Finite Group Databasebeta

← C2×#22626869 #34031952

Subgroups — C2×#22626869 #34031952

Order 18688.

1938 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626869C2116yesmaximal, direct product factor
2C2×#17989639C211yesmaximal, characteristic, complemented
3C2×#17989637C211yesmaximal, characteristic, complemented
4C2×#17989619C211yesmaximal, characteristic, complemented
5C2×#17989619C211yesmaximal, characteristic, complemented
6C2×#17989617C211yesmaximal, characteristic, complemented
7C2×#17989616C211yesmaximal, characteristic, complemented
8C2×#17989615C211yesmaximal, characteristic, complemented
9C2×#17989614C211yesmaximal, characteristic, complemented
10C2×#17989612C211yesmaximal, characteristic, complemented
11C2×#17989611C211yesmaximal, characteristic, complemented
12C2×#17989609C211yesmaximal, characteristic, complemented
13C2×#17989594C211yesmaximal, characteristic, complemented
14C2×#17989593C211yesmaximal, characteristic, complemented
15C2×#17989588C211yesmaximal, characteristic, complemented
16C2×#17989120C211yesmaximal, characteristic
17C22×#11924038C2211yescharacteristic
18C22×#11924037C2211yescharacteristic
19C22×#11924036C2211yescharacteristic
20C22×#11924036C2211yescharacteristic
21C22×#11924036C2211yescharacteristic
22C23×#10596833C2211yescharacteristic
23#17989639C2218yescomplemented
24#17989637C2218yescomplemented
25#17989619C2218yescomplemented
26#17989619C2218yescomplemented
27#17989617C2218yescomplemented
28#17989616C2218yescomplemented
29#17989615C2218yescomplemented
30#17989614C2218yescomplemented
31#17989612C2218yescomplemented
32#17989611C2218yescomplemented
33#17989609C2218yescomplemented
34#17989594C2218yescomplemented
35#17989593C2218yescomplemented
36C2×#14556658C2211yescharacteristic
37C2×#14556658C2211yescharacteristic
38C2×#14556658C2211yescharacteristic
39C2×#14556658C2211yescharacteristic
40#17989588C2218yescomplemented
41C2×C4⋊#10596833C2211yescharacteristic
42C2×C4⋊#10596833C2211yescharacteristic
43C2×C4⋊#10596833C2211yescharacteristic
44C2×C4⋊#10596833C2211yescharacteristic
45C2×C4⋊#10596833C2211yescharacteristic
46C2×C4⋊#10596833C2211yescharacteristic
47C2×#14556648C2211yescharacteristic
48C2×#14556648C2211yescharacteristic
49C2×#14556648C2211yescharacteristic
50C2×#14556648C2211yescharacteristic
51C2×C22⋊#10596833C2211yescharacteristic
52C2×C22⋊#10596833C2211yescharacteristic
53C2×#14556646C2211yescharacteristic
54C2×#14556646C2211yescharacteristic
55C2×#14556646C2211yescharacteristic
56C2×#14556646C2211yescharacteristic
57C2×C4×#10596833C2211yescharacteristic
58C2×C4×#10596833C2211yescharacteristic
59#17989120C418yes—
60#17989120C2218yes—
