Finite Group Databasebeta

← #14926061

Subgroups — #14926061

Order 2816.

3114 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623069C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3#13074242C212yesmaximal, complemented
4#13074240C212yesmaximal, complemented
5#13073814C212yesmaximal, complemented
6#13073585C212yesmaximal, complemented
7#13073106C211yesmaximal, characteristic, complemented
8#13073092C211yesmaximal, characteristic, complemented
9#13072265C211yesmaximal, characteristic, complemented
10#13072251C211yesmaximal, characteristic
11#13072004C211yesmaximal, characteristic, complemented
12#13072003C211yesmaximal, characteristic, complemented
13#13071999C211yesmaximal, characteristic, complemented
14#13071997C211yesmaximal, characteristic, complemented
15#13071860C212yesmaximal, complemented
16#13071858C212yesmaximal, complemented
17C4×#66993C212yesmaximal, complemented
18C4×#66938C212yesmaximal, complemented
19C4×#66935C211yesmaximal, characteristic, complemented
20C4×#67006C211yesmaximal, characteristic, complemented
21C4×#66990C211yesmaximal, characteristic, complemented
22C4×#66930C211yesmaximal, characteristic, complemented
23C4×C11×#120C211yesmaximal, characteristic, complemented
24C24×C4×C11C2211yescharacteristic
25C23×C22⋊D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C2×C11×#120C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2212yescomplemented
30C2×#67006C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C2×#66993C2212yes—
33C2×#66992C2211yescharacteristic
34C2×#66990C2211yescharacteristic
35C2×#66988C2211yescharacteristic
36C2×C4×C22⋊D11—28no—
37C2×C4×C22⋊D11C2211yescharacteristic
38C2×C4×C22⋊D11C2212yes—
39C2×C4×C22⋊D11C2212yes—
40C2×C4×C22⋊D11C2212yes—
41C2×C4×C22⋊D11C2212yes—
42C2×C4×C22⋊D11C2211yescharacteristic, complemented
43C2×C4×C22⋊D11C2212yescomplemented
44C2×C4×C22⋊D11C2212yescomplemented
45C22×(C2×D11)⋊C4C2211yescharacteristic
46C2×#66979C2211yescharacteristic, complemented
47C22×Dic11⋊C4C2211yescharacteristic
48C22×C4×Dic11C2211yescharacteristic
49#10623069—28no—
50C2×#66951C2211yescharacteristic, complemented
51C2×#66942C2211yescharacteristic, complemented
52C2×#66939C2211yescharacteristic
53C2×#66938C2212yes—
54C2×#66938C2211yescharacteristic, complemented
55C2×#66935C2211yescharacteristic
56C2×#66932C2211yescharacteristic, complemented
57C2×#66931C2211yescharacteristic
58C2×#66930C2211yescharacteristic
59C2×#66930C2211yescharacteristic
60C2×C4×D44C2212yescomplemented
61C2×#66925C2211yescharacteristic, complemented
62C2×C4×Dic22C2211yescharacteristic, complemented
63C11×#386C2211yescharacteristic
64C11×#386C2212yescomplemented
65C11×#385C2211yescharacteristic
66C11×#385C2212yescomplemented
67C11×#379C2211yescharacteristic
68C4×C11×C22⋊C4C2211yescharacteristic
69C4×C11×C22⋊C4C2212yescomplemented
70#10622860C2211yescharacteristic
71#10622836C2212yes—
72#10622835C2212yescomplemented
73#10622834C2212yescomplemented
74#10622833C2211yescharacteristic
75#10622826C2211yescharacteristic
76#10622826C2212yescomplemented
77#10622823C2211yescharacteristic
78#10622823C2212yescomplemented
79C4×C22⋊Dic11C2211yescharacteristic
80C4×C22⋊Dic11C2212yescomplemented
81#10622607C2212yescomplemented
82#10622602C2212yescomplemented
83#10622601C2212yescomplemented
84#10622597C2212yescomplemented
85#10622589C2212yescomplemented
86#10622574C2212yes—
