Finite Group Databasebeta

← C2×#13079726 #15625169

Subgroups — C2×#13079726 #15625169

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×#10623264C211yesmaximal, characteristic, complemented
2C2×#10623206C211yesmaximal, characteristic, complemented
3#13079726C2116yesmaximal, direct product factor
4C2×#10622328C211yesmaximal, characteristic, complemented
5C2×#10622672C211yesmaximal, characteristic, complemented
6C2×#10622706C211yesmaximal, characteristic, complemented
7C2×#10622380C211yesmaximal, characteristic, complemented
8C2×#10622406C211yesmaximal, characteristic, complemented
9C2×#10622400C211yesmaximal, characteristic, complemented
10C2×#10622431C211yesmaximal, characteristic, complemented
11C2×#10622396C211yesmaximal, characteristic, complemented
12C2×#10622394C211yesmaximal, characteristic
13C2×#10622421C211yesmaximal, characteristic, complemented
14C2×#10622419C211yesmaximal, characteristic, complemented
15C2×#10622322C211yesmaximal, characteristic, complemented
16C2×C11×#489C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2211yescharacteristic
18C22×#4341C2211yescharacteristic
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C11×#124C2211yescharacteristic
21C2×#67000—21no—
22C2×#66999—21no—
23C2×#66997C2211yescharacteristic
24C22×#4326C2211yescharacteristic
25C22×#4325C2211yescharacteristic
26C2×#66989C2211yescharacteristic
27C22×#4324C2211yescharacteristic
28C22×#4323C2211yescharacteristic
29C22×Dic44C2211yescharacteristic
30C22×Dic44C2211yescharacteristic
31C22×#4314C2211yescharacteristic
32C22×#4314C2211yescharacteristic
33#10623264—24no—
34#10623264C2218yescomplemented
35#10623206—24no—
36#10623206C2218yescomplemented
37C2×#66951—21no—
38C2×#66950C2211yescharacteristic
39C2×#66948C2211yescharacteristic
40C2×#66947—21no—
41C2×#66946C2211yescharacteristic
42C2×#66940C2211yescharacteristic
43C2×#66936—21no—
44C2×#66936—21no—
45C2×#66931—21no—
46C2×#66931—21no—
47C2×#66928C2211yescharacteristic
48C2×#66925C2211yescharacteristic
49C2×#66922C2211yescharacteristic
50C11×#489C2218yescomplemented
51C2×C11×#103C2211yescharacteristic
52C2×C11×#103C2211yescharacteristic
53C2×C11×#102C2211yescharacteristic
54C2×C11×#102C2211yescharacteristic
55C2×C11×#97C2211yescharacteristic
56C2×(C2×D11)⋊C8C2211yescharacteristic
57C2×(C2×D11)⋊C8C2211yescharacteristic
58C2×Dic11⋊C8C2211yescharacteristic
59C2×Dic11⋊C8C2211yescharacteristic
60#10622706C2218yescomplemented
61#10622672C2218yescomplemented
62C2×#66874C2211yescharacteristic
63C2×#66874C2211yescharacteristic
64C2×#66874C2211yescharacteristic
65C2×#66874C2211yescharacteristic
66C2×C4×C11⋊C8C2211yescharacteristic
67#10622431C2218yescomplemented
68#10622421C2218yescomplemented
69#10622419C2218yescomplemented
70#10622406C2218yescomplemented
71#10622400C2218yescomplemented
72#10622396C2218yescomplemented
73#10622394C2218yes—
74#10622380C2218yescomplemented
