Finite Group Databasebeta

← C2×#13080034 #15626690

Subgroups — C2×#13080034 #15626690

Order 2816.

1946 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623264C211yesmaximal, characteristic, complemented
2C2×#10623093C211yesmaximal, characteristic, complemented
3#13080034C2116yesmaximal, direct product factor
4C2×#10622490C211yesmaximal, characteristic, complemented
5C2×#10622504C211yesmaximal, characteristic, complemented
6C2×#10622697C211yesmaximal, characteristic, complemented
7C2×#10622395C211yesmaximal, characteristic, complemented
8C2×#10622499C211yesmaximal, characteristic, complemented
9C2×#10622496C211yesmaximal, characteristic, complemented
10C2×#10622391C211yesmaximal, characteristic, complemented
11C2×#10622375C211yesmaximal, characteristic, complemented
12C2×#10622457C211yesmaximal, characteristic, complemented
13C2×#10622629C211yesmaximal, characteristic, complemented
14C2×#10622399C211yesmaximal, characteristic, complemented
15C2×#10622452C211yesmaximal, characteristic, complemented
16C2×C11×#474C211yesmaximal, characteristic, complemented
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×#67000—21no—
20C2×#66999—21no—
21C2×#66993C2211yescharacteristic
22C2×#66991C2211yescharacteristic
23C22×#4324C2211yescharacteristic
24C22×#4323C2211yescharacteristic
25C2×#66983—21no—
26C2×#66982—21no—
27C22×D88C2211yescharacteristic
28C22×#4314C2211yescharacteristic
29C22×#4313C2211yescharacteristic
30C22×C8×D11C2211yescharacteristic
31#10623264—24no—
32#10623264C2218yescomplemented
33#10623093—24no—
34#10623093C2218yescomplemented
35C2×#66951—21no—
36C2×#66950C2211yescharacteristic
37C2×#66948C2211yescharacteristic
38C2×#66948C2211yescharacteristic
39C2×#66947—21no—
40C2×#66946C2211yescharacteristic
41C2×#66943C2211yescharacteristic
42C2×#66940C2211yescharacteristic
43C2×#66937—21no—
44C2×#66936—21no—
45C2×#66928C2211yescharacteristic
46C2×C4×D44C2211yescharacteristic
47C2×#66925C2211yescharacteristic
48C11×#474C2218yescomplemented
49C2×C11×#107C2211yescharacteristic
50C2×C11×#107C2211yescharacteristic
51C2×C11×C4⋊C8C2211yescharacteristic
52C2×C11×#102C2211yescharacteristic
53C2×C11×#102C2211yescharacteristic
54C2×#66885C2211yescharacteristic
55C2×#66880C2211yescharacteristic
56C2×Dic11⋊C8C2211yescharacteristic
57C2×Dic11⋊C8C2211yescharacteristic
58#10622697C2218yescomplemented
59#10622629C2218yescomplemented
60C2×#66874C2211yescharacteristic
61C2×#66873C2211yescharacteristic
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66872C2211yescharacteristic
65C2×#66872C2211yescharacteristic
66C2×C4⋊(C11⋊C8)C2211yescharacteristic
67#10622504C2218yescomplemented
68#10622499C2218yescomplemented
69#10622496C2218yescomplemented
70#10622490C2218yescomplemented
71#10622457C2218yescomplemented
72#10622452C2218yescomplemented
73#10622399C2218yescomplemented
74#10622395C2218yescomplemented
75#10622391C2218yescomplemented
