Finite Group Databasebeta

← C2×#13078862 #15622071

Subgroups — C2×#13078862 #15622071

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×#10623156C211yesmaximal, characteristic, complemented
2C2×#10623329C211yesmaximal, characteristic
3#13078862C2116yesmaximal, direct product factor
4C2×#10622336C211yesmaximal, characteristic, complemented
5C2×#10622658C211yesmaximal, characteristic, complemented
6C2×#10622376C211yesmaximal, characteristic, complemented
7C2×#10622379C211yesmaximal, characteristic, complemented
8C2×#10622775C211yesmaximal, characteristic, complemented
9C2×#10622775C211yesmaximal, characteristic, complemented
10C2×#10622831C211yesmaximal, characteristic
11C2×#10622777C211yesmaximal, characteristic, complemented
12C2×#10622370C211yesmaximal, characteristic, complemented
13C2×#10622371C211yesmaximal, characteristic, complemented
14C2×SD16×Dic11C211yesmaximal, characteristic, complemented
15C2×#10622333C211yesmaximal, characteristic, complemented
16C2×C11×#450C211yesmaximal, characteristic
17C23×D4×C11C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Dic11—21no—
22C22×C22⋊Dic11—21no—
23C2×Q8×Dic11C2211yescharacteristic, complemented
24C2×#66997C2211yescharacteristic, complemented
25#10623329—24no—
26#10623329C2218yes—
27C2×D4×Dic11—21no—
28C2×D4×Dic11—21no—
29C2×D4×Dic11C2211yescharacteristic
30C2×D4×Dic11C2211yescharacteristic
31C2×D4×Dic11C2211yescharacteristic
32C2×D4×Dic11C2211yescharacteristic
33C22×#4324C2211yescharacteristic
34C22×#4324C2211yescharacteristic
35C2×#66979C2211yescharacteristic
36C2×#66979C2211yescharacteristic
37C2×#66977C2211yescharacteristic
38#10623156—24no—
39#10623156C2218yescomplemented
40C2×#66943—21no—
41C2×#66943C2211yescharacteristic, complemented
42C2×#66942—21no—
43C2×#66940C2211yescharacteristic, complemented
44C2×#66932—21no—
45C2×#66932—21no—
46C11×#450C2218yes—
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×C22⋊C8C2211yescharacteristic
50C2×#66899C2211yescharacteristic, complemented
51C2×#66899C2211yescharacteristic, complemented
52#10622831C2218yes—
53C2×#66896C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×C22⋊(C11⋊C8)C2211yescharacteristic
56#10622777C2218yescomplemented
57#10622775C2218yescomplemented
58#10622775C2218yescomplemented
59SD16×Dic11C2218yescomplemented
60C2×#66882C2211yescharacteristic, complemented
61C2×#66881C2211yescharacteristic, complemented
62C2×#66880C2211yescharacteristic, complemented
63C2×#66880C2211yescharacteristic, complemented
64C2×#66879C2211yescharacteristic, complemented
65C2×Dic11⋊C8C2211yescharacteristic, complemented
66C2×Dic11⋊C8C2211yescharacteristic, complemented
67C2×C8×Dic11C2211yescharacteristic, complemented
68#10622658C2218yescomplemented
69C2×#66872C2211yescharacteristic, complemented
70C2×#66871C2211yescharacteristic, complemented
71#10622379C2218yescomplemented
72#10622376C2218yescomplemented
73#10622371C2218yescomplemented
74#10622370C2218yescomplemented
75#10622336C2218yescomplemented
76#10622333C2218yescomplemented
77C25×C11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11—24no—
80C22×D4×C11—24no—
81C22×D4×C11—21no—
82C22×D4×C11—22no—
83C22×D4×C11C2314yes—
84C22×D4×C11C2311yescharacteristic
85C22×D4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×Dic11—21no—
88C23×Dic11—21no—
89C23×Dic11—21no—
90C23×Dic11—21no—
91C22×Dic22C2311yescharacteristic
