Finite Group Databasebeta

← C2×#13080058 #15626717

Subgroups — C2×#13080058 #15626717

Order 2816.

1882 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623156C211yesmaximal, characteristic, complemented
2C2×#10623150C211yesmaximal, characteristic
3#13080058C2116yesmaximal, direct product factor
4C2×#10622409C211yesmaximal, characteristic, complemented
5C2×#10622490C211yesmaximal, characteristic, complemented
6C2×#10622504C211yesmaximal, characteristic, complemented
7C2×#10622379C211yesmaximal, characteristic, complemented
8C2×#10622747C211yesmaximal, characteristic, complemented
9C2×#10622661C211yesmaximal, characteristic, complemented
10C2×#10622654C211yesmaximal, characteristic, complemented
11C2×#10622375C211yesmaximal, characteristic, complemented
12C2×#10622776C211yesmaximal, characteristic, complemented
13C2×#10622431C211yesmaximal, characteristic, complemented
14C2×#10622775C211yesmaximal, characteristic, complemented
15C2×#10622732C211yesmaximal, characteristic, complemented
16C2×C11×#468C211yesmaximal, characteristic, complemented
17C22×C11×SD16C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C2×#66997C2211yescharacteristic
23C22×#4325C2211yescharacteristic
24C2×#66993C2211yescharacteristic
25C2×#66992—21no—
26C2×#66991—21no—
27C2×D4×Dic11C2211yescharacteristic
28C22×#4324C2211yescharacteristic
29C2×#66983C2211yescharacteristic
30C2×#66979C2211yescharacteristic
31C2×#66977C2211yescharacteristic
32C23×C11⋊C8C2211yescharacteristic
33C22×#4314C2211yescharacteristic
34#10623156—24no—
35#10623156C2218yescomplemented
36#10623150—24no—
37#10623150C2218yes—
38C2×#66946C2211yescharacteristic
39C2×#66943—21no—
40C2×#66943C2211yescharacteristic
41C2×#66943C2211yescharacteristic
42C2×#66942—21no—
43C2×#66940C2211yescharacteristic
44C2×#66939—21no—
45C2×#66936—21no—
46C2×#66932—21no—
47C2×#66932—21no—
48C11×#468C2218yescomplemented
49C2×C11×#107C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54#10622776C2218yescomplemented
55#10622775C2218yescomplemented
56#10622747C2218yescomplemented
57#10622732C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×#66882C2211yescharacteristic
60C2×#66880C2211yescharacteristic
61C2×Dic11⋊C8C2211yescharacteristic
62C2×Dic11⋊C8C2211yescharacteristic
63C2×Dic11⋊C8C2211yescharacteristic
64C2×Dic11⋊C8C2211yescharacteristic
65#10622661C2218yescomplemented
66#10622654C2218yescomplemented
67C2×#66874C2211yescharacteristic
68C2×#66873C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66872C2211yescharacteristic
71#10622504C2218yescomplemented
72#10622490C2218yescomplemented
73#10622431C2218yescomplemented
74#10622409C2218yescomplemented
75#10622379C2218yescomplemented
76#10622375C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C23×Dic11—21no—
85C22×D44C2311yescharacteristic
86C22×C4×D11—21no—
87C22×Dic22C2311yescharacteristic
88C2×C11×SD16—42no—
89C2×C11×SD16C2314yes—
90C2×C11×M16—42no—
91C2×C11×M16C2314yes—
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C11×C22⋊Q8—22no—
95C11×C22⋊Q8C2314yes—
96C11×#121—22no—
97C11×#121C2314yes—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11—21no—
105C2×C22⋊Dic11D411yescharacteristic
106C2×C22⋊Dic11D411yescharacteristic
107Q8×Dic11—22no—
108Q8×Dic11C2314yes—