75#10622328C2218yescomplemented
76#10622322C2218yescomplemented
77C22×Q8×C11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11C2311yescharacteristic
80C22×C22⋊D11—21no—
81C23×Dic11—21no—
82C2×Q8×D11—22no—
83C2×Q8×D11—42no—
84C2×Q8×D11—42no—
85C2×Q8×D11C2314yes—
86C2×#4341—22no—
87C2×#4341—42no—
88C2×#4341—42no—
89C2×#4341C2314yes—
90C22×D44—21no—
91C22×D44C2311yescharacteristic
92C22×C4×D11—21no—
93C22×C4×D11—21no—
94C22×C4×D11C2311yescharacteristic
95C22×Dic22—21no—
96C22×Dic22C2311yescharacteristic
97C22×Dic22C2311yescharacteristic
98C22×Dic22C2311yescharacteristic
99C22×C8×C11C2311yescharacteristic
100C22×C8×C11C2311yescharacteristic
101C11×C4⋊Q8—22no—
102C11×C4⋊Q8C2314yes—
103C11×#124—22no—
104C11×#124C2314yes—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C42×C11C2311yescharacteristic
111C2×C22⋊Dic11—21no—
112C2×C22⋊Dic11—21no—
113#67000—28no—
114#66999—28no—
115#66997—22no—
116#66997C2314yes—
117C2×#4326—42no—
118C2×#4326C2314yes—
119C2×#4325—42no—
120C2×#4325C2314yes—
121#66989—22no—
122#66989C2314yes—
123C2×#4324—42no—
124C2×#4324C2314yes—
125C2×#4323—42no—
126C2×#4323C2314yes—
127C2×(C2×D11)⋊C4—21no—
128C2×(C2×D11)⋊C4—21no—
129C2×(C2×D11)⋊C4—21no—
130C2×(C2×D11)⋊C4—21no—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4D411yescharacteristic
133C2×(C2×D11)⋊C4D411yescharacteristic
134C2×C4⋊Dic11—21no—
135C2×C4⋊Dic11—21no—
136C2×C4⋊Dic11—21no—
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4D411yescharacteristic
141C2×Dic11⋊C4D411yescharacteristic
142C2×C4×Dic11—21no—
143C2×C4×Dic11C2311yescharacteristic
144C22×C11⋊C8C2311yescharacteristic
145C22×C11⋊C8C2311yescharacteristic
146C2×Dic44—42no—
147C2×Dic44—42no—
148C2×Dic44C2314yes—
149C2×Dic44C2314yes—
150C2×#4314—42no—
151C2×#4314—42no—
152C2×#4314C2314yes—
153C2×#4314C2314yes—
154#66951—28no—
155#66950—22no—
156#66950C2314yes—
157#66948—22no—
158#66948C2314yes—
159#66947—28no—
160#66946—22no—
161#66946C2314yes—
162#66940—22no—
163#66940C2314yes—
164#66936—28no—
165#66936—28no—
166#66931—28no—
167#66931—28no—
168#66928—22no—
169#66928C2314yes—
170#66925D414yes—
171#66925C2314yes—
172#66922—22no—
173#66922C2314yes—
174C11×#103C2314yes—
175C11×#103C2314yes—
176C11×#102C2314yes—
177C11×#102C2314yes—
178C11×#97C2314yes—
179(C2×D11)⋊C8C2314yes—
180(C2×D11)⋊C8C2314yes—
181Dic11⋊C8C2314yes—
182Dic11⋊C8C2314yes—
183#66874C2314yes—
184#66874C2314yes—
185#66874C2314yes—
186#66874C2314yes—
187C4×C11⋊C8C2314yes—
188C2×#3225—111nomaximal, Sylow
189C24×C11—21no—
190C23×D11—21no—
191C23×D11C2×D411yescharacteristic
192C2×Q8×C11—21no—
193C2×Q8×C11—24no—
194C2×Q8×C11—22no—
195C2×Q8×C11—22no—
196C2×Q8×C11—82no—
197C2×Q8×C11C2412yes—
198C2×D4×C11—21no—
199C2×D4×C11—22no—
200C2×D4×C11—22no—
201C2×D4×C11C2412yes—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2411yescharacteristic
208C2×C22⋊D11—24no—
209C2×C22⋊D11—44no—
