Finite Group Databasebeta

← C2×#24913454 #35570872

Subgroups — C2×#24913454 #35570872

Order 21248.

2654 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24913454C2116yesmaximal, direct product factor
2C2×#19127640C211yesmaximal, characteristic, complemented
3C2×#19127628C211yesmaximal, characteristic, complemented
4C2×#19127627C211yesmaximal, characteristic, complemented
5C2×#19127618C211yesmaximal, characteristic, complemented
6C2×#19127617C211yesmaximal, characteristic, complemented
7C2×#19127617C211yesmaximal, characteristic, complemented
8C2×#19127610C211yesmaximal, characteristic
9C2×#19127602C211yesmaximal, characteristic, complemented
10C2×#19127593C211yesmaximal, characteristic, complemented
11C2×#19127591C211yesmaximal, characteristic, complemented
12C2×#19127587C211yesmaximal, characteristic, complemented
13C2×#19127578C211yesmaximal, characteristic, complemented
14C2×#19127578C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic83C211yesmaximal, characteristic, complemented
16C2×#396×C83C211yesmaximal, characteristic, complemented
17C23×D332C2211yescharacteristic
18C23×C22⋊D83C2211yescharacteristic
19C23×C22⋊D83C2211yescharacteristic
20C24×Dic83C2211yescharacteristic
21C22×C4⋊Dic83C2211yescharacteristic
22C22×C4⋊Dic83C2211yescharacteristic
23C22×C22⋊Dic83C2211yescharacteristic
24C22×(C2×D83)⋊C4C2211yescharacteristic
25C22×(C2×D83)⋊C4C2211yescharacteristic
26C22×(C2×D83)⋊C4C2211yescharacteristic
27C22×(C2×D83)⋊C4C2211yescharacteristic
28C22×(C2×D83)⋊C4C2211yescharacteristic
29C22×(C2×D83)⋊C4C2211yescharacteristic
30C22×(C2×D83)⋊C4C2211yescharacteristic
31C22×(C2×D83)⋊C4C2211yescharacteristic
32C22×(C2×D83)⋊C4C2211yescharacteristic
33C22×(C2×D83)⋊C4C2211yescharacteristic
34C22×C4×Dic83C2211yescharacteristic
35C22×C4×Dic83C2211yescharacteristic
36#19127640C2218yescomplemented
37#19127628C2218yescomplemented
38#19127627C2218yescomplemented
39#19127618C2218yescomplemented
40#19127617C2218yescomplemented
41#19127617C2218yescomplemented
42#19127610C2218yes—
43#19127602C2218yescomplemented
44#19127593C2218yescomplemented
45#19127591C2218yescomplemented
46#19127587C2218yescomplemented
47#19127578C2218yescomplemented
48#19127578C2218yescomplemented
49C22⋊C4×Dic83C2218yescomplemented
50C2×C83⋊#95C2211yescharacteristic
51C2×C83⋊#95C2211yescharacteristic
52C2×C83⋊#95C2211yescharacteristic
53C2×C83⋊#95C2211yescharacteristic
54C2×C83⋊#95C2211yescharacteristic
55C2×C83⋊#95C2211yescharacteristic
56C2×C83⋊#95C2211yescharacteristic
57C2×C83⋊#95C2211yescharacteristic
58C2×C83⋊#95C2211yescharacteristic
59C22×C4⋊C4×C83C2211yescharacteristic
60C22×C4⋊C4×C83C2211yescharacteristic
61C22×C4⋊C4×C83C2211yescharacteristic
62C22×C22⋊C4×C83C2211yescharacteristic
