Finite Group Databasebeta

← #14926698

Subgroups — #14926698

Order 2816.

2642 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623025C212yesmaximal, complemented
2#13076968C211yesmaximal, characteristic, complemented
3#13076961C211yesmaximal, characteristic, complemented
4#13076898C212yesmaximal, complemented
5#13074544C212yesmaximal, complemented
6#13074350C212yesmaximal, complemented
7#13073739C214yesmaximal, complemented
8#13073709C214yesmaximal, complemented
9#13073038C212yesmaximal, complemented
10#13072979C212yesmaximal, complemented
11#13072204C212yesmaximal, complemented
12#13072130C212yesmaximal, complemented
13#13071319C212yesmaximal, complemented
14C4×#66983C212yesmaximal, complemented
15C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C2×#67006C2214yes—
22C2×#66983C2212yes—
23C2×#66983C2212yes—
24C2×#66983C2212yes—
25C2×#66983C2212yes—
26C2×#66983C2212yes—
27C2×C4×C22⋊D11C2214yes—
28C2×#66977C2212yes—
29#10623025—216no—
30C2×#66938C2214yes—
31C2×#66937C2214yes—
32C2×#66936C2214yes—
33C2×#66932C2214yes—
34C2×#66927C2211yescharacteristic, complemented
35C2×C4×D44C2212yescomplemented
36C2×#66922C2211yescharacteristic, complemented
37C4×C11×C22⋊C4C2212yes—
38C4×C11×C22⋊C4C2212yes—
39C4×C11×C22⋊C4C2212yes—
40C4×C11×C22⋊C4C2212yes—
41C2×C11×#95C2211yescharacteristic
42C2×C11×#95C2211yescharacteristic
43#10622826C2214yes—
44#10622826C2214yes—
45#10622826C2214yes—
46#10622826C2214yes—
47#10622825C2212yes—
48#10622825C2212yes—
49#10622825C2212yes—
50#10622825C2212yes—
51#10622574C2214yes—
52#10622574C2214yes—
53#10622573C2214yes—
54#10622566C2214yes—
55#10622553C2214yescomplemented
56#10622552C2212yescomplemented
57#10622552C2212yescomplemented
58#10622552C2212yescomplemented
59#10622552C2212yescomplemented
60C4×(C2×D11)⋊C4C2214yescomplemented
61#10622548C2211yescharacteristic, complemented
62#10622548C2211yescharacteristic, complemented
63C4×C4⋊Dic11C2212yescomplemented
64#10622542C2212yescomplemented
65#10622541C2212yescomplemented
66#10622541C2212yescomplemented
67#10622541C2212yescomplemented
68#10622287C2214yescomplemented
69#10622286C2214yescomplemented
70#10622285C2214yescomplemented
71#10622283C2214yescomplemented
72#10622281C2214yescomplemented
73#10622278C2214yescomplemented
74#10622272C2214yescomplemented
75#10622266C2214yescomplemented
76C25×C11C2311yescharacteristic
77C23×C4×C11—24no—
78C23×C4×C11—42no—
79C23×C4×C11—42no—
80C23×C4×C11C2312yes—
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2312yes—
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C22×C22⋊D11C2314yes—
89C22×C22⋊D11C2314yes—
90C22×C22⋊D11C2314yes—
91C22×D44C2312yes—
92C22×D44C2312yes—
93C22×D44C2312yes—
94C22×C4×D11C2314yes—
95C22×Dic22C2312yes—
96C2×C11×C22⋊C4—24no—
97C2×C11×C22⋊C4D418yescomplemented
98C2×C11×C22⋊C4C2312yes—
99C2×C11×C22⋊C4C2312yes—
