Finite Group Databasebeta

← C2×#13079570 #15624981

Subgroups — C2×#13079570 #15624981

Order 2816.

2186 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623153C211yesmaximal, characteristic, complemented
2C2×#10623363C211yesmaximal, characteristic
3#13079570C2116yesmaximal, direct product factor
4C2×#10622794C211yesmaximal, characteristic, complemented
5C2×#10622788C211yesmaximal, characteristic, complemented
6C2×#10622405C211yesmaximal, characteristic, complemented
7C2×#10622373C211yesmaximal, characteristic, complemented
8C2×#10622411C211yesmaximal, characteristic, complemented
9C2×#10622798C211yesmaximal, characteristic, complemented
10C2×#10622380C211yesmaximal, characteristic, complemented
11C2×#10622779C211yesmaximal, characteristic, complemented
12C2×#10622346C211yesmaximal, characteristic, complemented
13C2×#10622852C211yesmaximal, characteristic, complemented
14C2×#10622660C211yesmaximal, characteristic, complemented
15C2×#10622331C211yesmaximal, characteristic, complemented
16C2×C11×#452C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×#4339C2211yescharacteristic
19C22×C11×Q16C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic
22#10623363—24no—
23#10623363C2218yes—
24C2×#67000C2211yescharacteristic
25C2×Q8×Dic11C2211yescharacteristic
26C2×#66997C2211yescharacteristic
27C2×#66997C2211yescharacteristic
28C22×#4326C2211yescharacteristic
29C22×#4326C2211yescharacteristic
30C22×#4325C2211yescharacteristic
31C2×#66993C2211yescharacteristic
32C2×#66992—21no—
33C2×#66992—21no—
34C2×#66989C2211yescharacteristic
35C22×#4324C2211yescharacteristic
36C2×C4×C22⋊D11—21no—
37C2×C4×C22⋊D11—21no—
38C2×#66977C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C22×Dic44C2211yescharacteristic
41C22×#4314C2211yescharacteristic
42#10623153—24no—
43#10623153C2218yescomplemented
44C2×#66942—21no—
45C2×#66941C2211yescharacteristic
46C2×#66940—21no—
47C2×#66940C2211yescharacteristic
48C2×#66931—21no—
49C2×#66930—21no—
50C11×#452C2218yescomplemented
51C2×C11×#103C2211yescharacteristic
52C2×C11×#102C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic
54#10622852C2218yescomplemented
55C2×#66899C2211yescharacteristic
56C2×#66896C2211yescharacteristic
57C2×C22⋊(C11⋊C8)C2211yescharacteristic
58#10622798C2218yescomplemented
59#10622794C2218yescomplemented
60#10622788C2218yescomplemented
61#10622779C2218yescomplemented
62C2×#66885C2211yescharacteristic
63C2×#66880C2211yescharacteristic
64C2×Dic11⋊C8C2211yescharacteristic
65C2×Dic11⋊C8C2211yescharacteristic
66C2×C8×Dic11C2211yescharacteristic
67C2×C8×Dic11C2211yescharacteristic
68#10622660C2218yescomplemented
69C2×#66874C2211yescharacteristic
70C2×#66873C2211yescharacteristic
71#10622411C2218yescomplemented
72#10622405C2218yescomplemented
73#10622380C2218yescomplemented
74#10622373C2218yescomplemented
75#10622346C2218yescomplemented
76#10622331C2218yescomplemented
77C2×C11×#41—22no—
78C2×C11×#41—42no—
79C2×C11×#41—42no—
80C2×C11×#41C2314yes—
81C22×Q8×C11C2311yescharacteristic
82C22×Q8×C11C2311yescharacteristic
