Finite Group Databasebeta

← C2×#13078866 #15622075

Subgroups — C2×#13078866 #15622075

Order 2816.

2210 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×#10623262C211yesmaximal, characteristic, complemented
2C2×#10623076C211yesmaximal, characteristic
3#13078866C2116yesmaximal, direct product factor
4C2×#10622427C211yesmaximal, characteristic, complemented
5C2×#10622428C211yesmaximal, characteristic, complemented
6C2×#10622460C211yesmaximal, characteristic, complemented
7C2×#10622622C211yesmaximal, characteristic, complemented
8C2×#10622696C211yesmaximal, characteristic, complemented
9C2×#10622782C211yesmaximal, characteristic
10C2×#10622782C211yesmaximal, characteristic
11C2×#10622430C211yesmaximal, characteristic, complemented
12C2×#10622777C211yesmaximal, characteristic, complemented
13C2×SD16×Dic11C211yesmaximal, characteristic, complemented
14C2×#10622401C211yesmaximal, characteristic, complemented
15C2×#10622453C211yesmaximal, characteristic, complemented
16C2×C11×#461C211yesmaximal, characteristic, complemented
17C22×D4×D11C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C2×C11×C4⋊Q8C2211yescharacteristic, complemented
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66999C2211yescharacteristic
23C2×#66999C2211yescharacteristic
24C2×Q8×Dic11C2211yescharacteristic, complemented
25C2×Q8×Dic11C2211yescharacteristic, complemented
26C22×#4325C2211yescharacteristic
27C22×#4325C2211yescharacteristic
28C2×D4×Dic11C2211yescharacteristic
29C2×C4×C22⋊D11—21no—
30C22×(C2×D11)⋊C4—21no—
31#10623262—24no—
32#10623262C2218yescomplemented
33#10623076—24no—
34#10623076C2218yes—
35C2×#66951—21no—
36C2×#66951—21no—
37C2×#66946C2211yescharacteristic
38C2×#66945C2211yescharacteristic
39C2×#66942—21no—
40C2×#66942—21no—
41C2×(C22⋊D11)⋊C4—21no—
42C2×C22⋊C4×D11—21no—
43C2×C4×D44C2211yescharacteristic
44C2×#66925C2211yescharacteristic
45C2×#66923C2211yescharacteristic, complemented
46C11×#461C2218yescomplemented
47C2×C11×C4⋊C8C2211yescharacteristic, complemented
48C2×C11×#103C2211yescharacteristic, complemented
49C2×C11×#103C2211yescharacteristic, complemented
50C2×#66899C2211yescharacteristic, complemented
51C2×#66899C2211yescharacteristic, complemented
52C2×#66896C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54#10622782C2218yes—
55#10622782C2218yes—
56#10622777C2218yescomplemented
57SD16×Dic11C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×#66885C2211yescharacteristic
60C2×(C2×D11)⋊C8C2211yescharacteristic
61C2×(C2×D11)⋊C8C2211yescharacteristic
62C2×#66882C2211yescharacteristic, complemented
63C2×#66881C2211yescharacteristic, complemented
64C2×#66879C2211yescharacteristic, complemented
65C2×C8×Dic11C2211yescharacteristic, complemented
66#10622696C2218yescomplemented
67#10622622C2218yescomplemented
68C2×#66872C2211yescharacteristic, complemented
69C2×#66871C2211yescharacteristic, complemented
70C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
71#10622460C2218yescomplemented
72#10622453C2218yescomplemented
73#10622430C2218yescomplemented
74#10622428C2218yescomplemented
75#10622427C2218yescomplemented
76#10622401C2218yescomplemented
