Finite Group Databasebeta

← #14925906

Subgroups — #14925906

Order 2816.

3206 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623078C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3#13074232C212yesmaximal, complemented
4#13074224C212yesmaximal, complemented
5#13074095C211yesmaximal, characteristic, complemented
6#13073995C211yesmaximal, characteristic, complemented
7#13073801C212yesmaximal, complemented
8#13073771C211yesmaximal, characteristic, complemented
9#13073575C212yesmaximal, complemented
10#13073544C211yesmaximal, characteristic, complemented
11#13072015C211yesmaximal, characteristic, complemented
12#13072010C211yesmaximal, characteristic, complemented
13#13071992C211yesmaximal, characteristic, complemented
14#13071986C211yesmaximal, characteristic, complemented
15#13071877C212yesmaximal, complemented
16#13071831C212yesmaximal, complemented
17C4×#66939C211yesmaximal, characteristic, complemented
18C4×#66988C211yesmaximal, characteristic, complemented
19C4×#66937C212yesmaximal, complemented
20C4×#66991C212yesmaximal, complemented
21C4×#67006C211yesmaximal, characteristic, complemented
22C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
23C4×C11×#120C211yesmaximal, characteristic, complemented
24C24×C4×C11C2211yescharacteristic
25C23×C22⋊D11C2211yescharacteristic
26C22×#4339C2211yescharacteristic, complemented
27C23×C4×D11C2211yescharacteristic
28C2×C11×#120C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×C4×D4×C11C2212yescomplemented
31C2×#67006C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C2×#66992C2211yescharacteristic
34C2×#66991C2212yes—
35C2×#66990C2211yescharacteristic
36C2×#66988C2211yescharacteristic
37C2×C4×C22⋊D11—28no—
38C2×C4×C22⋊D11C2211yescharacteristic
39C2×C4×C22⋊D11C2212yes—
40C2×C4×C22⋊D11C2212yes—
41C2×C4×C22⋊D11C2212yes—
42C2×C4×C22⋊D11C2212yes—
43C2×C4×C22⋊D11C2211yescharacteristic, complemented
44C2×C4×C22⋊D11C2212yescomplemented
45C22×(C2×D11)⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48#10623078—28no—
49C2×#66949C2211yescharacteristic, complemented
50C2×#66947C2211yescharacteristic, complemented
51C2×#66939C2211yescharacteristic
52C2×#66937C2212yes—
53C2×#66937C2211yescharacteristic, complemented
54C2×#66936C2211yescharacteristic, complemented
55C2×#66935C2211yescharacteristic
56C2×C22⋊C4×D11C2211yescharacteristic
57C2×C22⋊C4×D11C2211yescharacteristic
58C2×#66931C2211yescharacteristic
59C2×C4×D44C2211yescharacteristic, complemented
60C2×#66925C2211yescharacteristic, complemented
61C2×C42×D11C2212yescomplemented
62C11×#386C2211yescharacteristic
63C11×#386C2212yescomplemented
64C11×#385C2211yescharacteristic
65C11×#385C2212yescomplemented
66C11×#379C2211yescharacteristic
67C4×C11×C22⋊C4C2211yescharacteristic
68C4×C11×C22⋊C4C2212yescomplemented
69#10622860C2211yescharacteristic
70#10622836C2212yes—
71#10622836C2212yescomplemented
72#10622834C2212yescomplemented
73#10622833C2211yescharacteristic
74#10622826C2211yescharacteristic
75#10622826C2212yescomplemented
76#10622823C2211yescharacteristic
77#10622823C2212yescomplemented
78C4×C22⋊Dic11C2211yescharacteristic
79C4×C22⋊Dic11C2212yescomplemented
80C4×C22⋊Dic11C2212yescomplemented
81#10622604C2212yescomplemented
82#10622600C2212yescomplemented
83#10622592C2212yescomplemented
84#10622591C2212yescomplemented
85#10622586C2212yescomplemented
86#10622574C2212yes—
87#10622573C2212yes—
88#10622572C2212yes—
89#10622572C2212yescomplemented
90#10622572C2212yescomplemented
91#10622571C2211yescharacteristic