92C2×C11×SD16—24no—
93C2×C11×SD16—24no—
94C2×C11×SD16C2314yes—
95C2×C11×SD16C2314yes—
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C11×C22⋊Q8—22no—
99C11×C22⋊Q8C2314yes—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C22⋊C4—21no—
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11—21no—
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11—21no—
109C2×C22⋊Dic11—28no—
110C2×C22⋊Dic11—28no—
111C2×C22⋊Dic11D411yescharacteristic
112C2×C22⋊Dic11D411yescharacteristic
113Q8×Dic11—22no—
114Q8×Dic11C2314yescomplemented
115#66997—22no—
116#66997C2314yescomplemented
117D4×Dic11—28no—
118D4×Dic11—28no—
119D4×Dic11—22no—
120D4×Dic11—22no—
121D4×Dic11—22no—
122D4×Dic11—22no—
123D4×Dic11C2314yes—
124D4×Dic11C2314yes—
125D4×Dic11C2314yes—
126D4×Dic11C2314yes—
127C2×#4324—24no—
128C2×#4324—24no—
129C2×#4324C2314yes—
130C2×#4324C2314yes—
131#66979—22no—
132#66979D414yes—
133#66979C2314yes—
134#66979C2314yes—
135C2×C4⋊Dic11—21no—
136C2×C4⋊Dic11—21no—
137C2×C4⋊Dic11D411yescharacteristic
138C2×C4⋊Dic11D411yescharacteristic
139C2×C4⋊Dic11C2311yescharacteristic
140C2×C4⋊Dic11C2311yescharacteristic
141C2×C4⋊Dic11C2311yescharacteristic
142#66977—22no—
143#66977C2314yes—
144C2×Dic11⋊C4—21no—
145C2×Dic11⋊C4—21no—
146C2×Dic11⋊C4—21no—
147C2×Dic11⋊C4—21no—
148C2×Dic11⋊C4—21no—
149C2×C4×Dic11—21no—
150C2×C4×Dic11—21no—
151C2×C4×Dic11—21no—
152C2×C4×Dic11C2311yescharacteristic
153C2×C4×Dic11C2311yescharacteristic
154C22×C11⋊C8C2311yescharacteristic
155C22×C11⋊C8C2311yescharacteristic
156#66943—28no—
157#66943—22no—
158#66943C2314yescomplemented
159#66942—28no—
160#66940—22no—
161#66940C2314yescomplemented
162#66932—28no—
163#66932—28no—
164C11×#102C2314yes—
165C11×#102C2314yes—
166C11×C22⋊C8C2314yes—
167#66899C2314yescomplemented
168#66899C2314yescomplemented
169#66896C2314yes—
170#66896C2314yes—
171C22⋊(C11⋊C8)C2314yes—
172#66882C2314yescomplemented
173#66881C2314yescomplemented
174#66880C2314yescomplemented
175#66880C2314yescomplemented
176#66879C2314yescomplemented
177Dic11⋊C8C2314yescomplemented
178Dic11⋊C8C2314yescomplemented
179C8×Dic11C2314yescomplemented
180#66872C2314yescomplemented
181#66871C2314yescomplemented
182C2×#3123—111nomaximal, Sylow
183C24×C11—28no—
184C24×C11—21no—
185C24×C11—21no—
186C24×C11—24no—
187C24×C11—82no—
188C24×C11—82no—
189C24×C11C2×D411yescharacteristic
190C2×Q8×C11—21no—
191C2×Q8×C11—22no—
192C2×Q8×C11—22no—
193C2×Q8×C11C2412yes—
194C2×D4×C11—28no—
195C2×D4×C11—216no—
196C2×D4×C11—28no—
197C2×D4×C11—28no—
198C2×D4×C11—24no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—22no—
202C2×D4×C11—22no—
203C2×D4×C11#4114yes—
204C2×D4×C11#4114yes—
205C2×D4×C11C2412yes—
206C2×D4×C11C2412yes—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D412yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2411yescharacteristic
215C22×Dic11—24no—
216C22×Dic11—24no—
217C22×Dic11—24no—
218C22×Dic11—24no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—82no—
224C22×Dic11—82no—
225C22×Dic11—82no—
226C22×Dic11—82no—
227C22×Dic11C2×D411yescharacteristic
228C22×Dic11C2×D411yescharacteristic
229C22×Dic11C2×D411yescharacteristic
230C22×Dic11C2×D411yescharacteristic
231C2×Dic22—21no—
232C2×Dic22—22no—
233C2×Dic22—22no—
234C2×Dic22C2412yes—
235C11×SD16—28no—
236C11×SD16—28no—
237C2×C8×C11—22no—
238C2×C8×C11—22no—
239C2×C8×C11C2412yes—
240C2×C8×C11C2412yes—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—24no—
