Finite Group Databasebeta

← C2×#13079721 #15625166

Subgroups — C2×#13079721 #15625166

Order 2816.

2086 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623134C211yesmaximal, characteristic, complemented
2C2×#10623356C211yesmaximal, characteristic, complemented
3#13079721C2116yesmaximal, direct product factor
4C2×#10622780C211yesmaximal, characteristic, complemented
5C2×#10622768C211yesmaximal, characteristic, complemented
6C2×#10622378C211yesmaximal, characteristic, complemented
7C2×#10622405C211yesmaximal, characteristic, complemented
8C2×#10622380C211yesmaximal, characteristic, complemented
9C2×#10622406C211yesmaximal, characteristic, complemented
10C2×#10622766C211yesmaximal, characteristic, complemented
11C2×#10622775C211yesmaximal, characteristic, complemented
12C2×#10622852C211yesmaximal, characteristic, complemented
13C2×#10622352C211yesmaximal, characteristic, complemented
14C2×#10622653C211yesmaximal, characteristic, complemented
15C2×#10622333C211yesmaximal, characteristic, complemented
16C2×C11×#449C211yesmaximal, characteristic
17C22×C11×#41C2211yescharacteristic
18C23×Dic22C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22#10623356—24no—
23#10623356C2218yescomplemented
24C2×#66997C2211yescharacteristic
25C2×#66997C2211yescharacteristic
26C22×#4326C2211yescharacteristic
27C2×#66989—21no—
28C2×#66989C2211yescharacteristic
29C2×#66989C2211yescharacteristic
30C2×#66989C2211yescharacteristic
31C2×#66988—21no—
32C2×#66988—21no—
33C2×#66988—21no—
34C2×D4×Dic11C2211yescharacteristic
35C22×#4324C2211yescharacteristic
36C22×#4324C2211yescharacteristic
37C22×#4324C2211yescharacteristic
38C2×#66979C2211yescharacteristic
39C2×#66977—21no—
40C2×#66977—21no—
41C2×#66977C2211yescharacteristic
42C22×Dic44C2211yescharacteristic
43C22×Dic44C2211yescharacteristic
44#10623134—24no—
45#10623134C2218yescomplemented
46C2×#66941C2211yescharacteristic
47C2×#66940C2211yescharacteristic
48C2×#66932—21no—
49C2×#66931—21no—
50C11×#449C2218yes—
51C2×C11×#103C2211yescharacteristic
52C2×C11×#102C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic
54#10622852C2218yescomplemented
55C2×#66899C2211yescharacteristic
56C2×#66896C2211yescharacteristic
57C2×C22⋊(C11⋊C8)C2211yescharacteristic
58#10622780C2218yescomplemented
59#10622775C2218yescomplemented
60#10622768C2218yescomplemented
61#10622766C2218yescomplemented
62C2×#66880C2211yescharacteristic
63C2×#66880C2211yescharacteristic
64C2×#66879C2211yescharacteristic
65C2×Dic11⋊C8C2211yescharacteristic
66C2×Dic11⋊C8C2211yescharacteristic
67C2×C8×Dic11C2211yescharacteristic
68#10622653C2218yescomplemented
69C2×#66874C2211yescharacteristic
70C2×#66874C2211yescharacteristic
71#10622406C2218yescomplemented
72#10622405C2218yescomplemented
73#10622380C2218yescomplemented
74#10622378C2218yescomplemented
75#10622352C2218yescomplemented
76#10622333C2218yescomplemented
77C2×C11×#41—22no—
