Finite Group Databasebeta

← C2×#13081226 #15632506

Subgroups — C2×#13081226 #15632506

Order 2816.

1866 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623172C211yesmaximal, characteristic
2C2×#10623166C211yesmaximal, characteristic
3#13081226C2116yesmaximal, direct product factor
4C2×#10622468C211yesmaximal, characteristic, complemented
5C2×#10622427C211yesmaximal, characteristic, complemented
6C2×#10622658C211yesmaximal, characteristic, complemented
7C2×#10622418C211yesmaximal, characteristic, complemented
8C2×#10622656C211yesmaximal, characteristic, complemented
9C2×#10622407C211yesmaximal, characteristic, complemented
10C2×#10622404C211yesmaximal, characteristic, complemented
11C2×#10622802C211yesmaximal, characteristic, complemented
12C2×Q16×Dic11C211yesmaximal, characteristic, complemented
13C2×#10622741C211yesmaximal, characteristic
14C2×#10622734C211yesmaximal, characteristic, complemented
15C2×#10622474C211yesmaximal, characteristic, complemented
16C2×C11×#470C211yesmaximal, characteristic, complemented
17C22×C11×Q16C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×#66999C2211yescharacteristic
22C2×#66999C2211yescharacteristic
23C2×Q8×Dic11C2211yescharacteristic
24C2×Q8×Dic11C2211yescharacteristic
25C2×C4×C22⋊D11C2211yescharacteristic
26C2×#66979C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×#4313C2211yescharacteristic
29#10623172—24no—
30#10623172C2218yes—
31#10623166—24no—
32#10623166C2218yes—
33C2×#66951—21no—
34C2×#66950—21no—
35C2×#66945C2211yescharacteristic
36C2×C4⋊C4×D11C2211yescharacteristic
37C2×#66942—21no—
38C2×#66941C2211yescharacteristic
39C2×#66941C2211yescharacteristic
40C2×#66940—21no—
41C2×#66938—21no—
42C2×(C22⋊D11)⋊C4—21no—
43C2×#66932—21no—
44C2×#66931—21no—
45C11×#470C2218yescomplemented
46C2×C11×#106C2211yescharacteristic
47C2×C11×#103C2211yescharacteristic
48C2×C11×#103C2211yescharacteristic
49C2×#66899C2211yescharacteristic
50C2×#66899C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×C22⋊(C11⋊C8)C2211yescharacteristic
54#10622802C2218yescomplemented
55Q16×Dic11C2218yescomplemented
56#10622741C2218yes—
57#10622734C2218yescomplemented
58C2×(C2×D11)⋊C8C2211yescharacteristic
59C2×#66882C2211yescharacteristic
60C2×#66882C2211yescharacteristic
61C2×#66881C2211yescharacteristic
62C2×#66881C2211yescharacteristic
63C2×Dic11⋊C8C2211yescharacteristic
64C2×C8×Dic11C2211yescharacteristic
65#10622658C2218yescomplemented
66#10622656C2218yescomplemented
67C2×#66872C2211yescharacteristic
68C2×#66872C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71#10622474C2218yescomplemented
72#10622468C2218yescomplemented
73#10622427C2218yescomplemented
74#10622418C2218yescomplemented
75#10622407C2218yescomplemented
76#10622404C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11D411yescharacteristic
81C23×Dic11—21no—
82C22×C4×D11—21no—
83C22×C4×D11C2311yescharacteristic
84C22×Dic22—21no—
85C22×Dic22—21no—
86C2×C11×Q16—24no—
87C2×C11×Q16C2314yes—
88C2×C11×M16—24no—
89C2×C11×M16C2314yes—
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C11×C22⋊Q8—22no—
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8C2314yes—