77C24×D11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11—21no—
82C22×C22⋊D11—21no—
83C23×Dic11—21no—
84C2×D4×D11—24no—
85C2×D4×D11—24no—
86C2×D4×D11—22no—
87C2×D4×D11C2314yes—
88C22×D44C2311yescharacteristic
89C22×C4×D11—21no—
90C22×C4×D11—21no—
91C22×C4×D11C2311yescharacteristic
92C2×C11×SD16—24no—
93C2×C11×SD16—24no—
94C2×C11×SD16C2314yes—
95C2×C11×SD16C2314yes—
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C11×C4⋊Q8—22no—
99C11×C4⋊Q8C2314yescomplemented
100C4×D4×C11—22no—
101C4×D4×C11C2314yes—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C22⋊C4—21no—
106C2×C42×C11C2311yescharacteristic
107C2×C22⋊Dic11—21no—
108#66999—22no—
109#66999—22no—
110#66999C2314yes—
111#66999C2314yes—
112Q8×Dic11—22no—
113Q8×Dic11—22no—
114Q8×Dic11C2314yescomplemented
115Q8×Dic11C2314yescomplemented
116C2×#4325—24no—
117C2×#4325—24no—
118C2×#4325C2314yes—
119C2×#4325C2314yes—
120D4×Dic11—22no—
121D4×Dic11C2314yes—
122C4×C22⋊D11—28no—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4—21no—
125C2×(C2×D11)⋊C4—21no—
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4—21no—
128C2×(C2×D11)⋊C4—28no—
129C2×(C2×D11)⋊C4D411yescharacteristic
130C2×(C2×D11)⋊C4D411yescharacteristic
131C2×C4⋊Dic11—21no—
132C2×C4⋊Dic11—21no—
133C2×C4⋊Dic11C2311yescharacteristic
134C2×C4⋊Dic11C2311yescharacteristic
135C2×C4⋊Dic11C2311yescharacteristic
136C2×Dic11⋊C4—21no—
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4D411yescharacteristic
141C2×Dic11⋊C4D411yescharacteristic
142C2×C4×Dic11—21no—
143C2×C4×Dic11—21no—
144C2×C4×Dic11—21no—
145C2×C4×Dic11C2311yescharacteristic
146C22×C11⋊C8C2311yescharacteristic
147C22×C11⋊C8C2311yescharacteristic
148#66951—28no—
149#66951—28no—
150#66946—22no—
151#66946C2314yes—
152#66945—22no—
153#66945C2314yes—
154#66942—28no—
155#66942—28no—
156(C22⋊D11)⋊C4—28no—
157C22⋊C4×D11—28no—
158C4×D44—22no—
159C4×D44C2314yes—
160#66925D414yes—
161#66925C2314yes—
162#66923—22no—
163#66923C2314yescomplemented
164C11×C4⋊C8C2314yescomplemented
165C11×#103C2314yescomplemented
166C11×#103C2314yescomplemented
167#66899C2314yescomplemented
168#66899C2314yescomplemented
169#66896C2314yes—
170#66896C2314yes—
171#66885C2314yes—
172#66885C2314yes—
173(C2×D11)⋊C8C2314yes—
174(C2×D11)⋊C8C2314yes—
175#66882C2314yescomplemented
176#66881C2314yescomplemented
177#66879C2314yescomplemented
178C8×Dic11C2314yescomplemented
179#66872C2314yescomplemented
180#66871C2314yescomplemented
181C4⋊(C11⋊C8)C2314yescomplemented
182C2×#3123—111nomaximal, Sylow
183C24×C11—21no—
184C23×D11—21no—
185C23×D11—28no—
186C23×D11—24no—
187C23×D11—82no—
188C23×D11—82no—
189C23×D11C2×D411yescharacteristic
190C2×Q8×C11—21no—
191C2×Q8×C11—21no—
192C2×Q8×C11—22no—
193C2×Q8×C11—22no—
194C2×Q8×C11—22no—
195C2×Q8×C11—22no—
196C2×Q8×C11C2412yes—
197C2×Q8×C11C2412yes—
198C2×D4×C11—21no—
199C2×D4×C11—22no—
200C2×D4×C11#4114yes—
201C2×D4×C11C2412yes—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—24no—
206C22×C4×C11—82no—
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2411yescharacteristic
210C2×C22⋊D11—28no—
211C2×C22⋊D11—24no—
212C22×Dic11—24no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—82no—
