Finite Group Databasebeta

← C2×#13081644 #15634738

Subgroups — C2×#13081644 #15634738

Order 2816.

1906 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623252C211yesmaximal, characteristic, complemented
2C2×#10623202C211yesmaximal, characteristic
3#13081644C2116yesmaximal, direct product factor
4C2×#10622780C211yesmaximal, characteristic
5C2×#10622794C211yesmaximal, characteristic, complemented
6C2×#10622779C211yesmaximal, characteristic
7C2×#10622667C211yesmaximal, characteristic
8C2×#10622795C211yesmaximal, characteristic, complemented
9C2×#10622795C211yesmaximal, characteristic, complemented
10C2×#10622703C211yesmaximal, characteristic, complemented
11C2×#10622775C211yesmaximal, characteristic
12C2×#10622314C211yesmaximal, characteristic, complemented
13C2×#10622329C211yesmaximal, characteristic, complemented
14C2×#10622797C211yesmaximal, characteristic, complemented
15C2×SD16×Dic11C211yesmaximal, characteristic
16C2×C11×#497C211yesmaximal, characteristic
17C22×C11×Q16C2211yescharacteristic
18C22×C11×Q16C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C2×C11×C4⋊Q8C2211yescharacteristic
22C2×C11×#124C2211yescharacteristic
23C2×Q8×Dic11C2211yescharacteristic
24C2×Q8×Dic11C2211yescharacteristic
25C2×Q8×Dic11C2211yescharacteristic
26C2×#66997C2211yescharacteristic
27C2×#66997C2211yescharacteristic
28C2×#66997C2211yescharacteristic
29C22×#4326C2211yescharacteristic
30C22×#4326C2211yescharacteristic
31C22×#4326C2211yescharacteristic
32C2×#66989C2211yescharacteristic
33C2×D4×Dic11C2211yescharacteristic
34C22×#4324C2211yescharacteristic
35C22×Dic44C2211yescharacteristic
36#10623252—24no—
37#10623252C2218yescomplemented
38#10623202—24no—
39#10623202C2218yes—
40C2×#66943—21no—
41C2×#66942—21no—
42C2×#66942—21no—
43C2×#66940—21no—
44C2×#66932—21no—
45C2×#66932—21no—
46C2×#66931—21no—
47C2×#66930—21no—
48C2×C4×Dic22C2211yescharacteristic
49C2×C4×Dic22C2211yescharacteristic
50C2×C4×Dic22C2211yescharacteristic
51C11×#497C2218yes—
52C2×C11×#97C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×#66899C2211yescharacteristic
55C2×#66899C2211yescharacteristic
56C2×#66896C2211yescharacteristic
57#10622797C2218yescomplemented
58#10622795C2218yescomplemented
59#10622795C2218yescomplemented
60#10622794C2218yescomplemented
61#10622780C2218yes—
62#10622779C2218yes—
63#10622775C2218yes—
64SD16×Dic11C2218yes—
65C2×#66881C2211yescharacteristic
66C2×#66880C2211yescharacteristic
67C2×#66880C2211yescharacteristic
68C2×#66879C2211yescharacteristic
69C2×Dic11⋊C8C2211yescharacteristic
70C2×Dic11⋊C8C2211yescharacteristic
71C2×C8×Dic11C2211yescharacteristic
72#10622703C2218yescomplemented
73#10622667C2218yes—
74C2×C4⋊(C11⋊C8)C2211yescharacteristic
75#10622329C2218yescomplemented
76#10622314C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C23×Dic11—21no—
82C22×Dic22D411yescharacteristic
83C22×Dic22C2311yescharacteristic
84C22×Dic22C2311yescharacteristic
85C2×C11×Q16—24no—
86C2×C11×Q16—42no—
87C2×C11×Q16C2314yes—
88C2×C11×Q16C2314yes—
89C2×C11×SD16—24no—
90C2×C11×SD16—42no—
91C2×C11×SD16C2314yes—
92C2×C11×SD16C2314yes—
