Finite Group Databasebeta

← #14914714

Subgroups — #14914714

Order 2816.

3106 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623054C211yesmaximal, characteristic
2C2×#10623054C211yesmaximal, characteristic
3C2×C4×#4339C211yesmaximal, characteristic
4#13071536C212yesmaximal, complemented
5C4⋊C4×Dic22C212yesmaximal, complemented
6#13071527C212yesmaximal, complemented
7#13071522C214yesmaximal, complemented
8C4⋊C4×D44C212yesmaximal, complemented
9#13071514C214yesmaximal, complemented
10#13071239C211yesmaximal, characteristic, complemented
11#13071238C212yesmaximal, complemented
12#13071232C211yesmaximal, characteristic, complemented
13#13071231C212yesmaximal, complemented
14#13071097C212yesmaximal, complemented
15C2×#10622541C211yesmaximal, characteristic, complemented
16D11×#389C212yesmaximal, complemented
17C11×#2296C211yesmaximal, characteristic, complemented
18C22×#4339C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C2×C4×C22⋊D11C2212yes—
23C2×C4×C22⋊D11C2212yes—
24C2×#66979C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×Dic11⋊C4C2212yes—
28#10623054—28no—
29#10623054C4116yescomplemented
30C2×#66945C2212yes—
31C2×#66945C2212yes—
32C2×C4⋊C4×D11C2212yes—
33C2×C4⋊C4×D11C2214yes—
34C2×C4⋊C4×D11C2212yes—
35C2×(C22⋊D11)⋊C4C2214yes—
36C2×(C22⋊D11)⋊C4C2214yes—
37C4×#4339—28no—
38C2×C4×D44C2211yescharacteristic
39C2×C4×D44C2212yes—
40C2×C4×D44C2211yescharacteristic
41C2×C4×D44C2212yes—
42C2×#66925C2212yes—
43C2×C42×D11C2212yes—
44C2×C4×Dic22C2211yescharacteristic
45C2×C4×Dic22C2212yes—
46C2×C4×Dic22C2211yescharacteristic
47C2×C4×Dic22C2212yes—
48C11×#389C2211yescharacteristic
49C11×#389C2211yescharacteristic
50C11×#389C2211yescharacteristic
51C11×#389C2211yescharacteristic
52C11×#385C2212yes—
53C11×#385C2212yes—
54C4×C11×C4⋊C4C2212yes—
55C4×C11×C4⋊C4C2212yes—
56C2×C11⋊#95C2212yes—
57#10622602C2214yes—
58#10622602C2214yes—
59#10622600C2214yes—
60#10622598C2212yes—
61#10622598C2212yes—
62#10622589C2214yes—
63C4⋊C4×Dic11C2214yes—
64#10622586C2212yes—
65#10622586C2212yes—
66#10622585C2214yes—
67#10622585C2214yes—
68#10622563C2214yes—
69#10622555C2214yes—
70#10622549C2212yes—
71#10622548C2212yes—
72#10622541C2212yes—
73#10622541C2212yes—
74#10622541C2212yes—
75#10622541C2212yes—
76#10622541C2212yes—
77#10622541C2212yes—
78#10622281C2214yes—
79#10622281C2214yes—
80#10622280C2214yes—
81D11×#95C2214yes—
82#10622263C2214yes—
83#10622262C2214yes—
84#10622260C2214yes—
85#10622260C2214yes—
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C22×C22⋊D11C2312yes—
90C23×Dic11C2312yes—
91C23×Dic11C2312yes—
