Finite Group Databasebeta

← C2×#22626753 #34031539

Subgroups — C2×#22626753 #34031539

Order 18688.

1970 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#22626753C2116yesmaximal, direct product factor
2C2×#17989639C211yesmaximal, characteristic, complemented
3C2×#17989637C211yesmaximal, characteristic, complemented
4C2×#17989622C211yesmaximal, characteristic, complemented
5C2×#17989620C211yesmaximal, characteristic, complemented
6C2×#17989619C211yesmaximal, characteristic, complemented
7C2×#17989619C211yesmaximal, characteristic, complemented
8C2×#17989618C211yesmaximal, characteristic, complemented
9C2×#17989616C211yesmaximal, characteristic, complemented
10C2×#17989612C211yesmaximal, characteristic, complemented
11C2×#17989611C211yesmaximal, characteristic, complemented
12C2×#17989608C211yesmaximal, characteristic, complemented
13C2×#17989552C211yesmaximal, characteristic, complemented
14C2×#17989551C211yesmaximal, characteristic, complemented
15C2×C4×#11924037C211yesmaximal, characteristic, complemented
16C2×#17989114C211yesmaximal, characteristic
17C22×#11924038C2211yescharacteristic
18C22×#11924037C2211yescharacteristic
19C22×#11924037C2211yescharacteristic
20C22×#11924037C2211yescharacteristic
21C22×#11924036C2211yescharacteristic
22C23×#10596833C2211yescharacteristic
23#17989639C2218yescomplemented
24#17989637C2218yescomplemented
25#17989622C2218yescomplemented
26#17989620C2218yescomplemented
27#17989619C2218yescomplemented
28#17989619C2218yescomplemented
29#17989618C2218yescomplemented
30#17989616C2218yescomplemented
31#17989612C2218yescomplemented
32#17989611C2218yescomplemented
33#17989608C2218yescomplemented
34C2×#14556658C2211yescharacteristic
35C2×#14556658C2211yescharacteristic
36C2×C4⋊#10596833C2211yescharacteristic
37C2×C4⋊#10596833C2211yescharacteristic
38C2×C4⋊#10596833C2211yescharacteristic
39C2×C4⋊#10596833C2211yescharacteristic
40C2×#14556648C2211yescharacteristic
41C2×#14556648C2211yescharacteristic
42C2×C22⋊#10596833C2211yescharacteristic
43C2×C22⋊#10596833C2211yescharacteristic
44C2×C22⋊#10596833C2211yescharacteristic
45C2×C22⋊#10596833C2211yescharacteristic
46#17989552C2218yescomplemented
47#17989551C2218yescomplemented
48C4×#11924037C2218yescomplemented
49C2×#14556646C2211yescharacteristic
50C2×#14556646C2211yescharacteristic
51C2×#14556646C2211yescharacteristic
52C2×#14556646C2211yescharacteristic
53C2×#14556646C2211yescharacteristic
54C2×#14556646C2211yescharacteristic
55C2×C4×#10596833C2211yescharacteristic
56C2×C4×#10596833C2211yescharacteristic
57C2×C4×#10596833C2211yescharacteristic
58C2×C4×#10596833C2211yescharacteristic
59#17989114C418yes—
60#17989114C2218yes—
61C2×#14556586C411yescharacteristic
62C2×#14556584C411yescharacteristic
63C2×#14556581C411yescharacteristic
64C2×#14556577C411yescharacteristic
65C2×#14556574C411yescharacteristic
