Finite Group Databasebeta

← C2×#13079587 #15624988

Subgroups — C2×#13079587 #15624988

Order 2816.

2218 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623199C211yesmaximal, characteristic, complemented
2C2×#10623211C211yesmaximal, characteristic, complemented
3#13079587C2116yesmaximal, direct product factor
4C2×#10622672C211yesmaximal, characteristic, complemented
5C2×#10622310C211yesmaximal, characteristic, complemented
6C2×#10622669C211yesmaximal, characteristic, complemented
7C2×#10622795C211yesmaximal, characteristic, complemented
8C2×#10622776C211yesmaximal, characteristic, complemented
9C2×#10622775C211yesmaximal, characteristic, complemented
10C2×#10622763C211yesmaximal, characteristic, complemented
11C2×#10622800C211yesmaximal, characteristic, complemented
12C2×#10622786C211yesmaximal, characteristic, complemented
13C2×#10622785C211yesmaximal, characteristic, complemented
14C2×#10622771C211yesmaximal, characteristic, complemented
15C2×#10622298C211yesmaximal, characteristic, complemented
16C2×C11×#495C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×#4341C2211yescharacteristic
19C22×C11×Q16C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C22×C11×SD16C2211yescharacteristic
22C22×C11×D8C2211yescharacteristic
23C2×C11×#124C2211yescharacteristic
24C2×C11×#124C2211yescharacteristic
25C2×#66999C2211yescharacteristic
26C2×Q8×Dic11C2211yescharacteristic
27C2×#66997C2211yescharacteristic
28C22×#4326C2211yescharacteristic
29C22×#4325C2211yescharacteristic
30C2×#66993C2211yescharacteristic
31C2×#66991C2211yescharacteristic
32C2×D4×Dic11C2211yescharacteristic
33C22×#4324C2211yescharacteristic
34C22×#4323C2211yescharacteristic
35#10623211—24no—
36#10623211C2218yescomplemented
37#10623199—24no—
38#10623199C2218yescomplemented
39C2×#66937—21no—
40C2×#66937—21no—
41C2×#66936—21no—
42C2×(C22⋊D11)⋊C4—21no—
43C2×(C22⋊D11)⋊C4—21no—
44C2×(C22⋊D11)⋊C4—21no—
45C2×#66932—21no—
46C2×#66930—21no—
47C2×#66928C2211yescharacteristic
48C2×C42×D11C2211yescharacteristic
49C2×#66923C2211yescharacteristic
50C11×#495C2218yescomplemented
51C2×C4×C8×C11C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×#66896C2211yescharacteristic
56#10622800C2218yescomplemented
57#10622795C2218yescomplemented
58#10622786C2218yescomplemented
59#10622785C2218yescomplemented
60#10622776C2218yescomplemented
61#10622775C2218yescomplemented
62#10622771C2218yescomplemented
63#10622763C2218yescomplemented
64C2×#66885C2211yescharacteristic
65C2×#66885C2211yescharacteristic
66C2×(C2×D11)⋊C8C2211yescharacteristic
67C2×(C2×D11)⋊C8C2211yescharacteristic
68C2×#66880C2211yescharacteristic
69C2×#66880C2211yescharacteristic
70C2×Dic11⋊C8C2211yescharacteristic
71C2×Dic11⋊C8C2211yescharacteristic
72#10622672C2218yescomplemented
73#10622669C2218yescomplemented
74C2×C4×C11⋊C8C2211yescharacteristic
75#10622310C2218yescomplemented
76#10622298C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C23×Dic11—21no—
86C23×Dic11—21no—
87C2×#4343—22no—
88C2×#4343—42no—
89C2×#4343—42no—
90C2×#4343C2314yes—
