Finite Group Databasebeta

← C2×#13079172 #15623484

Subgroups — C2×#13079172 #15623484

Order 2816.

2286 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C211yesmaximal, characteristic, complemented
2C2×#10623079C211yesmaximal, characteristic
3#13079172C2116yesmaximal, direct product factor
4C2×#10622468C211yesmaximal, characteristic, complemented
5C2×#10622788C211yesmaximal, characteristic, complemented
6C2×#10622405C211yesmaximal, characteristic, complemented
7C2×#10622373C211yesmaximal, characteristic, complemented
8C2×#10622420C211yesmaximal, characteristic, complemented
9C2×#10622477C211yesmaximal, characteristic, complemented
10C2×#10622391C211yesmaximal, characteristic, complemented
11C2×#10622784C211yesmaximal, characteristic, complemented
12C2×C4×#4314C211yesmaximal, characteristic, complemented
13C2×C4×#4325C211yesmaximal, characteristic, complemented
14C2×C4×#4324C211yesmaximal, characteristic, complemented
15C2×C4×C8×D11C211yesmaximal, characteristic, complemented
16C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
17C22×#4339—21no—
18C22×C11×SD16C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×#66999C2211yescharacteristic
22C2×#66997C2211yescharacteristic
23C22×#4325C2211yescharacteristic
24C2×#66993C2211yescharacteristic
25C2×#66991C2211yescharacteristic
26C22×#4324C2211yescharacteristic
27C2×C4×C22⋊D11—21no—
28C22×#4314C2211yescharacteristic
29C22×C8×D11C2211yescharacteristic
30C22×C8×D11C2211yescharacteristic
31#10623109—24no—
32#10623109C2218yescomplemented
33#10623079—24no—
34#10623079C2218yes—
35C2×#66950C2211yescharacteristic
36C2×#66949—21no—
37C2×#66948C2211yescharacteristic
38C2×#66942—21no—
39C2×#66941C2211yescharacteristic
40C2×#66941C2211yescharacteristic
41C2×#66938—21no—
42C2×#66937—21no—
43C2×C4×D44C2211yescharacteristic
44C2×#66925—21no—
45C2×C42×D11C2211yescharacteristic
46C2×C4×Dic22—21no—
47C2×C4×Dic22C2211yescharacteristic
48C4×C11×SD16C2218yescomplemented
49C2×C11×#106C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×C4×C8×C11C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55#10622788C2218yescomplemented
56#10622784C2218yescomplemented
57C2×#66885C2211yescharacteristic
58C2×#66881C2211yescharacteristic
59C2×#66880C2211yescharacteristic
60C2×C8×Dic11C2211yescharacteristic
61C2×C8×Dic11C2211yescharacteristic
62C4×#4325C2218yescomplemented
63C4×#4324C2218yescomplemented
64C2×#66874C2211yescharacteristic
65C2×#66873C2211yescharacteristic
66C2×#66872C2211yescharacteristic
67C2×#66872C2211yescharacteristic
68C2×C4×C11⋊C8C2211yescharacteristic
69#10622477C2218yescomplemented
70#10622468C2218yescomplemented
71#10622420C2218yescomplemented
72#10622405C2218yescomplemented
73#10622391C2218yescomplemented
74#10622373C2218yescomplemented
75C4×#4314C2218yescomplemented
76C4×C8×D11C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C2×#4339—28no—
84C2×#4339—48no—
85C22×D44—21no—
