Finite Group Databasebeta

← C2×#13080694 #15630296

Subgroups — C2×#13080694 #15630296

Order 2816.

2298 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×#10623261C211yesmaximal, characteristic, complemented
2C2×#10623085C211yesmaximal, characteristic
3#13080694C2116yesmaximal, direct product factor
4C2×#10622702C211yesmaximal, characteristic, complemented
5C2×#10622497C211yesmaximal, characteristic, complemented
6C2×#10622495C211yesmaximal, characteristic, complemented
7C2×#10622499C211yesmaximal, characteristic, complemented
8C2×#10622500C211yesmaximal, characteristic, complemented
9C2×#10622458C211yesmaximal, characteristic, complemented
10C2×#10622396C211yesmaximal, characteristic, complemented
11C2×#10622389C211yesmaximal, characteristic, complemented
12C2×#10622631C211yesmaximal, characteristic, complemented
13C2×#10622449C211yesmaximal, characteristic, complemented
14C2×#10622384C211yesmaximal, characteristic, complemented
15C2×D11×#102C211yesmaximal, characteristic, complemented
16C2×C11×#474C211yesmaximal, characteristic, complemented
17C22×#4341C2211yescharacteristic
18C22×D4×D11C2211yescharacteristic
19C2×C11×C4⋊Q8C2211yescharacteristic, complemented
20C2×C4×D4×C11C2211yescharacteristic
21C2×#66999—21no—
22C2×#66999—21no—
23C22×#4324C2211yescharacteristic
24C2×#66983—21no—
25C22×(C2×D11)⋊C4—21no—
26C22×Dic44C2211yescharacteristic, complemented
27C22×#4314C2211yescharacteristic
28C22×#4313C2211yescharacteristic, complemented
29C22×C8×D11C2211yescharacteristic
30#10623261—24no—
31#10623261C2218yescomplemented
32#10623085—24no—
33#10623085C2218yes—
34C2×#66950C2211yescharacteristic
35C2×#66950C2211yescharacteristic
36C2×#66950C2211yescharacteristic, complemented
37C2×#66948C2211yescharacteristic
38C2×#66946—21no—
39C2×C4⋊C4×D11C2211yescharacteristic
40C2×C4⋊C4×D11C2211yescharacteristic, complemented
41C2×#66943—21no—
42C2×#66939—21no—
43C2×#66935—21no—
44C2×#66928C2211yescharacteristic
45C2×C4×D44C2211yescharacteristic
46C2×C4×Dic22C2211yescharacteristic, complemented
47C11×#474C2218yescomplemented
48C2×C11×#107C2211yescharacteristic, complemented
49C2×C11×#107C2211yescharacteristic, complemented
50C2×C11×C4⋊C8C2211yescharacteristic, complemented
51C2×C11×#102C2211yescharacteristic
52C2×C11×#102C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54C2×#66885C2211yescharacteristic
55C2×(C2×D11)⋊C8C2211yescharacteristic
56C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
57C2×#66880C2211yescharacteristic, complemented
58#10622702C2218yescomplemented
59#10622631C2218yescomplemented
60C2×#66874C2211yescharacteristic, complemented
61C2×#66874C2211yescharacteristic, complemented
62C2×#66874C2211yescharacteristic, complemented
63C2×#66873C2211yescharacteristic
64C2×#66873C2211yescharacteristic
65C2×#66871C2211yescharacteristic, complemented
