Finite Group Databasebeta

← C2×#13079617 #15625027

Subgroups — C2×#13079617 #15625027

Order 2816.

2242 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C211yesmaximal, characteristic, complemented
2C2×D11×#124C211yesmaximal, characteristic
3#13079617C2116yesmaximal, direct product factor
4C2×#10622803C211yesmaximal, characteristic, complemented
5C2×#10622780C211yesmaximal, characteristic, complemented
6C2×#10622408C211yesmaximal, characteristic, complemented
7C2×#10622378C211yesmaximal, characteristic, complemented
8C2×#10622458C211yesmaximal, characteristic, complemented
9C2×#10622641C211yesmaximal, characteristic, complemented
10C2×#10622667C211yesmaximal, characteristic, complemented
11C2×#10622421C211yesmaximal, characteristic, complemented
12C2×#10622799C211yesmaximal, characteristic, complemented
13C2×#10622389C211yesmaximal, characteristic
14C2×#10622782C211yesmaximal, characteristic
15C2×#10622448C211yesmaximal, 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×#66999C2211yescharacteristic
25C2×#66997C2211yescharacteristic, complemented
26C22×#4326C2211yescharacteristic, complemented
27C22×#4326C2211yescharacteristic, complemented
28C22×#4325C2211yescharacteristic
29C2×#66989C2211yescharacteristic
30C22×#4324C2211yescharacteristic
31C22×Dic44C2211yescharacteristic, complemented
32C22×#4314C2211yescharacteristic
33D11×#124—24no—
34D11×#124C2218yes—
35#10623109—24no—
36#10623109C2218yescomplemented
37C2×#66950C2211yescharacteristic
38C2×#66949—21no—
39C2×#66942—21no—
40C2×#66941C2211yescharacteristic, complemented
41C2×#66938—21no—
42C2×#66938—21no—
43C2×C22⋊C4×D11—21no—
44C2×C22⋊C4×D11—21no—
45C2×#66928C2211yescharacteristic
46C2×#66925—21no—
47C2×C42×D11C2211yescharacteristic
48C2×C4×Dic22—21no—
49C2×C4×Dic22C2211yescharacteristic, complemented
50C11×#464C2218yescomplemented
51C2×C11×C4⋊C8C2211yescharacteristic, complemented
52C2×C11×#103C2211yescharacteristic, complemented
53C2×C11×#102C2211yescharacteristic
54C2×#66899C2211yescharacteristic, complemented
55C2×#66896C2211yescharacteristic
56#10622803C2218yescomplemented
57#10622799C2218yescomplemented
58#10622782C2218yes—
59#10622780C2218yescomplemented
60C2×#66885C2211yescharacteristic
61C2×(C2×D11)⋊C8C2211yescharacteristic
62C2×(C2×D11)⋊C8C2211yescharacteristic
63C2×#66880C2211yescharacteristic, complemented
64C2×#66879C2211yescharacteristic, complemented
65C2×#66879C2211yescharacteristic, complemented
66#10622667C2218yescomplemented
67#10622641C2218yescomplemented
68C2×#66874C2211yescharacteristic, complemented
69C2×#66873C2211yescharacteristic
70C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
71#10622458C2218yescomplemented
72#10622448C2218yescomplemented
73#10622421C2218yescomplemented
74#10622408C2218yescomplemented
75#10622389C2218yes—
76#10622378C2218yescomplemented
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×D44C2311yescharacteristic
91C22×C4×D11—21no—
92C22×C4×D11D411yescharacteristic
93C22×C4×D11D411yescharacteristic
94C22×C4×D11C2311yescharacteristic
95C22×Dic22—21no—
96C22×Dic22—21no—
97C22×Dic22C2311yescharacteristic
98C22×Dic22C2311yescharacteristic
