Finite Group Databasebeta

← C2×#13080647 #15630438

Subgroups — C2×#13080647 #15630438

Order 2816.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623172C211yesmaximal, characteristic, complemented
2C2×#10623161C211yesmaximal, characteristic
3#13080647C2116yesmaximal, direct product factor
4C2×#10622408C211yesmaximal, characteristic, complemented
5C2×#10622658C211yesmaximal, characteristic, complemented
6C2×#10622479C211yesmaximal, characteristic, complemented
7C2×#10622483C211yesmaximal, characteristic, complemented
8C2×#10622420C211yesmaximal, characteristic, complemented
9C2×#10622798C211yesmaximal, characteristic, complemented
10C2×#10622800C211yesmaximal, characteristic, complemented
11C2×#10622659C211yesmaximal, characteristic, complemented
12C2×#10622430C211yesmaximal, characteristic, complemented
13C2×#10622740C211yesmaximal, characteristic, complemented
14C2×#10622744C211yesmaximal, characteristic, complemented
15C2×#10622417C211yesmaximal, characteristic, complemented
16C2×C11×#470C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C22×C11×Q16C2211yescharacteristic, complemented
20C22×C11×M16C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×#67000C2211yescharacteristic
24C2×#66999C2211yescharacteristic, complemented
25C2×Q8×Dic11C2211yescharacteristic, complemented
26C22×#4325C2211yescharacteristic
27C22×#4325C2211yescharacteristic
28C2×C4×C22⋊D11C2211yescharacteristic
29C2×#66979C2211yescharacteristic
30C22×C8×D11C2211yescharacteristic, complemented
31#10623172—24no—
32#10623172C2218yescomplemented
33#10623161—24no—
34#10623161C2218yes—
35C2×#66951—21no—
36C2×#66948—21no—
37C2×#66948C2211yescharacteristic
38C2×#66947—21no—
39C2×#66946C2211yescharacteristic
40C2×#66945C2211yescharacteristic, complemented
41C2×#66941C2211yescharacteristic, complemented
42C2×#66940—21no—
43C2×#66938—21no—
44C2×#66935—21no—
45C2×C22⋊C4×D11—21no—
46C2×#66932—21no—
47C11×#470C2218yescomplemented
48C2×C11×#106C2211yescharacteristic, complemented
49C2×C11×#103C2211yescharacteristic, complemented
50C2×C11×#103C2211yescharacteristic, complemented
51C2×#66899C2211yescharacteristic, complemented
52C2×#66899C2211yescharacteristic, complemented
53C2×C22⋊(C11⋊C8)C2211yescharacteristic
54#10622800C2218yescomplemented
55#10622798C2218yescomplemented
56#10622744C2218yescomplemented
57#10622740C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×#66885C2211yescharacteristic
60C2×#66885C2211yescharacteristic
61C2×#66885C2211yescharacteristic
62C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
63C2×#66879C2211yescharacteristic, complemented
64C2×Dic11⋊C8C2211yescharacteristic, complemented
65#10622659C2218yescomplemented
66#10622658C2218yescomplemented
67C2×#66873C2211yescharacteristic
68C2×#66873C2211yescharacteristic
69C2×#66872C2211yescharacteristic, complemented
70C2×#66871C2211yescharacteristic, complemented
71#10622483C2218yescomplemented
72#10622479C2218yescomplemented
73#10622430C2218yescomplemented
74#10622420C2218yescomplemented
75#10622417C2218yescomplemented
76#10622408C2218yescomplemented
77C24×D11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11D411yescharacteristic
82C2×#4343—22no—