63C22×C22⋊C4×C83C2211yescharacteristic
64C22×C22⋊C4×C83C2211yescharacteristic
65#396×C83C2218yescomplemented
66C2×#95×C83C2211yescharacteristic
67C24×D83C2311yescharacteristic
68C24×D83C2311yescharacteristic
69C22×D332—24no—
70C22×D332—42no—
71C22×D332—42no—
72C22×D332C2314yes—
73C22×C22⋊D83—24no—
74C22×C22⋊D83—24no—
75C22×C22⋊D83—42no—
76C22×C22⋊D83—42no—
77C22×C22⋊D83—42no—
78C22×C22⋊D83—42no—
79C22×C22⋊D83C2314yes—
80C22×C22⋊D83C2314yes—
81C23×Dic83—24no—
82C23×Dic83—42no—
83C23×Dic83—42no—
84C23×Dic83C2311yescharacteristic
85C23×Dic83C2311yescharacteristic
86C23×Dic83C2311yescharacteristic
87C23×Dic83C2311yescharacteristic
88C23×Dic83C2311yescharacteristic
89C23×Dic83C2311yescharacteristic
90C23×Dic83C2314yes—
91C2×C4⋊Dic83—42no—
92C2×C4⋊Dic83—42no—
93C2×C4⋊Dic83C2314yes—
94C2×C4⋊Dic83C2314yes—
95C2×C22⋊Dic83—24no—
96C2×C22⋊Dic83C2314yes—
97C2×(C2×D83)⋊C4—24no—
98C2×(C2×D83)⋊C4—24no—
99C2×(C2×D83)⋊C4—42no—
100C2×(C2×D83)⋊C4—42no—
101C2×(C2×D83)⋊C4—42no—
102C2×(C2×D83)⋊C4—42no—
103C2×(C2×D83)⋊C4—42no—
104C2×(C2×D83)⋊C4—42no—
105C2×(C2×D83)⋊C4—42no—
106C2×(C2×D83)⋊C4—42no—
107C2×(C2×D83)⋊C4C2314yes—
108C2×(C2×D83)⋊C4C2314yes—
109C2×(C2×D83)⋊C4C2314yes—
110C2×(C2×D83)⋊C4C2314yes—
111C2×(C2×D83)⋊C4C2314yes—
112C2×(C2×D83)⋊C4C2314yes—
113C2×(C2×D83)⋊C4C2314yes—
114C2×(C2×D83)⋊C4C2314yes—
115C2×(C2×D83)⋊C4C2314yes—
116C2×(C2×D83)⋊C4C2314yes—
117C2×C4×Dic83—42no—
118C2×C4×Dic83—42no—
119C2×C4×Dic83C2314yes—
120C2×C4×Dic83C2314yes—
121C83⋊#95C2314yes—
122C83⋊#95C2314yes—
123C83⋊#95C2314yes—
124C83⋊#95C2314yes—
125C83⋊#95C2314yes—
126C83⋊#95C2314yes—
127C83⋊#95C2314yes—
128C83⋊#95C2314yes—
129C83⋊#95C2314yes—
130C25×C83C2311yescharacteristic
131C23×C4×C83C2311yescharacteristic
132C23×C4×C83C2311yescharacteristic
133C23×C4×C83C2311yescharacteristic
134C23×C4×C83C2311yescharacteristic
135C23×C4×C83C2311yescharacteristic
136C23×C4×C83C2311yescharacteristic
137C2×C4⋊C4×C83—24no—
138C2×C4⋊C4×C83—42no—
139C2×C4⋊C4×C83—42no—
140C2×C4⋊C4×C83C2314yes—
141C2×C4⋊C4×C83C2314yes—
142C2×C4⋊C4×C83C2314yes—
143C2×C22⋊C4×C83—24no—
144C2×C22⋊C4×C83—42no—
145C2×C22⋊C4×C83—42no—
146C2×C22⋊C4×C83C2314yes—
147C2×C22⋊C4×C83C2314yes—
148C2×C22⋊C4×C83C2314yes—
149#95×C83C2314yes—
150C23×D83—22no—
151C23×D83—22no—
152C23×D83—22no—
153C23×D83—22no—
154C23×D83—22no—
155C23×D83—22no—
156C23×D83—22no—
157C23×D83—22no—
158C23×D83—22no—
159C23×D83—22no—
160C23×D83—22no—
161C23×D83—22no—
162C23×D83—22no—
163C23×D83—22no—
164C23×D83C2412yes—
165C23×D83C2412yes—
166C2×D332—28no—
167C2×D332—44no—
168C2×D332—44no—
169C2×D332—416no—
170C2×C22⋊D83—28no—
171C2×C22⋊D83—28no—
172C2×C22⋊D83—44no—
173C2×C22⋊D83—44no—
174C2×C22⋊D83—44no—
175C2×C22⋊D83—44no—
176C2×C22⋊D83—416no—
177C2×C22⋊D83—416no—
178C22×Dic83—22no—
179C22×Dic83—22no—
