Finite Group Databasebeta

← C2×#13081692 #15634790

Subgroups — C2×#13081692 #15634790

Order 2816.

1938 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623263C211yesmaximal, characteristic, complemented
2C2×#10623202C211yesmaximal, characteristic, complemented
3#13081692C2116yesmaximal, direct product factor
4C2×#10622803C211yesmaximal, characteristic, complemented
5C2×#10622781C211yesmaximal, characteristic
6C2×#10622798C211yesmaximal, characteristic, complemented
7C2×#10622779C211yesmaximal, characteristic, complemented
8C2×#10622795C211yesmaximal, characteristic, complemented
9C2×#10622703C211yesmaximal, characteristic, complemented
10C2×#10622778C211yesmaximal, characteristic
11C2×#10622670C211yesmaximal, characteristic
12C2×#10622314C211yesmaximal, characteristic, complemented
13C2×#10622323C211yesmaximal, characteristic, complemented
14C2×#10622777C211yesmaximal, characteristic, complemented
15C2×Q16×Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#497C211yesmaximal, characteristic, complemented
17C22×C11×Q16C2211yescharacteristic
18C22×C11×Q16C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C2×C11×C4⋊Q8C2211yescharacteristic
22C2×C11×#124C2211yescharacteristic
23C2×#67000C2211yescharacteristic
24C2×#67000C2211yescharacteristic
25C2×Q8×Dic11C2211yescharacteristic
26C2×Q8×Dic11C2211yescharacteristic
27C2×Q8×Dic11C2211yescharacteristic
28C2×#66997C2211yescharacteristic
29C22×#4326C2211yescharacteristic
30C22×#4326C2211yescharacteristic
31C22×#4325C2211yescharacteristic
32C2×#66989C2211yescharacteristic
33C2×D4×Dic11C2211yescharacteristic
34C22×#4323C2211yescharacteristic
35C22×#4314C2211yescharacteristic
36#10623263—24no—
37#10623263C2218yescomplemented
38#10623202—24no—
39#10623202C2218yescomplemented
40C2×#66951—21no—
41C2×#66951—21no—
42C2×#66950—21no—
43C2×#66945—21no—
44C2×#66932—21no—
45C2×#66932—21no—
46C2×#66931—21no—
47C2×#66930—21no—
48C2×C4×D44C2211yescharacteristic
49C2×C4×Dic22C2211yescharacteristic
50C2×C4×Dic22C2211yescharacteristic
51C11×#497C2218yescomplemented
52C2×C11×#97C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×#66899C2211yescharacteristic
55C2×#66899C2211yescharacteristic
56C2×#66896C2211yescharacteristic
57#10622803C2218yescomplemented
58#10622798C2218yescomplemented
59Q16×Dic11C2218yescomplemented
60#10622795C2218yescomplemented
61#10622781C2218yes—
62#10622779C2218yescomplemented
63#10622778C2218yes—
64#10622777C2218yescomplemented
65C2×#66885C2211yescharacteristic
66C2×#66882C2211yescharacteristic
67C2×#66880C2211yescharacteristic
68C2×#66879C2211yescharacteristic
69C2×Dic11⋊C8C2211yescharacteristic
70C2×Dic11⋊C8C2211yescharacteristic
71C2×C8×Dic11C2211yescharacteristic
72#10622703C2218yescomplemented
73#10622670C2218yes—
74C2×C4⋊(C11⋊C8)C2211yescharacteristic
75#10622323C2218yescomplemented
76#10622314C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C23×Dic11—21no—
82C22×D44C2311yescharacteristic
83C22×C4×D11—21no—
84C22×Dic22D411yescharacteristic
85C22×Dic22C2311yescharacteristic
86C2×C11×Q16—24no—
87C2×C11×Q16—42no—
88C2×C11×Q16C2314yes—
89C2×C11×Q16C2314yes—
90C2×C11×SD16—24no—
91C2×C11×SD16—42no—
92C2×C11×SD16C2314yes—
93C2×C11×SD16C2314yes—
