Finite Group Databasebeta

← C2×#13080611 #15630351

Subgroups — C2×#13080611 #15630351

Order 2816.

2374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623348C211yesmaximal, characteristic, complemented
2C2×#10623142C211yesmaximal, characteristic, complemented
3#13080611C2116yesmaximal, direct product factor
4C2×#10622408C211yesmaximal, characteristic, complemented
5C2×#10622422C211yesmaximal, characteristic, complemented
6C2×#10622349C211yesmaximal, characteristic, complemented
7C2×#10622407C211yesmaximal, characteristic, complemented
8C2×#10622787C211yesmaximal, characteristic, complemented
9C2×#10622651C211yesmaximal, characteristic, complemented
10C2×#10622778C211yesmaximal, characteristic, complemented
11C2×#10622785C211yesmaximal, characteristic, complemented
12C2×#10622777C211yesmaximal, characteristic, complemented
13C2×#10622343C211yesmaximal, characteristic, complemented
14C2×#10622416C211yesmaximal, characteristic, complemented
15C22×#66899C211yesmaximal, characteristic, complemented
16C2×C11×#448C211yesmaximal, characteristic, complemented
17C23×Q8×C11C2211yescharacteristic
18C22×#4343C2211yescharacteristic
19C22×#4341—21no—
20C22×C11×SD16C2211yescharacteristic
21C22×C11×SD16C2211yescharacteristic
22C2×C11×#121C2211yescharacteristic
23#10623348—24no—
24#10623348C2218yescomplemented
25C2×#67000—21no—
26C2×#67000C2211yescharacteristic
27C2×#66999—21no—
28C2×#66999C2211yescharacteristic
29C2×Q8×Dic11C2211yescharacteristic
30C2×#66991C2211yescharacteristic
31C2×#66988—21no—
32C2×D4×Dic11C2211yescharacteristic
33C22×#4323C2211yescharacteristic
34C2×#66983—21no—
35C2×#66983C2211yescharacteristic
36C2×C4×C22⋊D11—21no—
37C2×C4×C22⋊D11C2211yescharacteristic
38C22×C4⋊Dic11C2211yescharacteristic
39C23×C11⋊C8C2211yescharacteristic
40C22×#4313C2211yescharacteristic
41#10623142—24no—
42#10623142C2218yescomplemented
43C2×C4⋊C4×D11C2211yescharacteristic
44C2×#66941C2211yescharacteristic
45C2×#66936—21no—
46C2×#66931—21no—
47C11×#448C2218yescomplemented
48C2×C11×#103C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×#66899C2211yescharacteristic
55C2×#66899C2218yescomplemented
56C2×#66896C2211yescharacteristic
57#10622787C2218yescomplemented
58#10622785C2218yescomplemented
59#10622778C2218yescomplemented
60#10622777C2218yescomplemented
61C2×#66885C2211yescharacteristic
62C2×#66885C2211yescharacteristic
63C2×(C2×D11)⋊C8C2211yescharacteristic
64C2×#66882C2211yescharacteristic
65C2×#66882C2211yescharacteristic
66C2×#66879C2211yescharacteristic
67C2×Dic11⋊C8C2211yescharacteristic
68#10622651C2218yescomplemented
69C2×#66873C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71#10622422C2218yescomplemented