95C11×C22⋊Q8C2314yes—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C22⋊Dic11—21no—
103C2×C22⋊Dic11D411yescharacteristic
104#66999—22no—
105#66999—22no—
106#66999C2314yes—
107#66999C2314yes—
108Q8×Dic11—22no—
109Q8×Dic11—22no—
110Q8×Dic11C2314yes—
111Q8×Dic11C2314yes—
112C4×C22⋊D11D414yes—
113C4×C22⋊D11C2314yes—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4D411yescharacteristic
118#66979—22no—
119#66979C2314yes—
120C2×C4⋊Dic11—21no—
121C2×C4⋊Dic11—22no—
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11—21no—
124C2×C4⋊Dic11C2314yes—
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4⋊Dic11C2311yescharacteristic
128C2×C4⋊Dic11C2311yescharacteristic
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4D411yescharacteristic
135C2×C4×Dic11—21no—
136C2×C4×Dic11—21no—
137C2×C4×Dic11—21no—
138C2×C4×Dic11—21no—
139C2×C4×Dic11C2311yescharacteristic
140C22×C11⋊C8C2311yescharacteristic
141C22×C11⋊C8C2311yescharacteristic
142C2×#4313—24no—
143C2×#4313C2314yes—
144#66951—28no—
145#66950—28no—
146#66945—22no—
147#66945C2314yes—
148C4⋊C4×D11—22no—
149C4⋊C4×D11C2314yes—
150#66942—28no—
151#66941—22no—
152#66941—22no—
153#66941C2314yes—
154#66941C2314yes—
155#66940—28no—
156#66938—28no—
157(C22⋊D11)⋊C4—28no—
158#66932—28no—
159#66931—28no—
160C11×#106C2314yes—
161C11×#103C2314yes—
162C11×#103C2314yes—
163#66899C2314yes—
164#66899C2314yes—
165#66899C2314yes—
166#66899C2314yes—
167C22⋊(C11⋊C8)C2314yes—
168(C2×D11)⋊C8C2314yes—
169#66882C2314yes—
170#66882C2314yes—
171#66881C2314yes—
172#66881C2314yes—
173Dic11⋊C8C2314yes—
174C8×Dic11C2314yes—
175#66872C2314yes—
176#66872C2314yes—
177#66872C2314yes—
178#66871C2314yes—
179C2×#3356—111nomaximal, Sylow
180C24×C11C2×D411yescharacteristic
181C23×D11C2×D411yescharacteristic
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—22no—
185C2×Q8×C11—22no—
186C2×Q8×C11—22no—
187C2×Q8×C11—22no—
188C2×Q8×C11C2412yes—
189C2×Q8×C11C2412yes—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D412yes—
198C22×C4×C11C2412yes—
199C22×C4×C11C2411yescharacteristic
200C2×C22⋊D11—24no—
201C2×C22⋊D11C2×D414yes—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—24no—
207C22×Dic11—82no—
208C22×Dic11C2×D411yescharacteristic
209C22×Dic11C2×D411yescharacteristic
210C22×Dic11C2×D411yescharacteristic
211C2×C4×D11—24no—
212C2×C4×D11—22no—
213C2×C4×D11—22no—
214C2×C4×D11—82no—
215C2×C4×D11C2×D412yes—
216C2×C4×D11C2412yes—
217C2×Dic22—24no—
218C2×Dic22—24no—
219C2×Dic22—44no—
220C2×Dic22—82no—
221C11×Q16—28no—
222C11×M16—28no—
223C2×C8×C11—22no—
224C2×C8×C11#4114yes—
225C2×C8×C11C2412yes—
226C2×C8×C11C2412yes—
227C11×C4⋊C4—24no—
228C11×C4⋊C4—21no—
229C11×C4⋊C4—21no—
230C11×C4⋊C4—24no—
231C11×C4⋊C4C2412yes—
232C11×C4⋊C4C2412yes—
233C11×C22⋊C4—24no—
234C11×C22⋊C4—24no—
235C22⋊Dic11—24no—
236C22⋊Dic11C2×D414yes—
237(C2×D11)⋊C4—24no—
238(C2×D11)⋊C4—24no—
239(C2×D11)⋊C4—24no—
240(C2×D11)⋊C4C2×D414yes—
241C4⋊Dic11—24no—
242C4⋊Dic11—24no—
243C4⋊Dic11—21no—
244C4⋊Dic11—21no—
245C4⋊Dic11—24no—
246C4⋊Dic11—21no—
247C4⋊Dic11—21no—
248C4⋊Dic11C2412yes—
249C4⋊Dic11C2412yes—
250C4⋊Dic11C2412yes—
251C4⋊Dic11C2412yes—
252Dic11⋊C4—24no—
253Dic11⋊C4—24no—
254Dic11⋊C4—24no—
255Dic11⋊C4—24no—
