Finite Group Databasebeta

← C2×#13081631 #15634724

Subgroups — C2×#13081631 #15634724

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×#10623099C211yesmaximal, characteristic, complemented
2C2×#10623249C211yesmaximal, characteristic, complemented
3#13081631C2116yesmaximal, direct product factor
4C2×#10622687C211yesmaximal, characteristic, complemented
5C2×#10622789C211yesmaximal, characteristic, complemented
6C2×#10622788C211yesmaximal, characteristic, complemented
7C2×#10622375C211yesmaximal, characteristic, complemented
8C2×#10622778C211yesmaximal, characteristic, complemented
9C2×#10622457C211yesmaximal, characteristic, complemented
10C2×#10622775C211yesmaximal, characteristic, complemented
11C2×#10622399C211yesmaximal, characteristic, complemented
12C2×#10622441C211yesmaximal, characteristic, complemented
13C2×#10622639C211yesmaximal, characteristic, complemented
14C2×#10622370C211yesmaximal, characteristic, complemented
15C2×#10622369C211yesmaximal, characteristic, complemented
16C2×C11×#460C211yesmaximal, characteristic, complemented
17C22×#4341—21no—
18C22×C11×SD16C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C2×C11×#127C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×#67000C2211yescharacteristic
23C2×#66997C2211yescharacteristic
24C22×#4325C2211yescharacteristic
25C2×#66993C2211yescharacteristic
26C2×#66993C2211yescharacteristic
27C2×#66992—21no—
28C2×#66992—21no—
29C2×#66991—21no—
30C2×D4×Dic11C2211yescharacteristic
31C2×D4×Dic11C2211yescharacteristic
32C22×#4324C2211yescharacteristic
33C22×#4324C2211yescharacteristic
34C22×#4323C2211yescharacteristic
35C22×#4323C2211yescharacteristic
36C22×D88C2211yescharacteristic
37C22×#4314C2211yescharacteristic
38#10623249—24no—
39#10623249C2218yescomplemented
40#10623099—24no—
41#10623099C2218yescomplemented
42C2×#66951—21no—
43C2×#66949—21no—
44C2×#66946C2211yescharacteristic
45C2×#66940C2211yescharacteristic
46C2×#66929—21no—
47C2×#66928C2211yescharacteristic
48C2×C4×D44C2211yescharacteristic
49C2×#66925—21no—
50C2×C4×Dic22C2211yescharacteristic
51C11×#460C2218yescomplemented
52C2×C11×C4⋊C8C2211yescharacteristic
53C2×C11×#102C2211yescharacteristic
54C2×C11×#102C2211yescharacteristic
55C2×#66899C2211yescharacteristic
56#10622789C2218yescomplemented
57#10622788C2218yescomplemented
58#10622778C2218yescomplemented
59#10622775C2218yescomplemented
60C2×#66885C2211yescharacteristic
61C2×#66880C2211yescharacteristic
62C2×#66879C2211yescharacteristic
63C2×Dic11⋊C8C2211yescharacteristic
64C2×Dic11⋊C8C2211yescharacteristic
65C2×C8×Dic11C2211yescharacteristic
66#10622687C2218yescomplemented
67#10622639C2218yescomplemented
68C2×#66873C2211yescharacteristic
69C2×#66871C2211yescharacteristic
70C2×#66867C2211yescharacteristic
71#10622457C2218yescomplemented
72#10622441C2218yescomplemented
73#10622399C2218yescomplemented
74#10622375C2218yescomplemented
75#10622370C2218yescomplemented
76#10622369C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11C2311yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C23×Dic11—21no—
87C23×Dic11—21no—
88C2×#4341—28no—
89C2×#4341—48no—
90C22×D44C2311yescharacteristic
91C22×D44C2311yescharacteristic
92C22×C4×D11—21no—
93C22×C4×D11—21no—
94C22×Dic22D411yescharacteristic