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C11×C4⋊Q8—22no—
97C11×C4⋊Q8C2314yes—
98C11×#124—22no—
99C11×#124C2314yes—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C42×C11C2311yescharacteristic
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11—21no—
108#67000—22no—
109#67000—22no—
110#67000C2314yes—
111#67000C2314yes—
112Q8×Dic11—22no—
113Q8×Dic11—22no—
114Q8×Dic11—22no—
115Q8×Dic11C2314yes—
116Q8×Dic11C2314yes—
117Q8×Dic11C2314yes—
118#66997—22no—
119#66997C2314yes—
120C2×#4326—42no—
121C2×#4326—42no—
122C2×#4326C2314yes—
123C2×#4326C2314yes—
124C2×#4325—42no—
125C2×#4325C2314yes—
126#66989—22no—
127#66989C2314yes—
128D4×Dic11—22no—
129D4×Dic11C2314yes—
130C2×#4323—42no—
131C2×#4323C2314yes—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—21no—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4—21no—
137C2×C4⋊Dic11—21no—
138C2×C4⋊Dic11—21no—
139C2×C4⋊Dic11—21no—
140C2×C4⋊Dic11D411yescharacteristic
141C2×C4⋊Dic11C2311yescharacteristic
142C2×C4⋊Dic11C2311yescharacteristic
143C2×Dic11⋊C4—21no—
144C2×Dic11⋊C4—21no—
145C2×Dic11⋊C4—21no—
146C2×Dic11⋊C4D411yescharacteristic
147C2×Dic11⋊C4D411yescharacteristic
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×#4314—24no—
157C2×#4314C2314yes—
158#66951—28no—
159#66951—28no—
160#66950—28no—
161#66945—28no—
162#66932—28no—
163#66932—28no—
164#66931—28no—
165#66930—28no—
166C4×D44—22no—
167C4×D44C2314yes—
168C4×Dic22—22no—
169C4×Dic22D414yes—
170C4×Dic22C2314yes—
171C4×Dic22C2314yes—
172C11×#97C2314yes—
173#66899C2314yes—
174#66899C2314yes—
175#66899C2314yes—
176#66896C2314yes—
177#66885C2314yes—
178#66882C2314yes—
179#66880C2314yes—
180#66879C2314yes—
181Dic11⋊C8C2314yes—
182Dic11⋊C8C2314yes—
183C8×Dic11C2314yes—
184C4⋊(C11⋊C8)C2314yes—
185C2×#3402—111nomaximal, Sylow
186C24×C11—21no—
187C23×D11—21no—
188C2×Q8×C11—21no—
189C2×Q8×C11—21no—
190C2×Q8×C11—21no—
191C2×Q8×C11—22no—
192C2×Q8×C11—22no—
193C2×Q8×C11—22no—
194C2×Q8×C11—22no—
195C2×Q8×C11—22no—
196C2×Q8×C11—22no—
197C2×Q8×C11C2412yes—
198C2×Q8×C11C2412yes—
199C2×Q8×C11C2412yes—
200C2×D4×C11—21no—
201C2×D4×C11—22no—
202C2×D4×C11—22no—
203C2×D4×C11C2412yes—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2411yescharacteristic
210C22×Dic11—24no—
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×D44—21no—
220C2×D44—22no—
221C2×D44—22no—
222C2×D44C2412yes—
223C2×C4×D11—24no—
224C2×C4×D11—44no—
225C2×Dic22—21no—
226C2×Dic22—22no—
227C2×Dic22—22no—
228C2×Dic22—42no—
229C2×Dic22C2×D414yes—
230C2×Dic22C2412yes—
231C11×Q16—28no—
232C11×Q16—44no—
233C11×SD16—28no—
234C11×SD16—44no—
235C2×C8×C11—22no—
236C2×C8×C11#4114yes—
237C2×C8×C11C2412yes—
238C2×C8×C11C2412yes—
239C11×C4⋊C4—24no—
240C11×C4⋊C4—24no—
241C11×C22⋊C4—24no—
242C11×C22⋊C4—24no—
243C42×C11C2×D412yes—
244C42×C11C2412yes—
245C22⋊Dic11—24no—
246C22⋊Dic11—24no—
247C22⋊Dic11—24no—
248#4326—44no—
249#4326—44no—
250#4325—44no—
251#4323—44no—
252(C2×D11)⋊C4—24no—
253(C2×D11)⋊C4—24no—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—24no—
257C4⋊Dic11—24no—
258C4⋊Dic11—24no—
259C4⋊Dic11—24no—
260C4⋊Dic11—21no—
261C4⋊Dic11—21no—
262C4⋊Dic11C2×D414yes—
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×Dic11C2×D412yes—
276C4×Dic11C2412yes—
277C4×Dic11C2412yes—
