Finite Group Databasebeta

← C2×#13078904 #15622116

Subgroups — C2×#13078904 #15622116

Order 2816.

2122 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×#10623093C211yesmaximal, characteristic
2C2×#10623103C211yesmaximal, characteristic, complemented
3#13078904C2116yesmaximal, direct product factor
4C2×#10622479C211yesmaximal, characteristic, complemented
5C2×#10622392C211yesmaximal, characteristic, complemented
6C2×#10622470C211yesmaximal, characteristic, complemented
7C2×#10622412C211yesmaximal, characteristic, complemented
8C2×#10622375C211yesmaximal, characteristic, complemented
9C2×#10622776C211yesmaximal, characteristic, complemented
10C2×#10622419C211yesmaximal, characteristic, complemented
11C2×#10622783C211yesmaximal, characteristic, complemented
12C2×#10622631C211yesmaximal, characteristic, complemented
13C2×#10622639C211yesmaximal, characteristic, complemented
14C2×C4×#4314C211yesmaximal, characteristic, complemented
15C2×#10622303C211yesmaximal, characteristic, complemented
16C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C22×#4325C2211yescharacteristic
23C2×#66993C2211yescharacteristic
24C2×#66991C2211yescharacteristic
25C22×#4324C2211yescharacteristic
26C2×#66983—21no—
27C2×#66982—21no—
28C22×#4314C2211yescharacteristic
29#10623103—24no—
30#10623103C2218yescomplemented
31#10623093—24no—
32#10623093C2218yes—
33C2×#66948C2211yescharacteristic
34C2×#66945—21no—
35C2×#66945C2211yescharacteristic
36C2×#66943C2211yescharacteristic
37C2×#66940—21no—
38C2×#66940C2211yescharacteristic
39C2×#66937—21no—
40C2×#66936—21no—
41C2×C4×D44C2211yescharacteristic
42C2×#66925—21no—
43C2×#66925C2211yescharacteristic
44C2×C4×Dic22—21no—
45C2×C4×Dic22C2211yescharacteristic
46C4×C11×SD16C2218yescomplemented
47C2×C11×#106C2211yescharacteristic
48C2×C11×#103C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C4×C8×C11C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53#10622783C2218yescomplemented
54#10622776C2218yescomplemented
55C2×#66885C2211yescharacteristic
56C2×(C2×D11)⋊C8C2211yescharacteristic
57C2×(C2×D11)⋊C8C2211yescharacteristic
58C2×#66881C2211yescharacteristic
59C2×#66880C2211yescharacteristic
60C2×Dic11⋊C8C2211yescharacteristic
61C2×Dic11⋊C8C2211yescharacteristic
62#10622639C2218yescomplemented
63#10622631C2218yescomplemented
64C2×#66874C2211yescharacteristic
65C2×#66873C2211yescharacteristic
66C2×#66871C2211yescharacteristic
67C2×#66871C2211yescharacteristic
68C2×#66867C2211yescharacteristic
69#10622479C2218yescomplemented
70#10622470C2218yescomplemented
71#10622419C2218yescomplemented
72#10622412C2218yescomplemented
73#10622392C2218yescomplemented
74#10622375C2218yescomplemented
75C4×#4314C2218yescomplemented
76#10622303C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C2×Q8×D11—24no—
84C2×Q8×D11—22no—
85C2×Q8×D11—24no—
86C2×Q8×D11C2314yes—
87C22×D44—21no—
88C22×D44C2311yescharacteristic
89C22×C4×D11—21no—
90C22×C4×D11—21no—
91C22×C4×D11C2311yescharacteristic
92C22×Dic22—21no—
93C22×Dic22C2311yescharacteristic
94C2×C11×SD16—24no—
95C2×C11×SD16C2314yes—
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C4×Q8×C11—22no—
99C4×Q8×C11C2314yes—
100C4×D4×C11—22no—
101C4×D4×C11C2314yes—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C22⋊C4—21no—
106C2×C42×C11—21no—