99C2×C11×Q16—42no—
100C2×C11×Q16C2314yescomplemented
101C2×C11×SD16—42no—
102C2×C11×SD16C2314yes—
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C11×#124—22no—
106C11×#124C2314yes—
107C4×Q8×C11—22no—
108C4×Q8×C11C2314yescomplemented
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C42×C11—21no—
114C2×C42×C11C2311yescharacteristic
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11—21no—
117#67000—22no—
118#67000C2314yes—
119#66999—22no—
120#66999C2314yes—
121#66997—22no—
122#66997C2314yescomplemented
123C2×#4326—42no—
124C2×#4326—42no—
125C2×#4326C2314yescomplemented
126C2×#4326C2314yescomplemented
127C2×#4325—42no—
128C2×#4325C2314yes—
129#66989—22no—
130#66989C2314yes—
131C2×#4324—42no—
132C2×#4324C2314yes—
133C2×(C2×D11)⋊C4—21no—
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×C4⋊Dic11—21no—
140C2×C4⋊Dic11C2311yescharacteristic
141C2×Dic11⋊C4—21no—
142C2×Dic11⋊C4—21no—
143C2×Dic11⋊C4—21no—
144C2×Dic11⋊C4—21no—
145C2×Dic11⋊C4—21no—
146C2×C4×Dic11—21no—
147C2×C4×Dic11D411yescharacteristic
148C2×C4×Dic11D411yescharacteristic
149C2×C4×Dic11C2311yescharacteristic
150C22×C11⋊C8C2311yescharacteristic
151C22×C11⋊C8C2311yescharacteristic
152C2×Dic44—42no—
153C2×Dic44C2314yescomplemented
154C2×#4314—42no—
155C2×#4314C2314yes—
156#66950—22no—
157#66950C2314yes—
158#66949—28no—
159#66942—28no—
160#66941—22no—
161#66941C2314yescomplemented
162#66938—28no—
163#66938—28no—
164C22⋊C4×D11—28no—
165C22⋊C4×D11—28no—
166#66928—22no—
167#66928C2314yes—
168#66925—28no—
169C42×D11D414yes—
170C42×D11C2314yes—
171C4×Dic22—22no—
172C4×Dic22—28no—
173C4×Dic22C2314yescomplemented
174C11×C4⋊C8C2314yescomplemented
175C11×#103C2314yescomplemented
176C11×#102C2314yes—
177#66899C2314yescomplemented
178#66896C2314yes—
179#66885C2314yes—
180(C2×D11)⋊C8C2314yes—
181(C2×D11)⋊C8C2314yes—
182#66880C2314yescomplemented
183#66879C2314yescomplemented
184#66879C2314yescomplemented
185#66874C2314yescomplemented
186#66873C2314yes—
187C4⋊(C11⋊C8)C2314yescomplemented
188C2×#3215—111nomaximal, Sylow
189C24×C11—21no—
190C23×D11—21no—
191C23×D11—24no—
192C23×D11—44no—
193C23×D11—44no—
194C23×D11—44no—
195C23×D11C2×D411yescharacteristic
196C2×Q8×C11—21no—
197C2×Q8×C11—21no—
198C2×Q8×C11—22no—
199C2×Q8×C11—22no—
200C2×Q8×C11—22no—
201C2×Q8×C11—22no—
202C2×Q8×C11C2412yes—
203C2×Q8×C11C2412yes—
204C2×D4×C11—21no—
205C2×D4×C11—22no—
206C2×D4×C11—22no—
207C2×D4×C11C2412yes—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2411yescharacteristic
214C2×C22⋊D11—24no—
215C2×C22⋊D11—44no—
216C22×Dic11—21no—
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—21no—
229C2×D44—22no—
230C2×D44—22no—
231C2×D44C2412yes—
232C2×C4×D11—24no—
233C2×C4×D11—24no—
234C2×C4×D11—22no—
235C2×C4×D11—22no—
236C2×C4×D11—42no—
237C2×C4×D11—44no—
238C2×C4×D11C2×D412yes—
239C2×C4×D11C2×D414yes—
240C2×C4×D11C2×D414yes—
241C2×C4×D11C2412yes—
242C2×Dic22—24no—
243C2×Dic22—24no—
244C2×Dic22—21no—
245C2×Dic22—21no—
246C2×Dic22—22no—
247C2×Dic22—22no—
248C2×Dic22—22no—
249C2×Dic22—22no—
250C2×Dic22—44no—
251C2×Dic22—44no—
252C2×Dic22C2412yes—
253C2×Dic22C2412yes—
254C11×Q16—44no—
