Finite Group Databasebeta

← C2×#13078786 #15621920

Subgroups — C2×#13078786 #15621920

Order 2816.

2150 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623211C211yesmaximal, characteristic
2C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
3#13078786C2116yesmaximal, direct product factor
4C2×#10622422C211yesmaximal, characteristic, complemented
5C2×#10622390C211yesmaximal, characteristic
6C2×#10622442C211yesmaximal, characteristic, complemented
7C2×#10622635C211yesmaximal, characteristic, complemented
8C2×#10622667C211yesmaximal, characteristic, complemented
9C2×#10622799C211yesmaximal, characteristic, complemented
10C2×#10622783C211yesmaximal, characteristic
11C2×#10622797C211yesmaximal, characteristic, complemented
12C2×#10622402C211yesmaximal, characteristic, complemented
13C2×#10622777C211yesmaximal, characteristic, complemented
14C2×#10622370C211yesmaximal, characteristic, complemented
15C2×#10622448C211yesmaximal, characteristic, complemented
16C2×C11×#464C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2211yescharacteristic
18C22×C11×Q16C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C2×C11×#124C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×#66999C2211yescharacteristic
23C2×Q8×Dic11C2211yescharacteristic
24C2×Q8×Dic11C2211yescharacteristic
25C22×#4326C2211yescharacteristic
26C2×#66991C2211yescharacteristic
27C2×D4×Dic11C2211yescharacteristic
28C22×#4324C2211yescharacteristic
29#10623211—24no—
30#10623211C2218yes—
31C4×Q8×D11—24no—
32C4×Q8×D11C2218yescomplemented
33C2×C4⋊C4×D11—21no—
34C2×C4⋊C4×D11C2211yescharacteristic
35C2×#66940—21no—
36C2×#66940C2211yescharacteristic
37C2×#66936—21no—
38C2×(C22⋊D11)⋊C4—21no—
39C2×#66932—21no—
40C2×#66930—21no—
41C2×C42×D11—21no—
42C2×C42×D11C2211yescharacteristic
43C2×#66923C2211yescharacteristic
44C2×C4×Dic22—21no—
45C2×C4×Dic22C2211yescharacteristic
46C11×#464C2218yescomplemented
47C2×C11×C4⋊C8C2211yescharacteristic
48C2×C11×#103C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×#66899C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54#10622799C2218yescomplemented
55#10622797C2218yescomplemented
56#10622783C2218yes—
57#10622777C2218yescomplemented
58C2×(C2×D11)⋊C8C2211yescharacteristic
59C2×(C2×D11)⋊C8C2211yescharacteristic
60C2×#66882C2211yescharacteristic
61C2×#66881C2211yescharacteristic
62C2×#66880C2211yescharacteristic
63C2×#66880C2211yescharacteristic
64C2×#66879C2211yescharacteristic
65C2×#66879C2211yescharacteristic
66#10622667C2218yescomplemented
67#10622635C2218yescomplemented
68C2×#66872C2211yescharacteristic
69C2×#66871C2211yescharacteristic
70C2×C4⋊(C11⋊C8)C2211yescharacteristic
71#10622448C2218yescomplemented
72#10622442C2218yescomplemented
73#10622422C2218yescomplemented
74#10622402C2218yescomplemented
