Finite Group Databasebeta

← C2×#24920292 #36284171

Subgroups — C2×#24920292 #36284171

Order 21248.

1886 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
1C2×#19128424C211yesmaximal, characteristic, complemented
2C2×#19128411C211yesmaximal, characteristic, complemented
3#24920292C2116yesmaximal, direct product factor
4C2×#19128070C211yesmaximal, characteristic, complemented
5C2×#19128061C211yesmaximal, characteristic, complemented
6C2×#19128056C211yesmaximal, characteristic, complemented
7C2×#19128009C211yesmaximal, characteristic, complemented
8C2×#19127987C211yesmaximal, characteristic, complemented
9C2×#19128002C211yesmaximal, characteristic, complemented
10C2×#19127917C211yesmaximal, characteristic
11C2×#19127917C211yesmaximal, characteristic
12C2×#19127907C211yesmaximal, characteristic, complemented
13C2×#19127814C211yesmaximal, characteristic
14C2×#19127803C211yesmaximal, characteristic, complemented
15C2×C4×#13050579C211yesmaximal, characteristic, complemented
16C2×#446×C83C211yesmaximal, characteristic, complemented
17C22×#13050579C2211yescharacteristic
18C22×#13050579C2211yescharacteristic
19C22×D664C2211yescharacteristic
20#19128424—24no—
21#19128424C2218yescomplemented
22#19128411—24no—
23#19128411C2218yescomplemented
24C2×#14581792C2211yescharacteristic
25C2×#14581792C2211yescharacteristic
26C2×#14581787—21no—
27C2×#14581787—21no—
28C2×#14581784C2211yescharacteristic
29C2×#14581784C2211yescharacteristic
30C2×#14581780C2211yescharacteristic
31C2×#14581780C2211yescharacteristic
32C2×#14581770—21no—
33C2×#14581770—21no—
34C2×#14581768—21no—
35C2×#14581768—21no—
36C2×C4×Dic166C2211yescharacteristic
37C2×C4×Dic166C2211yescharacteristic
38C2×C4×D332C2211yescharacteristic
39C2×C4×D332C2211yescharacteristic
40C2×C4×D332C2211yescharacteristic
41C2×C4×D332C2211yescharacteristic
42C2×#14581750—21no—
43C2×C4⋊C4×D83—21no—
44#19128070C2218yescomplemented
45#19128061C2218yescomplemented
46#19128056C2218yescomplemented
47#19128009C2218yescomplemented
48#19128002C2218yescomplemented
49#19127987C2218yescomplemented
50#19127917C2218yes—
51#19127917C2218yes—
52#19127907C2218yescomplemented
53#19127814C2218yes—
54#19127803C2218yescomplemented
55C4×#13050579C2218yescomplemented
56C2×#14581726C2211yescharacteristic
57C2×#14581724C2211yescharacteristic
58C2×#14581724C2211yescharacteristic
59C2×#14581717C2211yescharacteristic
60C2×#14581717C2211yescharacteristic
61C2×#14581717C2211yescharacteristic
62C2×#14581717C2211yescharacteristic
63C2×#14581717C2211yescharacteristic
64C2×#14581717C2211yescharacteristic
65C2×#14581714C2211yescharacteristic
66C2×#14581714C2211yescharacteristic
67C2×#14581714C2211yescharacteristic
68C2×#14581714C2211yescharacteristic
69C2×C4×Q8×C83C2211yescharacteristic
70#446×C83C2218yescomplemented
71C2×C4⋊C8×C83C2211yescharacteristic
72C2×C4⋊C8×C83C2211yescharacteristic