92C2×#4339C2×C418yes—
93C2×#4339D418yes—
94C2×#4339Q818yes—
95C22×D44C2311yescharacteristic
96C22×C4×D11C2312yes—
97C22×C4×D11C2312yes—
98C22×C4×D11C2314yes—
99C22×C4×D11C2314yes—
100C22×C4×D11C2312yes—
101C22×Dic22C2311yescharacteristic
102C11×#117—24no—
103C11×#117C2×C418yescomplemented
104C2×C11×C4⋊C4C2312yes—
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2312yes—
108C2×C11×C4⋊C4C2312yes—
109C2×C11×C4⋊C4C2312yes—
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C22⋊C4C2312yes—
113C2×C11×C22⋊C4C2312yes—
114C2×C42×C11—24no—
115C2×C42×C11C2311yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C2×C42×C11C2312yes—
118C2×C42×C11C2311yescharacteristic
119C2×C42×C11C2311yescharacteristic
120C2×C42×C11C2312yes—
121C2×C22⋊Dic11C2312yes—
122C4×C22⋊D11—28no—
123C4×C22⋊D11—28no—
124C2×(C2×D11)⋊C4C2312yes—
125C2×(C2×D11)⋊C4C2312yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128#66979—24no—
129C2×C4⋊Dic11—24no—
130C2×C4⋊Dic11C2×C418yescomplemented
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2312yes—
133C2×C4⋊Dic11C2311yescharacteristic
134C2×C4⋊Dic11C2312yes—
135C2×C4⋊Dic11C2314yes—
136C2×C4⋊Dic11C2314yes—
137C2×C4⋊Dic11C2312yes—
138C2×C4⋊Dic11C2312yes—
139C2×Dic11⋊C4—44no—
140C2×Dic11⋊C4C2312yes—
141C2×Dic11⋊C4C2312yes—
142C2×Dic11⋊C4C2314yes—
143C2×Dic11⋊C4C2314yes—
144C2×Dic11⋊C4C2314yes—
145C2×Dic11⋊C4C2314yes—
146C2×Dic11⋊C4C2314yes—
147C2×Dic11⋊C4C2314yes—
148C2×C4×Dic11C2312yes—
149C2×C4×Dic11C2312yes—
150C2×C4×Dic11C2314yes—
151C2×C4×Dic11C2312yes—
152C2×C4×Dic11C2314yes—
153#66945—28no—
154#66945C2×C4116yescomplemented
155C4⋊C4×D11—28no—
156C4⋊C4×D11—48no—
157C4⋊C4×D11C2×C4116yescomplemented
158(C22⋊D11)⋊C4—216no—
159(C22⋊D11)⋊C4C2×C4132yescomplemented
160C4×D44—24no—
161C4×D44—24no—
162C4×D44—28no—
163C4×D44C2×C4116yescomplemented
164#66925—28no—
165C42×D11—28no—
166C4×Dic22—24no—
167C4×Dic22—24no—
168C4×Dic22—28no—
169C4×Dic22C2×C4116yescomplemented
170C11×#95C2312yes—
171C11×#95C2312yes—
172C11×#95C2312yes—
173C11×#95C2312yes—
174C11⋊#95C2314yes—
175C11⋊#95C2314yes—
176C11⋊#95C2314yes—
177C11⋊#95C2314yes—
178C11⋊#95C2314yes—
179C11⋊#95C2314yes—
180#34250—111nomaximal, Sylow
181C24×C11C2411yescharacteristic
182C23×D11C2412yes—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—41no—
188C22×C4×C11—41no—
189C22×C4×C11C22×C414yes—
190C22×C4×C11C2×D414yes—
191C22×C4×C11C2×Q814yes—
192C22×C4×C11C2411yescharacteristic
193C22×C4×C11C2412yes—
194C22×C4×C11C2412yes—
195C22×C4×C11C2411yescharacteristic
196C22×C4×C11C2412yes—
197C22×C4×C11C2412yes—
198C22×C4×C11C2411yescharacteristic
