Finite Group Databasebeta

← C2×#24919905 #36282937

Subgroups — C2×#24919905 #36282937

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×#19128391C211yesmaximal, characteristic, complemented
2C2×#19128355C211yesmaximal, characteristic
3#24919905C2116yesmaximal, direct product factor
4C2×#19128110C211yesmaximal, characteristic, complemented
5C2×#19128037C211yesmaximal, characteristic, complemented
6C2×#19128026C211yesmaximal, characteristic, complemented
7C2×#19128032C211yesmaximal, characteristic, complemented
8C2×#19128015C211yesmaximal, characteristic, complemented
9C2×#19127997C211yesmaximal, characteristic, complemented
10C2×#19128002C211yesmaximal, characteristic, complemented
11C2×#19127947C211yesmaximal, characteristic, complemented
12C2×#19127930C211yesmaximal, characteristic, complemented
13C2×#19127803C211yesmaximal, characteristic, complemented
14C2×#19127743C211yesmaximal, characteristic, complemented
15C22×#14581726C211yesmaximal, characteristic, complemented
16C2×#435×C83C211yesmaximal, characteristic, complemented
17C22×#13050589—21no—
18C22×#13050579C2211yescharacteristic
19#19128391—24no—
20#19128391C2218yescomplemented
21#19128355—24no—
22#19128355C2218yes—
23C2×#14581792C2211yescharacteristic
24C2×#14581785—21no—
25C2×#14581784C2211yescharacteristic
26C2×#14581782—21no—
27C2×#14581776—21no—
28C2×#14581776—21no—
29C2×#14581773—21no—
30C2×#14581772—21no—
31C2×#14581771C2211yescharacteristic
32C2×#14581771C2211yescharacteristic
33C2×#14581766C2211yescharacteristic
34C2×#14581766C2211yescharacteristic
35C2×C4×Dic166C2211yescharacteristic
36C2×C4×D332C2211yescharacteristic
37C2×#14581751C2211yescharacteristic
38C2×#14581748—21no—
39C22×C4⋊Dic83C2211yescharacteristic
40C22×C4⋊Dic83C2211yescharacteristic
41C22×C4⋊Dic83C2211yescharacteristic
42#19128110C2218yescomplemented
43#19128037C2218yescomplemented
44#19128032C2218yescomplemented
45#19128026C2218yescomplemented
46#19128015C2218yescomplemented
47#19128002C2218yescomplemented
48#19127997C2218yescomplemented
49#19127947C2218yescomplemented
50#19127930C2218yescomplemented
51#19127803C2218yescomplemented
52#19127743C2218yescomplemented
53C2×#14581726C2211yescharacteristic
54C2×#14581726C2211yescharacteristic
55C2×#14581726C2211yescharacteristic
56C2×#14581726C2211yescharacteristic
57C2×#14581726C2211yescharacteristic
58C2×#14581726C2211yescharacteristic
59C2×#14581726C2218yescomplemented
60C2×#14581724C2211yescharacteristic
61C2×#14581724C2211yescharacteristic
62C2×#14581724C2211yescharacteristic
63C2×#14581717C2211yescharacteristic
64C2×#14581717C2211yescharacteristic
65C2×#14581717C2211yescharacteristic
66C2×#14581714C2211yescharacteristic
67C2×#14581714C2211yescharacteristic
68C2×#14581714C2211yescharacteristic
69C22×M16×C83C2211yescharacteristic
70C23×C8×C83C2211yescharacteristic
71C2×C4×D4×C83C2211yescharacteristic
72#435×C83C2218yescomplemented
