Finite Group Databasebeta

← C2×#13079585 #15624949

Subgroups — C2×#13079585 #15624949

Order 2816.

2294 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623111C211yesmaximal, characteristic, complemented
2C2×D11×#124C211yesmaximal, characteristic, complemented
3#13079585C2116yesmaximal, direct product factor
4C2×#10622804C211yesmaximal, characteristic, complemented
5C2×#10622781C211yesmaximal, characteristic, complemented
6C2×#10622413C211yesmaximal, characteristic, complemented
7C2×#10622381C211yesmaximal, characteristic, complemented
8C2×#10622641C211yesmaximal, characteristic, complemented
9C2×#10622457C211yesmaximal, characteristic, complemented
10C2×#10622670C211yesmaximal, characteristic, complemented
11C2×#10622799C211yesmaximal, characteristic, complemented
12C2×#10622419C211yesmaximal, characteristic, complemented
13C2×#10622782C211yesmaximal, characteristic, complemented
14C2×#10622386C211yesmaximal, characteristic
15C2×#10622446C211yesmaximal, characteristic, complemented
16C2×C11×#464C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2211yescharacteristic
18C22×D4×D11C2211yescharacteristic
19C22×C11×Q16C2211yescharacteristic, complemented
20C22×C11×SD16C2211yescharacteristic
21C2×C11×#124C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic, complemented
23C2×#67000C2211yescharacteristic
24C2×#67000C2211yescharacteristic, complemented
25C2×#66999C2211yescharacteristic
26C22×#4326C2211yescharacteristic, complemented
27C22×#4325C2211yescharacteristic
28C22×#4325C2211yescharacteristic, complemented
29C2×#66989C2211yescharacteristic
30C22×#4323C2211yescharacteristic
31C22×D88C2211yescharacteristic
32C22×#4314C2211yescharacteristic, complemented
33D11×#124—24no—
34D11×#124C2218yescomplemented
35#10623111—24no—
36#10623111C2218yescomplemented
37C2×#66951—21no—
38C2×#66948C2211yescharacteristic
39C2×#66947—21no—
40C2×#66943C2211yescharacteristic, complemented
41C2×#66938—21no—
42C2×#66938—21no—
43C2×C22⋊C4×D11—21no—
44C2×C22⋊C4×D11—21no—
45C2×#66928C2211yescharacteristic
46C2×C4×D44—21no—
47C2×C4×D44C2211yescharacteristic, complemented
48C2×#66925—21no—
49C2×C42×D11C2211yescharacteristic
50C11×#464C2218yescomplemented
51C2×C11×C4⋊C8C2211yescharacteristic, complemented
52C2×C11×#103C2211yescharacteristic, complemented
53C2×C11×#102C2211yescharacteristic
54C2×#66899C2211yescharacteristic, complemented
55C2×#66896C2211yescharacteristic
56#10622804C2218yescomplemented
57#10622799C2218yescomplemented
58#10622782C2218yescomplemented
59#10622781C2218yescomplemented
60C2×#66885C2211yescharacteristic
61C2×(C2×D11)⋊C8C2211yescharacteristic
62C2×(C2×D11)⋊C8C2211yescharacteristic
63C2×#66880C2211yescharacteristic, complemented
64C2×C8×Dic11C2211yescharacteristic, complemented
65C2×C8×Dic11C2211yescharacteristic, complemented
66#10622670C2218yescomplemented
67#10622641C2218yescomplemented
