Finite Group Databasebeta

← #14914086

Subgroups — #14914086

Order 2816.

3246 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic
2C2×#10623054C211yesmaximal, characteristic, complemented
3#13071608C214yesmaximal, complemented
4#13071595C214yesmaximal, complemented
5#13071566C212yesmaximal, complemented
6#13071546C212yesmaximal, complemented
7#13071541C212yesmaximal, complemented
8C4⋊C4×C22⋊D11C212yesmaximal, complemented
9#13071309C212yesmaximal, complemented
10#13071298C212yesmaximal, complemented
11#13071236C211yesmaximal, characteristic, complemented
12#13071204C211yesmaximal, characteristic, complemented
13C4×#66977C212yesmaximal, complemented
14C4×#66983C212yesmaximal, complemented
15C2×#10622825C211yesmaximal, characteristic, complemented
16#13070972C211yesmaximal, characteristic, complemented
17C22×C11×#117C211yesmaximal, characteristic, complemented
18C24×C4×C11C2211yescharacteristic
19C22×#4339C2211yescharacteristic
20C2×C11×#117—28no—
21C2×C11×#117C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C2×C11×#117C2212yes—
24C2×C11×#117C2211yescharacteristic
25C2×C11×#117C2212yes—
26C2×C11×#117C2211yescharacteristic
27C22×C11×C4⋊C4C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2212yes—
30C22×C42×C11C2212yes—
31C2×#67006C2212yes—
32C22×C22⋊Dic11C2212yes—
33#10623322C4116yescomplemented
34C2×#66983C2211yescharacteristic
35C2×#66983C2211yescharacteristic
36C2×#66982C2212yes—
37C2×C4×C22⋊D11C2214yes—
38C2×C4×C22⋊D11C2212yes—
39C2×C4×C22⋊D11C2212yes—
40C2×#66979C2211yescharacteristic
41C22×C4⋊Dic11C2211yescharacteristic
42C22×C4⋊Dic11C2211yescharacteristic
43C2×#66977C2211yescharacteristic
44C2×#66977C2211yescharacteristic
45#10623054—28no—
46C2×#66945C2212yescomplemented
47C2×C4⋊C4×D11C2212yescomplemented
48C2×(C22⋊D11)⋊C4C2214yes—
49C2×C4×D44C2212yescomplemented
50C2×C4×Dic22C2212yescomplemented
51#10622826C2214yes—
52#10622825C2212yes—
53#10622825C2212yes—
54#10622825C2212yes—
55#10622825C2212yes—
56#10622823C2214yes—
57C4×C22⋊Dic11C2214yes—
58C2×C11⋊#95C2212yes—
59#10622603C2214yescomplemented
60#10622602C2214yescomplemented
61#10622600C2212yescomplemented
62#10622600C2212yescomplemented
63#10622591C2214yescomplemented
64#10622590C2212yescomplemented
65#10622589C2212yescomplemented
66C4⋊C4×Dic11C2212yescomplemented
67C4⋊C4×Dic11C2212yescomplemented
68#10622585C2214yescomplemented
69#10622571C2214yes—
70#10622570C2214yes—
71#10622569C2214yes—
72#10622559C2214yes—
73#10622558C2214yes—
74#10622557C2214yes—
75C22⋊C4×Dic11C2214yes—
76#10622553C2214yescomplemented
77#10622552C2212yescomplemented
78C4×(C2×D11)⋊C4C2214yescomplemented
