Finite Group Databasebeta

← C2×#24920008 #36283047

Subgroups — C2×#24920008 #36283047

Order 21248.

1898 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128397C211yesmaximal, characteristic
2#24920008C2116yesmaximal, direct product factor
3C2×#19128107C211yesmaximal, characteristic, complemented
4C2×#19128039C211yesmaximal, characteristic, complemented
5C2×#19128025C211yesmaximal, characteristic, complemented
6C2×#19128025C211yesmaximal, characteristic, complemented
7C2×#19128029C211yesmaximal, characteristic, complemented
8C2×#19128008C211yesmaximal, characteristic, complemented
9C2×#19127988C211yesmaximal, characteristic, complemented
10C2×#19127949C211yesmaximal, characteristic, complemented
11C2×#19127932C211yesmaximal, characteristic, complemented
12C2×#19127799C211yesmaximal, characteristic, complemented
13C2×#19127773C211yesmaximal, characteristic, complemented
14C2×#19127744C211yesmaximal, characteristic, complemented
15C2×#19127737C211yesmaximal, characteristic, complemented
16C2×#556×C83C211yesmaximal, characteristic, complemented
17C22×#13050577C2211yescharacteristic
18C22×#13050574C2211yescharacteristic
19C23×C83⋊C8C2211yescharacteristic
20#19128397—24no—
21#19128397C2218yes—
22C2×#14581787—21no—
23C2×#14581784C2211yescharacteristic
24C2×#14581774—21no—
25C2×#14581766C2211yescharacteristic
26C2×#14581766C2211yescharacteristic
27C2×#14581764—21no—
28C2×C4×D332C2211yescharacteristic
29C2×(C22⋊D83)⋊C4—21no—
30C2×#14581751C2211yescharacteristic
31C22×C4⋊Dic83C2211yescharacteristic
32#19128107C2218yescomplemented
33#19128039C2218yescomplemented
34#19128029C2218yescomplemented
35#19128025C2218yescomplemented
36#19128025C2218yescomplemented
37#19128008C2218yescomplemented
38#19127988C2218yescomplemented
39#19127949C2218yescomplemented
40#19127932C2218yescomplemented
41#19127799C2218yescomplemented
42#19127773C2218yescomplemented
43#19127744C2218yescomplemented
44#19127737C2218yescomplemented
45C2×#14581725C2211yescharacteristic
46C2×#14581725C2211yescharacteristic
47C2×#14581725C2211yescharacteristic
48C2×#14581725C2211yescharacteristic
49C2×#14581723C2211yescharacteristic
50C2×#14581723C2211yescharacteristic
51C2×#14581723C2211yescharacteristic
52C2×#14581723C2211yescharacteristic
53C2×#14581723C2211yescharacteristic
54C2×C4⋊(C83⋊C8)C2211yescharacteristic
55C2×#14581716C2211yescharacteristic
56C2×#14581716C2211yescharacteristic
57C2×#14581716C2211yescharacteristic
58C2×#14581712C2211yescharacteristic
59C2×#14581712C2211yescharacteristic
60C2×#14581712C2211yescharacteristic
61C2×C22⋊(C83⋊C8)C2211yescharacteristic
62C2×C22⋊(C83⋊C8)C2211yescharacteristic
63C2×#14581703C2211yescharacteristic
64#556×C83—24no—
65#556×C83C2218yescomplemented
66C2×C4⋊Q8×C83C2211yescharacteristic
67C2×#126×C83—21no—
68C2×#126×C83—21no—
69C2×#124×C83—21no—
70C2×C22⋊Q8×C83C2211yescharacteristic
71C2×C22⋊Q8×C83C2211yescharacteristic
