Finite Group Databasebeta

← #14926266

Subgroups — #14926266

Order 2816.

2962 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623079C211yesmaximal, characteristic, complemented
2C2×C4×#4339C211yesmaximal, characteristic, complemented
3#13074301C212yesmaximal, complemented
4#13074299C212yesmaximal, complemented
5#13073823C211yesmaximal, characteristic, complemented
6#13073786C211yesmaximal, characteristic, complemented
7#13073617C211yesmaximal, characteristic, complemented
8#13073559C211yesmaximal, characteristic, complemented
9#13073076C212yesmaximal, complemented
10#13072233C212yesmaximal, complemented
11#13072037C211yesmaximal, characteristic, complemented
12#13072036C211yesmaximal, characteristic, complemented
13#13072032C211yesmaximal, characteristic, complemented
14#13072030C211yesmaximal, characteristic, complemented
15#13071832C212yesmaximal, complemented
16#13071831C212yesmaximal, complemented
17C4×#66993C212yesmaximal, complemented
18C4×#66938C212yesmaximal, complemented
19C4×#66948C211yesmaximal, characteristic, complemented
20C4×#66983C211yesmaximal, characteristic, complemented
21C4×#66991C211yesmaximal, characteristic, complemented
22C4×#66945C211yesmaximal, characteristic, complemented
23C4×C11×#121C211yesmaximal, characteristic, complemented
24C22×#4339C2211yescharacteristic
25C22×#4339C2212yes—
26C2×C11×#121C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2212yes—
29C22×C42×C11C2211yescharacteristic
30C2×#66993C2211yescharacteristic
31C2×#66993C2212yes—
32C2×#66991C2211yescharacteristic
33C2×#66991C2211yescharacteristic
34C2×#66983C2211yescharacteristic
35C2×C4×C22⋊D11C2212yes—
36C2×C4×C22⋊D11C2211yescharacteristic
37C2×C4×C22⋊D11C2211yescharacteristic
38C2×C4×C22⋊D11C2211yescharacteristic
39C2×C4×C22⋊D11C2211yescharacteristic
40C2×C4×C22⋊D11C2212yes—
41C2×C4×C22⋊D11C2212yes—
42C2×#66979C2211yescharacteristic
43#10623079—28no—
44C2×#66948C2211yescharacteristic
45C2×#66948C2211yescharacteristic
46C2×#66945C2211yescharacteristic
47C2×#66945C2211yescharacteristic
48C2×#66941C2211yescharacteristic
49C2×#66938C2212yes—
50C2×#66938C2212yes—
51C2×#66937C2212yes—
52C4×#4339—28no—
53C2×C4×D44C2211yescharacteristic
54C2×C4×D44C2211yescharacteristic
55C2×C4×D44C2211yescharacteristic
56C2×C4×D44C2212yes—
57C2×#66925C2211yescharacteristic
58C2×#66925C2211yescharacteristic
59C2×C42×D11C2211yescharacteristic
60C2×C42×D11C2211yescharacteristic
61C2×C4×Dic22C2211yescharacteristic
62C2×C4×Dic22C2211yescharacteristic
63C11×#390C2211yescharacteristic
64C11×#389C2211yescharacteristic
65C11×#388C2212yes—
66C11×#386C2212yes—
67C11×#380C2211yescharacteristic
68C4×C11×C4⋊C4C2211yescharacteristic
69C4×C11×C22⋊C4C2212yes—
70#10622836C2212yes—
71#10622836C2212yes—
72#10622834C2211yescharacteristic
73#10622834C2212yes—
74#10622826C2212yes—
75#10622825C2211yescharacteristic
76C4×C22⋊Dic11C2212yes—
77#10622604C2212yes—
78#10622601C2211yescharacteristic
79#10622601C2212yes—
80#10622600C2211yescharacteristic
81#10622600C2211yescharacteristic
82#10622598C2211yescharacteristic
83#10622592C2212yes—
84#10622589C2212yes—
85C4⋊C4×Dic11C2211yescharacteristic
86C4⋊C4×Dic11C2211yescharacteristic
87#10622586C2211yescharacteristic
88#10622574C2212yes—
89#10622574C2212yes—
90#10622573C2212yes—
91#10622573C2212yes—