278C2×C11⋊C8—22no—
279C2×C11⋊C8—22no—
280C2×C11⋊C8C2412yes—
281C2×C11⋊C8C2412yes—
282#4314—28no—
283C2×#556—111no—
284C2×#556—111no—
285#3402—1116no—
286C2×#497—111no—
287C2×#497D1111yescharacteristic, complemented
288C2×#495—111no—
289C2×#464—111no—
290C2×#464—111no—
291C2×#462—111no—
292C2×#462—111no—
293C2×#463—111no—
294C2×#463—111no—
295C2×#446—111no—
296C2×#440—111no—
297C2×#440—111no—
298C2×C4×Q16—111no—
299C23×C11—22no—
300C23×C11—42no—
301C23×C11—42no—
302C23×C11—42no—
303C23×C11C22×D411yescharacteristic
304C22×D11—22no—
305C22×D11—42no—
306C22×D11—42no—
307C22×D11—42no—
308Q8×C11—22no—
309Q8×C11—22no—
310Q8×C11—22no—
311Q8×C11—22no—
312Q8×C11—22no—
313Q8×C11—22no—
314Q8×C11—42no—
315Q8×C11—42no—
316Q8×C11—42no—
317D4×C11—22no—
318D4×C11—22no—
319D4×C11—42no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—42no—
326C2×C4×C11—42no—
327C2×C4×C11—42no—
328C2×C4×C11C22×D412yes—
329C2×C4×C11C22×D412yes—
330C2×C4×C11C22×D411yescharacteristic
331C2×C4×C11C2×#4112yes—
332C2×C4×C11H(5,𝔽2)12yes—
333C2×C4×C11C2511yescharacteristic
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—48no—
342C2×Dic11—42no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11C22×D412yes—
346C2×Dic11C22×D412yes—
347C2×Dic11C22×D412yes—
348C2×Dic11C22×D412yes—
349D44—22no—
350D44—22no—
351D44—42no—
352C4×D11—48no—
353Dic22—22no—
354Dic22—22no—
355Dic22—44no—
356Dic22—42no—
357C8×C11—22no—
358C8×C11C2×#4114yes—
359C11⋊C8—22no—
360C11⋊C8—22no—
361C22×Q16—111no—
362C22×Q16—111no—
363C22×Q16C2×D1111yescharacteristic
364C22×Q16C2×D1111yescharacteristic
365C22×SD16—111no—
366C22×SD16—111no—
367C22×SD16C2×D1111yescharacteristic
368C22×SD16C2×D1111yescharacteristic
369C22×D8—111no—
370#556—118no—
371#556—118no—
372#556—224no—
373#556—224no—
374C2×C4⋊Q8—111no—
375C2×C4⋊Q8C2×D1111yescharacteristic
376C2×#126—221no—
377C2×#126—221no—
378C2×#126—221no—
379C2×#126—221no—
380C2×#124—111no—
381C2×#124—111no—
382C2×#124—111no—
383C2×#124C2×D1111yescharacteristic
384C2×C22⋊Q8—221no—
385C2×C22⋊Q8—221no—
386C2×C4×Q8—111no—
387C2×C4×Q8—111no—
388C2×C4×Q8—111no—
389C2×C4×Q8—111no—
390C2×C4×Q8—111no—
391C2×C4×D4—111no—
392C2×C4×D4—111no—
393C2×#117—221no—
394C2×#117—221no—
395#497—118no—
396#497C2×D1118yescomplemented
397#495—118no—
398#464—118no—
399#464—118no—
400#463—118no—
401#463—118no—
402#462—118no—
403#462—118no—
404#446—118no—
405#440—118no—
406#440—118no—
407C4×Q16—118no—
408C2×#107—111no—
409C2×C4⋊C8—111no—
410C2×C4⋊C8—111no—
411C2×C4⋊C8—111no—
412C2×#103—111no—
413C2×#103—111no—
414C2×#103—111no—
415C2×#103—111no—
416C2×#102—111no—
417C2×#102—111no—
418C2×#97—111no—
419C2×#97C2×D1111yescharacteristic
420C2×C4×C8—111no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—84no—
425C22×C11#55012yes—
426C22×C11#57512yes—
427C22×C11#57812yes—
428C22×C11C23×D411yescharacteristic
429C2×D11—42no—
430C2×D11—42no—
431C2×D11—42no—
432C2×D11—84no—
433C4×C11—22no—
434C4×C11—22no—
435C4×C11—42no—
436C4×C11—42no—
437C4×C11—42no—
438C4×C11#55012yes—
439C4×C11C22×#4111yescharacteristic
440C4×C11C2×H(5,𝔽2)11yescharacteristic
441Dic11—22no—
442Dic11—22no—
443Dic11—22no—
444Dic11—22no—
445Dic11—42no—
446Dic11—42no—
447Dic11—42no—
448C22×Q8—111no—
449C22×Q8—111no—