91C2×#4341—22no—
92C2×#4341—42no—
93C2×#4341—42no—
94C2×#4341C2314yes—
95C22×D44—21no—
96C22×D44C2311yescharacteristic
97C22×C4×D11—21no—
98C22×C4×D11D411yescharacteristic
99C22×C4×D11D411yescharacteristic
100C22×C4×D11C2311yescharacteristic
101C22×Dic22C2311yescharacteristic
102C2×C11×Q16—42no—
103C2×C11×Q16C2314yes—
104C2×C11×SD16—42no—
105C2×C11×SD16—42no—
106C2×C11×SD16C2314yes—
107C2×C11×SD16C2314yes—
108C2×C11×D8—42no—
109C2×C11×D8C2314yes—
110C22×C8×C11C2311yescharacteristic
111C22×C8×C11C2311yescharacteristic
112C11×#124—22no—
113C11×#124—22no—
114C11×#124C2314yes—
115C11×#124C2314yes—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C42×C11C2311yescharacteristic
121C2×C22⋊Dic11—21no—
122C2×C22⋊Dic11—21no—
123#66999—22no—
124#66999C2314yes—
125Q8×Dic11—22no—
126Q8×Dic11C2314yes—
127#66997—22no—
128#66997C2314yes—
129C2×#4326—42no—
130C2×#4326C2314yes—
131C2×#4325—42no—
132C2×#4325C2314yes—
133#66993—22no—
134#66993C2314yes—
135#66991—22no—
136#66991C2314yes—
137D4×Dic11—22no—
138D4×Dic11C2314yes—
139C2×#4324—42no—
140C2×#4324C2314yes—
141C2×#4323—42no—
142C2×#4323C2314yes—
143C2×(C2×D11)⋊C4—21no—
144C2×(C2×D11)⋊C4—21no—
145C2×(C2×D11)⋊C4—21no—
146C2×C4⋊Dic11—21no—
147C2×C4⋊Dic11C2311yescharacteristic
148C2×C4⋊Dic11C2311yescharacteristic
149C2×Dic11⋊C4—21no—
150C2×Dic11⋊C4—21no—
151C2×Dic11⋊C4—21no—
152C2×Dic11⋊C4—21no—
153C2×Dic11⋊C4—21no—
154C2×C4×Dic11—21no—
155C2×C4×Dic11D411yescharacteristic
156C2×C4×Dic11D411yescharacteristic
157C2×C4×Dic11C2311yescharacteristic
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160#66937—28no—
161#66937—28no—
162#66936—28no—
163(C22⋊D11)⋊C4—28no—
164(C22⋊D11)⋊C4—28no—
165(C22⋊D11)⋊C4—28no—
166#66932—28no—
167#66930—28no—
168#66928—22no—
169#66928C2314yes—
170C42×D11D414yes—
171C42×D11C2314yes—
172#66923—22no—
173#66923C2314yes—
174C4×C8×C11C2314yes—
175#66899C2314yes—
176#66899C2314yes—
177#66896C2314yes—
178#66896C2314yes—
179#66885C2314yes—
180#66885C2314yes—
181(C2×D11)⋊C8C2314yes—
182(C2×D11)⋊C8C2314yes—
183#66880C2314yes—
184#66880C2314yes—
185Dic11⋊C8C2314yes—
186Dic11⋊C8C2314yes—
187C4×C11⋊C8C2314yes—
188C2×#3212—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11—21no—
191C23×D11—21no—
192C23×D11C2×D411yescharacteristic
193C2×Q8×C11—21no—
194C2×Q8×C11—21no—
195C2×Q8×C11—22no—
196C2×Q8×C11—22no—
197C2×Q8×C11—22no—
198C2×Q8×C11—22no—
199C2×Q8×C11C2412yes—
200C2×Q8×C11C2412yes—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—22no—
204C2×D4×C11—22no—
205C2×D4×C11—22no—
206C2×D4×C11—22no—
207C2×D4×C11C2412yes—
208C2×D4×C11C2412yes—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2411yescharacteristic
214C2×C22⋊D11—24no—
215C2×C22⋊D11—24no—
216C2×C22⋊D11—24no—
217C2×C22⋊D11—24no—
218C2×C22⋊D11—44no—
219C2×C22⋊D11—44no—
220C2×C22⋊D11—44no—
221C2×C22⋊D11—44no—
222C22×Dic11—24no—
223C22×Dic11—24no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—44no—
228C22×Dic11—44no—
229C22×Dic11C2×D411yescharacteristic
230C22×Dic11C2×D411yescharacteristic
231C22×Dic11C2×D411yescharacteristic
232#4343—44no—