100C2×C11×C22⋊C4C2312yes—
101C2×C11×C22⋊C4C2312yes—
102C2×C42×C11—42no—
103C2×C42×C11—42no—
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2312yes—
106C2×C42×C11C2311yescharacteristic
107C2×C42×C11C2311yescharacteristic
108C2×C42×C11C2311yescharacteristic
109C2×C42×C11C2312yes—
110#67006—216no—
111C2×C22⋊Dic11C2314yes—
112C2×C22⋊Dic11C2314yes—
113C2×C22⋊Dic11C2314yes—
114#66983—28no—
115#66983—28no—
116#66983—28no—
117#66983—44no—
118#66983—44no—
119C4×C22⋊D11—216no—
120C2×(C2×D11)⋊C4C2314yes—
121C2×(C2×D11)⋊C4C2314yes—
122C2×(C2×D11)⋊C4C2314yes—
123C2×(C2×D11)⋊C4C2314yes—
124C2×(C2×D11)⋊C4C2314yes—
125C2×(C2×D11)⋊C4C2314yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×C4⋊Dic11C2312yes—
129C2×C4⋊Dic11C2312yes—
130C2×C4⋊Dic11C2312yes—
131C2×C4⋊Dic11C2312yes—
132C2×C4⋊Dic11C2312yes—
133C2×C4⋊Dic11C2312yes—
134C2×C4⋊Dic11C2312yes—
135C2×C4⋊Dic11C2312yes—
136#66977—28no—
137C2×Dic11⋊C4C2314yes—
138C2×Dic11⋊C4C2314yes—
139C2×C4×Dic11C2314yes—
140#66938—216no—
141#66937—216no—
142#66936—216no—
143#66932—216no—
144#66927—42no—
145C4×D44—44no—
146#66922—42no—
147C11×#95C2312yes—
148C11×#95C2312yes—
149C11×#95C2312yes—
150C11×#95C2312yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157#35005—111nomaximal, Sylow
158C24×C11—22no—
159C24×C11—22no—
160C24×C11—41no—
161C24×C11—41no—
162C24×C11—41no—
163C24×C11—41no—
164C24×C11C2×D414yes—
165C24×C11C2412yes—
166C24×C11C2411yescharacteristic
167C23×D11C2414yes—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—24no—
173C22×C4×C11—24no—
174C22×C4×C11—24no—
175C22×C4×C11—24no—
176C22×C4×C11—41no—
177C22×C4×C11—41no—
178C22×C4×C11—41no—
179C22×C4×C11—41no—
180C22×C4×C11—42no—
181C22×C4×C11—42no—
182C22×C4×C11—41no—
183C22×C4×C11—41no—
184C22×C4×C11—41no—
185C22×C4×C11—41no—
186C22×C4×C11—41no—
187C22×C4×C11—41no—
188C22×C4×C11—416no—
189C22×C4×C11C2×D414yes—
190C22×C4×C11C2×D414yes—
191C22×C4×C11#4114yes—
192C22×C4×C11#4114yes—
193C22×C4×C11C2412yes—
194C22×C4×C11C2412yes—
195C22×C4×C11C2412yes—
196C22×C4×C11C2411yescharacteristic
197C22×C4×C11C2411yescharacteristic
198C22×C4×C11C2411yescharacteristic
199C22×C4×C11C2411yescharacteristic
200C22×C4×C11C2411yescharacteristic
201C22×C4×C11C2411yescharacteristic
202C2×C22⋊D11—28no—
203C2×C22⋊D11—28no—
204C2×C22⋊D11—28no—
205C2×C22⋊D11—28no—
206C2×C22⋊D11—28no—
207C2×C22⋊D11—44no—
208C2×C22⋊D11—44no—
209C2×C22⋊D11—44no—
210C2×C22⋊D11—44no—
211C22×Dic11C2414yes—
212C22×Dic11C2414yes—
213C22×Dic11C2414yes—
214C2×D44—24no—
215C2×D44—24no—
216C2×D44—24no—
217C2×D44—24no—
218C2×D44—24no—
219C2×D44—42no—
220C2×D44—42no—
221C2×D44—42no—
222C2×D44—42no—
223C2×C4×D11—28no—
224C2×C4×D11—44no—
225C2×C4×D11—44no—
226C2×Dic22—24no—
227C2×Dic22—42no—
228C2×Dic22—42no—
229C11×C22⋊C4—24no—
230C11×C22⋊C4—24no—
231C11×C22⋊C4C2×D418yes—
232C11×C22⋊C4C2×D418yes—
233C42×C11—22no—