256Dic11⋊C4—24no—
257Dic11⋊C4C2×D414yes—
258C4×Dic11—24no—
259C4×Dic11—24no—
260C4×Dic11—24no—
261C4×Dic11—24no—
262C4×Dic11C2×D412yes—
263C4×Dic11C2412yes—
264C2×C11⋊C8—22no—
265C2×C11⋊C8—22no—
266C2×C11⋊C8C2412yes—
267C2×C11⋊C8C2412yes—
268#4313—28no—
269C2×#556—111no—
270C2×#554—111no—
271#3356—1116no—
272C2×#498—111no—
273C2×#485—111no—
274C2×#485—111no—
275C2×#483—111no—
276C2×#483—111no—
277C2×#477—111no—
278C2×#475—111no—
279C2×#470—111no—
280C2×#470D1111yescharacteristic, complemented
281C2×C4×Q16—111no—
282C2×#436—111no—
283C2×#428—111no—
284C2×#428—111no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11C22×D412yes—
289C23×C11C22×D411yescharacteristic
290C22×D11—22no—
291C22×D11—22no—
292C22×D11—22no—
293C22×D11C22×D412yes—
294Q8×C11—22no—
295Q8×C11—22no—
296Q8×C11—22no—
297Q8×C11—22no—
298Q8×C11—42no—
299Q8×C11—42no—
300C2×C4×C11—22no—
301C2×C4×C11—24no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11C22×D412yes—
313C2×C4×C11C22×D411yescharacteristic
314C2×C4×C11C2×#4112yes—
315C2×C4×C112−1+412yes—
316C2×C4×C11C2511yescharacteristic
317C22⋊D11—28no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—42no—
325C2×Dic11—42no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11—84no—
329C2×Dic11#13714yes—
330C2×Dic11C22×D412yes—
331C2×Dic11C22×D412yes—
332C2×Dic11C22×D412yes—
333C4×D11—24no—
334C4×D11—22no—
335C4×D11—22no—
336C4×D11—84no—
337Dic22—48no—
338Dic22—84no—
339C8×C11—22no—
340C8×C11C2×#4114yes—
341C11⋊C8—22no—
342C11⋊C8—22no—
343C22×Q16C2×D1111yescharacteristic
344C22×M16—111no—
345C22×M16C2×D1111yescharacteristic
346#556—118no—
347#556—224no—
348#554—118no—
349#554—224no—
350C2×C4⋊Q8—111no—
351C2×C4⋊Q8—111no—
352C2×#126—221no—
353C2×#126—221no—
354C2×#125—221no—
355C2×#124—221no—
356C2×C22⋊Q8—111no—
357C2×C22⋊Q8—111no—
358C2×C22⋊Q8—221no—
359C2×C22⋊Q8—221no—
360C2×C22⋊Q8C2×D1111yescharacteristic
361C2×C22⋊Q8C2×D1111yescharacteristic
362C2×C4×Q8—111no—
363C2×C4×Q8—111no—
364C2×C4×Q8—221no—
365C2×C4×D4—111no—
366C2×C4×D4—221no—
367C2×#117—111no—
368C2×#117—111no—
369C22×C4⋊C4—111no—
370C22×C4⋊C4—111no—
371#498—118no—
372#485—118no—
373#485—118no—
374#483—118no—
375#483—118no—
376#477—118no—
377#475—118no—
378#470—118no—
379#470C2×D1118yescomplemented
380C4×Q16—118no—
381#436—118no—
382#428—118no—
383#428—118no—
384C2×#107—111no—
385C2×#107—111no—
386C2×#107—111no—
387C2×#106—111no—
388C2×#106—111no—
389C2×#106—111no—
390C2×#106—111no—
391C2×#106—111no—
392C2×#106C2×D1111yescharacteristic
393C2×C4⋊C8—111no—
394C2×#103—111no—
395C2×#103—111no—
396C2×#103—111no—
397C2×#103—111no—
398C2×#103C2×D1111yescharacteristic
399C2×#103C2×D1111yescharacteristic
400C2×C22⋊C8—111no—
401C2×C22⋊C8—111no—
402C2×C4×C8—111no—
403C22×C11—22no—
404C22×C11—22no—
405C22×C11—22no—
406C22×C11—44no—
407C22×C11#54712yes—
408C22×C11C2×#13712yes—
409C22×C11#57712yes—
410C22×C11C23×D411yescharacteristic
411C2×D11—22no—
412C2×D11—22no—
413C2×D11—22no—
414C2×D11—44no—
415C4×C11—22no—
416C4×C11—42no—
417C4×C11—42no—
418C4×C11—42no—
419C4×C11—42no—
420C4×C11#54712yes—
421C4×C11C22×#4111yescharacteristic
422C4×C11C2×2−1+411yescharacteristic
423Dic11—22no—
424Dic11—22no—
425Dic11—42no—
