Finite Group Databasebeta

← C2×#13079294 #15623652

Subgroups — C2×#13079294 #15623652

Order 2816.

2034 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×#10623174C211yesmaximal, characteristic, complemented
2C2×#10623150C211yesmaximal, characteristic, complemented
3#13079294C2116yesmaximal, direct product factor
4C2×#10622469C211yesmaximal, characteristic, complemented
5C2×#10622789C211yesmaximal, characteristic, complemented
6C2×#10622413C211yesmaximal, characteristic, complemented
7C2×#10622373C211yesmaximal, characteristic, complemented
8C2×#10622652C211yesmaximal, characteristic, complemented
9C2×#10622662C211yesmaximal, characteristic, complemented
10C2×#10622728C211yesmaximal, characteristic, complemented
11C2×#10622482C211yesmaximal, characteristic, complemented
12C2×#10622777C211yesmaximal, characteristic, complemented
13C2×#10622401C211yesmaximal, characteristic, complemented
14C2×#10622369C211yesmaximal, characteristic, complemented
15C2×#10622714C211yesmaximal, characteristic, complemented
16C2×C11×#465C211yesmaximal, characteristic, complemented
17C22×C11×SD16C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×#67000C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23C22×#4325C2211yescharacteristic
24C2×#66993C2211yescharacteristic
25C2×#66992—21no—
26C2×#66991—21no—
27C2×D4×Dic11C2211yescharacteristic
28C22×#4323C2211yescharacteristic
29C2×#66983C2211yescharacteristic
30C2×#66983C2211yescharacteristic
31C2×#66979C2211yescharacteristic
32C22×#4318C2211yescharacteristic
33C22×D88C2211yescharacteristic
34#10623174—24no—
35#10623174C2218yescomplemented
36#10623150—24no—
37#10623150C2218yescomplemented
38C2×#66951—21no—
39C2×#66950—21no—
40C2×#66946C2211yescharacteristic
41C2×#66946C2211yescharacteristic
42C2×#66943C2211yescharacteristic
43C2×#66941C2211yescharacteristic
44C2×#66939—21no—
45C2×#66938—21no—
46C2×#66936—21no—
47C2×#66936—21no—
48C11×#465C2218yescomplemented
49C2×C11×#106C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54#10622789C2218yescomplemented
55#10622777C2218yescomplemented
56#10622728C2218yescomplemented
57C2×#66885C2211yescharacteristic
58C2×#66885C2211yescharacteristic
59C2×#66882C2211yescharacteristic
60#10622714C2218yescomplemented
61C2×#66879C2211yescharacteristic
62C2×#66879C2211yescharacteristic
63C2×C8×Dic11C2211yescharacteristic
64C2×C8×Dic11C2211yescharacteristic
65#10622662C2218yescomplemented
66#10622652C2218yescomplemented
67C2×#66873C2211yescharacteristic
68C2×#66873C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71#10622482C2218yescomplemented
72#10622469C2218yescomplemented
73#10622413C2218yescomplemented
74#10622401C2218yescomplemented
75#10622373C2218yescomplemented
76#10622369C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C23×Dic11—21no—
86C22×D44C2311yescharacteristic
87C22×D44C2311yescharacteristic
88C22×C4×D11—21no—
89C22×C4×D11—21no—
90C22×Dic22—21no—
91C2×C11×SD16—24no—
92C2×C11×SD16C2314yes—
93C22×C8×C11—24no—
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2314yes—
96C22×C8×C11C2311yescharacteristic
97C11×C22⋊Q8—22no—
98C11×C22⋊Q8C2314yes—
99C11×#121—22no—
100C11×#121C2314yes—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11D411yescharacteristic
108C2×C22⋊Dic11D411yescharacteristic
