Finite Group Databasebeta

← C2×#13077456 #15617879

Subgroups — C2×#13077456 #15617879

Order 2816.

2730 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66968C211yesmaximal, characteristic
2C2×#10623077C211yesmaximal, characteristic
3C2×#10623103C211yesmaximal, characteristic, complemented
4#13077456C2116yesmaximal, direct product factor
5C2×#10622329C211yesmaximal, characteristic, complemented
6C2×#10622402C211yesmaximal, characteristic, complemented
7C2×#10622370C211yesmaximal, characteristic, complemented
8C2×#10622486C211yesmaximal, characteristic, complemented
9C2×C4×#4326C211yesmaximal, characteristic, complemented
10C2×SD16×Dic11C211yesmaximal, characteristic, complemented
11C2×C4×#4324C211yesmaximal, characteristic, complemented
12C2×#10622494C211yesmaximal, characteristic, complemented
13C2×#10622385C211yesmaximal, characteristic
14C2×D11×#103C211yesmaximal, characteristic, complemented
15C2×#10622321C211yesmaximal, characteristic, complemented
16C2×C11×#440C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2211yescharacteristic
18C22×#4341C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23C22×#4326C2211yescharacteristic
24C2×D4×Dic11C2211yescharacteristic
25C22×#4324C2211yescharacteristic
26C2×C4×C22⋊D11—21no—
27C22×Dic11⋊C4—21no—
28C2×#66968C4116yescomplemented
29C2×#66968C2218yes—
30C22×Dic44C2211yescharacteristic
31C22×#4313C2211yescharacteristic
32C22×C8×D11C2211yescharacteristic
33#10623103—24no—
34#10623103C2218yescomplemented
35#10623077—24no—
36#10623077C2218yes—
37C2×#66945—21no—
38C2×#66945C2211yescharacteristic
39C2×C4⋊C4×D11C2211yescharacteristic
40C2×#66940—21no—
41C2×#66940C2211yescharacteristic
42C2×#66940C2211yescharacteristic
43C2×(C22⋊D11)⋊C4—21no—
44C2×#66930—21no—
45C2×#66925—21no—
46C2×#66925C2211yescharacteristic
47C2×C4×Dic22—21no—
48C2×C4×Dic22C2211yescharacteristic
49C2×C4×Dic22C2211yescharacteristic
50C11×#440C2218yescomplemented
51C2×C11×#107C2211yescharacteristic
52C2×C11×#103C2211yescharacteristic
53C2×C11×#102C2211yescharacteristic
54C2×C11×#97C2211yescharacteristic
55C2×#66899C2211yescharacteristic
56C2×#66896C2211yescharacteristic
57SD16×Dic11C2218yescomplemented
58C2×#66881C2211yescharacteristic
59C2×#66880C2211yescharacteristic
60C2×#66880C2211yescharacteristic
61C2×#66879C2211yescharacteristic
62C2×C8×Dic11C2211yescharacteristic
63C4×#4326C2218yescomplemented
64C4×#4324C2218yescomplemented
65C2×#66874C2211yescharacteristic
66C2×#66874C2211yescharacteristic
67C2×#66872C2211yescharacteristic
68C2×#66871C2211yescharacteristic
69C2×C4×C11⋊C8C2211yescharacteristic
70#10622494C2218yescomplemented