61C2×#14556585C411yescharacteristic
62C2×#14556581C411yescharacteristic
63C2×#14556577C411yescharacteristic
64C2×#14556576C411yescharacteristic
65C2×#14556573C411yescharacteristic
66C2×#14556569C411yescharacteristic
67C2×#14556564C411yescharacteristic
68C2×#14556556C2211yescharacteristic
69C2×#14556553C2211yescharacteristic
70C2×#14556551C2211yescharacteristic
71C2×#14556551C2211yescharacteristic
72C2×#14556549C2211yescharacteristic
73C2×#14556547C2211yescharacteristic
74C2×C42×D73C2211yescharacteristic
75C2×#126×C73C411yescharacteristic
76C2×#11924038—42no—
77C2×#11924038C2314yes—
78C2×#11924037—42no—
79C2×#11924037C2314yes—
80C2×#11924036—42no—
81C2×#11924036—42no—
82C2×#11924036—42no—
83C2×#11924036C2314yes—
84C2×#11924036C2314yes—
85C2×#11924036C2314yes—
86C22×#10596833—42no—
87C22×#10596833C2311yescharacteristic
88C22×#10596833C2311yescharacteristic
89C22×#10596833C2311yescharacteristic
90C22×#10596833C2311yescharacteristic
91C22×#10596833C2311yescharacteristic
92C22×#10596833C2311yescharacteristic
93C22×#10596833C2311yescharacteristic
94C22×#10596833C2311yescharacteristic
95C22×#10596833C2314yes—
96#14556658C2314yes—
97#14556658C2314yes—
98#14556658C2314yes—
99#14556658C2314yes—
100C4⋊#10596833C2314yes—
101C4⋊#10596833C2314yes—
102C4⋊#10596833C2314yes—
103C4⋊#10596833C2314yes—
104C4⋊#10596833C2314yes—
105C4⋊#10596833C2314yes—
106#14556648C2314yes—
107#14556648C2314yes—
108#14556648C2314yes—
109#14556648C2314yes—
110C22⋊#10596833C2314yes—
111C22⋊#10596833C2314yes—
112#14556646C2314yes—
113#14556646C2314yes—
114#14556646C2314yes—
115#14556646C2314yes—
116C4×#10596833C2314yes—
117C4×#10596833C2314yes—
118C22×Dic146C2×C411yescharacteristic
119C22×D292C2×C411yescharacteristic
120C22×C22⋊D73C2×C411yescharacteristic
121C22×C22⋊D73C2×C411yescharacteristic
122C23×Dic73C2311yescharacteristic
123C22×C4×D73C2×C411yescharacteristic
124C22×C4×D73C2×C411yescharacteristic
125C22×C4×D73C2311yescharacteristic
126C22×C4×D73C2311yescharacteristic
127#14556585C2×C418yes—
128#14556581C2×C418yes—
129#14556577C2×C418yes—
130#14556576C2×C418yes—
131#14556573C2×C418yes—
132#14556569C2×C418yes—
133#14556564C2×C418yes—
134#14556556C2×C414yes—
135#14556556C2314yes—
136#14556553C2×C414yes—
137#14556553C2314yes—
138#14556551C2×C414yes—
139#14556551C2×C414yes—
140#14556551C2314yes—
141#14556551C2314yes—
142#14556549C2×C414yes—
143#14556549C2314yes—
144#14556547C2×C414yes—
145#14556547C2314yes—
146C2×C4⋊Dic73C2×C411yescharacteristic
147C2×#11924007C2×C411yescharacteristic
148C2×#11924007C2×C411yescharacteristic
149C2×#11924007C2×C411yescharacteristic
150C2×#11924007C2×C411yescharacteristic
151C2×#11924007C2×C411yescharacteristic
