Finite Group Databasebeta

← C2×#22624361 #33993596

Subgroups — C2×#22624361 #33993596

Order 18688.

7086 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624361C2132yesmaximal, direct product factor
2C2×#17989339C214yesmaximal, complemented
3C2×#17989316C211yesmaximal, characteristic, complemented
4C2×#17989295C212yesmaximal, complemented
5C2×#17989281C212yesmaximal, complemented
6C2×Q8×D292C212yesmaximal, complemented
7C2×#17989252C211yesmaximal, characteristic, complemented
8C2×#17989245C212yesmaximal, complemented
9C2×#17989241C211yesmaximal, characteristic, complemented
10C2×#17989215C212yesmaximal, complemented
11C2×#17989210C212yesmaximal, complemented
12C2×#17989195C212yesmaximal, complemented
13C2×#17989178C214yesmaximal, complemented
14C2×#17989157C212yesmaximal, complemented
15C2×C4⋊Q8×D73C211yesmaximal, characteristic, complemented
16C2×#17989124C211yesmaximal, characteristic, complemented
17C2×#17989119C211yesmaximal, characteristic, complemented
18C2×#556×C73C211yesmaximal, characteristic, complemented
19C22×#11924027C2212yes—
20C22×Q8×D73C2212yes—
21C22×Q8×D73C2212yes—
22#17989339C22164yescomplemented
23#17989316C22116yescomplemented
24#17989295C22132yescomplemented
25#17989281C22132yescomplemented
26Q8×D292C22132yescomplemented
27#17989252C22116yescomplemented
28#17989245C22132yescomplemented
29#17989241C22116yescomplemented
30#17989215C22132yescomplemented
31#17989210C22132yescomplemented
32#17989195C22132yescomplemented
33#17989178C22164yescomplemented
34#17989157C22132yescomplemented
35C2×#14556591C2212yes—
36C2×#14556591C2211yescharacteristic
37C2×#14556591C2214yes—
38C2×#14556590C2212yes—
39C2×#14556590C2212yes—
40C2×#14556590C2212yes—
41C2×#14556589C2212yes—
42C4⋊Q8×D73C22116yescomplemented
43#17989124C22116yescomplemented
44#17989119C22116yescomplemented
45C2×#14556586C2214yes—
46C2×#14556586C2212yes—
47C2×#14556585C2214yes—
48C2×#14556584C2212yes—
49C2×#14556583C2214yes—
50C2×#14556582C2214yes—
51C2×#14556582C2212yes—
52C2×#14556582C2211yescharacteristic
53C2×#14556582C2211yescharacteristic
54C2×#14556581C2214yes—
55C2×#14556580C2211yescharacteristic
56C2×#14556578C2211yescharacteristic
57C2×#14556577C2214yes—
58C2×#14556576C2212yes—
59C2×#14556575C2214yes—
60C2×#14556573C2214yes—
61C2×#14556573C2214yes—
62C2×#14556573C2212yes—
63C2×#14556571C2214yes—
64C2×#14556571C2212yes—
65C2×#14556571C2214yes—
66C2×#14556571C2211yescharacteristic
67C2×#14556569C2214yes—
68C2×#14556568C2214yes—
69C2×#14556568C2214yes—
70C2×#14556568C2214yes—
71C2×#14556567C2212yes—
72C2×#14556567C2211yescharacteristic
