Finite Group Databasebeta

← C2×#13079998 #15626640

Subgroups — C2×#13079998 #15626640

Order 2816.

2146 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×#10623153C211yesmaximal, characteristic, complemented
2C2×#10623127C211yesmaximal, characteristic
3#13079998C2116yesmaximal, direct product factor
4C2×#10622488C211yesmaximal, characteristic, complemented
5C2×#10622407C211yesmaximal, characteristic, complemented
6C2×#10622503C211yesmaximal, characteristic, complemented
7C2×#10622372C211yesmaximal, characteristic, complemented
8C2×#10622662C211yesmaximal, characteristic, complemented
9C2×#10622747C211yesmaximal, characteristic, complemented
10C2×#10622655C211yesmaximal, characteristic, complemented
11C2×#10622375C211yesmaximal, characteristic, complemented
12C2×#10622776C211yesmaximal, characteristic, complemented
13C2×#10622431C211yesmaximal, characteristic, complemented
14C2×#10622775C211yesmaximal, characteristic, complemented
15C2×#10622731C211yesmaximal, characteristic, complemented
16C2×C11×#468C211yesmaximal, characteristic, complemented
17C22×#4341—21no—
18C22×C11×SD16C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23C2×#66997C2211yescharacteristic
24C22×#4325C2211yescharacteristic
25C2×#66993C2211yescharacteristic
26C2×#66992—21no—
27C2×D4×Dic11C2211yescharacteristic
28C22×#4324C2211yescharacteristic
29C2×#66983C2211yescharacteristic
30C2×#66977C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×#4318C2211yescharacteristic
33C22×#4314C2211yescharacteristic
34#10623153—24no—
35#10623153C2218yescomplemented
36#10623127—24no—
37#10623127C2218yes—
38C2×#66946C2211yescharacteristic
39C2×#66942—21no—
40C2×#66941C2211yescharacteristic
41C2×#66941C2211yescharacteristic
42C2×#66940—21no—
43C2×#66940C2211yescharacteristic
44C2×#66938—21no—
45C2×(C22⋊D11)⋊C4—21no—
46C2×#66931—21no—
47C2×#66930—21no—
48C11×#468C2218yescomplemented
49C2×C11×#107C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54#10622776C2218yescomplemented
55#10622775C2218yescomplemented
56#10622747C2218yescomplemented
57#10622731C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×#66882C2211yescharacteristic
60C2×#66880C2211yescharacteristic
61C2×Dic11⋊C8C2211yescharacteristic
62C2×Dic11⋊C8C2211yescharacteristic
63C2×Dic11⋊C8C2211yescharacteristic
64C2×Dic11⋊C8C2211yescharacteristic
65#10622662C2218yescomplemented
66#10622655C2218yescomplemented
67C2×#66874C2211yescharacteristic
68C2×#66873C2211yescharacteristic
69C2×#66871C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71#10622503C2218yescomplemented
72#10622488C2218yescomplemented
73#10622431C2218yescomplemented
74#10622407C2218yescomplemented
75#10622375C2218yescomplemented
76#10622372C2218yescomplemented
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—
84C23×Dic11—21no—
85C23×Dic11D411yescharacteristic
86C23×Dic11D411yescharacteristic
87C2×#4341—28no—
88C2×#4341—48no—
89C22×D44C2311yescharacteristic
90C22×C4×D11—21no—
91C22×Dic22—21no—
92C22×Dic22—21no—
93C22×Dic22C2311yescharacteristic
94C2×C11×SD16—42no—
95C2×C11×SD16C2314yes—
96C2×C11×M16—42no—
97C2×C11×M16C2314yes—
98C22×C8×C11C2311yescharacteristic
