Finite Group Databasebeta

← C2×#22624423 #33993819

Subgroups — C2×#22624423 #33993819

Order 18688.

6338 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624423C2132yesmaximal, direct product factor
2C2×C73⋊#564C214yesmaximal, complemented
3C2×#17989316C211yesmaximal, characteristic, complemented
4C2×#17989315C211yesmaximal, characteristic, complemented
5C2×#17989315C212yesmaximal, complemented
6C2×#17989314C212yesmaximal, complemented
7C2×#17989313C212yesmaximal, complemented
8C2×#17989312C211yesmaximal, characteristic, complemented
9C2×#17989312C212yesmaximal, complemented
10C2×#17989200C212yesmaximal
11C2×#17989198C212yesmaximal
12C2×#17989196C214yesmaximal
13C2×#17989195C212yesmaximal
14C2×#17989195C212yesmaximal
15C2×#17989142C211yesmaximal, characteristic
16C2×#17989141C211yesmaximal, characteristic
17C2×#17989141C211yesmaximal, characteristic
18C2×#557×C73C211yesmaximal, characteristic, complemented
19C73⋊#564C22164yescomplemented
20#17989316C22116yescomplemented
21#17989315C22116yescomplemented
22#17989315C22132yescomplemented
23#17989314C22132yescomplemented
24#17989313C22132yescomplemented
25#17989312C22116yescomplemented
26#17989312C22132yescomplemented
27#17989200C22132yes—
28#17989198C22132yes—
29#17989196C22164yes—
30#17989195C22132yes—
31#17989195C22132yes—
32#17989142C22116yes—
33#17989141C22116yes—
34#17989141C22116yes—
35C2×#14556591C2212yes—
36C2×#14556591C2211yescharacteristic
37C2×#14556590C2211yescharacteristic
38C2×#14556590C2214yes—
39C2×#14556590C2211yescharacteristic
40C2×#14556589C2212yes—
41C2×#14556589C2211yescharacteristic
42C2×#14556589C2212yes—
43C2×#14556589C2211yescharacteristic
44C2×#14556586C2214yes—
45C2×#14556586C2214yes—
46C2×#14556586C2214yes—
47C2×#14556585C2214yes—
48C2×#14556583C2212yes—
49C2×#14556583C2214yes—
50C2×#14556583C2214yes—
51C2×#14556582C2212yes—
52C2×#14556582C2214yes—
53C2×#14556582C2212yes—
54C2×#14556582C2214yes—
55C2×#14556582C2214yes—
56C2×#14556582C2212yes—
57C2×#14556581C2214yes—
58C2×#14556581C2214yes—
59C2×#14556581C2214yes—
60C2×#14556581C2214yes—
61C2×#14556581C2214yes—
62C2×#14556581C2214yes—
63C2×#14556581C2214yes—
64C2×#14556581C2212yes—
65C2×#14556581C2212yes—
66C2×#14556571C2211yescharacteristic
67C2×#14556571C2212yes—
68C2×#14556571C2211yescharacteristic
69C2×#14556569C2212yes—
70C2×#14556569C2212yes—
71C2×#14556567C2211yescharacteristic
72C2×#14556567C2212yes—
73C2×#14556567C2211yescharacteristic
74C2×Q8×Dic73C2212yes—
75C2×Q8×Dic73C2212yes—
76C2×Q8×Dic73C2212yes—
77C2×C4×Dic146C2212yes—
78C2×C4×Dic146C2212yes—
79C2×C4×Dic146C2211yescharacteristic
80C2×C4×Dic146C2211yescharacteristic
81C2×C4×Dic146C2214yes—
82C2×C4×Dic146C2212yes—
83C2×C4×Dic146C2212yes—