72C2×C4×Q8×C83—21no—
73C2×C4×Q8×C83C2211yescharacteristic
74C2×C4×D4×C83C2211yescharacteristic
75C2×#117×C83C2211yescharacteristic
76C2×#117×C83C2211yescharacteristic
77C22×D332C2311yescharacteristic
78C22×C22⋊D83—21no—
79C22×C22⋊D83—21no—
80C23×Dic83—21no—
81C22×C4×D83—21no—
82C2×#13050577—24no—
83C2×#13050577C2314yes—
84C2×#13050574—24no—
85C2×#13050574C2314yes—
86C22×C83⋊C8—24no—
87C22×C83⋊C8C2311yescharacteristic
88C22×C83⋊C8C2311yescharacteristic
89C22×C83⋊C8C2311yescharacteristic
90C22×C83⋊C8C2314yes—
91C22×C83⋊C8C2311yescharacteristic
92#14581787—28no—
93#14581784—22no—
94#14581784C2314yes—
95#14581774—28no—
96#14581766—22no—
97#14581766—22no—
98#14581766C2314yes—
99#14581766C2314yes—
100#14581764—28no—
101C4×D332—22no—
102C4×D332C2314yes—
103(C22⋊D83)⋊C4—28no—
104#14581751—22no—
105#14581751C2314yes—
106C2×C4⋊Dic83—22no—
107C2×C4⋊Dic83—21no—
108C2×C4⋊Dic83C2314yes—
109C2×C4⋊Dic83C2311yescharacteristic
110C2×C4⋊Dic83C2311yescharacteristic
111C2×C4⋊Dic83C2311yescharacteristic
112C2×Dic83⋊C4—21no—
113C2×Dic83⋊C4—21no—
114C2×C22⋊Dic83—21no—
115C2×(C2×D83)⋊C4—21no—
116C2×(C2×D83)⋊C4—21no—
117C2×(C2×D83)⋊C4—21no—
118C2×C4×Dic83—21no—
119#14581725C2314yes—
120#14581725C2314yes—
121#14581725C2314yes—
122#14581725C2314yes—
123#14581723C2314yes—
124#14581723C2314yes—
125#14581723C2314yes—
126#14581723C2314yes—
127#14581723C2314yes—
128C4⋊(C83⋊C8)C2314yes—
129#14581716C2314yes—
130#14581716C2314yes—
131#14581716C2314yes—
132#14581712C2314yes—
133#14581712C2314yes—
134#14581712C2314yes—
135C22⋊(C83⋊C8)C2314yes—
136C22⋊(C83⋊C8)C2314yes—
137#14581703C2314yes—
138C22×Q8×C83—21no—
139C22×Q8×C83C2311yescharacteristic
140C22×D4×C83D411yescharacteristic
141C23×C4×C83C2311yescharacteristic
142C23×C4×C83C2311yescharacteristic
143C4⋊Q8×C83—22no—
144C4⋊Q8×C83C2314yes—
145#126×C83—28no—
146#126×C83—28no—
147#124×C83—28no—
148C22⋊Q8×C83—22no—
149C22⋊Q8×C83—22no—
150C22⋊Q8×C83C2314yes—
151C22⋊Q8×C83C2314yes—
152C4×Q8×C83—28no—
153C4×Q8×C83—22no—
154C4×Q8×C83C2314yes—
155C4×D4×C83D414yes—
156C4×D4×C83C2314yes—
157#117×C83—22no—
158#117×C83—22no—
159#117×C83C2314yes—
160#117×C83C2314yes—
161C2×C4⋊C4×C83—21no—
162C2×C4⋊C4×C83—21no—
163C2×C4⋊C4×C83—21no—
164C2×C4⋊C4×C83—21no—
165C2×C4⋊C4×C83D411yescharacteristic
166C2×C4⋊C4×C83C2311yescharacteristic
167C2×C4⋊C4×C83C2311yescharacteristic
168C2×C4⋊C4×C83C2311yescharacteristic
169C2×C22⋊C4×C83—21no—
170C2×C22⋊C4×C83—21no—
171C2×C22⋊C4×C83—21no—
172C2×C22⋊C4×C83—21no—
173C2×C22⋊C4×C83D411yescharacteristic
174C2×C22⋊C4×C83D411yescharacteristic
175C2×C42×C83—21no—
176C2×C42×C83—21no—
177C2×C42×C83—21no—
178C2×C42×C83C2311yescharacteristic
179C23×D83—21no—
180C2×D332—22no—
181C2×D332—22no—
182C2×D332—21no—
183C2×D332C2412yes—
184C2×C22⋊D83—24no—
185C2×C22⋊D83—24no—
186C2×C22⋊D83—44no—
187C2×C22⋊D83—82no—
188C22×Dic83—21no—
189C22×Dic83—21no—
190C22×Dic83—21no—
191C22×Dic83—24no—
