Finite Group Databasebeta

← #14926723

Subgroups — #14926723

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×#10623025C212yesmaximal, complemented
2#13076980C211yesmaximal, characteristic, complemented
3#13076970C211yesmaximal, characteristic, complemented
4#13076960C211yesmaximal, characteristic, complemented
5#13076946C211yesmaximal, characteristic, complemented
6#13074757C212yesmaximal, complemented
7#13074746C212yesmaximal, complemented
8#13073690C212yesmaximal, complemented
9#13073678C212yesmaximal, complemented
10#13073203C211yesmaximal, characteristic, complemented
11#13072980C211yesmaximal, characteristic, complemented
12#13072736C212yesmaximal, complemented
13#13072382C211yesmaximal, characteristic, complemented
14#13072312C211yesmaximal, characteristic, complemented
15#13072249C211yesmaximal, characteristic, complemented
16#13072205C211yesmaximal, characteristic, complemented
17#13072152C212yesmaximal, complemented
18#13072050C211yesmaximal, characteristic, complemented
19#13071966C211yesmaximal, characteristic, complemented
20#13071274C212yesmaximal, complemented
21C4×#66983C211yesmaximal, characteristic, complemented
22C42×C22⋊D11C211yesmaximal, characteristic, complemented
23C2×C11×#390C211yesmaximal, characteristic, complemented
24C23×D4×C11C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2212yes—
27C22×C11×C22⋊C4C2212yes—
28C22×C42×C11C2211yescharacteristic
29C2×#67006C2212yes—
30C2×#67006C2212yes—
31C2×#67006C2212yes—
32C2×#66993C2211yescharacteristic
33C2×#66993C2211yescharacteristic
34C2×#66991C2211yescharacteristic
35C2×#66991C2211yescharacteristic
36C2×#66983C2212yes—
37C2×#66983C2211yescharacteristic
38C2×C4×C22⋊D11C2211yescharacteristic
39C2×C4×C22⋊D11C2212yes—
40C2×C4×C22⋊D11C2211yescharacteristic
41C2×C4×C22⋊D11C2211yescharacteristic
42C2×#66977C2212yes—
43C2×#66948C2211yescharacteristic, complemented
44C2×#66941C2211yescharacteristic, complemented
45#10623025—216no—
46C2×#66938C2212yescomplemented
47C2×#66938C2212yescomplemented
48C2×#66938C2212yescomplemented
49C2×#66937C2212yescomplemented
50C2×#66937C2212yescomplemented
51C2×#66937C2212yescomplemented
52C2×#66936C2212yescomplemented
53C2×#66936C2212yescomplemented
54C2×#66932C2212yescomplemented
55C2×#66932C2212yescomplemented
56C2×C4×D44C2211yescharacteristic, complemented
57C2×C42×D11C2211yescharacteristic, complemented
58C11×#390C2212yes—
59C11×#390C2211yescharacteristic
60C11×#390C2212yes—
61C11×#390C2211yescharacteristic
62C11×#390C2211yescharacteristic
63C11×#390C2211yescharacteristic
64#10622860C2212yes—
65#10622836C2212yes—
66#10622836C2212yes—
67#10622836C2212yes—
68#10622835C2212yes—
69#10622834C2211yescharacteristic
70#10622834C2211yescharacteristic
71#10622834C2211yescharacteristic
72#10622834C2211yescharacteristic
73#10622826C2212yes—
74#10622826C2212yes—
75#10622825C2211yescharacteristic
76#10622823C2212yes—
77C4×C22⋊Dic11C2211yescharacteristic
78C4×C22⋊Dic11C2211yescharacteristic
79C4×C22⋊Dic11C2211yescharacteristic
80#10622607C2212yescomplemented
81#10622604C2212yescomplemented
82#10622601C2211yescharacteristic, complemented
83#10622600C2211yescharacteristic, complemented
84#10622598C2211yescharacteristic, complemented
85#10622598C2211yescharacteristic, complemented
