Finite Group Databasebeta

← C2×#13081633 #15634726

Subgroups — C2×#13081633 #15634726

Order 2816.

2250 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623202C211yesmaximal, characteristic, complemented
2C2×#10623249C211yesmaximal, characteristic, complemented
3#13081633C2116yesmaximal, direct product factor
4C2×#10622767C211yesmaximal, characteristic, complemented
5C2×#10622788C211yesmaximal, characteristic, complemented
6C2×#10622776C211yesmaximal, characteristic, complemented
7C2×#10622688C211yesmaximal, characteristic, complemented
8C2×#10622766C211yesmaximal, characteristic, complemented
9C2×#10622670C211yesmaximal, characteristic, complemented
10C2×#10622775C211yesmaximal, characteristic, complemented
11C2×#10622763C211yesmaximal, characteristic, complemented
12C2×#10622314C211yesmaximal, characteristic, complemented
13C2×#10622323C211yesmaximal, characteristic, complemented
14C2×#10622777C211yesmaximal, characteristic, complemented
15C2×D8×Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#496C211yesmaximal, characteristic, complemented
17C22×#4341—21no—
18C22×C11×SD16C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic
21C22×C11×D8C2211yescharacteristic
22C2×C11×#127C2211yescharacteristic
23C2×C11×#124C2211yescharacteristic
24C2×Q8×Dic11C2211yescharacteristic
25C2×#66997C2211yescharacteristic
26C22×#4325C2211yescharacteristic
27C2×#66993C2211yescharacteristic
28C2×#66993C2211yescharacteristic
29C2×#66992—21no—
30C2×#66992—21no—
31C2×#66991—21no—
32C2×#66989C2211yescharacteristic
33C2×D4×Dic11C2211yescharacteristic
34C2×D4×Dic11C2211yescharacteristic
35C2×D4×Dic11C2211yescharacteristic
36C22×#4324C2211yescharacteristic
37C22×#4324C2211yescharacteristic
38C22×#4323C2211yescharacteristic
39C22×#4314C2211yescharacteristic
40#10623249—24no—
41#10623249C2218yescomplemented
42#10623202—24no—
43#10623202C2218yescomplemented
44C2×#66932—21no—
45C2×#66932—21no—
46C2×#66931—21no—
47C2×#66930—21no—
48C2×C4×D44C2211yescharacteristic
49C2×C4×Dic22C2211yescharacteristic
50C2×C4×Dic22C2211yescharacteristic
51C11×#496C2218yescomplemented
52C2×C11×#97C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×#66896C2211yescharacteristic
56C2×#66896C2211yescharacteristic
57#10622788C2218yescomplemented
58#10622777C2218yescomplemented
59#10622776C2218yescomplemented
60#10622775C2218yescomplemented
61#10622767C2218yescomplemented
62#10622766C2218yescomplemented
63#10622763C2218yescomplemented
64D8×Dic11C2218yescomplemented
65C2×#66885C2211yescharacteristic
66C2×#66882C2211yescharacteristic
67C2×#66880C2211yescharacteristic
68C2×#66879C2211yescharacteristic
69C2×Dic11⋊C8C2211yescharacteristic
70C2×Dic11⋊C8C2211yescharacteristic
71C2×C8×Dic11C2211yescharacteristic
72#10622688C2218yescomplemented
73#10622670C2218yescomplemented
74C2×C4⋊(C11⋊C8)C2211yescharacteristic
75#10622323C2218yescomplemented
76#10622314C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11C2311yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C22×C22⋊D11—21no—
