Finite Group Databasebeta

← C2×#24919920 #36282953

Subgroups — C2×#24919920 #36282953

Order 21248.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128408C211yesmaximal, characteristic
2C2×#19128391C211yesmaximal, characteristic
3#24919920C2116yesmaximal, direct product factor
4C2×#19128110C211yesmaximal, characteristic, complemented
5C2×#19128037C211yesmaximal, characteristic, complemented
6C2×#19128043C211yesmaximal, characteristic, complemented
7C2×#19128032C211yesmaximal, characteristic, complemented
8C2×#19128032C211yesmaximal, characteristic, complemented
9C2×#19128009C211yesmaximal, characteristic, complemented
10C2×#19127987C211yesmaximal, characteristic, complemented
11C2×#19127959C211yesmaximal, characteristic, complemented
12C2×#19127942C211yesmaximal, characteristic, complemented
13C2×#19127809C211yesmaximal, characteristic, complemented
14C2×#19127743C211yesmaximal, characteristic, complemented
15C22×#14581724C211yesmaximal, characteristic, complemented
16C2×#435×C83C211yesmaximal, characteristic
17C22×Dic332C2211yescharacteristic
18#19128408—24no—
19#19128408C2218yes—
20#19128391—24no—
21#19128391C2218yes—
22C2×#14581792C2211yescharacteristic
23C2×#14581785—21no—
24C2×#14581784C2211yescharacteristic
25C2×#14581783—21no—
26C2×#14581782—21no—
27C2×#14581773—21no—
28C2×#14581771C2211yescharacteristic
29C2×#14581771C2211yescharacteristic
30C2×#14581771C2211yescharacteristic
31C2×#14581771C2211yescharacteristic
32C2×#14581769—21no—
33C2×#14581769—21no—
34C2×C4×Dic166C2211yescharacteristic
35C2×C4×Dic166C2211yescharacteristic
36C2×D4×Dic83—21no—
37C2×#14581751C2211yescharacteristic
38C2×#14581748—21no—
39C22×C4⋊Dic83C2211yescharacteristic
40C22×C4⋊Dic83C2211yescharacteristic
41C22×C4⋊Dic83C2211yescharacteristic
42#19128110C2218yescomplemented
43#19128043C2218yescomplemented
44#19128037C2218yescomplemented
45#19128032C2218yescomplemented
46#19128032C2218yescomplemented
47#19128009C2218yescomplemented
48#19127987C2218yescomplemented
49#19127959C2218yescomplemented
50#19127942C2218yescomplemented
51#19127809C2218yescomplemented
52#19127743C2218yescomplemented
53C2×#14581726C2211yescharacteristic
54C2×#14581726C2211yescharacteristic
55C2×#14581726C2211yescharacteristic
56C2×#14581724C2211yescharacteristic
57C2×#14581724C2211yescharacteristic
58C2×#14581724C2211yescharacteristic
59C2×#14581724C2211yescharacteristic
60C2×#14581724C2211yescharacteristic
61C2×#14581724C2211yescharacteristic
62C2×#14581724C2218yescomplemented
63C2×#14581717C2211yescharacteristic
64C2×#14581717C2211yescharacteristic
65C2×#14581717C2211yescharacteristic
66C2×#14581717C2211yescharacteristic
67C2×#14581717C2211yescharacteristic
68C2×#14581717C2211yescharacteristic
69C22×M16×C83C2211yescharacteristic
70C23×C8×C83C2211yescharacteristic
71C2×C4×D4×C83C2211yescharacteristic
72#435×C83C2218yes—