210C22×Dic11—24no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—44no—
215C22×Dic11C2×D411yescharacteristic
216C22×Dic11C2×D411yescharacteristic
217C22×Dic11C2×D411yescharacteristic
218Q8×D11—44no—
219Q8×D11—44no—
220Q8×D11—48no—
221#4341—44no—
222#4341—44no—
223#4341—48no—
224C2×D44—24no—
225C2×D44—21no—
226C2×D44—22no—
227C2×D44—22no—
228C2×D44—82no—
229C2×D44C2412yes—
230C2×C4×D11—24no—
231C2×C4×D11—24no—
232C2×C4×D11—22no—
233C2×C4×D11—22no—
234C2×C4×D11—44no—
235C2×C4×D11—82no—
236C2×C4×D11C2×D412yes—
237C2×C4×D11C2412yes—
238C2×Dic22—24no—
239C2×Dic22—21no—
240C2×Dic22—21no—
241C2×Dic22—21no—
242C2×Dic22—22no—
243C2×Dic22—22no—
244C2×Dic22—22no—
245C2×Dic22—22no—
246C2×Dic22—22no—
247C2×Dic22—22no—
248C2×Dic22—44no—
249C2×Dic22C2412yes—
250C2×Dic22C2412yes—
251C2×Dic22C2412yes—
252C2×C8×C11—22no—
253C2×C8×C11—22no—
254C2×C8×C11C2412yes—
255C2×C8×C11C2412yes—
256C11×C4⋊C4—21no—
257C11×C4⋊C4—21no—
258C11×C4⋊C4—24no—
259C11×C4⋊C4C2412yes—
260C11×C4⋊C4C2412yes—
261C11×C22⋊C4—24no—
262C11×C22⋊C4—24no—
263C42×C11C2×D412yes—
264C42×C11C2412yes—
265C22⋊Dic11—24no—
266C22⋊Dic11—24no—
267#4326—44no—
268#4325—44no—
269#4324—44no—
270#4323—44no—
271(C2×D11)⋊C4—24no—
272(C2×D11)⋊C4—24no—
273(C2×D11)⋊C4—24no—
274(C2×D11)⋊C4—24no—
275(C2×D11)⋊C4—24no—
276(C2×D11)⋊C4C2×D414yes—
277(C2×D11)⋊C4C2×D414yes—
278C4⋊Dic11—24no—
279C4⋊Dic11—24no—
280C4⋊Dic11—24no—
281Dic11⋊C4—24no—
282Dic11⋊C4—24no—
283Dic11⋊C4—24no—
284Dic11⋊C4C2×D414yes—
285Dic11⋊C4C2×D414yes—
286C4×Dic11—24no—
287C4×Dic11C2×D412yes—
288C4×Dic11C2412yes—
289C2×C11⋊C8—22no—
290C2×C11⋊C8—22no—
291C2×C11⋊C8C2412yes—
292C2×C11⋊C8C2412yes—
293Dic44—44no—
294Dic44—44no—
295#4314—44no—
296#4314—44no—
297C2×#542—111no—
298C2×#536—111no—
299#3225—1116no—
300C2×#497—111no—
301C2×#495—111no—
302C2×#489D1111yescharacteristic, complemented
303C2×#487—111no—
304C2×#464—111no—
305C2×#462—111no—
306C2×#463—111no—
307C2×#461—111no—
308C2×#452—111no—
309C2×#449—111no—
310C2×#451—111no—
311C2×#448—111no—
312C2×#433—111no—
313C23×C11—22no—
314C23×C11—42no—
315C23×C11—42no—
316C23×C11—42no—
317C23×C11C22×D411yescharacteristic
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—42no—
323C22×D11—42no—
324C22×D11—42no—
325C22×D11C22×D412yes—
326Q8×C11—22no—
327Q8×C11—22no—
328Q8×C11—42no—
329Q8×C11—84no—
330D4×C11—22no—
331D4×C11—22no—
332D4×C11—42no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—42no—
339C2×C4×C11—42no—
340C2×C4×C11—42no—
341C2×C4×C11C22×D412yes—
342C2×C4×C11C22×D412yes—
343C2×C4×C11C22×D411yescharacteristic
344C2×C4×C11H(5,𝔽2)12yes—
345C2×C4×C11H(5,𝔽2)12yes—
346C2×C4×C11C2511yescharacteristic
347C22⋊D11—48no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—48no—
355C2×Dic11—42no—
356C2×Dic11—42no—
357C2×Dic11—42no—
358C2×Dic11C22×D412yes—
359C2×Dic11C22×D412yes—
360C2×Dic11C22×D412yes—
361D44—22no—
362D44—22no—
363D44—42no—
364D44—84no—
365C4×D11—24no—
366C4×D11—22no—
367C4×D11—22no—