243C11×C4⋊C4C2412yes—
244C11×C22⋊C4—24no—
245C22⋊Dic11—24no—
246C22⋊Dic11—24no—
247C22⋊Dic11—24no—
248C22⋊Dic11—24no—
249C22⋊Dic11—24no—
250C22⋊Dic11—24no—
251C22⋊Dic11C2×D414yes—
252C22⋊Dic11C2×D414yes—
253#4324—28no—
254#4324—28no—
255C4⋊Dic11—24no—
256C4⋊Dic11—24no—
257C4⋊Dic11—21no—
258C4⋊Dic11—21no—
259C4⋊Dic11—21no—
260C4⋊Dic11C2×D414yes—
261C4⋊Dic11C2×D414yes—
262C4⋊Dic11C2412yes—
263C4⋊Dic11C2412yes—
264C4⋊Dic11C2412yes—
265Dic11⋊C4—24no—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268Dic11⋊C4—24no—
269Dic11⋊C4—24no—
270C4×Dic11—24no—
271C4×Dic11—24no—
272C4×Dic11—24no—
273C4×Dic11C2×D412yes—
274C4×Dic11C2×D412yes—
275C4×Dic11C2412yes—
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×#461—111no—
290C2×#450—111no—
291C2×#450D1111yescharacteristic
292C2×#440—111no—
293C2×#440—111no—
294C2×C4×SD16—111no—
295C2×C4×SD16—111no—
296C2×#433—111no—
297C23×C11—216no—
298C23×C11—22no—
299C23×C11—24no—
300C23×C11—24no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—42no—
306C23×C11—42no—
307C23×C11—42no—
308C23×C11—42no—
309C23×C11—84no—
310C23×C11—84no—
311C23×C11—816no—
312C23×C11C22×D412yes—
313C23×C11C22×D411yescharacteristic
314Q8×C11—22no—
315Q8×C11—22no—
316Q8×C11—42no—
317D4×C11—216no—
318D4×C11—24no—
319D4×C11—24no—
320D4×C11—22no—
321D4×C11—22no—
322D4×C11C2×#4114yes—
323D4×C11C2×#4114yes—
324C2×C4×C11—22no—
325C2×C4×C11—24no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—42no—
331C2×C4×C11—42no—
332C2×C4×C11C22×D412yes—
333C2×C4×C11C22×D411yescharacteristic
334C2×C4×C11C2×#4112yes—
335C2×C4×C11C2×#4112yes—
336C2×C4×C11C2511yescharacteristic
337C2×Dic11—22no—
338C2×Dic11—22no—
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—42no—
349C2×Dic11—84no—
350C2×Dic11—84no—
351C2×Dic11—84no—
352C2×Dic11—84no—
353C2×Dic11C22×D412yes—
354C2×Dic11C22×D412yes—
355C2×Dic11C22×D412yes—
356C2×Dic11C22×D412yes—
357Dic22—22no—
358Dic22—22no—
359Dic22—42no—
360C8×C11—22no—
361C8×C11—22no—
362C11⋊C8—22no—
363C11⋊C8—22no—
364C23×D4C2×D1111yescharacteristic
365C22×SD16—111no—
366C22×SD16—111no—
367C22×SD16C2×D1111yescharacteristic
368C22×SD16C2×D1111yescharacteristic
369#541—118no—
370#541—224no—
371C2×C4⋊Q8—111no—
372C2×#126—221no—
373C2×#126—221no—
374C2×#125—111no—
375C2×#125—221no—
376C2×#125—221no—
377C2×C22⋊Q8—111no—
378C2×C22⋊Q8C2×D1111yescharacteristic
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—111no—
387C2×C4×D4—221no—
388C2×C4×D4—221no—
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#461—118no—
399#450—118no—
400#450C2×D1118yes—
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⋊C8—111no—
412C2×#103—111no—
413C2×#103—111no—
414C2×#103—111no—
415C2×#103—111no—
416C2×#102—111no—
417C2×#102—111no—
418C2×#102C2×D1111yescharacteristic
419C2×#102C2×D1111yescharacteristic
420C2×C22⋊C8—111no—
421C2×C22⋊C8C2×D1111yescharacteristic
422C2×#97—111no—
423C2×C4×C8—111no—
424C22×C11—22no—
425C22×C11—24no—
426C22×C11—24no—
427C22×C11—22no—
428C22×C11—22no—
429C22×C11—44no—
430C22×C11—48no—
431C22×C11—48no—
432C22×C11—42no—
433C22×C11—42no—
434C22×C11—42no—
435C22×C11—42no—
436C22×C11—816no—
437C22×C11#52512yes—
438C22×C11#57712yes—
439C22×C11#57712yes—
440C22×C11C23×D411yescharacteristic
441C4×C11—22no—
442C4×C11—42no—
443C4×C11—42no—
444C4×C11#52512yes—
445C4×C11C22×#4111yescharacteristic
446C4×C11C22×#4111yescharacteristic