233#4343—44no—
234#4343—48no—
235#4341—44no—
236#4341—44no—
237#4341—48no—
238C2×D44—24no—
239C2×D44—21no—
240C2×D44—22no—
241C2×D44—22no—
242C2×D44—44no—
243C2×D44C2412yes—
244C2×C4×D11—24no—
245C2×C4×D11—24no—
246C2×C4×D11—22no—
247C2×C4×D11—22no—
248C2×C4×D11—42no—
249C2×C4×D11—44no—
250C2×C4×D11C2×D412yes—
251C2×C4×D11C2×D414yes—
252C2×C4×D11C2×D414yes—
253C2×C4×D11C2412yes—
254C2×Dic22—21no—
255C2×Dic22—22no—
256C2×Dic22—22no—
257C2×Dic22C2412yes—
258C11×Q16—44no—
259C11×SD16—44no—
260C11×SD16—44no—
261C11×D8—44no—
262C2×C8×C11—22no—
263C2×C8×C11—22no—
264C2×C8×C11C2412yes—
265C2×C8×C11C2412yes—
266C11×C22⋊C4—24no—
267C11×C22⋊C4—24no—
268C11×C22⋊C4—24no—
269C11×C22⋊C4—24no—
270C42×C11C2×D412yes—
271C42×C11C2412yes—
272C22⋊Dic11—24no—
273C22⋊Dic11—24no—
274#4326—44no—
275#4325—44no—
276#4324—44no—
277#4323—44no—
278(C2×D11)⋊C4—24no—
279(C2×D11)⋊C4—24no—
280(C2×D11)⋊C4—24no—
281C4⋊Dic11—24no—
282C4⋊Dic11—21no—
283C4⋊Dic11—21no—
284C4⋊Dic11C2412yes—
285C4⋊Dic11C2412yes—
286Dic11⋊C4—24no—
287Dic11⋊C4—24no—
288Dic11⋊C4—24no—
289Dic11⋊C4—24no—
290Dic11⋊C4—24no—
291C4×Dic11—24no—
292C4×Dic11C2×D412yes—
293C4×Dic11C2×D414yes—
294C4×Dic11C2×D414yes—
295C4×Dic11C2412yes—
296C2×C11⋊C8—22no—
297C2×C11⋊C8—22no—
298C2×C11⋊C8C2412yes—
299C2×C11⋊C8C2412yes—
300C2×#532—111no—
301C2×#529—111no—
302#3212—1116no—
303C2×#495—111no—
304C2×#495D1111yescharacteristic, complemented
305C2×#488—111no—
306C2×#488—111no—
307C2×#462—111no—
308C2×#460—111no—
309C2×#461—111no—
310C2×#459—111no—
311C2×#452—111no—
312C2×#452—111no—
313C2×#449—111no—
314C2×#449—111no—
315C2×#431—111no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—42no—
319C23×C11—42no—
320C23×C11—42no—
321C23×C11—42no—
322C23×C11—42no—
323C23×C11—42no—
324C23×C11C22×D411yescharacteristic
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—42no—
330C22×D11—42no—
331C22×D11—42no—
332C22×D11C22×D412yes—
333Q8×C11—22no—
334Q8×C11—22no—
335Q8×C11—22no—
336Q8×C11—22no—
337Q8×C11—42no—
338Q8×C11—42no—
339D4×C11—22no—
340D4×C11—22no—
341D4×C11—22no—
342D4×C11—22no—
343D4×C11—42no—
344D4×C11—42no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—42no—
350C2×C4×C11—42no—
351C2×C4×C11C22×D412yes—
352C2×C4×C11C22×D412yes—
353C2×C4×C11C22×D411yescharacteristic
354C2×C4×C11H(5,𝔽2)12yes—
355C2×C4×C11H(5,𝔽2)12yes—
356C2×C4×C11C2511yescharacteristic
357C22⋊D11—48no—
358C22⋊D11—48no—
359C22⋊D11—48no—
360C22⋊D11—48no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—48no—
367C2×Dic11—42no—
368C2×Dic11—42no—
369C2×Dic11—42no—
370C2×Dic11—48no—
371C2×Dic11#13514yes—
372C2×Dic11C22×D412yes—
373C2×Dic11C22×D412yes—
374C2×Dic11C22×D412yes—
375D44—22no—
376D44—22no—
377D44—48no—
378D44—42no—
379C4×D11—24no—
380C4×D11—22no—
381C4×D11—22no—
382C4×D11—28no—
383C4×D11—44no—
384C4×D11—48no—
385Dic22—22no—
386Dic22—22no—
387Dic22—42no—
388C8×C11—22no—
389C8×C11—22no—
390C11⋊C8—22no—
391C11⋊C8—22no—
392C22×#41—111no—
393C22×#41—111no—
394C22×Q16—111no—
395C22×Q16C2×D1111yescharacteristic
396C22×SD16—111no—
397C22×SD16—111no—