92#10622570C2212yescomplemented
93#10622569C2212yes—
94#10622569C2212yes—
95#10622569C2212yescomplemented
96#10622565C2212yescomplemented
97#10622564C2212yescomplemented
98#10622563C2211yescharacteristic
99#10622562C2212yescomplemented
100#10622560C2212yescomplemented
101#10622559C2211yescharacteristic
102#10622557C2212yescomplemented
103#10622557C2212yescomplemented
104#10622557C2212yescomplemented
105#10622556C2211yescharacteristic
106#10622556C2211yescharacteristic
107C22⋊C4×Dic11C2211yescharacteristic
108C22⋊C4×Dic11C2211yescharacteristic
109C4×(C2×D11)⋊C4C2212yescomplemented
110C4×(C2×D11)⋊C4C2212yescomplemented
111C4×C4⋊Dic11C2212yescomplemented
112C4×Dic11⋊C4C2212yescomplemented
113#10622288C2212yescomplemented
114#10622287C2212yescomplemented
115#10622283C2212yescomplemented
116#10622282C2212yescomplemented
117#10622280C2212yescomplemented
118#10622279C2212yescomplemented
119#10622278C2212yescomplemented
120D11×#95C2212yescomplemented
121#10622271C2212yescomplemented
122#10622270C2212yescomplemented
123#10622266C2212yescomplemented
124#10622260C2212yescomplemented
125C25×C11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C22×D4×C11C2312yes—
129C23×C4×C11—24no—
130C23×C4×C11—44no—
131C23×C4×C11C2312yes—
132C23×C4×C11C2311yescharacteristic
133C23×C4×C11C2311yescharacteristic
134C23×C4×C11C2311yescharacteristic
135C23×C4×C11C2312yes—
136C22×C22⋊D11—24no—
137C22×C22⋊D11—28no—
138C22×C22⋊D11C2311yescharacteristic
139C22×C22⋊D11C2311yescharacteristic
140C22×C22⋊D11C2312yes—
141C22×C22⋊D11C2312yes—
142C22×C22⋊D11C2312yes—
143C22×C22⋊D11C2311yescharacteristic
144C22×C22⋊D11C2311yescharacteristic
145C23×Dic11C2311yescharacteristic
146C23×Dic11C2311yescharacteristic
147C23×Dic11C2311yescharacteristic
148C2×#4339—24no—
149C2×#4339—44no—
150C22×D44C2311yescharacteristic
151C22×D44C2311yescharacteristic
152C22×C4×D11—44no—
153C22×C4×D11D418yescomplemented
154C22×C4×D11C2311yescharacteristic
155C22×C4×D11C2312yes—
156C22×C4×D11C2312yes—
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2311yescharacteristic
159C22×C4×D11C2311yescharacteristic
160C22×C4×D11C2311yescharacteristic
161C22×Dic22C2311yescharacteristic
162C11×#120—24no—
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⋊C4C2311yescharacteristic
170C2×C11×C22⋊C4C2312yes—
171C2×C11×C22⋊C4C2312yes—
172C2×C11×C22⋊C4C2312yes—
173C2×C11×C22⋊C4C2312yes—
174C2×C11×C22⋊C4C2311yescharacteristic
175C2×C42×C11C2312yes—
176C2×C42×C11C2311yescharacteristic
177#67006—24no—
178C2×C22⋊Dic11—24no—
179C2×C22⋊Dic11C2311yescharacteristic
180C2×C22⋊Dic11C2311yescharacteristic
181C2×C22⋊Dic11C2311yescharacteristic
182C2×C22⋊Dic11C2312yes—
183C2×C22⋊Dic11C2312yes—
184C2×C22⋊Dic11C2312yes—
185C2×C22⋊Dic11C2312yes—
186C2×C22⋊Dic11C2312yes—
187C2×C22⋊Dic11C2312yes—
188C2×C22⋊Dic11C2312yes—
189C2×C22⋊Dic11C2311yescharacteristic
190#66992—24no—
191#66991—28no—
192#66990—24no—
193#66988—24no—
194C4×C22⋊D11—24no—
195C4×C22⋊D11—28no—
196C4×C22⋊D11—28no—
197C4×C22⋊D11—28no—
198C4×C22⋊D11—28no—
199C4×C22⋊D11—24no—
200C4×C22⋊D11—44no—
201C2×(C2×D11)⋊C4—24no—
202C2×(C2×D11)⋊C4C2311yescharacteristic
203C2×(C2×D11)⋊C4C2311yescharacteristic
204C2×(C2×D11)⋊C4C2311yescharacteristic
205C2×(C2×D11)⋊C4C2311yescharacteristic
206C2×(C2×D11)⋊C4C2312yes—
207C2×(C2×D11)⋊C4C2312yes—
208C2×(C2×D11)⋊C4C2311yescharacteristic
209C2×(C2×D11)⋊C4C2312yes—
210C2×(C2×D11)⋊C4C2311yescharacteristic
211C2×(C2×D11)⋊C4C2312yes—
212C2×(C2×D11)⋊C4C2312yes—
213C2×(C2×D11)⋊C4C2312yes—
214C2×(C2×D11)⋊C4C2312yes—
