Finite Group Databasebeta

← C2×#13078871 #15622081

Subgroups — C2×#13078871 #15622081

Order 2816.

2134 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623134C211yesmaximal, characteristic, complemented
2C2×#10623358C211yesmaximal, characteristic, complemented
3#13078871C2116yesmaximal, direct product factor
4C2×#10622335C211yesmaximal, characteristic, complemented
5C2×#10622646C211yesmaximal, characteristic, complemented
6C2×#10622407C211yesmaximal, characteristic, complemented
7C2×#10622372C211yesmaximal, characteristic, complemented
8C2×#10622779C211yesmaximal, characteristic, complemented
9C2×#10622766C211yesmaximal, characteristic, complemented
10C2×#10622852C211yesmaximal, characteristic, complemented
11C2×#10622777C211yesmaximal, characteristic, complemented
12C2×#10622370C211yesmaximal, characteristic, complemented
13C2×#10622403C211yesmaximal, characteristic, complemented
14C2×D8×Dic11C211yesmaximal, characteristic, complemented
15C2×#10622333C211yesmaximal, characteristic, complemented
16C2×C11×#449C211yesmaximal, characteristic
17C22×C11×#41C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×D8C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21#10623358—24no—
22#10623358C2218yescomplemented
23C2×Q8×Dic11C2211yescharacteristic
24C2×Q8×Dic11C2211yescharacteristic
25C22×#4326C2211yescharacteristic
26C2×#66989—21no—
27C2×#66989C2211yescharacteristic
28C2×#66988—21no—
29C2×D4×Dic11—21no—
30C2×D4×Dic11—21no—
31C2×D4×Dic11C2211yescharacteristic
32C2×D4×Dic11C2211yescharacteristic
33C2×D4×Dic11C2211yescharacteristic
34C22×#4324C2211yescharacteristic
35C2×#66979—21no—
36C2×#66979C2211yescharacteristic
37C22×C4⋊Dic11—21no—
38C22×C4⋊Dic11C2211yescharacteristic
39C2×#66977C2211yescharacteristic
40#10623134—24no—
41#10623134C2218yescomplemented
42C2×#66941C2211yescharacteristic
43C2×#66940C2211yescharacteristic
44C2×#66932—21no—
45C2×#66931—21no—
46C11×#449C2218yes—
47C2×C11×#103C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×C22⋊C8C2211yescharacteristic
50#10622852C2218yescomplemented
51C2×#66899C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×C22⋊(C11⋊C8)C2211yescharacteristic
56#10622779C2218yescomplemented
57#10622777C2218yescomplemented
58#10622766C2218yescomplemented
59D8×Dic11C2218yescomplemented
60C2×#66882C2211yescharacteristic
61C2×#66882C2211yescharacteristic
62C2×#66880C2211yescharacteristic
63C2×#66880C2211yescharacteristic
64C2×#66879C2211yescharacteristic
65C2×Dic11⋊C8C2211yescharacteristic
66C2×Dic11⋊C8C2211yescharacteristic
67C2×C8×Dic11C2211yescharacteristic
68#10622646C2218yescomplemented
69C2×#66871C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71#10622407C2218yescomplemented
72#10622403C2218yescomplemented
73#10622372C2218yescomplemented
74#10622370C2218yescomplemented
75#10622335C2218yescomplemented
76#10622333C2218yescomplemented