79C4×C4⋊Dic11C2212yescomplemented
80C4×C4⋊Dic11C2212yescomplemented
81#10622546C2214yescomplemented
82C4×Dic11⋊C4C2214yescomplemented
83#10622542C2212yescomplemented
84#10622541C2212yescomplemented
85#10622541C2212yescomplemented
86C25×C11C2311yescharacteristic
87C23×C4×C11—24no—
88C23×C4×C11—24no—
89C23×C4×C11C2×C418yescomplemented
90C23×C4×C11C2312yes—
91C23×C4×C11C2312yes—
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2311yescharacteristic
97C23×C4×C11C2311yescharacteristic
98C22×C22⋊D11C2312yes—
99C22×C22⋊D11C2312yes—
100C22×C22⋊D11C2312yes—
101C23×Dic11C2312yes—
102C23×Dic11C2312yes—
103C2×#4339—24no—
104C2×#4339—24no—
105C2×#4339C2×C418yescomplemented
106C22×D44C2311yescharacteristic
107C22×C4×D11C2312yes—
108C22×C4×D11C2314yes—
109C22×Dic22C2311yescharacteristic
110C11×#117—24no—
111C11×#117—24no—
112C11×#117—24no—
113C11×#117—28no—
114C11×#117—28no—
115C11×#117D418yescomplemented
116C2×C11×C4⋊C4—24no—
117C2×C11×C4⋊C4—24no—
118C2×C11×C4⋊C4C2312yes—
119C2×C11×C4⋊C4C2311yescharacteristic
120C2×C11×C4⋊C4C2311yescharacteristic
121C2×C11×C4⋊C4C2312yes—
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C4⋊C4C2311yescharacteristic
124C2×C11×C22⋊C4—28no—
125C2×C11×C22⋊C4C2312yes—
126C2×C11×C22⋊C4C2312yes—
127C2×C11×C22⋊C4C2312yes—
128C2×C11×C22⋊C4C2312yes—
129C2×C42×C11—28no—
130C2×C42×C11C2312yes—
131C2×C42×C11C2312yes—
132C2×C42×C11C2312yes—
133C2×C42×C11C2312yes—
134#67006C2×C4116yescomplemented
135C2×C22⋊Dic11—44no—
136C2×C22⋊Dic11C2314yes—
137C2×C22⋊Dic11C2314yes—
138C2×C22⋊Dic11C2312yes—
139C2×C22⋊Dic11C2312yes—
140C2×C22⋊Dic11C2312yes—
141#66983C2×C418yescomplemented
142#66983C2×C418yescomplemented
143#66982C2×C4116yescomplemented
144C4×C22⋊D11—48no—
145C4×C22⋊D11C2×C4116yescomplemented
146C4×C22⋊D11C2×C4116yescomplemented
147C2×(C2×D11)⋊C4C2314yes—
148C2×(C2×D11)⋊C4C2314yes—
149C2×(C2×D11)⋊C4C2314yes—
150C2×(C2×D11)⋊C4C2312yes—
151C2×(C2×D11)⋊C4C2312yes—
152#66979C2×C418yescomplemented
153C2×C4⋊Dic11—24no—
154C2×C4⋊Dic11—24no—
155C2×C4⋊Dic11C2312yes—
156C2×C4⋊Dic11C2312yes—
157C2×C4⋊Dic11C2312yes—
158C2×C4⋊Dic11C2312yes—
159C2×C4⋊Dic11C2311yescharacteristic
160C2×C4⋊Dic11C2311yescharacteristic
161#66977C2×C418yescomplemented
162#66977C2×C418yescomplemented
163C2×Dic11⋊C4C2314yes—
164C2×Dic11⋊C4C2314yes—
165C2×Dic11⋊C4C2314yes—
166C2×Dic11⋊C4C2312yes—
167C2×Dic11⋊C4C2312yes—
168C2×C4×Dic11C2314yes—
169C2×C4×Dic11C2314yes—
170C2×C4×Dic11C2314yes—
171C2×C4×Dic11C2312yes—
172#66945—28no—
173C4⋊C4×D11—28no—
174(C22⋊D11)⋊C4—216no—
175C4×D44—28no—
176C4×Dic22—28no—
177C11⋊#95C2314yes—
178C11⋊#95C2314yes—
179C11⋊#95C2314yes—
180C11⋊#95C2314yes—