68C2×#66874C2211yescharacteristic, complemented
69C2×#66873C2211yescharacteristic
70C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
71#10622457C2218yescomplemented
72#10622446C2218yescomplemented
73#10622419C2218yescomplemented
74#10622413C2218yescomplemented
75#10622386C2218yes—
76#10622381C2218yescomplemented
77C24×D11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C2×Q8×D11—22no—
83C2×Q8×D11—42no—
84C2×Q8×D11—42no—
85C2×Q8×D11C2314yes—
86C2×D4×D11—22no—
87C2×D4×D11—42no—
88C2×D4×D11—42no—
89C2×D4×D11C2314yes—
90C22×D44—21no—
91C22×D44C2311yescharacteristic
92C22×D44C2311yescharacteristic
93C22×C4×D11—21no—
94C22×C4×D11—21no—
95C22×C4×D11D411yescharacteristic
96C22×C4×D11D411yescharacteristic
97C22×C4×D11C2311yescharacteristic
98C22×Dic22—21no—
99C22×Dic22C2311yescharacteristic
100C2×C11×Q16—42no—
101C2×C11×Q16C2314yescomplemented
102C2×C11×SD16—42no—
103C2×C11×SD16C2314yes—
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C11×#124—22no—
107C11×#124C2314yes—
108C4×Q8×C11—22no—
109C4×Q8×C11C2314yescomplemented
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C42×C11—21no—
115C2×C42×C11C2311yescharacteristic
116C2×C22⋊Dic11—21no—
117C2×C22⋊Dic11—21no—
118#67000—22no—
119#67000—22no—
120#67000C2314yes—
121#67000C2314yescomplemented
122#66999—22no—
123#66999C2314yes—
124C2×#4326—42no—
125C2×#4326C2314yescomplemented
126C2×#4325—42no—
127C2×#4325—42no—
128C2×#4325C2314yes—
129C2×#4325C2314yescomplemented
130#66989—22no—
131#66989C2314yes—
132C2×#4323—42no—
133C2×#4323C2314yes—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4—21no—
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⋊Dic11—21no—
144C2×C4⋊Dic11C2311yescharacteristic
145C2×Dic11⋊C4—21no—
146C2×Dic11⋊C4—21no—
147C2×C4×Dic11D411yescharacteristic
148C2×C4×Dic11D411yescharacteristic
149C2×C4×Dic11C2311yescharacteristic
150C22×C11⋊C8C2311yescharacteristic
151C22×C11⋊C8C2311yescharacteristic
152C2×D88—42no—
153C2×D88C2314yes—
154C2×#4314—42no—
155C2×#4314C2314yescomplemented
156#66951—28no—
157#66948—22no—
158#66948C2314yes—
159#66947—28no—
160#66943—22no—
161#66943C2314yescomplemented
162#66938—28no—
163#66938—28no—
164C22⋊C4×D11—28no—
165C22⋊C4×D11—28no—
166#66928—22no—
167#66928C2314yes—
168C4×D44—28no—
169C4×D44—22no—
170C4×D44C2314yescomplemented
171#66925—28no—
172C42×D11D414yes—
173C42×D11C2314yes—
174C11×C4⋊C8C2314yescomplemented
175C11×#103C2314yescomplemented
176C11×#102C2314yes—
177#66899C2314yescomplemented
178#66896C2314yes—
179#66885C2314yes—
180(C2×D11)⋊C8C2314yes—
181(C2×D11)⋊C8C2314yes—
182#66880C2314yescomplemented
183C8×Dic11C2314yescomplemented
184C8×Dic11C2314yescomplemented
185#66874C2314yescomplemented
186#66873C2314yes—
187C4⋊(C11⋊C8)C2314yescomplemented
188C2×#3211—111nomaximal, Sylow
189C24×C11—21no—
190C23×D11—21no—
191C23×D11—21no—
192C23×D11—24no—
193C23×D11—44no—
