Finite Group Databasebeta

← C2×#24919899 #36282931

Subgroups — C2×#24919899 #36282931

Order 21248.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128386C211yesmaximal, characteristic, complemented
2C2×#19128352C211yesmaximal, characteristic
3#24919899C2116yesmaximal, direct product factor
4C2×#19128109C211yesmaximal, characteristic, complemented
5C2×#19128038C211yesmaximal, characteristic, complemented
6C2×#19128028C211yesmaximal, characteristic, complemented
7C2×#19128031C211yesmaximal, characteristic, complemented
8C2×#19128014C211yesmaximal, characteristic, complemented
9C2×#19127995C211yesmaximal, characteristic, complemented
10C2×#19128004C211yesmaximal, characteristic, complemented
11C2×#19127948C211yesmaximal, characteristic, complemented
12C2×#19127930C211yesmaximal, characteristic, complemented
13C2×#19127800C211yesmaximal, characteristic, complemented
14C2×#19127772C211yesmaximal, characteristic, complemented
15C2×#19127742C211yesmaximal, characteristic, complemented
16C22×#107×C83C211yesmaximal, characteristic, complemented
17C22×#13050590—21no—
18C22×#13050579C2211yescharacteristic
19C22×#13050573C2211yescharacteristic
20#19128386—24no—
21#19128386C2218yescomplemented
22#19128352—24no—
23#19128352C2218yes—
24C2×#14581791C2211yescharacteristic
25C2×#14581787—21no—
26C2×#14581783C2211yescharacteristic
27C2×#14581782—21no—
28C2×#14581777—21no—
29C2×#14581775—21no—
30C2×#14581775—21no—
31C2×#14581772C2211yescharacteristic
32C2×#14581771C2211yescharacteristic
33C2×#14581770—21no—
34C2×#14581767C2211yescharacteristic
35C2×#14581766C2211yescharacteristic
36C2×#14581757C2211yescharacteristic
37C2×#14581754C2211yescharacteristic
38C2×C4×C22⋊D83C2211yescharacteristic
39C2×#14581751—21no—
40C2×#14581750C2211yescharacteristic
41C2×C4⋊C4×D83C2211yescharacteristic
42#19128109C2218yescomplemented
43#19128038C2218yescomplemented
44#19128031C2218yescomplemented
45#19128028C2218yescomplemented
46#19128014C2218yescomplemented
47#19128004C2218yescomplemented
48#19127995C2218yescomplemented
49#19127948C2218yescomplemented
50#19127930C2218yescomplemented
51#19127800C2218yescomplemented
52#19127772C2218yescomplemented
53#19127742C2218yescomplemented
54C2×#14581725C2211yescharacteristic
55C2×#14581725C2211yescharacteristic
56C2×#14581724C2211yescharacteristic
57C2×#14581723C2211yescharacteristic
58C2×#14581723C2211yescharacteristic
59C2×Dic83⋊C8C2211yescharacteristic
60C2×#14581717C2211yescharacteristic
61C2×#14581715C2211yescharacteristic
62C2×#14581715C2211yescharacteristic
