Finite Group Databasebeta

← C2×#22623850 #33994488

Subgroups — C2×#22623850 #33994488

Order 18688.

7238 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623850C2132yesmaximal, direct product factor
2C2×#17989284C214yesmaximal, complemented
3C2×#17989282C214yesmaximal, complemented
4C2×#17989280C214yesmaximal, complemented
5C2×#17989274C214yesmaximal, complemented
6C2×#17989200C211yesmaximal, characteristic, complemented
7C2×#17989199C211yesmaximal, characteristic, complemented
8C2×#17989191C211yesmaximal, characteristic, complemented
9C2×#17989166C212yesmaximal, complemented
10C2×#17989135C211yesmaximal, characteristic, complemented
11C2×#17989119C212yesmaximal, complemented
12C2×#17989118C212yesmaximal, complemented
13C2×#125×D73C211yesmaximal, characteristic, complemented
14C2×#17989066C212yesmaximal, complemented
15C2×#17989055C211yesmaximal, characteristic, complemented
16C2×#540×C73C211yesmaximal, characteristic, complemented
17C22×#11924028C2211yescharacteristic
18C22×#11924027C2212yes—
19#17989284C22164yescomplemented
20#17989282C22164yescomplemented
21#17989280C22164yescomplemented
22#17989274C22164yescomplemented
23#17989200C22116yescomplemented
24#17989199C22116yescomplemented
25#17989191C22116yescomplemented
26#17989166C22132yescomplemented
27#17989135C22116yescomplemented
28C2×#14556591C2211yescharacteristic
29#17989119C22132yescomplemented
30#17989118C22132yescomplemented
31C2×#14556586C2214yes—
32C2×#14556584C2214yes—
33C2×#14556584C2214yes—
34C2×#14556584C2214yes—
35C2×#14556583C2211yescharacteristic
36C2×#14556582C2214yes—
37C2×#14556582C2212yes—
38C2×#14556581C2214yes—
39C2×#14556581C2214yes—
40#125×D73C22116yescomplemented
41C2×#14556578C2212yes—
42C2×#14556573C2214yes—
43C2×#14556572C2214yes—
44C2×#14556572C2214yes—
45C2×#14556571C2212yes—
46C2×#14556570C2212yes—
47C2×#14556568C2214yes—
48C2×#14556564C2214yes—
49C2×#14556563C2214yes—
50C2×#14556563C2214yes—
51C2×#14556562C2212yes—
52C2×#14556562C2214yes—
53C2×#14556562C2214yes—
54#17989066C22132yescomplemented
55#17989055C22116yescomplemented
56C2×C4×Dic146C2212yes—
57C2×#14556556C2212yes—
58C2×#14556556C2212yes—
59C2×D4×Dic73C2212yes—
60C2×D4×Dic73C2214yes—
61C2×D4×Dic73C2214yes—
62C2×#14556553C2212yes—
63C2×C4×C22⋊D73C2214yes—
64C2×C4×C22⋊D73C2214yes—
65C2×#14556551C2212yes—
66C2×#14556551C2212yes—
67C2×#14556551C2214yes—
68C2×#14556550C2214yes—
69C2×#14556548C2211yescharacteristic
70C2×#14556548C2211yescharacteristic
71C2×#14556547C2214yes—
72C2×#14556547C2214yes—
73C22×#11924007C2214yes—
74C2×C4⋊C4×D73C2212yes—
75C2×C4⋊C4×D73C2214yes—