92#10622573C2212yes—
93#10622572C2212yes—
94#10622572C2212yes—
95#10622570C2212yes—
96#10622570C2212yes—
97#10622570C2212yes—
98#10622570C2212yes—
99#10622570C2212yes—
100#10622569C2212yes—
101#10622564C2212yes—
102#10622560C2212yes—
103#10622557C2212yes—
104#10622557C2212yes—
105#10622553C2212yes—
106#10622552C2211yescharacteristic
107C4×(C2×D11)⋊C4C2212yes—
108C4×(C2×D11)⋊C4C2212yes—
109C4×(C2×D11)⋊C4C2212yes—
110C4×C4⋊Dic11C2211yescharacteristic
111C42×Dic11C2212yes—
112#10622541C2211yescharacteristic
113#10622286C2212yes—
114#10622285C2212yes—
115#10622284C2212yes—
116#10622283C2212yes—
117#10622283C2212yes—
118#10622282C2212yes—
119#10622279C2212yes—
120#10622278C2212yes—
121#10622269C2212yes—
122#10622263C2212yes—
123#10622261C2212yes—
124#10622259C2212yes—
125C22×D4×C11C2311yescharacteristic
126C22×D4×C11C2312yes—
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2312yes—
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2311yescharacteristic
133C22×C22⋊D11C2312yes—
134C22×C22⋊D11C2312yes—
135C22×C22⋊D11C2311yescharacteristic
136C22×C22⋊D11C2312yes—
137C22×C22⋊D11C2312yes—
138C2×#4339—24no—
139C2×#4339—24no—
140C2×#4339—28no—
141C2×#4339—24no—
142C2×#4339—44no—
143C2×#4339—44no—
144C22×D44C2311yescharacteristic
145C22×D44C2311yescharacteristic
146C22×D44C2312yes—
147C22×D44C2312yes—
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2312yes—
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2311yescharacteristic
154C22×C4×D11C2311yescharacteristic
155C22×Dic22C2311yescharacteristic
156C22×Dic22C2312yes—
157C11×#121—24no—
158C4×D4×C11—24no—
159C4×D4×C11—44no—
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C11×C4⋊C4C2311yescharacteristic
162C2×C11×C4⋊C4C2312yes—
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2312yes—
166C2×C11×C22⋊C4C2312yes—
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2312yes—
169C2×C42×C11—24no—
170C2×C42×C11C2311yescharacteristic
171C2×C42×C11C2311yescharacteristic
172C2×C42×C11C2311yescharacteristic
173C2×C42×C11C2312yes—
174C2×C42×C11C2311yescharacteristic
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2311yescharacteristic
178C2×C22⋊Dic11C2311yescharacteristic
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2312yes—
182#66993—28no—
183#66993—24no—
184#66991—24no—
185#66991—24no—
186#66983—24no—
187C4×C22⋊D11—24no—
188C4×C22⋊D11—24no—
189C4×C22⋊D11—24no—
190C4×C22⋊D11—24no—
191C4×C22⋊D11—28no—
192C4×C22⋊D11—44no—
193C4×C22⋊D11—44no—
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2311yescharacteristic
197C2×(C2×D11)⋊C4C2311yescharacteristic
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2312yes—
206C2×(C2×D11)⋊C4C2312yes—
207C2×(C2×D11)⋊C4C2312yes—
208C2×(C2×D11)⋊C4C2312yes—
209C2×(C2×D11)⋊C4C2312yes—
210#66979—24no—
211C2×C4⋊Dic11C2311yescharacteristic
212C2×C4⋊Dic11C2311yescharacteristic
213C2×C4⋊Dic11C2311yescharacteristic
214C2×C4⋊Dic11C2311yescharacteristic
215C2×C4⋊Dic11C2312yes—
216C2×C4⋊Dic11C2311yescharacteristic
217C2×Dic11⋊C4C2311yescharacteristic
218C2×Dic11⋊C4C2311yescharacteristic
219C2×Dic11⋊C4C2311yescharacteristic
220C2×Dic11⋊C4C2311yescharacteristic
221C2×Dic11⋊C4C2312yes—
222C2×Dic11⋊C4C2312yes—
223C2×Dic11⋊C4C2312yes—
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2311yescharacteristic
226C2×C4×Dic11C2311yescharacteristic