73C2×C4⋊C8×C83C2211yescharacteristic
74C2×C22⋊C8×C83C2211yescharacteristic
75C2×C22⋊C8×C83C2211yescharacteristic
76C2×#97×C83C2211yescharacteristic
77C22×Dic166—21no—
78C22×Dic166C2311yescharacteristic
79C22×Dic166C2311yescharacteristic
80C23×Dic83—21no—
81C23×Dic83—21no—
82C23×Dic83—21no—
83C2×Dic332—24no—
84C2×Dic332C2314yes—
85#14581792—22no—
86#14581792C2314yes—
87#14581785—28no—
88#14581784—22no—
89#14581784C2314yes—
90#14581783—28no—
91#14581782—28no—
92#14581773—28no—
93#14581771—22no—
94#14581771—22no—
95#14581771—22no—
96#14581771—22no—
97#14581771C2314yes—
98#14581771C2314yes—
99#14581771C2314yes—
100#14581771C2314yes—
101#14581769—28no—
102#14581769—28no—
103C4×Dic166—22no—
104C4×Dic166—22no—
105C4×Dic166C2314yes—
106C4×Dic166C2314yes—
107D4×Dic83—28no—
108#14581751—22no—
109#14581751C2314yes—
110#14581748—28no—
111C2×C4⋊Dic83—22no—
112C2×C4⋊Dic83—22no—
113C2×C4⋊Dic83—22no—
114C2×C4⋊Dic83—21no—
115C2×C4⋊Dic83—21no—
116C2×C4⋊Dic83—21no—
117C2×C4⋊Dic83—21no—
118C2×C4⋊Dic83C2314yes—
119C2×C4⋊Dic83C2311yescharacteristic
120C2×C4⋊Dic83C2314yes—
121C2×C4⋊Dic83C2314yes—
122C2×C4⋊Dic83C2311yescharacteristic
123C2×C4⋊Dic83C2311yescharacteristic
124C2×C4⋊Dic83C2311yescharacteristic
125C2×C4⋊Dic83C2311yescharacteristic
126C2×C4⋊Dic83C2311yescharacteristic
127C2×Dic83⋊C4—21no—
128C2×Dic83⋊C4—21no—
129C2×Dic83⋊C4—21no—
130C2×Dic83⋊C4—21no—
131C2×Dic83⋊C4—21no—
132C2×Dic83⋊C4—21no—
133C2×Dic83⋊C4—21no—
134C2×Dic83⋊C4—21no—
135C2×C22⋊Dic83—21no—
136C2×C22⋊Dic83—21no—
137C2×C22⋊Dic83—21no—
138C2×C22⋊Dic83—21no—
139C2×C22⋊Dic83—21no—
140C2×C4×Dic83—21no—
141C2×C4×Dic83—21no—
142C2×C4×Dic83—21no—
143#14581726C2314yes—
144#14581726C2314yes—
145#14581726C2314yes—
146#14581724C2314yes—
147#14581724C2314yes—
148#14581724C2314yes—
149#14581724C2314yes—
150#14581724C2314yes—
151#14581724C2314yes—
152#14581717C2314yes—
153#14581717C2314yes—
154#14581717C2314yes—
155#14581717C2314yes—
156#14581717C2314yes—
157#14581717C2314yes—
158C22×D4×C83D411yescharacteristic
159C23×C4×C83C2311yescharacteristic
160C23×C4×C83C2311yescharacteristic
161C2×M16×C83—24no—
162C2×M16×C83C2314yes—
163C22×C8×C83—24no—
164C22×C8×C83C2314yes—
165C22×C8×C83C2311yescharacteristic
166C22×C8×C83C2311yescharacteristic
167C22×C8×C83C2311yescharacteristic
168C22×C8×C83C2311yescharacteristic
169C4×D4×C83D414yes—
170C4×D4×C83C2314yes—
171C2×C4⋊C4×C83D411yescharacteristic
172C2×C22⋊C4×C83D411yescharacteristic
173C2×C22⋊C4×C83D411yescharacteristic
174C2×C42×C83C2311yescharacteristic
175C4⋊C8×C83C2314yes—
176C22⋊C8×C83C2314yes—
177C22⋊C8×C83C2314yes—
178#97×C83C2314yes—
179C2×Dic166—22no—
180C2×Dic166—22no—
181C2×Dic166—22no—
182C2×Dic166—22no—
183C2×Dic166—21no—
184C2×Dic166—21no—
185C2×Dic166—24no—
186C2×Dic166—82no—
187C2×Dic166C2412yes—
188C2×Dic166C2412yes—
189C22×Dic83—24no—
190C22×Dic83—21no—
191C22×Dic83—21no—
192C22×Dic83—21no—
