Finite Group Databasebeta

← C2×#13081570 #15634310

Subgroups — C2×#13081570 #15634310

Order 2816.

1898 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623110C211yesmaximal, characteristic, complemented
2#13081570C2116yesmaximal, direct product factor
3C2×#10622678C211yesmaximal, characteristic, complemented
4C2×#10622693C211yesmaximal, characteristic, complemented
5C2×#10622677C211yesmaximal, characteristic, complemented
6C2×#10622622C211yesmaximal, characteristic, complemented
7C2×#10622622C211yesmaximal, characteristic, complemented
8C2×#10622679C211yesmaximal, characteristic, complemented
9C2×#10622679C211yesmaximal, characteristic, complemented
10C2×#10622620C211yesmaximal, characteristic, complemented
11C2×#10622700C211yesmaximal, characteristic, complemented
12C2×#10622637C211yesmaximal, characteristic, complemented
13C2×#10622627C211yesmaximal, characteristic
14C2×#10622627C211yesmaximal, characteristic
15C2×C4×#4323C211yesmaximal, characteristic
16C2×C11×#554C211yesmaximal, characteristic, complemented
17C11×#554—24no—
18C11×#554C2218yescomplemented
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C11×#125C2211yescharacteristic
21C2×C11×#125C2211yescharacteristic
22C2×C11×C22⋊Q8—21no—
23C2×C11×C22⋊Q8—21no—
24C2×C11×C22⋊Q8—21no—
25C2×C4×Q8×C11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C22×C11×C4⋊C4—21no—
30C2×#66999—21no—
31C22×#4323C2211yescharacteristic
32#10623110—24no—
33#10623110C2218yescomplemented
34C2×#66949—21no—
35C2×#66949—21no—
36C2×C4⋊C4×D11—21no—
37C2×C4×D44C2211yescharacteristic
38C2×C4×D44C2211yescharacteristic
39C2×C4×D44C2211yescharacteristic
40C2×#66923C2211yescharacteristic
41C2×#66923C2211yescharacteristic
42C2×#66922C2211yescharacteristic
43C2×#66896C2211yescharacteristic
44C2×#66896C2211yescharacteristic
45C2×#66896C2211yescharacteristic
46#10622700C2218yescomplemented
47#10622693C2218yescomplemented
48#10622679C2218yescomplemented
49#10622679C2218yescomplemented
50#10622678C2218yescomplemented
51#10622677C2218yescomplemented
52#10622637C2218yescomplemented
53#10622627C2218yes—
54#10622627C2218yes—
55C4×#4323C2218yes—
56#10622622C2218yescomplemented
57#10622622C2218yescomplemented
58#10622620C2218yescomplemented
59C2×#66873C2211yescharacteristic
60C2×#66873C2211yescharacteristic
61C2×#66873C2211yescharacteristic
62C2×#66872C2211yescharacteristic
63C2×#66872C2211yescharacteristic
64C2×#66872C2211yescharacteristic
65C2×#66872C2211yescharacteristic
66C2×#66871C2211yescharacteristic
67C2×#66871C2211yescharacteristic
68C2×#66871C2211yescharacteristic
69C2×#66871C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71C2×C4⋊(C11⋊C8)C2211yescharacteristic