75#10622390C2218yes—
76#10622370C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11C2311yescharacteristic
80C22×C22⋊D11—21no—
81C23×Dic11—21no—
82C2×Q8×D11—24no—
83C2×Q8×D11—22no—
84C2×Q8×D11—24no—
85C2×Q8×D11C2314yes—
86C22×C4×D11—21no—
87C22×C4×D11—21no—
88C22×C4×D11D411yescharacteristic
89C22×C4×D11D411yescharacteristic
90C22×C4×D11C2311yescharacteristic
91C22×Dic22—21no—
92C22×Dic22C2311yescharacteristic
93C2×C11×Q16—24no—
94C2×C11×Q16C2314yes—
95C2×C11×SD16—24no—
96C2×C11×SD16C2314yes—
97C22×C8×C11C2311yescharacteristic
98C22×C8×C11C2311yescharacteristic
99C11×#124—22no—
100C11×#124C2314yes—
101C4×Q8×C11—22no—
102C4×Q8×C11C2314yes—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C42×C11—21no—
108C2×C42×C11C2311yescharacteristic
109C2×C22⋊Dic11—21no—
110C2×C22⋊Dic11—21no—
111#66999—22no—
112#66999C2314yes—
113Q8×Dic11—22no—
114Q8×Dic11—22no—
115Q8×Dic11C2314yes—
116Q8×Dic11C2314yes—
117C2×#4326—24no—
118C2×#4326C2314yes—
119#66991—22no—
120#66991C2314yes—
121D4×Dic11—22no—
122D4×Dic11C2314yes—
123C2×#4324—24no—
124C2×#4324C2314yes—
125C2×(C2×D11)⋊C4—21no—
126C2×C4⋊Dic11—21no—
127C2×C4⋊Dic11—21no—
128C2×C4⋊Dic11C2311yescharacteristic
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4—21no—
136C2×Dic11⋊C4—21no—
137C2×C4×Dic11—21no—
138C2×C4×Dic11—21no—
139C2×C4×Dic11—21no—
140C2×C4×Dic11—21no—
141C2×C4×Dic11D411yescharacteristic
142C2×C4×Dic11D411yescharacteristic
143C2×C4×Dic11C2311yescharacteristic
144C22×C11⋊C8C2311yescharacteristic
145C22×C11⋊C8C2311yescharacteristic
146C4⋊C4×D11—28no—
147C4⋊C4×D11—22no—
148C4⋊C4×D11C2314yes—
149#66940—28no—
150#66940—22no—
151#66940C2314yes—
152#66936—28no—
153(C22⋊D11)⋊C4—28no—
154#66932—28no—
155#66930—28no—
156C42×D11—28no—
157C42×D11D414yes—
158C42×D11C2314yes—
159#66923—22no—
160#66923C2314yes—
161C4×Dic22—22no—
162C4×Dic22—28no—
163C4×Dic22C2314yes—
164C11×C4⋊C8C2314yes—
165C11×#103C2314yes—
166C11×#102C2314yes—
167#66899C2314yes—
168#66899C2314yes—
169#66899C2314yes—
170#66896C2314yes—
171(C2×D11)⋊C8C2314yes—
172(C2×D11)⋊C8C2314yes—
173#66882C2314yes—
174#66881C2314yes—
175#66880C2314yes—
176#66880C2314yes—
177#66879C2314yes—
178#66879C2314yes—
179#66872C2314yes—
180#66871C2314yes—
181C4⋊(C11⋊C8)C2314yes—
182C2×#3117—111nomaximal, Sylow
183C24×C11—21no—
184C23×D11C2×D411yescharacteristic
185C2×Q8×C11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—22no—
188C2×Q8×C11—22no—
189C2×Q8×C11—22no—
190C2×Q8×C11#4114yes—
191C2×Q8×C11C2412yes—
192C2×Q8×C11C2412yes—
193C2×D4×C11—21no—
194C2×D4×C11—22no—
195C2×D4×C11—22no—
196C2×D4×C11C2412yes—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2411yescharacteristic
203C2×C22⋊D11—24no—
204C2×C22⋊D11—44no—
205C22×Dic11—24no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—44no—
211C22×Dic11C2×D411yescharacteristic
