Finite Group Databasebeta

← #14913387

Subgroups — #14913387

Order 2816.

3298 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623079C211yesmaximal, characteristic
2C2×#10623053C212yesmaximal, complemented
3#13071682C214yesmaximal, complemented
4#13071677C212yesmaximal, complemented
5#13071669C212yesmaximal, complemented
6#13071660C214yesmaximal, complemented
7#13071637C212yesmaximal, complemented
8#13071631C212yesmaximal, complemented
9#13071102C212yesmaximal, complemented
10#13071077C211yesmaximal, characteristic, complemented
11#13071055C212yesmaximal, complemented
12#13071053C212yesmaximal, complemented
13C42×D44C211yesmaximal, characteristic, complemented
14C4×D4×Dic11C211yesmaximal, characteristic, complemented
15C4×#66925C211yesmaximal, characteristic, complemented
16C4×C4⋊C4×D11C211yesmaximal, characteristic, complemented
17C11×#2293C211yesmaximal, characteristic, complemented
18C22×#4339C2212yes—
19C2×C4×D4×C11C2211yescharacteristic
20C2×C11×#117C2212yes—
21C2×#66993C2211yescharacteristic
22C2×#66991C2211yescharacteristic
23C2×D4×Dic11C2212yes—
24C2×C4×C22⋊D11C2212yes—
25C22×C4×Dic11C2212yes—
26#10623079C4116yescomplemented
27#10623053—216no—
28C2×#66948C2211yescharacteristic
29C2×#66946C2214yes—
30C2×C4⋊C4×D11C2212yes—
31C2×#66941C2211yescharacteristic
32C2×#66940C2214yes—
33C2×#66938C2212yes—
34C2×#66937C2212yes—
35C2×(C22⋊D11)⋊C4C2214yes—
36C2×(C22⋊D11)⋊C4C2214yes—
37C2×C4×D44C2212yes—
38C2×C4×D44C2211yescharacteristic
39C2×#66925C2211yescharacteristic
40C2×#66925C2212yes—
41C2×#66925C2211yescharacteristic
42C2×C42×D11C2212yes—
43C2×C42×D11C2212yes—
44C2×C42×D11C2211yescharacteristic
45C11×#390C2212yes—
46C11×#389C2212yes—
47C11×#388C2214yes—
48C4×C11×C4⋊C4C2211yescharacteristic
49C4×C11×C22⋊C4C2212yes—
50C43×C11C2211yescharacteristic
51C4×C22⋊Dic11C2212yes—
52#10622602C2214yes—
53#10622601C2212yes—
54#10622591C2214yes—
55C4⋊C4×Dic11C2212yes—
56C4⋊C4×Dic11C2212yes—
57#10622586C2212yes—
58#10622571C2214yes—
59#10622570C2214yes—
60#10622569C2214yes—
61#10622569C2214yes—
62#10622559C2214yes—
63#10622557C2214yes—
64C22⋊C4×Dic11C2214yes—
65C4×(C2×D11)⋊C4C2212yes—
66C4×(C2×D11)⋊C4C2212yes—
67C4×(C2×D11)⋊C4C2214yes—
68C4×(C2×D11)⋊C4C2212yes—
69C4×(C2×D11)⋊C4C2212yes—
70C4×C4⋊Dic11C2212yes—
71C4×C4⋊Dic11C2211yescharacteristic
72#10622545C2211yescharacteristic
73#10622545C2211yescharacteristic
74C4×Dic11⋊C4C2212yes—
75C4×Dic11⋊C4C2212yes—
76C4×Dic11⋊C4C2212yes—
77C42×Dic11C2211yescharacteristic
78#10622282C2214yes—
79#10622282C2214yes—
80#10622278C2214yes—