83C22×D4×C11—21no—
84C22×D4×C11C2311yescharacteristic
85C23×C4×C11—21no—
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11—21no—
88C22×C22⋊D11—21no—
89C22×C22⋊D11—21no—
90C23×Dic11D411yescharacteristic
91C23×Dic11D411yescharacteristic
92C2×#4339—22no—
93C2×#4339—42no—
94C2×#4339—42no—
95C2×#4339C2314yes—
96C22×D44C2311yescharacteristic
97C22×C4×D11—21no—
98C22×Dic22—21no—
99C22×Dic22C2311yescharacteristic
100C22×Dic22C2311yescharacteristic
101C2×C11×Q16—42no—
102C2×C11×Q16C2314yes—
103C2×C11×SD16—42no—
104C2×C11×SD16C2314yes—
105C22×C8×C11C2311yescharacteristic
106C22×C8×C11C2311yescharacteristic
107C11×C22⋊Q8—22no—
108C11×C22⋊Q8C2314yes—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C22⋊C4—21no—
112C2×C22⋊Dic11—21no—
113C2×C22⋊Dic11—21no—
114C2×C22⋊Dic11—21no—
115#67000—22no—
116#67000C2314yes—
117Q8×Dic11—22no—
118Q8×Dic11C2314yes—
119#66997—22no—
120#66997—22no—
121#66997C2314yes—
122#66997C2314yes—
123C2×#4326—42no—
124C2×#4326—42no—
125C2×#4326C2314yes—
126C2×#4326C2314yes—
127C2×#4325—42no—
128C2×#4325C2314yes—
129#66993—22no—
130#66993C2314yes—
131#66992—28no—
132#66992—28no—
133#66989—22no—
134#66989C2314yes—
135C2×#4324—42no—
136C2×#4324C2314yes—
137C4×C22⋊D11—28no—
138C4×C22⋊D11—28no—
139C2×(C2×D11)⋊C4—21no—
140C2×(C2×D11)⋊C4—21no—
141C2×C4⋊Dic11—21no—
142C2×C4⋊Dic11C2311yescharacteristic
143#66977—22no—
144#66977C2314yes—
145C2×Dic11⋊C4—21no—
146C2×Dic11⋊C4—21no—
147C2×Dic11⋊C4—21no—
148C2×Dic11⋊C4—21no—
149C2×Dic11⋊C4—21no—
150C2×Dic11⋊C4—21no—
151C2×Dic11⋊C4—21no—
152C2×C4×Dic11—21no—
153C2×C4×Dic11—21no—
154C2×C4×Dic11D411yescharacteristic
155C2×C4×Dic11D411yescharacteristic
156C2×C4×Dic11D414yes—
157C2×C4×Dic11C2311yescharacteristic
158C2×C4×Dic11C2311yescharacteristic
159C2×C4×Dic11C2314yes—
160C22×C11⋊C8C2311yescharacteristic
161C22×C11⋊C8C2311yescharacteristic
162C2×Dic44—42no—
163C2×Dic44C2314yes—
164C2×#4314—42no—
165C2×#4314C2314yes—
166#66942—28no—
167#66941—22no—
168#66941C2314yes—
169#66940—28no—
170#66940—22no—
171#66940C2314yes—
172#66931—28no—
173#66930—28no—
174C11×#103C2314yes—
175C11×#102C2314yes—
176C11×C22⋊C8C2314yes—
177#66899C2314yes—
178#66896C2314yes—
179C22⋊(C11⋊C8)C2314yes—
180#66885C2314yes—
181#66880C2314yes—
182Dic11⋊C8C2314yes—
183Dic11⋊C8C2314yes—
184C8×Dic11C2314yes—
185C8×Dic11C2314yes—
186#66874C2314yes—
187#66873C2314yes—
188C2×#3210—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11C2×D411yescharacteristic
191C23×D11—21no—
192C11×#41—44no—
193C11×#41—44no—
194C11×#41—48no—
195C2×Q8×C11—21no—
196C2×Q8×C11—21no—
197C2×Q8×C11—22no—
198C2×Q8×C11—22no—
199C2×Q8×C11—22no—
200C2×Q8×C11—22no—
201C2×Q8×C11C2412yes—
202C2×Q8×C11C2412yes—
203C2×D4×C11—24no—
204C2×D4×C11—21no—
205C2×D4×C11—22no—
206C2×D4×C11—22no—
207C2×D4×C11—44no—
208C2×D4×C11C2412yes—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—24no—
215C22×C4×C11—44no—
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D412yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2411yescharacteristic
220C2×C22⋊D11—24no—
221C2×C22⋊D11—24no—
