Finite Group Databasebeta

← C2×#13079303 #15623661

Subgroups — C2×#13079303 #15623661

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×#10623092C211yesmaximal, characteristic, complemented
2C2×#10623093C211yesmaximal, characteristic, complemented
3#13079303C2116yesmaximal, direct product factor
4C2×#10622489C211yesmaximal, characteristic, complemented
5C2×#10622767C211yesmaximal, characteristic, complemented
6C2×#10622381C211yesmaximal, characteristic, complemented
7C2×#10622373C211yesmaximal, characteristic, complemented
8C2×#10622772C211yesmaximal, characteristic, complemented
9C2×#10622499C211yesmaximal, characteristic, complemented
10C2×#10622388C211yesmaximal, characteristic, complemented
11C2×#10622391C211yesmaximal, characteristic, complemented
12C2×#10622627C211yesmaximal, characteristic, complemented
13C2×#10622631C211yesmaximal, characteristic, complemented
14C2×C4×#4314C211yesmaximal, characteristic, complemented
15C2×#10622302C211yesmaximal, characteristic, complemented
16C2×C4×C11×D8C211yesmaximal, characteristic, complemented
17C22×C11×D8C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×#66993C2211yescharacteristic
21C2×#66991C2211yescharacteristic
22C2×#66991C2211yescharacteristic
23C2×#66989C2211yescharacteristic
24C22×#4324C2211yescharacteristic
25C22×#4323C2211yescharacteristic
26C2×#66983—21no—
27C2×#66982—21no—
28C2×#66982—21no—
29C2×#66977—21no—
30C22×#4314C2211yescharacteristic
31C22×#4313C2211yescharacteristic
32C22×C8×D11C2211yescharacteristic
33#10623093—24no—
34#10623093C2218yescomplemented
35#10623092—24no—
36#10623092C2218yescomplemented
37C2×#66950C2211yescharacteristic
38C2×#66948C2211yescharacteristic
39C2×#66943C2211yescharacteristic
40C2×#66941C2211yescharacteristic
41C2×#66938—21no—
42C2×#66937—21no—
43C2×#66936—21no—
44C2×#66932—21no—
45C2×C4×D44C2211yescharacteristic
46C2×#66925C2211yescharacteristic
47C2×C4×Dic22C2211yescharacteristic
48C4×C11×D8C2218yescomplemented
49C2×C11×#107C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×C4×C8×C11C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55#10622772C2218yescomplemented
56#10622767C2218yescomplemented
57C2×#66885C2211yescharacteristic
58C2×#66881C2211yescharacteristic
59C2×#66880C2211yescharacteristic
60C2×#66879C2211yescharacteristic
61C2×C8×Dic11C2211yescharacteristic
62#10622631C2218yescomplemented
63#10622627C2218yescomplemented
64C2×#66874C2211yescharacteristic
65C2×#66873C2211yescharacteristic
66C2×#66872C2211yescharacteristic
67C2×#66871C2211yescharacteristic
68C2×#66867C2211yescharacteristic
69#10622499C2218yescomplemented
70#10622489C2218yescomplemented
71#10622391C2218yescomplemented
72#10622388C2218yescomplemented
73#10622381C2218yescomplemented
74#10622373C2218yescomplemented
75C4×#4314C2218yescomplemented
76#10622302C2218yescomplemented
77C22×D4×C11C2311yescharacteristic
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C23×C4×C11—21no—
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×D44—21no—
86C22×D44C2311yescharacteristic
87C22×C4×D11—21no—
88C22×C4×D11C2311yescharacteristic
89C22×Dic22—21no—
90C22×Dic22C2311yescharacteristic
91C2×C11×D8—24no—