215C2×C4⋊Dic11C2311yescharacteristic
216C2×C4⋊Dic11C2312yes—
217C2×C4⋊Dic11C2312yes—
218C2×Dic11⋊C4—24no—
219C2×Dic11⋊C4C2311yescharacteristic
220C2×Dic11⋊C4C2311yescharacteristic
221C2×Dic11⋊C4C2311yescharacteristic
222C2×Dic11⋊C4C2311yescharacteristic
223C2×Dic11⋊C4C2312yes—
224C2×Dic11⋊C4C2312yes—
225C2×Dic11⋊C4C2312yes—
226C2×Dic11⋊C4C2312yes—
227C2×Dic11⋊C4C2312yes—
228C2×C4×Dic11—24no—
229C2×C4×Dic11C2312yes—
230C2×C4×Dic11C2311yescharacteristic
231C2×C4×Dic11C2312yes—
232C2×C4×Dic11C2312yes—
233C2×C4×Dic11C2312yes—
234C2×C4×Dic11C2312yes—
235#66949—24no—
236#66947—24no—
237#66939—24no—
238#66937—28no—
239#66937—24no—
240#66936—24no—
241#66935—24no—
242C22⋊C4×D11—24no—
243C22⋊C4×D11—24no—
244#66931—24no—
245C4×D44—24no—
246#66925—24no—
247C42×D11—44no—
248C11×#95C2312yes—
249C11×#95C2312yes—
250C11×#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262C11⋊#95C2312yes—
263C11⋊#95C2312yes—
264#34957—111nomaximal, Sylow
265C24×C11—22no—
266C24×C11—24no—
267C24×C11—22no—
268C24×C11—22no—
269C24×C11—42no—
270C24×C11C2411yescharacteristic
271C24×C11C2412yes—
272C24×C11C2411yescharacteristic
273C23×D11—22no—
274C23×D11—22no—
275C23×D11—24no—
276C23×D11—42no—
277C23×D11C2×D414yes—
278C23×D11C2411yescharacteristic
279C23×D11C2411yescharacteristic
280C23×D11C2411yescharacteristic
281C2×D4×C11—22no—
282C2×D4×C11—22no—
283C2×D4×C11—24no—
284C2×D4×C11—22no—
285C2×D4×C11—24no—
286C2×D4×C11—42no—
287C22×C4×C11—24no—
288C22×C4×C11—22no—
289C22×C4×C11—24no—
290C22×C4×C11—24no—
291C22×C4×C11—22no—
292C22×C4×C11—24no—
293C22×C4×C11—24no—
294C22×C4×C11—24no—
295C22×C4×C11—42no—
296C22×C4×C11—42no—
297C22×C4×C11—42no—
298C22×C4×C11—416no—
299C22×C4×C11C2×D414yes—
300C22×C4×C11C2412yes—
301C22×C4×C11C2411yescharacteristic
302C22×C4×C11C2411yescharacteristic
303C22×C4×C11C2411yescharacteristic
304C22×C4×C11C2412yes—
305C22×C4×C11C2411yescharacteristic
306C22×C4×C11C2412yes—
307C22×C4×C11C2411yescharacteristic
308C2×C22⋊D11—232no—
309C2×C22⋊D11—22no—
310C2×C22⋊D11—24no—
311C2×C22⋊D11—24no—
312C2×C22⋊D11—22no—
313C2×C22⋊D11—24no—
314C2×C22⋊D11—24no—
315C2×C22⋊D11—22no—
316C2×C22⋊D11—22no—
317C2×C22⋊D11—24no—
318C2×C22⋊D11—24no—
319C2×C22⋊D11—22no—
320C2×C22⋊D11—22no—
321C2×C22⋊D11—24no—
322C2×C22⋊D11—24no—
323C2×C22⋊D11—42no—
324C2×C22⋊D11—42no—
325C2×C22⋊D11—42no—
326C2×C22⋊D11#4118yescomplemented
327C22×Dic11—24no—
328C22×Dic11—22no—
329C22×Dic11—22no—
330C22×Dic11—22no—
331C22×Dic11—22no—
332C22×Dic11—42no—
333C22×Dic11C2×D414yes—
334C22×Dic11C2412yes—
335C22×Dic11C2412yes—
336C22×Dic11C2411yescharacteristic
337C22×Dic11C2411yescharacteristic
338C22×Dic11C2411yescharacteristic
339C22×Dic11C2411yescharacteristic
340C22×Dic11C2411yescharacteristic
341C22×Dic11C2412yes—
342C22×Dic11C2412yes—
343#4339—416no—
344C2×D44—22no—
345C2×D44—22no—
346C2×D44—24no—
347C2×D44—42no—
348C2×C4×D11—24no—
349C2×C4×D11—24no—
350C2×C4×D11—24no—
351C2×C4×D11—22no—
352C2×C4×D11—24no—
353C2×C4×D11—24no—
354C2×C4×D11—24no—
355C2×C4×D11—24no—
356C2×C4×D11—42no—
357C2×C4×D11—42no—
358C2×C4×D11—42no—
359C2×C4×D11—42no—
360C2×C4×D11—416no—
361C2×C4×D11C2×D414yes—
362C2×C4×D11C2×D414yes—
363C2×C4×D11C2×D414yes—
364C2×C4×D11C2×D414yes—
365C2×Dic22—22no—
366C2×Dic22—42no—
367C11×C4⋊C4—22no—
368C11×C4⋊C4—42no—
369C11×C22⋊C4—22no—
370C11×C22⋊C4—22no—
371C11×C22⋊C4—24no—
372C11×C22⋊C4—22no—
373C11×C22⋊C4—24no—
374C11×C22⋊C4—42no—
375C11×C22⋊C4—42no—
376C11×C22⋊C4#4114yescomplemented
377C42×C11—22no—
378C42×C11—24no—
379C22⋊Dic11—22no—
