Finite Group Databasebeta

← C2×#13078773 #15621906

Subgroups — C2×#13078773 #15621906

Order 2816.

2150 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623153C211yesmaximal, characteristic, complemented
2C2×#10623053C211yesmaximal, characteristic
3#13078773C2116yesmaximal, direct product factor
4C2×#10622609C211yesmaximal, characteristic, complemented
5C2×#10622488C211yesmaximal, characteristic, complemented
6C2×#10622483C211yesmaximal, characteristic, complemented
7C2×#10622406C211yesmaximal, characteristic, complemented
8C2×#10622431C211yesmaximal, characteristic, complemented
9C2×#10622346C211yesmaximal, characteristic
10C2×#10622660C211yesmaximal, characteristic
11C2×#10622466C211yesmaximal, characteristic, complemented
12C2×#10622402C211yesmaximal, characteristic, complemented
13C2×#10622430C211yesmaximal, characteristic, complemented
14C2×#10622502C211yesmaximal, characteristic, complemented
15C2×#10622332C211yesmaximal, characteristic, complemented
16C2×C11×#485C211yesmaximal, characteristic, complemented
17C22×#4339C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×#66997C2211yescharacteristic
22C22×#4326C2211yescharacteristic
23C22×#4325C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C22×Dic44C2211yescharacteristic
27C22×#4314C2211yescharacteristic
28#10623153—24no—
29#10623153C2218yescomplemented
30#10623053—24no—
31#10623053C2218yes—
32C2×#66946C2211yescharacteristic
33C2×#66946C2211yescharacteristic
34C2×#66942—21no—
35C2×#66941C2211yescharacteristic
36C2×#66940—21no—
37C2×#66940C2211yescharacteristic
38C2×#66940C2211yescharacteristic
39C2×#66940C2211yescharacteristic
40C2×(C22⋊D11)⋊C4—21no—
41C2×(C22⋊D11)⋊C4—21no—
42C2×#66931—21no—
43C2×#66930—21no—
44C2×#66925—21no—
45C2×C42×D11—21no—
46C11×#485C2218yescomplemented
47C2×C11×#107C2211yescharacteristic
48C2×C11×#106C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C22⋊(C11⋊C8)C2211yescharacteristic
53C2×#66885C2211yescharacteristic
54C2×#66880C2211yescharacteristic
55C2×#66879C2211yescharacteristic
56C2×#66879C2211yescharacteristic
57C2×Dic11⋊C8C2211yescharacteristic
58C2×Dic11⋊C8C2211yescharacteristic
59#10622660C2218yes—
60#10622609C2218yescomplemented
61C2×#66874C2211yescharacteristic
62C2×#66874C2211yescharacteristic
63C2×#66874C2211yescharacteristic
64C2×#66873C2211yescharacteristic
65C2×#66872C2211yescharacteristic
66C2×#66871C2211yescharacteristic
67#10622502C2218yescomplemented
68#10622488C2218yescomplemented
69#10622483C2218yescomplemented
70#10622466C2218yescomplemented
71#10622431C2218yescomplemented
72#10622430C2218yescomplemented
73#10622406C2218yescomplemented
74#10622402C2218yescomplemented
75#10622346C2218yes—
76#10622332C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C22×C22⋊D11—21no—
80C23×Dic11D411yescharacteristic
81C23×Dic11D411yescharacteristic
82C2×#4339—22no—
83C2×#4339—24no—
84C2×#4339—24no—
85C2×#4339C2314yes—
86C22×D44C2311yescharacteristic
87C22×C4×D11—21no—
88C22×C4×D11—21no—
89C22×C4×D11—21no—
90C22×Dic22—21no—
91C22×Dic22C2311yescharacteristic
92C22×Dic22C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C11×C22⋊Q8—22no—
96C11×C22⋊Q8C2314yes—
97C11×#117—22no—
98C11×#117C2314yes—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C42×C11—21no—
106C2×C22⋊Dic11—21no—
107Q8×Dic11—22no—