180C22×Dic83—22no—
181C22×Dic83—22no—
182C22×Dic83—22no—
183C22×Dic83—22no—
184C22×Dic83—22no—
185C22×Dic83—22no—
186C22×Dic83—22no—
187C22×Dic83—22no—
188C22×Dic83—22no—
189C22×Dic83—22no—
190C22×Dic83—22no—
191C22×Dic83—22no—
192C22×Dic83—22no—
193C22×Dic83—22no—
194C22×Dic83—22no—
195C22×Dic83—28no—
196C22×Dic83—44no—
197C22×Dic83—44no—
198C22×Dic83—416no—
199C22×Dic83#4114yes—
200C22×Dic83C2412yes—
201C22×Dic83C2412yes—
202C22×Dic83C2412yes—
203C22×Dic83C2412yes—
204C22×Dic83C2412yes—
205C22×Dic83C2412yes—
206C4⋊Dic83—44no—
207C4⋊Dic83—44no—
208C22⋊Dic83—28no—
209(C2×D83)⋊C4—28no—
210(C2×D83)⋊C4—28no—
211(C2×D83)⋊C4—44no—
212(C2×D83)⋊C4—44no—
213(C2×D83)⋊C4—44no—
214(C2×D83)⋊C4—44no—
215(C2×D83)⋊C4—44no—
216(C2×D83)⋊C4—44no—
217(C2×D83)⋊C4—44no—
218(C2×D83)⋊C4—44no—
219C4×Dic83—44no—
220C4×Dic83—44no—
221C24×C83—22no—
222C24×C83—22no—
223C24×C83—22no—
224C24×C83—22no—
225C24×C83—22no—
226C24×C83—22no—
227C24×C83#4114yes—
228C24×C83C2412yes—
229C24×C83C2411yescharacteristic
230C22×C4×C83—22no—
231C22×C4×C83—22no—
232C22×C4×C83—22no—
233C22×C4×C83—22no—
234C22×C4×C83—22no—
235C22×C4×C83—22no—
236C22×C4×C83—22no—
237C22×C4×C83—22no—
238C22×C4×C83—22no—
239C22×C4×C83—22no—
240C22×C4×C83—22no—
241C22×C4×C83—22no—
242C22×C4×C83—22no—
243C22×C4×C83—22no—
244C22×C4×C83—22no—
245C22×C4×C83—22no—
246C22×C4×C83—22no—
247C22×C4×C83#4114yes—
248C22×C4×C83C2412yes—
249C22×C4×C83C2412yes—
250C22×C4×C83C2412yes—
251C22×C4×C83C2412yes—
252C22×C4×C83C2412yes—
253C22×C4×C83C2412yes—
254C4⋊C4×C83—28no—
255C4⋊C4×C83—44no—
256C4⋊C4×C83—44no—
257C22⋊C4×C83—28no—
258C22⋊C4×C83—44no—
259C22⋊C4×C83—44no—
260C23×C83—28no—
261C23×C83—28no—
262C23×C83—28no—
263C23×C83—22no—
264C23×C83—22no—
265C23×C83—22no—
266C23×C83—22no—
267C23×C83—22no—
268C23×C83—22no—
269C23×C83—44no—
270C23×C83—44no—
271C23×C83—44no—
272C23×C83—44no—
273C23×C83C2×#4112yes—
274C23×C83C2×#4112yes—
275C23×C83C2×#4114yes—
276C23×C83C2×#4112yes—
277C23×C83H(5,𝔽2)12yes—
278C23×C83H(5,𝔽2)12yes—
279C23×C83H(5,𝔽2)12yes—
280C23×C83H(5,𝔽2)12yes—
281C23×C83C2511yescharacteristic
282C22×D83—22no—
283C22×D83—22no—
284C22×D83—22no—
285C22×D83—22no—
286C22×D83—22no—
287C22×D83—22no—
288C22×D83—22no—
289C22×D83—22no—
290C22×D83—22no—
291C22×D83—22no—
292C22×D83—22no—
293C22×D83—22no—
294C22×D83—22no—
295C22×D83—22no—
296C22×D83—44no—
297C22×D83—44no—
298C22×D83—44no—
299C22×D83—44no—
300C22×D83—44no—
301C22×D83—44no—
302C22×D83—44no—
303C22×D83—44no—
304C22×D83—44no—
305C22×D83—44no—
306C22×D83—44no—
307C22×D83—44no—
308C22×D83—44no—
309C22×D83—44no—
310C2×C4×C83—28no—
311C2×C4×C83—22no—
312C2×C4×C83—22no—
313C2×C4×C83—22no—
314C2×C4×C83—22no—
315C2×C4×C83—22no—
316C2×C4×C83—22no—
317C2×C4×C83—22no—
318C2×C4×C83—22no—
319C2×C4×C83—22no—
