Finite Group Databasebeta

← C2×#13080837 #15630591

Subgroups — C2×#13080837 #15630591

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×#10623112C211yesmaximal, characteristic, complemented
2C2×#10623085C211yesmaximal, characteristic
3#13080837C2116yesmaximal, direct product factor
4C2×#10622310C211yesmaximal, characteristic, complemented
5C2×#10622476C211yesmaximal, characteristic, complemented
6C2×#10622480C211yesmaximal, characteristic, complemented
7C2×#10622622C211yesmaximal, characteristic, complemented
8C2×#10622429C211yesmaximal, characteristic, complemented
9C2×#10622425C211yesmaximal, characteristic, complemented
10C2×#10622641C211yesmaximal, characteristic, complemented
11C2×#10622786C211yesmaximal, characteristic, complemented
12C2×#10622782C211yesmaximal, characteristic, complemented
13C2×#10622301C211yesmaximal, characteristic, complemented
14C2×#10622384C211yesmaximal, characteristic, complemented
15C2×#10622383C211yesmaximal, characteristic, complemented
16C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
17C22×#4341C2211yescharacteristic
18C22×D4×D11C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic, complemented
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66999C2211yescharacteristic
23C2×#66999C2211yescharacteristic, complemented
24C22×#4326C2211yescharacteristic, complemented
25C22×#4325C2211yescharacteristic
26C2×#66983—21no—
27C22×(C2×D11)⋊C4—21no—
28C22×#4313C2211yescharacteristic
29C22×#4313C2211yescharacteristic, complemented
30#10623112—24no—
31#10623112C2218yescomplemented
32#10623085—24no—
33#10623085C2218yes—
34C2×#66950C2211yescharacteristic
35C2×#66948C2211yescharacteristic
36C2×#66947—21no—
37C2×#66945C2211yescharacteristic
38C2×C4⋊C4×D11C2211yescharacteristic, complemented
39C2×#66942—21no—
40C2×#66939—21no—
41C2×#66935—21no—
42C2×#66929—21no—
43C2×#66928C2211yescharacteristic
44C2×C4×D44C2211yescharacteristic
45C2×#66925—21no—
46C2×#66923C2211yescharacteristic, complemented
47C4×C11×SD16C2218yescomplemented
48C2×C11×#106C2211yescharacteristic, complemented
49C2×C11×#103C2211yescharacteristic, complemented
50C2×C11×#102C2211yescharacteristic
51C2×C4×C8×C11C2211yescharacteristic, complemented
52C2×#66896C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54#10622786C2218yescomplemented
55#10622782C2218yescomplemented
56C2×#66885C2211yescharacteristic
57C2×#66885C2211yescharacteristic
58C2×(C2×D11)⋊C8C2211yescharacteristic
59C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
60C2×#66880C2211yescharacteristic, complemented
61C2×#66880C2211yescharacteristic, complemented
62#10622641C2218yescomplemented
63#10622622C2218yescomplemented
64C2×#66874C2211yescharacteristic, complemented
65C2×#66873C2211yescharacteristic
66C2×#66872C2211yescharacteristic, complemented
67C2×#66871C2211yescharacteristic, complemented
68C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
69#10622480C2218yescomplemented
70#10622476C2218yescomplemented
71#10622429C2218yescomplemented
