Finite Group Databasebeta

← C2×#13080968 #15632191

Subgroups — C2×#13080968 #15632191

Order 2816.

2158 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623166C211yesmaximal, characteristic, complemented
2C2×#10623142C211yesmaximal, characteristic
3#13080968C2116yesmaximal, direct product factor
4C2×#10622468C211yesmaximal, characteristic, complemented
5C2×#10622390C211yesmaximal, characteristic, complemented
6C2×#10622647C211yesmaximal, characteristic, complemented
7C2×#10622418C211yesmaximal, characteristic, complemented
8C2×#10622656C211yesmaximal, characteristic, complemented
9C2×#10622404C211yesmaximal, characteristic, complemented
10C2×#10622374C211yesmaximal, characteristic, complemented
11C2×#10622784C211yesmaximal, characteristic, complemented
12C2×SD16×Dic11C211yesmaximal, characteristic, complemented
13C2×C8×C22⋊D11C211yesmaximal, characteristic, complemented
14C22×#66881C211yesmaximal, characteristic, complemented
15C2×D11×#106C211yesmaximal, characteristic, complemented
16C2×C11×#465C211yesmaximal, characteristic, complemented
17C22×#4341—21no—
18C22×C11×SD16C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×#66999C2211yescharacteristic
23C2×Q8×Dic11C2211yescharacteristic
24C2×#66991C2211yescharacteristic
25C2×#66988—21no—
26C2×D4×Dic11C2211yescharacteristic
27C2×C4×C22⋊D11C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×C8×D11C2211yescharacteristic
31#10623166—24no—
32#10623166C2218yescomplemented
33#10623142—24no—
34#10623142C2218yes—
35C2×#66950—21no—
36C2×C4⋊C4×D11C2211yescharacteristic
37C2×C4⋊C4×D11C2211yescharacteristic
38C2×#66942—21no—
39C2×#66941C2211yescharacteristic
40C2×#66941C2211yescharacteristic
41C2×#66936—21no—
42C2×(C22⋊D11)⋊C4—21no—
43C2×#66931—21no—
44C2×#66931—21no—
45C11×#465C2218yescomplemented
46C2×C11×#106C2211yescharacteristic
47C2×C11×#103C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×#66899C2211yescharacteristic
50C2×#66899C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×C22⋊(C11⋊C8)C2211yescharacteristic
54#10622784C2218yescomplemented
55SD16×Dic11C2218yescomplemented
56C8×C22⋊D11C2218yescomplemented
57C2×(C2×D11)⋊C8C2211yescharacteristic
58C2×#66881C2211yescharacteristic
59C2×#66881C2211yescharacteristic
60C2×#66881C2211yescharacteristic
61C2×#66881C2211yescharacteristic
62C2×#66881C2218yescomplemented
63C2×Dic11⋊C8C2211yescharacteristic
64C2×C8×Dic11C2211yescharacteristic
65#10622656C2218yescomplemented
66#10622647C2218yescomplemented
67C2×#66872C2211yescharacteristic
68C2×#66872C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66872C2211yescharacteristic
71D11×#106C2218yescomplemented
72#10622468C2218yescomplemented
73#10622418C2218yescomplemented
74#10622404C2218yescomplemented
75#10622390C2218yescomplemented
76#10622374C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×C22⋊D11D411yescharacteristic