73C2×#14556566C2211yescharacteristic
74C2×#14556565C2212yes—
75C2×#14556564C2214yes—
76C2×#14556562C2211yescharacteristic
77C2×Q8×Dic73C2212yes—
78C2×C4×Dic146C2212yes—
79C2×C4×Dic146C2211yescharacteristic
80C2×C4×D292C2214yes—
81C2×C4×D292C2211yescharacteristic
82C2×C4×D292C2212yes—
83C2×#14556553C2212yes—
84C2×C4×C22⋊D73C2212yes—
85C2×#14556551C2214yes—
86C2×#14556550C2212yes—
87C2×#14556548C2212yes—
88C22×C4⋊Dic73C2212yes—
89C2×C4⋊C4×D73C2212yes—
90C2×C4⋊C4×D73C2212yes—
91C2×C42×D73C2211yescharacteristic
92#556×C73C22116yescomplemented
93C2×C4⋊Q8×C73C2211yescharacteristic
94C2×#126×C73C2214yes—
95C2×#124×C73C2212yes—
96C2×C22⋊Q8×C73C2212yes—
97C2×C4×Q8×C73C2211yescharacteristic
98C2×C4×Q8×C73C2212yes—
99C2×C4×D4×C73C2211yescharacteristic
100C2×#117×C73C2212yes—
101C2×#11924027—48no—
102C2×#11924027C23116yes—
103C22×Dic146C2312yes—
104C22×Dic146C2311yescharacteristic
105C22×Dic146C2314yes—
106C22×Dic146C2314yes—
107C2×Q8×D73—48no—
108C2×Q8×D73—48no—
109C2×Q8×D73C23116yes—
110C2×Q8×D73C23116yes—
111C22×D292C2311yescharacteristic
112C22×D292C2312yes—
113C22×C22⋊D73C2312yes—
114C22×C22⋊D73C2314yes—
115C23×Dic73C2314yes—
116C22×C4×D73C2311yescharacteristic
117C22×C4×D73C2312yes—
118C22×C4×D73C2311yescharacteristic
119C22×C4×D73C2311yescharacteristic
120C22×C4×D73C2314yes—
121C22×C4×D73C2314yes—
122#14556591C2318yes—
123#14556591C23116yes—
124#14556591C23132yes—
125#14556590C23116yes—
126#14556590C23116yes—
127#14556590C23116yes—
128#14556589C23116yes—
129#14556586C23116yes—
130#14556586C23132yes—
131#14556585C23132yes—
132#14556584C23116yes—
133#14556583C23132yes—
134#14556582C2318yes—
135#14556582C23132yes—
136#14556582C2318yes—
137#14556582C23116yes—
138#14556581C23132yes—
139#14556580C2318yes—
140#14556578C2318yes—
141#14556577C23132yes—
142#14556576C23116yes—
143#14556575C23132yes—
144#14556573C23132yes—
145#14556573C23132yes—
146#14556573C23116yes—
147#14556571C23132yes—
148#14556571C23116yes—
149#14556571C23132yes—
150#14556571C2318yes—
151#14556569C23132yes—
152#14556568C23132yes—
153#14556568C23132yes—
154#14556568C23132yes—
155#14556567C2318yes—
156#14556567C23116yes—
157#14556566C2318yes—
158#14556565C23116yes—
159#14556564C23132yes—
160#14556562C2318yes—
161Q8×Dic73C23116yes—
162C4×Dic146C23116yes—
163C4×Dic146C2318yes—
164C4×D292C2318yes—
165C4×D292C23116yes—
166C4×D292C23132yes—
167#14556553C23116yes—
168C4×C22⋊D73C23116yes—
169#14556551C23132yes—
170#14556550C23116yes—
171#14556548C23116yes—
172C2×C4⋊Dic73C2311yescharacteristic
173C2×C4⋊Dic73C2312yes—
174C2×C4⋊Dic73C2312yes—
175C2×C4⋊Dic73C2312yes—
176C2×C4⋊Dic73C2312yes—