81D11×#95C2212yes—
82#10622265C2214yes—
83#10622262C2212yes—
84#10622259C2214yes—
85C22×D4×C11C2311yescharacteristic
86C23×C4×C11C2312yes—
87C22×C22⋊D11C2312yes—
88C22×C22⋊D11C2312yes—
89C22×C22⋊D11C2312yes—
90C23×Dic11C2314yes—
91C2×#4339—28no—
92C2×#4339—28no—
93C2×#4339C2×C4116yescomplemented
94C22×D44C2311yescharacteristic
95C22×D44C2312yes—
96C22×C4×D11C2314yes—
97C22×C4×D11C2314yes—
98C22×C4×D11C2312yes—
99C22×C4×D11C2311yescharacteristic
100C22×C4×D11C2311yescharacteristic
101C22×C4×D11C2311yescharacteristic
102C22×Dic22C2312yes—
103C4×D4×C11C2×C418yescomplemented
104C11×#117—28no—
105C2×C11×C4⋊C4C2314yes—
106C2×C11×C4⋊C4C2312yes—
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C22⋊C4C2314yes—
109C2×C11×C22⋊C4C2314yes—
110C2×C11×C22⋊C4C2312yes—
111C2×C42×C11C2312yes—
112C2×C42×C11C2311yescharacteristic
113C2×C42×C11C2312yes—
114C2×C42×C11C2312yes—
115C2×C42×C11C2311yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C2×C22⋊Dic11C2314yes—
118C2×C22⋊Dic11C2312yes—
119#66993C2×C418yescomplemented
120#66991C2×C418yescomplemented
121D4×Dic11—28no—
122C4×C22⋊D11C2×C4116yescomplemented
123C2×(C2×D11)⋊C4C2314yes—
124C2×(C2×D11)⋊C4C2312yes—
125C2×(C2×D11)⋊C4C2314yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2312yes—
128C2×(C2×D11)⋊C4C2312yes—
129C2×(C2×D11)⋊C4C2312yes—
130C2×C4⋊Dic11C2311yescharacteristic
131C2×C4⋊Dic11C2312yes—
132C2×Dic11⋊C4C2314yes—
133C2×Dic11⋊C4C2312yes—
134C2×Dic11⋊C4C2314yes—
135C2×Dic11⋊C4C2312yes—
136C2×Dic11⋊C4C2312yes—
137C2×C4×Dic11—28no—
138C2×C4×Dic11C2312yes—
139C2×C4×Dic11C2314yes—
140C2×C4×Dic11C2314yes—
141C2×C4×Dic11C2311yescharacteristic
142C2×C4×Dic11C2314yes—
143C2×C4×Dic11C2312yes—
144C2×C4×Dic11C2312yes—
145C2×C4×Dic11C2311yescharacteristic
146C2×C4×Dic11C2311yescharacteristic
147C2×C4×Dic11C2311yescharacteristic
148C2×C4×Dic11C2311yescharacteristic
149#66948C2×C418yescomplemented
150#66946—216no—
151C4⋊C4×D11—28no—
152#66941C2×C418yescomplemented
153#66940—216no—
154#66938C2×C4116yescomplemented
155#66937C2×C4116yescomplemented
156(C22⋊D11)⋊C4—216no—
157(C22⋊D11)⋊C4—216no—
158C4×D44—28no—
159C4×D44C2×C418yescomplemented
160#66925—24no—
161#66925—28no—
162#66925D418yescomplemented
163C42×D11—28no—
164C42×D11—28no—
165C42×D11C2×C418yescomplemented
166C11×#95C2314yes—
167C11×#95C2312yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2314yes—
171C11⋊#95C2312yes—
172C11⋊#95C2312yes—
173C11⋊#95C2314yes—
174C11⋊#95C2312yes—
175C11⋊#95C2312yes—
176C11⋊#95C2312yes—
177#34141—111nomaximal, Sylow
178C24×C11C2412yes—
179C23×D11C2412yes—