152C2×#11924007C2×C411yescharacteristic
153C2×C22⋊Dic73C2×C411yescharacteristic
154C2×#11924005C2×C411yescharacteristic
155C2×#11924005C2×C411yescharacteristic
156C2×#11924005C2×C411yescharacteristic
157C2×#11924005C2×C411yescharacteristic
158C2×#11924005C2×C411yescharacteristic
159C2×#11924005C2×C411yescharacteristic
160C2×C4×Dic73C2×C411yescharacteristic
161C2×C4×Dic73C2311yescharacteristic
162C2×C4×Dic73C2311yescharacteristic
163C2×C4×Dic73C2311yescharacteristic
164C2×C4×Dic73C2311yescharacteristic
165C42×D73C2×C414yes—
166C42×D73C2314yes—
167#126×C73C2×C418yes—
168C2×C4⋊C4×C73C2×C411yescharacteristic
169C2×C4⋊C4×C73C2×C411yescharacteristic
170C2×C4⋊C4×C73C2×C411yescharacteristic
171C2×C22⋊C4×C73C2×C411yescharacteristic
172C2×C22⋊C4×C73C2×C411yescharacteristic
173C2×C22⋊C4×C73C2×C411yescharacteristic
174C2×C42×C73C2×C411yescharacteristic
175#11924038—44no—
176#11924037—44no—
177#11924036—44no—
178#11924036—44no—
179#11924036—44no—
180C2×#10596833—22no—
181C2×#10596833—22no—
182C2×#10596833—22no—
183C2×#10596833—22no—
184C2×#10596833—22no—
185C2×#10596833—22no—
186C2×#10596833—22no—
187C2×#10596833—22no—
188C2×#10596833—44no—
189C2×#10596833C2412yes—
190C2×#10596833C2412yes—
191C2×#10596833C2412yes—
192C2×#10596833C2412yes—
193C2×#10596833C2412yes—
194C2×#10596833C2412yes—
195C2×#10596833C2412yes—
196C2×#10596833C2412yes—
197C23×D73C22×C411yescharacteristic
198C23×D73C22×C411yescharacteristic
199C2×Dic146—42no—
200C2×Dic146C22×C414yes—
201C2×D292—24no—
202C2×D292C22×C414yes—
203C2×C22⋊D73—24no—
204C2×C22⋊D73—42no—
205C2×C22⋊D73C22×C414yes—
206C2×C22⋊D73C22×C414yes—
207C22×Dic73—22no—
208C22×Dic73—22no—
209C22×Dic73C22×C411yescharacteristic
210C22×Dic73C22×C411yescharacteristic
211C22×Dic73C22×C411yescharacteristic
212C22×Dic73C22×C411yescharacteristic
213C22×Dic73C22×C411yescharacteristic
214C22×Dic73C22×C412yes—
215C22×Dic73C2412yes—
216C22×Dic73C2411yescharacteristic
217C2×C4×D73—24no—
218C2×C4×D73—22no—
219C2×C4×D73—22no—
220C2×C4×D73—22no—
221C2×C4×D73—22no—
222C2×C4×D73—42no—
223C2×C4×D73C22×C412yes—
224C2×C4×D73C22×C414yes—
225C2×C4×D73C22×C412yes—
226C2×C4×D73C22×C414yes—
227C2×C4×D73C2412yes—
228C2×C4×D73C2412yes—
229C4⋊Dic73C22×C414yes—
230#11924007C22×C414yes—
231#11924007C22×C414yes—
232#11924007C22×C414yes—
233#11924007C22×C414yes—
234#11924007C22×C414yes—
235#11924007C22×C414yes—
236C22⋊Dic73C22×C414yes—
237#11924005C22×C414yes—
238#11924005C22×C414yes—
239#11924005C22×C414yes—
240#11924005C22×C414yes—
241#11924005C22×C414yes—
242#11924005C22×C414yes—
243C4×Dic73C22×C412yes—
244C4×Dic73C22×C412yes—
245C4×Dic73C22×C414yes—
246C4×Dic73C22×C412yes—
247C4×Dic73C22×C412yes—
248C4×Dic73C2412yes—
