Finite Group Databasebeta

← C2×#13078978 #15623018

Subgroups — C2×#13078978 #15623018

Order 2816.

2070 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623260C211yesmaximal, characteristic, complemented
2C2×#10623206C211yesmaximal, characteristic
3#13078978C2116yesmaximal, direct product factor
4C2×#10622316C211yesmaximal, characteristic, complemented
5C2×#10622410C211yesmaximal, characteristic, complemented
6C2×#10622378C211yesmaximal, characteristic, complemented
7C2×#10622669C211yesmaximal, characteristic, complemented
8C2×#10622381C211yesmaximal, characteristic, complemented
9C2×#10622706C211yesmaximal, characteristic, complemented
10C2×#10622405C211yesmaximal, characteristic, complemented
11C2×#10622384C211yesmaximal, characteristic
12C2×#10622415C211yesmaximal, characteristic, complemented
13C2×#10622385C211yesmaximal, characteristic
14C2×D11×#103C211yesmaximal, characteristic, complemented
15C2×#10622321C211yesmaximal, characteristic, complemented
16C2×C11×#489C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2211yescharacteristic
18C22×#4341C2211yescharacteristic
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C11×#124C2211yescharacteristic
21C2×#66999—21no—
22C2×#66997—21no—
23C2×#66997C2211yescharacteristic
24C2×#66989C2211yescharacteristic
25C22×#4313C2211yescharacteristic
26C22×C8×D11C2211yescharacteristic
27#10623260—24no—
28#10623260C2218yescomplemented
29#10623206—24no—
30#10623206C2218yes—
31C2×#66949—21no—
32C2×#66945C2211yescharacteristic
33C2×C4⋊C4×D11C2211yescharacteristic
34C2×#66943C2211yescharacteristic
35C2×#66942—21no—
36C2×#66941C2211yescharacteristic
37C2×#66936—21no—
38C2×#66936—21no—
39C2×#66931—21no—
40C2×#66931—21no—
41C2×#66925C2211yescharacteristic
42C2×#66923C2211yescharacteristic
43C2×#66922C2211yescharacteristic
44C11×#489C2218yescomplemented
45C2×C11×#103C2211yescharacteristic
46C2×C11×#103C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×#97C2211yescharacteristic
50C2×#66899C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54C2×#66880C2211yescharacteristic
55C2×#66880C2211yescharacteristic
56C2×#66880C2211yescharacteristic
57C2×#66880C2211yescharacteristic
58C2×#66879C2211yescharacteristic
59C2×C8×Dic11C2211yescharacteristic
60#10622706C2218yescomplemented
61#10622669C2218yescomplemented
62C2×#66874C2211yescharacteristic
63C2×#66874C2211yescharacteristic
64C2×#66874C2211yescharacteristic
65C2×#66874C2211yescharacteristic
66C2×C4×C11⋊C8C2211yescharacteristic
67#10622415C2218yescomplemented
68D11×#103C2218yescomplemented
69#10622410C2218yescomplemented
70#10622405C2218yescomplemented
71#10622385C2218yes—
72#10622384C2218yes—
73#10622381C2218yescomplemented
74#10622378C2218yescomplemented
75#10622321C2218yescomplemented
76#10622316C2218yescomplemented
77C22×Q8×C11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11C2311yescharacteristic
80C22×C22⋊D11—21no—
81C23×Dic11—21no—
82C2×Q8×D11—22no—
83C2×Q8×D11—24no—
84C2×Q8×D11—24no—
85C2×Q8×D11C2314yes—
86C2×#4341—22no—
87C2×#4341—24no—
88C2×#4341—24no—
89C2×#4341C2314yes—
90C22×C4×D11—21no—
91C22×C4×D11—21no—
92C22×C4×D11C2311yescharacteristic
93C22×Dic22—21no—
94C22×Dic22—21no—
95C22×Dic22C2311yescharacteristic