63C2×#14581714C2211yescharacteristic
64C2×#14581712C2211yescharacteristic
65C2×#14581712C2211yescharacteristic
66C2×C22⋊(C83⋊C8)C2211yescharacteristic
67C2×(C2×D83)⋊C8C2211yescharacteristic
68C2×#14581702C2211yescharacteristic
69C23×C8×C83C2211yescharacteristic
70C22×C4⋊C4×C83C2211yescharacteristic
71C22×C4⋊C4×C83C2211yescharacteristic
72C2×#107×C83C2211yescharacteristic
73C2×#107×C83C2211yescharacteristic
74C2×#107×C83C2211yescharacteristic
75C2×#107×C83C2211yescharacteristic
76C2×#107×C83C2218yescomplemented
77C2×#13050590—28no—
78C2×#13050590—48no—
79C22×Dic166—21no—
80C22×Dic166C2311yescharacteristic
81C22×D332—21no—
82C22×D332C2311yescharacteristic
83C22×C22⋊D83—21no—
84C22×C22⋊D83D411yescharacteristic
85C22×C4×D83—21no—
86C22×C4×D83—21no—
87C22×C4×D83C2311yescharacteristic
88C2×#13050579—24no—
89C2×#13050579C2314yes—
90C2×#13050573—24no—
91C2×#13050573C2314yes—
92C22×C83⋊C8C2311yescharacteristic
93C22×C83⋊C8C2311yescharacteristic
94#14581791—22no—
95#14581791C2314yes—
96#14581787—28no—
97#14581783—22no—
98#14581783C2314yes—
99#14581782—28no—
100#14581777—28no—
101#14581775—28no—
102#14581775—28no—
103#14581772—22no—
104#14581772C2314yes—
105#14581771—22no—
106#14581771C2314yes—
107#14581770—28no—
108#14581767—22no—
109#14581767C2314yes—
110#14581766—22no—
111#14581766C2314yes—
112#14581757—22no—
113#14581757C2314yes—
114#14581754—22no—
115#14581754C2314yes—
116C4×C22⋊D83D414yes—
117C4×C22⋊D83C2314yes—
118#14581751—28no—
119#14581750—22no—
120#14581750C2314yes—
121C2×C4⋊Dic83—21no—
122C2×C4⋊Dic83—21no—
123C2×C4⋊Dic83C2311yescharacteristic
124C2×C4⋊Dic83C2311yescharacteristic
125C2×Dic83⋊C4—21no—
126C2×Dic83⋊C4—21no—
127C2×Dic83⋊C4—21no—
128C2×Dic83⋊C4—21no—
129C2×Dic83⋊C4—21no—
130C2×Dic83⋊C4D411yescharacteristic
131C4⋊C4×D83—22no—
132C4⋊C4×D83C2314yes—
133C2×C22⋊Dic83—21no—
134C2×C22⋊Dic83D411yescharacteristic
135C2×(C2×D83)⋊C4—21no—
136C2×(C2×D83)⋊C4—21no—
137C2×(C2×D83)⋊C4—21no—
138C2×(C2×D83)⋊C4—21no—
139C2×(C2×D83)⋊C4—21no—
140C2×(C2×D83)⋊C4D411yescharacteristic
141C2×C4×Dic83—21no—
142C2×C4×Dic83—21no—
143C2×C4×Dic83C2311yescharacteristic
144#14581725C2314yes—
145#14581725C2314yes—
146#14581724C2314yes—
147#14581723C2314yes—
148#14581723C2314yes—
149Dic83⋊C8C2314yes—
150#14581717C2314yes—
151#14581715C2314yes—
152#14581715C2314yes—
153#14581714C2314yes—
154#14581712C2314yes—
155#14581712C2314yes—
156C22⋊(C83⋊C8)C2314yes—
157(C2×D83)⋊C8C2314yes—
158#14581702C2314yes—
159C23×C4×C83—21no—
160C23×C4×C83—21no—
161C23×C4×C83C2311yescharacteristic
162C22×C8×C83—24no—
163C22×C8×C83C2311yescharacteristic