227C2×C4×Dic11C2312yes—
228C2×C4×Dic11C2312yes—
229C2×C4×Dic11C2312yes—
230C2×C4×Dic11C2312yes—
231C2×C4×Dic11C2312yes—
232C2×C4×Dic11C2311yescharacteristic
233C2×C4×Dic11C2311yescharacteristic
234C2×C4×Dic11C2311yescharacteristic
235#66948—24no—
236#66948—24no—
237#66945—24no—
238#66945—24no—
239#66941—24no—
240#66938—28no—
241#66938—28no—
242#66937—28no—
243C4×D44—24no—
244C4×D44—24no—
245C4×D44—24no—
246C4×D44—44no—
247#66925—24no—
248#66925—24no—
249C42×D11—24no—
250C42×D11D418yescomplemented
251C4×Dic22—24no—
252C4×Dic22—24no—
253C11×#95C2312yes—
254C11×#95C2312yes—
255C11×#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262C11⋊#95C2312yes—
263C11⋊#95C2312yes—
264C11⋊#95C2312yes—
265#34977—111nomaximal, Sylow
266C24×C11C2412yes—
267C24×C11C2411yescharacteristic
268C23×D11C2412yes—
269C23×D11C2411yescharacteristic
270C23×D11C2411yescharacteristic
271C2×D4×C11—24no—
272C2×D4×C11—22no—
273C2×D4×C11—22no—
274C2×D4×C11—24no—
275C2×D4×C11—22no—
276C2×D4×C11—42no—
277C22×C4×C11—22no—
278C22×C4×C11—22no—
279C22×C4×C11—22no—
280C22×C4×C11—22no—
281C22×C4×C11—22no—
282C22×C4×C11—24no—
283C22×C4×C11—22no—
284C22×C4×C11—22no—
285C22×C4×C11—22no—
286C22×C4×C11—24no—
287C22×C4×C11—22no—
288C22×C4×C11—24no—
289C22×C4×C11C2412yes—
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2412yes—
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2412yes—
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2411yescharacteristic
298C2×C22⋊D11—22no—
299C2×C22⋊D11—24no—
300C2×C22⋊D11—24no—
301C2×C22⋊D11—22no—
302C2×C22⋊D11—22no—
303C2×C22⋊D11—24no—
304C2×C22⋊D11—24no—
305C2×C22⋊D11—24no—
306C2×C22⋊D11—24no—
307C2×C22⋊D11—22no—
308C2×C22⋊D11—24no—
309C2×C22⋊D11—22no—
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#4114yescomplemented
319C22×Dic11C2412yes—
320C22×Dic11C2411yescharacteristic
321C22×Dic11C2412yes—
322C22×Dic11C2411yescharacteristic
323C22×Dic11C2411yescharacteristic
324C22×Dic11C2411yescharacteristic
325C22×Dic11C2412yes—
326C22×Dic11C2411yescharacteristic
327C22×Dic11C2411yescharacteristic
328#4339—232no—
329#4339—432no—
330C2×D44—22no—
331C2×D44—24no—
332C2×D44—22no—
333C2×D44—24no—
334C2×D44—22no—
335C2×D44—22no—
336C2×D44—24no—
337C2×D44—22no—
338C2×D44—22no—
339C2×D44—42no—
340C2×D44—42no—
341C2×D44—42no—
342C2×C4×D11—22no—
343C2×C4×D11—22no—
344C2×C4×D11—22no—
345C2×C4×D11—22no—
346C2×C4×D11—22no—
347C2×C4×D11—22no—
348C2×C4×D11—22no—
349C2×C4×D11—24no—
350C2×C4×D11—22no—
351C2×C4×D11—22no—
352C2×C4×D11—22no—
353C2×C4×D11—22no—
354C2×C4×D11—22no—
355C2×C4×D11—22no—
356C2×C4×D11—22no—
357C2×C4×D11—24no—
358C2×C4×D11—22no—
359C2×C4×D11—24no—
360C2×C4×D11C2×D414yes—
361C2×C4×D11C2×D414yes—
362C2×C4×D11C2×D414yes—
363C2×Dic22—22no—
364C2×Dic22—22no—
365C2×Dic22—24no—
366C2×Dic22—42no—
367C2×Dic22—42no—
368C2×Dic22#4114yescomplemented
369C11×C4⋊C4—22no—
370C11×C4⋊C4—22no—
371C11×C4⋊C4—42no—
372C11×C4⋊C4#4114yescomplemented
373C11×C22⋊C4—24no—
374C11×C22⋊C4—24no—
375C11×C22⋊C4—24no—
376C11×C22⋊C4—42no—
377C11×C22⋊C4—42no—
378C42×C11—22no—
379C42×C11—22no—
380C42×C11—22no—
381C42×C11—24no—
382C42×C11C2×D414yes—
383C22⋊Dic11—24no—
384C22⋊Dic11—22no—
385C22⋊Dic11—22no—
386C22⋊Dic11—24no—
387C22⋊Dic11—24no—
388C22⋊Dic11—42no—
389C22⋊Dic11—42no—
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—22no—