84C2×#14556556C2214yes—
85C2×#14556556C2212yes—
86C2×#14556556C2212yes—
87C2×#14556556C2212yes—
88C2×#14556549C2212yes—
89C2×#14556548C2212yes—
90C2×#14556548C2212yes—
91C2×C42×D73C2211yescharacteristic
92#557×C73C22116yescomplemented
93C2×C4⋊Q8×C73C2212yes—
94C2×C4⋊Q8×C73C2211yescharacteristic
95C2×#125×C73C2212yes—
96C2×#125×C73C2214yes—
97C2×C4×Q8×C73C2212yes—
98C2×C4×Q8×C73C2212yes—
99C2×C4×Q8×C73C2211yescharacteristic
100C2×C4×Q8×C73C2211yescharacteristic
101C22×Dic146C2311yescharacteristic
102C22×Dic146C2312yes—
103C22×Dic146C2311yescharacteristic
104C22×Dic146C2312yes—
105C22×Dic146C2312yes—
106C22×C4×D73C2311yescharacteristic
107C22×C4×D73C2311yescharacteristic
108C22×C4×D73C2311yescharacteristic
109#14556591C2318yes—
110#14556591C23116yes—
111#14556590C2318yes—
112#14556590C2318yes—
113#14556590C23132yes—
114#14556589C2318yes—
115#14556589C2318yes—
116#14556589C23116yes—
117#14556589C23116yes—
118#14556586C23132yes—
119#14556586C23132yes—
120#14556586C23132yes—
121#14556585C23132yes—
122#14556583C23132yes—
123#14556583C23132yes—
124#14556583C23116yes—
125#14556582C23116yes—
126#14556582C23116yes—
127#14556582C23116yes—
128#14556582C23132yes—
129#14556582C23132yes—
130#14556582C23132yes—
131#14556581C23116yes—
132#14556581C23116yes—
133#14556581C23132yes—
134#14556581C23132yes—
135#14556581C23132yes—
136#14556581C23132yes—
137#14556581C23132yes—
138#14556581C23132yes—
139#14556581C23132yes—
140#14556571C2318yes—
141#14556571C2318yes—
142#14556571C23116yes—
143#14556569C23116yes—
144#14556569C23116yes—
145#14556567C2318yes—
146#14556567C2318yes—
147#14556567C23116yes—
148Q8×Dic73C23116yes—
149Q8×Dic73C23116yes—
150Q8×Dic73C23116yes—
151C4×Dic146C23116yes—
152C4×Dic146C2318yes—
153C4×Dic146C2318yes—
154C4×Dic146C23116yes—
155C4×Dic146C23116yes—
156C4×Dic146C23116yes—
157C4×Dic146C23132yes—
158#14556556C23116yes—
159#14556556C23132yes—
160#14556556C23116yes—
161#14556556C23116yes—
162#14556549C23116yes—
163#14556548C23116yes—
164#14556548C23116yes—
165C2×C4⋊Dic73C2311yescharacteristic
166C2×C4⋊Dic73C2311yescharacteristic
167C2×C4⋊Dic73C2314yes—
168C2×C4⋊Dic73C2312yes—
169C2×C4⋊Dic73C2312yes—
170C2×C4⋊Dic73C2314yes—
171C2×C4⋊Dic73C2314yes—
172C2×C4⋊Dic73C2312yes—
173C2×C4⋊Dic73C2312yes—
174C2×C4⋊Dic73C2314yes—
175C2×#11924007C2312yes—
176C2×#11924007C2312yes—
177C2×#11924007C2312yes—
178C2×#11924007C2314yes—
179C2×#11924007C2314yes—
180C2×#11924007C2312yes—
181C2×#11924007C2314yes—
182C2×#11924007C2314yes—
183C2×#11924007C2312yes—
184C2×#11924007C2312yes—
185C2×#11924007C2314yes—
186C2×#11924007C2314yes—
187C2×#11924007C2314yes—
188C2×#11924007C2312yes—
189C2×#11924007C2312yes—
190C2×#11924007C2312yes—
191C2×#11924007C2312yes—