83C23×Dic11—21no—
84C23×Dic11—21no—
85C23×Dic11—21no—
86C2×#4341—28no—
87C2×#4341—48no—
88C22×C4×D11—21no—
89C22×C4×D11—21no—
90C22×C4×D11C2311yescharacteristic
91C22×Dic22—21no—
92C22×Dic22—21no—
93C2×C11×SD16—24no—
94C2×C11×SD16C2314yes—
95C22×C8×C11—24no—
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2314yes—
98C22×C8×C11C2311yescharacteristic
99C11×C22⋊Q8—22no—
100C11×C22⋊Q8C2314yes—
101C11×#121—22no—
102C11×#121C2314yes—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C22⋊Dic11—21no—
109C2×C22⋊Dic11—21no—
110C2×C22⋊Dic11D411yescharacteristic
111#66999—22no—
112#66999C2314yes—
113Q8×Dic11—22no—
114Q8×Dic11C2314yes—
115#66991—22no—
116#66991C2314yes—
117#66988—28no—
118D4×Dic11—22no—
119D4×Dic11C2314yes—
120C4×C22⋊D11D414yes—
121C4×C22⋊D11C2314yes—
122C2×(C2×D11)⋊C4—21no—
123C2×(C2×D11)⋊C4D411yescharacteristic
124C2×C4⋊Dic11—21no—
125C2×C4⋊Dic11—21no—
126C2×C4⋊Dic11—22no—
127C2×C4⋊Dic11—22no—
128C2×C4⋊Dic11—21no—
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2311yescharacteristic
133C2×C4⋊Dic11C2314yes—
134C2×C4⋊Dic11C2314yes—
135C2×Dic11⋊C4—21no—
136C2×Dic11⋊C4—21no—
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4D411yescharacteristic
141C2×C4×Dic11—21no—
142C2×C4×Dic11C2311yescharacteristic
143C22×C11⋊C8C2311yescharacteristic
144C22×C11⋊C8C2311yescharacteristic
145C2×C8×D11—24no—
146C2×C8×D11C2314yes—
147#66950—28no—
148C4⋊C4×D11—22no—
149C4⋊C4×D11—22no—
150C4⋊C4×D11C2314yes—
151C4⋊C4×D11C2314yes—
152#66942—28no—
153#66941—22no—
154#66941—22no—
155#66941C2314yes—
156#66941C2314yes—
157#66936—28no—
158(C22⋊D11)⋊C4—28no—
159#66931—28no—
160#66931—28no—
161C11×#106C2314yes—
162C11×#103C2314yes—
163C11×#102C2314yes—
164#66899C2314yes—
165#66899C2314yes—
166#66896C2314yes—
167#66896C2314yes—
168C22⋊(C11⋊C8)C2314yes—
169(C2×D11)⋊C8C2314yes—
170#66881C2314yes—
171#66881C2314yes—
172#66881C2314yes—
173#66881C2314yes—
174Dic11⋊C8C2314yes—
175C8×Dic11C2314yes—
176#66872C2314yes—
177#66872C2314yes—
178#66872C2314yes—
179#66872C2314yes—
180C2×#3335—111nomaximal, Sylow
181C24×C11—21no—
182C24×C11C2×D411yescharacteristic
183C23×D11C2×D411yescharacteristic
184C2×Q8×C11—21no—
185C2×Q8×C11—22no—
186C2×Q8×C11—22no—
187C2×Q8×C11C2412yes—
188C2×D4×C11—24no—
189C2×D4×C11—21no—
190C2×D4×C11—22no—
191C2×D4×C11—22no—
192C2×D4×C11—44no—
193C2×D4×C11C2412yes—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D412yes—
201C22×C4×C11C2412yes—
202C22×C4×C11C2411yescharacteristic
203C2×C22⋊D11—24no—
204C2×C22⋊D11—44no—
205C2×C22⋊D11SD1618yescomplemented
206C2×C22⋊D11C2×D414yes—
207C22×Dic11—24no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—24no—
213C22×Dic11—24no—
214C22×Dic11—44no—
215C22×Dic11—44no—
216C22×Dic11—82no—
217C22×Dic11C2×D411yescharacteristic
218C22×Dic11C2×D411yescharacteristic
219C22×Dic11C2×D411yescharacteristic
220#4341—432no—
221C2×C4×D11—24no—
222C2×C4×D11—24no—