447Dic11—22no—
448Dic11—22no—
449Dic11—22no—
450Dic11—22no—
451Dic11—42no—
452Dic11—42no—
453Dic11—42no—
454Dic11—42no—
455C25—21no—
456C22×Q8—111no—
457C22×Q8C22×D1111yescharacteristic
458C22×D4—24no—
459C22×D4—24no—
460C22×D4—21no—
461C22×D4—22no—
462C22×D4C22×D1114yes—
463C22×D4C22×D1111yescharacteristic
464C22×D4C22×D1111yescharacteristic
465C23×C4—221no—
466C23×C4—221no—
467C23×C4—221no—
468C23×C4—221no—
469C23×C4C22×D1111yescharacteristic
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—114no—
483C4⋊Q8—222no—
484#126—228no—
485#126—228no—
486#125—114no—
487#125—222no—
488#125—228no—
489#125—228no—
490C22⋊Q8—22no—
491C22⋊Q8—114no—
492C22⋊Q8—222no—
493C22⋊Q8C22×D1114yes—
494C4×Q8—114no—
495C4×Q8—114no—
496C4×Q8—222no—
497C4×Q8—222no—
498C4×D4—114no—
499C4×D4—114no—
500C4×D4—114no—
501C4×D4—114no—
502C4×D4—222no—
503C4×D4—222no—
504C4×D4—222no—
505C4×D4—222no—
506C4×D4—228no—
507C4×D4—228no—
508#117—114no—
509#117—114no—
510#117—114no—
511#117—222no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—111no—
514C2×C4⋊C4—111no—
515C2×C4⋊C4—111no—
516C2×C4⋊C4—111no—
517C2×C4⋊C4—111no—
518C2×C4⋊C4—221no—
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—111no—
539C2×C42—221no—
540C2×C42—221no—
541C2×C42—221no—
542#107—114no—
543#107—114no—
544#106—114no—
545#106—114no—
546C4⋊C8—114no—
547C4⋊C8—114no—
548#103—114no—
549#103—114no—
550#103—114no—
551#103—114no—
552#102—114no—
553#102—114no—
554#102C22×D1114yes—
555#102C22×D1114yes—
556C22⋊C8—114no—
557C22⋊C8C22×D1114yes—
558#97—114no—
559C4×C8—114no—
560C2×C11—42no—
561C2×C11—44no—
562C2×C11—44no—
563C2×C11#312314yescomplemented
564C2×C11C2×#52511yescharacteristic
565C2×C11C2×#57711yescharacteristic
566C2×C11C2×#57711yescharacteristic
567C24—28no—
568C24—21no—
569C24—21no—
570C24—24no—
571C24—82no—
572C24—82no—
573C24D4×D1111yescharacteristic
574C2×Q8—21no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—112no—
578C2×Q8—221no—
579C2×Q8—222no—
580C2×Q8—222no—
581C2×Q8C23×D1112yes—
582C2×D4—28no—
583C2×D4—216no—
584C2×D4—28no—
585C2×D4—28no—
586C2×D4—24no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4#434114yes—
592C2×D4#434114yes—
593C2×D4C23×D1112yes—
594C2×D4C23×D1112yes—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—111no—
600C22×C4—111no—
601C22×C4—111no—
602C22×C4—111no—
603C22×C4—224no—
604C22×C4—224no—
605C22×C4—224no—
606C22×C4—224no—
607C22×C4—221no—
608C22×C4—221no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—882no—
612C22×C4—882no—
613C22×C4—882no—
614C22×C4—882no—
615C22×C4D4×D1112yes—
616C22×C4D4×D1111yescharacteristic
617C22×C4C23×D1112yes—
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—21no—
633C4⋊C4—114no—
634C4⋊C4—114no—
635C4⋊C4—112no—
636C4⋊C4—112no—
637C4⋊C4—112no—
638C4⋊C4—224no—
639C4⋊C4—224no—
640C4⋊C4—224no—
641C4⋊C4—224no—
642C4⋊C4—224no—
643C4⋊C4—224no—
644C4⋊C4—221no—
645C4⋊C4—221no—
646C4⋊C4—221no—
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—112no—
661C42—112no—
662C42—224no—
663C42—224no—
664C42—224no—
665C11C2×#312311yescharacteristic, complemented, Sylow
666C23—216no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—24no—
671C23—24no—
672C23—22no—
673C23—22no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—84no—
679C23—84no—
680C23—816no—
681C23C2×D4×D1112yes—
682C23C2×D4×D1111yescharacteristic
683Q8—22no—
684Q8—22no—
685Q8—42no—
686Q8—222no—