72#10622416C2218yescomplemented
73#10622408C2218yescomplemented
74#10622407C2218yescomplemented
75#10622349C2218yescomplemented
76#10622343C2218yescomplemented
77C22×Q8×C11—21no—
78C22×Q8×C11—22no—
79C22×Q8×C11—24no—
80C22×Q8×C11—42no—
81C22×Q8×C11C2311yescharacteristic
82C22×Q8×C11C2314yes—
83C22×Q8×C11C2311yescharacteristic
84C22×D4×C11—21no—
85C22×D4×C11C2311yescharacteristic
86C23×C4×C11—21no—
87C23×C4×C11C2311yescharacteristic
88C22×C22⋊D11—21no—
89C22×C22⋊D11—21no—
90C22×C22⋊D11D411yescharacteristic
91C23×Dic11—21no—
92C23×Dic11—21no—
93C2×#4343—22no—
94C2×#4343—24no—
95C2×#4343—42no—
96C2×#4343C2314yes—
97C2×#4341—28no—
98C2×#4341—48no—
99C22×D44—21no—
100C22×D44C2311yescharacteristic
101C22×C4×D11—21no—
102C22×C4×D11—21no—
103C22×C4×D11C2311yescharacteristic
104C22×Dic22—21no—
105C2×C11×SD16—24no—
106C2×C11×SD16—42no—
107C2×C11×SD16C2314yes—
108C2×C11×SD16C2314yes—
109C22×C8×C11C2311yescharacteristic
110C22×C8×C11C2311yescharacteristic
111C11×#121—22no—
112C11×#121C2314yes—
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C22⋊C4—21no—
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11—21no—
117C2×C22⋊Dic11D411yescharacteristic
118#67000—28no—
119#67000—22no—
120#67000C2314yes—
121#66999—22no—
122#66999—28no—
123#66999C2314yes—
124Q8×Dic11—22no—
125Q8×Dic11C2314yes—
126#66991—22no—
127#66991C2314yes—
128#66988—28no—
129D4×Dic11—22no—
130D4×Dic11C2314yes—
131C2×#4323—42no—
132C2×#4323C2314yes—
133#66983—22no—
134#66983—28no—
135#66983C2314yes—
136C4×C22⋊D11—28no—
137C4×C22⋊D11D414yes—
138C4×C22⋊D11C2314yes—
139C2×(C2×D11)⋊C4—21no—
140C2×(C2×D11)⋊C4—21no—
141C2×(C2×D11)⋊C4—21no—
142C2×(C2×D11)⋊C4—21no—
143C2×(C2×D11)⋊C4D411yescharacteristic
144C2×C4⋊Dic11—21no—
145C2×C4⋊Dic11—22no—
146C2×C4⋊Dic11—21no—
147C2×C4⋊Dic11C2311yescharacteristic
148C2×C4⋊Dic11C2311yescharacteristic
149C2×C4⋊Dic11C2314yes—
150C2×C4⋊Dic11C2311yescharacteristic
151C2×Dic11⋊C4—21no—
152C2×Dic11⋊C4—21no—
153C2×Dic11⋊C4—21no—
154C2×Dic11⋊C4D411yescharacteristic
155C2×C4×Dic11—21no—
156C2×C4×Dic11C2311yescharacteristic
157C22×C11⋊C8—42no—
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C22×C11⋊C8C2314yes—
161C2×#4313—42no—
162C2×#4313C2314yes—
163C4⋊C4×D11—22no—
164C4⋊C4×D11C2314yes—
165#66941—22no—
166#66941C2314yes—
167#66936—28no—
168#66931—28no—
169C11×#103C2314yes—
170C11×#103C2314yes—
171C11×C22⋊C8C2314yes—
172#66899C2314yes—
173#66899C2314yes—
174#66899C2314yes—
175#66899C2314yes—
176#66896C2314yes—
177#66885C2314yes—
178#66885C2314yes—
179(C2×D11)⋊C8C2314yes—
180#66882C2314yes—
181#66882C2314yes—
182#66879C2314yes—
183Dic11⋊C8C2314yes—
184#66873C2314yes—
185#66871C2314yes—