73C2×C4⋊C8×C83C2211yescharacteristic
74C2×#97×C83C2211yescharacteristic
75C2×#97×C83C2211yescharacteristic
76C2×C4×C8×C83C2211yescharacteristic
77C22×Dic166—21no—
78C22×Dic166C2311yescharacteristic
79C22×Dic166C2311yescharacteristic
80C22×D332C2311yescharacteristic
81C22×D332C2311yescharacteristic
82C22×C4×D83—21no—
83C22×C4×D83—21no—
84C22×C4×D83—21no—
85C22×C4×D83—21no—
86C2×#13050579—24no—
87C2×#13050579—24no—
88C2×#13050579C2314yes—
89C2×#13050579C2314yes—
90C2×D664—24no—
91C2×D664C2314yes—
92#14581792—22no—
93#14581792—22no—
94#14581792C2314yes—
95#14581792C2314yes—
96#14581787—28no—
97#14581787—28no—
98#14581784—22no—
99#14581784—22no—
100#14581784C2314yes—
101#14581784C2314yes—
102#14581780—22no—
103#14581780—22no—
104#14581780C2314yes—
105#14581780C2314yes—
106#14581770—28no—
107#14581770—28no—
108#14581768—28no—
109#14581768—28no—
110C4×Dic166—22no—
111C4×Dic166—22no—
112C4×Dic166C2314yes—
113C4×Dic166C2314yes—
114C4×D332—22no—
115C4×D332—22no—
116C4×D332—22no—
117C4×D332—22no—
118C4×D332C2314yes—
119C4×D332C2314yes—
120C4×D332C2314yes—
121C4×D332C2314yes—
122#14581750—28no—
123C2×C4⋊Dic83—21no—
124C2×C4⋊Dic83—21no—
125C2×C4⋊Dic83—21no—
126C2×C4⋊Dic83C2311yescharacteristic
127C2×C4⋊Dic83C2311yescharacteristic
128C2×C4⋊Dic83C2311yescharacteristic
129C2×C4⋊Dic83C2311yescharacteristic
130C2×Dic83⋊C4—21no—
131C2×Dic83⋊C4—21no—
132C2×Dic83⋊C4—21no—
133C2×Dic83⋊C4—21no—
134C2×Dic83⋊C4—21no—
135C2×Dic83⋊C4—21no—
136C4⋊C4×D83—28no—
137C2×(C2×D83)⋊C4—21no—
138C2×(C2×D83)⋊C4—21no—
139C2×(C2×D83)⋊C4—21no—
140C2×(C2×D83)⋊C4—21no—
141C2×(C2×D83)⋊C4—21no—
142C2×(C2×D83)⋊C4—21no—
143C2×(C2×D83)⋊C4—21no—
144C2×(C2×D83)⋊C4—21no—
145C2×C4×Dic83—21no—
146C2×C4×Dic83—21no—
147#14581726C2314yes—
148#14581724C2314yes—
149#14581724C2314yes—
150#14581717C2314yes—
151#14581717C2314yes—
152#14581717C2314yes—
153#14581717C2314yes—
154#14581717C2314yes—
155#14581717C2314yes—
156#14581714C2314yes—
157#14581714C2314yes—
158#14581714C2314yes—
159#14581714C2314yes—
160C22×Q8×C83D411yescharacteristic
161C22×C8×C83C2311yescharacteristic
162C22×C8×C83C2311yescharacteristic
163C22×C8×C83C2311yescharacteristic
164C22×C8×C83C2311yescharacteristic
165C4×Q8×C83D414yes—
166C4×Q8×C83C2314yes—
167C2×C4⋊C4×C83D411yescharacteristic
168C2×C4⋊C4×C83D411yescharacteristic
169C2×C4⋊C4×C83D411yescharacteristic
170C2×C42×C83C2311yescharacteristic
171C2×C42×C83C2311yescharacteristic
172C2×C42×C83C2311yescharacteristic
173C4⋊C8×C83C2314yes—
174C4⋊C8×C83C2314yes—
175C4⋊C8×C83C2314yes—
176#97×C83C2314yes—
177#97×C83C2314yes—
178C4×C8×C83C2314yes—
179C23×D83—21no—
180C23×D83—21no—
181C2×Dic166—22no—
182C2×Dic166—22no—
183C2×Dic166—22no—
184C2×Dic166—22no—
185C2×Dic166—21no—
186C2×Dic166—21no—
187C2×Dic166—24no—
188C2×Dic166—82no—
189C2×Dic166C2412yes—
190C2×Dic166C2412yes—
191C2×D332—21no—
192C2×D332—22no—
193C2×D332—22no—
194C2×D332—22no—
195C2×D332—21no—