320C2×C4×C83—22no—
321C2×C4×C83—22no—
322C2×C4×C83—22no—
323C2×C4×C83—22no—
324C2×C4×C83—22no—
325C2×C4×C83—22no—
326C2×C4×C83—22no—
327C2×C4×C83—22no—
328C2×C4×C83—44no—
329C2×C4×C83—44no—
330C2×C4×C83—44no—
331C2×C4×C83—44no—
332C2×C4×C83—44no—
333C2×C4×C83C2×#4114yes—
334C22⋊D83—416no—
335C22⋊D83—416no—
336C2×Dic83—28no—
337C2×Dic83—22no—
338C2×Dic83—22no—
339C2×Dic83—22no—
340C2×Dic83—22no—
341C2×Dic83—22no—
342C2×Dic83—22no—
343C2×Dic83—22no—
344C2×Dic83—22no—
345C2×Dic83—22no—
346C2×Dic83—22no—
347C2×Dic83—22no—
348C2×Dic83—22no—
349C2×Dic83—22no—
350C2×Dic83—22no—
351C2×Dic83—22no—
352C2×Dic83—22no—
353C2×Dic83—22no—
354C2×Dic83—416no—
355C2×Dic83—44no—
356C2×Dic83—44no—
357C2×Dic83—44no—
358C2×Dic83—44no—
359C2×Dic83—44no—
360C2×Dic83C2×#4114yes—
361D332—416no—
362C22×C83—24no—
363C22×C83—24no—
364C22×C83—24no—
365C22×C83—416no—
366C22×C83—42no—
367C22×C83—42no—
368C22×C83—42no—
369C22×C83—42no—
370C22×C83#52914yes—
371C22×C83#53814yes—
372C22×C83#53814yes—
373C22×C83#53814yes—
374C22×C83#53814yes—
375C22×C83#54014yes—
376C22×C83#54014yes—
377C22×C83C22×#4111yescharacteristic
378C22×C83C22×#4111yescharacteristic
379C22×C83C22×#4111yescharacteristic
380C22×C83C2×H(5,𝔽2)11yescharacteristic
381C22×C83C2×H(5,𝔽2)11yescharacteristic
382C22×C83C2×H(5,𝔽2)11yescharacteristic
383C22×C83C2×H(5,𝔽2)11yescharacteristic
384C2×D83—42no—
385C2×D83—42no—
386C2×D83—42no—
387C2×D83—42no—
388C2×D83—42no—
389C2×D83—42no—
390C2×D83—42no—
391C2×D83—42no—
392C2×D83—42no—
393C2×D83—42no—
394C2×D83—42no—
395C2×D83—42no—
396C2×D83—42no—
397C2×D83—42no—
398C2×D83—88no—
399C2×D83—88no—
400C4×C83—24no—
401C4×C83—42no—
402C4×C83—42no—
403C4×C83—42no—
404C4×C83—42no—
405C4×C83—42no—
406Dic83—24no—
407Dic83—42no—
408Dic83—42no—
409Dic83—42no—
410Dic83—42no—
411Dic83—42no—
412C2×#2648—831nomaximal, Sylow
413C2×C83—44no—
414C2×C83#264818yescomplemented
415C2×C83C2×#52911yescharacteristic
416C2×C83C2×#53811yescharacteristic
417C2×C83C2×#53811yescharacteristic
418C2×C83C2×#53811yescharacteristic
419C2×C83C2×#53811yescharacteristic
420C2×C83C2×#54011yescharacteristic
421C2×C83C2×#54011yescharacteristic
422D83—82no—
423D83—82no—
424#2648—8316no—
425C2×#400—831no—
426C2×#397—831no—
427C2×#397—831no—
428C2×#396D8311yescharacteristic, complemented
429C2×#394—831no—
430C2×#394—831no—
431C2×#394—831no—
432C2×#392—831no—
433C2×#390—831no—
434C2×#388—831no—
435C2×#388—831no—
436C2×#387—831no—
437C2×#386—831no—
438C2×#386—831no—
439C2×C4×C22⋊C4—831no—
440C83C2×#264811yescharacteristic, complemented, Sylow
441C23×D4—831no—
442C23×D4—831no—
443C23×D4—831no—
444C24×C4—831no—
445C22×C4⋊C4—831no—
446C22×C4⋊C4—831no—
447C22×C4⋊C4C2×D8311yescharacteristic
448C22×C4⋊C4C2×D8311yescharacteristic
449C22×C4⋊C4C2×D8311yescharacteristic