93C22×C8×C11C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C11×C4⋊Q8—22no—
96C11×C4⋊Q8C2314yes—
97C11×#124—22no—
98C11×#124C2314yes—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C42×C11C2311yescharacteristic
104C2×C22⋊Dic11—21no—
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107Q8×Dic11—22no—
108Q8×Dic11—22no—
109Q8×Dic11—22no—
110Q8×Dic11C2314yes—
111Q8×Dic11C2314yes—
112Q8×Dic11C2314yes—
113#66997—22no—
114#66997—22no—
115#66997—22no—
116#66997C2314yes—
117#66997C2314yes—
118#66997C2314yes—
119C2×#4326—42no—
120C2×#4326—42no—
121C2×#4326—42no—
122C2×#4326C2314yes—
123C2×#4326C2314yes—
124C2×#4326C2314yes—
125#66989—22no—
126#66989C2314yes—
127D4×Dic11—22no—
128D4×Dic11C2314yes—
129C2×#4324—42no—
130C2×#4324C2314yes—
131C2×C4⋊Dic11—21no—
132C2×C4⋊Dic11—21no—
133C2×C4⋊Dic11—21no—
134C2×C4⋊Dic11D411yescharacteristic
135C2×C4⋊Dic11C2311yescharacteristic
136C2×C4⋊Dic11C2311yescharacteristic
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C2×Dic11⋊C4—21no—
142C2×Dic11⋊C4—21no—
143C2×Dic11⋊C4—21no—
144C2×Dic11⋊C4—21no—
145C2×Dic11⋊C4D411yescharacteristic
146C2×Dic11⋊C4D411yescharacteristic
147C2×C4×Dic11—21no—
148C2×C4×Dic11—21no—
149C2×C4×Dic11—21no—
150C2×C4×Dic11—21no—
151C2×C4×Dic11—21no—
152C2×C4×Dic11C2311yescharacteristic
153C2×C4×Dic11C2311yescharacteristic
154C22×C11⋊C8C2311yescharacteristic
155C22×C11⋊C8C2311yescharacteristic
156C2×Dic44—24no—
157C2×Dic44C2314yes—
158#66943—28no—
159#66942—28no—
160#66942—28no—
161#66940—28no—
162#66932—28no—
163#66932—28no—
164#66931—28no—
165#66930—28no—
166C4×Dic22—22no—
167C4×Dic22—22no—
168C4×Dic22D414yes—
169C4×Dic22C2314yes—
170C4×Dic22C2314yes—
171C4×Dic22C2314yes—
172C11×#97C2314yes—
173#66899C2314yes—
174#66899C2314yes—
175#66899C2314yes—
176#66896C2314yes—
177#66881C2314yes—
178#66880C2314yes—
179#66880C2314yes—
180#66879C2314yes—
181Dic11⋊C8C2314yes—
182Dic11⋊C8C2314yes—
183C8×Dic11C2314yes—
184C4⋊(C11⋊C8)C2314yes—
185C2×#3398—111nomaximal, Sylow
186C24×C11—21no—
187C2×Q8×C11—21no—
188C2×Q8×C11—21no—
189C2×Q8×C11—21no—
190C2×Q8×C11—22no—
191C2×Q8×C11—22no—
192C2×Q8×C11—22no—
193C2×Q8×C11—22no—
194C2×Q8×C11—22no—
195C2×Q8×C11—22no—
196C2×Q8×C11C2412yes—
197C2×Q8×C11C2412yes—
198C2×Q8×C11C2412yes—
199C2×D4×C11—21no—
200C2×D4×C11—22no—
201C2×D4×C11—22no—
202C2×D4×C11C2412yes—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2411yescharacteristic
209C22×Dic11—24no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—44no—
215C22×Dic11C2×D411yescharacteristic
216C22×Dic11C2×D411yescharacteristic
217C22×Dic11C2×D411yescharacteristic
218C22×Dic11C2×D411yescharacteristic
219C2×Dic22—24no—
220C2×Dic22—21no—
221C2×Dic22—21no—
222C2×Dic22—22no—
223C2×Dic22—22no—
224C2×Dic22—22no—
225C2×Dic22—22no—
226C2×Dic22C2×D414yes—
227C2×Dic22C2412yes—
228C2×Dic22C2412yes—
229C11×Q16—28no—
230C11×Q16—44no—
231C11×SD16—28no—
232C11×SD16—44no—
233C2×C8×C11—22no—
234C2×C8×C11#4114yes—
235C2×C8×C11C2412yes—
236C2×C8×C11C2412yes—
237C11×C4⋊C4—24no—
238C11×C4⋊C4—24no—
239C11×C22⋊C4—24no—
240C11×C22⋊C4—24no—
241C42×C11C2×D412yes—
242C42×C11C2412yes—
243C22⋊Dic11—24no—
244C22⋊Dic11—24no—
245C22⋊Dic11—24no—
