Finite Group Databasebeta

← C2×#24913432 #35570846

Subgroups — C2×#24913432 #35570846

Order 21248.

2374 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24913432C2116yesmaximal, direct product factor
2C2×#19127643C211yesmaximal, characteristic, complemented
3C2×#19127643C211yesmaximal, characteristic, complemented
4C2×#19127642C211yesmaximal, characteristic, complemented
5C2×#19127639C211yesmaximal, characteristic, complemented
6C2×#19127634C211yesmaximal, characteristic, complemented
7C2×#19127632C211yesmaximal, characteristic, complemented
8C2×#19127631C211yesmaximal, characteristic, complemented
9C2×#19127575C211yesmaximal, characteristic
10C2×#19127572C211yesmaximal, characteristic
11C2×#19127572C211yesmaximal, characteristic
12C2×#19127572C211yesmaximal, characteristic
13C2×#19127560C211yesmaximal, characteristic
14C2×#19127558C211yesmaximal, characteristic
15C2×#95×D83C211yesmaximal, characteristic
16C2×#398×C83C211yesmaximal, characteristic, complemented
17C23×C4×D83C2211yescharacteristic
18C23×C4×D83C2211yescharacteristic
19C23×C4×D83C2211yescharacteristic
20C22×C4⋊Dic83C2211yescharacteristic
21C22×C4⋊Dic83C2211yescharacteristic
22C22×Dic83⋊C4C2211yescharacteristic
23C22×Dic83⋊C4C2211yescharacteristic
24C22×Dic83⋊C4C2211yescharacteristic
25C22×Dic83⋊C4C2211yescharacteristic
26C22×Dic83⋊C4C2211yescharacteristic
27C22×Dic83⋊C4C2211yescharacteristic
28C22×(C2×D83)⋊C4C2211yescharacteristic
29C22×(C2×D83)⋊C4C2211yescharacteristic
30C22×(C2×D83)⋊C4C2211yescharacteristic
31C22×(C2×D83)⋊C4C2211yescharacteristic
32#19127643C2218yescomplemented
33#19127643C2218yescomplemented
34#19127642C2218yescomplemented
35#19127639C2218yescomplemented
36#19127634C2218yescomplemented
37#19127632C2218yescomplemented
38#19127631C2218yescomplemented
39#19127575C2218yes—
40#19127572C2218yes—
41#19127572C2218yes—
42#19127572C2218yes—
43#19127560C2218yes—
44#19127558C2218yes—
45C2×C83⋊#95C2211yescharacteristic
46C2×C83⋊#95C2211yescharacteristic
47C2×C83⋊#95C2211yescharacteristic
48C2×C83⋊#95C2211yescharacteristic
49C2×C83⋊#95C2211yescharacteristic
50C2×C83⋊#95C2211yescharacteristic
51C2×C83⋊#95C2211yescharacteristic
52C2×C83⋊#95C2211yescharacteristic
53C2×C83⋊#95C2211yescharacteristic
54C2×C83⋊#95C2211yescharacteristic
55C2×C83⋊#95C2211yescharacteristic
56C2×C83⋊#95C2211yescharacteristic
57C2×C83⋊#95C2211yescharacteristic
58#95×D83C2218yes—
59C22×C4⋊C4×C83C2211yescharacteristic
60C22×C4⋊C4×C83C2211yescharacteristic
61C22×C4⋊C4×C83C2211yescharacteristic
62C22×C4⋊C4×C83C2211yescharacteristic
63#398×C83C2218yescomplemented
64C2×#95×C83C2211yescharacteristic
65C2×#95×C83C2211yescharacteristic
66C2×#95×C83C2211yescharacteristic
67C24×D83C2311yescharacteristic
68C23×Dic83C2311yescharacteristic