96C22×Dic22C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C22×C8×C11C2311yescharacteristic
99C11×C4⋊Q8—22no—
100C11×C4⋊Q8C2314yes—
101C11×#124—22no—
102C11×#124C2314yes—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C42×C11C2311yescharacteristic
109C2×C22⋊Dic11—21no—
110C2×C22⋊Dic11—21no—
111#66999—28no—
112#66997—28no—
113#66997—22no—
114#66997C2314yes—
115#66989—22no—
116#66989C2314yes—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4D411yescharacteristic
119C2×(C2×D11)⋊C4D411yescharacteristic
120C2×C4⋊Dic11—21no—
121C2×C4⋊Dic11—21no—
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4—21no—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4D411yescharacteristic
133C2×Dic11⋊C4D411yescharacteristic
134C2×C4×Dic11—21no—
135C2×C4×Dic11C2311yescharacteristic
136C22×C11⋊C8C2311yescharacteristic
137C22×C11⋊C8C2311yescharacteristic
138C2×#4313—24no—
139C2×#4313C2314yes—
140C2×C8×D11—24no—
141C2×C8×D11C2314yes—
142#66949—28no—
143#66945—22no—
144#66945C2314yes—
145C4⋊C4×D11—22no—
146C4⋊C4×D11C2314yes—
147#66943—22no—
148#66943C2314yes—
149#66942—28no—
150#66941—22no—
151#66941C2314yes—
152#66936—28no—
153#66936—28no—
154#66931—28no—
155#66931—28no—
156#66925D414yes—
157#66925C2314yes—
158#66923—22no—
159#66923C2314yes—
160#66922—22no—
161#66922C2314yes—
162C11×#103C2314yes—
163C11×#103C2314yes—
164C11×#102C2314yes—
165C11×#102C2314yes—
166C11×#97C2314yes—
167#66899C2314yes—
168#66899C2314yes—
169#66896C2314yes—
170#66896C2314yes—
171#66880C2314yes—
172#66880C2314yes—
173#66880C2314yes—
174#66880C2314yes—
175#66879C2314yes—
176C8×Dic11C2314yes—
177#66874C2314yes—
178#66874C2314yes—
179#66874C2314yes—
180#66874C2314yes—
181C4×C11⋊C8C2314yes—
182C2×#3137—111nomaximal, Sylow
183C24×C11—21no—
184C23×D11C2×D411yescharacteristic
185C2×Q8×C11—21no—
186C2×Q8×C11—24no—
187C2×Q8×C11—22no—
188C2×Q8×C11—22no—
189C2×Q8×C11—82no—
190C2×Q8×C11C2412yes—
191C2×D4×C11—21no—
192C2×D4×C11—22no—
193C2×D4×C11—22no—
194C2×D4×C11C2412yes—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2411yescharacteristic
201C2×C22⋊D11—24no—
202C2×C22⋊D11—44no—
203C22×Dic11—24no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—44no—
209C22×Dic11C2×D411yescharacteristic
210C22×Dic11C2×D411yescharacteristic
211C22×Dic11C2×D411yescharacteristic
212Q8×D11—28no—
213Q8×D11—28no—
214Q8×D11—48no—
215#4341—28no—
216#4341—28no—
217#4341—48no—
218C2×C4×D11—24no—
219C2×C4×D11—24no—
220C2×C4×D11—44no—
221C2×C4×D11—82no—
222C2×C4×D11C2×D412yes—
223C2×C4×D11#4114yes—
224C2×C4×D11#4114yes—
225C2×C4×D11C2412yes—
226C2×Dic22—24no—
227C2×Dic22—24no—
228C2×Dic22—21no—
229C2×Dic22—21no—
230C2×Dic22—22no—
231C2×Dic22—22no—
232C2×Dic22—22no—
233C2×Dic22—22no—
234C2×Dic22—44no—
235C2×Dic22—82no—
236C2×Dic22C2412yes—
237C2×Dic22C2412yes—
238C2×C8×C11—22no—
239C2×C8×C11—22no—
240C2×C8×C11C2412yes—
241C2×C8×C11C2412yes—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—24no—
244C11×C4⋊C4—21no—
245C11×C4⋊C4C2412yes—
246C11×C4⋊C4C2412yes—
247C11×C22⋊C4—24no—
248C11×C22⋊C4—24no—
249C42×C11C2×D412yes—
250C42×C11C2412yes—
251C22⋊Dic11—24no—
252C22⋊Dic11—24no—
253(C2×D11)⋊C4—24no—
254(C2×D11)⋊C4C2×D414yes—
255(C2×D11)⋊C4C2×D414yes—
256C4⋊Dic11—24no—
257C4⋊Dic11—24no—
258C4⋊Dic11—24no—
259C4⋊Dic11—21no—
260C4⋊Dic11—21no—
261C4⋊Dic11C2412yes—