199C22×C4×C11C2411yescharacteristic
200C22×C4×C11C2411yescharacteristic
201C22×C4×C11C2411yescharacteristic
202C2×C22⋊D11C22×C418yes—
203C2×C22⋊D11C2×D418yes—
204C2×C22⋊D11C2×Q818yes—
205C22×Dic11—24no—
206C22×Dic11—42no—
207C22×Dic11—42no—
208C22×Dic11—42no—
209C22×Dic11—42no—
210C22×Dic11C22×C418yes—
211C22×Dic11C2412yes—
212C22×Dic11C2414yes—
213C22×Dic11C2412yes—
214C22×Dic11C2414yes—
215C22×Dic11C2412yes—
216#4339C4⋊C4164yescomplemented
217C2×D44C22×C414yes—
218C2×D44C2×D414yes—
219C2×D44C2×Q814yes—
220C2×C4×D11—24no—
221C2×C4×D11—24no—
222C2×C4×D11—28no—
223C2×C4×D11—24no—
224C2×C4×D11—24no—
225C2×C4×D11—44no—
226C2×C4×D11—44no—
227C2×C4×D11—42no—
228C2×C4×D11—42no—
229C2×C4×D11—44no—
230C2×C4×D11—44no—
231C2×C4×D11C22×C4116yes—
232C2×C4×D11C22×C418yes—
233C2×C4×D11C2×D418yes—
234C2×C4×D11C2×Q818yes—
235C2×Dic22C22×C414yes—
236C2×Dic22C2×D414yes—
237C2×Dic22C2×Q814yes—
238C11×C4⋊C4—22no—
239C11×C4⋊C4—22no—
240C11×C4⋊C4—24no—
241C11×C4⋊C4—24no—
242C11×C4⋊C4—42no—
243C11×C4⋊C4—42no—
244C11×C4⋊C4C22×C414yes—
245C11×C4⋊C4C22×C414yes—
246C11×C22⋊C4—24no—
247C11×C22⋊C4C22×C418yes—
248C42×C11—22no—
249C42×C11—22no—
250C42×C11—24no—
251C42×C11—22no—
252C42×C11—22no—
253C42×C11C22×C418yes—
254C22⋊Dic11—24no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—28no—
258(C2×D11)⋊C4C22×C4116yes—
259C4⋊Dic11—24no—
260C4⋊Dic11—22no—
261C4⋊Dic11—22no—
262C4⋊Dic11—24no—
263C4⋊Dic11—44no—
264C4⋊Dic11—44no—
265C4⋊Dic11C22×C418yes—
266C4⋊Dic11C22×C418yes—
267Dic11⋊C4—24no—
268Dic11⋊C4—24no—
269Dic11⋊C4—28no—
270Dic11⋊C4—28no—
271Dic11⋊C4—44no—
272Dic11⋊C4—44no—
273Dic11⋊C4—44no—
274Dic11⋊C4C22×C4116yes—
275C4×Dic11—24no—
276C4×Dic11—24no—
277C4×Dic11—28no—
278C4×Dic11—24no—
279C4×Dic11C22×C4116yes—
280C2×#520—111no—
281C2×#520—111no—
282C2×C4×#41—111no—
283#2351—112no—
284Q8×C4⋊C4—112no—
285#2349—114no—
286#2349—112no—
287D4×C4⋊C4—114no—
288D4×C4⋊C4—112no—
289#2317—112no—
290#2317—111no—
291#2316—112no—
292#2316—111no—
293#2296—112no—
294#2296D1111yescharacteristic, complemented
295C2×#389—111no—
296C2×#389—112no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11C23×C412yes—
302C23×C11C22×D412yes—
303C23×C11C22×Q812yes—
304C23×C11C2511yescharacteristic
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11C23×C414yes—
310C22×D11C22×D414yes—
311C22×D11C22×Q814yes—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—22no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—22no—
324C2×C4×C11—21no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—21no—