76#10622375C2218yescomplemented
77C22×Q8×C11—21no—
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C22×D44—21no—
84C22×D44—21no—
85C22×D44C2311yescharacteristic
86C22×D44C2311yescharacteristic
87C22×C4×D11—21no—
88C22×C4×D11—21no—
89C22×C4×D11C2311yescharacteristic
90C22×Dic22C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C22×C8×C11C2311yescharacteristic
93C11×C4⋊Q8—22no—
94C11×C4⋊Q8C2314yes—
95C4×D4×C11—22no—
96C4×D4×C11C2314yes—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C22⋊C4—21no—
102C2×C42×C11C2311yescharacteristic
103C2×C22⋊Dic11—21no—
104#67000—28no—
105#66999—28no—
106#66993—22no—
107#66993C2314yes—
108#66991—22no—
109#66991C2314yes—
110C2×#4324—42no—
111C2×#4324C2314yes—
112C2×#4323—42no—
113C2×#4323C2314yes—
114#66983—28no—
115#66982—28no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
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)⋊C4D411yescharacteristic
124C2×(C2×D11)⋊C4D411yescharacteristic
125C2×C4⋊Dic11—21no—
126C2×C4⋊Dic11—21no—
127C2×C4⋊Dic11C2311yescharacteristic
128C2×Dic11⋊C4—21no—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4D411yescharacteristic
131C2×Dic11⋊C4D411yescharacteristic
132C2×C4×Dic11—21no—
133C2×C4×Dic11C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135C22×C11⋊C8C2311yescharacteristic
136C2×D88—42no—
137C2×D88C2314yes—
138C2×#4314—42no—
139C2×#4314C2314yes—
140C2×#4313—42no—
141C2×#4313C2314yes—
142C2×C8×D11—42no—
143C2×C8×D11C2314yes—
144#66951—28no—
145#66950—22no—
146#66950C2314yes—
147#66948—22no—
148#66948—22no—
149#66948C2314yes—
150#66948C2314yes—
151#66947—28no—
152#66946—22no—
153#66946C2314yes—
154#66943—22no—
155#66943C2314yes—
156#66940—22no—
157#66940C2314yes—
158#66937—28no—
159#66936—28no—
160#66928—22no—
161#66928C2314yes—
162C4×D44—22no—
163C4×D44C2314yes—
164#66925D414yes—
165#66925C2314yes—
166C11×#107C2314yes—
167C11×#107C2314yes—
168C11×C4⋊C8C2314yes—
169C11×#102C2314yes—
170C11×#102C2314yes—
171#66885C2314yes—
172#66880C2314yes—
173Dic11⋊C8C2314yes—
174Dic11⋊C8C2314yes—
175#66874C2314yes—
176#66873C2314yes—
177#66873C2314yes—
178#66873C2314yes—
179#66872C2314yes—
180#66872C2314yes—
181C4⋊(C11⋊C8)C2314yes—
182C2×#3257—111nomaximal, Sylow
183C24×C11—21no—
184C23×D11—21no—
185C23×D11—21no—
186C23×D11C2×D411yescharacteristic
187C2×Q8×C11—24no—
188C2×Q8×C11—82no—
189C2×D4×C11—21no—
190C2×D4×C11—22no—
191C2×D4×C11—22no—
192C2×D4×C11C2412yes—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—24no—
197C22×C4×C11—82no—
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2411yescharacteristic
201C2×C22⋊D11—24no—
202C2×C22⋊D11—24no—
203C2×C22⋊D11—24no—
204C2×C22⋊D11—82no—
205C2×C22⋊D11—82no—
206C2×C22⋊D11—82no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11C2×D411yescharacteristic
210C22×Dic11C2×D411yescharacteristic
211C22×Dic11C2×D411yescharacteristic
212C2×D44—24no—
213C2×D44—24no—
214C2×D44—21no—
215C2×D44—21no—
216C2×D44—22no—