109#66997—22no—
110#66997C2314yes—
111C2×#4325—42no—
112C2×#4325C2314yes—
113#66993—22no—
114#66993C2314yes—
115#66992—28no—
116#66991—28no—
117D4×Dic11—22no—
118D4×Dic11C2314yes—
119C2×#4324—42no—
120C2×#4324C2314yes—
121#66983—22no—
122#66983C2314yes—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4—21no—
125#66979D414yes—
126#66979C2314yes—
127C2×C4⋊Dic11—21no—
128C2×C4⋊Dic11—21no—
129C2×C4⋊Dic11—21no—
130C2×C4⋊Dic11D411yescharacteristic
131C2×C4⋊Dic11D411yescharacteristic
132C2×C4⋊Dic11C2311yescharacteristic
133C2×C4⋊Dic11C2311yescharacteristic
134#66977—22no—
135#66977C2314yes—
136C2×Dic11⋊C4—21no—
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C2×Dic11⋊C4—21no—
142C2×C4×Dic11—21no—
143C2×C4×Dic11—21no—
144C2×C4×Dic11C2311yescharacteristic
145C2×C4×Dic11C2311yescharacteristic
146C22×C11⋊C8—42no—
147C22×C11⋊C8C2311yescharacteristic
148C22×C11⋊C8C2311yescharacteristic
149C22×C11⋊C8C2314yes—
150C2×#4314—42no—
151C2×#4314C2314yes—
152#66946—22no—
153#66946C2314yes—
154#66943—28no—
155#66943—22no—
156#66943—22no—
157#66943C2314yes—
158#66943C2314yes—
159#66942—28no—
160#66940—22no—
161#66940C2314yes—
162#66939—28no—
163#66936—28no—
164#66932—28no—
165#66932—28no—
166C11×#107C2314yes—
167C11×#103C2314yes—
168C11×#102C2314yes—
169#66899C2314yes—
170#66896C2314yes—
171#66885C2314yes—
172#66882C2314yes—
173#66880C2314yes—
174Dic11⋊C8C2314yes—
175Dic11⋊C8C2314yes—
176Dic11⋊C8C2314yes—
177Dic11⋊C8C2314yes—
178#66874C2314yes—
179#66873C2314yes—
180#66872C2314yes—
181#66872C2314yes—
182C2×#3260—111nomaximal, Sylow
183C24×C11—21no—
184C24×C11C2×D411yescharacteristic
185C23×D11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—22no—
188C2×Q8×C11—22no—
189C2×Q8×C11C2412yes—
190C2×D4×C11—24no—
191C2×D4×C11—21no—
192C2×D4×C11—22no—
193C2×D4×C11—22no—
194C2×D4×C11—82no—
195C2×D4×C11C2412yes—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D412yes—
203C22×C4×C11C2412yes—
204C22×C4×C11C2411yescharacteristic
205C2×C22⋊D11—24no—
206C2×C22⋊D11—24no—
207C2×C22⋊D11—24no—
208C2×C22⋊D11—82no—
209C2×C22⋊D11—82no—
210C2×C22⋊D11—82no—
211C22×Dic11—24no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—82no—
216C22×Dic11C2×D411yescharacteristic
217C22×Dic11C2×D411yescharacteristic
218C22×Dic11C2×D411yescharacteristic
219C22×Dic11C2×D411yescharacteristic
220C2×D44—21no—
221C2×D44—22no—
222C2×D44—22no—
223C2×D44C2412yes—
224C2×C4×D11—24no—
225C2×C4×D11—82no—
226C2×Dic22—21no—
227C2×Dic22—22no—
228C2×Dic22—22no—
229C2×Dic22C2412yes—
230C11×SD16—44no—
231C11×M16—44no—
232C2×C8×C11—22no—
233C2×C8×C11—22no—
234C2×C8×C11C2412yes—
235C2×C8×C11C2412yes—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—24no—
238C11×C4⋊C4—21no—
239C11×C4⋊C4C2412yes—
240C11×C4⋊C4C2412yes—
241C11×C22⋊C4—24no—
242C11×C22⋊C4—24no—
243C22⋊Dic11—24no—
244C22⋊Dic11—24no—
245C22⋊Dic11C2×D414yes—
246C22⋊Dic11C2×D414yes—
247#4325—44no—
248#4324—44no—
249(C2×D11)⋊C4—24no—
250(C2×D11)⋊C4—24no—
251C4⋊Dic11—24no—
252C4⋊Dic11—24no—
253C4⋊Dic11—24no—
254C4⋊Dic11—21no—
255C4⋊Dic11—21no—
256C4⋊Dic11C2×D414yes—
257C4⋊Dic11C2×D414yes—
258C4⋊Dic11C2412yes—
259C4⋊Dic11C2412yes—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266C4×Dic11—24no—
267C4×Dic11—24no—
268C4×Dic11C2×D412yes—