177C2×C4⋊Dic73C2314yes—
178C2×C4⋊Dic73C2314yes—
179C2×C4⋊Dic73C2314yes—
180C2×C4⋊Dic73C23116yes—
181C2×C4⋊Dic73C2312yes—
182C2×C4⋊Dic73C2311yescharacteristic
183C2×#11924007C2314yes—
184C2×#11924007C2314yes—
185C2×#11924007C2314yes—
186C2×#11924007C2312yes—
187C2×#11924007C2312yes—
188C2×#11924007C2312yes—
189C2×#11924007C2314yes—
190C2×#11924007C2312yes—
191C4⋊C4×D73C23116yes—
192C4⋊C4×D73C23116yes—
193C2×C22⋊Dic73C2312yes—
194C2×C22⋊Dic73C2312yes—
195C2×C22⋊Dic73C2312yes—
196C2×#11924005C2312yes—
197C2×#11924005C2312yes—
198C2×#11924005C2312yes—
199C2×#11924005C2312yes—
200C2×#11924005C2314yes—
201C2×#11924005C2314yes—
202C2×#11924005C2312yes—
203C2×#11924005C2312yes—
204C2×C4×Dic73C2311yescharacteristic
205C2×C4×Dic73C2311yescharacteristic
206C2×C4×Dic73C2311yescharacteristic
207C2×C4×Dic73C2312yes—
208C2×C4×Dic73C2314yes—
209C42×D73C2318yes—
210C22×Q8×C73C2312yes—
211C22×Q8×C73C2311yescharacteristic
212C22×D4×C73C2311yescharacteristic
213C23×C4×C73C2312yes—
214C4⋊Q8×C73C2318yes—
215#126×C73C23132yes—
216#124×C73C23116yes—
217C22⋊Q8×C73C23116yes—
218C4×Q8×C73C2318yes—
219C4×Q8×C73C23116yes—
220C4×D4×C73C2318yes—
221#117×C73C23116yes—
222C2×C4⋊C4×C73C2312yes—
223C2×C4⋊C4×C73C2312yes—
224C2×C4⋊C4×C73C2311yescharacteristic
225C2×C4⋊C4×C73C2311yescharacteristic
226C2×C4⋊C4×C73C2314yes—
227C2×C4⋊C4×C73C2312yes—
228C2×C22⋊C4×C73C2314yes—
229C2×C22⋊C4×C73C2312yes—
230C2×C22⋊C4×C73C2314yes—
231C2×C42×C73C2314yes—
232C2×C42×C73C2311yescharacteristic
233C2×C42×C73C2312yes—
234C23×D73C2412yes—
235C23×D73C2411yescharacteristic
236#11924027—432no—
237C2×Dic146—24no—
238C2×Dic146—28no—
239C2×Dic146—48no—
240C2×Dic146—48no—
241C2×Dic146C2414yes—
242C2×Dic146C2418yes—
243C2×Dic146C24116yes—
244C2×Dic146C24116yes—
245Q8×D73—432no—
246Q8×D73—432no—
247C2×D292—28no—
248C2×D292—24no—
249C2×D292C2414yes—
250C2×D292C2418yes—
251C2×C22⋊D73—28no—
252C2×C22⋊D73—48no—
253C2×C22⋊D73C2418yes—
254C2×C22⋊D73C24116yes—
255C22×Dic73—48no—
256C22×Dic73C2412yes—
257C22×Dic73C2411yescharacteristic
258C22×Dic73C2411yescharacteristic
259C22×Dic73C2411yescharacteristic
260C22×Dic73C2412yes—
261C22×Dic73C2414yes—
262C22×Dic73C2412yes—
263C22×Dic73C24116yes—
264C2×C4×D73—24no—
265C2×C4×D73—24no—
266C2×C4×D73—28no—
267C2×C4×D73—24no—
268C2×C4×D73—48no—
269C2×C4×D73—48no—
270C2×C4×D73C2414yes—
271C2×C4×D73C2414yes—
272C2×C4×D73C2414yes—
273C2×C4×D73C2418yes—
274C2×C4×D73C24116yes—
275C2×C4×D73C24116yes—
276C4⋊Dic73C2418yes—
277C4⋊Dic73C2418yes—
278C4⋊Dic73C2414yes—
279C4⋊Dic73C24116yes—
280C4⋊Dic73C2418yes—
281C4⋊Dic73C2418yes—
282C4⋊Dic73C2418yes—
283C4⋊Dic73C24116yes—