86C22×D44C2311yescharacteristic
87C22×C4×D11—21no—
88C22×C4×D11D411yescharacteristic
89C22×C4×D11D411yescharacteristic
90C22×C4×D11C2311yescharacteristic
91C22×Dic22—21no—
92C22×Dic22—21no—
93C22×Dic22C2311yescharacteristic
94C2×C11×SD16—24no—
95C2×C11×SD16C2314yes—
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C4×Q8×C11—22no—
99C4×Q8×C11C2314yes—
100C4×D4×C11—22no—
101C4×D4×C11C2314yes—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C22⋊C4—21no—
106C2×C42×C11—21no—
107C2×C42×C11C2311yescharacteristic
108C2×C22⋊Dic11—21no—
109#66999—22no—
110#66999C2314yes—
111#66997—22no—
112#66997C2314yes—
113C2×#4325—24no—
114C2×#4325C2314yes—
115#66993—22no—
116#66993C2314yes—
117#66991—22no—
118#66991C2314yes—
119C2×#4324—24no—
120C2×#4324C2314yes—
121C4×C22⋊D11—28no—
122C2×(C2×D11)⋊C4—21no—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4—21no—
125C2×(C2×D11)⋊C4—21no—
126C2×C4⋊Dic11—21no—
127C2×C4⋊Dic11C2311yescharacteristic
128C2×C4⋊Dic11C2311yescharacteristic
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×C4×Dic11—21no—
136C2×C4×Dic11D411yescharacteristic
137C2×C4×Dic11D411yescharacteristic
138C2×C4×Dic11C2311yescharacteristic
139C22×C11⋊C8C2311yescharacteristic
140C22×C11⋊C8C2311yescharacteristic
141C2×#4314—24no—
142C2×#4314C2314yes—
143C2×C8×D11—24no—
144C2×C8×D11—24no—
145C2×C8×D11C2314yes—
146C2×C8×D11C2314yes—
147#66950—22no—
148#66950C2314yes—
149#66949—28no—
150#66948—22no—
151#66948C2314yes—
152#66942—28no—
153#66941—22no—
154#66941—22no—
155#66941C2314yes—
156#66941C2314yes—
157#66938—28no—
158#66937—28no—
159C4×D44—22no—
160C4×D44C2314yes—
161#66925—28no—
162C42×D11D414yes—
163C42×D11C2314yes—
164C4×Dic22—22no—
165C4×Dic22—28no—
166C4×Dic22C2314yes—
167C11×#106C2314yes—
168C11×#103C2314yes—
169C11×#102C2314yes—
170C4×C8×C11C2314yes—
171#66899C2314yes—
172#66896C2314yes—
173#66885C2314yes—
174#66881C2314yes—
175#66880C2314yes—
176C8×Dic11C2314yes—
177C8×Dic11C2314yes—
178#66874C2314yes—
179#66873C2314yes—
180#66872C2314yes—
181#66872C2314yes—
182C4×C11⋊C8C2314yes—
183C2×#3167—111nomaximal, Sylow
184C24×C11—21no—
185C23×D11—21no—
186C23×D11C2×D411yescharacteristic
187C2×Q8×C11—21no—
188C2×Q8×C11—22no—
189C2×Q8×C11—22no—
190C2×Q8×C11C2412yes—
191C2×D4×C11—21no—
192C2×D4×C11—22no—
193C2×D4×C11—22no—
194C2×D4×C11C2412yes—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—24no—
199C22×C4×C11—44no—
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2411yescharacteristic
203C2×C22⋊D11—24no—
204C2×C22⋊D11—24no—
205C2×C22⋊D11—24no—
206C2×C22⋊D11—44no—
207C2×C22⋊D11—44no—
208C2×C22⋊D11—44no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11C2×D411yescharacteristic
213C22×Dic11C2×D411yescharacteristic
214C22×Dic11C2×D411yescharacteristic
215#4339—432no—
216C2×D44—24no—
217C2×D44—21no—
218C2×D44—22no—
219C2×D44—22no—
220C2×D44—44no—
221C2×D44C2412yes—
222C2×C4×D11—24no—
223C2×C4×D11—24no—
224C2×C4×D11—22no—