66C2×#66867C2211yescharacteristic, complemented
67#10622500C2218yescomplemented
68#10622499C2218yescomplemented
69#10622497C2218yescomplemented
70#10622495C2218yescomplemented
71#10622458C2218yescomplemented
72#10622449C2218yescomplemented
73#10622396C2218yescomplemented
74#10622389C2218yescomplemented
75#10622384C2218yescomplemented
76D11×#102C2218yescomplemented
77C24×D11—21no—
78C22×Q8×C11—21no—
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11—21no—
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C23×Dic11—21no—
84C2×#4341—24no—
85C2×#4341—22no—
86C2×#4341—42no—
87C2×#4341C2314yes—
88C2×D4×D11—24no—
89C2×D4×D11—22no—
90C2×D4×D11—42no—
91C2×D4×D11C2314yes—
92C22×D44—21no—
93C22×D44D411yescharacteristic
94C22×D44C2311yescharacteristic
95C22×C4×D11—21no—
96C22×C4×D11—21no—
97C22×C4×D11C2311yescharacteristic
98C22×C4×D11C2311yescharacteristic
99C22×Dic22C2311yescharacteristic
100C22×Dic22C2311yescharacteristic
101C22×C8×C11C2311yescharacteristic
102C22×C8×C11C2311yescharacteristic
103C11×C4⋊Q8—22no—
104C11×C4⋊Q8C2314yescomplemented
105C4×D4×C11—22no—
106C4×D4×C11C2314yes—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C22⋊C4—21no—
112C2×C42×C11C2311yescharacteristic
113#66999—28no—
114#66999—28no—
115C2×#4324—24no—
116C2×#4324C2314yes—
117#66983—28no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4—21no—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4—28no—
125C2×(C2×D11)⋊C4D411yescharacteristic
126C2×(C2×D11)⋊C4D411yescharacteristic
127C2×C4⋊Dic11—21no—
128C2×C4⋊Dic11—21no—
129C2×C4⋊Dic11—21no—
130C2×C4⋊Dic11D411yescharacteristic
131C2×C4⋊Dic11C2311yescharacteristic
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×C4×Dic11—21no—
136C22×C11⋊C8C2311yescharacteristic
137C22×C11⋊C8C2311yescharacteristic
138C2×Dic44—42no—
139C2×Dic44C2314yescomplemented
140C2×#4314—42no—
141C2×#4314C2314yes—
142C2×#4313—42no—
143C2×#4313C2314yescomplemented
144C2×C8×D11—42no—
145C2×C8×D11C2314yes—
146#66950—22no—
147#66950—22no—
148#66950—22no—
149#66950C2314yes—
150#66950C2314yes—
151#66950C2314yescomplemented
152#66948—22no—
153#66948C2314yes—
154#66946—28no—
155C4⋊C4×D11—22no—
156C4⋊C4×D11—22no—
157C4⋊C4×D11C2314yes—
158C4⋊C4×D11C2314yescomplemented
159#66943—28no—
160#66939—28no—
161#66935—28no—
162#66928—22no—
163#66928C2314yes—
164C4×D44D414yes—
165C4×D44C2314yes—
166C4×Dic22—22no—
167C4×Dic22C2314yescomplemented
168C11×#107C2314yescomplemented
169C11×#107C2314yescomplemented
170C11×C4⋊C8C2314yescomplemented
171C11×#102C2314yes—
172C11×#102C2314yes—
173#66896C2314yes—
174#66885C2314yes—
175(C2×D11)⋊C8C2314yes—
176(C2×D11)⋊C8C2314yescomplemented
177#66880C2314yescomplemented
178#66874C2314yescomplemented
179#66874C2314yescomplemented
180#66874C2314yescomplemented
181#66873C2314yes—
182#66873C2314yes—
183#66871C2314yescomplemented