284C4⋊Dic73C2414yes—
285C4⋊Dic73C24116yes—
286#11924007C24116yes—
287#11924007C24116yes—
288#11924007C2418yes—
289#11924007C2418yes—
290#11924007C24116yes—
291#11924007C2418yes—
292#11924007C24116yes—
293#11924007C2418yes—
294C22⋊Dic73C2418yes—
295C22⋊Dic73C2418yes—
296C22⋊Dic73C2418yes—
297#11924005C2418yes—
298#11924005C2418yes—
299#11924005C2418yes—
300#11924005C2418yes—
301#11924005C24116yes—
302#11924005C24116yes—
303#11924005C2418yes—
304#11924005C2418yes—
305C4×Dic73C2414yes—
306C4×Dic73C2414yes—
307C4×Dic73C2414yes—
308C4×Dic73C2418yes—
309C4×Dic73C24116yes—
310C24×C73C2412yes—
311C2×Q8×C73—28no—
312C2×Q8×C73—24no—
313C2×Q8×C73C2414yes—
314C2×Q8×C73C2418yes—
315C2×D4×C73—24no—
316C2×D4×C73C2414yes—
317C22×C4×C73—28no—
318C22×C4×C73C2412yes—
319C22×C4×C73C2412yes—
320C22×C4×C73C2411yescharacteristic
321C22×C4×C73C2412yes—
322C22×C4×C73C2414yes—
323C22×C4×C73C2418yes—
324C22×C4×C73C2411yescharacteristic
325C22×C4×C73C2411yescharacteristic
326C4⋊C4×C73C2414yes—
327C4⋊C4×C73C2418yes—
328C4⋊C4×C73C2414yes—
329C4⋊C4×C73C24116yes—
330C4⋊C4×C73C2418yes—
331C4⋊C4×C73C2418yes—
332C22⋊C4×C73C24116yes—
333C22⋊C4×C73C2418yes—
334C22⋊C4×C73C24116yes—
335C42×C73C24116yes—
336C42×C73C2414yes—
337C42×C73C2418yes—
338C23×C73—24no—
339C23×C73—24no—
340C23×C73—24no—
341C23×C73C2514yes—
342C23×C73C2511yescharacteristic
343C22×D73—22no—
344C22×D73—22no—
345C22×D73—24no—
346C22×D73—24no—
347C22×D73—24no—
348C22×D732−1+414yes—
349C22×D73C2514yes—
350C22×D73C2512yes—
351Q8×C73—216no—
352Q8×C73—28no—
353D4×C73—28no—
354C2×C4×C73—28no—
355C2×C4×C73—24no—
356C2×C4×C73—24no—
357C2×C4×C73—22no—
358C2×C4×C73—24no—
359C2×C4×C73—216no—
360C2×C4×C73H(5,𝔽2)14yes—
361C2×C4×C732−1+414yes—
362C2×C4×C73C2514yes—
363C2×C4×C73C2514yes—
364C2×C4×C73C2512yes—
365C2×C4×C73C2514yes—
366C2×C4×C73C2518yes—
367C2×C4×C73C2512yes—
368C2×C4×C73C2512yes—
369C22⋊D73—216no—
370C22⋊D73—416no—
371C2×Dic73—24no—
372C2×Dic73—22no—
373C2×Dic73—24no—
374C2×Dic73—28no—
375C2×Dic73—22no—
376C2×Dic73—22no—
377C2×Dic73—24no—
378C2×Dic73—416no—
379C2×Dic73C2514yes—
380C2×Dic73C2512yes—
381C2×Dic73C2512yes—
382C2×Dic73C2512yes—
383C2×Dic73C2514yes—
384C2×Dic73C2518yes—
385C2×Dic73C2514yes—
386D292—216no—
387D292—28no—
388C4×D73—28no—
389C4×D73—28no—
390C4×D73—216no—
391C4×D73—28no—
392C4×D73—416no—
393C4×D73—416no—
394Dic146—28no—
395Dic146—216no—
396Dic146—416no—
397Dic146—416no—
398C22×C73—24no—
399C22×C73—24no—
400C22×C73—24no—
401C22×C73—48no—
402C22×C73C2×H(5,𝔽2)12yes—
403C22×C73C2×2−1+412yes—
404C22×C73C2×2−1+412yes—
405C22×C73C2611yescharacteristic
406C2×D73—22no—
407C2×D73—22no—
408C2×D73—28no—