398(C2×D11)⋊C4—24no—
399(C2×D11)⋊C4—24no—
400(C2×D11)⋊C4—24no—
401(C2×D11)⋊C4—24no—
402(C2×D11)⋊C4—42no—
403(C2×D11)⋊C4—42no—
404(C2×D11)⋊C4—42no—
405(C2×D11)⋊C4—42no—
406C4⋊Dic11—22no—
407C4⋊Dic11—22no—
408C4⋊Dic11—22no—
409C4⋊Dic11—22no—
410C4⋊Dic11—42no—
411C4⋊Dic11#4114yescomplemented
412Dic11⋊C4—22no—
413Dic11⋊C4—22no—
414Dic11⋊C4—22no—
415Dic11⋊C4—22no—
416Dic11⋊C4—24no—
417Dic11⋊C4—42no—
418Dic11⋊C4—42no—
419C4×Dic11—24no—
420C4×Dic11—24no—
421C4×Dic11—24no—
422C4×Dic11—22no—
423C4×Dic11—22no—
424C4×Dic11—22no—
425C4×Dic11—24no—
426C4×Dic11—24no—
427C4×Dic11C2×D414yes—
428C4×Dic11C2×D414yes—
429C4×Dic11C2×D414yes—
430C2×#532—111no—
431C2×C4×#41—111no—
432#2610—112no—
433#2610—112no—
434#2567—111no—
435#2563—111no—
436#2548—111no—
437#2541—111no—
438#2500—112no—
439#2431—112no—
440#2414—111no—
441#2414—111no—
442#2414—111no—
443#2414—111no—
444#2388—112no—
445#2388—112no—
446C4×#127—112no—
447C4×#124—112no—
448C4×#121—111no—
449C4×#121—111no—
450C4×#121—111no—
451C4×#121D1111yescharacteristic, complemented
452C4×#117—111no—
453C23×C11—21no—
454C23×C11—21no—
455C23×C11—21no—
456C23×C11—21no—
457C23×C11—21no—
458C23×C11—21no—
459C23×C11—22no—
460C23×C11—22no—
461C23×C11—22no—
462C23×C11—22no—
463C23×C11—22no—
464C23×C11—22no—
465C23×C11—22no—
466C23×C11C2×#4112yes—
467C23×C11C2511yescharacteristic
468C22×D11—21no—
469C22×D11—21no—
470C22×D11—21no—
471C22×D11—21no—
472C22×D11—21no—
473C22×D11—21no—
474C22×D11—21no—
475C22×D11—21no—
476C22×D11—21no—
477C22×D11—21no—
478C22×D11—21no—
479C22×D11—21no—
480C22×D11—22no—
481C22×D11—22no—
482C22×D11—22no—
483C22×D11—22no—
484C22×D11—22no—
485C22×D11—22no—
486C22×D11—22no—
487C22×D11C22×D412yes—
488C22×D11C2×#4112yes—
489D4×C11—48no—
490D4×C11—44no—
491C2×C4×C11—28no—
492C2×C4×C11—21no—
493C2×C4×C11—22no—
494C2×C4×C11—21no—
495C2×C4×C11—21no—
496C2×C4×C11—21no—
497C2×C4×C11—22no—
498C2×C4×C11—21no—
499C2×C4×C11—21no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—21no—
504C2×C4×C11—21no—
505C2×C4×C11—21no—
506C2×C4×C11—22no—
507C2×C4×C11—22no—
508C2×C4×C11—21no—
509C2×C4×C11—22no—
510C2×C4×C11—44no—
511C2×C4×C11—48no—
512C2×C4×C11—44no—
513C2×C4×C11C22×D412yes—
514C2×C4×C11C22×D412yes—
515C2×C4×C11C22×D412yes—
516C2×C4×C11C2×#4114yes—
517C2×C4×C11C2×#4112yes—
518C2×C4×C11C2×#4112yes—
519C2×C4×C11C2×#4112yes—
520C2×C4×C11H(5,𝔽2)12yes—
521C2×C4×C11H(5,𝔽2)12yes—
522C22⋊D11—28no—
523C22⋊D11—28no—
524C22⋊D11—48no—
525C22⋊D11—48no—
526C22⋊D11—48no—
527C22⋊D11—48no—
528C22⋊D11—48no—
529C2×Dic11—21no—
530C2×Dic11—21no—
531C2×Dic11—21no—
532C2×Dic11—22no—
533C2×Dic11—21no—
534C2×Dic11—22no—
535C2×Dic11—21no—
536C2×Dic11—21no—
537C2×Dic11—21no—
538C2×Dic11—21no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—21no—
543C2×Dic11—21no—
544C2×Dic11—22no—
545C2×Dic11—21no—
546C2×Dic11—22no—
547C2×Dic11—21no—
548C2×Dic11—22no—
549C2×Dic11C22×D412yes—
550C2×Dic11C22×D412yes—
551C2×Dic11C22×D412yes—
552C2×Dic11C2×#4114yes—
553C2×Dic11C2×#4112yes—
554C2×Dic11C2×#4112yes—
555C2×Dic11C2×#4112yes—
556D44—28no—
557D44—48no—
558D44—48no—
559D44—44no—
560C4×D11—28no—
561C4×D11—28no—
562C4×D11—28no—
563C4×D11—28no—
564C4×D11—44no—
565C4×D11—44no—
566C4×D11—48no—
567Dic22—28no—
568Dic22—48no—
569C22×#41—111no—
570C22×#41—112no—
571#532—228no—
572C2×C4⋊Q8—111no—