87#10622573C2212yes—
88#10622572C2212yes—
89#10622572C2212yescomplemented
90#10622572C2212yescomplemented
91#10622571C2211yescharacteristic
92#10622570C2212yes—
93#10622570C2212yes—
94#10622570C2212yescomplemented
95#10622570C2212yescomplemented
96#10622570C2212yescomplemented
97#10622569C2212yescomplemented
98#10622568C2211yescharacteristic
99#10622568C2211yescharacteristic
100#10622565C2212yescomplemented
101#10622564C2212yescomplemented
102#10622563C2211yescharacteristic
103#10622561C2212yescomplemented
104#10622561C2212yescomplemented
105#10622559C2211yescharacteristic
106#10622557C2212yescomplemented
107C22⋊C4×Dic11C2211yescharacteristic
108C22⋊C4×Dic11C2211yescharacteristic
109C4×(C2×D11)⋊C4C2212yescomplemented
110C4×(C2×D11)⋊C4C2212yescomplemented
111C4×Dic11⋊C4C2212yescomplemented
112C42×Dic11C2212yescomplemented
113#10622289C2212yescomplemented
114#10622288C2212yescomplemented
115#10622285C2212yescomplemented
116#10622283C2212yescomplemented
117#10622282C2212yescomplemented
118#10622281C2212yescomplemented
119#10622278C2212yescomplemented
120#10622270C2212yescomplemented
121#10622263C2212yescomplemented
122#10622262C2212yescomplemented
123#10622261C2212yescomplemented
124#10622259C2212yescomplemented
125C25×C11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C22×D4×C11C2312yes—
129C23×C4×C11—24no—
130C23×C4×C11—44no—
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2312yes—
133C23×C4×C11C2311yescharacteristic
134C23×C4×C11C2311yescharacteristic
135C23×C4×C11C2312yes—
136C22×C22⋊D11—28no—
137C22×C22⋊D11—24no—
138C22×C22⋊D11C2311yescharacteristic
139C22×C22⋊D11C2311yescharacteristic
140C22×C22⋊D11C2312yes—
141C22×C22⋊D11C2312yes—
142C22×C22⋊D11C2312yes—
143C22×C22⋊D11C2312yes—
144C23×Dic11C2311yescharacteristic
145C23×Dic11C2311yescharacteristic
146C23×Dic11C2311yescharacteristic
147C22×D44C2312yes—
148C22×C4×D11—24no—
149C22×C4×D11—44no—
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2312yes—
152C22×C4×D11C2312yes—
153C22×Dic22C2311yescharacteristic
154C11×#120—24no—
155C4×D4×C11—24no—
156C4×D4×C11—44no—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2312yes—
159C2×C11×C22⋊C4C2311yescharacteristic
160C2×C11×C22⋊C4C2311yescharacteristic
161C2×C11×C22⋊C4C2311yescharacteristic
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2312yes—
166C2×C11×C22⋊C4C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2312yes—
169#67006—24no—
170C2×C22⋊Dic11—24no—
171C2×C22⋊Dic11C2311yescharacteristic
172C2×C22⋊Dic11C2311yescharacteristic
173C2×C22⋊Dic11C2311yescharacteristic
174C2×C22⋊Dic11C2311yescharacteristic
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2311yescharacteristic
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2312yes—
182C2×C22⋊Dic11C2311yescharacteristic
183#66993—28no—
184#66992—24no—
185#66990—24no—
186#66988—24no—
187C4×C22⋊D11—24no—
188C4×C22⋊D11—28no—
189C4×C22⋊D11—28no—
190C4×C22⋊D11—28no—
191C4×C22⋊D11—28no—
192C4×C22⋊D11—24no—
193C4×C22⋊D11—44no—
194C4×C22⋊D11—44no—
195C2×(C2×D11)⋊C4—24no—
196C2×(C2×D11)⋊C4C2311yescharacteristic
197C2×(C2×D11)⋊C4C2311yescharacteristic
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2311yescharacteristic
202C2×(C2×D11)⋊C4C2311yescharacteristic
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⋊Dic11C2312yes—
215C2×Dic11⋊C4—24no—
216C2×Dic11⋊C4C2311yescharacteristic
217C2×Dic11⋊C4C2311yescharacteristic