409C2×D73—24no—
410C2×D73—24no—
411C2×D73—24no—
412C2×D73—48no—
413C2×D73C2×2−1+414yes—
414C4×C73—28no—
415C4×C73—22no—
416C4×C73—24no—
417C4×C73—24no—
418C4×C73—24no—
419C4×C73C2×H(5,𝔽2)14yes—
420C4×C73C2×2−1+414yes—
421Dic73—24no—
422Dic73—28no—
423Dic73—22no—
424Dic73—24no—
425Dic73—22no—
426Dic73—22no—
427Dic73—24no—
428C2×#3552—731nomaximal, Sylow
429C2×C73—44no—
430C2×C73#355214yescomplemented
431C2×C73C22×H(5,𝔽2)11yescharacteristic
432C2×C73C22×2−1+411yescharacteristic
433C2×C73C22×2−1+411yescharacteristic
434D73—24no—
435D73—44no—
436#3552—7332no—
437C2×#563—734no—
438C2×#557—731no—
439C2×#556D7311yescharacteristic, complemented
440C2×#554—732no—
441C2×#553—732no—
442C2×D4×Q8—731no—
443C2×D4×Q8—732no—
444C2×#548—732no—
445C2×#547—731no—
446C2×#544—732no—
447C2×#542—732no—
448C2×#541—732no—
449C2×#539—734no—
450C2×#536—732no—
451C22×C4⋊Q8—731no—
452C2×#529—731no—
453C2×#529—731no—
454C73C2×#355211yescharacteristic, complemented, Sylow
455C22×#41—732no—
456C23×Q8—732no—
457C23×Q8—732no—
458#563—7364no—
459#557—7316no—
460#556C2×D73116yescomplemented
461#554—7332no—
462#553—7332no—
463D4×Q8—7316no—
464D4×Q8—7332no—
465#548—7332no—
466#547—7316no—
467#544—7332no—
468#542—7332no—
469#541—7332no—
470#539—7364no—
471#536—7332no—
472C2×C4⋊Q8—732no—
473C2×C4⋊Q8—7316no—
474C2×C4⋊Q8—732no—
475C2×C4⋊Q8—732no—
476C2×C4⋊Q8—732no—
477C2×C4⋊Q8—731no—
478C2×C4⋊Q8—732no—
479C2×C4⋊Q8—734no—
480C2×C4⋊Q8C2×D7311yescharacteristic
481#529—7316no—
482#529—7316no—
483C2×#126—732no—
484C2×#126—734no—
485C2×#126—732no—
486C2×#126—734no—
487C2×#126C2×D7314yes—
488C2×#125—731no—
489C2×#125—731no—
490C2×#125—734no—
491C2×#125—734no—
492C2×#125—732no—
493C2×#125—734no—
494C2×#124—731no—
495C2×#124—731no—
496C2×#124—734no—
497C2×#124C2×D7312yes—
498C2×#123—732no—
499C2×#123—732no—
500C2×#123—734no—
501C2×#123—734no—
502C2×#123—734no—
503C2×C22⋊Q8—731no—
504C2×C22⋊Q8—732no—
505C2×C22⋊Q8—731no—
506C2×C22⋊Q8—734no—
507C2×C22⋊Q8—734no—
508C2×C22⋊Q8—732no—
509C2×C22⋊Q8—734no—
510C2×C22⋊Q8—734no—
511C2×C22⋊Q8—734no—
512C2×C22⋊Q8—734no—
513C2×C22⋊Q8C2×D7312yes—
514C2×#121—731no—
515C2×#121—732no—
516C2×#121—731no—
517C2×#121—734no—
518C2×C4×Q8—732no—
519C2×C4×Q8—731no—
520C2×C4×Q8—732no—
521C2×C4×Q8C2×D7311yescharacteristic
522C2×C4×Q8C2×D7312yes—
523C2×C4×D4—732no—
524C2×C4×D4—732no—
525C2×C4×D4—734no—
526C2×C4×D4—731no—
527C2×C4×D4—732no—
528C2×C4×D4—734no—
529C2×C4×D4C2×D7311yescharacteristic
530C2×#117—732no—
531C2×#117—732no—
532C2×#117C2×D7312yes—
533C22×C4⋊C4—732no—
534C22×C4⋊C4—732no—
535C22×C4⋊C4—732no—
536C22×C42—731no—
537C2×#41—2928no—