184#66867C2314yescomplemented
185C2×#3314—111nomaximal, Sylow
186C24×C11—21no—
187C23×D11—21no—
188C23×D11—24no—
189C23×D11—44no—
190C23×D11—44no—
191C23×D11—82no—
192C23×D11C2×D411yescharacteristic
193C23×D11C2×D411yescharacteristic
194C2×Q8×C11—24no—
195C2×Q8×C11—82no—
196C2×D4×C11—21no—
197C2×D4×C11—22no—
198C2×D4×C11#4114yes—
199C2×D4×C11C2412yes—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—24no—
204C22×C4×C11—82no—
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2411yescharacteristic
208C2×C22⋊D11—24no—
209C2×C22⋊D11—24no—
210C2×C22⋊D11—44no—
211C2×C22⋊D11—44no—
212C22×Dic11—24no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—44no—
217C22×Dic11C2×D411yescharacteristic
218C22×Dic11C2×D411yescharacteristic
219#4341—28no—
220#4341—44no—
221#4341—48no—
222D4×D11—28no—
223D4×D11—44no—
224D4×D11—48no—
225C2×D44—24no—
226C2×D44—24no—
227C2×D44—21no—
228C2×D44—22no—
229C2×D44—22no—
230C2×D44—82no—
231C2×D44C2×D414yes—
232C2×D44C2412yes—
233C2×C4×D11—24no—
234C2×C4×D11—24no—
235C2×C4×D11—22no—
236C2×C4×D11—22no—
237C2×C4×D11—22no—
238C2×C4×D11—22no—
239C2×C4×D11—82no—
240C2×C4×D11—82no—
241C2×C4×D11C2×D412yes—
242C2×C4×D11C2×D412yes—
243C2×C4×D11C2412yes—
244C2×C4×D11C2412yes—
245C2×Dic22—21no—
246C2×Dic22—21no—
247C2×Dic22—22no—
248C2×Dic22—22no—
249C2×Dic22—22no—
250C2×Dic22—22no—
251C2×Dic22C2412yes—
252C2×Dic22C2412yes—
253C2×C8×C11—22no—
254C2×C8×C11—22no—
255C2×C8×C11C2412yes—
256C2×C8×C11C2412yes—
257C11×C4⋊C4—24no—
258C11×C4⋊C4—21no—
259C11×C4⋊C4—21no—
260C11×C4⋊C4—21no—
261C11×C4⋊C4C2412yes—
262C11×C4⋊C4C2412yes—
263C11×C4⋊C4C2412yes—
264C11×C22⋊C4—24no—
265C42×C11C2×D412yes—
266C42×C11C2412yes—
267#4324—28no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4—24no—
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—
275(C2×D11)⋊C4C2×D414yes—
276C4⋊Dic11—24no—
277C4⋊Dic11—24no—
278C4⋊Dic11—24no—
279C4⋊Dic11—21no—
280C4⋊Dic11C2×D414yes—
281C4⋊Dic11C2412yes—
282Dic11⋊C4—24no—
283Dic11⋊C4—24no—
284Dic11⋊C4—24no—
285C4×Dic11—24no—
286C2×C11⋊C8—22no—
287C2×C11⋊C8—22no—
288C2×C11⋊C8C2412yes—
289C2×C11⋊C8C2412yes—
290Dic44—44no—
291#4314—44no—
292#4313—44no—
293C8×D11—44no—
294C2×#554—111no—
295C2×#546—111no—
296#3314—1116no—
297C2×#489—111no—
298C2×#484—111no—
299C2×#480—111no—
300C2×#474D1111yescharacteristic, complemented
301C2×#468—111no—
302C2×#467—111no—
303C2×#464—111no—
304C2×#452—111no—
305C2×#450—111no—
306C2×#440—111no—
307C2×#435—111no—
308C2×#417—111no—
309C22×#102—111no—
310C23×C11—24no—
311C23×C11—22no—
312C23×C11—42no—
313C23×C11—42no—
314C23×C11C22×D411yescharacteristic
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—48no—
322C22×D11—42no—
323C22×D11—42no—
324C22×D11—42no—
325C22×D11—48no—
326C22×D11—84no—
327C22×D11—816no—
328C22×D11#13714yes—
329C22×D11C22×D412yes—
330C22×D11C22×D412yes—
331Q8×C11—84no—
