Finite Group Databasebeta

← #14913614

Subgroups — #14913614

Order 2816.

3268 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623257C211yesmaximal, characteristic
2C2×C4×#4343C212yesmaximal, complemented
3#13071639C212yesmaximal, complemented
4#13071634C212yesmaximal, complemented
5#13071615C214yesmaximal, complemented
6#13071563C211yesmaximal, characteristic, complemented
7C4⋊C4×D44C211yesmaximal, characteristic, complemented
8#13071484C212yesmaximal, complemented
9#13071445C212yesmaximal, complemented
10C4⋊Q8×Dic11C211yesmaximal, characteristic, complemented
11#13071154C212yesmaximal, complemented
12#13071137C214yesmaximal, complemented
13#13071124C212yesmaximal, complemented
14C4×#66946C211yesmaximal, characteristic, complemented
15C4×#66946C211yesmaximal, characteristic, complemented
16C4×C4⋊C4×D11C212yesmaximal, complemented
17C11×#2365C211yesmaximal, characteristic, complemented
18C22×#4343C2212yes—
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C4×Q8×C11C2212yes—
21C2×#66999C2212yes—
22C2×Q8×Dic11C2212yes—
23#10623257C4116yescomplemented
24C4×#4343—216no—
25C2×#66948C2212yes—
26C2×#66947C2214yes—
27C2×#66946C2211yescharacteristic
28C2×#66946C2211yescharacteristic
29C2×#66946C2214yes—
30C2×#66946C2211yescharacteristic
31C2×#66946C2211yescharacteristic
32C2×#66945C2212yes—
33C2×#66945C2214yes—
34C2×C4⋊C4×D11C2212yes—
35C2×C4⋊C4×D11C2212yes—
36C2×C4×D44C2214yes—
37C2×C4×D44C2212yes—
38C2×C4×D44C2211yescharacteristic
39C2×C4×D44C2211yescharacteristic
40C2×C42×D11C2212yes—
41C2×C42×D11C2214yes—
42C2×C42×D11C2212yes—
43C11×#391C2212yes—
44C11×#389C2212yes—
45C11×#387C2214yes—
46C4×C11×C4⋊C4C2212yes—
47C4×C11×C4⋊C4C2211yescharacteristic
48C4×C11×C4⋊C4C2211yescharacteristic
49#10622843C2212yes—
50#10622603C2214yes—
51#10622600C2212yes—
52#10622600C2212yes—
53#10622598C2212yes—
54#10622598C2212yes—
55#10622591C2214yes—
56C4⋊C4×Dic11C2212yes—
57C4⋊C4×Dic11C2211yescharacteristic
58C4⋊C4×Dic11C2212yes—
59C4⋊C4×Dic11C2211yescharacteristic
60C4⋊C4×Dic11C2211yescharacteristic
61C4⋊C4×Dic11C2211yescharacteristic
62#10622553C2214yes—
63#10622552C2212yes—
64C4×(C2×D11)⋊C4C2212yes—
65C4×(C2×D11)⋊C4C2212yes—
66#10622548C2211yescharacteristic
67C4×C4⋊Dic11C2212yes—
68C4×Dic11⋊C4C2214yes—
69C42×Dic11C2211yescharacteristic
70#10622541C2212yes—
71#10622283C2214yes—
72#10622281C2214yes—
73#10622281C2214yes—
74#10622279C2214yes—
75#10622279C2212yes—
76#10622279C2212yes—
77#10622279C2212yes—
78#10622279C2212yes—
79#10622278C2214yes—
80#10622278C2214yes—
81#10622277C2214yes—
82D11×#95C2214yes—
