Finite Group Databasebeta

← #15622213

Subgroups — #15622213

Order 2816.

2148 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4339C211yesmaximal, characteristic
2#13078772C214yesmaximal, complemented
3#13078742C212yesmaximal, complemented
4#13078711C212yesmaximal, complemented
5#13078681C214yesmaximal, complemented
6#13078651C212yesmaximal, complemented
7#13078620C212yesmaximal, complemented
8#13078560C212yesmaximal, complemented
9#13078425C212yesmaximal, complemented
10#13078099C212yesmaximal, complemented
11#13077874C212yesmaximal
12C4×#66995C214yesmaximal, complemented
13#13077249C211yesmaximal, characteristic, complemented
14C2×C11×#533C211yesmaximal, characteristic, complemented
15C22×#4339C2211yescharacteristic
16C11×#533—21no—
17C11×#533—21no—
18C11×#533—21no—
19C11×#533—21no—
20C11×#533C2212yes—
21C11×#533C2212yes—
22C11×#533C2212yescomplemented
23C11×#533C2212yescomplemented
24C2×C11×C4⋊Q8C2211yescharacteristic, complemented
25C2×C11×C4⋊Q8C2211yescharacteristic, complemented
26C2×C11×#125—21no—
27C2×C11×C22⋊Q8—21no—
28C2×C11×C22⋊Q8C2212yes—
29C2×C4×Q8×C11—21no—
30C2×C4×Q8×C11C2212yescomplemented
31C2×C11×#117—21no—
32C22×C42×C11C2211yescharacteristic
33C2×#66995C2214yes—
34C2×C4×C22⋊D11—21no—
35C2×C4×C22⋊D11—21no—
36C2×#66979C2211yescharacteristic
37C4×#4339—21no—
38C4×#4339—21no—
39C4×#4339—21no—
40C4×#4339—21no—
41C4×#4339C2212yes—
42C4×#4339C2212yes—
43C4×#4339C2212yes—
44C4×#4339C2212yes—
45C2×C4×D44C2211yescharacteristic
46C2×C4×D44C2211yescharacteristic
47C2×#66925—21no—
48C2×C42×D11—21no—
49C2×C4×Dic22C2211yescharacteristic
50C2×C4×Dic22C2211yescharacteristic
51#10622838C2214yescomplemented
52#10622820C2212yes—
53#10622707C2214yescomplemented
54#10622704C2214yescomplemented
55#10622703C2214yescomplemented
56#10622703C2214yescomplemented
57#10622700C2214yescomplemented
58#10622697C2214yescomplemented
59#10622696C2214yescomplemented
60#10622696C2214yescomplemented
61#10622663C2214yes—
62#10622660C2218yes—
63#10622659C2214yes—
64#10622658C2218yescomplemented
65#10622657C2214yes—
66#10622656C2214yes—
67#10622643C2218yescomplemented
68C4×#4326C2218yescomplemented
69#10622639C2218yescomplemented
70C4×#4325C2218yescomplemented
71#10622579C2214yes—
72#10622577C2214yescomplemented
73#10622539C2212yes—
74#10622539C2212yescomplemented
75#10622538C2212yes—
76#10622538C2212yescomplemented
77#10622537C2212yescomplemented
78C4×#4318C2212yescomplemented
79C22×Q8×C11—21no—
80C22×Q8×C11C2312yes—
81C23×C4×C11D411yescharacteristic
82C23×C4×C11D411yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C22×C22⋊D11—21no—
85C2×#4339—21no—
86C2×#4339—21no—
87C2×#4339—28no—
88C2×#4339C2312yes—
89C2×#4339C2312yes—
90C22×D44C2311yescharacteristic
91C22×C4×D11—21no—
92C22×C4×D11—21no—
93C22×C4×D11—21no—
94C22×Dic22C2311yescharacteristic