71#10622486C2218yescomplemented
72D11×#103C2218yescomplemented
73#10622402C2218yescomplemented
74#10622385C2218yes—
75#10622370C2218yescomplemented
76#10622329C2218yescomplemented
77#10622321C2218yescomplemented
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11—21no—
81C22×C22⋊D11—21no—
82C23×Dic11—21no—
83C23×Dic11—21no—
84C2×Q8×D11—22no—
85C2×Q8×D11—24no—
86C2×Q8×D11C2×C418yescomplemented
87C2×Q8×D11C2314yes—
88C2×#4341—22no—
89C2×#4341—24no—
90C2×#4341C2×C418yes—
91C2×#4341C2314yes—
92C22×C4×D11—21no—
93C22×C4×D11—21no—
94C22×C4×D11C2311yescharacteristic
95C22×Dic22—21no—
96C22×Dic22C2311yescharacteristic
97C22×Dic22C2311yescharacteristic
98C2×C11×SD16C2×C418yescomplemented
99C2×C11×SD16C2314yes—
100C22×C8×C11C2311yescharacteristic
101C22×C8×C11C2311yescharacteristic
102C4×Q8×C11—22no—
103C4×Q8×C11C2314yes—
104C4×D4×C11—22no—
105C4×D4×C11C2314yes—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C22⋊C4—21no—
110C2×C42×C11—21no—
111C2×C42×C11C2311yescharacteristic
112C2×C22⋊Dic11—21no—
113Q8×Dic11—22no—
114Q8×Dic11C2314yes—
115C2×#4326C2×C418yescomplemented
116C2×#4326C2314yes—
117D4×Dic11—22no—
118D4×Dic11C2314yes—
119C2×#4324C2×C418yescomplemented
120C2×#4324C2314yes—
121C4×C22⋊D11—28no—
122C2×(C2×D11)⋊C4—21no—
123C2×(C2×D11)⋊C4D411yescharacteristic
124C2×(C2×D11)⋊C4D411yescharacteristic
125C2×C4⋊Dic11—21no—
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4⋊Dic11C2311yescharacteristic
128C2×Dic11⋊C4—21no—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4—28no—
134C2×Dic11⋊C4D411yescharacteristic
135C2×Dic11⋊C4D411yescharacteristic
136C2×C4×Dic11—21no—
137C2×C4×Dic11—21no—
138C2×C4×Dic11—21no—
139C2×C4×Dic11—21no—
140C2×C4×Dic11—21no—
141C2×C4×Dic11—21no—
142C2×C4×Dic11C2311yescharacteristic
143C22×C11⋊C8C2311yescharacteristic
144C22×C11⋊C8C2311yescharacteristic
145#66968C2×C4164yescomplemented
146C2×Dic44C2×C418yescomplemented
147C2×Dic44C2314yes—
148C2×#4313C2×C418yescomplemented
149C2×#4313C2314yes—
150C2×C8×D11—24no—
151C2×C8×D11C2314yes—
152#66945—22no—
153#66945—28no—
154#66945C2314yes—
155C4⋊C4×D11—22no—
156C4⋊C4×D11C2314yes—
157#66940—28no—
158#66940—22no—
159#66940—22no—
160#66940C2314yes—
161#66940C2314yes—
162(C22⋊D11)⋊C4—28no—
163#66930—28no—
164#66925—28no—
165#66925D414yes—
166#66925C2314yes—
167C4×Dic22—22no—
168C4×Dic22—22no—
169C4×Dic22—28no—
170C4×Dic22C2314yes—
171C4×Dic22C2314yes—
172C11×#107C2314yes—
173C11×#103C2314yes—
174C11×#102C2314yes—
175C11×#97C2314yes—
176#66899C2314yes—
177#66896C2314yes—
178#66881C2314yes—
179#66880C2314yes—
180#66880C2314yes—
181#66879C2314yes—
182C8×Dic11C2314yes—
183#66874C2314yes—