66C2×#14556568C411yescharacteristic
67C2×#14556563C411yescharacteristic
68C2×#14556556C2211yescharacteristic
69C2×D4×Dic73C2211yescharacteristic
70C2×#14556551C2211yescharacteristic
71C2×#14556551C2211yescharacteristic
72C2×#14556549C2211yescharacteristic
73C2×#14556547C2211yescharacteristic
74C22×C4×Dic73C2211yescharacteristic
75C2×#123×C73C411yescharacteristic
76C2×#11924038—24no—
77C2×#11924038C2314yes—
78C2×#11924037—24no—
79C2×#11924037—24no—
80C2×#11924037—24no—
81C2×#11924037C2314yes—
82C2×#11924037C2314yes—
83C2×#11924037C2314yes—
84C2×#11924036—24no—
85C2×#11924036C2314yes—
86C22×#10596833—24no—
87C22×#10596833C2311yescharacteristic
88C22×#10596833C2314yes—
89C22×#10596833C2311yescharacteristic
90C22×#10596833C2311yescharacteristic
91C22×#10596833C2311yescharacteristic
92C22×#10596833C2311yescharacteristic
93C22×#10596833C2311yescharacteristic
94C22×#10596833C2311yescharacteristic
95C22×#10596833C2311yescharacteristic
96#14556658C2314yes—
97#14556658C2314yes—
98C4⋊#10596833C2314yes—
99C4⋊#10596833C2314yes—
100C4⋊#10596833C2314yes—
101C4⋊#10596833C2314yes—
102#14556648C2314yes—
103#14556648C2314yes—
104C22⋊#10596833C2314yes—
105C22⋊#10596833C2314yes—
106C22⋊#10596833C2314yes—
107C22⋊#10596833C2314yes—
108#14556646C2314yes—
109#14556646C2314yes—
110#14556646C2314yes—
111#14556646C2314yes—
112#14556646C2314yes—
113#14556646C2314yes—
114C4×#10596833C2314yes—
115C4×#10596833C2314yes—
116C4×#10596833C2314yes—
117C4×#10596833C2314yes—
118C22×Dic146C2×C411yescharacteristic
119C22×C22⋊D73C2×C411yescharacteristic
120C22×C22⋊D73C2×C411yescharacteristic
121C23×Dic73C2×C411yescharacteristic
122C23×Dic73C2311yescharacteristic
123C23×Dic73C2311yescharacteristic
124C22×C4×D73C2311yescharacteristic
125#14556586C2×C418yes—
126#14556584C2×C418yes—
127#14556581C2×C418yes—
128#14556577C2×C418yes—
129#14556574C2×C418yes—
130#14556568C2×C418yes—
131#14556563C2×C418yes—
132#14556556C2×C414yes—
133#14556556C2314yes—
134D4×Dic73C2×C414yes—
135D4×Dic73C2314yes—
136#14556551C2×C414yes—
137#14556551C2×C414yes—
138#14556551C2314yes—
139#14556551C2314yes—
140#14556549C2×C414yes—
141#14556549C2314yes—
142#14556547C2×C414yes—
143#14556547C2314yes—
144C2×C4⋊Dic73C2×C411yescharacteristic
145C2×C4⋊Dic73C2×C411yescharacteristic
146C2×#11924007C2×C411yescharacteristic
147C2×#11924007C2×C411yescharacteristic
148C2×#11924007C2×C411yescharacteristic
149C2×#11924007C2×C411yescharacteristic
150C2×#11924007C2×C411yescharacteristic
151C2×#11924007C2×C411yescharacteristic
152C2×C22⋊Dic73C2×C411yescharacteristic
153C2×C22⋊Dic73C2×C411yescharacteristic
154C2×C22⋊Dic73C2×C411yescharacteristic
155C2×#11924005C2×C411yescharacteristic
156C2×#11924005C2×C411yescharacteristic
157C2×#11924005C2×C411yescharacteristic
158C2×#11924005C2×C411yescharacteristic
159C2×C4×Dic73C2×C411yescharacteristic
160C2×C4×Dic73C2×C411yescharacteristic
161C2×C4×Dic73C2×C414yes—