212C22×Dic11C2×D411yescharacteristic
213C22×Dic11C2×D411yescharacteristic
214Q8×D11—216no—
215Q8×D11—28no—
216Q8×D11—28no—
217C2×C4×D11—28no—
218C2×C4×D11—24no—
219C2×C4×D11—24no—
220C2×C4×D11—24no—
221C2×C4×D11—22no—
222C2×C4×D11—22no—
223C2×C4×D11—42no—
224C2×C4×D11—44no—
225C2×C4×D11C2×D414yes—
226C2×C4×D11C2×D412yes—
227C2×C4×D11C2×D414yes—
228C2×C4×D11C2412yes—
229C2×Dic22—28no—
230C2×Dic22—24no—
231C2×Dic22—21no—
232C2×Dic22—22no—
233C2×Dic22#4114yes—
234C2×Dic22C2412yes—
235C11×Q16—28no—
236C11×SD16—28no—
237C2×C8×C11—22no—
238C2×C8×C11—22no—
239C2×C8×C11C2412yes—
240C2×C8×C11C2412yes—
241C11×C4⋊C4—24no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4C2412yes—
244C11×C22⋊C4—24no—
245C11×C22⋊C4—24no—
246C42×C11—24no—
247C42×C11C2×D412yes—
248C42×C11C2412yes—
249C22⋊Dic11—24no—
250C22⋊Dic11—24no—
251#4326—28no—
252#4324—28no—
253(C2×D11)⋊C4—24no—
254C4⋊Dic11—24no—
255C4⋊Dic11—24no—
256C4⋊Dic11—21no—
257C4⋊Dic11—21no—
258C4⋊Dic11—21no—
259C4⋊Dic11C2412yes—
260C4⋊Dic11C2412yes—
261C4⋊Dic11C2412yes—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268C4×Dic11—24no—
269C4×Dic11—24no—
270C4×Dic11—24no—
271C4×Dic11—24no—
272C4×Dic11C2×D414yes—
273C4×Dic11C2×D412yes—
274C4×Dic11C2×D414yes—
275C4×Dic11C2412yes—
276C2×C11⋊C8—22no—
277C2×C11⋊C8—22no—
278C2×C11⋊C8C2412yes—
279C2×C11⋊C8C2412yes—
280C2×#529—111no—
281C22×C4×Q8—111no—
282#3117—1116no—
283C2×#484—111no—
284C2×#481—111no—
285C2×#479—111no—
286C2×#479—111no—
287C2×#464—111no—
288C2×#464D1111yescharacteristic, complemented
289C2×#451—111no—
290C2×#448—111no—
291C2×#441—111no—
292C2×#441—111no—
293C2×#440—111no—
294C2×#440—111no—
295C2×#432—111no—
296C23×C11—22no—
297C23×C11—42no—
298C23×C11—42no—
299C23×C11—42no—
300C23×C11C22×D411yescharacteristic
301C22×D11—22no—
302C22×D11—22no—
303C22×D11#13714yes—
304C22×D11C22×D412yes—
305Q8×C11—24no—
306Q8×C11—22no—
307Q8×C11—22no—
308Q8×C11—22no—
309Q8×C11—42no—
310Q8×C11C2×#4114yes—
311D4×C11—22no—
312D4×C11—22no—
313D4×C11—42no—
314C2×C4×C11—24no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—42no—
321C2×C4×C11—42no—
322C2×C4×C11C22×D412yes—
323C2×C4×C11C22×D412yes—
324C2×C4×C11C22×D411yescharacteristic
325C2×C4×C11C2×#4112yes—
326C2×C4×C11C2×#4112yes—
327C2×C4×C11C2511yescharacteristic
328C22⋊D11—48no—
329C2×Dic11—22no—
330C2×Dic11—24no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—48no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11C22×D412yes—
342C2×Dic11C22×D412yes—
343C2×Dic11C22×D412yes—
344C4×D11—216no—
345C4×D11—28no—
346C4×D11—24no—
347C4×D11—22no—
348C4×D11—22no—
349C4×D11—44no—
350C4×D11—48no—
351Dic22—216no—
352Dic22—24no—
353Dic22—22no—
354Dic22C2×#4114yes—
355C8×C11—22no—
356C8×C11—22no—
357C11⋊C8—22no—
358C11⋊C8—22no—
359C23×Q8—111no—
360C22×Q16—111no—