193C22×Dic83—21no—
194C22×Dic83—21no—
195C22×Dic83—21no—
196C22×Dic83—21no—
197C22×Dic83—21no—
198C22×Dic83—24no—
199C22×Dic83—24no—
200C22×Dic83—44no—
201C22×Dic83—82no—
202C22×Dic83—82no—
203Dic332—28no—
204C4⋊Dic83—24no—
205C4⋊Dic83—24no—
206C4⋊Dic83—21no—
207C4⋊Dic83—21no—
208C4⋊Dic83—21no—
209C4⋊Dic83—21no—
210C4⋊Dic83—24no—
211C4⋊Dic83—24no—
212C4⋊Dic83—21no—
213C4⋊Dic83—21no—
214C4⋊Dic83C2412yes—
215C4⋊Dic83C2412yes—
216C4⋊Dic83C2412yes—
217C4⋊Dic83C2412yes—
218C4⋊Dic83C2412yes—
219C4⋊Dic83C2412yes—
220Dic83⋊C4—24no—
221Dic83⋊C4—24no—
222Dic83⋊C4—24no—
223Dic83⋊C4—24no—
224Dic83⋊C4—24no—
225Dic83⋊C4—24no—
226Dic83⋊C4—24no—
227Dic83⋊C4—24no—
228C22⋊Dic83—24no—
229C22⋊Dic83—24no—
230C22⋊Dic83—24no—
231C22⋊Dic83—24no—
232C22⋊Dic83—24no—
233C4×Dic83—24no—
234C4×Dic83—24no—
235C4×Dic83—24no—
236C24×C83C2×D411yescharacteristic
237C24×C83C2×D411yescharacteristic
238C2×D4×C83—24no—
239C2×D4×C83C2×D414yes—
240C22×C4×C83—22no—
241C22×C4×C83—22no—
242C22×C4×C83—22no—
243C22×C4×C83—22no—
244C22×C4×C83C2×D412yes—
245C22×C4×C83C2×D412yes—
246C22×C4×C83C2×D411yescharacteristic
247C22×C4×C83C2×D411yescharacteristic
248C22×C4×C83C2×D411yescharacteristic
249C22×C4×C83C2×D411yescharacteristic
250C22×C4×C83C2412yes—
251C22×C4×C83C2412yes—
252C22×C4×C83C2411yescharacteristic
253M16×C83—28no—
254C2×C8×C83—22no—
255C2×C8×C83—22no—
256C2×C8×C83—22no—
257C2×C8×C83—28no—
258C2×C8×C83#4114yes—
259C2×C8×C83C2412yes—
260C2×C8×C83C2412yes—
261C2×C8×C83C2412yes—
262C2×C8×C83C2412yes—
263C4⋊C4×C83C2×D414yes—
264C22⋊C4×C83C2×D414yes—
265C22⋊C4×C83C2×D414yes—
266C42×C83C2×D412yes—
267C42×C83C2412yes—
268C23×C83—22no—
269C23×C83—22no—
270C23×C83—22no—
271C23×C83—22no—
272C23×C83—22no—
273C23×C83#13714yes—
274C23×C83C22×D412yes—
275C23×C83C22×D412yes—
276C23×C83C22×D411yescharacteristic
277D4×C83—28no—
278C2×C4×C83—22no—
279C2×C4×C83—22no—
280C2×C4×C83—22no—
281C2×C4×C83—22no—
282C2×C4×C83—24no—
283C2×C4×C83—24no—
284C2×C4×C83—22no—
285C2×C4×C83—22no—
286C2×C4×C83—22no—
287C2×C4×C83—22no—
288C2×C4×C83C22×D412yes—
289C2×C4×C83C22×D412yes—
290C2×C4×C83C22×D412yes—
291C2×C4×C83C22×D412yes—
292C2×C4×C83C22×D411yescharacteristic
293C2×C4×C83C2×#4112yes—
294C2×C4×C832−1+412yes—
295C2×C4×C83C2511yescharacteristic
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—42no—
305C2×Dic83—42no—
306C2×Dic83—48no—
307C2×Dic83—42no—
308C2×Dic83—42no—
309C2×Dic83—42no—
310C2×Dic83—42no—
311C2×Dic83—42no—
312C2×Dic83—42no—
313C2×Dic83—84no—
314C2×Dic83—84no—
315Dic166—22no—
316Dic166—22no—
317Dic166—22no—
318Dic166—22no—
319Dic166—42no—
320Dic166—42no—
321Dic166—84no—
322C8×C83—22no—
323C8×C83—22no—
324C8×C83—22no—
325C8×C83C2×#4114yes—
326C22×C83—28no—
327C22×C83—22no—
328C22×C83—22no—
329C22×C83—22no—
330C22×C83—22no—
331C22×C83—22no—
332C22×C83—44no—
333C22×C83#54712yes—
334C22×C83C2×#13714yes—
335C22×C83C2×#13712yes—
336C22×C83#57712yes—