223C2×C4×D11—22no—
224C2×C4×D11—22no—
225C2×C4×D11—44no—
226C2×C4×D11—82no—
227C2×C4×D11C2×D412yes—
228C2×C4×D11C2412yes—
229C2×Dic22—24no—
230C2×Dic22—24no—
231C2×Dic22—44no—
232C2×Dic22—82no—
233C11×SD16—28no—
234C2×C8×C11—28no—
235C2×C8×C11—22no—
236C2×C8×C11#4114yescomplemented
237C2×C8×C11C2412yes—
238C2×C8×C11C2412yes—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—24no—
242C11×C4⋊C4C2412yes—
243C11×C4⋊C4C2412yes—
244C11×C22⋊C4—24no—
245C11×C22⋊C4—24no—
246C22⋊Dic11—24no—
247C22⋊Dic11—24no—
248C22⋊Dic11C2×D414yes—
249(C2×D11)⋊C4—24no—
250(C2×D11)⋊C4C2×D414yes—
251C4⋊Dic11—24no—
252C4⋊Dic11—24no—
253C4⋊Dic11—21no—
254C4⋊Dic11—21no—
255C4⋊Dic11—24no—
256C4⋊Dic11—21no—
257C4⋊Dic11—21no—
258C4⋊Dic11C2412yes—
259C4⋊Dic11C2412yes—
260C4⋊Dic11C2412yes—
261C4⋊Dic11C2412yes—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266Dic11⋊C4—24no—
267Dic11⋊C4C2×D414yes—
268C4×Dic11—24no—
269C4×Dic11C2×D412yes—
270C4×Dic11C2412yes—
271C2×C11⋊C8—22no—
272C2×C11⋊C8—22no—
273C2×C11⋊C8C2412yes—
274C2×C11⋊C8C2412yes—
275C8×D11—28no—
276C2×#554—111no—
277C2×#547—111no—
278#3335—1116no—
279C2×#498—111no—
280C2×#481—111no—
281C2×#481—111no—
282C2×#483—111no—
283C2×#483—111no—
284C2×#475—111no—
285C2×#476—111no—
286C2×#465—111no—
287C2×#465D1111yescharacteristic, complemented
288C2×C4×SD16—111no—
289C2×C8×D4—111no—
290C22×#106—111no—
291C22×#106—111no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—42no—
296C23×C11—42no—
297C23×C11—42no—
298C23×C11C2×SD1614yes—
299C23×C11C22×D412yes—
300C23×C11C22×D411yescharacteristic
301C22×D11—22no—
302C22×D11—22no—
303C22×D11C2×SD1614yes—
304C22×D11C22×D412yes—
305Q8×C11—22no—
306Q8×C11—22no—
307Q8×C11—42no—
308D4×C11—22no—
309D4×C11—22no—
310D4×C11—48no—
311D4×C11—42no—
312C2×C4×C11—22no—
313C2×C4×C11—24no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—42no—
320C2×C4×C11—42no—
321C2×C4×C11—42no—
322C2×C4×C11C22×D412yes—
323C2×C4×C11C22×D411yescharacteristic
324C2×C4×C11C2×#4112yes—
325C2×C4×C112−1+412yes—
326C2×C4×C11C2511yescharacteristic
327C22⋊D11—48no—
328C22⋊D11C2×SD16116yescomplemented
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11—48no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—48no—
341C2×Dic11—84no—
342C2×Dic11C2×SD1614yes—
343C2×Dic11C22×D412yes—
344C2×Dic11C22×D412yes—
345C2×Dic11C22×D412yes—
346C4×D11—24no—
347C4×D11—22no—
348C4×D11—22no—
349C4×D11—48no—
350C4×D11—84no—
351Dic22—48no—
352Dic22—84no—
353C8×C11—22no—
354C8×C11C2×#4114yescomplemented
355C11⋊C8—22no—
356C11⋊C8—22no—
357C22×#41—221no—
358C22×SD16C2×D1111yescharacteristic
359C23×C8—111no—
360C23×C8C2×D1111yescharacteristic
361#554—118no—
362#554—224no—
363#547—118no—
364#547—224no—
365C2×C4⋊Q8—111no—
366C2×C4⋊Q8—111no—
367C2×#125—221no—
368C2×#123—221no—
369C2×#123—221no—
370C2×C22⋊Q8—111no—
371C2×C22⋊Q8—221no—
372C2×C22⋊Q8—221no—
373C2×C22⋊Q8—221no—