192C2×#11924005C2312yes—
193C2×#11924005C2312yes—
194C2×#11924005C2312yes—
195C2×#11924005C2312yes—
196C2×#11924005C2314yes—
197C2×C4×Dic73C2311yescharacteristic
198C2×C4×Dic73C2311yescharacteristic
199C2×C4×Dic73C2312yes—
200C2×C4×Dic73C2312yes—
201C2×C4×Dic73C2314yes—
202C2×C4×Dic73C2311yescharacteristic
203C2×C4×Dic73C2314yes—
204C2×C4×Dic73C2314yes—
205C2×C4×Dic73C2314yes—
206C42×D73C2318yes—
207C22×Q8×C73C2311yescharacteristic
208C22×Q8×C73C2312yes—
209C22×Q8×C73C2311yescharacteristic
210C4⋊Q8×C73C2318yes—
211C4⋊Q8×C73C23116yes—
212#125×C73C23132yes—
213#125×C73C23116yes—
214C4×Q8×C73C2318yes—
215C4×Q8×C73C2318yes—
216C4×Q8×C73C23116yes—
217C4×Q8×C73C23116yes—
218C2×C4⋊C4×C73C2311yescharacteristic
219C2×C4⋊C4×C73C2311yescharacteristic
220C2×C4⋊C4×C73C2314yes—
221C2×C4⋊C4×C73C2312yes—
222C2×C4⋊C4×C73C2312yes—
223C2×C4⋊C4×C73C2312yes—
224C2×C4⋊C4×C73C2314yes—
225C2×C4⋊C4×C73C2312yes—
226C2×C4⋊C4×C73C2314yes—
227C2×C42×C73C2312yes—
228C2×C42×C73C2311yescharacteristic
229C2×C42×C73C2314yes—
230C2×C42×C73C2312yes—
231C23×D73C2411yescharacteristic
232C2×Dic146—24no—
233C2×Dic146—28no—
234C2×Dic146—24no—
235C2×Dic146—28no—
236C2×Dic146—28no—
237C2×Dic146C2418yes—
238C2×Dic146C2418yes—
239C2×Dic146C2414yes—
240C2×Dic146C2418yes—
241C2×Dic146C2414yes—
242C22×Dic73C2412yes—
243C22×Dic73C2412yes—
244C22×Dic73C2412yes—
245C22×Dic73C2412yes—
246C22×Dic73C2414yes—
247C22×Dic73C2411yescharacteristic
248C22×Dic73C2411yescharacteristic
249C22×Dic73C2411yescharacteristic
250C2×C4×D73—24no—
251C2×C4×D73—24no—
252C2×C4×D73—24no—
253C2×C4×D73C2414yes—
254C2×C4×D73C2414yes—
255C2×C4×D73C2414yes—
256C4⋊Dic73C2418yes—
257C4⋊Dic73C2414yes—
258C4⋊Dic73C2418yes—
259C4⋊Dic73C2414yes—
260C4⋊Dic73C2418yes—
261C4⋊Dic73C2418yes—
262C4⋊Dic73C24116yes—
263C4⋊Dic73C24116yes—
264C4⋊Dic73C24116yes—
265C4⋊Dic73C24116yes—
266#11924007C2418yes—
267#11924007C2418yes—
268#11924007C2418yes—
269#11924007C2418yes—
270#11924007C2418yes—
271#11924007C24116yes—
272#11924007C24116yes—
273#11924007C24116yes—
274#11924007C24116yes—
275#11924007C2418yes—
276#11924007C2418yes—
277#11924007C2418yes—
278#11924007C2418yes—
279#11924007C2418yes—
280#11924007C24116yes—
281#11924007C24116yes—
282#11924007C24116yes—
283#11924005C2418yes—
284#11924005C2418yes—
285#11924005C2418yes—
286#11924005C2418yes—
287#11924005C24116yes—
288C4×Dic73C2414yes—
289C4×Dic73C2414yes—
290C4×Dic73C2414yes—
291C4×Dic73C2418yes—
292C4×Dic73C2418yes—
293C4×Dic73C24116yes—
294C4×Dic73C24116yes—
295C4×Dic73C24116yes—
296C4×Dic73C24116yes—
297C2×Q8×C73—28no—
298C2×Q8×C73—24no—
299C2×Q8×C73—24no—
300C2×Q8×C73C2414yes—
301C2×Q8×C73C2414yes—
302C2×Q8×C73C2418yes—
303C22×C4×C73C2412yes—
304C22×C4×C73C2412yes—