246#4326—44no—
247#4326—44no—
248#4326—44no—
249#4324—44no—
250C4⋊Dic11—24no—
251C4⋊Dic11—24no—
252C4⋊Dic11—24no—
253C4⋊Dic11—21no—
254C4⋊Dic11—21no—
255C4⋊Dic11C2×D414yes—
256C4⋊Dic11C2412yes—
257C4⋊Dic11C2412yes—
258Dic11⋊C4—24no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266Dic11⋊C4C2×D414yes—
267Dic11⋊C4C2×D414yes—
268C4×Dic11—24no—
269C4×Dic11—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—
281Dic44—28no—
282C2×#557—111no—
283C2×#556—111no—
284#3398—1116no—
285C2×#497—111no—
286C2×#497D1111yescharacteristic
287C2×#494—111no—
288C2×#464—111no—
289C2×#464—111no—
290C2×#462—111no—
291C2×#462—111no—
292C2×#462—111no—
293C2×#461—111no—
294C2×#446—111no—
295C2×#441—111no—
296C2×#441—111no—
297C2×C4×SD16—111no—
298C23×C11—22no—
299C23×C11—42no—
300C23×C11—42no—
301C23×C11—42no—
302C23×C11C22×D411yescharacteristic
303Q8×C11—22no—
304Q8×C11—22no—
305Q8×C11—22no—
306Q8×C11—22no—
307Q8×C11—22no—
308Q8×C11—22no—
309Q8×C11—42no—
310Q8×C11—42no—
311Q8×C11—42no—
312D4×C11—22no—
313D4×C11—22no—
314D4×C11—42no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—42no—
321C2×C4×C11—42no—
322C2×C4×C11—42no—
323C2×C4×C11C22×D412yes—
324C2×C4×C11C22×D412yes—
325C2×C4×C11C22×D411yescharacteristic
326C2×C4×C11C2×#4112yes—
327C2×C4×C11H(5,𝔽2)12yes—
328C2×C4×C11C2511yescharacteristic
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—48no—
341C2×Dic11#13714yes—
342C2×Dic11C22×D412yes—
343C2×Dic11C22×D412yes—
344C2×Dic11C22×D412yes—
345C2×Dic11C22×D412yes—
346Dic22—28no—
347Dic22—22no—
348Dic22—22no—
349Dic22—22no—
350Dic22—22no—
351Dic22—42no—
352Dic22—42no—
353C8×C11—22no—
354C8×C11C2×#4114yes—
355C11⋊C8—22no—
356C11⋊C8—22no—
357C22×Q16—111no—
358C22×Q16—111no—
359C22×Q16—111no—
360C22×Q16—111no—
361C22×Q16C2×D1111yescharacteristic
362C22×Q16C2×D1111yescharacteristic
363C22×SD16—111no—
364C22×SD16C2×D1111yescharacteristic
365C22×SD16C2×D1111yescharacteristic
366#557—118no—
367#557—224no—
368#556—118no—
369#556—224no—
370C2×C4⋊Q8—111no—
371C2×C4⋊Q8—111no—
372C2×C4⋊Q8—111no—
373C2×C4⋊Q8C2×D1111yescharacteristic
374C2×#126—221no—
375C2×#126—221no—
376C2×#125—221no—
377C2×#125—221no—
378C2×#125—221no—
379C2×#124—111no—
380C2×#124C2×D1111yescharacteristic
381C2×C22⋊Q8—221no—
382C2×C4×Q8—111no—
383C2×C4×Q8—111no—
384C2×C4×Q8—111no—
385C2×C4×Q8—111no—
386C2×C4×Q8—111no—
387C2×C4×Q8—111no—
388C2×C4×Q8—221no—
389C2×C4×D4—111no—
390C2×#117—221no—
391#497—118no—
392#497C2×D1118yes—
393#494—118no—
394#464—118no—
395#464—118no—
396#462—118no—
397#462—118no—
398#462—118no—
399#461—118no—
400#446—118no—
401#441—118no—
402#441—118no—
403C4×SD16—118no—
404C2×#106—111no—
405C2×C4⋊C8—111no—
406C2×C4⋊C8—111no—
407C2×C4⋊C8—111no—
408C2×#103—111no—
409C2×#103—111no—
410C2×#103—111no—
411C2×#103—111no—
412C2×#103—111no—
413C2×#102—111no—
414C2×#97—111no—
415C2×#97C2×D1111yescharacteristic
416C2×C4×C8—111no—
417C22×C11—42no—
418C22×C11—42no—
419C22×C11—42no—
420C22×C11—84no—
421C22×C11#55012yes—
422C22×C11C2×#13712yes—
423C22×C11#57812yes—
424C22×C11C23×D411yescharacteristic
425C4×C11—22no—
426C4×C11—22no—
427C4×C11—42no—
428C4×C11—42no—
429C4×C11—42no—