83#10622268C2214yes—
84#10622262C2214yes—
85C22×Q8×C11C2312yes—
86C2×#4343—28no—
87C2×#4343—28no—
88C2×#4343C2×C4116yescomplemented
89C22×D44C2311yescharacteristic
90C22×D44C2314yes—
91C22×D44C2311yescharacteristic
92C22×C4×D11C2312yes—
93C22×C4×D11C2314yes—
94C22×C4×D11C2312yes—
95C22×C4×D11C2312yes—
96C22×C4×D11C2312yes—
97C22×C4×D11C2312yes—
98C22×C4×D11C2314yes—
99C22×C4×D11C2312yes—
100C11×C4⋊Q8C2×C418yescomplemented
101C4×Q8×C11—28no—
102C2×C11×C4⋊C4C2314yes—
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2312yes—
106C2×C11×C4⋊C4C2312yes—
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C42×C11C2312yes—
110C2×C42×C11C2314yes—
111C2×C42×C11C2312yes—
112C2×C42×C11C2311yescharacteristic
113#66999C2×C4116yescomplemented
114Q8×Dic11—28no—
115C2×(C2×D11)⋊C4C2314yes—
116C2×(C2×D11)⋊C4C2314yes—
117C2×(C2×D11)⋊C4C2312yes—
118C2×(C2×D11)⋊C4C2312yes—
119C2×(C2×D11)⋊C4C2312yes—
120C2×(C2×D11)⋊C4C2314yes—
121C2×(C2×D11)⋊C4C2312yes—
122C2×(C2×D11)⋊C4C2312yes—
123C2×(C2×D11)⋊C4C2314yes—
124C2×(C2×D11)⋊C4C2312yes—
125C2×C4⋊Dic11C2314yes—
126C2×C4⋊Dic11C2312yes—
127C2×C4⋊Dic11C2312yes—
128C2×C4⋊Dic11C2312yes—
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131C2×Dic11⋊C4C2314yes—
132C2×Dic11⋊C4C2314yes—
133C2×C4×Dic11C2312yes—
134C2×C4×Dic11C2312yes—
135C2×C4×Dic11C2314yes—
136C2×C4×Dic11C2312yes—
137C2×C4×Dic11C2314yes—
138C2×C4×Dic11C2312yes—
139C2×C4×Dic11C2311yescharacteristic
140C2×C4×Dic11C2311yescharacteristic
141C2×C4×Dic11C2311yescharacteristic
142C2×C4×Dic11C2311yescharacteristic
143C2×C4×Dic11C2311yescharacteristic
144C2×C4×Dic11C2311yescharacteristic
145#66948C2×C4116yescomplemented
146#66947C2×C4132yescomplemented
147#66946—24no—
148#66946—216no—
149#66946—24no—
150#66946—24no—
151#66946D418yescomplemented
152#66945—28no—
153#66945—216no—
154C4⋊C4×D11—28no—
155C4⋊C4×D11C2×C4116yescomplemented
156C4×D44—28no—
157C4×D44—216no—
158C4×D44C2×C418yescomplemented
159C4×D44C2×C418yescomplemented
160C42×D11—216no—
161C42×D11—28no—
162C42×D11—28no—
163C11×#95C2314yes—
164C11×#95C2314yes—
165C11×#95C2312yes—
166C11×#95C2312yes—
167C11⋊#95C2314yes—
168C11⋊#95C2312yes—
169C11⋊#95C2314yes—
170C11⋊#95C2312yes—
171C11⋊#95C2314yes—
172C11⋊#95C2312yes—
173C11⋊#95C2314yes—
174C11⋊#95C2312yes—
175C4×#547—111nomaximal, Sylow
176C23×D11C2412yes—
177C23×D11C2412yes—
178C2×Q8×C11—24no—
179C2×Q8×C11—24no—
180C2×Q8×C11C22×C418yes—
181C22×C4×C11C2412yes—
182C22×C4×C11C2412yes—
183C22×C4×C11C2414yes—
184C22×C4×C11C2411yescharacteristic
185C22×C4×C11C2412yes—
186C22×C4×C11C2412yes—
187C22×C4×C11C2411yescharacteristic