162C2×C4×Dic73C2311yescharacteristic
163C2×C4×Dic73C2311yescharacteristic
164C2×C4×Dic73C2311yescharacteristic
165C2×C4×Dic73C2311yescharacteristic
166C2×C4×Dic73C2314yes—
167C22×D4×C73C2×C411yescharacteristic
168C23×C4×C73C2×C411yescharacteristic
169#123×C73C2×C418yes—
170C2×C4⋊C4×C73C2×C411yescharacteristic
171C2×C4⋊C4×C73C2×C411yescharacteristic
172C2×C22⋊C4×C73C2×C411yescharacteristic
173C2×C22⋊C4×C73C2×C411yescharacteristic
174C2×C22⋊C4×C73C2×C411yescharacteristic
175#11924038—28no—
176#11924037—28no—
177#11924037—28no—
178#11924037—28no—
179#11924036—28no—
180C2×#10596833—22no—
181C2×#10596833—22no—
182C2×#10596833—22no—
183C2×#10596833—22no—
184C2×#10596833—22no—
185C2×#10596833—22no—
186C2×#10596833—28no—
187C2×#10596833#4114yes—
188C2×#10596833#4114yes—
189C2×#10596833C2412yes—
190C2×#10596833C2412yes—
191C2×#10596833C2412yes—
192C2×#10596833C2412yes—
193C2×#10596833C2412yes—
194C2×#10596833C2412yes—
195C2×#10596833C2412yes—
196C2×#10596833C2412yes—
197C23×D73C22×C411yescharacteristic
198C2×Dic146—42no—
199C2×Dic146C22×C414yes—
200C2×C22⋊D73—42no—
201C2×C22⋊D73—42no—
202C2×C22⋊D73C22×C414yes—
203C2×C22⋊D73C22×C414yes—
204C22×Dic73—22no—
205C22×Dic73—22no—
206C22×Dic73—22no—
207C22×Dic73—22no—
208C22×Dic73—42no—
209C22×Dic73C22×C411yescharacteristic
210C22×Dic73C22×C412yes—
211C22×Dic73C22×C411yescharacteristic
212C22×Dic73C22×C411yescharacteristic
213C22×Dic73C22×C411yescharacteristic
214C22×Dic73C22×C411yescharacteristic
215C22×Dic73C22×C411yescharacteristic
216C22×Dic73C22×C412yes—
217C22×Dic73C22×C414yes—
218C22×Dic73C2412yes—
219C22×Dic73C2412yes—
220C22×Dic73C2411yescharacteristic
221C2×C4×D73—22no—
222C2×C4×D73—22no—
223C2×C4×D73C22×C412yes—
224C2×C4×D73C2412yes—
225C4⋊Dic73C22×C414yes—
226C4⋊Dic73C22×C414yes—
227#11924007C22×C414yes—
228#11924007C22×C414yes—
229#11924007C22×C414yes—
230#11924007C22×C414yes—
231#11924007C22×C414yes—
232#11924007C22×C414yes—
233C22⋊Dic73C22×C414yes—
234C22⋊Dic73C22×C414yes—
235C22⋊Dic73C22×C414yes—
236#11924005C22×C414yes—
237#11924005C22×C414yes—
238#11924005C22×C414yes—
239#11924005C22×C414yes—
240C4×Dic73C22×C412yes—
241C4×Dic73C22×C412yes—
242C4×Dic73C22×C414yes—
243C4×Dic73C22×C414yes—
244C4×Dic73C22×C412yes—
245C4×Dic73C22×C412yes—
246C4×Dic73C2412yes—
247C4×Dic73C2412yes—
248C4×Dic73C2412yes—
249C4×Dic73C2412yes—
250C24×C73C22×C411yescharacteristic
251C24×C73C22×C411yescharacteristic
252C2×D4×C73—42no—
253C2×D4×C73C22×C414yes—
254C22×C4×C73—42no—
255C22×C4×C73C22×C411yescharacteristic
256C22×C4×C73C22×C411yescharacteristic
257C22×C4×C73C22×C411yescharacteristic
258C22×C4×C73C22×C411yescharacteristic
259C22×C4×C73C22×C411yescharacteristic
260C22×C4×C73C22×C414yes—
261C4⋊C4×C73C22×C414yes—
262C4⋊C4×C73C22×C414yes—
263C22⋊C4×C73C22×C414yes—
264C22⋊C4×C73C22×C414yes—
265C22⋊C4×C73C22×C414yes—
266C23×C73—22no—
267C23×C73—22no—