450C22×C22⋊C4—831no—
451C22×C22⋊C4—831no—
452C22×C22⋊C4—831no—
453C22×C22⋊C4—831no—
454C22×C22⋊C4—831no—
455C22×C22⋊C4—831no—
456C22×C22⋊C4—831no—
457C22×C22⋊C4—831no—
458C22×C22⋊C4—831no—
459C22×C22⋊C4—831no—
460C22×C22⋊C4—831no—
461C22×C22⋊C4C2×D8311yescharacteristic
462C22×C22⋊C4C2×D8311yescharacteristic
463C22×C22⋊C4C2×D8311yescharacteristic
464C22×C42—831no—
465C22×C42—831no—
466#400—838no—
467#397—838no—
468#397—838no—
469#396C2×D8318yescomplemented
470#394—838no—
471#394—838no—
472#394—838no—
473#392—838no—
474#390—838no—
475#388—838no—
476#388—838no—
477#387—838no—
478#386—838no—
479#386—838no—
480C4×C22⋊C4—838no—
481C2×#95—831no—
482C2×#95—831no—
483C2×#95—831no—
484C2×#95—831no—
485C2×#95—831no—
486C2×#95—831no—
487C2×#95—831no—
488C2×#95—831no—
489C2×#95—831no—
490C2×#95C2×D8311yescharacteristic
491C25—831no—
492C25—831no—
493C25C22×D8311yescharacteristic
494C22×D4—3322no—
495C22×D4—3322no—
496C22×D4—3322no—
497C22×D4—3322no—
498C22×D4—3322no—
499C22×D4—3322no—
500C22×D4—834no—
501C22×D4—834no—
502C22×D4—834no—
503C22×D4—1664no—
504C22×D4—1664no—
505C22×D4—1664no—
506C23×C4—3322no—
507C23×C4—3322no—
508C23×C4—834no—
509C23×C4—831no—
510C23×C4—831no—
511C23×C4—831no—
512C23×C4—831no—
513C23×C4—831no—
514C23×C4—831no—
515C23×C4—1664no—
516C23×C4C22×D8311yescharacteristic
517C23×C4C22×D8311yescharacteristic
518C23×C4C22×D8311yescharacteristic
519C23×C4C22×D8311yescharacteristic
520C23×C4C22×D8311yescharacteristic
521C23×C4C22×D8311yescharacteristic
522C2×C4⋊C4—24no—
523C2×C4⋊C4—42no—
524C2×C4⋊C4—42no—
525C2×C4⋊C4—3322no—
526C2×C4⋊C4—3322no—
527C2×C4⋊C4—834no—
528C2×C4⋊C4—834no—
529C2×C4⋊C4C22×D8314yes—
530C2×C4⋊C4C22×D8314yes—
531C2×C4⋊C4C22×D8314yes—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—3322no—
536C2×C22⋊C4—3322no—
537C2×C22⋊C4—3322no—
538C2×C22⋊C4—3322no—
539C2×C22⋊C4—3322no—
540C2×C22⋊C4—3322no—
541C2×C22⋊C4—3322no—
542C2×C22⋊C4—3322no—
543C2×C22⋊C4—834no—
544C2×C22⋊C4—834no—
545C2×C22⋊C4—834no—
546C2×C22⋊C4—834no—
547C2×C22⋊C4—834no—
548C2×C22⋊C4—834no—
549C2×C22⋊C4—834no—
550C2×C22⋊C4—834no—
551C2×C22⋊C4—834no—
552C2×C22⋊C4—834no—
553C2×C22⋊C4—834no—
554C2×C22⋊C4—1664no—
555C2×C22⋊C4—1664no—
556C2×C22⋊C4—1664no—
557C2×C22⋊C4C22×D8314yes—
558C2×C22⋊C4C22×D8314yes—
559C2×C22⋊C4C22×D8314yes—
560C2×C42—3322no—
561C2×C42—3322no—
562C2×C42—834no—
563C2×C42—834no—
564#95—834no—
565#95—834no—
566#95—834no—
567#95—834no—
568#95—834no—
569#95—834no—
570#95—834no—
571#95—834no—
572#95—834no—
573#95C22×D8314yes—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—832no—
581C24—832no—
582C24—1662no—
583C24—1662no—
584C24—1662no—
585C24—1662no—
586C24—1662no—
587C24—1662no—
588C24—1662no—
589C24—1662no—
590C24—1662no—
591C24—1662no—
592C24—1662no—