374C2×C22⋊Q8C2×D1111yescharacteristic
375C2×#121—111no—
376C2×#121C2×D1111yescharacteristic
377C2×C4×Q8—111no—
378C2×C4×D4—111no—
379C2×C4×D4—111no—
380C2×C4×D4—221no—
381C22×C4⋊C4—111no—
382C22×C4⋊C4—111no—
383C22×C4⋊C4—111no—
384C22×C4⋊C4—111no—
385#498—118no—
386#483—118no—
387#483—118no—
388#481—118no—
389#481—118no—
390#476—118no—
391#475—118no—
392#465—118no—
393#465C2×D1118yescomplemented
394C4×SD16—118no—
395C8×D4—118no—
396C2×#106—111no—
397C2×#106—118no—
398C2×#106—111no—
399C2×#106—111no—
400C2×#106—111no—
401C2×#106—111no—
402C2×#106—111no—
403C2×#106—111no—
404C2×#106—111no—
405C2×#106—118no—
406C2×#106C2×D1111yescharacteristic
407C2×C4⋊C8—111no—
408C2×#103—111no—
409C2×#103—111no—
410C2×#103C2×D1111yescharacteristic
411C2×#102—111no—
412C2×#102—111no—
413C2×#102C2×D1111yescharacteristic
414C2×C22⋊C8—111no—
415C2×C22⋊C8—111no—
416C2×C4×C8—111no—
417C22×C11—28no—
418C22×C11—22no—
419C22×C11—22no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—84no—
424C22×C11#54712yes—
425C22×C11C22×SD1614yes—
426C22×C11C22×SD1612yes—
427C22×C11#57712yes—
428C22×C11C23×D411yescharacteristic
429C2×D11—28no—
430C2×D11—22no—
431C2×D11—22no—
432C2×D11C22×SD1614yes—
433C4×C11—22no—
434C4×C11—42no—
435C4×C11—42no—
436C4×C11—42no—
437C4×C11#54712yes—
438C4×C11C22×#4111yescharacteristic
439C4×C11C2×2−1+411yescharacteristic
440Dic11—22no—
441Dic11—22no—
442Dic11—42no—
443Dic11—42no—
444Dic11—42no—
445Dic11—42no—
446Dic11C22×SD1614yes—
447C2×#41—228no—
448C2×#41—448no—
449C22×Q8—221no—
450C22×Q8—221no—
451C22×Q8C22×D1111yescharacteristic
452C22×D4—21no—
453C22×D4—111no—
454C22×D4—221no—
455C22×D4C22×D1111yescharacteristic
456C23×C4—111no—
457C23×C4—221no—
458C23×C4—221no—
459C23×C4—221no—
460C23×C4—221no—
461C23×C4—221no—
462C23×C4C22×D1111yescharacteristic
463C2×SD16—24no—
464C2×SD16C22×D1114yes—
465C22×C8—24no—
466C22×C8—111no—
467C22×C8—111no—
468C22×C8—114no—
469C22×C8—224no—
470C22×C8C22×D1111yescharacteristic
471C22×C8C22×D1114yes—
472C22×C8C22×D1111yescharacteristic
473C4⋊Q8—114no—
474C4⋊Q8—114no—
475C4⋊Q8—222no—
476C4⋊Q8—222no—
477#125—228no—
478#123—228no—
479#123—228no—
480C22⋊Q8—22no—
481C22⋊Q8—114no—
482C22⋊Q8—228no—
483C22⋊Q8—228no—
484C22⋊Q8—228no—
485C22⋊Q8—222no—
486C22⋊Q8C22×D1114yes—
487#121—22no—
488#121—114no—
489#121—222no—
490#121C22×D1114yes—
491C4×Q8—114no—
492C4×Q8—222no—
493C4×D4—114no—
494C4×D4—114no—
495C4×D4—114no—
496C4×D4—222no—
497C4×D4—228no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—111no—
500C2×C4⋊C4—111no—
501C2×C4⋊C4—111no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4—111no—
504C2×C4⋊C4—114no—
505C2×C4⋊C4—114no—
506C2×C4⋊C4—114no—
507C2×C4⋊C4—114no—
508C2×C4⋊C4—222no—
509C2×C4⋊C4—222no—
510C2×C4⋊C4—221no—
511C2×C4⋊C4—221no—
512C2×C4⋊C4—221no—
513C2×C4⋊C4—221no—
514C2×C4⋊C4—221no—
515C2×C4⋊C4—221no—
516C2×C4⋊C4—221no—
517C2×C4⋊C4—221no—
518C2×C4⋊C4—222no—