328C2×C4×C11—22no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—22no—
332C2×C4×C11—44no—
333C2×C4×C11—44no—
334C2×C4×C11C2×C4⋊C4116yescomplemented
335C2×C4×C11C23×C414yes—
336C2×C4×C11C23×C414yes—
337C2×C4×C11C23×C412yes—
338C2×C4×C11C23×C412yes—
339C2×C4×C11C22×D412yes—
340C2×C4×C11C22×D412yes—
341C2×C4×C11C22×Q812yes—
342C2×C4×C11C22×Q812yes—
343C2×C4×C11H(5,𝔽2)12yes—
344C2×C4×C112−1+412yes—
345C22⋊D11C2×C4⋊C4132yescomplemented
346C2×Dic11—24no—
347C2×Dic11—24no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—24no—
351C2×Dic11—24no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—24no—
357C2×Dic11—48no—
358C2×Dic11—84no—
359C2×Dic11C23×C418yes—
360C2×Dic11C23×C414yes—
361C2×Dic11C22×D414yes—
362C2×Dic11C22×Q814yes—
363D44C2×C4⋊C4116yescomplemented
364C4×D11—416no—
365C4×D11—48no—
366C4×D11—48no—
367C4×D11—88no—
368C4×D11C2×C4⋊C4132yescomplemented
369Dic22C2×C4⋊C4116yescomplemented
370C22×#41—111no—
371#520—1116no—
372#520—228no—
373C4×#41—228no—
374C2×C4×Q8—112no—
375C2×C4×Q8—111no—
376C2×C4×Q8—112no—
377C2×C4×Q8—111no—
378C2×C4×D4—112no—
379C2×C4×D4—112no—
380C2×C4×D4—114no—
381C2×C4×D4—114no—
382C2×C4×D4—112no—
383C2×C4×D4—111no—
384C2×C4×D4—112no—
385C2×C4×D4—111no—
386C2×#117—111no—
387C2×#117—112no—
388C2×#117—112no—
389C2×#117—112no—
390C2×#117C2×D1111yescharacteristic
391C2×#117C2×D1111yescharacteristic
392C22×C4⋊C4—111no—
393C22×C4⋊C4—112no—
394C22×C4⋊C4—111no—
395C22×C4⋊C4—112no—
396C22×C4⋊C4—112no—
397C22×C4⋊C4—114no—
398C22×C42—112no—
399C22×C42C2×D1111yescharacteristic
400#389—112no—
401#389—112no—
402#389—112no—
403#389—114no—
404#389—112no—
405#389—114no—
406#389—112no—
407#389—112no—
408#389—112no—
409#389—112no—
410#389—112no—
411#389—112no—
412#389—114no—
413#389—114no—
414#389C2×D1111yescharacteristic
415#389C2×D1111yescharacteristic
416#389C2×D1111yescharacteristic
417#389C2×D1111yescharacteristic
418#385—114no—
419#385—114no—
420#385—114no—
421#385—114no—
422#385—114no—
423#385C2×D1112yes—
424#385C2×D1112yes—
425#384—114no—
426#384—112no—
427#382—112no—
428#382—114no—
429#380—114no—
430#380—114no—
431#380—114no—
432C4×C4⋊C4—114no—
433C4×C4⋊C4—114no—
434C4×C4⋊C4C2×D1112yes—
435C4×C4⋊C4C2×D1112yes—
436C2×#95—112no—
437C2×#95—114no—
438C22×C11—22no—
439C22×C11—22no—
440C22×C11—22no—
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—22no—
444C22×C11C22×C4⋊C414yes—
445C22×C11C24×C411yescharacteristic
446C22×C11C23×D411yescharacteristic
447C22×C11C23×Q811yescharacteristic
448C22×C11C2×H(5,𝔽2)11yescharacteristic
449C22×C11C2×2−1+411yescharacteristic
450C22×C11#58511yescharacteristic