332D4×C11—24no—
333D4×C11—22no—
334D4×C11C2×#4114yes—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—42no—
341C2×C4×C11—42no—
342C2×C4×C11—42no—
343C2×C4×C11—84no—
344C2×C4×C11C22×D412yes—
345C2×C4×C11C22×D412yes—
346C2×C4×C11C22×D411yescharacteristic
347C2×C4×C11C2×#4112yes—
348C2×C4×C11H(5,𝔽2)12yes—
349C2×C4×C11C2511yescharacteristic
350C22⋊D11—48no—
351C22⋊D11—48no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—48no—
358C2×Dic11—42no—
359C2×Dic11—42no—
360C2×Dic11—42no—
361C2×Dic11C22×D412yes—
362C2×Dic11C22×D412yes—
363D44—28no—
364D44—22no—
365D44—22no—
366D44—42no—
367D44—84no—
368C4×D11—24no—
369C4×D11—24no—
370C4×D11—22no—
371C4×D11—22no—
372C4×D11—22no—
373C4×D11—22no—
374C4×D11—84no—
375C4×D11—84no—
376Dic22—22no—
377Dic22—22no—
378Dic22—22no—
379Dic22—22no—
380Dic22—42no—
381Dic22—42no—
382C8×C11—22no—
383C8×C11—22no—
384C11⋊C8—22no—
385C11⋊C8—22no—
386C22×#41—111no—
387C23×D4—111no—
388C22×Q16—111no—
389C22×SD16—111no—
390C22×SD16—111no—
391C22×M16—111no—
392C23×C8—111no—
393#554—118no—
394#554—224no—
395#546—118no—
396#546—224no—
397C2×C4⋊Q8C2×D1111yescharacteristic, complemented
398C2×#125—221no—
399C2×#124—111no—
400C2×#123—221no—
401C2×C22⋊Q8—111no—
402C2×C22⋊Q8—111no—
403C2×C22⋊Q8—111no—
404C2×C22⋊Q8—221no—
405C2×C22⋊Q8—221no—
406C2×#121—111no—
407C2×#121—221no—
408C2×#120—221no—
409C2×C4×Q8—111no—
410C2×C4×D4—111no—
411C2×C4×D4—221no—
412C2×C4×D4C2×D1111yescharacteristic
413C22×C4⋊C4—111no—
414C22×C4⋊C4—111no—
415C22×C22⋊C4—221no—
416#489—118no—
417#484—118no—
418#480—118no—
419#474C2×D1118yescomplemented
420#468—118no—
421#467—118no—
422#464—118no—
423#452—118no—
424#450—118no—
425#440—118no—
426#435—118no—
427C2×#107—111no—
428C2×#107C2×D1111yescharacteristic, complemented
429C2×#107C2×D1111yescharacteristic, complemented
430C2×C4⋊C8C2×D1111yescharacteristic, complemented
431#417—118no—
432C2×#103—111no—
433C2×#103—111no—
434C2×#103—111no—
435C2×#103—111no—
436C2×#102—111no—
437C2×#102—111no—
438C2×#102—111no—
439C2×#102—111no—
440C2×#102—118no—
441C2×#102C2×D1111yescharacteristic
442C2×#102C2×D1111yescharacteristic
443C2×C22⋊C8—111no—
444C2×C22⋊C8—111no—
445C2×#97—111no—
446C22×C11—24no—
447C22×C11—48no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11#54612yes—
451C22×C11C2×#13712yes—
452C22×C11#57612yes—
453C22×C11C23×D411yescharacteristic
454C2×D11—22no—
455C2×D11—28no—
456C2×D11—22no—
457C2×D11—22no—
458C2×D11—22no—
459C2×D11—22no—
460C2×D11—44no—
461C2×D11—42no—
462C2×D11—42no—
463C2×D11—42no—
464C2×D11—816no—
465C2×D11—84no—
466C2×D11C2×#13714yes—
467C4×C11—22no—
468C4×C11—22no—
469C4×C11—42no—
470C4×C11—42no—
471C4×C11—42no—
472C4×C11#54612yes—
473C4×C11C22×#4111yescharacteristic
474C4×C11C2×H(5,𝔽2)11yescharacteristic
475Dic11—22no—
476Dic11—22no—
477Dic11—42no—
478Dic11—42no—
479Dic11—42no—
480C25—221no—
481C2×#41—114no—