181C11⋊#95C2314yes—
182C11⋊#95C2314yes—
183C11⋊#95C2314yes—
184C11⋊#95C2314yes—
185#34202—111nomaximal, Sylow
186C24×C11—22no—
187C24×C11—22no—
188C24×C11—22no—
189C24×C11—22no—
190C24×C11—41no—
191C24×C11—41no—
192C24×C11C22×C414yes—
193C24×C11C2411yescharacteristic
194C24×C11C2411yescharacteristic
195C24×C11C2411yescharacteristic
196C23×D11C2412yes—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—232no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—24no—
209C22×C4×C11—24no—
210C22×C4×C11—24no—
211C22×C4×C11—24no—
212C22×C4×C11—42no—
213C22×C4×C11—42no—
214C22×C4×C11C22×C414yes—
215C22×C4×C11C22×C414yes—
216C22×C4×C11C22×C414yes—
217C22×C4×C11C22×C414yes—
218C22×C4×C11C22×C414yes—
219C22×C4×C11C22×C414yes—
220C22×C4×C11C2×D414yes—
221C22×C4×C11#4114yes—
222C22×C4×C11C2412yes—
223C22×C4×C11C2412yes—
224C22×C4×C11C2411yescharacteristic
225C22×C4×C11C2411yescharacteristic
226C22×C4×C11C2412yes—
227C22×C4×C11C2412yes—
228C22×C4×C11C2411yescharacteristic
229C22×C4×C11C2411yescharacteristic
230C2×C22⋊D11—24no—
231C2×C22⋊D11—24no—
232C2×C22⋊D11—24no—
233C2×C22⋊D11—24no—
234C2×C22⋊D11—42no—
235C2×C22⋊D11—42no—
236C2×C22⋊D11C22×C418yes—
237C2×C22⋊D11C22×C418yes—
238C2×C22⋊D11C22×C418yes—
239C22×Dic11—24no—
240C22×Dic11—24no—
241C22×Dic11—42no—
242C22×Dic11—42no—
243C22×Dic11—42no—
244C22×Dic11—42no—
245C22×Dic11C2414yes—
246C22×Dic11C2414yes—
247C22×Dic11C2412yes—
248C22×Dic11C2412yes—
249C22×Dic11C2412yes—
250#4339—232no—
251C2×D44—22no—
252C2×D44—22no—
253C2×D44C22×C414yes—
254C2×C4×D11—24no—
255C2×C4×D11—28no—
256C2×C4×D11—24no—
257C2×C4×D11—44no—
258C2×C4×D11—44no—
259C2×C4×D11C22×C418yes—
260C2×Dic22—22no—
261C2×Dic22—22no—
262C2×Dic22C22×C414yes—
263C11×C4⋊C4—24no—
264C11×C4⋊C4—24no—
265C11×C4⋊C4—22no—
266C11×C4⋊C4—22no—
267C11×C4⋊C4C2×D414yes—
268C11×C4⋊C4C2×D414yes—
269C11×C22⋊C4—24no—
270C11×C22⋊C4—24no—
271C11×C22⋊C4—24no—
272C11×C22⋊C4C2×D418yes—
273C42×C11—24no—
274C42×C11—24no—
275C42×C11—24no—
276C42×C11C2×D418yes—
277C22⋊Dic11—28no—
278C22⋊Dic11—44no—
279C22⋊Dic11C22×C418yes—
280C22⋊Dic11C22×C418yes—
281C22⋊Dic11C22×C418yes—
282(C2×D11)⋊C4—28no—
283(C2×D11)⋊C4—44no—
284(C2×D11)⋊C4—44no—
285(C2×D11)⋊C4C22×C418yes—
286(C2×D11)⋊C4C22×C418yes—
287C4⋊Dic11—24no—
288C4⋊Dic11—24no—
289C4⋊Dic11—24no—
290C4⋊Dic11—24no—
291C4⋊Dic11C22×C414yes—
292C4⋊Dic11C22×C414yes—
293Dic11⋊C4—28no—
294Dic11⋊C4—44no—
295Dic11⋊C4—44no—
296Dic11⋊C4C22×C418yes—
297Dic11⋊C4C22×C418yes—
298C4×Dic11—28no—
299C4×Dic11—44no—
300C4×Dic11—44no—
301C4×Dic11C22×C418yes—
302C2×#525—111no—
303C2×#520—111no—
304C22×#117D1111yescharacteristic, complemented