538C2×#41—7316no—
539C22×Q8—2928no—
540C22×Q8—2928no—
541C22×Q8—7316no—
542C22×Q8—7316no—
543C22×Q8—734no—
544C22×Q8—734no—
545C22×Q8—731no—
546C22×Q8—732no—
547C22×Q8C22×D7311yescharacteristic
548C22×Q8C22×D7312yes—
549C22×D4—734no—
550C22×D4—732no—
551C22×D4—732no—
552C22×D4—731no—
553C22×D4C22×D7311yescharacteristic
554C23×C4—734no—
555C23×C4—734no—
556C23×C4—734no—
557C23×C4—731no—
558C23×C4—731no—
559C23×C4—732no—
560C23×C4—731no—
561C23×C4C22×D7312yes—
562C4⋊Q8—7316no—
563C4⋊Q8—7316no—
564C4⋊Q8—7316no—
565C4⋊Q8—7316no—
566C4⋊Q8—738no—
567C4⋊Q8—7316no—
568C4⋊Q8—7332no—
569C4⋊Q8C22×D7318yes—
570#126—7316no—
571#126—7332no—
572#126—7316no—
573#126—7332no—
574#126C22×D73132yes—
575#125—738no—
576#125—738no—
577#125—7332no—
578#125—7332no—
579#125—7316no—
580#125—7332no—
581#124—738no—
582#124—738no—
583#124—7332no—
584#124C22×D73116yes—
585#123—7316no—
586#123—7316no—
587#123—7332no—
588#123—7332no—
589#123—7332no—
590C22⋊Q8—738no—
591C22⋊Q8—7316no—
592C22⋊Q8—738no—
593C22⋊Q8—7332no—
594C22⋊Q8—7332no—
595C22⋊Q8—7316no—
596C22⋊Q8—7332no—
597C22⋊Q8—7332no—
598C22⋊Q8—7332no—
599C22⋊Q8—7332no—
600C22⋊Q8C22×D73116yes—
601#121—738no—
602#121—7316no—
603#121—738no—
604#121—7332no—
605C4×Q8—7316no—
606C4×Q8—738no—
607C4×Q8—7316no—
608C4×Q8C22×D7318yes—
609C4×Q8C22×D73116yes—
610C4×D4—7316no—
611C4×D4—7316no—
612C4×D4—7332no—
613C4×D4—738no—
614C4×D4—7316no—
615C4×D4—7332no—
616C4×D4C22×D7318yes—
617#117—7316no—
618#117—7316no—
619#117C22×D73116yes—
620C2×C4⋊C4—731no—
621C2×C4⋊C4—732no—
622C2×C4⋊C4—734no—
623C2×C4⋊C4—734no—
624C2×C4⋊C4—734no—
625C2×C4⋊C4—732no—
626C2×C4⋊C4—7316no—
627C2×C4⋊C4—732no—
628C2×C4⋊C4—732no—
629C2×C4⋊C4—732no—
630C2×C4⋊C4—732no—
631C2×C4⋊C4—734no—
632C2×C4⋊C4—732no—
633C2×C4⋊C4—734no—
634C2×C4⋊C4—732no—
635C2×C4⋊C4—731no—
636C2×C4⋊C4—734no—
637C2×C4⋊C4—734no—
638C2×C4⋊C4—732no—
639C2×C4⋊C4—7316no—
640C2×C4⋊C4—7316no—
641C2×C4⋊C4C22×D7312yes—
642C2×C4⋊C4C22×D7312yes—
643C2×C4⋊C4C22×D7311yescharacteristic
644C2×C4⋊C4C22×D7311yescharacteristic
645C2×C4⋊C4C22×D7314yes—
646C2×C4⋊C4C22×D7312yes—
647C2×C22⋊C4—732no—
648C2×C22⋊C4—732no—
649C2×C22⋊C4—732no—
650C2×C22⋊C4—732no—
651C2×C22⋊C4—732no—
652C2×C22⋊C4—732no—
653C2×C22⋊C4—732no—
654C2×C22⋊C4—734no—
655C2×C22⋊C4—734no—
656C2×C22⋊C4—732no—
657C2×C22⋊C4—732no—
658C2×C22⋊C4C22×D7314yes—
659C2×C22⋊C4C22×D7314yes—
660C2×C22⋊C4C22×D7312yes—
661C2×C42—731no—
662C2×C42—731no—
663C2×C42—732no—
664C2×C42—734no—
665C2×C42—731no—
666C2×C42—738no—
667C2×C42C22×D7312yes—
668C2×C42C22×D7314yes—
669C2×C42C22×D7311yescharacteristic
670C24—731no—
671C24—732no—
672C24C23×D7312yes—