217C2×D44—22no—
218C2×D44—22no—
219C2×D44—22no—
220C2×D44—82no—
221C2×D44—82no—
222C2×D44C2412yes—
223C2×D44C2412yes—
224C2×C4×D11—24no—
225C2×C4×D11—24no—
226C2×C4×D11—22no—
227C2×C4×D11—22no—
228C2×C4×D11—82no—
229C2×C4×D11—82no—
230C2×C4×D11C2×D412yes—
231C2×C4×D11C2412yes—
232C2×Dic22—21no—
233C2×Dic22—22no—
234C2×Dic22—22no—
235C2×Dic22C2412yes—
236C2×C8×C11—22no—
237C2×C8×C11—22no—
238C2×C8×C11C2412yes—
239C2×C8×C11C2412yes—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—24no—
244C11×C4⋊C4C2412yes—
245C11×C4⋊C4C2412yes—
246C11×C4⋊C4C2412yes—
247C11×C22⋊C4—24no—
248C42×C11C2×D412yes—
249C42×C11C2412yes—
250C22⋊Dic11—24no—
251#4324—44no—
252#4323—44no—
253(C2×D11)⋊C4—24no—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—24no—
258(C2×D11)⋊C4—24no—
259(C2×D11)⋊C4—24no—
260(C2×D11)⋊C4C2×D414yes—
261(C2×D11)⋊C4C2×D414yes—
262C4⋊Dic11—24no—
263C4⋊Dic11—24no—
264C4⋊Dic11—21no—
265C4⋊Dic11C2412yes—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268Dic11⋊C4C2×D414yes—
269Dic11⋊C4C2×D414yes—
270C4×Dic11—24no—
271C4×Dic11C2×D412yes—
272C4×Dic11C2412yes—
273C2×C11⋊C8—22no—
274C2×C11⋊C8—22no—
275C2×C11⋊C8C2412yes—
276C2×C11⋊C8C2412yes—
277D88—44no—
278#4314—44no—
279#4313—44no—
280C8×D11—44no—
281C2×#542—111no—
282C2×#540—111no—
283#3257—1116no—
284C2×#479—111no—
285C2×#478—111no—
286C2×#476—111no—
287C2×#474D1111yescharacteristic, complemented
288C2×#469—111no—
289C2×#468—111no—
290C2×#466—111no—
291C2×#465—111no—
292C2×#460—111no—
293C2×#463—111no—
294C2×#463—111no—
295C2×#459—111no—
296C2×#424—111no—
297C23×C11—22no—
298C23×C11—42no—
299C23×C11—42no—
300C23×C11—42no—
301C23×C11C22×D411yescharacteristic
302C22×D11—22no—
303C22×D11—22no—
304C22×D11—22no—
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—42no—
308C22×D11—42no—
309C22×D11—42no—
310C22×D11—42no—
311C22×D11—42no—
312C22×D11—42no—
313C22×D11C22×D412yes—
314Q8×C11—84no—
315D4×C11—22no—
316D4×C11—22no—
317D4×C11—42no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—42no—
324C2×C4×C11—42no—
325C2×C4×C11—42no—
326C2×C4×C11—84no—
327C2×C4×C11C22×D412yes—
328C2×C4×C11C22×D412yes—
329C2×C4×C11C22×D411yescharacteristic
330C2×C4×C11H(5,𝔽2)12yes—
331C2×C4×C112−1+412yes—
332C2×C4×C11C2511yescharacteristic
333C22⋊D11—84no—
334C22⋊D11—84no—
335C22⋊D11—84no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11C22×D412yes—
344C2×Dic11C22×D412yes—
345C2×Dic11C22×D412yes—
346D44—22no—
347D44—22no—
348D44—22no—
349D44—22no—
350D44—42no—
351D44—42no—
352D44—84no—
353D44—84no—
354C4×D11—24no—
355C4×D11—22no—
356C4×D11—22no—
357C4×D11—84no—
358C4×D11—84no—
359Dic22—22no—
360Dic22—22no—
361Dic22—42no—
362C8×C11—22no—
363C8×C11—22no—
364C11⋊C8—22no—
365C11⋊C8—22no—
366C22×SD16—111no—
367C22×SD16—111no—
368C22×D8—111no—
369C22×D8—111no—
370C22×M16—111no—
371C23×C8—111no—
372#542—118no—
373#542—224no—
374#540—118no—
375#540—224no—
376C2×C4⋊Q8C2×D1111yescharacteristic