77C2×C11×#41—24no—
78C2×C11×#41—24no—
79C2×C11×#41—22no—
80C2×C11×#41C2314yes—
81C22×Q8×C11C2311yescharacteristic
82C22×D4×C11—21no—
83C22×D4×C11—21no—
84C22×D4×C11C2311yescharacteristic
85C22×D4×C11C2311yescharacteristic
86C23×C4×C11—21no—
87C23×C4×C11C2311yescharacteristic
88C23×Dic11—21no—
89C23×Dic11—21no—
90C23×Dic11—21no—
91C23×Dic11—21no—
92C22×Dic22—21no—
93C22×Dic22C2311yescharacteristic
94C2×C11×SD16—24no—
95C2×C11×SD16C2314yes—
96C2×C11×D8—24no—
97C2×C11×D8C2314yes—
98C22×C8×C11C2311yescharacteristic
99C22×C8×C11C2311yescharacteristic
100C11×#121—22no—
101C11×#121C2314yes—
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C22⋊C4—21no—
104C2×C22⋊Dic11—21no—
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11—21no—
109C2×C22⋊Dic11—21no—
110C2×C22⋊Dic11D411yescharacteristic
111C2×C22⋊Dic11D411yescharacteristic
112Q8×Dic11—22no—
113Q8×Dic11—22no—
114Q8×Dic11C2314yes—
115Q8×Dic11C2314yes—
116C2×#4326—24no—
117C2×#4326C2314yes—
118#66989—28no—
119#66989—22no—
120#66989C2314yes—
121#66988—28no—
122D4×Dic11—28no—
123D4×Dic11—28no—
124D4×Dic11—22no—
125D4×Dic11—22no—
126D4×Dic11—22no—
127D4×Dic11C2314yes—
128D4×Dic11C2314yes—
129D4×Dic11C2314yes—
130C2×#4324—24no—
131C2×#4324C2314yes—
132#66979—28no—
133#66979D414yes—
134#66979C2314yes—
135C2×C4⋊Dic11—21no—
136C2×C4⋊Dic11—22no—
137C2×C4⋊Dic11—21no—
138C2×C4⋊Dic11—21no—
139C2×C4⋊Dic11—28no—
140C2×C4⋊Dic11D411yescharacteristic
141C2×C4⋊Dic11D411yescharacteristic
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4⋊Dic11C2311yescharacteristic
144C2×C4⋊Dic11C2311yescharacteristic
145C2×C4⋊Dic11C2314yes—
146#66977—22no—
147#66977C2314yes—
148C2×Dic11⋊C4—21no—
149C2×Dic11⋊C4—21no—
150C2×Dic11⋊C4—21no—
151C2×C4×Dic11—21no—
152C2×C4×Dic11—21no—
153C2×C4×Dic11—21no—
154C2×C4×Dic11C2311yescharacteristic
155C2×C4×Dic11C2311yescharacteristic
156C22×C11⋊C8C2311yescharacteristic
157C22×C11⋊C8C2311yescharacteristic
158#66941—22no—
159#66941C2314yes—
160#66940—22no—
161#66940C2314yes—
162#66932—28no—
163#66931—28no—
164C11×#103C2314yes—
165C11×#102C2314yes—
166C11×C22⋊C8C2314yes—
167#66899C2314yes—
168#66896C2314yes—
169#66896C2314yes—
170#66896C2314yes—
171C22⋊(C11⋊C8)C2314yes—
172#66882C2314yes—
173#66882C2314yes—
174#66880C2314yes—
175#66880C2314yes—
176#66879C2314yes—
177Dic11⋊C8C2314yes—
178Dic11⋊C8C2314yes—
179C8×Dic11C2314yes—
180#66871C2314yes—
181#66871C2314yes—
182C2×#3124—111nomaximal, Sylow
183C24×C11—21no—
184C24×C11—21no—
185C24×C11C2×D411yescharacteristic
186C11×#41—216no—
187C11×#41—28no—
188C11×#41—28no—
189C2×Q8×C11—21no—
190C2×Q8×C11—22no—
191C2×Q8×C11#4114yes—
192C2×Q8×C11C2412yes—
193C2×D4×C11—28no—
194C2×D4×C11—24no—
195C2×D4×C11—24no—
196C2×D4×C11—21no—
197C2×D4×C11—21no—
198C2×D4×C11—22no—
199C2×D4×C11—22no—
200C2×D4×C11—22no—
201C2×D4×C11—82no—
202C2×D4×C11#4114yes—
203C2×D4×C11C2412yes—
204C2×D4×C11C2412yes—
205C22×C4×C11—28no—