108Q8×Dic11C2314yes—
109#66997—22no—
110#66997C2314yes—
111C2×#4326—24no—
112C2×#4326C2314yes—
113C2×#4325—24no—
114C2×#4325C2314yes—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×C4⋊Dic11—21no—
118C2×C4⋊Dic11C2311yescharacteristic
119#66977—22no—
120#66977C2314yes—
121C2×Dic11⋊C4—21no—
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4—21no—
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4—21no—
128C2×C4×Dic11—21no—
129C2×C4×Dic11—21no—
130C2×C4×Dic11—21no—
131C2×C4×Dic11—21no—
132C2×C4×Dic11D411yescharacteristic
133C2×C4×Dic11D411yescharacteristic
134C2×C4×Dic11D414yes—
135C2×C4×Dic11C2311yescharacteristic
136C2×C4×Dic11C2311yescharacteristic
137C2×C4×Dic11C2314yes—
138C22×C11⋊C8C2311yescharacteristic
139C22×C11⋊C8C2311yescharacteristic
140C2×Dic44—24no—
141C2×Dic44C2314yes—
142C2×#4314—24no—
143C2×#4314C2314yes—
144#66946—22no—
145#66946—22no—
146#66946C2314yes—
147#66946C2314yes—
148#66942—28no—
149#66941—22no—
150#66941C2314yes—
151#66940—28no—
152#66940—22no—
153#66940—22no—
154#66940—22no—
155#66940C2314yes—
156#66940C2314yes—
157#66940C2314yes—
158(C22⋊D11)⋊C4—28no—
159(C22⋊D11)⋊C4—28no—
160#66931—28no—
161#66930—28no—
162#66925—28no—
163C42×D11—28no—
164C11×#107C2314yes—
165C11×#106C2314yes—
166C11×#103C2314yes—
167C11×#103C2314yes—
168C11×C22⋊C8C2314yes—
169C22⋊(C11⋊C8)C2314yes—
170#66885C2314yes—
171#66880C2314yes—
172#66879C2314yes—
173#66879C2314yes—
174Dic11⋊C8C2314yes—
175Dic11⋊C8C2314yes—
176#66874C2314yes—
177#66874C2314yes—
178#66874C2314yes—
179#66873C2314yes—
180#66872C2314yes—
181#66871C2314yes—
182C2×#3116—111nomaximal, Sylow
183C24×C11C2×D411yescharacteristic
184C23×D11—21no—
185C2×Q8×C11—21no—
186C2×Q8×C11—22no—
187C2×Q8×C11—22no—
188C2×Q8×C11C2412yes—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D412yes—
197C22×C4×C11C2412yes—
198C22×C4×C11C2411yescharacteristic
199C2×C22⋊D11—28no—
200C2×C22⋊D11—24no—
201C22×Dic11—24no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—42no—
206C22×Dic11C2×D414yes—
207C22×Dic11C2×D411yescharacteristic
208C22×Dic11C2×D411yescharacteristic
209C22×Dic11C2×D411yescharacteristic
210C22×Dic11C2×D414yes—
211C22×Dic11C2×D411yescharacteristic
212#4339—216no—
213#4339—28no—
214#4339—28no—
215C2×D44—21no—
216C2×D44—22no—
217C2×D44#4114yes—
218C2×D44C2412yes—
219C2×C4×D11—28no—
220C2×C4×D11—24no—
221C2×C4×D11—24no—
222C2×C4×D11—24no—
223C2×C4×D11—44no—
224C2×C4×D11—44no—
225C2×Dic22—24no—
226C2×Dic22—21no—
227C2×Dic22—21no—
228C2×Dic22—22no—
229C2×Dic22—22no—
230C2×Dic22—22no—
231C2×Dic22—44no—
232C2×Dic22#4114yes—
233C2×Dic22C2412yes—
234C2×Dic22C2412yes—
235C2×C8×C11—22no—
236C2×C8×C11—22no—
237C2×C8×C11C2412yes—
238C2×C8×C11C2412yes—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—24no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4C2412yes—
244C11×C4⋊C4C2412yes—
245C11×C4⋊C4C2412yes—
246C11×C22⋊C4—24no—
247C11×C22⋊C4—24no—
248C42×C11—24no—
249C22⋊Dic11—24no—
250#4326—28no—
251#4325—28no—
252(C2×D11)⋊C4—24no—
253(C2×D11)⋊C4—24no—
254C4⋊Dic11—24no—
255C4⋊Dic11—21no—
256C4⋊Dic11C2412yes—
257Dic11⋊C4—24no—
258Dic11⋊C4—24no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264C4×Dic11—24no—
265C4×Dic11—24no—
266C4×Dic11—24no—
267C4×Dic11—24no—
268C4×Dic11C2×D414yes—
269C4×Dic11C2×D414yes—
270C4×Dic11C2×D412yes—
271C4×Dic11C2×D412yes—