194C23×D11—44no—
195C23×D11—44no—
196C23×D11C2×D411yescharacteristic
197C2×Q8×C11—21no—
198C2×Q8×C11—21no—
199C2×Q8×C11—22no—
200C2×Q8×C11—22no—
201C2×Q8×C11—22no—
202C2×Q8×C11—22no—
203C2×Q8×C11C2412yes—
204C2×Q8×C11C2412yes—
205C2×D4×C11—21no—
206C2×D4×C11—22no—
207C2×D4×C11—22no—
208C2×D4×C11C2412yes—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2411yescharacteristic
215C2×C22⋊D11—24no—
216C2×C22⋊D11—44no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11C2×D411yescharacteristic
220C22×Dic11C2×D411yescharacteristic
221C22×Dic11C2×D411yescharacteristic
222Q8×D11—44no—
223Q8×D11—44no—
224Q8×D11—48no—
225D4×D11—44no—
226D4×D11—44no—
227D4×D11—48no—
228C2×D44—24no—
229C2×D44—21no—
230C2×D44—21no—
231C2×D44—22no—
232C2×D44—22no—
233C2×D44—22no—
234C2×D44—22no—
235C2×D44—44no—
236C2×D44C2412yes—
237C2×D44C2412yes—
238C2×C4×D11—24no—
239C2×C4×D11—24no—
240C2×C4×D11—24no—
241C2×C4×D11—22no—
242C2×C4×D11—22no—
243C2×C4×D11—42no—
244C2×C4×D11—44no—
245C2×C4×D11—44no—
246C2×C4×D11C2×D412yes—
247C2×C4×D11C2×D414yes—
248C2×C4×D11C2×D414yes—
249C2×C4×D11C2412yes—
250C2×Dic22—24no—
251C2×Dic22—21no—
252C2×Dic22—22no—
253C2×Dic22—22no—
254C2×Dic22—44no—
255C2×Dic22C2412yes—
256C11×Q16—44no—
257C11×SD16—44no—
258C2×C8×C11—22no—
259C2×C8×C11—22no—
260C2×C8×C11C2412yes—
261C2×C8×C11C2412yes—
262C11×C4⋊C4—21no—
263C11×C4⋊C4—24no—
264C11×C4⋊C4C2412yes—
265C11×C22⋊C4—24no—
266C11×C22⋊C4—24no—
267C42×C11—24no—
268C42×C11C2×D412yes—
269C42×C11C2412yes—
270C22⋊Dic11—24no—
271C22⋊Dic11—24no—
272#4326—44no—
273#4325—44no—
274#4325—44no—
275#4323—44no—
276(C2×D11)⋊C4—24no—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4—24no—
279(C2×D11)⋊C4—24no—
280(C2×D11)⋊C4—24no—
281(C2×D11)⋊C4—24no—
282(C2×D11)⋊C4—24no—
283(C2×D11)⋊C4—24no—
284(C2×D11)⋊C4—24no—
285C4⋊Dic11—24no—
286C4⋊Dic11—21no—
287C4⋊Dic11C2412yes—
288Dic11⋊C4—24no—
289Dic11⋊C4—24no—
290C4×Dic11C2×D412yes—
291C4×Dic11C2×D414yes—
292C4×Dic11C2×D414yes—
293C4×Dic11C2412yes—
294C2×C11⋊C8—22no—
295C2×C11⋊C8—22no—
296C2×C11⋊C8C2412yes—
297C2×C11⋊C8C2412yes—
298D88—44no—
299#4314—44no—
300C2×#529—111no—
301C22×#124—111no—
302#3211—1116no—
303C2×#495—111no—
304C2×#495—111no—
305C2×#488—111no—
306C2×#488—111no—
307C2×#464—111no—
308C2×#464D1111yescharacteristic, complemented
309C2×#463—111no—
310C2×#463—111no—
311C2×#451—111no—
312C2×#448—111no—
313C2×#450—111no—
314C2×#447—111no—
315C2×#431—111no—
316C23×C11—22no—
317C23×C11—42no—
318C23×C11—42no—
319C23×C11—42no—
320C23×C11C22×D411yescharacteristic
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—48no—
326C22×D11—48no—
327C22×D11—42no—
328C22×D11—42no—
329C22×D11—42no—
330C22×D11—42no—
331C22×D11—42no—
332C22×D11—42no—
333C22×D11—48no—
334C22×D11—816no—
335C22×D11#13514yes—
336C22×D11C22×D412yes—
337Q8×C11—22no—
338Q8×C11—22no—
339Q8×C11—22no—
340Q8×C11—22no—
341Q8×C11—42no—
342Q8×C11—42no—