217C22×Dic11C2×D411yescharacteristic
218C22×Dic11C2×D411yescharacteristic
219C22×Dic11C2×D411yescharacteristic
220D4×D11—216no—
221D4×D11—28no—
222D4×D11—28no—
223C2×D44—21no—
224C2×D44—22no—
225C2×D44#4114yes—
226C2×D44C2412yes—
227C2×C4×D11—24no—
228C2×C4×D11—24no—
229C2×C4×D11—22no—
230C2×C4×D11—22no—
231C2×C4×D11—82no—
232C2×C4×D11—82no—
233C2×C4×D11C2×D412yes—
234C2×C4×D11C2412yes—
235C11×SD16—28no—
236C11×SD16—28no—
237C2×C8×C11—22no—
238C2×C8×C11—22no—
239C2×C8×C11C2412yes—
240C2×C8×C11C2412yes—
241C11×C4⋊C4—24no—
242C11×C4⋊C4—24no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4C2412yes—
245C11×C22⋊C4—24no—
246C42×C11C2×D412yes—
247C42×C11C2412yes—
248C22⋊Dic11—24no—
249#4325—28no—
250#4325—28no—
251(C2×D11)⋊C4—24no—
252(C2×D11)⋊C4—24no—
253(C2×D11)⋊C4—24no—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4C2×D414yes—
257(C2×D11)⋊C4C2×D414yes—
258C4⋊Dic11—24no—
259C4⋊Dic11—24no—
260C4⋊Dic11—21no—
261C4⋊Dic11—21no—
262C4⋊Dic11—21no—
263C4⋊Dic11C2412yes—
264C4⋊Dic11C2412yes—
265C4⋊Dic11C2412yes—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268Dic11⋊C4—24no—
269Dic11⋊C4—24no—
270Dic11⋊C4C2×D414yes—
271Dic11⋊C4C2×D414yes—
272C4×Dic11—24no—
273C4×Dic11—24no—
274C4×Dic11—24no—
275C4×Dic11C2×D412yes—
276C4×Dic11C2412yes—
277C2×C11⋊C8—22no—
278C2×C11⋊C8—22no—
279C2×C11⋊C8C2412yes—
280C2×C11⋊C8C2412yes—
281C2×#541—111no—
282C2×#518—111no—
283#3123—1116no—
284C2×#485—111no—
285C2×#485—111no—
286C2×#478—111no—
287C2×#478—111no—
288C2×#461—111no—
289C2×#461D1111yescharacteristic, complemented
290C2×#450—111no—
291C2×#450—111no—
292C2×#440—111no—
293C2×#440—111no—
294C2×C4×SD16—111no—
295C2×C4×SD16—111no—
296C2×#433—111no—
297C23×C11—24no—
298C23×C11—22no—
299C23×C11—42no—
300C23×C11—42no—
301C23×C11C22×D411yescharacteristic
302C22×D11—22no—
303C22×D11—24no—
304C22×D11—22no—
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—216no—
308C22×D11—42no—
309C22×D11—42no—
310C22×D11—84no—
311C22×D11—84no—
312C22×D11—816no—
313C22×D11C22×D412yes—
314Q8×C11—22no—
315Q8×C11—22no—
316Q8×C11—22no—
317Q8×C11—22no—
318Q8×C11—42no—
319Q8×C11—42no—
320D4×C11—24no—
321D4×C11—22no—
322D4×C11C2×#4114yes—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—42no—
329C2×C4×C11—42no—
330C2×C4×C11—42no—
331C2×C4×C11—84no—
332C2×C4×C11C22×D412yes—
333C2×C4×C11C22×D412yes—
334C2×C4×C11C22×D411yescharacteristic
335C2×C4×C11C2×#4112yes—
336C2×C4×C11C2×#4112yes—
337C2×C4×C11C2511yescharacteristic
338C22⋊D11—216no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11—84no—
349C2×Dic11C22×D412yes—
350C2×Dic11C22×D412yes—
351C2×Dic11C22×D412yes—
352D44—24no—
353D44—22no—
354D44C2×#4114yes—
355C4×D11—24no—
356C4×D11—22no—
357C4×D11—22no—
358C4×D11—84no—
359C4×D11—84no—
360C8×C11—22no—
361C8×C11—22no—
362C11⋊C8—22no—
363C11⋊C8—22no—
364C23×D4—111no—
365C22×SD16—111no—
366C22×SD16—111no—
367C22×SD16C2×D1111yescharacteristic
368C22×SD16C2×D1111yescharacteristic
369#541—118no—
370#541—224no—
371C2×C4⋊Q8C2×D1111yescharacteristic, complemented
372C2×#126—221no—
373C2×#126—221no—
374C2×#125—111no—
375C2×#125—221no—
376C2×#125—221no—
377C2×C22⋊Q8—111no—
378C2×C22⋊Q8—111no—