87C23×Dic11—21no—
88C23×Dic11—21no—
89C23×Dic11—21no—
90C2×#4341—28no—
91C2×#4341—48no—
92C22×D44C2311yescharacteristic
93C22×C4×D11—21no—
94C22×Dic22D411yescharacteristic
95C22×Dic22C2311yescharacteristic
96C2×C11×SD16—24no—
97C2×C11×SD16—42no—
98C2×C11×SD16C2314yes—
99C2×C11×SD16C2314yes—
100C2×C11×D8—24no—
101C2×C11×D8—42no—
102C2×C11×D8C2314yes—
103C2×C11×D8C2314yes—
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C11×#127—22no—
107C11×#127C2314yes—
108C11×#124—22no—
109C11×#124C2314yes—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C42×C11C2311yescharacteristic
113C2×C22⋊Dic11—21no—
114C2×C22⋊Dic11—21no—
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11—21no—
117C2×C22⋊Dic11—21no—
118Q8×Dic11—22no—
119Q8×Dic11C2314yes—
120#66997—22no—
121#66997C2314yes—
122C2×#4325—42no—
123C2×#4325C2314yes—
124#66993—22no—
125#66993—22no—
126#66993C2314yes—
127#66993C2314yes—
128#66992—28no—
129#66992—28no—
130#66991—28no—
131#66989—22no—
132#66989C2314yes—
133D4×Dic11—22no—
134D4×Dic11—22no—
135D4×Dic11—22no—
136D4×Dic11C2314yes—
137D4×Dic11C2314yes—
138D4×Dic11C2314yes—
139C2×#4324—42no—
140C2×#4324—42no—
141C2×#4324C2314yes—
142C2×#4324C2314yes—
143C2×#4323—42no—
144C2×#4323C2314yes—
145C2×(C2×D11)⋊C4—21no—
146C2×C4⋊Dic11—21no—
147C2×C4⋊Dic11D411yescharacteristic
148C2×C4⋊Dic11C2311yescharacteristic
149C2×C4⋊Dic11C2311yescharacteristic
150C2×Dic11⋊C4—21no—
151C2×Dic11⋊C4—21no—
152C2×Dic11⋊C4—21no—
153C2×Dic11⋊C4D411yescharacteristic
154C2×Dic11⋊C4D411yescharacteristic
155C2×C4×Dic11—21no—
156C2×C4×Dic11—21no—
157C2×C4×Dic11C2311yescharacteristic
158C2×C4×Dic11C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C22×C11⋊C8C2311yescharacteristic
161C2×#4314—24no—
162C2×#4314C2314yes—
163#66932—28no—
164#66932—28no—
165#66931—28no—
166#66930—28no—
167C4×D44—22no—
168C4×D44C2314yes—
169C4×Dic22—22no—
170C4×Dic22D414yes—
171C4×Dic22C2314yes—
172C4×Dic22C2314yes—
173C11×#97C2314yes—
174#66899C2314yes—
175#66896C2314yes—
176#66896C2314yes—
177#66896C2314yes—
178#66885C2314yes—
179#66882C2314yes—
180#66880C2314yes—
181#66879C2314yes—
182Dic11⋊C8C2314yes—
183Dic11⋊C8C2314yes—
184C8×Dic11C2314yes—
185C4⋊(C11⋊C8)C2314yes—
186C2×#3397—111nomaximal, Sylow
187C24×C11—21no—
188C24×C11—21no—
189C24×C11—21no—
190C23×D11—21no—
191C2×Q8×C11—21no—
192C2×Q8×C11—22no—
193C2×Q8×C11—22no—
194C2×Q8×C11C2412yes—
195C2×D4×C11—21no—
196C2×D4×C11—21no—
197C2×D4×C11—21no—
198C2×D4×C11—24no—
199C2×D4×C11—24no—
200C2×D4×C11—22no—
201C2×D4×C11—22no—
202C2×D4×C11—22no—
203C2×D4×C11—22no—
204C2×D4×C11—22no—
205C2×D4×C11—22no—
206C2×D4×C11—44no—
207C2×D4×C11—82no—
208C2×D4×C11C2412yes—
209C2×D4×C11C2412yes—
210C2×D4×C11C2412yes—
211C22×C4×C11—21no—
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2411yescharacteristic
215C2×C22⋊D11—24no—
216C2×C22⋊D11—24no—
217C2×C22⋊D11—24no—
218C2×C22⋊D11—24no—
219C2×C22⋊D11—44no—
220C2×C22⋊D11—44no—
221C2×C22⋊D11—82no—
222C2×C22⋊D11—82no—
223C22×Dic11—24no—
224C22×Dic11—24no—
225C22×Dic11—24no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—44no—