78C2×C11×#41—42no—
79C2×C11×#41—42no—
80C2×C11×#41C2314yes—
81C22×Q8×C11C2311yescharacteristic
82C22×D4×C11—21no—
83C22×D4×C11—21no—
84C22×D4×C11C2311yescharacteristic
85C22×D4×C11C2311yescharacteristic
86C23×C4×C11—21no—
87C23×C4×C11C2311yescharacteristic
88C23×Dic11—21no—
89C23×Dic11—21no—
90C22×Dic22—21no—
91C22×Dic22—22no—
92C22×Dic22—21no—
93C22×Dic22—42no—
94C22×Dic22—42no—
95C22×Dic22C2311yescharacteristic
96C22×Dic22C2311yescharacteristic
97C22×Dic22C2311yescharacteristic
98C22×Dic22C2314yes—
99C2×C11×SD16—42no—
100C2×C11×SD16C2314yes—
101C2×C11×D8—42no—
102C2×C11×D8C2314yes—
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C11×#121—22no—
106C11×#121C2314yes—
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C22⋊C4—21no—
109C2×C22⋊Dic11—21no—
110C2×C22⋊Dic11—21no—
111C2×C22⋊Dic11—21no—
112C2×C22⋊Dic11—21no—
113C2×C22⋊Dic11—21no—
114C2×C22⋊Dic11—21no—
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11—21no—
117C2×C22⋊Dic11D411yescharacteristic
118C2×C22⋊Dic11D411yescharacteristic
119#66997—22no—
120#66997—22no—
121#66997C2314yes—
122#66997C2314yes—
123C2×#4326—42no—
124C2×#4326C2314yes—
125#66989—28no—
126#66989—22no—
127#66989—22no—
128#66989—22no—
129#66989C2314yes—
130#66989C2314yes—
131#66989C2314yes—
132#66988—28no—
133#66988—28no—
134#66988—28no—
135D4×Dic11—22no—
136D4×Dic11C2314yes—
137C2×#4324—42no—
138C2×#4324—42no—
139C2×#4324—42no—
140C2×#4324C2314yes—
141C2×#4324C2314yes—
142C2×#4324C2314yes—
143#66979D414yes—
144#66979C2314yes—
145C2×C4⋊Dic11D411yescharacteristic
146C2×C4⋊Dic11D411yescharacteristic
147C2×C4⋊Dic11C2311yescharacteristic
148#66977—22no—
149#66977—28no—
150#66977—28no—
151#66977C2314yes—
152C2×Dic11⋊C4—21no—
153C2×Dic11⋊C4—21no—
154C2×Dic11⋊C4—21no—
155C2×Dic11⋊C4—21no—
156C2×Dic11⋊C4—21no—
157C2×Dic11⋊C4—21no—
158C2×Dic11⋊C4—21no—
159C2×C4×Dic11—21no—
160C2×C4×Dic11C2311yescharacteristic
161C2×C4×Dic11C2311yescharacteristic
162C22×C11⋊C8C2311yescharacteristic
163C22×C11⋊C8C2311yescharacteristic
164C2×Dic44—42no—
165C2×Dic44—42no—
166C2×Dic44C2314yes—
167C2×Dic44C2314yes—
168#66941—22no—
169#66941C2314yes—
170#66940—22no—
171#66940C2314yes—
172#66932—28no—
173#66931—28no—
174C11×#103C2314yes—
175C11×#102C2314yes—
176C11×C22⋊C8C2314yes—
177#66899C2314yes—
178#66896C2314yes—
179C22⋊(C11⋊C8)C2314yes—
180#66880C2314yes—
181#66880C2314yes—
182#66879C2314yes—
183Dic11⋊C8C2314yes—
184Dic11⋊C8C2314yes—
185C8×Dic11C2314yes—
186#66874C2314yes—
187#66874C2314yes—
188C2×#3225—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11—21no—
191C24×C11C2×D411yescharacteristic
192C11×#41—44no—
193C11×#41—44no—
194C11×#41—48no—
195C2×Q8×C11—21no—
196C2×Q8×C11—22no—
197C2×Q8×C11—22no—
198C2×Q8×C11C2412yes—
199C2×D4×C11—24no—
200C2×D4×C11—24no—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—22no—
204C2×D4×C11—22no—
205C2×D4×C11—22no—
206C2×D4×C11—22no—
207C2×D4×C11—44no—