184#66874C2314yes—
185#66872C2314yes—
186#66871C2314yes—
187C4×C11⋊C8C2314yes—
188C2×#2947—111nomaximal, Sylow
189C24×C11—21no—
190C23×D11C2×D411yescharacteristic
191C2×Q8×C11—21no—
192C2×Q8×C11—22no—
193C2×Q8×C11C22×C414yes—
194C2×Q8×C11C2412yes—
195C2×D4×C11—21no—
196C2×D4×C11—22no—
197C2×D4×C11C22×C414yes—
198C2×D4×C11C2412yes—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—24no—
203C22×C4×C11—82no—
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2411yescharacteristic
207C2×C22⋊D11—28no—
208C2×C22⋊D11—24no—
209C22×Dic11—28no—
210C22×Dic11—24no—
211C22×Dic11—24no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—82no—
217C22×Dic11C2×D411yescharacteristic
218C22×Dic11C2×D411yescharacteristic
219C22×Dic11C2×D411yescharacteristic
220Q8×D11—216no—
221Q8×D11—28no—
222Q8×D11C22×C4116yescomplemented
223#4341—216no—
224#4341—28no—
225#4341C22×C4116yes—
226C2×C4×D11—28no—
227C2×C4×D11—24no—
228C2×C4×D11—24no—
229C2×C4×D11—82no—
230C2×C4×D11C22×C414yes—
231C2×C4×D11C2×D412yes—
232C2×C4×D11#4114yes—
233C2×C4×D11C2412yes—
234C2×Dic22—28no—
235C2×Dic22—24no—
236C2×Dic22—21no—
237C2×Dic22—21no—
238C2×Dic22—22no—
239C2×Dic22—22no—
240C2×Dic22C22×C414yes—
241C2×Dic22C22×C414yes—
242C2×Dic22C2412yes—
243C2×Dic22C2412yes—
244C11×SD16C22×C4116yescomplemented
245C2×C8×C11—22no—
246C2×C8×C11C22×C414yes—
247C2×C8×C11C2412yes—
248C2×C8×C11C2412yes—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—24no—
251C11×C4⋊C4—21no—
252C11×C4⋊C4C2412yes—
253C11×C4⋊C4C2412yes—
254C11×C22⋊C4—24no—
255C42×C11—24no—
256C42×C11C2×D412yes—
257C42×C11C2412yes—
258C22⋊Dic11—24no—
259#4326C22×C4116yescomplemented
260#4324C22×C4116yescomplemented
261(C2×D11)⋊C4—24no—
262(C2×D11)⋊C4C2×D414yes—
263(C2×D11)⋊C4C2×D414yes—
264C4⋊Dic11—24no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11C2412yes—
268C4⋊Dic11C2412yes—
269Dic11⋊C4—24no—
270Dic11⋊C4—24no—
271Dic11⋊C4—24no—
272Dic11⋊C4—24no—
273Dic11⋊C4—24no—
274Dic11⋊C4C2×D414yes—
275Dic11⋊C4C2×D414yes—
276C4×Dic11—24no—
277C4×Dic11—24no—
278C4×Dic11—24no—
279C4×Dic11—24no—
280C4×Dic11—24no—
281C4×Dic11—24no—
282C4×Dic11C2×D412yes—
283C4×Dic11C2412yes—
284C2×C11⋊C8—22no—
285C2×C11⋊C8C22×C414yes—
286C2×C11⋊C8C2412yes—
287C2×C11⋊C8C2412yes—
288Dic44C22×C4116yescomplemented
289#4313C22×C4116yescomplemented
290C8×D11—28no—
291C22×#137—111no—
292C2×#520—111no—
293C2×#519—111no—
294#2947—1116no—
295C2×#441—111no—
296C2×#441—111no—
297C2×#440—111no—
298C2×#440D1111yescharacteristic, complemented
299C2×C4×Q16—111no—
300C2×C4×Q16—111no—
301C2×C4×SD16—111no—
302C2×C4×SD16—111no—
303C2×#428—111no—
304C2×#416—111no—
305C22×#103—111no—