305C22×C4×C73C2412yes—
306C22×C4×C73C2411yescharacteristic
307C22×C4×C73C2412yes—
308C22×C4×C73C2414yes—
309C22×C4×C73C2411yescharacteristic
310C22×C4×C73C2411yescharacteristic
311C4⋊C4×C73C2414yes—
312C4⋊C4×C73C2414yes—
313C4⋊C4×C73C2418yes—
314C4⋊C4×C73C2418yes—
315C4⋊C4×C73C24116yes—
316C4⋊C4×C73C2418yes—
317C4⋊C4×C73C24116yes—
318C4⋊C4×C73C2418yes—
319C4⋊C4×C73C24116yes—
320C42×C73C2418yes—
321C42×C73C24116yes—
322C42×C73C2414yes—
323C42×C73C2418yes—
324C23×C73C2511yescharacteristic
325C22×D73—22no—
326C22×D73—22no—
327C22×D73—22no—
328C22×D73C2512yes—
329Q8×C73—28no—
330Q8×C73—216no—
331Q8×C73—28no—
332C2×C4×C73—24no—
333C2×C4×C73—28no—
334C2×C4×C73—24no—
335C2×C4×C73—22no—
336C2×C4×C73—24no—
337C2×C4×C73—24no—
338C2×C4×C732−1+414yes—
339C2×C4×C732−1+414yes—
340C2×C4×C73C2514yes—
341C2×C4×C73C2514yes—
342C2×C4×C73C2514yes—
343C2×C4×C73C2512yes—
344C2×C4×C73C2514yes—
345C2×C4×C73C2518yes—
346C2×C4×C73C2512yes—
347C2×C4×C73C2512yes—
348C2×Dic73—22no—
349C2×Dic73—22no—
350C2×Dic73—24no—
351C2×Dic73—24no—
352C2×Dic73—24no—
353C2×Dic73—24no—
354C2×Dic73—28no—
355C2×Dic732−1+414yes—
356C2×Dic73C2514yes—
357C2×Dic73C2514yes—
358C2×Dic73C2514yes—
359C2×Dic73C2514yes—
360C2×Dic73C2518yes—
361C2×Dic73C2512yes—
362C2×Dic73C2512yes—
363C2×Dic73C2512yes—
364C4×D73—28no—
365C4×D73—28no—
366C4×D73—28no—
367Dic146—28no—
368Dic146—216no—
369Dic146—28no—
370Dic146—216no—
371Dic146—216no—
372C22×C73C2×2−1+412yes—
373C22×C73C2×2−1+412yes—
374C22×C73C2×2−1+412yes—
375C22×C73C2611yescharacteristic
376C2×D73—22no—
377C2×D73—22no—
378C2×D73—22no—
379C2×D73—44no—
380C4×C73—24no—
381C4×C73—24no—
382C4×C73—22no—
383C4×C73—24no—
384C4×C73—28no—
385C4×C73—24no—
386C4×C73C2×2−1+414yes—
387C4×C73C2×2−1+414yes—
388Dic73—24no—
389Dic73—24no—
390Dic73—24no—
391Dic73—24no—
392Dic73—28no—
393Dic73—22no—
394Dic73—22no—
395Dic73C2×2−1+414yes—
396C2×#3556—731nomaximal, Sylow
397C2×C73#355614yescomplemented
398C2×C73C22×2−1+411yescharacteristic
399C2×C73C22×2−1+411yescharacteristic
400C2×C73C22×2−1+411yescharacteristic
401D73—42no—
402#3556—7332no—
403C2×#564—734no—
404C2×#557—732no—
405C2×#557—731no—
406C2×#557—732no—
407C2×#557—732no—
408C2×#557—732no—
409C2×#557—731no—
410C2×#557—731no—
411C2×#557D7311yescharacteristic, complemented
412C2×#541—732no—
413C2×#541—734no—
414C2×#541—732no—
415C2×#541—732no—
416C2×#541—732no—
417C2×#533—731no—
418C2×#533—731no—
419C2×#533—731no—
420C73C2×#355611yescharacteristic, complemented, Sylow
421#564—7364no—
422#557—7332no—
423#557—7316no—
424#557—7332no—
425#557—7332no—
426#557—7332no—
427#557—7316no—
428#557—7316no—
429#557C2×D73116yescomplemented
430#541—7332no—
431#541—7364no—
432#541—7332no—
433#541—7332no—
434#541—7332no—