255C11×SD16—44no—
256C2×C8×C11—22no—
257C2×C8×C11—22no—
258C2×C8×C11C2412yes—
259C2×C8×C11C2412yes—
260C11×C4⋊C4—21no—
261C11×C4⋊C4—24no—
262C11×C4⋊C4C2412yes—
263C11×C22⋊C4—24no—
264C11×C22⋊C4—24no—
265C42×C11—24no—
266C42×C11C2×D412yes—
267C42×C11C2412yes—
268C22⋊Dic11—24no—
269C22⋊Dic11—24no—
270#4326—44no—
271#4326—44no—
272#4325—44no—
273#4324—44no—
274(C2×D11)⋊C4—24no—
275(C2×D11)⋊C4—24no—
276(C2×D11)⋊C4—24no—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4—24no—
279(C2×D11)⋊C4—24no—
280C4⋊Dic11—24no—
281C4⋊Dic11—21no—
282C4⋊Dic11C2412yes—
283Dic11⋊C4—24no—
284Dic11⋊C4—24no—
285Dic11⋊C4—24no—
286Dic11⋊C4—24no—
287Dic11⋊C4—24no—
288C4×Dic11—24no—
289C4×Dic11C2×D414yes—
290C4×Dic11C2×D412yes—
291C4×Dic11C2×D414yes—
292C4×Dic11C2412yes—
293C2×C11⋊C8—22no—
294C2×C11⋊C8—22no—
295C2×C11⋊C8C2412yes—
296C2×C11⋊C8C2412yes—
297Dic44—44no—
298#4314—44no—
299C2×#533—111no—
300C22×#124—111no—
301#3215—1116no—
302C2×#497—111no—
303C2×#497—111no—
304C2×#489—111no—
305C2×#489—111no—
306C2×#464—111no—
307C2×#464—111no—
308C2×#464—111no—
309C2×#464D1111yescharacteristic, complemented
310C2×#451—111no—
311C2×#451—111no—
312C2×#450—111no—
313C2×#450—111no—
314C2×#432—111no—
315C23×C11—22no—
316C23×C11—42no—
317C23×C11—42no—
318C23×C11—42no—
319C23×C11C22×D411yescharacteristic
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—48no—
324C22×D11—48no—
325C22×D11—42no—
326C22×D11—42no—
327C22×D11—42no—
328C22×D11—48no—
329C22×D11—816no—
330C22×D11#13714yes—
331C22×D11C22×D412yes—
332Q8×C11—22no—
333Q8×C11—22no—
334Q8×C11—22no—
335Q8×C11—22no—
336Q8×C11—42no—
337Q8×C11—42no—
338D4×C11—22no—
339D4×C11—22no—
340D4×C11—42no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—42no—
347C2×C4×C11—42no—
348C2×C4×C11—42no—
349C2×C4×C11C22×D412yes—
350C2×C4×C11C22×D412yes—
351C2×C4×C11C22×D411yescharacteristic
352C2×C4×C11H(5,𝔽2)12yes—
353C2×C4×C11H(5,𝔽2)12yes—
354C2×C4×C11C2511yescharacteristic
355C22⋊D11—48no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—42no—
363C2×Dic11—42no—
364C2×Dic11—42no—
365C2×Dic11C22×D412yes—
366C2×Dic11C22×D412yes—
367C2×Dic11C22×D412yes—
368D44—22no—
369D44—22no—
370D44—42no—
371C4×D11—28no—
372C4×D11—24no—
373C4×D11—22no—
374C4×D11—22no—
375C4×D11—44no—
376C4×D11—48no—
377Dic22—22no—
378Dic22—22no—
379Dic22—22no—
380Dic22—22no—
381Dic22—48no—
382Dic22—48no—
383Dic22—42no—
384Dic22—42no—
385C8×C11—22no—
386C8×C11—22no—
387C11⋊C8—22no—
388C11⋊C8—22no—
389C23×Q8—111no—
390C23×D4—111no—
391C22×Q16—111no—
392C22×Q16—111no—
393C22×Q16—111no—
394C22×Q16C2×D1111yescharacteristic, complemented
395C22×SD16—111no—
396C22×SD16—111no—
397C22×SD16—111no—
398C22×SD16C2×D1111yescharacteristic
399#533—118no—
400#533—224no—
401C2×C4⋊Q8—111no—
402C2×C4⋊Q8—111no—
403C2×#125—221no—
404C2×#124—111no—
405C2×#124—111no—
406C2×#124—118no—
407C2×#124—111no—
408C2×#124—221no—
409C2×#124—221no—
410C2×#124—224no—
411C2×#124C2×D1111yescharacteristic
412C2×C22⋊Q8—111no—
413C2×C22⋊Q8—111no—
414C2×C22⋊Q8—221no—
415C2×C4×Q8—111no—
416C2×C4×Q8—221no—
417C2×C4×Q8C2×D1111yescharacteristic, complemented
418C2×#117—221no—
419C22×C22⋊C4—221no—
420C22×C22⋊C4—221no—