186C2×#3308—111nomaximal, Sylow
187C24×C11—21no—
188C24×C11C2×D411yescharacteristic
189C23×D11—21no—
190C23×D11C2×D411yescharacteristic
191C2×Q8×C11—21no—
192C2×Q8×C11—24no—
193C2×Q8×C11—21no—
194C2×Q8×C11—22no—
195C2×Q8×C11—28no—
196C2×Q8×C11—22no—
197C2×Q8×C11—22no—
198C2×Q8×C11—44no—
199C2×Q8×C11—44no—
200C2×Q8×C11—48no—
201C2×Q8×C11#4114yescomplemented
202C2×Q8×C11C2412yes—
203C2×Q8×C11C2412yes—
204C2×D4×C11—24no—
205C2×D4×C11—21no—
206C2×D4×C11—22no—
207C2×D4×C11—22no—
208C2×D4×C11—44no—
209C2×D4×C11C2412yes—
210C22×C4×C11—21no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—24no—
216C22×C4×C11—44no—
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D412yes—
219C22×C4×C11C2412yes—
220C22×C4×C11C2411yescharacteristic
221C2×C22⋊D11—24no—
222C2×C22⋊D11—24no—
223C2×C22⋊D11—24no—
224C2×C22⋊D11—44no—
225C2×C22⋊D11—44no—
226C2×C22⋊D11C2×D414yes—
227C22×Dic11—24no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—24no—
232C22×Dic11—44no—
233C22×Dic11—44no—
234C22×Dic11C2×D411yescharacteristic
235C22×Dic11C2×D411yescharacteristic
236C22×Dic11C2×D411yescharacteristic
237#4343—28no—
238#4343—44no—
239#4343—48no—
240#4341—432no—
241C2×D44—24no—
242C2×D44—21no—
243C2×D44—22no—
244C2×D44—22no—
245C2×D44—44no—
246C2×D44C2412yes—
247C2×C4×D11—24no—
248C2×C4×D11—24no—
249C2×C4×D11—22no—
250C2×C4×D11—22no—
251C2×C4×D11—44no—
252C2×C4×D11—44no—
253C2×C4×D11C2×D412yes—
254C2×C4×D11C2412yes—
255C2×Dic22—24no—
256C2×Dic22—44no—
257C11×SD16—28no—
258C11×SD16—44no—
259C2×C8×C11—22no—
260C2×C8×C11—22no—
261C2×C8×C11C2412yes—
262C2×C8×C11C2412yes—
263C11×C4⋊C4—21no—
264C11×C4⋊C4C2412yes—
265C11×C22⋊C4—24no—
266C22⋊Dic11—24no—
267C22⋊Dic11—24no—
268C22⋊Dic11C2×D414yes—
269#4323—44no—
270(C2×D11)⋊C4—24no—
271(C2×D11)⋊C4—24no—
272(C2×D11)⋊C4—24no—
273(C2×D11)⋊C4—24no—
274(C2×D11)⋊C4C2×D414yes—
275C4⋊Dic11—24no—
276C4⋊Dic11—24no—
277C4⋊Dic11—21no—
278C4⋊Dic11—21no—
279C4⋊Dic11—21no—
280C4⋊Dic11C2412yes—
281C4⋊Dic11C2412yes—
282C4⋊Dic11C2412yes—
283Dic11⋊C4—24no—
284Dic11⋊C4—24no—
285Dic11⋊C4—24no—
286Dic11⋊C4C2×D414yes—
287C4×Dic11—24no—
288C4×Dic11C2×D412yes—
289C4×Dic11C2412yes—
290C2×C11⋊C8—22no—
291C2×C11⋊C8—22no—
292C2×C11⋊C8—44no—
293C2×C11⋊C8C2412yes—
294C2×C11⋊C8C2412yes—
295#4313—44no—
296C2×#548—111no—
297C2×#547—111no—
298#3308—1116no—
299C2×#489—111no—
300C2×#484—111no—
301C2×#480—111no—
302C2×#477—111no—
303C2×#468—111no—
304C2×#466—111no—
305C2×#463—111no—
306C2×#449—111no—
307C2×#448D1111yescharacteristic, complemented
308C2×#440—111no—
309C2×#435—111no—
310C2×#417—111no—
311C22×#103—111no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—42no—
316C23×C11—42no—
317C23×C11—42no—
