Finite Group Databasebeta

← C2×#22624396 #33993609

Subgroups — C2×#22624396 #33993609

Order 18688.

7182 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624396C2132yesmaximal, direct product factor
2C2×#17989332C214yesmaximal, complemented
3C2×#17989323C211yesmaximal, characteristic, complemented
4C2×#17989320C212yesmaximal, complemented
5C2×#17989312C211yesmaximal, characteristic, complemented
6C2×#17989296C212yesmaximal, complemented
7C2×#17989257C211yesmaximal, characteristic, complemented
8C2×#17989252C211yesmaximal, characteristic, complemented
9C2×#17989244C212yesmaximal, complemented
10C2×#17989236C212yesmaximal, complemented
11C2×#17989206C212yesmaximal, complemented
12C2×#17989204C212yesmaximal, complemented
13C2×#17989190C212yesmaximal, complemented
14C2×#17989179C214yesmaximal, complemented
15C2×#17989157C212yesmaximal, complemented
16C2×#17989144C211yesmaximal, characteristic, complemented
17C2×#17989121C211yesmaximal, characteristic, complemented
18C2×#532×C73C211yesmaximal, characteristic, complemented
19C22×#11924027C2212yes—
20C22×Q8×D73C2212yes—
21#17989332C22164yescomplemented
22#17989323C22116yescomplemented
23#17989320C22132yescomplemented
24#17989312C22116yescomplemented
25#17989296C22132yescomplemented
26#17989257C22116yescomplemented
27#17989252C22116yescomplemented
28#17989244C22132yescomplemented
29#17989236C22132yescomplemented
30#17989206C22132yescomplemented
31#17989204C22132yescomplemented
32#17989190C22132yescomplemented
33#17989179C22164yescomplemented
34#17989157C22132yescomplemented
35#17989144C22116yescomplemented
36C2×#14556591C2211yescharacteristic
37C2×#14556591C2211yescharacteristic
38C2×#14556590C2212yes—
39C2×#14556589C2212yes—
40C2×#14556587C2212yes—
41#17989121C22116yescomplemented
42C2×#14556585C2212yes—
43C2×#14556584C2214yes—
44C2×#14556583C2212yes—
45C2×#14556583C2211yescharacteristic
46C2×#14556582C2212yes—
47C2×#14556581C2214yes—
48C2×#14556579C2211yescharacteristic
49C2×#14556578C2212yes—
50C2×#14556578C2212yes—
51C2×#14556578C2214yes—
52C2×#14556577C2214yes—
53C2×#14556575C2214yes—
54C2×#14556574C2214yes—
55C2×#14556574C2212yes—
56C2×#14556573C2214yes—
57C2×#14556573C2214yes—
58C2×#14556572C2214yes—
59C2×#14556572C2214yes—
60C2×#14556570C2214yes—
61C2×#14556570C2212yes—
62C2×#14556570C2211yescharacteristic
63C2×#14556570C2211yescharacteristic
64C2×#14556570C2211yescharacteristic
65C2×#14556569C2214yes—
66C2×#14556568C2214yes—