673#41—29232no—
674C2×Q8—28no—
675C2×Q8—24no—
676C2×Q8—2928no—
677C2×Q8—2928no—
678C2×Q8—29232no—
679C2×Q8—29232no—
680C2×Q8—7316no—
681C2×Q8—7316no—
682C2×Q8—734no—
683C2×Q8—738no—
684C2×Q8—1464no—
685C2×Q8—1468no—
686C2×Q8C23×D7314yes—
687C2×Q8C23×D7318yes—
688C2×D4—24no—
689C2×D4—2928no—
690C2×D4—7316no—
691C2×D4—738no—
692C2×D4—738no—
693C2×D4—734no—
694C2×D4—1468no—
695C2×D4—1468no—
696C2×D4—1464no—
697C2×D4C23×D7314yes—
698C22×C4—28no—
699C22×C4—2928no—
700C22×C4—2928no—
701C22×C4—2928no—
702C22×C4—7316no—
703C22×C4—7316no—
704C22×C4—7316no—
705C22×C4—732no—
706C22×C4—731no—
707C22×C4—731no—
708C22×C4—731no—
709C22×C4—732no—
710C22×C4—734no—
711C22×C4—732no—
712C22×C4—734no—
713C22×C4—734no—
714C22×C4—734no—
715C22×C4—738no—
716C22×C4—1464no—
717C22×C4—1464no—
718C22×C4—1468no—
719C22×C4—1464no—
720C22×C4C23×D7318yes—
721C22×C4C23×D7312yes—
722C22×C4C23×D7311yescharacteristic
723C22×C4C23×D7312yes—
724C22×C4C23×D7312yes—
725C22×C4C23×D7314yes—
726C22×C4C23×D7311yescharacteristic
727C22×C4C23×D7311yescharacteristic
728C4⋊C4—7316no—
729C4⋊C4—7316no—
730C4⋊C4—738no—
731C4⋊C4—738no—
732C4⋊C4—7316no—
733C4⋊C4—738no—
734C4⋊C4—7316no—
735C4⋊C4—738no—
736C4⋊C4—734no—
737C4⋊C4—738no—
738C4⋊C4—7316no—
739C4⋊C4—738no—
740C4⋊C4—738no—
741C4⋊C4—738no—
742C4⋊C4—738no—
743C4⋊C4—7316no—
744C4⋊C4—734no—
745C4⋊C4—7316no—
746C4⋊C4C23×D7318yes—
747C4⋊C4C23×D7318yes—
748C4⋊C4C23×D7314yes—
749C4⋊C4C23×D7314yes—
750C4⋊C4C23×D73116yes—
751C4⋊C4C23×D7318yes—
752C22⋊C4—738no—
753C22⋊C4—738no—
754C22⋊C4—738no—
755C22⋊C4—738no—
756C22⋊C4—738no—
757C22⋊C4—738no—
758C22⋊C4—738no—
759C22⋊C4—7316no—
760C22⋊C4—7316no—
761C22⋊C4—738no—
762C22⋊C4—738no—
763C22⋊C4C23×D73116yes—
764C22⋊C4C23×D73116yes—
765C22⋊C4C23×D7318yes—
766C42—734no—
767C42—734no—
768C42—734no—
769C42—738no—
770C42—7316no—
771C42C23×D7314yes—
772C42C23×D7318yes—
773C42C23×D73116yes—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—734no—
778C23—732no—
779C23—734no—
780C23—1464no—
781C23—1464no—
782C23—1464no—
783C23—1462no—
784C23—1462no—
785C23C24×D7314yes—
786C23C24×D7311yescharacteristic
787Q8—216no—
788Q8—28no—
789Q8—29216no—
790Q8—29216no—
791Q8—1468no—
792Q8—14616no—
793D4—28no—
794D4—29216no—
795D4—14616no—
796D4—14616no—
797D4—1468no—
798C2×C4—28no—
799C2×C4—22no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—216no—
804C2×C4—29216no—
805C2×C4—29216no—
806C2×C4—29216no—
807C2×C4—734no—
808C2×C4—732no—
809C2×C4—732no—
810C2×C4—732no—
811C2×C4—734no—
812C2×C4—738no—
813C2×C4—734no—
814C2×C4—1468no—
815C2×C4—1464no—
816C2×C4—1468no—
817C2×C4—1464no—
818C2×C4—1462no—
819C2×C4—1462no—