450C22×Q8C22×D1111yescharacteristic
451C22×Q8C22×D1111yescharacteristic
452C22×Q8C22×D1111yescharacteristic
453C22×D4—111no—
454C22×D4C22×D1111yescharacteristic
455C23×C4—221no—
456C23×C4—221no—
457C2×Q16—24no—
458C2×Q16—42no—
459C2×Q16—114no—
460C2×Q16—114no—
461C2×Q16—442no—
462C2×Q16—442no—
463C2×Q16C22×D1114yes—
464C2×Q16C22×D1114yes—
465C2×SD16—24no—
466C2×SD16—42no—
467C2×SD16—114no—
468C2×SD16—114no—
469C2×SD16—224no—
470C2×SD16—442no—
471C2×SD16C22×D1114yes—
472C2×SD16C22×D1114yes—
473C2×D8—114no—
474C2×D8—442no—
475C22×C8—111no—
476C22×C8—111no—
477C22×C8C22×D1111yescharacteristic
478C22×C8C22×D1111yescharacteristic
479C4⋊Q8—22no—
480C4⋊Q8—114no—
481C4⋊Q8—222no—
482C4⋊Q8C22×D1114yes—
483#126—228no—
484#126—228no—
485#126—228no—
486#126—228no—
487#124—22no—
488#124—114no—
489#124—114no—
490#124—114no—
491#124—222no—
492#124—222no—
493#124—222no—
494#124C22×D1114yes—
495C22⋊Q8—228no—
496C22⋊Q8—228no—
497C4×Q8—114no—
498C4×Q8—114no—
499C4×Q8—114no—
500C4×Q8—114no—
501C4×Q8—114no—
502C4×Q8—114no—
503C4×Q8—222no—
504C4×Q8—222no—
505C4×Q8—222no—
506C4×Q8—222no—
507C4×D4—114no—
508C4×D4—114no—
509C4×D4—222no—
510C4×D4—222no—
511#117—228no—
512#117—228no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—111no—
516C2×C4⋊C4—111no—
517C2×C4⋊C4—111no—
518C2×C4⋊C4—111no—
519C2×C4⋊C4—111no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4—221no—
522C2×C4⋊C4—221no—
523C2×C4⋊C4—221no—
524C2×C4⋊C4—221no—
525C2×C4⋊C4—221no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—221no—
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×C22⋊C4—221no—
536C2×C42—111no—
537C2×C42—111no—
538C2×C42—221no—
539C2×C42—221no—
540C2×C42—221no—
541C2×C42—221no—
542C2×C42C22×D1111yescharacteristic
543#107—114no—
544C4⋊C8—114no—
545C4⋊C8—114no—
546C4⋊C8—114no—
547#103—114no—
548#103—114no—
549#103—114no—
550#103—114no—
551#102—114no—
552#102—114no—
553#97—114no—
554#97C22×D1114yes—
555C4×C8—114no—
556C2×C11—82no—
557C2×C11#340214yescomplemented
558C2×C11C2×#55011yescharacteristic
559C2×C11C2×#57511yescharacteristic
560C2×C11C2×#57811yescharacteristic
561D11—82no—
562C24—21no—
563C24—221no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8—114no—
574C2×Q8—112no—
575C2×Q8—221no—
576C2×Q8—222no—
577C2×Q8—222no—
578C2×Q8—442no—
579C2×Q8C23×D1112yes—
580C2×Q8C23×D1112yes—
581C2×Q8C23×D1112yes—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—112no—
586C2×D4—221no—
587C2×D4—222no—
588C2×D4—222no—
589C2×D4C23×D1112yes—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—111no—
594C22×C4—111no—
595C22×C4—111no—
596C22×C4—111no—
597C22×C4—224no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—224no—
602C22×C4—444no—
603C22×C4—444no—
604C22×C4D4×D1111yescharacteristic
605C22×C4D4×D1111yescharacteristic
606C22×C4C23×D1111yescharacteristic
607Q16—28no—
608Q16—44no—
609Q16—444no—
610Q16—444no—
611SD16—28no—
612SD16—44no—
613SD16—228no—
614SD16—444no—
615D8—444no—
616C2×C8—22no—
617C2×C8—112no—
618C2×C8—112no—
619C2×C8—222no—
620C2×C8—222no—
621C2×C8#434114yes—
622C2×C8C23×D1112yes—
623C2×C8C23×D1112yes—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—114no—
627C4⋊C4—114no—
628C4⋊C4—114no—
629C4⋊C4—112no—
630C4⋊C4—112no—
631C4⋊C4—224no—
632C4⋊C4—224no—