83C2×#4343—24no—
84C2×#4343—42no—
85C2×#4343C2314yes—
86C22×D44—24no—
87C22×D44—21no—
88C22×D44—21no—
89C22×D44—22no—
90C22×D44—21no—
91C22×D44—42no—
92C22×D44C2311yescharacteristic
93C22×D44C2314yes—
94C22×D44C2311yescharacteristic
95C22×C4×D11—21no—
96C22×C4×D11—21no—
97C22×C4×D11C2311yescharacteristic
98C22×Dic22—21no—
99C2×C11×Q16—42no—
100C2×C11×Q16C2314yescomplemented
101C2×C11×M16—42no—
102C2×C11×M16C2314yes—
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C11×C22⋊Q8—22no—
106C11×C22⋊Q8—22no—
107C11×C22⋊Q8C2314yes—
108C11×C22⋊Q8C2314yes—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11D411yescharacteristic
117#67000—22no—
118#67000C2314yes—
119#66999—22no—
120#66999C2314yescomplemented
121Q8×Dic11—22no—
122Q8×Dic11C2314yescomplemented
123C2×#4325—24no—
124C2×#4325—42no—
125C2×#4325C2314yes—
126C2×#4325C2314yes—
127C4×C22⋊D11D414yes—
128C4×C22⋊D11C2314yes—
129C2×(C2×D11)⋊C4—21no—
130C2×(C2×D11)⋊C4—21no—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—21no—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4D411yescharacteristic
136#66979—22no—
137#66979C2314yes—
138C2×C4⋊Dic11—21no—
139C2×C4⋊Dic11C2311yescharacteristic
140C2×C4⋊Dic11C2311yescharacteristic
141C2×Dic11⋊C4—21no—
142C2×Dic11⋊C4—21no—
143C2×Dic11⋊C4D411yescharacteristic
144C2×C4×Dic11—21no—
145C2×C4×Dic11—21no—
146C2×C4×Dic11—21no—
147C2×C4×Dic11C2311yescharacteristic
148C22×C11⋊C8C2311yescharacteristic
149C22×C11⋊C8C2311yescharacteristic
150C2×C8×D11—42no—
151C2×C8×D11C2314yescomplemented
152#66951—28no—
153#66948—22no—
154#66948—28no—
155#66948C2314yes—
156#66947—28no—
157#66946—22no—
158#66946C2314yes—
159#66945—22no—
160#66945C2314yescomplemented
161#66941—22no—
162#66941C2314yescomplemented
163#66940—28no—
164#66938—28no—
165#66935—28no—
166C22⋊C4×D11—28no—
167#66932—28no—
168C11×#106C2314yescomplemented
169C11×#103C2314yescomplemented
170C11×#103C2314yescomplemented
171#66899C2314yescomplemented
172#66899C2314yescomplemented
173C22⋊(C11⋊C8)C2314yes—
174#66885C2314yes—
175#66885C2314yes—
176#66885C2314yes—
177#66885C2314yes—
178(C2×D11)⋊C8C2314yescomplemented
179#66879C2314yescomplemented
180Dic11⋊C8C2314yescomplemented
181#66873C2314yes—
182#66873C2314yes—
183#66872C2314yescomplemented
184#66871C2314yescomplemented
185C2×#3311—111nomaximal, Sylow
186C24×C11C2×D411yescharacteristic
187C23×D11—21no—
188C23×D11—21no—
189C23×D11—24no—
190C23×D11—44no—
191C23×D11—44no—
192C23×D11—82no—
193C23×D11C2×D411yescharacteristic
194C2×Q8×C11—21no—
195C2×Q8×C11—21no—
196C2×Q8×C11—22no—
197C2×Q8×C11—22no—
198C2×Q8×C11—22no—
199C2×Q8×C11—22no—
200C2×Q8×C11C2412yes—
201C2×Q8×C11C2412yes—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2411yescharacteristic
212C2×C22⋊D11—42no—
213C2×C22⋊D11C2×D414yes—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11C2×D411yescharacteristic
217C22×Dic11C2×D411yescharacteristic
218C22×Dic11C2×D411yescharacteristic
219#4343—28no—
220#4343—44no—
221#4343—48no—
222C2×D44—24no—
223C2×D44—24no—
224C2×D44—28no—
225C2×D44—21no—
226C2×D44—24no—
227C2×D44—21no—
228C2×D44—22no—
229C2×D44—22no—
230C2×D44—22no—
231C2×D44—44no—
232C2×D44—44no—
233C2×D44—48no—
234C2×D44—44no—
235C2×D44—82no—
236C2×D44#4114yes—