67C2×#14556568C2214yes—
68C2×#14556568C2214yes—
69C2×#14556567C2212yes—
70C2×#14556565C2211yescharacteristic
71C2×#14556563C2214yes—
72C2×#14556563C2214yes—
73C2×#14556562C2214yes—
74C2×#14556562C2212yes—
75C2×Q8×Dic73C2212yes—
76C2×C4×Dic146C2211yescharacteristic
77C2×C4×Dic146C2211yescharacteristic
78C2×C4×Dic146C2212yes—
79C2×C4×Dic146C2211yescharacteristic
80C2×#14556556C2212yes—
81C2×C4×D292C2211yescharacteristic
82C2×D4×Dic73C2212yes—
83C2×D4×Dic73C2212yes—
84C2×D4×Dic73C2212yes—
85C2×#14556553C2212yes—
86C2×C4×C22⋊D73C2214yes—
87C2×C4×C22⋊D73C2212yes—
88C2×#14556550C2212yes—
89C2×#14556548C2212yes—
90C22×#11924007C2214yes—
91C22×#41×C73C2212yes—
92#532×C73C22116yescomplemented
93C2×C4⋊Q8×C73C2211yescharacteristic
94C2×#127×C73C2211yescharacteristic
95C2×#124×C73C2212yes—
96C2×#121×C73C2212yes—
97C2×#121×C73C2212yes—
98C2×C4×D4×C73C2212yes—
99C2×C4×D4×C73C2212yes—
100C22×C42×C73C2211yescharacteristic
101C2×#11924027—48no—
102C2×#11924027C23116yes—
103C22×Dic146C2311yescharacteristic
104C22×Dic146C2311yescharacteristic
105C22×Dic146C2311yescharacteristic
106C22×Dic146C2314yes—
107C22×Dic146C2312yes—
108C2×Q8×D73—48no—
109C2×Q8×D73C23116yes—
110C22×D292C2311yescharacteristic
111C22×C22⋊D73C2314yes—
112C22×C22⋊D73C2314yes—
113C22×C22⋊D73C2312yes—
114C23×Dic73C2314yes—
115C23×Dic73C2314yes—
116C22×C4×D73C2312yes—
117C22×C4×D73C2314yes—
118#14556591C2318yes—
119#14556591C2318yes—
120#14556590C23116yes—
121#14556589C23116yes—
122#14556587C23116yes—
123#14556585C23116yes—
124#14556584C23132yes—
125#14556583C2318yes—
126#14556583C23116yes—
127#14556582C23116yes—
128#14556581C23132yes—
129#14556579C2318yes—
130#14556578C23116yes—
131#14556578C23132yes—
132#14556578C23116yes—
133#14556577C23132yes—
134#14556575C23132yes—
135#14556574C23116yes—
136#14556574C23132yes—
137#14556573C23132yes—
138#14556573C23132yes—
139#14556572C23132yes—
140#14556572C23132yes—
141#14556570C2318yes—
142#14556570C2318yes—
143#14556570C2318yes—
144#14556570C23116yes—
145#14556570C23132yes—
146#14556569C23132yes—
147#14556568C23132yes—
148#14556568C23132yes—
149#14556568C23132yes—
150#14556567C23116yes—
151#14556565C2318yes—
152#14556563C23132yes—
153#14556563C23132yes—
154#14556562C23132yes—
155#14556562C23116yes—
156Q8×Dic73C23116yes—
157C4×Dic146C2318yes—
158C4×Dic146C2318yes—
159C4×Dic146C2318yes—
160C4×Dic146C23116yes—
161#14556556C23116yes—
162C4×D292C2318yes—
163D4×Dic73C23116yes—
164D4×Dic73C23116yes—
165D4×Dic73C23116yes—