435#533—7316no—
436#533—7316no—
437#533—7316no—
438C2×C4⋊Q8—731no—
439C2×C4⋊Q8—731no—
440C2×C4⋊Q8—732no—
441C2×C4⋊Q8—732no—
442C2×C4⋊Q8—731no—
443C2×C4⋊Q8—731no—
444C2×C4⋊Q8—734no—
445C2×C4⋊Q8—731no—
446C2×C4⋊Q8—732no—
447C2×C4⋊Q8C2×D7311yescharacteristic
448C2×C4⋊Q8C2×D7312yes—
449C2×#126—734no—
450C2×#126—734no—
451C2×#126—734no—
452C2×#126—734no—
453C2×#125—732no—
454C2×#125—732no—
455C2×#125—732no—
456C2×#125—734no—
457C2×#125—732no—
458C2×#125—732no—
459C2×#125—734no—
460C2×#125—734no—
461C2×#125—734no—
462C2×#125—734no—
463C2×#125—734no—
464C2×#125—734no—
465C2×#125—734no—
466C2×#125—734no—
467C2×#125—734no—
468C2×#125—732no—
469C2×#125—734no—
470C2×#125—734no—
471C2×#125C2×D7312yes—
472C2×#125C2×D7314yes—
473C2×C22⋊Q8—732no—
474C2×C22⋊Q8—731no—
475C2×C22⋊Q8—731no—
476C2×C22⋊Q8—732no—
477C2×C22⋊Q8—732no—
478C2×C22⋊Q8—732no—
479C2×C22⋊Q8—731no—
480C2×C22⋊Q8—731no—
481C2×C4×Q8—732no—
482C2×C4×Q8—732no—
483C2×C4×Q8—732no—
484C2×C4×Q8—732no—
485C2×C4×Q8—734no—
486C2×C4×Q8—732no—
487C2×C4×Q8—732no—
488C2×C4×Q8—731no—
489C2×C4×Q8—731no—
490C2×C4×Q8—732no—
491C2×C4×Q8—732no—
492C2×C4×Q8—734no—
493C2×C4×Q8—732no—
494C2×C4×Q8—732no—
495C2×C4×Q8C2×D7311yescharacteristic
496C2×C4×Q8C2×D7311yescharacteristic
497C2×C4×Q8C2×D7312yes—
498C2×C4×Q8C2×D7312yes—
499C2×#117—732no—
500C2×#117—732no—
501C2×#117—732no—
502C22×C42—731no—
503C22×Q8—732no—
504C22×Q8—732no—
505C22×Q8—731no—
506C22×Q8—732no—
507C22×Q8—731no—
508C22×Q8C22×D7312yes—
509C22×Q8C22×D7311yescharacteristic
510C22×Q8C22×D7311yescharacteristic
511C23×C4—731no—
512C23×C4—731no—
513C23×C4—731no—
514C4⋊Q8—738no—
515C4⋊Q8—738no—
516C4⋊Q8—7316no—
517C4⋊Q8—7316no—
518C4⋊Q8—738no—
519C4⋊Q8—738no—
520C4⋊Q8—7332no—
521C4⋊Q8—738no—
522C4⋊Q8—7316no—
523C4⋊Q8C22×D7318yes—
524C4⋊Q8C22×D73116yes—
525#126—7332no—
526#126—7332no—
527#126—7332no—
528#126—7332no—
529#125—7316no—
530#125—7316no—
531#125—7316no—
532#125—7332no—
533#125—7316no—
534#125—7316no—
535#125—7332no—
536#125—7332no—
537#125—7332no—
538#125—7332no—
539#125—7332no—
540#125—7332no—
541#125—7332no—
542#125—7332no—
543#125—7332no—
544#125—7316no—
545#125—7332no—
546#125—7332no—
547#125C22×D73116yes—
548#125C22×D73132yes—
549C22⋊Q8—7316no—
550C22⋊Q8—738no—
551C22⋊Q8—738no—
552C22⋊Q8—7316no—
553C22⋊Q8—7316no—
554C22⋊Q8—7316no—
555C22⋊Q8—738no—
556C22⋊Q8—738no—
557C4×Q8—7316no—
558C4×Q8—7316no—
559C4×Q8—7316no—
560C4×Q8—7316no—
561C4×Q8—7332no—
562C4×Q8—7316no—
563C4×Q8—7316no—
564C4×Q8—7316no—
565C4×Q8—7316no—
566C4×Q8—738no—
567C4×Q8—738no—
568C4×Q8—7332no—
569C4×Q8—7316no—
570C4×Q8—7316no—
571C4×Q8C22×D7318yes—
572C4×Q8C22×D7318yes—
573C4×Q8C22×D73116yes—
574C4×Q8C22×D73116yes—
575#117—7316no—
576#117—7316no—
577#117—7316no—