268C23×C73—22no—
269C23×C73—22no—
270C23×C73—22no—
271C23×C73—22no—
272C23×C73C23×C412yes—
273C23×C73C23×C412yes—
274C23×C73C23×C411yescharacteristic
275C22×D73—22no—
276C22×D73—22no—
277C22×D73—22no—
278C22×D73C23×C412yes—
279D4×C73—44no—
280C2×C4×C73—22no—
281C2×C4×C73—22no—
282C2×C4×C73—22no—
283C2×C4×C73—22no—
284C2×C4×C73—22no—
285C2×C4×C73—44no—
286C2×C4×C73C23×C412yes—
287C2×C4×C73C23×C412yes—
288C2×C4×C73C23×C412yes—
289C2×C4×C73C23×C412yes—
290C2×C4×C73C23×C412yes—
291C22⋊D73—44no—
292C22⋊D73—44no—
293C2×Dic73—22no—
294C2×Dic73—22no—
295C2×Dic73—22no—
296C2×Dic73—22no—
297C2×Dic73—22no—
298C2×Dic73—22no—
299C2×Dic73—24no—
300C2×Dic73—24no—
301C2×Dic73—22no—
302C2×Dic73—22no—
303C2×Dic73—22no—
304C2×Dic73—22no—
305C2×Dic73—44no—
306C2×Dic73C23×C412yes—
307C2×Dic73C23×C412yes—
308C2×Dic73C23×C412yes—
309C2×Dic73C23×C412yes—
310C2×Dic73C23×C412yes—
311C2×Dic73C23×C412yes—
312C2×Dic73C23×C411yescharacteristic
313C2×Dic73C2×#4112yes—
314C2×Dic73C2×#4112yes—
315C2×Dic73C2511yescharacteristic
316C4×D73—24no—
317C4×D73—22no—
318C4×D73—22no—
319Dic146—44no—
320#10596833—22no—
321#10596833—22no—
322#10596833—22no—
323#10596833—22no—
324#10596833—22no—
325#10596833—22no—
326#10596833C2×#4114yes—
327#10596833C2×#4114yes—
328C22×C73—22no—
329C22×C73—22no—
330C22×C73—22no—
331C22×C73—22no—
332C22×C73—22no—
333C22×C73—22no—
334C22×C73—44no—
335C22×C73—44no—
336C22×C73C4×#4112yes—
337C22×C73#56812yes—
338C22×C73#56812yes—
339C22×C73C24×C411yescharacteristic
340C2×D73—22no—
341C2×D73—22no—
342C2×D73—22no—
343C2×D73—44no—
344C4×C73—22no—
345C4×C73—22no—
346C4×C73—22no—
347C4×C73—22no—
348C4×C73—22no—
349Dic73—22no—
350Dic73—22no—
351Dic73—22no—
352Dic73—22no—
353Dic73—22no—
354Dic73—22no—
355Dic73C4×#4112yes—
356Dic73C22×#4111yescharacteristic
357Dic73C22×#4111yescharacteristic
358C2×#2967—731nomaximal, Sylow
359C2×C73—42no—
360C2×C73—42no—
361C2×C73#296714yescomplemented
362C2×C73C2×C4×#4111yescharacteristic
363C2×C73C2×#56811yescharacteristic
364C2×C73C2×#56811yescharacteristic
365D73—42no—
366C2×#529—731no—
367#2967—7316no—
368C2×#446—731no—
369C2×#446—731no—
370C2×#436—731no—
371C2×#436—731no—
372C2×#435—731no—
373C2×#435—731no—
374C2×#435—731no—
375C2×#435—731no—
376C2×#433—731no—
377C2×#433—731no—
378C2×#432—731no—
379C2×#405—731no—
380C2×#405—731no—
381C2×C4×M16—731no—
382C73C2×#296711yescharacteristic, complemented, Sylow
383C22×M16—731no—
384C22×M16—731no—
385C22×M16—731no—
386C22×M16—731no—
387C23×C8—731no—
388C23×C8—731no—
389#529—738no—
390#529—738no—
391C2×#126—731no—
392C2×#126—731no—
393C2×#125—731no—
394C2×#124—731no—
395C2×#123—731no—
396C2×#123#6440811yescharacteristic
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#436—738no—
409#436—738no—
410#435—738no—
411#435—738no—
412#435—738no—
413#435—738no—
414#433—738no—
415#433—738no—
416#432—738no—
417C2×C4⋊C8—731no—
418C2×C4⋊C8—731no—