230C22×Dic11—44no—
231C22×Dic11—44no—
232C22×Dic11C2×D411yescharacteristic
233C22×Dic11C2×D411yescharacteristic
234C22×Dic11C2×D411yescharacteristic
235C22×Dic11C2×D411yescharacteristic
236#4341—432no—
237C2×D44—21no—
238C2×D44—22no—
239C2×D44—22no—
240C2×D44C2412yes—
241C2×C4×D11—24no—
242C2×C4×D11—44no—
243C2×Dic22—24no—
244C2×Dic22—21no—
245C2×Dic22—22no—
246C2×Dic22—22no—
247C2×Dic22C2×D414yes—
248C2×Dic22C2412yes—
249C11×SD16—28no—
250C11×SD16—44no—
251C11×D8—28no—
252C11×D8—44no—
253C2×C8×C11—22no—
254C2×C8×C11#4114yescomplemented
255C2×C8×C11C2412yes—
256C2×C8×C11C2412yes—
257C11×C22⋊C4—24no—
258C11×C22⋊C4—24no—
259C42×C11C2×D412yes—
260C42×C11C2412yes—
261C22⋊Dic11—24no—
262C22⋊Dic11—24no—
263C22⋊Dic11—24no—
264C22⋊Dic11—24no—
265C22⋊Dic11—24no—
266#4325—44no—
267#4324—44no—
268#4324—44no—
269#4323—44no—
270(C2×D11)⋊C4—24no—
271C4⋊Dic11—24no—
272C4⋊Dic11—21no—
273C4⋊Dic11—21no—
274C4⋊Dic11C2×D414yes—
275C4⋊Dic11C2412yes—
276C4⋊Dic11C2412yes—
277Dic11⋊C4—24no—
278Dic11⋊C4—24no—
279Dic11⋊C4—24no—
280Dic11⋊C4C2×D414yes—
281Dic11⋊C4C2×D414yes—
282C4×Dic11—24no—
283C4×Dic11—24no—
284C4×Dic11C2×D412yes—
285C4×Dic11C2×D412yes—
286C4×Dic11C2412yes—
287C4×Dic11C2412yes—
288C2×C11⋊C8—22no—
289C2×C11⋊C8—22no—
290C2×C11⋊C8C2412yes—
291C2×C11⋊C8C2412yes—
292#4314—28no—
293C2×#556—111no—
294C2×#550—111no—
295#3397—1116no—
296C2×#496—111no—
297C2×#496D1111yescharacteristic, complemented
298C2×#492—111no—
299C2×#460—111no—
300C2×#460—111no—
301C2×#463—111no—
302C2×#463—111no—
303C2×#461—111no—
304C2×#459—111no—
305C2×#446—111no—
306C2×#440—111no—
307C2×#440—111no—
308C2×C4×D8—111no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—42no—
313C23×C11—42no—
314C23×C11—42no—
315C23×C11—42no—
316C23×C11—42no—
317C23×C11—42no—
318C23×C11—42no—
319C23×C11—42no—
320C23×C11—42no—
321C23×C11C22×D411yescharacteristic
322C22×D11—22no—
323C22×D11—42no—
324C22×D11—42no—
325C22×D11—42no—
326Q8×C11—22no—
327Q8×C11—22no—
328Q8×C11—42no—
329D4×C11—22no—
330D4×C11—22no—
331D4×C11—22no—
332D4×C11—22no—
333D4×C11—22no—
334D4×C11—22no—
335D4×C11—48no—
336D4×C11—42no—
337D4×C11—42no—
338D4×C11—42no—
339D4×C11—84no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—42no—
344C2×C4×C11C22×D412yes—
345C2×C4×C11C22×D412yes—
346C2×C4×C11C22×D411yescharacteristic
347C2×C4×C11C2×#4112yes—
348C2×C4×C11H(5,𝔽2)12yes—
349C2×C4×C11C2511yescharacteristic
350C22⋊D11—48no—
351C22⋊D11—48no—
352C22⋊D11—84no—
353C22⋊D11—84no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—48no—
361C2×Dic11—42no—
362C2×Dic11—42no—
363C2×Dic11—42no—
364C2×Dic11—48no—
365C2×Dic11—48no—
366C2×Dic11AGL(1,ℤ/8)14yes—
367C2×Dic11C22×D412yes—
368C2×Dic11C22×D412yes—
369C2×Dic11C22×D412yes—
370C2×Dic11C22×D412yes—
371D44—22no—
372D44—22no—
373D44—42no—
374C4×D11—48no—
375Dic22—28no—
376Dic22—22no—
377Dic22—22no—
378Dic22—42no—
379C8×C11—22no—
380C8×C11C2×#4114yescomplemented
381C11⋊C8—22no—
382C11⋊C8—22no—
383C22×#41—221no—
384C22×SD16—111no—
385C22×SD16—111no—
386C22×SD16—111no—