69C23×Dic83C2311yescharacteristic
70C23×Dic83C2311yescharacteristic
71C23×Dic83C2311yescharacteristic
72C23×Dic83C2311yescharacteristic
73C23×Dic83C2311yescharacteristic
74C23×Dic83C2311yescharacteristic
75C22×C4×D83—24no—
76C22×C4×D83—24no—
77C22×C4×D83—42no—
78C22×C4×D83—42no—
79C22×C4×D83—42no—
80C22×C4×D83—42no—
81C22×C4×D83—42no—
82C22×C4×D83—42no—
83C22×C4×D83Q818yes—
84C22×C4×D83C2314yes—
85C22×C4×D83C2314yes—
86C22×C4×D83C2314yes—
87C2×C4⋊Dic83—42no—
88C2×C4⋊Dic83—42no—
89C2×C4⋊Dic83C2314yes—
90C2×C4⋊Dic83C2314yes—
91C2×Dic83⋊C4—42no—
92C2×Dic83⋊C4—42no—
93C2×Dic83⋊C4—42no—
94C2×Dic83⋊C4—42no—
95C2×Dic83⋊C4—42no—
96C2×Dic83⋊C4—42no—
97C2×Dic83⋊C4C2314yes—
98C2×Dic83⋊C4C2314yes—
99C2×Dic83⋊C4C2314yes—
100C2×Dic83⋊C4C2314yes—
101C2×Dic83⋊C4C2314yes—
102C2×Dic83⋊C4C2314yes—
103C2×(C2×D83)⋊C4—24no—
104C2×(C2×D83)⋊C4—24no—
105C2×(C2×D83)⋊C4—24no—
106C2×(C2×D83)⋊C4—24no—
107C2×(C2×D83)⋊C4C2314yes—
108C2×(C2×D83)⋊C4C2314yes—
109C2×(C2×D83)⋊C4C2314yes—
110C2×(C2×D83)⋊C4C2314yes—
111C83⋊#95C2314yes—
112C83⋊#95C2314yes—
113C83⋊#95C2314yes—
114C83⋊#95C2314yes—
115C83⋊#95C2314yes—
116C83⋊#95C2314yes—
117C83⋊#95C2314yes—
118C83⋊#95C2314yes—
119C83⋊#95C2314yes—
120C83⋊#95C2314yes—
121C83⋊#95C2314yes—
122C83⋊#95C2314yes—
123C83⋊#95C2314yes—
124C23×C4×C83C2311yescharacteristic
125C23×C4×C83C2311yescharacteristic
126C23×C4×C83C2311yescharacteristic
127C23×C4×C83C2311yescharacteristic
128C23×C4×C83C2311yescharacteristic
129C23×C4×C83C2311yescharacteristic
130C23×C4×C83C2311yescharacteristic
131C2×C4⋊C4×C83—42no—
132C2×C4⋊C4×C83—42no—
133C2×C4⋊C4×C83—42no—
134C2×C4⋊C4×C83—42no—
135C2×C4⋊C4×C83C2314yes—
136C2×C4⋊C4×C83C2314yes—
137C2×C4⋊C4×C83C2314yes—
138C2×C4⋊C4×C83C2314yes—
139#95×C83C2314yes—
140#95×C83C2314yes—
141#95×C83C2314yes—
142C23×D83—22no—
143C23×D83—22no—
144C23×D83—22no—
145C23×D83—22no—
146C23×D83C2×Q814yes—
147C23×D83#4114yes—
148C23×D83#4114yes—
149C23×D83C2412yes—
150C22×Dic83—22no—
151C22×Dic83—22no—
152C22×Dic83—22no—
153C22×Dic83—22no—
154C22×Dic83—22no—
155C22×Dic83—22no—
156C22×Dic83—22no—
157C22×Dic83—22no—
158C22×Dic83—22no—
159C22×Dic83—22no—
160C22×Dic83—22no—
161C22×Dic83—22no—
162C22×Dic83—22no—
163C22×Dic83—22no—
164C22×Dic83—22no—
165C22×Dic83—22no—
166C22×Dic83—22no—
167C22×Dic83—22no—
168C22×Dic83—22no—
169C22×Dic83—22no—
170C22×Dic83C2×Q814yes—
171C22×Dic83C2412yes—
172C22×Dic83C2412yes—
173C22×Dic83C2412yes—
174C22×Dic83C2412yes—
175C22×Dic83C2412yes—
176C22×Dic83C2412yes—
177C22×Dic83C2412yes—
178C2×C4×D83—28no—
179C2×C4×D83—28no—
180C2×C4×D83—416no—
181C2×C4×D83—44no—
182C2×C4×D83—44no—
183C2×C4×D83—44no—
184C2×C4×D83—44no—
185C2×C4×D83—44no—
186C2×C4×D83—44no—
187C2×C4×D83—416no—
188C2×C4×D83—416no—
189C2×C4×D83C2×Q8116yes—