380C22⋊Dic11—24no—
381C22⋊Dic11—24no—
382C22⋊Dic11—24no—
383C22⋊Dic11—24no—
384C22⋊Dic11—24no—
385C22⋊Dic11—22no—
386C22⋊Dic11—22no—
387C22⋊Dic11—24no—
388C22⋊Dic11—42no—
389C22⋊Dic11#4114yescomplemented
390(C2×D11)⋊C4—22no—
391(C2×D11)⋊C4—24no—
392(C2×D11)⋊C4—24no—
393(C2×D11)⋊C4—22no—
394(C2×D11)⋊C4—22no—
395(C2×D11)⋊C4—22no—
396(C2×D11)⋊C4—22no—
397(C2×D11)⋊C4—24no—
398(C2×D11)⋊C4—24no—
399(C2×D11)⋊C4—22no—
400(C2×D11)⋊C4—24no—
401(C2×D11)⋊C4—24no—
402(C2×D11)⋊C4—42no—
403C4⋊Dic11—22no—
404C4⋊Dic11—24no—
405C4⋊Dic11—24no—
406Dic11⋊C4—22no—
407Dic11⋊C4—22no—
408Dic11⋊C4—22no—
409Dic11⋊C4—24no—
410Dic11⋊C4—24no—
411Dic11⋊C4—24no—
412Dic11⋊C4—24no—
413Dic11⋊C4—22no—
414Dic11⋊C4—42no—
415C4×Dic11—22no—
416C4×Dic11—24no—
417C4×Dic11—24no—
418C4×Dic11—24no—
419C4×Dic11—42no—
420C4×Dic11—42no—
421C2×#525—111no—
422C22×C4×D4—111no—
423#2602—112no—
424#2602—112no—
425#2591—111no—
426#2583—111no—
427#2564—112no—
428#2561—111no—
429#2543—112no—
430#2539—111no—
431#2412—111no—
432#2412—111no—
433#2410—111no—
434#2410—111no—
435#2395—112no—
436#2388—112no—
437C4×#123—111no—
438C4×#123—111no—
439C4×#121—112no—
440C4×#121—112no—
441C4×#120—111no—
442C4×#120D1111yescharacteristic, complemented
443C2×C4×C22⋊C4—111no—
444C23×C11—22no—
445C23×C11—22no—
446C23×C11—28no—
447C23×C11—22no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11—22no—
451C23×C11—22no—
452C23×C11—22no—
453C23×C11—21no—
454C23×C11—21no—
455C23×C11—22no—
456C23×C11—21no—
457C23×C11—22no—
458C23×C11—48no—
459C23×C11—48no—
460C23×C11—44no—
461C23×C11—44no—
462C23×C11C22×D412yes—
463C23×C11C2×#4112yes—
464C23×C11C2×#4114yes—
465C23×C11C2×#4112yes—
466C23×C11C2511yescharacteristic
467C22×D11—21no—
468C22×D11—21no—
469C22×D11—22no—
470C22×D11—28no—
471C22×D11—21no—
472C22×D11—21no—
473C22×D11—22no—
474C22×D11—22no—
475C22×D11—28no—
476C22×D11—21no—
477C22×D11—21no—
478C22×D11—22no—
479C22×D11—21no—
480C22×D11—22no—
481C22×D11—44no—
482C22×D11—48no—
483C22×D11—48no—
484C22×D11C22×D412yes—
485C22×D11C22×D412yes—
486C22×D11C2×#4114yes—
487D4×C11—48no—
488D4×C11—44no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—28no—
493C2×C4×C11—22no—
494C2×C4×C11—21no—
495C2×C4×C11—21no—
496C2×C4×C11—21no—
497C2×C4×C11—21no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—21no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—22no—
506C2×C4×C11—48no—
507C2×C4×C11—44no—
508C2×C4×C11—44no—
509C2×C4×C11—48no—
510C2×C4×C11C22×D412yes—
511C2×C4×C11C22×D412yes—
512C2×C4×C11C2×#4114yes—
513C2×C4×C11H(5,𝔽2)14yes—
514C22⋊D11—216no—
515C22⋊D11—216no—
516C22⋊D11—48no—
517C22⋊D11—44no—
518C22⋊D11—44no—
519C22⋊D11—44no—
520C22⋊D11—44no—
521C2×Dic11—28no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—22no—
529C2×Dic11—21no—
530C2×Dic11—21no—
531C2×Dic11—21no—
532C2×Dic11—22no—
533C2×Dic11—21no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—21no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—44no—
542C2×Dic11—44no—
543C2×Dic11C22×D412yes—
544C2×Dic11C22×D412yes—
545C2×Dic11C2×#4114yes—
546C2×Dic11C2×#4114yes—
547D44—44no—
548D44—44no—
549C4×D11—28no—
550C4×D11—28no—
551C4×D11—44no—
552C4×D11—44no—
553C4×D11—48no—
554C4×D11—48no—
555C4×D11—44no—
556Dic22—44no—
557C22×#41—111no—
558C23×D4—111no—
559C24×C4—111no—
560C24×C4C2×D1111yescharacteristic
561#525—228no—
562C2×#123—111no—
563C2×#123—111no—
564C2×#123—111no—
565C2×#123—111no—
566C2×C22⋊Q8—111no—
567C2×C22⋊Q8—111no—
568C2×#121—111no—
569C2×#121—112no—
570C2×#121—112no—
571C2×#121—111no—
572C2×#120—111no—