262C4⋊Dic11C2412yes—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268Dic11⋊C4—24no—
269Dic11⋊C4—24no—
270Dic11⋊C4C2×D414yes—
271Dic11⋊C4C2×D414yes—
272C4×Dic11—24no—
273C4×Dic11C2×D412yes—
274C4×Dic11C2412yes—
275C2×C11⋊C8—22no—
276C2×C11⋊C8—22no—
277C2×C11⋊C8C2412yes—
278C2×C11⋊C8C2412yes—
279#4313—28no—
280C8×D11—28no—
281C2×#544—111no—
282C2×#536—111no—
283#3137—1116no—
284C2×#491—111no—
285C2×#491—111no—
286C2×#489—111no—
287C2×#489D1111yescharacteristic, complemented
288C2×#488—111no—
289C2×#488—111no—
290C2×#487—111no—
291C2×#487—111no—
292C2×#417—111no—
293C2×#419—111no—
294C2×#416—111no—
295C22×#103—111no—
296C2×#405—111no—
297C23×C11—22no—
298C23×C11—42no—
299C23×C11—42no—
300C23×C11—42no—
301C23×C11C22×D411yescharacteristic
302C22×D11—22no—
303C22×D11—22no—
304C22×D11#12414yes—
305C22×D11C22×D412yes—
306Q8×C11—22no—
307Q8×C11—22no—
308Q8×C11—42no—
309Q8×C11—84no—
310D4×C11—22no—
311D4×C11—22no—
312D4×C11—42no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—42no—
319C2×C4×C11—42no—
320C2×C4×C11—42no—
321C2×C4×C11C22×D412yes—
322C2×C4×C11C22×D412yes—
323C2×C4×C11C22×D411yescharacteristic
324C2×C4×C11C2×#4112yes—
325C2×C4×C11C2×#4112yes—
326C2×C4×C11C2511yescharacteristic
327C22⋊D11—48no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11—48no—
339C2×Dic11#12414yes—
340C2×Dic11C22×D412yes—
341C2×Dic11C22×D412yes—
342C2×Dic11C22×D412yes—
343C4×D11—48no—
344C4×D11—84no—
345C4×D11#12418yes—
346C4×D11C2×#4114yes—
347C4×D11C2×#4114yes—
348Dic22—22no—
349Dic22—22no—
350Dic22—22no—
351Dic22—22no—
352Dic22—42no—
353Dic22—42no—
354Dic22—48no—
355Dic22—84no—
356C8×C11—22no—
357C8×C11—22no—
358C11⋊C8—22no—
359C11⋊C8—22no—
360C22×#41—111no—
361C23×Q8—111no—
362C22×M16—111no—
363C23×C8—111no—
364#544—118no—
365#544—224no—
366#536—118no—
367#536—224no—
368C2×C4⋊Q8—111no—
369C2×C4⋊Q8—111no—
370C2×C4⋊Q8—111no—
371C2×C4⋊Q8—221no—
372C2×C4⋊Q8C2×D1111yescharacteristic
373C2×#125—111no—
374C2×#125—111no—
375C2×#125—221no—
376C2×#124—111no—
377C2×#124C2×D1111yescharacteristic
378C2×#123—221no—
379C2×#123—221no—
380C2×C22⋊Q8—221no—
381C2×C22⋊Q8—221no—
382C2×C22⋊Q8—221no—
383C2×C22⋊Q8—221no—
384C2×#117—111no—
385C2×#117—111no—
386C22×C4⋊C4—111no—
387#491—118no—
388#491—118no—
389#489—118no—
390#489C2×D1118yescomplemented
391#488—118no—
392#488—118no—
393#487—118no—
394#487—118no—
395#419—118no—
396#417—118no—
397#416—118no—
398C2×#103—111no—
399C2×#103—111no—
400C2×#103—111no—
401C2×#103—111no—
402C2×#103—111no—
403C2×#103—111no—
404C2×#103—111no—
405C2×#103—111no—
406C2×#103—111no—
407C2×#103—111no—
408C2×#103—118no—
409C2×#103C2×D1111yescharacteristic
410C2×#103C2×D1111yescharacteristic
411C2×#102—111no—
412C2×#102—111no—
413C2×#102C2×D1111yescharacteristic
414C2×#102C2×D1111yescharacteristic
415#405—118no—
416C2×#97—111no—
417C2×#97C2×D1111yescharacteristic
418C2×C4×C8—111no—
419C2×C4×C8—111no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—84no—
424C22×C11C2×#12412yes—
425C22×C11#57712yes—
426C22×C11#57812yes—
427C22×C11C23×D411yescharacteristic
428C2×D11—28no—
429C2×D11—22no—
430C2×D11—22no—
431C2×D11C2×#12414yes—
432C4×C11—22no—
433C4×C11—22no—
434C4×C11—42no—
435C4×C11—42no—
436C4×C11—42no—
437C4×C11C2×#12412yes—
438C4×C11C22×#4111yescharacteristic
439C4×C11C22×#4111yescharacteristic