190C4⋊Dic83—44no—
191C4⋊Dic83—44no—
192Dic83⋊C4—44no—
193Dic83⋊C4—44no—
194Dic83⋊C4—44no—
195Dic83⋊C4—44no—
196Dic83⋊C4—44no—
197Dic83⋊C4—44no—
198(C2×D83)⋊C4—28no—
199(C2×D83)⋊C4—28no—
200(C2×D83)⋊C4—28no—
201(C2×D83)⋊C4—28no—
202C24×C83C2411yescharacteristic
203C22×C4×C83—22no—
204C22×C4×C83—22no—
205C22×C4×C83—22no—
206C22×C4×C83—22no—
207C22×C4×C83—22no—
208C22×C4×C83—22no—
209C22×C4×C83—22no—
210C22×C4×C83—22no—
211C22×C4×C83—22no—
212C22×C4×C83—22no—
213C22×C4×C83—22no—
214C22×C4×C83—22no—
215C22×C4×C83—22no—
216C22×C4×C83—22no—
217C22×C4×C83—22no—
218C22×C4×C83—22no—
219C22×C4×C83—22no—
220C22×C4×C83—22no—
221C22×C4×C83—22no—
222C22×C4×C83—22no—
223C22×C4×C83C2×Q814yes—
224C22×C4×C83C2412yes—
225C22×C4×C83C2412yes—
226C22×C4×C83C2412yes—
227C22×C4×C83C2412yes—
228C22×C4×C83C2412yes—
229C22×C4×C83C2412yes—
230C22×C4×C83C2412yes—
231C4⋊C4×C83—44no—
232C4⋊C4×C83—44no—
233C4⋊C4×C83—44no—
234C4⋊C4×C83—44no—
235C23×C83C22×Q812yes—
236C23×C83C2×#4112yes—
237C23×C83C2×#4112yes—
238C23×C83H(5,𝔽2)12yes—
239C23×C83H(5,𝔽2)12yes—
240C23×C83H(5,𝔽2)12yes—
241C23×C832−1+412yes—
242C23×C83C2511yescharacteristic
243C22×D83—28no—
244C22×D83—28no—
245C22×D83—28no—
246C22×D83—28no—
247C22×D83—28no—
248C22×D83—28no—
249C22×D83—22no—
250C22×D83—22no—
251C22×D83—22no—
252C22×D83—22no—
253C22×D83#125116yes—
254C22×D83C22×Q814yes—
255C22×D83C2×#4114yes—
256C22×D83C2×#4114yes—
257C2×C4×C83—28no—
258C2×C4×C83—22no—
259C2×C4×C83—22no—
260C2×C4×C83—22no—
261C2×C4×C83—22no—
262C2×C4×C83—22no—
263C2×C4×C83—22no—
264C2×C4×C83—22no—
265C2×C4×C83—22no—
266C2×C4×C83—22no—
267C2×C4×C83—22no—
268C2×C4×C83—22no—
269C2×C4×C83—22no—
270C2×C4×C83—22no—
271C2×C4×C83—22no—
272C2×C4×C83—22no—
273C2×C4×C83—22no—
274C2×C4×C83—22no—
275C2×C4×C83—22no—
276C2×C4×C83—22no—
277C2×C4×C83—22no—
278C2×C4×C83—44no—
279C2×C4×C83—44no—
280C2×C4×C83—44no—
281C2×C4×C83—44no—
282C2×C4×C83—44no—
283C2×C4×C83—44no—
284C2×C4×C83C22×Q814yes—
285C2×Dic83—28no—
286C2×Dic83—22no—
287C2×Dic83—22no—
288C2×Dic83—22no—
289C2×Dic83—22no—
290C2×Dic83—22no—
291C2×Dic83—22no—
292C2×Dic83—22no—
293C2×Dic83—22no—
294C2×Dic83—22no—
295C2×Dic83—22no—
296C2×Dic83—22no—
297C2×Dic83—22no—
298C2×Dic83—22no—
299C2×Dic83—22no—
300C2×Dic83—22no—
301C2×Dic83—22no—
302C2×Dic83—22no—
303C2×Dic83—22no—
304C2×Dic83—22no—
305C2×Dic83—22no—
306C2×Dic83—44no—
307C2×Dic83—44no—
308C2×Dic83—44no—
309C2×Dic83—44no—
310C2×Dic83—44no—
311C2×Dic83—44no—
312C2×Dic83C22×Q814yes—
313C4×D83—416no—
314C4×D83—416no—
315C4×D83—416no—
316C22×C83C2×#12514yes—
317C22×C83#53814yes—
318C22×C83#53814yes—
319C22×C83#53914yes—
320C22×C83#53914yes—
321C22×C83#54314yes—
322C22×C83#54414yes—
323C22×C83C23×Q811yescharacteristic
324C22×C83C22×#4111yescharacteristic