421C22×C42—111no—
422#497—118no—
423#497—118no—
424#489—118no—
425#489—118no—
426#464—118no—
427#464—118no—
428#464—118no—
429#464C2×D1118yescomplemented
430#451—118no—
431#451—118no—
432#450—118no—
433#450—118no—
434#432—118no—
435C2×C4⋊C8—111no—
436C2×C4⋊C8C2×D1111yescharacteristic, complemented
437C2×#103—111no—
438C2×#103—111no—
439C2×#103—111no—
440C2×#103C2×D1111yescharacteristic, complemented
441C2×#102—111no—
442C2×#102—111no—
443C2×#102—111no—
444C2×#102C2×D1111yescharacteristic
445C2×C22⋊C8—111no—
446C2×C22⋊C8—111no—
447C2×#97—111no—
448C2×#97—111no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—84no—
453C22×C11#53512yes—
454C22×C11C2×#13712yes—
455C22×C11#57512yes—
456C22×C11C23×D411yescharacteristic
457C2×D11—22no—
458C2×D11—28no—
459C2×D11—22no—
460C2×D11—42no—
461C2×D11—42no—
462C2×D11—42no—
463C2×D11—816no—
464C2×D11—84no—
465C2×D11C2×#13714yes—
466C4×C11—22no—
467C4×C11—22no—
468C4×C11—42no—
469C4×C11—42no—
470C4×C11—42no—
471C4×C11#53512yes—
472C4×C11C2×H(5,𝔽2)11yescharacteristic
473C4×C11C2×H(5,𝔽2)11yescharacteristic
474Dic11—22no—
475Dic11—22no—
476Dic11—22no—
477Dic11—42no—
478Dic11—42no—
479Dic11—42no—
480C25—221no—
481C22×Q8—114no—
482C22×Q8—111no—
483C22×Q8—111no—
484C22×Q8—221no—
485C22×Q8—221no—
486C22×Q8—222no—
487C22×Q8—442no—
488C22×Q8—442no—
489C22×Q8C22×D1111yescharacteristic
490C22×Q8C22×D1111yescharacteristic
491C22×D4—114no—
492C22×D4—111no—
493C22×D4—222no—
494C22×D4—221no—
495C22×D4—442no—
496C22×D4—442no—
497C22×D4C22×D1111yescharacteristic
498C23×C4—111no—
499C23×C4—111no—
500C23×C4—111no—
501C23×C4—221no—
502C2×Q16—42no—
503C2×Q16—114no—
504C2×Q16—114no—
505C2×Q16—114no—
506C2×Q16—442no—
507C2×Q16—442no—
508C2×Q16—442no—
509C2×Q16C22×D1114yescomplemented
510C2×SD16—42no—
511C2×SD16—114no—
512C2×SD16—114no—
513C2×SD16—114no—
514C2×SD16—442no—
515C2×SD16—442no—
516C2×SD16—442no—
517C2×SD16C22×D1114yes—
518C22×C8—111no—
519C22×C8—111no—
520C22×C8C22×D1111yescharacteristic
521C22×C8C22×D1111yescharacteristic
522C4⋊Q8—114no—
523C4⋊Q8—114no—
524C4⋊Q8—222no—
525C4⋊Q8—222no—
526#125—228no—
527#124—22no—
528#124—114no—
529#124—114no—
530#124—114no—
531#124—228no—
532#124—228no—
533#124—222no—
534#124—222no—
535#124—222no—
536#124C22×D1114yes—
537C22⋊Q8—114no—
538C22⋊Q8—114no—
539C22⋊Q8—222no—
540C22⋊Q8—228no—
541C22⋊Q8—222no—
542C4×Q8—22no—
543C4×Q8—114no—
544C4×Q8—228no—
545C4×Q8—222no—
546C4×Q8C22×D1114yescomplemented
547#117—228no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—111no—
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—21no—
559C2×C22⋊C4—228no—
560C2×C22⋊C4—228no—
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×C22⋊C4—221no—
569C2×C42—21no—
570C2×C42—111no—
571C2×C42—111no—
572C2×C42—111no—
573C2×C42—114no—
574C2×C42—114no—
575C2×C42—221no—
576C2×C42C22×D1111yescharacteristic
577C4⋊C8—114no—
578C4⋊C8C22×D1114yescomplemented
579#103—114no—
580#103—114no—
581#103—114no—
582#103C22×D1114yescomplemented
583#102—114no—
584#102—114no—
585#102—114no—
586#102C22×D1114yes—
587C22⋊C8—114no—
588C22⋊C8—114no—
589#97—114no—
590#97—114no—
591C2×C11—82no—
592C2×C11#321514yescomplemented