368C4×D11—48no—
369C4×D11—84no—
370Dic22—22no—
371Dic22—22no—
372Dic22—22no—
373Dic22—22no—
374Dic22—22no—
375Dic22—22no—
376Dic22—48no—
377Dic22—42no—
378Dic22—42no—
379Dic22—42no—
380C8×C11—22no—
381C8×C11—22no—
382C11⋊C8—22no—
383C11⋊C8—22no—
384C22×#41—111no—
385C23×Q8—111no—
386C22×Q16—111no—
387C22×Q16—111no—
388C22×Q16—111no—
389C22×SD16—111no—
390C22×SD16—111no—
391C22×SD16—111no—
392C22×SD16—111no—
393C22×D8—111no—
394#542—118no—
395#542—224no—
396#536—118no—
397#536—224no—
398C2×C4⋊Q8—111no—
399C2×C4⋊Q8—111no—
400C2×C4⋊Q8C2×D1111yescharacteristic
401C2×#126—221no—
402C2×#124—111no—
403C2×#124—111no—
404C2×#124—221no—
405C2×#124C2×D1111yescharacteristic
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×#121—111no—
414C2×C4×Q8—111no—
415C2×C4×D4—111no—
416C2×#117—111no—
417#497—118no—
418#495—118no—
419#489C2×D1118yescomplemented
420#487—118no—
421#464—118no—
422#463—118no—
423#462—118no—
424#461—118no—
425#452—118no—
426#451—118no—
427#449—118no—
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×#103C2×D1111yescharacteristic
437C2×#103C2×D1111yescharacteristic
438C2×#102C2×D1111yescharacteristic
439C2×#102C2×D1111yescharacteristic
440C2×C22⋊C8—111no—
441C2×C22⋊C8—111no—
442C2×#97C2×D1111yescharacteristic
443C2×C4×C8—111no—
444C22×C11—42no—
445C22×C11—42no—
446C22×C11—42no—
447C22×C11—84no—
448C22×C11#53512yes—
449C22×C11#57712yes—
450C22×C11#57812yes—
451C22×C11C23×D411yescharacteristic
452C2×D11—22no—
453C2×D11—22no—
454C2×D11—22no—
455C2×D11—44no—
456C2×D11—42no—
457C2×D11—42no—
458C2×D11—42no—
459C2×D11—84no—
460C4×C11—22no—
461C4×C11—22no—
462C4×C11—42no—
463C4×C11—42no—
464C4×C11—42no—
465C4×C11#53512yes—
466C4×C11C2×H(5,𝔽2)11yescharacteristic
467C4×C11C2×H(5,𝔽2)11yescharacteristic
468Dic11—22no—
469Dic11—22no—
470Dic11—22no—
471Dic11—42no—
472Dic11—42no—
473Dic11—42no—
474C2×#41—114no—
475C2×#41—222no—
476C2×#41—442no—
477C2×#41—442no—
478C22×Q8—21no—
479C22×Q8—114no—
480C22×Q8—111no—
481C22×Q8—111no—
482C22×Q8—111no—
483C22×Q8—221no—
484C22×Q8—222no—
485C22×Q8—442no—
486C22×Q8—442no—
487C22×Q8C22×D1111yescharacteristic
488C22×D4—111no—
489C22×D4—221no—
490C22×D4—221no—
491C22×D4C22×D1111yescharacteristic
492C23×C4—111no—
493C23×C4—221no—
494C23×C4—221no—
495C23×C4—221no—
496C2×Q16—114no—
497C2×Q16—114no—
498C2×Q16—114no—
499C2×Q16—442no—
500C2×Q16—442no—
501C2×Q16—442no—
502C2×SD16—114no—
503C2×SD16—114no—
504C2×SD16—114no—
505C2×SD16—114no—
506C2×SD16—442no—
507C2×SD16—442no—
508C2×SD16—442no—
509C2×SD16—442no—
510C2×D8—114no—
511C2×D8—442no—
512C22×C8—111no—
513C22×C8—111no—
514C22×C8C22×D1111yescharacteristic
515C22×C8C22×D1111yescharacteristic
516C4⋊Q8—22no—
517C4⋊Q8—114no—
518C4⋊Q8—114no—
519C4⋊Q8—222no—
520C4⋊Q8—222no—
521C4⋊Q8C22×D1114yes—
522#126—228no—
523#124—22no—
524#124—114no—
525#124—114no—
526#124—222no—
527#124—228no—
528#124—222no—
529#124C22×D1114yes—
530#123—228no—
531#123—228no—