86#10622597C2212yescomplemented
87#10622592C2212yescomplemented
88#10622589C2211yescharacteristic, complemented
89#10622586C2211yescharacteristic, complemented
90#10622574C2212yescomplemented
91#10622573C2212yescomplemented
92#10622572C2212yescomplemented
93#10622572C2212yescomplemented
94#10622572C2212yescomplemented
95#10622570C2212yescomplemented
96#10622570C2212yescomplemented
97#10622570C2212yescomplemented
98#10622570C2212yescomplemented
99#10622569C2212yescomplemented
100#10622569C2212yescomplemented
101#10622569C2212yescomplemented
102#10622565C2212yescomplemented
103#10622564C2212yescomplemented
104#10622564C2212yescomplemented
105#10622561C2212yescomplemented
106#10622560C2212yescomplemented
107#10622558C2212yescomplemented
108#10622558C2212yescomplemented
109#10622557C2212yescomplemented
110#10622557C2212yescomplemented
111#10622557C2212yescomplemented
112#10622553C2212yescomplemented
113#10622552C2211yescharacteristic, complemented
114C4×(C2×D11)⋊C4C2212yescomplemented
115C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
116C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
117C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
118C4×C4⋊Dic11C2211yescharacteristic, complemented
119C4×Dic11⋊C4C2211yescharacteristic, complemented
120C4×Dic11⋊C4C2211yescharacteristic, complemented
121C4×Dic11⋊C4C2211yescharacteristic, complemented
122C42×Dic11C2211yescharacteristic, complemented
123#10622541C2211yescharacteristic, complemented
124C25×C11C2312yes—
125C22×D4×C11—24no—
126C22×D4×C11—42no—
127C22×D4×C11—42no—
128C22×D4×C11C2311yescharacteristic
129C22×D4×C11C2311yescharacteristic
130C22×D4×C11C2312yes—
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2311yescharacteristic
133C23×C4×C11C2312yes—
134C23×C4×C11C2311yescharacteristic
135C22×C22⋊D11C2312yes—
136C22×C22⋊D11C2311yescharacteristic
137C22×C22⋊D11C2312yes—
138C22×C22⋊D11C2312yes—
139C22×C22⋊D11C2312yes—
140C22×C22⋊D11C2312yes—
141C22×C22⋊D11C2312yes—
142C22×C22⋊D11C2312yes—
143C22×D44C2311yescharacteristic
144C22×D44C2312yes—
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2312yes—
148C22×C4×D11C2311yescharacteristic
149C22×Dic22C2312yes—
150C2×C11×C4⋊C4—42no—
151C2×C11×C4⋊C4C2311yescharacteristic
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C4⋊C4C2312yes—
154C2×C11×C22⋊C4—28no—
155C2×C11×C22⋊C4—44no—
156C2×C11×C22⋊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×C11×C22⋊C4C2312yes—
164C2×C42×C11—42no—
165C2×C42×C11C2311yescharacteristic
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2311yescharacteristic
169#67006—28no—
170#67006—28no—
171#67006—28no—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2311yescharacteristic
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2312yes—
182C2×C22⋊Dic11C2312yes—
183C2×C22⋊Dic11C2312yes—
184C2×C22⋊Dic11C2311yescharacteristic
185C2×C22⋊Dic11C2311yescharacteristic
186#66993—42no—
187#66993—42no—
188#66991—42no—
189#66991—42no—
190#66983—24no—
191#66983—28no—
192C4×C22⋊D11—28no—
193C4×C22⋊D11—24no—
194C4×C22⋊D11—24no—
195C4×C22⋊D11D418yescomplemented
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2311yescharacteristic
201C2×(C2×D11)⋊C4C2311yescharacteristic
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2312yes—