430C4×C11#55012yes—
431C4×C11C22×#4111yescharacteristic
432C4×C11C2×H(5,𝔽2)11yescharacteristic
433Dic11—22no—
434Dic11—22no—
435Dic11—22no—
436Dic11—42no—
437Dic11—42no—
438Dic11—42no—
439Dic11—42no—
440Dic11C2×#13714yes—
441C22×Q8—111no—
442C22×Q8—111no—
443C22×Q8—111no—
444C22×Q8C22×D1111yescharacteristic
445C22×Q8C22×D1111yescharacteristic
446C22×Q8C22×D1111yescharacteristic
447C22×D4C22×D1111yescharacteristic
448C23×C4—221no—
449C2×Q16—24no—
450C2×Q16—42no—
451C2×Q16—114no—
452C2×Q16—114no—
453C2×Q16—114no—
454C2×Q16—114no—
455C2×Q16—224no—
456C2×Q16—442no—
457C2×Q16—442no—
458C2×Q16—442no—
459C2×Q16C22×D1114yes—
460C2×Q16C22×D1114yes—
461C2×SD16—24no—
462C2×SD16—42no—
463C2×SD16—114no—
464C2×SD16—442no—
465C2×SD16C22×D1114yes—
466C2×SD16C22×D1114yes—
467C22×C8—111no—
468C22×C8—111no—
469C22×C8C22×D1111yescharacteristic
470C22×C8C22×D1111yescharacteristic
471C4⋊Q8—22no—
472C4⋊Q8—114no—
473C4⋊Q8—114no—
474C4⋊Q8—114no—
475C4⋊Q8—222no—
476C4⋊Q8—222no—
477C4⋊Q8—222no—
478C4⋊Q8C22×D1114yes—
479#126—228no—
480#126—228no—
481#125—228no—
482#125—228no—
483#125—228no—
484#124—22no—
485#124—114no—
486#124—222no—
487#124C22×D1114yes—
488C22⋊Q8—228no—
489C4×Q8—114no—
490C4×Q8—114no—
491C4×Q8—114no—
492C4×Q8—114no—
493C4×Q8—114no—
494C4×Q8—114no—
495C4×Q8—114no—
496C4×Q8—222no—
497C4×Q8—222no—
498C4×Q8—222no—
499C4×Q8—228no—
500C4×Q8—222no—
501C4×Q8—222no—
502C4×D4—114no—
503C4×D4—222no—
504#117—228no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—111no—
508C2×C4⋊C4—111no—
509C2×C4⋊C4—111no—
510C2×C4⋊C4—111no—
511C2×C4⋊C4—111no—
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⋊C4—221no—
521C2×C4⋊C4—221no—
522C2×C4⋊C4—221no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—221no—
526C2×C22⋊C4—221no—
527C2×C22⋊C4—221no—
528C2×C42—111no—
529C2×C42—111no—
530C2×C42—221no—
531C2×C42—221no—
532C2×C42—221no—
533C2×C42—221no—
534C2×C42—221no—
535C2×C42C22×D1111yescharacteristic
536#106—114no—
537C4⋊C8—114no—
538C4⋊C8—114no—
539C4⋊C8—114no—
540#103—114no—
541#103—114no—
542#103—114no—
543#103—114no—
544#103—114no—
545#102—114no—
546#97—114no—
547#97C22×D1114yes—
548C4×C8—114no—
549C2×C11—82no—
550C2×C11#339814yescomplemented
551C2×C11C2×#55011yescharacteristic
552C2×C11C22×#13711yescharacteristic
553C2×C11C2×#57811yescharacteristic
554C24—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—114no—
565C2×Q8—112no—
566C2×Q8—112no—
567C2×Q8—224no—
568C2×Q8—221no—
569C2×Q8—221no—
570C2×Q8—222no—
571C2×Q8—222no—
572C2×Q8—222no—
573C2×Q8—222no—
574C2×Q8C23×D1112yes—
575C2×Q8C23×D1112yes—
576C2×Q8C23×D1112yes—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4C23×D1112yes—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—111no—
585C22×C4—111no—
586C22×C4—111no—
587C22×C4—111no—
588C22×C4—224no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4—221no—
593C22×C4—444no—
594C22×C4D4×D1111yescharacteristic
595C22×C4D4×D1111yescharacteristic
596C22×C4C23×D1111yescharacteristic
597Q16—28no—
598Q16—44no—
599Q16—228no—
600Q16—444no—
601Q16—444no—
602Q16—444no—
603SD16—28no—
604SD16—44no—
605SD16—444no—
606C2×C8—22no—
607C2×C8—112no—