180C23×D11C2411yescharacteristic
181C2×D4×C11—24no—
182C2×D4×C11C22×C414yes—
183C22×C4×C11—24no—
184C22×C4×C11—24no—
185C22×C4×C11C22×C418yes—
186C22×C4×C11C2412yes—
187C22×C4×C11C2414yes—
188C22×C4×C11C2411yescharacteristic
189C22×C4×C11C2412yes—
190C22×C4×C11C2412yes—
191C22×C4×C11C2411yescharacteristic
192C22×C4×C11C2411yescharacteristic
193C2×C22⋊D11—24no—
194C2×C22⋊D11—24no—
195C2×C22⋊D11—24no—
196C2×C22⋊D11—24no—
197C2×C22⋊D11—44no—
198C2×C22⋊D11C22×C418yes—
199C2×C22⋊D11C22×C418yes—
200C2×C22⋊D11C22×C418yes—
201C22×Dic11—28no—
202C22×Dic11—28no—
203C22×Dic11—44no—
204C22×Dic11C2412yes—
205C22×Dic11C2411yescharacteristic
206C22×Dic11C2411yescharacteristic
207C22×Dic11C2412yes—
208C22×Dic11C2412yes—
209C22×Dic11C2414yes—
210C22×Dic11C2411yescharacteristic
211#4339—264no—
212C2×D44—24no—
213C2×D44—24no—
214C2×D44—24no—
215C2×D44C22×C414yes—
216C2×D44C22×C418yes—
217C2×C4×D11—28no—
218C2×C4×D11—28no—
219C2×C4×D11—28no—
220C2×C4×D11—24no—
221C2×C4×D11—28no—
222C2×C4×D11—24no—
223C2×C4×D11—24no—
224C2×C4×D11—42no—
225C2×C4×D11—44no—
226C2×C4×D11—44no—
227C2×C4×D11C22×C414yes—
228C2×C4×D11C22×C418yes—
229C2×C4×D11C22×C414yes—
230C2×C4×D11C22×C414yes—
231C2×C4×D11C2×D414yes—
232C2×C4×D11#4114yes—
233C2×Dic22—24no—
234C2×Dic22—24no—
235C2×Dic22C22×C418yes—
236C11×C4⋊C4—28no—
237C11×C4⋊C4—24no—
238C11×C4⋊C4C22×C414yes—
239C11×C22⋊C4—28no—
240C11×C22⋊C4—44no—
241C11×C22⋊C4C22×C418yes—
242C42×C11—24no—
243C42×C11—22no—
244C42×C11—24no—
245C42×C11—42no—
246C42×C11C22×C414yes—
247C42×C11C2×D414yes—
248C22⋊Dic11—28no—
249C22⋊Dic11C22×C418yes—
250(C2×D11)⋊C4—28no—
251(C2×D11)⋊C4—28no—
252(C2×D11)⋊C4—24no—
253(C2×D11)⋊C4—44no—
254(C2×D11)⋊C4C22×C418yes—
255(C2×D11)⋊C4C22×C418yes—
256(C2×D11)⋊C4C2×D418yes—
257C4⋊Dic11C22×C414yes—
258C4⋊Dic11#4118yescomplemented
259Dic11⋊C4—28no—
260Dic11⋊C4—24no—
261Dic11⋊C4—28no—
262Dic11⋊C4C22×C418yes—
263Dic11⋊C4C2×D418yes—
264C4×Dic11—28no—
265C4×Dic11—28no—
266C4×Dic11—24no—
267C4×Dic11—28no—
268C4×Dic11—22no—
269C4×Dic11—24no—
270C4×Dic11—42no—
271C4×Dic11C22×C414yes—
272C4×Dic11C22×C414yes—
273C4×Dic11C22×C414yes—
274C4×Dic11C2×D414yes—
275C2×#532—111no—
276C2×C4×#41—112no—
277#2367—114no—
278#2366—112no—
279#2365—112no—
280#2364—114no—
281#2361—112no—
282#2361—112no—
283#2297—112no—
284#2293—111no—
285#2293D1111yescharacteristic, complemented
286#2290—112no—
287#2290—112no—
288C42×D4—111no—
289C42×D4—111no—
290C4×#117—111no—
291C2×C4×C4⋊C4—111no—
292C23×C11—22no—
293C23×C11—24no—
294C23×C11—22no—
295C23×C11—24no—
296C23×C11C23×C414yes—