820C2×C4—1464no—
821C2×C4—1462no—
822C2×C4—1468no—
823C2×C4—14616no—
824C2×C4—1468no—
825C2×C4#1455663714yes—
826C2×C4#1455663814yes—
827C2×C4C24×D7314yes—
828C2×C4C24×D7312yes—
829C2×C4C24×D7314yes—
830C2×C4C24×D7314yes—
831C2×C4C24×D7318yes—
832C2×C4C24×D7312yes—
833C2×C4C24×D7312yes—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—48no—
838C22—2928no—
839C22—734no—
840C22—1464no—
841C22—1464no—
842C22—1464no—
843C22—1468no—
844C22—1462no—
845C22—1462no—
846C22C2×#1455663712yes—
847C222−1+4×D7312yes—
848C22C2×#1455663812yes—
849C22C25×D7311yescharacteristic
850C4—28no—
851C4—22no—
852C4—24no—
853C4—24no—
854C4—24no—
855C4—1464no—
856C4—1468no—
857C4—1464no—
858C4—1462no—
859C4—1462no—
860C4—1464no—
861C4—1462no—
862C4C2×#1455663714yes—
863C4C2×#1455663814yes—
864C2—44no—
865C2—2924no—
866C2—1464no—
867C2#2262436114yesdirect product factor
868C2C22×#1455663711yescharacteristic
869C2C2×2−1+4×D7311yescharacteristic
870C2C22×#1455663811yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#556×C73C2
socleC23×C73C25
hypercenterC2×#556D73
hypocenterC73C2×#3552
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #22624361C2direct (N × H)
2. C2×#17989339C2semidirect
3. C2×#17989316C2semidirect
4. C2×#17989295C2semidirect
5. C2×#17989281C2semidirect
6. C2×Q8×D292C2semidirect
7. C2×#17989252C2semidirect
8. C2×#17989245C2semidirect
9. C2×#17989241C2semidirect
10. C2×#17989215C2semidirect
11. C2×#17989210C2semidirect
12. C2×#17989195C2semidirect
13. C2×#17989178C2semidirect
14. C2×#17989157C2semidirect
15. C2×C4⋊Q8×D73C2semidirect
16. C2×#17989124C2semidirect
17. C2×#17989119C2semidirect
18. C2×#556×C73C2semidirect
22. #17989339C22semidirect
23. #17989316C22semidirect
24. #17989295C22semidirect
25. #17989281C22semidirect
26. Q8×D292C22semidirect
27. #17989252C22semidirect
28. #17989245C22semidirect
29. #17989241C22semidirect
30. #17989215C22semidirect
31. #17989210C22semidirect
32. #17989195C22semidirect
33. #17989178C22semidirect
34. #17989157C22semidirect
42. C4⋊Q8×D73C22semidirect
43. #17989124C22semidirect
44. #17989119C22semidirect
92. #556×C73C22semidirect
430. C2×C73#3552semidirect
439. C2×#556D73semidirect
454. C73C2×#3552semidirect
460. #556C2×D73semidirect
867. C2#22624361direct (N × H)

Maximal subgroups

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

subgroupindex
#226243612
C2×#179893392
C2×#179893162
C2×#179892952
C2×#179892812
C2×Q8×D2922
C2×#179892522
C2×#179892452
C2×#179892412
C2×#179892152
C2×#179892102
C2×#179891952
C2×#179891782
C2×#179891572
C2×C4⋊Q8×D732
C2×#179891242
C2×#179891192
C2×#556×C732
C2×#355273