72#10622425C2218yescomplemented
73#10622384C2218yescomplemented
74#10622383C2218yescomplemented
75#10622310C2218yescomplemented
76#10622301C2218yescomplemented
77C24×D11—21no—
78C22×Q8×C11C2311yescharacteristic
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×D11C2311yescharacteristic
97C22×C4×D11C2311yescharacteristic
98C22×Dic22C2311yescharacteristic
99C2×C11×SD16—24no—
100C2×C11×SD16C2314yes—
101C22×C8×C11C2311yescharacteristic
102C22×C8×C11C2311yescharacteristic
103C4×Q8×C11—22no—
104C4×Q8×C11C2314yescomplemented
105C4×D4×C11—22no—
106C4×D4×C11C2314yes—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C22⋊C4—21no—
111C2×C42×C11—21no—
112C2×C42×C11C2311yescharacteristic
113#66999—22no—
114#66999—22no—
115#66999C2314yes—
116#66999C2314yescomplemented
117C2×#4326—42no—
118C2×#4326C2314yescomplemented
119C2×#4325—42no—
120C2×#4325C2314yes—
121#66983—28no—
122C2×(C2×D11)⋊C4—21no—
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—21no—
129C2×(C2×D11)⋊C4—28no—
130C2×(C2×D11)⋊C4D411yescharacteristic
131C2×(C2×D11)⋊C4D411yescharacteristic
132C2×C4⋊Dic11—21no—
133C2×C4⋊Dic11D411yescharacteristic
134C2×C4⋊Dic11C2311yescharacteristic
135C2×C4⋊Dic11C2311yescharacteristic
136C2×Dic11⋊C4—21no—
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C2×C4×Dic11—21no—
142C22×C11⋊C8C2311yescharacteristic
143C22×C11⋊C8C2311yescharacteristic
144C2×#4313—42no—
145C2×#4313—42no—
146C2×#4313C2314yes—
147C2×#4313C2314yescomplemented
148#66950—22no—
149#66950C2314yes—
150#66948—22no—
151#66948C2314yes—
152#66947—28no—
153#66945—22no—
154#66945C2314yes—
155C4⋊C4×D11—22no—
156C4⋊C4×D11C2314yescomplemented
157#66942—28no—
158#66939—28no—
159#66935—28no—
160#66929—28no—
161#66928—22no—
162#66928C2314yes—
163C4×D44D414yes—
164C4×D44C2314yes—
165#66925—28no—
166#66923—22no—
167#66923C2314yescomplemented
168C11×#106C2314yescomplemented
169C11×#103C2314yescomplemented
170C11×#102C2314yes—
171C4×C8×C11C2314yescomplemented
172#66896C2314yes—
173#66896C2314yes—
174#66885C2314yes—
175#66885C2314yes—
176(C2×D11)⋊C8C2314yes—
177(C2×D11)⋊C8C2314yescomplemented
178#66880C2314yescomplemented
179#66880C2314yescomplemented
180#66874C2314yescomplemented
181#66873C2314yes—
182#66872C2314yescomplemented
183#66871C2314yescomplemented
184C4⋊(C11⋊C8)C2314yescomplemented
185C2×#3323—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—21no—
195C2×Q8×C11—22no—
196C2×Q8×C11—22no—
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—24no—
211C2×C22⋊D11—24no—
212C2×C22⋊D11—44no—
213C2×C22⋊D11—44no—
214C22×Dic11—24no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—44no—
219C22×Dic11C2×D411yescharacteristic
220C22×Dic11C2×D411yescharacteristic
221#4341—28no—
222#4341—44no—
223#4341—48no—
224D4×D11—28no—
225D4×D11—44no—
226D4×D11—48no—
227C2×D44—24no—
228C2×D44—21no—
229C2×D44—22no—
230C2×D44—22no—
231C2×D44—42no—
232C2×D44—82no—
233C2×D44C2×D414yes—
234C2×D44C2412yes—
235C2×C4×D11—24no—
236C2×C4×D11—22no—
237C2×C4×D11—22no—
238C2×C4×D11—22no—
239C2×C4×D11—22no—
240C2×C4×D11—44no—