343D4×C11—22no—
344D4×C11—22no—
345D4×C11—42no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—42no—
352C2×C4×C11—42no—
353C2×C4×C11—42no—
354C2×C4×C11C22×D412yes—
355C2×C4×C11C22×D412yes—
356C2×C4×C11C22×D411yescharacteristic
357C2×C4×C11H(5,𝔽2)12yes—
358C2×C4×C11H(5,𝔽2)12yes—
359C2×C4×C11C2511yescharacteristic
360C22⋊D11—48no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—42no—
367C2×Dic11—42no—
368C2×Dic11C22×D412yes—
369C2×Dic11C22×D412yes—
370C2×Dic11C22×D412yes—
371D44—22no—
372D44—22no—
373D44—22no—
374D44—22no—
375D44—48no—
376D44—42no—
377D44—42no—
378C4×D11—28no—
379C4×D11—24no—
380C4×D11—22no—
381C4×D11—22no—
382C4×D11—44no—
383C4×D11—48no—
384C4×D11—48no—
385Dic22—22no—
386Dic22—22no—
387Dic22—48no—
388Dic22—42no—
389C8×C11—22no—
390C8×C11—22no—
391C11⋊C8—22no—
392C11⋊C8—22no—
393C23×Q8—111no—
394C23×D4—111no—
395C22×Q16—111no—
396C22×Q16C2×D1111yescharacteristic, complemented
397C22×SD16—111no—
398C22×SD16—111no—
399C22×SD16—111no—
400C22×SD16C2×D1111yescharacteristic
401C22×D8—111no—
402C22×D8—111no—
403#529—118no—
404#529—224no—
405C2×#126—221no—
406C2×#125—111no—
407C2×#124—111no—
408C2×#124—111no—
409C2×#124—111no—
410C2×#124—118no—
411C2×#124—111no—
412C2×#124—221no—
413C2×#124—221no—
414C2×#124—224no—
415C2×#124C2×D1111yescharacteristic
416C2×#123—221no—
417C2×C22⋊Q8—111no—
418C2×#121—111no—
419C2×C4×Q8C2×D1111yescharacteristic, complemented
420C2×C4×D4—111no—
421C2×C4×D4—221no—
422C2×#117—221no—
423C22×C22⋊C4—221no—
424C22×C22⋊C4—221no—
425C22×C42—111no—
426#495—118no—
427#495—118no—
428#488—118no—
429#488—118no—
430#464—118no—
431#464C2×D1118yescomplemented
432#463—118no—
433#463—118no—
434#451—118no—
435#450—118no—
436#448—118no—
437#447—118no—
438#431—118no—
439C2×C4⋊C8—111no—
440C2×C4⋊C8C2×D1111yescharacteristic, complemented
441C2×#103—111no—
442C2×#103—111no—
443C2×#103—111no—
444C2×#103C2×D1111yescharacteristic, complemented
445C2×#102—111no—
446C2×#102—111no—
447C2×#102—111no—
448C2×#102C2×D1111yescharacteristic
449C2×C22⋊C8—111no—
450C2×C22⋊C8—111no—
451C2×C4×C8—111no—
452C2×C4×C8—111no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—84no—
457C22×C11#53512yes—
458C22×C11C2×#13512yes—
459C22×C11#57512yes—
460C22×C11C23×D411yescharacteristic
461C2×D11—22no—
462C2×D11—28no—
463C2×D11—22no—
464C2×D11—42no—
465C2×D11—42no—
466C2×D11—42no—
467C2×D11—42no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—816no—
471C2×D11—84no—
472C2×D11—84no—
473C2×D11C2×#13514yes—
474C4×C11—22no—
475C4×C11—22no—
476C4×C11—42no—
477C4×C11—42no—
478C4×C11—42no—
479C4×C11#53512yes—
480C4×C11C2×H(5,𝔽2)11yescharacteristic
481C4×C11C2×H(5,𝔽2)11yescharacteristic
482Dic11—22no—
483Dic11—22no—
484Dic11—22no—
485Dic11—42no—
486Dic11—42no—
487C25—221no—
488C22×Q8—114no—
489C22×Q8—111no—
490C22×Q8—221no—
491C22×Q8—222no—
492C22×Q8—442no—
493C22×Q8—442no—