72C2×C4⋊(C11⋊C8)C2211yescharacteristic
73C2×C4⋊(C11⋊C8)C2211yescharacteristic
74C2×#66867C2211yescharacteristic
75C2×#66867C2211yescharacteristic
76C2×C4×C11⋊C8C2211yescharacteristic
77C22×Q8×C11—21no—
78C22×Q8×C11D411yescharacteristic
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11—21no—
81C23×C4×C11—21no—
82C23×C4×C11—21no—
83C22×D44C2311yescharacteristic
84C22×C4×D11—21no—
85C22×C4×D11—21no—
86C22×C4×D11—21no—
87C22×Dic22—21no—
88C11×C4⋊Q8—22no—
89C11×C4⋊Q8C2314yes—
90C11×#125—22no—
91C11×#125—22no—
92C11×#125C2314yes—
93C11×#125C2314yes—
94C11×C22⋊Q8—28no—
95C11×C22⋊Q8—28no—
96C11×C22⋊Q8—28no—
97C4×Q8×C11D414yes—
98C4×Q8×C11C2314yes—
99C4×D4×C11—22no—
100C4×D4×C11—22no—
101C4×D4×C11—22no—
102C4×D4×C11C2314yes—
103C4×D4×C11C2314yes—
104C4×D4×C11C2314yes—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4—28no—
111C2×C11×C4⋊C4D411yescharacteristic
112C2×C11×C4⋊C4D411yescharacteristic
113C2×C11×C4⋊C4D411yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C42×C11C2311yescharacteristic
121C2×C42×C11C2311yescharacteristic
122C2×C42×C11C2311yescharacteristic
123#66999—28no—
124C2×#4323Q818yescomplemented
125C2×#4323C2314yes—
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4—21no—
128C2×(C2×D11)⋊C4—21no—
129C2×C4⋊Dic11—21no—
130C2×C4⋊Dic11C2311yescharacteristic
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2311yescharacteristic
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4—21no—
136C2×Dic11⋊C4—21no—
137C22×C11⋊C8C2311yescharacteristic
138C22×C11⋊C8C2311yescharacteristic
139C22×C11⋊C8C2311yescharacteristic
140C22×C11⋊C8C2311yescharacteristic
141#66949—28no—
142#66949—28no—
143C4⋊C4×D11—28no—
144C4×D44—22no—
145C4×D44—22no—
146C4×D44—22no—
147C4×D44C2314yes—
148C4×D44C2314yes—
149C4×D44C2314yes—
150#66923—22no—
151#66923—22no—
152#66923C2314yes—
153#66923C2314yes—
154#66922—22no—
155#66922C2314yes—
156#66896C2314yes—
157#66896C2314yes—
158#66896C2314yes—
159#66873C2314yes—
160#66873C2314yes—
161#66873C2314yes—
162#66872C2314yes—
163#66872C2314yes—
164#66872C2314yes—
165#66872C2314yes—
166#66871C2314yes—
167#66871C2314yes—
168#66871C2314yes—
169#66871C2314yes—
170#66871C2314yes—
171C4⋊(C11⋊C8)C2314yes—
172C4⋊(C11⋊C8)C2314yes—
173C4⋊(C11⋊C8)C2314yes—
174#66867C2314yes—
175#66867C2314yes—
176C4×C11⋊C8C2314yes—
177C2×#3389—111nomaximal, Sylow
178C24×C11—21no—
179C23×D11—21no—
180C2×Q8×C11—24no—
181C2×Q8×C11—42no—
182C2×Q8×C11—82no—
183C2×Q8×C11C2×D414yes—
184C2×D4×C11—21no—
185C2×D4×C11—22no—
186C2×D4×C11C2×Q814yes—
187C2×D4×C11C2412yes—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—24no—
192C22×C4×C11—24no—
193C22×C4×C11—24no—
194C22×C4×C11—44no—
195C22×C4×C11—82no—
196C22×C4×C11—82no—