398C22×SD16C2×D1111yescharacteristic
399C22×SD16C2×D1111yescharacteristic
400C22×D8—111no—
401C22×D8C2×D1111yescharacteristic
402#532—118no—
403#532—224no—
404C2×C4⋊Q8—111no—
405C2×#127—111no—
406#529—118no—
407#529—224no—
408C2×#126—221no—
409C2×#125—111no—
410C2×#124—111no—
411C2×#124C2×D1111yescharacteristic
412C2×#124C2×D1111yescharacteristic
413C2×#123—221no—
414C2×C22⋊Q8—111no—
415C2×#121—111no—
416C2×#121—221no—
417C2×#121—221no—
418C2×C4×Q8—111no—
419C2×C4×D4—111no—
420C2×C4×D4—221no—
421C2×C4×D4—221no—
422C2×C4×D4—221no—
423C2×#117—221no—
424C22×C42—111no—
425#495—118no—
426#495C2×D1118yescomplemented
427#488—118no—
428#488—118no—
429#462—118no—
430#461—118no—
431#460—118no—
432#459—118no—
433#452—118no—
434#452—118no—
435#449—118no—
436#449—118no—
437#431—118no—
438C2×C4⋊C8—111no—
439C2×C4⋊C8—111no—
440C2×#103—111no—
441C2×#103—111no—
442C2×#103—111no—
443C2×#103—111no—
444C2×#102—111no—
445C2×#102—111no—
446C2×#102—111no—
447C2×#102—111no—
448C2×C22⋊C8—111no—
449C2×C22⋊C8—111no—
450C2×C4×C8—111no—
451C2×C4×C8C2×D1111yescharacteristic
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—84no—
459C22×C11—84no—
460C22×C11#53512yes—
461C22×C11C2×#13512yes—
462C22×C11#57512yes—
463C22×C11C23×D411yescharacteristic
464C2×D11—22no—
465C2×D11—22no—
466C2×D11—22no—
467C2×D11—44no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—84no—
472C4×C11—22no—
473C4×C11—22no—
474C4×C11—42no—
475C4×C11—42no—
476C4×C11#53512yes—
477C4×C11C2×H(5,𝔽2)11yescharacteristic
478C4×C11C2×H(5,𝔽2)11yescharacteristic
479Dic11—22no—
480Dic11—22no—
481Dic11—42no—
482Dic11—42no—
483Dic11—42no—
484Dic11C2×#13514yes—
485C2×#41—114no—
486C2×#41—114no—
487C2×#41—222no—
488C2×#41—222no—
489C2×#41—442no—
490C2×#41—442no—
491C2×#41—442no—
492C2×#41—442no—
493C22×Q8—111no—
494C22×Q8C22×D1111yescharacteristic
495C22×Q8C22×D1111yescharacteristic
496C22×D4—111no—
497C22×D4—221no—
498C22×D4—221no—
499C22×D4—221no—
500C22×D4—221no—
501C22×D4—221no—
502C22×D4C22×D1111yescharacteristic
503C22×D4C22×D1111yescharacteristic
504C23×C4—111no—
505C23×C4—111no—
506C23×C4—111no—
507C23×C4—221no—
508C23×C4—221no—
509C23×C4—221no—
510C2×Q16—42no—
511C2×Q16—114no—
512C2×Q16—442no—
513C2×Q16C22×D1114yes—
514C2×SD16—42no—
515C2×SD16—42no—
516C2×SD16—114no—
517C2×SD16—114no—
518C2×SD16—442no—
519C2×SD16—442no—
520C2×SD16C22×D1114yes—
521C2×SD16C22×D1114yes—
522C2×D8—42no—
523C2×D8—114no—
524C2×D8—442no—
525C2×D8C22×D1114yes—
526C22×C8—111no—
527C22×C8—111no—
528C22×C8C22×D1111yescharacteristic
529C22×C8C22×D1111yescharacteristic
530C4⋊Q8—114no—
531C4⋊Q8—222no—
532#127—114no—
533#127—222no—
534#126—228no—
535#125—114no—
536#125—222no—
537#124—22no—
538#124—22no—
539#124—114no—
540#124—222no—
541#124C22×D1114yes—
542#124C22×D1114yes—
543#123—228no—
544C22⋊Q8—114no—
545C22⋊Q8—222no—
546#121—114no—
547#121—228no—
548#121—228no—
549#121—222no—
550C4×Q8—114no—
551C4×Q8—222no—
552C4×D4—114no—
553C4×D4—228no—
554C4×D4—228no—
555C4×D4—222no—
556C4×D4—228no—
557#117—228no—
558C2×C4⋊C4—111no—
559C2×C4⋊C4—111no—
560C2×C4⋊C4—221no—