269C4×Dic11C2×D412yes—
270C4×Dic11C2412yes—
271C4×Dic11C2412yes—
272C2×C11⋊C8—22no—
273C2×C11⋊C8—22no—
274C2×C11⋊C8—44no—
275C2×C11⋊C8C2412yes—
276C2×C11⋊C8C2412yes—
277#4314—44no—
278C2×#541—111no—
279C2×#540—111no—
280#3260—1116no—
281C2×#479—111no—
282C2×#479—111no—
283C2×#478—111no—
284C2×#478—111no—
285C2×#468—111no—
286C2×#468D1111yescharacteristic, complemented
287C2×#465—111no—
288C2×#465—111no—
289C2×#460—111no—
290C2×#460—111no—
291C2×#461—111no—
292C2×#461—111no—
293C2×#424—111no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—42no—
299C23×C11—42no—
300C23×C11—42no—
301C23×C11C22×D412yes—
302C23×C11C22×D411yescharacteristic
303C22×D11—22no—
304C22×D11—42no—
305C22×D11—42no—
306C22×D11—42no—
307Q8×C11—22no—
308Q8×C11—22no—
309Q8×C11—42no—
310D4×C11—22no—
311D4×C11—22no—
312D4×C11—42no—
313D4×C11—84no—
314C2×C4×C11—22no—
315C2×C4×C11—24no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—42no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11C22×D412yes—
325C2×C4×C11C22×D411yescharacteristic
326C2×C4×C11H(5,𝔽2)12yes—
327C2×C4×C112−1+412yes—
328C2×C4×C11C2511yescharacteristic
329C22⋊D11—84no—
330C22⋊D11—84no—
331C22⋊D11—84no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11—84no—
343C2×Dic11C22×D412yes—
344C2×Dic11C22×D412yes—
345C2×Dic11C22×D412yes—
346C2×Dic11C22×D412yes—
347D44—22no—
348D44—22no—
349D44—42no—
350C4×D11—84no—
351Dic22—22no—
352Dic22—22no—
353Dic22—42no—
354C8×C11—22no—
355C8×C11—22no—
356C11⋊C8—22no—
357C11⋊C8—22no—
358C22×SD16—111no—
359C22×SD16—111no—
360C22×SD16—111no—
361C22×SD16C2×D1111yescharacteristic
362C22×M16C2×D1111yescharacteristic
363C23×C8—111no—
364#541—118no—
365#541—224no—
366#540—118no—
367#540—224no—
368C2×C4⋊Q8—111no—
369C2×#127—111no—
370C2×#126—221no—
371C2×#126—221no—
372C2×#125—111no—
373C2×#125—111no—
374C2×#125—221no—
375C2×#125—221no—
376C2×#123—221no—
377C2×#123—221no—
378C2×C22⋊Q8—111no—
379C2×C22⋊Q8C2×D1111yescharacteristic
380C2×#121—111no—
381C2×#121—221no—
382C2×#121—221no—
383C2×#121C2×D1111yescharacteristic
384C2×C4×Q8—111no—
385C2×C4×Q8—111no—
386C2×C4×D4—111no—
387C2×C4×D4—111no—
388C2×#117—111no—
389#479—118no—
390#479—118no—
391#478—118no—
392#478—118no—
393#468—118no—
394#468C2×D1118yescomplemented
395#465—118no—
396#465—118no—
397#461—118no—
398#461—118no—
399#460—118no—
400#460—118no—
401C2×#107—111no—
402C2×#107C2×D1111yescharacteristic
403C2×#106—111no—
404C2×#106—111no—
405#424—118no—
406C2×C4⋊C8—111no—
407C2×C4⋊C8—111no—
408C2×C4⋊C8—111no—
409C2×C4⋊C8—111no—
410C2×#103—111no—
411C2×#103—111no—
412C2×#103—111no—
413C2×#103C2×D1111yescharacteristic
414C2×#102—111no—
415C2×#102—111no—
416C2×#102—111no—
417C2×#102C2×D1111yescharacteristic
418C22×C11—22no—
419C22×C11—22no—
420C22×C11—22no—
421C22×C11—44no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—42no—
425C22×C11—84no—
426C22×C11#53712yes—
427C22×C11#57712yes—
428C22×C11#57712yes—
429C22×C11C23×D411yescharacteristic
430C2×D11—42no—
431C2×D11—42no—
432C2×D11—42no—
433C2×D11—84no—
434C4×C11—22no—
435C4×C11—42no—
436C4×C11—42no—
437C4×C11—42no—
438C4×C11#53712yes—
439C4×C11C2×H(5,𝔽2)11yescharacteristic
440C4×C11C2×2−1+411yescharacteristic
441Dic11—22no—
442Dic11—22no—
443Dic11—22no—
444Dic11—22no—
445Dic11—42no—
446Dic11—42no—