519C2×C4⋊C4—222no—
520C2×C4⋊C4C22×D1111yescharacteristic
521C2×C4⋊C4C22×D1111yescharacteristic
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—111no—
525C2×C22⋊C4—111no—
526C2×C22⋊C4—221no—
527C2×C22⋊C4—221no—
528C2×C22⋊C4—221no—
529C2×C42—111no—
530C2×C42—221no—
531#106—114no—
532#106—114no—
533#106—114no—
534#106—114no—
535#106—114no—
536#106—114no—
537#106—114no—
538#106—114no—
539#106C22×D1114yes—
540C4⋊C8—114no—
541#103—114no—
542#103—114no—
543#103C22×D1114yes—
544#102—114no—
545#102—114no—
546#102C22×D1114yes—
547C22⋊C8—114no—
548C22⋊C8—114no—
549C4×C8—114no—
550C2×C11—24no—
551C2×C11—82no—
552C2×C11#333514yescomplemented
553C2×C11C2×#54711yescharacteristic
554C2×C11C23×SD1611yescharacteristic
555C2×C11C2×#57711yescharacteristic
556D11—24no—
557C24—21no—
558C24—111no—
559C24D4×D1111yescharacteristic
560#41—4432no—
561C2×Q8—21no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—224no—
565C2×Q8—224no—
566C2×Q8—444no—
567C2×Q8—882no—
568C2×Q8C23×D1112yes—
569C2×D4—24no—
570C2×D4—21no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—44no—
574C2×D4—118no—
575C2×D4—114no—
576C2×D4—224no—
577C2×D4—444no—
578C2×D4C23×D1112yes—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—111no—
585C22×C4—111no—
586C22×C4—111no—
587C22×C4—112no—
588C22×C4—112no—
589C22×C4—224no—
590C22×C4—224no—
591C22×C4—224no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—224no—
595C22×C4—221no—
596C22×C4—221no—
597C22×C4—221no—
598C22×C4—221no—
599C22×C4—224no—
600C22×C4—444no—
601C22×C4—444no—
602C22×C4—444no—
603C22×C4—882no—
604C22×C4—882no—
605C22×C4D4×D1112yes—
606C22×C4D4×D1111yescharacteristic
607C22×C4C23×D1112yes—
608C22×C4C23×D1111yescharacteristic
609SD16—28no—
610C2×C8—22no—
611C2×C8—28no—
612C2×C8—112no—
613C2×C8—112no—
614C2×C8—222no—
615C2×C8—222no—
616C2×C8—228no—
617C2×C8#434114yescomplemented
618C2×C8C23×D1112yes—
619C2×C8C23×D1112yes—
620C4⋊C4—24no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—114no—
624C4⋊C4—112no—
625C4⋊C4—112no—
626C4⋊C4—112no—
627C4⋊C4—112no—
628C4⋊C4—224no—
629C4⋊C4—224no—
630C4⋊C4—224no—
631C4⋊C4—224no—
632C4⋊C4—224no—
633C4⋊C4—224no—
634C4⋊C4—221no—
635C4⋊C4—221no—
636C4⋊C4—221no—
637C4⋊C4—224no—
638C4⋊C4—224no—
639C4⋊C4—221no—
640C4⋊C4C23×D1112yes—
641C4⋊C4C23×D1112yes—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—114no—
645C22⋊C4—114no—
646C22⋊C4—224no—
647C22⋊C4—224no—
648C22⋊C4—224no—
649C42—112no—
650C42—112no—
651C42—224no—
652C11C2×#333511yescharacteristic, complemented, Sylow
653C23—22no—
654C23—22no—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—114no—
660C23—112no—
661C23—222no—
662C23—222no—
663C23SD16×D1114yes—
664C23C2×D4×D1112yes—
665C23C2×D4×D1111yescharacteristic
666Q8—22no—
667Q8—22no—
668Q8—42no—
669Q8—448no—
670Q8—884no—
671D4—22no—
672D4—22no—
673D4—48no—
674D4—42no—
675D4—1116no—