494C22×Q8C22×D1111yescharacteristic
495C22×Q8C22×D1111yescharacteristic
496C22×D4—114no—
497C22×D4—111no—
498C22×D4—111no—
499C22×D4—221no—
500C22×D4—222no—
501C22×D4—221no—
502C22×D4—442no—
503C22×D4—442no—
504C22×D4C22×D1111yescharacteristic
505C23×C4—111no—
506C23×C4—111no—
507C23×C4—111no—
508C23×C4—221no—
509C23×C4—221no—
510C2×Q16—42no—
511C2×Q16—114no—
512C2×Q16—442no—
513C2×Q16C22×D1114yescomplemented
514C2×SD16—42no—
515C2×SD16—114no—
516C2×SD16—114no—
517C2×SD16—114no—
518C2×SD16—442no—
519C2×SD16—442no—
520C2×SD16—442no—
521C2×SD16C22×D1114yes—
522C2×D8—114no—
523C2×D8—114no—
524C2×D8—442no—
525C2×D8—442no—
526C22×C8—111no—
527C22×C8—111no—
528C22×C8C22×D1111yescharacteristic
529C22×C8C22×D1111yescharacteristic
530#126—228no—
531#125—114no—
532#125—222no—
533#124—22no—
534#124—114no—
535#124—114no—
536#124—114no—
537#124—114no—
538#124—228no—
539#124—228no—
540#124—222no—
541#124—222no—
542#124—222no—
543#124—222no—
544#124C22×D1114yes—
545#123—228no—
546C22⋊Q8—114no—
547C22⋊Q8—222no—
548#121—114no—
549#121—222no—
550C4×Q8—22no—
551C4×Q8C22×D1114yescomplemented
552C4×D4—114no—
553C4×D4—228no—
554C4×D4—222no—
555#117—228no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—111no—
558C2×C4⋊C4—221no—
559C2×C4⋊C4—221no—
560C2×C4⋊C4—221no—
561C2×C4⋊C4C22×D1111yescharacteristic
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—228no—
565C2×C22⋊C4—228no—
566C2×C22⋊C4—221no—
567C2×C22⋊C4—221no—
568C2×C22⋊C4—221no—
569C2×C22⋊C4—221no—
570C2×C22⋊C4—221no—
571C2×C22⋊C4—221no—
572C2×C22⋊C4—221no—
573C2×C22⋊C4—221no—
574C2×C22⋊C4—221no—
575C2×C22⋊C4—221no—
576C2×C22⋊C4—221no—
577C2×C42—21no—
578C2×C42—111no—
579C2×C42—111no—
580C2×C42—111no—
581C2×C42—114no—
582C2×C42—114no—
583C2×C42C22×D1111yescharacteristic
584C4⋊C8—114no—
585C4⋊C8C22×D1114yescomplemented
586#103—114no—
587#103—114no—
588#103—114no—
589#103C22×D1114yescomplemented
590#102—114no—
591#102—114no—
592#102—114no—
593#102C22×D1114yes—
594C22⋊C8—114no—
595C22⋊C8—114no—
596C4×C8—114no—
597C4×C8—114no—
598C2×C11—82no—
599C2×C11#321114yescomplemented
600C2×C11C2×#53511yescharacteristic
601C2×C11C22×#13511yescharacteristic
602C2×C11C2×#57511yescharacteristic
603D11—24no—
604D11—82no—
605D11—82no—
606C24—21no—
607C24—111no—
608C24—224no—
609C24—221no—
610C24—221no—
611C24—444no—
612C24—444no—
613C24—444no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—22no—
617C2×Q8—22no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8—112no—
621C2×Q8—224no—
622C2×Q8—221no—
623C2×Q8—222no—
624C2×Q8—222no—
625C2×Q8—444no—
626C2×Q8—444no—
627C2×Q8—444no—
628C2×Q8—448no—
629C2×Q8C23×D1112yes—
630C2×Q8C23×D1112yes—
631C2×D4—21no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—112no—
635C2×D4—112no—
636C2×D4—224no—
637C2×D4—224no—
638C2×D4—221no—
639C2×D4—221no—
640C2×D4—222no—
641C2×D4—222no—
642C2×D4—222no—
643C2×D4—222no—
644C2×D4—444no—