305#2359—114no—
306#2358—114no—
307#2354—112no—
308#2352—112no—
309#2352—112no—
310D4×C4⋊C4—112no—
311#2324—112no—
312#2323—112no—
313#2317—111no—
314#2311—111no—
315C4×C22⋊Q8—112no—
316C4×#121—112no—
317C2×#380—111no—
318#2274—111no—
319C23×C11—21no—
320C23×C11—21no—
321C23×C11—21no—
322C23×C11—21no—
323C23×C11—21no—
324C23×C11—21no—
325C23×C11—21no—
326C23×C11—21no—
327C23×C11—28no—
328C23×C11—28no—
329C23×C11—21no—
330C23×C11—21no—
331C23×C11—21no—
332C23×C11—21no—
333C23×C11—21no—
334C23×C11—21no—
335C23×C11—44no—
336C23×C11—44no—
337C23×C11—44no—
338C23×C11—44no—
339C23×C11—44no—
340C23×C11C23×C412yes—
341C23×C11C23×C412yes—
342C23×C11C23×C412yes—
343C23×C11C22×D412yes—
344C23×C11C2×#4112yes—
345C23×C11H(5,𝔽2)12yes—
346C23×C112−1+412yes—
347C23×C11C2511yescharacteristic
348C22×D11—22no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11C23×C414yes—
355C2×C4×C11—28no—
356C2×C4×C11—21no—
357C2×C4×C11—21no—
358C2×C4×C11—21no—
359C2×C4×C11—21no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—28no—
365C2×C4×C11—28no—
366C2×C4×C11—28no—
367C2×C4×C11—28no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—48no—
375C2×C4×C11—48no—
376C2×C4×C11C4×D4116yescomplemented
377C2×C4×C11C23×C412yes—
378C2×C4×C11C23×C412yes—
379C2×C4×C11C23×C412yes—
380C2×C4×C11C23×C412yes—
381C2×C4×C11C22×D414yes—
382C2×C4×C11C22×D414yes—
383C2×C4×C11C22×D412yes—
384C2×C4×C11C22×D412yes—
385C2×C4×C11C2×#4112yes—
386C2×C4×C11C2×#4112yes—
387C22⋊D11—216no—
388C22⋊D11—216no—
389C22⋊D11—48no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—24no—
397C2×Dic11—24no—
398C2×Dic11—24no—
399C2×Dic11—24no—
400C2×Dic11—24no—
401C2×Dic11—24no—
402C2×Dic11—84no—
403C2×Dic11—84no—
404C2×Dic11C23×C414yes—
405C2×Dic11C23×C414yes—
406C2×Dic11C23×C414yes—
407D44—28no—
408C4×D11—216no—
409C4×D11—88no—
410Dic22—28no—
411C22×#41—111no—
412C24×C4C2×D1111yescharacteristic
413#525—1116no—
414C2×#123—112no—
415C2×C22⋊Q8—111no—
416C2×C22⋊Q8—111no—
417C2×#121—111no—
418C2×#121—111no—
419C2×#120—112no—
420#520—228no—
421C2×C4×Q8—112no—
422C2×C4×D4—112no—
423C2×C4×D4—112no—
424C2×C4×D4—114no—
425C2×C4×D4—114no—
426C2×C4×D4—112no—
427C2×#117—28no—
428C2×#117—111no—
429C2×#117—112no—
430C2×#117C2×D1111yescharacteristic
431C2×#117C2×D1112yes—
432C2×#117C2×D1111yescharacteristic
433C2×#117C2×D1111yescharacteristic
434C2×#117C2×D1112yes—
435C2×#117C2×D1111yescharacteristic
436C22×C4⋊C4—111no—
437C22×C4⋊C4—111no—
438C22×C4⋊C4—112no—
439C22×C4⋊C4C2×D1111yescharacteristic
440C22×C4⋊C4C2×D1111yescharacteristic
441C22×C22⋊C4—112no—
442C22×C22⋊C4C2×D1112yes—
443C22×C42C2×D1112yes—
444#391—112no—
445#390—114no—