218C2×Dic11⋊C4C2311yescharacteristic
219C2×Dic11⋊C4C2311yescharacteristic
220C2×Dic11⋊C4C2312yes—
221C2×Dic11⋊C4C2312yes—
222C2×Dic11⋊C4C2311yescharacteristic
223C2×Dic11⋊C4C2311yescharacteristic
224C2×Dic11⋊C4C2312yes—
225C2×Dic11⋊C4C2312yes—
226C2×Dic11⋊C4C2312yes—
227C2×Dic11⋊C4C2312yes—
228C2×C4×Dic11D418yescomplemented
229C2×C4×Dic11C2311yescharacteristic
230C2×C4×Dic11C2312yes—
231C2×C4×Dic11C2312yes—
232C2×C4×Dic11C2312yes—
233C2×C4×Dic11C2312yes—
234C2×C4×Dic11C2312yes—
235C2×C4×Dic11C2311yescharacteristic
236C2×C4×Dic11C2311yescharacteristic
237C2×C4×Dic11C2311yescharacteristic
238C2×C4×Dic11C2311yescharacteristic
239#66951—24no—
240#66942—24no—
241#66939—24no—
242#66938—28no—
243#66938—24no—
244#66935—24no—
245#66932—24no—
246#66931—24no—
247#66930—24no—
248#66930—24no—
249C4×D44—44no—
250#66925—24no—
251C4×Dic22—24no—
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#34965—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—24no—
275C23×D11—22no—
276C23×D11—22no—
277C23×D11—42no—
278C23×D11C2411yescharacteristic
279C23×D11C2412yes—
280C2×D4×C11—22no—
281C2×D4×C11—22no—
282C2×D4×C11—24no—
283C2×D4×C11—22no—
284C2×D4×C11—24no—
285C2×D4×C11—42no—
286C22×C4×C11—24no—
287C22×C4×C11—22no—
288C22×C4×C11—22no—
289C22×C4×C11—24no—
290C22×C4×C11—24no—
291C22×C4×C11—24no—
292C22×C4×C11—24no—
293C22×C4×C11—24no—
294C22×C4×C11—42no—
295C22×C4×C11—42no—
296C22×C4×C11—42no—
297C22×C4×C11—416no—
298C22×C4×C11C2×D414yes—
299C22×C4×C11C2412yes—
300C22×C4×C11C2411yescharacteristic
301C22×C4×C11C2412yes—
302C22×C4×C11C2411yescharacteristic
303C22×C4×C11C2411yescharacteristic
304C22×C4×C11C2411yescharacteristic
305C22×C4×C11C2412yes—
306C22×C4×C11C2411yescharacteristic
307C2×C22⋊D11—232no—
308C2×C22⋊D11—24no—
309C2×C22⋊D11—24no—
310C2×C22⋊D11—22no—
311C2×C22⋊D11—24no—
312C2×C22⋊D11—24no—
313C2×C22⋊D11—24no—
314C2×C22⋊D11—24no—
315C2×C22⋊D11—22no—
316C2×C22⋊D11—24no—
317C2×C22⋊D11—22no—
318C2×C22⋊D11—24no—
319C2×C22⋊D11—22no—
320C2×C22⋊D11—24no—
321C2×C22⋊D11—24no—
322C2×C22⋊D11—42no—
323C2×C22⋊D11—42no—
324C2×C22⋊D11#4118yes—
325C22×Dic11—24no—
326C22×Dic11—22no—
327C22×Dic11—22no—
328C22×Dic11—22no—
329C22×Dic11—42no—
330C22×Dic11C2×D414yes—
331C22×Dic11C2×D414yes—
332C22×Dic11C2412yes—
333C22×Dic11C2411yescharacteristic
334C22×Dic11C2411yescharacteristic
335C22×Dic11C2412yes—
336C22×Dic11C2411yescharacteristic
337C22×Dic11C2411yescharacteristic
338C22×Dic11C2411yescharacteristic
339C22×Dic11C2411yescharacteristic
340C22×Dic11C2412yes—
341C22×Dic11C2411yescharacteristic
342C2×D44—24no—
343C2×D44—24no—
344C2×D44—42no—
345C2×C4×D11—22no—
346C2×C4×D11—24no—
347C2×C4×D11—24no—
348C2×C4×D11—24no—
349C2×C4×D11—24no—
350C2×C4×D11—24no—
351C2×C4×D11—42no—
352C2×C4×D11—42no—
353C2×C4×D11—416no—
354C2×Dic22—22no—
355C2×Dic22—24no—
356C11×C4⋊C4—22no—
357C11×C4⋊C4—42no—
358C11×C22⋊C4—22no—
359C11×C22⋊C4—22no—
360C11×C22⋊C4—24no—
361C11×C22⋊C4—22no—
362C11×C22⋊C4—24no—
363C11×C22⋊C4—42no—
364C11×C22⋊C4—42no—
365C11×C22⋊C4#4114yes—
366C42×C11—22no—
367C42×C11—24no—
368C22⋊Dic11—22no—
369C22⋊Dic11—22no—
370C22⋊Dic11—22no—
371C22⋊Dic11—24no—
372C22⋊Dic11—24no—
373C22⋊Dic11—24no—
374C22⋊Dic11—22no—
375C22⋊Dic11—22no—
376C22⋊Dic11—24no—
377C22⋊Dic11—42no—
378C22⋊Dic11—42no—
379C22⋊Dic11#4114yes—
380(C2×D11)⋊C4—22no—
381(C2×D11)⋊C4—22no—
382(C2×D11)⋊C4—22no—
383(C2×D11)⋊C4—24no—
384(C2×D11)⋊C4—24no—
