Finite Group Databasebeta

← C2×#13081086 #15632336

Subgroups — C2×#13081086 #15632336

Order 2816.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623096C211yesmaximal, characteristic, complemented
2#13081086C2116yesmaximal, direct product factor
3C2×#10622693C211yesmaximal, characteristic, complemented
4C2×#10622581C211yesmaximal, characteristic, complemented
5C2×#10622647C211yesmaximal, characteristic, complemented
6C2×#10622648C211yesmaximal, characteristic, complemented
7C2×#10622580C211yesmaximal, characteristic, complemented
8C2×#10622622C211yesmaximal, characteristic, complemented
9C2×#10622697C211yesmaximal, characteristic, complemented
10C2×#10622652C211yesmaximal, characteristic, complemented
11C2×#10622651C211yesmaximal, characteristic, complemented
12C2×#10622627C211yesmaximal, characteristic, complemented
13C2×#10622624C211yesmaximal, characteristic, complemented
14C2×#10622577C211yesmaximal, characteristic, complemented
15C22×#66872C211yesmaximal, characteristic, complemented
16C2×C11×#547C211yesmaximal, characteristic, complemented
17C22×C11×#41—21no—
18C11×#547—24no—
19C11×#547C2218yescomplemented
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×#123—21no—
22C2×C11×#123—21no—
23C2×C11×C22⋊Q8—21no—
24C2×C11×#121C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C22×C11×C4⋊C4C2211yescharacteristic
30C2×#66992—21no—
31C22×#4323C2211yescharacteristic
32C2×#66983C2211yescharacteristic
33C2×#66983C2211yescharacteristic
34C2×#66979C2211yescharacteristic
35C22×C4⋊Dic11C2211yescharacteristic
36C22×#4318C2211yescharacteristic
37C23×C11⋊C8C2211yescharacteristic
38#10623096—24no—
39#10623096C2218yescomplemented
40C2×#66951—21no—
41C2×#66936—21no—
42C2×(C22⋊D11)⋊C4—21no—
43C2×C4×D44C2211yescharacteristic
44C2×#66923C2211yescharacteristic
45C2×#66896C2211yescharacteristic
46C2×#66896C2211yescharacteristic
47C2×#66896C2211yescharacteristic
48C2×C22⋊(C11⋊C8)C2211yescharacteristic
49C2×C22⋊(C11⋊C8)C2211yescharacteristic
50#10622697C2218yescomplemented
51#10622693C2218yescomplemented
52#10622652C2218yescomplemented
53#10622651C2218yescomplemented
54#10622648C2218yescomplemented
55#10622647C2218yescomplemented
56#10622627C2218yescomplemented
57#10622624C2218yescomplemented
58#10622622C2218yescomplemented
59#10622581C2218yescomplemented
60#10622580C2218yescomplemented
61C2×#66873C2211yescharacteristic
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64#10622577C2218yescomplemented
65C2×#66872C2211yescharacteristic
66C2×#66872C2211yescharacteristic
67C2×#66872C2211yescharacteristic
68C2×#66872C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66872C2211yescharacteristic
71C2×#66872C2218yescomplemented
72C2×#66871C2211yescharacteristic
73C2×#66871C2211yescharacteristic
74C2×#66871C2211yescharacteristic
75C2×C4⋊(C11⋊C8)C2211yescharacteristic
76C2×#66867C2211yescharacteristic