306C2×#405—111no—
307C23×C11—24no—
308C23×C11—22no—
309C23×C11—42no—
310C23×C11—42no—
311C23×C11C22×D411yescharacteristic
312C22×D11—22no—
313C22×D11—22no—
314C22×D11C4×D414yes—
315C22×D11C22×D412yes—
316Q8×C11—24no—
317Q8×C11—22no—
318Q8×C11C23×C414yes—
319D4×C11—24no—
320D4×C11—22no—
321D4×C11C23×C414yes—
322C2×C4×C11—24no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—42no—
329C2×C4×C11—42no—
330C2×C4×C11—84no—
331C2×C4×C11C23×C412yes—
332C2×C4×C11C22×D412yes—
333C2×C4×C11C22×D412yes—
334C2×C4×C11C22×D411yescharacteristic
335C2×C4×C11C2×#4112yes—
336C2×C4×C11C2511yescharacteristic
337C22⋊D11—216no—
338C2×Dic11—24no—
339C2×Dic11—24no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—216no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—42no—
348C2×Dic11—42no—
349C2×Dic11—84no—
350C2×Dic11C4×D414yes—
351C2×Dic11C22×D412yes—
352C2×Dic11C22×D412yes—
353C2×Dic11C22×D412yes—
354C4×D11—216no—
355C4×D11—84no—
356C4×D11C4×D418yes—
357C4×D11C23×C414yes—
358C4×D11C2×#4114yes—
359Dic22—24no—
360Dic22—24no—
361Dic22—22no—
362Dic22—22no—
363Dic22—216no—
364Dic22C23×C414yes—
365Dic22C23×C414yes—
366C8×C11—22no—
367C8×C11C23×C414yes—
368C11⋊C8—22no—
369C11⋊C8C23×C414yes—
370C22×#41—111no—
371C23×Q8—111no—
372C2×#137—118no—
373C2×#137—1116no—
374C22×Q16—111no—
375C22×Q16—111no—
376C22×SD16—111no—
377C22×SD16C2×D1111yescharacteristic
378C22×M16—111no—
379C23×C8—111no—
380#520—118no—
381#520—224no—
382#519—118no—
383#519—224no—
384C2×C4×Q8—111no—
385C2×C4×Q8—111no—
386C2×C4×Q8—111no—
387C2×C4×Q8—111no—
388C2×C4×Q8—111no—
389C2×C4×Q8—221no—
390C2×C4×Q8—221no—
391C2×C4×Q8C2×D1111yescharacteristic
392C2×C4×D4—111no—
393C2×C4×D4—221no—
394C2×C4×D4—221no—
395C2×C4×D4C2×D1111yescharacteristic
396C2×#117—111no—
397C2×#117—111no—
398C2×#117—221no—
399C2×#117—221no—
400C2×#117—221no—
401C22×C4⋊C4—111no—
402C22×C4⋊C4—221no—
403#441—118no—
404#441—118no—
405#440—118no—
406#440C2×D1118yescomplemented
407C4×Q16—118no—
408C4×Q16—118no—
409C4×SD16—118no—
410C4×SD16—118no—
411#428—118no—
412C2×#107—111no—
413C2×#107C2×D1111yescharacteristic
414C2×#106—111no—
415C2×#106—111no—
416#416—118no—
417C2×#103—111no—
418C2×#103—111no—
419C2×#103—111no—
420C2×#103—111no—
421C2×#103—111no—
422C2×#103—118no—
423C2×#103C2×D1111yescharacteristic
424C2×#102—111no—
425C2×#102C2×D1111yescharacteristic
426#405—118no—
427C2×#97—111no—
428C2×#97C2×D1111yescharacteristic
429C2×C4×C8—111no—
430C2×C4×C8—111no—
431C22×C11—24no—
432C22×C11—48no—
433C22×C11—42no—
434C22×C11—42no—
435C22×C11C2×C4×D412yes—
436C22×C11#57712yes—
437C22×C11#57812yes—
438C22×C11C23×D411yescharacteristic