92C2×C11×D8C2314yes—
93C22×C8×C11C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C4×D4×C11—22no—
96C4×D4×C11—22no—
97C4×D4×C11C2314yes—
98C4×D4×C11C2314yes—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C42×C11C2311yescharacteristic
104C2×C22⋊Dic11—21no—
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11—21no—
108#66993—22no—
109#66993C2314yes—
110#66991—22no—
111#66991—22no—
112#66991C2314yes—
113#66991C2314yes—
114#66989—22no—
115#66989C2314yes—
116C2×#4324—24no—
117C2×#4324C2314yes—
118C2×#4323—24no—
119C2×#4323C2314yes—
120#66983—28no—
121#66982—28no—
122#66982—28no—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4—21no—
125C2×(C2×D11)⋊C4—21no—
126C2×(C2×D11)⋊C4D411yescharacteristic
127C2×(C2×D11)⋊C4D411yescharacteristic
128C2×C4⋊Dic11—21no—
129C2×C4⋊Dic11—21no—
130C2×C4⋊Dic11C2311yescharacteristic
131C2×C4⋊Dic11C2311yescharacteristic
132#66977—28no—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4—21no—
136C2×Dic11⋊C4D411yescharacteristic
137C2×Dic11⋊C4D411yescharacteristic
138C2×C4×Dic11—21no—
139C2×C4×Dic11C2311yescharacteristic
140C22×C11⋊C8C2311yescharacteristic
141C22×C11⋊C8C2311yescharacteristic
142C2×#4314—24no—
143C2×#4314C2314yes—
144C2×#4313—24no—
145C2×#4313C2314yes—
146C2×C8×D11—24no—
147C2×C8×D11C2314yes—
148#66950—22no—
149#66950C2314yes—
150#66948—22no—
151#66948C2314yes—
152#66943—22no—
153#66943C2314yes—
154#66941—22no—
155#66941C2314yes—
156#66938—28no—
157#66937—28no—
158#66936—28no—
159#66932—28no—
160C4×D44—22no—
161C4×D44C2314yes—
162#66925D414yes—
163#66925C2314yes—
164C4×Dic22—22no—
165C4×Dic22C2314yes—
166C11×#107C2314yes—
167C11×#102C2314yes—
168C11×#102C2314yes—
169C4×C8×C11C2314yes—
170#66896C2314yes—
171#66896C2314yes—
172#66885C2314yes—
173#66881C2314yes—
174#66880C2314yes—
175#66879C2314yes—
176C8×Dic11C2314yes—
177#66874C2314yes—
178#66873C2314yes—
179#66872C2314yes—
180#66871C2314yes—
181#66867C2314yes—
182C2×#3179—111nomaximal, Sylow
183C24×C11—21no—
184C24×C11—21no—
185C23×D11—21no—
186C23×D11C2×D411yescharacteristic
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11—22no—
190C2×D4×C11—22no—
191C2×D4×C11—22no—
192C2×D4×C11—22no—
193C2×D4×C11C2412yes—
194C2×D4×C11C2412yes—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—24no—
198C22×C4×C11—24no—
199C22×C4×C11—82no—
200C22×C4×C11—82no—
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2411yescharacteristic
204C2×C22⋊D11—24no—
205C2×C22⋊D11—24no—
206C2×C22⋊D11—24no—
207C2×C22⋊D11—24no—
208C2×C22⋊D11—82no—
209C2×C22⋊D11—82no—
210C2×C22⋊D11—82no—
211C2×C22⋊D11—82no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11C2×D411yescharacteristic
216C22×Dic11C2×D411yescharacteristic
217C22×Dic11C2×D411yescharacteristic
218C2×D44—24no—
219C2×D44—21no—
220C2×D44—22no—
221C2×D44—22no—
222C2×D44—82no—
223C2×D44C2412yes—
224C2×C4×D11—24no—
225C2×C4×D11—22no—
226C2×C4×D11—22no—
227C2×C4×D11—82no—
228C2×C4×D11C2×D412yes—
229C2×C4×D11C2412yes—
230C2×Dic22—24no—
231C2×Dic22—21no—
232C2×Dic22—22no—
233C2×Dic22—22no—
234C2×Dic22—82no—
235C2×Dic22C2412yes—
236C11×D8—28no—
237C2×C8×C11—22no—
238C2×C8×C11#4114yes—
239C2×C8×C11C2412yes—
240C2×C8×C11C2412yes—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4C2412yes—