573C2×#127—112no—
574C2×#127—111no—
575C2×#124—112no—
576C2×#124—112no—
577C2×#121—111no—
578C2×#121—111no—
579C2×#121—111no—
580C2×#121—111no—
581C2×#121—111no—
582C2×#121—112no—
583C2×#121C2×D1111yescharacteristic
584C4×#41—228no—
585C2×C4×Q8—111no—
586C2×C4×Q8—111no—
587C2×C4×D4—111no—
588C2×C4×D4—112no—
589C2×C4×D4—111no—
590C2×C4×D4—111no—
591C2×C4×D4—111no—
592C2×C4×D4—112no—
593C2×C4×D4—112no—
594C2×C4×D4—111no—
595C2×C4×D4—111no—
596C2×C4×D4—111no—
597C2×C4×D4—112no—
598C2×C4×D4C2×D1111yescharacteristic
599C2×C4×D4C2×D1112yes—
600C2×#117—111no—
601C2×#117—111no—
602C2×#117—111no—
603C2×#117—111no—
604C2×#117—111no—
605C22×C42—111no—
606C22×C42—111no—
607C22×C42C2×D1111yescharacteristic
608#395—112no—
609#395—112no—
610#394—112no—
611#394—112no—
612#394—112no—
613#394—112no—
614#394—112no—
615#394—112no—
616#393—112no—
617#393—112no—
618#392—112no—
619#392—112no—
620#392—112no—
621#392—112no—
622#392—112no—
623#392—112no—
624#391—112no—
625#390—112no—
626#390—111no—
627#390—112no—
628#390—111no—
629#390—112no—
630#390—112no—
631#390—112no—
632#390—112no—
633#390—112no—
634#390—111no—
635#390C2×D1111yescharacteristic
636#389—111no—
637#389—111no—
638#389—111no—
639#389C2×D1111yescharacteristic
640#388—112no—
641#388—112no—
642#388—112no—
643#388—112no—
644#388—112no—
645#388—112no—
646#388—112no—
647#388C2×D1112yes—
648#386—112no—
649#386—112no—
650#386—112no—
651#386C2×D1112yes—
652#384—112no—
653#382—112no—
654#380—111no—
655#380—111no—
656#380—111no—
657#380C2×D1111yescharacteristic
658C4×C4⋊C4—111no—
659C4×C4⋊C4—111no—
660C4×C4⋊C4—111no—
661C4×C4⋊C4C2×D1111yescharacteristic
662C4×C22⋊C4—112no—
663C4×C22⋊C4—112no—
664C4×C22⋊C4—112no—
665C4×C22⋊C4—112no—
666C4×C22⋊C4—112no—
667C4×C22⋊C4C2×D1112yes—
668#376—112no—
669C43—112no—
670C22×C11—22no—
671C22×C11—22no—
672C22×C11—22no—
673C22×C11—41no—
674C22×C11—41no—
675C22×C11—41no—
676C22×C11—41no—
677C22×C11—42no—
678C22×C11—42no—
679C22×C11—42no—
680C22×C11—42no—
681C22×C11—42no—
682C22×C11—42no—
683C22×C11—42no—
684C22×C11C23×D411yescharacteristic
685C22×C11C22×#4111yescharacteristic
686C22×C11C22×#4111yescharacteristic
687C22×C11C22×#4111yescharacteristic
688C22×C11C22×#4111yescharacteristic
689C22×C11C2×H(5,𝔽2)11yescharacteristic
690C22×C11C2×H(5,𝔽2)11yescharacteristic
691C2×D11—22no—
692C2×D11—22no—
693C2×D11—22no—
694C2×D11—22no—
695C2×D11—22no—
696C2×D11—22no—
697C2×D11—41no—
698C2×D11—41no—
699C2×D11—41no—
700C2×D11—41no—
701C2×D11—41no—
702C2×D11—41no—
703C2×D11—41no—
704C2×D11—41no—
705C2×D11—42no—
706C2×D11—42no—
707C2×D11—42no—
708C2×D11—42no—
709C2×D11—42no—
710C2×D11—42no—
711C2×D11—42no—
712C4×C11—22no—
713C4×C11—22no—
714C4×C11—24no—
715C4×C11—41no—
716C4×C11—41no—
717C4×C11—42no—
718C4×C11—42no—
719C4×C11#53214yes—
720C4×C11#53514yes—
721Dic11—22no—
722Dic11—22no—
723Dic11—22no—
724Dic11—24no—
725Dic11—41no—
726Dic11—42no—
727Dic11—41no—
728Dic11—42no—
729Dic11#52514yes—
730C2×#41—224no—
731C2×#41—228no—
732C2×#41—224no—
733C2×#41—224no—
734C2×#41—444no—
735C2×#41—444no—
736C22×Q8—111no—
737C22×Q8—112no—
738C22×D4—111no—
739C22×D4—111no—
740C22×D4—112no—
741C22×D4—112no—
742C22×D4—112no—
743C22×D4—112no—
744C22×D4—112no—
745C22×D4—111no—
746C22×D4—111no—
747C22×D4—112no—
748C22×D4—112no—
749C22×D4C22×D1111yescharacteristic
750C22×D4C22×D1112yes—