99C22×C8×C11C2311yescharacteristic
100C11×C22⋊Q8—22no—
101C11×C22⋊Q8C2314yes—
102C11×#121—22no—
103C11×#121C2314yes—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
109C2×C22⋊Dic11—21no—
110C2×C22⋊Dic11—21no—
111Q8×Dic11—22no—
112Q8×Dic11C2314yes—
113#66997—22no—
114#66997C2314yes—
115C2×#4325—42no—
116C2×#4325C2314yes—
117#66993—22no—
118#66993C2314yes—
119#66992—28no—
120D4×Dic11—22no—
121D4×Dic11C2314yes—
122C2×#4324—42no—
123C2×#4324C2314yes—
124#66983—22no—
125#66983C2314yes—
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4—21no—
128C2×C4⋊Dic11—21no—
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131#66977—22no—
132#66977C2314yes—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4—21no—
136C2×Dic11⋊C4—21no—
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4—21no—
139C2×C4×Dic11—21no—
140C2×C4×Dic11—21no—
141C2×C4×Dic11D411yescharacteristic
142C2×C4×Dic11D411yescharacteristic
143C2×C4×Dic11D414yes—
144C2×C4×Dic11C2314yes—
145C2×C4×Dic11C2311yescharacteristic
146C2×C4×Dic11C2311yescharacteristic
147C2×#4318—42no—
148C2×#4318C2314yes—
149C22×C11⋊C8C2311yescharacteristic
150C22×C11⋊C8C2311yescharacteristic
151C2×#4314—42no—
152C2×#4314C2314yes—
153#66946—22no—
154#66946C2314yes—
155#66942—28no—
156#66941—22no—
157#66941—22no—
158#66941C2314yes—
159#66941C2314yes—
160#66940—28no—
161#66940—22no—
162#66940C2314yes—
163#66938—28no—
164(C22⋊D11)⋊C4—28no—
165#66931—28no—
166#66930—28no—
167C11×#107C2314yes—
168C11×#103C2314yes—
169C11×#102C2314yes—
170#66899C2314yes—
171#66896C2314yes—
172#66885C2314yes—
173#66882C2314yes—
174#66880C2314yes—
175Dic11⋊C8C2314yes—
176Dic11⋊C8C2314yes—
177Dic11⋊C8C2314yes—
178Dic11⋊C8C2314yes—
179#66874C2314yes—
180#66873C2314yes—
181#66871C2314yes—
182#66871C2314yes—
183C2×#3254—111nomaximal, Sylow
184C24×C11—21no—
185C24×C11C2×D411yescharacteristic
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—44no—
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—44no—
210C2×C22⋊D11—44no—
211C2×C22⋊D11—44no—
212C22×Dic11—24no—
213C22×Dic11—24no—
214C22×Dic11—24no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—44no—
219C22×Dic11C2×D414yes—
220C22×Dic11C2×D414yes—
221C22×Dic11C2×D411yescharacteristic
222C22×Dic11C2×D411yescharacteristic
223C22×Dic11C2×D411yescharacteristic
224C22×Dic11C2×D411yescharacteristic
225#4341—432no—
226C2×D44—21no—
227C2×D44—22no—
228C2×D44—22no—
229C2×D44C2412yes—
230C2×C4×D11—24no—
231C2×C4×D11—44no—
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—44no—
241C11×M16—44no—
242C2×C8×C11—22no—
243C2×C8×C11—22no—
244C2×C8×C11C2412yes—
245C2×C8×C11C2412yes—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—24no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4C2412yes—
250C11×C4⋊C4C2412yes—
251C11×C22⋊C4—24no—
252C11×C22⋊C4—24no—
253C22⋊Dic11—24no—
254C22⋊Dic11—24no—
255#4325—44no—
256#4324—44no—
257(C2×D11)⋊C4—24no—
258(C2×D11)⋊C4—24no—
259C4⋊Dic11—24no—
260C4⋊Dic11—21no—
261C4⋊Dic11—21no—
262C4⋊Dic11C2412yes—
263C4⋊Dic11C2412yes—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268Dic11⋊C4—24no—
269Dic11⋊C4—24no—
270C4×Dic11—24no—
271C4×Dic11—24no—