593C2×C11C2×#53511yescharacteristic
594C2×C11C22×#13711yescharacteristic
595C2×C11C2×#57511yescharacteristic
596D11—24no—
597D11—82no—
598C24—21no—
599C24—111no—
600C24—224no—
601C24—221no—
602C24—444no—
603C24—444no—
604C24—444no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—22no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—112no—
612C2×Q8—112no—
613C2×Q8—224no—
614C2×Q8—224no—
615C2×Q8—221no—
616C2×Q8—221no—
617C2×Q8—222no—
618C2×Q8—222no—
619C2×Q8—222no—
620C2×Q8—222no—
621C2×Q8—444no—
622C2×Q8—444no—
623C2×Q8—444no—
624C2×Q8—444no—
625C2×Q8—448no—
626C2×Q8C23×D1112yes—
627C2×Q8C23×D1112yes—
628C2×D4—21no—
629C2×D4—22no—
630C2×D4—22no—
631C2×D4—112no—
632C2×D4—224no—
633C2×D4—221no—
634C2×D4—222no—
635C2×D4—222no—
636C2×D4—444no—
637C2×D4—444no—
638C2×D4—448no—
639C2×D4—444no—
640C2×D4C23×D1112yes—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—111no—
645C22×C4—111no—
646C22×C4—111no—
647C22×C4—114no—
648C22×C4—112no—
649C22×C4—112no—
650C22×C4—114no—
651C22×C4—224no—
652C22×C4—224no—
653C22×C4—222no—
654C22×C4—222no—
655C22×C4—221no—
656C22×C4—221no—
657C22×C4—221no—
658C22×C4—442no—
659C22×C4—444no—
660C22×C4D4×D1111yescharacteristic
661C22×C4D4×D1111yescharacteristic
662C22×C4C23×D1111yescharacteristic
663Q16—44no—
664Q16—444no—
665Q16—444no—
666Q16—444no—
667SD16—44no—
668SD16—444no—
669SD16—444no—
670SD16—444no—
671C2×C8—22no—
672C2×C8—22no—
673C2×C8—112no—
674C2×C8—112no—
675C2×C8—222no—
676C2×C8—222no—
677C2×C8C23×D1112yes—
678C2×C8C23×D1112yes—
679C4⋊C4—24no—
680C4⋊C4—21no—
681C4⋊C4—112no—
682C4⋊C4—224no—
683C4⋊C4—224no—
684C4⋊C4—224no—
685C4⋊C4—224no—
686C4⋊C4—224no—
687C4⋊C4—221no—
688C4⋊C4—224no—
689C4⋊C4C23×D1112yes—
690C22⋊C4—24no—
691C22⋊C4—24no—
692C22⋊C4—224no—
693C22⋊C4—224no—
694C22⋊C4—224no—
695C22⋊C4—224no—
696C22⋊C4—224no—
697C22⋊C4—224no—
698C22⋊C4—224no—
699C22⋊C4—224no—
700C42—24no—
701C42—114no—
702C42—114no—
703C42—112no—
704C42—112no—
705C42—224no—
706C42D4×D1112yes—
707C42C23×D1112yes—
708C11C2×#321511yescharacteristic, complemented, Sylow
709C23—22no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—114no—
714C23—112no—
715C23—222no—
716C23—222no—
717C23—222no—
718C23—448no—
719C23—448no—
720C23—448no—
721C23—442no—
722C23—442no—
723C23—442no—
724C23—8816no—
725C23C2×D4×D1111yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—22no—
729Q8—22no—
730Q8—42no—
731Q8—42no—
732Q8—222no—
733Q8—222no—
734Q8—222no—
735Q8—222no—
736Q8—448no—
737Q8—448no—
738Q8—442no—
739Q8—442no—
740D4—22no—
741D4—22no—
742D4—42no—
743D4—222no—
744D4—222no—
745D4—448no—
746D4—442no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—112no—
756C2×C4—112no—
757C2×C4—112no—
758C2×C4—228no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—224no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—222no—
767C2×C4—222no—
768C2×C4—444no—
769C2×C4—448no—
770C2×C4—442no—
771C2×C4—442no—
772C2×C4—442no—
773C2×C4C2×D4×D1112yes—
774C2×C4C2×D4×D1112yes—
775C2×C4C2×D4×D1111yescharacteristic
776C2×C4#6703712yes—
777C2×C4#6704212yes—
778C2×C4C24×D1111yescharacteristic
779C8—22no—
780C8—22no—
781C8—222no—