751C23×C4—111no—
752C23×C4—111no—
753C23×C4—111no—
754C23×C4—111no—
755C23×C4—111no—
756C23×C4—111no—
757C23×C4—112no—
758C23×C4C22×D1111yescharacteristic
759C23×C4C22×D1111yescharacteristic
760C23×C4C22×D1111yescharacteristic
761C23×C4C22×D1112yes—
762C4⋊Q8—224no—
763#127—224no—
764#127—228no—
765#124—228no—
766#124—228no—
767#121—24no—
768#121—228no—
769#121—224no—
770#121—224no—
771#121—224no—
772#121—224no—
773#121—224no—
774C4×Q8—224no—
775C4×Q8—224no—
776C4×D4—24no—
777C4×D4—44no—
778C4×D4—224no—
779C4×D4—224no—
780C4×D4—224no—
781C4×D4—224no—
782C4×D4—228no—
783C4×D4—224no—
784C4×D4—224no—
785C4×D4—224no—
786C4×D4—444no—
787C4×D4—444no—
788C4×D4—444no—
789#117—224no—
790#117—224no—
791#117—224no—
792#117—224no—
793#117—224no—
794C2×C4⋊C4—111no—
795C2×C4⋊C4—111no—
796C2×C4⋊C4—111no—
797C2×C4⋊C4—111no—
798C2×C4⋊C4—111no—
799C2×C4⋊C4—111no—
800C2×C4⋊C4—111no—
801C2×C4⋊C4—111no—
802C2×C4⋊C4—111no—
803C2×C4⋊C4—112no—
804C2×C4⋊C4—112no—
805C2×C4⋊C4—112no—
806C2×C4⋊C4—112no—
807C2×C4⋊C4C22×D1111yescharacteristic
808C2×C4⋊C4C22×D1111yescharacteristic
809C2×C4⋊C4C22×D1112yes—
810C2×C4⋊C4C22×D1111yescharacteristic
811C2×C22⋊C4—111no—
812C2×C22⋊C4—111no—
813C2×C22⋊C4—112no—
814C2×C22⋊C4—112no—
815C2×C22⋊C4—112no—
816C2×C22⋊C4—111no—
817C2×C22⋊C4—111no—
818C2×C22⋊C4—111no—
819C2×C22⋊C4—111no—
820C2×C22⋊C4—112no—
821C2×C22⋊C4—112no—
822C2×C22⋊C4—112no—
823C2×C22⋊C4—112no—
824C2×C22⋊C4—112no—
825C2×C22⋊C4—112no—
826C2×C22⋊C4—112no—
827C2×C22⋊C4—112no—
828C2×C22⋊C4—112no—
829C2×C22⋊C4—112no—
830C2×C22⋊C4—112no—
831C2×C22⋊C4—112no—
832C2×C22⋊C4—112no—
833C2×C22⋊C4—112no—
834C2×C22⋊C4C22×D1112yes—
835C2×C22⋊C4C22×D1112yes—
836C2×C22⋊C4C22×D1112yes—
837C2×C22⋊C4C22×D1112yes—
838C2×C22⋊C4C22×D1112yes—
839C2×C42—24no—
840C2×C42—111no—
841C2×C42—111no—
842C2×C42—111no—
843C2×C42—118no—
844C2×C42—111no—
845C2×C42—112no—
846C2×C42—112no—
847C2×C42—111no—
848C2×C42—112no—
849C2×C42—112no—
850C2×C42—112no—
851C2×C42—111no—
852C2×C42—224no—
853C2×C42C22×D1111yescharacteristic
854C2×C42C22×D1111yescharacteristic
855C2×C42C22×D1112yes—
856C2×C42C22×D1111yescharacteristic
857C2×C42C22×D1111yescharacteristic
858#95—112no—
859#95—112no—
860#95—112no—
861#95—112no—
862#95—112no—
863#95—112no—
864#95—112no—
865#95—112no—
866#95—112no—
867#95C22×D1112yes—
868#95C22×D1112yes—
869#95C22×D1112yes—
870C2×C11—42no—
871C2×C11—82no—
872C2×C11C2×#52511yescharacteristic
873C2×C11C2×#53211yescharacteristic
874C2×C11C2×#53511yescharacteristic
875C2×C11#348111yescharacteristic
876C2×C11#348111yescharacteristic
877C2×C11#348311yescharacteristic
878C2×C11#348311yescharacteristic
879D11—42no—
880D11—42no—
881D11—82no—
882C24—111no—
883C24—111no—
884C24—112no—
885C24C23×D1112yes—
886C24C23×D1111yescharacteristic
887#41—2232no—
888#41—4432no—
889C2×Q8—114no—
890C2×Q8—222no—
891C2×Q8—222no—
892C2×Q8—224no—
893C2×Q8—442no—
894C2×Q8—442no—
895C2×D4—24no—
896C2×D4—24no—
897C2×D4—22no—
898C2×D4—22no—
899C2×D4—22no—
900C2×D4—42no—
901C2×D4—114no—
902C2×D4—222no—
903C2×D4—222no—
904C2×D4—224no—
905C2×D4—224no—
906C2×D4—222no—
907C2×D4—222no—
908C2×D4—222no—
909C2×D4—224no—
910C2×D4—224no—
911C2×D4—224no—
912C2×D4—224no—
913C2×D4—224no—
914C2×D4—224no—
915C2×D4—222no—
916C2×D4—222no—
917C2×D4—224no—
918C2×D4—224no—
919C2×D4—224no—
920C2×D4—224no—
921C2×D4—222no—
