Finite Group Databasebeta

← C2×#24920014 #36283053

Subgroups — C2×#24920014 #36283053

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×#19128422C211yesmaximal, characteristic, complemented
2C2×#19128398C211yesmaximal, characteristic
3#24920014C2116yesmaximal, direct product factor
4C2×#19128108C211yesmaximal, characteristic, complemented
5C2×#19128039C211yesmaximal, characteristic, complemented
6C2×#19128024C211yesmaximal, characteristic, complemented
7C2×#19128022C211yesmaximal, characteristic, complemented
8C2×#19128030C211yesmaximal, characteristic, complemented
9C2×#19128006C211yesmaximal, characteristic, complemented
10C2×#19127989C211yesmaximal, characteristic, complemented
11C2×#19127944C211yesmaximal, characteristic, complemented
12C2×#19127802C211yesmaximal, characteristic, complemented
13C2×#19127772C211yesmaximal, characteristic, complemented
14C2×#19127740C211yesmaximal, characteristic, complemented
15C2×#19127739C211yesmaximal, characteristic, complemented
16C2×#465×C83C211yesmaximal, characteristic, complemented
17C22×#13050573C2211yescharacteristic
18#19128422—24no—
19#19128422C2218yescomplemented
20#19128398—24no—
21#19128398C2218yes—
22C2×#14581791C2211yescharacteristic
23C2×#14581787—21no—
24C2×#14581785—21no—
25C2×#14581785—21no—
26C2×#14581783C2211yescharacteristic
27C2×#14581778—21no—
28C2×#14581773—21no—
29C2×#14581768C2211yescharacteristic
30C2×#14581763—21no—
31C2×#14581763C2211yescharacteristic
32C2×Q8×Dic83C2211yescharacteristic
33C2×#14581757—21no—
34C2×D4×Dic83C2211yescharacteristic
35C2×C4×C22⋊D83C2211yescharacteristic
36C2×(C22⋊D83)⋊C4—21no—
37C2×#14581751C2211yescharacteristic
38C2×#14581751C2211yescharacteristic
39C2×#14581750C2211yescharacteristic
40C2×C4⋊C4×D83C2211yescharacteristic
41#19128108C2218yescomplemented
42#19128039C2218yescomplemented
43#19128030C2218yescomplemented
44#19128024C2218yescomplemented
45#19128022C2218yescomplemented
46#19128006C2218yescomplemented
47#19127989C2218yescomplemented
48#19127944C2218yescomplemented
49#19127802C2218yescomplemented
50#19127772C2218yescomplemented
51#19127740C2218yescomplemented
52#19127739C2218yescomplemented
53C2×#14581726C2211yescharacteristic
54C2×#14581726C2211yescharacteristic
55C2×#14581725C2211yescharacteristic
56C2×#14581725C2211yescharacteristic
57C2×#14581724C2211yescharacteristic
58C2×#14581724C2211yescharacteristic
59C2×#14581723C2211yescharacteristic
60C2×#14581723C2211yescharacteristic
61C2×Dic83⋊C8C2211yescharacteristic
62C2×#14581716C2211yescharacteristic
63C2×#14581716C2211yescharacteristic
64C2×#14581713C2211yescharacteristic
65C2×#14581713C2211yescharacteristic
66C2×C22⋊(C83⋊C8)C2211yescharacteristic
67C2×(C2×D83)⋊C8C2211yescharacteristic
68C2×#14581702C2211yescharacteristic
69C22×SD16×C83C2211yescharacteristic
70C23×C8×C83C2211yescharacteristic