95C11×C4⋊Q8—21no—
96C11×C4⋊Q8—21no—
97C11×C4⋊Q8—21no—
98C11×C4⋊Q8—21no—
99C11×C4⋊Q8C2312yes—
100C11×C4⋊Q8C2312yes—
101C11×C4⋊Q8C2312yes—
102C11×C4⋊Q8C2312yes—
103C11×#125—22no—
104C11×#125—22no—
105C11×#125—22no—
106C11×#125—22no—
107C11×C22⋊Q8—22no—
108C11×C22⋊Q8—22no—
109C11×C22⋊Q8—22no—
110C11×C22⋊Q8—22no—
111C11×C22⋊Q8—22no—
112C11×C22⋊Q8—22no—
113C11×C22⋊Q8C2314yes—
114C11×C22⋊Q8C2314yes—
115C4×Q8×C11—22no—
116C4×Q8×C11—22no—
117C4×Q8×C11—22no—
118C4×Q8×C11—22no—
119C4×Q8×C11—22no—
120C4×Q8×C11—22no—
121C4×Q8×C11C2314yes—
122C4×Q8×C11C2314yes—
123C11×#117—22no—
124C11×#117—22no—
125C11×#117—22no—
126C11×#117—22no—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4—21no—
129C2×C11×C4⋊C4—21no—
130C2×C11×C4⋊C4—22no—
131C2×C11×C4⋊C4—22no—
132C2×C11×C4⋊C4C2312yes—
133C2×C11×C22⋊C4—22no—
134C2×C42×C11—22no—
135C2×C42×C11D411yescharacteristic
136C2×C42×C11D411yescharacteristic
137C2×C42×C11D411yescharacteristic
138C2×C42×C11D411yescharacteristic
139C2×C42×C11D411yescharacteristic
140C2×C42×C11D411yescharacteristic
141C2×C42×C11C2311yescharacteristic
142C2×C42×C11C2311yescharacteristic
143C2×C42×C11C2311yescharacteristic
144C2×C42×C11C2311yescharacteristic
145C2×C42×C11C2311yescharacteristic
146C2×C42×C11C2311yescharacteristic
147C2×C22⋊Dic11—21no—
148C2×#4326C2318yes—
149#66995—216no—
150C2×#4325C2318yes—
151C4×C22⋊D11—22no—
152C4×C22⋊D11—22no—
153C4×C22⋊D11—22no—
154C4×C22⋊D11—22no—
155C4×C22⋊D11—22no—
156C4×C22⋊D11—22no—
157C4×C22⋊D11—22no—
158C4×C22⋊D11—22no—
159C2×(C2×D11)⋊C4—21no—
160C2×(C2×D11)⋊C4—21no—
161#66979—21no—
162#66979—21no—
163#66979C2312yes—
164#66979C2312yes—
165C2×C4⋊Dic11C2311yescharacteristic
166C2×C4⋊Dic11C2311yescharacteristic
167C2×Dic11⋊C4—21no—
168C2×Dic11⋊C4—21no—
169C2×C4×Dic11—21no—
170C2×C4×Dic11—21no—
171C2×C4×Dic11—21no—
172C2×#4318C2314yes—
173C4×D44—21no—
174C4×D44—21no—
175C4×D44—21no—
176C4×D44—21no—
177C4×D44C2312yes—
178C4×D44C2312yes—
179C4×D44C2312yes—
180C4×D44C2312yes—
181#66925—22no—
182#66925—22no—
183#66925—22no—
184#66925—22no—
185C42×D11—22no—
186C42×D11—22no—
187C42×D11—22no—
188C42×D11—22no—
189C4×Dic22—21no—
190C4×Dic22—21no—
191C4×Dic22—21no—
192C4×Dic22—21no—
193C4×Dic22C2312yes—
194C4×Dic22C2312yes—
195C4×Dic22C2312yes—
196C4×Dic22C2312yes—
197#66899C2318yes—
198#66899C2318yes—
199C22⋊(C11⋊C8)C2314yes—
200C22⋊(C11⋊C8)C2314yes—
201#66874C2318yes—
202#66873C2318yes—
203#66872C2318yes—
204#66871C2318yes—
205C4⋊(C11⋊C8)C2314yes—
206C4⋊(C11⋊C8)C2314yes—
207#66867C2314yes—
208C4×C11⋊C8C2314yes—
209#60562—111nomaximal, Sylow
210C24×C11C2×D411yescharacteristic
211C23×D11—21no—
212C2×Q8×C11—22no—
213C2×Q8×C11—22no—
214C2×Q8×C11—22no—
215C2×Q8×C11—28no—
216C2×Q8×C11—44no—
217C2×Q8×C11C2414yes—
218C22×C4×C11—24no—
219C22×C4×C11—24no—
220C22×C4×C11—22no—
221C22×C4×C11—22no—
222C22×C4×C11—42no—