225C2×C4×D11—22no—
226C2×C4×D11—44no—
227C2×C4×D11SD1618yescomplemented
228C2×C4×D11C2×D412yes—
229C2×C4×D11C2×D414yes—
230C2×C4×D11C2×D414yes—
231C2×C4×D11C2412yes—
232C2×Dic22—24no—
233C2×Dic22—24no—
234C2×Dic22—21no—
235C2×Dic22—22no—
236C2×Dic22—22no—
237C2×Dic22—44no—
238C2×Dic22—44no—
239C2×Dic22C2412yes—
240C11×SD16—28no—
241C2×C8×C11—22no—
242C2×C8×C11#4114yescomplemented
243C2×C8×C11C2412yes—
244C2×C8×C11C2412yes—
245C11×C4⋊C4—21no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—24no—
248C11×C4⋊C4C2412yes—
249C11×C4⋊C4C2412yes—
250C11×C22⋊C4—24no—
251C42×C11—24no—
252C42×C11C2×D412yes—
253C42×C11C2412yes—
254C22⋊Dic11—24no—
255#4325—28no—
256#4324—28no—
257(C2×D11)⋊C4—24no—
258(C2×D11)⋊C4—24no—
259(C2×D11)⋊C4—24no—
260(C2×D11)⋊C4—24no—
261C4⋊Dic11—24no—
262C4⋊Dic11—21no—
263C4⋊Dic11—21no—
264C4⋊Dic11C2412yes—
265C4⋊Dic11C2412yes—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268Dic11⋊C4—24no—
269Dic11⋊C4—24no—
270Dic11⋊C4—24no—
271Dic11⋊C4—24no—
272C4×Dic11—24no—
273C4×Dic11C2×D414yes—
274C4×Dic11C2×D412yes—
275C4×Dic11C2×D414yes—
276C4×Dic11C2412yes—
277C2×C11⋊C8—22no—
278C2×C11⋊C8#4114yescomplemented
279C2×C11⋊C8C2412yes—
280C2×C11⋊C8C2412yes—
281#4314—28no—
282C8×D11—28no—
283C8×D11—28no—
284C2×#533—111no—
285C2×#532—111no—
286#3167—1116no—
287C2×#498—111no—
288C2×#492—111no—
289C2×#487—111no—
290C2×#486—111no—
291C2×#465—111no—
292C2×#465—111no—
293C2×#465—111no—
294C2×#465—111no—
295C2×C4×SD16—111no—
296C2×C4×SD16—111no—
297C2×C4×SD16—111no—
298C2×C4×SD16D1111yescharacteristic, complemented
299C22×C4×C8—111no—
300C23×C11—22no—
301C23×C11—42no—
302C23×C11—42no—
303C23×C11—42no—
304C23×C11C22×D411yescharacteristic
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—42no—
309C22×D11—42no—
310C22×D11—42no—
311C22×D11C2×SD1614yes—
312C22×D11C22×D412yes—
313Q8×C11—22no—
314Q8×C11—22no—
315Q8×C11—42no—
316D4×C11—22no—
317D4×C11—22no—
318D4×C11—42no—
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—48no—
327C2×C4×C11C2×SD1614yes—
328C2×C4×C11C22×D412yes—
329C2×C4×C11C22×D411yescharacteristic
330C2×C4×C11C22×D412yes—
331C2×C4×C11C2×#4112yes—
332C2×C4×C11C2×#4112yes—
333C2×C4×C11C2511yescharacteristic
334C22⋊D11—48no—
335C22⋊D11—48no—
336C22⋊D11—48no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11—42no—
344C2×Dic11C2×SD1614yes—
345C2×Dic11#13514yes—
346C2×Dic11C22×D412yes—
347C2×Dic11C22×D412yes—
348C2×Dic11C22×D412yes—
349D44—22no—
350D44—22no—
351D44—48no—
352D44—42no—
353C4×D11—24no—
354C4×D11—22no—
355C4×D11—22no—
356C4×D11—28no—
357C4×D11—48no—
358C4×D11C2×SD16116yescomplemented
359Dic22—22no—
360Dic22—22no—
361Dic22—42no—
362Dic22—48no—
363Dic22—48no—
364C8×C11—22no—
365C8×C11C2×#4114yescomplemented
366C11⋊C8—22no—
367C11⋊C8C2×#4114yescomplemented
368C22×#41—221no—
369C22×SD16—111no—
370C22×SD16—111no—
371C22×SD16—111no—
372C22×SD16C2×D1111yescharacteristic
373C23×C8—111no—
374C23×C8—111no—