241C2×C4×D11C2×D412yes—
242C2×C4×D11C2×D412yes—
243C2×C4×D11C2412yes—
244C2×C4×D11C2412yes—
245C2×Dic22—21no—
246C2×Dic22—22no—
247C2×Dic22—22no—
248C2×Dic22C2412yes—
249C11×SD16—28no—
250C2×C8×C11—22no—
251C2×C8×C11—22no—
252C2×C8×C11C2412yes—
253C2×C8×C11C2412yes—
254C11×C4⋊C4—24no—
255C11×C4⋊C4—21no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4C2412yes—
258C11×C4⋊C4C2412yes—
259C11×C22⋊C4—24no—
260C42×C11—24no—
261C42×C11C2×D412yes—
262C42×C11C2412yes—
263#4326—44no—
264#4325—44no—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4—24no—
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)⋊C4C2×D414yes—
273(C2×D11)⋊C4C2×D414yes—
274C4⋊Dic11—24no—
275C4⋊Dic11—21no—
276C4⋊Dic11—21no—
277C4⋊Dic11C2×D414yes—
278C4⋊Dic11C2412yes—
279C4⋊Dic11C2412yes—
280Dic11⋊C4—24no—
281Dic11⋊C4—24no—
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—
290#4313—44no—
291#4313—44no—
292C2×#552—111no—
293C2×#546—111no—
294#3323—1116no—
295C2×#488—111no—
296C2×#481—111no—
297C2×#485—111no—
298C2×#478—111no—
299C2×#470—111no—
300C2×#468—111no—
301C2×#464—111no—
302C2×#452—111no—
303C2×#450—111no—
304C2×C4×SD16D1111yescharacteristic, complemented
305C2×#436—111no—
306C2×#417—111no—
307C2×#418—111no—
308C23×C11—24no—
309C23×C11—22no—
310C23×C11—42no—
311C23×C11—42no—
312C23×C11C22×D411yescharacteristic
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—48no—
321C22×D11—48no—
322C22×D11—42no—
323C22×D11—42no—
324C22×D11—42no—
325C22×D11—84no—
326C22×D11—816no—
327C22×D11C22×D412yes—
328C22×D11C22×D412yes—
329Q8×C11—22no—
330Q8×C11—22no—
331Q8×C11—42no—
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—22no—
364D44—22no—
365D44—44no—
366D44—42no—
367D44—84no—
368C4×D11—24no—
369C4×D11—24no—
370C4×D11—22no—
371C4×D11—22no—
372C4×D11—22no—
373C4×D11—22no—
374C4×D11—48no—
375Dic22—22no—
376Dic22—22no—
377Dic22—42no—
378C8×C11—22no—
379C8×C11—22no—
380C11⋊C8—22no—
381C11⋊C8—22no—
382C22×#41—111no—
383C23×D4—111no—
384C22×Q16—111no—
385C22×SD16—111no—
386C22×SD16C2×D1111yescharacteristic
387C22×M16—111no—
388C22×M16—111no—
389#552—118no—
390#552—224no—
391#546—118no—
392#546—224no—
393C2×#126—221no—
394C2×#125—111no—
395C2×#125—221no—
396C2×#124—111no—
397C2×#123—221no—
398C2×#123—221no—
399C2×C22⋊Q8—111no—
400C2×C22⋊Q8—111no—
401C2×C22⋊Q8—111no—
402C2×#121—111no—
403C2×#121—221no—
404C2×#120—221no—
405C2×C4×Q8C2×D1111yescharacteristic, complemented
406C2×C4×D4—111no—
407C2×C4×D4C2×D1111yescharacteristic
408C2×#117—111no—
409C2×#117—221no—
410C22×C4⋊C4—111no—
411C22×C22⋊C4—221no—
412#488—118no—
413#485—118no—
414#481—118no—
415#478—118no—
416#470—118no—
417#468—118no—
418#464—118no—
419#452—118no—
420#450—118no—
421C4×SD16C2×D1118yescomplemented
422#436—118no—
423C2×#107—111no—
424C2×#106—111no—
425C2×#106C2×D1111yescharacteristic, complemented
426C2×C4⋊C8—111no—
427#418—118no—
428#417—118no—
429C2×#103—111no—
430C2×#103—111no—
431C2×#103—111no—
432C2×#103C2×D1111yescharacteristic, complemented
433C2×#102—111no—
434C2×#102—111no—