451C22×C11#58511yescharacteristic
452C2×D11—24no—
453C2×D11—24no—
454C2×D11—24no—
455C2×D11—24no—
456C2×D11—24no—
457C2×D11—24no—
458C2×D11C22×C4⋊C418yes—
459C4×C11—24no—
460C4×C11—24no—
461C4×C11—22no—
462C4×C11—22no—
463C4×C11—41no—
464C4×C11—42no—
465C4×C11—42no—
466C4×C11—41no—
467C4×C11C22×C4⋊C414yes—
468C4×C11C22×C4⋊C414yes—
469Dic11—28no—
470Dic11—42no—
471Dic11—44no—
472Dic11—42no—
473Dic11C22×C4⋊C418yes—
474C2×#41—118no—
475C2×#41—118no—
476C2×#41—118no—
477C22×Q8—111no—
478C22×D4—112no—
479C22×D4—111no—
480C23×C4—112no—
481C23×C4—112no—
482C23×C4—114no—
483C23×C4—112no—
484C23×C4—112no—
485C23×C4—112no—
486C23×C4—114no—
487C23×C4C22×D1111yescharacteristic
488C23×C4C22×D1111yescharacteristic
489C23×C4C22×D1111yescharacteristic
490C4×Q8—1116no—
491C4×Q8—224no—
492C4×Q8—224no—
493C4×Q8—228no—
494C4×D4—1132no—
495C4×D4—1116no—
496C4×D4—224no—
497C4×D4—224no—
498C4×D4—228no—
499C4×D4—2216no—
500C4×D4—228no—
501C4×D4—228no—
502#117—24no—
503#117—1116no—
504#117—228no—
505#117—228no—
506#117—224no—
507#117C4×D1118yescomplemented
508C2×C4⋊C4—118no—
509C2×C4⋊C4—112no—
510C2×C4⋊C4—114no—
511C2×C4⋊C4—112no—
512C2×C4⋊C4—1116no—
513C2×C4⋊C4—112no—
514C2×C4⋊C4—114no—
515C2×C4⋊C4—114no—
516C2×C4⋊C4—112no—
517C2×C4⋊C4—112no—
518C2×C4⋊C4—111no—
519C2×C4⋊C4—112no—
520C2×C4⋊C4—111no—
521C2×C4⋊C4—114no—
522C2×C4⋊C4—114no—
523C2×C4⋊C4—114no—
524C2×C4⋊C4—114no—
525C2×C4⋊C4—114no—
526C2×C4⋊C4—228no—
527C2×C4⋊C4—224no—
528C2×C4⋊C4—448no—
529C2×C4⋊C4—444no—
530C2×C4⋊C4C22×D1111yescharacteristic
531C2×C4⋊C4C22×D1112yes—
532C2×C4⋊C4C22×D1111yescharacteristic
533C2×C4⋊C4C22×D1112yes—
534C2×C4⋊C4C22×D1112yes—
535C2×C4⋊C4C22×D1112yes—
536C2×C4⋊C4C22×D1111yescharacteristic
537C2×C4⋊C4C22×D1111yescharacteristic
538C2×C22⋊C4—114no—
539C2×C22⋊C4—112no—
540C2×C22⋊C4—112no—
541C2×C22⋊C4—114no—
542C2×C22⋊C4—112no—
543C2×C22⋊C4C22×D1112yes—
544C2×C22⋊C4C22×D1112yes—
545C2×C42—24no—
546C2×C42—114no—
547C2×C42—112no—
548C2×C42—114no—
549C2×C42—112no—
550C2×C42—112no—
551C2×C42—228no—
552C2×C42C22×D1111yescharacteristic
553C2×C42C22×D1112yes—
554C2×C42C22×D1111yescharacteristic
555C2×C42C22×D1111yescharacteristic
556C2×C42C22×D1111yescharacteristic
557C2×C42C22×D1112yes—
558#95—114no—
559#95—114no—
560#95—114no—
561#95—114no—
562#95—114no—
563#95—114no—
564#95C22×D1112yes—
565#95C22×D1112yes—
566#95C22×D1112yes—
567#95C22×D1112yes—
568C2×C11—24no—
569C2×C11C23×C4⋊C411yescharacteristic
570C2×C11C4×H(5,𝔽2)11yescharacteristic
571C2×C11C4×2−1+411yescharacteristic
572C2×C11#348811yescharacteristic
573C2×C11#348911yescharacteristic