337C22×C83C23×D411yescharacteristic
338C4×C83—22no—
339C4×C83—22no—
340C4×C83—22no—
341C4×C83—22no—
342C4×C83#54712yes—
343C4×C83C22×#4111yescharacteristic
344C4×C83C2×2−1+411yescharacteristic
345Dic83—42no—
346Dic83—42no—
347Dic83—42no—
348Dic83—42no—
349Dic83—42no—
350Dic83—42no—
351Dic83—42no—
352Dic83—42no—
353C2×#3344—831nomaximal, Sylow
354C2×C83—24no—
355C2×C83—42no—
356C2×C83#334414yescomplemented
357C2×C83C2×#54711yescharacteristic
358C2×C83C22×#13711yescharacteristic
359C2×C83C2×#57711yescharacteristic
360C2×#554—831no—
361C2×#552—831no—
362#3344—8316no—
363C2×#501—831no—
364C2×#484—831no—
365C2×#485—831no—
366C2×#483—831no—
367C2×#483—831no—
368C2×#479—831no—
369C2×#475—831no—
370C2×#470—831no—
371C2×#467—831no—
372C2×#441—831no—
373C2×#435D8311yescharacteristic
374C2×#428—831no—
375C22×#106—831no—
376C83C2×#334411yescharacteristic, complemented, Sylow
377C22×Q16—831no—
378C22×M16C2×D8311yescharacteristic
379C23×C8C2×D8311yescharacteristic
380#554—838no—
381#554—1664no—
382#552—838no—
383#552—1664no—
384C2×C4⋊Q8—831no—
385C2×#126—1661no—
386C2×#125—831no—
387C2×#125—1661no—
388C2×#125—1661no—
389C2×#123—1661no—
390C2×C22⋊Q8—831no—
391C2×C22⋊Q8—831no—
392C2×C22⋊Q8—831no—
393C2×C22⋊Q8—831no—
394C2×C22⋊Q8—1661no—
395C2×C22⋊Q8—1661no—
396C2×C4×Q8—831no—
397C2×C4×Q8—831no—
398C2×C4×D4—1661no—
399C2×C4×D4C2×D8311yescharacteristic
400C2×#117—831no—
401C2×#117—1661no—
402C22×C4⋊C4—831no—
403C22×C4⋊C4—831no—
404C22×C4⋊C4—831no—
405#501—838no—
406#485—838no—
407#484—838no—
408#483—838no—
409#483—838no—
410#479—838no—
411#475—838no—
412#470—838no—
413#467—838no—
414#441—838no—
415#435C2×D8318yes—
416#428—838no—
417C2×#107—831no—
418C2×#107—831no—
419C2×#107—831no—
420C2×#106—831no—
421C2×#106—831no—
422C2×#106—831no—
423C2×#106—831no—
424C2×#106—838no—
425C2×#106—831no—
426C2×#106—831no—
427C2×C4⋊C8C2×D8311yescharacteristic
428C2×#103—831no—
429C2×#103—831no—
430C2×#103—831no—
431C2×#103—831no—
432C2×#103—831no—
433C2×#103—831no—
434C2×C22⋊C8C2×D8311yescharacteristic
435C2×C22⋊C8C2×D8311yescharacteristic
436C2×#97C2×D8311yescharacteristic
437C22×Q8—831no—
438C22×Q8—831no—
439C22×Q8—1661no—
440C22×D4D33211yescharacteristic
441C23×C4—1661no—
442C23×C4—1661no—
443C23×C4—1661no—
444C23×C4C22×D8311yescharacteristic
445C23×C4C22×D8311yescharacteristic
446C2×Q16—834no—
447C2×Q16—1664no—
448C2×M16—24no—
449C2×M16C22×D8314yes—
450C22×C8—24no—
451C22×C8C22×D8311yescharacteristic
452C22×C8C22×D8314yes—
453C22×C8C22×D8311yescharacteristic
454C22×C8C22×D8311yescharacteristic
455C22×C8C22×D8311yescharacteristic
456C4⋊Q8—834no—
457C4⋊Q8—1662no—
458#126—1668no—
459#125—834no—
460#125—1668no—
461#125—1668no—
462#125—1662no—
463#123—1668no—
464C22⋊Q8—834no—
465C22⋊Q8—834no—
466C22⋊Q8—834no—
467C22⋊Q8—834no—
468C22⋊Q8—1662no—
469C22⋊Q8—1662no—
470C22⋊Q8—1662no—
471C22⋊Q8—1662no—
472C22⋊Q8—1668no—