922C2×D4—222no—
923C2×D4—222no—
924C2×D4—222no—
925C2×D4—442no—
926C2×D4—442no—
927C2×D4—442no—
928C2×D4—442no—
929C2×D4—442no—
930C2×D4—442no—
931C2×D4—442no—
932C2×D4—442no—
933C2×D4—442no—
934C22×C4—22no—
935C22×C4—22no—
936C22×C4—22no—
937C22×C4—22no—
938C22×C4—22no—
939C22×C4—22no—
940C22×C4—24no—
941C22×C4—22no—
942C22×C4—24no—
943C22×C4—22no—
944C22×C4—22no—
945C22×C4—24no—
946C22×C4—111no—
947C22×C4—112no—
948C22×C4—111no—
949C22×C4—111no—
950C22×C4—111no—
951C22×C4—114no—
952C22×C4—114no—
953C22×C4—114no—
954C22×C4—112no—
955C22×C4—111no—
956C22×C4—112no—
957C22×C4—111no—
958C22×C4—222no—
959C22×C4—222no—
960C22×C4—222no—
961C22×C4—222no—
962C22×C4—222no—
963C22×C4—222no—
964C22×C4—222no—
965C22×C4—222no—
966C22×C4—222no—
967C22×C4—222no—
968C22×C4—222no—
969C22×C4—222no—
970C22×C4—224no—
971C22×C4—222no—
972C22×C4—224no—
973C22×C4—222no—
974C22×C4—222no—
975C22×C4—224no—
976C22×C4C23×D1112yes—
977C22×C4C23×D1111yescharacteristic
978C22×C4C23×D1112yes—
979C22×C4C23×D1111yescharacteristic
980C22×C4C23×D1112yes—
981C22×C4C23×D1111yescharacteristic
982C22×C4C23×D1111yescharacteristic
983C22×C4C23×D1111yescharacteristic
984C22×C4C23×D1111yescharacteristic
985C4⋊C4—22no—
986C4⋊C4—22no—
987C4⋊C4—42no—
988C4⋊C4—114no—
989C4⋊C4—222no—
990C4⋊C4—222no—
991C4⋊C4—222no—
992C4⋊C4—222no—
993C4⋊C4—222no—
994C4⋊C4—222no—
995C4⋊C4—224no—
996C4⋊C4—222no—
997C4⋊C4—222no—
998C4⋊C4—442no—
999C4⋊C4—442no—
1000C4⋊C4—442no—
1001C4⋊C4#433914yescomplemented
1002C22⋊C4—24no—
1003C22⋊C4—24no—
1004C22⋊C4—24no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—222no—
1008C22⋊C4—222no—
1009C22⋊C4—224no—
1010C22⋊C4—224no—
1011C22⋊C4—224no—
1012C22⋊C4—224no—
1013C22⋊C4—222no—
1014C22⋊C4—222no—
1015C22⋊C4—222no—
1016C22⋊C4—222no—
1017C22⋊C4—224no—
1018C22⋊C4—224no—
1019C22⋊C4—224no—
1020C22⋊C4—224no—
1021C22⋊C4—224no—
1022C22⋊C4—224no—
1023C22⋊C4—224no—
1024C22⋊C4—442no—
1025C22⋊C4—442no—
1026C22⋊C4—442no—
1027C22⋊C4—442no—
1028C22⋊C4—442no—
1029C22⋊C4—442no—
1030C42—22no—
1031C42—22no—
1032C42—22no—
1033C42—24no—
1034C42—114no—
1035C42—114no—
1036C42—114no—
1037C42—224no—
1038C42—224no—
1039C42—224no—
1040C42—224no—
1041C42—222no—
1042C42—222no—
1043C42—222no—
1044C42—224no—
1045C42D4×D1114yes—
1046C11#3497711yescharacteristic, complemented, Sylow
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—112no—
1061C23—112no—
1062C23—221no—
1063C23—221no—
1064C23—221no—
1065C23—221no—
1066C23—221no—
1067C23—221no—
1068C23—221no—
1069C23—221no—
1070C23—221no—
1071C23—221no—
1072C23—221no—
1073C23—221no—
1074C23—222no—
1075C23—222no—
1076C23—222no—
1077C23—222no—
1078C23—222no—
1079C23—222no—
1080C23—222no—
1081C23#41×D1112yes—
1082C23C24×D1111yescharacteristic
1083Q8—228no—
1084Q8—448no—
1085D4—48no—
1086D4—44no—
1087D4—228no—
1088D4—228no—
1089D4—228no—
1090D4—448no—
1091D4—448no—
1092D4—448no—
1093D4—448no—
1094D4—448no—
1095D4—448no—
1096D4—448no—
1097D4—444no—
1098C2×C4—28no—
1099C2×C4—21no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—21no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—22no—
1117C2×C4—44no—
1118C2×C4—44no—
1119C2×C4—48no—
1120C2×C4—112no—
1121C2×C4—112no—
1122C2×C4—112no—
1123C2×C4—112no—
1124C2×C4—112no—
1125C2×C4—114no—
1126C2×C4—112no—
1127C2×C4—228no—
1128C2×C4—228no—
1129C2×C4—221no—