71C2×C22⋊Q8×C83C2211yescharacteristic
72C2×#121×C83C2211yescharacteristic
73#465×C83C2218yescomplemented
74C2×#106×C83C2211yescharacteristic
75C2×#103×C83C2211yescharacteristic
76C2×#102×C83C2211yescharacteristic
77C22×Dic166—21no—
78C22×C22⋊D83—21no—
79C22×C22⋊D83D411yescharacteristic
80C23×Dic83—21no—
81C22×C4×D83—21no—
82C22×C4×D83C2311yescharacteristic
83C2×#13050573—24no—
84C2×#13050573C2314yes—
85C22×C83⋊C8C2311yescharacteristic
86C22×C83⋊C8C2311yescharacteristic
87#14581791—22no—
88#14581791C2314yes—
89#14581787—28no—
90#14581785—28no—
91#14581785—28no—
92#14581783—22no—
93#14581783C2314yes—
94#14581778—28no—
95#14581773—28no—
96#14581768—22no—
97#14581768C2314yes—
98#14581763—28no—
99#14581763—22no—
100#14581763C2314yes—
101Q8×Dic83—22no—
102Q8×Dic83C2314yes—
103#14581757—28no—
104D4×Dic83—22no—
105D4×Dic83C2314yes—
106C4×C22⋊D83D414yes—
107C4×C22⋊D83C2314yes—
108(C22⋊D83)⋊C4—28no—
109#14581751—22no—
110#14581751—22no—
111#14581751C2314yes—
112#14581751C2314yes—
113#14581750—22no—
114#14581750C2314yes—
115C2×C4⋊Dic83—21no—
116C2×C4⋊Dic83—21no—
117C2×C4⋊Dic83C2311yescharacteristic
118C2×C4⋊Dic83C2311yescharacteristic
119C2×C4⋊Dic83C2311yescharacteristic
120C2×C4⋊Dic83C2311yescharacteristic
121C2×Dic83⋊C4—21no—
122C2×Dic83⋊C4—21no—
123C2×Dic83⋊C4—21no—
124C2×Dic83⋊C4—21no—
125C2×Dic83⋊C4D411yescharacteristic
126C4⋊C4×D83—22no—
127C4⋊C4×D83C2314yes—
128C2×C22⋊Dic83—21no—
129C2×C22⋊Dic83—21no—
130C2×C22⋊Dic83—21no—
131C2×C22⋊Dic83—21no—
132C2×C22⋊Dic83D411yescharacteristic
133C2×(C2×D83)⋊C4—21no—
134C2×(C2×D83)⋊C4—21no—
135C2×(C2×D83)⋊C4D411yescharacteristic
136C2×C4×Dic83—21no—
137C2×C4×Dic83—21no—
138C2×C4×Dic83—21no—
139C2×C4×Dic83—21no—
140C2×C4×Dic83C2311yescharacteristic
141#14581726C2314yes—
142#14581726C2314yes—
143#14581725C2314yes—
144#14581725C2314yes—
145#14581724C2314yes—
146#14581724C2314yes—
147#14581723C2314yes—
148#14581723C2314yes—
149Dic83⋊C8C2314yes—
150#14581716C2314yes—
151#14581716C2314yes—
152#14581713C2314yes—
153#14581713C2314yes—
154C22⋊(C83⋊C8)C2314yes—
155(C2×D83)⋊C8C2314yes—
156#14581702C2314yes—
157C22×Q8×C83C2311yescharacteristic
158C22×D4×C83—21no—
159C22×D4×C83C2311yescharacteristic
160C23×C4×C83C2311yescharacteristic
161C2×SD16×C83—24no—
162C2×SD16×C83C2314yes—
163C22×C8×C83—24no—
164C22×C8×C83C2314yes—
165C22×C8×C83C2311yescharacteristic
166C22×C8×C83C2311yescharacteristic
167C22⋊Q8×C83—22no—
168C22⋊Q8×C83C2314yes—
169#121×C83—22no—
170#121×C83C2314yes—
171C2×C4⋊C4×C83—21no—
172C2×C4⋊C4×C83C2311yescharacteristic
173C2×C4⋊C4×C83C2311yescharacteristic
174C2×C22⋊C4×C83—21no—
175C2×C22⋊C4×C83—21no—
176#106×C83C2314yes—
177#103×C83C2314yes—
178#102×C83C2314yes—
179C23×D83C2×D411yescharacteristic
180C2×Dic166—24no—
181C2×Dic166—44no—
182C2×C22⋊D83—24no—
183C2×C22⋊D83—42no—
184C2×C22⋊D83—44no—