297C23×C11C2511yescharacteristic
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—24no—
302C22×D11—22no—
303C22×D11—24no—
304C22×D11C23×C414yes—
305C22×D11C23×C412yes—
306C22×D11C22×D412yes—
307C22×D11C2×#4112yes—
308D4×C11—28no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—216no—
315C2×C4×C11—24no—
316C2×C4×C11—22no—
317C2×C4×C11—24no—
318C2×C4×C11—22no—
319C2×C4×C11—24no—
320C2×C4×C11—22no—
321C2×C4×C11C23×C412yes—
322C2×C4×C11C23×C414yes—
323C2×C4×C11C23×C412yes—
324C2×C4×C11C23×C412yes—
325C2×C4×C11C22×D414yes—
326C2×C4×C11C22×D412yes—
327C2×C4×C11C2×#4112yes—
328C2×C4×C11C2×#4114yes—
329C22⋊D11—216no—
330C22⋊D11—216no—
331C22⋊D11—48no—
332C2×Dic11—24no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—24no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—416no—
344C2×Dic11C23×C412yes—
345C2×Dic11C23×C412yes—
346C2×Dic11C23×C414yes—
347C2×Dic11C23×C412yes—
348C2×Dic11C22×D414yes—
349C2×Dic11C22×D412yes—
350C2×Dic11C2×#4118yes—
351C2×Dic11C2×#4112yes—
352D44—216no—
353D44—28no—
354C4×D11—216no—
355C4×D11—28no—
356C4×D11—44no—
357C4×D11—416no—
358C4×D11—416no—
359C4×D11C4×D4116yescomplemented
360Dic22—216no—
361C22×#41—112no—
362#532—1116no—
363C2×C4⋊Q8—111no—
364C2×#127—111no—
365C2×#124—112no—
366C2×#121—111no—
367C2×#121—111no—
368C2×#121—112no—
369C4×#41—2216no—
370C2×C4×Q8—114no—
371C2×C4×D4—112no—
372C2×C4×D4—112no—
373C2×C4×D4—114no—
374C2×C4×D4—114no—
375C2×C4×D4—114no—
376C2×C4×D4—111no—
377C2×C4×D4—112no—
378C2×C4×D4C2×D1111yescharacteristic
379C2×#117—111no—
380C2×#117—112no—
381C2×#117—111no—
382C2×#117C2×D1112yes—
383C22×C4⋊C4—112no—
384C22×C42—111no—
385C22×C42—112no—
386C22×C42—112no—
387C22×C42—112no—
388#391—114no—
389#390—112no—
390#390—114no—
391#390C2×D1112yes—
392#389—112no—
393#389C2×D1112yes—
394#388—114no—
395#388—114no—
396#388—114no—
397#388C2×D1114yes—
398#387—114no—
399#387—114no—
400#386—114no—
401#386—114no—
402#386—114no—
403#386—114no—
404#385—114no—
405#385—114no—
406C4×C4⋊C4—112no—
407C4×C4⋊C4—112no—
408C4×C4⋊C4—112no—
409C4×C4⋊C4—112no—
410C4×C4⋊C4—112no—
411C4×C4⋊C4—112no—
412C4×C4⋊C4—111no—
413C4×C4⋊C4—112no—
414C4×C4⋊C4C2×D1111yescharacteristic
415C4×C22⋊C4—112no—
416C4×C22⋊C4—114no—
417C4×C22⋊C4—112no—
418C4×C22⋊C4—112no—
419C4×C22⋊C4—114no—
420C4×C22⋊C4—112no—
421C4×C22⋊C4—112no—
422C4×C22⋊C4C2×D1112yes—
423#376—111no—
424#376—111no—
425C2×#95—112no—
426C43—111no—
427C43C2×D1111yescharacteristic
428C22×C11—24no—
429C22×C11—24no—
430C22×C11—24no—
431C22×C11—44no—
432C22×C11—44no—
433C22×C11C24×C411yescharacteristic