206C22×C4×C11—21no—
207C22×C4×C11—24no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—21no—
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D412yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2411yescharacteristic
215C22×Dic11—24no—
216C22×Dic11—24no—
217C22×Dic11—24no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—24no—
223C22×Dic11—82no—
224C22×Dic11—82no—
225C22×Dic11—82no—
226C22×Dic11—82no—
227C22×Dic11C2×D411yescharacteristic
228C22×Dic11C2×D411yescharacteristic
229C22×Dic11C2×D411yescharacteristic
230C22×Dic11C2×D411yescharacteristic
231C2×Dic22—24no—
232C2×Dic22—21no—
233C2×Dic22—22no—
234C2×Dic22—22no—
235C2×Dic22—82no—
236C2×Dic22C2412yes—
237C11×SD16—28no—
238C11×D8—28no—
239C2×C8×C11—22no—
240C2×C8×C11—22no—
241C2×C8×C11C2412yes—
242C2×C8×C11C2412yes—
243C11×C4⋊C4—21no—
244C11×C4⋊C4C2412yes—
245C11×C22⋊C4—24no—
246C22⋊Dic11—24no—
247C22⋊Dic11—24no—
248C22⋊Dic11—24no—
249C22⋊Dic11—24no—
250C22⋊Dic11—24no—
251C22⋊Dic11—24no—
252C22⋊Dic11C2×D414yes—
253C22⋊Dic11C2×D414yes—
254#4326—28no—
255#4324—28no—
256C4⋊Dic11—24no—
257C4⋊Dic11—24no—
258C4⋊Dic11—21no—
259C4⋊Dic11—24no—
260C4⋊Dic11—21no—
261C4⋊Dic11—21no—
262C4⋊Dic11C2×D414yes—
263C4⋊Dic11C2×D414yes—
264C4⋊Dic11C2412yes—
265C4⋊Dic11C2412yes—
266C4⋊Dic11C2412yes—
267Dic11⋊C4—24no—
268Dic11⋊C4—24no—
269Dic11⋊C4—24no—
270C4×Dic11—24no—
271C4×Dic11—24no—
272C4×Dic11—24no—
273C4×Dic11C2×D412yes—
274C4×Dic11C2×D412yes—
275C4×Dic11C2412yes—
276C4×Dic11C2412yes—
277C2×C11⋊C8—22no—
278C2×C11⋊C8—22no—
279C2×C11⋊C8C2412yes—
280C2×C11⋊C8C2412yes—
281C2×#542—111no—
282C2×#520—111no—
283#3124—1116no—
284C2×#484—111no—
285C2×#480—111no—
286C2×#477—111no—
287C2×#474—111no—
288C2×#464—111no—
289C2×#463—111no—
290C2×#452—111no—
291C2×#449D1111yescharacteristic
292C2×#440—111no—
293C2×#440—111no—
294C2×C4×Q16—111no—
295C2×C4×D8—111no—
296C2×#433—111no—
297C23×C11—22no—
298C23×C11—24no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—42no—
304C23×C11—42no—
305C23×C11—42no—
306C23×C11—42no—
307C23×C11—42no—
308C23×C11C22×D412yes—
309C23×C11C22×D411yescharacteristic
310Q8×C11—24no—
311Q8×C11—22no—
312Q8×C11C2×#4114yes—
313D4×C11—216no—
314D4×C11—24no—
315D4×C11—22no—
316D4×C11—22no—
317D4×C11—22no—
318D4×C11—42no—
319D4×C11—84no—
320D4×C11C2×#4114yes—
321C2×C4×C11—216no—
322C2×C4×C11—22no—
323C2×C4×C11—24no—
324C2×C4×C11—22no—
325C2×C4×C11—24no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—42no—
330C2×C4×C11C22×D412yes—
331C2×C4×C11C22×D411yescharacteristic
332C2×C4×C11C2×#4112yes—
333C2×C4×C11C2×#4112yes—
334C2×C4×C11C2511yescharacteristic
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—84no—
348C2×Dic11—84no—
349C2×Dic11—84no—
350C2×Dic11—84no—
351C2×Dic11C22×D412yes—
352C2×Dic11C22×D412yes—
353C2×Dic11C22×D412yes—
354C2×Dic11C22×D412yes—
355Dic22—22no—
356Dic22—22no—
357Dic22—42no—
358Dic22—84no—
359C8×C11—22no—