645C2×D4—444no—
646C2×D4—444no—
647C2×D4—448no—
648C2×D4—444no—
649C2×D4C23×D1112yes—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—111no—
654C22×C4—111no—
655C22×C4—111no—
656C22×C4—114no—
657C22×C4—112no—
658C22×C4—112no—
659C22×C4—114no—
660C22×C4—224no—
661C22×C4—224no—
662C22×C4—222no—
663C22×C4—222no—
664C22×C4—221no—
665C22×C4—221no—
666C22×C4—224no—
667C22×C4—442no—
668C22×C4—444no—
669C22×C4—444no—
670C22×C4D4×D1111yescharacteristic
671C22×C4D4×D1111yescharacteristic
672C22×C4C23×D1111yescharacteristic
673Q16—44no—
674Q16—444no—
675SD16—44no—
676SD16—444no—
677SD16—444no—
678SD16—444no—
679D8—444no—
680D8—444no—
681C2×C8—22no—
682C2×C8—22no—
683C2×C8—112no—
684C2×C8—112no—
685C2×C8—222no—
686C2×C8—222no—
687C2×C8C23×D1112yes—
688C2×C8C23×D1112yes—
689C4⋊C4—24no—
690C4⋊C4—21no—
691C4⋊C4—112no—
692C4⋊C4—224no—
693C4⋊C4—224no—
694C4⋊C4—224no—
695C4⋊C4—221no—
696C4⋊C4C23×D1112yes—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—224no—
700C22⋊C4—224no—
701C22⋊C4—224no—
702C22⋊C4—224no—
703C22⋊C4—224no—
704C22⋊C4—224no—
705C22⋊C4—224no—
706C22⋊C4—224no—
707C22⋊C4—224no—
708C22⋊C4—224no—
709C22⋊C4—224no—
710C42—24no—
711C42—114no—
712C42—112no—
713C42—114no—
714C42—112no—
715C42D4×D1112yes—
716C42C23×D1112yes—
717C11C2×#321111yescharacteristic, complemented, Sylow
718C23—22no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—114no—
723C23—112no—
724C23—222no—
725C23—222no—
726C23—222no—
727C23—222no—
728C23—448no—
729C23—448no—
730C23—448no—
731C23—442no—
732C23—442no—
733C23—442no—
734C23—442no—
735C23—442no—
736C23—442no—
737C23—8816no—
738C23C2×D4×D1111yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—22no—
742Q8—22no—
743Q8—42no—
744Q8—42no—
745Q8—222no—
746Q8—222no—
747Q8—448no—
748Q8—442no—
749D4—22no—
750D4—22no—
751D4—42no—
752D4—222no—
753D4—222no—
754D4—222no—
755D4—222no—
756D4—448no—
757D4—448no—
758D4—442no—
759D4—442no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—112no—
769C2×C4—112no—
770C2×C4—112no—
771C2×C4—228no—
772C2×C4—222no—
773C2×C4—222no—
774C2×C4—222no—
775C2×C4—224no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—222no—
779C2×C4—222no—
780C2×C4—444no—
781C2×C4—448no—
782C2×C4—448no—
783C2×C4—442no—
784C2×C4—442no—
785C2×C4C2×D4×D1112yes—
786C2×C4C2×D4×D1112yes—
787C2×C4C2×D4×D1111yescharacteristic
788C2×C4#6703712yes—
789C2×C4#6704212yes—
790C2×C4C24×D1111yescharacteristic
791C8—22no—
792C8—22no—
793C8—222no—
794C8—222no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—84no—
799C22—114no—
800C22—228no—
801C22—222no—
802C22—222no—
803C22—442no—
804C22—442no—
805C22—442no—
806C22—442no—
807C22—442no—
808C22—442no—
809C22—8816no—
810C22—884no—
811C22—884no—
812C22#1062313812yes—
813C22D11×#13512yes—
814C22#1062330812yes—
815C22C22×D4×D1111yescharacteristic
816C4—22no—
817C4—22no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—222no—