73C2×C4⋊C8×C83C2211yescharacteristic
74C2×C22⋊C8×C83C2211yescharacteristic
75C2×C22⋊C8×C83C2211yescharacteristic
76C2×#97×C83C2211yescharacteristic
77C2×#13050589—28no—
78C2×#13050589—48no—
79C22×Dic166—21no—
80C22×Dic166C2311yescharacteristic
81C22×D332C2311yescharacteristic
82C22×C22⋊D83—21no—
83C22×C22⋊D83—21no—
84C23×Dic83—21no—
85C23×Dic83—21no—
86C23×Dic83—21no—
87C22×C4×D83—21no—
88C2×#13050579—24no—
89C2×#13050579C2314yes—
90#14581792—22no—
91#14581792C2314yes—
92#14581785—28no—
93#14581784—22no—
94#14581784C2314yes—
95#14581782—28no—
96#14581776—28no—
97#14581776—28no—
98#14581773—28no—
99#14581772—28no—
100#14581771—22no—
101#14581771—22no—
102#14581771C2314yes—
103#14581771C2314yes—
104#14581766—22no—
105#14581766—22no—
106#14581766C2314yes—
107#14581766C2314yes—
108C4×Dic166—22no—
109C4×Dic166C2314yes—
110C4×D332—22no—
111C4×D332C2314yes—
112#14581751—22no—
113#14581751C2314yes—
114#14581748—28no—
115C2×C4⋊Dic83—22no—
116C2×C4⋊Dic83—22no—
117C2×C4⋊Dic83—22no—
118C2×C4⋊Dic83—21no—
119C2×C4⋊Dic83—21no—
120C2×C4⋊Dic83—21no—
121C2×C4⋊Dic83—21no—
122C2×C4⋊Dic83C2314yes—
123C2×C4⋊Dic83C2314yes—
124C2×C4⋊Dic83C2314yes—
125C2×C4⋊Dic83C2311yescharacteristic
126C2×C4⋊Dic83C2311yescharacteristic
127C2×C4⋊Dic83C2311yescharacteristic
128C2×C4⋊Dic83C2311yescharacteristic
129C2×C4⋊Dic83C2311yescharacteristic
130C2×C4⋊Dic83C2311yescharacteristic
131C2×Dic83⋊C4—21no—
132C2×Dic83⋊C4—21no—
133C2×Dic83⋊C4—21no—
134C2×Dic83⋊C4—21no—
135C2×Dic83⋊C4—21no—
136C2×C22⋊Dic83—21no—
137C2×C22⋊Dic83—21no—
138C2×C22⋊Dic83—21no—
139C2×(C2×D83)⋊C4—21no—
140C2×(C2×D83)⋊C4—21no—
141C2×(C2×D83)⋊C4—21no—
142C2×C4×Dic83—21no—
143C2×C4×Dic83—21no—
144#14581726C2314yes—
145#14581726C2314yes—
146#14581726C2314yes—
147#14581726C2314yes—
148#14581726C2314yes—
149#14581726C2314yes—
150#14581724C2314yes—
151#14581724C2314yes—
152#14581724C2314yes—
153#14581717C2314yes—
154#14581717C2314yes—
155#14581717C2314yes—
156#14581714C2314yes—
157#14581714C2314yes—
158#14581714C2314yes—
159C22×D4×C83D411yescharacteristic
160C23×C4×C83C2311yescharacteristic
161C23×C4×C83C2311yescharacteristic
162C2×M16×C83—24no—
163C2×M16×C83C2314yes—
164C22×C8×C83—24no—
165C22×C8×C83C2314yes—
166C22×C8×C83C2311yescharacteristic
167C22×C8×C83C2311yescharacteristic
168C22×C8×C83C2311yescharacteristic
169C22×C8×C83C2311yescharacteristic
170C4×D4×C83D414yes—
171C4×D4×C83C2314yes—
172C2×C4⋊C4×C83D411yescharacteristic
173C2×C22⋊C4×C83D411yescharacteristic
174C2×C22⋊C4×C83D411yescharacteristic
175C2×C42×C83C2311yescharacteristic
176C4⋊C8×C83C2314yes—
177C22⋊C8×C83C2314yes—
178C22⋊C8×C83C2314yes—
179#97×C83C2314yes—
180C23×D83—21no—
181#13050589—432no—
182C2×Dic166—22no—
183C2×Dic166—22no—
184C2×Dic166—21no—
185C2×Dic166—24no—
186C2×Dic166—44no—
187C2×Dic166C2412yes—
188C2×D332—22no—
189C2×D332—22no—
190C2×D332—21no—
191C2×D332C2412yes—
192C2×C22⋊D83—24no—
193C2×C22⋊D83—24no—
194C2×C22⋊D83—44no—
195C2×C22⋊D83—44no—