244C11×C4⋊C4C2412yes—
245C11×C22⋊C4—24no—
246C11×C22⋊C4—24no—
247C42×C11C2×D412yes—
248C42×C11C2412yes—
249C22⋊Dic11—24no—
250C22⋊Dic11—24no—
251C22⋊Dic11—24no—
252C22⋊Dic11—24no—
253#4324—28no—
254#4323—28no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—24no—
258(C2×D11)⋊C4C2×D414yes—
259(C2×D11)⋊C4C2×D414yes—
260C4⋊Dic11—24no—
261C4⋊Dic11—24no—
262C4⋊Dic11—21no—
263C4⋊Dic11—21no—
264C4⋊Dic11C2412yes—
265C4⋊Dic11C2412yes—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268Dic11⋊C4—24no—
269Dic11⋊C4C2×D414yes—
270Dic11⋊C4C2×D414yes—
271C4×Dic11—24no—
272C4×Dic11C2×D412yes—
273C4×Dic11C2412yes—
274C2×C11⋊C8—22no—
275C2×C11⋊C8#4114yes—
276C2×C11⋊C8C2412yes—
277C2×C11⋊C8C2412yes—
278#4314—28no—
279#4313—28no—
280C8×D11—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×#465—111no—
292C2×#442—111no—
293C2×#440—111no—
294C2×C4×SD16—111no—
295C2×C4×D8D1111yescharacteristic, complemented
296C2×#405—111no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—42no—
300C23×C11—42no—
301C23×C11—42no—
302C23×C11—42no—
303C23×C11—42no—
304C23×C11—42no—
305C23×C11C22×D411yescharacteristic
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—42no—
311C22×D11—42no—
312C22×D11—42no—
313C22×D11C22×D412yes—
314D4×C11—22no—
315D4×C11—22no—
316D4×C11—22no—
317D4×C11—22no—
318D4×C11—42no—
319D4×C11—42no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—42no—
325C2×C4×C11—42no—
326C2×C4×C11—84no—
327C2×C4×C11—84no—
328C2×C4×C11C22×D412yes—
329C2×C4×C11C22×D412yes—
330C2×C4×C11C22×D411yescharacteristic
331C2×C4×C11C2×#4112yes—
332C2×C4×C11C2×#4112yes—
333C2×C4×C11C2511yescharacteristic
334C22⋊D11—84no—
335C22⋊D11—84no—
336C22⋊D11—84no—
337C22⋊D11—84no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11C22×D412yes—
348C2×Dic11C22×D412yes—
349C2×Dic11C22×D412yes—
350D44—22no—
351D44—22no—
352D44—42no—
353D44—84no—
354C4×D11—24no—
355C4×D11—22no—
356C4×D11—22no—
357C4×D11—84no—
358Dic22—22no—
359Dic22—22no—
360Dic22—42no—
361Dic22—84no—
362C8×C11—22no—
363C8×C11C2×#4114yes—
364C11⋊C8—22no—
365C11⋊C8C2×#4114yes—
366C22×SD16—111no—
367C22×SD16—111no—
368C22×D8—111no—
369C22×D8C2×D1111yescharacteristic
370C22×M16—111no—
371C23×C8—111no—
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—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×D4C2×D1111yescharacteristic
395C2×C4×D4C2×D1111yescharacteristic
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#465—118no—
405#442—118no—
406#440—118no—
407C4×SD16—118no—
408C4×D8C2×D1118yescomplemented
409C2×#107—111no—
410C2×#107C2×D1111yescharacteristic
411C2×#106—111no—
412C2×#106—111no—
413C2×#103—111no—
414C2×#103—111no—
415C2×#102—111no—
416C2×#102—111no—
417C2×#102—111no—
418C2×#102—111no—
419C2×#102C2×D1111yescharacteristic
420C2×#102C2×D1111yescharacteristic
421#405—118no—
422C2×#97—111no—
423C2×#97—111no—
424C2×C4×C8—111no—
425C2×C4×C8C2×D1111yescharacteristic
426C22×C11—42no—
427C22×C11—42no—
428C22×C11—42no—
429C22×C11—42no—
430C22×C11—42no—
431C22×C11—42no—
432C22×C11—84no—
433C22×C11—84no—
434C22×C11#53212yes—
435C22×C11#57612yes—
436C22×C11#57712yes—
437C22×C11C23×D411yescharacteristic
438C2×D11—22no—