687Q8—222no—
688Q8—442no—
689D4—216no—
690D4—24no—
691D4—24no—
692D4—22no—
693D4—22no—
694D4C2×#434114yes—
695D4C2×#434114yes—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—112no—
705C2×C4—112no—
706C2×C4—112no—
707C2×C4—112no—
708C2×C4—222no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—442no—
717C2×C4—442no—
718C2×C4—442no—
719C2×C4—442no—
720C2×C4—884no—
721C2×C4—884no—
722C2×C4—884no—
723C2×C4—884no—
724C2×C4C2×D4×D1112yes—
725C2×C4C2×D4×D1111yescharacteristic
726C2×C4C2×#434112yes—
727C2×C4C2×#434112yes—
728C2×C4C24×D1111yescharacteristic
729C8—22no—
730C8—22no—
731C8—222no—
732C8—222no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—24no—
737C22—24no—
738C22—44no—
739C22—48no—
740C22—48no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—816no—
746C22#1062311712yes—
747C22#1062329312yes—
748C22#1062330612yes—
749C22C22×D4×D1111yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—222no—
754C4—222no—
755C4—222no—
756C4—222no—
757C4—442no—
758C4—442no—
759C4—442no—
760C4—442no—
761C4#1062311712yes—
762C4C22×#434111yescharacteristic
763C4C22×#434111yescharacteristic
764C2—42no—
765C2—44no—
766C2—44no—
767C2#1307886214yesdirect product factor
768C2C2×#1062311711yescharacteristic
769C2C2×#1062329311yescharacteristic
770C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#450C2
socleC23×C11C22×D4
prime radicalC23×D4×C11C22
hypercenterC2×#450D11
hypocenterC11C2×#3123
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. C2×#10623156C2semidirect
3. #13078862C2direct (N × H)
4. C2×#10622336C2semidirect
5. C2×#10622658C2semidirect
6. C2×#10622376C2semidirect
7. C2×#10622379C2semidirect
8. C2×#10622775C2semidirect
9. C2×#10622775C2semidirect
11. C2×#10622777C2semidirect
12. C2×#10622370C2semidirect
13. C2×#10622371C2semidirect
14. C2×SD16×Dic11C2semidirect
15. C2×#10622333C2semidirect
23. C2×Q8×Dic11C22semidirect
24. C2×#66997C22semidirect
39. #10623156C22semidirect
41. C2×#66943C22semidirect
43. C2×#66940C22semidirect
50. C2×#66899C22semidirect
51. C2×#66899C22semidirect
56. #10622777C22semidirect
57. #10622775C22semidirect
58. #10622775C22semidirect
59. SD16×Dic11C22semidirect
60. C2×#66882C22semidirect
61. C2×#66881C22semidirect
62. C2×#66880C22semidirect
63. C2×#66880C22semidirect
64. C2×#66879C22semidirect
65. C2×Dic11⋊C8C22semidirect
66. C2×Dic11⋊C8C22semidirect
67. C2×C8×Dic11C22semidirect
68. #10622658C22semidirect
69. C2×#66872C22semidirect
70. C2×#66871C22semidirect
71. #10622379C22semidirect
72. #10622376C22semidirect
73. #10622371C22semidirect
74. #10622370C22semidirect
75. #10622336C22semidirect
76. #10622333C22semidirect
114. Q8×Dic11C23semidirect
116. #66997C23semidirect
158. #66943C23semidirect
161. #66940C23semidirect
167. #66899C23semidirect
168. #66899C23semidirect
172. #66882C23semidirect
173. #66881C23semidirect
174. #66880C23semidirect
175. #66880C23semidirect
176. #66879C23semidirect
177. Dic11⋊C8C23semidirect
178. Dic11⋊C8C23semidirect
179. C8×Dic11C23semidirect
180. #66872C23semidirect
181. #66871C23semidirect
563. C2×C11#3123semidirect
665. C11C2×#3123semidirect
767. C2#13078862direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231562
C2×#106233292
#130788622
C2×#106223362
C2×#106226582
C2×#106223762
C2×#106223792
C2×#106227752
C2×#106228312
C2×#106227772
C2×#106223702
C2×#106223712
C2×SD16×Dic112
C2×#106223332
C2×C11×#4502
C2×#312311