196C22×Dic83—24no—
197C22×Dic83—24no—
198C22×Dic83—24no—
199C22×Dic83—21no—
200C22×Dic83—21no—
201C22×Dic83—21no—
202C22×Dic83—21no—
203C22×Dic83—21no—
204C22×Dic83—21no—
205C22×Dic83—21no—
206C22×Dic83—44no—
207C22×Dic83—44no—
208C22×Dic83—44no—
209C2×C4×D83—24no—
210C2×C4×D83—44no—
211#13050579—28no—
212C4⋊Dic83—21no—
213C4⋊Dic83—21no—
214C4⋊Dic83—21no—
215C4⋊Dic83—21no—
216C4⋊Dic83—24no—
217C4⋊Dic83—24no—
218C4⋊Dic83—24no—
219C4⋊Dic83—24no—
220C4⋊Dic83—21no—
221C4⋊Dic83—21no—
222C4⋊Dic83C2412yes—
223C4⋊Dic83C2412yes—
224C4⋊Dic83C2412yes—
225C4⋊Dic83C2412yes—
226C4⋊Dic83C2412yes—
227C4⋊Dic83C2412yes—
228Dic83⋊C4—24no—
229Dic83⋊C4—24no—
230Dic83⋊C4—24no—
231Dic83⋊C4—24no—
232Dic83⋊C4—24no—
233C22⋊Dic83—24no—
234C22⋊Dic83—24no—
235C22⋊Dic83—24no—
236(C2×D83)⋊C4—24no—
237(C2×D83)⋊C4—24no—
238(C2×D83)⋊C4—24no—
239C4×Dic83—24no—
240C4×Dic83—24no—
241C24×C83C2×D411yescharacteristic
242C24×C83C2×D411yescharacteristic
243C2×D4×C83—24no—
244C2×D4×C83C2×D414yes—
245C22×C4×C83—22no—
246C22×C4×C83—22no—
247C22×C4×C83—22no—
248C22×C4×C83—22no—
249C22×C4×C83C2×D412yes—
250C22×C4×C83C2×D412yes—
251C22×C4×C83C2×D411yescharacteristic
252C22×C4×C83C2×D411yescharacteristic
253C22×C4×C83C2×D411yescharacteristic
254C22×C4×C83C2×D411yescharacteristic
255C22×C4×C83C2412yes—
256C22×C4×C83C2412yes—
257C22×C4×C83C2411yescharacteristic
258M16×C83—28no—
259C2×C8×C83—22no—
260C2×C8×C83—22no—
261C2×C8×C83—22no—
262C2×C8×C83—28no—
263C2×C8×C83#4114yescomplemented
264C2×C8×C83C2412yes—
265C2×C8×C83C2412yes—
266C2×C8×C83C2412yes—
267C2×C8×C83C2412yes—
268C4⋊C4×C83C2×D414yes—
269C22⋊C4×C83C2×D414yes—
270C22⋊C4×C83C2×D414yes—
271C42×C83C2×D412yes—
272C42×C83C2412yes—
273C23×C83—22no—
274C23×C83—22no—
275C23×C83—22no—
276C23×C83—22no—
277C23×C83—22no—
278C23×C83AGL(1,ℤ/8)14yes—
279C23×C83C22×D412yes—
280C23×C83C22×D412yes—
281C23×C83C22×D411yescharacteristic
282C22×D83—22no—
283C22×D83—42no—
284C22×D83—42no—
285C22×D83—42no—
286D4×C83—28no—
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×C83C22×D412yes—
298C2×C4×C83C22×D412yes—
299C2×C4×C83C22×D412yes—
300C2×C4×C83C22×D412yes—
301C2×C4×C83C22×D411yescharacteristic
302C2×C4×C83C2×#4112yes—
303C2×C4×C832−1+412yes—
304C2×C4×C83C2511yescharacteristic
305C22⋊D83—48no—
306C22⋊D83—48no—
307C2×Dic83—22no—
308C2×Dic83—22no—
309C2×Dic83—22no—
310C2×Dic83—22no—
311C2×Dic83—22no—
312C2×Dic83—22no—
313C2×Dic83—22no—
314C2×Dic83—48no—
315C2×Dic83—42no—
316C2×Dic83—42no—
317C2×Dic83—48no—
318C2×Dic83—42no—
319C2×Dic83—42no—
320C2×Dic83—42no—
321C2×Dic83—42no—
322C2×Dic83—48no—
323C2×Dic83—42no—
324D332—22no—
325D332—22no—
326D332—42no—
327C4×D83—48no—
328Dic166—22no—
329Dic166—22no—
330Dic166—48no—
331Dic166—42no—
332C8×C83—22no—
333C8×C83—22no—
334C8×C83—22no—
335C8×C83C2×#4114yescomplemented
336C22×C83—28no—
337C22×C83—22no—
338C22×C83—22no—
339C22×C83—22no—
340C22×C83—22no—
341C22×C83—22no—
342C22×C83—44no—
343C22×C83#54712yes—