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D411yescharacteristic
226C22×C4×C11C2×D411yescharacteristic
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2×D411yescharacteristic
238C22×C4×C11C2411yescharacteristic
239C22×C4×C11C2411yescharacteristic
240C22×C4×C11C2411yescharacteristic
241C2×C22⋊D11—28no—
242C2×C22⋊D11—22no—
243C2×C22⋊D11—22no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247#4339—28no—
248#4339—28no—
249#4339—24no—
250#4339—24no—
251#4339—24no—
252#4339#4118yes—
253C2×D44—24no—
254C2×D44—21no—
255C2×D44C2412yes—
256C2×C4×D11—28no—
257C2×C4×D11—22no—
258C2×C4×D11—22no—
259C2×C4×D11—22no—
260C2×C4×D11—22no—
261C2×C4×D11—22no—
262C2×C4×D11—22no—
263C2×C4×D11—44no—
264C2×C4×D11—44no—
265C2×Dic22—24no—
266C2×Dic22—21no—
267C2×Dic22C2412yes—
268C11×C4⋊C4—22no—
269C11×C4⋊C4—22no—
270C11×C4⋊C4—22no—
271C11×C4⋊C4—22no—
272C11×C4⋊C4—22no—
273C11×C4⋊C4—22no—
274C11×C4⋊C4—24no—
275C11×C4⋊C4—24no—
276C11×C4⋊C4—24no—
277C11×C4⋊C4—24no—
278C11×C4⋊C4—22no—
279C11×C4⋊C4C2414yes—
280C11×C22⋊C4—24no—
281C11×C22⋊C4—24no—
282C42×C11—24no—
283C42×C11—24no—
284C42×C11C2×D411yescharacteristic
285C42×C11C2×D411yescharacteristic
286C42×C11C2×D411yescharacteristic
287C42×C11C2×D411yescharacteristic
288C42×C11C2×D411yescharacteristic
289C42×C11C2×D411yescharacteristic
290C42×C11C2×D411yescharacteristic
291C42×C11C2×D411yescharacteristic
292C42×C11C2×D411yescharacteristic
293C42×C11C2×D411yescharacteristic
294C42×C11C2×D411yescharacteristic
295C42×C11C2×D411yescharacteristic
296C42×C11C2411yescharacteristic
297C42×C11C2411yescharacteristic
298C42×C11C2411yescharacteristic
299C42×C11C2411yescharacteristic
300C22⋊Dic11—22no—
301C22⋊Dic11—22no—
302#4326—216no—
303#4325—216no—
304(C2×D11)⋊C4—22no—
305(C2×D11)⋊C4—22no—
306(C2×D11)⋊C4—22no—
307(C2×D11)⋊C4—22no—
308C4⋊Dic11—21no—
309C4⋊Dic11—21no—
310C4⋊Dic11C2412yes—
311C4⋊Dic11C2412yes—
312Dic11⋊C4—22no—
313Dic11⋊C4—22no—
314Dic11⋊C4—22no—
315Dic11⋊C4—22no—
316C4×Dic11—22no—
317C4×Dic11—22no—
318C4×Dic11—22no—
319C4×Dic11—22no—
320C4×Dic11—22no—
321C4×Dic11—22no—
322#4318—28no—
323C2×C11⋊C8C2418yes—
324C2×#533D1111yescharacteristic, complemented
325C2×C4×#41—111no—
326#3116—114no—
327#3113—112no—
328#3110—112no—
329#3107—114no—
330#3104—112no—
331#3101—112no—
332#3095—112no—
333#3079—112no—
334#3039—112no—
335#3007—112no—
336C4×#137—114no—
337#2920—111no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11—41no—
341C23×C11C22×D411yescharacteristic
342C23×C11C22×D411yescharacteristic
343C23×C11C22×D411yescharacteristic
344C22×D11—24no—
345C22×D11—22no—
346C22×D11—42no—
347C22×D11—42no—
348Q8×C11—28no—
349Q8×C11—44no—
350Q8×C11—44no—
351Q8×C11—44no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—24no—
366C2×C4×C11—24no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—44no—