234C42×C11—24no—
235C42×C11—22no—
236C42×C11—41no—
237C42×C11—41no—
238C42×C11—42no—
239C22⋊Dic11—28no—
240C22⋊Dic11—28no—
241C22⋊Dic11—28no—
242(C2×D11)⋊C4—28no—
243(C2×D11)⋊C4—28no—
244(C2×D11)⋊C4—28no—
245(C2×D11)⋊C4—28no—
246(C2×D11)⋊C4—44no—
247(C2×D11)⋊C4—44no—
248(C2×D11)⋊C4—44no—
249(C2×D11)⋊C4—44no—
250C4⋊Dic11—24no—
251C4⋊Dic11—24no—
252C4⋊Dic11—24no—
253C4⋊Dic11—24no—
254C4⋊Dic11—24no—
255C4⋊Dic11—24no—
256C4⋊Dic11—42no—
257C4⋊Dic11—42no—
258Dic11⋊C4—28no—
259Dic11⋊C4—28no—
260C4×Dic11—28no—
261C2×#538—112no—
262#2857—111no—
263#2856—111no—
264#2847—112no—
265#2639—112no—
266#2617—112no—
267#2559—114no—
268#2557—114no—
269#2496—112no—
270#2491—112no—
271#2428—112no—
272#2422—112no—
273#2325—112no—
274C4×#121—112no—
275C2×C4×C22⋊C4D1111yescharacteristic, complemented
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—28no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—44no—
288C23×C11—44no—
289C23×C11—44no—
290C23×C11—44no—
291C23×C11—44no—
292C23×C11—44no—
293C23×C11C22×D414yes—
294C23×C11C22×D412yes—
295C23×C11C2×#4112yes—
296C23×C11C2×#4112yes—
297C23×C11C2511yescharacteristic
298C22×D11—24no—
299C22×D11—24no—
300C22×D11—24no—
301C22×D11—24no—
302C22×D11—24no—
303C22×D11—24no—
304C22×D11—24no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—22no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—22no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—28no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—44no—
325C2×C4×C11—44no—
326C2×C4×C11—44no—
327C2×C4×C11—48no—
328C2×C4×C11—44no—
329C2×C4×C11—44no—
330C2×C4×C11—48no—
331C2×C4×C11C22×D414yes—
332C2×C4×C11C22×D412yes—
333C2×C4×C11C22×D412yes—
334C2×C4×C11C2×#4112yes—
335C2×C4×C11C2×#4112yes—
336C2×C4×C11C2×#4112yes—
337C2×C4×C11C2×#4112yes—
338C2×C4×C11H(5,𝔽2)12yes—
339C2×C4×C11H(5,𝔽2)12yes—
340C22⋊D11—416no—
341C22⋊D11—88no—
342C22⋊D11—88no—
343C2×Dic11—24no—
344C2×Dic11—24no—
345C2×Dic11—24no—
346C2×Dic11—24no—
347C2×Dic11—24no—
348C2×Dic11—24no—
349C2×Dic11—24no—
350C2×Dic11—24no—
351C2×Dic11—24no—
352D44—48no—
353D44—84no—
354D44—84no—
355C4×D11—88no—
356Dic22—84no—
357C24×C4C2×D1111yescharacteristic
358#538—2216no—
359C2×C4⋊Q8—111no—
360C2×#127—111no—
361C2×#126—114no—
362C2×#124—114no—
363C2×#123—114no—
364C2×C22⋊Q8—112no—
365C2×#121—112no—
366C2×#121—112no—
367C2×#121—112no—
368C2×#121—112no—
369C2×#121—112no—
370C2×#121—114no—
371C2×#120—114no—
372C2×C4×D4—114no—
373C2×C4×D4—112no—
374C22×C22⋊C4C2×D1111yescharacteristic
375C22×C22⋊C4C2×D1111yescharacteristic
376C22×C42C2×D1111yescharacteristic
377C22×C42C2×D1111yescharacteristic
378#400—114no—
379#397—114no—
380#397—114no—
381#394—114no—
382#394—114no—
383#394—114no—
384#393—114no—
385#392—114no—
386#391—112no—
387#390—112no—
388#390—112no—
389#390—112no—
390#390—112no—
391#389—112no—
392#389—112no—
393#389—112no—