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2411yescharacteristic
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C2×D44—21no—
208C2×D44—22no—
209C2×D44C2×Q814yes—
210C2×D44C2412yes—
211C2×C4×D11—24no—
212C2×C4×D11—24no—
213C2×C4×D11—24no—
214C2×C4×D11—44no—
215C2×C4×D11—82no—
216C2×C4×D11—82no—
217C2×Dic22—24no—
218C2×Dic22—82no—
219C11×C4⋊C4—24no—
220C11×C4⋊C4—24no—
221C11×C4⋊C4—24no—
222C11×C4⋊C4—24no—
223C11×C4⋊C4—24no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—21no—
227C11×C4⋊C4C2×D414yes—
228C11×C4⋊C4C2×D414yes—
229C11×C4⋊C4C2×D414yes—
230C11×C4⋊C4C2412yes—
231C11×C4⋊C4C2412yes—
232C11×C4⋊C4C2412yes—
233C11×C22⋊C4—24no—
234C11×C22⋊C4—24no—
235C11×C22⋊C4—24no—
236C42×C11C2×D412yes—
237C42×C11C2×D412yes—
238C42×C11C2×D412yes—
239C42×C11C2412yes—
240C42×C11C2412yes—
241C42×C11C2412yes—
242#4323C2×Q8116yescomplemented
243(C2×D11)⋊C4—24no—
244(C2×D11)⋊C4—24no—
245(C2×D11)⋊C4—24no—
246C4⋊Dic11—21no—
247C4⋊Dic11—21no—
248C4⋊Dic11—24no—
249C4⋊Dic11—21no—
250C4⋊Dic11C2412yes—
251C4⋊Dic11C2412yes—
252C4⋊Dic11C2412yes—
253Dic11⋊C4—24no—
254Dic11⋊C4—24no—
255Dic11⋊C4—24no—
256Dic11⋊C4—24no—
257C2×C11⋊C8—22no—
258C2×C11⋊C8—22no—
259C2×C11⋊C8—22no—
260C2×C11⋊C8C2×Q814yes—
261C2×C11⋊C8C2412yes—
262C2×C11⋊C8C2412yes—
263C2×C11⋊C8C2412yes—
264C2×C11⋊C8C2412yes—
265C2×#554—111no—
266C2×#554D1111yescharacteristic, complemented
267#3389—1116no—
268C2×#501—111no—
269C2×#501—111no—
270C2×#499—111no—
271C2×#478—111no—
272C2×#478—111no—
273C2×#478—111no—
274C2×#478—111no—
275C2×#474—111no—
276C2×#474—111no—
277C2×#446—111no—
278C2×#442—111no—
279C2×#442—111no—
280C2×C4×D8—111no—
281C23×C11—24no—
282C23×C11—22no—
283C23×C11—42no—
284C23×C11—42no—
285C23×C11C22×D411yescharacteristic
286C22×D11—24no—
287C22×D11—22no—
288C22×D11—42no—
289C22×D11—42no—
290Q8×C11—44no—
291Q8×C11—84no—
292D4×C11—24no—
293D4×C11—22no—
294D4×C11C22×Q814yes—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—48no—
305C2×C4×C11—42no—
306C2×C4×C11—42no—
307C2×C4×C11—42no—
308C2×C4×C11—84no—
309C2×C4×C11—84no—
310C2×C4×C11C22×D412yes—
311C2×C4×C11C22×D412yes—
312C2×C4×C11C22×D412yes—
313C2×C4×C11C22×D412yes—
314C2×C4×C11C22×D412yes—
315C2×C4×C11C22×D412yes—
316C2×C4×C11C22×D411yescharacteristic
317C2×C4×C11C22×Q812yes—
318C2×C4×C112−1+412yes—
319C2×C4×C11C2511yescharacteristic
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—42no—
324C2×Dic11—42no—
325C2×Dic11—42no—
326D44—24no—
327D44—22no—
328D44C22×Q814yes—
329C4×D11—48no—
330C4×D11—84no—
331C4×D11—84no—
332Dic22—84no—
333C11⋊C8—22no—
334C11⋊C8—22no—
335C11⋊C8—22no—
336C11⋊C8C22×Q814yes—
337C22×D8—111no—
338#554—24no—
339#554—118no—
340#554—224no—
341#554C2×D1118yescomplemented
342C2×C4⋊Q8—111no—