166#14556553C23116yes—
167C4×C22⋊D73C23116yes—
168C4×C22⋊D73C23132yes—
169#14556550C23116yes—
170#14556548C23116yes—
171C2×C4⋊Dic73C2311yescharacteristic
172C2×C4⋊Dic73C2312yes—
173C2×C4⋊Dic73C2312yes—
174C2×C4⋊Dic73C2311yescharacteristic
175C2×C4⋊Dic73C2311yescharacteristic
176C2×C4⋊Dic73C2312yes—
177C2×C4⋊Dic73C2311yescharacteristic
178C2×C4⋊Dic73C2314yes—
179C2×#11924007C2314yes—
180C2×#11924007C2314yes—
181C2×#11924007C2314yes—
182C2×#11924007C23132yes—
183C2×#11924007C2312yes—
184C2×#11924007C2312yes—
185C2×#11924007C2312yes—
186C2×#11924007C2312yes—
187C2×#11924007C2312yes—
188C2×#11924007C2312yes—
189C2×#11924007C2312yes—
190C2×#11924007C2312yes—
191C2×C22⋊Dic73C2312yes—
192C2×C22⋊Dic73C2312yes—
193C2×C22⋊Dic73C2314yes—
194C2×C22⋊Dic73C2312yes—
195C2×C22⋊Dic73C2314yes—
196C2×C22⋊Dic73C2314yes—
197C2×C22⋊Dic73C2314yes—
198C2×#11924005C2312yes—
199C2×#11924005C2312yes—
200C2×#11924005C2312yes—
201C2×#11924005C2314yes—
202C2×#11924005C2312yes—
203C2×C4×Dic73C2312yes—
204C2×C4×Dic73C2312yes—
205C2×C4×Dic73C2312yes—
206C2×C4×Dic73C2314yes—
207C2×#41×C73—48no—
208C2×#41×C73C23116yes—
209C22×Q8×C73C2312yes—
210C22×D4×C73C2312yes—
211C22×D4×C73C2312yes—
212C22×D4×C73C2312yes—
213C22×D4×C73C2314yes—
214C23×C4×C73C2311yescharacteristic
215C23×C4×C73C2311yescharacteristic
216C23×C4×C73C2311yescharacteristic
217C23×C4×C73C2314yes—
218C4⋊Q8×C73C2318yes—
219#127×C73C2318yes—
220#124×C73C23116yes—
221#121×C73C23116yes—
222#121×C73C23116yes—
223C4×D4×C73C23116yes—
224C4×D4×C73C23116yes—
225C2×C4⋊C4×C73C2312yes—
226C2×C4⋊C4×C73C2312yes—
227C2×C22⋊C4×C73C2314yes—
228C2×C22⋊C4×C73C2314yes—
229C2×C42×C73C2318yes—
230C2×C42×C73C2311yescharacteristic
231C2×C42×C73C2311yescharacteristic
232C2×C42×C73C2311yescharacteristic
233C2×C42×C73C2311yescharacteristic
234C23×D73C2412yes—
235#11924027—432no—
236C2×Dic146—24no—
237C2×Dic146—24no—
238C2×Dic146—24no—
239C2×Dic146—48no—
240C2×Dic146—44no—
241C2×Dic146C2414yes—
242C2×Dic146C2414yes—
243C2×Dic146C2414yes—
244C2×Dic146C2418yes—
245C2×Dic146C24116yes—
246Q8×D73—432no—
247C2×D292—24no—
248C2×D292C2414yes—
249C2×C22⋊D73—44no—
250C2×C22⋊D73—48no—
251C2×C22⋊D73—48no—
252C2×C22⋊D73C2418yes—
253C2×C22⋊D73C24116yes—
254C2×C22⋊D73C24116yes—
255C22×Dic73—48no—
256C22×Dic73—48no—
257C22×Dic73C2412yes—
258C22×Dic73C2412yes—
259C22×Dic73C2412yes—
260C22×Dic73C2412yes—
261C22×Dic73C2412yes—
262C22×Dic73C2412yes—
263C22×Dic73C2412yes—
264C22×Dic73C24116yes—
265C22×Dic73C24116yes—