344C22×C83C2×AGL(1,ℤ/8)14yes—
345C22×C83C2×AGL(1,ℤ/8)12yes—
346C22×C83#57812yes—
347C22×C83C23×D411yescharacteristic
348C2×D83—42no—
349C2×D83—42no—
350C2×D83—42no—
351C2×D83—84no—
352C4×C83—22no—
353C4×C83—22no—
354C4×C83—22no—
355C4×C83—22no—
356C4×C83#54712yes—
357C4×C83C22×#4111yescharacteristic
358C4×C83C2×2−1+411yescharacteristic
359Dic83—42no—
360Dic83—42no—
361Dic83—42no—
362Dic83—42no—
363Dic83—42no—
364Dic83—42no—
365Dic83—42no—
366C2×#3343—831nomaximal, Sylow
367C2×C83—24no—
368C2×C83—42no—
369C2×C83#334314yescomplemented
370C2×C83C2×#54711yescharacteristic
371C2×C83C22×AGL(1,ℤ/8)11yescharacteristic
372C2×C83C2×#57811yescharacteristic
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×#435D8311yescharacteristic, complemented
388C2×#428—831no—
389C22×#107—831no—
390C83C2×#334311yescharacteristic, complemented, Sylow
391C22×#41—1661no—
392C22×SD16—831no—
393C22×M16C2×D8311yescharacteristic
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×D4C2×D8311yescharacteristic
414C2×#117—831no—
415C2×#117—1661no—
416C22×C4⋊C4—831no—
417C22×C4⋊C4—831no—
418C22×C4⋊C4—831no—
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#435C2×D8318yescomplemented
430#428—838no—
431C2×#107—831no—
432C2×#107—831no—
433C2×#107—831no—
434C2×#107—831no—
435C2×#107—838no—
436C2×#107—831no—
437C2×#107—831no—
438C2×#106—831no—
439C2×#106—831no—
440C2×#106—831no—
441C2×C4⋊C8C2×D8311yescharacteristic
442C2×#103—831no—
443C2×#103—831no—
444C2×#103—831no—
445C2×#102—831no—
446C2×#102—831no—
447C2×#102—831no—
448C2×C22⋊C8C2×D8311yescharacteristic
449C2×C22⋊C8C2×D8311yescharacteristic
450C2×#97C2×D8311yescharacteristic
451C2×#41—3328no—
452C2×#41—1668no—
453C22×Q8—831no—
454C22×Q8—1661no—
455C22×D4—831no—
456C22×D4—1661no—
457C22×D4—1661no—
458C22×D4D33211yescharacteristic
459C23×C4—1661no—
460C23×C4—1661no—
461C23×C4—1661no—
462C23×C4—1661no—
463C23×C4C22×D8311yescharacteristic
464C23×C4C22×D8311yescharacteristic
465C2×SD16—834no—
466C2×SD16—1664no—
467C2×M16—24no—
468C2×M16C22×D8314yes—
469C22×C8—24no—
470C22×C8C22×D8311yescharacteristic
471C22×C8C22×D8314yes—
472C22×C8C22×D8311yescharacteristic
473C22×C8C22×D8311yescharacteristic
474C22×C8C22×D8311yescharacteristic
475C4⋊Q8—834no—
476C4⋊Q8—1662no—
477#126—1668no—
478#125—834no—
479#125—1668no—
480#125—1662no—
481#123—1668no—
482#123—1668no—
483#123—1668no—
484C22⋊Q8—834no—
485C22⋊Q8—834no—
486C22⋊Q8—1662no—
487C22⋊Q8—1662no—
488C22⋊Q8—1668no—
489#121—834no—
490#121—834no—
491#121—1662no—
492#121—1662no—
493C4×Q8—834no—
494C4×Q8—1662no—
495C4×D4—834no—
496C4×D4—1662no—
497C4×D4D33214yes—
498C4×D4C22×D8314yes—
499#117—834no—
500#117—1662no—
501#117—1668no—
502C2×C4⋊C4—831no—
503C2×C4⋊C4—831no—
504C2×C4⋊C4—831no—
505C2×C4⋊C4—831no—
506C2×C4⋊C4—831no—
507C2×C4⋊C4—834no—
508C2×C4⋊C4—834no—
509C2×C4⋊C4—834no—
510C2×C4⋊C4—831no—
511C2×C4⋊C4—1661no—
512C2×C4⋊C4—1661no—
513C2×C4⋊C4—1661no—
514C2×C4⋊C4—1662no—