107C2×C42×C11C2311yescharacteristic
108C2×C22⋊Dic11—21no—
109Q8×Dic11—22no—
110Q8×Dic11C2314yes—
111C2×#4325—24no—
112C2×#4325C2314yes—
113#66993—22no—
114#66993C2314yes—
115#66991—22no—
116#66991C2314yes—
117C2×#4324—24no—
118C2×#4324C2314yes—
119#66983—28no—
120#66982—28no—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4—21no—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4D411yescharacteristic
125C2×(C2×D11)⋊C4D411yescharacteristic
126C2×C4⋊Dic11—21no—
127C2×C4⋊Dic11—21no—
128C2×C4⋊Dic11C2311yescharacteristic
129C2×C4⋊Dic11C2311yescharacteristic
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4D411yescharacteristic
134C2×Dic11⋊C4D411yescharacteristic
135C2×C4×Dic11—21no—
136C2×C4×Dic11—21no—
137C2×C4×Dic11—21no—
138C2×C4×Dic11—21no—
139C2×C4×Dic11C2311yescharacteristic
140C22×C11⋊C8C2311yescharacteristic
141C22×C11⋊C8C2311yescharacteristic
142C2×#4314—24no—
143C2×#4314C2314yes—
144#66948—22no—
145#66948C2314yes—
146#66945—22no—
147#66945—28no—
148#66945C2314yes—
149#66943—22no—
150#66943C2314yes—
151#66940—28no—
152#66940—22no—
153#66940C2314yes—
154#66937—28no—
155#66936—28no—
156C4×D44—22no—
157C4×D44C2314yes—
158#66925—28no—
159#66925D414yes—
160#66925C2314yes—
161C4×Dic22—22no—
162C4×Dic22—28no—
163C4×Dic22C2314yes—
164C11×#106C2314yes—
165C11×#103C2314yes—
166C11×#102C2314yes—
167C4×C8×C11C2314yes—
168#66899C2314yes—
169#66896C2314yes—
170#66885C2314yes—
171(C2×D11)⋊C8C2314yes—
172(C2×D11)⋊C8C2314yes—
173#66881C2314yes—
174#66880C2314yes—
175Dic11⋊C8C2314yes—
176Dic11⋊C8C2314yes—
177#66874C2314yes—
178#66873C2314yes—
179#66871C2314yes—
180#66871C2314yes—
181#66867C2314yes—
182C2×#3126—111nomaximal, Sylow
183C24×C11—21no—
184C23×D11—21no—
185C23×D11C2×D411yescharacteristic
186C2×Q8×C11—21no—
187C2×Q8×C11—22no—
188C2×Q8×C11#4114yes—
189C2×Q8×C11C2412yes—
190C2×D4×C11—21no—
191C2×D4×C11—22no—
192C2×D4×C11—22no—
193C2×D4×C11C2412yes—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—24no—
198C22×C4×C11—82no—
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2411yescharacteristic
202C2×C22⋊D11—24no—
203C2×C22⋊D11—24no—
204C2×C22⋊D11—24no—
205C2×C22⋊D11—82no—
206C2×C22⋊D11—82no—
207C2×C22⋊D11—82no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11C2×D411yescharacteristic
212C22×Dic11C2×D411yescharacteristic
213C22×Dic11C2×D411yescharacteristic
214Q8×D11—216no—
215Q8×D11—28no—
216Q8×D11—28no—
217C2×D44—24no—
218C2×D44—21no—
219C2×D44—22no—
220C2×D44—22no—
221C2×D44—82no—
222C2×D44C2412yes—
223C2×C4×D11—28no—
224C2×C4×D11—24no—
225C2×C4×D11—24no—
226C2×C4×D11—22no—
227C2×C4×D11—22no—
228C2×C4×D11—82no—
229C2×C4×D11C2×D412yes—
230C2×C4×D11C2412yes—
231C2×Dic22—28no—
232C2×Dic22—24no—
233C2×Dic22—21no—
234C2×Dic22—22no—
235C2×Dic22#4114yes—
236C2×Dic22C2412yes—
237C11×SD16—28no—
238C2×C8×C11—22no—
239C2×C8×C11—22no—
240C2×C8×C11C2412yes—
241C2×C8×C11C2412yes—
242C11×C4⋊C4—24no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4—21no—
245C11×C4⋊C4C2412yes—
246C11×C4⋊C4C2412yes—
247C11×C22⋊C4—24no—
248C42×C11—24no—
249C42×C11C2×D412yes—
250C42×C11C2412yes—
251C22⋊Dic11—24no—
252#4325—28no—
253#4324—28no—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4C2×D414yes—
258(C2×D11)⋊C4C2×D414yes—
259C4⋊Dic11—24no—
260C4⋊Dic11—24no—
261C4⋊Dic11—21no—
262C4⋊Dic11—21no—
263C4⋊Dic11C2412yes—