360C8×C11—22no—
361C11⋊C8—22no—
362C11⋊C8—22no—
363C22×#41C2×D1111yescharacteristic
364C22×Q16—111no—
365C22×SD16—111no—
366C22×SD16C2×D1111yescharacteristic
367C22×D8C2×D1111yescharacteristic
368#542—118no—
369#542—224no—
370C2×C4⋊Q8—111no—
371C2×#126—221no—
372C2×#124—111no—
373C2×#124—221no—
374C2×#123—221no—
375C2×C22⋊Q8—111no—
376C2×C22⋊Q8—221no—
377C2×#121C2×D1111yescharacteristic
378#520—118no—
379#520—224no—
380C2×C4×Q8—111no—
381C2×C4×Q8—111no—
382C2×C4×Q8—111no—
383C2×C4×D4—111no—
384C2×C4×D4—111no—
385C2×C4×D4—111no—
386C2×C4×D4—221no—
387C2×C4×D4—221no—
388C2×#117—111no—
389C2×#117—221no—
390C22×C4⋊C4—111no—
391C22×C4⋊C4—221no—
392#484—118no—
393#480—118no—
394#477—118no—
395#474—118no—
396#464—118no—
397#463—118no—
398#452—118no—
399#449C2×D1118yes—
400#440—118no—
401#440—118no—
402C4×Q16—118no—
403C4×D8—118no—
404#433—118no—
405C2×#107—111no—
406C2×#107—111no—
407C2×#107—111no—
408C2×#107—111no—
409C2×C4⋊C8—111no—
410C2×C4⋊C8—111no—
411C2×#103—111no—
412C2×#103—111no—
413C2×#103—111no—
414C2×#103C2×D1111yescharacteristic
415C2×#102—111no—
416C2×#102—111no—
417C2×#102—111no—
418C2×#102C2×D1111yescharacteristic
419C2×C22⋊C8—111no—
420C2×C22⋊C8C2×D1111yescharacteristic
421C2×#97—111no—
422C2×C4×C8—111no—
423C22×C11—22no—
424C22×C11—24no—
425C22×C11—22no—
426C22×C11—22no—
427C22×C11—44no—
428C22×C11—48no—
429C22×C11—42no—
430C22×C11—42no—
431C22×C11—42no—
432C22×C11—42no—
433C22×C11—42no—
434C22×C11—84no—
435C22×C11#52512yes—
436C22×C11#57612yes—
437C22×C11#57812yes—
438C22×C11C23×D411yescharacteristic
439C4×C11—22no—
440C4×C11—24no—
441C4×C11—42no—
442C4×C11#52512yes—
443C4×C11C22×#4111yescharacteristic
444C4×C11C22×#4111yescharacteristic
445Dic11—22no—
446Dic11—22no—
447Dic11—22no—
448Dic11—22no—
449Dic11—42no—
450Dic11—42no—
451Dic11—42no—
452Dic11—42no—
453C2×#41—24no—
454C2×#41—24no—
455C2×#41—22no—
456C2×#41C22×D1114yes—
457C22×Q8—111no—
458C22×Q8—221no—
459C22×Q8C22×D1111yescharacteristic
460C22×D4—21no—
461C22×D4—21no—
462C22×D4C22×D1111yescharacteristic
463C22×D4C22×D1111yescharacteristic
464C23×C4—21no—
465C23×C4—221no—
466C23×C4—221no—
467C23×C4—221no—
468C23×C4—221no—
469C23×C4C22×D1111yescharacteristic
470C2×Q16—114no—
471C2×Q16—224no—
472C2×SD16—24no—
473C2×SD16—114no—
474C2×SD16—224no—
475C2×SD16C22×D1114yes—
476C2×D8—24no—
477C2×D8C22×D1114yes—
478C22×C8—111no—
479C22×C8—111no—
480C22×C8C22×D1111yescharacteristic
481C22×C8C22×D1111yescharacteristic
482C4⋊Q8—114no—
483C4⋊Q8—222no—
484#126—228no—
485#124—114no—
486#124—222no—
487#124—228no—
488#123—228no—
489C22⋊Q8—114no—
490C22⋊Q8—228no—
491C22⋊Q8—222no—
492#121—22no—
493#121C22×D1114yes—
494C4×Q8—114no—
495C4×Q8—114no—
496C4×Q8—114no—
497C4×Q8—222no—
498C4×Q8—222no—
499C4×Q8—222no—
500C4×D4—114no—
501C4×D4—114no—
502C4×D4—114no—
503C4×D4—222no—
504C4×D4—222no—
505C4×D4—222no—
506C4×D4—228no—
507C4×D4—228no—
508#117—114no—