222C2×C22⋊D11—24no—
223C2×C22⋊D11—44no—
224C2×C22⋊D11—44no—
225C2×C22⋊D11—44no—
226C22×Dic11—24no—
227C22×Dic11—24no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11C2×D414yes—
232C22×Dic11C2×D414yes—
233C22×Dic11C2×D411yescharacteristic
234C22×Dic11C2×D411yescharacteristic
235C22×Dic11C2×D411yescharacteristic
236C22×Dic11C2×D411yescharacteristic
237#4339—44no—
238#4339—44no—
239#4339—48no—
240C2×D44—21no—
241C2×D44—22no—
242C2×D44—22no—
243C2×D44C2412yes—
244C2×C4×D11—24no—
245C2×C4×D11—44no—
246C2×Dic22—24no—
247C2×Dic22—21no—
248C2×Dic22—21no—
249C2×Dic22—22no—
250C2×Dic22—22no—
251C2×Dic22—22no—
252C2×Dic22—22no—
253C2×Dic22—44no—
254C2×Dic22C2412yes—
255C2×Dic22C2412yes—
256C11×Q16—44no—
257C11×SD16—44no—
258C2×C8×C11—22no—
259C2×C8×C11—22no—
260C2×C8×C11C2412yes—
261C2×C8×C11C2412yes—
262C11×C4⋊C4—21no—
263C11×C4⋊C4—24no—
264C11×C4⋊C4C2412yes—
265C11×C22⋊C4—24no—
266C22⋊Dic11—24no—
267C22⋊Dic11—24no—
268C22⋊Dic11—24no—
269#4326—44no—
270#4326—44no—
271#4325—44no—
272#4324—44no—
273(C2×D11)⋊C4—24no—
274(C2×D11)⋊C4—24no—
275C4⋊Dic11—24no—
276C4⋊Dic11—21no—
277C4⋊Dic11C2412yes—
278Dic11⋊C4—24no—
279Dic11⋊C4—24no—
280Dic11⋊C4—24no—
281Dic11⋊C4—24no—
282Dic11⋊C4—24no—
283Dic11⋊C4—24no—
284Dic11⋊C4—24no—
285C4×Dic11—24no—
286C4×Dic11—24no—
287C4×Dic11C2×D414yes—
288C4×Dic11C2×D412yes—
289C4×Dic11C2×D412yes—
290C4×Dic11C2×D414yes—
291C4×Dic11C2412yes—
292C4×Dic11C2412yes—
293C2×C11⋊C8—22no—
294C2×C11⋊C8—22no—
295C2×C11⋊C8C2412yes—
296C2×C11⋊C8C2412yes—
297Dic44—44no—
298#4314—44no—
299C2×#533—111no—
300C2×#532—111no—
301#3210—1116no—
302C2×#494—111no—
303C2×#492—111no—
304C2×#487—111no—
305C2×#486—111no—
306C2×#464—111no—
307C2×#464—111no—
308C2×#464—111no—
309C2×#464—111no—
310C2×#452—111no—
311C2×#452—111no—
312C2×#452—111no—
313C2×#452D1111yescharacteristic, complemented
314C2×#431—111no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—42no—
320C23×C11—42no—
321C23×C11—42no—
322C23×C11C22×D412yes—
323C23×C11C22×D411yescharacteristic
324C22×D11—22no—
325C22×D11—42no—
326C22×D11—42no—
327C22×D11—42no—
328Q8×C11—22no—
329Q8×C11—22no—
330Q8×C11—22no—
331Q8×C11—22no—
332Q8×C11—42no—
333Q8×C11—42no—
334D4×C11—22no—
335D4×C11—22no—
336D4×C11—48no—
337D4×C11—42no—
338C2×C4×C11—22no—
339C2×C4×C11—24no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—48no—
346C2×C4×C11—42no—
347C2×C4×C11—42no—
348C2×C4×C11—42no—
349C2×C4×C11C22×D412yes—
350C2×C4×C11C22×D411yescharacteristic
351C2×C4×C11H(5,𝔽2)12yes—
352C2×C4×C11H(5,𝔽2)12yes—
353C2×C4×C11C2511yescharacteristic
354C22⋊D11—48no—
355C22⋊D11—48no—
356C22⋊D11—48no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—28no—
360C2×Dic11—28no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—42no—
365C2×Dic11—42no—
366C2×Dic11—42no—
367C2×Dic11#13514yes—
368C2×Dic11#13714yes—
369C2×Dic11C22×D412yes—
370C2×Dic11C22×D412yes—
371C2×Dic11C22×D412yes—
372C2×Dic11C22×D412yes—
373D44—22no—
374D44—22no—
375D44—42no—
376C4×D11—48no—
377Dic22—22no—
378Dic22—22no—
379Dic22—22no—
380Dic22—22no—
381Dic22—42no—