77C2×C11×#41—28no—
78C2×C11×#41—48no—
79C22×Q8×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11—21no—
82C22×D4×C11D411yescharacteristic
83C22×D4×C11C2311yescharacteristic
84C23×C4×C11—21no—
85C23×C4×C11—21no—
86C23×C4×C11—21no—
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C22×C22⋊D11—21no—
90C22×C22⋊D11—21no—
91C23×Dic11—21no—
92C22×D44C2311yescharacteristic
93C22×C4×D11—21no—
94C11×C4⋊Q8—22no—
95C11×C4⋊Q8C2314yes—
96C11×#123—28no—
97C11×#123—28no—
98C11×C22⋊Q8—28no—
99C11×#121—22no—
100C11×#121—22no—
101C11×#121C2314yes—
102C11×#121C2314yes—
103C4×D4×C11—22no—
104C4×D4×C11D414yes—
105C4×D4×C11C2314yes—
106C4×D4×C11C2314yes—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4—22no—
110C2×C11×C4⋊C4—22no—
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4D411yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2314yes—
117C2×C11×C4⋊C4C2314yes—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4D411yescharacteristic
122C2×C11×C22⋊C4D411yescharacteristic
123C2×C42×C11C2311yescharacteristic
124C2×C22⋊Dic11—21no—
125#66992—28no—
126C2×#4323—24no—
127C2×#4323C2314yes—
128#66983—22no—
129#66983—22no—
130#66983C2314yes—
131#66983C2314yes—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—21no—
134C2×(C2×D11)⋊C4—21no—
135#66979—22no—
136#66979C2314yes—
137C2×C4⋊Dic11—21no—
138C2×C4⋊Dic11—22no—
139C2×C4⋊Dic11C2311yescharacteristic
140C2×C4⋊Dic11C2311yescharacteristic
141C2×C4⋊Dic11C2311yescharacteristic
142C2×C4⋊Dic11C2314yes—
143C2×Dic11⋊C4—21no—
144C2×Dic11⋊C4—21no—
145C2×C4×Dic11—21no—
146C2×#4318—24no—
147C2×#4318C2314yes—
148C22×C11⋊C8—24no—
149C22×C11⋊C8C2311yescharacteristic
150C22×C11⋊C8C2311yescharacteristic
151C22×C11⋊C8C2311yescharacteristic
152C22×C11⋊C8C2314yes—
153C22×C11⋊C8C2311yescharacteristic
154#66951—28no—
155#66936—28no—
156(C22⋊D11)⋊C4—28no—
157C4×D44—22no—
158C4×D44C2314yes—
159#66923—22no—
160#66923C2314yes—
161#66896C2314yes—
162#66896C2314yes—
163#66896C2314yes—
164C22⋊(C11⋊C8)C2314yes—
165C22⋊(C11⋊C8)C2314yes—
166#66873C2314yes—
167#66873C2314yes—
168#66873C2314yes—
169#66872C2314yes—
170#66872C2314yes—
171#66872C2314yes—
172#66872C2314yes—
173#66872C2314yes—
174#66872C2314yes—
175#66871C2314yes—
176#66871C2314yes—
177#66871C2314yes—
178C4⋊(C11⋊C8)C2314yes—
179#66867C2314yes—
180C2×#3345—111nomaximal, Sylow
181C24×C11—21no—
182C24×C11C2×D411yescharacteristic
183C24×C11C2×D411yescharacteristic
184C23×D11—21no—
185C11×#41—432no—
186C2×Q8×C11—24no—
187C2×Q8×C11—44no—
188C2×D4×C11—24no—
189C2×D4×C11—24no—
190C2×D4×C11—24no—
191C2×D4×C11—21no—
192C2×D4×C11—22no—
193C2×D4×C11—22no—
194C2×D4×C11—44no—
195C2×D4×C11—44no—
196C2×D4×C11C2×D414yes—
197C2×D4×C11C2412yes—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—24no—
206C22×C4×C11—24no—
207C22×C4×C11—24no—
208C22×C4×C11—44no—
209C22×C4×C11—44no—
210C22×C4×C11—44no—