318C23×C11AGL(1,ℤ/8)14yes—
319C23×C11C22×D412yes—
320C23×C11C22×D411yescharacteristic
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—42no—
326C22×D11—42no—
327C22×D11—42no—
328C22×D11C22×D412yes—
329Q8×C11—24no—
330Q8×C11—22no—
331Q8×C11—22no—
332Q8×C11—22no—
333Q8×C11—48no—
334Q8×C11—42no—
335Q8×C11C2×#4114yescomplemented
336D4×C11—22no—
337D4×C11—22no—
338D4×C11—48no—
339D4×C11—42no—
340C2×C4×C11—24no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—24no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—48no—
349C2×C4×C11—42no—
350C2×C4×C11—42no—
351C2×C4×C11C22×D412yes—
352C2×C4×C11C22×D411yescharacteristic
353C2×C4×C11C2×#4112yes—
354C2×C4×C11H(5,𝔽2)12yes—
355C2×C4×C11C2511yescharacteristic
356C22⋊D11—28no—
357C22⋊D11—48no—
358C22⋊D11—48no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—48no—
366C2×Dic11—42no—
367C2×Dic11—42no—
368C2×Dic11—48no—
369C2×Dic11—42no—
370C2×Dic11C22×D412yes—
371C2×Dic11C22×D412yes—
372C2×Dic11C22×D412yes—
373D44—22no—
374D44—22no—
375D44—48no—
376D44—42no—
377C4×D11—24no—
378C4×D11—22no—
379C4×D11—22no—
380C4×D11—48no—
381C4×D11—48no—
382Dic22—48no—
383C8×C11—22no—
384C8×C11—22no—
385C11⋊C8—22no—
386C11⋊C8—22no—
387C22×#41—111no—
388C22×#41—221no—
389C23×Q8C2×D1111yescharacteristic
390C22×SD16C2×D1111yescharacteristic
391C22×SD16C2×D1111yescharacteristic
392C22×D8—111no—
393C22×M16—111no—
394C23×C8—111no—
395#548—118no—
396#548—224no—
397#547—118no—
398#547—224no—
399C2×C4⋊Q8—111no—
400C2×#124—111no—
401C2×#124—221no—
402C2×#123—221no—
403C2×#123—221no—
404C2×C22⋊Q8—111no—
405C2×C22⋊Q8—221no—
406C2×C22⋊Q8—221no—
407C2×#121—111no—
408C2×#121—111no—
409C2×#121—221no—
410C2×#121C2×D1111yescharacteristic
411C2×C4×Q8—111no—
412C2×C4×D4—111no—
413C2×C4×D4—111no—
414C2×C4×D4—221no—
415C22×C4⋊C4—111no—
416C22×C4⋊C4—111no—
417#489—118no—
418#484—118no—
419#480—118no—
420#477—118no—
421#468—118no—
422#466—118no—
423#463—118no—
424#449—118no—
425#448C2×D1118yescomplemented
426#440—118no—
427#435—118no—
428C2×#107—111no—
429C2×#107—111no—
430C2×#107—111no—
431C2×C4⋊C8—111no—
432#417—118no—
433C2×#103—111no—
434C2×#103—111no—
435C2×#103—111no—
436C2×#103—111no—
437C2×#103—118no—
438C2×#103C2×D1111yescharacteristic
439C2×#103C2×D1111yescharacteristic
440C2×#102—111no—
441C2×#102—111no—
442C2×#102—111no—
443C2×#102—111no—
444C2×C22⋊C8—111no—
445C2×C22⋊C8C2×D1111yescharacteristic
446C2×#97—111no—
447C22×C11—22no—
448C22×C11—28no—
449C22×C11—22no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—84no—
454C22×C11#54612yes—
455C22×C11C2×AGL(1,ℤ/8)14yes—
456C22×C11C2×AGL(1,ℤ/8)12yes—
457C22×C11#57812yes—
458C22×C11C23×D411yescharacteristic
459C2×D11—22no—