192C22×Dic83—82no—
193C2×C4×D83—24no—
194C2×C4×D83—82no—
195#13050577—28no—
196#13050574—28no—
197C2×C83⋊C8—22no—
198C2×C83⋊C8—22no—
199C2×C83⋊C8—22no—
200C2×C83⋊C8—28no—
201C2×C83⋊C8#4114yes—
202C2×C83⋊C8C2412yes—
203C2×C83⋊C8C2412yes—
204C2×C83⋊C8C2412yes—
205C2×C83⋊C8C2412yes—
206C4⋊Dic83—21no—
207C4⋊Dic83—21no—
208C4⋊Dic83—24no—
209C4⋊Dic83—21no—
210C4⋊Dic83C2412yes—
211C4⋊Dic83C2412yes—
212C4⋊Dic83C2412yes—
213Dic83⋊C4—24no—
214Dic83⋊C4—24no—
215C22⋊Dic83—24no—
216(C2×D83)⋊C4—24no—
217(C2×D83)⋊C4—24no—
218(C2×D83)⋊C4—24no—
219C4×Dic83—24no—
220C24×C83C2×D411yescharacteristic
221C24×C83C2×D411yescharacteristic
222C2×Q8×C83—21no—
223C2×Q8×C83—24no—
224C2×Q8×C83—22no—
225C2×Q8×C83—22no—
226C2×Q8×C83—44no—
227C2×Q8×C83C2412yes—
228C2×D4×C83—42no—
229C2×D4×C83C2×D414yes—
230C22×C4×C83—22no—
231C22×C4×C83—22no—
232C22×C4×C83—22no—
233C22×C4×C83—22no—
234C22×C4×C83—21no—
235C22×C4×C83—21no—
236C22×C4×C83—21no—
237C22×C4×C83—21no—
238C22×C4×C83C2×D412yes—
239C22×C4×C83C2×D412yes—
240C22×C4×C83C2×D411yescharacteristic
241C22×C4×C83C2×D411yescharacteristic
242C22×C4×C83C2×D411yescharacteristic
243C22×C4×C83C2×D411yescharacteristic
244C22×C4×C83C2412yes—
245C22×C4×C83C2412yes—
246C22×C4×C83C2411yescharacteristic
247C4⋊C4×C83—24no—
248C4⋊C4×C83—24no—
249C4⋊C4×C83—24no—
250C4⋊C4×C83—24no—
251C4⋊C4×C83—21no—
252C4⋊C4×C83—21no—
253C4⋊C4×C83—21no—
254C4⋊C4×C83C2×D414yes—
255C4⋊C4×C83C2412yes—
256C4⋊C4×C83C2412yes—
257C4⋊C4×C83C2412yes—
258C22⋊C4×C83—24no—
259C22⋊C4×C83—24no—
260C22⋊C4×C83—24no—
261C22⋊C4×C83—24no—
262C22⋊C4×C83C2×D414yes—
263C22⋊C4×C83C2×D414yes—
264C42×C83—24no—
265C42×C83—24no—
266C42×C83—24no—
267C42×C83C2×D412yes—
268C42×C83C2412yes—
269C23×C83—22no—
270C23×C83—22no—
271C23×C83—22no—
272C23×C83—22no—
273C23×C83—22no—
274C23×C83—22no—
275C23×C83C22×D412yes—
276C23×C83C22×D412yes—
277C23×C83C22×D411yescharacteristic
278C22×D83—22no—
279C22×D83—42no—
280C22×D83—42no—
281C22×D83—42no—
282Q8×C83—22no—
283Q8×C83—22no—
284Q8×C83—48no—
285Q8×C83—42no—
286D4×C83—44no—
287C2×C4×C83—22no—
288C2×C4×C83—22no—
289C2×C4×C83—22no—
290C2×C4×C83—22no—
291C2×C4×C83—24no—
292C2×C4×C83—24no—
293C2×C4×C83—22no—
294C2×C4×C83—22no—
295C2×C4×C83—22no—
296C2×C4×C83—22no—
297C2×C4×C83—22no—
298C2×C4×C83—22no—
299C2×C4×C83—22no—
300C2×C4×C83—22no—
301C2×C4×C83—42no—
302C2×C4×C83—42no—
303C2×C4×C83—42no—
304C2×C4×C83—42no—
305C2×C4×C83C22×D412yes—
306C2×C4×C83C22×D412yes—
307C2×C4×C83C22×D412yes—
308C2×C4×C83C22×D412yes—
309C2×C4×C83C22×D411yescharacteristic
310C2×C4×C83C2×#4112yes—
311C2×C4×C832−1+412yes—
312C2×C4×C83C2511yescharacteristic
313C22⋊D83—48no—
314C22⋊D83—84no—
315C2×Dic83—22no—
316C2×Dic83—22no—
317C2×Dic83—22no—
318C2×Dic83—42no—
319C2×Dic83—42no—
320C2×Dic83—42no—
321C2×Dic83—84no—
322D332—22no—
323D332—22no—
324D332—42no—
325C4×D83—84no—
326C83⋊C8—22no—
327C83⋊C8—22no—
328C83⋊C8—22no—
329C83⋊C8C2×#4114yes—