608C2×C8—112no—
609C2×C8—222no—
610C2×C8—222no—
611C2×C8#434114yes—
612C2×C8C23×D1112yes—
613C2×C8C23×D1112yes—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—114no—
617C4⋊C4—114no—
618C4⋊C4—114no—
619C4⋊C4—112no—
620C4⋊C4—112no—
621C4⋊C4—224no—
622C4⋊C4—224no—
623C4⋊C4—224no—
624C4⋊C4—224no—
625C4⋊C4—224no—
626C4⋊C4—224no—
627C4⋊C4—224no—
628C4⋊C4—224no—
629C4⋊C4—224no—
630C4⋊C4—221no—
631C4⋊C4—221no—
632C4⋊C4—224no—
633C4⋊C4—224no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—224no—
637C22⋊C4—224no—
638C22⋊C4—224no—
639C42—112no—
640C42—112no—
641C42—112no—
642C42—112no—
643C42—224no—
644C42—224no—
645C42—224no—
646C42—224no—
647C42—224no—
648C42D4×D1112yes—
649C42C23×D1112yes—
650C11C2×#339811yescharacteristic, complemented, Sylow
651C23—22no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23C2×D4×D1111yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—42no—
664Q8—42no—
665Q8—228no—
666Q8—222no—
667Q8—222no—
668Q8—222no—
669Q8—222no—
670Q8—442no—
671Q8—442no—
672D4—22no—
673D4—22no—
674D4—42no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—114no—
684C2×C4—112no—
685C2×C4—112no—
686C2×C4—112no—
687C2×C4—112no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—222no—
694C2×C4—222no—
695C2×C4—448no—
696C2×C4—442no—
697C2×C4—442no—
698C2×C4—442no—
699C2×C4—442no—
700C2×C4C2×D4×D1112yes—
701C2×C4C2×D4×D1112yes—
702C2×C4C2×D4×D1111yescharacteristic
703C2×C4C2×#434112yes—
704C2×C4#6703712yes—
705C2×C4C24×D1111yescharacteristic
706C8—22no—
707C8—222no—
708C8—222no—
709C8C2×#434114yes—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22#1062324912yes—
715C22D11×#13712yes—
716C22#1062331012yes—
717C22C22×D4×D1111yescharacteristic
718C4—22no—
719C4—22no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—114no—
724C4—222no—
725C4—222no—
726C4—222no—
727C4—442no—
728C4—442no—
729C4—442no—
730C4—442no—
731C4#1062324912yes—
732C4C22×#434111yescharacteristic
733C4C2×#6703711yescharacteristic
734C2—82no—
735C2#1308164414yesdirect product factor
736C2C2×#1062324911yescharacteristic
737C2C2×D11×#13711yescharacteristic
738C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#497C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×#497D11
hypocenterC11C2×#3398
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
1. C2×#10623252C2semidirect
3. #13081644C2direct (N × H)
5. C2×#10622794C2semidirect
8. C2×#10622795C2semidirect
9. C2×#10622795C2semidirect
10. C2×#10622703C2semidirect
12. C2×#10622314C2semidirect
13. C2×#10622329C2semidirect
14. C2×#10622797C2semidirect
37. #10623252C22semidirect
57. #10622797C22semidirect
58. #10622795C22semidirect
59. #10622795C22semidirect
60. #10622794C22semidirect
72. #10622703C22semidirect
75. #10622329C22semidirect
76. #10622314C22semidirect
550. C2×C11#3398semidirect
650. C11C2×#3398semidirect
735. C2#13081644direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232522
C2×#106232022
#130816442
C2×#106227802
C2×#106227942
C2×#106227792
C2×#106226672
C2×#106227952
C2×#106227032
C2×#106227752
C2×#106223142
C2×#106223292
C2×#106227972
C2×SD16×Dic112
C2×C11×#4972
C2×#339811