95C22×Dic22C2311yescharacteristic
96C2×C11×SD16—42no—
97C2×C11×SD16—42no—
98C2×C11×SD16C2314yes—
99C2×C11×SD16C2314yes—
100C22×C8×C11C2311yescharacteristic
101C22×C8×C11C2311yescharacteristic
102C11×#127—22no—
103C11×#127C2314yes—
104C4×Q8×C11—22no—
105C4×Q8×C11C2314yes—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C42×C11—21no—
109C2×C42×C11C2311yescharacteristic
110C2×C22⋊Dic11—21no—
111C2×C22⋊Dic11—21no—
112#67000—22no—
113#67000C2314yes—
114#66997—22no—
115#66997C2314yes—
116C2×#4325—24no—
117C2×#4325C2314yes—
118#66993—22no—
119#66993—22no—
120#66993C2314yes—
121#66993C2314yes—
122#66992—28no—
123#66992—28no—
124#66991—28no—
125D4×Dic11—22no—
126D4×Dic11—22no—
127D4×Dic11C2314yes—
128D4×Dic11C2314yes—
129C2×#4324—24no—
130C2×#4324—42no—
131C2×#4324C2314yes—
132C2×#4324C2314yes—
133C2×#4323—24no—
134C2×#4323—42no—
135C2×#4323C2314yes—
136C2×#4323C2314yes—
137C2×(C2×D11)⋊C4—21no—
138C2×(C2×D11)⋊C4—21no—
139C2×(C2×D11)⋊C4—21no—
140C2×(C2×D11)⋊C4—21no—
141C2×(C2×D11)⋊C4—21no—
142C2×(C2×D11)⋊C4—21no—
143C2×C4⋊Dic11D411yescharacteristic
144C2×C4⋊Dic11C2311yescharacteristic
145C2×Dic11⋊C4—21no—
146C2×Dic11⋊C4—21no—
147C2×Dic11⋊C4—21no—
148C2×Dic11⋊C4D411yescharacteristic
149C2×Dic11⋊C4D411yescharacteristic
150C2×C4×Dic11—21no—
151C2×C4×Dic11C2311yescharacteristic
152C2×C4×Dic11C2311yescharacteristic
153C22×C11⋊C8C2311yescharacteristic
154C22×C11⋊C8C2311yescharacteristic
155C2×D88—42no—
156C2×D88C2314yes—
157C2×#4314—42no—
158C2×#4314C2314yes—
159#66951—28no—
160#66949—28no—
161#66946—22no—
162#66946C2314yes—
163#66940—22no—
164#66940C2314yes—
165#66929—28no—
166#66928—22no—
167#66928C2314yes—
168C4×D44—22no—
169C4×D44C2314yes—
170#66925—28no—
171C4×Dic22D414yes—
172C4×Dic22C2314yes—
173C11×C4⋊C8C2314yes—
174C11×#102C2314yes—
175C11×#102C2314yes—
176#66899C2314yes—
177#66885C2314yes—
178#66880C2314yes—
179#66879C2314yes—
180Dic11⋊C8C2314yes—
181Dic11⋊C8C2314yes—
182C8×Dic11C2314yes—
183#66873C2314yes—
184#66871C2314yes—
185#66867C2314yes—
186C2×#3397—111nomaximal, Sylow
187C24×C11—21no—
188C24×C11—21no—
189C23×D11—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—24no—
198C2×D4×C11—24no—
199C2×D4×C11—22no—
200C2×D4×C11—22no—
201C2×D4×C11—22no—
202C2×D4×C11—22no—
203C2×D4×C11—44no—
204C2×D4×C11—82no—
205C2×D4×C11C2412yes—
206C2×D4×C11C2412yes—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2411yescharacteristic
212C2×C22⋊D11—24no—
213C2×C22⋊D11—24no—
214C2×C22⋊D11—24no—
215C2×C22⋊D11—24no—
216C2×C22⋊D11—44no—
217C2×C22⋊D11—44no—
218C2×C22⋊D11—82no—
219C2×C22⋊D11—82no—
220C22×Dic11—24no—
221C22×Dic11—24no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—44no—
225C22×Dic11—44no—
226C22×Dic11C2×D411yescharacteristic
227C22×Dic11C2×D411yescharacteristic
228C22×Dic11C2×D411yescharacteristic
229C22×Dic11C2×D411yescharacteristic
230#4341—432no—
231C2×D44—21no—
232C2×D44—21no—
233C2×D44—22no—
234C2×D44—22no—
235C2×D44—22no—
236C2×D44—22no—
237C2×D44C2412yes—
238C2×D44C2412yes—
239C2×C4×D11—24no—
240C2×C4×D11—24no—
241C2×C4×D11—44no—
242C2×C4×D11—44no—
243C2×Dic22—24no—
244C2×Dic22—21no—
245C2×Dic22—22no—
246C2×Dic22—22no—
247C2×Dic22C2×D414yes—
248C2×Dic22C2412yes—
249C11×SD16—44no—
250C11×SD16—44no—
251C2×C8×C11—22no—
252C2×C8×C11—22no—