185C2×C22⋊D83C2×D414yes—
186C22×Dic83—21no—
187C22×Dic83—21no—
188C22×Dic83—21no—
189C22×Dic83—21no—
190C22×Dic83—24no—
191C22×Dic83—82no—
192C22×Dic83C2×D411yescharacteristic
193C22×Dic83C2×D411yescharacteristic
194C22×Dic83C2×D411yescharacteristic
195C2×C4×D83—22no—
196C2×C4×D83—22no—
197C2×C4×D83—24no—
198C2×C4×D83—82no—
199C2×C4×D83C2×D412yes—
200C2×C4×D83C2412yes—
201#13050573—28no—
202C2×C83⋊C8—22no—
203C2×C83⋊C8—22no—
204C2×C83⋊C8C2412yes—
205C2×C83⋊C8C2412yes—
206C4⋊Dic83—21no—
207C4⋊Dic83—21no—
208C4⋊Dic83—21no—
209C4⋊Dic83—21no—
210C4⋊Dic83—24no—
211C4⋊Dic83—24no—
212C4⋊Dic83C2412yes—
213C4⋊Dic83C2412yes—
214C4⋊Dic83C2412yes—
215C4⋊Dic83C2412yes—
216Dic83⋊C4—24no—
217Dic83⋊C4—24no—
218Dic83⋊C4—24no—
219Dic83⋊C4—24no—
220Dic83⋊C4C2×D414yes—
221C22⋊Dic83—24no—
222C22⋊Dic83—24no—
223C22⋊Dic83—24no—
224C22⋊Dic83—24no—
225C22⋊Dic83C2×D414yes—
226(C2×D83)⋊C4—24no—
227(C2×D83)⋊C4—24no—
228(C2×D83)⋊C4C2×D414yes—
229C4×Dic83—24no—
230C4×Dic83—24no—
231C4×Dic83—24no—
232C4×Dic83—24no—
233C4×Dic83C2×D412yes—
234C4×Dic83C2412yes—
235C24×C83—21no—
236C24×C83C2×D411yescharacteristic
237C2×Q8×C83—21no—
238C2×Q8×C83—22no—
239C2×Q8×C83—22no—
240C2×Q8×C83C2412yes—
241C2×D4×C83—24no—
242C2×D4×C83—21no—
243C2×D4×C83—22no—
244C2×D4×C83—22no—
245C2×D4×C83—82no—
246C2×D4×C83C2412yes—
247C22×C4×C83—22no—
248C22×C4×C83—22no—
249C22×C4×C83—21no—
250C22×C4×C83—21no—
251C22×C4×C83—21no—
252C22×C4×C83C2×D411yescharacteristic
253C22×C4×C83C2×D412yes—
254C22×C4×C83C2412yes—
255C22×C4×C83C2411yescharacteristic
256SD16×C83—28no—
257C2×C8×C83—22no—
258C2×C8×C83—28no—
259C2×C8×C83#4114yes—
260C2×C8×C83C2412yes—
261C2×C8×C83C2412yes—
262C4⋊C4×C83—21no—
263C4⋊C4×C83—24no—
264C4⋊C4×C83—21no—
265C4⋊C4×C83C2412yes—
266C4⋊C4×C83C2412yes—
267C22⋊C4×C83—24no—
268C22⋊C4×C83—24no—
269C23×C83—22no—
270C23×C83—22no—
271C23×C83—22no—
272C23×C83—22no—
273C23×C83—42no—
274C23×C83—42no—
275C23×C83—42no—
276C23×C83C22×D412yes—
277C23×C83C22×D411yescharacteristic
278C22×D83—22no—
279C22×D83—22no—
280C22×D83—22no—
281C22×D83C22×D412yes—
282Q8×C83—22no—
283Q8×C83—22no—
284Q8×C83—42no—
285D4×C83—22no—
286D4×C83—22no—
287D4×C83—42no—
288D4×C83—84no—
289C2×C4×C83—22no—
290C2×C4×C83—24no—
291C2×C4×C83—22no—
292C2×C4×C83—22no—
293C2×C4×C83—22no—
294C2×C4×C83—22no—
295C2×C4×C83—22no—
296C2×C4×C83—42no—
297C2×C4×C83—42no—
298C2×C4×C83—42no—
299C2×C4×C83C22×D412yes—
300C2×C4×C83C22×D411yescharacteristic
301C2×C4×C83C2×#4112yes—
302C2×C4×C832−1+412yes—
303C2×C4×C83C2511yescharacteristic
304C22⋊D83—44no—
305C22⋊D83—48no—
306C2×Dic83—22no—
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×Dic83—42no—
317C2×Dic83—84no—
318C2×Dic83C22×D412yes—
319C2×Dic83C22×D412yes—
320C2×Dic83C22×D412yes—
321C4×D83—24no—
322C4×D83—22no—
323C4×D83—22no—
324C4×D83—84no—
325Dic166—48no—
326C8×C83—22no—
327C8×C83C2×#4114yes—