208C2×D4×C11—82no—
209C2×D4×C11C2412yes—
210C2×D4×C11C2412yes—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—24no—
216C22×C4×C11—44no—
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D412yes—
219C22×C4×C11C2412yes—
220C22×C4×C11C2411yescharacteristic
221C22×Dic11—24no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—24no—
227C22×Dic11—44no—
228C22×Dic11—82no—
229C22×Dic11C2×D411yescharacteristic
230C22×Dic11C2×D411yescharacteristic
231C22×Dic11C2×D411yescharacteristic
232C22×Dic11C2×D411yescharacteristic
233C2×Dic22—24no—
234C2×Dic22—21no—
235C2×Dic22—24no—
236C2×Dic22—21no—
237C2×Dic22—21no—
238C2×Dic22—22no—
239C2×Dic22—22no—
240C2×Dic22—22no—
241C2×Dic22—22no—
242C2×Dic22—22no—
243C2×Dic22—22no—
244C2×Dic22—44no—
245C2×Dic22—44no—
246C2×Dic22—44no—
247C2×Dic22—48no—
248C2×Dic22—82no—
249C2×Dic22C2412yes—
250C2×Dic22C2412yes—
251C2×Dic22C2412yes—
252C11×SD16—44no—
253C11×D8—44no—
254C2×C8×C11—22no—
255C2×C8×C11—22no—
256C2×C8×C11C2412yes—
257C2×C8×C11C2412yes—
258C11×C4⋊C4—21no—
259C11×C4⋊C4C2412yes—
260C11×C22⋊C4—24no—
261C22⋊Dic11—24no—
262C22⋊Dic11—24no—
263C22⋊Dic11—24no—
264C22⋊Dic11—24no—
265C22⋊Dic11—24no—
266C22⋊Dic11—24no—
267C22⋊Dic11—24no—
268C22⋊Dic11—24no—
269C22⋊Dic11C2×D414yes—
270C22⋊Dic11C2×D414yes—
271#4326—44no—
272#4324—44no—
273#4324—44no—
274#4324—44no—
275C4⋊Dic11—21no—
276C4⋊Dic11C2×D414yes—
277C4⋊Dic11C2×D414yes—
278C4⋊Dic11C2412yes—
279Dic11⋊C4—24no—
280Dic11⋊C4—24no—
281Dic11⋊C4—24no—
282Dic11⋊C4—24no—
283Dic11⋊C4—24no—
284Dic11⋊C4—24no—
285Dic11⋊C4—24no—
286C4×Dic11—24no—
287C4×Dic11C2×D412yes—
288C4×Dic11C2×D412yes—
289C4×Dic11C2412yes—
290C4×Dic11C2412yes—
291C2×C11⋊C8—22no—
292C2×C11⋊C8—22no—
293C2×C11⋊C8C2412yes—
294C2×C11⋊C8C2412yes—
295Dic44—44no—
296Dic44—44no—
297C2×#542—111no—
298C2×#536—111no—
299#3225—1116no—
300C2×#497—111no—
301C2×#495—111no—
302C2×#489—111no—
303C2×#487—111no—
304C2×#464—111no—
305C2×#462—111no—
306C2×#463—111no—
307C2×#461—111no—
308C2×#452—111no—
309C2×#449D1111yescharacteristic
310C2×#451—111no—
311C2×#448—111no—
312C2×#433—111no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—42no—
319C23×C11—42no—
320C23×C11—42no—
321C23×C11—42no—
322C23×C11—42no—
323C23×C11—42no—
324C23×C11C22×D412yes—
325C23×C11C22×D411yescharacteristic
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—24no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—48no—
344C2×C4×C11—42no—
345C2×C4×C11—42no—
346C2×C4×C11C22×D412yes—
347C2×C4×C11C22×D411yescharacteristic
348C2×C4×C11H(5,𝔽2)12yes—
349C2×C4×C11H(5,𝔽2)12yes—
350C2×C4×C11C2511yescharacteristic
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—48no—
360C2×Dic11—42no—
361C2×Dic11—42no—
362C2×Dic11—42no—
363C2×Dic11—42no—
364C2×Dic11—84no—
365C2×Dic11C22×D412yes—
366C2×Dic11C22×D412yes—
367C2×Dic11C22×D412yes—
368C2×Dic11C22×D412yes—
369Dic22—22no—
370Dic22—22no—
371Dic22—22no—
372Dic22—22no—
373Dic22—22no—