439C2×D11—28no—
440C2×D11—22no—
441C2×D11—22no—
442C2×D11C2×C4×D414yes—
443C4×C11—24no—
444C4×C11—22no—
445C4×C11—22no—
446C4×C11—42no—
447C4×C11—42no—
448C4×C11C2×C4×D412yes—
449C4×C11C24×C411yescharacteristic
450C4×C11C22×#4111yescharacteristic
451Dic11—24no—
452Dic11—24no—
453Dic11—22no—
454Dic11—22no—
455Dic11—42no—
456Dic11—42no—
457Dic11C2×C4×D414yes—
458C2×#41—118no—
459C2×#41—114no—
460C2×#41—222no—
461C2×#41—224no—
462C22×Q8—118no—
463C22×Q8—114no—
464C22×Q8—111no—
465C22×Q8—111no—
466C22×Q8—221no—
467C22×Q8—222no—
468C22×Q8—224no—
469C22×Q8C22×D1111yescharacteristic
470C22×D4—221no—
471C22×D4C22×D1111yescharacteristic
472C23×C4—21no—
473C23×C4—111no—
474C23×C4—221no—
475C23×C4—221no—
476C23×C4—221no—
477C23×C4—221no—
478#137—1164no—
479C2×Q16—118no—
480C2×Q16—114no—
481C2×Q16—118no—
482C2×Q16—114no—
483C2×SD16—118no—
484C2×SD16—114no—
485C2×SD16C4×D1118yescomplemented
486C2×SD16C22×D1114yes—
487C2×M16—118no—
488C2×M16—114no—
489C22×C8—111no—
490C22×C8—111no—
491C22×C8—114no—
492C22×C8—224no—
493C22×C8C22×D1111yescharacteristic
494C22×C8C22×D1111yescharacteristic
495C4×Q8—22no—
496C4×Q8—114no—
497C4×Q8—114no—
498C4×Q8—114no—
499C4×Q8—114no—
500C4×Q8—114no—
501C4×Q8—228no—
502C4×Q8—222no—
503C4×Q8—222no—
504C4×Q8—222no—
505C4×Q8—228no—
506C4×Q8—222no—
507C4×Q8—222no—
508C4×Q8C22×D1114yes—
509C4×D4—22no—
510C4×D4—114no—
511C4×D4—222no—
512C4×D4—228no—
513C4×D4—228no—
514C4×D4C22×D1114yes—
515#117—114no—
516#117—114no—
517#117—114no—
518#117—228no—
519#117—228no—
520#117—228no—
521#117—222no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—111no—
524C2×C4⋊C4—111no—
525C2×C4⋊C4—111no—
526C2×C4⋊C4—111no—
527C2×C4⋊C4—114no—
528C2×C4⋊C4—222no—
529C2×C4⋊C4—228no—
530C2×C4⋊C4—221no—
531C2×C4⋊C4—221no—
532C2×C4⋊C4—221no—
533C2×C4⋊C4—221no—
534C2×C4⋊C4—221no—
535C2×C4⋊C4—221no—
536C2×C4⋊C4C22×D1111yescharacteristic
537C2×C4⋊C4C22×D1111yescharacteristic
538C2×C22⋊C4—21no—
539C2×C22⋊C4—111no—
540C2×C22⋊C4—111no—
541C2×C22⋊C4—221no—
542C2×C22⋊C4—221no—
543C2×C42—21no—
544C2×C42—111no—
545C2×C42—221no—
546C2×C42—221no—
547C2×C42—221no—
548C2×C42—221no—
549C2×C42—221no—
550C2×C42—221no—
551C2×C42C22×D1111yescharacteristic
552#107—114no—
553#107C22×D1114yes—
554#106—114no—
555#106—114no—
556#103—114no—
557#103—114no—
558#103—114no—
559#103—114no—
560#103—114no—
561#103C22×D1114yes—
562#102—114no—
563#102C22×D1114yes—
564#97—114no—
565#97C22×D1114yes—
566C4×C8—114no—
567C4×C8—114no—
568C2×C11—44no—
569C2×C11#294714yescomplemented
570C2×C11C22×C4×D411yescharacteristic
571C2×C11C2×#57711yescharacteristic
572C2×C11C2×#57811yescharacteristic
573D11—24no—
574C24—21no—