385(C2×D11)⋊C4—24no—
386(C2×D11)⋊C4—24no—
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4—22no—
389(C2×D11)⋊C4—24no—
390(C2×D11)⋊C4—42no—
391(C2×D11)⋊C4—42no—
392(C2×D11)⋊C4—42no—
393(C2×D11)⋊C4—42no—
394C4⋊Dic11—22no—
395C4⋊Dic11—22no—
396C4⋊Dic11—22no—
397C4⋊Dic11—42no—
398Dic11⋊C4—22no—
399Dic11⋊C4—22no—
400Dic11⋊C4—22no—
401Dic11⋊C4—22no—
402Dic11⋊C4—22no—
403Dic11⋊C4—24no—
404Dic11⋊C4—24no—
405Dic11⋊C4—24no—
406Dic11⋊C4—22no—
407Dic11⋊C4—24no—
408Dic11⋊C4—42no—
409Dic11⋊C4—42no—
410C4×Dic11—24no—
411C4×Dic11—24no—
412C4×Dic11—24no—
413C4×Dic11—22no—
414C4×Dic11—24no—
415C4×Dic11—24no—
416C4×Dic11C2×D414yes—
417C4×Dic11C2×D414yes—
418C4×Dic11C2×D414yes—
419C4×Dic11C2×D414yes—
420C2×#529—111no—
421C22×C4×D4—111no—
422#2603—112no—
423#2603—112no—
424#2566—112no—
425#2544—112no—
426#2504—111no—
427#2502—111no—
428#2435—111no—
429#2433—111no—
430#2411—111no—
431#2411—111no—
432#2411—111no—
433#2411—111no—
434#2392—112no—
435#2392—112no—
436C4×#127—112no—
437C4×#124—112no—
438C4×#120—111no—
439C4×#120—111no—
440C4×#120—111no—
441C4×#120D1111yescharacteristic, complemented
442C4×#117—111no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—28no—
446C23×C11—22no—
447C23×C11—22no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11—22no—
451C23×C11—22no—
452C23×C11—21no—
453C23×C11—22no—
454C23×C11—21no—
455C23×C11—21no—
456C23×C11—22no—
457C23×C11—48no—
458C23×C11—48no—
459C23×C11—44no—
460C23×C11—44no—
461C23×C11C22×D412yes—
462C23×C11C2×#4112yes—
463C23×C11C2×#4114yes—
464C23×C11C2×#4112yes—
465C23×C11C2511yescharacteristic
466C22×D11—28no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—22no—
473C22×D11—21no—
474C22×D11—21no—
475C22×D11—22no—
476C22×D11—21no—
477C22×D11—22no—
478C22×D11—48no—
479C22×D11—48no—
480C22×D11—44no—
481C22×D11—44no—
482C22×D11C2×#4114yes—
483D4×C11—48no—
484D4×C11—44no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—28no—
489C2×C4×C11—21no—
490C2×C4×C11—22no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—21no—
496C2×C4×C11—22no—
497C2×C4×C11—21no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—48no—
503C2×C4×C11—44no—
504C2×C4×C11—44no—
505C2×C4×C11—48no—
506C2×C4×C11C22×D412yes—
507C2×C4×C11C22×D412yes—
508C2×C4×C11C2×#4114yes—
509C2×C4×C11H(5,𝔽2)14yes—
510C22⋊D11—216no—
511C22⋊D11—216no—
512C22⋊D11—48no—
513C22⋊D11—48no—
514C22⋊D11—44no—
515C22⋊D11—44no—
516C2×Dic11—28no—
517C2×Dic11—21no—
518C2×Dic11—21no—
519C2×Dic11—22no—
520C2×Dic11—21no—
521C2×Dic11—21no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—28no—
525C2×Dic11—21no—
526C2×Dic11—21no—
527C2×Dic11—21no—
528C2×Dic11—22no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—21no—
532C2×Dic11—22no—
533C2×Dic11—21no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—44no—
539C2×Dic11C22×D412yes—
540C2×Dic11C22×D412yes—
541C2×Dic11C22×D412yes—
542C2×Dic11C22×D412yes—
543C2×Dic11C2×#4114yes—
544C2×Dic11C2×#4114yes—
545D44—48no—
546C4×D11—48no—
547C4×D11—44no—
548C4×D11—48no—
549Dic22—44no—
550C23×D4—111no—
551C24×C4—111no—
552C24×C4C2×D1111yescharacteristic
553C2×#127—112no—
554#529—228no—
555C2×#126—111no—
556C2×#126—111no—
557C2×#125—111no—
558C2×#124—112no—
559C2×#124—111no—
560C2×#123—111no—
561C2×#123—111no—
562C2×C22⋊Q8—111no—
563C2×#121—111no—
564C2×#120—111no—
565C2×#120—111no—
566C2×#120—111no—
567C2×#120C2×D1111yescharacteristic
568C2×C4×Q8—111no—
569C2×C4×D4—111no—