253C2×C8×C11C2412yes—
254C2×C8×C11C2412yes—
255C11×C4⋊C4—21no—
256C11×C4⋊C4—24no—
257C11×C4⋊C4C2412yes—
258C42×C11—24no—
259C42×C11C2×D412yes—
260C42×C11C2412yes—
261C22⋊Dic11—24no—
262C22⋊Dic11—24no—
263#4325—28no—
264#4324—28no—
265#4324—44no—
266#4323—28no—
267#4323—44no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4—24no—
270(C2×D11)⋊C4—24no—
271(C2×D11)⋊C4—24no—
272(C2×D11)⋊C4—24no—
273(C2×D11)⋊C4—24no—
274C4⋊Dic11—21no—
275C4⋊Dic11C2×D414yes—
276C4⋊Dic11C2412yes—
277Dic11⋊C4—24no—
278Dic11⋊C4—24no—
279Dic11⋊C4—24no—
280Dic11⋊C4C2×D414yes—
281Dic11⋊C4C2×D414yes—
282C4×Dic11—24no—
283C4×Dic11C2×D412yes—
284C4×Dic11C2×D412yes—
285C4×Dic11C2412yes—
286C4×Dic11C2412yes—
287C2×C11⋊C8—22no—
288C2×C11⋊C8#4114yescomplemented
289C2×C11⋊C8C2412yes—
290C2×C11⋊C8C2412yes—
291D88—44no—
292#4314—44no—
293C2×#556—111no—
294C2×#550—111no—
295#3397—1116no—
296C2×#496—111no—
297C2×#496—111no—
298C2×#492—111no—
299C2×#460—111no—
300C2×#460D1111yescharacteristic, complemented
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—42no—
312C23×C11—42no—
313C23×C11—42no—
314C23×C11—42no—
315C23×C11—42no—
316C23×C11—42no—
317C23×C11C22×D411yescharacteristic
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—42no—
321C22×D11—42no—
322C22×D11—42no—
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—48no—
334D4×C11—42no—
335D4×C11—42no—
336D4×C11—84no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—42no—
342C2×C4×C11—42no—
343C2×C4×C11C22×D412yes—
344C2×C4×C11C22×D412yes—
345C2×C4×C11C22×D411yescharacteristic
346C2×C4×C11C2×#4112yes—
347C2×C4×C11H(5,𝔽2)12yes—
348C2×C4×C11C2511yescharacteristic
349C22⋊D11—48no—
350C22⋊D11—48no—
351C22⋊D11—84no—
352C22⋊D11—84no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—48no—
359C2×Dic11—42no—
360C2×Dic11—42no—
361C2×Dic11—48no—
362C2×Dic11AGL(1,ℤ/8)14yes—
363C2×Dic11C22×D412yes—
364C2×Dic11C22×D412yes—
365C2×Dic11C22×D412yes—
366C2×Dic11C22×D412yes—
367D44—22no—
368D44—22no—
369D44—22no—
370D44—22no—
371D44—42no—
372D44—42no—
373C4×D11—48no—
374C4×D11—48no—
375Dic22—28no—
376Dic22—22no—
377Dic22—22no—
378Dic22—42no—
379C8×C11—22no—
380C8×C11—22no—
381C11⋊C8—22no—
382C11⋊C8C2×#4114yescomplemented
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×D8—111no—
392C22×D8—111no—
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×#124—111no—
405C2×C22⋊Q8—221no—
406C2×#121—221no—
407C2×#121—221no—
408C2×#121—221no—
409C2×C4×Q8—111no—
410C2×C4×Q8—111no—
411C2×C4×Q8C2×D1111yescharacteristic
412C2×C4×D4—111no—
413C2×C4×D4—111no—
414C2×C4×D4—111no—
415C2×C4×D4—111no—
416C2×#117—221no—
417#496—118no—
418#496—118no—
419#492—118no—
420#463—118no—
421#463—118no—
422#461—118no—
423#460—118no—
424#460C2×D1118yescomplemented
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⋊C8C2×D1111yescharacteristic
434C2×#103—111no—
435C2×#103—111no—
436C2×#102—111no—
437C2×#102—111no—
438C2×#102C2×D1111yescharacteristic
439C2×#102C2×D1111yescharacteristic
440C2×#97—111no—
441C2×#97—111no—
442C2×C4×C8—111no—
443C22×C11—42no—
444C22×C11—42no—
445C22×C11—42no—
446C22×C11—42no—
447C22×C11—42no—
448C22×C11—42no—
449C22×C11—84no—
450C22×C11—84no—
451C22×C11#55012yes—
452C22×C11C2×AGL(1,ℤ/8)12yes—
453C22×C11#57712yes—
454C22×C11C23×D411yescharacteristic