325C22×C83C22×#4111yescharacteristic
326C22×C83C2×H(5,𝔽2)11yescharacteristic
327C22×C83C2×H(5,𝔽2)11yescharacteristic
328C22×C83C2×H(5,𝔽2)11yescharacteristic
329C22×C83C2×2−1+411yescharacteristic
330C2×D83—232no—
331C2×D83—24no—
332C2×D83—24no—
333C2×D83—24no—
334C2×D83—24no—
335C2×D83—24no—
336C2×D83—24no—
337C2×D83C2×#12518yes—
338C4×C83—24no—
339C4×C83—42no—
340C4×C83—42no—
341C4×C83—42no—
342C4×C83—42no—
343C4×C83—42no—
344C4×C83—42no—
345Dic83—24no—
346Dic83—42no—
347Dic83—42no—
348Dic83—42no—
349Dic83—42no—
350Dic83—42no—
351Dic83—42no—
352C2×#2646—831nomaximal, Sylow
353C2×C83#264618yescomplemented
354C2×C83C22×#12511yescharacteristic
355C2×C83C2×#53811yescharacteristic
356C2×C83C2×#53811yescharacteristic
357C2×C83C2×#53911yescharacteristic
358C2×C83C2×#53911yescharacteristic
359C2×C83C2×#54311yescharacteristic
360C2×C83C2×#54411yescharacteristic
361D83—28no—
362#2646—8316no—
363C2×#400—831no—
364C2×#400—831no—
365C2×#400—831no—
366C2×#400—831no—
367C2×#398—831no—
368C2×#398—831no—
369C2×#398—831no—
370C2×#398D8311yescharacteristic, complemented
371C2×#385—831no—
372C2×#385—831no—
373C2×#385—831no—
374C2×#385—831no—
375C2×#380—831no—
376C2×#380—831no—
377C22×#95—831no—
378C83C2×#264611yescharacteristic, complemented, Sylow
379C24×C4—831no—
380C24×C4—831no—
381C24×C4—831no—
382C22×C4⋊C4—831no—
383C22×C4⋊C4—831no—
384C22×C4⋊C4—831no—
385C22×C4⋊C4—831no—
386C22×C4⋊C4—831no—
387C22×C4⋊C4—831no—
388C22×C4⋊C4—831no—
389C22×C4⋊C4—831no—
390C22×C4⋊C4C2×D8311yescharacteristic
391C22×C4⋊C4C2×D8311yescharacteristic
392C22×C4⋊C4C2×D8311yescharacteristic
393C22×C4⋊C4C2×D8311yescharacteristic
394C22×C22⋊C4—831no—
395C22×C22⋊C4—831no—
396C22×C22⋊C4—831no—
397C22×C22⋊C4—831no—
398#400—838no—
399#400—838no—
400#400—838no—
401#400—838no—
402#398—838no—
403#398—838no—
404#398—838no—
405#398C2×D8318yescomplemented
406#385—838no—
407#385—838no—
408#385—838no—
409#385—838no—
410#380—838no—
411#380—838no—
412C2×#95—831no—
413C2×#95—831no—
414C2×#95—831no—
415C2×#95—831no—
416C2×#95—831no—
417C2×#95—831no—
418C2×#95—831no—
419C2×#95—831no—
420C2×#95—831no—
421C2×#95—831no—
422C2×#95—831no—
423C2×#95—831no—
424C2×#95—831no—
425C2×#95—838no—
426C2×#95C2×D8311yescharacteristic
427C2×#95C2×D8311yescharacteristic
428C2×#95C2×D8311yescharacteristic
429C25—831no—
430C23×C4—3322no—
431C23×C4—3322no—
432C23×C4—3322no—
433C23×C4—3322no—
434C23×C4—3322no—
435C23×C4—3322no—
436C23×C4—838no—
437C23×C4—834no—
438C23×C4—834no—
439C23×C4—834no—
440C23×C4—831no—
441C23×C4—831no—
442C23×C4—831no—
443C23×C4—831no—
444C23×C4—831no—
445C23×C4—831no—
446C23×C4—831no—
447C23×C4—1664no—
448C23×C4—1664no—
449C23×C4C22×D8311yescharacteristic
450C23×C4C22×D8311yescharacteristic
451C23×C4C22×D8311yescharacteristic