509#117—114no—
510#117—228no—
511C2×C4⋊C4—111no—
512C2×C4⋊C4—111no—
513C2×C4⋊C4—111no—
514C2×C4⋊C4—111no—
515C2×C4⋊C4—114no—
516C2×C4⋊C4—111no—
517C2×C4⋊C4—228no—
518C2×C4⋊C4—221no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4—221no—
522C2×C4⋊C4—221no—
523C2×C4⋊C4—222no—
524C2×C4⋊C4—221no—
525C2×C4⋊C4C22×D1111yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—111no—
528C2×C22⋊C4—111no—
529C2×C22⋊C4—221no—
530C2×C22⋊C4—221no—
531C2×C22⋊C4—221no—
532C2×C22⋊C4—221no—
533C2×C22⋊C4—221no—
534C2×C22⋊C4—221no—
535C2×C42—111no—
536C2×C42—111no—
537C2×C42—221no—
538C2×C42—221no—
539C2×C42—221no—
540#107—114no—
541#107—114no—
542#107—114no—
543#107—114no—
544C4⋊C8—114no—
545C4⋊C8—114no—
546#103—114no—
547#103—114no—
548#103—114no—
549#103C22×D1114yes—
550#102—114no—
551#102—114no—
552#102—114no—
553#102C22×D1114yes—
554C22⋊C8—114no—
555C22⋊C8C22×D1114yes—
556#97—114no—
557C4×C8—114no—
558C2×C11—42no—
559C2×C11—44no—
560C2×C11—82no—
561C2×C11#312414yescomplemented
562C2×C11C2×#52511yescharacteristic
563C2×C11C2×#57611yescharacteristic
564C2×C11C2×#57811yescharacteristic
565C24—21no—
566C24—21no—
567C24D4×D1111yescharacteristic
568#41—216no—
569#41—28no—
570#41—28no—
571C2×Q8—21no—
572C2×Q8—22no—
573C2×Q8—112no—
574C2×Q8—224no—
575C2×Q8—221no—
576C2×Q8—222no—
577C2×Q8—222no—
578C2×Q8—882no—
579C2×Q8#434114yes—
580C2×Q8C23×D1112yes—
581C2×D4—28no—
582C2×D4—24no—
583C2×D4—24no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—82no—
590C2×D4#434114yes—
591C2×D4C23×D1112yes—
592C2×D4C23×D1112yes—
593C22×C4—28no—
594C22×C4—21no—
595C22×C4—24no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—111no—
600C22×C4—111no—
601C22×C4—111no—
602C22×C4—111no—
603C22×C4—224no—
604C22×C4—224no—
605C22×C4—224no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4—221no—
609C22×C4—221no—
610C22×C4—224no—
611C22×C4—882no—
612C22×C4—882no—
613C22×C4—882no—
614C22×C4—882no—
615C22×C4D4×D1112yes—
616C22×C4D4×D1111yescharacteristic
617C22×C4C23×D1112yes—
618C22×C4C23×D1111yescharacteristic
619Q16—228no—
620SD16—28no—
621SD16—228no—
622D8—28no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—112no—
626C2×C8—112no—
627C2×C8—222no—
628C2×C8—222no—
629C2×C8C23×D1112yes—
630C2×C8C23×D1112yes—
631C4⋊C4—21no—
632C4⋊C4—114no—
633C4⋊C4—114no—
634C4⋊C4—112no—
635C4⋊C4—112no—
636C4⋊C4—112no—
637C4⋊C4—224no—
638C4⋊C4—224no—
639C4⋊C4—224no—
640C4⋊C4—224no—
641C4⋊C4—224no—
642C4⋊C4—221no—
643C4⋊C4—221no—
644C4⋊C4—221no—
645C4⋊C4—224no—
646C4⋊C4C23×D1112yes—
647C22⋊C4—24no—
648C22⋊C4—114no—
649C22⋊C4—114no—
650C22⋊C4—224no—
651C22⋊C4—224no—
652C22⋊C4—224no—
653C22⋊C4—224no—
654C22⋊C4—224no—
655C22⋊C4—224no—
656C42—112no—
657C42—112no—
658C42—112no—
659C42—112no—
660C42—224no—
661C42—224no—
662C42—224no—
663C11C2×#312411yescharacteristic, complemented, Sylow
664C23—22no—
665C23—22no—
666C23—22no—
667C23—24no—
668C23—22no—