570C2×C4×D4—112no—
571C2×C4×D4—112no—
572C2×C4×D4—112no—
573C2×C4×D4—112no—
574C2×C4×D4—111no—
575C2×C4×D4—112no—
576C2×C4×D4—112no—
577C2×C4×D4—112no—
578C2×C4×D4—228no—
579C2×C4×D4C2×D1111yescharacteristic
580C2×C4×D4C2×D1112yescomplemented
581C2×#117—111no—
582C2×#117—111no—
583C2×#117—111no—
584C2×#117—111no—
585C22×C4⋊C4—111no—
586C22×C22⋊C4—111no—
587C22×C22⋊C4—111no—
588C22×C42—111no—
589#398—112no—
590#398—112no—
591#397—112no—
592#397—112no—
593#396—112no—
594#396—112no—
595#396—112no—
596#396—112no—
597#394—112no—
598#394—112no—
599#394—112no—
600#394—112no—
601#394—112no—
602#394—112no—
603#392—112no—
604#392—112no—
605#391—112no—
606#390—112no—
607#390—112no—
608#390—112no—
609#390—112no—
610#390—112no—
611#390—112no—
612#390—112no—
613#388—112no—
614#388—112no—
615#388—112no—
616#388—112no—
617#386—111no—
618#386—112no—
619#386—111no—
620#386—112no—
621#386—111no—
622#386—112no—
623#386C2×D1111yescharacteristic
624#386C2×D1112yescomplemented
625#385—112no—
626#385—111no—
627#385—112no—
628#385—111no—
629#385—111no—
630#385—112no—
631#385C2×D1111yescharacteristic
632#385C2×D1112yescomplemented
633#384—112no—
634#382—112no—
635#379—111no—
636#379—111no—
637#379—111no—
638#379C2×D1111yescharacteristic
639C4×C4⋊C4—112no—
640C4×C4⋊C4—112no—
641C4×C22⋊C4—112no—
642C4×C22⋊C4—111no—
643C4×C22⋊C4—111no—
644C4×C22⋊C4—111no—
645C4×C22⋊C4—112no—
646C4×C22⋊C4—112no—
647C4×C22⋊C4C2×D1111yescharacteristic
648C4×C22⋊C4C2×D1112yescomplemented
649#376—112no—
650C43—112no—
651C22×C11—22no—
652C22×C11—22no—
653C22×C11—24no—
654C22×C11—24no—
655C22×C11—24no—
656C22×C11—24no—
657C22×C11—24no—
658C22×C11—416no—
659C22×C11—42no—
660C22×C11—42no—
661C22×C11—42no—
662C22×C11—42no—
663C22×C11—41no—
664C22×C11—41no—
665C22×C11—41no—
666C22×C11—42no—
667C22×C11—42no—
668C22×C11#53214yes—
669C22×C11C23×D411yescharacteristic
670C22×C11C22×#4111yescharacteristic
671C22×C11C22×#4112yes—
672C22×C11C22×#4111yescharacteristic
673C22×C11C2×H(5,𝔽2)12yes—
674C2×D11—24no—
675C2×D11—24no—
676C2×D11—24no—
677C2×D11—416no—
678C2×D11—42no—
679C2×D11—42no—
680C2×D11—42no—
681C2×D11—42no—
682C2×D11—41no—
683C2×D11—41no—
684C2×D11—41no—
685C2×D11—42no—
686C2×D11—42no—
687C4×C11—22no—
688C4×C11—24no—
689C4×C11—41no—
690C4×C11—41no—
691C4×C11—41no—
692C4×C11—42no—
693C4×C11—42no—
694C4×C11#53514yes—
695Dic11—22no—
696Dic11—22no—
697Dic11—22no—
698Dic11—24no—
699Dic11—41no—
700Dic11—41no—
701Dic11—42no—
702Dic11—41no—
703Dic11—42no—
704Dic11#52514yes—
705C25—111no—
706C25C22×D1111yescharacteristic
707C22×Q8—111no—
708C22×D4—112no—
709C22×D4—112no—
710C22×D4—111no—
711C22×D4—111no—
712C22×D4—112no—
713C22×D4—112no—
714C22×D4—112no—
715C22×D4—224no—
716C22×D4—228no—
717C22×D4C22×D1111yescharacteristic
718C22×D4C22×D1112yes—
719C23×C4—24no—
720C23×C4—44no—
721C23×C4—111no—
722C23×C4—111no—
723C23×C4—111no—
724C23×C4—111no—
725C23×C4—112no—
726C23×C4—112no—
727C23×C4—224no—
728C23×C4—444no—
729C23×C4C22×D1111yescharacteristic
730C23×C4C22×D1112yes—
731C23×C4C22×D1111yescharacteristic
732C23×C4C22×D1111yescharacteristic
733C23×C4C22×D1112yes—
734#127—228no—
735#126—224no—
736#126—224no—
737#125—224no—
738#124—224no—
739#124—228no—
740#123—224no—
741#123—224no—
742C22⋊Q8—224no—
743#121—224no—
744#120—24no—
745#120—224no—
746#120—224no—
747#120—224no—
748C4×Q8—224no—
749C4×D4—24no—
750C4×D4—44no—
751C4×D4—228no—
752C4×D4—228no—