371C2×C4×C11—44no—
372C2×C4×C11#13714yescomplemented
373C2×C4×C11C22×D411yescharacteristic
374C2×C4×C11C22×D411yescharacteristic
375C2×C4×C11C22×D411yescharacteristic
376C2×C4×C11C22×D411yescharacteristic
377C2×C4×C11C22×D411yescharacteristic
378C2×C4×C11C22×D411yescharacteristic
379C2×C4×C11C22×D411yescharacteristic
380C2×C4×C11C22×D411yescharacteristic
381C2×C4×C11C22×D411yescharacteristic
382C2×C4×C11C22×D411yescharacteristic
383C2×C4×C11C22×D411yescharacteristic
384C2×C4×C11C2×#4114yes—
385C2×C4×C11C2511yescharacteristic
386C22⋊D11—28no—
387C22⋊D11—28no—
388C2×Dic11—24no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—42no—
393C2×Dic11—42no—
394D44—24no—
395D44—22no—
396D44C2×#4114yes—
397C4×D11—28no—
398C4×D11—28no—
399C4×D11—44no—
400C4×D11—44no—
401C4×D11—44no—
402C4×D11—44no—
403Dic22—24no—
404Dic22—22no—
405Dic22C2×#4114yes—
406C11⋊C8—28no—
407C22×#41—111no—
408C2×#137—114no—
409#533—21no—
410#533—21no—
411#533—21no—
412#533—21no—
413#533C2×D1112yes—
414#533C2×D1112yes—
415#533C2×D1112yescomplemented
416#533C2×D1112yescomplemented
417C2×C4⋊Q8C2×D1111yescharacteristic, complemented
418C2×C4⋊Q8C2×D1111yescharacteristic, complemented
419C2×#125—21no—
420C2×C22⋊Q8—21no—
421C2×C22⋊Q8C2×D1112yes—
422C4×#41—112no—
423C4×#41—112no—
424C4×#41—112no—
425C4×#41—112no—
426C4×#41—221no—
427C4×#41—221no—
428C4×#41—221no—
429C4×#41—221no—
430C2×C4×Q8—21no—
431C2×C4×Q8—111no—
432C2×C4×Q8—111no—
433C2×C4×Q8C2×D1112yescomplemented
434C2×C4×D4—111no—
435C2×C4×D4—111no—
436C2×C4×D4—221no—
437C2×C4×D4—221no—
438C2×#117—21no—
439C2×#117—111no—
440C2×#117—221no—
441C22×C42—221no—
442C22×C42C2×D1111yescharacteristic
443#485—118no—
444#484—114no—
445#483—114no—
446#477—114no—
447#476—114no—
448#475—114no—
449#474—114no—
450#462—114no—
451#462—114no—
452#461—114no—
453#461—114no—
454#452—118no—
455#451—114no—
456#450—114no—
457#441—118no—
458#440—118no—
459C4×Q16—118no—
460C4×SD16—118no—
461#432—112no—
462#432—112no—
463#431—112no—
464#431—112no—
465#428—114no—
466#423—112no—
467#419—114no—
468#417—114no—
469#407—112no—
470C4×M16—112no—
471C22×C11—21no—
472C22×C11—21no—
473C22×C11—21no—
474C22×C11—21no—
475C22×C11—21no—
476C22×C11—21no—
477C22×C11—21no—
478C22×C11—44no—
479C22×C11#52512yes—
480C22×C11C2×#13712yes—
481C22×C11C23×D411yescharacteristic
482C2×D11—24no—
483C2×D11—48no—
484C2×D11—42no—
485C2×D11—42no—
486C4×C11—21no—
487C4×C11—21no—
488C4×C11—21no—
489C4×C11—21no—
490C4×C11—21no—
491C4×C11—21no—
492C4×C11—21no—
493C4×C11—44no—
494C4×C11—44no—
495C4×C11#52512yes—
496C4×C11C2×#13712yes—
497C4×C11C2×#13712yes—
498C4×C11#57512yes—
499C4×C11C22×#4112yes—
500Dic11—24no—
501Dic11—42no—
502Dic11—42no—
503C2×#41—112no—
504C2×#41—112no—
505C2×#41—228no—
506C2×#41—221no—
507C2×#41—221no—
508C22×Q8—21no—
509C22×Q8—111no—
510C22×Q8C22×D1112yes—