196C2×D332#4114yes—
197C2×D332C2412yes—
198C2×D332C2412yes—
199C22×Dic83—21no—
200C22×Dic83—21no—
201C22×Dic83—21no—
202C22×Dic83—21no—
203C22×Dic83—21no—
204C22×Dic83—21no—
205C2×C4×D83—24no—
206C2×C4×D83—24no—
207C2×C4×D83—24no—
208C2×C4×D83—24no—
209C2×C4×D83—44no—
210C2×C4×D83—44no—
211C2×C4×D83—82no—
212C2×C4×D83—82no—
213#13050579—28no—
214#13050579—28no—
215D664—28no—
216C4⋊Dic83—24no—
217C4⋊Dic83—24no—
218C4⋊Dic83—21no—
219C4⋊Dic83—21no—
220C4⋊Dic83—21no—
221C4⋊Dic83—24no—
222C4⋊Dic83—21no—
223C4⋊Dic83C2412yes—
224C4⋊Dic83C2412yes—
225C4⋊Dic83C2412yes—
226C4⋊Dic83C2412yes—
227Dic83⋊C4—24no—
228Dic83⋊C4—24no—
229Dic83⋊C4—24no—
230Dic83⋊C4—24no—
231Dic83⋊C4—24no—
232Dic83⋊C4—24no—
233(C2×D83)⋊C4—24no—
234(C2×D83)⋊C4—24no—
235(C2×D83)⋊C4—24no—
236(C2×D83)⋊C4—24no—
237(C2×D83)⋊C4—24no—
238(C2×D83)⋊C4—24no—
239(C2×D83)⋊C4—24no—
240(C2×D83)⋊C4—24no—
241C4×Dic83—24no—
242C4×Dic83—24no—
243C2×Q8×C83—42no—
244C2×Q8×C83C2×D414yes—
245C22×C4×C83C2×D411yescharacteristic
246C22×C4×C83C2×D411yescharacteristic
247C22×C4×C83C2×D411yescharacteristic
248C22×C4×C83C2×D411yescharacteristic
249C22×C4×C83C2×D411yescharacteristic
250C22×C4×C83C2×D411yescharacteristic
251C22×C4×C83C2411yescharacteristic
252C2×C8×C83—22no—
253C2×C8×C83—22no—
254C2×C8×C83—22no—
255C2×C8×C83—22no—
256C2×C8×C83C2412yes—
257C2×C8×C83C2412yes—
258C2×C8×C83C2412yes—
259C2×C8×C83C2412yes—
260C4⋊C4×C83C2×D414yes—
261C4⋊C4×C83C2×D414yes—
262C4⋊C4×C83C2×D414yes—
263C42×C83C2×D412yes—
264C42×C83C2×D412yes—
265C42×C83C2×D412yes—
266C42×C83C2412yes—
267C42×C83C2412yes—
268C42×C83C2412yes—
269C23×C83C22×D411yescharacteristic
270C22×D83—24no—
271C22×D83—22no—
272C22×D83—22no—
273C22×D83—42no—
274C22×D83—42no—
275C22×D83—42no—
276C22×D83—42no—
277C22×D83—42no—
278Q8×C83—44no—
279C2×C4×C83—22no—
280C2×C4×C83—22no—
281C2×C4×C83—22no—
282C2×C4×C83—22no—
283C2×C4×C83—22no—
284C2×C4×C83—22no—
285C2×C4×C83C22×D412yes—
286C2×C4×C83C22×D412yes—
287C2×C4×C83C22×D412yes—
288C2×C4×C83C22×D412yes—
289C2×C4×C83C22×D412yes—
290C2×C4×C83C22×D412yes—
291C2×C4×C83C22×D411yescharacteristic
292C2×C4×C83C2×#4112yes—
293C2×C4×C832−1+412yes—
294C2×C4×C83C2511yescharacteristic
295C2×Dic83—22no—
296C2×Dic83—22no—
297C2×Dic83—22no—
298C2×Dic83—22no—
299C2×Dic83—22no—
300C2×Dic83—22no—
301C2×Dic83—42no—
302C2×Dic83—42no—
303C2×Dic83—42no—
304C2×Dic83—42no—
305C2×Dic83—42no—
306C2×Dic83—42no—
307D332—24no—
308D332—22no—
309D332—22no—
310D332—22no—
311D332—42no—
312D332C2×#4114yes—
313C4×D83—48no—
314C4×D83—48no—
315C4×D83—84no—
316C4×D83—84no—
317Dic166—22no—
318Dic166—22no—
319Dic166—22no—
320Dic166—22no—
321Dic166—42no—
322Dic166—42no—
323Dic166—84no—
324C8×C83—22no—
325C8×C83—22no—
326C8×C83—22no—
327C8×C83—22no—
328C22×C83#54812yes—
329C22×C83#57512yes—
330C22×C83#57712yes—
331C22×C83C23×D411yescharacteristic
332C2×D83—24no—
333C2×D83—48no—
334C2×D83—42no—
335C2×D83—42no—