76C22×C4×Dic73C2211yescharacteristic
77C2×C42×D73C2211yescharacteristic
78C2×C42×D73C2211yescharacteristic
79#540×C73C22116yescomplemented
80C2×#127×C73C2211yescharacteristic
81C2×#125×C73C2211yescharacteristic
82C2×#123×C73C2214yes—
83C2×#121×C73C2212yes—
84C2×#121×C73C2214yes—
85C2×C4×D4×C73C2212yes—
86C2×#117×C73C2211yescharacteristic
87C2×#11924028—28no—
88C2×#11924028C2318yes—
89C2×#11924027—216no—
90C2×#11924027C23116yes—
91C22×Dic146C2312yes—
92C22×Dic146C2311yescharacteristic
93C22×D292C2311yescharacteristic
94C22×C22⋊D73C2314yes—
95C22×C22⋊D73C2311yescharacteristic
96C22×C22⋊D73C2311yescharacteristic
97C22×C22⋊D73C2314yes—
98C23×Dic73C2314yes—
99C23×Dic73C2312yes—
100C23×Dic73C2314yes—
101C22×C4×D73C2311yescharacteristic
102C22×C4×D73C2312yes—
103C22×C4×D73C2312yes—
104C22×C4×D73C2314yes—
105C22×C4×D73C2311yescharacteristic
106#14556591C2318yes—
107#14556586C23132yes—
108#14556584C23132yes—
109#14556584C23132yes—
110#14556584C23132yes—
111#14556583C2318yes—
112#14556582C23132yes—
113#14556582C23116yes—
114#14556581C23132yes—
115#14556581C23132yes—
116#14556578C23116yes—
117#14556573C23132yes—
118#14556572C23132yes—
119#14556572C23132yes—
120#14556571C23116yes—
121#14556570C23116yes—
122#14556568C23132yes—
123#14556564C23132yes—
124#14556563C23132yes—
125#14556563C23132yes—
126#14556562C23132yes—
127#14556562C23116yes—
128#14556562C23132yes—
129C4×Dic146C23116yes—
130#14556556C23116yes—
131#14556556C23116yes—
132D4×Dic73C23132yes—
133D4×Dic73C23116yes—
134D4×Dic73C23132yes—
135#14556553C23116yes—
136C4×C22⋊D73C23132yes—
137C4×C22⋊D73C23132yes—
138#14556551C23116yes—
139#14556551C23132yes—
140#14556551C23116yes—
141#14556550C23132yes—
142#14556548C2318yes—
143#14556548C2318yes—
144#14556547C23132yes—
145#14556547C23132yes—
146C2×C4⋊Dic73C2314yes—
147C2×C4⋊Dic73C2314yes—
148C2×C4⋊Dic73C2312yes—
149C2×C4⋊Dic73C2314yes—
150C2×#11924007C23132yes—
151C2×#11924007C2314yes—
152C2×#11924007C2314yes—
153C2×#11924007C2314yes—
154C2×#11924007C2312yes—
155C2×#11924007C2314yes—
156C2×#11924007C2314yes—
157C2×#11924007C2314yes—
158C2×#11924007C2312yes—
159C4⋊C4×D73C23116yes—
160C4⋊C4×D73C23132yes—
161C2×C22⋊Dic73C2314yes—
162C2×C22⋊Dic73C2314yes—
163C2×C22⋊Dic73C2314yes—
164C2×C22⋊Dic73C2314yes—
165C2×C22⋊Dic73C2314yes—
166C2×#11924005C2312yes—
167C2×#11924005C2312yes—
168C2×#11924005C2314yes—
169C2×C4×Dic73C2311yescharacteristic
170C2×C4×Dic73C2312yes—
171C2×C4×Dic73C2312yes—
172C2×C4×Dic73C2312yes—
173C2×C4×Dic73C2311yescharacteristic
174C2×C4×Dic73C2318yes—
175C2×C4×Dic73C2314yes—
176C2×C4×Dic73C2314yes—
177C42×D73C2318yes—
