—444no—
1138C2×C4—884no—
1139C2×C4—884no—
1140C2×C4C2×D4×D1112yes—
1141C2×C4C2×D4×D1112yes—
1142C2×C4C2×D4×D1112yes—
1143C2×C4#41×D1112yes—
1144C2×C4#41×D1112yes—
1145C2×C4#6704212yes—
1146C2×C4#6704212yes—
1147C2×C4#6704212yes—
1148C22—42no—
1149C22—42no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—42no—
1154C22—42no—
1155C22—114no—
1156C22—222no—
1157C22—222no—
1158C22—222no—
1159C22—222no—
1160C22—222no—
1161C22—222no—
1162C22—222no—
1163C22—222no—
1164C22—222no—
1165C22—441no—
1166C22—441no—
1167C22—441no—
1168C22—441no—
1169C22—442no—
1170C22—442no—
1171C22—442no—
1172C22—442no—
1173C22—442no—
1174C22—442no—
1175C22—442no—
1176C22—442no—
1177C22—442no—
1178C22—442no—
1179C22—442no—
1180C22—442no—
1181C22—442no—
1182C22—442no—
1183C22—8816no—
1184C22C22×D4×D1111yescharacteristic
1185C22C2×#41×D1111yescharacteristic
1186C22C2×#41×D1111yescharacteristic
1187C22C2×#6704211yescharacteristic
1188C22C2×#6704211yescharacteristic
1189C22C2×#6704211yescharacteristic
1190C22#1062345311yescharacteristic
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—22no—
1195C4—22no—
1196C4—42no—
1197C4—42no—
1198C4—42no—
1199C4—41no—
1200C4—222no—
1201C4—222no—
1202C4—222no—
1203C4—222no—
1204C4—442no—
1205C4—442no—
1206C4—441no—
1207C4—441no—
1208C4#1062323514yescomplemented
1209C2—82no—
1210C2—224no—
1211C2—442no—
1212C2—882no—
1213C2—882no—
1214C2D11×#53211yescharacteristic
1215C2C2×#1062323511yescharacteristic
1216C2#1308203711yescharacteristic
1217C2#1308237811yescharacteristic
1218C2#1308238911yescharacteristic
1219C2#1308256511yescharacteristic
1220C2#1308265011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2860C2
hypercenter#2860D11
hypocenterC11#35007
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2860

Complements

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

NH ≅ G/Ntype
1. C2×#10623235C2semidirect
2. #13076973C2semidirect
3. #13076960C2semidirect
4. #13076949C2semidirect
5. #13074756C2semidirect
6. #13074748C2semidirect
7. #13073692C2semidirect
8. #13073675C2semidirect
9. #13073205C2semidirect
10. #13072977C2semidirect
11. #13072746C2semidirect
12. #13072384C2semidirect
13. #13072320C2semidirect
14. #13072252C2semidirect
15. #13072202C2semidirect
16. #13072157C2semidirect
17. #13072054C2semidirect
18. #13071970C2semidirect
19. #13071269C2semidirect
20. #13071124C2semidirect
21. D11×#390C2semidirect
22. C42×D44C2semidirect
23. C11×#2860C2semidirect
25. C2×C11×#126C22semidirect
29. C2×#66951C22semidirect
34. C2×#66948C22semidirect
35. C2×#66948C22semidirect
36. C2×#66947C22semidirect
38. C2×#66946C22semidirect
40. C2×#66938C22semidirect
41. C2×#66937C22semidirect
42. C2×#66937C22semidirect
43. C2×#66936C22semidirect
49. C2×#66928C22semidirect
50. C2×#66928C22semidirect
56. C2×C42×D11C22semidirect
57. C2×#66922C22semidirect
61. C11×#389C22semidirect
62. C11×#389C22semidirect
63. C11×#389C22semidirect
64. C11×#388C22semidirect
65. C11×#388C22semidirect
66. C11×#388C22semidirect
67. C43×C11C22semidirect
69. #10622607C22semidirect
70. #10622607C22semidirect
71. #10622604C22semidirect
72. #10622603C22semidirect
73. #10622603C22semidirect
77. #10622600C22semidirect
78. #10622592C22semidirect
79. #10622589C22semidirect
80. C4⋊C4×Dic11C22semidirect
81. #10622586C22semidirect
83. #10622574C22semidirect
84. #10622574C22semidirect
88. #10622572C22semidirect
91. #10622570C22semidirect
92. #10622570C22semidirect
93. #10622569C22semidirect
95. #10622564C22semidirect
96. #10622560C22semidirect
99. #10622552C22semidirect
100. #10622552C22semidirect
101. #10622552C22semidirect
102. #10622552C22semidirect
106. C4×(C2×D11)⋊C4C22semidirect
107. C4×(C2×D11)⋊C4C22semidirect
108. C4×(C2×D11)⋊C4C22semidirect
109. C4×C4⋊Dic11C22semidirect
110. C4×C4⋊Dic11C22semidirect
111. C4×C4⋊Dic11C22semidirect
112. #10622288C22semidirect
113. #10622285C22semidirect
114. #10622284C22semidirect
115. #10622282C22semidirect
116. #10622282C22semidirect
118. #10622279C22semidirect
121. #10622278C22semidirect
122. #10622278C22semidirect
123. #10622270C22semidirect
241. C4×D44D4semidirect
351. C2×C4×D11C2×D4semidirect
374. C42×C11C2×D4semidirect
400. (C2×D11)⋊C4C2×D4semidirect
407. C4⋊Dic11C2×D4semidirect
420. #2860D11semidirect
567. C2×#126C2×D11semidirect
628. #389C2×D11semidirect
629. #389C2×D11semidirect
630. #389C2×D11semidirect
636. #388C2×D11semidirect
637. #388C2×D11semidirect
638. #388C2×D11semidirect
660. C43C2×D11semidirect
713. C4×C11#538semidirect
1027. C42D4×D11semidirect
1028. C11#35007semidirect
1208. C4#10623235semidirect

Maximal subgroups

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

subgroupindex
C2×#106232352
#130769732
#130769602
#130769492
#130747562
#130747482
#130736922
#130736752
#130732052
#130729772
#130727462
#130723842
#130723202
#130722522
#130722022
#130721572
#130720542
#130719702
#130712692
#130711242
D11×#3902
C42×D442
C11×#28602
#3500711