633C4⋊C4—224no—
634C4⋊C4—224no—
635C4⋊C4—224no—
636C4⋊C4—221no—
637C4⋊C4—221no—
638C4⋊C4—224no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—224no—
642C22⋊C4—224no—
643C22⋊C4—224no—
644C22⋊C4—224no—
645C22⋊C4—224no—
646C22⋊C4—224no—
647C22⋊C4—224no—
648C22⋊C4—224no—
649C42—112no—
650C42—112no—
651C42—112no—
652C42—112no—
653C42—224no—
654C42—224no—
655C42—224no—
656C42—224no—
657C42D4×D1112yes—
658C42C23×D1112yes—
659C11C2×#340211yescharacteristic, complemented, Sylow
660C23—22no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—222no—
665C23—442no—
666C23—442no—
667C23—442no—
668C23C2×D4×D1111yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—22no—
673Q8—22no—
674Q8—22no—
675Q8—42no—
676Q8—42no—
677Q8—42no—
678Q8—222no—
679Q8—222no—
680Q8—444no—
681Q8—442no—
682D4—22no—
683D4—22no—
684D4—42no—
685D4—222no—
686D4—222no—
687D4—442no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—112no—
697C2×C4—112no—
698C2×C4—112no—
699C2×C4—112no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—222no—
706C2×C4—222no—
707C2×C4—448no—
708C2×C4—448no—
709C2×C4—442no—
710C2×C4—442no—
711C2×C4—442no—
712C2×C4C2×D4×D1112yes—
713C2×C4C2×D4×D1112yes—
714C2×C4C2×D4×D1111yescharacteristic
715C2×C4C2×#434112yes—
716C2×C4#6703712yes—
717C2×C4C24×D1111yescharacteristic
718C8—22no—
719C8—222no—
720C8—222no—
721C8C2×#434114yes—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—442no—
727C22—442no—
728C22—442no—
729C22—884no—
730C22#1062324912yes—
731C22#1062330812yes—
732C22#1062331012yes—
733C22C22×D4×D1111yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—222no—
740C4—222no—
741C4—222no—
742C4—222no—
743C4—442no—
744C4—442no—
745C4—442no—
746C4#1062324912yes—
747C4C22×#434111yescharacteristic
748C4C2×#6703711yescharacteristic
749C2—82no—
750C2—882no—
751C2#1308169214yesdirect product factor
752C2C2×#1062324911yescharacteristic
753C2C2×#1062330811yescharacteristic
754C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#497C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenterC2×#497D11
hypocenterC11C2×#3402
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×#10623263C2semidirect
2. C2×#10623202C2semidirect
3. #13081692C2direct (N × H)
4. C2×#10622803C2semidirect
6. C2×#10622798C2semidirect
7. C2×#10622779C2semidirect
8. C2×#10622795C2semidirect
9. C2×#10622703C2semidirect
12. C2×#10622314C2semidirect
13. C2×#10622323C2semidirect
14. C2×#10622777C2semidirect
15. C2×Q16×Dic11C2semidirect
16. C2×C11×#497C2semidirect
37. #10623263C22semidirect
39. #10623202C22semidirect
51. C11×#497C22semidirect
57. #10622803C22semidirect
58. #10622798C22semidirect
59. Q16×Dic11C22semidirect
60. #10622795C22semidirect
62. #10622779C22semidirect
64. #10622777C22semidirect
72. #10622703C22semidirect
75. #10622323C22semidirect
76. #10622314C22semidirect
287. C2×#497D11semidirect
396. #497C2×D11semidirect
557. C2×C11#3402semidirect
659. C11C2×#3402semidirect
751. C2#13081692direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232632
C2×#106232022
#130816922
C2×#106228032
C2×#106227812
C2×#106227982
C2×#106227792
C2×#106227952
C2×#106227032
C2×#106227782
C2×#106226702
C2×#106223142
C2×#106223232
C2×#106227772
C2×Q16×Dic112
C2×C11×#4972
C2×#340211