249C4×Dic73C2412yes—
250C4×Dic73C2412yes—
251C4×Dic73C2412yes—
252C24×C73C22×C411yescharacteristic
253C22×C4×C73C22×C411yescharacteristic
254C22×C4×C73C22×C411yescharacteristic
255C22×C4×C73C22×C411yescharacteristic
256C22×C4×C73C22×C411yescharacteristic
257C22×C4×C73C22×C411yescharacteristic
258C22×C4×C73C22×C411yescharacteristic
259C4⋊C4×C73C22×C414yes—
260C4⋊C4×C73C22×C414yes—
261C4⋊C4×C73C22×C414yes—
262C22⋊C4×C73C22×C414yes—
263C22⋊C4×C73C22×C414yes—
264C22⋊C4×C73C22×C414yes—
265C42×C73C22×C414yes—
266C23×C73—22no—
267C23×C73—22no—
268C23×C73—22no—
269C23×C73C23×C412yes—
270C23×C73C23×C411yescharacteristic
271C22×D73—22no—
272C22×D73—22no—
273C22×D73—22no—
274C22×D73—22no—
275C22×D73—22no—
276C22×D73#13114yes—
277C22×D73C23×C412yes—
278C22×D73C23×C412yes—
279C2×C4×C73—22no—
280C2×C4×C73—22no—
281C2×C4×C73—22no—
282C2×C4×C73—22no—
283C2×C4×C73—22no—
284C2×C4×C73—22no—
285C2×C4×C73C23×C412yes—
286C2×C4×C73C23×C412yes—
287C2×C4×C73C23×C412yes—
288C2×C4×C73C23×C412yes—
289C2×C4×C73C23×C412yes—
290C2×C4×C73C23×C412yes—
291C22⋊D73—28no—
292C22⋊D73—44no—
293C2×Dic73—22no—
294C2×Dic73—22no—
295C2×Dic73—22no—
296C2×Dic73—22no—
297C2×Dic73—22no—
298C2×Dic73—24no—
299C2×Dic73—22no—
300C2×Dic73—22no—
301C2×Dic73C23×C412yes—
302C2×Dic73C23×C412yes—
303C2×Dic73C23×C412yes—
304C2×Dic73C23×C412yes—
305C2×Dic73C23×C412yes—
306C2×Dic73C23×C411yescharacteristic
307C2×Dic73H(5,𝔽2)12yes—
308C2×Dic732−1+412yes—
309C2×Dic73C2511yescharacteristic
310D292—28no—
311C4×D73—28no—
312C4×D73—24no—
313C4×D73—24no—
314C4×D73—22no—
315C4×D73—22no—
316C4×D73—22no—
317C4×D73—22no—
318C4×D73—44no—
319Dic146—44no—
320#10596833—22no—
321#10596833—22no—
322#10596833—22no—
323#10596833—22no—
324#10596833—22no—
325#10596833—22no—
326#10596833—22no—
327#10596833—22no—
328C22×C73—22no—
329C22×C73—22no—
330C22×C73—22no—
331C22×C73—44no—
332C22×C73#52012yes—
333C22×C73C2×#13112yes—
334C22×C73#56812yes—
335C22×C73C24×C411yescharacteristic
336C2×D73—22no—
337C2×D73—28no—
338C2×D73—22no—
339C2×D73—22no—
340C2×D73—22no—
341C2×D73—22no—
342C2×D73—44no—
343C2×D73C2×#13114yes—
344C4×C73—22no—
345C4×C73—22no—
346C4×C73—22no—
347C4×C73—22no—
348C4×C73—22no—
349C4×C73—22no—
350Dic73—22no—
351Dic73—22no—
352Dic73—22no—
353Dic73—22no—
354Dic73—22no—
355Dic73#52012yes—
356Dic73C2×H(5,𝔽2)11yescharacteristic
357Dic73C2×2−1+411yescharacteristic
358C2×#2992—731nomaximal, Sylow
359C2×C73—42no—
360C2×C73#299214yescomplemented
361C2×C73C2×#52011yescharacteristic
362C2×C73C22×#13111yescharacteristic
363C2×C73C2×#56811yescharacteristic
364D73—24no—
365D73—42no—
366C2×#529—731no—
367#2992—7316no—
368C2×#446—731no—
369C2×#446—731no—
370C2×#435—731no—