272C4×Dic11C2412yes—
273C4×Dic11C2412yes—
274C2×C11⋊C8—22no—
275C2×C11⋊C8—22no—
276C2×C11⋊C8C2412yes—
277C2×C11⋊C8C2412yes—
278Dic44—28no—
279#4314—28no—
280C2×#533—111no—
281C2×C4×#41—111no—
282#3116—1116no—
283C2×#485—111no—
284C2×#485D1111yescharacteristic, complemented
285C2×#477—111no—
286C2×#476—111no—
287C2×#462—111no—
288C2×#461—111no—
289C2×#452—111no—
290C2×#452—111no—
291C2×#441—111no—
292C2×#441—111no—
293C2×#440—111no—
294C2×#440—111no—
295C2×#432—111no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11C22×D412yes—
300C23×C11C22×D411yescharacteristic
301C22×D11—24no—
302C22×D11—22no—
303C22×D11—42no—
304C22×D11—42no—
305Q8×C11—22no—
306Q8×C11—22no—
307Q8×C11—42no—
308C2×C4×C11—22no—
309C2×C4×C11—24no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—42no—
317C2×C4×C11—42no—
318C2×C4×C11—42no—
319C2×C4×C11—42no—
320C2×C4×C11C22×D412yes—
321C2×C4×C11C22×D411yescharacteristic
322C2×C4×C11C2×#4112yes—
323C2×C4×C11C2×#4112yes—
324C2×C4×C11C2511yescharacteristic
325C22⋊D11—216no—
326C2×Dic11—24no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—28no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—44no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11#13714yes—
338C2×Dic11C22×D412yes—
339C2×Dic11C22×D412yes—
340C2×Dic11C22×D412yes—
341C2×Dic11C22×D412yes—
342D44—24no—
343D44—22no—
344D44C2×#4114yes—
345C4×D11—216no—
346C4×D11—48no—
347C4×D11—48no—
348Dic22—24no—
349Dic22—22no—
350Dic22—22no—
351Dic22—22no—
352Dic22—48no—
353Dic22—42no—
354Dic22C2×#4114yes—
355C8×C11—22no—
356C8×C11—22no—
357C11⋊C8—22no—
358C11⋊C8—22no—
359C22×#41—111no—
360C22×Q16—111no—
361C22×Q16—111no—
362C22×SD16—111no—
363C22×SD16—111no—
364#533—118no—
365#533—224no—
366C2×C4⋊Q8—111no—
367C2×C4⋊Q8—111no—
368C2×#125—221no—
369C2×C22⋊Q8—111no—
370C2×C22⋊Q8—221no—
371C2×C22⋊Q8C2×D1111yescharacteristic
372C4×#41—118no—
373C4×#41—224no—
374C2×C4×Q8—111no—
375C2×C4×Q8—111no—
376C2×C4×Q8—111no—
377C2×C4×Q8—111no—
378C2×C4×Q8—221no—
379C2×C4×D4—111no—
380C2×C4×D4—111no—
381C2×C4×D4—221no—
382C2×C4×D4—221no—
383C2×#117—221no—
384C2×#117—221no—
385C2×#117C2×D1111yescharacteristic
386C22×C42—111no—
387C22×C42—221no—
388#485—118no—
389#485C2×D1118yescomplemented
390#477—118no—
391#476—118no—
392#462—118no—
393#461—118no—
394#452—118no—
395#452—118no—
396#441—118no—
397#441—118no—
398#440—118no—
399#440—118no—
400#432—118no—
401C2×#107—111no—
402C2×#107C2×D1111yescharacteristic
403C2×#106—111no—
404C2×#106C2×D1111yescharacteristic
405C2×C4⋊C8—111no—
406C2×C4⋊C8—111no—
407C2×#103—111no—
408C2×#103—111no—
409C2×#103—111no—
410C2×#103—111no—
411C2×#103C2×D1111yescharacteristic
412C2×#103C2×D1111yescharacteristic
413C2×#102—111no—
414C2×#102—111no—
415C2×C22⋊C8—111no—
416C2×C22⋊C8C2×D1111yescharacteristic
417C2×#97—111no—
418C2×#97—111no—
419C22×C11—22no—
420C22×C11—22no—
421C22×C11—22no—
422C22×C11—44no—
423C22×C11#52512yes—
424C22×C11C2×#13712yes—
425C22×C11#57512yes—
426C22×C11C23×D411yescharacteristic
427C2×D11—24no—
428C2×D11—48no—
429C2×D11—42no—
430C2×D11—42no—
431C4×C11—22no—
432C4×C11—42no—
433C4×C11—42no—
434C4×C11—42no—
435C4×C11—42no—
436C4×C11#52512yes—
437C4×C11C22×#4111yescharacteristic
438C4×C11C22×#4111yescharacteristic
439Dic11—24no—
440Dic11—22no—
441Dic11—22no—
442Dic11—22no—
443Dic11—42no—
444Dic11—42no—