336C2×D83—42no—
337C2×D83—42no—
338C2×D83—42no—
339C2×D83—84no—
340C4×C83—22no—
341C4×C83—22no—
342C4×C83—22no—
343C4×C83—22no—
344C4×C83—22no—
345C4×C83—22no—
346C4×C83#54812yes—
347C4×C83C22×#4111yescharacteristic
348C4×C83C2×2−1+411yescharacteristic
349Dic83—42no—
350Dic83—42no—
351Dic83—42no—
352Dic83—42no—
353Dic83—42no—
354Dic83—42no—
355C2×#3376—831nomaximal, Sylow
356C2×C83#337614yescomplemented
357C2×C83C2×#54811yescharacteristic
358C2×C83C2×#57511yescharacteristic
359C2×C83C2×#57711yescharacteristic
360D83—44no—
361D83—82no—
362C2×#556—831no—
363C2×#554—831no—
364#3376—8316no—
365C2×#491—831no—
366C2×#489—831no—
367C2×#488—831no—
368C2×#479—831no—
369C2×#475—831no—
370C2×#478—831no—
371C2×#463—831no—
372C2×#463—831no—
373C2×#461—831no—
374C2×#446D8311yescharacteristic, complemented
375C2×#442—831no—
376C2×#440—831no—
377C2×C4×SD16—831no—
378C83C2×#337611yescharacteristic, complemented, Sylow
379C22×SD16—831no—
380C22×SD16—831no—
381C22×D8—831no—
382#556—838no—
383#556—1664no—
384#554—838no—
385#554—1664no—
386C2×C4⋊Q8—831no—
387C2×C4⋊Q8—831no—
388C2×#126—1661no—
389C2×#126—1661no—
390C2×#125—831no—
391C2×#125—831no—
392C2×#124—831no—
393C2×#124—831no—
394C2×C22⋊Q8—1661no—
395C2×C22⋊Q8—1661no—
396C2×C22⋊Q8—1661no—
397C2×C22⋊Q8—1661no—
398C2×C4×Q8—831no—
399C2×C4×Q8—831no—
400C2×C4×Q8C2×D8311yescharacteristic
401C2×C4×D4—831no—
402C2×C4×D4—831no—
403C2×C4×D4—831no—
404C2×C4×D4—831no—
405C2×#117—1661no—
406C22×C4⋊C4—1661no—
407#491—838no—
408#489—838no—
409#488—838no—
410#479—838no—
411#478—838no—
412#475—838no—
413#463—838no—
414#463—838no—
415#461—838no—
416#446C2×D8318yescomplemented
417#442—838no—
418#440—838no—
419C4×SD16—838no—
420C2×#107—831no—
421C2×#106—831no—
422C2×#106—831no—
423C2×C4⋊C8C2×D8311yescharacteristic
424C2×C4⋊C8C2×D8311yescharacteristic
425C2×C4⋊C8C2×D8311yescharacteristic
426C2×#103—831no—
427C2×#103—831no—
428C2×#103—831no—
429C2×#103—831no—
430C2×#103—831no—
431C2×#103—831no—
432C2×#102—831no—
433C2×#102—831no—
434C2×#102—831no—
435C2×#102—831no—
436C2×#97C2×D8311yescharacteristic
437C2×#97C2×D8311yescharacteristic
438C2×C4×C8C2×D8311yescharacteristic
439C22×Q8—831no—
440C22×Q8—831no—
441C22×Q8—1661no—
442C22×Q8D33211yescharacteristic
443C22×D4—831no—
444C22×D4—831no—
445C23×C4—1661no—
446C23×C4—1661no—
447C23×C4—1661no—
448C23×C4—1661no—
449C2×SD16—834no—
450C2×SD16—834no—
451C2×SD16—1664no—
452C2×SD16—1664no—
453C2×D8—834no—
454C2×D8—1664no—
455C22×C8C22×D8311yescharacteristic
456C22×C8C22×D8311yescharacteristic
457C22×C8C22×D8311yescharacteristic
458C22×C8C22×D8311yescharacteristic
459C4⋊Q8—834no—
460C4⋊Q8—834no—
461C4⋊Q8—1662no—
462C4⋊Q8—1662no—
463#126—1668no—
464#126—1668no—
465#125—834no—
466#125—834no—
467#125—1662no—
468#125—1662no—
469#124—834no—
470#124—834no—
471#124—1662no—
472#124—1662no—
473C22⋊Q8—1668no—
474C22⋊Q8—1668no—
475C22⋊Q8—1668no—