206C2×(C2×D11)⋊C4C2311yescharacteristic
207C2×C4⋊Dic11C2311yescharacteristic
208C2×C4⋊Dic11C2312yes—
209C2×C4⋊Dic11C2312yes—
210C2×C4⋊Dic11C2311yescharacteristic
211C2×C4⋊Dic11C2311yescharacteristic
212#66977—28no—
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2312yes—
215C2×Dic11⋊C4C2312yes—
216C2×Dic11⋊C4C2311yescharacteristic
217C2×Dic11⋊C4C2311yescharacteristic
218C2×Dic11⋊C4C2312yes—
219C2×Dic11⋊C4C2312yes—
220C2×Dic11⋊C4C2311yescharacteristic
221C2×C4×Dic11C2311yescharacteristic
222C2×C4×Dic11C2312yes—
223C2×C4×Dic11C2311yescharacteristic
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2311yescharacteristic
226C2×C4×Dic11C2311yescharacteristic
227C2×C4×Dic11C2311yescharacteristic
228C2×C4×Dic11C2311yescharacteristic
229C2×C4×Dic11C2311yescharacteristic
230C2×C4×Dic11C2311yescharacteristic
231#66948—42no—
232#66941—42no—
233#66938—28no—
234#66938—28no—
235#66938—44no—
236#66937—28no—
237#66937—28no—
238#66937—44no—
239#66936—28no—
240#66936—28no—
241#66932—28no—
242#66932—28no—
243C4×D44—42no—
244C42×D11—42no—
245C11⋊#95C2312yes—
246C11⋊#95C2311yescharacteristic
247C11⋊#95C2311yescharacteristic
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2311yescharacteristic
250C11⋊#95C2311yescharacteristic
251C11⋊#95C2311yescharacteristic
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258#35007—111nomaximal, Sylow
259C24×C11—24no—
260C24×C11—24no—
261C24×C11—24no—
262C24×C11—42no—
263C24×C11—42no—
264C24×C11—42no—
265C24×C11—42no—
266C24×C11C2412yes—
267C24×C11C2412yes—
268C24×C11C2411yescharacteristic
269C23×D11C2412yes—
270C23×D11C2411yescharacteristic
271C2×D4×C11—24no—
272C2×D4×C11—22no—
273C2×D4×C11—22no—
274C2×D4×C11—22no—
275C2×D4×C11—22no—
276C2×D4×C11—22no—
277C2×D4×C11—22no—
278C2×D4×C11—42no—
279C2×D4×C11—42no—
280C2×D4×C11—416no—
281C22×C4×C11—22no—
282C22×C4×C11—22no—
283C22×C4×C11—22no—
284C22×C4×C11—24no—
285C22×C4×C11—22no—
286C22×C4×C11—41no—
287C22×C4×C11—41no—
288C22×C4×C11—41no—
289C22×C4×C11—42no—
290C22×C4×C11—42no—
291C22×C4×C11C2×D414yes—
292C22×C4×C11#4114yes—
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2412yes—
295C22×C4×C11C2412yes—
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2411yescharacteristic
300C22×C4×C11C2411yescharacteristic
301C2×C22⋊D11—24no—
302C2×C22⋊D11—24no—
303C2×C22⋊D11—24no—
304C2×C22⋊D11—24no—
305C2×C22⋊D11—24no—
306C2×C22⋊D11—22no—
307C2×C22⋊D11—22no—
308C2×C22⋊D11—24no—
309C2×C22⋊D11—24no—
310C2×C22⋊D11—24no—
311C2×C22⋊D11—24no—
312C2×C22⋊D11—42no—
313C2×C22⋊D11—42no—
314C2×C22⋊D11—42no—
315C2×C22⋊D11—42no—
316C2×C22⋊D11—42no—
317C2×C22⋊D11—42no—
318C2×C22⋊D11—42no—
319C2×C22⋊D11—42no—
320C2×C22⋊D11—42no—
321C2×C22⋊D11—42no—
322C2×C22⋊D11—42no—
323C2×C22⋊D11—42no—
324C2×C22⋊D11C2×D414yes—
325C22×Dic11C2411yescharacteristic
326C22×Dic11C2411yescharacteristic
327C22×Dic11C2412yes—
328C22×Dic11C2412yes—
329C22×Dic11C2412yes—
330C22×Dic11C2411yescharacteristic
331C22×Dic11C2411yescharacteristic
332C22×Dic11C2411yescharacteristic
333C22×Dic11C2411yescharacteristic
334C22×Dic11C2411yescharacteristic
335C2×D44—24no—
336C2×D44—22no—
337C2×D44—22no—
338C2×D44—22no—
339C2×D44—42no—
340C2×D44—42no—
341C2×C4×D11—22no—
342C2×C4×D11—24no—
343C2×C4×D11—22no—
344C2×C4×D11—22no—
345C2×C4×D11—22no—