578C2×C4⋊C4—732no—
579C2×C4⋊C4—732no—
580C2×C4⋊C4—732no—
581C2×C4⋊C4—732no—
582C2×C4⋊C4—732no—
583C2×C4⋊C4—732no—
584C2×C4⋊C4—732no—
585C2×C4⋊C4—732no—
586C2×C4⋊C4—731no—
587C2×C4⋊C4—731no—
588C2×C4⋊C4—732no—
589C2×C4⋊C4—732no—
590C2×C4⋊C4—734no—
591C2×C4⋊C4—732no—
592C2×C4⋊C4—732no—
593C2×C4⋊C4—734no—
594C2×C4⋊C4—732no—
595C2×C4⋊C4—732no—
596C2×C4⋊C4—734no—
597C2×C4⋊C4—734no—
598C2×C4⋊C4—734no—
599C2×C4⋊C4—734no—
600C2×C4⋊C4—734no—
601C2×C4⋊C4—734no—
602C2×C4⋊C4—734no—
603C2×C4⋊C4—734no—
604C2×C4⋊C4—734no—
605C2×C4⋊C4C22×D7312yes—
606C2×C4⋊C4C22×D7312yes—
607C2×C4⋊C4C22×D7311yescharacteristic
608C2×C4⋊C4C22×D7314yes—
609C2×C4⋊C4C22×D7311yescharacteristic
610C2×C4⋊C4C22×D7312yes—
611C2×C4⋊C4C22×D7312yes—
612C2×C4⋊C4C22×D7314yes—
613C2×C4⋊C4C22×D7314yes—
614C2×C22⋊C4—734no—
615C2×C22⋊C4—732no—
616C2×C22⋊C4—732no—
617C2×C22⋊C4—732no—
618C2×C22⋊C4—732no—
619C2×C42—734no—
620C2×C42—732no—
621C2×C42—732no—
622C2×C42—731no—
623C2×C42—731no—
624C2×C42—734no—
625C2×C42—734no—
626C2×C42—734no—
627C2×C42—731no—
628C2×C42—738no—
629C2×C42C22×D7312yes—
630C2×C42C22×D7312yes—
631C2×C42C22×D7311yescharacteristic
632C2×C42C22×D7314yes—
633C24—731no—
634C2×Q8—28no—
635C2×Q8—24no—
636C2×Q8—24no—
637C2×Q8—738no—
638C2×Q8—738no—
639C2×Q8—734no—
640C2×Q8—738no—
641C2×Q8—734no—
642C2×Q8—1468no—
643C2×Q8—1468no—
644C2×Q8—1464no—
645C2×Q8—1468no—
646C2×Q8—1464no—
647C2×Q8C23×D7318yes—
648C2×Q8C23×D7314yes—
649C2×Q8C23×D7314yes—
650C22×C4—731no—
651C22×C4—732no—
652C22×C4—732no—
653C22×C4—732no—
654C22×C4—732no—
655C22×C4—734no—
656C22×C4—731no—
657C22×C4—731no—
658C22×C4—734no—
659C22×C4—734no—
660C22×C4—734no—
661C22×C4—1464no—
662C22×C4—1464no—
663C22×C4—1464no—
664C22×C4C23×D7314yes—
665C22×C4C23×D7312yes—
666C22×C4C23×D7312yes—
667C22×C4C23×D7311yescharacteristic
668C22×C4C23×D7312yes—
669C22×C4C23×D7312yes—
670C22×C4C23×D7311yescharacteristic
671C22×C4C23×D7311yescharacteristic
672C4⋊C4—738no—
673C4⋊C4—738no—
674C4⋊C4—738no—
675C4⋊C4—738no—
676C4⋊C4—738no—
677C4⋊C4—738no—
678C4⋊C4—738no—
679C4⋊C4—738no—
680C4⋊C4—7316no—
681C4⋊C4—738no—
682C4⋊C4—738no—
683C4⋊C4—7316no—
684C4⋊C4—7316no—
685C4⋊C4—7316no—
686C4⋊C4—7316no—
687C4⋊C4—7316no—
688C4⋊C4—7316no—
689C4⋊C4—738no—
690C4⋊C4—738no—
691C4⋊C4—734no—
692C4⋊C4—734no—
693C4⋊C4—7316no—
694C4⋊C4—738no—
695C4⋊C4—738no—
696C4⋊C4—7316no—
697C4⋊C4—7316no—
698C4⋊C4—7316no—
699C4⋊C4C23×D7318yes—
700C4⋊C4C23×D7318yes—
701C4⋊C4C23×D7314yes—
702C4⋊C4C23×D73116yes—
703C4⋊C4C23×D7314yes—
704C4⋊C4C23×D7318yes—
705C4⋊C4C23×D7318yes—
706C4⋊C4C23×D73116yes—
707C4⋊C4C23×D73116yes—
708C22⋊C4—738no—
709C22⋊C4—7316no—
710C22⋊C4—738no—
711C22⋊C4—738no—
712C22⋊C4—738no—
713C42—734no—
714C42—734no—
715C42—734no—
716C42—7316no—
717C42—738no—