361C22×Q16C2×D1111yescharacteristic
362C22×SD16—111no—
363C22×SD16C2×D1111yescharacteristic
364#529—118no—
365#529—224no—
366C2×#126—221no—
367C2×#125—111no—
368C2×#124C2×D1111yescharacteristic
369C2×#123—221no—
370C2×C22⋊Q8—111no—
371C2×#121—111no—
372C2×C4×Q8—111no—
373C2×C4×Q8—111no—
374C2×C4×Q8—118no—
375C2×C4×Q8—111no—
376C2×C4×Q8—111no—
377C2×C4×Q8—221no—
378C2×C4×Q8—221no—
379C2×C4×Q8—224no—
380C2×C4×Q8C2×D1111yescharacteristic
381C2×C4×D4—111no—
382C2×C4×D4—221no—
383C2×#117—221no—
384C22×C4⋊C4—111no—
385C22×C4⋊C4—221no—
386C22×C42—111no—
387C22×C42—221no—
388#484—118no—
389#481—118no—
390#479—118no—
391#479—118no—
392#464—118no—
393#464C2×D1118yescomplemented
394#451—118no—
395#448—118no—
396#441—118no—
397#441—118no—
398#440—118no—
399#440—118no—
400#432—118no—
401C2×#107—111no—
402C2×#107—111no—
403C2×#106—111no—
404C2×#106—111no—
405C2×C4⋊C8—111no—
406C2×C4⋊C8C2×D1111yescharacteristic
407C2×#103—111no—
408C2×#103—111no—
409C2×#103—111no—
410C2×#103—111no—
411C2×#103—111no—
412C2×#103C2×D1111yescharacteristic
413C2×#102—111no—
414C2×#102C2×D1111yescharacteristic
415C2×C22⋊C8—111no—
416C2×C22⋊C8—111no—
417C2×#97—111no—
418C2×#97—111no—
419C22×C11—42no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—84no—
423C22×C11#52512yes—
424C22×C11C2×#13712yes—
425C22×C11#57512yes—
426C22×C11C23×D411yescharacteristic
427C2×D11—28no—
428C2×D11—22no—
429C2×D11—22no—
430C2×D11C2×#13714yes—
431C4×C11—24no—
432C4×C11—22no—
433C4×C11—22no—
434C4×C11—42no—
435C4×C11—42no—
436C4×C11#52512yes—
437C4×C11C22×#4111yescharacteristic
438C4×C11C22×#4111yescharacteristic
439Dic11—22no—
440Dic11—24no—
441Dic11—22no—
442Dic11—22no—
443Dic11—42no—
444Dic11—42no—
445Dic11—42no—
446C22×Q8—114no—
447C22×Q8—111no—
448C22×Q8—221no—
449C22×Q8—222no—
450C22×Q8—224no—
451C22×Q8—224no—
452C22×Q8C22×D1111yescharacteristic
453C22×Q8C22×D1111yescharacteristic
454C22×D4—221no—
455C22×D4C22×D1111yescharacteristic
456C23×C4—111no—
457C23×C4—111no—
458C23×C4—111no—
459C23×C4—221no—
460C23×C4—221no—
461C23×C4—221no—
462C2×Q16—24no—
463C2×Q16—114no—
464C2×Q16—224no—
465C2×Q16C22×D1114yes—
466C2×SD16—24no—
467C2×SD16—114no—
468C2×SD16—224no—
469C2×SD16C22×D1114yes—
470C22×C8—111no—
471C22×C8—111no—
472C22×C8C22×D1111yescharacteristic
473C22×C8C22×D1111yescharacteristic
474#126—228no—
475#125—114no—
476#125—222no—
477#124—22no—
478#124C22×D1114yes—
479#123—228no—
480C22⋊Q8—114no—
481C22⋊Q8—222no—
482#121—114no—
483#121—222no—
484C4×Q8—22no—
485C4×Q8—114no—
486C4×Q8—114no—
487C4×Q8—114no—
488C4×Q8—114no—
489C4×Q8—228no—
490C4×Q8—222no—
491C4×Q8—228no—
492C4×Q8—222no—
493C4×Q8—222no—
494C4×Q8—222no—
495C4×Q8C22×D1114yes—
496C4×D4—114no—
497C4×D4—222no—
498C4×D4—228no—
499#117—228no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—111no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4—111no—