346C2×C4×D11—22no—
347C2×C4×D11—41no—
348C2×C4×D11—41no—
349C2×C4×D11—41no—
350C2×C4×D11—42no—
351C2×C4×D11—42no—
352C2×C4×D11C2×D414yescomplemented
353C2×Dic22—24no—
354C2×Dic22—42no—
355C2×Dic22—42no—
356C11×C4⋊C4—22no—
357C11×C4⋊C4—22no—
358C11×C4⋊C4—42no—
359C11×C22⋊C4—24no—
360C11×C22⋊C4—24no—
361C11×C22⋊C4—24no—
362C11×C22⋊C4—24no—
363C11×C22⋊C4—24no—
364C11×C22⋊C4—24no—
365C11×C22⋊C4—42no—
366C11×C22⋊C4—42no—
367C42×C11—22no—
368C42×C11—22no—
369C42×C11—41no—
370C42×C11—41no—
371C22⋊Dic11—24no—
372C22⋊Dic11—24no—
373C22⋊Dic11—24no—
374C22⋊Dic11—24no—
375C22⋊Dic11—24no—
376C22⋊Dic11—24no—
377C22⋊Dic11—24no—
378C22⋊Dic11—22no—
379C22⋊Dic11—42no—
380C22⋊Dic11—42no—
381C22⋊Dic11—42no—
382C22⋊Dic11—42no—
383C22⋊Dic11C2×D414yes—
384C22⋊Dic11#4114yes—
385(C2×D11)⋊C4—24no—
386(C2×D11)⋊C4—22no—
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4—24no—
389(C2×D11)⋊C4—22no—
390(C2×D11)⋊C4—24no—
391(C2×D11)⋊C4—24no—
392(C2×D11)⋊C4—42no—
393(C2×D11)⋊C4—42no—
394(C2×D11)⋊C4—42no—
395(C2×D11)⋊C4C2×D414yescomplemented
396C4⋊Dic11—24no—
397C4⋊Dic11—24no—
398C4⋊Dic11—22no—
399C4⋊Dic11—22no—
400C4⋊Dic11—22no—
401Dic11⋊C4—24no—
402Dic11⋊C4—24no—
403Dic11⋊C4—22no—
404Dic11⋊C4—24no—
405Dic11⋊C4—22no—
406Dic11⋊C4—42no—
407Dic11⋊C4—42no—
408Dic11⋊C4C2×D414yescomplemented
409C4×Dic11—22no—
410C4×Dic11—24no—
411C4×Dic11—22no—
412C4×Dic11—22no—
413C4×Dic11—22no—
414C4×Dic11—22no—
415C4×Dic11—41no—
416C4×Dic11—41no—
417C4×Dic11—41no—
418C4×Dic11C2×D414yescomplemented
419C2×#538—112no—
420#2860—111no—
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×#390D1111yescharacteristic, complemented
441C42×D4—111no—
442C23×C11—21no—
443C23×C11—21no—
444C23×C11—21no—
445C23×C11—21no—
446C23×C11—22no—
447C23×C11—22no—
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×C11—22no—
458C23×C11—22no—
459C23×C11—22no—
460C23×C11—48no—
461C23×C11—48no—
462C23×C11—48no—
463C23×C11—84no—
464C23×C11—84no—
465C23×C11—84no—
466C23×C11—84no—
467C23×C11C22×D412yes—
468C23×C11C2×#4112yes—
469C23×C11C2×#4112yes—
470C23×C11C2511yescharacteristic
471C22×D11—21no—
472C22×D11—21no—
473C22×D11—21no—
474C22×D11—21no—
475C22×D11—21no—
476C22×D11—21no—
477C22×D11—22no—
478C22×D11—22no—
479C22×D11—22no—
480C22×D11—22no—
481C22×D11—22no—
482C22×D11—22no—
483C22×D11—22no—
484C22×D11C22×D412yes—
485D4×C11—48no—
486D4×C11—44no—
487D4×C11—44no—
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—28no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—21no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—21no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—21no—
506C2×C4×C11—44no—
507C2×C4×C11—44no—
508C2×C4×C11—84no—
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—28no—
517C22⋊D11—48no—
518C22⋊D11—84no—
519C22⋊D11—84no—
520C22⋊D11—84no—
521C22⋊D11—84no—
522C22⋊D11—84no—
523C22⋊D11—84no—
524C2×Dic11—21no—
525C2×Dic11—21no—
526C2×Dic11—21no—
527C2×Dic11—21no—
528C2×Dic11—21no—
529C2×Dic11—21no—
530C2×Dic11—21no—
531C2×Dic11—21no—
532C2×Dic11—21no—
533C2×Dic11—21no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—21no—
538C2×Dic11—21no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—21no—
542C2×Dic11—21no—
543C2×Dic11—22no—
544C2×Dic11—22no—
545C2×Dic11—22no—
546C2×Dic11—21no—
547C2×Dic11—21no—