178C42×D73C2318yes—
179C22×D4×C73C2312yes—
180C22×D4×C73C2314yes—
181C22×D4×C73C2314yes—
182C23×C4×C73C2311yescharacteristic
183C23×C4×C73C2314yes—
184#127×C73C2318yes—
185#125×C73C2318yes—
186#123×C73C23132yes—
187#121×C73C23116yes—
188#121×C73C23132yes—
189C4×D4×C73C23116yes—
190#117×C73C2318yes—
191C2×C4⋊C4×C73C2312yes—
192C2×C4⋊C4×C73C2312yes—
193C2×C4⋊C4×C73C2314yes—
194C2×C22⋊C4×C73C2312yes—
195C2×C22⋊C4×C73C2314yes—
196C2×C22⋊C4×C73C2314yes—
197C2×C42×C73C2311yescharacteristic
198C2×C42×C73C2311yescharacteristic
199C23×D73C2411yescharacteristic
200C23×D73C2411yescharacteristic
201#11924028—232no—
202#11924027—264no—
203C2×Dic146—28no—
204C2×Dic146—24no—
205C2×Dic146C2414yes—
206C2×Dic146C2418yes—
207C2×D292—24no—
208C2×D292C2414yes—
209C2×C22⋊D73—216no—
210C2×C22⋊D73—24no—
211C2×C22⋊D73—24no—
212C2×C22⋊D73—48no—
213C2×C22⋊D73C2414yes—
214C2×C22⋊D73C2414yes—
215C2×C22⋊D73C24116yes—
216C2×C22⋊D73C24116yes—
217C22×Dic73—216no—
218C22×Dic73—44no—
219C22×Dic73—48no—
220C22×Dic73C2412yes—
221C22×Dic73C2412yes—
222C22×Dic73C2414yes—
223C22×Dic73C2411yescharacteristic
224C22×Dic73C2414yes—
225C22×Dic73C24116yes—
226C22×Dic73C2418yes—
227C22×Dic73C24116yes—
228C22×Dic73C2411yescharacteristic
229C2×C4×D73—24no—
230C2×C4×D73—44no—
231C2×C4×D73—44no—
232C2×C4×D73—48no—
233C2×C4×D73#4118yes—
234C2×C4×D73C2414yes—
235C2×C4×D73C2418yes—
236C2×C4×D73C2418yes—
237C2×C4×D73C24116yes—
238C2×C4×D73C2414yes—
239C4⋊Dic73C24116yes—
240C4⋊Dic73C2418yes—
241C4⋊Dic73C24116yes—
242C4⋊Dic73C24116yes—
243#11924007C24116yes—
244#11924007C24116yes—
245#11924007C24116yes—
246#11924007C2418yes—
247#11924007C24116yes—
248#11924007C24116yes—
249#11924007C24116yes—
250#11924007C2418yes—
251C22⋊Dic73C24116yes—
252C22⋊Dic73C24116yes—
253C22⋊Dic73C24116yes—
254C22⋊Dic73C24116yes—
255C22⋊Dic73C24116yes—
256#11924005C2418yes—
257#11924005C2418yes—
258#11924005C24116yes—
259C4×Dic73C2414yes—
260C4×Dic73C2418yes—
261C4×Dic73C2418yes—
262C4×Dic73C2418yes—
263C4×Dic73C2414yes—
264C4×Dic73C24116yes—
265C4×Dic73C24116yes—
266C24×C73C2411yescharacteristic
267C24×C73C2414yes—
268C2×D4×C73—28no—
269C2×D4×C73—48no—
270C2×D4×C73—48no—
271C2×D4×C73C2418yes—
272C2×D4×C73C24116yes—
273C2×D4×C73C24116yes—
274C22×C4×C73—24no—
275C22×C4×C73—48no—
276C22×C4×C73C2412yes—
277C22×C4×C73C2412yes—
278C22×C4×C73C2411yescharacteristic
279C22×C4×C73C2414yes—
280C22×C4×C73C2414yes—
281C22×C4×C73C24116yes—
282C22×C4×C73C2411yescharacteristic
283C4⋊C4×C73C2418yes—
284C4⋊C4×C73C2418yes—
285C4⋊C4×C73C24116yes—
286C22⋊C4×C73C2418yes—
287C22⋊C4×C73C24116yes—
288C22⋊C4×C73C24116yes—
289C42×C73C2414yes—