460C2×D11—22no—
461C2×D11—22no—
462C2×D11—44no—
463C2×D11—42no—
464C2×D11—42no—
465C2×D11—42no—
466C2×D11—84no—
467C4×C11—22no—
468C4×C11—24no—
469C4×C11—42no—
470C4×C11—42no—
471C4×C11#54612yes—
472C4×C11C22×#4111yescharacteristic
473C4×C11C2×H(5,𝔽2)11yescharacteristic
474Dic11—22no—
475Dic11—22no—
476Dic11—22no—
477Dic11—42no—
478Dic11—42no—
479Dic11—42no—
480C2×#41—114no—
481C2×#41—222no—
482C2×#41—228no—
483C2×#41—224no—
484C2×#41—442no—
485C2×#41—448no—
486C22×Q8—21no—
487C22×Q8—22no—
488C22×Q8—24no—
489C22×Q8—42no—
490C22×Q8—221no—
491C22×Q8C22×D1111yescharacteristic
492C22×Q8C22×D1114yes—
493C22×Q8C22×D1111yescharacteristic
494C22×D4—21no—
495C22×D4—111no—
496C22×D4—111no—
497C22×D4—221no—
498C22×D4—221no—
499C22×D4—221no—
500C22×D4C22×D1111yescharacteristic
501C23×C4—21no—
502C23×C4—111no—
503C23×C4—221no—
504C23×C4—221no—
505C23×C4—221no—
506C23×C4—221no—
507C23×C4C22×D1111yescharacteristic
508C2×SD16—24no—
509C2×SD16—42no—
510C2×SD16C22×D1114yes—
511C2×SD16C22×D1114yes—
512C2×D8—114no—
513C2×D8—442no—
514C2×M16—114no—
515C2×M16—442no—
516C22×C8—111no—
517C22×C8—111no—
518C22×C8—114no—
519C22×C8—442no—
520C22×C8C22×D1111yescharacteristic
521C22×C8C22×D1111yescharacteristic
522C4⋊Q8—114no—
523C4⋊Q8—222no—
524#124—114no—
525#124—222no—
526#124—228no—
527#123—228no—
528#123—228no—
529C22⋊Q8—114no—
530C22⋊Q8—228no—
531C22⋊Q8—228no—
532C22⋊Q8—222no—
533#121—22no—
534#121—114no—
535#121—114no—
536#121—228no—
537#121—222no—
538#121—222no—
539#121C22×D1114yes—
540C4×Q8—114no—
541C4×Q8—222no—
542C4×D4—114no—
543C4×D4—114no—
544C4×D4—114no—
545C4×D4—222no—
546C4×D4—228no—
547C2×C4⋊C4—111no—
548C2×C4⋊C4—111no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—114no—
551C2×C4⋊C4—111no—
552C2×C4⋊C4—114no—
553C2×C4⋊C4—222no—
554C2×C4⋊C4—221no—
555C2×C4⋊C4—221no—
556C2×C4⋊C4—221no—
557C2×C4⋊C4—221no—
558C2×C4⋊C4—221no—
559C2×C4⋊C4—222no—
560C2×C4⋊C4C22×D1111yescharacteristic
561C2×C22⋊C4—21no—
562C2×C22⋊C4—111no—
563C2×C22⋊C4—111no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—221no—
567C2×C22⋊C4—221no—
568C2×C22⋊C4—221no—
569C2×C22⋊C4—221no—
570C2×C42—111no—
571C2×C42—221no—
572#107—114no—
573#107—114no—
574#107—114no—
575C4⋊C8—114no—
576#103—114no—
577#103—114no—
578#103—114no—
579#103—114no—
580#103C22×D1114yes—
581#103C22×D1114yes—
582#102—114no—
583#102—114no—
584#102—114no—
585#102—114no—
586C22⋊C8—114no—
587C22⋊C8C22×D1114yes—
588#97—114no—
589C2×C11—24no—
590C2×C11—82no—
591C2×C11#330814yescomplemented
592C2×C11C2×#54611yescharacteristic
593C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
594C2×C11C2×#57811yescharacteristic
595D11—42no—
596D11—82no—
597C24—21no—
598C24—111no—