574C2×C11#350311yescharacteristic
575C2×C11#350411yescharacteristic
576D11—28no—
577C24—112no—
578C24C23×D1111yescharacteristic
579#41—1164no—
580C2×Q8—114no—
581C2×Q8—114no—
582C2×Q8—114no—
583C2×D4—118no—
584C2×D4—118no—
585C2×D4—118no—
586C2×D4—114no—
587C2×D4—114no—
588C2×D4—114no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—112no—
596C22×C4—118no—
597C22×C4—118no—
598C22×C4—118no—
599C22×C4—114no—
600C22×C4—118no—
601C22×C4—1116no—
602C22×C4—112no—
603C22×C4—114no—
604C22×C4—112no—
605C22×C4—224no—
606C22×C4—224no—
607C22×C4—228no—
608C22×C4—224no—
609C22×C4—224no—
610C22×C4—224no—
611C22×C4—444no—
612C22×C4—444no—
613C22×C4—442no—
614C22×C4—442no—
615C22×C4—444no—
616C22×C4—444no—
617C22×C4—442no—
618C22×C4—442no—
619C22×C4—442no—
620C22×C4—442no—
621C22×C4C2×C4×D1114yes—
622C22×C4D4×D1114yes—
623C22×C4Q8×D1114yes—
624C22×C4C23×D1111yescharacteristic
625C22×C4C23×D1112yes—
626C22×C4C23×D1112yes—
627C22×C4C23×D1111yescharacteristic
628C22×C4C23×D1112yes—
629C22×C4C23×D1112yes—
630C22×C4C23×D1111yescharacteristic
631C22×C4C23×D1111yescharacteristic
632C22×C4C23×D1111yescharacteristic
633C22×C4C23×D1111yescharacteristic
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—118no—
641C4⋊C4—1116no—
642C4⋊C4—118no—
643C4⋊C4—228no—
644C4⋊C4—224no—
645C4⋊C4—224no—
646C4⋊C4—224no—
647C4⋊C4—224no—
648C4⋊C4—222no—
649C4⋊C4—222no—
650C4⋊C4—228no—
651C4⋊C4—444no—
652C4⋊C4—444no—
653C4⋊C4—444no—
654C4⋊C4—444no—
655C4⋊C4—444no—
656C4⋊C4C2×C4×D1114yes—
657C4⋊C4C2×C4×D1114yes—
658C22⋊C4—24no—
659C22⋊C4—1116no—
660C22⋊C4—224no—
661C22⋊C4—224no—
662C22⋊C4—228no—
663C22⋊C4—224no—
664C22⋊C4C2×C4×D1118yes—
665C42—22no—
666C42—22no—
667C42—22no—
668C42—22no—
669C42—24no—
670C42—1116no—
671C42—224no—
672C42—224no—
673C42—228no—
674C42—224no—
675C42C2×C4×D1118yes—
676C11#3425011yescharacteristic, complemented, Sylow
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—114no—
682C23—114no—
683C23—114no—
684C23—222no—
685C23—222no—
686C23—222no—
687C23—222no—
688C23C22×C4×D1112yes—
689C23C2×D4×D1112yes—
690C23C2×Q8×D1112yes—
691C23C24×D1111yescharacteristic
692Q8—1116no—
693D4—1132no—
694D4—1116no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—114no—
718C2×C4—114no—
719C2×C4—114no—
720C2×C4—1132no—
721C2×C4—118no—
722C2×C4—224no—
723C2×C4—224no—
724C2×C4—222no—
725C2×C4—222no—
726C2×C4—224no—
727C2×C4—224no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—224no—
733C2×C4—4416no—
734C2×C4—448no—
735C2×C4—448no—
736C2×C4—448no—
737C2×C4—888no—
738C2×C4—884no—
739C2×C4C4⋊C4×D11116yescomplemented
740C2×C4C22×C4×D1114yes—