548C2×Dic11—22no—
549C2×Dic11C22×D412yes—
550C2×Dic11C22×D412yes—
551C2×Dic11C22×D412yes—
552C2×Dic11C2×#4112yes—
553C2×Dic11C2×#4112yes—
554D44—44no—
555D44—84no—
556C4×D11—44no—
557C4×D11—44no—
558C4×D11—44no—
559C4×D11—84no—
560Dic22—84no—
561C23×D4C2×D1111yescharacteristic
562#538—2216no—
563C2×C4⋊Q8—111no—
564C2×#127—111no—
565C2×#127—111no—
566C2×#126—112no—
567C2×#126—112no—
568C2×#124—112no—
569C2×#124—112no—
570C2×#124—112no—
571C2×#123—112no—
572C2×#123—112no—
573C2×C22⋊Q8—112no—
574C2×#121—112no—
575C2×#121—111no—
576C2×#121—111no—
577C2×#121—111no—
578C2×#121—111no—
579C2×#121—112no—
580C2×#121—112no—
581C2×#121—112no—
582C2×#120—112no—
583C2×#120—112no—
584C2×#120—112no—
585C2×C4×D4—111no—
586C2×C4×D4—112no—
587C2×C4×D4—111no—
588C2×C4×D4—111no—
589C2×C4×D4—111no—
590C22×C4⋊C4C2×D1111yescharacteristic
591C22×C22⋊C4C2×D1112yes—
592C22×C22⋊C4C2×D1112yes—
593C22×C42—111no—
594C22×C42C2×D1111yescharacteristic
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—111no—
615#390—111no—
616#390—112no—
617#390—112no—
618#390—112no—
619#390—112no—
620#390—111no—
621#390C2×D1111yescharacteristic
622#390C2×D1111yescharacteristic
623#390C2×D1112yes—
624#390C2×D1111yescharacteristic
625#390C2×D1111yescharacteristic
626#390C2×D1112yes—
627#389—111no—
628#389—111no—
629#389—111no—
630#389—111no—
631#388—112no—
632#388—112no—
633#388—112no—
634#388—112no—
635#388—112no—
636#388—112no—
637#388—112no—
638#388—112no—
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—
660C43—111no—
661C22×C11—22no—
662C22×C11—22no—
663C22×C11—22no—
664C22×C11—22no—
665C22×C11—22no—
666C22×C11—22no—
667C22×C11—42no—
668C22×C11—42no—
669C22×C11—42no—
670C22×C11—42no—
671C22×C11—42no—
672C22×C11—42no—
673C22×C11—42no—
674C22×C11—42no—
675C22×C11—42no—
676C22×C11—42no—
677C22×C11—42no—
678C22×C11—42no—
679C22×C11—42no—
680C22×C11—42no—
681C22×C11—816no—
682C22×C11#53214yes—
683C22×C11C23×D411yescharacteristic
684C22×C11C22×#4111yescharacteristic
685C22×C11C22×#4111yescharacteristic
686C22×C11C2×H(5,𝔽2)11yescharacteristic
687C22×C11C2×H(5,𝔽2)11yescharacteristic
688C22×C11C2×H(5,𝔽2)11yescharacteristic
689C22×C11#58511yescharacteristic
690C2×D11—22no—
691C2×D11—22no—
692C2×D11—22no—
693C2×D11—41no—
694C2×D11—41no—
695C2×D11—41no—
696C2×D11—41no—
697C2×D11—42no—
698C2×D11—42no—
699C2×D11—42no—
700C2×D11—42no—
701C2×D11—42no—
702C2×D11—42no—
703C2×D11—42no—
704C4×C11—22no—
705C4×C11—22no—
706C4×C11—22no—
707C4×C11—22no—
708C4×C11—42no—
709C4×C11—42no—
710C4×C11—41no—
711C4×C11#53814yescomplemented
712Dic11—22no—
713Dic11—22no—
714Dic11—22no—
715Dic11—22no—
716Dic11—22no—
717Dic11—42no—
718Dic11—41no—
719Dic11—41no—
720Dic11—42no—
721Dic11—42no—
722C25C22×D1112yes—
723C22×Q8—112no—
724C22×D4—24no—
725C22×D4—42no—
726C22×D4—42no—
727C22×D4—111no—
728C22×D4—112no—
729C22×D4—112no—
730C22×D4—112no—
731C22×D4—112no—
732C22×D4—112no—
733C22×D4—112no—
734C22×D4—112no—
735C22×D4—111no—
736C22×D4—112no—
737C22×D4C22×D1111yescharacteristic
738C22×D4C22×D1111yescharacteristic
739C22×D4C22×D1112yes—
740C23×C4—111no—
741C23×C4—111no—
742C23×C4—111no—
743C23×C4—112no—
744C23×C4C22×D1111yescharacteristic
745C23×C4C22×D1111yescharacteristic
746C23×C4C22×D1112yes—
747C23×C4C22×D1111yescharacteristic