188C22×C4×C11C2411yescharacteristic
189C22×Dic11C2411yescharacteristic
190C22×Dic11C2414yes—
191C22×Dic11C2412yes—
192C22×Dic11C2412yes—
193C22×Dic11C2411yescharacteristic
194C22×Dic11C2411yescharacteristic
195C22×Dic11C2411yescharacteristic
196#4343—264no—
197C2×D44—28no—
198C2×D44—28no—
199C2×D44—22no—
200C2×D44—22no—
201C2×D44C22×C414yes—
202C2×D44C22×C4116yes—
203C2×D44C22×C414yes—
204C2×D44C2×D414yes—
205C2×D44#4114yes—
206C2×C4×D11—24no—
207C2×C4×D11—24no—
208C2×C4×D11—24no—
209C2×C4×D11—24no—
210C2×C4×D11—24no—
211C2×C4×D11—24no—
212C2×C4×D11—24no—
213C2×C4×D11—28no—
214C2×C4×D11—28no—
215C2×C4×D11—28no—
216C2×C4×D11—24no—
217C2×C4×D11—24no—
218C2×C4×D11—24no—
219C2×C4×D11—24no—
220C2×C4×D11—24no—
221C2×C4×D11—28no—
222C2×C4×D11—24no—
223C2×C4×D11—44no—
224C2×C4×D11—42no—
225C2×C4×D11—42no—
226C2×C4×D11C22×C418yes—
227C2×C4×D11C22×C418yes—
228C2×C4×D11C22×C4116yes—
229C2×C4×D11C2×D418yes—
230C11×C4⋊C4—28no—
231C11×C4⋊C4—22no—
232C11×C4⋊C4—22no—
233C11×C4⋊C4C22×C418yes—
234C11×C4⋊C4C22×C418yes—
235C11×C4⋊C4C2×D414yes—
236C11×C4⋊C4#4114yescomplemented
237C42×C11—28no—
238C42×C11—24no—
239C42×C11—24no—
240C42×C11C22×C414yes—
241(C2×D11)⋊C4—24no—
242(C2×D11)⋊C4—28no—
243(C2×D11)⋊C4—24no—
244(C2×D11)⋊C4—28no—
245(C2×D11)⋊C4—24no—
246(C2×D11)⋊C4—44no—
247(C2×D11)⋊C4C22×C418yes—
248(C2×D11)⋊C4C22×C418yes—
249(C2×D11)⋊C4C22×C4116yes—
250(C2×D11)⋊C4C2×D418yes—
251C4⋊Dic11—28no—
252C4⋊Dic11—24no—
253C4⋊Dic11—24no—
254C4⋊Dic11—42no—
255C4⋊Dic11C22×C414yes—
256C4⋊Dic11C22×C414yes—
257Dic11⋊C4—28no—
258Dic11⋊C4C22×C4116yes—
259C4×Dic11—24no—
260C4×Dic11—24no—
261C4×Dic11—28no—
262C4×Dic11—24no—
263C4×Dic11—24no—
264C4×Dic11—22no—
265C4×Dic11—28no—
266C4×Dic11—22no—
267C4×Dic11—22no—
268C4×Dic11—41no—
269C4×Dic11C2×D414yes—
270C4×Dic11#4114yescomplemented
271C2×#547—111no—
272C2×C4×#41—112no—
273#2365D1111yescharacteristic, complemented
274#2362—112no—
275#2361—112no—
276#2359—114no—
277#2354—111no—
278D4×C4⋊C4—111no—
279#2344—112no—
280#2339—112no—
281C4×C4⋊Q8—111no—
282C4×C22⋊Q8—112no—
283C4×#123—114no—
284C4×#121—112no—
285C42×D4—111no—
286C42×D4—111no—
287C2×C4×C4⋊C4—112no—
288C23×C11C2511yescharacteristic
289C22×D11—22no—
290C22×D11—22no—
291C22×D11—22no—
292C22×D11—22no—
293C22×D11—22no—
294C22×D11—22no—
295C22×D11—22no—
296C22×D11—22no—
297C22×D11—22no—
298C22×D11—22no—
299C22×D11C23×C414yes—
300C22×D11C23×C414yes—
301C22×D11C22×D414yes—
302C22×D11C2×#4114yes—
303Q8×C11—216no—
304C2×C4×C11—24no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—24no—
308C2×C4×C11—21no—