264C4⋊Dic11C2412yes—
265Dic11⋊C4—24no—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268Dic11⋊C4C2×D414yes—
269Dic11⋊C4C2×D414yes—
270C4×Dic11—24no—
271C4×Dic11—24no—
272C4×Dic11—24no—
273C4×Dic11—24no—
274C4×Dic11C2×D412yes—
275C4×Dic11C2412yes—
276C2×C11⋊C8—22no—
277C2×C11⋊C8—22no—
278C2×C11⋊C8C2412yes—
279C2×C11⋊C8C2412yes—
280#4314—28no—
281C2×#540—111no—
282C2×#519—111no—
283#3126—1116no—
284C2×#482—111no—
285C2×#482—111no—
286C2×#479—111no—
287C2×#479—111no—
288C2×#460—111no—
289C2×#460—111no—
290C2×#448—111no—
291C2×#448—111no—
292C2×#440—111no—
293C2×#440—111no—
294C2×C4×SD16—111no—
295C2×C4×SD16D1111yescharacteristic, complemented
296C2×#433—111no—
297C23×C11—22no—
298C23×C11—42no—
299C23×C11—42no—
300C23×C11—42no—
301C23×C11C22×D411yescharacteristic
302C22×D11—22no—
303C22×D11—22no—
304C22×D11—22no—
305C22×D11—22no—
306C22×D11—42no—
307C22×D11—42no—
308C22×D11—42no—
309C22×D11C22×D412yes—
310Q8×C11—24no—
311Q8×C11—22no—
312Q8×C11C2×#4114yes—
313D4×C11—22no—
314D4×C11—22no—
315D4×C11—42no—
316C2×C4×C11—24no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11—84no—
325C2×C4×C11C22×D412yes—
326C2×C4×C11C22×D412yes—
327C2×C4×C11C22×D411yescharacteristic
328C2×C4×C11C2×#4112yes—
329C2×C4×C11C2×#4112yes—
330C2×C4×C11C2511yescharacteristic
331C22⋊D11—84no—
332C22⋊D11—84no—
333C22⋊D11—84no—
334C2×Dic11—22no—
335C2×Dic11—24no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11C22×D412yes—
344C2×Dic11C22×D412yes—
345C2×Dic11C22×D412yes—
346D44—22no—
347D44—22no—
348D44—42no—
349D44—84no—
350C4×D11—216no—
351C4×D11—24no—
352C4×D11—22no—
353C4×D11—22no—
354C4×D11—84no—
355Dic22—216no—
356Dic22—24no—
357Dic22—22no—
358Dic22C2×#4114yes—
359C8×C11—22no—
360C8×C11—22no—
361C11⋊C8—22no—
362C11⋊C8—22no—
363C23×Q8—111no—
364C22×SD16—111no—
365C22×SD16—111no—
366C22×SD16—111no—
367C22×SD16C2×D1111yescharacteristic
368#540—118no—
369#540—224no—
370C2×#127—111no—
371C2×#125—111no—
372C2×#123—221no—
373C2×#123—221no—
374C2×#121—111no—
375C2×#121—111no—
376C2×#121—221no—
377C2×#121—221no—
378#519—118no—
379#519—224no—
380C2×C4×Q8—111no—
381C2×C4×Q8—111no—
382C2×C4×Q8—111no—
383C2×C4×Q8—221no—
384C2×C4×Q8—221no—
385C2×C4×Q8C2×D1111yescharacteristic
386C2×C4×D4—111no—
387C2×C4×D4C2×D1111yescharacteristic
388C2×#117—111no—
389C2×#117—111no—
390C2×#117—221no—
391C2×#117—221no—
392#482—118no—
393#482—118no—
394#479—118no—
395#479—118no—
396#460—118no—
397#460—118no—
398#448—118no—
399#448—118no—
400#440—118no—
401#440—118no—
402C4×SD16—118no—
403C4×SD16C2×D1118yescomplemented
404#433—118no—
405C2×#107—111no—
406C2×#107—111no—
407C2×#106—111no—
408C2×#106C2×D1111yescharacteristic
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⋊C8—111no—
421C2×#97—111no—
422C2×C4×C8C2×D1111yescharacteristic
423C22×C11—42no—
424C22×C11—42no—
425C22×C11—42no—
426C22×C11—84no—
427C22×C11#52512yes—
428C22×C11#57712yes—
429C22×C11#57712yes—
430C22×C11C23×D411yescharacteristic
431C2×D11—22no—
432C2×D11—22no—
433C2×D11—22no—
434C2×D11—44no—
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—84no—
439C4×C11—24no—
440C4×C11—22no—
441C4×C11—22no—
442C4×C11—42no—
443C4×C11—42no—
444C4×C11#52512yes—
445C4×C11C22×#4111yescharacteristic
446C4×C11C22×#4111yescharacteristic
447Dic11—22no—
448Dic11—24no—
449Dic11—22no—
450Dic11—22no—