237C2×D44C2412yes—
238C2×D44C2412yes—
239C2×C4×D11—24no—
240C2×C4×D11—24no—
241C2×C4×D11—22no—
242C2×C4×D11—22no—
243C2×C4×D11—44no—
244C2×C4×D11—82no—
245C2×C4×D11C2×D412yes—
246C2×C4×D11C2412yes—
247C2×Dic22—24no—
248C2×Dic22—44no—
249C11×Q16—44no—
250C11×M16—44no—
251C2×C8×C11—22no—
252C2×C8×C11—22no—
253C2×C8×C11C2412yes—
254C2×C8×C11C2412yes—
255C11×C4⋊C4—24no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4—21no—
258C11×C4⋊C4—24no—
259C11×C4⋊C4C2412yes—
260C11×C4⋊C4C2412yes—
261C11×C22⋊C4—24no—
262C11×C22⋊C4—24no—
263C22⋊Dic11—24no—
264C22⋊Dic11C2×D414yes—
265#4325—28no—
266#4325—44no—
267(C2×D11)⋊C4—24no—
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)⋊C4C2×D414yes—
274C4⋊Dic11—24no—
275C4⋊Dic11—21no—
276C4⋊Dic11—21no—
277C4⋊Dic11C2412yes—
278C4⋊Dic11C2412yes—
279Dic11⋊C4—24no—
280Dic11⋊C4—24no—
281Dic11⋊C4C2×D414yes—
282C4×Dic11—24no—
283C4×Dic11—24no—
284C4×Dic11—24no—
285C4×Dic11C2×D412yes—
286C4×Dic11C2412yes—
287C2×C11⋊C8—22no—
288C2×C11⋊C8—22no—
289C2×C11⋊C8C2412yes—
290C2×C11⋊C8C2412yes—
291C8×D11—44no—
292C2×#556—111no—
293C2×#546—111no—
294#3311—1116no—
295C2×#489—111no—
296C2×#485—111no—
297C2×#482—111no—
298C2×#476—111no—
299C2×#470D1111yescharacteristic, complemented
300C2×#465—111no—
301C2×#464—111no—
302C2×#452—111no—
303C2×#450—111no—
304C2×#440—111no—
305C2×#435—111no—
306C2×#418—111no—
307C2×#416—111no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11C22×D412yes—
312C23×C11C22×D411yescharacteristic
313C22×D11—22no—
314C22×D11—24no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—48no—
320C22×D11—42no—
321C22×D11—42no—
322C22×D11—48no—
323C22×D11—42no—
324C22×D11—42no—
325C22×D11—42no—
326C22×D11—84no—
327C22×D11—816no—
328C22×D11C22×D412yes—
329Q8×C11—22no—
330Q8×C11—22no—
331Q8×C11—22no—
332Q8×C11—22no—
333Q8×C11—42no—
334Q8×C11—42no—
335C2×C4×C11—22no—
336C2×C4×C11—24no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—42no—
344C2×C4×C11—42no—
345C2×C4×C11—42no—
346C2×C4×C11—42no—
347C2×C4×C11C22×D412yes—
348C2×C4×C11C22×D411yescharacteristic
349C2×C4×C11C2×#4112yes—
350C2×C4×C11H(5,𝔽2)12yes—
351C2×C4×C11C2511yescharacteristic
352C22⋊D11—44no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—42no—
359C2×Dic11—42no—
360C2×Dic11C22×D412yes—
361C2×Dic11C22×D412yes—
362C2×Dic11C22×D412yes—
363D44—24no—
364D44—22no—
365D44—22no—
366D44—22no—
367D44—48no—
368D44—48no—
369D44—42no—
370D44—84no—
371D44C2×#4114yes—
372C4×D11—24no—
373C4×D11—22no—
374C4×D11—22no—
375C4×D11—48no—
376C4×D11—84no—
377Dic22—48no—
378C8×C11—22no—
379C8×C11—22no—
380C11⋊C8—22no—
381C11⋊C8—22no—
382C22×#41—111no—
383C23×D4—111no—
384C22×Q16C2×D1111yescharacteristic, complemented
385C22×SD16—111no—
386C22×SD16—111no—
387C22×M16C2×D1111yescharacteristic
388C23×C8—111no—
389#556—118no—
390#556—224no—
391#546—118no—
392#546—224no—
393C2×C4⋊Q8—111no—
394C2×#126—221no—
395C2×#126—221no—
396C2×#124—111no—
397C2×#124—221no—
398C2×#123—221no—
399C2×C22⋊Q8—111no—
400C2×C22⋊Q8C2×D1111yescharacteristic
401C2×C22⋊Q8C2×D1111yescharacteristic
402C2×#121—111no—
403C2×#121—221no—
404C2×#120—221no—
405C2×C4×Q8—111no—
406C2×C4×Q8—221no—
407C2×C4×D4—111no—
408C2×C4×D4—111no—
409C2×#117—111no—