266C2×C4×D73—28no—
267C2×C4×D73—48no—
268C2×C4×D73C2418yes—
269C2×C4×D73C24116yes—
270C4⋊Dic73C2418yes—
271C4⋊Dic73C2418yes—
272C4⋊Dic73C2414yes—
273C4⋊Dic73C2414yes—
274C4⋊Dic73C2414yes—
275C4⋊Dic73C2414yes—
276C4⋊Dic73C2418yes—
277C4⋊Dic73C24116yes—
278#11924007C2418yes—
279#11924007C2418yes—
280#11924007C24116yes—
281#11924007C24116yes—
282#11924007C2418yes—
283#11924007C2418yes—
284#11924007C2418yes—
285#11924007C24116yes—
286#11924007C2418yes—
287#11924007C2418yes—
288#11924007C2418yes—
289C22⋊Dic73C2418yes—
290C22⋊Dic73C2418yes—
291C22⋊Dic73C24116yes—
292C22⋊Dic73C2418yes—
293C22⋊Dic73C24116yes—
294C22⋊Dic73C24116yes—
295C22⋊Dic73C24116yes—
296#11924005C2418yes—
297#11924005C2418yes—
298#11924005C2418yes—
299#11924005C24116yes—
300#11924005C2418yes—
301C4×Dic73C2418yes—
302C4×Dic73C2418yes—
303C4×Dic73C2418yes—
304C4×Dic73C24116yes—
305C24×C73C2414yes—
306C24×C73C2411yescharacteristic
307#41×C73—432no—
308C2×Q8×C73—28no—
309C2×Q8×C73C2418yes—
310C2×D4×C73—28no—
311C2×D4×C73—28no—
312C2×D4×C73—44no—
313C2×D4×C73—48no—
314C2×D4×C73C2418yes—
315C2×D4×C73C2418yes—
316C2×D4×C73C2418yes—
317C2×D4×C73C24116yes—
318C22×C4×C73—24no—
319C22×C4×C73—24no—
320C22×C4×C73—42no—
321C22×C4×C73—48no—
322C22×C4×C73C2411yescharacteristic
323C22×C4×C73C2411yescharacteristic
324C22×C4×C73C2411yescharacteristic
325C22×C4×C73C2414yes—
326C22×C4×C73C2411yescharacteristic
327C22×C4×C73C2414yes—
328C22×C4×C73C2414yes—
329C22×C4×C73C2414yes—
330C22×C4×C73C24116yes—
331C22×C4×C73C2411yescharacteristic
332C22×C4×C73C2411yescharacteristic
333C4⋊C4×C73C2418yes—
334C4⋊C4×C73C2418yes—
335C22⋊C4×C73C24116yes—
336C22⋊C4×C73C24116yes—
337C42×C73C2414yes—
338C42×C73C2414yes—
339C42×C73C2414yes—
340C42×C73C2414yes—
341C23×C73—22no—
342C23×C73—28no—
343C23×C73—22no—
344C23×C73—28no—
345C23×C73—22no—
346C23×C73—28no—
347C23×C73C2518yes—
348C23×C73C2512yes—
349C23×C73C2511yescharacteristic
350C22×D73—24no—
351C22×D73—24no—
352C22×D73—24no—
353C22×D73C2514yes—
354Q8×C73—216no—
355D4×C73—216no—
356D4×C73—216no—
357D4×C73—48no—
358D4×C73—416no—
359C2×C4×C73—22no—
360C2×C4×C73—28no—
361C2×C4×C73—22no—
362C2×C4×C73—22no—
363C2×C4×C73—22no—
364C2×C4×C73—28no—
365C2×C4×C73—28no—
366C2×C4×C73—44no—
367C2×C4×C73—416no—
368C2×C4×C73H(5,𝔽2)14yes—
369C2×C4×C732−1+414yes—
370C2×C4×C73C2512yes—
371C2×C4×C73C2512yes—
372C2×C4×C73C2512yes—
373C2×C4×C73C2512yes—
374C2×C4×C73C2518yes—
375C2×C4×C73C2512yes—
376C2×C4×C73C2512yes—
377C22⋊D73—416no—