109#67000—22no—
110#67000C2314yes—
111Q8×Dic11—22no—
112Q8×Dic11C2314yes—
113C2×#4325—24no—
114C2×#4325C2314yes—
115#66993—22no—
116#66993C2314yes—
117#66992—28no—
118#66991—28no—
119D4×Dic11—22no—
120D4×Dic11C2314yes—
121C2×#4323—24no—
122C2×#4323C2314yes—
123#66983—22no—
124#66983—22no—
125#66983C2314yes—
126#66983C2314yes—
127C2×(C2×D11)⋊C4—21no—
128C2×(C2×D11)⋊C4—21no—
129C2×(C2×D11)⋊C4—21no—
130C2×(C2×D11)⋊C4—21no—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4—21no—
133#66979D414yes—
134#66979C2314yes—
135C2×C4⋊Dic11—21no—
136C2×C4⋊Dic11—21no—
137C2×C4⋊Dic11D411yescharacteristic
138C2×C4⋊Dic11D411yescharacteristic
139C2×C4⋊Dic11C2311yescharacteristic
140C2×C4⋊Dic11C2311yescharacteristic
141C2×Dic11⋊C4—21no—
142C2×Dic11⋊C4—21no—
143C2×C4×Dic11—21no—
144C2×C4×Dic11C2311yescharacteristic
145C2×C4×Dic11C2311yescharacteristic
146C2×#4318—24no—
147C2×#4318C2314yes—
148C22×C11⋊C8C2311yescharacteristic
149C22×C11⋊C8C2311yescharacteristic
150C2×D88—24no—
151C2×D88C2314yes—
152#66951—28no—
153#66950—28no—
154#66946—22no—
155#66946—22no—
156#66946C2314yes—
157#66946C2314yes—
158#66943—22no—
159#66943C2314yes—
160#66941—22no—
161#66941C2314yes—
162#66939—28no—
163#66938—28no—
164#66936—28no—
165#66936—28no—
166C11×#106C2314yes—
167C11×#103C2314yes—
168C11×#102C2314yes—
169#66899C2314yes—
170#66896C2314yes—
171#66885C2314yes—
172#66885C2314yes—
173#66882C2314yes—
174#66879C2314yes—
175#66879C2314yes—
176C8×Dic11C2314yes—
177C8×Dic11C2314yes—
178#66873C2314yes—
179#66873C2314yes—
180#66872C2314yes—
181#66871C2314yes—
182C2×#3179—111nomaximal, Sylow
183C24×C11—21no—
184C24×C11C2×D411yescharacteristic
185C23×D11—21no—
186C23×D11—21no—
187C2×Q8×C11—21no—
188C2×Q8×C11—22no—
189C2×Q8×C11—22no—
190C2×Q8×C11C2412yes—
191C2×D4×C11—24no—
192C2×D4×C11—21no—
193C2×D4×C11—22no—
194C2×D4×C11—22no—
195C2×D4×C11—82no—
196C2×D4×C11C2412yes—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D412yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2411yescharacteristic
206C2×C22⋊D11—24no—
207C2×C22⋊D11—24no—
208C2×C22⋊D11—24no—
209C2×C22⋊D11—24no—
210C2×C22⋊D11—82no—
211C2×C22⋊D11—82no—
212C2×C22⋊D11—82no—
213C2×C22⋊D11—82no—
214C22×Dic11—24no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—82no—
218C22×Dic11C2×D411yescharacteristic
219C22×Dic11C2×D411yescharacteristic
220C22×Dic11C2×D411yescharacteristic
221C22×Dic11C2×D411yescharacteristic
222C2×D44—21no—
223C2×D44—21no—
224C2×D44—22no—
225C2×D44—22no—
226C2×D44—22no—
227C2×D44—22no—
228C2×D44C2412yes—
229C2×D44C2412yes—
230C2×C4×D11—24no—
231C2×C4×D11—24no—
232C2×C4×D11—82no—
233C2×C4×D11—82no—
234C2×Dic22—24no—
235C2×Dic22—82no—
236C11×SD16—28no—
237C2×C8×C11—28no—
238C2×C8×C11—22no—
239C2×C8×C11#4114yes—
240C2×C8×C11C2412yes—
241C2×C8×C11C2412yes—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4—24no—
245C11×C4⋊C4C2412yes—
246C11×C4⋊C4C2412yes—
247C11×C22⋊C4—24no—
248C11×C22⋊C4—24no—
249C22⋊Dic11—24no—
250C22⋊Dic11C2×D414yes—
251C22⋊Dic11C2×D414yes—
252#4325—28no—
253#4323—28no—
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—
260C4⋊Dic11—24no—
261C4⋊Dic11—24no—
262C4⋊Dic11—21no—
263C4⋊Dic11—21no—
264C4⋊Dic11C2×D414yes—
265C4⋊Dic11C2×D414yes—
266C4⋊Dic11C2412yes—
267C4⋊Dic11C2412yes—
268Dic11⋊C4—24no—
269Dic11⋊C4—24no—