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D412yes—
216C22×C4×C11C2×D412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2411yescharacteristic
220C2×C22⋊D11—24no—
221C2×C22⋊D11—24no—
222C2×C22⋊D11—44no—
223C2×C22⋊D11—82no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—24no—
228C22×Dic11—82no—
229C2×D44—21no—
230C2×D44—22no—
231C2×D44—22no—
232C2×D44C2412yes—
233C2×C4×D11—24no—
234C2×C4×D11—82no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—21no—
238C11×C4⋊C4—24no—
239C11×C4⋊C4—24no—
240C11×C4⋊C4—24no—
241C11×C4⋊C4C2×D414yes—
242C11×C4⋊C4C2412yes—
243C11×C4⋊C4C2412yes—
244C11×C4⋊C4C2412yes—
245C11×C22⋊C4—24no—
246C11×C22⋊C4—24no—
247C11×C22⋊C4—24no—
248C11×C22⋊C4C2×D414yes—
249C11×C22⋊C4C2×D414yes—
250C42×C11C2×D412yes—
251C42×C11C2412yes—
252C22⋊Dic11—24no—
253#4323—28no—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—24no—
257C4⋊Dic11—21no—
258C4⋊Dic11—21no—
259C4⋊Dic11—21no—
260C4⋊Dic11—24no—
261C4⋊Dic11C2412yes—
262C4⋊Dic11C2412yes—
263C4⋊Dic11C2412yes—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266C4×Dic11—24no—
267#4318—28no—
268C2×C11⋊C8—28no—
269C2×C11⋊C8—22no—
270C2×C11⋊C8—22no—
271C2×C11⋊C8—22no—
272C2×C11⋊C8#4114yescomplemented
273C2×C11⋊C8C2412yes—
274C2×C11⋊C8C2412yes—
275C2×C11⋊C8C2412yes—
276C2×C11⋊C8C2412yes—
277C2×#553—111no—
278C2×#547D1111yescharacteristic, complemented
279#3345—1116no—
280C2×#501—111no—
281C2×#481—111no—
282C2×#481—111no—
283C2×#482—111no—
284C2×#480—111no—
285C2×#478—111no—
286C2×#476—111no—
287C2×#469—111no—
288C2×#466—111no—
289C2×#442—111no—
290C2×#435—111no—
291C2×#428—111no—
292C22×#106—111no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—42no—
300C23×C11—42no—
301C23×C11—42no—
302C23×C11AGL(1,ℤ/8)14yes—
303C23×C11C22×D412yes—
304C23×C11C22×D412yes—
305C23×C11C22×D411yescharacteristic
306C22×D11—22no—
307C22×D11—42no—
308C22×D11—42no—
309C22×D11—42no—
310Q8×C11—48no—
311D4×C11—28no—
312D4×C11—22no—
313D4×C11—22no—
314D4×C11—48no—
315D4×C11—48no—
316D4×C11—42no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—24no—
322C2×C4×C11—24no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—48no—
331C2×C4×C11—48no—
332C2×C4×C11—42no—
333C2×C4×C11—42no—
334C2×C4×C11—42no—
335C2×C4×C11—48no—
336C2×C4×C11C22×D412yes—
337C2×C4×C11C22×D412yes—
338C2×C4×C11C22×D412yes—
339C2×C4×C11C22×D412yes—
340C2×C4×C11C22×D411yescharacteristic
341C2×C4×C11C2×#4112yes—
342C2×C4×C112−1+412yes—
343C2×C4×C11C2511yescharacteristic
344C22⋊D11—48no—
345C22⋊D11—84no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—42no—
350C2×Dic11—42no—
351C2×Dic11—42no—
352C2×Dic11—84no—
353D44—22no—
354D44—22no—
355D44—42no—
356C4×D11—84no—
357C11⋊C8—22no—
358C11⋊C8—22no—
359C11⋊C8—22no—
360C11⋊C8C2×#4114yescomplemented
361C22×#41—21no—
362C22×D8—111no—
363C22×M16—111no—
364C23×C8—111no—
365#553—118no—
366#553—224no—
367#547—24no—