375#533—118no—
376#533—224no—
377#532—118no—
378#532—224no—
379C2×C4⋊Q8—111no—
380C2×C4⋊Q8—111no—
381C2×C4⋊Q8—111no—
382C2×#127—111no—
383C2×#125—221no—
384C2×#124—221no—
385C2×C22⋊Q8—111no—
386C2×C22⋊Q8—111no—
387C2×C22⋊Q8—221no—
388C2×#121—111no—
389C2×#121—111no—
390C2×#121—221no—
391C2×C4×Q8—111no—
392C2×C4×Q8—221no—
393C2×C4×Q8C2×D1111yescharacteristic
394C2×C4×D4—111no—
395C2×C4×D4—221no—
396C2×C4×D4C2×D1111yescharacteristic
397C2×#117—221no—
398C22×C42—111no—
399#498—118no—
400#492—118no—
401#487—118no—
402#486—118no—
403#465—118no—
404#465—118no—
405#465—118no—
406#465—118no—
407C4×SD16—118no—
408C4×SD16—118no—
409C4×SD16—118no—
410C4×SD16C2×D1118yescomplemented
411C2×#106—111no—
412C2×#106—111no—
413C2×#106—111no—
414C2×#106C2×D1111yescharacteristic
415C2×#103—111no—
416C2×#103—111no—
417C2×#103—111no—
418C2×#103C2×D1111yescharacteristic
419C2×#102—111no—
420C2×#102—111no—
421C2×#102—111no—
422C2×#102C2×D1111yescharacteristic
423C2×C4×C8—111no—
424C2×C4×C8—111no—
425C2×C4×C8—111no—
426C2×C4×C8—118no—
427C2×C4×C8C2×D1111yescharacteristic
428C22×C11—42no—
429C22×C11—42no—
430C22×C11—42no—
431C22×C11—84no—
432C22×C11#53212yes—
433C22×C11C22×SD1612yes—
434C22×C11C2×#13512yes—
435C22×C11C23×D411yescharacteristic
436C2×D11—28no—
437C2×D11—22no—
438C2×D11—22no—
439C2×D11—42no—
440C2×D11—42no—
441C2×D11—42no—
442C2×D11—84no—
443C2×D11C22×SD1614yes—
444C4×C11—22no—
445C4×C11—42no—
446C4×C11—42no—
447C4×C11—42no—
448C4×C11#53212yes—
449C4×C11C22×SD1614yes—
450C4×C11C22×#4111yescharacteristic
451C4×C11C22×#4111yescharacteristic
452Dic11—22no—
453Dic11—42no—
454Dic11—42no—
455Dic11—42no—
456Dic11C22×SD1614yes—
457Dic11C2×#13514yes—
458C2×#41—228no—
459C2×#41—448no—
460C22×Q8—111no—
461C22×Q8—221no—
462C22×Q8—221no—
463C22×Q8C22×D1111yescharacteristic
464C22×D4—111no—
465C22×D4—221no—
466C22×D4—221no—
467C22×D4—221no—
468C22×D4—221no—
469C22×D4C22×D1111yescharacteristic
470C23×C4—21no—
471C23×C4—111no—
472C23×C4—111no—
473C23×C4—111no—
474C23×C4—221no—
475C2×SD16—24no—
476C2×SD16—114no—
477C2×SD16—114no—
478C2×SD16—114no—
479C2×SD16—224no—
480C2×SD16—224no—
481C2×SD16—224no—
482C2×SD16C22×D1114yes—
483C22×C8—111no—
484C22×C8—111no—
485C22×C8—114no—
486C22×C8—114no—
487C22×C8—224no—
488C22×C8—224no—
489C22×C8C22×D1111yescharacteristic
490C22×C8C22×D1111yescharacteristic
491C4⋊Q8—114no—
492C4⋊Q8—114no—
493C4⋊Q8—114no—
494C4⋊Q8—222no—
495C4⋊Q8—222no—
496C4⋊Q8—222no—
497#127—114no—
498#127—222no—
499#125—228no—
500#124—228no—
501C22⋊Q8—114no—
502C22⋊Q8—114no—
503C22⋊Q8—222no—
504C22⋊Q8—228no—
505C22⋊Q8—222no—
506#121—114no—
507#121—114no—
508#121—228no—
509#121—222no—
510#121—222no—
511C4×Q8—22no—
512C4×Q8—114no—
513C4×Q8—228no—
514C4×Q8—222no—
515C4×Q8C22×D1114yes—
516C4×D4—22no—
517C4×D4—114no—
518C4×D4—228no—
519C4×D4—222no—
520C4×D4C22×D1114yes—
521#117—228no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—111no—
524C2×C4⋊C4—111no—