532#123—228no—
533C22⋊Q8—114no—
534C22⋊Q8—228no—
535C22⋊Q8—228no—
536C22⋊Q8—222no—
537C22⋊Q8—228no—
538#121—114no—
539#121—222no—
540C4×Q8—114no—
541C4×Q8—222no—
542C4×D4—114no—
543C4×D4—222no—
544#117—114no—
545#117—114no—
546C2×C4⋊C4—21no—
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⋊C4C22×D1111yescharacteristic
556C2×C4⋊C4C22×D1111yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—111no—
560C2×C22⋊C4—111no—
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—221no—
570C2×C42C22×D1111yescharacteristic
571C4⋊C8—114no—
572C4⋊C8—114no—
573#103—114no—
574#103—114no—
575#103—114no—
576#103—114no—
577#103C22×D1114yes—
578#103C22×D1114yes—
579#102C22×D1114yes—
580#102C22×D1114yes—
581C22⋊C8—114no—
582C22⋊C8—114no—
583#97C22×D1114yes—
584C4×C8—114no—
585C2×C11—82no—
586C2×C11#322514yescomplemented
587C2×C11C2×#53511yescharacteristic
588C2×C11C2×#57711yescharacteristic
589C2×C11C2×#57811yescharacteristic
590D11—42no—
591D11—82no—
592C24—21no—
593C24—111no—
594C24—221no—
595#41—444no—
596#41—444no—
597#41—448no—
598C2×Q8—21no—
599C2×Q8—24no—
600C2×Q8—22no—
601C2×Q8—22no—
602C2×Q8—82no—
603C2×Q8—112no—
604C2×Q8—112no—
605C2×Q8—112no—
606C2×Q8—224no—
607C2×Q8—221no—
608C2×Q8—221no—
609C2×Q8—221no—
610C2×Q8—222no—
611C2×Q8—222no—
612C2×Q8—222no—
613C2×Q8—222no—
614C2×Q8—222no—
615C2×Q8—222no—
616C2×Q8—444no—
617C2×Q8—444no—
618C2×Q8—444no—
619C2×Q8—448no—
620C2×Q8C23×D1112yes—
621C2×D4—21no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—112no—
625C2×D4—224no—
626C2×D4—224no—
627C2×D4—221no—
628C2×D4—222no—
629C2×D4—222no—
630C2×D4—444no—
631C2×D4—882no—
632C2×D4C23×D1112yes—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—111no—
637C22×C4—111no—
638C22×C4—111no—
639C22×C4—112no—
640C22×C4—112no—
641C22×C4—224no—
642C22×C4—224no—
643C22×C4—224no—
644C22×C4—222no—
645C22×C4—222no—
646C22×C4—221no—
647C22×C4—221no—
648C22×C4—221no—
649C22×C4—444no—
650C22×C4—444no—
651C22×C4—882no—
652C22×C4D4×D1111yescharacteristic
653C22×C4D4×D1111yescharacteristic
654C22×C4C23×D1111yescharacteristic
655Q16—444no—
656Q16—444no—
657Q16—444no—
658SD16—444no—
659SD16—444no—
660SD16—444no—
661SD16—444no—
662D8—444no—
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—24no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—114no—
675C4⋊C4—114no—
676C4⋊C4—224no—
677C4⋊C4—224no—
678C4⋊C4—224no—
679C4⋊C4—224no—
680C4⋊C4—224no—
681C4⋊C4—224no—
682C4⋊C4C23×D1112yes—
683C4⋊C4C23×D1112yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—114no—
687C22⋊C4—114no—
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—224no—
698C42D4×D1112yes—
699C42C23×D1112yes—
700C11C2×#322511yescharacteristic, complemented, Sylow
701C23—22no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—112no—
706C23—222no—
707C23—222no—
708C23—222no—
709C23—222no—
710C23—442no—
711C23—442no—
712C23—442no—