511C22×D4—111no—
512C22×D4—221no—
513C23×C4—221no—
514C23×C4—221no—
515C23×C4—221no—
516C23×C4C22⋊D1111yescharacteristic
517C23×C4C22⋊D1111yescharacteristic
518C23×C4C22×D1111yescharacteristic
519#137—2216no—
520C2×Q16—118no—
521C2×SD16—118no—
522C2×M16—114no—
523C4⋊Q8—21no—
524C4⋊Q8—21no—
525C4⋊Q8—21no—
526C4⋊Q8—21no—
527C4⋊Q8C22×D1112yes—
528C4⋊Q8C22×D1112yes—
529C4⋊Q8C22×D1112yes—
530C4⋊Q8C22×D1112yes—
531#125—22no—
532#125—22no—
533#125—22no—
534#125—22no—
535C22⋊Q8—22no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538C22⋊Q8—22no—
539C22⋊Q8—22no—
540C22⋊Q8—22no—
541C22⋊Q8C22×D1114yes—
542C22⋊Q8C22×D1114yes—
543C4×Q8—22no—
544C4×Q8—22no—
545C4×Q8—22no—
546C4×Q8—22no—
547C4×Q8—22no—
548C4×Q8—22no—
549C4×Q8—112no—
550C4×Q8—112no—
551C4×Q8—112no—
552C4×Q8—112no—
553C4×Q8—221no—
554C4×Q8—221no—
555C4×Q8—221no—
556C4×Q8—221no—
557C4×Q8C22×D1114yes—
558C4×Q8C22×D1114yes—
559C4×D4—112no—
560C4×D4—112no—
561C4×D4—112no—
562C4×D4—112no—
563C4×D4—222no—
564C4×D4—222no—
565C4×D4—222no—
566C4×D4—222no—
567C4×D4—222no—
568C4×D4—222no—
569C4×D4—222no—
570C4×D4—222no—
571C4×D4—221no—
572C4×D4—221no—
573C4×D4—221no—
574C4×D4—221no—
575#117—22no—
576#117—22no—
577#117—22no—
578#117—22no—
579#117—112no—
580#117—112no—
581#117—221no—
582#117—221no—
583#117—222no—
584#117—222no—
585#117—222no—
586#117—222no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—111no—
593C2×C4⋊C4—111no—
594C2×C4⋊C4—221no—
595C2×C4⋊C4—221no—
596C2×C4⋊C4C22×D1112yes—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—221no—
599C2×C22⋊C4—221no—
600C2×C22⋊C4—221no—
601C2×C42—22no—
602C2×C42—221no—
603C2×C42—221no—
604C2×C42—221no—
605C2×C42—222no—
606C2×C42—222no—
607C2×C42—222no—
608C2×C42—222no—
609C2×C42C22⋊D1111yescharacteristic
610C2×C42C22⋊D1111yescharacteristic
611C2×C42C22⋊D1111yescharacteristic
612C2×C42C22⋊D1111yescharacteristic
613C2×C42C22⋊D1111yescharacteristic
614C2×C42C22⋊D1111yescharacteristic
615C2×C42C22×D1111yescharacteristic
616C2×C42C22×D1111yescharacteristic
617C2×C42C22×D1111yescharacteristic
618C2×C42C22×D1111yescharacteristic
619C2×C42C22×D1111yescharacteristic
620C2×C42C22×D1111yescharacteristic
621#107—118no—
622#106—118no—
623C4⋊C8—114no—
624C4⋊C8—114no—
625#103—118no—
626#103—118no—
627#103—118no—
628#102—118no—
629C22⋊C8—114no—
630C22⋊C8—114no—
631#97—114no—
632C4×C8—114no—
633C2×C11—22no—
634C2×C11—22no—
635C2×C11—41no—
636C2×C11C2×#52511yescharacteristic
637C2×C11C22×#13711yescharacteristic
638C2×C11C2×#57511yescharacteristic
639D11—44no—
640C24—221no—
641C24C2×C22⋊D1111yescharacteristic
642#41—118no—
643#41—224no—
644#41—224no—
645#41—228no—
646#41—228no—
647#41—224no—
648C2×Q8—22no—
649C2×Q8—22no—
650C2×Q8—22no—
651C2×Q8—28no—
652C2×Q8—44no—
653C2×Q8—112no—
654C2×Q8—224no—
655C2×Q8—221no—
656C2×Q8C23×D1114yes—
657C2×D4—112no—