270C4×Dic11—24no—
271C4×Dic11C2×D412yes—
272C4×Dic11C2×D412yes—
273C4×Dic11C2412yes—
274C4×Dic11C2412yes—
275#4318—28no—
276C2×C11⋊C8—22no—
277C2×C11⋊C8#4114yes—
278C2×C11⋊C8C2412yes—
279C2×C11⋊C8C2412yes—
280D88—28no—
281C2×#542—111no—
282C2×#540—111no—
283#3179—1116no—
284C2×#501—111no—
285C2×#496—111no—
286C2×#488—111no—
287C2×#486—111no—
288C2×#469—111no—
289C2×#468—111no—
290C2×#466—111no—
291C2×#465D1111yescharacteristic, complemented
292C2×#442—111no—
293C2×#440—111no—
294C2×C4×SD16—111no—
295C2×C4×D8—111no—
296C2×#405—111no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—42no—
302C23×C11—42no—
303C23×C11—42no—
304C23×C11C22×D412yes—
305C23×C11C22×D411yescharacteristic
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—42no—
309C22×D11—42no—
310C22×D11—42no—
311C22×D11—42no—
312C22×D11—42no—
313C22×D11—42no—
314Q8×C11—22no—
315Q8×C11—22no—
316Q8×C11—42no—
317D4×C11—22no—
318D4×C11—22no—
319D4×C11—42no—
320D4×C11—84no—
321C2×C4×C11—22no—
322C2×C4×C11—24no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—42no—
329C2×C4×C11—42no—
330C2×C4×C11—42no—
331C2×C4×C11C22×D412yes—
332C2×C4×C11C22×D411yescharacteristic
333C2×C4×C11C2×#4112yes—
334C2×C4×C11C2×#4112yes—
335C2×C4×C11C2511yescharacteristic
336C22⋊D11—84no—
337C22⋊D11—84no—
338C22⋊D11—84no—
339C22⋊D11—84no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11—84no—
349C2×Dic11C22×D412yes—
350C2×Dic11C22×D412yes—
351C2×Dic11C22×D412yes—
352C2×Dic11C22×D412yes—
353D44—22no—
354D44—22no—
355D44—22no—
356D44—22no—
357D44—42no—
358D44—42no—
359C4×D11—84no—
360C4×D11—84no—
361Dic22—84no—
362C8×C11—22no—
363C8×C11C2×#4114yes—
364C11⋊C8—22no—
365C11⋊C8C2×#4114yes—
366C22×SD16—111no—
367C22×SD16C2×D1111yescharacteristic
368C22×D8—111no—
369C22×D8—111no—
370C22×M16—111no—
371C23×C8C2×D1111yescharacteristic
372#542—118no—
373#542—224no—
374#540—118no—
375#540—224no—
376C2×C4⋊Q8—111no—
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—221no—
386C2×C22⋊Q8C2×D1111yescharacteristic
387C2×#121—111no—
388C2×#121—111no—
389C2×#121—221no—
390C2×#121—221no—
391C2×#121C2×D1111yescharacteristic
392C2×C4×Q8—111no—
393C2×C4×D4—111no—
394C2×C4×D4—111no—
395C2×C4×D4—111no—
396C2×#117—111no—
397#501—118no—
398#496—118no—
399#488—118no—
400#486—118no—
401#469—118no—
402#468—118no—
403#466—118no—
404#465C2×D1118yescomplemented
405#442—118no—
406#440—118no—
407C4×SD16—118no—
408C4×D8—118no—
409C2×#107—111no—
410C2×#107—111no—
411C2×#106—111no—
412C2×#106C2×D1111yescharacteristic
413C2×#103—111no—
414C2×#103C2×D1111yescharacteristic
415C2×#102—111no—
416C2×#102—111no—
417C2×#102—111no—
418C2×#102—111no—
419C2×#102—111no—
420C2×#102C2×D1111yescharacteristic
421#405—118no—
422C2×#97—111no—
423C2×#97—111no—
424C2×C4×C8—111no—
425C2×C4×C8—111no—
426C22×C11—22no—
427C22×C11—22no—
428C22×C11—22no—
429C22×C11—44no—
430C22×C11—42no—
431C22×C11—42no—
432C22×C11—42no—
433C22×C11—84no—
434C22×C11#53212yes—
435C22×C11#57612yes—
436C22×C11#57712yes—
437C22×C11C23×D411yescharacteristic
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—42no—
448C4×C11—42no—
449C4×C11—42no—
450C4×C11#53212yes—
451C4×C11C22×#4111yescharacteristic
452C4×C11C22×#4111yescharacteristic
453Dic11—22no—
454Dic11—22no—
455Dic11—22no—
456Dic11—22no—
457Dic11—42no—
458Dic11—42no—