482C2×#41—222no—
483C2×#41—224no—
484C2×#41—442no—
485C22×Q8—21no—
486C22×Q8—111no—
487C22×Q8—111no—
488C22×D4—114no—
489C22×D4—111no—
490C22×D4—111no—
491C22×D4—221no—
492C22×D4—222no—
493C22×D4—221no—
494C22×D4—224no—
495C22×D4—221no—
496C22×D4—442no—
497C22×D4C22×D1111yescharacteristic
498C23×C4—21no—
499C23×C4—111no—
500C23×C4—111no—
501C23×C4—221no—
502C23×C4—221no—
503C23×C4—221no—
504C2×Q16—114no—
505C2×Q16—442no—
506C2×SD16—114no—
507C2×SD16—114no—
508C2×SD16—224no—
509C2×SD16—442no—
510C2×M16—114no—
511C2×M16—442no—
512C22×C8—111no—
513C22×C8—111no—
514C22×C8—114no—
515C22×C8—442no—
516C22×C8C22×D1111yescharacteristic
517C22×C8C22×D1111yescharacteristic
518C4⋊Q8—22no—
519C4⋊Q8C22×D1114yescomplemented
520#125—228no—
521#124—114no—
522#124—222no—
523#123—228no—
524C22⋊Q8—114no—
525C22⋊Q8—114no—
526C22⋊Q8—114no—
527C22⋊Q8—228no—
528C22⋊Q8—228no—
529C22⋊Q8—222no—
530C22⋊Q8—222no—
531C22⋊Q8—222no—
532#121—114no—
533#121—228no—
534#121—222no—
535#120—228no—
536C4×Q8—114no—
537C4×Q8—222no—
538C4×D4—22no—
539C4×D4—114no—
540C4×D4—114no—
541C4×D4—228no—
542C4×D4C22×D1114yes—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—111no—
545C2×C4⋊C4—111no—
546C2×C4⋊C4—114no—
547C2×C4⋊C4—114no—
548C2×C4⋊C4—222no—
549C2×C4⋊C4—222no—
550C2×C4⋊C4—221no—
551C2×C4⋊C4—221no—
552C2×C4⋊C4—221no—
553C2×C4⋊C4—221no—
554C2×C4⋊C4—221no—
555C2×C4⋊C4—221no—
556C2×C4⋊C4C22×D1111yescharacteristic
557C2×C4⋊C4C22×D1111yescharacteristic
558C2×C4⋊C4C22×D1111yescharacteristic
559C2×C22⋊C4—21no—
560C2×C22⋊C4—111no—
561C2×C22⋊C4—111no—
562C2×C22⋊C4—228no—
563C2×C22⋊C4—221no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—221no—
567C2×C22⋊C4—221no—
568C2×C22⋊C4—221no—
569C2×C42—221no—
570C2×C42C22×D1111yescharacteristic
571#107—114no—
572#107C22×D1114yescomplemented
573#107C22×D1114yescomplemented
574C4⋊C8C22×D1114yescomplemented
575#103—114no—
576#103—114no—
577#103—114no—
578#103—114no—
579#102—114no—
580#102—114no—
581#102—114no—
582#102—114no—
583#102C22×D1114yes—
584#102C22×D1114yes—
585C22⋊C8—114no—
586C22⋊C8—114no—
587#97—114no—
588C2×C11—44no—
589C2×C11#331414yescomplemented
590C2×C11C2×#54611yescharacteristic
591C2×C11C22×#13711yescharacteristic
592C2×C11C2×#57611yescharacteristic
593D11—24no—
594D11—42no—
595D11—82no—
596C24—21no—
597C24—111no—
598C24—111no—
599C24—224no—
600C24—221no—
601C24—444no—
602C24—444no—
603C24—882no—
604#41—228no—
605#41—444no—
606#41—448no—
607C2×Q8—24no—
608C2×Q8—82no—
609C2×Q8—112no—
610C2×Q8—112no—
611C2×Q8—221no—
612C2×Q8—221no—
613C2×Q8—222no—
614C2×Q8—222no—
615C2×Q8—222no—
616C2×Q8—222no—
617C2×D4—21no—
618C2×D4—22no—
619C2×D4—114no—
620C2×D4—112no—
621C2×D4—224no—
622C2×D4—224no—
623C2×D4—224no—
624C2×D4—228no—
625C2×D4—224no—
626C2×D4—221no—
627C2×D4—222no—
628C2×D4—222no—
629C2×D4—444no—
630C2×D4—448no—
631C2×D4—444no—