452C23×C4C22×D8311yescharacteristic
453C23×C4C22×D8311yescharacteristic
454C23×C4C22×D8311yescharacteristic
455C23×C4C22×D8311yescharacteristic
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—3322no—
461C2×C4⋊C4—3322no—
462C2×C4⋊C4—3322no—
463C2×C4⋊C4—3322no—
464C2×C4⋊C4—3322no—
465C2×C4⋊C4—3322no—
466C2×C4⋊C4—3322no—
467C2×C4⋊C4—3322no—
468C2×C4⋊C4—834no—
469C2×C4⋊C4—834no—
470C2×C4⋊C4—834no—
471C2×C4⋊C4—834no—
472C2×C4⋊C4—834no—
473C2×C4⋊C4—834no—
474C2×C4⋊C4—834no—
475C2×C4⋊C4—834no—
476C2×C4⋊C4C22×D8314yes—
477C2×C4⋊C4C22×D8314yes—
478C2×C4⋊C4C22×D8314yes—
479C2×C4⋊C4C22×D8314yes—
480C2×C22⋊C4—834no—
481C2×C22⋊C4—834no—
482C2×C22⋊C4—834no—
483C2×C22⋊C4—834no—
484C2×C22⋊C4—1664no—
485C2×C22⋊C4—1664no—
486C2×C22⋊C4—1664no—
487C2×C22⋊C4—1664no—
488#95—834no—
489#95—834no—
490#95—834no—
491#95—834no—
492#95—834no—
493#95—834no—
494#95—834no—
495#95—834no—
496#95—834no—
497#95—834no—
498#95—834no—
499#95—834no—
500#95—834no—
501#95C22×D8314yes—
502#95C22×D8314yes—
503#95C22×D8314yes—
504C24—834no—
505C24—834no—
506C24—834no—
507C24—832no—
508C24—1662no—
509C24—1662no—
510C24—1662no—
511C24—1662no—
512C24C23×D8311yescharacteristic
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—33216no—
534C22×C4—3324no—
535C22×C4—3324no—
536C22×C4—3324no—
537C22×C4—3324no—
538C22×C4—3324no—
539C22×C4—3324no—
540C22×C4—33216no—
541C22×C4—33216no—
542C22×C4—8316no—
543C22×C4—834no—
544C22×C4—832no—
545C22×C4—832no—
546C22×C4—832no—
547C22×C4—832no—
548C22×C4—832no—
549C22×C4—832no—
550C22×C4—832no—
551C22×C4—1668no—
552C22×C4—1668no—
553C22×C4—1662no—
554C22×C4—1662no—
555C22×C4—1662no—
556C22×C4—1662no—
557C22×C4—1662no—
558C22×C4—1662no—
559C22×C4—1662no—
560C22×C4—1662no—
561C22×C4—1662no—
562C22×C4—1662no—
563C22×C4—1662no—
564C22×C4—1662no—
565C22×C4—1662no—
566C22×C4—1662no—
567C22×C4—1662no—
568C22×C4—1662no—
569C22×C4—1662no—
570C22×C4—1662no—
571C22×C4—1662no—
572C22×C4—1662no—
573C22×C4Q8×D8314yes—
574C22×C4C23×D8312yes—
575C22×C4C23×D8312yes—
576C22×C4C23×D8312yes—
577C22×C4C23×D8312yes—
578C22×C4C23×D8312yes—
579C22×C4C23×D8312yes—
580C22×C4C23×D8312yes—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—44no—
585C4⋊C4—3324no—
586C4⋊C4—3324no—
587C4⋊C4—3324no—
588C4⋊C4—3324no—
589C4⋊C4—3324no—
590C4⋊C4—3324no—
591C4⋊C4—3324no—
592C4⋊C4—3324no—
593C22⋊C4—1668no—
594C22⋊C4—1668no—
595C22⋊C4—1668no—
596C22⋊C4—1668no—
597C23—8316no—
598C23—834no—
599C23—834no—
600C23—834no—
601C23—1668no—
602C23—1668no—
603C23—1662no—
604C23—1662no—
605C23—1662no—
606C23—1662no—
607C23—1668no—
608C23—1668no—
609C23—1668no—
610C23—1668no—
611C23C2×Q8×D8312yes—
612C23#41×D8312yes—
613C23#41×D8312yes—
614C23#1458183712yes—
615C23#1458183712yes—
616C23#1458183812yes—
617C23#1458184012yes—