561C2×C4⋊C4—221no—
562C2×C4⋊C4—221no—
563C2×C4⋊C4—221no—
564C2×C4⋊C4—221no—
565C2×C4⋊C4—221no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—221no—
571C2×C22⋊C4—221no—
572C2×C22⋊C4—221no—
573C2×C22⋊C4—221no—
574C2×C22⋊C4—221no—
575C2×C42—111no—
576C2×C42—111no—
577C2×C42—111no—
578C2×C42—114no—
579C2×C42—114no—
580C2×C42—221no—
581C2×C42C22×D1111yescharacteristic
582C4⋊C8—114no—
583C4⋊C8—114no—
584#103—114no—
585#103—114no—
586#103—114no—
587#103—114no—
588#102—114no—
589#102—114no—
590#102—114no—
591#102—114no—
592C22⋊C8—114no—
593C22⋊C8—114no—
594C4×C8—114no—
595C4×C8C22×D1114yes—
596C2×C11—82no—
597C2×C11—82no—
598C2×C11#321214yescomplemented
599C2×C11C2×#53511yescharacteristic
600C2×C11C22×#13511yescharacteristic
601C2×C11C2×#57511yescharacteristic
602D11—42no—
603D11—82no—
604C24—21no—
605C24—21no—
606C24—111no—
607C24—221no—
608#41—444no—
609#41—444no—
610#41—448no—
611#41—444no—
612#41—444no—
613#41—448no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—22no—
617C2×Q8—22no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8—112no—
621C2×Q8—221no—
622C2×Q8—222no—
623C2×Q8—222no—
624C2×Q8C23×D1112yes—
625C2×Q8C23×D1112yes—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—22no—
629C2×D4—22no—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—112no—
633C2×D4—224no—
634C2×D4—224no—
635C2×D4—224no—
636C2×D4—224no—
637C2×D4—224no—
638C2×D4—221no—
639C2×D4—222no—
640C2×D4—222no—
641C2×D4—444no—
642C2×D4—444no—
643C2×D4—444no—
644C2×D4—444no—
645C2×D4—444no—
646C2×D4C23×D1112yes—
647C2×D4C23×D1112yes—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—111no—
651C22×C4—111no—
652C22×C4—111no—
653C22×C4—114no—
654C22×C4—112no—
655C22×C4—112no—
656C22×C4—114no—
657C22×C4—224no—
658C22×C4—224no—
659C22×C4—224no—
660C22×C4—224no—
661C22×C4—222no—
662C22×C4—222no—
663C22×C4—221no—
664C22×C4—221no—
665C22×C4—221no—
666C22×C4—442no—
667C22×C4—444no—
668C22×C4—444no—
669C22×C4—444no—
670C22×C4D4×D1111yescharacteristic
671C22×C4D4×D1111yescharacteristic
672C22×C4C23×D1111yescharacteristic
673Q16—44no—
674Q16—444no—
675SD16—44no—
676SD16—44no—
677SD16—444no—
678SD16—444no—
679D8—44no—
680D8—444no—
681C2×C8—22no—
682C2×C8—22no—
683C2×C8—112no—
684C2×C8—112no—
685C2×C8—222no—
686C2×C8—222no—
687C2×C8C23×D1112yes—
688C2×C8C23×D1112yes—
689C4⋊C4—112no—
690C4⋊C4—112no—
691C4⋊C4—224no—
692C4⋊C4—224no—
693C4⋊C4—224no—
694C4⋊C4—224no—
695C4⋊C4—221no—
696C4⋊C4—221no—
697C4⋊C4—224no—
698C4⋊C4—224no—
699C22⋊C4—24no—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—224no—
704C22⋊C4—224no—
705C22⋊C4—224no—
706C22⋊C4—224no—
707C22⋊C4—224no—
708C42—114no—
709C42—114no—
710C42—112no—
711C42—112no—
712C42—224no—
713C42D4×D1112yes—
714C42C23×D1112yes—
715C11C2×#321211yescharacteristic, complemented, Sylow
716C23—22no—
717C23—22no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—112no—
725C23—222no—
726C23—222no—
727C23—222no—
728C23—222no—
729C23—442no—
730C23—442no—
731C23—442no—
732C23C2×D4×D1111yescharacteristic
733Q8—22no—
734Q8—22no—
735Q8—22no—
736Q8—22no—
737Q8—42no—