445Dic11C2×#13714yes—
446C2×#41—114no—
447C2×#41—224no—
448C2×#41—224no—
449C2×#41—222no—
450C22×Q8—111no—
451C22×Q8—111no—
452C22×Q8—221no—
453C22×Q8C22×D1111yescharacteristic
454C22×D4—111no—
455C22×D4—221no—
456C23×C4—111no—
457C23×C4—111no—
458C23×C4—221no—
459C23×C4—221no—
460C23×C4—221no—
461C23×C4C22×D1111yescharacteristic
462C2×Q16—114no—
463C2×Q16—114no—
464C2×Q16—224no—
465C2×Q16—224no—
466C2×SD16—114no—
467C2×SD16—114no—
468C2×SD16—224no—
469C2×SD16—224no—
470C22×C8—111no—
471C22×C8—111no—
472C22×C8C22×D1111yescharacteristic
473C22×C8C22×D1111yescharacteristic
474C4⋊Q8—114no—
475C4⋊Q8—114no—
476C4⋊Q8—222no—
477C4⋊Q8—222no—
478#125—228no—
479C22⋊Q8—22no—
480C22⋊Q8—114no—
481C22⋊Q8—228no—
482C22⋊Q8—222no—
483C22⋊Q8C22×D1114yes—
484C4×Q8—114no—
485C4×Q8—114no—
486C4×Q8—114no—
487C4×Q8—114no—
488C4×Q8—222no—
489C4×Q8—222no—
490C4×Q8—222no—
491C4×Q8—228no—
492C4×Q8—222no—
493C4×D4—114no—
494C4×D4—114no—
495C4×D4—222no—
496C4×D4—222no—
497C4×D4—228no—
498C4×D4—228no—
499#117—22no—
500#117—228no—
501#117—228no—
502#117C22×D1114yes—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—111no—
505C2×C4⋊C4—221no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4—221no—
508C2×C4⋊C4—221no—
509C2×C4⋊C4—221no—
510C2×C4⋊C4—221no—
511C2×C4⋊C4—221no—
512C2×C4⋊C4—221no—
513C2×C4⋊C4C22×D1111yescharacteristic
514C2×C4⋊C4C22×D1111yescharacteristic
515C2×C4⋊C4C22×D1111yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C42—21no—
522C2×C42—111no—
523C2×C42—114no—
524C2×C42—111no—
525C2×C42—111no—
526C2×C42—111no—
527C2×C42—114no—
528C2×C42—228no—
529C2×C42—221no—
530C2×C42—221no—
531C2×C42—221no—
532C2×C42—221no—
533#107—114no—
534#107C22×D1114yes—
535#106—114no—
536#106C22×D1114yes—
537C4⋊C8—114no—
538C4⋊C8—114no—
539#103—114no—
540#103—114no—
541#103—114no—
542#103—114no—
543#103C22×D1114yes—
544#103C22×D1114yes—
545#102—114no—
546#102—114no—
547C22⋊C8—114no—
548C22⋊C8C22×D1114yes—
549#97—114no—
550#97—114no—
551C2×C11—42no—
552C2×C11#311614yescomplemented
553C2×C11C2×#52511yescharacteristic
554C2×C11C22×#13711yescharacteristic
555C2×C11C2×#57511yescharacteristic
556D11—44no—
557C24—221no—
558C24D4×D1111yescharacteristic
559#41—228no—
560#41—228no—
561#41—2216no—
562C2×Q8—21no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—114no—
566C2×Q8—112no—
567C2×Q8—112no—
568C2×Q8—224no—
569C2×Q8—221no—
570C2×Q8—221no—
571C2×Q8—222no—
572C2×Q8—222no—
573C2×Q8—222no—
574C2×Q8—444no—
575C2×Q8C23×D1112yes—
576C2×D4—114no—
577C2×D4—112no—
578C2×D4—228no—
579C2×D4—224no—
580C2×D4—221no—
581C2×D4—222no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—111no—
589C22×C4—114no—
590C22×C4—111no—
591C22×C4—111no—
592C22×C4—111no—
593C22×C4—114no—
594C22×C4—224no—
595C22×C4—224no—
596C22×C4—228no—
597C22×C4—224no—
598C22×C4—221no—
599C22×C4—224no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4—444no—
603C22×C4—444no—
604C22×C4—442no—
605C22×C4D4×D1112yes—
606C22×C4D4×D1111yescharacteristic
607C22×C4C23×D1112yes—
608C22×C4C23×D1111yescharacteristic
609Q16—228no—
610Q16—228no—
611SD16—228no—
612SD16—228no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—112no—
616C2×C8—112no—
617C2×C8—222no—
618C2×C8—222no—
619C2×C8C23×D1112yes—
620C2×C8C23×D1112yes—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—112no—
626C4⋊C4—224no—