455C2×D11—42no—
456C2×D11—42no—
457C2×D11—42no—
458C2×D11—42no—
459C2×D11—42no—
460C2×D11—42no—
461C2×D11—84no—
462C2×D11—84no—
463C4×C11—22no—
464C4×C11—22no—
465C4×C11—42no—
466C4×C11—42no—
467C4×C11#55012yes—
468C4×C11C22×#4111yescharacteristic
469C4×C11C2×H(5,𝔽2)11yescharacteristic
470Dic11—22no—
471Dic11—22no—
472Dic11—22no—
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—111no—
485C22×D4—221no—
486C22×D4—221no—
487C22×D4—221no—
488C22×D4—221no—
489C22×D4C22×D1111yescharacteristic
490C22×D4C22×D1111yescharacteristic
491C23×C4—221no—
492C23×C4—221no—
493C23×C4—221no—
494C23×C4—221no—
495C2×SD16—42no—
496C2×SD16—42no—
497C2×SD16—114no—
498C2×SD16—114no—
499C2×SD16—114no—
500C2×SD16—114no—
501C2×SD16—224no—
502C2×SD16—224no—
503C2×SD16—442no—
504C2×SD16—442no—
505C2×SD16C22×D1114yes—
506C2×SD16C22×D1114yes—
507C2×D8—114no—
508C2×D8—114no—
509C2×D8—114no—
510C2×D8—224no—
511C2×D8—442no—
512C2×D8—442no—
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—114no—
528#124—114no—
529#124—222no—
530#124—222no—
531C22⋊Q8—228no—
532#121—228no—
533#121—228no—
534#121—228no—
535C4×Q8—22no—
536C4×Q8—114no—
537C4×Q8—114no—
538C4×Q8—114no—
539C4×Q8—222no—
540C4×Q8C22×D1114yes—
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—21no—
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⋊C4C22×D1111yescharacteristic
559C2×C22⋊C4—221no—
560C2×C22⋊C4—221no—
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—21no—
568C2×C42—111no—
569C2×C42—111no—
570C2×C42—221no—
571C2×C42C22×D1111yescharacteristic
572#107—114no—
573C4⋊C8—114no—
574C4⋊C8—114no—
575C4⋊C8C22×D1114yes—
576#103—114no—
577#103—114no—
578#102—114no—
579#102—114no—
580#102C22×D1114yes—
581#102C22×D1114yes—
582#97—114no—
583#97—114no—
584C4×C8—114no—
585C2×C11—82no—
586C2×C11—82no—
587C2×C11#339714yescomplemented
588C2×C11C2×#55011yescharacteristic
589C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
590C2×C11C2×#57711yescharacteristic
591D11—82no—
592D11—82no—
593C24—21no—
594C24—21no—
595C24—221no—
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—24no—
611C2×D4—24no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—44no—
617C2×D4—82no—
618C2×D4—112no—
619C2×D4—112no—
620C2×D4—224no—
621C2×D4—224no—
622C2×D4—224no—
623C2×D4—224no—
624C2×D4—221no—
625C2×D4—221no—
626C2×D4—222no—
627C2×D4—222no—
628C2×D4—222no—
629C2×D4—222no—
630C2×D4—444no—
631C2×D4—444no—
632C2×D4—882no—
633C2×D4—882no—
634C2×D4C23×D1112yes—
635C2×D4C23×D1112yes—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—111no—
639C22×C4—111no—
640C22×C4—111no—
641C22×C4—111no—
642C22×C4—224no—
643C22×C4—224no—
644C22×C4—224no—
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—44no—
656SD16—44no—
657SD16—228no—
658SD16—228no—
659SD16—444no—
660SD16—444no—
661D8—228no—
662D8—444no—
663D8—444no—
664C2×C8—22no—
665C2×C8—22no—
666C2×C8—114no—
667C2×C8—112no—
668C2×C8—112no—
669C2×C8—222no—
670C2×C8C23×D1112yes—
671C2×C8C23×D1112yes—
672C4⋊C4—24no—
673C4⋊C4—21no—
674C4⋊C4—114no—
675C4⋊C4—114no—
676C4⋊C4—114no—
677C4⋊C4—112no—
678C4⋊C4—224no—
679C4⋊C4—224no—
680C4⋊C4—224no—
681C4⋊C4—221no—
682C4⋊C4C23×D1112yes—
683C22⋊C4—224no—
684C22⋊C4—224no—
685C22⋊C4—224no—
686C22⋊C4—224no—
687C22⋊C4—224no—
688C22⋊C4—224no—
689C22⋊C4—224no—