387C22×SD16—111no—
388C22×SD16C2×D1111yescharacteristic
389C22×SD16C2×D1111yescharacteristic
390C22×D8—111no—
391C22×D8C2×D1111yescharacteristic
392C22×D8C2×D1111yescharacteristic
393#556—118no—
394#556—224no—
395#550—118no—
396#550—224no—
397C2×C4⋊Q8—111no—
398C2×#127—111no—
399C2×#127—111no—
400C2×#127C2×D1111yescharacteristic
401C2×#126—221no—
402C2×#126—221no—
403C2×#124—111no—
404C2×#124C2×D1111yescharacteristic
405C2×C22⋊Q8—221no—
406C2×#121—221no—
407C2×#121—221no—
408C2×#121—221no—
409C2×C4×Q8—111no—
410C2×C4×Q8—111no—
411C2×C4×Q8—111no—
412C2×C4×D4—111no—
413C2×C4×D4—111no—
414C2×C4×D4—111no—
415C2×C4×D4—111no—
416C2×#117—221no—
417#496—118no—
418#496C2×D1118yescomplemented
419#492—118no—
420#463—118no—
421#463—118no—
422#461—118no—
423#460—118no—
424#460—118no—
425#459—118no—
426#446—118no—
427#440—118no—
428#440—118no—
429C4×D8—118no—
430C2×#107—111no—
431C2×C4⋊C8—111no—
432C2×C4⋊C8—111no—
433C2×C4⋊C8—111no—
434C2×#103—111no—
435C2×#103—111no—
436C2×#102—111no—
437C2×#102—111no—
438C2×#102—111no—
439C2×#102—111no—
440C2×#97—111no—
441C2×#97C2×D1111yescharacteristic
442C2×C4×C8—111no—
443C22×C11—42no—
444C22×C11—42no—
445C22×C11—42no—
446C22×C11—42no—
447C22×C11—42no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—84no—
453C22×C11—84no—
454C22×C11—84no—
455C22×C11#55012yes—
456C22×C11C2×AGL(1,ℤ/8)12yes—
457C22×C11#57712yes—
458C22×C11C23×D411yescharacteristic
459C2×D11—42no—
460C2×D11—42no—
461C2×D11—42no—
462C2×D11—84no—
463C4×C11—22no—
464C4×C11—22no—
465C4×C11—42no—
466C4×C11#55012yes—
467C4×C11C22×#4111yescharacteristic
468C4×C11C2×H(5,𝔽2)11yescharacteristic
469Dic11—22no—
470Dic11—22no—
471Dic11—22no—
472Dic11—42no—
473Dic11—42no—
474Dic11—42no—
475Dic11C2×AGL(1,ℤ/8)14yes—
476C2×#41—228no—
477C2×#41—448no—
478C22×Q8—111no—
479C22×Q8—111no—
480C22×Q8C22×D1111yescharacteristic
481C22×D4—21no—
482C22×D4—21no—
483C22×D4—111no—
484C22×D4—221no—
485C22×D4—221no—
486C22×D4—221no—
487C22×D4—221no—
488C22×D4C22×D1111yescharacteristic
489C22×D4C22×D1111yescharacteristic
490C22×D4C22×D1111yescharacteristic
491C23×C4—221no—
492C23×C4—221no—
493C23×C4—221no—
494C23×C4—221no—
495C2×SD16—24no—
496C2×SD16—42no—
497C2×SD16—114no—
498C2×SD16—114no—
499C2×SD16—114no—
500C2×SD16—114no—
501C2×SD16—224no—
502C2×SD16—442no—
503C2×SD16—442no—
504C2×SD16—442no—
505C2×SD16C22×D1114yes—
506C2×SD16C22×D1114yes—
507C2×D8—24no—
508C2×D8—42no—
509C2×D8—114no—
510C2×D8—442no—
511C2×D8C22×D1114yes—
512C2×D8C22×D1114yes—
513C22×C8—111no—
514C22×C8—111no—
515C22×C8C22×D1111yescharacteristic
516C22×C8C22×D1111yescharacteristic
517C4⋊Q8—114no—
518C4⋊Q8—222no—
519#127—22no—
520#127—114no—
521#127—114no—
522#127—222no—
523#127—222no—
524#127C22×D1114yes—
525#126—228no—
526#126—228no—
527#124—22no—
528#124—114no—
529#124—222no—
530#124C22×D1114yes—
531C22⋊Q8—228no—
532#121—228no—
533#121—228no—
534#121—228no—
535C4×Q8—114no—
536C4×Q8—114no—
537C4×Q8—114no—
538C4×Q8—114no—
539C4×Q8—222no—
540C4×Q8—222no—
541C4×D4—114no—
542C4×D4—114no—
543C4×D4—114no—
544C4×D4—114no—