371C2×#435—731no—
372C2×#435—731no—
373C2×#435—731no—
374C2×C8×D4—731no—
375C2×C8×D4—731no—
376C2×#433—731no—
377C2×#433—731no—
378C2×#432—731no—
379C2×#424—731no—
380C2×#424—731no—
381C22×C4⋊C8—731no—
382C73C2×#299211yescharacteristic, complemented, Sylow
383C22×M16—731no—
384C22×M16—731no—
385C23×C8—731no—
386C23×C8—731no—
387C23×C8—731no—
388C23×C8—731no—
389#529—738no—
390#529—738no—
391C2×#126—731no—
392C2×#126#6440811yescharacteristic
393C2×#125—731no—
394C2×#124—731no—
395C2×#123—731no—
396C2×#123—731no—
397C2×C22⋊Q8—731no—
398C2×#121—731no—
399C2×C4×Q8—731no—
400C2×C4×D4—731no—
401C2×C4×D4—731no—
402C2×C4×D4—731no—
403C2×#117—731no—
404C2×#117—731no—
405C22×C42—731no—
406#446—738no—
407#446—738no—
408#435—738no—
409#435—738no—
410#435—738no—
411#435—738no—
412C8×D4—738no—
413C8×D4—738no—
414#433—738no—
415#433—738no—
416#432—738no—
417#424—738no—
418#424—738no—
419C2×C4⋊C8—731no—
420C2×C4⋊C8—731no—
421C2×C4⋊C8—731no—
422C2×C4⋊C8—731no—
423C2×C4⋊C8—738no—
424C2×C4⋊C8—731no—
425C2×C4⋊C8—731no—
426C2×C4⋊C8—731no—
427C2×C4⋊C8—731no—
428C2×C4⋊C8—731no—
429C2×C4⋊C8—731no—
430C2×C22⋊C8—731no—
431C2×C22⋊C8—731no—
432C2×C22⋊C8—731no—
433C2×C22⋊C8—731no—
434C2×C22⋊C8—731no—
435C2×C22⋊C8—731no—
436C2×#97—731no—
437C2×#97—731no—
438C2×#97—731no—
439C2×#97—731no—
440C2×C4×C8—731no—
441C2×C4×C8—731no—
442C22×Q8—731no—
443C22×D4—731no—
444C22×D4—731no—
445C22×D4—731no—
446C23×C4—731no—
447C23×C4—731no—
448C23×C4—731no—
449C23×C4—731no—
450C23×C4—731no—
451C2×M16—2922no—
452C2×M16—2922no—
453C2×M16—734no—
454C2×M16—734no—
455C22×C8—2922no—
456C22×C8—2922no—
457C22×C8—2922no—
458C22×C8—2922no—
459C22×C8—734no—
460C22×C8—734no—
461C22×C8—734no—
462C22×C8—734no—
463C22×C8—731no—
464C22×C8—731no—
465C22×C8—731no—
466C22×C8—731no—
467C22×C8—731no—
468C22×C8—731no—
469C22×C8—731no—
470C22×C8—731no—
471#126—738no—
472#126C2×#6440818yes—
473#125—738no—
474#124—738no—
475#123—738no—
476#123—738no—
477C22⋊Q8—738no—
478#121—738no—
479C4×Q8—734no—
480C4×Q8—734no—
481C4×D4—734no—
482C4×D4—734no—
483C4×D4—734no—
484C4×D4—734no—
485C4×D4—734no—
486C4×D4—734no—
487#117—734no—
488#117—734no—
489#117—734no—
490#117—734no—
491C2×C4⋊C4—731no—
492C2×C4⋊C4—731no—
493C2×C4⋊C4—731no—
494C2×C4⋊C4—731no—
495C2×C4⋊C4—731no—
496C2×C4⋊C4—731no—
497C2×C4⋊C4—731no—
498C2×C4⋊C4C2×#6440811yescharacteristic
499C2×C4⋊C4C2×#6440811yescharacteristic
500C2×C4⋊C4C2×#6440811yescharacteristic
501C2×C22⋊C4—731no—
502C2×C22⋊C4—731no—
503C2×C22⋊C4—731no—
504C2×C22⋊C4—731no—
505C2×C22⋊C4—731no—
506C2×C22⋊C4—731no—
507C2×C22⋊C4—731no—
508C2×C22⋊C4C2×#6440811yescharacteristic
509C2×C22⋊C4C2×#6440811yescharacteristic
510C2×C22⋊C4C2×#6440811yescharacteristic