632C2×D4—444no—
633C2×D4—882no—
634C2×D4#434314yes—
635C2×D4C23×D1112yes—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—82no—
641C22×C4—111no—
642C22×C4—111no—
643C22×C4—112no—
644C22×C4—112no—
645C22×C4—112no—
646C22×C4—112no—
647C22×C4—224no—
648C22×C4—224no—
649C22×C4—224no—
650C22×C4—222no—
651C22×C4—222no—
652C22×C4—222no—
653C22×C4—222no—
654C22×C4—221no—
655C22×C4—221no—
656C22×C4—221no—
657C22×C4—444no—
658C22×C4—882no—
659C22×C4—882no—
660C22×C4D4×D1111yescharacteristic
661C22×C4D4×D1111yescharacteristic
662C22×C4C23×D1111yescharacteristic
663Q16—444no—
664SD16—228no—
665SD16—444no—
666M16—444no—
667C2×C8—22no—
668C2×C8—22no—
669C2×C8—112no—
670C2×C8—112no—
671C2×C8—222no—
672C2×C8—222no—
673C2×C8—444no—
674C2×C8C23×D1112yes—
675C2×C8C23×D1112yes—
676C4⋊C4—24no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—114no—
681C4⋊C4—112no—
682C4⋊C4—224no—
683C4⋊C4—224no—
684C4⋊C4—224no—
685C4⋊C4—224no—
686C4⋊C4—224no—
687C4⋊C4—221no—
688C4⋊C4—224no—
689C4⋊C4C23×D1112yes—
690C4⋊C4C23×D1112yes—
691C4⋊C4C23×D1112yes—
692C22⋊C4—24no—
693C22⋊C4—114no—
694C22⋊C4—114no—
695C22⋊C4—224no—
696C22⋊C4—224no—
697C22⋊C4—224no—
698C22⋊C4—224no—
699C22⋊C4—224no—
700C22⋊C4—224no—
701C42—224no—
702C42D4×D1112yes—
703C42C23×D1112yes—
704C11C2×#331411yescharacteristic, complemented, Sylow
705C23—24no—
706C23—22no—
707C23—42no—
708C23—42no—
709C23—114no—
710C23—112no—
711C23—112no—
712C23—222no—
713C23—222no—
714C23—222no—
715C23—222no—
716C23—222no—
717C23—222no—
718C23—448no—
719C23—448no—
720C23—442no—
721C23—442no—
722C23—442no—
723C23—884no—
724C23—8816no—
725C23C2×D4×D1111yescharacteristic
726Q8—84no—
727Q8—222no—
728Q8—222no—
729Q8—222no—
730Q8—222no—
731Q8—442no—
732Q8—442no—
733D4—24no—
734D4—22no—
735D4—228no—
736D4—222no—
737D4—222no—
738D4—448no—
739D4—448no—
740D4—442no—
741D4—884no—
742D4C2×#434314yes—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—84no—
752C2×C4—112no—
753C2×C4—112no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—224no—
757C2×C4—224no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—448no—
766C2×C4—442no—
767C2×C4—442no—
768C2×C4—442no—
769C2×C4—884no—
770C2×C4—884no—
771C2×C4C2×D4×D1112yes—
772C2×C4C2×D4×D1112yes—
773C2×C4C2×D4×D1111yescharacteristic
774C2×C4C2×#434312yes—
775C2×C4#6704212yes—
776C2×C4C24×D1111yescharacteristic
777C8—22no—
778C8—22no—
779C8—222no—
780C8—222no—
781C22—24no—
782C22—48no—
783C22—42no—
784C22—42no—
785C22—114no—
786C22—228no—
787C22—222no—
788C22—222no—
789C22—222no—
790C22—222no—
791C22—222no—
792C22—444no—
793C22—442no—
794C22—442no—
795C22—442no—
796C22—8816no—
797C22—884no—
798C22#1062316112yes—
799C22#1062328812yes—
800C22D11×#13712yes—
801C22C22×D4×D1111yescharacteristic
802C4—22no—
803C4—22no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—222no—
808C4—222no—
809C4—442no—