328C83⋊C8—22no—
329C83⋊C8—22no—
330C22×C83—22no—
331C22×C83—22no—
332C22×C83—22no—
333C22×C83—44no—
334C22×C83—42no—
335C22×C83—42no—
336C22×C83—42no—
337C22×C83—84no—
338C22×C83#54712yes—
339C22×C83#57512yes—
340C22×C83#57712yes—
341C22×C83C23×D411yescharacteristic
342C2×D83—22no—
343C2×D83—22no—
344C2×D83—22no—
345C2×D83—44no—
346C4×C83—22no—
347C4×C83—42no—
348C4×C83—42no—
349C4×C83—42no—
350C4×C83#54712yes—
351C4×C83C22×#4111yescharacteristic
352C4×C83C2×2−1+411yescharacteristic
353Dic83—22no—
354Dic83—22no—
355Dic83—22no—
356Dic83—42no—
357Dic83—42no—
358Dic83—42no—
359Dic83—42no—
360C2×#3350—831nomaximal, Sylow
361C2×C83—42no—
362C2×C83—82no—
363C2×C83#335014yescomplemented
364C2×C83C2×#54711yescharacteristic
365C2×C83C2×#57511yescharacteristic
366C2×C83C2×#57711yescharacteristic
367D83—42no—
368C2×#556—831no—
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×#465D8311yescharacteristic, complemented
380C2×#440—831no—
381C2×#435—831no—
382C2×#428—831no—
383C2×#427—831no—
384C83C2×#335011yescharacteristic, complemented, Sylow
385C22×SD16C2×D8311yescharacteristic
386C22×M16—831no—
387C23×C8C2×D8311yescharacteristic
388#556—838no—
389#556—1664no—
390#553—838no—
391#553—1664no—
392C2×C4⋊Q8—831no—
393C2×#126—1661no—
394C2×#126—1661no—
395C2×#126—1661no—
396C2×#125—831no—
397C2×#124—1661no—
398C2×#123—1661no—
399C2×C22⋊Q8—831no—
400C2×C22⋊Q8C2×D8311yescharacteristic
401C2×#121—831no—
402C2×#121—1661no—
403C2×#121C2×D8311yescharacteristic
404C2×C4×Q8—831no—
405C2×C4×Q8—1661no—
406C2×C4×D4—831no—
407C2×C4×D4—831no—
408C2×C4×D4—1661no—
409C2×#117—831no—
410C2×#117—831no—
411C2×#117—831no—
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#465C2×D8318yescomplemented
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×#106C2×D8311yescharacteristic
435C2×C4⋊C8—831no—
436C2×#103—831no—
437C2×#103—831no—
438C2×#103C2×D8311yescharacteristic
439C2×#102—831no—
440C2×#102—831no—
441C2×#102C2×D8311yescharacteristic
442C2×C22⋊C8—831no—
443C2×C22⋊C8—831no—
444C2×#97—831no—
445C22×Q8—1661no—
446C22×Q8C22×D8311yescharacteristic
447C22×D4—21no—
448C22×D4—831no—
449C22×D4—1661no—
450C22×D4C22×D8311yescharacteristic
451C23×C4—831no—
452C23×C4—1661no—
453C23×C4—1661no—
454C23×C4C22×D8311yescharacteristic
455C2×SD16—24no—
456C2×SD16C22×D8314yes—
457C2×M16—834no—
458C2×M16—1664no—
459C22×C8—24no—
460C22×C8—831no—
461C22×C8—831no—
462C22×C8C22×D8311yescharacteristic
463C22×C8C22×D8314yes—
464C22×C8C22×D8311yescharacteristic
465C4⋊Q8—834no—
466C4⋊Q8—1662no—
467#126—1668no—
468#126—1668no—
469#126—1668no—
470#125—834no—
471#125—1662no—
472#124—1668no—
473#123—1668no—
474C22⋊Q8—22no—
475C22⋊Q8—834no—
476C22⋊Q8—1662no—
477C22⋊Q8C22×D8314yes—
478#121—22no—
479#121—834no—
480#121—1662no—
481#121—1668no—
482#121C22×D8314yes—
483C4×Q8—834no—
484C4×Q8—1662no—
485C4×Q8—1668no—