330C22×C83—22no—
331C22×C83—22no—
332C22×C83—22no—
333C22×C83—22no—
334C22×C83—22no—
335C22×C83—22no—
336C22×C83—44no—
337C22×C83—44no—
338C22×C83#54712yes—
339C22×C83#57512yes—
340C22×C83#57712yes—
341C22×C83C23×D411yescharacteristic
342C2×D83—42no—
343C2×D83—42no—
344C2×D83—42no—
345C2×D83—84no—
346C4×C83—22no—
347C4×C83—22no—
348C4×C83—22no—
349C4×C83—22no—
350C4×C83—42no—
351C4×C83—42no—
352C4×C83—42no—
353C4×C83—42no—
354C4×C83#54712yes—
355C4×C83C22×#4111yescharacteristic
356C4×C83C2×2−1+411yescharacteristic
357Dic83—42no—
358Dic83—42no—
359Dic83—42no—
360C2×#3350—831nomaximal, Sylow
361C2×C83—42no—
362C2×C83—42no—
363C2×C83#335014yescomplemented
364C2×C83C2×#54711yescharacteristic
365C2×C83C2×#57511yescharacteristic
366C2×C83C2×#57711yescharacteristic
367D83—82no—
368C2×#556D8311yescharacteristic, complemented
369C2×#553—831no—
370#3350—8316no—
371C2×#501—831no—
372C2×#485—831no—
373C2×#482—831no—
374C2×#482—831no—
375C2×#483—831no—
376C2×#479—831no—
377C2×#476—831no—
378C2×#468—831no—
379C2×#465—831no—
380C2×#440—831no—
381C2×#435—831no—
382C2×#428—831no—
383C2×#427—831no—
384C83C2×#335011yescharacteristic, complemented, Sylow
385C22×SD16—831no—
386C22×M16—831no—
387C23×C8—831no—
388#556—24no—
389#556C2×D8318yescomplemented
390#553—838no—
391#553—1664no—
392C2×C4⋊Q8C2×D8311yescharacteristic
393C2×#126—21no—
394C2×#126—21no—
395C2×#126—1661no—
396C2×#125—831no—
397C2×#124—21no—
398C2×#123—1661no—
399C2×C22⋊Q8C2×D8311yescharacteristic
400C2×C22⋊Q8C2×D8311yescharacteristic
401C2×#121—831no—
402C2×#121—831no—
403C2×#121—1661no—
404C2×C4×Q8—21no—
405C2×C4×Q8C2×D8311yescharacteristic
406C2×C4×D4—831no—
407C2×C4×D4—1661no—
408C2×C4×D4C2×D8311yescharacteristic
409C2×#117—831no—
410C2×#117C2×D8311yescharacteristic
411C2×#117C2×D8311yescharacteristic
412C22×C4⋊C4—831no—
413#501—838no—
414#485—838no—
415#483—838no—
416#482—838no—
417#482—838no—
418#479—838no—
419#476—838no—
420#468—838no—
421#465—838no—
422#440—838no—
423#435—838no—
424#428—838no—
425#427—838no—
426C2×#107—831no—
427C2×#107—831no—
428C2×#107—831no—
429C2×#107—831no—
430C2×#106—831no—
431C2×#106—831no—
432C2×#106—831no—
433C2×#106—831no—
434C2×#106—831no—
435C2×C4⋊C8—831no—
436C2×#103—831no—
437C2×#103—831no—
438C2×#103—831no—
439C2×#102—831no—
440C2×#102—831no—
441C2×#102—831no—
442C2×C22⋊C8—831no—
443C2×C22⋊C8—831no—
444C2×#97—831no—
445C22×Q8—21no—
446C22×Q8C22×D8311yescharacteristic
447C22×D4—831no—
448C22×D4—1661no—
449C22×D4—1661no—
450C22×D4C22⋊D8311yescharacteristic
451C23×C4—1661no—
452C23×C4—1661no—
453C23×C4C22×D8311yescharacteristic
454C23×C4C22×D8311yescharacteristic
455C2×SD16—834no—
456C2×SD16—1664no—
457C2×M16—834no—
458C2×M16—1664no—
459C22×C8—831no—
460C22×C8—831no—
461C22×C8—834no—
462C22×C8—831no—
463C22×C8—831no—
464C22×C8—1664no—
465C4⋊Q8—22no—
466C4⋊Q8C22×D8314yes—
467#126—28no—
468#126—28no—
469#126—1668no—
470#125—834no—