164C22×C8×C83C2314yes—
165C22×C8×C83C2311yescharacteristic
166C2×C4⋊C4×C83—22no—
167C2×C4⋊C4×C83—22no—
168C2×C4⋊C4×C83—21no—
169C2×C4⋊C4×C83—21no—
170C2×C4⋊C4×C83C2314yes—
171C2×C4⋊C4×C83C2314yes—
172C2×C4⋊C4×C83C2311yescharacteristic
173C2×C4⋊C4×C83C2311yescharacteristic
174C2×C4⋊C4×C83C2311yescharacteristic
175C2×C4⋊C4×C83C2311yescharacteristic
176#107×C83C2314yes—
177#107×C83C2314yes—
178#107×C83C2314yes—
179#107×C83C2314yes—
180C23×D83—21no—
181C23×D83C2×D411yescharacteristic
182#13050590—432no—
183C2×Dic166—22no—
184C2×Dic166—22no—
185C2×Dic166—21no—
186C2×Dic166—24no—
187C2×Dic166—44no—
188C2×Dic166C2412yes—
189C2×D332—22no—
190C2×D332—22no—
191C2×D332—24no—
192C2×D332—21no—
193C2×D332—44no—
194C2×D332C2412yes—
195C2×C22⋊D83—24no—
196C2×C22⋊D83—24no—
197C2×C22⋊D83—44no—
198C2×C22⋊D83C2×D414yes—
199C22×Dic83—21no—
200C22×Dic83—21no—
201C22×Dic83—21no—
202C22×Dic83C2×D411yescharacteristic
203C22×Dic83C2×D411yescharacteristic
204C22×Dic83C2×D411yescharacteristic
205C2×C4×D83—22no—
206C2×C4×D83—22no—
207C2×C4×D83—24no—
208C2×C4×D83—24no—
209C2×C4×D83—44no—
210C2×C4×D83—44no—
211C2×C4×D83C2×D412yes—
212C2×C4×D83C2412yes—
213#13050579—28no—
214#13050573—28no—
215C2×C83⋊C8—22no—
216C2×C83⋊C8—22no—
217C2×C83⋊C8C2412yes—
218C2×C83⋊C8C2412yes—
219C4⋊Dic83—21no—
220C4⋊Dic83—21no—
221C4⋊Dic83—24no—
222C4⋊Dic83—24no—
223C4⋊Dic83C2412yes—
224C4⋊Dic83C2412yes—
225Dic83⋊C4—24no—
226Dic83⋊C4—24no—
227Dic83⋊C4—24no—
228Dic83⋊C4—24no—
229Dic83⋊C4—24no—
230Dic83⋊C4C2×D414yes—
231C22⋊Dic83—24no—
232C22⋊Dic83C2×D414yes—
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)⋊C4C2×D414yes—
239C4×Dic83—24no—
240C4×Dic83—24no—
241C4×Dic83C2×D412yes—
242C4×Dic83C2412yes—
243C24×C83C2×D411yescharacteristic
244C22×C4×C83—22no—
245C22×C4×C83—22no—
246C22×C4×C83—24no—
247C22×C4×C83—24no—
248C22×C4×C83—21no—
249C22×C4×C83—21no—
250C22×C4×C83—21no—
251C22×C4×C83—21no—
252C22×C4×C83—44no—
253C22×C4×C83—44no—
254C22×C4×C83C2×D412yes—
255C22×C4×C83C2×D411yescharacteristic
256C22×C4×C83C2412yes—
257C22×C4×C83C2411yescharacteristic
258C2×C8×C83—22no—
259C2×C8×C83—28no—
260C2×C8×C83#4114yescomplemented
261C2×C8×C83C2412yes—
262C2×C8×C83C2412yes—
263C4⋊C4×C83—21no—
264C4⋊C4×C83—24no—
265C4⋊C4×C83—21no—
266C4⋊C4×C83—24no—
267C4⋊C4×C83—21no—
268C4⋊C4×C83—21no—
269C4⋊C4×C83C2412yes—
270C4⋊C4×C83C2412yes—
271C4⋊C4×C83C2412yes—
272C4⋊C4×C83C2412yes—
273C23×C83—22no—
274C23×C83—22no—
275C23×C83AGL(1,ℤ/8)14yes—
276C23×C83C22×D412yes—
277C23×C83C22×D411yescharacteristic
278C22×D83—22no—
279C22×D83—22no—
280C22×D83—22no—