459C22×Q8—221no—
460C22×Q8C22×D1111yescharacteristic
461C22×D4—21no—
462C22×D4—111no—
463C22×D4—111no—
464C22×D4—221no—
465C22×D4—221no—
466C22×D4—221no—
467C22×D4—221no—
468C22×D4C22×D1111yescharacteristic
469C23×C4—221no—
470C23×C4—221no—
471C23×C4—221no—
472C23×C4C22×D1111yescharacteristic
473C2×SD16—24no—
474C2×SD16—114no—
475C2×SD16—224no—
476C2×SD16C22×D1114yes—
477C2×D8—114no—
478C2×D8—114no—
479C2×D8—224no—
480C2×D8—224no—
481C2×M16—114no—
482C2×M16—224no—
483C22×C8—24no—
484C22×C8—111no—
485C22×C8—111no—
486C22×C8C22×D1111yescharacteristic
487C22×C8C22×D1114yes—
488C22×C8C22×D1111yescharacteristic
489C4⋊Q8—114no—
490C4⋊Q8—222no—
491#127—114no—
492#127—222no—
493#126—228no—
494#125—114no—
495#125—222no—
496#124—114no—
497#124—222no—
498#124—228no—
499#123—228no—
500#123—228no—
501#123—228no—
502C22⋊Q8—22no—
503C22⋊Q8—228no—
504C22⋊Q8C22×D1114yes—
505#121—22no—
506#121—114no—
507#121—114no—
508#121—228no—
509#121—228no—
510#121—222no—
511#121—222no—
512#121C22×D1114yes—
513C4×Q8—114no—
514C4×Q8—222no—
515C4×D4—114no—
516C4×D4—114no—
517C4×D4—114no—
518C4×D4—222no—
519C4×D4—222no—
520C4×D4—222no—
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—111no—
528C2×C4⋊C4—221no—
529C2×C4⋊C4—221no—
530C2×C4⋊C4—221no—
531C2×C4⋊C4—221no—
532C2×C4⋊C4C22×D1111yescharacteristic
533C2×C4⋊C4C22×D1111yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—111no—
537C2×C22⋊C4—111no—
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—111no—
547C2×C42—221no—
548#107—114no—
549#107—114no—
550#106—114no—
551#106C22×D1114yes—
552#103—114no—
553#103C22×D1114yes—
554#102—114no—
555#102—114no—
556#102—114no—
557#102—114no—
558#102—114no—
559#102C22×D1114yes—
560#97—114no—
561#97—114no—
562C4×C8—114no—
563C4×C8—114no—
564C2×C11—42no—
565C2×C11—82no—
566C2×C11#317914yescomplemented
567C2×C11C2×#53211yescharacteristic
568C2×C11C2×#57611yescharacteristic
569C2×C11C2×#57711yescharacteristic
570D11—82no—
571D11—82no—
572C24—21no—
573C24—221no—
574C24—221no—
575C24D4×D1111yescharacteristic
576C2×Q8—21no—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8—224no—
580C2×Q8—882no—
581C2×Q8C23×D1112yes—
582C2×D4—24no—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—82no—
587C2×D4—112no—
588C2×D4—112no—
589C2×D4—224no—
590C2×D4—224no—
591C2×D4—224no—
592C2×D4—224no—
593C2×D4—221no—
594C2×D4—221no—
595C2×D4—222no—
596C2×D4—222no—
597C2×D4—222no—
598C2×D4—222no—
599C2×D4—882no—
600C2×D4—882no—
601C2×D4—882no—
602C2×D4—882no—
603C2×D4C23×D1112yes—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—111no—
610C22×C4—111no—
611C22×C4—111no—
612C22×C4—111no—
613C22×C4—224no—
614C22×C4—224no—
615C22×C4—224no—
616C22×C4—221no—
617C22×C4—221no—
618C22×C4—882no—
619C22×C4—882no—
620C22×C4—882no—
621C22×C4D4×D1112yes—
622C22×C4D4×D1111yescharacteristic
623C22×C4C23×D1112yes—
624C22×C4C23×D1111yescharacteristic
625SD16—28no—
626SD16—228no—
627D8—228no—
628D8—228no—
629M16—228no—
630C2×C8—22no—
631C2×C8—28no—
632C2×C8—114no—
633C2×C8—112no—
634C2×C8—112no—
635C2×C8—222no—
636C2×C8#434114yes—
637C2×C8C23×D1112yes—
638C2×C8C23×D1112yes—
639C4⋊C4—24no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—114no—
643C4⋊C4—114no—
644C4⋊C4—112no—
645C4⋊C4—112no—
646C4⋊C4—224no—
647C4⋊C4—224no—
648C4⋊C4—224no—
649C4⋊C4—224no—