504C2×C4⋊C4—114no—
505C2×C4⋊C4—222no—
506C2×C4⋊C4—228no—
507C2×C4⋊C4—221no—
508C2×C4⋊C4—221no—
509C2×C4⋊C4—221no—
510C2×C4⋊C4—221no—
511C2×C4⋊C4—221no—
512C2×C4⋊C4—221no—
513C2×C4⋊C4—221no—
514C2×C4⋊C4—221no—
515C2×C4⋊C4C22×D1111yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C42—21no—
522C2×C42—111no—
523C2×C42—111no—
524C2×C42—111no—
525C2×C42—114no—
526C2×C42—114no—
527C2×C42—228no—
528C2×C42—221no—
529C2×C42—221no—
530C2×C42—221no—
531C2×C42—221no—
532C2×C42C22×D1111yescharacteristic
533#107—114no—
534#107—114no—
535#106—114no—
536#106—114no—
537C4⋊C8—114no—
538C4⋊C8C22×D1114yes—
539#103—114no—
540#103—114no—
541#103—114no—
542#103—114no—
543#103—114no—
544#103C22×D1114yes—
545#102—114no—
546#102C22×D1114yes—
547C22⋊C8—114no—
548C22⋊C8—114no—
549#97—114no—
550#97—114no—
551C2×C11—82no—
552C2×C11#311714yescomplemented
553C2×C11C2×#52511yescharacteristic
554C2×C11C22×#13711yescharacteristic
555C2×C11C2×#57511yescharacteristic
556D11—24no—
557C24—21no—
558C24—111no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—114no—
565C2×Q8—112no—
566C2×Q8—224no—
567C2×Q8—228no—
568C2×Q8—228no—
569C2×Q8—2216no—
570C2×Q8—228no—
571C2×Q8—221no—
572C2×Q8—222no—
573C2×Q8#434114yes—
574C2×Q8C23×D1112yes—
575C2×Q8C23×D1112yes—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—224no—
580C2×D4—444no—
581C2×D4C23×D1112yes—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—111no—
586C22×C4—111no—
587C22×C4—111no—
588C22×C4—114no—
589C22×C4—112no—
590C22×C4—112no—
591C22×C4—114no—
592C22×C4—224no—
593C22×C4—224no—
594C22×C4—228no—
595C22×C4—224no—
596C22×C4—224no—
597C22×C4—221no—
598C22×C4—222no—
599C22×C4—222no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4—221no—
603C22×C4—442no—
604C22×C4—444no—
605C22×C4—444no—
606C22×C4D4×D1111yescharacteristic
607C22×C4D4×D1111yescharacteristic
608C22×C4C23×D1111yescharacteristic
609Q16—28no—
610Q16—228no—
611SD16—28no—
612SD16—228no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—112no—
616C2×C8—112no—
617C2×C8—222no—
618C2×C8—222no—
619C2×C8C23×D1112yes—
620C2×C8C23×D1112yes—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—112no—
624C4⋊C4—112no—
625C4⋊C4—112no—
626C4⋊C4—224no—
627C4⋊C4—224no—
628C4⋊C4—224no—
629C4⋊C4—224no—
630C4⋊C4—224no—
631C4⋊C4—221no—
632C4⋊C4—221no—
633C4⋊C4—221no—
634C4⋊C4—224no—
635C4⋊C4—224no—
636C4⋊C4—224no—
637C4⋊C4C23×D1112yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—224no—
641C22⋊C4—224no—
642C22⋊C4—224no—
643C42—24no—
644C42—114no—
645C42—112no—
646C42—114no—
647C42—112no—
648C42—224no—
649C42—224no—
650C42—224no—
651C42—224no—
652C42D4×D1112yes—
653C42C23×D1112yes—
654C11C2×#311711yescharacteristic, complemented, Sylow
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—114no—