573C2×#120—111no—
574C2×#120—111no—
575C2×#120C2×D1111yescharacteristic
576C2×C4×D4—112no—
577C2×C4×D4—112no—
578C2×C4×D4—112no—
579C2×C4×D4—112no—
580C2×C4×D4—111no—
581C2×C4×D4—111no—
582C2×C4×D4—112no—
583C2×C4×D4—111no—
584C2×C4×D4—228no—
585C2×C4×D4C2×D1111yescharacteristic
586C2×C4×D4C2×D1112yescomplemented
587C2×#117—111no—
588C22×C4⋊C4—111no—
589C22×C22⋊C4—111no—
590C22×C22⋊C4—111no—
591C22×C22⋊C4—111no—
592C22×C22⋊C4—111no—
593C22×C42—111no—
594C22×C42—112no—
595#400—112no—
596#399—112no—
597#398—112no—
598#397—112no—
599#397—112no—
600#397—112no—
601#395—112no—
602#394—112no—
603#394—112no—
604#394—112no—
605#394—112no—
606#394—112no—
607#393—112no—
608#392—112no—
609#392—112no—
610#392—112no—
611#390—112no—
612#390—112no—
613#389—112no—
614#389—112no—
615#388—112no—
616#388—112no—
617#388—112no—
618#388—112no—
619#388—112no—
620#388—112no—
621#387—112no—
622#387—112no—
623#386—111no—
624#386—111no—
625#386—112no—
626#386—112no—
627#386—112no—
628#386—111no—
629#386—112no—
630#386—112no—
631#386C2×D1111yescharacteristic
632#386C2×D1112yescomplemented
633#385—112no—
634#385—111no—
635#385—111no—
636#385—111no—
637#385C2×D1111yescharacteristic
638#385C2×D1112yescomplemented
639#381—111no—
640#381—111no—
641#380—112no—
642#380—112no—
643#379—111no—
644#379C2×D1111yescharacteristic
645C4×C4⋊C4—112no—
646C4×C4⋊C4—112no—
647C4×C22⋊C4—112no—
648C4×C22⋊C4—112no—
649C4×C22⋊C4—111no—
650C4×C22⋊C4—111no—
651C4×C22⋊C4—111no—
652C4×C22⋊C4—112no—
653C4×C22⋊C4—112no—
654C4×C22⋊C4—112no—
655C4×C22⋊C4C2×D1111yescharacteristic
656C4×C22⋊C4C2×D1112yescomplemented
657C2×#95—112no—
658C22×C11—22no—
659C22×C11—22no—
660C22×C11—24no—
661C22×C11—24no—
662C22×C11—24no—
663C22×C11—24no—
664C22×C11—24no—
665C22×C11—416no—
666C22×C11—42no—
667C22×C11—42no—
668C22×C11—42no—
669C22×C11—42no—
670C22×C11—41no—
671C22×C11—41no—
672C22×C11—41no—
673C22×C11—42no—
674C22×C11—42no—
675C22×C11#53214yes—
676C22×C11C23×D411yescharacteristic
677C22×C11C22×#4111yescharacteristic
678C22×C11C22×#4112yes—
679C22×C11C22×#4111yescharacteristic
680C22×C11C2×H(5,𝔽2)12yes—
681C2×D11—22no—
682C2×D11—22no—
683C2×D11—24no—
684C2×D11—24no—
685C2×D11—22no—
686C2×D11—22no—
687C2×D11—22no—
688C2×D11—416no—
689C2×D11—42no—
690C2×D11—42no—
691C2×D11—41no—
692C2×D11—41no—
693C2×D11—41no—
694C2×D11—42no—
695C2×D11—42no—
696C2×D11#52514yes—
697C4×C11—22no—
698C4×C11—24no—
699C4×C11—41no—
700C4×C11—41no—
701C4×C11—42no—
702C4×C11—41no—
703C4×C11—42no—
704C4×C11#53414yes—
705Dic11—24no—
706Dic11—22no—
707Dic11—22no—
708Dic11—24no—
709Dic11—41no—
710Dic11—42no—
711Dic11—41no—
712Dic11—41no—
713Dic11—42no—
714C25—111no—
715C25C22×D1111yescharacteristic
716C2×#41—224no—
717C2×#41—444no—
718C22×Q8—111no—
719C22×D4—112no—
720C22×D4—112no—
721C22×D4—111no—
722C22×D4—111no—
723C22×D4—112no—
724C22×D4—111no—
725C22×D4—111no—
726C22×D4—111no—
727C22×D4—111no—
728C22×D4—228no—
729C22×D4—224no—
730C22×D4C22×D1111yescharacteristic
731C22×D4C22×D1112yes—
732C23×C4—24no—
733C23×C4—44no—
734C23×C4—111no—
735C23×C4—111no—
736C23×C4—111no—
737C23×C4—118no—
738C23×C4—111no—
739C23×C4—111no—
740C23×C4—111no—
741C23×C4—111no—
742C23×C4—111no—
743C23×C4—112no—
744C23×C4—112no—
745C23×C4—444no—
746C23×C4C22×D1112yes—
747C23×C4C22×D1111yescharacteristic
748C23×C4C22×D1111yescharacteristic
749C23×C4C22×D1111yescharacteristic
750C23×C4C22×D1112yes—
751#123—224no—
752#123—224no—
753#123—224no—
754#123—224no—
755C22⋊Q8—224no—
756C22⋊Q8—224no—
757#121—224no—
758#121—228no—
759#121—224no—