748C4⋊Q8—442no—
749#127—442no—
750#127—442no—
751#126—228no—
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—228no—
762#121—224no—
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—42no—
776C2×C4⋊C4—111no—
777C2×C4⋊C4—111no—
778C2×C4⋊C4—112no—
779C2×C4⋊C4—111no—
780C2×C4⋊C4—111no—
781C2×C4⋊C4—112no—
782C2×C4⋊C4—112no—
783C2×C4⋊C4—112no—
784C2×C4⋊C4—111no—
785C2×C4⋊C4—111no—
786C2×C4⋊C4—112no—
787C2×C4⋊C4—112no—
788C2×C4⋊C4—112no—
789C2×C4⋊C4C22×D1111yescharacteristic
790C2×C4⋊C4C22×D1111yescharacteristic
791C2×C4⋊C4C22×D1112yes—
792C2×C22⋊C4—28no—
793C2×C22⋊C4—44no—
794C2×C22⋊C4—111no—
795C2×C22⋊C4—111no—
796C2×C22⋊C4—111no—
797C2×C22⋊C4—112no—
798C2×C22⋊C4—111no—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—111no—
807C2×C22⋊C4—111no—
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⋊C4C22×D1112yes—
820C2×C22⋊C4C22×D1112yes—
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—42no—
828C2×C42—111no—
829C2×C42—112no—
830C2×C42—111no—
831C2×C42—111no—
832C2×C42—111no—
833C2×C42—111no—
834C2×C42—111no—
835C2×C42—111no—
836C2×C42—111no—
837C2×C42—111no—
838C2×C42—442no—
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#95—112no—
854#95—112no—
855#95—112no—
856C2×C11—24no—
857C2×C11—82no—
858C2×C11—82no—
859C2×C11C2×#53211yescharacteristic
860C2×C11C2×#53811yescharacteristic
861C2×C11#346011yescharacteristic
862C2×C11#349611yescharacteristic
863C2×C11#349811yescharacteristic
864C2×C11#351411yescharacteristic
865C2×C11#351911yescharacteristic
866D11—42no—
867D11—82no—
868C24—24no—
869C24—24no—
870C24—24no—
871C24—42no—
872C24—42no—
873C24—42no—
874C24—42no—
875C24—111no—
876C24—112no—
877C24C23×D1112yes—
878C24C23×D1112yes—
879C24C23×D1111yescharacteristic
880C2×Q8—224no—
881C2×Q8—442no—
882C2×Q8—442no—
883C2×D4—24no—
884C2×D4—22no—
885C2×D4—22no—
886C2×D4—22no—
887C2×D4—22no—
888C2×D4—22no—
889C2×D4—22no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—416no—
893C2×D4—114no—
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—224no—
903C2×D4—224no—
904C2×D4—224no—
905C2×D4—224no—
906C2×D4—222no—
907C2×D4—222no—
908C2×D4—222no—
909C2×D4—442no—
910C2×D4—442no—
911C2×D4—442no—
912C2×D4—442no—
913C2×D4—442no—
914C2×D4—442no—
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—22no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—24no—
927C22×C4—22no—
928C22×C4—41no—
929C22×C4—41no—
930C22×C4—41no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—111no—
934C22×C4—111no—
935C22×C4—111no—
936C22×C4—111no—
937C22×C4—111no—
938C22×C4—114no—
939C22×C4—111no—
940C22×C4—111no—
941C22×C4—112no—
942C22×C4—112no—
943C22×C4—112no—
944C22×C4—222no—
945C22×C4—222no—
946C22×C4—222no—
947C22×C4—222no—
948C22×C4—222no—
949C22×C4—224no—
950C22×C4—441no—
951C22×C4—441no—
952C22×C4—441no—
953C22×C4—442no—
954C22×C4—442no—
955C22×C4#433914yes—
956C22×C4D4×D1114yes—
957C22×C4C23×D1111yescharacteristic
958C22×C4C23×D1112yes—
959C22×C4C23×D1112yes—
960C22×C4C23×D1111yescharacteristic
961C22×C4C23×D1111yescharacteristic
962C22×C4C23×D1111yescharacteristic
963C22×C4C23×D1111yescharacteristic
964C22×C4C23×D1111yescharacteristic
965C4⋊C4—22no—
966C4⋊C4—22no—
967C4⋊C4—42no—
968C4⋊C4—114no—
969C4⋊C4—222no—
970C4⋊C4—224no—
971C4⋊C4—224no—
972C4⋊C4—224no—
973C4⋊C4—224no—