343C2×C4⋊Q8C2×D1111yescharacteristic
344C2×#125—111no—
345C2×#125—111no—
346C2×#125C2×D1111yescharacteristic
347C2×#125C2×D1111yescharacteristic
348C2×C22⋊Q8—21no—
349C2×C22⋊Q8—21no—
350C2×C22⋊Q8—21no—
351C2×C22⋊Q8—221no—
352C2×C22⋊Q8—221no—
353C2×C22⋊Q8—221no—
354C2×C4×Q8C2×D1111yescharacteristic
355C2×C4×D4—111no—
356C2×C4×D4—111no—
357C2×C4×D4—111no—
358C2×C4×D4C2×D1111yescharacteristic
359C2×C4×D4C2×D1111yescharacteristic
360C2×C4×D4C2×D1111yescharacteristic
361C22×C4⋊C4—21no—
362C22×C4⋊C4—221no—
363#501—118no—
364#501—118no—
365#499—118no—
366#478—118no—
367#478—118no—
368#478—118no—
369#478—118no—
370#474—118no—
371#474—118no—
372#446—118no—
373#442—118no—
374#442—118no—
375C4×D8—118no—
376C2×#107—111no—
377C2×#107—111no—
378C2×#107—111no—
379C2×#107—111no—
380C2×#107—111no—
381C2×#106—111no—
382C2×#106—111no—
383C2×#106—111no—
384C2×#106—111no—
385C2×C4⋊C8—111no—
386C2×C4⋊C8—111no—
387C2×C4⋊C8—111no—
388C2×#102—111no—
389C2×#102—111no—
390C2×#102—111no—
391C2×#102—111no—
392C2×#102—111no—
393C2×#102—111no—
394C2×#97—111no—
395C2×#97—111no—
396C2×C4×C8—111no—
397C22×C11—24no—
398C22×C11—48no—
399C22×C11—42no—
400C22×C11—42no—
401C22×C11D4×Q812yes—
402C22×C11#57512yes—
403C22×C11#57612yes—
404C22×C11C23×D411yescharacteristic
405C2×D11—24no—
406C2×D11—48no—
407C2×D11—42no—
408C2×D11—42no—
409C4×C11—22no—
410C4×C11—22no—
411C4×C11—22no—
412C4×C11—22no—
413C4×C11—22no—
414C4×C11—22no—
415C4×C11—42no—
416C4×C11—42no—
417C4×C11—42no—
418C4×C11D4×Q812yes—
419C4×C11C23×Q811yescharacteristic
420C4×C11C2×2−1+411yescharacteristic
421Dic11—42no—
422Dic11—42no—
423Dic11—42no—
424C22×Q8—21no—
425C22×Q8—221no—
426C22×Q8C22⋊D1111yescharacteristic
427C22×D4—111no—
428C22×D4C22×D1111yescharacteristic
429C23×C4—21no—
430C23×C4—21no—
431C23×C4—21no—
432C23×C4—221no—
433C23×C4—221no—
434C23×C4—221no—
435C2×D8—118no—
436C2×D8—114no—
437C22×C8—111no—
438C22×C8—111no—
439C22×C8—111no—
440C22×C8—111no—
441C4⋊Q8—22no—
442C4⋊Q8—114no—
443C4⋊Q8—222no—
444C4⋊Q8C22×D1114yes—
445#125—22no—
446#125—22no—
447#125—114no—
448#125—114no—
449#125—222no—
450#125—222no—
451#125C22×D1114yes—
452#125C22×D1114yes—
453C22⋊Q8—28no—
454C22⋊Q8—28no—
455C22⋊Q8—28no—
456C22⋊Q8—228no—
457C22⋊Q8—228no—
458C22⋊Q8—228no—
459C4×Q8C22⋊D1114yes—
460C4×Q8C22×D1114yes—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—22no—
464C4×D4—114no—
465C4×D4—114no—
466C4×D4—114no—
467C4×D4—222no—
468C4×D4—222no—
469C4×D4—222no—
470C4×D4C22×D1114yes—
471C4×D4C22×D1114yes—
472C4×D4C22×D1114yes—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—28no—
479C2×C4⋊C4—111no—
480C2×C4⋊C4—111no—
481C2×C4⋊C4—111no—
482C2×C4⋊C4—221no—
483C2×C4⋊C4—221no—
484C2×C4⋊C4—221no—