511C2×C42—731no—
512C2×C42—731no—
513C2×C42—731no—
514C2×C42—731no—
515C2×C42—731no—
516C2×C42—734no—
517C2×C42—734no—
518C2×C42C2×#6440811yescharacteristic
519C4⋊C8—734no—
520C4⋊C8—734no—
521C4⋊C8—734no—
522C4⋊C8—734no—
523C4⋊C8—734no—
524C4⋊C8—734no—
525C4⋊C8—734no—
526C4⋊C8—734no—
527C4⋊C8—734no—
528C4⋊C8—734no—
529C22⋊C8—734no—
530C22⋊C8—734no—
531C22⋊C8—734no—
532C22⋊C8—734no—
533C22⋊C8—734no—
534C22⋊C8—734no—
535#97—734no—
536#97—734no—
537#97—734no—
538#97—734no—
539C4×C8—734no—
540C4×C8—734no—
541C24—731no—
542C24—731no—
543C24C22×#6440811yescharacteristic
544C2×Q8—2922no—
545C2×Q8—734no—
546C2×D4—2922no—
547C2×D4—734no—
548C2×D4—734no—
549C2×D4—734no—
550C2×D4—1464no—
551C2×D4—1464no—
552C22×C4—2922no—
553C22×C4—734no—
554C22×C4—731no—
555C22×C4—732no—
556C22×C4—732no—
557C22×C4—731no—
558C22×C4—731no—
559C22×C4—731no—
560C22×C4—731no—
561C22×C4—731no—
562C22×C4—732no—
563C22×C4—734no—
564C22×C4—732no—
565C22×C4—732no—
566C22×C4—732no—
567C22×C4—1462no—
568C22×C4—1462no—
569C22×C4—1462no—
570C22×C4—1462no—
571C22×C4—1464no—
572C22×C4—1462no—
573C22×C4—1462no—
574C22×C4C22×#6440811yescharacteristic
575C22×C4C22×#6440811yescharacteristic
576C22×C4C22×#6440811yescharacteristic
577C22×C4C22×#6440811yescharacteristic
578C22×C4C22×#6440811yescharacteristic
579C22×C4C22×#6440811yescharacteristic
580M16—2924no—
581M16—2924no—
582C2×C8—2924no—
583C2×C8—2924no—
584C2×C8—2924no—
585C2×C8—2924no—
586C2×C8—732no—
587C2×C8—732no—
588C2×C8—732no—
589C2×C8—732no—
590C2×C8—732no—
591C2×C8—732no—
592C2×C8—732no—
593C2×C8—732no—
594C2×C8—1462no—
595C2×C8—1462no—
596C2×C8—1462no—
597C2×C8—1462no—
598C2×C8—1462no—
599C2×C8—1462no—
600C2×C8—1462no—
601C2×C8—1462no—
602C4⋊C4—734no—
603C4⋊C4—734no—
604C4⋊C4—734no—
605C4⋊C4—734no—
606C4⋊C4—734no—
607C4⋊C4—734no—
608C4⋊C4—734no—
609C4⋊C4C22×#6440814yes—
610C4⋊C4C22×#6440814yes—
611C4⋊C4C22×#6440814yes—
612C22⋊C4—734no—
613C22⋊C4—734no—
614C22⋊C4—734no—
615C22⋊C4—734no—
616C22⋊C4—734no—
617C22⋊C4—734no—
618C22⋊C4—734no—
619C22⋊C4C22×#6440814yes—
620C22⋊C4C22×#6440814yes—
621C22⋊C4C22×#6440814yes—
622C42—732no—
623C42—732no—
624C42—734no—
625C42—732no—
626C42—732no—
627C42—732no—
628C42—732no—
629C42—732no—
630C42—732no—
631C42C22×#6440814yes—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—734no—
636C23—732no—
637C23—732no—
638C23—1462no—
639C23—1462no—
640C23—1462no—
641C23—1462no—
642C23—1462no—
643C23C23×#6440812yes—
644C23C23×#6440811yescharacteristic
645Q8—2924no—
646D4—2924no—
647D4—1468no—
648D4—1468no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—2924no—
656C2×C4—732no—
657C2×C4—732no—
658C2×C4—731no—
659C2×C4—731no—
660C2×C4—732no—