435C2×#102—111no—
436C2×#102—111no—
437C2×#102—111no—
438C2×#102C2×D1111yescharacteristic
439C2×C22⋊C8—111no—
440C2×C22⋊C8—111no—
441C2×C4×C8C2×D1111yescharacteristic, complemented
442C22×C11—24no—
443C22×C11—48no—
444C22×C11—42no—
445C22×C11—42no—
446C22×C11#54612yes—
447C22×C11#57512yes—
448C22×C11#57712yes—
449C22×C11C23×D411yescharacteristic
450C2×D11—22no—
451C2×D11—22no—
452C2×D11—22no—
453C2×D11—22no—
454C2×D11—22no—
455C2×D11—22no—
456C2×D11—44no—
457C2×D11—44no—
458C2×D11—42no—
459C2×D11—42no—
460C2×D11—42no—
461C2×D11—816no—
462C2×D11—84no—
463C4×C11—22no—
464C4×C11—22no—
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—42no—
474Dic11—42no—
475Dic11—42no—
476C25—221no—
477C2×#41—114no—
478C2×#41—222no—
479C2×#41—224no—
480C2×#41—442no—
481C22×Q8—111no—
482C22×Q8C22×D1111yescharacteristic
483C22×D4—114no—
484C22×D4—111no—
485C22×D4—111no—
486C22×D4—221no—
487C22×D4—222no—
488C22×D4—221no—
489C22×D4—224no—
490C22×D4—221no—
491C22×D4—442no—
492C22×D4C22×D1111yescharacteristic
493C23×C4—21no—
494C23×C4—111no—
495C23×C4—111no—
496C23×C4—221no—
497C23×C4—221no—
498C2×Q16—114no—
499C2×Q16—442no—
500C2×SD16—24no—
501C2×SD16—114no—
502C2×SD16—442no—
503C2×SD16C22×D1114yes—
504C2×M16—114no—
505C2×M16—114no—
506C2×M16—442no—
507C2×M16—442no—
508C22×C8—111no—
509C22×C8—111no—
510C22×C8C22×D1111yescharacteristic
511C22×C8C22×D1111yescharacteristic
512#126—228no—
513#125—114no—
514#125—228no—
515#125—222no—
516#124—114no—
517#124—222no—
518#123—228no—
519#123—228no—
520C22⋊Q8—114no—
521C22⋊Q8—114no—
522C22⋊Q8—114no—
523C22⋊Q8—222no—
524C22⋊Q8—222no—
525C22⋊Q8—222no—
526#121—114no—
527#121—228no—
528#121—222no—
529#120—228no—
530C4×Q8—22no—
531C4×Q8C22×D1114yescomplemented
532C4×D4—22no—
533C4×D4—114no—
534C4×D4—114no—
535C4×D4C22×D1114yes—
536#117—114no—
537#117—228no—
538#117—222no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—111no—
541C2×C4⋊C4—111no—
542C2×C4⋊C4—111no—
543C2×C4⋊C4—114no—
544C2×C4⋊C4—222no—
545C2×C4⋊C4—221no—
546C2×C4⋊C4—221no—
547C2×C4⋊C4—221no—
548C2×C4⋊C4—221no—
549C2×C4⋊C4—221no—
550C2×C4⋊C4—221no—
551C2×C4⋊C4C22×D1111yescharacteristic
552C2×C4⋊C4C22×D1111yescharacteristic
553C2×C22⋊C4—21no—
554C2×C22⋊C4—111no—
555C2×C22⋊C4—111no—
556C2×C22⋊C4—228no—
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×C22⋊C4—221no—
564C2×C42—21no—
565C2×C42—221no—
566C2×C42C22×D1111yescharacteristic
567#107—114no—
568#106—114no—
569#106C22×D1114yescomplemented
570C4⋊C8—114no—
571#103—114no—
572#103—114no—
573#103—114no—
574#103C22×D1114yescomplemented
575#102—114no—
576#102—114no—
577#102—114no—
578#102—114no—
579#102—114no—
580#102C22×D1114yes—
581C22⋊C8—114no—
582C22⋊C8—114no—
583C4×C8C22×D1114yescomplemented
584C2×C11—44no—
585C2×C11#332314yescomplemented
586C2×C11C2×#54611yescharacteristic
587C2×C11C2×#57511yescharacteristic
588C2×C11C2×#57711yescharacteristic
589D11—42no—
590D11—42no—
591D11—82no—
592C24—21no—
593C24—111no—
594C24—111no—
595C24—224no—
596C24—221no—
597C24—444no—
598C24—444no—
599C24—882no—