525C2×C4⋊C4—221no—
526C2×C4⋊C4—221no—
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—221no—
536C2×C22⋊C4—221no—
537C2×C22⋊C4—221no—
538C2×C22⋊C4—221no—
539C2×C22⋊C4—221no—
540C2×C42—21no—
541C2×C42—111no—
542C2×C42—111no—
543C2×C42—111no—
544C2×C42—114no—
545C2×C42—114no—
546C2×C42—221no—
547C2×C42C22×D1111yescharacteristic
548#106—114no—
549#106—114no—
550#106—114no—
551#106C22×D1114yes—
552#103—114no—
553#103—114no—
554#103—114no—
555#103C22×D1114yes—
556#102—114no—
557#102—114no—
558#102—114no—
559#102C22×D1114yes—
560C4×C8—114no—
561C4×C8—114no—
562C4×C8—114no—
563C4×C8C22×D1114yes—
564C2×C11—82no—
565C2×C11#316714yescomplemented
566C2×C11C2×#53211yescharacteristic
567C2×C11C23×SD1611yescharacteristic
568C2×C11C22×#13511yescharacteristic
569D11—24no—
570D11—82no—
571C24—21no—
572C24—111no—
573C24—221no—
574#41—4432no—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—112no—
579C2×Q8—224no—
580C2×Q8—224no—
581C2×Q8—221no—
582C2×Q8—222no—
583C2×Q8—222no—
584C2×Q8—444no—
585C2×Q8—444no—
586C2×Q8C23×D1112yes—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—22no—
590C2×D4—112no—
591C2×D4—224no—
592C2×D4—224no—
593C2×D4—224no—
594C2×D4—224no—
595C2×D4—222no—
596C2×D4—221no—
597C2×D4—222no—
598C2×D4—444no—
599C2×D4—444no—
600C2×D4—444no—
601C2×D4—444no—
602C2×D4C23×D1112yes—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—24no—
607C22×C4—44no—
608C22×C4—111no—
609C22×C4—111no—
610C22×C4—118no—
611C22×C4—114no—
612C22×C4—111no—
613C22×C4—114no—
614C22×C4—112no—
615C22×C4—112no—
616C22×C4—224no—
617C22×C4—222no—
618C22×C4—222no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4—221no—
622C22×C4—224no—
623C22×C4—444no—
624C22×C4D4×D1111yescharacteristic
625C22×C4D4×D1111yescharacteristic
626C22×C4C23×D1111yescharacteristic
627SD16—28no—
628SD16—228no—
629SD16—228no—
630SD16—228no—
631C2×C8—22no—
632C2×C8—114no—
633C2×C8—112no—
634C2×C8—112no—
635C2×C8—228no—
636C2×C8—222no—
637C2×C8—228no—
638C2×C8#433914yescomplemented
639C2×C8C23×D1112yes—
640C2×C8C23×D1112yes—
641C4⋊C4—24no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—112no—
645C4⋊C4—112no—
646C4⋊C4—224no—
647C4⋊C4—224no—
648C4⋊C4—224no—
649C4⋊C4—224no—
650C4⋊C4—224no—
651C4⋊C4—224no—
652C4⋊C4—221no—
653C4⋊C4—221no—
654C4⋊C4—224no—
655C4⋊C4C23×D1112yes—
656C4⋊C4C23×D1112yes—
657C22⋊C4—24no—
658C22⋊C4—224no—
659C22⋊C4—224no—
660C22⋊C4—224no—
661C22⋊C4—224no—
662C22⋊C4—224no—
663C42—24no—
664C42—114no—
665C42—114no—
666C42—112no—
667C42—112no—
668C42—224no—
669C42D4×D1112yes—
670C42C23×D1112yes—
671C11C2×#316711yescharacteristic, complemented, Sylow
672C23—22no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—114no—
677C23—112no—
678C23—222no—
679C23—222no—
680C23—222no—
681C23—442no—
682C23—442no—
683C23—442no—
684C23C2×D4×D1111yescharacteristic
685Q8—22no—
686Q8—22no—
687Q8—42no—
688Q8—222no—
689Q8—222no—
690Q8—448no—
691Q8—448no—
692Q8—442no—