281C22×D83—22no—
282C22×D83—42no—
283C22×D83—42no—
284C22×D83—42no—
285C22×D83C22×D412yes—
286C2×C4×C83—22no—
287C2×C4×C83—24no—
288C2×C4×C83—22no—
289C2×C4×C83—22no—
290C2×C4×C83—22no—
291C2×C4×C83—22no—
292C2×C4×C83—22no—
293C2×C4×C83—22no—
294C2×C4×C83—48no—
295C2×C4×C83—42no—
296C2×C4×C83—42no—
297C2×C4×C83—42no—
298C2×C4×C83—42no—
299C2×C4×C83—48no—
300C2×C4×C83C22×D412yes—
301C2×C4×C83C22×D411yescharacteristic
302C2×C4×C83C2×#4112yes—
303C2×C4×C832−1+412yes—
304C2×C4×C83C2511yescharacteristic
305C22⋊D83—28no—
306C22⋊D83—48no—
307C2×Dic83—22no—
308C2×Dic83—22no—
309C2×Dic83—22no—
310C2×Dic83—22no—
311C2×Dic83—22no—
312C2×Dic83—22no—
313C2×Dic83—42no—
314C2×Dic83—42no—
315C2×Dic83—42no—
316C2×Dic83C22×D412yes—
317C2×Dic83C22×D412yes—
318C2×Dic83C22×D412yes—
319D332—22no—
320D332—22no—
321D332—48no—
322D332—42no—
323C4×D83—24no—
324C4×D83—22no—
325C4×D83—22no—
326C4×D83—48no—
327C4×D83—48no—
328Dic166—22no—
329Dic166—22no—
330Dic166—48no—
331Dic166—42no—
332C8×C83—22no—
333C8×C83C2×#4114yescomplemented
334C83⋊C8—22no—
335C83⋊C8—22no—
336C22×C83—28no—
337C22×C83—22no—
338C22×C83—22no—
339C22×C83#54712yes—
340C22×C83C2×AGL(1,ℤ/8)14yes—
341C22×C83C2×AGL(1,ℤ/8)12yes—
342C22×C83#57812yes—
343C22×C83C23×D411yescharacteristic
344C2×D83—22no—
345C2×D83—22no—
346C2×D83—22no—
347C2×D83—44no—
348C2×D83—42no—
349C2×D83—42no—
350C2×D83—42no—
351C2×D83—84no—
352C4×C83—22no—
353C4×C83—42no—
354C4×C83—42no—
355C4×C83—42no—
356C4×C83—42no—
357C4×C83#54712yes—
358C4×C83C22×#4111yescharacteristic
359C4×C83C2×2−1+411yescharacteristic
360Dic83—22no—
361Dic83—22no—
362Dic83—22no—
363Dic83—42no—
364Dic83—42no—
365Dic83—42no—
366C2×#3343—831nomaximal, Sylow
367C2×C83—24no—
368C2×C83#334314yescomplemented
369C2×C83C2×#54711yescharacteristic
370C2×C83C22×AGL(1,ℤ/8)11yescharacteristic
371C2×C83C2×#57811yescharacteristic
372D83—42no—
373D83—82no—
374C2×#552—831no—
375C2×#547—831no—
376#3343—8316no—
377C2×#501—831no—
378C2×#484—831no—
379C2×#482—831no—
380C2×#483—831no—
381C2×#480—831no—
382C2×#477—831no—
383C2×#478—831no—
384C2×#468—831no—
385C2×#465—831no—
386C2×#440—831no—
387C2×#435—831no—
388C2×#428—831no—
389C22×#107D8311yescharacteristic, complemented
390C83C2×#334311yescharacteristic, complemented, Sylow
391C22×#41—1661no—
392C22×SD16—831no—
393C22×M16—831no—
394C23×C8C2×D8311yescharacteristic
395#552—838no—
396#552—1664no—
397#547—838no—
398#547—1664no—
399C2×C4⋊Q8—831no—
400C2×#126—1661no—
401C2×#125—831no—
402C2×#125—1661no—
403C2×#123—1661no—
404C2×#123—1661no—
405C2×#123—1661no—
406C2×C22⋊Q8—831no—