426Dic11—42no—
427Dic11—42no—
428Dic11—42no—
429Dic11C2×#13714yes—
430C22×Q8—221no—
431C22×Q8—221no—
432C22×Q8C22×D1111yescharacteristic
433C22×Q8C22×D1111yescharacteristic
434C22×D4—111no—
435C23×C4—111no—
436C23×C4—221no—
437C23×C4—221no—
438C23×C4C22×D1111yescharacteristic
439C2×Q16—24no—
440C2×Q16C22×D1114yes—
441C2×M16—24no—
442C2×M16—114no—
443C2×M16—224no—
444C2×M16C22×D1114yes—
445C22×C8—111no—
446C22×C8—111no—
447C22×C8C22×D1111yescharacteristic
448C22×C8C22×D1111yescharacteristic
449C4⋊Q8—114no—
450C4⋊Q8—114no—
451C4⋊Q8—222no—
452C4⋊Q8—222no—
453#126—228no—
454#126—228no—
455#125—228no—
456#124—228no—
457C22⋊Q8—22no—
458C22⋊Q8—22no—
459C22⋊Q8—114no—
460C22⋊Q8—114no—
461C22⋊Q8—228no—
462C22⋊Q8—228no—
463C22⋊Q8—222no—
464C22⋊Q8—222no—
465C22⋊Q8C22×D1114yes—
466C22⋊Q8C22×D1114yes—
467C4×Q8—114no—
468C4×Q8—114no—
469C4×Q8—222no—
470C4×Q8—222no—
471C4×Q8—228no—
472C4×D4—114no—
473C4×D4—114no—
474C4×D4—228no—
475#117—114no—
476#117—114no—
477#117—222no—
478#117—222no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—111no—
482C2×C4⋊C4—111no—
483C2×C4⋊C4—111no—
484C2×C4⋊C4—114no—
485C2×C4⋊C4—111no—
486C2×C4⋊C4—111no—
487C2×C4⋊C4—114no—
488C2×C4⋊C4—222no—
489C2×C4⋊C4—221no—
490C2×C4⋊C4—221no—
491C2×C4⋊C4—221no—
492C2×C4⋊C4—221no—
493C2×C4⋊C4—221no—
494C2×C4⋊C4—221no—
495C2×C4⋊C4—221no—
496C2×C4⋊C4—221no—
497C2×C4⋊C4—222no—
498C2×C4⋊C4C22×D1111yescharacteristic
499C2×C4⋊C4C22×D1111yescharacteristic
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—111no—
503C2×C22⋊C4—111no—
504C2×C22⋊C4—221no—
505C2×C22⋊C4—221no—
506C2×C22⋊C4—221no—
507C2×C22⋊C4—221no—
508C2×C42—111no—
509C2×C42—221no—
510C2×C42—221no—
511C2×C42—221no—
512C2×C42—221no—
513#107—114no—
514#107—114no—
515#107—114no—
516#106—114no—
517#106—114no—
518#106—114no—
519#106—114no—
520#106—114no—
521#106C22×D1114yes—
522C4⋊C8—114no—
523#103—114no—
524#103—114no—
525#103—114no—
526#103—114no—
527#103C22×D1114yes—
528#103C22×D1114yes—
529C22⋊C8—114no—
530C22⋊C8—114no—
531C4×C8—114no—
532C2×C11—42no—
533C2×C11#335614yescomplemented
534C2×C11C2×#54711yescharacteristic
535C2×C11C22×#13711yescharacteristic
536C2×C11C2×#57711yescharacteristic
537D11—42no—
538C24—111no—
539C24D4×D1111yescharacteristic
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—224no—
547C2×Q8—224no—
548C2×Q8—444no—
549C2×Q8—882no—
550C2×Q8C23×D1112yes—
551C2×Q8C23×D1112yes—
552C2×D4—114no—
553C2×D4—224no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—111no—
561C22×C4—111no—
562C22×C4—111no—
563C22×C4—112no—
564C22×C4—112no—
565C22×C4—224no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—221no—
571C22×C4—221no—
572C22×C4—224no—
573C22×C4—882no—
574C22×C4—882no—
575C22×C4D4×D1112yes—
576C22×C4D4×D1111yescharacteristic
577C22×C4C23×D1112yes—
578C22×C4C23×D1111yescharacteristic
579Q16—28no—
580M16—28no—
581M16—228no—
582C2×C8—22no—
583C2×C8—112no—
584C2×C8—112no—
585C2×C8—222no—
586C2×C8—222no—
587C2×C8#434114yes—
588C2×C8C23×D1112yes—
589C2×C8C23×D1112yes—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—114no—
595C4⋊C4—112no—
596C4⋊C4—112no—
597C4⋊C4—112no—
598C4⋊C4—112no—
599C4⋊C4—224no—
600C4⋊C4—224no—
601C4⋊C4—224no—
602C4⋊C4—224no—