382Dic22—42no—
383Dic22—48no—
384C8×C11—22no—
385C8×C11—22no—
386C11⋊C8—22no—
387C11⋊C8—22no—
388C22×#41—111no—
389C22×#41C2×D1111yescharacteristic
390C22×Q16—111no—
391C22×Q16—111no—
392C22×Q16—111no—
393C22×Q16C2×D1111yescharacteristic
394C22×SD16—111no—
395C22×SD16—111no—
396C22×SD16—111no—
397C22×SD16C2×D1111yescharacteristic
398#533—118no—
399#533—224no—
400#532—118no—
401#532—224no—
402C2×C4⋊Q8—111no—
403C2×C4⋊Q8—111no—
404C2×C4⋊Q8—111no—
405C2×#127—111no—
406C2×#125—221no—
407C2×#124—111no—
408C2×#124—111no—
409C2×C22⋊Q8—111no—
410C2×C22⋊Q8—221no—
411C2×C22⋊Q8C2×D1111yescharacteristic
412C2×#121—221no—
413C2×#121—221no—
414C2×C4×Q8—111no—
415C2×C4×Q8—111no—
416C2×C4×Q8—221no—
417C2×C4×D4—221no—
418C2×C4×D4—221no—
419C2×#117—221no—
420C22×C42—111no—
421#494—118no—
422#492—118no—
423#487—118no—
424#486—118no—
425#464—118no—
426#464—118no—
427#464—118no—
428#464—118no—
429#452—118no—
430#452—118no—
431#452—118no—
432#452C2×D1118yescomplemented
433#431—118no—
434C2×C4⋊C8—111no—
435C2×C4⋊C8—111no—
436C2×#103—111no—
437C2×#103—111no—
438C2×#103—111no—
439C2×#103C2×D1111yescharacteristic
440C2×#102—111no—
441C2×#102—111no—
442C2×#102—111no—
443C2×#102C2×D1111yescharacteristic
444C2×C22⋊C8—111no—
445C2×C22⋊C8C2×D1111yescharacteristic
446C2×C4×C8—111no—
447C2×C4×C8—111no—
448C22×C11—22no—
449C22×C11—22no—
450C22×C11—22no—
451C22×C11—44no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—84no—
456C22×C11#53512yes—
457C22×C11C2×#13512yes—
458C22×C11C2×#13712yes—
459C22×C11C23×D411yescharacteristic
460C2×D11—42no—
461C2×D11—42no—
462C2×D11—42no—
463C2×D11—84no—
464C4×C11—22no—
465C4×C11—42no—
466C4×C11—42no—
467C4×C11—42no—
468C4×C11#53512yes—
469C4×C11C2×H(5,𝔽2)11yescharacteristic
470C4×C11C2×H(5,𝔽2)11yescharacteristic
471Dic11—22no—
472Dic11—22no—
473Dic11—42no—
474Dic11—42no—
475Dic11—42no—
476Dic11C2×#13514yes—
477Dic11C2×#13714yes—
478C2×#41—22no—
479C2×#41—42no—
480C2×#41—42no—
481C2×#41—114no—
482C2×#41—222no—
483C2×#41—442no—
484C2×#41—442no—
485C2×#41C22×D1114yes—
486C22×Q8—111no—
487C22×Q8—111no—
488C22×Q8—221no—
489C22×Q8C22×D1111yescharacteristic
490C22×Q8C22×D1111yescharacteristic
491C22×D4—21no—
492C22×D4—111no—
493C22×D4—221no—
494C22×D4—221no—
495C22×D4—221no—
496C22×D4C22×D1111yescharacteristic
497C23×C4—21no—
498C23×C4—111no—
499C23×C4—111no—
500C23×C4—221no—
501C23×C4C22×D1111yescharacteristic
502C2×Q16—42no—
503C2×Q16—114no—
504C2×Q16—114no—
505C2×Q16—114no—
506C2×Q16—442no—
507C2×Q16—442no—
508C2×Q16—442no—
509C2×Q16C22×D1114yes—
510C2×SD16—42no—
511C2×SD16—114no—
512C2×SD16—114no—
513C2×SD16—114no—
514C2×SD16—442no—
515C2×SD16—442no—
516C2×SD16—442no—
517C2×SD16C22×D1114yes—
518C22×C8—111no—
519C22×C8—111no—
520C22×C8C22×D1111yescharacteristic
521C22×C8C22×D1111yescharacteristic
522C4⋊Q8—114no—
523C4⋊Q8—114no—
524C4⋊Q8—114no—
525C4⋊Q8—222no—
526C4⋊Q8—222no—
527C4⋊Q8—222no—
528#127—114no—
529#127—222no—
530#125—228no—
531#124—114no—
532#124—114no—
533#124—222no—
534#124—222no—
535C22⋊Q8—22no—
536C22⋊Q8—114no—
537C22⋊Q8—228no—
538C22⋊Q8—222no—