600#41—228no—
601#41—444no—
602#41—448no—
603C2×Q8—21no—
604C2×Q8—22no—
605C2×Q8—22no—
606C2×Q8—112no—
607C2×Q8—221no—
608C2×Q8—222no—
609C2×Q8—222no—
610C2×Q8C23×D1112yes—
611C2×D4—21no—
612C2×D4—22no—
613C2×D4—114no—
614C2×D4—112no—
615C2×D4—224no—
616C2×D4—224no—
617C2×D4—228no—
618C2×D4—224no—
619C2×D4—222no—
620C2×D4—221no—
621C2×D4—222no—
622C2×D4—442no—
623C2×D4—444no—
624C2×D4—448no—
625C2×D4—444no—
626C2×D4—444no—
627C2×D4—882no—
628C2×D4#433914yes—
629C2×D4C23×D1112yes—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—24no—
634C22×C4—82no—
635C22×C4—111no—
636C22×C4—111no—
637C22×C4—112no—
638C22×C4—112no—
639C22×C4—112no—
640C22×C4—112no—
641C22×C4—224no—
642C22×C4—224no—
643C22×C4—222no—
644C22×C4—222no—
645C22×C4—222no—
646C22×C4—222no—
647C22×C4—221no—
648C22×C4—221no—
649C22×C4—221no—
650C22×C4—444no—
651C22×C4—444no—
652C22×C4D4×D1111yescharacteristic
653C22×C4D4×D1111yescharacteristic
654C22×C4C23×D1111yescharacteristic
655Q16—444no—
656SD16—28no—
657SD16—444no—
658M16—444no—
659M16—444no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—112no—
663C2×C8—112no—
664C2×C8—222no—
665C2×C8—222no—
666C2×C8C23×D1112yes—
667C2×C8C23×D1112yes—
668C4⋊C4—24no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—114no—
672C4⋊C4—112no—
673C4⋊C4—112no—
674C4⋊C4—224no—
675C4⋊C4—224no—
676C4⋊C4—224no—
677C4⋊C4—224no—
678C4⋊C4—221no—
679C4⋊C4—221no—
680C4⋊C4—224no—
681C4⋊C4—224no—
682C4⋊C4C23×D1112yes—
683C4⋊C4C23×D1112yes—
684C22⋊C4—24no—
685C22⋊C4—114no—
686C22⋊C4—114no—
687C22⋊C4—224no—
688C22⋊C4—224no—
689C22⋊C4—224no—
690C22⋊C4—224no—
691C22⋊C4—224no—
692C22⋊C4—224no—
693C22⋊C4—224no—
694C42—24no—
695C42—224no—
696C42D4×D1112yes—
697C42C23×D1112yes—
698C11C2×#332311yescharacteristic, complemented, Sylow
699C23—24no—
700C23—22no—
701C23—42no—
702C23—42no—
703C23—112no—
704C23—112no—
705C23—222no—
706C23—222no—
707C23—222no—
708C23—222no—
709C23—222no—
710C23—222no—
711C23—222no—
712C23—448no—
713C23—448no—
714C23—442no—
715C23—442no—
716C23—442no—
717C23—884no—
718C23—8816no—
719C23C2×D4×D1111yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—42no—
723Q8—222no—
724Q8—222no—
725Q8—442no—
726D4—24no—
727D4—22no—
728D4—222no—
729D4—222no—
730D4—444no—
731D4—448no—
732D4—448no—
733D4—442no—
734D4—884no—
735D4C2×#433914yes—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—84no—
745C2×C4—112no—
746C2×C4—112no—
747C2×C4—222no—
748C2×C4—222no—
749C2×C4—224no—
750C2×C4—224no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—448no—
759C2×C4—448no—
760C2×C4—442no—
761C2×C4—442no—
762C2×C4—442no—
763C2×C4C2×#433912yes—
764C2×C4C2×D4×D1112yes—
765C2×C4C2×D4×D1112yes—
766C2×C4C2×D4×D1111yescharacteristic
767C2×C4#6704212yes—
768C2×C4C24×D1111yescharacteristic
769C8—22no—
770C8—22no—
771C8—222no—
772C8—222no—
773C22—24no—
774C22—48no—
775C22—42no—
776C22—42no—
777C22—222no—
778C22—222no—
779C22—222no—
780C22—222no—
781C22—222no—
782C22—222no—
783C22—444no—
784C22—444no—
785C22—442no—
786C22—442no—
787C22—442no—
788C22—8816no—