515C2×C4⋊C4—1662no—
516C2×C4⋊C4—1662no—
517C2×C4⋊C4—1661no—
518C2×C4⋊C4—1661no—
519C2×C4⋊C4—1661no—
520C2×C4⋊C4—1661no—
521C2×C4⋊C4—1661no—
522C2×C4⋊C4—1661no—
523C2×C4⋊C4D33211yescharacteristic
524C2×C22⋊C4—1661no—
525C2×C22⋊C4—1661no—
526C2×C22⋊C4—1661no—
527C2×C22⋊C4—1661no—
528C2×C22⋊C4—1661no—
529C2×C22⋊C4—1661no—
530C2×C22⋊C4D33211yescharacteristic
531C2×C22⋊C4D33211yescharacteristic
532C2×C42—1661no—
533C2×C42—1661no—
534C2×C42C22×D8311yescharacteristic
535#107—834no—
536#107—834no—
537#107—834no—
538#107—834no—
539#107—834no—
540#107—834no—
541#106—834no—
542#106—834no—
543#106—834no—
544C4⋊C8C22×D8314yes—
545#103—834no—
546#103—834no—
547#103—834no—
548#102—834no—
549#102—834no—
550#102—834no—
551C22⋊C8C22×D8314yes—
552C22⋊C8C22×D8314yes—
553#97C22×D8314yes—
554C24—1661no—
555C24C2×D33211yescharacteristic
556C24C2×D33211yescharacteristic
557#41—33232no—
558C2×Q8—3324no—
559C2×Q8—832no—
560C2×Q8—1662no—
561C2×Q8—1662no—
562C2×Q8—1661no—
563C2×Q8—1664no—
564C2×D4—24no—
565C2×D4—3324no—
566C2×D4—3324no—
567C2×D4—832no—
568C2×D4—1664no—
569C2×D4—1664no—
570C2×D4—1661no—
571C2×D4—1662no—
572C2×D4—1662no—
573C2×D4C2×D33214yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—3324no—
579C22×C4—3324no—
580C22×C4—3324no—
581C22×C4—3324no—
582C22×C4—1664no—
583C22×C4—1664no—
584C22×C4—1664no—
585C22×C4—1661no—
586C22×C4—1661no—
587C22×C4—1661no—
588C22×C4—1661no—
589C22×C4—1661no—
590C22×C4—1661no—
591C22×C4—1661no—
592C22×C4—1664no—
593C22×C4C2×D33212yes—
594C22×C4C2×D33212yes—
595C22×C4C2×D33211yescharacteristic
596C22×C4C2×D33211yescharacteristic
597C22×C4C2×D33211yescharacteristic
598C22×C4C2×D33211yescharacteristic
599C22×C4C23×D8312yes—
600C22×C4C23×D8312yes—
601C22×C4C23×D8311yescharacteristic
602SD16—1668no—
603M16—28no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—28no—
608C2×C8#1305058914yescomplemented
609C2×C8C23×D8312yes—
610C2×C8C23×D8312yes—
611C2×C8C23×D8312yes—
612C2×C8C23×D8312yes—
613C4⋊C4—832no—
614C4⋊C4—832no—
615C4⋊C4—832no—
616C4⋊C4—832no—
617C4⋊C4—832no—
618C4⋊C4—832no—
619C4⋊C4—1661no—
620C4⋊C4—1661no—
621C4⋊C4—1661no—
622C4⋊C4—1661no—
623C4⋊C4—1664no—
624C4⋊C4—1664no—
625C4⋊C4—1661no—
626C4⋊C4—1664no—
627C4⋊C4—1661no—
628C4⋊C4—1664no—
629C4⋊C4—1664no—
630C4⋊C4—1664no—
631C4⋊C4—1664no—
632C4⋊C4—1664no—
633C4⋊C4—1664no—
634C4⋊C4C2×D33214yes—
635C22⋊C4—1664no—
636C22⋊C4—1664no—
637C22⋊C4—1664no—
638C22⋊C4—1664no—
639C22⋊C4—1664no—
640C22⋊C4—1664no—
641C22⋊C4C2×D33214yes—
642C22⋊C4C2×D33214yes—
643C42—1664no—
644C42—1664no—
645C42C2×D33212yes—
646C42C23×D8312yes—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—3322no—
653C23—3322no—
654C23—3322no—
655C23—1662no—
656C23#1458182014yes—
657C23C22×D33212yes—
658C23C22×D33212yes—
659C23C22×D33211yescharacteristic
660Q8—3328no—
661Q8—3322no—
662Q8—1662no—
663Q8—1662no—
664D4—28no—
665D4—3328no—
666D4—3328no—
667D4—3322no—
668D4—1662no—