693D4—22no—
694D4—22no—
695D4—42no—
696D4—222no—
697D4—222no—
698D4—448no—
699D4—448no—
700D4—448no—
701D4—448no—
702D4—442no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—48no—
711C2×C4—114no—
712C2×C4—114no—
713C2×C4—112no—
714C2×C4—112no—
715C2×C4—1116no—
716C2×C4—112no—
717C2×C4—228no—
718C2×C4—222no—
719C2×C4—224no—
720C2×C4—222no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—222no—
725C2×C4—442no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—448no—
729C2×C4SD16×D1114yes—
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×#433914yescomplemented
740C22—42no—
741C22—42no—
742C22—42no—
743C22—84no—
744C22—114no—
745C22—222no—
746C22—228no—
747C22—222no—
748C22—442no—
749C22—442no—
750C22—442no—
751C22—884no—
752C22#1062307912yes—
753C22C2×SD16×D1112yes—
754C22D11×#13512yes—
755C22C22×D4×D1111yescharacteristic
756C4—22no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—114no—
761C4—114no—
762C4—222no—
763C4—442no—
764C4—442no—
765C4—442no—
766C4#1062307912yes—
767C4C2×SD16×D1114yes—
768C4C22×#433911yescharacteristic
769C4C2×#41×D1111yescharacteristic
770C2—82no—
771C2—224no—
772C2—882no—
773C2#1307917214yesdirect product factor
774C2C2×#1062307911yescharacteristic
775C2C22×SD16×D1111yescharacteristic
776C2C2×D11×#13511yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
prime radicalC2×#10623079C2
hypercenterC2×C4×SD16D11
hypocenterC11C2×#3167
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#10623109C2semidirect
3. #13079172C2direct (N × H)
4. C2×#10622468C2semidirect
5. C2×#10622788C2semidirect
6. C2×#10622405C2semidirect
7. C2×#10622373C2semidirect
8. C2×#10622420C2semidirect
9. C2×#10622477C2semidirect
10. C2×#10622391C2semidirect
11. C2×#10622784C2semidirect
12. C2×C4×#4314C2semidirect
13. C2×C4×#4325C2semidirect
14. C2×C4×#4324C2semidirect
15. C2×C4×C8×D11C2semidirect
16. C2×C4×C11×SD16C2semidirect
32. #10623109C22semidirect
48. C4×C11×SD16C22semidirect
55. #10622788C22semidirect
56. #10622784C22semidirect
62. C4×#4325C22semidirect
63. C4×#4324C22semidirect
69. #10622477C22semidirect
70. #10622468C22semidirect
71. #10622420C22semidirect
72. #10622405C22semidirect
73. #10622391C22semidirect
74. #10622373C22semidirect
75. C4×#4314C22semidirect
76. C4×C8×D11C22semidirect
227. C2×C4×D11SD16semidirect
242. C2×C8×C11#41semidirect
278. C2×C11⋊C8#41semidirect
298. C2×C4×SD16D11semidirect
358. C4×D11C2×SD16semidirect
365. C8×C11C2×#41semidirect
367. C11⋊C8C2×#41semidirect
410. C4×SD16C2×D11semidirect
565. C2×C11#3167semidirect
638. C2×C8#4339semidirect
671. C11C2×#3167semidirect
739. C8C2×#4339semidirect
773. C2#13079172direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231092
C2×#106230792
#130791722
C2×#106224682
C2×#106227882
C2×#106224052
C2×#106223732
C2×#106224202
C2×#106224772
C2×#106223912
C2×#106227842
C2×C4×#43142
C2×C4×#43252
C2×C4×#43242
C2×C4×C8×D112
C2×C4×C11×SD162
C2×#316711