394#388—114no—
395#388—114no—
396#387—114no—
397#386—114no—
398#386—114no—
399#386—114no—
400#386—114no—
401#386—114no—
402#385—114no—
403#384—111no—
404#384—111no—
405#380—112no—
406#380—112no—
407#380—112no—
408#380—112no—
409C4×C4⋊C4—112no—
410C4×C22⋊C4—114no—
411C4×C22⋊C4C2×D1112yes—
412C4×C22⋊C4C2×D1112yes—
413C4×C22⋊C4C2×D1112yes—
414C4×C22⋊C4C2×D1112yes—
415C2×#95C2×D1111yescharacteristic
416C2×#95C2×D1111yescharacteristic
417C22×C11—22no—
418C22×C11—22no—
419C22×C11—22no—
420C22×C11—22no—
421C22×C11—22no—
422C22×C11—22no—
423C22×C11—24no—
424C22×C11—24no—
425C22×C11—24no—
426C22×C11—416no—
427C22×C11—42no—
428C22×C11—42no—
429C22×C11—42no—
430C22×C11—42no—
431C22×C11#53214yes—
432C22×C11C23×D411yescharacteristic
433C22×C11C22×#4111yescharacteristic
434C22×C11C22×#4111yescharacteristic
435C22×C11C2×H(5,𝔽2)11yescharacteristic
436C22×C11C2×H(5,𝔽2)11yescharacteristic
437C22×C11#58511yescharacteristic
438C22×C11#58511yescharacteristic
439C2×D11—44no—
440C2×D11—44no—
441C2×D11—44no—
442C2×D11—44no—
443C2×D11—44no—
444C2×D11—44no—
445C2×D11—44no—
446C4×C11—22no—
447C4×C11—22no—
448C4×C11—24no—
449C4×C11—22no—
450C4×C11—22no—
451C4×C11—22no—
452C4×C11—42no—
453C4×C11—42no—
454C4×C11#53814yescomplemented
455Dic11—44no—
456Dic11—44no—
457Dic11—44no—
458C25C22×D1111yescharacteristic
459C22×Q8—112no—
460C22×D4—114no—
461C22×D4—114no—
462C22×D4—114no—
463C22×D4—112no—
464C22×D4—112no—
465C22×D4—112no—
466C23×C4—24no—
467C23×C4—42no—
468C23×C4—42no—
469C23×C4—114no—
470C23×C4C22×D1112yes—
471C23×C4C22×D1111yescharacteristic
472C23×C4C22×D1111yescharacteristic
473C23×C4C22×D1111yescharacteristic
474C23×C4C22×D1112yes—
475C23×C4C22×D1111yescharacteristic
476C23×C4C22×D1111yescharacteristic
477C23×C4C22×D1111yescharacteristic
478C4⋊Q8—442no—
479#127—442no—
480#126—2216no—
481#124—2216no—
482#123—2216no—
483C22⋊Q8—228no—
484#121—228no—
485#121—228no—
486#121—228no—
487#121—2216no—
488#121—444no—
489#121—444no—
490#120—2216no—
491C4×D4—2216no—
492C4×D4—444no—
493C2×C4⋊C4—112no—
494C2×C4⋊C4—114no—
495C2×C4⋊C4—114no—
496C2×C4⋊C4—112no—
497C2×C4⋊C4—112no—
498C2×C4⋊C4—112no—
499C2×C4⋊C4—112no—
500C2×C4⋊C4—112no—
501C2×C4⋊C4—112no—
502C2×C4⋊C4—112no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—114no—
505C2×C22⋊C4—114no—
506C2×C22⋊C4—114no—
507C2×C22⋊C4—114no—
508C2×C22⋊C4—114no—
509C2×C22⋊C4—114no—
510C2×C22⋊C4—114no—
511C2×C22⋊C4—114no—
512C2×C22⋊C4—114no—
513C2×C22⋊C4—114no—
514C2×C22⋊C4—114no—
515C2×C22⋊C4D4418yescomplemented
516C2×C22⋊C4C22×D1112yes—
517C2×C22⋊C4C22×D1112yes—
518C2×C22⋊C4C22×D1112yes—
519C2×C22⋊C4C22×D1112yes—
520C2×C42—42no—
521C2×C42—42no—
522C2×C42—114no—
523C2×C42C22×D1112yes—
524C2×C42C22×D1111yescharacteristic
525C2×C42C22×D1111yescharacteristic
526C2×C42C22×D1112yes—
527C2×C42C22×D1111yescharacteristic
528C2×C42C22×D1111yescharacteristic