545C4×D4—222no—
546C4×D4—222no—
547C4×D4—222no—
548C4×D4—222no—
549#117—228no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—111no—
552C2×C4⋊C4—111no—
553C2×C4⋊C4—111no—
554C2×C4⋊C4—111no—
555C2×C4⋊C4—221no—
556C2×C4⋊C4—221no—
557C2×C4⋊C4—221no—
558C2×C4⋊C4—221no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—221no—
562C2×C22⋊C4—221no—
563C2×C22⋊C4—221no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—221no—
567C2×C42—111no—
568C2×C42—111no—
569C2×C42—221no—
570C2×C42—221no—
571C2×C42C22×D1111yescharacteristic
572#107—114no—
573C4⋊C8—114no—
574C4⋊C8—114no—
575C4⋊C8—114no—
576#103—114no—
577#103—114no—
578#102—114no—
579#102—114no—
580#102—114no—
581#102—114no—
582#97—114no—
583#97C22×D1114yes—
584C4×C8—114no—
585C2×C11—82no—
586C2×C11—82no—
587C2×C11—82no—
588C2×C11#339714yescomplemented
589C2×C11C2×#55011yescharacteristic
590C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
591C2×C11C2×#57711yescharacteristic
592D11—82no—
593C24—21no—
594C24—21no—
595C24—21no—
596C24—221no—
597#41—4432no—
598C2×Q8—21no—
599C2×Q8—22no—
600C2×Q8—22no—
601C2×Q8—114no—
602C2×Q8—112no—
603C2×Q8—224no—
604C2×Q8—221no—
605C2×Q8—222no—
606C2×Q8—222no—
607C2×Q8C23×D1112yes—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—44no—
620C2×D4—82no—
621C2×D4—112no—
622C2×D4—224no—
623C2×D4—224no—
624C2×D4—224no—
625C2×D4—224no—
626C2×D4—221no—
627C2×D4—222no—
628C2×D4—222no—
629C2×D4—444no—
630C2×D4—444no—
631C2×D4—882no—
632C2×D4—882no—
633C2×D4C23×D1112yes—
634C2×D4C23×D1112yes—
635C2×D4C23×D1112yes—
636C22×C4—21no—
637C22×C4—111no—
638C22×C4—111no—
639C22×C4—111no—
640C22×C4—111no—
641C22×C4—224no—
642C22×C4—224no—
643C22×C4—224no—
644C22×C4—221no—
645C22×C4—221no—
646C22×C4—221no—
647C22×C4—224no—
648C22×C4—444no—
649C22×C4—444no—
650C22×C4—444no—
651C22×C4—444no—
652C22×C4D4×D1111yescharacteristic
653C22×C4D4×D1111yescharacteristic
654C22×C4C23×D1111yescharacteristic
655SD16—28no—
656SD16—44no—
657SD16—228no—
658SD16—444no—
659SD16—444no—
660SD16—444no—
661D8—28no—
662D8—44no—
663D8—444no—
664C2×C8—22no—
665C2×C8—112no—
666C2×C8—112no—
667C2×C8—222no—
668C2×C8—222no—
669C2×C8#434114yescomplemented
670C2×C8C23×D1112yes—
671C2×C8C23×D1112yes—
672C4⋊C4—114no—
673C4⋊C4—114no—
674C4⋊C4—114no—
675C4⋊C4—112no—
676C4⋊C4—112no—
677C4⋊C4—224no—
678C4⋊C4—224no—
679C4⋊C4—224no—
680C4⋊C4—221no—
681C4⋊C4—221no—
682C4⋊C4—224no—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—224no—
686C22⋊C4—224no—
687C22⋊C4—224no—
688C22⋊C4—224no—
689C22⋊C4—224no—
690C22⋊C4—224no—
691C42—112no—
692C42—112no—
693C42—112no—
694C42—112no—
695C42—224no—
696C42—224no—
697C42D4×D1112yes—
698C42C23×D1112yes—
699C11C2×#339711yescharacteristic, complemented, Sylow
700C23—22no—
701C23—22no—
702C23—22no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—222no—
713C23—442no—
714C23—442no—
715C23—442no—
716C23C2×D4×D1111yescharacteristic
717Q8—22no—
718Q8—22no—
719Q8—42no—
720Q8—228no—
721Q8—222no—
722Q8—222no—
723Q8—442no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—22no—