419C2×C4⋊C8—731no—
420C2×C4⋊C8—731no—
421C2×C4⋊C8—731no—
422C2×C4⋊C8—731no—
423C2×C22⋊C8—731no—
424C2×C22⋊C8—731no—
425C2×C22⋊C8—731no—
426C2×C22⋊C8—731no—
427C2×C22⋊C8—731no—
428C2×C22⋊C8—731no—
429#405—738no—
430#405—738no—
431C4×M16—738no—
432C2×#97—731no—
433C2×#97—731no—
434C2×#97—731no—
435C2×#97—731no—
436C2×#97—731no—
437C2×#97—731no—
438C2×C4×C8—731no—
439C2×C4×C8—731no—
440C2×C4×C8—731no—
441C2×C4×C8—731no—
442C22×Q8—731no—
443C22×D4—731no—
444C22×D4—731no—
445C22×D4C2×#6440811yescharacteristic
446C23×C4—731no—
447C23×C4—731no—
448C23×C4—731no—
449C23×C4—731no—
450C23×C4C2×#6440811yescharacteristic
451C2×M16—734no—
452C2×M16—734no—
453C2×M16—734no—
454C2×M16—734no—
455C2×M16—1464no—
456C2×M16—1464no—
457C2×M16—1464no—
458C2×M16—1464no—
459C22×C8—731no—
460C22×C8—731no—
461C22×C8—731no—
462C22×C8—731no—
463C22×C8—734no—
464C22×C8—731no—
465C22×C8—731no—
466C22×C8—731no—
467C22×C8—731no—
468C22×C8—734no—
469C22×C8—1464no—
470C22×C8—1464no—
471#126—738no—
472#126—738no—
473#125—738no—
474#124—738no—
475#123—738no—
476#123C2×#6440818yes—
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⋊C4—731no—
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—731no—
517C2×C42—734no—
518C2×C42—734no—
519C4⋊C8—734no—
520C4⋊C8—734no—
521C4⋊C8—734no—
522C4⋊C8—734no—
523C4⋊C8—734no—
524C4⋊C8—734no—
525C22⋊C8—734no—
526C22⋊C8—734no—
527C22⋊C8—734no—
528C22⋊C8—734no—
529C22⋊C8—734no—
530C22⋊C8—734no—
531#97—734no—
532#97—734no—
533#97—734no—
534#97—734no—
535#97—734no—
536#97—734no—
537C4×C8—734no—
538C4×C8—734no—
539C4×C8—734no—
540C4×C8—734no—
541C24—731no—
542C24C22×#6440811yescharacteristic
543C24C22×#6440811yescharacteristic
544C2×Q8—2922no—
545C2×Q8—734no—
546C2×D4—42no—
547C2×D4—2922no—
548C2×D4—2922no—
549C2×D4—734no—
550C2×D4—734no—
551C2×D4C22×#6440814yes—
552C22×C4—42no—
553C22×C4—2922no—
554C22×C4—734no—
555C22×C4—731no—
556C22×C4—732no—
557C22×C4—732no—
558C22×C4—732no—
559C22×C4—732no—
560C22×C4—731no—
561C22×C4—731no—
562C22×C4—731no—
563C22×C4—731no—
564C22×C4—731no—
565C22×C4—731no—
566C22×C4—732no—
567C22×C4—732no—
568C22×C4—1462no—
569C22×C4—1462no—
570C22×C4—1462no—
571C22×C4—1462no—
572C22×C4—1462no—
573C22×C4—1462no—
574C22×C4C22×#6440811yescharacteristic
575C22×C4C22×#6440811yescharacteristic
576C22×C4C22×#6440811yescharacteristic
577C22×C4C22×#6440811yescharacteristic
578C22×C4C22×#6440811yescharacteristic
579C22×C4C22×#6440814yes—
580M16—1468no—
581M16—1468no—
582M16—1468no—
583M16—1468no—
584C2×C8—734no—
585C2×C8—734no—
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—1468no—
595C2×C8—1468no—
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⋊C4—734no—
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—734no—
626C42—732no—
627C42—732no—
628C42—732no—
629C42—732no—
630C42—732no—
631C42—732no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—732no—
639C23—1462no—