368#547C2×D1118yescomplemented
369C2×C4⋊Q8C2×D1111yescharacteristic
370C2×#126—221no—
371C2×#125—111no—
372C2×#123—21no—
373C2×#123—21no—
374C2×#123—221no—
375C2×C22⋊Q8—21no—
376C2×#121—111no—
377C2×#121—111no—
378C2×#121—221no—
379C2×#121C2×D1111yescharacteristic
380C2×#121C2×D1111yescharacteristic
381C2×C4×D4—111no—
382C2×C4×D4—221no—
383C2×C4×D4C2×D1111yescharacteristic
384C2×C4×D4C2×D1111yescharacteristic
385C2×#117—111no—
386C22×C4⋊C4—111no—
387C22×C4⋊C4C2×D1111yescharacteristic
388C22×C4⋊C4C2×D1111yescharacteristic
389#501—118no—
390#482—118no—
391#481—118no—
392#481—118no—
393#480—118no—
394#478—118no—
395#476—118no—
396#469—118no—
397#466—118no—
398#442—118no—
399#435—118no—
400#428—118no—
401C2×#107—111no—
402C2×#107—111no—
403C2×#107—111no—
404C2×#106—111no—
405C2×#106—111no—
406C2×#106—111no—
407C2×#106—111no—
408C2×#106—118no—
409C2×#106—111no—
410C2×#106—111no—
411C2×C4⋊C8—111no—
412C2×#102—111no—
413C2×#102—111no—
414C2×#102—111no—
415C2×#102—111no—
416C2×#102—111no—
417C2×#102—111no—
418C2×C22⋊C8—111no—
419C2×C22⋊C8—111no—
420C2×#97—111no—
421C22×C11—28no—
422C22×C11—22no—
423C22×C11—22no—
424C22×C11—22no—
425C22×C11—22no—
426C22×C11—22no—
427C22×C11—44no—
428C22×C11—42no—
429C22×C11—42no—
430C22×C11—42no—
431C22×C11—84no—
432C22×C11#54712yes—
433C22×C11C2×AGL(1,ℤ/8)14yes—
434C22×C11C2×AGL(1,ℤ/8)12yes—
435C22×C11#57712yes—
436C22×C11C23×D411yescharacteristic
437C2×D11—42no—
438C2×D11—42no—
439C2×D11—42no—
440C2×D11—84no—
441C4×C11—22no—
442C4×C11—22no—
443C4×C11—22no—
444C4×C11—22no—
445C4×C11—42no—
446C4×C11—42no—
447C4×C11—42no—
448C4×C11#54712yes—
449C4×C11C22×#4111yescharacteristic
450C4×C11C2×2−1+411yescharacteristic
451Dic11—42no—
452Dic11—42no—
453Dic11—42no—
454C2×#41—28no—
455C2×#41—48no—
456C22×Q8—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—111no—
460C22×D4—221no—
461C22×D4—221no—
462C22×D4C22⋊D1111yescharacteristic
463C22×D4C22×D1111yescharacteristic
464C23×C4—21no—
465C23×C4—21no—
466C23×C4—21no—
467C23×C4—221no—
468C23×C4—221no—
469C23×C4C22×D1111yescharacteristic
470C23×C4C22×D1111yescharacteristic
471C2×D8—114no—
472C2×D8—224no—
473C2×M16—114no—
474C2×M16—224no—
475C22×C8—111no—
476C22×C8—111no—
477C22×C8—114no—
478C22×C8—111no—
479C22×C8—111no—
480C22×C8—224no—
481C4⋊Q8—22no—
482C4⋊Q8C22×D1114yes—
483#126—228no—
484#125—114no—
485#125—222no—
486#123—28no—
487#123—28no—
488#123—228no—
489C22⋊Q8—28no—
490#121—22no—
491#121—22no—
492#121—114no—
493#121—114no—
494#121—228no—
495#121—222no—
496#121—222no—
497#121C22×D1114yes—
498#121C22×D1114yes—
499C4×D4—22no—
500C4×D4—114no—
501C4×D4—228no—
502C4×D4—222no—
503C4×D4C22⋊D1114yes—
504C4×D4C22×D1114yes—
505C4×D4C22×D1114yes—
506#117—114no—
507#117—222no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—111no—
514C2×C4⋊C4—111no—
515C2×C4⋊C4—114no—
516C2×C4⋊C4—111no—
517C2×C4⋊C4—221no—