434C22×C11C23×D411yescharacteristic
435C22×C11C22×#4111yescharacteristic
436C22×C11C22×#4112yes—
437C22×C11#58512yes—
438C2×D11—22no—
439C2×D11—22no—
440C2×D11—24no—
441C2×D11—24no—
442C2×D11—24no—
443C2×D11—24no—
444C2×D11—24no—
445C2×D11—44no—
446C2×D11—44no—
447C2×D11C2×C4×D414yes—
448C4×C11—24no—
449C4×C11—22no—
450C4×C11—24no—
451C4×C11—44no—
452C4×C11—42no—
453C4×C11C2×C4×D414yes—
454C4×C11C4×#4114yescomplemented
455Dic11—24no—
456Dic11—22no—
457Dic11—22no—
458Dic11—28no—
459Dic11—24no—
460Dic11—42no—
461Dic11C2×C4×D414yes—
462C2×#41—1116no—
463C2×#41—228no—
464C2×#41—228no—
465C22×Q8—112no—
466C22×D4—112no—
467C22×D4—112no—
468C22×D4—112no—
469C22×D4—111no—
470C22×D4—112no—
471C22×D4C22×D1111yescharacteristic
472C23×C4—111no—
473C23×C4—111no—
474C23×C4—112no—
475C23×C4—111no—
476C23×C4—114no—
477C23×C4—114no—
478C23×C4—114no—
479C23×C4C22×D1112yes—
480C4⋊Q8—118no—
481#127—118no—
482#124—1116no—
483#121—118no—
484#121—118no—
485#121—1116no—
486C4×Q8—2216no—
487C4×D4—1116no—
488C4×D4—118no—
489C4×D4—228no—
490C4×D4—2216no—
491C4×D4—2216no—
492C4×D4—2216no—
493C4×D4—228no—
494C4×D4C4×D1118yescomplemented
495#117—28no—
496#117—118no—
497#117—228no—
498#117—224no—
499C2×C4⋊C4—112no—
500C2×C4⋊C4—112no—
501C2×C4⋊C4—111no—
502C2×C4⋊C4—112no—
503C2×C4⋊C4—114no—
504C2×C4⋊C4—114no—
505C2×C4⋊C4—112no—
506C2×C4⋊C4—228no—
507C2×C4⋊C4C22×D1112yes—
508C2×C4⋊C4C22×D1114yes—
509C2×C4⋊C4C22×D1111yescharacteristic
510C2×C22⋊C4—112no—
511C2×C22⋊C4—112no—
512C2×C22⋊C4—112no—
513C2×C22⋊C4—112no—
514C2×C22⋊C4—114no—
515C2×C22⋊C4—114no—
516C2×C22⋊C4—112no—
517C2×C22⋊C4—114no—
518C2×C22⋊C4—114no—
519C2×C22⋊C4C22×D1114yes—
520C2×C22⋊C4C22×D1114yes—
521C2×C22⋊C4C22×D1112yes—
522C2×C42—111no—
523C2×C42—111no—
524C2×C42—111no—
525C2×C42—111no—
526C2×C42—118no—
527C2×C42—114no—
528C2×C42—114no—
529C2×C42—114no—
530C2×C42—112no—
531C2×C42—111no—
532C2×C42—112no—
533C2×C42—112no—
534C2×C42—228no—
535C2×C42—228no—
536C2×C42—228no—
537C2×C42C22×D1112yes—
538C2×C42C22×D1112yes—
539C2×C42C22×D1111yescharacteristic
540C2×C42C22×D1112yes—
541C2×C42C22×D1111yescharacteristic
542C2×C42C22×D1111yescharacteristic
543#95—112no—
544#95—114no—
545#95—112no—
546#95—112no—
547#95—112no—
548#95—112no—
549#95—114no—
550#95—114no—
551#95—114no—
552#95C22×D1112yes—
553#95C22×D1114yes—
554C2×C11—44no—
555C2×C11C22×C4×D411yescharacteristic
556C2×C11C2×C4×#4111yescharacteristic
557C2×C11#342811yescharacteristic
558C2×C11D4×#4112yes—
559C2×C11#348012yes—
560D11—24no—
561D11—44no—
562C24—111no—
563C24—112no—
564C24C23×D1112yes—