378C22⋊D73—48no—
379C22⋊D73—416no—
380C2×Dic73—24no—
381C2×Dic73—24no—
382C2×Dic73—24no—
383C2×Dic73—24no—
384C2×Dic73—24no—
385C2×Dic73—24no—
386C2×Dic73—24no—
387C2×Dic73—416no—
388C2×Dic73—416no—
389C2×Dic73C2514yes—
390C2×Dic73C2514yes—
391C2×Dic73C2514yes—
392C2×Dic73C2514yes—
393C2×Dic73C2514yes—
394C2×Dic73C2514yes—
395C2×Dic73C2514yes—
396D292—28no—
397C4×D73—216no—
398C4×D73—416no—
399Dic146—28no—
400Dic146—28no—
401Dic146—28no—
402Dic146—416no—
403Dic146—48no—
404C22×C73—28no—
405C22×C73—22no—
406C22×C73—22no—
407C22×C73—28no—
408C22×C73—28no—
409C22×C73—22no—
410C22×C73—44no—
411C22×C73—416no—
412C22×C73C2×H(5,𝔽2)12yes—
413C22×C73C2×2−1+412yes—
414C22×C73#58512yes—
415C22×C73C2611yescharacteristic
416C2×D73—24no—
417C2×D73—24no—
418C2×D73—24no—
419C2×D73—48no—
420C4×C73—28no—
421C4×C73—22no—
422C4×C73—22no—
423C4×C73—22no—
424C4×C73—22no—
425C4×C73C2×H(5,𝔽2)14yes—
426C4×C73C2×2−1+414yes—
427Dic73—24no—
428Dic73—24no—
429Dic73—24no—
430Dic73—24no—
431Dic73—24no—
432Dic73—24no—
433Dic73—24no—
434C2×#3554—731nomaximal, Sylow
435C2×C73—48no—
436C2×C73—42no—
437C2×C73#355414yescomplemented
438C2×C73C22×H(5,𝔽2)11yescharacteristic
439C2×C73C22×2−1+411yescharacteristic
440C2×C73C2×#58511yescharacteristic
441D73—44no—
442#3554—7332no—
443C2×#562—734no—
444C2×#559—731no—
445C2×#559—732no—
446C2×#557—731no—
447C2×#554—732no—
448C2×#550—731no—
449C2×D4×Q8—731no—
450C2×#548—732no—
451C2×#547—732no—
452C2×#542—732no—
453C2×#542—732no—
454C2×#540—732no—
455C2×#539—734no—
456C2×#536—732no—
457C2×#533—731no—
458C2×#532D7311yescharacteristic, complemented
459C2×#529—731no—
460C73C2×#355411yescharacteristic, complemented, Sylow
461C22×#41—732no—
462C22×#41C2×D7312yes—
463C23×Q8—732no—
464#562—7364no—
465#559—7316no—
466#559—7332no—
467#557—7316no—
468#554—7332no—
469#550—7316no—
470D4×Q8—7316no—
471#548—7332no—
472#547—7332no—
473#542—7332no—
474#542—7332no—
475#540—7332no—
476#539—7364no—
477#536—7332no—
478#533—7316no—
479#532C2×D73116yescomplemented
480C2×C4⋊Q8—732no—
481C2×C4⋊Q8—732no—
482C2×C4⋊Q8—731no—
483C2×C4⋊Q8—731no—
484C2×C4⋊Q8C2×D7311yescharacteristic
485C2×#127—732no—
486C2×#127C2×D7311yescharacteristic
487#529—7316no—
488C2×#126—734no—
489C2×#126—732no—
490C2×#125—734no—
491C2×#125—732no—
492C2×#125—731no—
493C2×#125—732no—
494C2×#124—732no—
495C2×#124—734no—
496C2×#124—732no—
497C2×#124—734no—
498C2×#124—731no—
499C2×#124C2×D7312yes—
500C2×#123—734no—
501C2×#123—734no—