309C2×C4×C11—22no—
310C2×C4×C11—21no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11C23×C418yes—
319C2×C4×C11C23×C412yes—
320C2×C4×C11C23×C412yes—
321C2×C4×C11C23×C412yes—
322C2×C4×C11C22×D414yes—
323C2×C4×C11C22×D412yes—
324C2×C4×C11C2×#4114yes—
325C2×C4×C11C2×#4112yes—
326C2×C4×C11C2×#4112yes—
327C2×C4×C11C2×#4112yes—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—21no—
331C2×Dic11—21no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—21no—
335C2×Dic11—21no—
336C2×Dic11—24no—
337C2×Dic11—21no—
338C2×Dic11—21no—
339C2×Dic11—24no—
340C2×Dic11—21no—
341C2×Dic11—24no—
342C2×Dic11C23×C414yes—
343C2×Dic11C23×C414yes—
344C2×Dic11C22×D412yes—
345C2×Dic11C22×D412yes—
346C2×Dic11C2×#4112yes—
347C2×Dic11C2×#4112yes—
348C2×Dic112−1+412yes—
349D44—232no—
350D44—28no—
351D44C4×D4116yescomplemented
352C4×D11—232no—
353C4×D11—216no—
354C4×D11—216no—
355C4×D11—216no—
356C4×D11—48no—
357C4×D11—48no—
358C4×D11—416no—
359C4×D11—48no—
360C22×#41—112no—
361#547—1116no—
362C2×C4⋊Q8C2×D1111yescharacteristic
363C2×#123—114no—
364C2×C22⋊Q8—112no—
365C2×#121—112no—
366C4×#41—2216no—
367C2×C4×Q8—112no—
368C2×C4×Q8C2×D1112yes—
369C2×C4×D4—111no—
370C2×C4×D4—111no—
371C2×C4×D4—111no—
372C2×C4×D4—114no—
373C2×C4×D4—111no—
374C2×C4×D4—111no—
375C2×C4×D4—111no—
376C2×C4×D4—112no—
377C2×C4×D4—114no—
378C2×#117—114no—
379C2×#117—112no—
380C22×C4⋊C4—112no—
381C22×C4⋊C4—112no—
382C22×C42—114no—
383C22×C42—112no—
384C22×C42—112no—
385#391—112no—
386#391C2×D1112yes—
387#390—112no—
388#389—112no—
389#389—112no—
390#389—112no—
391#389C2×D1112yes—
392#388—114no—
393#388—114no—
394#388—114no—
395#387—114no—
396#387—114no—
397#387C2×D1114yes—
398#386—114no—
399#386—114no—
400#385—114no—
401#385—114no—
402#384—111no—
403#381—114no—
404#380—112no—
405#380—112no—
406C4×C4⋊C4—112no—
407C4×C4⋊C4—112no—
408C4×C4⋊C4—111no—
409C4×C4⋊C4—111no—
410C4×C4⋊C4—111no—
411C4×C4⋊C4—111no—
412C4×C4⋊C4—112no—
413C4×C4⋊C4—114no—
414C4×C4⋊C4—114no—
415C4×C4⋊C4C2×D1111yescharacteristic
416C4×C4⋊C4C2×D1111yescharacteristic
417C4×C4⋊C4C2×D1112yes—
418C4×C22⋊C4—112no—
419C4×C22⋊C4—112no—
420C4×C22⋊C4—112no—
421C4×C22⋊C4—112no—
422C4×C22⋊C4—112no—
423C4×C22⋊C4—112no—
424C4×C22⋊C4—114no—
425C2×#95—114no—
426C43—111no—
427C22×C11C24×C411yescharacteristic
428C22×C11C23×D411yescharacteristic
429C22×C11C22×#4111yescharacteristic
430C22×C11C22×#4111yescharacteristic
431C22×C11C22×#4111yescharacteristic
432C22×C11C2×2−1+411yescharacteristic
433C22×C11#58511yescharacteristic
434C2×D11—24no—
435C2×D11—24no—
436C2×D11—24no—
437C2×D11—24no—
438C2×D11—24no—