439C2×D11—22no—
440C2×D11—22no—
441C2×D11—44no—
442C2×D11—42no—
443C2×D11—42no—
444C2×D11—42no—
445C2×D11—84no—
446C4×C11—22no—
447C4×C11—22no—
448C4×C11—42no—
449C4×C11—42no—
450C4×C11#53212yes—
451C4×C11C22×#4111yescharacteristic
452C4×C11C22×#4111yescharacteristic
453Dic11—22no—
454Dic11—22no—
455Dic11—22no—
456Dic11—42no—
457Dic11—42no—
458Dic11—42no—
459C22×Q8—111no—
460C22×Q8—221no—
461C22×D4—111no—
462C22×D4—221no—
463C22×D4—221no—
464C22×D4—221no—
465C22×D4—221no—
466C22×D4—221no—
467C22×D4C22×D1111yescharacteristic
468C22×D4C22×D1111yescharacteristic
469C23×C4—21no—
470C23×C4—21no—
471C23×C4—111no—
472C23×C4—221no—
473C2×SD16—114no—
474C2×SD16—114no—
475C2×SD16—224no—
476C2×SD16—224no—
477C2×D8—24no—
478C2×D8—114no—
479C2×D8—224no—
480C2×D8C22×D1114yes—
481C2×M16—114no—
482C2×M16—224no—
483C22×C8—111no—
484C22×C8—111no—
485C22×C8—114no—
486C22×C8—224no—
487C22×C8C22×D1111yescharacteristic
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—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—22no—
517C4×D4—114no—
518C4×D4—222no—
519C4×D4C22×D1114yes—
520C4×D4C22×D1114yes—
521#117—114no—
522#117—114no—
523C2×C4⋊C4—111no—
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⋊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—221no—
547C2×C42C22×D1111yescharacteristic
548#107—114no—
549#107C22×D1114yes—
550#106—114no—
551#106—114no—
552#103—114no—
553#103—114no—
554#102—114no—
555#102—114no—
556#102—114no—
557#102—114no—
558#102C22×D1114yes—
559#102C22×D1114yes—
560#97—114no—
561#97—114no—
562C4×C8—114no—
563C4×C8C22×D1114yes—
564C2×C11—82no—
565C2×C11—82no—
566C2×C11#317914yescomplemented
567C2×C11C2×#53211yescharacteristic
568C2×C11C2×#57611yescharacteristic
569C2×C11C2×#57711yescharacteristic
570D11—42no—
571D11—82no—
572C24—21no—
573C24—21no—
574C24—111no—
575C24—221no—
576C2×Q8—112no—
577C2×Q8—224no—
578C2×Q8—221no—
579C2×Q8—222no—
580C2×Q8—222no—
581C2×Q8—882no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—112no—
589C2×D4—224no—
590C2×D4—224no—
591C2×D4—224no—
592C2×D4—224no—
593C2×D4—224no—
594C2×D4—222no—
595C2×D4—221no—
596C2×D4—222no—
597C2×D4—882no—
598C2×D4—882no—
599C2×D4—882no—
600C2×D4—882no—
601C2×D4—882no—
602C2×D4C23×D1112yes—
603C2×D4C23×D1112yes—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—82no—
609C22×C4—82no—
610C22×C4—111no—
611C22×C4—111no—
612C22×C4—111no—
613C22×C4—112no—
614C22×C4—112no—
615C22×C4—222no—
616C22×C4—222no—
617C22×C4—221no—
618C22×C4—221no—
619C22×C4—221no—
620C22×C4—224no—
621C22×C4—882no—
622C22×C4D4×D1111yescharacteristic
623C22×C4D4×D1111yescharacteristic
624C22×C4C23×D1111yescharacteristic
625SD16—228no—
626SD16—228no—
627D8—28no—
628D8—228no—
629M16—228no—
630C2×C8—22no—
631C2×C8—114no—
632C2×C8—112no—
633C2×C8—112no—
634C2×C8—228no—
635C2×C8—222no—
636C2×C8#433914yes—
637C2×C8C23×D1112yes—
638C2×C8C23×D1112yes—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—114no—
642C4⋊C4—114no—
643C4⋊C4—112no—
644C4⋊C4—112no—
645C4⋊C4—224no—
646C4⋊C4—224no—
647C4⋊C4—224no—
648C4⋊C4—224no—
649C4⋊C4—221no—
650C4⋊C4—221no—
651C4⋊C4—224no—
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—224no—
668C42D4×D1112yes—