471#125—1662no—
472#124—28no—
473#123—1668no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476C22⋊Q8C22×D8314yes—
477C22⋊Q8C22×D8314yes—
478#121—834no—
479#121—834no—
480#121—1668no—
481#121—1662no—
482#121—1662no—
483C4×Q8—28no—
484C4×Q8—22no—
485C4×Q8C22×D8314yes—
486C4×D4—834no—
487C4×D4—1668no—
488C4×D4—1662no—
489C4×D4C22⋊D8314yes—
490C4×D4C22×D8314yes—
491#117—22no—
492#117—22no—
493#117—834no—
494#117—1662no—
495#117C22×D8314yes—
496#117C22×D8314yes—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—831no—
502C2×C4⋊C4—831no—
503C2×C4⋊C4—834no—
504C2×C4⋊C4—831no—
505C2×C4⋊C4—1661no—
506C2×C4⋊C4—1662no—
507C2×C4⋊C4—1661no—
508C2×C4⋊C4—1661no—
509C2×C4⋊C4C22⋊D8311yescharacteristic
510C2×C4⋊C4C22×D8311yescharacteristic
511C2×C4⋊C4C22×D8311yescharacteristic
512C2×C4⋊C4C22×D8311yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—1661no—
518C2×C22⋊C4—1661no—
519C2×C22⋊C4—1661no—
520C2×C22⋊C4—1661no—
521C2×C22⋊C4C22⋊D8311yescharacteristic
522C2×C22⋊C4C22⋊D8311yescharacteristic
523C2×C42—21no—
524C2×C42—21no—
525C2×C42—21no—
526C2×C42—1661no—
527C2×C42C22×D8311yescharacteristic
528#107—834no—
529#107—834no—
530#107—834no—
531#107—834no—
532#106—834no—
533#106—834no—
534#106—834no—
535#106—834no—
536#106—834no—
537C4⋊C8—834no—
538#103—834no—
539#103—834no—
540#103—834no—
541#102—834no—
542#102—834no—
543#102—834no—
544C22⋊C8—834no—
545C22⋊C8—834no—
546#97—834no—
547C24—1661no—
548C24C2×C22⋊D8311yescharacteristic
549C24C2×C22⋊D8311yescharacteristic
550C2×Q8—21no—
551C2×Q8—24no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—44no—
555C2×Q8C23×D8312yes—
556C2×D4—42no—
557C2×D4—3324no—
558C2×D4—832no—
559C2×D4—6642no—
560C2×D4—1664no—
561C2×D4—1664no—
562C2×D4—1661no—
563C2×D4—1662no—
564C2×D4—1662no—
565C2×D4C2×C22⋊D8314yes—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—6642no—
575C22×C4—6642no—
576C22×C4—1661no—
577C22×C4—1661no—
578C22×C4—1661no—
579C22×C4—1664no—
580C22×C4—1664no—
581C22×C4C2×C22⋊D8312yes—
582C22×C4C2×C22⋊D8312yes—
583C22×C4C2×C22⋊D8311yescharacteristic
584C22×C4C2×C22⋊D8311yescharacteristic
585C22×C4C2×C22⋊D8311yescharacteristic
586C22×C4C2×C22⋊D8311yescharacteristic
587C22×C4C23×D8312yes—
588C22×C4C23×D8312yes—
589C22×C4C23×D8311yescharacteristic
590SD16—1668no—
591M16—1668no—
592C2×C8—834no—
593C2×C8—832no—
594C2×C8—832no—
595C2×C8—832no—
596C2×C8—832no—
597C2×C8—1668no—
598C2×C8—1662no—
599C2×C8—1662no—
600C2×C8—1662no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—832no—
609C4⋊C4—832no—
610C4⋊C4—832no—
611C4⋊C4—1661no—
612C4⋊C4—1661no—
613C4⋊C4—1664no—
614C4⋊C4—1661no—
615C4⋊C4—1664no—
616C4⋊C4—1664no—
617C4⋊C4C2×C22⋊D8314yes—
618C4⋊C4C23×D8312yes—
619C4⋊C4C23×D8312yes—
620C4⋊C4C23×D8312yes—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—1664no—
626C22⋊C4—1664no—
627C22⋊C4—1664no—
628C22⋊C4—1664no—
629C22⋊C4C2×C22⋊D8314yes—
630C22⋊C4C2×C22⋊D8314yes—