760#121—228no—
761#120—24no—
762#120—224no—
763#120—224no—
764#120—224no—
765C4×D4—24no—
766C4×D4—44no—
767C4×D4—224no—
768C4×D4—228no—
769C4×D4—228no—
770C4×D4—228no—
771C4×D4—228no—
772C4×D4—224no—
773C4×D4—224no—
774C4×D4—444no—
775#117—224no—
776C2×C4⋊C4—112no—
777C2×C4⋊C4—112no—
778C2×C4⋊C4—111no—
779C2×C4⋊C4—111no—
780C2×C4⋊C4—111no—
781C2×C4⋊C4—111no—
782C2×C4⋊C4—111no—
783C2×C4⋊C4—112no—
784C2×C4⋊C4—112no—
785C2×C4⋊C4—112no—
786C2×C4⋊C4—112no—
787C2×C4⋊C4—112no—
788C2×C4⋊C4—224no—
789C2×C4⋊C4C22×D1111yescharacteristic
790C2×C4⋊C4C22×D1112yes—
791C2×C22⋊C4—111no—
792C2×C22⋊C4—112no—
793C2×C22⋊C4—112no—
794C2×C22⋊C4—111no—
795C2×C22⋊C4—111no—
796C2×C22⋊C4—111no—
797C2×C22⋊C4—112no—
798C2×C22⋊C4—112no—
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—111no—
806C2×C22⋊C4—111no—
807C2×C22⋊C4—111no—
808C2×C22⋊C4—111no—
809C2×C22⋊C4—111no—
810C2×C22⋊C4—111no—
811C2×C22⋊C4—112no—
812C2×C22⋊C4—112no—
813C2×C22⋊C4—112no—
814C2×C22⋊C4—112no—
815C2×C22⋊C4—224no—
816C2×C22⋊C4—224no—
817C2×C22⋊C4—224no—
818C2×C22⋊C4—224no—
819C2×C22⋊C4C22×D1111yescharacteristic
820C2×C22⋊C4C22×D1111yescharacteristic
821C2×C22⋊C4C22×D1111yescharacteristic
822C2×C22⋊C4C22×D1112yes—
823C2×C22⋊C4C22×D1112yes—
824C2×C22⋊C4C22×D1112yes—
825C2×C22⋊C4C22×D1112yes—
826C2×C22⋊C4C22×D1111yescharacteristic
827C2×C42—112no—
828C2×C42—111no—
829C2×C42—112no—
830C2×C42—112no—
831C2×C42—112no—
832C2×C42—112no—
833C2×C42—224no—
834C2×C42—444no—
835C2×C42C22×D1111yescharacteristic
836C2×C42C22×D1112yes—
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#95—112no—
846#95—112no—
847#95—112no—
848#95—112no—
849#95—112no—
850#95C22×D1112yes—
851#95C22×D1112yes—
852#95C22×D1112yes—
853C2×C11—24no—
854C2×C11—44no—
855C2×C11—81no—
856C2×C11C2×#52511yescharacteristic
857C2×C11C2×#53211yescharacteristic
858C2×C11C2×#53411yescharacteristic
859C2×C11#348112yes—
860C2×C11#348112yes—
861D11—24no—
862D11—42no—
863D11—81no—
864C24—22no—
865C24—24no—
866C24—22no—
867C24—22no—
868C24—42no—
869C24—111no—
870C24—111no—
871C24—114no—
872C24—111no—
873C24—224no—
874C24—222no—
875C24—222no—
876C24—442no—
877C24C23×D1111yescharacteristic
878C24C23×D1112yes—
879C24C23×D1111yescharacteristic
880#41—4416no—
881C2×Q8—222no—
882C2×Q8—442no—
883C2×D4—22no—
884C2×D4—22no—
885C2×D4—24no—
886C2×D4—22no—
887C2×D4—24no—
888C2×D4—42no—
889C2×D4—118no—
890C2×D4—222no—
891C2×D4—222no—
892C2×D4—224no—
893C2×D4—224no—
894C2×D4—224no—
895C2×D4—222no—
896C2×D4—224no—
897C2×D4—224no—
898C2×D4—224no—
899C2×D4—2232no—
900C2×D4—224no—
901C2×D4—222no—
902C2×D4—222no—
903C2×D4—224no—
904C2×D4—222no—
905C2×D4—222no—
906C2×D4—222no—
907C2×D4—224no—
908C2×D4—442no—
909C2×D4—442no—
910C2×D4—442no—
911C2×D4—442no—
912C22×C4—24no—
913C22×C4—22no—
914C22×C4—22no—
915C22×C4—24no—
916C22×C4—24no—
917C22×C4—24no—
918C22×C4—24no—
919C22×C4—24no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—416no—
924C22×C4—112no—
925C22×C4—112no—
926C22×C4—111no—
927C22×C4—111no—
928C22×C4—114no—
929C22×C4—114no—
930C22×C4—114no—
931C22×C4—114no—
932C22×C4—114no—
933C22×C4—112no—
934C22×C4—112no—
935C22×C4—111no—
936C22×C4—111no—
937C22×C4—111no—
938C22×C4—224no—
939C22×C4—224no—
940C22×C4—224no—
941C22×C4—224no—
942C22×C4—222no—
943C22×C4—224no—
944C22×C4—224no—
945C22×C4—222no—
946C22×C4—222no—
947C22×C4—222no—
948C22×C4—224no—
949C22×C4—222no—
950C22×C4—224no—
951C22×C4—4416no—
952C22×C4—442no—
953C22×C4—442no—
954C22×C4—442no—
955C22×C4—442no—
956C22×C4—442no—
957C22×C4D4×D1114yes—
958C22×C4C23×D1112yes—