476C22⋊Q8—1668no—
477C4×Q8—834no—
478C4×Q8—834no—
479C4×Q8—1662no—
480C4×Q8—1662no—
481C4×Q8D33214yes—
482C4×Q8C22×D8314yes—
483C4×D4—834no—
484C4×D4—834no—
485C4×D4—834no—
486C4×D4—834no—
487C4×D4—1662no—
488C4×D4—1662no—
489C4×D4—1662no—
490C4×D4—1662no—
491#117—1668no—
492C2×C4⋊C4—831no—
493C2×C4⋊C4—831no—
494C2×C4⋊C4—831no—
495C2×C4⋊C4—831no—
496C2×C4⋊C4—1661no—
497C2×C4⋊C4—1661no—
498C2×C4⋊C4—1661no—
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—1668no—
506C2×C4⋊C4D33211yescharacteristic
507C2×C4⋊C4D33211yescharacteristic
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⋊C4—1661no—
515C2×C22⋊C4—1661no—
516C2×C22⋊C4—1661no—
517C2×C42—1661no—
518C2×C42—1661no—
519C2×C42C22×D8311yescharacteristic
520C2×C42C22×D8311yescharacteristic
521C2×C42C22×D8311yescharacteristic
522#107—834no—
523#106—834no—
524#106—834no—
525C4⋊C8C22×D8314yes—
526C4⋊C8C22×D8314yes—
527C4⋊C8C22×D8314yes—
528#103—834no—
529#103—834no—
530#103—834no—
531#103—834no—
532#103—834no—
533#103—834no—
534#102—834no—
535#102—834no—
536#102—834no—
537#102—834no—
538#97C22×D8314yes—
539#97C22×D8314yes—
540C4×C8C22×D8314yes—
541C24—1661no—
542C24—1661no—
543C2×Q8—42no—
544C2×Q8—832no—
545C2×Q8—832no—
546C2×Q8—6642no—
547C2×Q8—1662no—
548C2×Q8—1662no—
549C2×Q8—1662no—
550C2×Q8—1662no—
551C2×Q8—1661no—
552C2×Q8—1661no—
553C2×Q8—1664no—
554C2×Q8C2×D33214yes—
555C2×D4—834no—
556C2×D4—832no—
557C2×D4—832no—
558C2×D4—1661no—
559C2×D4—1661no—
560C2×D4—1662no—
561C2×D4—1662no—
562C2×D4—1662no—
563C22×C4—3324no—
564C22×C4—3324no—
565C22×C4—6642no—
566C22×C4—6642no—
567C22×C4—1661no—
568C22×C4—1661no—
569C22×C4—1661no—
570C22×C4—1661no—
571C22×C4—1661no—
572C22×C4—1661no—
573C22×C4—1664no—
574C22×C4—1664no—
575C22×C4—1664no—
576C22×C4—1664no—
577C22×C4C2×D33211yescharacteristic
578C22×C4C2×D33211yescharacteristic
579C22×C4C2×D33211yescharacteristic
580C22×C4C2×D33211yescharacteristic
581C22×C4C2×D33211yescharacteristic
582C22×C4C2×D33211yescharacteristic
583C22×C4C23×D8311yescharacteristic
584SD16—1668no—
585SD16—1668no—
586D8—1668no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8C23×D8312yes—
592C2×C8C23×D8312yes—
593C2×C8C23×D8312yes—
594C2×C8C23×D8312yes—
595C4⋊C4—832no—
596C4⋊C4—832no—
597C4⋊C4—832no—
598C4⋊C4—832no—
599C4⋊C4—1661no—
600C4⋊C4—1661no—
601C4⋊C4—1661no—
602C4⋊C4—1661no—
603C4⋊C4—1664no—
604C4⋊C4—1664no—
605C4⋊C4—1664no—
606C4⋊C4—1664no—
607C4⋊C4—1664no—
608C4⋊C4—1664no—
609C4⋊C4—1664no—
610C4⋊C4—1664no—
611C4⋊C4—1664no—
612C4⋊C4C2×D33214yes—
613C4⋊C4C2×D33214yes—
614C4⋊C4C2×D33214yes—
615C22⋊C4—1664no—
616C22⋊C4—1664no—
617C22⋊C4—1664no—
618C22⋊C4—1664no—
619C22⋊C4—1664no—
620C22⋊C4—1664no—
621C22⋊C4—1664no—
622C22⋊C4—1664no—
623C42—1664no—
624C42—1664no—
625C42C2×D33212yes—
626C42C2×D33212yes—
627C42C2×D33212yes—
628C42C23×D8312yes—
629C42C23×D8312yes—
630C42C23×D8312yes—
631C23—3322no—
632C23—3322no—
633C23—3322no—