272C4×Dic11C2×D414yes—
273C4×Dic11C2×D414yes—
274C4×Dic11C2×D412yes—
275C4×Dic11C2×D412yes—
276C4×Dic11C2412yes—
277C4×Dic11C2412yes—
278#4318—44no—
279C2×C11⋊C8—22no—
280C2×C11⋊C8—22no—
281C2×C11⋊C8C2412yes—
282C2×C11⋊C8C2412yes—
283#4314—44no—
284C2×#533—111no—
285C2×#532—111no—
286#3254—1116no—
287C2×#477—111no—
288C2×#477—111no—
289C2×#474—111no—
290C2×#474—111no—
291C2×#468—111no—
292C2×#468—111no—
293C2×#468—111no—
294C2×#468D1111yescharacteristic, complemented
295C2×#460—111no—
296C2×#460—111no—
297C2×#461—111no—
298C2×#461—111no—
299C2×#423—111no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—42no—
305C23×C11—42no—
306C23×C11—42no—
307C23×C11C22×D412yes—
308C23×C11C22×D411yescharacteristic
309C22×D11—22no—
310C22×D11—42no—
311C22×D11—42no—
312C22×D11—42no—
313Q8×C11—22no—
314Q8×C11—22no—
315Q8×C11—42no—
316D4×C11—22no—
317D4×C11—22no—
318D4×C11—48no—
319D4×C11—42no—
320C2×C4×C11—22no—
321C2×C4×C11—24no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—42no—
328C2×C4×C11—42no—
329C2×C4×C11—42no—
330C2×C4×C11C22×D412yes—
331C2×C4×C11C22×D411yescharacteristic
332C2×C4×C11H(5,𝔽2)12yes—
333C2×C4×C112−1+412yes—
334C2×C4×C11C2511yescharacteristic
335C22⋊D11—48no—
336C22⋊D11—48no—
337C22⋊D11—48no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—28no—
341C2×Dic11—28no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11—48no—
349C2×Dic11AGL(1,ℤ/8)14yes—
350C2×Dic11#13714yes—
351C2×Dic11C22×D412yes—
352C2×Dic11C22×D412yes—
353C2×Dic11C22×D412yes—
354C2×Dic11C22×D412yes—
355D44—22no—
356D44—22no—
357D44—42no—
358C4×D11—48no—
359Dic22—22no—
360Dic22—22no—
361Dic22—48no—
362Dic22—42no—
363Dic22—48no—
364C8×C11—22no—
365C8×C11—22no—
366C11⋊C8—22no—
367C11⋊C8—22no—
368C22×#41—221no—
369C22×SD16—111no—
370C22×SD16—111no—
371C22×SD16—111no—
372C22×SD16C2×D1111yescharacteristic
373C22×M16—111no—
374C22×M16C2×D1111yescharacteristic
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—221no—
387C2×C22⋊Q8C2×D1111yescharacteristic
388C2×#121—111no—
389C2×#121—221no—
390C2×#121C2×D1111yescharacteristic
391C2×C4×Q8—111no—
392C2×C4×Q8—111no—
393C2×C4×Q8—221no—
394C2×C4×D4—111no—
395C2×C4×D4—111no—
396C2×C4×D4—221no—
397C2×#117—221no—
398C22×C42—111no—
399#477—118no—
400#477—118no—
401#474—118no—
402#474—118no—
403#468—118no—
404#468—118no—
405#468—118no—
406#468C2×D1118yescomplemented
407#461—118no—
408#461—118no—
409#460—118no—
410#460—118no—
411C2×#107—111no—
412C2×#107—111no—
413C2×#107—111no—
414C2×#107C2×D1111yescharacteristic
415#423—118no—
416C2×C4⋊C8—111no—
417C2×C4⋊C8—111no—
418C2×C4⋊C8—111no—
419C2×C4⋊C8—111no—
420C2×#103—111no—
421C2×#103—111no—
422C2×#103—111no—
423C2×#103C2×D1111yescharacteristic
424C2×#102—111no—
425C2×#102—111no—
426C2×#102—111no—
427C2×#102C2×D1111yescharacteristic
428C22×C11—22no—
429C22×C11—22no—
430C22×C11—22no—
431C22×C11—44no—
432C22×C11—42no—
433C22×C11—42no—
434C22×C11—42no—
435C22×C11—84no—
436C22×C11#53712yes—
437C22×C11C2×AGL(1,ℤ/8)12yes—
438C22×C11C2×#13712yes—
439C22×C11C23×D411yescharacteristic
440C2×D11—42no—
441C2×D11—42no—
442C2×D11—42no—
443C2×D11—84no—
444C4×C11—22no—
445C4×C11—42no—