439C2×D11—24no—
440C2×D11—24no—
441C2×D11—24no—
442C2×D11—24no—
443C2×D11—42no—
444C2×D11—42no—
445C2×D11—42no—
446C2×D11—42no—
447C2×D11C2×C4×D418yes—
448C4×C11—28no—
449C4×C11—22no—
450C4×C11—24no—
451C4×C11—24no—
452C4×C11—42no—
453C4×C11—42no—
454C4×C11C2×C4×D414yes—
455C4×C11C4×#4114yescomplemented
456Dic11—24no—
457Dic11—24no—
458Dic11—22no—
459Dic11—22no—
460Dic11—44no—
461Dic11—41no—
462Dic11#54714yescomplemented
463C2×#41—1116no—
464C2×#41—228no—
465C2×#41—228no—
466C22×Q8C22×D1112yes—
467C22×D4—111no—
468C22×D4—111no—
469C22×D4—114no—
470C23×C4—112no—
471C23×C4—114no—
472C23×C4—112no—
473C23×C4—112no—
474C23×C4—112no—
475C23×C4—114no—
476C23×C4—112no—
477C23×C4—112no—
478C4⋊Q8C4×D1118yescomplemented
479#123—1132no—
480C22⋊Q8—1116no—
481#121—1116no—
482C4×Q8—28no—
483C4×Q8—228no—
484C4×D4—118no—
485C4×D4—118no—
486C4×D4—118no—
487C4×D4—2216no—
488C4×D4—228no—
489C4×D4—224no—
490C4×D4—2216no—
491C4×D4—224no—
492C4×D4—224no—
493#117—2216no—
494#117—228no—
495C2×C4⋊C4—111no—
496C2×C4⋊C4—114no—
497C2×C4⋊C4—111no—
498C2×C4⋊C4—1116no—
499C2×C4⋊C4—112no—
500C2×C4⋊C4—114no—
501C2×C4⋊C4—112no—
502C2×C4⋊C4—114no—
503C2×C4⋊C4—112no—
504C2×C4⋊C4—228no—
505C2×C4⋊C4C22×D1114yes—
506C2×C4⋊C4C22×D1111yescharacteristic
507C2×C4⋊C4C22×D1111yescharacteristic
508C2×C4⋊C4C22×D1112yes—
509C2×C4⋊C4C22×D1112yes—
510C2×C4⋊C4C22×D1111yescharacteristic
511C2×C4⋊C4C22×D1111yescharacteristic
512C2×C22⋊C4—112no—
513C2×C22⋊C4—112no—
514C2×C22⋊C4—112no—
515C2×C22⋊C4—114no—
516C2×C22⋊C4—114no—
517C2×C22⋊C4—114no—
518C2×C22⋊C4—112no—
519C2×C22⋊C4—112no—
520C2×C22⋊C4—112no—
521C2×C22⋊C4—114no—
522C2×C42—111no—
523C2×C42—111no—
524C2×C42—112no—
525C2×C42—114no—
526C2×C42—114no—
527C2×C42—111no—
528C2×C42—111no—
529C2×C42—111no—
530C2×C42—112no—
531C2×C42—112no—
532C2×C42—112no—
533C2×C42—111no—
534C2×C42—228no—
535C2×C42—228no—
536C2×C42—2216no—
537C2×C42C22×D1112yes—
538C2×C42C22×D1114yes—
539C2×C42C22×D1112yes—
540C2×C42C22×D1111yescharacteristic
541#95—112no—
542#95—114no—
543#95—114no—
544#95—112no—
545#95—112no—
546#95—112no—
547#95—114no—
548#95—114no—
549#95C22×D1114yes—
550#95C22×D1112yes—
551#95C22×D1112yes—
552#95C22×D1114yes—
553C2×C11C22×C4×D411yescharacteristic
554C2×C11C2×C4×#4111yescharacteristic
555C2×C11C4×2−1+411yescharacteristic
556C2×C11C2×#54711yescharacteristic
557C2×C11D4×#4111yescharacteristic
558C2×C11#347511yescharacteristic
559C2×C11#348211yescharacteristic
560D11—28no—
561D11—44no—
562C24—112no—
563C24—112no—
564#41—2264no—
565C2×Q8—24no—
566C2×Q8—24no—
567C2×Q8C2×C4×D1118yes—
568C2×D4—114no—