407C2×C22⋊Q8—831no—
408C2×C22⋊Q8—1661no—
409C2×#121—831no—
410C2×#121—831no—
411C2×C4×Q8—831no—
412C2×C4×D4—831no—
413C2×C4×D4—831no—
414C2×#117—831no—
415C2×#117—1661no—
416C22×C4⋊C4—831no—
417C22×C4⋊C4C2×D8311yescharacteristic
418C22×C4⋊C4C2×D8311yescharacteristic
419#501—838no—
420#484—838no—
421#483—838no—
422#482—838no—
423#480—838no—
424#478—838no—
425#477—838no—
426#468—838no—
427#465—838no—
428#440—838no—
429#435—838no—
430#428—838no—
431C2×#107—831no—
432C2×#107—831no—
433C2×#107C2×D8311yescharacteristic
434C2×#107C2×D8311yescharacteristic
435C2×#107C2×D8311yescharacteristic
436C2×#107C2×D8311yescharacteristic
437C2×#107C2×D8318yescomplemented
438C2×#106—831no—
439C2×#106—831no—
440C2×#106—831no—
441C2×C4⋊C8—831no—
442C2×#103—831no—
443C2×#103—831no—
444C2×#103—831no—
445C2×#102—831no—
446C2×#102—831no—
447C2×#102—831no—
448C2×C22⋊C8—831no—
449C2×C22⋊C8—831no—
450C2×#97—831no—
451C2×#41—3328no—
452C2×#41—1668no—
453C22×Q8—831no—
454C22×Q8—1661no—
455C22×D4—831no—
456C22×D4—831no—
457C22×D4—1661no—
458C22×D4—1661no—
459C23×C4—21no—
460C23×C4—21no—
461C23×C4—831no—
462C23×C4—1661no—
463C23×C4—1661no—
464C23×C4C22×D8311yescharacteristic
465C2×SD16—834no—
466C2×SD16—1664no—
467C2×M16—834no—
468C2×M16—1664no—
469C22×C8—24no—
470C22×C8—831no—
471C22×C8—831no—
472C22×C8C22×D8311yescharacteristic
473C22×C8C22×D8314yes—
474C22×C8C22×D8311yescharacteristic
475C4⋊Q8—834no—
476C4⋊Q8—1662no—
477#126—1668no—
478#125—834no—
479#125—1662no—
480#125—1668no—
481#123—1668no—
482#123—1668no—
483#123—1668no—
484C22⋊Q8—834no—
485C22⋊Q8—834no—
486C22⋊Q8—1668no—
487C22⋊Q8—1662no—
488C22⋊Q8—1662no—
489#121—834no—
490#121—834no—
491#121—1662no—
492#121—1662no—
493C4×Q8—834no—
494C4×Q8—1662no—
495C4×D4—834no—
496C4×D4—834no—
497C4×D4—834no—
498C4×D4—1662no—
499#117—834no—
500#117—1668no—
501#117—1662no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—831no—
507C2×C4⋊C4—831no—
508C2×C4⋊C4—831no—
509C2×C4⋊C4—834no—
510C2×C4⋊C4—1662no—
511C2×C4⋊C4—1661no—
512C2×C4⋊C4—1661no—
513C2×C4⋊C4—1661no—
514C2×C4⋊C4—1661no—
515C2×C4⋊C4—1661no—
516C2×C4⋊C4—1661no—
517C2×C4⋊C4—1661no—
518C2×C4⋊C4C22×D8311yescharacteristic
519C2×C4⋊C4C22×D8311yescharacteristic
520C2×C4⋊C4C22×D8311yescharacteristic
521C2×C4⋊C4C22×D8311yescharacteristic
522C2×C4⋊C4C22×D8314yes—
523C2×C4⋊C4C22×D8314yes—
524C2×C22⋊C4—831no—
525C2×C22⋊C4—831no—
526C2×C22⋊C4—1661no—
527C2×C22⋊C4—1661no—
528C2×C22⋊C4—1661no—
529C2×C22⋊C4—1661no—
530C2×C22⋊C4—1661no—
531C2×C22⋊C4—1661no—
532C2×C42—831no—
533C2×C42—1661no—
534C2×C42—1661no—