486C4×D4—834no—
487C4×D4—834no—
488C4×D4—834no—
489C4×D4—1662no—
490C4×D4—1668no—
491#117—834no—
492#117—834no—
493#117—834no—
494#117—1662no—
495#117—1662no—
496#117—1662no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—831no—
499C2×C4⋊C4—831no—
500C2×C4⋊C4—831no—
501C2×C4⋊C4—831no—
502C2×C4⋊C4—831no—
503C2×C4⋊C4—834no—
504C2×C4⋊C4—1662no—
505C2×C4⋊C4—1661no—
506C2×C4⋊C4—1661no—
507C2×C4⋊C4—1661no—
508C2×C4⋊C4—1661no—
509C2×C4⋊C4—1661no—
510C2×C4⋊C4—1661no—
511C2×C4⋊C4C22×D8311yescharacteristic
512C2×C4⋊C4C22×D8311yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—831no—
516C2×C22⋊C4—831no—
517C2×C22⋊C4—1661no—
518C2×C22⋊C4—1661no—
519C2×C22⋊C4—1661no—
520C2×C22⋊C4—1661no—
521C2×C22⋊C4—1661no—
522C2×C22⋊C4—1661no—
523C2×C42—831no—
524C2×C42—1661no—
525C2×C42—1661no—
526C2×C42—1661no—
527C2×C42—1661no—
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#106C22×D8314yes—
537C4⋊C8—834no—
538#103—834no—
539#103—834no—
540#103C22×D8314yes—
541#102—834no—
542#102—834no—
543#102C22×D8314yes—
544C22⋊C8—834no—
545C22⋊C8—834no—
546#97—834no—
547C24—21no—
548C24—831no—
549C24D4×D8311yescharacteristic
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—3324no—
554C2×Q8—1664no—
555C2×Q8C23×D8312yes—
556C2×D4—24no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—82no—
561C2×D4—3324no—
562C2×D4—3322no—
563C2×D4—834no—
564C2×D4—1664no—
565C2×D4C23×D8312yes—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—831no—
572C22×C4—831no—
573C22×C4—831no—
574C22×C4—832no—
575C22×C4—832no—
576C22×C4—6642no—
577C22×C4—6642no—
578C22×C4—1664no—
579C22×C4—1661no—
580C22×C4—1661no—
581C22×C4—1661no—
582C22×C4—1661no—
583C22×C4—1664no—
584C22×C4—1662no—
585C22×C4—1662no—
586C22×C4D4×D8312yes—
587C22×C4D4×D8311yescharacteristic
588C22×C4C23×D8312yes—
589C22×C4C23×D8311yescharacteristic
590SD16—28no—
591M16—1668no—
592C2×C8—22no—
593C2×C8—28no—
594C2×C8—832no—
595C2×C8—832no—
596C2×C8—1662no—
597C2×C8—1662no—
598C2×C8#1305058914yes—
599C2×C8C23×D8312yes—
600C2×C8C23×D8312yes—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—834no—
605C4⋊C4—832no—
606C4⋊C4—832no—
607C4⋊C4—832no—
608C4⋊C4—832no—
609C4⋊C4—1664no—
610C4⋊C4—1664no—
611C4⋊C4—1664no—
612C4⋊C4—1664no—
613C4⋊C4—1664no—
614C4⋊C4—1664no—
615C4⋊C4—1661no—
616C4⋊C4—1661no—
617C4⋊C4—1661no—
618C4⋊C4—1661no—
619C4⋊C4C23×D8312yes—
620C4⋊C4C23×D8312yes—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—834no—
624C22⋊C4—834no—
625C22⋊C4—1664no—
626C22⋊C4—1664no—
627C22⋊C4—1664no—
628C22⋊C4—1664no—
629C22⋊C4—1664no—
630C22⋊C4—1664no—
631C42—832no—
632C42—832no—
633C42—1664no—
634C42—1664no—
635C42—1664no—
636C42—1664no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—832no—
645C23—1662no—
646C23—1662no—
647C23—1662no—
648C23C2×D4×D8312yes—
649C23C2×D4×D8311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—3328no—