741C2×C4C22×C4×D1114yes—
742C2×C4C22×C4×D1112yes—
743C2×C4C22×C4×D1112yes—
744C2×C4C2×D4×D1112yes—
745C2×C4C2×D4×D1112yes—
746C2×C4C2×Q8×D1112yes—
747C2×C4C2×Q8×D1112yes—
748C2×C4#6704212yes—
749C2×C4#6704312yes—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—118no—
757C22—224no—
758C22—224no—
759C22—224no—
760C22—224no—
761C22—224no—
762C22—224no—
763C22C2×C4⋊C4×D1114yes—
764C22C23×C4×D1111yescharacteristic
765C22C22×D4×D1111yescharacteristic
766C22C22×Q8×D1111yescharacteristic
767C22C2×#6704211yescharacteristic
768C22C2×#6704311yescharacteristic
769C22#1062345311yescharacteristic
770C22#1062345311yescharacteristic
771C4—22no—
772C4—22no—
773C4—24no—
774C4—24no—
775C4—41no—
776C4—42no—
777C4—41no—
778C4—42no—
779C4—118no—
780C4—228no—
781C4—442no—
782C4—444no—
783C4—442no—
784C4C2×C4⋊C4×D1114yes—
785C4C2×C4⋊C4×D1114yes—
786C2—24no—
787C2—228no—
788C2C22×C4⋊C4×D1111yescharacteristic
789C2C4×#6704211yescharacteristic
790C2C4×#6704311yescharacteristic
791C2#1308227711yescharacteristic
792C2#1308228811yescharacteristic
793C2#1308242811yescharacteristic
794C2#1308243711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2296C2
socle, cosocleC23×C11C25
prime radicalC22×#4339C22
hypercenter#2296D11
hypocenterC11#34250
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2296

Complements

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

NH ≅ G/Ntype
4. #13071536C2semidirect
5. C4⋊C4×Dic22C2semidirect
6. #13071527C2semidirect
7. #13071522C2semidirect
8. C4⋊C4×D44C2semidirect
9. #13071514C2semidirect
10. #13071239C2semidirect
11. #13071238C2semidirect
12. #13071232C2semidirect
13. #13071231C2semidirect
14. #13071097C2semidirect
15. C2×#10622541C2semidirect
16. D11×#389C2semidirect
17. C11×#2296C2semidirect
29. #10623054C4semidirect
103. C11×#117C2×C4semidirect
130. C2×C4⋊Dic11C2×C4semidirect
154. #66945C2×C4semidirect
157. C4⋊C4×D11C2×C4semidirect
159. (C22⋊D11)⋊C4C2×C4semidirect
163. C4×D44C2×C4semidirect
169. C4×Dic22C2×C4semidirect
216. #4339C4⋊C4semidirect
294. #2296D11semidirect
334. C2×C4×C11C2×C4⋊C4semidirect
345. C22⋊D11C2×C4⋊C4semidirect
363. D44C2×C4⋊C4semidirect
368. C4×D11C2×C4⋊C4semidirect
369. Dic22C2×C4⋊C4semidirect
507. #117C4×D11semidirect
676. C11#34250semidirect
739. C2×C4C4⋊C4×D11semidirect

Maximal subgroups

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

subgroupindex
C2×#106230542
C2×C4×#43392
#130715362
C4⋊C4×Dic222
#130715272
#130715222
C4⋊C4×D442
#130715142
#130712392
#130712382
#130712322
#130712312
#130710972
C2×#106225412
D11×#3892
C11×#22962
#3425011