539C22⋊Q8C22×D1114yes—
540#121—228no—
541#121—228no—
542C4×Q8—114no—
543C4×Q8—114no—
544C4×Q8—222no—
545C4×Q8—228no—
546C4×Q8—222no—
547C4×D4—228no—
548C4×D4—228no—
549#117—228no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—111no—
552C2×C4⋊C4—221no—
553C2×C4⋊C4—221no—
554C2×C4⋊C4—221no—
555C2×C4⋊C4—221no—
556C2×C4⋊C4—221no—
557C2×C4⋊C4—221no—
558C2×C4⋊C4—221no—
559C2×C4⋊C4—221no—
560C2×C4⋊C4C22×D1111yescharacteristic
561C2×C22⋊C4—21no—
562C2×C22⋊C4—221no—
563C2×C22⋊C4—221no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—221no—
567C2×C42—111no—
568C2×C42—111no—
569C2×C42—114no—
570C2×C42—111no—
571C2×C42—111no—
572C2×C42—114no—
573C2×C42—221no—
574C2×C42—221no—
575C4⋊C8—114no—
576C4⋊C8—114no—
577#103—114no—
578#103—114no—
579#103—114no—
580#103C22×D1114yes—
581#102—114no—
582#102—114no—
583#102—114no—
584#102C22×D1114yes—
585C22⋊C8—114no—
586C22⋊C8C22×D1114yes—
587C4×C8—114no—
588C4×C8—114no—
589C2×C11—42no—
590C2×C11—82no—
591C2×C11#321014yescomplemented
592C2×C11C2×#53511yescharacteristic
593C2×C11C22×#13511yescharacteristic
594C2×C11C22×#13711yescharacteristic
595D11—82no—
596C24—21no—
597C24—221no—
598C24D4×D1111yescharacteristic
599#41—44no—
600#41—44no—
601#41—48no—
602#41—444no—
603#41—444no—
604#41—448no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—22no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—112no—
612C2×Q8—112no—
613C2×Q8—224no—
614C2×Q8—221no—
615C2×Q8—221no—
616C2×Q8—222no—
617C2×Q8—222no—
618C2×Q8—222no—
619C2×Q8—222no—
620C2×Q8—444no—
621C2×Q8C23×D1112yes—
622C2×Q8C23×D1112yes—
623C2×D4—24no—
624C2×D4—21no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—44no—
628C2×D4—112no—
629C2×D4—224no—
630C2×D4—224no—
631C2×D4—224no—
632C2×D4—221no—
633C2×D4—222no—
634C2×D4—222no—
635C2×D4—444no—
636C2×D4—444no—
637C2×D4—444no—
638C2×D4C23×D1112yes—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—24no—
645C22×C4—44no—
646C22×C4—111no—
647C22×C4—111no—
648C22×C4—114no—
649C22×C4—114no—
650C22×C4—111no—
651C22×C4—111no—
652C22×C4—224no—
653C22×C4—224no—
654C22×C4—221no—
655C22×C4—221no—
656C22×C4—221no—
657C22×C4—224no—
658C22×C4—444no—
659C22×C4D4×D1112yes—
660C22×C4D4×D1111yescharacteristic
661C22×C4C23×D1112yes—
662C22×C4C23×D1111yescharacteristic
663Q16—44no—
664Q16—444no—
665Q16—444no—
666Q16—444no—
667SD16—44no—
668SD16—444no—
669SD16—444no—
670SD16—444no—
671C2×C8—22no—
672C2×C8—22no—
673C2×C8—112no—
674C2×C8—112no—
675C2×C8—222no—
676C2×C8—222no—
677C2×C8C23×D1112yes—
678C2×C8C23×D1112yes—
679C4⋊C4—24no—
680C4⋊C4—21no—
681C4⋊C4—112no—
682C4⋊C4—224no—
683C4⋊C4—224no—
684C4⋊C4—224no—
685C4⋊C4—224no—
686C4⋊C4—224no—
687C4⋊C4—224no—
688C4⋊C4—224no—
689C4⋊C4—221no—
690C4⋊C4—224no—
691C4⋊C4C23×D1112yes—
692C22⋊C4—24no—
693C22⋊C4—224no—
694C22⋊C4—224no—
695C22⋊C4—224no—
696C22⋊C4—224no—
697C22⋊C4—224no—
698C42—114no—
699C42—114no—
700C42—112no—
701C42—112no—
702C42—112no—
703C42—112no—
704C42—224no—
705C42—224no—
706C11C2×#321011yescharacteristic, complemented, Sylow
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—222no—