569C2×D4—114no—
570C2×D4—1116no—
571C2×D4—114no—
572C2×D4—114no—
573C2×D4—228no—
574C2×D4—228no—
575C2×D4—222no—
576C2×D4—222no—
577C22×C4—111no—
578C22×C4—111no—
579C22×C4—112no—
580C22×C4—112no—
581C22×C4—111no—
582C22×C4—118no—
583C22×C4—1116no—
584C22×C4—118no—
585C22×C4—118no—
586C22×C4—111no—
587C22×C4—114no—
588C22×C4—224no—
589C22×C4—224no—
590C22×C4—224no—
591C22×C4—224no—
592C22×C4—224no—
593C22×C4—224no—
594C22×C4—224no—
595C22×C4—228no—
596C22×C4—228no—
597C22×C4—228no—
598C22×C4—224no—
599C22×C4—224no—
600C22×C4—224no—
601C22×C4—224no—
602C22×C4—224no—
603C22×C4—228no—
604C22×C4—224no—
605C22×C4—442no—
606C22×C4—444no—
607C22×C4—442no—
608C22×C4C23×D1112yes—
609C22×C4C23×D1112yes—
610C22×C4C23×D1114yes—
611C22×C4C23×D1111yescharacteristic
612C22×C4C23×D1112yes—
613C22×C4C23×D1112yes—
614C22×C4C23×D1111yescharacteristic
615C22×C4C23×D1111yescharacteristic
616C4⋊C4—28no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—114no—
620C4⋊C4—1116no—
621C4⋊C4—114no—
622C4⋊C4—228no—
623C4⋊C4—224no—
624C4⋊C4—228no—
625C4⋊C4—224no—
626C4⋊C4—442no—
627C4⋊C4C2×C4×D1118yes—
628C4⋊C4C2×C4×D1118yes—
629C4⋊C4D4×D1114yes—
630C4⋊C4#434314yescomplemented
631C22⋊C4—118no—
632C22⋊C4—118no—
633C22⋊C4—1116no—
634C22⋊C4—118no—
635C22⋊C4—224no—
636C22⋊C4—228no—
637C22⋊C4—224no—
638C22⋊C4—228no—
639C22⋊C4—224no—
640C22⋊C4—444no—
641C42—28no—
642C42—24no—
643C42—24no—
644C42—114no—
645C42—114no—
646C42—224no—
647C42—224no—
648C42—228no—
649C42—224no—
650C42—224no—
651C42—222no—
652C42—228no—
653C42—222no—
654C42—222no—
655C42—441no—
656C42C2×C4×D1114yes—
657C11C4×#54711yescharacteristic, complemented, Sylow
658C23—114no—
659C23—114no—
660C23—114no—
661C23—114no—
662C23—222no—
663C23—222no—
664C23—222no—
665C23—222no—
666C23—222no—
667C23—222no—
668C23—222no—
669C23—222no—
670C23—222no—
671C23—222no—
672C23C24×D1111yescharacteristic
673Q8—216no—
674D4—1116no—
675D4—2232no—
676D4—228no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—112no—
692C2×C4—112no—
693C2×C4—112no—
694C2×C4—114no—
695C2×C4—114no—
696C2×C4—112no—
697C2×C4—112no—
698C2×C4—2216no—
699C2×C4—2232no—
700C2×C4—222no—
701C2×C4—221no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—221no—
705C2×C4—222no—
706C2×C4—221no—
707C2×C4—221no—
708C2×C4—2216no—
709C2×C4—2216no—
710C2×C4—224no—
711C2×C4—221no—
712C2×C4—224no—
713C2×C4—221no—
714C2×C4—221no—
715C2×C4—224no—
716C2×C4—448no—
717C2×C4—4416no—
718C2×C4—448no—
719C2×C4—448no—
720C2×C4C22×C4×D1112yes—
721C2×C4C22×C4×D1118yes—
722C2×C4C22×C4×D1112yes—
723C2×C4C22×C4×D1112yes—