518C2×C4⋊C4—222no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4C22⋊D1111yescharacteristic
522C2×C4⋊C4C22×D1111yescharacteristic
523C2×C4⋊C4C22×D1111yescharacteristic
524C2×C4⋊C4C22×D1111yescharacteristic
525C2×C4⋊C4C22×D1114yes—
526C2×C4⋊C4C22×D1114yes—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—221no—
531C2×C22⋊C4—221no—
532C2×C22⋊C4—221no—
533C2×C22⋊C4—221no—
534C2×C22⋊C4C22⋊D1111yescharacteristic
535C2×C22⋊C4C22⋊D1111yescharacteristic
536C2×C42—221no—
537C2×C42C22×D1111yescharacteristic
538#107—114no—
539#107—114no—
540#107—114no—
541#106—114no—
542#106—114no—
543#106—114no—
544#106—114no—
545#106—114no—
546#106—114no—
547C4⋊C8—114no—
548#102—114no—
549#102—114no—
550#102—114no—
551#102—114no—
552#102—114no—
553#102—114no—
554C22⋊C8—114no—
555C22⋊C8—114no—
556#97—114no—
557C2×C11—24no—
558C2×C11—42no—
559C2×C11—82no—
560C2×C11#334514yescomplemented
561C2×C11C2×#54711yescharacteristic
562C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
563C2×C11C2×#57711yescharacteristic
564D11—82no—
565C24—21no—
566C24—221no—
567C24C2×C22⋊D1111yescharacteristic
568C24C2×C22⋊D1111yescharacteristic
569#41—432no—
570C2×Q8—24no—
571C2×Q8—44no—
572C2×D4—24no—
573C2×D4—24no—
574C2×D4—24no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—44no—
579C2×D4—44no—
580C2×D4—112no—
581C2×D4—224no—
582C2×D4—224no—
583C2×D4—222no—
584C2×D4—222no—
585C2×D4—221no—
586C2×D4—444no—
587C2×D4—882no—
588C2×D4C2×C22⋊D1114yes—
589C2×D4C23×D1112yes—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—221no—
606C22×C4—224no—
607C22×C4—224no—
608C22×C4—882no—
609C22×C4—882no—
610C22×C4C2×C22⋊D1112yes—
611C22×C4C2×C22⋊D1112yes—
612C22×C4C2×C22⋊D1111yescharacteristic
613C22×C4C2×C22⋊D1111yescharacteristic
614C22×C4C2×C22⋊D1111yescharacteristic
615C22×C4C2×C22⋊D1111yescharacteristic
616C22×C4C23×D1112yes—
617C22×C4C23×D1112yes—
618C22×C4C23×D1111yescharacteristic
619D8—228no—
620M16—228no—
621C2×C8—114no—
622C2×C8—112no—
623C2×C8—112no—
624C2×C8—112no—
625C2×C8—112no—
626C2×C8—228no—
627C2×C8—222no—
628C2×C8—222no—
629C2×C8—222no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—112no—
637C4⋊C4—112no—
638C4⋊C4—112no—
639C4⋊C4—221no—
640C4⋊C4—221no—
641C4⋊C4—224no—
642C4⋊C4—221no—
643C4⋊C4—224no—
644C4⋊C4—224no—
645C4⋊C4C2×C22⋊D1114yes—
646C4⋊C4C23×D1112yes—
647C4⋊C4C23×D1112yes—
648C4⋊C4C23×D1112yes—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—224no—
653C22⋊C4—224no—
654C22⋊C4—224no—
655C22⋊C4—224no—
656C22⋊C4C2×C22⋊D1114yes—
657C22⋊C4C2×C22⋊D1114yes—
658C42—224no—
659C42C2×C22⋊D1112yes—
660C42C23×D1112yes—
661C11C2×#334511yescharacteristic, complemented, Sylow
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—222no—
672C23—442no—
673C23—442no—
674C23—442no—
675C23#6698514yes—
676C23C22×C22⋊D1112yes—
677C23C22×C22⋊D1112yes—
678C23C22×C22⋊D1111yescharacteristic
679Q8—48no—