959C22×C4C23×D1111yescharacteristic
960C22×C4C23×D1111yescharacteristic
961C22×C4C23×D1111yescharacteristic
962C22×C4C23×D1112yes—
963C22×C4C23×D1112yes—
964C22×C4C23×D1111yescharacteristic
965C22×C4C23×D1111yescharacteristic
966C4⋊C4—22no—
967C4⋊C4—42no—
968C4⋊C4—224no—
969C4⋊C4—224no—
970C4⋊C4—222no—
971C4⋊C4—222no—
972C4⋊C4—222no—
973C4⋊C4—222no—
974C4⋊C4—224no—
975C4⋊C4—224no—
976C4⋊C4—224no—
977C4⋊C4—224no—
978C4⋊C4—222no—
979C4⋊C4—442no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—24no—
983C22⋊C4—24no—
984C22⋊C4—22no—
985C22⋊C4—42no—
986C22⋊C4—42no—
987C22⋊C4—114no—
988C22⋊C4—224no—
989C22⋊C4—222no—
990C22⋊C4—224no—
991C22⋊C4—224no—
992C22⋊C4—224no—
993C22⋊C4—222no—
994C22⋊C4—222no—
995C22⋊C4—222no—
996C22⋊C4—222no—
997C22⋊C4—224no—
998C22⋊C4—224no—
999C22⋊C4—222no—
1000C22⋊C4—224no—
1001C22⋊C4—224no—
1002C22⋊C4—224no—
1003C22⋊C4—222no—
1004C22⋊C4—222no—
1005C22⋊C4—224no—
1006C22⋊C4—224no—
1007C22⋊C4—224no—
1008C22⋊C4—222no—
1009C22⋊C4—442no—
1010C22⋊C4—442no—
1011C22⋊C4#433914yescomplemented
1012C42—22no—
1013C42—24no—
1014C42—224no—
1015C42—224no—
1016C42—222no—
1017C42—224no—
1018C42—442no—
1019C42—442no—
1020C11#3495711yescharacteristic, complemented, Sylow
1021C23—22no—
1022C23—22no—
1023C23—28no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—21no—
1031C23—21no—
1032C23—22no—
1033C23—21no—
1034C23—22no—
1035C23—48no—
1036C23—48no—
1037C23—44no—
1038C23—44no—
1039C23—112no—
1040C23—114no—
1041C23—112no—
1042C23—228no—
1043C23—221no—
1044C23—222no—
1045C23—221no—
1046C23—228no—
1047C23—221no—
1048C23—222no—
1049C23—221no—
1050C23—222no—
1051C23—221no—
1052C23—221no—
1053C23—222no—
1054C23—222no—
1055C23—221no—
1056C23—444no—
1057C23—448no—
1058C23—448no—
1059C23C2×#433912yes—
1060C23C2×D4×D1112yes—
1061C23#41×D1114yes—
1062C23#41×D1112yes—
1063C23C24×D1111yescharacteristic
1064Q8—444no—
1065D4—48no—
1066D4—44no—
1067D4—2216no—
1068D4—2216no—
1069D4—444no—
1070D4—444no—
1071D4—448no—
1072D4—444no—
1073D4—444no—
1074D4—444no—
1075D4—444no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—28no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—21no—
1093C2×C4—48no—
1094C2×C4—44no—
1095C2×C4—48no—
1096C2×C4—44no—
1097C2×C4—112no—
1098C2×C4—112no—
1099C2×C4—114no—
1100C2×C4—114no—
1101C2×C4—228no—
1102C2×C4—222no—
1103C2×C4—222no—
1104C2×C4—222no—
1105C2×C4—222no—
1106C2×C4—222no—
1107C2×C4—222no—
1108C2×C4—228no—
1109C2×C4—228no—
1110C2×C4—222no—
1111C2×C4—222no—
1112C2×C4—221no—
1113C2×C4—222no—
1114C2×C4—221no—
1115C2×C4—221no—
1116C2×C4—221no—
1117C2×C4—222no—
1118C2×C4—222no—
1119C2×C4—222no—
1120C2×C4—221no—
1121C2×C4—222no—
1122C2×C4—222no—
1123C2×C4—444no—
1124C2×C4—444no—
1125C2×C4—448no—
1126C2×C4—448no—
1127C2×C4—444no—
1128C2×C4—444no—
1129C2×C4—444no—
1130C2×C4C2×#433914yes—
1131C2×C4C2×D4×D1112yes—
1132C2×C4C2×D4×D1112yes—
1133C2×C4#6703714yes—
1134C22—22no—
1135C22—24no—
1136C22—24no—
1137C22—22no—
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—416no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—41no—
1147C22—41no—
1148C22—42no—
1149C22—42no—
1150C22—41no—
1151C22—114no—
1152C22—222no—
1153C22—222no—
1154C22—224no—
1155C22—224no—
1156C22—222no—
1157C22—222no—
1158C22—222no—
1159C22—4416no—
1160C22—442no—
1161C22—442no—
1162C22—441no—
1163C22—441no—
1164C22—442no—
1165C22—442no—
1166C22—441no—
1167C22#1062307914yes—
1168C22C22×#433911yescharacteristic
1169C22C22×D4×D1111yescharacteristic
1170C22C2×#6703712yes—
1171C22C2×#41×D1111yescharacteristic