575C24—111no—
576#41—1116no—
577#41—2216no—
578#41—228no—
579C2×Q8—21no—
580C2×Q8—22no—
581C2×Q8—1116no—
582C2×Q8—114no—
583C2×Q8—114no—
584C2×Q8—112no—
585C2×Q8—112no—
586C2×Q8—224no—
587C2×Q8—228no—
588C2×Q8—2216no—
589C2×Q8—228no—
590C2×Q8—221no—
591C2×Q8—221no—
592C2×Q8—222no—
593C2×Q8—222no—
594C2×Q8C2×C4×D1114yes—
595C2×Q8C23×D1112yes—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—224no—
599C2×D4—228no—
600C2×D4C2×C4×D1114yes—
601C2×D4C23×D1112yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—24no—
606C22×C4—82no—
607C22×C4—111no—
608C22×C4—114no—
609C22×C4—112no—
610C22×C4—114no—
611C22×C4—112no—
612C22×C4—111no—
613C22×C4—111no—
614C22×C4—224no—
615C22×C4—228no—
616C22×C4—224no—
617C22×C4—224no—
618C22×C4—228no—
619C22×C4—224no—
620C22×C4—221no—
621C22×C4—221no—
622C22×C4—221no—
623C22×C4—221no—
624C22×C4—882no—
625C22×C4—882no—
626C22×C4D4×D1111yescharacteristic
627C22×C4D4×D1111yescharacteristic
628C22×C4C23×D1111yescharacteristic
629Q16—1116no—
630Q16—1116no—
631SD16—1116no—
632SD16C2×C4×D11116yescomplemented
633M16—1116no—
634C2×C8—22no—
635C2×C8—114no—
636C2×C8—112no—
637C2×C8—112no—
638C2×C8—228no—
639C2×C8—222no—
640C2×C8C2×C4×D1114yes—
641C2×C8C23×D1112yes—
642C2×C8C23×D1112yes—
643C4⋊C4—24no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—114no—
647C4⋊C4—114no—
648C4⋊C4—112no—
649C4⋊C4—112no—
650C4⋊C4—224no—
651C4⋊C4—224no—
652C4⋊C4—224no—
653C4⋊C4—224no—
654C4⋊C4—221no—
655C4⋊C4—221no—
656C4⋊C4—224no—
657C4⋊C4—224no—
658C4⋊C4C23×D1112yes—
659C4⋊C4C23×D1112yes—
660C22⋊C4—24no—
661C22⋊C4—114no—
662C22⋊C4—114no—
663C22⋊C4—224no—
664C22⋊C4—224no—
665C42—24no—
666C42—112no—
667C42—112no—
668C42—224no—
669C42—224no—
670C42—224no—
671C42—224no—
672C42—224no—
673C42—224no—
674C42D4×D1112yes—
675C42C23×D1112yes—
676C11C2×#294711yescharacteristic, complemented, Sylow
677C23—24no—
678C23—22no—
679C23—42no—
680C23—42no—
681C23—114no—
682C23—112no—
683C23—222no—
684C23—222no—
685C23C2×D4×D1111yescharacteristic
686Q8—24no—
687Q8—22no—
688Q8—114no—
689Q8—114no—
690Q8—2216no—
691Q8—224no—
692Q8—224no—
693Q8—222no—
694Q8—222no—
695Q8C22×C4×D1114yes—
696D4—24no—
697D4—22no—
698D4—2216no—
699D4C22×C4×D1114yes—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—84no—
709C2×C4—114no—
710C2×C4—112no—
711C2×C4—118no—
712C2×C4—114no—
713C2×C4—114no—
714C2×C4—112no—
715C2×C4—112no—
716C2×C4—2216no—
717C2×C4—2216no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—224no—
721C2×C4—224no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—222no—
725C2×C4—222no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—884no—
729C2×C4—884no—