290C42×C73C2414yes—
291C23×C73—22no—
292C23×C73—28no—
293C23×C73—28no—
294C23×C73—24no—
295C23×C73—28no—
296C23×C73C2518yes—
297C23×C73C2512yes—
298C23×C73C2511yescharacteristic
299C22×D73—24no—
300C22×D73—22no—
301C22×D73—24no—
302C22×D73C2×#4114yes—
303C22×D73C2512yes—
304C22×D73C2512yes—
305D4×C73—216no—
306D4×C73—416no—
307D4×C73—416no—
308C2×C4×C73—22no—
309C2×C4×C73—24no—
310C2×C4×C73—28no—
311C2×C4×C73—24no—
312C2×C4×C73—28no—
313C2×C4×C73—416no—
314C2×C4×C73C2×#4114yes—
315C2×C4×C73C2514yes—
316C2×C4×C73C2514yes—
317C2×C4×C73C2512yes—
318C2×C4×C73C2518yes—
319C2×C4×C73C2512yes—
320C22⋊D73—232no—
321C22⋊D73—28no—
322C22⋊D73—28no—
323C22⋊D73—416no—
324C2×Dic73—22no—
325C2×Dic73—28no—
326C2×Dic73—24no—
327C2×Dic73—28no—
328C2×Dic73—24no—
329C2×Dic73—232no—
330C2×Dic73—48no—
331C2×Dic73—416no—
332C2×Dic73C2×#4114yes—
333C2×Dic73C2514yes—
334C2×Dic73C2514yes—
335C2×Dic73C2518yes—
336C2×Dic73C2512yes—
337C2×Dic73C2518yes—
338C2×Dic73C2512yes—
339D292—28no—
340C4×D73—28no—
341C4×D73—48no—
342C4×D73—48no—
343C4×D73—416no—
344C4×D73C2×#41116yes—
345Dic146—216no—
346Dic146—28no—
347C22×C73—28no—
348C22×C73—22no—
349C22×C73—28no—
350C22×C73—24no—
351C22×C73—28no—
352C22×C73—44no—
353C22×C73—416no—
354C22×C73C22×#4112yes—
355C22×C73#58514yes—
356C22×C73C2611yescharacteristic
357C2×D73—24no—
358C2×D73—28no—
359C2×D73—22no—
360C2×D73—24no—
361C2×D73—44no—
362C2×D73C22×#4114yes—
363C4×C73—22no—
364C4×C73—24no—
365C4×C73—28no—
366C4×C73—24no—
367C4×C73C22×#4114yes—
368Dic73—22no—
369Dic73—28no—
370Dic73—24no—
371Dic73—28no—
372Dic73—24no—
373Dic73C22×#4114yes—
374C2×#3512—731nomaximal, Sylow
375C2×C73—48no—
376C2×C73—42no—
377C2×C73#351214yescomplemented
378C2×C73C23×#4111yescharacteristic
379C2×C73C2×#58512yes—
380D73—24no—
381D73—42no—
382#3512—7332no—
383C2×#553—734no—
384C2×#553—734no—
385C2×#553—734no—
386C2×#552—734no—
387C2×#541—731no—
388C2×#541—731no—
389C2×#540—731no—
390C2×#540D7311yescharacteristic, complemented
391C2×#537—732no—
392C2×#532—731no—
393C2×#529—732no—
394C2×#529—732no—
395C22×#125—731no—
396C2×#520—732no—
397C2×C4×#41—731no—
398C73C2×#351211yescharacteristic, complemented, Sylow
399C22×#41—732no—
400C22×#41—731no—
401#553—7364no—
402#553—7364no—
403#553—7364no—
404#552—7364no—
405#541—7316no—
406#541—7316no—
407#540—7316no—
408#540C2×D73116yescomplemented
409#537—7332no—
410#532—7316no—
411C2×C4⋊Q8—731no—
412C2×#127C2×D7311yescharacteristic
413#529—7332no—
414#529—7332no—
415C2×#126—734no—
416C2×#126—734no—
417C2×#126—734no—
418C2×#126—734no—
419C2×#125—7316no—
420C2×#125—732no—
421C2×#125—734no—