715C23—442no—
716C23—442no—
717C23—442no—
718C23C2×D4×D1112yes—
719C23C2×D4×D1111yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—22no—
724Q8—42no—
725Q8—42no—
726Q8—222no—
727Q8—222no—
728Q8—222no—
729Q8—222no—
730Q8—448no—
731Q8—442no—
732Q8—442no—
733D4—22no—
734D4—22no—
735D4—48no—
736D4—42no—
737D4—222no—
738D4—222no—
739D4—448no—
740D4—448no—
741D4—448no—
742D4—442no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—48no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—114no—
755C2×C4—114no—
756C2×C4—112no—
757C2×C4—112no—
758C2×C4—112no—
759C2×C4—112no—
760C2×C4—228no—
761C2×C4—228no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—222no—
767C2×C4—448no—
768C2×C4—442no—
769C2×C4—442no—
770C2×C4—442no—
771C2×C4C2×D4×D1112yes—
772C2×C4C2×D4×D1111yescharacteristic
773C2×C4#6703712yes—
774C2×C4#6703712yes—
775C2×C4C24×D1111yescharacteristic
776C8—22no—
777C8—22no—
778C8—222no—
779C8—222no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—44no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—84no—
788C22—442no—
789C22—442no—
790C22—442no—
791C22—884no—
792C22#1062312312yes—
793C22D11×#13512yes—
794C22D11×#13712yes—
795C22C22×D4×D1111yescharacteristic
796C4—22no—
797C4—42no—
798C4—42no—
799C4—42no—
800C4—114no—
801C4—114no—
802C4—222no—
803C4—222no—
804C4—442no—
805C4—442no—
806C4—442no—
807C4#1062312312yes—
808C4C2×#6703711yescharacteristic
809C4C2×#6703711yescharacteristic
810C2—42no—
811C2—82no—
812C2—882no—
813C2#1307957014yesdirect product factor
814C2C2×#1062312311yescharacteristic
815C2C2×D11×#13511yescharacteristic
816C2C2×D11×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#452C2
socleC23×C11C22×D4
prime radicalC2×#10623363C2
hypercenterC2×#452D11
hypocenterC11C2×#3210
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#10623153C2semidirect
3. #13079570C2direct (N × H)
4. C2×#10622794C2semidirect
5. C2×#10622788C2semidirect
6. C2×#10622405C2semidirect
7. C2×#10622373C2semidirect
8. C2×#10622411C2semidirect
9. C2×#10622798C2semidirect
10. C2×#10622380C2semidirect
11. C2×#10622779C2semidirect
12. C2×#10622346C2semidirect
13. C2×#10622852C2semidirect
14. C2×#10622660C2semidirect
15. C2×#10622331C2semidirect
16. C2×C11×#452C2semidirect
43. #10623153C22semidirect
50. C11×#452C22semidirect
54. #10622852C22semidirect
58. #10622798C22semidirect
59. #10622794C22semidirect
60. #10622788C22semidirect
61. #10622779C22semidirect
68. #10622660C22semidirect
71. #10622411C22semidirect
72. #10622405C22semidirect
73. #10622380C22semidirect
74. #10622373C22semidirect
75. #10622346C22semidirect
76. #10622331C22semidirect
313. C2×#452D11semidirect
432. #452C2×D11semidirect
591. C2×C11#3210semidirect
706. C11C2×#3210semidirect
813. C2#13079570direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231532
C2×#106233632
#130795702
C2×#106227942
C2×#106227882
C2×#106224052
C2×#106223732
C2×#106224112
C2×#106227982
C2×#106223802
C2×#106227792
C2×#106223462
C2×#106228522
C2×#106226602
C2×#106223312
C2×C11×#4522
C2×#321011