753C4×D4—228no—
754C4×D4—228no—
755C4×D4—224no—
756C4×D4—224no—
757C4×D4—444no—
758C4×D4—444no—
759C4×D4—444no—
760#117—224no—
761#117—224no—
762#117—224no—
763#117—224no—
764C2×C4⋊C4—112no—
765C2×C4⋊C4—112no—
766C2×C4⋊C4—111no—
767C2×C4⋊C4—111no—
768C2×C4⋊C4—111no—
769C2×C4⋊C4—111no—
770C2×C4⋊C4—112no—
771C2×C4⋊C4—112no—
772C2×C4⋊C4—111no—
773C2×C4⋊C4—111no—
774C2×C4⋊C4—111no—
775C2×C4⋊C4—111no—
776C2×C4⋊C4—111no—
777C2×C4⋊C4—112no—
778C2×C4⋊C4—112no—
779C2×C4⋊C4—112no—
780C2×C4⋊C4—224no—
781C2×C4⋊C4C22×D1111yescharacteristic
782C2×C4⋊C4C22×D1112yes—
783C2×C22⋊C4—111no—
784C2×C22⋊C4—112no—
785C2×C22⋊C4—112no—
786C2×C22⋊C4—111no—
787C2×C22⋊C4—111no—
788C2×C22⋊C4—111no—
789C2×C22⋊C4—111no—
790C2×C22⋊C4—111no—
791C2×C22⋊C4—112no—
792C2×C22⋊C4—112no—
793C2×C22⋊C4—112no—
794C2×C22⋊C4—112no—
795C2×C22⋊C4—111no—
796C2×C22⋊C4—111no—
797C2×C22⋊C4—111no—
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—112no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—112no—
809C2×C22⋊C4—224no—
810C2×C22⋊C4—224no—
811C2×C22⋊C4C22×D1111yescharacteristic
812C2×C22⋊C4C22×D1111yescharacteristic
813C2×C22⋊C4C22×D1111yescharacteristic
814C2×C22⋊C4C22×D1112yes—
815C2×C22⋊C4C22×D1112yes—
816C2×C22⋊C4C22×D1112yes—
817C2×C22⋊C4C22×D1112yes—
818C2×C22⋊C4C22×D1111yescharacteristic
819C2×C42—118no—
820C2×C42—111no—
821C2×C42—111no—
822C2×C42—111no—
823C2×C42—111no—
824C2×C42—112no—
825C2×C42—112no—
826C2×C42—112no—
827C2×C42—112no—
828C2×C42—111no—
829C2×C42—112no—
830C2×C42C22×D1111yescharacteristic
831C2×C42C22×D1112yes—
832#95—112no—
833#95—112no—
834#95—112no—
835#95—112no—
836#95—112no—
837#95—112no—
838#95—112no—
839#95—112no—
840#95—112no—
841#95C22×D1112yes—
842#95C22×D1112yes—
843#95C22×D1112yes—
844C2×C11—24no—
845C2×C11—44no—
846C2×C11—81no—
847C2×C11C2×#52511yescharacteristic
848C2×C11C2×#53211yescharacteristic
849C2×C11C2×#53511yescharacteristic
850C2×C11#348112yes—
851C2×C11#348112yes—
852D11—44no—
853D11—81no—
854C24—22no—
855C24—24no—
856C24—22no—
857C24—22no—
858C24—42no—
859C24—112no—
860C24—111no—
861C24—224no—
862C24—222no—
863C24—222no—
864C24—222no—
865C24—442no—
866C24C23×D1111yescharacteristic
867C24C23×D1112yes—
868C24C23×D1111yescharacteristic
869C2×Q8—222no—
870C2×Q8—224no—
871C2×D4—22no—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—24no—
875C2×D4—24no—
876C2×D4—42no—
877C2×D4—118no—
878C2×D4—224no—
879C2×D4—224no—
880C2×D4—224no—
881C2×D4—224no—
882C2×D4—222no—
883C2×D4—224no—
884C2×D4—224no—
885C2×D4—224no—
886C2×D4—224no—
887C2×D4—2232no—
888C2×D4—224no—
889C2×D4—224no—
890C2×D4—222no—
891C2×D4—222no—
892C2×D4—222no—
893C2×D4—224no—
894C2×D4—224no—
895C2×D4—442no—
896C2×D4—442no—
897C2×D4—442no—
898C22×C4—24no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—24no—
902C22×C4—24no—
903C22×C4—24no—
904C22×C4—24no—
905C22×C4—24no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—416no—
910C22×C4—111no—
911C22×C4—114no—
912C22×C4—114no—
913C22×C4—112no—
914C22×C4—111no—
915C22×C4—111no—
916C22×C4—111no—
917C22×C4—112no—
918C22×C4—111no—
919C22×C4—111no—
920C22×C4—112no—
921C22×C4—111no—
922C22×C4—224no—
923C22×C4—222no—
924C22×C4—222no—
925C22×C4—222no—
926C22×C4—222no—
927C22×C4—224no—
928C22×C4—224no—
929C22×C4—224no—
930C22×C4—224no—
931C22×C4—224no—
932C22×C4—442no—
933C22×C4—442no—
934C22×C4—4416no—
935C22×C4—442no—
936C22×C4D4×D1114yes—
937C22×C4C23×D1112yes—