669D4—1662no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—3328no—
681C2×C4—3328no—
682C2×C4—3322no—
683C2×C4—3322no—
684C2×C4—3322no—
685C2×C4—3322no—
686C2×C4—3328no—
687C2×C4—3328no—
688C2×C4—3322no—
689C2×C4—3322no—
690C2×C4—3322no—
691C2×C4—1662no—
692C2×C4—1662no—
693C2×C4—1662no—
694C2×C4—1662no—
695C2×C4—1662no—
696C2×C4—1662no—
697C2×C4—1662no—
698C2×C4C22×D33212yes—
699C2×C4C22×D33212yes—
700C2×C4C22×D33212yes—
701C2×C4C22×D33212yes—
702C2×C4C22×D33211yescharacteristic
703C2×C4C2×#1305058912yes—
704C2×C4#1458183912yes—
705C2×C4C24×D8311yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8C2×#1305058914yescomplemented
710C22—22no—
711C22—28no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—3322no—
718C22—3322no—
719C22—3322no—
720C22—6644no—
721C22#1912835512yes—
722C22C2×#1458182014yes—
723C22C2×#1458182012yes—
724C22#1912851812yes—
725C22C23×D33211yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—3322no—
731C4—3322no—
732C4—3322no—
733C4—3322no—
734C4—3322no—
735C4—3322no—
736C4—3322no—
737C4#1912835512yes—
738C4C22×#1305058911yescharacteristic
739C4C2×#1458183911yescharacteristic
740C2—24no—
741C2—42no—
742C2—6642no—
743C2#2491990514yesdirect product factor
744C2C2×#1912835511yescharacteristic
745C2C22×#1458182011yescharacteristic
746C2C2×#1912851811yescharacteristic
subgroupG/H
centerC23C22×D332
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#435×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128355C2
hypercenterC2×#435D83
hypocenterC83C2×#3343
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
1. C2×#19128391C2semidirect
3. #24919905C2direct (N × H)
4. C2×#19128110C2semidirect
5. C2×#19128037C2semidirect
6. C2×#19128026C2semidirect
7. C2×#19128032C2semidirect
8. C2×#19128015C2semidirect
9. C2×#19127997C2semidirect
10. C2×#19128002C2semidirect
11. C2×#19127947C2semidirect
12. C2×#19127930C2semidirect
13. C2×#19127803C2semidirect
14. C2×#19127743C2semidirect
15. C22×#14581726C2semidirect
16. C2×#435×C83C2semidirect
20. #19128391C22semidirect
42. #19128110C22semidirect
43. #19128037C22semidirect
44. #19128032C22semidirect
45. #19128026C22semidirect
46. #19128015C22semidirect
47. #19128002C22semidirect
48. #19127997C22semidirect
49. #19127947C22semidirect
50. #19127930C22semidirect
51. #19127803C22semidirect
52. #19127743C22semidirect
59. C2×#14581726C22semidirect
72. #435×C83C22semidirect
263. C2×C8×C83#41semidirect
335. C8×C83C2×#41semidirect
369. C2×C83#3343semidirect
387. C2×#435D83semidirect
390. C83C2×#3343semidirect
429. #435C2×D83semidirect
608. C2×C8#13050589semidirect
709. C8C2×#13050589semidirect
743. C2#24919905direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283912
C2×#191283552
#249199052
C2×#191281102
C2×#191280372
C2×#191280262
C2×#191280322
C2×#191280152
C2×#191279972
C2×#191280022
C2×#191279472
C2×#191279302
C2×#191278032
C2×#191277432
C22×#145817262
C2×#435×C832
C2×#334383