374Dic22—22no—
375Dic22—48no—
376Dic22—42no—
377Dic22—42no—
378Dic22—42no—
379Dic22—84no—
380C8×C11—22no—
381C8×C11—22no—
382C11⋊C8—22no—
383C11⋊C8—22no—
384C22×#41C2×D1111yescharacteristic
385C23×Q8—111no—
386C22×Q16—111no—
387C22×Q16—111no—
388C22×Q16—111no—
389C22×SD16—111no—
390C22×SD16—111no—
391C22×SD16—111no—
392C22×SD16C2×D1111yescharacteristic
393C22×D8C2×D1111yescharacteristic
394#542—118no—
395#542—224no—
396#536—118no—
397#536—224no—
398C2×C4⋊Q8—111no—
399C2×C4⋊Q8—111no—
400C2×C4⋊Q8—111no—
401C2×#126—221no—
402C2×#124—111no—
403C2×#124—111no—
404C2×#124—111no—
405C2×#124—221no—
406C2×#123—221no—
407C2×#123—221no—
408C2×#123—221no—
409C2×C22⋊Q8—111no—
410C2×C22⋊Q8—221no—
411C2×C22⋊Q8—221no—
412C2×C22⋊Q8—221no—
413C2×#121C2×D1111yescharacteristic
414C2×C4×Q8—111no—
415C2×C4×D4—111no—
416C2×#117—111no—
417#497—118no—
418#495—118no—
419#489—118no—
420#487—118no—
421#464—118no—
422#463—118no—
423#462—118no—
424#461—118no—
425#452—118no—
426#451—118no—
427#449C2×D1118yes—
428#448—118no—
429#433—118no—
430C2×C4⋊C8—111no—
431C2×C4⋊C8—111no—
432C2×#103—111no—
433C2×#103—111no—
434C2×#103—111no—
435C2×#103—111no—
436C2×#103—111no—
437C2×#103C2×D1111yescharacteristic
438C2×#102—111no—
439C2×#102C2×D1111yescharacteristic
440C2×C22⋊C8—111no—
441C2×C22⋊C8C2×D1111yescharacteristic
442C2×#97—111no—
443C2×C4×C8—111no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—22no—
447C22×C11—44no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—84no—
455C22×C11—84no—
456C22×C11#53512yes—
457C22×C11#57712yes—
458C22×C11#57812yes—
459C22×C11C23×D411yescharacteristic
460C4×C11—22no—
461C4×C11—42no—
462C4×C11—42no—
463C4×C11#53512yes—
464C4×C11C2×H(5,𝔽2)11yescharacteristic
465C4×C11C2×H(5,𝔽2)11yescharacteristic
466Dic11—22no—
467Dic11—22no—
468Dic11—22no—
469Dic11—22no—
470Dic11—42no—
471Dic11—42no—
472Dic11—42no—
473Dic11—42no—
474C2×#41—22no—
475C2×#41—42no—
476C2×#41—42no—
477C2×#41C22×D1114yes—
478C22×Q8—111no—
479C22×Q8—111no—
480C22×Q8—111no—
481C22×Q8—114no—
482C22×Q8—221no—
483C22×Q8—221no—
484C22×Q8—222no—
485C22×Q8—442no—
486C22×Q8—442no—
487C22×Q8C22×D1111yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4C22×D1111yescharacteristic
491C22×D4C22×D1111yescharacteristic
492C23×C4—21no—
493C23×C4—221no—
494C23×C4—221no—
495C23×C4C22×D1111yescharacteristic
496C2×Q16—114no—
497C2×Q16—114no—
498C2×Q16—114no—
499C2×Q16—442no—
500C2×Q16—442no—
501C2×Q16—442no—
502C2×SD16—42no—
503C2×SD16—114no—
504C2×SD16—114no—
505C2×SD16—114no—
506C2×SD16—442no—
507C2×SD16—442no—
508C2×SD16—442no—
509C2×SD16C22×D1114yes—
510C2×D8—42no—
511C2×D8C22×D1114yes—
512C22×C8—111no—
513C22×C8—111no—
514C22×C8C22×D1111yescharacteristic
515C22×C8C22×D1111yescharacteristic
516C4⋊Q8—114no—
517C4⋊Q8—114no—
518C4⋊Q8—114no—
519C4⋊Q8—222no—
520C4⋊Q8—222no—
521C4⋊Q8—222no—
522#126—228no—
523#124—114no—
524#124—114no—
525#124—114no—
526#124—222no—