690C22⋊C4—224no—
691C42—24no—
692C42—112no—
693C42—112no—
694C42—112no—
695C42—112no—
696C42—224no—
697C42D4×D1112yes—
698C42C23×D1112yes—
699C11C2×#339711yescharacteristic, complemented, Sylow
700C23—22no—
701C23—22no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—222no—
709C23—222no—
710C23—442no—
711C23—442no—
712C23—442no—
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—48no—
729D4—42no—
730D4—42no—
731D4—84no—
732D4—222no—
733D4—222no—
734D4—222no—
735D4—222no—
736D4—448no—
737D4—448no—
738D4—442no—
739D4—442no—
740D4—884no—
741D4—884no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—114no—
749C2×C4—112no—
750C2×C4—112no—
751C2×C4—112no—
752C2×C4—112no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—448no—
759C2×C4—448no—
760C2×C4—448no—
761C2×C4—448no—
762C2×C4—442no—
763C2×C4—442no—
764C2×C4C2×D4×D1112yes—
765C2×C4C2×D4×D1112yes—
766C2×C4C2×D4×D1111yescharacteristic
767C2×C4#6703712yes—
768C2×C4#41×D1112yes—
769C2×C4C24×D1111yescharacteristic
770C8—22no—
771C8—22no—
772C8—114no—
773C8—222no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—84no—
781C22—84no—
782C22—442no—
783C22—442no—
784C22—442no—
785C22—442no—
786C22—442no—
787C22—442no—
788C22—884no—
789C22—884no—
790C22#1062313012yes—
791C22#1062329312yes—
792C22D11×AGL(1,ℤ/8)12yes—
793C22C22×D4×D1111yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—42no—
798C4—114no—
799C4—222no—
800C4—222no—
801C4—222no—
802C4—442no—
803C4—442no—
804C4#1062313012yes—
805C4C2×#6703711yescharacteristic
806C4C2×#41×D1111yescharacteristic
807C2—82no—
808C2—82no—
809C2—882no—
810C2—882no—
811C2#1308163114yesdirect product factor
812C2C2×#1062313011yescharacteristic
813C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
814C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#460C2
socleC23×C11C22×D4
hypercenterC2×#460D11
hypocenterC11C2×#3397
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
1. C2×#10623099C2semidirect
2. C2×#10623249C2semidirect
3. #13081631C2direct (N × H)
4. C2×#10622687C2semidirect
5. C2×#10622789C2semidirect
6. C2×#10622788C2semidirect
7. C2×#10622375C2semidirect
8. C2×#10622778C2semidirect
9. C2×#10622457C2semidirect
10. C2×#10622775C2semidirect
11. C2×#10622399C2semidirect
12. C2×#10622441C2semidirect
13. C2×#10622639C2semidirect
14. C2×#10622370C2semidirect
15. C2×#10622369C2semidirect
16. C2×C11×#460C2semidirect
39. #10623249C22semidirect
41. #10623099C22semidirect
51. C11×#460C22semidirect
56. #10622789C22semidirect
57. #10622788C22semidirect
58. #10622778C22semidirect
59. #10622775C22semidirect
66. #10622687C22semidirect
67. #10622639C22semidirect
71. #10622457C22semidirect
72. #10622441C22semidirect
73. #10622399C22semidirect
74. #10622375C22semidirect
75. #10622370C22semidirect
76. #10622369C22semidirect
288. C2×C11⋊C8#41semidirect
300. C2×#460D11semidirect
382. C11⋊C8C2×#41semidirect
424. #460C2×D11semidirect
587. C2×C11#3397semidirect
699. C11C2×#3397semidirect
811. C2#13081631direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230992
C2×#106232492
#130816312
C2×#106226872
C2×#106227892
C2×#106227882
C2×#106223752
C2×#106227782
C2×#106224572
C2×#106227752
C2×#106223992
C2×#106224412
C2×#106226392
C2×#106223702
C2×#106223692
C2×C11×#4602
C2×#339711