377C2×#127—111no—
378C2×#126—221no—
379C2×#125—111no—
380C2×#124—111no—
381C2×#124—221no—
382C2×#123—221no—
383C2×#123—221no—
384C2×#123—221no—
385C2×C22⋊Q8—111no—
386C2×C22⋊Q8—221no—
387C2×#121—111no—
388C2×#121—111no—
389C2×#121—111no—
390C2×#121—221no—
391C2×#121—221no—
392C2×C4×Q8—111no—
393C2×C4×D4—111no—
394C2×C4×D4—111no—
395C2×C4×D4C2×D1111yescharacteristic
396C2×#117—111no—
397#479—118no—
398#478—118no—
399#476—118no—
400#474C2×D1118yescomplemented
401#469—118no—
402#468—118no—
403#466—118no—
404#465—118no—
405#463—118no—
406#463—118no—
407#460—118no—
408#459—118no—
409C2×#107C2×D1111yescharacteristic
410C2×#107C2×D1111yescharacteristic
411C2×#106—111no—
412C2×#106—111no—
413#424—118no—
414C2×C4⋊C8—111no—
415C2×C4⋊C8—111no—
416C2×C4⋊C8—111no—
417C2×C4⋊C8C2×D1111yescharacteristic
418C2×#103—111no—
419C2×#103—111no—
420C2×#102—111no—
421C2×#102—111no—
422C2×#102—111no—
423C2×#102—111no—
424C2×#102C2×D1111yescharacteristic
425C2×#102C2×D1111yescharacteristic
426C22×C11—42no—
427C22×C11—42no—
428C22×C11—42no—
429C22×C11—84no—
430C22×C11#53712yes—
431C22×C11#57612yes—
432C22×C11#57712yes—
433C22×C11C23×D411yescharacteristic
434C2×D11—22no—
435C2×D11—22no—
436C2×D11—22no—
437C2×D11—44no—
438C2×D11—42no—
439C2×D11—42no—
440C2×D11—42no—
441C2×D11—42no—
442C2×D11—42no—
443C2×D11—42no—
444C2×D11—84no—
445C2×D11—84no—
446C4×C11—22no—
447C4×C11—22no—
448C4×C11—42no—
449C4×C11—42no—
450C4×C11—42no—
451C4×C11#53712yes—
452C4×C11C2×H(5,𝔽2)11yescharacteristic
453C4×C11C2×2−1+411yescharacteristic
454Dic11—22no—
455Dic11—22no—
456Dic11—22no—
457Dic11—42no—
458Dic11—42no—
459C22×Q8—21no—
460C22×Q8—111no—
461C22×D4—111no—
462C22×D4—111no—
463C22×D4—221no—
464C22×D4—221no—
465C22×D4—221no—
466C22×D4—221no—
467C22×D4—221no—
468C22×D4C22×D1111yescharacteristic
469C23×C4—21no—
470C23×C4—111no—
471C23×C4—221no—
472C23×C4—221no—
473C2×SD16—114no—
474C2×SD16—114no—
475C2×SD16—442no—
476C2×SD16—442no—
477C2×D8—114no—
478C2×D8—114no—
479C2×D8—442no—
480C2×D8—442no—
481C2×M16—114no—
482C2×M16—442no—
483C22×C8—111no—
484C22×C8—111no—
485C22×C8—114no—
486C22×C8—442no—
487C22×C8C22×D1111yescharacteristic
488C22×C8C22×D1111yescharacteristic
489C4⋊Q8—22no—
490C4⋊Q8C22×D1114yes—
491#127—114no—
492#127—222no—
493#126—228no—
494#125—114no—
495#125—222no—
496#124—114no—
497#124—228no—
498#124—222no—
499#123—228no—
500#123—228no—
501#123—228no—
502C22⋊Q8—114no—
503C22⋊Q8—222no—
504C22⋊Q8—228no—
505#121—114no—
506#121—114no—
507#121—114no—
508#121—228no—
509#121—228no—
510#121—222no—
511#121—222no—
512#121—222no—
513C4×Q8—114no—
514C4×Q8—222no—
515C4×D4—22no—
516C4×D4—114no—
517C4×D4—114no—
518C4×D4—222no—
519C4×D4—222no—
520C4×D4C22×D1114yes—
521#117—114no—
522#117—114no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—111no—
525C2×C4⋊C4—111no—
526C2×C4⋊C4—111no—
527C2×C4⋊C4—221no—
528C2×C4⋊C4—221no—
529C2×C4⋊C4—221no—
530C2×C4⋊C4—221no—