440Dic11—22no—
441Dic11—22no—
442Dic11—42no—
443Dic11—42no—
444Dic11—42no—
445Dic11—42no—
446Dic11C2×#12414yes—
447C2×#41—114no—
448C2×#41—222no—
449C2×#41—224no—
450C2×#41—224no—
451C22×Q8—21no—
452C22×Q8—114no—
453C22×Q8—111no—
454C22×Q8—111no—
455C22×Q8—221no—
456C22×Q8—221no—
457C22×Q8—222no—
458C22×Q8—224no—
459C22×Q8—224no—
460C22×Q8C22×D1111yescharacteristic
461C22×D4—221no—
462C22×D4C22×D1111yescharacteristic
463C23×C4—111no—
464C23×C4—221no—
465C23×C4—221no—
466C23×C4—221no—
467C2×M16—114no—
468C2×M16—224no—
469C22×C8—111no—
470C22×C8—111no—
471C22×C8—114no—
472C22×C8—224no—
473C22×C8C22×D1111yescharacteristic
474C22×C8C22×D1111yescharacteristic
475C4⋊Q8—22no—
476C4⋊Q8—114no—
477C4⋊Q8—114no—
478C4⋊Q8—114no—
479C4⋊Q8—222no—
480C4⋊Q8—222no—
481C4⋊Q8—228no—
482C4⋊Q8—222no—
483C4⋊Q8C22×D1114yes—
484#125—114no—
485#125—114no—
486#125—222no—
487#125—228no—
488#125—222no—
489#124—22no—
490#124—114no—
491#124—222no—
492#124C22×D1114yes—
493#123—228no—
494#123—228no—
495C22⋊Q8—228no—
496C22⋊Q8—228no—
497C22⋊Q8—228no—
498C22⋊Q8—228no—
499#117—114no—
500#117—114no—
501#117—114no—
502#117—222no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—111no—
505C2×C4⋊C4—111no—
506C2×C4⋊C4—111no—
507C2×C4⋊C4—111no—
508C2×C4⋊C4—114no—
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—221no—
519C2×C4⋊C4—221no—
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—
531C2×C42C22×D1111yescharacteristic
532#103—114no—
533#103—114no—
534#103—114no—
535#103—114no—
536#103—114no—
537#103—114no—
538#103—114no—
539#103—114no—
540#103—114no—
541#103—114no—
542#103C22×D1114yes—
543#103C22×D1114yes—
544#102—114no—
545#102—114no—
546#102C22×D1114yes—
547#102C22×D1114yes—
548#97—114no—
549#97C22×D1114yes—
550C4×C8—114no—
551C4×C8—114no—
552C2×C11—82no—
553C2×C11#313714yescomplemented
554C2×C11C22×#12411yescharacteristic
555C2×C11C2×#57711yescharacteristic
556C2×C11C2×#57811yescharacteristic
557D11—24no—
558C24—21no—
559C24—111no—
560#41—228no—
561#41—228no—
562#41—448no—
563C2×Q8—21no—
564C2×Q8—24no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—82no—
568C2×Q8—112no—
569C2×Q8—112no—
570C2×Q8—224no—
571C2×Q8—224no—
572C2×Q8—228no—
573C2×Q8—228no—
574C2×Q8—221no—
575C2×Q8—221no—
576C2×Q8—222no—
577C2×Q8—222no—
578C2×Q8—222no—
579C2×Q8—222no—
580C2×Q8—444no—
581C2×Q8—448no—
582C2×Q8—882no—
583C2×Q8C23×D1112yes—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—224no—
588C2×D4—444no—
589C2×D4C23×D1112yes—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—111no—
594C22×C4—112no—
595C22×C4—114no—
596C22×C4—114no—
597C22×C4—112no—
598C22×C4—111no—
599C22×C4—111no—
600C22×C4—224no—
601C22×C4—224no—
602C22×C4—224no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—221no—
606C22×C4—221no—
607C22×C4—444no—
608C22×C4—444no—
609C22×C4—882no—
610C22×C4D4×D1111yescharacteristic
611C22×C4D4×D1111yescharacteristic
612C22×C4C23×D1111yescharacteristic
613M16—228no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—112no—
617C2×C8—112no—
618C2×C8—228no—
619C2×C8—222no—
620C2×C8—222no—
621C2×C8C23×D1112yes—
622C2×C8C23×D1112yes—
623C4⋊C4—24no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—114no—
627C4⋊C4—114no—
628C4⋊C4—112no—
629C4⋊C4—112no—
630C4⋊C4—224no—
631C4⋊C4—224no—