485C2×C4⋊C4—221no—
486C2×C4⋊C4—221no—
487C2×C4⋊C4—228no—
488C2×C4⋊C4C22⋊D1111yescharacteristic
489C2×C4⋊C4C22⋊D1111yescharacteristic
490C2×C4⋊C4C22⋊D1111yescharacteristic
491C2×C4⋊C4C22×D1111yescharacteristic
492C2×C4⋊C4C22×D1111yescharacteristic
493C2×C4⋊C4C22×D1111yescharacteristic
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—221no—
498C2×C22⋊C4—221no—
499C2×C22⋊C4—221no—
500C2×C42C22×D1111yescharacteristic
501C2×C42C22×D1111yescharacteristic
502C2×C42C22×D1111yescharacteristic
503#107—114no—
504#107—114no—
505#107—114no—
506#107—114no—
507#107—114no—
508#106—114no—
509#106—114no—
510#106—114no—
511#106—114no—
512C4⋊C8—114no—
513C4⋊C8—114no—
514C4⋊C8—114no—
515#102—114no—
516#102—114no—
517#102—114no—
518#102—114no—
519#102—114no—
520#102—114no—
521#97—114no—
522#97—114no—
523C4×C8—114no—
524C2×C11—44no—
525C2×C11#338914yescomplemented
526C2×C11C2×D4×Q811yescharacteristic
527C2×C11C2×#57511yescharacteristic
528C2×C11C2×#57611yescharacteristic
529D11—44no—
530C24—21no—
531C24—221no—
532C2×Q8—24no—
533C2×Q8—42no—
534C2×Q8—82no—
535C2×Q8—224no—
536C2×Q8—882no—
537C2×Q8C2×C22⋊D1114yes—
538C2×D4—22no—
539C2×D4—21no—
540C2×D4—114no—
541C2×D4—112no—
542C2×D4—222no—
543C2×D4—221no—
544C2×D4Q8×D1114yes—
545C2×D4C23×D1112yes—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—44no—
553C22×C4—82no—
554C22×C4—82no—
555C22×C4—221no—
556C22×C4—221no—
557C22×C4—221no—
558C22×C4—224no—
559C22×C4—224no—
560C22×C4—224no—
561C22×C4—444no—
562C22×C4—882no—
563C22×C4—882no—
564C22×C4C2×C22⋊D1111yescharacteristic
565C22×C4C2×C22⋊D1111yescharacteristic
566C22×C4C2×C22⋊D1111yescharacteristic
567C22×C4C2×C22⋊D1111yescharacteristic
568C22×C4C2×C22⋊D1111yescharacteristic
569C22×C4C2×C22⋊D1111yescharacteristic
570C22×C4C23×D1111yescharacteristic
571D8—1116no—
572C2×C8—114no—
573C2×C8—112no—
574C2×C8—112no—
575C2×C8—112no—
576C2×C8—112no—
577C2×C8—222no—
578C2×C8—222no—
579C2×C8—222no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—112no—
589C4⋊C4—112no—
590C4⋊C4—112no—
591C4⋊C4—221no—
592C4⋊C4—221no—
593C4⋊C4—221no—
594C4⋊C4—224no—
595C4⋊C4—224no—
596C4⋊C4—224no—
597C4⋊C4—224no—
598C4⋊C4—224no—
599C4⋊C4C2×C22⋊D1114yes—
600C4⋊C4C2×C22⋊D1114yes—
601C4⋊C4C2×C22⋊D1114yes—
602C4⋊C4C23×D1112yes—
603C4⋊C4C23×D1112yes—
604C4⋊C4C23×D1112yes—
605C22⋊C4—24no—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—224no—
609C22⋊C4—224no—
610C22⋊C4—224no—
611C42C2×C22⋊D1112yes—
612C42C2×C22⋊D1112yes—
613C42C2×C22⋊D1112yes—
614C42C23×D1112yes—
615C42C23×D1112yes—
616C42C23×D1112yes—
617C11C2×#338911yescharacteristic, complemented, Sylow
618C23—24no—
619C23—22no—
620C23—42no—
621C23—42no—
622C23—224no—
623C23—222no—
624C23—442no—
625C23—442no—