718C42—738no—
719C42—7316no—
720C42—7316no—
721C42—7316no—
722C42C23×D7314yes—
723C42C23×D7318yes—
724C42C23×D7318yes—
725C42C23×D73116yes—
726C23—732no—
727C23—1462no—
728C23—1462no—
729C23—1462no—
730C23C24×D7311yescharacteristic
731Q8—216no—
732Q8—28no—
733Q8—28no—
734Q8—14616no—
735Q8—14616no—
736Q8—1468no—
737Q8—14616no—
738Q8—1468no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—28no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—734no—
746C2×C4—732no—
747C2×C4—734no—
748C2×C4—734no—
749C2×C4—734no—
750C2×C4—734no—
751C2×C4—738no—
752C2×C4—732no—
753C2×C4—732no—
754C2×C4—1468no—
755C2×C4—1464no—
756C2×C4—1464no—
757C2×C4—1462no—
758C2×C4—1464no—
759C2×C4—1462no—
760C2×C4—1464no—
761C2×C4—1468no—
762C2×C4—1468no—
763C2×C4—1468no—
764C2×C4#1455663814yes—
765C2×C4#1455663914yes—
766C2×C4C24×D7318yes—
767C2×C4C24×D7314yes—
768C2×C4C24×D7314yes—
769C2×C4C24×D7312yes—
770C2×C4C24×D7314yes—
771C2×C4C24×D7314yes—
772C2×C4C24×D7312yes—
773C2×C4C24×D7312yes—
774C22—2924no—
775C22—1462no—
776C22—1462no—
777C22—1462no—
778C222−1+4×D7312yes—
779C22C2×#1455663812yes—
780C22C2×#1455663912yes—
781C22C25×D7311yescharacteristic
782C4—22no—
783C4—24no—
784C4—24no—
785C4—28no—
786C4—24no—
787C4—24no—
788C4—734no—
789C4—1464no—
790C4—1464no—
791C4—1462no—
792C4—1464no—
793C4—1462no—
794C4—1464no—
795C4—1468no—
796C4C2×#1455663814yes—
797C4C2×#1455663914yes—
798C2—2922no—
799C2#2262442314yesdirect product factor
800C2C2×2−1+4×D7311yescharacteristic
801C2C22×#1455663811yescharacteristic
802C2C22×#1455663911yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#557×C73C2
socleC23×C73C25
prime radicalC23×D73C24
hypercenterC2×#557D73
hypocenterC73C2×#3556
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #22624423C2direct (N × H)
2. C2×C73⋊#564C2semidirect
3. C2×#17989316C2semidirect
4. C2×#17989315C2semidirect
5. C2×#17989315C2semidirect
6. C2×#17989314C2semidirect
7. C2×#17989313C2semidirect
8. C2×#17989312C2semidirect
9. C2×#17989312C2semidirect
18. C2×#557×C73C2semidirect
19. C73⋊#564C22semidirect
20. #17989316C22semidirect
21. #17989315C22semidirect
22. #17989315C22semidirect
23. #17989314C22semidirect
24. #17989313C22semidirect
25. #17989312C22semidirect
26. #17989312C22semidirect
92. #557×C73C22semidirect
397. C2×C73#3556semidirect
411. C2×#557D73semidirect
420. C73C2×#3556semidirect
429. #557C2×D73semidirect
799. C2#22624423direct (N × H)

Maximal subgroups

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

subgroupindex
#226244232
C2×C73⋊#5642
C2×#179893162
C2×#179893152
C2×#179893142
C2×#179893132
C2×#179893122
C2×#179892002
C2×#179891982
C2×#179891962
C2×#179891952
C2×#179891422
C2×#179891412
C2×#557×C732
C2×#355673