713C23C2×D4×D1111yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—84no—
718Q8—222no—
719Q8—222no—
720Q8—222no—
721Q8—222no—
722Q8—222no—
723Q8—222no—
724Q8—448no—
725Q8—442no—
726Q8—442no—
727Q8—442no—
728D4—22no—
729D4—22no—
730D4—42no—
731D4—222no—
732D4—222no—
733D4—448no—
734D4—442no—
735D4—884no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—112no—
745C2×C4—112no—
746C2×C4—112no—
747C2×C4—222no—
748C2×C4—222no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—224no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—448no—
757C2×C4—448no—
758C2×C4—442no—
759C2×C4—442no—
760C2×C4—442no—
761C2×C4—884no—
762C2×C4C2×D4×D1112yes—
763C2×C4C2×D4×D1112yes—
764C2×C4C2×D4×D1111yescharacteristic
765C2×C4#6704212yes—
766C2×C4#6704212yes—
767C2×C4C24×D1111yescharacteristic
768C8—22no—
769C8—22no—
770C8—222no—
771C8—222no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—84no—
776C22—222no—
777C22—222no—
778C22—222no—
779C22—444no—
780C22—442no—
781C22—442no—
782C22—442no—
783C22—884no—
784C22#1062320512yes—
785C22#1062330612yes—
786C22#1062331012yes—
787C22C22×D4×D1111yescharacteristic
788C4—22no—
789C4—22no—
790C4—42no—
791C4—42no—
792C4—42no—
793C4—222no—
794C4—222no—
795C4—222no—
796C4—442no—
797C4—442no—
798C4—442no—
799C4#1062320512yes—
800C4C2×#6704211yescharacteristic
801C4C2×#6704211yescharacteristic
802C2—82no—
803C2—442no—
804C2—882no—
805C2#1307972614yesdirect product factor
806C2C2×#1062320511yescharacteristic
807C2C2×#1062330611yescharacteristic
808C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#489C2
socleC23×C11C22×D4
prime radicalC2×#10622394C2
hypercenterC2×#489D11
hypocenterC11C2×#3225
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#10623264C2semidirect
2. C2×#10623206C2semidirect
3. #13079726C2direct (N × H)
4. C2×#10622328C2semidirect
5. C2×#10622672C2semidirect
6. C2×#10622706C2semidirect
7. C2×#10622380C2semidirect
8. C2×#10622406C2semidirect
9. C2×#10622400C2semidirect
10. C2×#10622431C2semidirect
11. C2×#10622396C2semidirect
13. C2×#10622421C2semidirect
14. C2×#10622419C2semidirect
15. C2×#10622322C2semidirect
16. C2×C11×#489C2semidirect
34. #10623264C22semidirect
36. #10623206C22semidirect
50. C11×#489C22semidirect
60. #10622706C22semidirect
61. #10622672C22semidirect
67. #10622431C22semidirect
68. #10622421C22semidirect
69. #10622419C22semidirect
70. #10622406C22semidirect
71. #10622400C22semidirect
72. #10622396C22semidirect
74. #10622380C22semidirect
75. #10622328C22semidirect
76. #10622322C22semidirect
302. C2×#489D11semidirect
419. #489C2×D11semidirect
586. C2×C11#3225semidirect
700. C11C2×#3225semidirect
805. C2#13079726direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232642
C2×#106232062
#130797262
C2×#106223282
C2×#106226722
C2×#106227062
C2×#106223802
C2×#106224062
C2×#106224002
C2×#106224312
C2×#106223962
C2×#106223942
C2×#106224212
C2×#106224192
C2×#106223222
C2×C11×#4892
C2×#322511