974C4⋊C4—222no—
975C4⋊C4—222no—
976C4⋊C4—224no—
977C4⋊C4—222no—
978C4⋊C4—222no—
979C4⋊C4—442no—
980C4⋊C4—442no—
981C22⋊C4—24no—
982C22⋊C4—24no—
983C22⋊C4—24no—
984C22⋊C4—24no—
985C22⋊C4—24no—
986C22⋊C4—24no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—114no—
990C22⋊C4—114no—
991C22⋊C4—114no—
992C22⋊C4—222no—
993C22⋊C4—224no—
994C22⋊C4—224no—
995C22⋊C4—224no—
996C22⋊C4—224no—
997C22⋊C4—224no—
998C22⋊C4—224no—
999C22⋊C4—224no—
1000C22⋊C4—224no—
1001C22⋊C4—222no—
1002C22⋊C4—224no—
1003C22⋊C4—222no—
1004C22⋊C4—224no—
1005C22⋊C4—224no—
1006C22⋊C4—224no—
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—41no—
1017C42—41no—
1018C42—114no—
1019C42—222no—
1020C42—222no—
1021C42—224no—
1022C42—222no—
1023C42—222no—
1024C42—222no—
1025C42—441no—
1026C42—441no—
1027C42—441no—
1028C11#3500711yescharacteristic, complemented, Sylow
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—48no—
1048C23—48no—
1049C23—48no—
1050C23—84no—
1051C23—84no—
1052C23—84no—
1053C23—84no—
1054C23—112no—
1055C23—221no—
1056C23—221no—
1057C23—221no—
1058C23—221no—
1059C23—221no—
1060C23—221no—
1061C23—222no—
1062C23—222no—
1063C23—222no—
1064C23—222no—
1065C23—222no—
1066C23—222no—
1067C23—222no—
1068C23C2×#433912yes—
1069C23C2×D4×D1112yes—
1070C23#41×D1112yes—
1071C23C24×D1111yescharacteristic
1072Q8—884no—
1073D4—48no—
1074D4—44no—
1075D4—44no—
1076D4—228no—
1077D4—448no—
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—28no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—21no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—21no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—21no—
1104C2×C4—44no—
1105C2×C4—44no—
1106C2×C4—84no—
1107C2×C4—112no—
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—221no—
1121C2×C4—221no—
1122C2×C4—221no—
1123C2×C4—221no—
1124C2×C4—222no—
1125C2×C4—222no—
1126C2×C4—222no—
1127C2×C4—222no—
1128C2×C4—221no—
1129C2×C4—221no—
1130C2×C4—222no—
1131C2×C4—221no—
1132C2×C4—222no—
1133C2×C4—222no—
1134C2×C4—222no—
1135C2×C4—221no—
1136C2×C4—222no—
1137C2×C4—444no—
1138C2×C4—444no—
1139C2×C4—444no—
1140C2×C4—884no—
1141C2×C4C2×#433912yes—
1142C2×C4C2×#433912yes—
1143C2×C4C2×D4×D1112yes—
1144C2×C4C2×D4×D1112yes—
1145C2×C4#6703712yes—
1146C2×C4#6703712yes—
1147C2×C4#6703712yes—
1148C22—22no—
1149C22—22no—
1150C22—22no—
1151C22—22no—
1152C22—22no—
1153C22—22no—
1154C22—42no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22—42no—
1168C22—816no—
1169C22—222no—
1170C22—222no—
1171C22—222no—
1172C22—441no—
1173C22—441no—
1174C22—441no—
1175C22—441no—
1176C22—442no—
1177C22—442no—
1178C22—442no—
1179C22—442no—
1180C22—442no—
1181C22—442no—
1182C22—442no—
1183C22#1062307914yes—
1184C22C22×#433911yescharacteristic
1185C22C22×D4×D1111yescharacteristic
1186C22C2×#6703711yescharacteristic
1187C22C2×#6703711yescharacteristic
1188C22C2×#6703711yescharacteristic
1189C22C2×#41×D1111yescharacteristic
1190C22#1062345311yescharacteristic
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—22no—
1195C4—41no—
1196C4—42no—
1197C4—42no—
1198C4—222no—
1199C4—222no—
1200C4—222no—
1201C4—222no—
1202C4—222no—
1203C4—442no—
1204C4—442no—
1205C4—442no—
1206C4—441no—
1207C4—441no—
1208C4#1062302514yescomplemented
1209C2—24no—
1210C2—82no—
1211C2—82no—
1212C2—442no—