531C2×C4⋊C4C22×D1111yescharacteristic
532C2×C4⋊C4C22×D1111yescharacteristic
533C2×C4⋊C4C22×D1111yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—111no—
536C2×C22⋊C4—111no—
537C2×C22⋊C4—221no—
538C2×C22⋊C4—221no—
539C2×C22⋊C4—221no—
540C2×C22⋊C4—221no—
541C2×C22⋊C4—221no—
542C2×C22⋊C4—221no—
543C2×C22⋊C4—221no—
544C2×C22⋊C4—221no—
545C2×C42—111no—
546C2×C42—221no—
547C2×C42C22×D1111yescharacteristic
548#107C22×D1114yes—
549#107C22×D1114yes—
550#106—114no—
551#106—114no—
552C4⋊C8—114no—
553C4⋊C8—114no—
554C4⋊C8—114no—
555C4⋊C8C22×D1114yes—
556#103—114no—
557#103—114no—
558#102—114no—
559#102—114no—
560#102—114no—
561#102—114no—
562#102C22×D1114yes—
563#102C22×D1114yes—
564C2×C11—82no—
565C2×C11#325714yescomplemented
566C2×C11C2×#53711yescharacteristic
567C2×C11C2×#57611yescharacteristic
568C2×C11C2×#57711yescharacteristic
569D11—42no—
570D11—82no—
571D11—82no—
572C24—21no—
573C24—111no—
574C24—221no—
575C24—221no—
576C2×Q8—24no—
577C2×Q8—82no—
578C2×Q8—112no—
579C2×Q8—221no—
580C2×Q8—222no—
581C2×Q8—222no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—112no—
586C2×D4—112no—
587C2×D4—224no—
588C2×D4—224no—
589C2×D4—224no—
590C2×D4—224no—
591C2×D4—224no—
592C2×D4—221no—
593C2×D4—221no—
594C2×D4—222no—
595C2×D4—222no—
596C2×D4—222no—
597C2×D4—222no—
598C2×D4—882no—
599C2×D4—882no—
600C2×D4—882no—
601C2×D4—882no—
602C2×D4—882no—
603C2×D4C23×D1112yes—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—24no—
608C22×C4—82no—
609C22×C4—111no—
610C22×C4—111no—
611C22×C4—111no—
612C22×C4—112no—
613C22×C4—112no—
614C22×C4—224no—
615C22×C4—222no—
616C22×C4—222no—
617C22×C4—221no—
618C22×C4—221no—
619C22×C4—224no—
620C22×C4—882no—
621C22×C4—882no—
622C22×C4D4×D1111yescharacteristic
623C22×C4D4×D1111yescharacteristic
624C22×C4C23×D1111yescharacteristic
625SD16—444no—
626SD16—444no—
627D8—444no—
628D8—444no—
629M16—444no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—112no—
633C2×C8—112no—
634C2×C8—222no—
635C2×C8—222no—
636C2×C8—444no—
637C2×C8C23×D1112yes—
638C2×C8C23×D1112yes—
639C4⋊C4—24no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—114no—
644C4⋊C4—114no—
645C4⋊C4—112no—
646C4⋊C4—224no—
647C4⋊C4—224no—
648C4⋊C4—224no—
649C4⋊C4—224no—
650C4⋊C4—221no—
651C4⋊C4C23×D1112yes—
652C4⋊C4C23×D1112yes—
653C4⋊C4C23×D1112yes—
654C22⋊C4—24no—
655C22⋊C4—114no—
656C22⋊C4—114no—
657C22⋊C4—224no—
658C22⋊C4—224no—
659C22⋊C4—224no—
660C22⋊C4—224no—
661C22⋊C4—224no—
662C22⋊C4—224no—
663C22⋊C4—224no—
664C22⋊C4—224no—
665C42—112no—
666C42—112no—
667C42—224no—
668C42D4×D1112yes—
669C42C23×D1112yes—
670C11C2×#325711yescharacteristic, complemented, Sylow
671C23—22no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—112no—
676C23—222no—
677C23—222no—
678C23—222no—
679C23—222no—
680C23—222no—
681C23—442no—
682C23—442no—
683C23—442no—
684C23—442no—
685C23—442no—
686C23—442no—
687C23C2×D4×D1111yescharacteristic
688Q8—84no—
689Q8—222no—
690Q8—222no—