810C4—442no—
811C4—442no—
812C4#1062316112yes—
813C4C22×#434311yescharacteristic
814C4C2×#6704211yescharacteristic
815C2—44no—
816C2—224no—
817C2—442no—
818C2—882no—
819C2#1308069414yesdirect product factor
820C2C2×#1062316111yescharacteristic
821C2C2×D11×#13711yescharacteristic
822C2C2×#1062328811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#474C2
socleC23×C11C22×D4
prime radicalC2×#10623085C2
hypercenterC2×#474D11
hypocenterC11C2×#3314
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#10623261C2semidirect
3. #13080694C2direct (N × H)
4. C2×#10622702C2semidirect
5. C2×#10622497C2semidirect
6. C2×#10622495C2semidirect
7. C2×#10622499C2semidirect
8. C2×#10622500C2semidirect
9. C2×#10622458C2semidirect
10. C2×#10622396C2semidirect
11. C2×#10622389C2semidirect
12. C2×#10622631C2semidirect
13. C2×#10622449C2semidirect
14. C2×#10622384C2semidirect
15. C2×D11×#102C2semidirect
16. C2×C11×#474C2semidirect
19. C2×C11×C4⋊Q8C22semidirect
26. C22×Dic44C22semidirect
28. C22×#4313C22semidirect
31. #10623261C22semidirect
36. C2×#66950C22semidirect
40. C2×C4⋊C4×D11C22semidirect
46. C2×C4×Dic22C22semidirect
47. C11×#474C22semidirect
48. C2×C11×#107C22semidirect
49. C2×C11×#107C22semidirect
50. C2×C11×C4⋊C8C22semidirect
56. C2×(C2×D11)⋊C8C22semidirect
57. C2×#66880C22semidirect
58. #10622702C22semidirect
59. #10622631C22semidirect
60. C2×#66874C22semidirect
61. C2×#66874C22semidirect
62. C2×#66874C22semidirect
65. C2×#66871C22semidirect
66. C2×#66867C22semidirect
67. #10622500C22semidirect
68. #10622499C22semidirect
69. #10622497C22semidirect
70. #10622495C22semidirect
71. #10622458C22semidirect
72. #10622449C22semidirect
73. #10622396C22semidirect
74. #10622389C22semidirect
75. #10622384C22semidirect
76. D11×#102C22semidirect
104. C11×C4⋊Q8C23semidirect
139. C2×Dic44C23semidirect
143. C2×#4313C23semidirect
151. #66950C23semidirect
158. C4⋊C4×D11C23semidirect
167. C4×Dic22C23semidirect
168. C11×#107C23semidirect
169. C11×#107C23semidirect
170. C11×C4⋊C8C23semidirect
176. (C2×D11)⋊C8C23semidirect
177. #66880C23semidirect
178. #66874C23semidirect
179. #66874C23semidirect
180. #66874C23semidirect
183. #66871C23semidirect
184. #66867C23semidirect
300. C2×#474D11semidirect
397. C2×C4⋊Q8C2×D11semidirect
419. #474C2×D11semidirect
428. C2×#107C2×D11semidirect
429. C2×#107C2×D11semidirect
430. C2×C4⋊C8C2×D11semidirect
519. C4⋊Q8C22×D11semidirect
572. #107C22×D11semidirect
573. #107C22×D11semidirect
574. C4⋊C8C22×D11semidirect
589. C2×C11#3314semidirect
704. C11C2×#3314semidirect
819. C2#13080694direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232612
C2×#106230852
#130806942
C2×#106227022
C2×#106224972
C2×#106224952
C2×#106224992
C2×#106225002
C2×#106224582
C2×#106223962
C2×#106223892
C2×#106226312
C2×#106224492
C2×#106223842
C2×D11×#1022
C2×C11×#4742
C2×#331411