527#124—222no—
528#124—222no—
529#124—228no—
530#123—228no—
531#123—228no—
532#123—228no—
533C22⋊Q8—114no—
534C22⋊Q8—228no—
535C22⋊Q8—228no—
536C22⋊Q8—228no—
537C22⋊Q8—222no—
538#121—22no—
539#121C22×D1114yes—
540C4×Q8—114no—
541C4×Q8—222no—
542C4×D4—114no—
543C4×D4—222no—
544#117—114no—
545#117—114no—
546C2×C4⋊C4—111no—
547C2×C4⋊C4—111no—
548C2×C4⋊C4—111no—
549C2×C4⋊C4—221no—
550C2×C4⋊C4—221no—
551C2×C4⋊C4—221no—
552C2×C4⋊C4—221no—
553C2×C4⋊C4—221no—
554C2×C4⋊C4—221no—
555C2×C4⋊C4—221no—
556C2×C4⋊C4C22×D1111yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—111no—
559C2×C22⋊C4—111no—
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×C22⋊C4—221no—
568C2×C42—111no—
569C2×C42—111no—
570C2×C42—221no—
571C4⋊C8—114no—
572C4⋊C8—114no—
573#103—114no—
574#103—114no—
575#103—114no—
576#103—114no—
577#103—114no—
578#103C22×D1114yes—
579#102—114no—
580#102C22×D1114yes—
581C22⋊C8—114no—
582C22⋊C8C22×D1114yes—
583#97—114no—
584C4×C8—114no—
585C2×C11—42no—
586C2×C11—82no—
587C2×C11—82no—
588C2×C11#322514yescomplemented
589C2×C11C2×#53511yescharacteristic
590C2×C11C2×#57711yescharacteristic
591C2×C11C2×#57811yescharacteristic
592C24—21no—
593C24—21no—
594C24D4×D1111yescharacteristic
595#41—44no—
596#41—44no—
597#41—48no—
598C2×Q8—21no—
599C2×Q8—22no—
600C2×Q8—22no—
601C2×Q8—112no—
602C2×Q8—112no—
603C2×Q8—112no—
604C2×Q8—224no—
605C2×Q8—221no—
606C2×Q8—224no—
607C2×Q8—221no—
608C2×Q8—221no—
609C2×Q8—222no—
610C2×Q8—222no—
611C2×Q8—222no—
612C2×Q8—222no—
613C2×Q8—222no—
614C2×Q8—222no—
615C2×Q8—444no—
616C2×Q8—444no—
617C2×Q8—444no—
618C2×Q8—448no—
619C2×Q8—882no—
620C2×Q8C23×D1112yes—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—22no—
629C2×D4—44no—
630C2×D4—82no—
631C2×D4C23×D1112yes—
632C2×D4C23×D1112yes—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—24no—
638C22×C4—44no—
639C22×C4—111no—
640C22×C4—111no—
641C22×C4—111no—
642C22×C4—111no—
643C22×C4—224no—
644C22×C4—224no—
645C22×C4—221no—
646C22×C4—221no—
647C22×C4—221no—
648C22×C4—221no—
649C22×C4—444no—
650C22×C4—882no—
651C22×C4D4×D1112yes—
652C22×C4D4×D1111yescharacteristic
653C22×C4C23×D1112yes—
654C22×C4C23×D1111yescharacteristic
655Q16—444no—
656Q16—444no—
657Q16—444no—
658SD16—44no—
659SD16—444no—
660SD16—444no—
661SD16—444no—
662D8—44no—
663C2×C8—22no—
664C2×C8—22no—
665C2×C8—112no—
666C2×C8—112no—
667C2×C8—222no—
668C2×C8—222no—
669C2×C8C23×D1112yes—
670C2×C8C23×D1112yes—
671C4⋊C4—21no—
672C4⋊C4—114no—
673C4⋊C4—114no—
674C4⋊C4—112no—
675C4⋊C4—224no—
676C4⋊C4—224no—
677C4⋊C4—224no—
678C4⋊C4—224no—
679C4⋊C4—224no—
680C4⋊C4—224no—
681C4⋊C4—221no—
682C4⋊C4—224no—
683C4⋊C4C23×D1112yes—
684C22⋊C4—24no—
685C22⋊C4—114no—
686C22⋊C4—114no—
687C22⋊C4—224no—
688C22⋊C4—224no—
689C22⋊C4—224no—
690C22⋊C4—224no—
691C22⋊C4—224no—
692C22⋊C4—224no—
693C22⋊C4—224no—
694C22⋊C4—224no—
695C42—112no—
696C42—112no—
697C42—112no—
698C42—112no—
699C42—224no—