473C22⋊Q8—1668no—
474C4×Q8—834no—
475C4×Q8—834no—
476C4×Q8—1662no—
477C4×Q8—1662no—
478C4×D4—1668no—
479C4×D4D33214yes—
480C4×D4C22×D8314yes—
481#117—834no—
482#117—1662no—
483#117—1668no—
484C2×C4⋊C4—831no—
485C2×C4⋊C4—831no—
486C2×C4⋊C4—831no—
487C2×C4⋊C4—831no—
488C2×C4⋊C4—831no—
489C2×C4⋊C4—834no—
490C2×C4⋊C4—834no—
491C2×C4⋊C4—834no—
492C2×C4⋊C4—831no—
493C2×C4⋊C4—1661no—
494C2×C4⋊C4—1661no—
495C2×C4⋊C4—1661no—
496C2×C4⋊C4—1662no—
497C2×C4⋊C4—1662no—
498C2×C4⋊C4—1662no—
499C2×C4⋊C4—1661no—
500C2×C4⋊C4—1661no—
501C2×C4⋊C4—1661no—
502C2×C4⋊C4—1661no—
503C2×C4⋊C4—1661no—
504C2×C4⋊C4—1661no—
505C2×C4⋊C4—1661no—
506C2×C4⋊C4—1661no—
507C2×C4⋊C4—1661no—
508C2×C4⋊C4D33211yescharacteristic
509C2×C22⋊C4—1661no—
510C2×C22⋊C4—1661no—
511C2×C22⋊C4—1661no—
512C2×C22⋊C4—1661no—
513C2×C22⋊C4—1661no—
514C2×C22⋊C4D33211yescharacteristic
515C2×C22⋊C4D33211yescharacteristic
516C2×C42—1661no—
517C2×C42—1661no—
518C2×C42—1661no—
519C2×C42C22×D8311yescharacteristic
520#107—834no—
521#107—834no—
522#107—834no—
523#106—834no—
524#106—834no—
525#106—834no—
526#106—834no—
527#106—834no—
528#106—834no—
529C4⋊C8C22×D8314yes—
530#103—834no—
531#103—834no—
532#103—834no—
533#103—834no—
534#103—834no—
535#103—834no—
536C22⋊C8C22×D8314yes—
537C22⋊C8C22×D8314yes—
538#97C22×D8314yes—
539C24C2×D33211yescharacteristic
540C24C2×D33211yescharacteristic
541C2×Q8—832no—
542C2×Q8—832no—
543C2×Q8—6642no—
544C2×Q8—1662no—
545C2×Q8—1662no—
546C2×Q8—1662no—
547C2×Q8—1662no—
548C2×Q8—1661no—
549C2×Q8—1661no—
550C2×Q8—1664no—
551C2×D4—24no—
552C2×D4C2×D33214yes—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—3324no—
558C22×C4—6642no—
559C22×C4—6642no—
560C22×C4—1664no—
561C22×C4—1661no—
562C22×C4—1661no—
563C22×C4—1661no—
564C22×C4—1661no—
565C22×C4—1661no—
566C22×C4—1661no—
567C22×C4—1661no—
568C22×C4—1661no—
569C22×C4—1664no—
570C22×C4—1664no—
571C22×C4C2×D33212yes—
572C22×C4C2×D33212yes—
573C22×C4C2×D33211yescharacteristic
574C22×C4C2×D33211yescharacteristic
575C22×C4C2×D33211yescharacteristic
576C22×C4C2×D33211yescharacteristic
577C22×C4C23×D8312yes—
578C22×C4C23×D8312yes—
579C22×C4C23×D8311yescharacteristic
580Q16—1668no—
581M16—28no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—28no—
586C2×C8#1305058914yes—
587C2×C8C23×D8312yes—
588C2×C8C23×D8312yes—
589C2×C8C23×D8312yes—
590C2×C8C23×D8312yes—
591C4⋊C4—832no—
592C4⋊C4—832no—
593C4⋊C4—832no—
594C4⋊C4—832no—
595C4⋊C4—832no—
596C4⋊C4—832no—
597C4⋊C4—1661no—
598C4⋊C4—1661no—
599C4⋊C4—1664no—
600C4⋊C4—1664no—
601C4⋊C4—1661no—
602C4⋊C4—1661no—
603C4⋊C4—1661no—
604C4⋊C4—1664no—
605C4⋊C4—1661no—
606C4⋊C4—1664no—
607C4⋊C4—1664no—
608C4⋊C4—1664no—
609C4⋊C4—1664no—
610C4⋊C4—1664no—
611C4⋊C4—1664no—
612C4⋊C4—1664no—
613C4⋊C4—1664no—
614C4⋊C4—1664no—
615C4⋊C4C2×D33214yes—
616C22⋊C4—1664no—
617C22⋊C4—1664no—
618C22⋊C4—1664no—
619C22⋊C4—1664no—
620C22⋊C4—1664no—