724C2×C4C2×D4×D1114yes—
725C2×C4C2×D4×D1112yes—
726C2×C4C2×#434314yes—
727C2×C4C2×#434312yes—
728C2×C4#41×D1112yes—
729C2×C4#41×D1112yes—
730C22—118no—
731C22—224no—
732C22—224no—
733C22—224no—
734C22—224no—
735C22—224no—
736C22—224no—
737C22—224no—
738C22—224no—
739C22—224no—
740C22—442no—
741C22—442no—
742C22—442no—
743C22—442no—
744C22C23×C4×D1111yescharacteristic
745C22C22×D4×D1111yescharacteristic
746C22C22×#434311yescharacteristic
747C22C2×#41×D1111yescharacteristic
748C22C2×#41×D1111yescharacteristic
749C22D11×2−1+411yescharacteristic
750C22#1062345711yescharacteristic
751C4—28no—
752C4—24no—
753C4—22no—
754C4—24no—
755C4—42no—
756C4—42no—
757C4—114no—
758C4—222no—
759C4—224no—
760C4—224no—
761C4—222no—
762C4—441no—
763C4—444no—
764C4C4×D4×D1114yes—
765C4C4×#434314yescomplemented
766C2—228no—
767C2—444no—
768C2C2×C4×D4×D1111yescharacteristic
769C2C2×C4×#434311yescharacteristic
770C2#1308182511yescharacteristic
771C2D11×#54711yescharacteristic
772C2D4×#434311yescharacteristic
773C2#1308217711yescharacteristic
774C2#1308223611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2365C2
socle, cosocleC23×C11C25
prime radicalC2×#10623257C2
hypercenter#2365D11
hypocenterC11C4×#547
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2365

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4343C2semidirect
3. #13071639C2semidirect
4. #13071634C2semidirect
5. #13071615C2semidirect
6. #13071563C2semidirect
7. C4⋊C4×D44C2semidirect
8. #13071484C2semidirect
9. #13071445C2semidirect
10. C4⋊Q8×Dic11C2semidirect
11. #13071154C2semidirect
12. #13071137C2semidirect
13. #13071124C2semidirect
14. C4×#66946C2semidirect
15. C4×#66946C2semidirect
16. C4×C4⋊C4×D11C2semidirect
17. C11×#2365C2semidirect
23. #10623257C4semidirect
88. C2×#4343C2×C4semidirect
100. C11×C4⋊Q8C2×C4semidirect
113. #66999C2×C4semidirect
145. #66948C2×C4semidirect
146. #66947C2×C4semidirect
151. #66946D4semidirect
155. C4⋊C4×D11C2×C4semidirect
158. C4×D44C2×C4semidirect
159. C4×D44C2×C4semidirect
236. C11×C4⋊C4#41semidirect
270. C4×Dic11#41semidirect
273. #2365D11semidirect
351. D44C4×D4semidirect
455. C4×C11C4×#41semidirect
462. Dic11#547semidirect
478. C4⋊Q8C4×D11semidirect
630. C4⋊C4#4343semidirect
657. C11C4×#547semidirect
765. C4C4×#4343semidirect

Maximal subgroups

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

subgroupindex
C2×#106232572
C2×C4×#43432
#130716392
#130716342
#130716152
#130715632
C4⋊C4×D442
#130714842
#130714452
C4⋊Q8×Dic112
#130711542
#130711372
#130711242
C4×#669462
C4×C4⋊C4×D112
C11×#23652
C4×#54711