669C23—22no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23C2×D4×D1112yes—
676C23C2×D4×D1111yescharacteristic
677Q8—24no—
678Q8—22no—
679Q8—222no—
680Q8—222no—
681Q8—442no—
682Q8—884no—
683Q8C2×#434114yes—
684D4—216no—
685D4—24no—
686D4—22no—
687D4—22no—
688D4—22no—
689D4—42no—
690D4—84no—
691D4C2×#434114yes—
692C2×C4—216no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—42no—
701C2×C4—112no—
702C2×C4—112no—
703C2×C4—112no—
704C2×C4—112no—
705C2×C4—222no—
706C2×C4—222no—
707C2×C4—222no—
708C2×C4—222no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—442no—
714C2×C4—442no—
715C2×C4—442no—
716C2×C4—442no—
717C2×C4—884no—
718C2×C4—884no—
719C2×C4—884no—
720C2×C4—884no—
721C2×C4C2×D4×D1112yes—
722C2×C4C2×D4×D1111yescharacteristic
723C2×C4C2×#434112yes—
724C2×C4C2×#434112yes—
725C2×C4C24×D1111yescharacteristic
726C8—22no—
727C8—22no—
728C8—222no—
729C8—222no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—24no—
734C22—44no—
735C22—48no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—84no—
742C22#1062311712yes—
743C22#1062330212yes—
744C22#1062330512yes—
745C22C22×D4×D1111yescharacteristic
746C4—22no—
747C4—24no—
748C4—42no—
749C4—222no—
750C4—222no—
751C4—222no—
752C4—222no—
753C4—442no—
754C4—442no—
755C4—442no—
756C4—442no—
757C4#1062311712yes—
758C4C22×#434111yescharacteristic
759C4C22×#434111yescharacteristic
760C2—42no—
761C2—44no—
762C2—82no—
763C2#1307887114yesdirect product factor
764C2C2×#1062311711yescharacteristic
765C2C2×#1062330511yescharacteristic
766C2C2×#1062330211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#449C2
socleC23×C11C22×D4
hypercenterC2×#449D11
hypocenterC11C2×#3124
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#10623134C2semidirect
2. C2×#10623358C2semidirect
3. #13078871C2direct (N × H)
4. C2×#10622335C2semidirect
5. C2×#10622646C2semidirect
6. C2×#10622407C2semidirect
7. C2×#10622372C2semidirect
8. C2×#10622779C2semidirect
9. C2×#10622766C2semidirect
10. C2×#10622852C2semidirect
11. C2×#10622777C2semidirect
12. C2×#10622370C2semidirect
13. C2×#10622403C2semidirect
14. C2×D8×Dic11C2semidirect
15. C2×#10622333C2semidirect
22. #10623358C22semidirect
41. #10623134C22semidirect
50. #10622852C22semidirect
56. #10622779C22semidirect
57. #10622777C22semidirect
58. #10622766C22semidirect
59. D8×Dic11C22semidirect
68. #10622646C22semidirect
71. #10622407C22semidirect
72. #10622403C22semidirect
73. #10622372C22semidirect
74. #10622370C22semidirect
75. #10622335C22semidirect
76. #10622333C22semidirect
561. C2×C11#3124semidirect
663. C11C2×#3124semidirect
763. C2#13078871direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231342
C2×#106233582
#130788712
C2×#106223352
C2×#106226462
C2×#106224072
C2×#106223722
C2×#106227792
C2×#106227662
C2×#106228522
C2×#106227772
C2×#106223702
C2×#106224032
C2×D8×Dic112
C2×#106223332
C2×C11×#4492
C2×#312411