634C23—3322no—
635C23—3322no—
636C23—1662no—
637C23—1664no—
638C23—1662no—
639C23C22×D33211yescharacteristic
640Q8—44no—
641Q8—3322no—
642Q8—3322no—
643Q8—6644no—
644Q8—1662no—
645Q8—1662no—
646Q8—1662no—
647Q8—1662no—
648D4—3322no—
649D4—834no—
650D4—1664no—
651D4—1662no—
652D4—1662no—
653D4—1662no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—3328no—
661C2×C4—3328no—
662C2×C4—3322no—
663C2×C4—3322no—
664C2×C4—3322no—
665C2×C4—3322no—
666C2×C4—3322no—
667C2×C4—3322no—
668C2×C4—6644no—
669C2×C4—6644no—
670C2×C4—1662no—
671C2×C4—1662no—
672C2×C4—1662no—
673C2×C4—1662no—
674C2×C4—1662no—
675C2×C4—1662no—
676C2×C4C22×D33212yes—
677C2×C4C22×D33212yes—
678C2×C4C22×D33212yes—
679C2×C4C22×D33212yes—
680C2×C4C22×D33212yes—
681C2×C4C22×D33212yes—
682C2×C4C22×D33211yescharacteristic
683C2×C4#41×D8312yes—
684C2×C4#1458184012yes—
685C2×C4C24×D8311yescharacteristic
686C8—22no—
687C8—22no—
688C8—22no—
689C8—22no—
690C22—3322no—
691C22—3322no—
692C22—3328no—
693C22—3322no—
694C22—3322no—
695C22—3322no—
696C22—6644no—
697C22—1664no—
698C22#1912836312yes—
699C22#1912850112yes—
700C22#1912851312yes—
701C22C23×D33211yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—3322no—
709C4—3322no—
710C4—3322no—
711C4—3322no—
712C4—3322no—
713C4—3322no—
714C4#1912836312yes—
715C4C2×#41×D8311yescharacteristic
716C4C2×#1458184011yescharacteristic
717C2—3324no—
718C2—6642no—
719C2#2492029214yesdirect product factor
720C2C2×#1912836311yescharacteristic
721C2C2×#1912850111yescharacteristic
722C2C2×#1912851311yescharacteristic
subgroupG/H
centerC23C22×D332
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#446×C83C2
socleC23×C83C22×D4
prime radicalC22×D664C22
hypercenterC2×#446D83
hypocenterC83C2×#3376
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
1. C2×#19128424C2semidirect
2. C2×#19128411C2semidirect
3. #24920292C2direct (N × H)
4. C2×#19128070C2semidirect
5. C2×#19128061C2semidirect
6. C2×#19128056C2semidirect
7. C2×#19128009C2semidirect
8. C2×#19127987C2semidirect
9. C2×#19128002C2semidirect
12. C2×#19127907C2semidirect
14. C2×#19127803C2semidirect
15. C2×C4×#13050579C2semidirect
16. C2×#446×C83C2semidirect
21. #19128424C22semidirect
23. #19128411C22semidirect
44. #19128070C22semidirect
45. #19128061C22semidirect
46. #19128056C22semidirect
47. #19128009C22semidirect
48. #19128002C22semidirect
49. #19127987C22semidirect
52. #19127907C22semidirect
54. #19127803C22semidirect
55. C4×#13050579C22semidirect
70. #446×C83C22semidirect
356. C2×C83#3376semidirect
374. C2×#446D83semidirect
378. C83C2×#3376semidirect
416. #446C2×D83semidirect
719. C2#24920292direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284242
C2×#191284112
#249202922
C2×#191280702
C2×#191280612
C2×#191280562
C2×#191280092
C2×#191279872
C2×#191280022
C2×#191279172
C2×#191279072
C2×#191278142
C2×#191278032
C2×C4×#130505792
C2×#446×C832
C2×#337683