535#107—834no—
536#107—834no—
537#107C22×D8314yes—
538#107C22×D8314yes—
539#107C22×D8314yes—
540#107C22×D8314yes—
541#106—834no—
542#106—834no—
543#106—834no—
544C4⋊C8—834no—
545#103—834no—
546#103—834no—
547#103—834no—
548#102—834no—
549#102—834no—
550#102—834no—
551C22⋊C8—834no—
552C22⋊C8—834no—
553#97—834no—
554C24—831no—
555C24—1661no—
556C24D4×D8311yescharacteristic
557#41—33232no—
558C2×Q8—3324no—
559C2×Q8—832no—
560C2×Q8—1664no—
561C2×Q8—1662no—
562C2×Q8—1662no—
563C2×Q8—1661no—
564C2×D4—3324no—
565C2×D4—3324no—
566C2×D4—834no—
567C2×D4—832no—
568C2×D4—1664no—
569C2×D4—1664no—
570C2×D4—1664no—
571C2×D4—1661no—
572C2×D4—1662no—
573C2×D4—1662no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—3324no—
585C22×C4—3324no—
586C22×C4—831no—
587C22×C4—831no—
588C22×C4—831no—
589C22×C4—832no—
590C22×C4—832no—
591C22×C4—1664no—
592C22×C4—1664no—
593C22×C4—1661no—
594C22×C4—1661no—
595C22×C4—1661no—
596C22×C4—1662no—
597C22×C4—1662no—
598C22×C4D4×D8312yes—
599C22×C4D4×D8311yescharacteristic
600C22×C4C23×D8312yes—
601C22×C4C23×D8311yescharacteristic
602SD16—1668no—
603M16—1668no—
604C2×C8—22no—
605C2×C8—28no—
606C2×C8—832no—
607C2×C8—832no—
608C2×C8—1662no—
609C2×C8—1662no—
610C2×C8#1305059014yescomplemented
611C2×C8C23×D8312yes—
612C2×C8C23×D8312yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—24no—
617C4⋊C4—21no—
618C4⋊C4—24no—
619C4⋊C4—834no—
620C4⋊C4—832no—
621C4⋊C4—832no—
622C4⋊C4—1664no—
623C4⋊C4—1664no—
624C4⋊C4—1664no—
625C4⋊C4—1664no—
626C4⋊C4—1664no—
627C4⋊C4—1664no—
628C4⋊C4—1661no—
629C4⋊C4—1661no—
630C4⋊C4—1664no—
631C4⋊C4C23×D8312yes—
632C4⋊C4C23×D8312yes—
633C4⋊C4C23×D8312yes—
634C4⋊C4C23×D8312yes—
635C22⋊C4—834no—
636C22⋊C4—834no—
637C22⋊C4—1664no—
638C22⋊C4—1664no—
639C22⋊C4—1664no—
640C22⋊C4—1664no—
641C22⋊C4—1664no—
642C22⋊C4—1664no—
643C42—832no—
644C42—832no—
645C42—1664no—
646C42—1664no—
647C23—22no—
648C23—22no—
649C23—3322no—
650C23—3322no—
651C23—3322no—
652C23—832no—
653C23—1662no—
654C23—1662no—
655C23—1662no—
656C23—1662no—
657C23#1458181614yes—
658C23C2×D4×D8312yes—
659C23C2×D4×D8311yescharacteristic
660Q8—3328no—
661Q8—3322no—
662Q8—1662no—
663Q8—1662no—
664D4—3328no—
665D4—3328no—
666D4—3322no—
667D4—1668no—
668D4—1662no—
669D4—1662no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—48no—
681C2×C4—48no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—3328no—
685C2×C4—3328no—
686C2×C4—3322no—
687C2×C4—3322no—
688C2×C4—3322no—
689C2×C4—832no—
690C2×C4—832no—
691C2×C4—832no—
692C2×C4—1662no—
693C2×C4—1662no—
694C2×C4—1662no—
695C2×C4—1662no—