661C2×C4—732no—
662C2×C4—732no—
663C2×C4—732no—
664C2×C4—732no—
665C2×C4—1462no—
666C2×C4—1462no—
667C2×C4—1462no—
668C2×C4—1462no—
669C2×C4—1464no—
670C2×C4—1464no—
671C2×C4—1468no—
672C2×C4—1462no—
673C2×C4—1462no—
674C2×C4—1464no—
675C2×C4—1462no—
676C2×C4—1462no—
677C2×C4—1462no—
678C2×C4—1462no—
679C2×C4—1462no—
680C2×C4C23×#6440812yes—
681C2×C4C23×#6440812yes—
682C2×C4C23×#6440812yes—
683C2×C4C23×#6440812yes—
684C2×C4C23×#6440812yes—
685C2×C4C23×#6440812yes—
686C8—1462no—
687C8—1462no—
688C8—1462no—
689C8—1462no—
690C8—1462no—
691C8—1462no—
692C8—1462no—
693C8—1462no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—44no—
698C22—2924no—
699C22—734no—
700C22—1462no—
701C22—1462no—
702C22—1462no—
703C22—1468no—
704C22—1462no—
705C22—1462no—
706C22#1798965612yes—
707C22D73⋊#13112yes—
708C22#1798966612yes—
709C22C24×#6440811yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—731no—
717C4—731no—
718C4—732no—
719C4—1462no—
720C4—1462no—
721C4—1462no—
722C4—1462no—
723C4—1462no—
724C2—42no—
725C2—2922no—
726C2—1464no—
727C2#2262686914yesdirect product factor
728C2C2×#1798965611yescharacteristic
729C2C2×D73⋊#13111yescharacteristic
730C2C2×#1798966611yescharacteristic
subgroupG/H
centerC23C23×#64408
commutatorC22×C73C24×C4
FrattiniC22C24×#64408
FittingC2×#126×C73C4
socleC23×C73C23×C4
prime radicalC2×#14556564C4
cosocleC2×Dic73C25
hypercenterC2×#126#64408
hypocenterC73C2×#2992
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #22626869C2direct (N × H)
2. C2×#17989639C2semidirect
3. C2×#17989637C2semidirect
4. C2×#17989619C2semidirect
5. C2×#17989619C2semidirect
6. C2×#17989617C2semidirect
7. C2×#17989616C2semidirect
8. C2×#17989615C2semidirect
9. C2×#17989614C2semidirect
10. C2×#17989612C2semidirect
11. C2×#17989611C2semidirect
12. C2×#17989609C2semidirect
13. C2×#17989594C2semidirect
14. C2×#17989593C2semidirect
15. C2×#17989588C2semidirect
23. #17989639C22semidirect
24. #17989637C22semidirect
25. #17989619C22semidirect
26. #17989619C22semidirect
27. #17989617C22semidirect
28. #17989616C22semidirect
29. #17989615C22semidirect
30. #17989614C22semidirect
31. #17989612C22semidirect
32. #17989611C22semidirect
33. #17989609C22semidirect
34. #17989594C22semidirect
35. #17989593C22semidirect
40. #17989588C22semidirect
360. C2×C73#2992semidirect
382. C73C2×#2992semidirect
727. C2#22626869direct (N × H)

Maximal subgroups

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

subgroupindex
#226268692
C2×#179896392
C2×#179896372
C2×#179896192
C2×#179896172
C2×#179896162
C2×#179896152
C2×#179896142
C2×#179896122
C2×#179896112
C2×#179896092
C2×#179895942
C2×#179895932
C2×#179895882
C2×#179891202
C2×#299273