938C22×C4C23×D1111yescharacteristic
939C22×C4C23×D1111yescharacteristic
940C22×C4C23×D1112yes—
941C22×C4C23×D1111yescharacteristic
942C22×C4C23×D1112yes—
943C22×C4C23×D1111yescharacteristic
944C22×C4C23×D1111yescharacteristic
945C4⋊C4—22no—
946C4⋊C4—42no—
947C4⋊C4—224no—
948C4⋊C4—224no—
949C4⋊C4—222no—
950C4⋊C4—222no—
951C4⋊C4—222no—
952C4⋊C4—222no—
953C4⋊C4—224no—
954C4⋊C4—222no—
955C4⋊C4—222no—
956C4⋊C4—222no—
957C4⋊C4—222no—
958C4⋊C4—224no—
959C4⋊C4—222no—
960C4⋊C4—442no—
961C4⋊C4—442no—
962C4⋊C4—442no—
963C22⋊C4—22no—
964C22⋊C4—22no—
965C22⋊C4—24no—
966C22⋊C4—24no—
967C22⋊C4—22no—
968C22⋊C4—42no—
969C22⋊C4—42no—
970C22⋊C4—114no—
971C22⋊C4—224no—
972C22⋊C4—224no—
973C22⋊C4—222no—
974C22⋊C4—222no—
975C22⋊C4—222no—
976C22⋊C4—224no—
977C22⋊C4—224no—
978C22⋊C4—224no—
979C22⋊C4—224no—
980C22⋊C4—224no—
981C22⋊C4—222no—
982C22⋊C4—222no—
983C22⋊C4—222no—
984C22⋊C4—224no—
985C22⋊C4—222no—
986C22⋊C4—222no—
987C22⋊C4—224no—
988C22⋊C4—224no—
989C22⋊C4—222no—
990C22⋊C4—442no—
991C22⋊C4—442no—
992C22⋊C4—442no—
993C22⋊C4—442no—
994C22⋊C4—442no—
995C22⋊C4—442no—
996C22⋊C4#433914yes—
997C42—22no—
998C42—24no—
999C42—114no—
1000C42—114no—
1001C42—114no—
1002C42—114no—
1003C42—224no—
1004C42—224no—
1005C42—224no—
1006C42—224no—
1007C42—222no—
1008C42—224no—
1009C11#3496511yescharacteristic, complemented, Sylow
1010C23—22no—
1011C23—22no—
1012C23—28no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—21no—
1020C23—21no—
1021C23—22no—
1022C23—21no—
1023C23—22no—
1024C23—48no—
1025C23—48no—
1026C23—44no—
1027C23—44no—
1028C23—114no—
1029C23—228no—
1030C23—222no—
1031C23—222no—
1032C23—222no—
1033C23—222no—
1034C23—222no—
1035C23—222no—
1036C23—221no—
1037C23—221no—
1038C23—222no—
1039C23—221no—
1040C23—222no—
1041C23—448no—
1042C23—448no—
1043C23—444no—
1044C23—444no—
1045C23C2×#433912yes—
1046C23C2×D4×D1112yes—
1047C23#41×D1114yes—
1048C23#41×D1112yes—
1049C23C24×D1111yescharacteristic
1050Q8—444no—
1051D4—48no—
1052D4—44no—
1053D4—2216no—
1054D4—2216no—
1055D4—448no—
1056D4—444no—
1057D4—448no—
1058D4—448no—
1059D4—444no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—28no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—21no—
1077C2×C4—48no—
1078C2×C4—44no—
1079C2×C4—44no—
1080C2×C4—48no—
1081C2×C4—112no—
1082C2×C4—114no—
1083C2×C4—112no—
1084C2×C4—112no—
1085C2×C4—112no—
1086C2×C4—114no—
1087C2×C4—228no—
1088C2×C4—228no—
1089C2×C4—221no—
1090C2×C4—221no—
1091C2×C4—222no—
1092C2×C4—221no—
1093C2×C4—222no—
1094C2×C4—221no—
1095C2×C4—222no—
1096C2×C4—222no—
1097C2×C4—221no—
1098C2×C4—221no—
1099C2×C4—221no—
1100C2×C4—221no—
1101C2×C4—222no—
1102C2×C4—222no—
1103C2×C4—222no—
1104C2×C4—222no—
1105C2×C4—222no—
1106C2×C4—222no—
1107C2×C4—221no—
1108C2×C4—222no—
1109C2×C4—448no—
1110C2×C4—444no—
1111C2×C4—448no—
1112C2×C4—444no—
1113C2×C4C2×#433914yes—
1114C2×C4C2×D4×D1112yes—
1115C2×C4C2×D4×D1112yes—
1116C2×C4#6703714yes—
1117C22—22no—
1118C22—24no—
1119C22—24no—
1120C22—22no—
1121C22—24no—
1122C22—24no—
1123C22—24no—
1124C22—416no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—41no—
1130C22—41no—
1131C22—42no—
1132C22—42no—
1133C22—41no—
1134C22—224no—
1135C22—224no—
1136C22—224no—
1137C22—4416no—
1138C22—442no—
1139C22—442no—
1140C22—442no—
1141C22—442no—
1142C22—441no—
1143C22—441no—
1144C22—442no—
1145C22—442no—
1146C22—441no—
1147C22#1062307914yes—
1148C22C22×#433911yescharacteristic