447Dic11—42no—
448C22×Q8—111no—
449C22×Q8C22×D1111yescharacteristic
450C22×D4—21no—
451C22×D4—111no—
452C22×D4—221no—
453C22×D4—221no—
454C22×D4—221no—
455C22×D4C22×D1111yescharacteristic
456C23×C4—221no—
457C23×C4—221no—
458C23×C4C22×D1111yescharacteristic
459C2×SD16—42no—
460C2×SD16—114no—
461C2×SD16—114no—
462C2×SD16—114no—
463C2×SD16—442no—
464C2×SD16—442no—
465C2×SD16—442no—
466C2×SD16C22×D1114yes—
467C2×M16—42no—
468C2×M16C22×D1114yes—
469C22×C8—111no—
470C22×C8—111no—
471C22×C8—114no—
472C22×C8—442no—
473C22×C8C22×D1111yescharacteristic
474C22×C8C22×D1111yescharacteristic
475C4⋊Q8—114no—
476C4⋊Q8—222no—
477#127—114no—
478#127—222no—
479#126—228no—
480#126—228no—
481#125—114no—
482#125—114no—
483#125—222no—
484#125—222no—
485#125—228no—
486#125—228no—
487#123—228no—
488#123—228no—
489C22⋊Q8—22no—
490C22⋊Q8—114no—
491C22⋊Q8—222no—
492C22⋊Q8C22×D1114yes—
493#121—22no—
494#121—114no—
495#121—228no—
496#121—228no—
497#121—222no—
498#121C22×D1114yes—
499C4×Q8—114no—
500C4×Q8—114no—
501C4×Q8—222no—
502C4×Q8—222no—
503C4×D4—114no—
504C4×D4—114no—
505C4×D4—222no—
506C4×D4—222no—
507#117—114no—
508#117—114no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—111no—
511C2×C4⋊C4—111no—
512C2×C4⋊C4—111no—
513C2×C4⋊C4—111no—
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⋊C4—221no—
521C2×C4⋊C4—221no—
522C2×C4⋊C4—221no—
523C2×C4⋊C4C22×D1111yescharacteristic
524C2×C4⋊C4C22×D1111yescharacteristic
525C2×C22⋊C4—21no—
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—111no—
534C2×C42—111no—
535C2×C42—221no—
536C2×C42—221no—
537#107—114no—
538#107C22×D1114yes—
539#106—114no—
540#106—114no—
541C4⋊C8—114no—
542C4⋊C8—114no—
543C4⋊C8—114no—
544C4⋊C8—114no—
545#103—114no—
546#103—114no—
547#103—114no—
548#103C22×D1114yes—
549#102—114no—
550#102—114no—
551#102—114no—
552#102C22×D1114yes—
553C2×C11—42no—
554C2×C11—82no—
555C2×C11#326014yescomplemented
556C2×C11C2×#53711yescharacteristic
557C2×C11C2×#57711yescharacteristic
558C2×C11C2×#57711yescharacteristic
559D11—82no—
560C24—21no—
561C24—221no—
562C24D4×D1111yescharacteristic
563C2×Q8—21no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—112no—
567C2×Q8—221no—
568C2×Q8—222no—
569C2×Q8—222no—
570C2×Q8C23×D1112yes—
571C2×D4—24no—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—82no—
576C2×D4—112no—
577C2×D4—224no—
578C2×D4—224no—
579C2×D4—224no—
580C2×D4—221no—
581C2×D4—222no—
582C2×D4—222no—
583C2×D4—882no—
584C2×D4—882no—
585C2×D4—882no—
586C2×D4C23×D1112yes—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—111no—
593C22×C4—111no—
594C22×C4—111no—
595C22×C4—111no—
596C22×C4—224no—
597C22×C4—224no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—882no—
602C22×C4—882no—
603C22×C4D4×D1112yes—
604C22×C4D4×D1111yescharacteristic
605C22×C4C23×D1112yes—
606C22×C4C23×D1111yescharacteristic
607SD16—44no—
608SD16—444no—
609SD16—444no—
610SD16—444no—
611M16—44no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—112no—
615C2×C8—112no—
616C2×C8—222no—
617C2×C8—222no—
618C2×C8—444no—
619C2×C8C23×D1112yes—
620C2×C8C23×D1112yes—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—114no—
625C4⋊C4—114no—
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—224no—
635C4⋊C4—224no—
636C4⋊C4—221no—