680D4—28no—
681D4—22no—
682D4—22no—
683D4—48no—
684D4—48no—
685D4—42no—
686D4—222no—
687D4—222no—
688D4—448no—
689D4—442no—
690D4—884no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—48no—
705C2×C4—48no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—48no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—442no—
714C2×C4—442no—
715C2×C4—442no—
716C2×C4—884no—
717C2×C4—884no—
718C2×C4#41×D1112yes—
719C2×C4#6704312yes—
720C2×C4C22×C22⋊D1112yes—
721C2×C4C22×C22⋊D1112yes—
722C2×C4C22×C22⋊D1112yes—
723C2×C4C22×C22⋊D1112yes—
724C2×C4C22×C22⋊D1111yescharacteristic
725C2×C4C24×D1111yescharacteristic
726C8—114no—
727C8—222no—
728C8—222no—
729C8—222no—
730C22—22no—
731C22—22no—
732C22—28no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—44no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—84no—
741C22—442no—
742C22—442no—
743C22—442no—
744C22—884no—
745C22C2×#6698514yes—
746C22C2×#6698512yes—
747C22#1062335512yes—
748C22#1062336812yes—
749C22C23×C22⋊D1111yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—442no—
758C4—442no—
759C4—442no—
760C4#1062335512yes—
761C4C2×#41×D1111yescharacteristic
762C4C2×#6704311yescharacteristic
763C2—24no—
764C2—42no—
765C2—82no—
766C2—882no—
767C2#1308108614yesdirect product factor
768C2C2×#1062335511yescharacteristic
769C2C22×#6698511yescharacteristic
770C2C2×#1062336811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#547C2
socleC23×C11C22×D4
hypercenterC2×#547D11
hypocenterC11C2×#3345
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#10623096C2semidirect
2. #13081086C2direct (N × H)
3. C2×#10622693C2semidirect
4. C2×#10622581C2semidirect
5. C2×#10622647C2semidirect
6. C2×#10622648C2semidirect
7. C2×#10622580C2semidirect
8. C2×#10622622C2semidirect
9. C2×#10622697C2semidirect
10. C2×#10622652C2semidirect
11. C2×#10622651C2semidirect
12. C2×#10622627C2semidirect
13. C2×#10622624C2semidirect
14. C2×#10622577C2semidirect
15. C22×#66872C2semidirect
16. C2×C11×#547C2semidirect
19. C11×#547C22semidirect
39. #10623096C22semidirect
50. #10622697C22semidirect
51. #10622693C22semidirect
52. #10622652C22semidirect
53. #10622651C22semidirect
54. #10622648C22semidirect
55. #10622647C22semidirect
56. #10622627C22semidirect
57. #10622624C22semidirect
58. #10622622C22semidirect
59. #10622581C22semidirect
60. #10622580C22semidirect
64. #10622577C22semidirect
71. C2×#66872C22semidirect
272. C2×C11⋊C8#41semidirect
278. C2×#547D11semidirect
360. C11⋊C8C2×#41semidirect
368. #547C2×D11semidirect
560. C2×C11#3345semidirect
661. C11C2×#3345semidirect
767. C2#13081086direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230962
#130810862
C2×#106226932
C2×#106225812
C2×#106226472
C2×#106226482
C2×#106225802
C2×#106226222
C2×#106226972
C2×#106226522
C2×#106226512
C2×#106226272
C2×#106226242
C2×#106225772
C22×#668722
C2×C11×#5472
C2×#334511