451Dic11—42no—
452Dic11—42no—
453C22×Q8—114no—
454C22×Q8—111no—
455C22×Q8—221no—
456C22×Q8—222no—
457C22×Q8—224no—
458C22×Q8—224no—
459C22×Q8C22×D1111yescharacteristic
460C22×D4—111no—
461C22×D4—221no—
462C22×D4—221no—
463C22×D4—221no—
464C22×D4—221no—
465C22×D4C22×D1111yescharacteristic
466C23×C4—21no—
467C23×C4—111no—
468C23×C4—221no—
469C23×C4—221no—
470C2×SD16—24no—
471C2×SD16—114no—
472C2×SD16—114no—
473C2×SD16—114no—
474C2×SD16—224no—
475C2×SD16—224no—
476C2×SD16—224no—
477C2×SD16C22×D1114yes—
478C22×C8—111no—
479C22×C8—111no—
480C22×C8C22×D1111yescharacteristic
481C22×C8C22×D1111yescharacteristic
482#127—114no—
483#127—222no—
484#125—114no—
485#125—222no—
486#123—228no—
487#123—228no—
488#121—114no—
489#121—114no—
490#121—228no—
491#121—228no—
492#121—222no—
493#121—222no—
494C4×Q8—22no—
495C4×Q8—114no—
496C4×Q8—114no—
497C4×Q8—114no—
498C4×Q8—228no—
499C4×Q8—222no—
500C4×Q8—222no—
501C4×Q8—228no—
502C4×Q8—222no—
503C4×Q8C22×D1114yes—
504C4×D4—22no—
505C4×D4—114no—
506C4×D4—222no—
507C4×D4C22×D1114yes—
508#117—114no—
509#117—114no—
510#117—114no—
511#117—228no—
512#117—228no—
513#117—222no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—111no—
516C2×C4⋊C4—111no—
517C2×C4⋊C4—111no—
518C2×C4⋊C4—111no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4—221no—
522C2×C4⋊C4—221no—
523C2×C4⋊C4—221no—
524C2×C4⋊C4C22×D1111yescharacteristic
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×C42—21no—
534C2×C42—111no—
535C2×C42—221no—
536C2×C42—221no—
537C2×C42—221no—
538C2×C42—221no—
539C2×C42C22×D1111yescharacteristic
540#107—114no—
541#107—114no—
542#106—114no—
543#106C22×D1114yes—
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⋊C8—114no—
556#97—114no—
557C4×C8C22×D1114yes—
558C2×C11—82no—
559C2×C11#312614yescomplemented
560C2×C11C2×#52511yescharacteristic
561C2×C11C2×#57711yescharacteristic
562C2×C11C2×#57711yescharacteristic
563D11—42no—
564D11—82no—
565C24—21no—
566C24—111no—
567C24—221no—
568C2×Q8—21no—
569C2×Q8—22no—
570C2×Q8—114no—
571C2×Q8—112no—
572C2×Q8—224no—
573C2×Q8—228no—
574C2×Q8—228no—
575C2×Q8—2216no—
576C2×Q8—228no—
577C2×Q8—222no—
578C2×Q8—221no—
579C2×Q8#433914yes—
580C2×Q8C23×D1112yes—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—112no—
585C2×D4—224no—
586C2×D4—224no—
587C2×D4—224no—
588C2×D4—224no—
589C2×D4—222no—
590C2×D4—221no—
591C2×D4—222no—
592C2×D4—882no—
593C2×D4—882no—
594C2×D4—882no—
595C2×D4—882no—
596C2×D4C23×D1112yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—24no—
601C22×C4—82no—
602C22×C4—111no—
603C22×C4—111no—
604C22×C4—111no—
605C22×C4—112no—
606C22×C4—112no—
607C22×C4—224no—
608C22×C4—228no—
609C22×C4—221no—
610C22×C4—222no—
611C22×C4—222no—
612C22×C4—221no—
613C22×C4—221no—
614C22×C4—224no—
615C22×C4—882no—
616C22×C4D4×D1111yescharacteristic
617C22×C4D4×D1111yescharacteristic
618C22×C4C23×D1111yescharacteristic
619SD16—28no—
620SD16—228no—
621SD16—228no—
622SD16—228no—
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—24no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—114no—
635C4⋊C4—114no—
636C4⋊C4—112no—
637C4⋊C4—112no—
638C4⋊C4—224no—
639C4⋊C4—224no—
640C4⋊C4—224no—
641C4⋊C4—224no—
642C4⋊C4—221no—
643C4⋊C4—221no—
644C4⋊C4—224no—
645C4⋊C4C23×D1112yes—
646C4⋊C4C23×D1112yes—
647C22⋊C4—24no—
648C22⋊C4—114no—
649C22⋊C4—114no—