599C24—221no—
600C24D4×D1111yescharacteristic
601#41—228no—
602#41—444no—
603#41—448no—
604#41—4432no—
605C2×Q8—21no—
606C2×Q8—24no—
607C2×Q8—21no—
608C2×Q8—22no—
609C2×Q8—28no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—44no—
613C2×Q8—44no—
614C2×Q8—48no—
615C2×Q8—224no—
616C2×Q8—444no—
617C2×Q8#434114yescomplemented
618C2×Q8C23×D1112yes—
619C2×Q8C23×D1112yes—
620C2×D4—24no—
621C2×D4—21no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—44no—
625C2×D4—114no—
626C2×D4—112no—
627C2×D4—224no—
628C2×D4—224no—
629C2×D4—224no—
630C2×D4—224no—
631C2×D4—221no—
632C2×D4—222no—
633C2×D4—222no—
634C2×D4—444no—
635C2×D4—444no—
636C2×D4—444no—
637C2×D4C23×D1112yes—
638C22×C4—21no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—24no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—44no—
645C22×C4—111no—
646C22×C4—111no—
647C22×C4—111no—
648C22×C4—112no—
649C22×C4—112no—
650C22×C4—224no—
651C22×C4—224no—
652C22×C4—224no—
653C22×C4—222no—
654C22×C4—222no—
655C22×C4—224no—
656C22×C4—221no—
657C22×C4—221no—
658C22×C4—221no—
659C22×C4—444no—
660C22×C4—444no—
661C22×C4—444no—
662C22×C4—444no—
663C22×C4D4×D1112yes—
664C22×C4D4×D1111yescharacteristic
665C22×C4C23×D1112yes—
666C22×C4C23×D1111yescharacteristic
667SD16—28no—
668SD16—44no—
669D8—444no—
670M16—444no—
671C2×C8—22no—
672C2×C8—22no—
673C2×C8—112no—
674C2×C8—112no—
675C2×C8—222no—
676C2×C8—222no—
677C2×C8—444no—
678C2×C8C23×D1112yes—
679C2×C8C23×D1112yes—
680C4⋊C4—21no—
681C4⋊C4—114no—
682C4⋊C4—112no—
683C4⋊C4—112no—
684C4⋊C4—112no—
685C4⋊C4—224no—
686C4⋊C4—224no—
687C4⋊C4—224no—
688C4⋊C4—224no—
689C4⋊C4—221no—
690C4⋊C4—221no—
691C4⋊C4—224no—
692C4⋊C4—221no—
693C4⋊C4C23×D1112yes—
694C22⋊C4—24no—
695C22⋊C4—114no—
696C22⋊C4—114no—
697C22⋊C4—224no—
698C22⋊C4—224no—
699C22⋊C4—224no—
700C22⋊C4—224no—
701C22⋊C4—224no—
702C22⋊C4—224no—
703C42—112no—
704C42—112no—
705C42—224no—
706C11C2×#330811yescharacteristic, complemented, Sylow
707C23—22no—
708C23—22no—
709C23—22no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—112no—
714C23—222no—
715C23—222no—
716C23—222no—
717C23—222no—
718C23—442no—
719C23—442no—
720C23—442no—
721C23#6696714yes—
722C23C2×D4×D1112yes—
723C23C2×D4×D1111yescharacteristic
724Q8—24no—
725Q8—22no—
726Q8—22no—
727Q8—22no—
728Q8—48no—
729Q8—42no—
730Q8—448no—
731Q8C2×#434114yescomplemented
732D4—22no—
733D4—22no—
734D4—48no—
735D4—42no—
736D4—228no—
737D4—222no—
738D4—222no—
739D4—448no—
740D4—448no—
741D4—448no—
742D4—442no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—48no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—112no—
755C2×C4—112no—
756C2×C4—112no—