446#390—112no—
447#389—114no—
448#389—112no—
449#389—112no—
450#388—114no—
451#388—114no—
452#388—114no—
453#388—114no—
454#387—114no—
455#387—114no—
456#386—114no—
457#386—114no—
458#386—114no—
459#385—114no—
460#385—114no—
461#385—114no—
462#384—112no—
463#382—112no—
464#380—112no—
465#380—112no—
466#380—112no—
467#380—112no—
468#380—112no—
469#380—112no—
470C4×C4⋊C4—112no—
471C4×C4⋊C4—112no—
472C4×C4⋊C4—112no—
473C4×C4⋊C4—112no—
474C4×C4⋊C4—114no—
475C4×C22⋊C4—114no—
476C4×C22⋊C4—114no—
477C4×C22⋊C4—114no—
478C2×#95—112no—
479C22×C11—22no—
480C22×C11—22no—
481C22×C11—22no—
482C22×C11—22no—
483C22×C11—22no—
484C22×C11—22no—
485C22×C11—22no—
486C22×C11—22no—
487C22×C11—22no—
488C22×C11—22no—
489C22×C11—22no—
490C22×C11—22no—
491C22×C11—22no—
492C22×C11—22no—
493C22×C11—22no—
494C22×C11—416no—
495C22×C11—41no—
496C22×C11—41no—
497C22×C11—41no—
498C22×C11—41no—
499C22×C11C2×C4×D414yes—
500C22×C11#52014yescomplemented
501C22×C11C24×C411yescharacteristic
502C22×C11C23×D411yescharacteristic
503C22×C11C22×#4111yescharacteristic
504C22×C11C2×H(5,𝔽2)11yescharacteristic
505C22×C11C2×2−1+411yescharacteristic
506C22×C11#58511yescharacteristic
507C22×C11#58511yescharacteristic
508C2×D11—24no—
509C2×D11—24no—
510C2×D11—24no—
511C2×D11—42no—
512C2×D11—42no—
513C2×D11—42no—
514C2×D11—42no—
515C4×C11—22no—
516C4×C11—22no—
517C4×C11—24no—
518C4×C11—24no—
519C4×C11—42no—
520C4×C11—42no—
521C4×C11C2×C4×D414yes—
522C4×C11C2×C4×D414yes—
523Dic11—24no—
524Dic11—24no—
525Dic11—24no—
526Dic11—44no—
527Dic11—44no—
528C25C22×D1111yescharacteristic
529C2×#41—118no—
530C2×#41—224no—
531C2×#41—224no—
532C22×Q8—111no—
533C22×D4—112no—
534C22×D4—112no—
535C22×D4—112no—
536C22×D4—111no—
537C23×C4—24no—
538C23×C4—24no—
539C23×C4—112no—
540C23×C4—112no—
541C23×C4—112no—
542C23×C4—114no—
543C23×C4C4×D1118yescomplemented
544C23×C4C22×D1112yes—
545C23×C4C22×D1112yes—
546C23×C4C22×D1111yescharacteristic
547C23×C4C22×D1111yescharacteristic
548C23×C4C22×D1111yescharacteristic
549C23×C4C22×D1111yescharacteristic
550C23×C4C22×D1111yescharacteristic
551C23×C4C22×D1111yescharacteristic
552#123—1116no—
553C22⋊Q8—118no—
554C22⋊Q8—118no—
555#121—118no—
556#121—118no—
557#120—1116no—
558C4×Q8—228no—
559C4×D4—1116no—
560C4×D4—1116no—
561C4×D4—2216no—
562C4×D4—228no—
563C4×D4—448no—
564#117—24no—
565#117—24no—
566#117—24no—
567#117—28no—
568#117—28no—
569#117—118no—
570#117—228no—
571#117C22⋊D1118yescomplemented
572C2×C4⋊C4—24no—
573C2×C4⋊C4—24no—
574C2×C4⋊C4—111no—
575C2×C4⋊C4—111no—
576C2×C4⋊C4—112no—
577C2×C4⋊C4—112no—
578C2×C4⋊C4—112no—
579C2×C4⋊C4—112no—
580C2×C4⋊C4—114no—
581C2×C4⋊C4—112no—