650C22⋊C4—224no—
651C22⋊C4—224no—
652C22⋊C4—224no—
653C22⋊C4—224no—
654C42—24no—
655C42—112no—
656C42—112no—
657C42—224no—
658C42—224no—
659C42—224no—
660C42—224no—
661C42D4×D1112yes—
662C42C23×D1112yes—
663C11C2×#312611yescharacteristic, complemented, Sylow
664C23—22no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—112no—
669C23—222no—
670C23—222no—
671C23—222no—
672C23—222no—
673C23—442no—
674C23—442no—
675C23—442no—
676C23C2×D4×D1111yescharacteristic
677Q8—24no—
678Q8—22no—
679Q8—114no—
680Q8—2216no—
681Q8—224no—
682Q8—222no—
683Q8C2×#433914yes—
684D4—22no—
685D4—22no—
686D4—42no—
687D4—222no—
688D4—222no—
689D4—442no—
690D4—884no—
691D4—884no—
692D4—884no—
693D4—884no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—84no—
703C2×C4—112no—
704C2×C4—112no—
705C2×C4—112no—
706C2×C4—2216no—
707C2×C4—222no—
708C2×C4—222no—
709C2×C4—222no—
710C2×C4—224no—
711C2×C4—222no—
712C2×C4—224no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—442no—
718C2×C4—442no—
719C2×C4—884no—
720C2×C4C2×#433912yes—
721C2×C4C2×D4×D1112yes—
722C2×C4C2×D4×D1112yes—
723C2×C4C2×D4×D1111yescharacteristic
724C2×C4#41×D1112yes—
725C2×C4C24×D1111yescharacteristic
726C8—22no—
727C8—22no—
728C8—222no—
729C8—222no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—84no—
734C22—222no—
735C22—222no—
736C22—222no—
737C22—444no—
738C22—442no—
739C22—442no—
740C22—442no—
741C22—884no—
742C22#1062307812yes—
743C22#1062329312yes—
744C22#1062330112yes—
745C22C22×D4×D1111yescharacteristic
746C4—24no—
747C4—22no—
748C4—22no—
749C4—42no—
750C4—42no—
751C4—222no—
752C4—224no—
753C4—222no—
754C4—222no—
755C4—442no—
756C4—442no—
757C4#1062307812yes—
758C4C22×#433911yescharacteristic
759C4C2×#41×D1111yescharacteristic
760C2—82no—
761C2—442no—
762C2—882no—
763C2#1307890414yesdirect product factor
764C2C2×#1062307811yescharacteristic
765C2C2×#1062329311yescharacteristic
766C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
prime radicalC2×#10623093C2
hypercenterC2×C4×SD16D11
hypocenterC11C2×#3126
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#10623103C2semidirect
3. #13078904C2direct (N × H)
4. C2×#10622479C2semidirect
5. C2×#10622392C2semidirect
6. C2×#10622470C2semidirect
7. C2×#10622412C2semidirect
8. C2×#10622375C2semidirect
9. C2×#10622776C2semidirect
10. C2×#10622419C2semidirect
11. C2×#10622783C2semidirect
12. C2×#10622631C2semidirect
13. C2×#10622639C2semidirect
14. C2×C4×#4314C2semidirect
15. C2×#10622303C2semidirect
16. C2×C4×C11×SD16C2semidirect
30. #10623103C22semidirect
46. C4×C11×SD16C22semidirect
53. #10622783C22semidirect
54. #10622776C22semidirect
62. #10622639C22semidirect
63. #10622631C22semidirect
69. #10622479C22semidirect
70. #10622470C22semidirect
71. #10622419C22semidirect
72. #10622412C22semidirect
73. #10622392C22semidirect
74. #10622375C22semidirect
75. C4×#4314C22semidirect
76. #10622303C22semidirect
295. C2×C4×SD16D11semidirect
403. C4×SD16C2×D11semidirect
559. C2×C11#3126semidirect
663. C11C2×#3126semidirect
763. C2#13078904direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230932
C2×#106231032
#130789042
C2×#106224792
C2×#106223922
C2×#106224702
C2×#106224122
C2×#106223752
C2×#106227762
C2×#106224192
C2×#106227832
C2×#106226312
C2×#106226392
C2×C4×#43142
C2×#106223032
C2×C4×C11×SD162
C2×#312611