379#518—118no—
380#518—224no—
381C2×C4×Q8—111no—
382C2×C4×Q8—111no—
383C2×C4×D4—111no—
384C2×C4×D4—111no—
385C2×C4×D4—111no—
386C2×C4×D4—221no—
387C2×C4×D4—221no—
388C2×C4×D4C2×D1111yescharacteristic
389C2×#117—111no—
390C2×#117—111no—
391C22×C22⋊C4—221no—
392C22×C22⋊C4—221no—
393#485—118no—
394#485—118no—
395#478—118no—
396#478—118no—
397#461—118no—
398#461C2×D1118yescomplemented
399#450—118no—
400#450—118no—
401#440—118no—
402#440—118no—
403C4×SD16—118no—
404C4×SD16—118no—
405#433—118no—
406C2×#107—111no—
407C2×#107—111no—
408C2×#106—111no—
409C2×#106—111no—
410C2×C4⋊C8—111no—
411C2×C4⋊C8C2×D1111yescharacteristic, complemented
412C2×#103—111no—
413C2×#103—111no—
414C2×#103C2×D1111yescharacteristic, complemented
415C2×#103C2×D1111yescharacteristic, complemented
416C2×#102—111no—
417C2×#102—111no—
418C2×#102—111no—
419C2×#102—111no—
420C2×C22⋊C8—111no—
421C2×C22⋊C8—111no—
422C2×#97—111no—
423C2×C4×C8—111no—
424C22×C11—24no—
425C22×C11—48no—
426C22×C11—42no—
427C22×C11—42no—
428C22×C11#52512yes—
429C22×C11#57712yes—
430C22×C11#57712yes—
431C22×C11C23×D411yescharacteristic
432C2×D11—22no—
433C2×D11—24no—
434C2×D11—22no—
435C2×D11—22no—
436C2×D11—44no—
437C2×D11—48no—
438C2×D11—42no—
439C2×D11—42no—
440C2×D11—816no—
441C4×C11—22no—
442C4×C11—22no—
443C4×C11—42no—
444C4×C11—42no—
445C4×C11—42no—
446C4×C11#52512yes—
447C4×C11C22×#4111yescharacteristic
448C4×C11C22×#4111yescharacteristic
449Dic11—22no—
450Dic11—22no—
451Dic11—22no—
452Dic11—42no—
453Dic11—42no—
454Dic11—42no—
455C25—221no—
456C22×Q8C22×D1111yescharacteristic
457C22×Q8C22×D1111yescharacteristic
458C22×D4—114no—
459C22×D4—111no—
460C22×D4—222no—
461C22×D4—221no—
462C22×D4—224no—
463C22×D4—224no—
464C22×D4C22×D1111yescharacteristic
465C23×C4—21no—
466C23×C4—111no—
467C23×C4—221no—
468C23×C4—221no—
469C23×C4—221no—
470C2×SD16—24no—
471C2×SD16—24no—
472C2×SD16—114no—
473C2×SD16—114no—
474C2×SD16—224no—
475C2×SD16—224no—
476C2×SD16C22×D1114yes—
477C2×SD16C22×D1114yes—
478C22×C8—111no—
479C22×C8—111no—
480C22×C8C22×D1111yescharacteristic
481C22×C8C22×D1111yescharacteristic
482C4⋊Q8—22no—
483C4⋊Q8C22×D1114yescomplemented
484#126—228no—
485#126—228no—
486#125—114no—
487#125—228no—
488#125—228no—
489#125—222no—
490C22⋊Q8—114no—
491C22⋊Q8—114no—
492C22⋊Q8—222no—
493C22⋊Q8—222no—
494C4×Q8—114no—
495C4×Q8—114no—
496C4×Q8—222no—
497C4×Q8—222no—
498C4×D4—22no—
499C4×D4—114no—
500C4×D4—114no—
501C4×D4—114no—
502C4×D4—222no—
503C4×D4—222no—
504C4×D4—228no—
505C4×D4—228no—
506C4×D4—222no—
507C4×D4C22×D1114yes—
508#117—114no—
509#117—114no—
510#117—114no—
511#117—222no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—111no—
515C2×C4⋊C4—111no—
516C2×C4⋊C4—111no—
517C2×C4⋊C4—111no—
518C2×C4⋊C4—111no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4—221no—
522C2×C4⋊C4—221no—
523C2×C4⋊C4—221no—
524C2×C4⋊C4—221no—
525C2×C4⋊C4C22×D1111yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—111no—
528C2×C22⋊C4—111no—
529C2×C22⋊C4—228no—
530C2×C22⋊C4—228no—
531C2×C22⋊C4—221no—
532C2×C22⋊C4—221no—
533C2×C22⋊C4—221no—
534C2×C22⋊C4—221no—
535C2×C22⋊C4—221no—
536C2×C22⋊C4—221no—
537C2×C42—111no—
538C2×C42—221no—