627C4⋊C4—224no—
628C4⋊C4—224no—
629C4⋊C4—224no—
630C4⋊C4—224no—
631C4⋊C4—224no—
632C4⋊C4—224no—
633C4⋊C4—221no—
634C4⋊C4—224no—
635C4⋊C4C23×D1112yes—
636C4⋊C4C23×D1112yes—
637C4⋊C4C23×D1112yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—224no—
641C22⋊C4—224no—
642C22⋊C4—224no—
643C42—24no—
644C42—114no—
645C42—114no—
646C42—112no—
647C42—112no—
648C42—112no—
649C42—112no—
650C42—224no—
651C42—224no—
652C42—224no—
653C42—224no—
654C11C2×#311611yescharacteristic, complemented, Sylow
655C23—22no—
656C23—22no—
657C23—22no—
658C23—224no—
659C23—222no—
660C23—442no—
661C23—442no—
662C23C2×D4×D1112yes—
663C23C2×D4×D1111yescharacteristic
664Q8—22no—
665Q8—22no—
666Q8—42no—
667Q8—114no—
668Q8—224no—
669Q8—222no—
670Q8—222no—
671Q8—222no—
672Q8—448no—
673Q8—442no—
674D4—114no—
675D4—2216no—
676D4—224no—
677D4—222no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—114no—
691C2×C4—112no—
692C2×C4—112no—
693C2×C4—112no—
694C2×C4—112no—
695C2×C4—2216no—
696C2×C4—228no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—224no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—448no—
705C2×C4—448no—
706C2×C4—444no—
707C2×C4—442no—
708C2×C4—442no—
709C2×C4C2×D4×D1112yes—
710C2×C4C2×D4×D1111yescharacteristic
711C2×C4#41×D1112yes—
712C2×C4#41×D1112yes—
713C2×C4C24×D1111yescharacteristic
714C8—22no—
715C8—22no—
716C8—222no—
717C8—222no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—44no—
722C22—224no—
723C22—442no—
724C22—442no—
725C22—448no—
726C22#1062318712yes—
727C22#1062329912yes—
728C22D11×#13712yes—
729C22C22×D4×D1111yescharacteristic
730C4—22no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—114no—
736C4—222no—
737C4—222no—
738C4—222no—
739C4—224no—
740C4—442no—
741C4—442no—
742C4#1062318712yes—
743C4C2×#41×D1111yescharacteristic
744C4C2×#41×D1111yescharacteristic
745C2—42no—
746C2—444no—
747C2#1307877314yesdirect product factor
748C2C2×#1062318711yescharacteristic
749C2C2×D11×#13711yescharacteristic
750C2C2×#1062329911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#485C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
hypercenterC2×#485D11
hypocenterC11C2×#3116
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#10623153C2semidirect
3. #13078773C2direct (N × H)
4. C2×#10622609C2semidirect
5. C2×#10622488C2semidirect
6. C2×#10622483C2semidirect
7. C2×#10622406C2semidirect
8. C2×#10622431C2semidirect
11. C2×#10622466C2semidirect
12. C2×#10622402C2semidirect
13. C2×#10622430C2semidirect
14. C2×#10622502C2semidirect
15. C2×#10622332C2semidirect
16. C2×C11×#485C2semidirect
29. #10623153C22semidirect
46. C11×#485C22semidirect
60. #10622609C22semidirect
67. #10622502C22semidirect
68. #10622488C22semidirect
69. #10622483C22semidirect
70. #10622466C22semidirect
71. #10622431C22semidirect
72. #10622430C22semidirect
73. #10622406C22semidirect
74. #10622402C22semidirect
76. #10622332C22semidirect
284. C2×#485D11semidirect
389. #485C2×D11semidirect
552. C2×C11#3116semidirect
654. C11C2×#3116semidirect
747. C2#13078773direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231532
C2×#106230532
#130787732
C2×#106226092
C2×#106224882
C2×#106224832
C2×#106224062
C2×#106224312
C2×#106223462
C2×#106226602
C2×#106224662
C2×#106224022
C2×#106224302
C2×#106225022
C2×#106223322
C2×C11×#4852
C2×#311611