738Q8—42no—
739Q8—222no—
740Q8—222no—
741Q8—442no—
742D4—22no—
743D4—22no—
744D4—22no—
745D4—22no—
746D4—42no—
747D4—42no—
748D4—222no—
749D4—222no—
750D4—448no—
751D4—448no—
752D4—448no—
753D4—448no—
754D4—448no—
755D4—442no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—114no—
763C2×C4—112no—
764C2×C4—112no—
765C2×C4—112no—
766C2×C4—228no—
767C2×C4—222no—
768C2×C4—222no—
769C2×C4—224no—
770C2×C4—222no—
771C2×C4—222no—
772C2×C4—222no—
773C2×C4—222no—
774C2×C4—222no—
775C2×C4—444no—
776C2×C4—448no—
777C2×C4—448no—
778C2×C4—448no—
779C2×C4—442no—
780C2×C4—442no—
781C2×C4—442no—
782C2×C4C2×D4×D1112yes—
783C2×C4C2×D4×D1112yes—
784C2×C4C2×D4×D1111yescharacteristic
785C2×C4#6703712yes—
786C2×C4#6703712yes—
787C2×C4C24×D1111yescharacteristic
788C8—22no—
789C8—22no—
790C8—222no—
791C8—222no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—84no—
799C22—84no—
800C22—222no—
801C22—222no—
802C22—222no—
803C22—444no—
804C22—442no—
805C22—442no—
806C22—442no—
807C22—884no—
808C22#1062324612yes—
809C22D11×#13512yes—
810C22#1062329912yes—
811C22C22×D4×D1111yescharacteristic
812C4—22no—
813C4—22no—
814C4—42no—
815C4—42no—
816C4—114no—
817C4—222no—
818C4—222no—
819C4—442no—
820C4—442no—
821C4—442no—
822C4#1062324612yes—
823C4C2×#6703711yescharacteristic
824C4C2×#6703711yescharacteristic
825C2—82no—
826C2—82no—
827C2—442no—
828C2—882no—
829C2#1307958714yesdirect product factor
830C2C2×#1062324611yescharacteristic
831C2C2×D11×#13511yescharacteristic
832C2C2×#1062329911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#495C2
socleC23×C11C22×D4
hypercenterC2×#495D11
hypocenterC11C2×#3212
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#495

Complements

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

NH ≅ G/Ntype
1. C2×#10623199C2semidirect
2. C2×#10623211C2semidirect
3. #13079587C2direct (N × H)
4. C2×#10622672C2semidirect
5. C2×#10622310C2semidirect
6. C2×#10622669C2semidirect
7. C2×#10622795C2semidirect
8. C2×#10622776C2semidirect
9. C2×#10622775C2semidirect
10. C2×#10622763C2semidirect
11. C2×#10622800C2semidirect
12. C2×#10622786C2semidirect
13. C2×#10622785C2semidirect
14. C2×#10622771C2semidirect
15. C2×#10622298C2semidirect
16. C2×C11×#495C2semidirect
36. #10623211C22semidirect
38. #10623199C22semidirect
50. C11×#495C22semidirect
56. #10622800C22semidirect
57. #10622795C22semidirect
58. #10622786C22semidirect
59. #10622785C22semidirect
60. #10622776C22semidirect
61. #10622775C22semidirect
62. #10622771C22semidirect
63. #10622763C22semidirect
72. #10622672C22semidirect
73. #10622669C22semidirect
75. #10622310C22semidirect
76. #10622298C22semidirect
304. C2×#495D11semidirect
426. #495C2×D11semidirect
598. C2×C11#3212semidirect
715. C11C2×#3212semidirect
829. C2#13079587direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231992
C2×#106232112
#130795872
C2×#106226722
C2×#106223102
C2×#106226692
C2×#106227952
C2×#106227762
C2×#106227752
C2×#106227632
C2×#106228002
C2×#106227862
C2×#106227852
C2×#106227712
C2×#106222982
C2×C11×#4952
C2×#321211