658C2×D4—224no—
659C2×D4—228no—
660C2×D4—222no—
661C2×D4—222no—
662C2×D4—221no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—42no—
668C22×C4—228no—
669C22×C4—221no—
670C22×C4—222no—
671C22×C4—222no—
672C22×C4—221no—
673C22×C4—221no—
674C22×C4—222no—
675C22×C4—222no—
676C22×C4—222no—
677C22×C4—222no—
678C22×C4—444no—
679C22×C4—444no—
680C22×C4C2×C22⋊D1111yescharacteristic
681C22×C4C2×C22⋊D1111yescharacteristic
682C22×C4C2×C22⋊D1111yescharacteristic
683C22×C4C2×C22⋊D1111yescharacteristic
684C22×C4C2×C22⋊D1111yescharacteristic
685C22×C4C2×C22⋊D1111yescharacteristic
686C22×C4C2×C22⋊D1111yescharacteristic
687C22×C4C2×C22⋊D1111yescharacteristic
688C22×C4C2×C22⋊D1111yescharacteristic
689C22×C4C2×C22⋊D1111yescharacteristic
690C22×C4C2×C22⋊D1111yescharacteristic
691C22×C4C2×C22⋊D1111yescharacteristic
692C22×C4C2×C22⋊D1111yescharacteristic
693C22×C4C2×C22⋊D1111yescharacteristic
694C22×C4C2×C22⋊D1111yescharacteristic
695C22×C4C23×D1111yescharacteristic
696C22×C4C23×D1111yescharacteristic
697C22×C4C23×D1111yescharacteristic
698Q16—2216no—
699SD16—2216no—
700M16—228no—
701C2×C8—118no—
702C4⋊C4—22no—
703C4⋊C4—22no—
704C4⋊C4—22no—
705C4⋊C4—22no—
706C4⋊C4—22no—
707C4⋊C4—22no—
708C4⋊C4—24no—
709C4⋊C4—24no—
710C4⋊C4—24no—
711C4⋊C4—24no—
712C4⋊C4—22no—
713C4⋊C4—112no—
714C4⋊C4—112no—
715C4⋊C4—221no—
716C4⋊C4—221no—
717C4⋊C4—222no—
718C4⋊C4—222no—
719C4⋊C4—222no—
720C4⋊C4—222no—
721C4⋊C4C23×D1114yes—
722C22⋊C4—24no—
723C22⋊C4—24no—
724C22⋊C4—222no—
725C22⋊C4—222no—
726C22⋊C4—222no—
727C22⋊C4—222no—
728C22⋊C4—222no—
729C22⋊C4—222no—
730C42—24no—
731C42—24no—
732C42—222no—
733C42—222no—
734C42—222no—
735C42—222no—
736C42—222no—
737C42—222no—
738C42C2×C22⋊D1111yescharacteristic
739C42C2×C22⋊D1111yescharacteristic
740C42C2×C22⋊D1111yescharacteristic
741C42C2×C22⋊D1111yescharacteristic
742C42C2×C22⋊D1111yescharacteristic
743C42C2×C22⋊D1111yescharacteristic
744C42C2×C22⋊D1111yescharacteristic
745C42C2×C22⋊D1111yescharacteristic
746C42C2×C22⋊D1111yescharacteristic
747C42C2×C22⋊D1111yescharacteristic
748C42C2×C22⋊D1111yescharacteristic
749C42C2×C22⋊D1111yescharacteristic
750C42C23×D1111yescharacteristic
751C42C23×D1111yescharacteristic
752C42C23×D1111yescharacteristic
753C42C23×D1111yescharacteristic
754C11#6056211yescharacteristic, complemented, Sylow
755C23—22no—
756C23—22no—
757C23—41no—
758C23—224no—
759C23—222no—
760C23—442no—
761C23—442no—
762C23C22×C22⋊D1111yescharacteristic
763C23C22×C22⋊D1111yescharacteristic
764C23C22×C22⋊D1111yescharacteristic
765Q8—28no—
766Q8—44no—
767Q8—44no—
768Q8—44no—
769Q8—114no—
770Q8—224no—
771Q8—222no—
772D4—114no—
773D4—224no—
774D4—228no—
775D4—228no—
776D4—222no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—228no—
798C2×C4—224no—
799C2×C4—222no—
800C2×C4—228no—
801C2×C4—222no—
802C2×C4—222no—
803C2×C4—444no—