603C4⋊C4—224no—
604C4⋊C4—224no—
605C4⋊C4—224no—
606C4⋊C4—221no—
607C4⋊C4—224no—
608C4⋊C4—221no—
609C4⋊C4—221no—
610C4⋊C4—221no—
611C4⋊C4C23×D1112yes—
612C4⋊C4C23×D1112yes—
613C22⋊C4—24no—
614C22⋊C4—24no—
615C22⋊C4—114no—
616C22⋊C4—114no—
617C22⋊C4—224no—
618C22⋊C4—224no—
619C22⋊C4—224no—
620C22⋊C4—224no—
621C42—112no—
622C42—112no—
623C42—224no—
624C42—224no—
625C42—224no—
626C42—224no—
627C11C2×#335611yescharacteristic, complemented, Sylow
628C23—22no—
629C23—22no—
630C23—22no—
631C23—112no—
632C23—222no—
633C23—222no—
634C23—222no—
635C23C2×D4×D1112yes—
636C23C2×D4×D1111yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—22no—
640Q8—22no—
641Q8—42no—
642Q8—42no—
643Q8—448no—
644Q8—884no—
645D4—228no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—114no—
659C2×C4—112no—
660C2×C4—112no—
661C2×C4—112no—
662C2×C4—222no—
663C2×C4—222no—
664C2×C4—224no—
665C2×C4—222no—
666C2×C4—222no—
667C2×C4—222no—
668C2×C4—222no—
669C2×C4—222no—
670C2×C4—222no—
671C2×C4—442no—
672C2×C4—442no—
673C2×C4—442no—
674C2×C4—442no—
675C2×C4—884no—
676C2×C4—884no—
677C2×C4C2×D4×D1112yes—
678C2×C4C2×D4×D1111yescharacteristic
679C2×C4C2×#434112yes—
680C2×C4#6704312yes—
681C2×C4C24×D1111yescharacteristic
682C8—22no—
683C8—222no—
684C8—222no—
685C8C2×#434114yes—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—44no—
690C22—222no—
691C22—222no—
692C22—222no—
693C22—444no—
694C22#1062314212yes—
695C22D11×#13712yes—
696C22#1062330912yes—
697C22C22×D4×D1111yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—114no—
704C4—222no—
705C4—222no—
706C4—442no—
707C4—442no—
708C4—442no—
709C4—442no—
710C4#1062314212yes—
711C4C22×#434111yescharacteristic
712C4C2×#6704311yescharacteristic
713C2—42no—
714C2—442no—
715C2#1308122614yesdirect product factor
716C2C2×#1062314211yescharacteristic
717C2C2×D11×#13711yescharacteristic
718C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#470C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
hypercenterC2×#470D11
hypocenterC11C2×#3356
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
3. #13081226C2direct (N × H)
4. C2×#10622468C2semidirect
5. C2×#10622427C2semidirect
6. C2×#10622658C2semidirect
7. C2×#10622418C2semidirect
8. C2×#10622656C2semidirect
9. C2×#10622407C2semidirect
10. C2×#10622404C2semidirect
11. C2×#10622802C2semidirect
12. C2×Q16×Dic11C2semidirect
14. C2×#10622734C2semidirect
15. C2×#10622474C2semidirect
16. C2×C11×#470C2semidirect
45. C11×#470C22semidirect
54. #10622802C22semidirect
55. Q16×Dic11C22semidirect
57. #10622734C22semidirect
65. #10622658C22semidirect
66. #10622656C22semidirect
71. #10622474C22semidirect
72. #10622468C22semidirect
73. #10622427C22semidirect
74. #10622418C22semidirect
75. #10622407C22semidirect
76. #10622404C22semidirect
280. C2×#470D11semidirect
379. #470C2×D11semidirect
533. C2×C11#3356semidirect
627. C11C2×#3356semidirect
715. C2#13081226direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231722
C2×#106231662
#130812262
C2×#106224682
C2×#106224272
C2×#106226582
C2×#106224182
C2×#106226562
C2×#106224072
C2×#106224042
C2×#106228022
C2×Q16×Dic112
C2×#106227412
C2×#106227342
C2×#106224742
C2×C11×#4702
C2×#335611