782C8—222no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—84no—
787C22—114no—
788C22—228no—
789C22—222no—
790C22—222no—
791C22—442no—
792C22—442no—
793C22—442no—
794C22—8816no—
795C22—884no—
796C22#1062313812yes—
797C22#1062329912yes—
798C22D11×#13712yes—
799C22C22×D4×D1111yescharacteristic
800C4—22no—
801C4—22no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—222no—
806C4—222no—
807C4—222no—
808C4—442no—
809C4—442no—
810C4—442no—
811C4#1062313812yes—
812C4C2×#6703711yescharacteristic
813C4C2×#6704211yescharacteristic
814C2—82no—
815C2—224no—
816C2—882no—
817C2#1307961714yesdirect product factor
818C2C2×#1062313811yescharacteristic
819C2C2×D11×#13711yescharacteristic
820C2C2×#1062329911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#464C2
socleC23×C11C22×D4
prime radicalC22×D4×D11C22
hypercenterC2×#464D11
hypocenterC11C2×#3215
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×#10623109C2semidirect
3. #13079617C2direct (N × H)
4. C2×#10622803C2semidirect
5. C2×#10622780C2semidirect
6. C2×#10622408C2semidirect
7. C2×#10622378C2semidirect
8. C2×#10622458C2semidirect
9. C2×#10622641C2semidirect
10. C2×#10622667C2semidirect
11. C2×#10622421C2semidirect
12. C2×#10622799C2semidirect
15. C2×#10622448C2semidirect
16. C2×C11×#464C2semidirect
19. C22×C11×Q16C22semidirect
22. C2×C4×Q8×C11C22semidirect
25. C2×#66997C22semidirect
26. C22×#4326C22semidirect
27. C22×#4326C22semidirect
31. C22×Dic44C22semidirect
36. #10623109C22semidirect
40. C2×#66941C22semidirect
49. C2×C4×Dic22C22semidirect
50. C11×#464C22semidirect
51. C2×C11×C4⋊C8C22semidirect
52. C2×C11×#103C22semidirect
54. C2×#66899C22semidirect
56. #10622803C22semidirect
57. #10622799C22semidirect
59. #10622780C22semidirect
63. C2×#66880C22semidirect
64. C2×#66879C22semidirect
65. C2×#66879C22semidirect
66. #10622667C22semidirect
67. #10622641C22semidirect
68. C2×#66874C22semidirect
70. C2×C4⋊(C11⋊C8)C22semidirect
71. #10622458C22semidirect
72. #10622448C22semidirect
73. #10622421C22semidirect
74. #10622408C22semidirect
76. #10622378C22semidirect
100. C2×C11×Q16C23semidirect
108. C4×Q8×C11C23semidirect
122. #66997C23semidirect
125. C2×#4326C23semidirect
126. C2×#4326C23semidirect
153. C2×Dic44C23semidirect
161. #66941C23semidirect
173. C4×Dic22C23semidirect
174. C11×C4⋊C8C23semidirect
175. C11×#103C23semidirect
177. #66899C23semidirect
182. #66880C23semidirect
183. #66879C23semidirect
184. #66879C23semidirect
185. #66874C23semidirect
187. C4⋊(C11⋊C8)C23semidirect
309. C2×#464D11semidirect
394. C22×Q16C2×D11semidirect
417. C2×C4×Q8C2×D11semidirect
429. #464C2×D11semidirect
436. C2×C4⋊C8C2×D11semidirect
440. C2×#103C2×D11semidirect
509. C2×Q16C22×D11semidirect
546. C4×Q8C22×D11semidirect
578. C4⋊C8C22×D11semidirect
582. #103C22×D11semidirect
592. C2×C11#3215semidirect
708. C11C2×#3215semidirect
817. C2#13079617direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231092
C2×D11×#1242
#130796172
C2×#106228032
C2×#106227802
C2×#106224082
C2×#106223782
C2×#106224582
C2×#106226412
C2×#106226672
C2×#106224212
C2×#106227992
C2×#106223892
C2×#106227822
C2×#106224482
C2×C11×#4642
C2×#321511