660C23—112no—
661C23—222no—
662C23—222no—
663C23C2×D4×D1111yescharacteristic
664Q8—24no—
665Q8—22no—
666Q8—22no—
667Q8—22no—
668Q8—42no—
669Q8—114no—
670Q8—2216no—
671Q8—224no—
672Q8—222no—
673Q8C2×#434114yes—
674D4—22no—
675D4—22no—
676D4—42no—
677D4—448no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—112no—
687C2×C4—112no—
688C2×C4—112no—
689C2×C4—228no—
690C2×C4—2216no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—222no—
694C2×C4—224no—
695C2×C4—222no—
696C2×C4—224no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—444no—
703C2×C4—448no—
704C2×C4—448no—
705C2×C4—442no—
706C2×C4—442no—
707C2×C4—442no—
708C2×C4C2×D4×D1112yes—
709C2×C4C2×D4×D1112yes—
710C2×C4C2×D4×D1111yescharacteristic
711C2×C4C2×#434112yes—
712C2×C4#41×D1112yes—
713C2×C4C24×D1111yescharacteristic
714C8—22no—
715C8—22no—
716C8—222no—
717C8—222no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—84no—
722C22—114no—
723C22—222no—
724C22—228no—
725C22—222no—
726C22#1062313712yes—
727C22#1062329912yes—
728C22D11×#13712yes—
729C22C22×D4×D1111yescharacteristic
730C4—24no—
731C4—22no—
732C4—22no—
733C4—42no—
734C4—42no—
735C4—222no—
736C4—224no—
737C4—222no—
738C4—222no—
739C4—442no—
740C4—442no—
741C4—442no—
742C4#1062313712yes—
743C4C22×#434111yescharacteristic
744C4C2×#41×D1111yescharacteristic
745C2—82no—
746C2—224no—
747C2#1307878614yesdirect product factor
748C2C2×#1062313711yescharacteristic
749C2C2×D11×#13711yescharacteristic
750C2C2×#1062329911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#464C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenterC2×#464D11
hypocenterC11C2×#3117
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D11C2semidirect
3. #13078786C2direct (N × H)
4. C2×#10622422C2semidirect
6. C2×#10622442C2semidirect
7. C2×#10622635C2semidirect
8. C2×#10622667C2semidirect
9. C2×#10622799C2semidirect
11. C2×#10622797C2semidirect
12. C2×#10622402C2semidirect
13. C2×#10622777C2semidirect
14. C2×#10622370C2semidirect
15. C2×#10622448C2semidirect
16. C2×C11×#464C2semidirect
32. C4×Q8×D11C22semidirect
46. C11×#464C22semidirect
54. #10622799C22semidirect
55. #10622797C22semidirect
57. #10622777C22semidirect
66. #10622667C22semidirect
67. #10622635C22semidirect
71. #10622448C22semidirect
72. #10622442C22semidirect
73. #10622422C22semidirect
74. #10622402C22semidirect
76. #10622370C22semidirect
288. C2×#464D11semidirect
393. #464C2×D11semidirect
552. C2×C11#3117semidirect
654. C11C2×#3117semidirect
747. C2#13078786direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232112
C2×C4×Q8×D112
#130787862
C2×#106224222
C2×#106223902
C2×#106224422
C2×#106226352
C2×#106226672
C2×#106227992
C2×#106227832
C2×#106227972
C2×#106224022
C2×#106227772
C2×#106223702
C2×#106224482
C2×C11×#4642
C2×#311711