700C11C2×#322511yescharacteristic, complemented, Sylow
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23C2×D4×D1112yes—
713C23C2×D4×D1111yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—222no—
718Q8—222no—
719Q8—222no—
720Q8—222no—
721Q8—222no—
722Q8—222no—
723Q8—448no—
724Q8—442no—
725Q8—442no—
726Q8—442no—
727Q8—884no—
728D4—22no—
729D4—22no—
730D4—22no—
731D4—22no—
732D4—48no—
733D4—42no—
734D4—42no—
735D4—84no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—48no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—112no—
746C2×C4—112no—
747C2×C4—112no—
748C2×C4—112no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—448no—
758C2×C4—442no—
759C2×C4—442no—
760C2×C4—442no—
761C2×C4—442no—
762C2×C4—884no—
763C2×C4C2×D4×D1112yes—
764C2×C4C2×D4×D1111yescharacteristic
765C2×C4#6703712yes—
766C2×C4#6703712yes—
767C2×C4C24×D1111yescharacteristic
768C8—22no—
769C8—22no—
770C8—222no—
771C8—222no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—44no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—84no—
783C22—84no—
784C22#1062312312yes—
785C22#1062330212yes—
786C22#1062330612yes—
787C22C22×D4×D1111yescharacteristic
788C4—22no—
789C4—42no—
790C4—42no—
791C4—222no—
792C4—222no—
793C4—222no—
794C4—222no—
795C4—442no—
796C4—442no—
797C4—442no—
798C4—442no—
799C4#1062312312yes—
800C4C2×#6703711yescharacteristic
801C4C2×#6703711yescharacteristic
802C2—42no—
803C2—82no—
804C2—82no—
805C2#1307972114yesdirect product factor
806C2C2×#1062312311yescharacteristic
807C2C2×#1062330611yescharacteristic
808C2C2×#1062330211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#449C2
socleC23×C11C22×D4
hypercenterC2×#449D11
hypocenterC11C2×#3225
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#10623134C2semidirect
2. C2×#10623356C2semidirect
3. #13079721C2direct (N × H)
4. C2×#10622780C2semidirect
5. C2×#10622768C2semidirect
6. C2×#10622378C2semidirect
7. C2×#10622405C2semidirect
8. C2×#10622380C2semidirect
9. C2×#10622406C2semidirect
10. C2×#10622766C2semidirect
11. C2×#10622775C2semidirect
12. C2×#10622852C2semidirect
13. C2×#10622352C2semidirect
14. C2×#10622653C2semidirect
15. C2×#10622333C2semidirect
23. #10623356C22semidirect
45. #10623134C22semidirect
54. #10622852C22semidirect
58. #10622780C22semidirect
59. #10622775C22semidirect
60. #10622768C22semidirect
61. #10622766C22semidirect
68. #10622653C22semidirect
71. #10622406C22semidirect
72. #10622405C22semidirect
73. #10622380C22semidirect
74. #10622378C22semidirect
75. #10622352C22semidirect
76. #10622333C22semidirect
588. C2×C11#3225semidirect
700. C11C2×#3225semidirect
805. C2#13079721direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231342
C2×#106233562
#130797212
C2×#106227802
C2×#106227682
C2×#106223782
C2×#106224052
C2×#106223802
C2×#106224062
C2×#106227662
C2×#106227752
C2×#106228522
C2×#106223522
C2×#106226532
C2×#106223332
C2×C11×#4492
C2×#322511