789C22—884no—
790C22#1062308112yes—
791C22#1062329312yes—
792C22#1062329912yes—
793C22C22×D4×D1111yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—222no—
800C4—222no—
801C4—442no—
802C4—442no—
803C4—442no—
804C4#1062308112yes—
805C4C22×#433911yescharacteristic
806C4C2×#6704211yescharacteristic
807C2—44no—
808C2—442no—
809C2—442no—
810C2—882no—
811C2#1308083714yesdirect product factor
812C2C2×#1062308111yescharacteristic
813C2C2×#1062329911yescharacteristic
814C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
prime radicalC2×#10623085C2
hypercenterC2×C4×SD16D11
hypocenterC11C2×#3323
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#10623112C2semidirect
3. #13080837C2direct (N × H)
4. C2×#10622310C2semidirect
5. C2×#10622476C2semidirect
6. C2×#10622480C2semidirect
7. C2×#10622622C2semidirect
8. C2×#10622429C2semidirect
9. C2×#10622425C2semidirect
10. C2×#10622641C2semidirect
11. C2×#10622786C2semidirect
12. C2×#10622782C2semidirect
13. C2×#10622301C2semidirect
14. C2×#10622384C2semidirect
15. C2×#10622383C2semidirect
16. C2×C4×C11×SD16C2semidirect
20. C2×C4×Q8×C11C22semidirect
23. C2×#66999C22semidirect
24. C22×#4326C22semidirect
29. C22×#4313C22semidirect
31. #10623112C22semidirect
38. C2×C4⋊C4×D11C22semidirect
46. C2×#66923C22semidirect
47. C4×C11×SD16C22semidirect
48. C2×C11×#106C22semidirect
49. C2×C11×#103C22semidirect
51. C2×C4×C8×C11C22semidirect
54. #10622786C22semidirect
55. #10622782C22semidirect
59. C2×(C2×D11)⋊C8C22semidirect
60. C2×#66880C22semidirect
61. C2×#66880C22semidirect
62. #10622641C22semidirect
63. #10622622C22semidirect
64. C2×#66874C22semidirect
66. C2×#66872C22semidirect
67. C2×#66871C22semidirect
68. C2×C4⋊(C11⋊C8)C22semidirect
69. #10622480C22semidirect
70. #10622476C22semidirect
71. #10622429C22semidirect
72. #10622425C22semidirect
73. #10622384C22semidirect
74. #10622383C22semidirect
75. #10622310C22semidirect
76. #10622301C22semidirect
104. C4×Q8×C11C23semidirect
116. #66999C23semidirect
118. C2×#4326C23semidirect
147. C2×#4313C23semidirect
156. C4⋊C4×D11C23semidirect
167. #66923C23semidirect
168. C11×#106C23semidirect
169. C11×#103C23semidirect
171. C4×C8×C11C23semidirect
177. (C2×D11)⋊C8C23semidirect
178. #66880C23semidirect
179. #66880C23semidirect
180. #66874C23semidirect
182. #66872C23semidirect
183. #66871C23semidirect
184. C4⋊(C11⋊C8)C23semidirect
304. C2×C4×SD16D11semidirect
405. C2×C4×Q8C2×D11semidirect
421. C4×SD16C2×D11semidirect
425. C2×#106C2×D11semidirect
432. C2×#103C2×D11semidirect
441. C2×C4×C8C2×D11semidirect
531. C4×Q8C22×D11semidirect
569. #106C22×D11semidirect
574. #103C22×D11semidirect
583. C4×C8C22×D11semidirect
585. C2×C11#3323semidirect
698. C11C2×#3323semidirect
811. C2#13080837direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231122
C2×#106230852
#130808372
C2×#106223102
C2×#106224762
C2×#106224802
C2×#106226222
C2×#106224292
C2×#106224252
C2×#106226412
C2×#106227862
C2×#106227822
C2×#106223012
C2×#106223842
C2×#106223832
C2×C4×C11×SD162
C2×#332311