593C24—1662no—
594C24—1662no—
595C24—1662no—
596C24#1305059114yes—
597C24C23×D8312yes—
598C24C23×D8311yescharacteristic
599C2×D4—33216no—
600C2×D4—3324no—
601C2×D4—3324no—
602C2×D4—33216no—
603C2×D4—33216no—
604C2×D4—3324no—
605C2×D4—3324no—
606C2×D4—3324no—
607C2×D4—3324no—
608C2×D4—1668no—
609C2×D4—1668no—
610C2×D4—1668no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—33216no—
629C22×C4—3324no—
630C22×C4—3324no—
631C22×C4—834no—
632C22×C4—832no—
633C22×C4—832no—
634C22×C4—832no—
635C22×C4—832no—
636C22×C4—832no—
637C22×C4—832no—
638C22×C4—1668no—
639C22×C4—1662no—
640C22×C4—1662no—
641C22×C4—1662no—
642C22×C4—1662no—
643C22×C4—1662no—
644C22×C4—1662no—
645C22×C4—1662no—
646C22×C4—1662no—
647C22×C4—1662no—
648C22×C4—1662no—
649C22×C4—1662no—
650C22×C4—1662no—
651C22×C4—1662no—
652C22×C4—1662no—
653C22×C4—1662no—
654C22×C4—1662no—
655C22×C4—1662no—
656C22×C4#1305058914yes—
657C22×C4C23×D8312yes—
658C22×C4C23×D8312yes—
659C22×C4C23×D8312yes—
660C22×C4C23×D8312yes—
661C22×C4C23×D8312yes—
662C22×C4C23×D8312yes—
663C4⋊C4—28no—
664C4⋊C4—44no—
665C4⋊C4—44no—
666C4⋊C4—3324no—
667C4⋊C4—3324no—
668C22⋊C4—28no—
669C22⋊C4—44no—
670C22⋊C4—44no—
671C22⋊C4—3324no—
672C22⋊C4—3324no—
673C22⋊C4—3324no—
674C22⋊C4—3324no—
675C22⋊C4—3324no—
676C22⋊C4—3324no—
677C22⋊C4—3324no—
678C22⋊C4—3324no—
679C22⋊C4—1668no—
680C22⋊C4—1668no—
681C22⋊C4—1668no—
682C42—3324no—
683C42—3324no—
684C23—28no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—28no—
692C23—28no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—3324no—
698C23—3324no—
699C23—3324no—
700C23—3324no—
701C23—3324no—
702C23—3324no—
703C23—3324no—
704C23—3324no—
705C23—3324no—
706C23—3324no—
707C23—3324no—
708C23—3324no—
709C23—3324no—
710C23—3324no—
711C23—1662no—
712C23—1662no—
713C23—1662no—
714C23—1662no—
715C23—1662no—
716C23—1662no—
717C23—1662no—
718C23—1662no—
719C23—1662no—
720C23—1662no—
721C23—1662no—
722C23—1662no—
723C23—1662no—
724C23—1662no—
725C23#41×D8312yes—
726C23C2×#1305058912yes—
727C23C2×#1305059114yes—
728C23C2×#1305059112yes—
729C23#1458183712yes—
730C23#1458183712yes—
731C23#1458183812yes—
732C23#1458183812yes—
733C23C24×D8311yescharacteristic
734D4—33216no—
735D4—33216no—
736D4—33216no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—28no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—3324no—
761C2×C4—3324no—
762C2×C4—3324no—
763C2×C4—3324no—
764C2×C4—3324no—
765C2×C4—33216no—
766C2×C4—834no—
767C2×C4—1662no—
768C2×C4—1662no—
769C2×C4—1662no—
770C2×C4—1662no—
771C2×C4—1662no—
772C2×C4—1662no—
773C2×C4—1662no—
774C2×C4—1662no—
775C2×C4—1662no—
776C2×C4—1662no—
777C2×C4—1662no—
778C2×C4—1662no—
779C2×C4—1662no—
780C2×C4—1662no—
781C2×C4—1662no—
782C2×C4—1662no—
783C2×C4—1662no—
784C2×C4—1668no—