730C2×C4C22×C4×D1112yes—
731C2×C4C2×D4×D1112yes—
732C2×C4C2×D4×D1112yes—
733C2×C4C2×D4×D1111yescharacteristic
734C2×C4#41×D1112yes—
735C2×C4C24×D1111yescharacteristic
736C8—22no—
737C8—114no—
738C8—222no—
739C8C22×C4×D1114yes—
740C22—24no—
741C22—48no—
742C22—42no—
743C22—42no—
744C22—114no—
745C22—228no—
746C22—222no—
747C22—222no—
748C22C4×D4×D1112yes—
749C22#1062330612yes—
750C22#1062331012yes—
751C22C22×D4×D1111yescharacteristic
752C4—24no—
753C4—22no—
754C4—22no—
755C4—42no—
756C4—42no—
757C4—114no—
758C4—224no—
759C4—224no—
760C4—222no—
761C4—222no—
762C4—442no—
763C4—442no—
764C4C4×D4×D1112yes—
765C4C23×C4×D1111yescharacteristic
766C4C2×#41×D1111yescharacteristic
767C2—44no—
768C2—224no—
769C2#1307745614yesdirect product factor
770C2C2×C4×D4×D1111yescharacteristic
771C2C2×#1062330611yescharacteristic
772C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C11×#440C2
socleC23×C11C22×D4
prime radicalC22×#4341C22
cosocleC2×C4×C11C25
hypercenterC2×#440D11
hypocenterC11C2×#2947
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
3. C2×#10623103C2semidirect
4. #13077456C2direct (N × H)
5. C2×#10622329C2semidirect
6. C2×#10622402C2semidirect
7. C2×#10622370C2semidirect
8. C2×#10622486C2semidirect
9. C2×C4×#4326C2semidirect
10. C2×SD16×Dic11C2semidirect
11. C2×C4×#4324C2semidirect
12. C2×#10622494C2semidirect
14. C2×D11×#103C2semidirect
15. C2×#10622321C2semidirect
16. C2×C11×#440C2semidirect
28. C2×#66968C4semidirect
34. #10623103C22semidirect
50. C11×#440C22semidirect
57. SD16×Dic11C22semidirect
63. C4×#4326C22semidirect
64. C4×#4324C22semidirect
70. #10622494C22semidirect
71. #10622486C22semidirect
72. D11×#103C22semidirect
73. #10622402C22semidirect
75. #10622370C22semidirect
76. #10622329C22semidirect
77. #10622321C22semidirect
86. C2×Q8×D11C2×C4semidirect
98. C2×C11×SD16C2×C4semidirect
115. C2×#4326C2×C4semidirect
119. C2×#4324C2×C4semidirect
145. #66968C2×C4semidirect
146. C2×Dic44C2×C4semidirect
148. C2×#4313C2×C4semidirect
222. Q8×D11C22×C4semidirect
244. C11×SD16C22×C4semidirect
259. #4326C22×C4semidirect
260. #4324C22×C4semidirect
288. Dic44C22×C4semidirect
289. #4313C22×C4semidirect
298. C2×#440D11semidirect
406. #440C2×D11semidirect
485. C2×SD16C4×D11semidirect
569. C2×C11#2947semidirect
632. SD16C2×C4×D11semidirect
676. C11C2×#2947semidirect
769. C2#13077456direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669682
C2×#106230772
C2×#106231032
#130774562
C2×#106223292
C2×#106224022
C2×#106223702
C2×#106224862
C2×C4×#43262
C2×SD16×Dic112
C2×C4×#43242
C2×#106224942
C2×#106223852
C2×D11×#1032
C2×#106223212
C2×C11×#4402
C2×#294711