529#95—114no—
530#95—114no—
531#95—114no—
532#95—114no—
533#95—114no—
534#95—114no—
535#95C22×D1112yes—
536#95C22×D1112yes—
537#95C22×D1112yes—
538#95C22×D1112yes—
539C2×C11—24no—
540C2×C11—44no—
541C2×C11C2×#53211yescharacteristic
542C2×C11C2×#53811yescharacteristic
543C2×C11#345511yescharacteristic
544C2×C11#349611yescharacteristic
545C2×C11#349611yescharacteristic
546C2×C11#350511yescharacteristic
547C2×C11#350611yescharacteristic
548D11—84no—
549C24—22no—
550C24—22no—
551C24—41no—
552C24—41no—
553C24—41no—
554C24—41no—
555C24—114no—
556C24C2×D4414yes—
557C24C23×D1112yes—
558C24C23×D1111yescharacteristic
559C2×Q8—224no—
560C2×Q8—442no—
561C2×Q8—442no—
562C2×D4—228no—
563C2×D4—228no—
564C2×D4—228no—
565C2×D4—228no—
566C2×D4—228no—
567C2×D4—224no—
568C2×D4—224no—
569C2×D4—224no—
570C2×D4—224no—
571C2×D4—224no—
572C2×D4—442no—
573C2×D4—442no—
574C2×D4—442no—
575C2×D4—442no—
576C2×D4—444no—
577C2×D4—444no—
578C2×D4—444no—
579C2×D4—444no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—416no—
601C22×C4—114no—
602C22×C4—114no—
603C22×C4—114no—
604C22×C4—228no—
605C22×C4—444no—
606C22×C4—444no—
607C22×C4C2×D4414yes—
608C22×C4C2×D4414yes—
609C22×C4#433914yes—
610C22×C4#433914yes—
611C22×C4C23×D1112yes—
612C22×C4C23×D1112yes—
613C22×C4C23×D1112yes—
614C22×C4C23×D1111yescharacteristic
615C22×C4C23×D1111yescharacteristic
616C22×C4C23×D1111yescharacteristic
617C22×C4C23×D1111yescharacteristic
618C22×C4C23×D1111yescharacteristic
619C22×C4C23×D1111yescharacteristic
620C4⋊C4—228no—
621C4⋊C4—228no—
622C4⋊C4—224no—
623C4⋊C4—224no—
624C4⋊C4—224no—
625C4⋊C4—224no—
626C4⋊C4—224no—
627C4⋊C4—224no—
628C4⋊C4—442no—
629C4⋊C4—442no—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—228no—
633C22⋊C4—228no—
634C22⋊C4—228no—
635C22⋊C4—228no—
636C22⋊C4—228no—
637C22⋊C4—228no—
638C22⋊C4—228no—
639C22⋊C4—444no—
640C22⋊C4—444no—
641C22⋊C4—444no—
642C22⋊C4—444no—
643C22⋊C4C2×D4418yes—
644C22⋊C4C2×D4418yes—
645C42—24no—
646C42—22no—
647C42—22no—
648C42—41no—
649C42—42no—
650C42—41no—
651C42—228no—
652C11#3500511yescharacteristic, complemented, Sylow
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—28no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—224no—
671C23—224no—
672C23—224no—
673C23—224no—
674C23—224no—
675C23—224no—
676C23—224no—
677C23C22×D4414yes—
678C23C22×D4412yes—
679C23C2×#433912yes—
680C23C2×#433912yes—
681C23C24×D1111yescharacteristic
682Q8—884no—
683D4—4416no—
684D4—448no—
685D4—884no—
686D4—884no—
687D4—888no—
688D4—888no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—28no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—48no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—48no—
715C2×C4—224no—
716C2×C4—224no—
717C2×C4—224no—
718C2×C4—224no—
719C2×C4—224no—
720C2×C4—224no—
721C2×C4—224no—
722C2×C4—224no—
723C2×C4—224no—
724C2×C4—888no—