539C2×C42—221no—
540C2×C42—221no—
541C2×C42C22×D1111yescharacteristic
542#107—114no—
543#107—114no—
544#106—114no—
545#106—114no—
546C4⋊C8—114no—
547C4⋊C8C22×D1114yescomplemented
548#103—114no—
549#103—114no—
550#103C22×D1114yescomplemented
551#103C22×D1114yescomplemented
552#102—114no—
553#102—114no—
554#102—114no—
555#102—114no—
556C22⋊C8—114no—
557C22⋊C8—114no—
558#97—114no—
559C4×C8—114no—
560C2×C11—44no—
561C2×C11#312314yescomplemented
562C2×C11C2×#52511yescharacteristic
563C2×C11C2×#57711yescharacteristic
564C2×C11C2×#57711yescharacteristic
565D11—42no—
566D11—44no—
567C24—21no—
568C24—111no—
569C24—224no—
570C24—228no—
571C24—221no—
572C24—882no—
573C24—882no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8C23×D1112yes—
581C2×Q8C23×D1112yes—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—114no—
585C2×D4—112no—
586C2×D4—224no—
587C2×D4—228no—
588C2×D4—2216no—
589C2×D4—228no—
590C2×D4—228no—
591C2×D4—221no—
592C2×D4—222no—
593C2×D4#434114yes—
594C2×D4C23×D1112yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—24no—
599C22×C4—82no—
600C22×C4—111no—
601C22×C4—111no—
602C22×C4—111no—
603C22×C4—112no—
604C22×C4—112no—
605C22×C4—224no—
606C22×C4—224no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4—224no—
613C22×C4—882no—
614C22×C4—882no—
615C22×C4—882no—
616C22×C4D4×D1111yescharacteristic
617C22×C4D4×D1111yescharacteristic
618C22×C4C23×D1111yescharacteristic
619SD16—28no—
620SD16—28no—
621SD16—228no—
622SD16—228no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—112no—
626C2×C8—112no—
627C2×C8—222no—
628C2×C8—222no—
629C2×C8C23×D1112yes—
630C2×C8C23×D1112yes—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—114no—
635C4⋊C4—114no—
636C4⋊C4—112no—
637C4⋊C4—112no—
638C4⋊C4—112no—
639C4⋊C4—224no—
640C4⋊C4—224no—
641C4⋊C4—224no—
642C4⋊C4—224no—
643C4⋊C4—221no—
644C4⋊C4—221no—
645C4⋊C4—221no—
646C4⋊C4—224no—
647C4⋊C4—224no—
648C4⋊C4C23×D1112yes—
649C22⋊C4—24no—
650C22⋊C4—114no—
651C22⋊C4—114no—
652C22⋊C4—224no—
653C22⋊C4—224no—
654C22⋊C4—224no—
655C22⋊C4—224no—
656C22⋊C4—224no—
657C22⋊C4—224no—
658C42—112no—
659C42—112no—
660C42—224no—
661C42—224no—
662C42—224no—
663C42D4×D1112yes—
664C42C23×D1112yes—
665C11C2×#312311yescharacteristic, complemented, Sylow
666C23—24no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—112no—
671C23—2216no—
672C23—222no—
673C23—222no—
674C23—222no—
675C23—224no—
676C23—222no—
677C23—442no—
678C23—442no—
679C23—884no—
680C23—884no—
681C23—8816no—
682C23C2×D4×D1111yescharacteristic
683Q8—22no—
684Q8—22no—
685Q8—22no—
686Q8—22no—
687Q8—42no—
688Q8—42no—
689D4—24no—
690D4—22no—
691D4—114no—
692D4—2216no—
693D4—224no—
694D4—222no—
695D4C2×#434114yes—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—84no—
705C2×C4—112no—
706C2×C4—112no—
707C2×C4—112no—
708C2×C4—222no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—224no—
712C2×C4—222no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—442no—
718C2×C4—442no—
719C2×C4—442no—
720C2×C4—884no—
721C2×C4—884no—
722C2×C4—884no—
723C2×C4C2×D4×D1112yes—
724C2×C4C2×D4×D1112yes—
725C2×C4C2×D4×D1111yescharacteristic
726C2×C4C2×#434112yes—
727C2×C4#41×D1112yes—