785C2×C4C2×#1305058914yes—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—416no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—3322no—
795C22—3322no—
796C22—3322no—
797C22—3322no—
798C22—3322no—
799C22—3322no—
800C22—3322no—
801C22—3322no—
802C22—3322no—
803C22—3322no—
804C22—3322no—
805C22—3322no—
806C22—3322no—
807C22—3322no—
808C22—6648no—
809C22—6648no—
810C22#1912823714yes—
811C22#1912828814yes—
812C22#1912829014yes—
813C22#1912829114yes—
814C22#1912829114yes—
815C22#1912830114yes—
816C22#1912830414yes—
817C22C2×#41×D8311yescharacteristic
818C22C22×#1305058911yescharacteristic
819C22C22×#1305059111yescharacteristic
820C22C2×#1458183711yescharacteristic
821C22C2×#1458183711yescharacteristic
822C22C2×#1458183811yescharacteristic
823C22C2×#1458183811yescharacteristic
824C4—24no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—42no—
830C4—3322no—
831C4—3322no—
832C4—3322no—
833C4—3322no—
834C4—3322no—
835C4—1664no—
836C2—44no—
837C2—6642no—
838C2—6642no—
839C2#2491345418yesdirect product factor
840C2C2×#1912823711yescharacteristic
841C2C2×#1912828811yescharacteristic
842C2C2×#1912829011yescharacteristic
843C2C2×#1912829111yescharacteristic
844C2C2×#1912829111yescharacteristic
845C2C2×#1912830111yescharacteristic
846C2C2×#1912830411yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#396×C83C2
socleC24×C83C24
prime radicalC2×#19127610C2
hypercenterC2×#396D83
hypocenterC83C2×#2648
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. #24913454C2direct (N × H)
2. C2×#19127640C2semidirect
3. C2×#19127628C2semidirect
4. C2×#19127627C2semidirect
5. C2×#19127618C2semidirect
6. C2×#19127617C2semidirect
7. C2×#19127617C2semidirect
9. C2×#19127602C2semidirect
10. C2×#19127593C2semidirect
11. C2×#19127591C2semidirect
12. C2×#19127587C2semidirect
13. C2×#19127578C2semidirect
14. C2×#19127578C2semidirect
15. C2×C22⋊C4×Dic83C2semidirect
16. C2×#396×C83C2semidirect
36. #19127640C22semidirect
37. #19127628C22semidirect
38. #19127627C22semidirect
39. #19127618C22semidirect
40. #19127617C22semidirect
41. #19127617C22semidirect
43. #19127602C22semidirect
44. #19127593C22semidirect
45. #19127591C22semidirect
46. #19127587C22semidirect
47. #19127578C22semidirect
48. #19127578C22semidirect
49. C22⋊C4×Dic83C22semidirect
65. #396×C83C22semidirect
414. C2×C83#2648semidirect
428. C2×#396D83semidirect
440. C83C2×#2648semidirect
469. #396C2×D83semidirect
839. C2#24913454direct (N × H)

Maximal subgroups

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

subgroupindex
#249134542
C2×#191276402
C2×#191276282
C2×#191276272
C2×#191276182
C2×#191276172
C2×#191276102
C2×#191276022
C2×#191275932
C2×#191275912
C2×#191275872
C2×#191275782
C2×C22⋊C4×Dic832
C2×#396×C832
C2×#264883