582C2×C4⋊C4—112no—
583C2×C4⋊C4—114no—
584C2×C4⋊C4—114no—
585C2×C4⋊C4—224no—
586C2×C4⋊C4—224no—
587C2×C4⋊C4—228no—
588C2×C4⋊C4C22×D1111yescharacteristic
589C2×C4⋊C4C22×D1111yescharacteristic
590C2×C4⋊C4C22×D1112yes—
591C2×C4⋊C4C22×D1112yes—
592C2×C4⋊C4C22×D1111yescharacteristic
593C2×C4⋊C4C22×D1111yescharacteristic
594C2×C22⋊C4—28no—
595C2×C22⋊C4—112no—
596C2×C22⋊C4—112no—
597C2×C22⋊C4—112no—
598C2×C22⋊C4—112no—
599C2×C22⋊C4—112no—
600C2×C22⋊C4—114no—
601C2×C22⋊C4—114no—
602C2×C22⋊C4—114no—
603C2×C22⋊C4—114no—
604C2×C22⋊C4—114no—
605C2×C22⋊C4—444no—
606C2×C22⋊C4C22×D1112yes—
607C2×C22⋊C4C22×D1112yes—
608C2×C22⋊C4C22×D1112yes—
609C2×C22⋊C4C22×D1112yes—
610C2×C42—28no—
611C2×C42—112no—
612C2×C42—114no—
613C2×C42—114no—
614C2×C42—114no—
615C2×C42C22×D1112yes—
616C2×C42C22×D1112yes—
617C2×C42C22×D1112yes—
618C2×C42C22×D1112yes—
619#95—114no—
620#95—114no—
621#95—114no—
622#95—114no—
623#95—114no—
624#95—114no—
625#95—114no—
626#95—114no—
627C2×C11—24no—
628C2×C11—24no—
629C2×C11—42no—
630C2×C11C22×C4×D411yescharacteristic
631C2×C11C2×#52011yescharacteristic
632C2×C11#342811yescharacteristic
633C2×C11#348811yescharacteristic
634C2×C11#348911yescharacteristic
635C2×C11#349411yescharacteristic
636C2×C11#349511yescharacteristic
637D11—44no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—41no—
643C24—41no—
644C24—112no—
645C24C2×C4×D1114yes—
646C24C23×D1111yescharacteristic
647C24C23×D1111yescharacteristic
648C24C23×D1111yescharacteristic
649#41—2232no—
650C2×Q8—114no—
651C2×Q8—222no—
652C2×Q8—222no—
653C2×D4—118no—
654C2×D4—118no—
655C2×D4—118no—
656C2×D4—114no—
657C2×D4—224no—
658C2×D4—224no—
659C2×D4—224no—
660C2×D4—224no—
661C2×D4—222no—
662C2×D4—222no—
663C2×D4—442no—
664C2×D4—442no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—232no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—24no—
677C22×C4—24no—
678C22×C4—24no—
679C22×C4—24no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—112no—
683C22×C4—112no—
684C22×C4—112no—
685C22×C4—118no—
686C22×C4—114no—
687C22×C4—114no—
688C22×C4—224no—
689C22×C4—224no—
690C22×C4—224no—
691C22×C4—224no—
692C22×C4—228no—
693C22×C4—444no—
694C22×C4—444no—
695C22×C4—442no—
696C22×C4—442no—
697C22×C4—442no—
698C22×C4—442no—
699C22×C4C2×C4×D1114yes—
700C22×C4C2×C4×D1114yes—
701C22×C4C2×C4×D1114yes—
702C22×C4C2×C4×D1114yes—
703C22×C4C2×C4×D1114yes—
704C22×C4C2×C4×D1114yes—
705C22×C4#433914yes—
706C22×C4C2×C22⋊D1114yes—
707C22×C4C23×D1112yes—
708C22×C4C23×D1112yes—
709C22×C4C23×D1111yescharacteristic
710C22×C4C23×D1111yescharacteristic
711C22×C4C23×D1112yes—
712C22×C4C23×D1112yes—