422C2×#125—734no—
423C2×#125—734no—
424C2×#125—731no—
425C2×#125C2×D7311yescharacteristic
426C2×#124—732no—
427C2×#123—734no—
428C2×#123—734no—
429C2×#123—734no—
430C2×#123C2×D7314yes—
431C2×C22⋊Q8—732no—
432C2×C22⋊Q8—732no—
433C2×C22⋊Q8—734no—
434C2×#121—732no—
435C2×#121—734no—
436C2×#121—734no—
437C2×#121—734no—
438C2×#121—734no—
439C2×#121—734no—
440C2×#121C2×D7312yes—
441C2×#121C2×D7314yes—
442#520—7332no—
443C4×#41—7316no—
444C2×C4×Q8—732no—
445C2×C4×Q8—732no—
446C2×C4×Q8—732no—
447C2×C4×D4—732no—
448C2×C4×D4—734no—
449C2×C4×D4—734no—
450C2×C4×D4—734no—
451C2×C4×D4—734no—
452C2×C4×D4—732no—
453C2×C4×D4—732no—
454C2×C4×D4—732no—
455C2×C4×D4—734no—
456C2×C4×D4C2×D7312yes—
457C2×#117—734no—
458C2×#117—734no—
459C2×#117—734no—
460C2×#117—731no—
461C2×#117—731no—
462C2×#117C2×D7311yescharacteristic
463C22×C4⋊C4—734no—
464C22×C4⋊C4—732no—
465C22×C4⋊C4—734no—
466C22×C42—731no—
467C22×C42—731no—
468C22×C42—731no—
469C2×#41—7316no—
470C2×#41—738no—
471C2×#41—1468no—
472C2×#41—14616no—
473C22×Q8—731no—
474C22×Q8—732no—
475C22×D4—734no—
476C22×D4—731no—
477C22×D4—734no—
478C22×D4—731no—
479C22×D4—731no—
480C22×D4C22×D7312yes—
481C22×D4C22×D7314yes—
482C22×D4C22×D7314yes—
483C23×C4—734no—
484C23×C4—732no—
485C23×C4—734no—
486C23×C4—732no—
487C23×C4—732no—
488C23×C4—731no—
489C23×C4—734no—
490C23×C4—731no—
491C23×C4C22×D7311yescharacteristic
492C23×C4C22×D7314yes—
493C4⋊Q8—738no—
494#127C22×D7318yes—
495#126—7332no—
496#126—7332no—
497#126—7332no—
498#126—7332no—
499#125—7316no—
500#125—7332no—
501#125—7332no—
502#125—7332no—
503#125—738no—
504#125C22×D7318yes—
505#124—7316no—
506#123—7332no—
507#123—7332no—
508#123—7332no—
509#123C22×D73132yes—
510C22⋊Q8—7316no—
511C22⋊Q8—7316no—
512C22⋊Q8—7332no—
513#121—7316no—
514#121—7332no—
515#121—7332no—
516#121—7332no—
517#121—7332no—
518#121—7332no—
519#121C22×D73116yes—
520#121C22×D73132yes—
521C4×Q8—7316no—
522C4×Q8—7316no—
523C4×Q8—7316no—
524C4×D4—7316no—
525C4×D4—7332no—
526C4×D4—7332no—
527C4×D4—7332no—
528C4×D4—7332no—
529C4×D4—7316no—
530C4×D4—7316no—
531C4×D4—7316no—
532C4×D4—7332no—
533C4×D4C22×D73116yes—
534#117—7332no—
535#117—7332no—
536#117—7332no—
537#117—738no—
538#117—738no—
539#117C22×D7318yes—
540C2×C4⋊C4—732no—
541C2×C4⋊C4—734no—
542C2×C4⋊C4—734no—
543C2×C4⋊C4—734no—
544C2×C4⋊C4—732no—
545C2×C4⋊C4—734no—
546C2×C4⋊C4—734no—
547C2×C4⋊C4—7332no—
548C2×C4⋊C4—734no—
549C2×C4⋊C4—732no—
550C2×C4⋊C4—734no—
551C2×C4⋊C4—734no—
552C2×C4⋊C4—734no—
553C2×C4⋊C4—7316no—
554C2×C4⋊C4—7332no—
555C2×C4⋊C4C22×D7312yes—
556C2×C4⋊C4C22×D7314yes—
557C2×C4⋊C4C22×D7312yes—
558C2×C22⋊C4—734no—