502C2×#123—732no—
503C2×#123—734no—
504C2×#123—734no—
505C2×#123—734no—
506C2×#123—734no—
507C2×C22⋊Q8—732no—
508C2×C22⋊Q8—731no—
509C2×C22⋊Q8—731no—
510C2×C22⋊Q8—731no—
511C2×C22⋊Q8—732no—
512C2×C22⋊Q8—734no—
513C2×C22⋊Q8—734no—
514C2×C22⋊Q8—734no—
515C2×C22⋊Q8—734no—
516C2×C22⋊Q8—734no—
517C2×#121—734no—
518C2×#121—734no—
519C2×#121—734no—
520C2×#121—732no—
521C2×#121—731no—
522C2×#121C2×D7312yes—
523C2×#121C2×D7312yes—
524C2×C4×Q8—732no—
525C2×C4×Q8—732no—
526C2×C4×Q8—731no—
527C2×C4×Q8—731no—
528C2×C4×Q8—731no—
529C2×C4×Q8—732no—
530C2×C4×D4—732no—
531C2×C4×D4—732no—
532C2×C4×D4—732no—
533C2×C4×D4—732no—
534C2×C4×D4—734no—
535C2×C4×D4—732no—
536C2×C4×D4—731no—
537C2×C4×D4C2×D7312yes—
538C2×C4×D4C2×D7312yes—
539C2×#117—732no—
540C2×#117—732no—
541C22×C4⋊C4—734no—
542C22×C42C2×D7311yescharacteristic
543C2×#41—48no—
544C2×#41—2928no—
545C2×#41—7316no—
546C2×#41C22×D73116yes—
547C22×Q8—2928no—
548C22×Q8—7316no—
549C22×Q8—732no—
550C22×Q8—734no—
551C22×Q8—731no—
552C22×Q8—731no—
553C22×Q8—731no—
554C22×Q8C22×D7312yes—
555C22×D4—732no—
556C22×D4—734no—
557C22×D4—734no—
558C22×D4—731no—
559C22×D4C22×D7312yes—
560C22×D4C22×D7312yes—
561C22×D4C22×D7312yes—
562C22×D4C22×D7314yes—
563C23×C4—734no—
564C23×C4—734no—
565C23×C4—734no—
566C23×C4—732no—
567C23×C4C22×D7311yescharacteristic
568C23×C4C22×D7311yescharacteristic
569C23×C4C22×D7314yes—
570C23×C4C22×D7311yescharacteristic
571C4⋊Q8—7316no—
572C4⋊Q8—7316no—
573C4⋊Q8—738no—
574C4⋊Q8—738no—
575C4⋊Q8C22×D7318yes—
576#127—7316no—
577#127C22×D7318yes—
578#126—7332no—
579#126—7316no—
580#125—7332no—
581#125—7316no—
582#125—738no—
583#125—7316no—
584#124—7316no—
585#124—7332no—
586#124—7316no—
587#124—7332no—
588#124—738no—
589#124C22×D73116yes—
590#123—7332no—
591#123—7332no—
592#123—7316no—
593#123—7332no—
594#123—7332no—
595#123—7332no—
596#123—7332no—
597C22⋊Q8—7316no—
598C22⋊Q8—738no—
599C22⋊Q8—738no—
600C22⋊Q8—738no—
601C22⋊Q8—7316no—
602C22⋊Q8—7332no—
603C22⋊Q8—7332no—
604C22⋊Q8—7332no—
605C22⋊Q8—7332no—
606C22⋊Q8—7332no—
607#121—7332no—
608#121—7332no—
609#121—7332no—
610#121—7316no—
611#121—738no—
612#121C22×D73116yes—
613#121C22×D73116yes—
614C4×Q8—7316no—
615C4×Q8—7316no—
616C4×Q8—738no—
617C4×Q8—738no—
618C4×Q8—738no—
619C4×Q8—7316no—
620C4×D4—7316no—
621C4×D4—7316no—
622C4×D4—7316no—
623C4×D4—7316no—
624C4×D4—7332no—
625C4×D4—7316no—
626C4×D4—738no—
627C4×D4C22×D73116yes—
628C4×D4C22×D73116yes—
629#117—7316no—
630#117—7316no—
631C2×C4⋊C4—732no—