640C23—1462no—
641C23—1462no—
642C23C23×#6440812yes—
643C23C23×#6440812yes—
644C23C23×#6440811yescharacteristic
645Q8—2924no—
646D4—44no—
647D4—2924no—
648D4—2924no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—44no—
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—732no—
666C2×C4—1462no—
667C2×C4—1462no—
668C2×C4—1464no—
669C2×C4—1462no—
670C2×C4—1462no—
671C2×C4—1462no—
672C2×C4—1462no—
673C2×C4—1464no—
674C2×C4—1464no—
675C2×C4—1462no—
676C2×C4—1462no—
677C2×C4—1462no—
678C2×C4—1462no—
679C2×C4—1462no—
680C2×C4—1462no—
681C2×C4C23×#6440812yes—
682C2×C4C23×#6440812yes—
683C2×C4C23×#6440812yes—
684C2×C4C23×#6440812yes—
685C2×C4C23×#6440812yes—
686C8—734no—
687C8—734no—
688C8—1462no—
689C8—1462no—
690C8—1462no—
691C8—1462no—
692C8—1462no—
693C8—1462no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—44no—
701C22—44no—
702C22—2924no—
703C22—1462no—
704C22—1462no—
705C22—1462no—
706C22#41×#6440812yes—
707C22#1798966512yes—
708C22#1798966612yes—
709C22C24×#6440811yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—22no—
715C4—731no—
716C4—731no—
717C4—732no—
718C4—1462no—
719C4—1462no—
720C4—1462no—
721C4—1462no—
722C4—1462no—
723C4—1462no—
724C2—42no—
725C2—42no—
726C2—2922no—
727C2#2262675314yesdirect product factor
728C2C2×#41×#6440811yescharacteristic
729C2C2×#1798966511yescharacteristic
730C2C2×#1798966611yescharacteristic
subgroupG/H
centerC23C23×#64408
commutatorC22×C73C24×C4
FrattiniC22C24×#64408
FittingC2×#123×C73C4
socleC23×C73C23×C4
prime radicalC2×#14556563C4
cosocleC2×Dic73C25
hypercenterC2×#123#64408
hypocenterC73C2×#2967
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. #22626753C2direct (N × H)
2. C2×#17989639C2semidirect
3. C2×#17989637C2semidirect
4. C2×#17989622C2semidirect
5. C2×#17989620C2semidirect
6. C2×#17989619C2semidirect
7. C2×#17989619C2semidirect
8. C2×#17989618C2semidirect
9. C2×#17989616C2semidirect
10. C2×#17989612C2semidirect
11. C2×#17989611C2semidirect
12. C2×#17989608C2semidirect
13. C2×#17989552C2semidirect
14. C2×#17989551C2semidirect
15. C2×C4×#11924037C2semidirect
23. #17989639C22semidirect
24. #17989637C22semidirect
25. #17989622C22semidirect
26. #17989620C22semidirect
27. #17989619C22semidirect
28. #17989619C22semidirect
29. #17989618C22semidirect
30. #17989616C22semidirect
31. #17989612C22semidirect
32. #17989611C22semidirect
33. #17989608C22semidirect
46. #17989552C22semidirect
47. #17989551C22semidirect
48. C4×#11924037C22semidirect
361. C2×C73#2967semidirect
382. C73C2×#2967semidirect
727. C2#22626753direct (N × H)

Maximal subgroups

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

subgroupindex
#226267532
C2×#179896392
C2×#179896372
C2×#179896222
C2×#179896202
C2×#179896192
C2×#179896182
C2×#179896162
C2×#179896122
C2×#179896112
C2×#179896082
C2×#179895522
C2×#179895512
C2×C4×#119240372
C2×#179891142
C2×#296773