559C2×C22⋊C4—734no—
560C2×C22⋊C4—734no—
561C2×C22⋊C4—734no—
562C2×C22⋊C4—734no—
563C2×C22⋊C4—732no—
564C2×C22⋊C4—732no—
565C2×C22⋊C4—734no—
566C2×C22⋊C4C22×D7314yes—
567C2×C22⋊C4C22×D7314yes—
568C2×C22⋊C4C22×D7312yes—
569C2×C42—731no—
570C2×C42—734no—
571C2×C42—734no—
572C2×C42—732no—
573C2×C42—732no—
574C2×C42—732no—
575C2×C42—738no—
576C2×C42—731no—
577C2×C42—738no—
578C2×C42—738no—
579C2×C42C22×D7311yescharacteristic
580C2×C42C22×D7311yescharacteristic
581C24—731no—
582C24—731no—
583C24C23×D7311yescharacteristic
584C24C23×D7314yes—
585#41—14632no—
586#41—14664no—
587C2×Q8—734no—
588C2×Q8—738no—
589C2×Q8—1464no—
590C2×Q8—1468no—
591C2×D4—28no—
592C2×D4—48no—
593C2×D4—48no—
594C2×D4—2928no—
595C2×D4—7316no—
596C2×D4—734no—
597C2×D4—734no—
598C2×D4—7316no—
599C2×D4—734no—
600C2×D4—1464no—
601C2×D4—1464no—
602C2×D4—1464no—
603C2×D4—14616no—
604C2×D4C23×D7318yes—
605C2×D4C23×D73116yes—
606C2×D4C23×D73116yes—
607C22×C4—24no—
608C22×C4—48no—
609C22×C4—2924no—
610C22×C4—2928no—
611C22×C4—2924no—
612C22×C4—2924no—
613C22×C4—2928no—
614C22×C4—738no—
615C22×C4—7316no—
616C22×C4—738no—
617C22×C4—738no—
618C22×C4—7316no—
619C22×C4—731no—
620C22×C4—738no—
621C22×C4—734no—
622C22×C4—7316no—
623C22×C4—732no—
624C22×C4—732no—
625C22×C4—734no—
626C22×C4—731no—
627C22×C4—734no—
628C22×C4—734no—
629C22×C4—14616no—
630C22×C4—1464no—
631C22×C4C23×D7314yes—
632C22×C4C23×D7312yes—
633C22×C4C23×D7311yescharacteristic
634C22×C4C23×D7312yes—
635C22×C4C23×D7314yes—
636C22×C4C23×D73116yes—
637C22×C4C23×D7311yescharacteristic
638C4⋊C4—738no—
639C4⋊C4—7316no—
640C4⋊C4—7316no—
641C4⋊C4—7316no—
642C4⋊C4—7316no—
643C4⋊C4—7316no—
644C4⋊C4—738no—
645C4⋊C4—7316no—
646C4⋊C4—7316no—
647C4⋊C4—738no—
648C4⋊C4—7316no—
649C4⋊C4—7316no—
650C4⋊C4C23×D7318yes—
651C4⋊C4C23×D73116yes—
652C4⋊C4C23×D7318yes—
653C22⋊C4—7316no—
654C22⋊C4—7316no—
655C22⋊C4—7316no—
656C22⋊C4—7316no—
657C22⋊C4—7316no—
658C22⋊C4—738no—
659C22⋊C4—738no—
660C22⋊C4—7316no—
661C22⋊C4C23×D73116yes—
662C22⋊C4C23×D73116yes—
663C22⋊C4C23×D7318yes—
664C42—734no—
665C42—734no—
666C42—738no—
667C42—738no—
668C42—738no—
669C42—7316no—
670C42—7316no—
671C42C23×D7314yes—
672C42C23×D7314yes—
673C23—22no—
674C23—28no—
675C23—28no—
676C23—24no—
677C23—28no—
678C23—734no—
679C23—732no—
680C23—732no—
681C23—1462no—
682C23—1464no—
683C23—1464no—
684C23C24×D7312yes—
685C23C24×D7318yes—
686C23C24×D7311yescharacteristic
687Q8—1468no—
688Q8—14616no—
689D4—216no—
690D4—416no—
691D4—416no—
692D4—29216no—
693D4—1468no—
694D4—1468no—
695D4—1468no—
696D4—14632no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—28no—