632C4⋊C4—224no—
633C4⋊C4—224no—
634C4⋊C4—224no—
635C4⋊C4—224no—
636C4⋊C4—221no—
637C4⋊C4—221no—
638C4⋊C4—224no—
639C4⋊C4—224no—
640C4⋊C4—224no—
641C4⋊C4—224no—
642C4⋊C4C23×D1112yes—
643C4⋊C4C23×D1112yes—
644C22⋊C4—24no—
645C22⋊C4—24no—
646C22⋊C4—114no—
647C22⋊C4—114no—
648C22⋊C4—224no—
649C22⋊C4—224no—
650C22⋊C4—224no—
651C42—112no—
652C42—112no—
653C42—224no—
654C42D4×D1112yes—
655C42C23×D1112yes—
656C11C2×#313711yescharacteristic, complemented, Sylow
657C23—22no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—112no—
662C23—114no—
663C23—222no—
664C23—222no—
665C23C2×D4×D1111yescharacteristic
666Q8—22no—
667Q8—22no—
668Q8—42no—
669Q8—84no—
670Q8—222no—
671Q8—222no—
672Q8—222no—
673Q8—222no—
674Q8—448no—
675Q8—442no—
676Q8—442no—
677Q8—884no—
678D4—22no—
679D4—22no—
680D4—42no—
681D4—448no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—112no—
691C2×C4—114no—
692C2×C4—114no—
693C2×C4—114no—
694C2×C4—118no—
695C2×C4—112no—
696C2×C4—112no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—448no—
704C2×C4—448no—
705C2×C4—442no—
706C2×C4—442no—
707C2×C4—442no—
708C2×C4—442no—
709C2×C4—884no—
710C2×C4C2×D4×D1112yes—
711C2×C4C2×D4×D1112yes—
712C2×C4C2×D4×D1111yescharacteristic
713C2×C4#41×D1112yes—
714C2×C4#41×D1112yes—
715C2×C4C24×D1111yescharacteristic
716C8—22no—
717C8—22no—
718C8—222no—
719C8—222no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—84no—
724C22—114no—
725C22—228no—
726C22—222no—
727C22—222no—
728C22D11×#12412yes—
729C22#1062330612yes—
730C22#1062331012yes—
731C22C22×D4×D1111yescharacteristic
732C4—22no—
733C4—22no—
734C4—42no—
735C4—42no—
736C4—42no—
737C4—114no—
738C4—222no—
739C4—222no—
740C4—442no—
741C4—442no—
742C4—442no—
743C4—442no—
744C4D11×#12412yes—
745C4C2×#41×D1111yescharacteristic
746C4C2×#41×D1111yescharacteristic
747C2—82no—
748C2—224no—
749C2#1307897814yesdirect product factor
750C2C2×D11×#12411yescharacteristic
751C2C2×#1062330611yescharacteristic
752C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#489C2
socleC23×C11C22×D4
prime radicalC22×#4341C22
hypercenterC2×#489D11
hypocenterC11C2×#3137
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#10623260C2semidirect
3. #13078978C2direct (N × H)
4. C2×#10622316C2semidirect
5. C2×#10622410C2semidirect
6. C2×#10622378C2semidirect
7. C2×#10622669C2semidirect
8. C2×#10622381C2semidirect
9. C2×#10622706C2semidirect
10. C2×#10622405C2semidirect
12. C2×#10622415C2semidirect
14. C2×D11×#103C2semidirect
15. C2×#10622321C2semidirect
16. C2×C11×#489C2semidirect
28. #10623260C22semidirect
44. C11×#489C22semidirect
60. #10622706C22semidirect
61. #10622669C22semidirect
67. #10622415C22semidirect
68. D11×#103C22semidirect
69. #10622410C22semidirect
70. #10622405C22semidirect
73. #10622381C22semidirect
74. #10622378C22semidirect
75. #10622321C22semidirect
76. #10622316C22semidirect
287. C2×#489D11semidirect
390. #489C2×D11semidirect
553. C2×C11#3137semidirect
656. C11C2×#3137semidirect
749. C2#13078978direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232602
C2×#106232062
#130789782
C2×#106223162
C2×#106224102
C2×#106223782
C2×#106226692
C2×#106223812
C2×#106227062
C2×#106224052
C2×#106223842
C2×#106224152
C2×#106223852
C2×D11×#1032
C2×#106223212
C2×C11×#4892
C2×#313711