696C2×C4—1662no—
697C2×C4—1662no—
698C2×C4—1664no—
699C2×C4—1662no—
700C2×C4—1662no—
701C2×C4C2×D4×D8312yes—
702C2×C4C2×D4×D8311yescharacteristic
703C2×C4C2×#1305059012yes—
704C2×C4#1458184012yes—
705C2×C4C24×D8311yescharacteristic
706C8—22no—
707C8—1662no—
708C8—1662no—
709C8C2×#1305059014yescomplemented
710C22—22no—
711C22—28no—
712C22—22no—
713C22—3324no—
714C22—3322no—
715C22—3322no—
716C22—3322no—
717C22—6644no—
718C22—1662no—
719C22—1662no—
720C22—1662no—
721C22#1912835212yes—
722C22C2×#1458181614yes—
723C22C2×#1458181612yes—
724C22#1912851412yes—
725C22C22×D4×D8311yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—3322no—
732C4—3322no—
733C4—3322no—
734C4—1662no—
735C4—1662no—
736C4—1662no—
737C4#1912835212yes—
738C4C22×#1305059011yescharacteristic
739C4C2×#1458184011yescharacteristic
740C2—24no—
741C2—3322no—
742C2—6642no—
743C2#2491989914yesdirect product factor
744C2C2×#1912835211yescharacteristic
745C2C22×#1458181611yescharacteristic
746C2C2×#1912851411yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC22×#107×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128352C2
hypercenterC22×#107D83
hypocenterC83C2×#3343
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
1. C2×#19128386C2semidirect
3. #24919899C2direct (N × H)
4. C2×#19128109C2semidirect
5. C2×#19128038C2semidirect
6. C2×#19128028C2semidirect
7. C2×#19128031C2semidirect
8. C2×#19128014C2semidirect
9. C2×#19127995C2semidirect
10. C2×#19128004C2semidirect
11. C2×#19127948C2semidirect
12. C2×#19127930C2semidirect
13. C2×#19127800C2semidirect
14. C2×#19127772C2semidirect
15. C2×#19127742C2semidirect
16. C22×#107×C83C2semidirect
21. #19128386C22semidirect
42. #19128109C22semidirect
43. #19128038C22semidirect
44. #19128031C22semidirect
45. #19128028C22semidirect
46. #19128014C22semidirect
47. #19128004C22semidirect
48. #19127995C22semidirect
49. #19127948C22semidirect
50. #19127930C22semidirect
51. #19127800C22semidirect
52. #19127772C22semidirect
53. #19127742C22semidirect
76. C2×#107×C83C22semidirect
260. C2×C8×C83#41semidirect
333. C8×C83C2×#41semidirect
368. C2×C83#3343semidirect
389. C22×#107D83semidirect
390. C83C2×#3343semidirect
437. C2×#107C2×D83semidirect
610. C2×C8#13050590semidirect
709. C8C2×#13050590semidirect
743. C2#24919899direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283862
C2×#191283522
#249198992
C2×#191281092
C2×#191280382
C2×#191280282
C2×#191280312
C2×#191280142
C2×#191279952
C2×#191280042
C2×#191279482
C2×#191279302
C2×#191278002
C2×#191277722
C2×#191277422
C22×#107×C832
C2×#334383