410C2×#117—111no—
411C22×C22⋊C4—221no—
412#489—118no—
413#485—118no—
414#482—118no—
415#476—118no—
416#470C2×D1118yescomplemented
417#465—118no—
418#464—118no—
419#452—118no—
420#450—118no—
421#440—118no—
422#435—118no—
423C2×#107—111no—
424C2×#106—111no—
425C2×#106C2×D1111yescharacteristic, complemented
426C2×C4⋊C8—111no—
427#418—118no—
428#416—118no—
429C2×#103—111no—
430C2×#103—111no—
431C2×#103C2×D1111yescharacteristic, complemented
432C2×#103C2×D1111yescharacteristic, complemented
433C2×#102—111no—
434C2×#102—111no—
435C2×#102—111no—
436C2×#102—111no—
437C2×#102—111no—
438C2×#102—111no—
439C2×C22⋊C8—111no—
440C2×C22⋊C8—111no—
441C2×#97—111no—
442C22×C11—22no—
443C22×C11—22no—
444C22×C11—22no—
445C22×C11—44no—
446C22×C11#54612yes—
447C22×C11#57512yes—
448C22×C11#57712yes—
449C22×C11C23×D411yescharacteristic
450C2×D11—24no—
451C2×D11—22no—
452C2×D11—22no—
453C2×D11—22no—
454C2×D11—44no—
455C2×D11—48no—
456C2×D11—42no—
457C2×D11—42no—
458C2×D11—42no—
459C2×D11—42no—
460C2×D11—42no—
461C2×D11—816no—
462C2×D11—84no—
463C4×C11—22no—
464C4×C11—42no—
465C4×C11—42no—
466C4×C11—42no—
467C4×C11—42no—
468C4×C11#54612yes—
469C4×C11C22×#4111yescharacteristic
470C4×C11C2×H(5,𝔽2)11yescharacteristic
471Dic11—22no—
472Dic11—22no—
473Dic11—22no—
474Dic11—42no—
475Dic11—42no—
476C25—221no—
477C2×#41—114no—
478C2×#41—222no—
479C2×#41—224no—
480C2×#41—442no—
481C22×Q8—221no—
482C22×Q8C22×D1111yescharacteristic
483C22×Q8C22×D1111yescharacteristic
484C22×D4—111no—
485C22×D4—111no—
486C22×D4—111no—
487C22×D4—114no—
488C22×D4—224no—
489C22×D4—221no—
490C22×D4—221no—
491C22×D4—221no—
492C22×D4—222no—
493C22×D4—442no—
494C23×C4—111no—
495C23×C4—221no—
496C23×C4—221no—
497C23×C4C22×D1111yescharacteristic
498C2×Q16—42no—
499C2×Q16C22×D1114yescomplemented
500C2×SD16—114no—
501C2×SD16—114no—
502C2×SD16—224no—
503C2×SD16—442no—
504C2×M16—42no—
505C2×M16C22×D1114yes—
506C22×C8—111no—
507C22×C8—111no—
508C22×C8—114no—
509C22×C8—442no—
510C22×C8C22×D1111yescharacteristic
511C22×C8C22×D1111yescharacteristic
512C4⋊Q8—114no—
513C4⋊Q8—222no—
514#126—228no—
515#126—228no—
516#124—114no—
517#124—222no—
518#124—228no—
519#123—228no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522C22⋊Q8—114no—
523C22⋊Q8—222no—
524C22⋊Q8C22×D1114yes—
525C22⋊Q8C22×D1114yes—
526#121—114no—
527#121—228no—
528#121—222no—
529#120—228no—
530C4×Q8—114no—
531C4×Q8—222no—
532C4×Q8—228no—
533C4×D4—114no—
534C4×D4—114no—
535C4×D4—114no—
536C4×D4—222no—
537#117—114no—
538#117—114no—
539#117—222no—
540#117—222no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—111no—
544C2×C4⋊C4—111no—
545C2×C4⋊C4—111no—
546C2×C4⋊C4—221no—
547C2×C4⋊C4—221no—
548C2×C4⋊C4—221no—
549C2×C4⋊C4C22×D1111yescharacteristic
550C2×C4⋊C4C22×D1111yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—111no—
554C2×C22⋊C4—111no—
555C2×C22⋊C4—228no—
556C2×C22⋊C4—221no—
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4—221no—
561C2×C22⋊C4—221no—
562C2×C22⋊C4—221no—
563C2×C42—111no—
564C2×C42—221no—
565C2×C42—221no—
566C2×C42—221no—
567#107—114no—
568#106—114no—
569#106C22×D1114yescomplemented
570C4⋊C8—114no—
571#103—114no—
572#103—114no—
573#103C22×D1114yescomplemented