618C23C24×D8311yescharacteristic
619C2×C4—28no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—33216no—
647C2×C4—33216no—
648C2×C4—33216no—
649C2×C4—3324no—
650C2×C4—3324no—
651C2×C4—3324no—
652C2×C4—3324no—
653C2×C4—3324no—
654C2×C4—3324no—
655C2×C4—834no—
656C2×C4—1662no—
657C2×C4—1662no—
658C2×C4—1662no—
659C2×C4—1662no—
660C2×C4—1662no—
661C2×C4—1662no—
662C2×C4—1662no—
663C2×C4—1662no—
664C2×C4—1662no—
665C2×C4—1662no—
666C2×C4—1662no—
667C2×C4—1662no—
668C2×C4—1662no—
669C2×C4—1662no—
670C2×C4—1662no—
671C2×C4—1662no—
672C2×C4—1662no—
673C2×C4—1662no—
674C2×C4—1668no—
675C2×C4—1662no—
676C2×C4—1662no—
677C2×C4C2×Q8×D8314yes—
678C22—838no—
679C22—16632no—
680C22—1664no—
681C22—1664no—
682C22—1664no—
683C22—1664no—
684C22—1664no—
685C22—1664no—
686C22#125×D8314yes—
687C22#1912828314yes—
688C22#1912828714yes—
689C22#1912829714yes—
690C22#1912829914yes—
691C22#1912832614yes—
692C22#1912832814yes—
693C22C22×Q8×D8311yescharacteristic
694C22C2×#41×D8311yescharacteristic
695C22C2×#41×D8311yescharacteristic
696C22C2×#1458183711yescharacteristic
697C22C2×#1458183711yescharacteristic
698C22C2×#1458183811yescharacteristic
699C22C2×#1458184011yescharacteristic
700C4—24no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—3322no—
708C4—3322no—
709C4—3322no—
710C4—3322no—
711C4—3322no—
712C4—3322no—
713C4—1664no—
714C2—1668no—
715C2#2491343218yesdirect product factor
716C2C2×#125×D8311yescharacteristic
717C2C2×#1912828311yescharacteristic
718C2C2×#1912828711yescharacteristic
719C2C2×#1912829711yescharacteristic
720C2C2×#1912829911yescharacteristic
721C2C2×#1912832611yescharacteristic
722C2C2×#1912832811yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#398×C83C2
socleC24×C83C24
prime radicalC24×D83C23
hypercenterC2×#398D83
hypocenterC83C2×#2646
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. #24913432C2direct (N × H)
2. C2×#19127643C2semidirect
3. C2×#19127643C2semidirect
4. C2×#19127642C2semidirect
5. C2×#19127639C2semidirect
6. C2×#19127634C2semidirect
7. C2×#19127632C2semidirect
8. C2×#19127631C2semidirect
16. C2×#398×C83C2semidirect
32. #19127643C22semidirect
33. #19127643C22semidirect
34. #19127642C22semidirect
35. #19127639C22semidirect
36. #19127634C22semidirect
37. #19127632C22semidirect
38. #19127631C22semidirect
63. #398×C83C22semidirect
353. C2×C83#2646semidirect
370. C2×#398D83semidirect
378. C83C2×#2646semidirect
405. #398C2×D83semidirect
715. C2#24913432direct (N × H)

Maximal subgroups

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

subgroupindex
#249134322
C2×#191276432
C2×#191276422
C2×#191276392
C2×#191276342
C2×#191276322
C2×#191276312
C2×#191275752
C2×#191275722
C2×#191275602
C2×#191275582
C2×#95×D832
C2×#398×C832
C2×#264683