446C4×C11—42no—
447C4×C11—42no—
448C4×C11#53712yes—
449C4×C11C2×H(5,𝔽2)11yescharacteristic
450C4×C11C2×2−1+411yescharacteristic
451Dic11—22no—
452Dic11—22no—
453Dic11—42no—
454Dic11—42no—
455Dic11—42no—
456Dic11C2×AGL(1,ℤ/8)14yes—
457Dic11C2×#13714yes—
458C2×#41—228no—
459C2×#41—448no—
460C22×Q8—111no—
461C22×Q8—221no—
462C22×Q8—221no—
463C22×Q8C22×D1111yescharacteristic
464C22×D4—21no—
465C22×D4—111no—
466C22×D4—221no—
467C22×D4—221no—
468C22×D4—221no—
469C22×D4C22×D1111yescharacteristic
470C23×C4—111no—
471C23×C4—111no—
472C23×C4—221no—
473C23×C4—221no—
474C23×C4C22×D1111yescharacteristic
475C2×SD16—42no—
476C2×SD16—114no—
477C2×SD16—114no—
478C2×SD16—114no—
479C2×SD16—442no—
480C2×SD16—442no—
481C2×SD16—442no—
482C2×SD16C22×D1114yes—
483C2×M16—42no—
484C2×M16—114no—
485C2×M16—442no—
486C2×M16C22×D1114yes—
487C22×C8—111no—
488C22×C8—111no—
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—22no—
502C22⋊Q8—114no—
503C22⋊Q8—228no—
504C22⋊Q8—222no—
505C22⋊Q8C22×D1114yes—
506#121—22no—
507#121—114no—
508#121—228no—
509#121—222no—
510#121C22×D1114yes—
511C4×Q8—114no—
512C4×Q8—114no—
513C4×Q8—222no—
514C4×Q8—228no—
515C4×Q8—222no—
516C4×D4—114no—
517C4×D4—114no—
518C4×D4—228no—
519C4×D4—222no—
520C4×D4—222no—
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—21no—
536C2×C22⋊C4—221no—
537C2×C22⋊C4—221no—
538C2×C22⋊C4—221no—
539C2×C22⋊C4—221no—
540C2×C42—111no—
541C2×C42—111no—
542C2×C42—114no—
543C2×C42—111no—
544C2×C42—111no—
545C2×C42—114no—
546C2×C42—221no—
547C2×C42—221no—
548#107—114no—
549#107—114no—
550#107—114no—
551#107C22×D1114yes—
552C4⋊C8—114no—
553C4⋊C8—114no—
554C4⋊C8—114no—
555C4⋊C8—114no—
556#103—114no—
557#103—114no—
558#103—114no—
559#103C22×D1114yes—
560#102—114no—
561#102—114no—
562#102—114no—
563#102C22×D1114yes—
564C2×C11—42no—
565C2×C11—82no—
566C2×C11#325414yescomplemented
567C2×C11C2×#53711yescharacteristic
568C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
569C2×C11C22×#13711yescharacteristic
570D11—82no—
571C24—21no—
572C24—221no—
573C24D4×D1111yescharacteristic
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—24no—
588C2×D4—21no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—44no—
592C2×D4—112no—
593C2×D4—224no—
594C2×D4—224no—
595C2×D4—224no—
596C2×D4—221no—
597C2×D4—222no—
598C2×D4—222no—
599C2×D4—444no—
600C2×D4—444no—
601C2×D4—444no—
602C2×D4C23×D1112yes—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—111no—
609C22×C4—111no—
610C22×C4—114no—
611C22×C4—114no—
612C22×C4—111no—
613C22×C4—111no—
614C22×C4—224no—
615C22×C4—224no—
616C22×C4—224no—
617C22×C4—224no—
618C22×C4—221no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4—444no—
622C22×C4—444no—
623C22×C4D4×D1112yes—
624C22×C4D4×D1111yescharacteristic
625C22×C4C23×D1112yes—
626C22×C4C23×D1111yescharacteristic
627SD16—44no—
628SD16—444no—
629SD16—444no—
630SD16—444no—
631M16—44no—
632M16—444no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—112no—
636C2×C8—112no—
637C2×C8—222no—
638C2×C8—222no—
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—24no—
659C22⋊C4—224no—
660C22⋊C4—224no—
661C22⋊C4—224no—
662C22⋊C4—224no—
663C42—114no—