1172C22C2×#41×D1112yes—
1173C4—22no—
1174C4—24no—
1175C4—41no—
1176C4—42no—
1177C4—41no—
1178C4—42no—
1179C4—41no—
1180C4—222no—
1181C4—222no—
1182C4—224no—
1183C4—224no—
1184C4—442no—
1185C4—441no—
1186C4—441no—
1187C4—442no—
1188C4—441no—
1189C4#1062312014yes—
1190C2—24no—
1191C2—44no—
1192C2—81no—
1193C2—224no—
1194C2—442no—
1195C2—881no—
1196C2D11×#52511yescharacteristic
1197C2C2×#1062307911yescharacteristic
1198C2C2×#1062312011yescharacteristic
1199C2#1308221812yes—
1200C2#1308222012yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC4×C11×#120C2
hypercenterC4×#120D11
hypocenterC11#34957
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#120

Complements

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

NH ≅ G/Ntype
1. C2×#10623078C2semidirect
2. C22×C4×C22⋊D11C2semidirect
3. #13074232C2semidirect
4. #13074224C2semidirect
5. #13074095C2semidirect
6. #13073995C2semidirect
7. #13073801C2semidirect
8. #13073771C2semidirect
9. #13073575C2semidirect
10. #13073544C2semidirect
11. #13072015C2semidirect
12. #13072010C2semidirect
13. #13071992C2semidirect
14. #13071986C2semidirect
15. #13071877C2semidirect
16. #13071831C2semidirect
17. C4×#66939C2semidirect
18. C4×#66988C2semidirect
19. C4×#66937C2semidirect
20. C4×#66991C2semidirect
21. C4×#67006C2semidirect
22. C4×C22⋊C4×D11C2semidirect
23. C4×C11×#120C2semidirect
26. C22×#4339C22semidirect
30. C2×C4×D4×C11C22semidirect
43. C2×C4×C22⋊D11C22semidirect
44. C2×C4×C22⋊D11C22semidirect
49. C2×#66949C22semidirect
50. C2×#66947C22semidirect
53. C2×#66937C22semidirect
54. C2×#66936C22semidirect
59. C2×C4×D44C22semidirect
60. C2×#66925C22semidirect
61. C2×C42×D11C22semidirect
63. C11×#386C22semidirect
65. C11×#385C22semidirect
68. C4×C11×C22⋊C4C22semidirect
71. #10622836C22semidirect
72. #10622834C22semidirect
75. #10622826C22semidirect
77. #10622823C22semidirect
79. C4×C22⋊Dic11C22semidirect
80. C4×C22⋊Dic11C22semidirect
81. #10622604C22semidirect
82. #10622600C22semidirect
83. #10622592C22semidirect
84. #10622591C22semidirect
85. #10622586C22semidirect
89. #10622572C22semidirect
90. #10622572C22semidirect
92. #10622570C22semidirect
95. #10622569C22semidirect
96. #10622565C22semidirect
97. #10622564C22semidirect
99. #10622562C22semidirect
100. #10622560C22semidirect
102. #10622557C22semidirect
103. #10622557C22semidirect
104. #10622557C22semidirect
109. C4×(C2×D11)⋊C4C22semidirect
110. C4×(C2×D11)⋊C4C22semidirect
111. C4×C4⋊Dic11C22semidirect
112. C4×Dic11⋊C4C22semidirect
113. #10622288C22semidirect
114. #10622287C22semidirect
115. #10622283C22semidirect
116. #10622282C22semidirect
117. #10622280C22semidirect
118. #10622279C22semidirect
119. #10622278C22semidirect
120. D11×#95C22semidirect
121. #10622271C22semidirect
122. #10622270C22semidirect
123. #10622266C22semidirect
124. #10622260C22semidirect
153. C22×C4×D11D4semidirect
326. C2×C22⋊D11#41semidirect
376. C11×C22⋊C4#41semidirect
389. C22⋊Dic11#41semidirect
442. C4×#120D11semidirect
586. C2×C4×D4C2×D11semidirect
632. #386C2×D11semidirect
638. #385C2×D11semidirect
656. C4×C22⋊C4C2×D11semidirect
1011. C22⋊C4#4339semidirect
1020. C11#34957semidirect

Maximal subgroups

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

subgroupindex
C2×#106230782
C22×C4×C22⋊D112
#130742322
#130742242
#130740952
#130739952
#130738012
#130737712
#130735752
#130735442
#130720152
#130720102
#130719922
#130719862
#130718772
#130718312
C4×#669392
C4×#669882
C4×#669372
C4×#669912
C4×#670062
C4×C22⋊C4×D112
C4×C11×#1202
#3495711