631C42—24no—
632C42—24no—
633C42—24no—
634C42—1664no—
635C42C2×C22⋊D8312yes—
636C42C23×D8312yes—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—3322no—
644C23—3322no—
645C23—3322no—
646C23—1662no—
647C23C22×C22⋊D8312yes—
648C23C22×C22⋊D8312yes—
649C23C22×C22⋊D8311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—48no—
653Q8—42no—
654D4—44no—
655D4—3328no—
656D4—3322no—
657D4—6644no—
658D4—1662no—
659D4—1662no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—3322no—
679C2×C4—3322no—
680C2×C4—3322no—
681C2×C4—6644no—
682C2×C4—6644no—
683C2×C4—1662no—
684C2×C4—1662no—
685C2×C4—1662no—
686C2×C4C22×C22⋊D8312yes—
687C2×C4C22×C22⋊D8312yes—
688C2×C4C22×C22⋊D8312yes—
689C2×C4C22×C22⋊D8312yes—
690C2×C4C22×C22⋊D8311yescharacteristic
691C2×C4#41×D8312yes—
692C2×C4#1458183912yes—
693C2×C4C24×D8311yescharacteristic
694C8—834no—
695C8—1662no—
696C8—1662no—
697C8—1662no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—44no—
705C22—44no—
706C22—3322no—
707C22—3322no—
708C22—3322no—
709C22—6644no—
710C22#1912835012yes—
711C22#1912849912yes—
712C22#1912850912yes—
713C22C23×C22⋊D8311yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—3322no—
723C4—3322no—
724C4—3322no—
725C4#1912835012yes—
726C4C2×#41×D8311yescharacteristic
727C4C2×#1458183911yescharacteristic
728C2—42no—
729C2—42no—
730C2—6642no—
731C2#2492000814yesdirect product factor
732C2C2×#1912835011yescharacteristic
733C2C2×#1912849911yescharacteristic
734C2C2×#1912850911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#556×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128397C2
hypercenterC2×#556D83
hypocenterC83C2×#3350
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
2. #24920008C2direct (N × H)
3. C2×#19128107C2semidirect
4. C2×#19128039C2semidirect
5. C2×#19128025C2semidirect
6. C2×#19128025C2semidirect
7. C2×#19128029C2semidirect
8. C2×#19128008C2semidirect
9. C2×#19127988C2semidirect
10. C2×#19127949C2semidirect
11. C2×#19127932C2semidirect
12. C2×#19127799C2semidirect
13. C2×#19127773C2semidirect
14. C2×#19127744C2semidirect
15. C2×#19127737C2semidirect
16. C2×#556×C83C2semidirect
32. #19128107C22semidirect
33. #19128039C22semidirect
34. #19128029C22semidirect
35. #19128025C22semidirect
36. #19128025C22semidirect
37. #19128008C22semidirect
38. #19127988C22semidirect
39. #19127949C22semidirect
40. #19127932C22semidirect
41. #19127799C22semidirect
42. #19127773C22semidirect
43. #19127744C22semidirect
44. #19127737C22semidirect
65. #556×C83C22semidirect
363. C2×C83#3350semidirect
368. C2×#556D83semidirect
384. C83C2×#3350semidirect
389. #556C2×D83semidirect
731. C2#24920008direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283972
#249200082
C2×#191281072
C2×#191280392
C2×#191280252
C2×#191280292
C2×#191280082
C2×#191279882
C2×#191279492
C2×#191279322
C2×#191277992
C2×#191277732
C2×#191277442
C2×#191277372
C2×#556×C832
C2×#335083