725C2×C4C22×D4414yes—
726C2×C4C22×D4412yes—
727C2×C4C22×D4412yes—
728C2×C4C2×#433912yes—
729C2×C4C2×#433912yes—
730C2×C4C2×#433912yes—
731C2×C4C2×#433912yes—
732C2×C4#6703712yes—
733C2×C4#6703712yes—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—24no—
741C22—24no—
742C22—24no—
743C22—416no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—444no—
749C22—444no—
750C22—444no—
751C22—444no—
752C22—444no—
753C22—444no—
754C22—444no—
755C22#1062300814yes—
756C22C23×D4411yescharacteristic
757C22C22×#433911yescharacteristic
758C22C22×#433911yescharacteristic
759C22C2×#6703711yescharacteristic
760C22C2×#6703711yescharacteristic
761C22#1062345311yescharacteristic
762C22#1062345311yescharacteristic
763C4—24no—
764C4—22no—
765C4—22no—
766C4—22no—
767C4—22no—
768C4—22no—
769C4—42no—
770C4—42no—
771C4—444no—
772C4—444no—
773C4—444no—
774C4#1062302514yescomplemented
775C2—24no—
776C2—44no—
777C2—884no—
778C2C2×#1062300811yescharacteristic
779C2C2×#1062302511yescharacteristic
780C2#1308200611yescharacteristic
781C2#1308238011yescharacteristic
782C2#1308238011yescharacteristic
783C2#1308245511yescharacteristic
784C2#1308246811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C4×C11×C22⋊C4C2
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#35005
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10623025C2semidirect
2. #13076968C2semidirect
3. #13076961C2semidirect
4. #13076898C2semidirect
5. #13074544C2semidirect
6. #13074350C2semidirect
7. #13073739C2semidirect
8. #13073709C2semidirect
9. #13073038C2semidirect
10. #13072979C2semidirect
11. #13072204C2semidirect
12. #13072130C2semidirect
13. #13071319C2semidirect
14. C4×#66983C2semidirect
15. C2×C4×C11×C22⋊C4C2semidirect
34. C2×#66927C22semidirect
35. C2×C4×D44C22semidirect
36. C2×#66922C22semidirect
55. #10622553C22semidirect
56. #10622552C22semidirect
57. #10622552C22semidirect
58. #10622552C22semidirect
59. #10622552C22semidirect
60. C4×(C2×D11)⋊C4C22semidirect
61. #10622548C22semidirect
62. #10622548C22semidirect
63. C4×C4⋊Dic11C22semidirect
64. #10622542C22semidirect
65. #10622541C22semidirect
66. #10622541C22semidirect
67. #10622541C22semidirect
68. #10622287C22semidirect
69. #10622286C22semidirect
70. #10622285C22semidirect
71. #10622283C22semidirect
72. #10622281C22semidirect
73. #10622278C22semidirect
74. #10622272C22semidirect
75. #10622266C22semidirect
97. C2×C11×C22⋊C4D4semidirect
275. C2×C4×C22⋊C4D11semidirect
454. C4×C11#538semidirect
515. C2×C22⋊C4D44semidirect
652. C11#35005semidirect
774. C4#10623025semidirect

Maximal subgroups

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

subgroupindex
C2×#106230252
#130769682
#130769612
#130768982
#130745442
#130743502
#130737392
#130737092
#130730382
#130729792
#130722042
#130721302
#130713192
C4×#669832
C2×C4×C11×C22⋊C42
#3500511