565#41—2264no—
566C2×Q8—118no—
567C2×Q8—224no—
568C2×Q8—224no—
569C2×D4—24no—
570C2×D4—118no—
571C2×D4—118no—
572C2×D4—118no—
573C2×D4—114no—
574C2×D4—118no—
575C2×D4—224no—
576C2×D4—224no—
577C2×D4—224no—
578C2×D4—224no—
579C2×D4—224no—
580C2×D4—224no—
581C2×D4—224no—
582C2×D4—444no—
583C2×D4C2×C4×D1114yes—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—111no—
587C22×C4—114no—
588C22×C4—114no—
589C22×C4—114no—
590C22×C4—111no—
591C22×C4—114no—
592C22×C4—111no—
593C22×C4—112no—
594C22×C4—112no—
595C22×C4—114no—
596C22×C4—118no—
597C22×C4—114no—
598C22×C4—112no—
599C22×C4—228no—
600C22×C4—228no—
601C22×C4—228no—
602C22×C4—228no—
603C22×C4—228no—
604C22×C4—224no—
605C22×C4—224no—
606C22×C4—224no—
607C22×C4—228no—
608C22×C4—442no—
609C22×C4—444no—
610C22×C4—444no—
611C22×C4—444no—
612C22×C4C2×C4×D1118yes—
613C22×C4C23×D1112yes—
614C22×C4C23×D1114yes—
615C22×C4C23×D1111yescharacteristic
616C22×C4C23×D1112yes—
617C22×C4C23×D1112yes—
618C22×C4C23×D1111yescharacteristic
619C22×C4C23×D1111yescharacteristic
620C4⋊C4—28no—
621C4⋊C4—24no—
622C4⋊C4—118no—
623C4⋊C4—114no—
624C4⋊C4—118no—
625C4⋊C4—118no—
626C4⋊C4—228no—
627C4⋊C4—228no—
628C4⋊C4—224no—
629C4⋊C4C2×C4×D1114yes—
630C22⋊C4—28no—
631C22⋊C4—44no—
632C22⋊C4—118no—
633C22⋊C4—118no—
634C22⋊C4—118no—
635C22⋊C4—118no—
636C22⋊C4—228no—
637C22⋊C4—228no—
638C22⋊C4—224no—
639C22⋊C4—228no—
640C22⋊C4—444no—
641C22⋊C4C2×C4×D1118yes—
642C42—24no—
643C42—22no—
644C42—24no—
645C42—42no—
646C42—114no—
647C42—114no—
648C42—114no—
649C42—114no—
650C42—228no—
651C42—228no—
652C42—224no—
653C42—228no—
654C42—222no—
655C42—224no—
656C42—442no—
657C42C2×C4×D1114yes—
658C42D4×D1114yes—
659C11#3414111yescharacteristic, complemented, Sylow
660C23—22no—
661C23—24no—
662C23—22no—
663C23—24no—
664C23—112no—
665C23—112no—
666C23—112no—
667C23—114no—
668C23—222no—
669C23—222no—
670C23—222no—
671C23—224no—
672C23—222no—
673C23—224no—
674C23C22×C4×D1114yes—
675C23C24×D1111yescharacteristic
676Q8—2216no—
677D4—28no—
678D4—2216no—
679D4—2216no—
680D4—2216no—
681D4—228no—
682D4—448no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—216no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—112no—
696C2×C4—112no—
697C2×C4—112no—
698C2×C4—1116no—
699C2×C4—112no—
700C2×C4—112no—
701C2×C4—114no—
702C2×C4—114no—
703C2×C4—118no—
704C2×C4—224no—
705C2×C4—222no—
706C2×C4—222no—
707C2×C4—222no—
708C2×C4—222no—
709C2×C4—222no—
710C2×C4—224no—
711C2×C4—222no—
712C2×C4—228no—
713C2×C4—2216no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—444no—
718C2×C4—4416no—