654D4—22no—
655D4—22no—
656D4—42no—
657D4—84no—
658D4—3328no—
659D4—3324no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—3322no—
671C2×C4—3322no—
672C2×C4—3322no—
673C2×C4—3322no—
674C2×C4—832no—
675C2×C4—832no—
676C2×C4—832no—
677C2×C4—6644no—
678C2×C4—6644no—
679C2×C4—1662no—
680C2×C4—1662no—
681C2×C4—1662no—
682C2×C4—1662no—
683C2×C4—1662no—
684C2×C4—1662no—
685C2×C4—1662no—
686C2×C4—1664no—
687C2×C4—1662no—
688C2×C4—1662no—
689C2×C4C2×D4×D8312yes—
690C2×C4C2×D4×D8311yescharacteristic
691C2×C4C2×#1305058912yes—
692C2×C4#1458183912yes—
693C2×C4C24×D8311yescharacteristic
694C8—22no—
695C8—1662no—
696C8—1662no—
697C8C2×#1305058914yes—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—44no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—84no—
706C22—3324no—
707C22—1662no—
708C22—1662no—
709C22—1662no—
710C22#1912835112yes—
711C22#1912849812yes—
712C22#1912850712yes—
713C22C22×D4×D8311yescharacteristic
714C4—22no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—3322no—
719C4—3322no—
720C4—3322no—
721C4—3322no—
722C4—1662no—
723C4—1662no—
724C4—1662no—
725C4#1912835112yes—
726C4C22×#1305058911yescharacteristic
727C4C2×#1458183911yescharacteristic
728C2—42no—
729C2—82no—
730C2—3322no—
731C2#2492001414yesdirect product factor
732C2C2×#1912835111yescharacteristic
733C2C2×#1912849811yescharacteristic
734C2C2×#1912850711yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#465×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128398C2
hypercenterC2×#465D83
hypocenterC83C2×#3350
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#19128422C2semidirect
3. #24920014C2direct (N × H)
4. C2×#19128108C2semidirect
5. C2×#19128039C2semidirect
6. C2×#19128024C2semidirect
7. C2×#19128022C2semidirect
8. C2×#19128030C2semidirect
9. C2×#19128006C2semidirect
10. C2×#19127989C2semidirect
11. C2×#19127944C2semidirect
12. C2×#19127802C2semidirect
13. C2×#19127772C2semidirect
14. C2×#19127740C2semidirect
15. C2×#19127739C2semidirect
16. C2×#465×C83C2semidirect
19. #19128422C22semidirect
41. #19128108C22semidirect
42. #19128039C22semidirect
43. #19128030C22semidirect
44. #19128024C22semidirect
45. #19128022C22semidirect
46. #19128006C22semidirect
47. #19127989C22semidirect
48. #19127944C22semidirect
49. #19127802C22semidirect
50. #19127772C22semidirect
51. #19127740C22semidirect
52. #19127739C22semidirect
73. #465×C83C22semidirect
363. C2×C83#3350semidirect
379. C2×#465D83semidirect
384. C83C2×#3350semidirect
421. #465C2×D83semidirect
731. C2#24920014direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284222
C2×#191283982
#249200142
C2×#191281082
C2×#191280392
C2×#191280242
C2×#191280222
C2×#191280302
C2×#191280062
C2×#191279892
C2×#191279442
C2×#191278022
C2×#191277722
C2×#191277402
C2×#191277392
C2×#465×C832
C2×#335083