637C4⋊C4—221no—
638C4⋊C4—224no—
639C4⋊C4C23×D1112yes—
640C4⋊C4C23×D1112yes—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—114no—
644C22⋊C4—114no—
645C22⋊C4—224no—
646C22⋊C4—224no—
647C22⋊C4—224no—
648C22⋊C4—224no—
649C42—112no—
650C42—112no—
651C42—112no—
652C42—112no—
653C42—224no—
654C42—224no—
655C11C2×#326011yescharacteristic, complemented, Sylow
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—222no—
664C23—442no—
665C23—442no—
666C23—442no—
667C23C2×D4×D1112yes—
668C23C2×D4×D1111yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—222no—
673Q8—222no—
674Q8—442no—
675D4—22no—
676D4—22no—
677D4—42no—
678D4—84no—
679D4—222no—
680D4—222no—
681D4—442no—
682D4—884no—
683D4—884no—
684D4—884no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—112no—
696C2×C4—112no—
697C2×C4—112no—
698C2×C4—112no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—222no—
706C2×C4—442no—
707C2×C4—442no—
708C2×C4—442no—
709C2×C4—884no—
710C2×C4—884no—
711C2×C4C2×D4×D1112yes—
712C2×C4C2×D4×D1111yescharacteristic
713C2×C4#6703712yes—
714C2×C4#6704312yes—
715C2×C4C24×D1111yescharacteristic
716C8—22no—
717C8—22no—
718C8—222no—
719C8—222no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—44no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—84no—
728C22—442no—
729C22—442no—
730C22—442no—
731C22—884no—
732C22#1062312812yes—
733C22#1062330612yes—
734C22#1062330912yes—
735C22C22×D4×D1111yescharacteristic
736C4—22no—
737C4—42no—
738C4—42no—
739C4—42no—
740C4—222no—
741C4—222no—
742C4—222no—
743C4—222no—
744C4—442no—
745C4—442no—
746C4—442no—
747C4#1062312812yes—
748C4C2×#6703711yescharacteristic
749C4C2×#6704311yescharacteristic
750C2—42no—
751C2—82no—
752C2—882no—
753C2#1308005814yesdirect product factor
754C2C2×#1062312811yescharacteristic
755C2C2×#1062330911yescharacteristic
756C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#468C2
socleC23×C11C22×D4
prime radicalC2×#10623150C2
hypercenterC2×#468D11
hypocenterC11C2×#3260
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#10623156C2semidirect
3. #13080058C2direct (N × H)
4. C2×#10622409C2semidirect
5. C2×#10622490C2semidirect
6. C2×#10622504C2semidirect
7. C2×#10622379C2semidirect
8. C2×#10622747C2semidirect
9. C2×#10622661C2semidirect
10. C2×#10622654C2semidirect
11. C2×#10622375C2semidirect
12. C2×#10622776C2semidirect
13. C2×#10622431C2semidirect
14. C2×#10622775C2semidirect
15. C2×#10622732C2semidirect
16. C2×C11×#468C2semidirect
35. #10623156C22semidirect
48. C11×#468C22semidirect
54. #10622776C22semidirect
55. #10622775C22semidirect
56. #10622747C22semidirect
57. #10622732C22semidirect
65. #10622661C22semidirect
66. #10622654C22semidirect
71. #10622504C22semidirect
72. #10622490C22semidirect
73. #10622431C22semidirect
74. #10622409C22semidirect
75. #10622379C22semidirect
76. #10622375C22semidirect
286. C2×#468D11semidirect
394. #468C2×D11semidirect
555. C2×C11#3260semidirect
655. C11C2×#3260semidirect
753. C2#13080058direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231562
C2×#106231502
#130800582
C2×#106224092
C2×#106224902
C2×#106225042
C2×#106223792
C2×#106227472
C2×#106226612
C2×#106226542
C2×#106223752
C2×#106227762
C2×#106224312
C2×#106227752
C2×#106227322
C2×C11×#4682
C2×#326011