691Q8—442no—
692D4—22no—
693D4—22no—
694D4—42no—
695D4—222no—
696D4—222no—
697D4—222no—
698D4—222no—
699D4—442no—
700D4—442no—
701D4—884no—
702D4—884no—
703D4—884no—
704D4—884no—
705D4—884no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—84no—
715C2×C4—112no—
716C2×C4—112no—
717C2×C4—112no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—222no—
721C2×C4—224no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—222no—
725C2×C4—222no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—884no—
729C2×C4—884no—
730C2×C4C2×D4×D1112yes—
731C2×C4C2×D4×D1112yes—
732C2×C4C2×D4×D1111yescharacteristic
733C2×C4#6704012yes—
734C2×C4#6704212yes—
735C2×C4C24×D1111yescharacteristic
736C8—22no—
737C8—22no—
738C8—222no—
739C8—222no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—84no—
744C22—222no—
745C22—222no—
746C22—222no—
747C22—444no—
748C22—442no—
749C22—442no—
750C22—442no—
751C22—442no—
752C22—442no—
753C22—442no—
754C22—884no—
755C22—884no—
756C22#1062316012yes—
757C22#1062328812yes—
758C22#1062330912yes—
759C22C22×D4×D1111yescharacteristic
760C4—22no—
761C4—22no—
762C4—42no—
763C4—42no—
764C4—42no—
765C4—222no—
766C4—222no—
767C4—222no—
768C4—442no—
769C4—442no—
770C4#1062316012yes—
771C4C2×#6704011yescharacteristic
772C4C2×#6704211yescharacteristic
773C2—82no—
774C2—442no—
775C2—882no—
776C2—882no—
777C2#1308003414yesdirect product factor
778C2C2×#1062316011yescharacteristic
779C2C2×#1062328811yescharacteristic
780C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#474C2
socleC23×C11C22×D4
hypercenterC2×#474D11
hypocenterC11C2×#3257
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×#10623264C2semidirect
2. C2×#10623093C2semidirect
3. #13080034C2direct (N × H)
4. C2×#10622490C2semidirect
5. C2×#10622504C2semidirect
6. C2×#10622697C2semidirect
7. C2×#10622395C2semidirect
8. C2×#10622499C2semidirect
9. C2×#10622496C2semidirect
10. C2×#10622391C2semidirect
11. C2×#10622375C2semidirect
12. C2×#10622457C2semidirect
13. C2×#10622629C2semidirect
14. C2×#10622399C2semidirect
15. C2×#10622452C2semidirect
16. C2×C11×#474C2semidirect
32. #10623264C22semidirect
34. #10623093C22semidirect
48. C11×#474C22semidirect
58. #10622697C22semidirect
59. #10622629C22semidirect
67. #10622504C22semidirect
68. #10622499C22semidirect
69. #10622496C22semidirect
70. #10622490C22semidirect
71. #10622457C22semidirect
72. #10622452C22semidirect
73. #10622399C22semidirect
74. #10622395C22semidirect
75. #10622391C22semidirect
76. #10622375C22semidirect
287. C2×#474D11semidirect
400. #474C2×D11semidirect
565. C2×C11#3257semidirect
670. C11C2×#3257semidirect
777. C2#13080034direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232642
C2×#106230932
#130800342
C2×#106224902
C2×#106225042
C2×#106226972
C2×#106223952
C2×#106224992
C2×#106224962
C2×#106223912
C2×#106223752
C2×#106224572
C2×#106226292
C2×#106223992
C2×#106224522
C2×C11×#4742
C2×#325711