804C2×C4—442no—
805C2×C4—442no—
806C2×C4—444no—
807C2×C4—444no—
808C2×C4—444no—
809C2×C4#6699514yescomplemented
810C2×C4#41×D1114yes—
811C2×C4C22×C22⋊D1111yescharacteristic
812C2×C4C22×C22⋊D1111yescharacteristic
813C2×C4C22×C22⋊D1111yescharacteristic
814C2×C4C22×C22⋊D1111yescharacteristic
815C2×C4C22×C22⋊D1111yescharacteristic
816C2×C4C22×C22⋊D1111yescharacteristic
817C2×C4C22×C22⋊D1111yescharacteristic
818C2×C4C22×C22⋊D1111yescharacteristic
819C2×C4C22×C22⋊D1111yescharacteristic
820C2×C4C22×C22⋊D1111yescharacteristic
821C2×C4C22×C22⋊D1111yescharacteristic
822C2×C4C24×D1111yescharacteristic
823C8—228no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—44no—
832C22—224no—
833C22—448no—
834C22—442no—
835C22—442no—
836C22C2×#6699512yes—
837C22#1062335912yes—
838C22C23×C22⋊D1111yescharacteristic
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—21no—
846C4—44no—
847C4—44no—
848C4—224no—
849C4—442no—
850C4—442no—
851C4C2×#6699512yes—
852C4C2×#6699512yes—
853C4#1062335312yes—
854C4#1062335912yes—
855C4C2×#41×D1112yes—
856C2—22no—
857C2—22no—
858C2—41no—
859C2—444no—
860C2C2×#1062335911yescharacteristic
861C2C22×#6699511yescharacteristic
862C2C2×#1062335311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#533C2
socleC22×C11C23×D4
prime radicalC22×#4339C22
hypercenterC2×#533D11
hypocenterC11#60562
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
2. #13078772C2semidirect
3. #13078742C2semidirect
4. #13078711C2semidirect
5. #13078681C2semidirect
6. #13078651C2semidirect
7. #13078620C2semidirect
8. #13078560C2semidirect
9. #13078425C2semidirect
10. #13078099C2semidirect
12. C4×#66995C2semidirect
13. #13077249C2semidirect
14. C2×C11×#533C2semidirect
22. C11×#533C22semidirect
23. C11×#533C22semidirect
24. C2×C11×C4⋊Q8C22semidirect
25. C2×C11×C4⋊Q8C22semidirect
30. C2×C4×Q8×C11C22semidirect
51. #10622838C22semidirect
53. #10622707C22semidirect
54. #10622704C22semidirect
55. #10622703C22semidirect
56. #10622703C22semidirect
57. #10622700C22semidirect
58. #10622697C22semidirect
59. #10622696C22semidirect
60. #10622696C22semidirect
64. #10622658C22semidirect
67. #10622643C22semidirect
68. C4×#4326C22semidirect
69. #10622639C22semidirect
70. C4×#4325C22semidirect
72. #10622577C22semidirect
74. #10622539C22semidirect
76. #10622538C22semidirect
77. #10622537C22semidirect
78. C4×#4318C22semidirect
324. C2×#533D11semidirect
372. C2×C4×C11#137semidirect
415. #533C2×D11semidirect
416. #533C2×D11semidirect
417. C2×C4⋊Q8C2×D11semidirect
418. C2×C4⋊Q8C2×D11semidirect
433. C2×C4×Q8C2×D11semidirect
754. C11#60562semidirect
809. C2×C4#66995semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43392
#130787722
#130787422
#130787112
#130786812
#130786512
#130786202
#130785602
#130784252
#130780992
#130778742
C4×#669952
#130772492
C2×C11×#5332
#6056211