713C22×C4C23×D1111yescharacteristic
714C22×C4C23×D1111yescharacteristic
715C4⋊C4—24no—
716C4⋊C4—24no—
717C4⋊C4—22no—
718C4⋊C4—22no—
719C4⋊C4—114no—
720C4⋊C4—114no—
721C4⋊C4—118no—
722C4⋊C4—118no—
723C4⋊C4—224no—
724C4⋊C4—224no—
725C4⋊C4—224no—
726C4⋊C4—228no—
727C4⋊C4—224no—
728C4⋊C4—444no—
729C4⋊C4—444no—
730C4⋊C4C2×C22⋊D1114yes—
731C4⋊C4C2×C22⋊D1114yes—
732C22⋊C4—24no—
733C22⋊C4—24no—
734C22⋊C4—24no—
735C22⋊C4—118no—
736C22⋊C4—118no—
737C22⋊C4—118no—
738C22⋊C4—118no—
739C22⋊C4—118no—
740C22⋊C4—228no—
741C22⋊C4—228no—
742C22⋊C4—444no—
743C22⋊C4—444no—
744C22⋊C4—444no—
745C22⋊C4C2×C22⋊D1118yes—
746C42—24no—
747C42—24no—
748C42—24no—
749C42—118no—
750C42—228no—
751C42—444no—
752C42—444no—
753C42C2×C22⋊D1118yes—
754C11#3420211yescharacteristic, complemented, Sylow
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—28no—
764C23—28no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—44no—
772C23—44no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—114no—
777C23—222no—
778C23—222no—
779C23—222no—
780C23—222no—
781C23—222no—
782C23—222no—
783C23C22×C4×D1112yes—
784C23C22×C4×D1112yes—
785C23C22×C4×D1112yes—
786C23C2×#433912yes—
787C23#6704212yes—
788C23#6704312yes—
789C23C22×C22⋊D1112yes—
790C23C24×D1111yescharacteristic
791Q8—228no—
792D4—2216no—
793D4—2216no—
794D4—228no—
795D4—448no—
796C2×C4—28no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—28no—
806C2×C4—28no—
807C2×C4—28no—
808C2×C4—28no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—48no—
816C2×C4—48no—
817C2×C4—114no—
818C2×C4—114no—
819C2×C4—114no—
820C2×C4—222no—
821C2×C4—222no—
822C2×C4—222no—
823C2×C4—222no—
824C2×C4—222no—
825C2×C4—222no—
826C2×C4—2216no—
827C2×C4—224no—
828C2×C4—224no—
829C2×C4—224no—
830C2×C4—224no—
831C2×C4—224no—
832C2×C4—224no—
833C2×C4—888no—
834C2×C4—884no—
835C2×C4—884no—
836C2×C4C4×C22⋊D11116yescomplemented
837C2×C4C22×C4×D1112yes—
838C2×C4C22×C4×D1112yes—
839C2×C4C22×C4×D1112yes—
840C2×C4C22×C4×D1112yes—
841C2×C4C2×#433912yes—
842C2×C4C2×#433912yes—
843C2×C4C22×C22⋊D1114yes—
844C2×C4C22×C22⋊D1114yes—
845C2×C4C22×C22⋊D1112yes—
846C2×C4C22×C22⋊D1112yes—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—416no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—224no—
868C22—224no—
869C22—224no—
870C22—442no—
871C22—442no—
872C22—442no—
873C22—442no—
874C22#1062305414yescomplemented
875C22C2×C4×C22⋊D1114yes—
876C22C23×C4×D1111yescharacteristic
877C22C22×#433911yescharacteristic
878C22C2×#6704211yescharacteristic
879C22C2×#6704311yescharacteristic
880C22#1062345311yescharacteristic
881C22#1062345311yescharacteristic
882C22C23×C22⋊D1111yescharacteristic