728C2×C4C24×D1111yescharacteristic
729C8—22no—
730C8—22no—
731C8—222no—
732C8—222no—
733C22—24no—
734C22—48no—
735C22—42no—
736C22—42no—
737C22—222no—
738C22—224no—
739C22—222no—
740C22—222no—
741C22—444no—
742C22—448no—
743C22—442no—
744C22—442no—
745C22—8816no—
746C22#1062313712yes—
747C22#1062329312yes—
748C22#1062330912yes—
749C22C22×D4×D1111yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—222no—
756C4—222no—
757C4—222no—
758C4—442no—
759C4—442no—
760C4—442no—
761C4#1062313712yes—
762C4C22×#434111yescharacteristic
763C4C2×#41×D1111yescharacteristic
764C2—44no—
765C2—442no—
766C2—444no—
767C2#1307886614yesdirect product factor
768C2C2×#1062313711yescharacteristic
769C2C2×#1062329311yescharacteristic
770C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#461C2
socleC23×C11C22×D4
prime radicalC22×D4×D11C22
hypercenterC2×#461D11
hypocenterC11C2×#3123
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#10623262C2semidirect
3. #13078866C2direct (N × H)
4. C2×#10622427C2semidirect
5. C2×#10622428C2semidirect
6. C2×#10622460C2semidirect
7. C2×#10622622C2semidirect
8. C2×#10622696C2semidirect
11. C2×#10622430C2semidirect
12. C2×#10622777C2semidirect
13. C2×SD16×Dic11C2semidirect
14. C2×#10622401C2semidirect
15. C2×#10622453C2semidirect
16. C2×C11×#461C2semidirect
20. C2×C11×C4⋊Q8C22semidirect
24. C2×Q8×Dic11C22semidirect
25. C2×Q8×Dic11C22semidirect
32. #10623262C22semidirect
45. C2×#66923C22semidirect
46. C11×#461C22semidirect
47. C2×C11×C4⋊C8C22semidirect
48. C2×C11×#103C22semidirect
49. C2×C11×#103C22semidirect
50. C2×#66899C22semidirect
51. C2×#66899C22semidirect
56. #10622777C22semidirect
57. SD16×Dic11C22semidirect
62. C2×#66882C22semidirect
63. C2×#66881C22semidirect
64. C2×#66879C22semidirect
65. C2×C8×Dic11C22semidirect
66. #10622696C22semidirect
67. #10622622C22semidirect
68. C2×#66872C22semidirect
69. C2×#66871C22semidirect
70. C2×C4⋊(C11⋊C8)C22semidirect
71. #10622460C22semidirect
72. #10622453C22semidirect
73. #10622430C22semidirect
74. #10622428C22semidirect
75. #10622427C22semidirect
76. #10622401C22semidirect
99. C11×C4⋊Q8C23semidirect
114. Q8×Dic11C23semidirect
115. Q8×Dic11C23semidirect
163. #66923C23semidirect
164. C11×C4⋊C8C23semidirect
165. C11×#103C23semidirect
166. C11×#103C23semidirect
167. #66899C23semidirect
168. #66899C23semidirect
175. #66882C23semidirect
176. #66881C23semidirect
177. #66879C23semidirect
178. C8×Dic11C23semidirect
179. #66872C23semidirect
180. #66871C23semidirect
181. C4⋊(C11⋊C8)C23semidirect
289. C2×#461D11semidirect
371. C2×C4⋊Q8C2×D11semidirect
398. #461C2×D11semidirect
411. C2×C4⋊C8C2×D11semidirect
414. C2×#103C2×D11semidirect
415. C2×#103C2×D11semidirect
483. C4⋊Q8C22×D11semidirect
547. C4⋊C8C22×D11semidirect
550. #103C22×D11semidirect
551. #103C22×D11semidirect
561. C2×C11#3123semidirect
665. C11C2×#3123semidirect
767. C2#13078866direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232622
C2×#106230762
#130788662
C2×#106224272
C2×#106224282
C2×#106224602
C2×#106226222
C2×#106226962
C2×#106227822
C2×#106224302
C2×#106227772
C2×SD16×Dic112
C2×#106224012
C2×#106224532
C2×C11×#4612
C2×#312311