621C22⋊C4C2×D33214yes—
622C22⋊C4C2×D33214yes—
623C42—1664no—
624C42—1664no—
625C42—1664no—
626C42C2×D33212yes—
627C42C23×D8312yes—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23#1458182514yes—
634C23C22×D33212yes—
635C23C22×D33212yes—
636C23C22×D33211yescharacteristic
637Q8—3322no—
638Q8—3322no—
639Q8—6644no—
640Q8—1662no—
641Q8—1662no—
642Q8—1662no—
643Q8—1662no—
644D4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—3322no—
656C2×C4—3322no—
657C2×C4—3328no—
658C2×C4—3322no—
659C2×C4—3322no—
660C2×C4—3322no—
661C2×C4—3322no—
662C2×C4—3322no—
663C2×C4—3322no—
664C2×C4—6644no—
665C2×C4—6644no—
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×C4C22×D33212yes—
675C2×C4C22×D33212yes—
676C2×C4C22×D33212yes—
677C2×C4C22×D33212yes—
678C2×C4C22×D33211yescharacteristic
679C2×C4C2×#1305058912yes—
680C2×C4#1458183912yes—
681C2×C4C24×D8311yescharacteristic
682C8—22no—
683C8—22no—
684C8—22no—
685C8C2×#1305058914yes—
686C22—22no—
687C22—28no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—44no—
693C22#1912835512yes—
694C22C2×#1458182514yes—
695C22C2×#1458182512yes—
696C22#1912851312yes—
697C22C23×D33211yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—3322no—
703C4—3322no—
704C4—3322no—
705C4—3322no—
706C4—3322no—
707C4—3322no—
708C4—3322no—
709C4—3322no—
710C4#1912835512yes—
711C4C22×#1305058911yescharacteristic
712C4C2×#1458183911yescharacteristic
713C2—24no—
714C2—42no—
715C2#2491992014yesdirect product factor
716C2C2×#1912835511yescharacteristic
717C2C22×#1458182511yescharacteristic
718C2C2×#1912851311yescharacteristic
subgroupG/H
centerC23C22×D332
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#435×C83C2
socleC23×C83C22×D4
prime radicalC22×D4×C83D4
hypercenterC2×#435D83
hypocenterC83C2×#3344
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
3. #24919920C2direct (N × H)
4. C2×#19128110C2semidirect
5. C2×#19128037C2semidirect
6. C2×#19128043C2semidirect
7. C2×#19128032C2semidirect
8. C2×#19128032C2semidirect
9. C2×#19128009C2semidirect
10. C2×#19127987C2semidirect
11. C2×#19127959C2semidirect
12. C2×#19127942C2semidirect
13. C2×#19127809C2semidirect
14. C2×#19127743C2semidirect
15. C22×#14581724C2semidirect
42. #19128110C22semidirect
43. #19128043C22semidirect
44. #19128037C22semidirect
45. #19128032C22semidirect
46. #19128032C22semidirect
47. #19128009C22semidirect
48. #19127987C22semidirect
49. #19127959C22semidirect
50. #19127942C22semidirect
51. #19127809C22semidirect
52. #19127743C22semidirect
62. C2×#14581724C22semidirect
356. C2×C83#3344semidirect
376. C83C2×#3344semidirect
715. C2#24919920direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284082
C2×#191283912
#249199202
C2×#191281102
C2×#191280372
C2×#191280432
C2×#191280322
C2×#191280092
C2×#191279872
C2×#191279592
C2×#191279422
C2×#191278092
C2×#191277432
C22×#145817242
C2×#435×C832
C2×#334483