719C2×C4—4416no—
720C2×C4—4416no—
721C2×C4C22×C4×D1112yes—
722C2×C4C22×C4×D1114yes—
723C2×C4C22×C4×D1112yes—
724C2×C4C22×C4×D1112yes—
725C2×C4C2×D4×D1114yes—
726C2×C4C2×D4×D1112yes—
727C2×C4#41×D1114yes—
728C2×C4#41×D1112yes—
729C22—24no—
730C22—24no—
731C22—24no—
732C22—44no—
733C22—44no—
734C22—114no—
735C22—224no—
736C22—222no—
737C22—222no—
738C22—224no—
739C22—224no—
740C22—224no—
741C22—224no—
742C22—444no—
743C22—444no—
744C22C23×C4×D1111yescharacteristic
745C22C22×D4×D1111yescharacteristic
746C22C2×#41×D1111yescharacteristic
747C22C2×#41×D1112yes—
748C22#1062345312yes—
749C4—24no—
750C4—22no—
751C4—24no—
752C4—42no—
753C4—44no—
754C4—114no—
755C4—224no—
756C4—222no—
757C4—222no—
758C4—228no—
759C4—224no—
760C4—442no—
761C4#1062305314yescomplemented
762C4C4×D4×D1114yes—
763C2—44no—
764C2—224no—
765C2—444no—
766C2C2×C4×D4×D1111yescharacteristic
767C2C2×#1062305311yescharacteristic
768C2#1308181511yescharacteristic
769C2#1308210212yes—
770C2#1308220712yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC11×#2293C2
socle, cosocleC23×C11C25
prime radicalC2×#10623079C2
hypercenter#2293D11
hypocenterC11#34141
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2293

Complements

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

NH ≅ G/Ntype
2. C2×#10623053C2semidirect
3. #13071682C2semidirect
4. #13071677C2semidirect
5. #13071669C2semidirect
6. #13071660C2semidirect
7. #13071637C2semidirect
8. #13071631C2semidirect
9. #13071102C2semidirect
10. #13071077C2semidirect
11. #13071055C2semidirect
12. #13071053C2semidirect
13. C42×D44C2semidirect
14. C4×D4×Dic11C2semidirect
15. C4×#66925C2semidirect
16. C4×C4⋊C4×D11C2semidirect
17. C11×#2293C2semidirect
26. #10623079C4semidirect
93. C2×#4339C2×C4semidirect
103. C4×D4×C11C2×C4semidirect
119. #66993C2×C4semidirect
120. #66991C2×C4semidirect
122. C4×C22⋊D11C2×C4semidirect
149. #66948C2×C4semidirect
152. #66941C2×C4semidirect
154. #66938C2×C4semidirect
155. #66937C2×C4semidirect
159. C4×D44C2×C4semidirect
162. #66925D4semidirect
165. C42×D11C2×C4semidirect
258. C4⋊Dic11#41semidirect
285. #2293D11semidirect
359. C4×D11C4×D4semidirect
454. C4×C11C4×#41semidirect
494. C4×D4C4×D11semidirect
659. C11#34141semidirect
761. C4#10623053semidirect

Maximal subgroups

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

subgroupindex
C2×#106230792
C2×#106230532
#130716822
#130716772
#130716692
#130716602
#130716372
#130716312
#130711022
#130710772
#130710552
#130710532
C42×D442
C4×D4×Dic112
C4×#669252
C4×C4⋊C4×D112
C11×#22932
#3414111