728D4—22no—
729D4—22no—
730D4—48no—
731D4—42no—
732D4—42no—
733D4—42no—
734D4—84no—
735D4—222no—
736D4—222no—
737D4—448no—
738D4—448no—
739D4—442no—
740D4—884no—
741D4—884no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—42no—
746C2×C4—114no—
747C2×C4—112no—
748C2×C4—112no—
749C2×C4—112no—
750C2×C4—112no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—448no—
758C2×C4—448no—
759C2×C4—448no—
760C2×C4—448no—
761C2×C4—442no—
762C2×C4—442no—
763C2×C4—442no—
764C2×C4C2×D4×D1112yes—
765C2×C4C2×D4×D1112yes—
766C2×C4C2×D4×D1111yescharacteristic
767C2×C4C2×#434112yes—
768C2×C4#6703712yes—
769C2×C4C24×D1111yescharacteristic
770C8—22no—
771C8—222no—
772C8—222no—
773C8C2×#434114yescomplemented
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—84no—
784C22—84no—
785C22—84no—
786C22—442no—
787C22—442no—
788C22—442no—
789C22—884no—
790C22#1062324912yes—
791C22D11×AGL(1,ℤ/8)12yes—
792C22#1062330612yes—
793C22C22×D4×D1111yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—114no—
798C4—222no—
799C4—222no—
800C4—222no—
801C4—442no—
802C4—442no—
803C4—442no—
804C4#1062324912yes—
805C4C22×#434111yescharacteristic
806C4C2×#6703711yescharacteristic
807C2—82no—
808C2—82no—
809C2—82no—
810C2—882no—
811C2#1308163314yesdirect product factor
812C2C2×#1062324911yescharacteristic
813C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
814C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#496C2
socleC23×C11C22×D4
hypercenterC2×#496D11
hypocenterC11C2×#3397
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#496

Complements

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

NH ≅ G/Ntype
1. C2×#10623202C2semidirect
2. C2×#10623249C2semidirect
3. #13081633C2direct (N × H)
4. C2×#10622767C2semidirect
5. C2×#10622788C2semidirect
6. C2×#10622776C2semidirect
7. C2×#10622688C2semidirect
8. C2×#10622766C2semidirect
9. C2×#10622670C2semidirect
10. C2×#10622775C2semidirect
11. C2×#10622763C2semidirect
12. C2×#10622314C2semidirect
13. C2×#10622323C2semidirect
14. C2×#10622777C2semidirect
15. C2×D8×Dic11C2semidirect
16. C2×C11×#496C2semidirect
41. #10623249C22semidirect
43. #10623202C22semidirect
51. C11×#496C22semidirect
57. #10622788C22semidirect
58. #10622777C22semidirect
59. #10622776C22semidirect
60. #10622775C22semidirect
61. #10622767C22semidirect
62. #10622766C22semidirect
63. #10622763C22semidirect
64. D8×Dic11C22semidirect
72. #10622688C22semidirect
73. #10622670C22semidirect
75. #10622323C22semidirect
76. #10622314C22semidirect
254. C2×C8×C11#41semidirect
297. C2×#496D11semidirect
380. C8×C11C2×#41semidirect
418. #496C2×D11semidirect
588. C2×C11#3397semidirect
669. C2×C8#4341semidirect
699. C11C2×#3397semidirect
773. C8C2×#4341semidirect
811. C2#13081633direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232022
C2×#106232492
#130816332
C2×#106227672
C2×#106227882
C2×#106227762
C2×#106226882
C2×#106227662
C2×#106226702
C2×#106227752
C2×#106227632
C2×#106223142
C2×#106223232
C2×#106227772
C2×D8×Dic112
C2×C11×#4962
C2×#339711