1130C2×C4—221no—
1131C2×C4—221no—
1132C2×C4—221no—
1133C2×C4—222no—
1134C2×C4—221no—
1135C2×C4—222no—
1136C2×C4—221no—
1137C2×C4—228no—
1138C2×C4—228no—
1139C2×C4—222no—
1140C2×C4—221no—
1141C2×C4—221no—
1142C2×C4—221no—
1143C2×C4—222no—
1144C2×C4—221no—
1145C2×C4—222no—
1146C2×C4—222no—
1147C2×C4—221no—
1148C2×C4—222no—
1149C2×C4—221no—
1150C2×C4—222no—
1151C2×C4—444no—
1152C2×C4—448no—
1153C2×C4—444no—
1154C2×C4C2×#433914yes—
1155C2×C4C2×#433912yes—
1156C2×C4C2×D4×D1112yes—
1157C2×C4C2×D4×D1112yes—
1158C2×C4C2×D4×D1112yes—
1159C2×C4#6703712yes—
1160C2×C4#41×D1112yes—
1161C2×C4#41×D1112yes—
1162C2×C4#6704212yes—
1163C22—22no—
1164C22—22no—
1165C22—22no—
1166C22—41no—
1167C22—41no—
1168C22—41no—
1169C22—41no—
1170C22—42no—
1171C22—42no—
1172C22—42no—
1173C22—42no—
1174C22—42no—
1175C22—42no—
1176C22—42no—
1177C22—222no—
1178C22—222no—
1179C22—222no—
1180C22—222no—
1181C22—222no—
1182C22—222no—
1183C22—441no—
1184C22—441no—
1185C22—441no—
1186C22—441no—
1187C22—441no—
1188C22—441no—
1189C22—441no—
1190C22—441no—
1191C22—442no—
1192C22—442no—
1193C22—442no—
1194C22—442no—
1195C22—442no—
1196C22—442no—
1197C22—442no—
1198C22C22×#433911yescharacteristic
1199C22C22×D4×D1111yescharacteristic
1200C22C2×#6703711yescharacteristic
1201C22C2×#41×D1111yescharacteristic
1202C22C2×#41×D1111yescharacteristic
1203C22C2×#41×D1111yescharacteristic
1204C22C2×#6704211yescharacteristic
1205C4—24no—
1206C4—22no—
1207C4—22no—
1208C4—41no—
1209C4—42no—
1210C4—41no—
1211C4—42no—
1212C4—114no—
1213C4—222no—
1214C4—222no—
1215C4—224no—
1216C4—222no—
1217C4—441no—
1218C4—442no—
1219C4—441no—
1220C4—442no—
1221C4#1062307914yes—
1222C4#1062313814yes—
1223C2—42no—
1224C2—82no—
1225C2—442no—
1226C2—442no—
1227C2—882no—
1228C2D11×#52511yescharacteristic
1229C2C2×#1062307911yescharacteristic
1230C2C2×#1062313811yescharacteristic
1231C2#1308222011yescharacteristic
1232C2#1308222211yescharacteristic
1233C2#1308224011yescharacteristic
1234C2#1308224211yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC4×C11×#121C2
hypercenterC4×#121D11
hypocenterC11#34977
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×#10623079C2semidirect
2. C2×C4×#4339C2semidirect
3. #13074301C2semidirect
4. #13074299C2semidirect
5. #13073823C2semidirect
6. #13073786C2semidirect
7. #13073617C2semidirect
8. #13073559C2semidirect
9. #13073076C2semidirect
10. #13072233C2semidirect
11. #13072037C2semidirect
12. #13072036C2semidirect
13. #13072032C2semidirect
14. #13072030C2semidirect
15. #13071832C2semidirect
16. #13071831C2semidirect
17. C4×#66993C2semidirect
18. C4×#66938C2semidirect
19. C4×#66948C2semidirect
20. C4×#66983C2semidirect
21. C4×#66991C2semidirect
22. C4×#66945C2semidirect
23. C4×C11×#121C2semidirect
250. C42×D11D4semidirect
318. C2×C22⋊D11#41semidirect
368. C2×Dic22#41semidirect
372. C11×C4⋊C4#41semidirect
411. C4⋊Dic11#41semidirect
451. C4×#121D11semidirect
1001. C4⋊C4#4339semidirect
1046. C11#34977semidirect

Maximal subgroups

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

subgroupindex
C2×#106230792
C2×C4×#43392
#130743012
#130742992
#130738232
#130737862
#130736172
#130735592
#130730762
#130722332
#130720372
#130720362
#130720322
#130720302
#130718322
#130718312
C4×#669932
C4×#669382
C4×#669482
C4×#669832
C4×#669912
C4×#669452
C4×C11×#1212
#3497711