626C23C22×C22⋊D1111yescharacteristic
627Q8—44no—
628Q8—84no—
629Q8—884no—
630D4—24no—
631D4—22no—
632D4—114no—
633D4—224no—
634D4—222no—
635D4C2×Q8×D1114yes—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—48no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—84no—
650C2×C4—84no—
651C2×C4—222no—
652C2×C4—222no—
653C2×C4—222no—
654C2×C4—448no—
655C2×C4—442no—
656C2×C4—442no—
657C2×C4—442no—
658C2×C4—884no—
659C2×C4—884no—
660C2×C4C2×Q8×D1112yes—
661C2×C4#6704012yes—
662C2×C4C22×C22⋊D1112yes—
663C2×C4C22×C22⋊D1112yes—
664C2×C4C22×C22⋊D1112yes—
665C2×C4C22×C22⋊D1112yes—
666C2×C4C22×C22⋊D1112yes—
667C2×C4C22×C22⋊D1112yes—
668C2×C4C22×C22⋊D1111yescharacteristic
669C2×C4C24×D1111yescharacteristic
670C8—114no—
671C8—222no—
672C8—222no—
673C8—222no—
674C22—24no—
675C22—42no—
676C22—48no—
677C22—42no—
678C22—224no—
679C22—442no—
680C22—448no—
681C22—442no—
682C22Q8×C22⋊D1112yes—
683C22#1062335312yes—
684C22#1062336612yes—
685C22C23×C22⋊D1111yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—22no—
691C4—22no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—442no—
696C4—442no—
697C4—442no—
698C4Q8×C22⋊D1112yes—
699C4C22×Q8×D1111yescharacteristic
700C4C2×#6704011yescharacteristic
701C2—44no—
702C2—444no—
703C2#1308157014yesdirect product factor
704C2C2×Q8×C22⋊D1111yescharacteristic
705C2C2×#1062335311yescharacteristic
706C2C2×#1062336611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#554C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenterC2×#554D11
hypocenterC11C2×#3389
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#10623110C2semidirect
2. #13081570C2direct (N × H)
3. C2×#10622678C2semidirect
4. C2×#10622693C2semidirect
5. C2×#10622677C2semidirect
6. C2×#10622622C2semidirect
7. C2×#10622622C2semidirect
8. C2×#10622679C2semidirect
9. C2×#10622679C2semidirect
10. C2×#10622620C2semidirect
11. C2×#10622700C2semidirect
12. C2×#10622637C2semidirect
16. C2×C11×#554C2semidirect
18. C11×#554C22semidirect
33. #10623110C22semidirect
46. #10622700C22semidirect
47. #10622693C22semidirect
48. #10622679C22semidirect
49. #10622679C22semidirect
50. #10622678C22semidirect
51. #10622677C22semidirect
52. #10622637C22semidirect
56. #10622622C22semidirect
57. #10622622C22semidirect
58. #10622620C22semidirect
124. C2×#4323Q8semidirect
242. #4323C2×Q8semidirect
266. C2×#554D11semidirect
341. #554C2×D11semidirect
525. C2×C11#3389semidirect
617. C11C2×#3389semidirect
703. C2#13081570direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231102
#130815702
C2×#106226782
C2×#106226932
C2×#106226772
C2×#106226222
C2×#106226792
C2×#106226202
C2×#106227002
C2×#106226372
C2×#106226272
C2×C4×#43232
C2×C11×#5542
C2×#338911