676D4—448no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—114no—
688C2×C4—112no—
689C2×C4—112no—
690C2×C4—112no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—224no—
694C2×C4—222no—
695C2×C4—222no—
696C2×C4—222no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—448no—
701C2×C4—448no—
702C2×C4—442no—
703C2×C4—442no—
704C2×C4—448no—
705C2×C4—442no—
706C2×C4—442no—
707C2×C4—884no—
708C2×C4—884no—
709C2×C4C2×D4×D1112yes—
710C2×C4C2×D4×D1111yescharacteristic
711C2×C4C2×#434112yes—
712C2×C4#6704312yes—
713C2×C4C24×D1111yescharacteristic
714C8—22no—
715C8—222no—
716C8—222no—
717C8C2×#434114yescomplemented
718C22—28no—
719C22—22no—
720C22—22no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—84no—
725C22—114no—
726C22—228no—
727C22—222no—
728C22—222no—
729C22#1062314212yes—
730C22C2×SD16×D1114yes—
731C22C2×SD16×D1112yes—
732C22#1062330112yes—
733C22C22×D4×D1111yescharacteristic
734C4—22no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—114no—
739C4—222no—
740C4—222no—
741C4—442no—
742C4—442no—
743C4—442no—
744C4—442no—
745C4#1062314212yes—
746C4C22×#434111yescharacteristic
747C4C2×#6704311yescharacteristic
748C2—24no—
749C2—82no—
750C2—224no—
751C2#1308096814yesdirect product factor
752C2C2×#1062314211yescharacteristic
753C2C22×SD16×D1111yescharacteristic
754C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#465C2
socleC23×C11C22×D4
prime radicalC2×#10623142C2
hypercenterC2×#465D11
hypocenterC11C2×#3335
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#10623166C2semidirect
3. #13080968C2direct (N × H)
4. C2×#10622468C2semidirect
5. C2×#10622390C2semidirect
6. C2×#10622647C2semidirect
7. C2×#10622418C2semidirect
8. C2×#10622656C2semidirect
9. C2×#10622404C2semidirect
10. C2×#10622374C2semidirect
11. C2×#10622784C2semidirect
12. C2×SD16×Dic11C2semidirect
13. C2×C8×C22⋊D11C2semidirect
14. C22×#66881C2semidirect
15. C2×D11×#106C2semidirect
16. C2×C11×#465C2semidirect
32. #10623166C22semidirect
45. C11×#465C22semidirect
54. #10622784C22semidirect
55. SD16×Dic11C22semidirect
56. C8×C22⋊D11C22semidirect
62. C2×#66881C22semidirect
65. #10622656C22semidirect
66. #10622647C22semidirect
71. D11×#106C22semidirect
72. #10622468C22semidirect
73. #10622418C22semidirect
74. #10622404C22semidirect
75. #10622390C22semidirect
76. #10622374C22semidirect
205. C2×C22⋊D11SD16semidirect
236. C2×C8×C11#41semidirect
287. C2×#465D11semidirect
328. C22⋊D11C2×SD16semidirect
354. C8×C11C2×#41semidirect
393. #465C2×D11semidirect
552. C2×C11#3335semidirect
617. C2×C8#4341semidirect
652. C11C2×#3335semidirect
717. C8C2×#4341semidirect
751. C2#13080968direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231662
C2×#106231422
#130809682
C2×#106224682
C2×#106223902
C2×#106226472
C2×#106224182
C2×#106226562
C2×#106224042
C2×#106223742
C2×#106227842
C2×SD16×Dic112
C2×C8×C22⋊D112
C22×#668812
C2×D11×#1062
C2×C11×#4652
C2×#333511