669C42C23×D1112yes—
670C11C2×#317911yescharacteristic, complemented, Sylow
671C23—22no—
672C23—22no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—112no—
680C23—222no—
681C23—222no—
682C23—222no—
683C23—222no—
684C23—442no—
685C23—442no—
686C23—442no—
687C23C2×D4×D1111yescharacteristic
688Q8—222no—
689Q8—222no—
690Q8—442no—
691Q8—884no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—22no—
696D4—42no—
697D4—42no—
698D4—222no—
699D4—222no—
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—42no—
711C2×C4—42no—
712C2×C4—84no—
713C2×C4—84no—
714C2×C4—112no—
715C2×C4—112no—
716C2×C4—112no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—224no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—222no—
725C2×C4—222no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—442no—
729C2×C4—884no—
730C2×C4C2×#433912yes—
731C2×C4C2×D4×D1112yes—
732C2×C4C2×D4×D1112yes—
733C2×C4C2×D4×D1111yescharacteristic
734C2×C4#41×D1112yes—
735C2×C4C24×D1111yescharacteristic
736C8—22no—
737C8—114no—
738C8—222no—
739C8C2×#433914yes—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—84no—
747C22—84no—
748C22—222no—
749C22—222no—
750C22—222no—
751C22—444no—
752C22—442no—
753C22—442no—
754C22—442no—
755C22—884no—
756C22#1062307912yes—
757C22#1062328812yes—
758C22#1062330112yes—
759C22C22×D4×D1111yescharacteristic
760C4—22no—
761C4—22no—
762C4—42no—
763C4—42no—
764C4—222no—
765C4—222no—
766C4—222no—
767C4—442no—
768C4—442no—
769C4—442no—
770C4#1062307912yes—
771C4C22×#433911yescharacteristic
772C4C2×#41×D1111yescharacteristic
773C2—82no—
774C2—82no—
775C2—442no—
776C2—882no—
777C2#1307930314yesdirect product factor
778C2C2×#1062307911yescharacteristic
779C2C2×#1062328811yescharacteristic
780C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×D8C2
socleC23×C11C22×D4
hypercenterC2×C4×D8D11
hypocenterC11C2×#3179
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#10623092C2semidirect
2. C2×#10623093C2semidirect
3. #13079303C2direct (N × H)
4. C2×#10622489C2semidirect
5. C2×#10622767C2semidirect
6. C2×#10622381C2semidirect
7. C2×#10622373C2semidirect
8. C2×#10622772C2semidirect
9. C2×#10622499C2semidirect
10. C2×#10622388C2semidirect
11. C2×#10622391C2semidirect
12. C2×#10622627C2semidirect
13. C2×#10622631C2semidirect
14. C2×C4×#4314C2semidirect
15. C2×#10622302C2semidirect
16. C2×C4×C11×D8C2semidirect
34. #10623093C22semidirect
36. #10623092C22semidirect
48. C4×C11×D8C22semidirect
55. #10622772C22semidirect
56. #10622767C22semidirect
62. #10622631C22semidirect
63. #10622627C22semidirect
69. #10622499C22semidirect
70. #10622489C22semidirect
71. #10622391C22semidirect
72. #10622388C22semidirect
73. #10622381C22semidirect
74. #10622373C22semidirect
75. C4×#4314C22semidirect
76. #10622302C22semidirect
295. C2×C4×D8D11semidirect
408. C4×D8C2×D11semidirect
566. C2×C11#3179semidirect
670. C11C2×#3179semidirect
777. C2#13079303direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230922
C2×#106230932
#130793032
C2×#106224892
C2×#106227672
C2×#106223812
C2×#106223732
C2×#106227722
C2×#106224992
C2×#106223882
C2×#106223912
C2×#106226272
C2×#106226312
C2×C4×#43142
C2×#106223022
C2×C4×C11×D82
C2×#317911