822C4—222no—
823C4—222no—
824C4—442no—
825C4—442no—
826C4#1062313812yes—
827C4C2×#6703711yescharacteristic
828C4C2×#6704211yescharacteristic
829C2—82no—
830C2—224no—
831C2—882no—
832C2—882no—
833C2#1307958514yesdirect product factor
834C2C2×#1062313811yescharacteristic
835C2C2×D11×#13511yescharacteristic
836C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#464C2
socleC23×C11C22×D4
prime radicalC2×#10622386C2
hypercenterC2×#464D11
hypocenterC11C2×#3211
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#10623111C2semidirect
2. C2×D11×#124C2semidirect
3. #13079585C2direct (N × H)
4. C2×#10622804C2semidirect
5. C2×#10622781C2semidirect
6. C2×#10622413C2semidirect
7. C2×#10622381C2semidirect
8. C2×#10622641C2semidirect
9. C2×#10622457C2semidirect
10. C2×#10622670C2semidirect
11. C2×#10622799C2semidirect
12. C2×#10622419C2semidirect
13. C2×#10622782C2semidirect
15. C2×#10622446C2semidirect
16. C2×C11×#464C2semidirect
19. C22×C11×Q16C22semidirect
22. C2×C4×Q8×C11C22semidirect
24. C2×#67000C22semidirect
26. C22×#4326C22semidirect
28. C22×#4325C22semidirect
32. C22×#4314C22semidirect
34. D11×#124C22semidirect
36. #10623111C22semidirect
40. C2×#66943C22semidirect
47. C2×C4×D44C22semidirect
50. C11×#464C22semidirect
51. C2×C11×C4⋊C8C22semidirect
52. C2×C11×#103C22semidirect
54. C2×#66899C22semidirect
56. #10622804C22semidirect
57. #10622799C22semidirect
58. #10622782C22semidirect
59. #10622781C22semidirect
63. C2×#66880C22semidirect
64. C2×C8×Dic11C22semidirect
65. C2×C8×Dic11C22semidirect
66. #10622670C22semidirect
67. #10622641C22semidirect
68. C2×#66874C22semidirect
70. C2×C4⋊(C11⋊C8)C22semidirect
71. #10622457C22semidirect
72. #10622446C22semidirect
73. #10622419C22semidirect
74. #10622413C22semidirect
76. #10622381C22semidirect
101. C2×C11×Q16C23semidirect
109. C4×Q8×C11C23semidirect
121. #67000C23semidirect
125. C2×#4326C23semidirect
129. C2×#4325C23semidirect
155. C2×#4314C23semidirect
161. #66943C23semidirect
170. C4×D44C23semidirect
174. C11×C4⋊C8C23semidirect
175. C11×#103C23semidirect
177. #66899C23semidirect
182. #66880C23semidirect
183. C8×Dic11C23semidirect
184. C8×Dic11C23semidirect
185. #66874C23semidirect
187. C4⋊(C11⋊C8)C23semidirect
308. C2×#464D11semidirect
396. C22×Q16C2×D11semidirect
419. C2×C4×Q8C2×D11semidirect
431. #464C2×D11semidirect
440. C2×C4⋊C8C2×D11semidirect
444. C2×#103C2×D11semidirect
513. C2×Q16C22×D11semidirect
551. C4×Q8C22×D11semidirect
585. C4⋊C8C22×D11semidirect
589. #103C22×D11semidirect
599. C2×C11#3211semidirect
717. C11C2×#3211semidirect
833. C2#13079585direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231112
C2×D11×#1242
#130795852
C2×#106228042
C2×#106227812
C2×#106224132
C2×#106223812
C2×#106226412
C2×#106224572
C2×#106226702
C2×#106227992
C2×#106224192
C2×#106227822
C2×#106223862
C2×#106224462
C2×C11×#4642
C2×#321111