1213C2—882no—
1214C2C2×#1062307911yescharacteristic
1215C2C2×#1062302511yescharacteristic
1216C2#1308203811yescharacteristic
1217C2#1308237311yescharacteristic
1218C2#1308239211yescharacteristic
1219C2#1308257111yescharacteristic
1220C2#1308264211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#390C2
hypercenterC2×#390D11
hypocenterC11#35007
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C2×#10623025C2semidirect
2. #13076980C2semidirect
3. #13076970C2semidirect
4. #13076960C2semidirect
5. #13076946C2semidirect
6. #13074757C2semidirect
7. #13074746C2semidirect
8. #13073690C2semidirect
9. #13073678C2semidirect
10. #13073203C2semidirect
11. #13072980C2semidirect
12. #13072736C2semidirect
13. #13072382C2semidirect
14. #13072312C2semidirect
15. #13072249C2semidirect
16. #13072205C2semidirect
17. #13072152C2semidirect
18. #13072050C2semidirect
19. #13071966C2semidirect
20. #13071274C2semidirect
21. C4×#66983C2semidirect
22. C42×C22⋊D11C2semidirect
23. C2×C11×#390C2semidirect
43. C2×#66948C22semidirect
44. C2×#66941C22semidirect
46. C2×#66938C22semidirect
47. C2×#66938C22semidirect
48. C2×#66938C22semidirect
49. C2×#66937C22semidirect
50. C2×#66937C22semidirect
51. C2×#66937C22semidirect
52. C2×#66936C22semidirect
53. C2×#66936C22semidirect
54. C2×#66932C22semidirect
55. C2×#66932C22semidirect
56. C2×C4×D44C22semidirect
57. C2×C42×D11C22semidirect
80. #10622607C22semidirect
81. #10622604C22semidirect
82. #10622601C22semidirect
83. #10622600C22semidirect
84. #10622598C22semidirect
85. #10622598C22semidirect
86. #10622597C22semidirect
87. #10622592C22semidirect
88. #10622589C22semidirect
89. #10622586C22semidirect
90. #10622574C22semidirect
91. #10622573C22semidirect
92. #10622572C22semidirect
93. #10622572C22semidirect
94. #10622572C22semidirect
95. #10622570C22semidirect
96. #10622570C22semidirect
97. #10622570C22semidirect
98. #10622570C22semidirect
99. #10622569C22semidirect
100. #10622569C22semidirect
101. #10622569C22semidirect
102. #10622565C22semidirect
103. #10622564C22semidirect
104. #10622564C22semidirect
105. #10622561C22semidirect
106. #10622560C22semidirect
107. #10622558C22semidirect
108. #10622558C22semidirect
109. #10622557C22semidirect
110. #10622557C22semidirect
111. #10622557C22semidirect
112. #10622553C22semidirect
113. #10622552C22semidirect
114. C4×(C2×D11)⋊C4C22semidirect
115. C4×(C2×D11)⋊C4C22semidirect
116. C4×(C2×D11)⋊C4C22semidirect
117. C4×(C2×D11)⋊C4C22semidirect
118. C4×C4⋊Dic11C22semidirect
119. C4×Dic11⋊C4C22semidirect
120. C4×Dic11⋊C4C22semidirect
121. C4×Dic11⋊C4C22semidirect
122. C42×Dic11C22semidirect
123. #10622541C22semidirect
195. C4×C22⋊D11D4semidirect
352. C2×C4×D11C2×D4semidirect
395. (C2×D11)⋊C4C2×D4semidirect
408. Dic11⋊C4C2×D4semidirect
418. C4×Dic11C2×D4semidirect
440. C2×#390D11semidirect
711. C4×C11#538semidirect
1028. C11#35007semidirect
1208. C4#10623025semidirect

Maximal subgroups

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

subgroupindex
C2×#106230252
#130769802
#130769702
#130769602
#130769462
#130747572
#130747462
#130736902
#130736782
#130732032
#130729802
#130727362
#130723822
#130723122
#130722492
#130722052
#130721522
#130720502
#130719662
#130712742
C4×#669832
C42×C22⋊D112
C2×C11×#3902
#3500711