883C4—24no—
884C4—24no—
885C4—22no—
886C4—22no—
887C4—42no—
888C4—42no—
889C4—224no—
890C4—224no—
891C4—224no—
892C4—444no—
893C4—444no—
894C4C2×C4×C22⋊D1114yes—
895C4C2×C4×C22⋊D1114yes—
896C2—24no—
897C2—24no—
898C2—42no—
899C2—444no—
900C2C22×C4×C22⋊D1111yescharacteristic
901C2C2×#1062305411yescharacteristic
902C2#1308181711yescharacteristic
903C2#1308228511yescharacteristic
904C2#1308229611yescharacteristic
905C2#1308235111yescharacteristic
906C2#1308236811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC22×C11×#117C2
socle, cosocleC23×C11C25
prime radicalC2×#10623322C2
hypercenterC22×#117D11
hypocenterC11#34202
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
2. C2×#10623054C2semidirect
3. #13071608C2semidirect
4. #13071595C2semidirect
5. #13071566C2semidirect
6. #13071546C2semidirect
7. #13071541C2semidirect
8. C4⋊C4×C22⋊D11C2semidirect
9. #13071309C2semidirect
10. #13071298C2semidirect
11. #13071236C2semidirect
12. #13071204C2semidirect
13. C4×#66977C2semidirect
14. C4×#66983C2semidirect
15. C2×#10622825C2semidirect
16. #13070972C2semidirect
17. C22×C11×#117C2semidirect
33. #10623322C4semidirect
46. C2×#66945C22semidirect
47. C2×C4⋊C4×D11C22semidirect
49. C2×C4×D44C22semidirect
50. C2×C4×Dic22C22semidirect
59. #10622603C22semidirect
60. #10622602C22semidirect
61. #10622600C22semidirect
62. #10622600C22semidirect
63. #10622591C22semidirect
64. #10622590C22semidirect
65. #10622589C22semidirect
66. C4⋊C4×Dic11C22semidirect
67. C4⋊C4×Dic11C22semidirect
68. #10622585C22semidirect
76. #10622553C22semidirect
77. #10622552C22semidirect
78. C4×(C2×D11)⋊C4C22semidirect
79. C4×C4⋊Dic11C22semidirect
80. C4×C4⋊Dic11C22semidirect
81. #10622546C22semidirect
82. C4×Dic11⋊C4C22semidirect
83. #10622542C22semidirect
84. #10622541C22semidirect
85. #10622541C22semidirect
89. C23×C4×C11C2×C4semidirect
105. C2×#4339C2×C4semidirect
115. C11×#117D4semidirect
134. #67006C2×C4semidirect
141. #66983C2×C4semidirect
142. #66983C2×C4semidirect
143. #66982C2×C4semidirect
145. C4×C22⋊D11C2×C4semidirect
146. C4×C22⋊D11C2×C4semidirect
152. #66979C2×C4semidirect
161. #66977C2×C4semidirect
162. #66977C2×C4semidirect
304. C22×#117D11semidirect
376. C2×C4×C11C4×D4semidirect
500. C22×C11#520semidirect
543. C23×C4C4×D11semidirect
571. #117C22⋊D11semidirect
754. C11#34202semidirect
836. C2×C4C4×C22⋊D11semidirect
874. C22#10623054semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
C2×#106230542
#130716082
#130715952
#130715662
#130715462
#130715412
C4⋊C4×C22⋊D112
#130713092
#130712982
#130712362
#130712042
C4×#669772
C4×#669832
C2×#106228252
#130709722
C22×C11×#1172
#3420211