574#103C22×D1114yescomplemented
575#102—114no—
576#102—114no—
577#102—114no—
578#102—114no—
579#102—114no—
580#102—114no—
581C22⋊C8—114no—
582C22⋊C8—114no—
583#97—114no—
584C2×C11—42no—
585C2×C11#331114yescomplemented
586C2×C11C2×#54611yescharacteristic
587C2×C11C2×#57511yescharacteristic
588C2×C11C2×#57711yescharacteristic
589D11—42no—
590D11—44no—
591D11—82no—
592C24—111no—
593C24—221no—
594C24—221no—
595C24—224no—
596C24—444no—
597C24—444no—
598C24—882no—
599C24D4×D1111yescharacteristic
600#41—228no—
601#41—444no—
602#41—448no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—22no—
609C2×Q8—224no—
610C2×Q8—444no—
611C2×Q8C23×D1112yes—
612C2×Q8C23×D1112yes—
613C2×D4—114no—
614C2×D4—114no—
615C2×D4—112no—
616C2×D4—112no—
617C2×D4—228no—
618C2×D4—224no—
619C2×D4—224no—
620C2×D4—221no—
621C2×D4—224no—
622C2×D4—221no—
623C2×D4—222no—
624C2×D4—222no—
625C2×D4—222no—
626C2×D4—444no—
627C2×D4—448no—
628C2×D4—444no—
629C2×D4—444no—
630C2×D4—442no—
631C2×D4—882no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—111no—
639C22×C4—111no—
640C22×C4—111no—
641C22×C4—112no—
642C22×C4—112no—
643C22×C4—224no—
644C22×C4—224no—
645C22×C4—222no—
646C22×C4—222no—
647C22×C4—221no—
648C22×C4—221no—
649C22×C4—444no—
650C22×C4—882no—
651C22×C4D4×D1112yes—
652C22×C4D4×D1111yescharacteristic
653C22×C4C23×D1112yes—
654C22×C4C23×D1111yescharacteristic
655Q16—44no—
656SD16—228no—
657SD16—444no—
658M16—44no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—112no—
662C2×C8—112no—
663C2×C8—222no—
664C2×C8—222no—
665C2×C8—444no—
666C2×C8C23×D1112yes—
667C2×C8C23×D1112yes—
668C4⋊C4—24no—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—114no—
673C4⋊C4—112no—
674C4⋊C4—112no—
675C4⋊C4—224no—
676C4⋊C4—224no—
677C4⋊C4—224no—
678C4⋊C4—221no—
679C4⋊C4—221no—
680C4⋊C4C23×D1112yes—
681C4⋊C4C23×D1112yes—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—114no—
685C22⋊C4—114no—
686C22⋊C4—224no—
687C22⋊C4—224no—
688C22⋊C4—224no—
689C22⋊C4—224no—
690C22⋊C4—224no—
691C22⋊C4—224no—
692C22⋊C4—224no—
693C42—112no—
694C42—112no—
695C42—224no—
696C42—224no—
697C42—224no—
698C11C2×#331111yescharacteristic, complemented, Sylow
699C23—22no—
700C23—22no—
701C23—22no—
702C23—112no—
703C23—222no—
704C23—222no—
705C23—222no—
706C23—224no—
707C23—222no—
708C23—222no—
709C23—448no—
710C23—448no—
711C23—442no—
712C23—442no—
713C23—442no—
714C23—442no—
715C23—442no—
716C23—884no—
717C23—8816no—
718C23C2×D4×D1112yes—
719C23C2×D4×D1111yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—22no—
724Q8—42no—
725Q8—42no—
726Q8—448no—
727D4—114no—
728D4—224no—
729D4—222no—
730D4—222no—
731D4—222no—
732D4—448no—
733D4—448no—
734D4—444no—
735D4—442no—
736D4—884no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—112no—
750C2×C4—112no—
751C2×C4—112no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—224no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—448no—
761C2×C4—442no—
762C2×C4—442no—
763C2×C4—884no—
764C2×C4C2×D4×D1112yes—
765C2×C4C2×D4×D1111yescharacteristic
766C2×C4#6703712yes—
767C2×C4#41×D1112yes—
768C2×C4C24×D1111yescharacteristic
769C8—22no—
770C8—22no—
771C8—222no—
772C8—222no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—222no—