664C42—112no—
665C42—112no—
666C42—114no—
667C42—112no—
668C42—112no—
669C42—224no—
670C42—224no—
671C11C2×#325411yescharacteristic, complemented, Sylow
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—222no—
680C23—442no—
681C23—442no—
682C23—442no—
683C23C2×D4×D1112yes—
684C23C2×D4×D1111yescharacteristic
685Q8—22no—
686Q8—22no—
687Q8—42no—
688Q8—222no—
689Q8—222no—
690Q8—448no—
691Q8—448no—
692Q8—442no—
693D4—22no—
694D4—22no—
695D4—48no—
696D4—42no—
697D4—222no—
698D4—222no—
699D4—448no—
700D4—448no—
701D4—448no—
702D4—442no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—114no—
714C2×C4—114no—
715C2×C4—112no—
716C2×C4—112no—
717C2×C4—112no—
718C2×C4—112no—
719C2×C4—228no—
720C2×C4—228no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—222no—
725C2×C4—222no—
726C2×C4—448no—
727C2×C4—448no—
728C2×C4—442no—
729C2×C4—442no—
730C2×C4—442no—
731C2×C4C2×D4×D1112yes—
732C2×C4C2×D4×D1111yescharacteristic
733C2×C4#6703712yes—
734C2×C4#6704312yes—
735C2×C4C24×D1111yescharacteristic
736C8—22no—
737C8—22no—
738C8—222no—
739C8—222no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—84no—
748C22—442no—
749C22—442no—
750C22—442no—
751C22—884no—
752C22#1062312812yes—
753C22D11×AGL(1,ℤ/8)12yes—
754C22D11×#13712yes—
755C22C22×D4×D1111yescharacteristic
756C4—22no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—114no—
761C4—114no—
762C4—222no—
763C4—222no—
764C4—442no—
765C4—442no—
766C4—442no—
767C4#1062312812yes—
768C4C2×#6703711yescharacteristic
769C4C2×#6704311yescharacteristic
770C2—42no—
771C2—82no—
772C2—882no—
773C2#1307999814yesdirect product factor
774C2C2×#1062312811yescharacteristic
775C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
776C2C2×D11×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#468C2
socleC23×C11C22×D4
prime radicalC2×#10623127C2
hypercenterC2×#468D11
hypocenterC11C2×#3254
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#10623153C2semidirect
3. #13079998C2direct (N × H)
4. C2×#10622488C2semidirect
5. C2×#10622407C2semidirect
6. C2×#10622503C2semidirect
7. C2×#10622372C2semidirect
8. C2×#10622662C2semidirect
9. C2×#10622747C2semidirect
10. C2×#10622655C2semidirect
11. C2×#10622375C2semidirect
12. C2×#10622776C2semidirect
13. C2×#10622431C2semidirect
14. C2×#10622775C2semidirect
15. C2×#10622731C2semidirect
16. C2×C11×#468C2semidirect
35. #10623153C22semidirect
48. C11×#468C22semidirect
54. #10622776C22semidirect
55. #10622775C22semidirect
56. #10622747C22semidirect
57. #10622731C22semidirect
65. #10622662C22semidirect
66. #10622655C22semidirect
71. #10622503C22semidirect
72. #10622488C22semidirect
73. #10622431C22semidirect
74. #10622407C22semidirect
75. #10622375C22semidirect
76. #10622372C22semidirect
294. C2×#468D11semidirect
406. #468C2×D11semidirect
566. C2×C11#3254semidirect
671. C11C2×#3254semidirect
773. C2#13079998direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231532
C2×#106231272
#130799982
C2×#106224882
C2×#106224072
C2×#106225032
C2×#106223722
C2×#106226622
C2×#106227472
C2×#106226552
C2×#106223752
C2×#106227762
C2×#106224312
C2×#106227752
C2×#106227312
C2×C11×#4682
C2×#325411