1149C22C22×D4×D1111yescharacteristic
1150C22C2×#6703712yes—
1151C22C2×#41×D1111yescharacteristic
1152C22C2×#41×D1112yes—
1153C4—22no—
1154C4—24no—
1155C4—41no—
1156C4—42no—
1157C4—41no—
1158C4—42no—
1159C4—41no—
1160C4—114no—
1161C4—222no—
1162C4—222no—
1163C4—224no—
1164C4—222no—
1165C4—441no—
1166C4—442no—
1167C4—441no—
1168C4—442no—
1169C4—441no—
1170C4#1062312314yes—
1171C2—24no—
1172C2—44no—
1173C2—81no—
1174C2—444no—
1175C2—881no—
1176C2D11×#52511yescharacteristic
1177C2C2×#1062307911yescharacteristic
1178C2C2×#1062312311yescharacteristic
1179C2#1308221812yes—
1180C2#1308222012yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC4×C11×#120C2
prime radical#13072251C2
hypercenterC4×#120D11
hypocenterC11#34965
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×#10623069C2semidirect
2. C22×C4×C22⋊D11C2semidirect
3. #13074242C2semidirect
4. #13074240C2semidirect
5. #13073814C2semidirect
6. #13073585C2semidirect
7. #13073106C2semidirect
8. #13073092C2semidirect
9. #13072265C2semidirect
11. #13072004C2semidirect
12. #13072003C2semidirect
13. #13071999C2semidirect
14. #13071997C2semidirect
15. #13071860C2semidirect
16. #13071858C2semidirect
17. C4×#66993C2semidirect
18. C4×#66938C2semidirect
19. C4×#66935C2semidirect
20. C4×#67006C2semidirect
21. C4×#66990C2semidirect
22. C4×#66930C2semidirect
23. C4×C11×#120C2semidirect
29. C2×C4×D4×C11C22semidirect
42. C2×C4×C22⋊D11C22semidirect
43. C2×C4×C22⋊D11C22semidirect
44. C2×C4×C22⋊D11C22semidirect
46. C2×#66979C22semidirect
50. C2×#66951C22semidirect
51. C2×#66942C22semidirect
54. C2×#66938C22semidirect
56. C2×#66932C22semidirect
60. C2×C4×D44C22semidirect
61. C2×#66925C22semidirect
62. C2×C4×Dic22C22semidirect
64. C11×#386C22semidirect
66. C11×#385C22semidirect
69. C4×C11×C22⋊C4C22semidirect
72. #10622835C22semidirect
73. #10622834C22semidirect
76. #10622826C22semidirect
78. #10622823C22semidirect
80. C4×C22⋊Dic11C22semidirect
81. #10622607C22semidirect
82. #10622602C22semidirect
83. #10622601C22semidirect
84. #10622597C22semidirect
85. #10622589C22semidirect
89. #10622572C22semidirect
90. #10622572C22semidirect
94. #10622570C22semidirect
95. #10622570C22semidirect
96. #10622570C22semidirect
97. #10622569C22semidirect
100. #10622565C22semidirect
101. #10622564C22semidirect
103. #10622561C22semidirect
104. #10622561C22semidirect
106. #10622557C22semidirect
109. C4×(C2×D11)⋊C4C22semidirect
110. C4×(C2×D11)⋊C4C22semidirect
111. C4×Dic11⋊C4C22semidirect
112. C42×Dic11C22semidirect
113. #10622289C22semidirect
114. #10622288C22semidirect
115. #10622285C22semidirect
116. #10622283C22semidirect
117. #10622282C22semidirect
118. #10622281C22semidirect
119. #10622278C22semidirect
120. #10622270C22semidirect
121. #10622263C22semidirect
122. #10622262C22semidirect
123. #10622261C22semidirect
124. #10622259C22semidirect
228. C2×C4×Dic11D4semidirect
441. C4×#120D11semidirect
580. C2×C4×D4C2×D11semidirect
624. #386C2×D11semidirect
632. #385C2×D11semidirect
648. C4×C22⋊C4C2×D11semidirect
1009. C11#34965semidirect

Maximal subgroups

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

subgroupindex
C2×#106230692
C22×C4×C22⋊D112
#130742422
#130742402
#130738142
#130735852
#130731062
#130730922
#130722652
#130722512
#130720042
#130720032
#130719992
#130719972
#130718602
#130718582
C4×#669932
C4×#669382
C4×#669352
C4×#670062
C4×#669902
C4×#669302
C4×C11×#1202
#3496511