778C22—224no—
779C22—222no—
780C22—222no—
781C22—444no—
782C22—448no—
783C22—442no—
784C22—442no—
785C22—442no—
786C22—442no—
787C22—442no—
788C22—8816no—
789C22—884no—
790C22#1062314112yes—
791C22#1062330812yes—
792C22#1062330912yes—
793C22C22×D4×D1111yescharacteristic
794C4—22no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—222no—
800C4—222no—
801C4—222no—
802C4—442no—
803C4—442no—
804C4#1062314112yes—
805C4C2×#6703711yescharacteristic
806C4C2×#41×D1111yescharacteristic
807C2—42no—
808C2—442no—
809C2—444no—
810C2—882no—
811C2#1308064714yesdirect product factor
812C2C2×#1062314111yescharacteristic
813C2C2×#1062330811yescharacteristic
814C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#470C2
socleC23×C11C22×D4
prime radicalC2×#10623161C2
hypercenterC2×#470D11
hypocenterC11C2×#3311
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
1. C2×#10623172C2semidirect
3. #13080647C2direct (N × H)
4. C2×#10622408C2semidirect
5. C2×#10622658C2semidirect
6. C2×#10622479C2semidirect
7. C2×#10622483C2semidirect
8. C2×#10622420C2semidirect
9. C2×#10622798C2semidirect
10. C2×#10622800C2semidirect
11. C2×#10622659C2semidirect
12. C2×#10622430C2semidirect
13. C2×#10622740C2semidirect
14. C2×#10622744C2semidirect
15. C2×#10622417C2semidirect
16. C2×C11×#470C2semidirect
19. C22×C11×Q16C22semidirect
24. C2×#66999C22semidirect
25. C2×Q8×Dic11C22semidirect
30. C22×C8×D11C22semidirect
32. #10623172C22semidirect
40. C2×#66945C22semidirect
41. C2×#66941C22semidirect
47. C11×#470C22semidirect
48. C2×C11×#106C22semidirect
49. C2×C11×#103C22semidirect
50. C2×C11×#103C22semidirect
51. C2×#66899C22semidirect
52. C2×#66899C22semidirect
54. #10622800C22semidirect
55. #10622798C22semidirect
56. #10622744C22semidirect
57. #10622740C22semidirect
62. C2×(C2×D11)⋊C8C22semidirect
63. C2×#66879C22semidirect
64. C2×Dic11⋊C8C22semidirect
65. #10622659C22semidirect
66. #10622658C22semidirect
69. C2×#66872C22semidirect
70. C2×#66871C22semidirect
71. #10622483C22semidirect
72. #10622479C22semidirect
73. #10622430C22semidirect
74. #10622420C22semidirect
75. #10622417C22semidirect
76. #10622408C22semidirect
100. C2×C11×Q16C23semidirect
120. #66999C23semidirect
122. Q8×Dic11C23semidirect
151. C2×C8×D11C23semidirect
160. #66945C23semidirect
162. #66941C23semidirect
168. C11×#106C23semidirect
169. C11×#103C23semidirect
170. C11×#103C23semidirect
171. #66899C23semidirect
172. #66899C23semidirect
178. (C2×D11)⋊C8C23semidirect
179. #66879C23semidirect
180. Dic11⋊C8C23semidirect
183. #66872C23semidirect
184. #66871C23semidirect
299. C2×#470D11semidirect
384. C22×Q16C2×D11semidirect
416. #470C2×D11semidirect
425. C2×#106C2×D11semidirect
431. C2×#103C2×D11semidirect
432. C2×#103C2×D11semidirect
499. C2×Q16C22×D11semidirect
569. #106C22×D11semidirect
573. #103C22×D11semidirect
574. #103C22×D11semidirect
585. C2×C11#3311semidirect
698. C11C2×#3311semidirect
811. C2#13080647direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231722
C2×#106231612
#130806472
C2×#106224082
C2×#106226582
C2×#106224792
C2×#106224832
C2×#106224202
C2×#106227982
C2×#106228002
C2×#106226592
C2×#106224302
C2×#106227402
C2×#106227442
C2×#106224172
C2×C11×#4702
C2×#331111