757C2×C4—222no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—224no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—448no—
767C2×C4—448no—
768C2×C4—448no—
769C2×C4—442no—
770C2×C4—442no—
771C2×C4—448no—
772C2×C4—442no—
773C2×C4C2×D4×D1112yes—
774C2×C4C2×D4×D1111yescharacteristic
775C2×C4C2×#434112yes—
776C2×C4#6703712yes—
777C2×C4C24×D1111yescharacteristic
778C8—22no—
779C8—22no—
780C8—222no—
781C8—222no—
782C22—28no—
783C22—22no—
784C22—22no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—84no—
789C22—222no—
790C22—222no—
791C22—222no—
792C22—444no—
793C22—442no—
794C22—442no—
795C22—442no—
796C22—884no—
797C22#1062312212yes—
798C22C2×#6696714yes—
799C22C2×#6696712yes—
800C22#1062331012yes—
801C22C22×D4×D1111yescharacteristic
802C4—22no—
803C4—24no—
804C4—42no—
805C4—42no—
806C4—222no—
807C4—222no—
808C4—222no—
809C4—442no—
810C4—442no—
811C4—442no—
812C4#1062312212yes—
813C4C22×#434111yescharacteristic
814C4C2×#6703711yescharacteristic
815C2—24no—
816C2—82no—
817C2—442no—
818C2—882no—
819C2#1308061114yesdirect product factor
820C2C2×#1062312211yescharacteristic
821C2C22×#6696711yescharacteristic
822C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#448C2
socleC23×C11C22×D4
hypercenterC2×#448D11
hypocenterC11C2×#3308
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C2×#10623348C2semidirect
2. C2×#10623142C2semidirect
3. #13080611C2direct (N × H)
4. C2×#10622408C2semidirect
5. C2×#10622422C2semidirect
6. C2×#10622349C2semidirect
7. C2×#10622407C2semidirect
8. C2×#10622787C2semidirect
9. C2×#10622651C2semidirect
10. C2×#10622778C2semidirect
11. C2×#10622785C2semidirect
12. C2×#10622777C2semidirect
13. C2×#10622343C2semidirect
14. C2×#10622416C2semidirect
15. C22×#66899C2semidirect
16. C2×C11×#448C2semidirect
24. #10623348C22semidirect
42. #10623142C22semidirect
47. C11×#448C22semidirect
55. C2×#66899C22semidirect
57. #10622787C22semidirect
58. #10622785C22semidirect
59. #10622778C22semidirect
60. #10622777C22semidirect
68. #10622651C22semidirect
71. #10622422C22semidirect
72. #10622416C22semidirect
73. #10622408C22semidirect
74. #10622407C22semidirect
75. #10622349C22semidirect
76. #10622343C22semidirect
201. C2×Q8×C11#41semidirect
307. C2×#448D11semidirect
335. Q8×C11C2×#41semidirect
425. #448C2×D11semidirect
591. C2×C11#3308semidirect
617. C2×Q8#4341semidirect
706. C11C2×#3308semidirect
731. Q8C2×#4341semidirect
819. C2#13080611direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233482
C2×#106231422
#130806112
C2×#106224082
C2×#106224222
C2×#106223492
C2×#106224072
C2×#106227872
C2×#106226512
C2×#106227782
C2×#106227852
C2×#106227772
C2×#106223432
C2×#106224162
C22×#668992
C2×C11×#4482
C2×#330811