700C2×C4—24no—
701C2×C4—28no—
702C2×C4—416no—
703C2×C4—2928no—
704C2×C4—29216no—
705C2×C4—2928no—
706C2×C4—2928no—
707C2×C4—29216no—
708C2×C4—734no—
709C2×C4—732no—
710C2×C4—7316no—
711C2×C4—734no—
712C2×C4—734no—
713C2×C4—732no—
714C2×C4—738no—
715C2×C4—738no—
716C2×C4—14632no—
717C2×C4—1468no—
718C2×C4—1462no—
719C2×C4—1464no—
720C2×C4—1464no—
721C2×C4—1468no—
722C2×C4—1468no—
723C2×C4#41×D7314yes—
724C2×C4C24×D7314yes—
725C2×C4C24×D7312yes—
726C2×C4C24×D7314yes—
727C2×C4C24×D7318yes—
728C2×C4C24×D7312yes—
729C22—22no—
730C22—28no—
731C22—28no—
732C22—24no—
733C22—28no—
734C22—44no—
735C22—416no—
736C22—2924no—
737C22—734no—
738C22—1462no—
739C22—1464no—
740C22—1468no—
741C22—1464no—
742C22C2×#41×D7312yes—
743C22#1798942214yes—
744C22C25×D7311yescharacteristic
745C4—22no—
746C4—24no—
747C4—28no—
748C4—24no—
749C4—734no—
750C4—1468no—
751C4—1462no—
752C4—1464no—
753C4—1464no—
754C4—1468no—
755C4C2×#41×D7314yes—
756C2—42no—
757C2—48no—
758C2—2922no—
759C2—1464no—
760C2#2262385014yesdirect product factor
761C2C22×#41×D7311yescharacteristic
762C2C2×#1798942212yes—
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#540×C73C2
socleC23×C73C25
hypercenterC2×#540D73
hypocenterC73C2×#3512
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. #22623850C2direct (N × H)
2. C2×#17989284C2semidirect
3. C2×#17989282C2semidirect
4. C2×#17989280C2semidirect
5. C2×#17989274C2semidirect
6. C2×#17989200C2semidirect
7. C2×#17989199C2semidirect
8. C2×#17989191C2semidirect
9. C2×#17989166C2semidirect
10. C2×#17989135C2semidirect
11. C2×#17989119C2semidirect
12. C2×#17989118C2semidirect
13. C2×#125×D73C2semidirect
14. C2×#17989066C2semidirect
15. C2×#17989055C2semidirect
16. C2×#540×C73C2semidirect
19. #17989284C22semidirect
20. #17989282C22semidirect
21. #17989280C22semidirect
22. #17989274C22semidirect
23. #17989200C22semidirect
24. #17989199C22semidirect
25. #17989191C22semidirect
26. #17989166C22semidirect
27. #17989135C22semidirect
29. #17989119C22semidirect
30. #17989118C22semidirect
40. #125×D73C22semidirect
54. #17989066C22semidirect
55. #17989055C22semidirect
79. #540×C73C22semidirect
377. C2×C73#3512semidirect
390. C2×#540D73semidirect
398. C73C2×#3512semidirect
408. #540C2×D73semidirect
760. C2#22623850direct (N × H)

Maximal subgroups

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

subgroupindex
#226238502
C2×#179892842
C2×#179892822
C2×#179892802
C2×#179892742
C2×#179892002
C2×#179891992
C2×#179891912
C2×#179891662
C2×#179891352
C2×#179891192
C2×#179891182
C2×#125×D732
C2×#179890662
C2×#179890552
C2×#540×C732
C2×#351273