650C4⋊C4—221no—
651C4⋊C4—221no—
652C4⋊C4C23×D1112yes—
653C4⋊C4C23×D1112yes—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—114no—
657C22⋊C4—114no—
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—112no—
668C42—112no—
669C42—224no—
670C11C2×#317911yescharacteristic, complemented, Sylow
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—222no—
679C23—222no—
680C23—442no—
681C23—442no—
682C23—442no—
683C23—442no—
684C23—442no—
685C23—442no—
686C23C2×D4×D1112yes—
687C23C2×D4×D1111yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—42no—
691Q8—884no—
692D4—22no—
693D4—22no—
694D4—42no—
695D4—84no—
696D4—222no—
697D4—222no—
698D4—222no—
699D4—222no—
700D4—442no—
701D4—442no—
702D4—884no—
703D4—884no—
704D4—884no—
705D4—884no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—112no—
717C2×C4—112no—
718C2×C4—112no—
719C2×C4—112no—
720C2×C4—222no—
721C2×C4—222no—
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×C4—884no—
731C2×C4C2×D4×D1112yes—
732C2×C4C2×D4×D1111yescharacteristic
733C2×C4C2×#434112yes—
734C2×C4#41×D1112yes—
735C2×C4C24×D1111yescharacteristic
736C8—22no—
737C8—114no—
738C8—222no—
739C8C2×#434114yes—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—84no—
748C22—442no—
749C22—442no—
750C22—442no—
751C22—442no—
752C22—442no—
753C22—442no—
754C22—884no—
755C22—884no—
756C22#1062312712yes—
757C22#1062329312yes—
758C22#1062330012yes—
759C22C22×D4×D1111yescharacteristic
760C4—22no—
761C4—42no—
762C4—42no—
763C4—42no—
764C4—222no—
765C4—222no—
766C4—222no—
767C4—222no—
768C4—442no—
769C4—442no—
770C4#1062312712yes—
771C4C22×#434111yescharacteristic
772C4C2×#41×D1111yescharacteristic
773C2—42no—
774C2—82no—
775C2—882no—
776C2—882no—
777C2#1307929414yesdirect product factor
778C2C2×#1062312711yescharacteristic
779C2C2×#1062330011yescharacteristic
780C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#465C2
socleC23×C11C22×D4
hypercenterC2×#465D11
hypocenterC11C2×#3179
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#10623174C2semidirect
2. C2×#10623150C2semidirect
3. #13079294C2direct (N × H)
4. C2×#10622469C2semidirect
5. C2×#10622789C2semidirect
6. C2×#10622413C2semidirect
7. C2×#10622373C2semidirect
8. C2×#10622652C2semidirect
9. C2×#10622662C2semidirect
10. C2×#10622728C2semidirect
11. C2×#10622482C2semidirect
12. C2×#10622777C2semidirect
13. C2×#10622401C2semidirect
14. C2×#10622369C2semidirect
15. C2×#10622714C2semidirect
16. C2×C11×#465C2semidirect
35. #10623174C22semidirect
37. #10623150C22semidirect
48. C11×#465C22semidirect
54. #10622789C22semidirect
55. #10622777C22semidirect
56. #10622728C22semidirect
60. #10622714C22semidirect
65. #10622662C22semidirect
66. #10622652C22semidirect
71. #10622482C22semidirect
72. #10622469C22semidirect
73. #10622413C22semidirect
74. #10622401C22semidirect
75. #10622373C22semidirect
76. #10622369C22semidirect
291. C2×#465D11semidirect
404. #465C2×D11semidirect
566. C2×C11#3179semidirect
670. C11C2×#3179semidirect
777. C2#13079294direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231742
C2×#106231502
#130792942
C2×#106224692
C2×#106227892
C2×#106224132
C2×#106223732
C2×#106226522
C2×#106226622
C2×#106227282
C2×#106224822
C2×#106227772
C2×#106224012
C2×#106223692
C2×#106227142
C2×C11×#4652
C2×#317911