632C2×C4⋊C4—732no—
633C2×C4⋊C4—734no—
634C2×C4⋊C4—734no—
635C2×C4⋊C4—7332no—
636C2×C4⋊C4—732no—
637C2×C4⋊C4—732no—
638C2×C4⋊C4—732no—
639C2×C4⋊C4—732no—
640C2×C4⋊C4—731no—
641C2×C4⋊C4—731no—
642C2×C4⋊C4—732no—
643C2×C4⋊C4—731no—
644C2×C4⋊C4—731no—
645C2×C4⋊C4—732no—
646C2×C4⋊C4—734no—
647C2×C4⋊C4—732no—
648C2×C4⋊C4—732no—
649C2×C4⋊C4—734no—
650C2×C4⋊C4—732no—
651C2×C4⋊C4C22×D7312yes—
652C2×C4⋊C4C22×D7312yes—
653C2×C22⋊C4—732no—
654C2×C22⋊C4—732no—
655C2×C22⋊C4—734no—
656C2×C22⋊C4—734no—
657C2×C22⋊C4—732no—
658C2×C22⋊C4—734no—
659C2×C22⋊C4—734no—
660C2×C22⋊C4—732no—
661C2×C22⋊C4—732no—
662C2×C22⋊C4—732no—
663C2×C22⋊C4—732no—
664C2×C22⋊C4—734no—
665C2×C22⋊C4C22×D7314yes—
666C2×C22⋊C4C22×D7314yes—
667C2×C42—732no—
668C2×C42—732no—
669C2×C42—732no—
670C2×C42—734no—
671C2×C42C22×D7311yescharacteristic
672C2×C42C22×D7311yescharacteristic
673C2×C42C22×D7311yescharacteristic
674C2×C42C22×D7311yescharacteristic
675C2×C42C22×D7318yes—
676C24—732no—
677C24C23×D7311yescharacteristic
678C24C23×D7314yes—
679#41—432no—
680#41—29232no—
681C2×Q8—28no—
682C2×Q8—2928no—
683C2×Q8—2924no—
684C2×Q8—29232no—
685C2×Q8—738no—
686C2×Q8—7316no—
687C2×Q8—734no—
688C2×Q8—734no—
689C2×Q8—734no—
690C2×Q8—1464no—
691C2×Q8—1464no—
692C2×Q8—1464no—
693C2×Q8C23×D7318yes—
694C2×D4—28no—
695C2×D4—28no—
696C2×D4—44no—
697C2×D4—48no—
698C2×D4—2924no—
699C2×D4—2928no—
700C2×D4—2928no—
701C2×D4—738no—
702C2×D4—7316no—
703C2×D4—7316no—
704C2×D4—734no—
705C2×D4—1464no—
706C2×D4C23×D7318yes—
707C2×D4C23×D7318yes—
708C2×D4C23×D7318yes—
709C2×D4C23×D73116yes—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—42no—
713C22×C4—48no—
714C22×C4—2928no—
715C22×C4—2928no—
716C22×C4—2928no—
717C22×C4—7316no—
718C22×C4—7316no—
719C22×C4—7316no—
720C22×C4—732no—
721C22×C4—732no—
722C22×C4—732no—
723C22×C4—732no—
724C22×C4—732no—
725C22×C4—732no—
726C22×C4—732no—
727C22×C4—738no—
728C22×C4—1468no—
729C22×C4C23×D7314yes—
730C22×C4C23×D7314yes—
731C22×C4C23×D7314yes—
732C22×C4C23×D7311yescharacteristic
733C22×C4C23×D7311yescharacteristic
734C22×C4C23×D7311yescharacteristic
735C22×C4C23×D7311yescharacteristic
736C22×C4C23×D7314yes—
737C22×C4C23×D73116yes—
738C22×C4C23×D7311yescharacteristic
739C22×C4C23×D7311yescharacteristic
740C4⋊C4—738no—
741C4⋊C4—738no—
742C4⋊C4—7316no—
743C4⋊C4—7316no—
744C4⋊C4—738no—
745C4⋊C4—738no—
746C4⋊C4—738no—
747C4⋊C4—738no—
748C4⋊C4—738no—
749C4⋊C4—7316no—
750C4⋊C4—738no—
751C4⋊C4—738no—
752C4⋊C4—738no—
753C4⋊C4—734no—
754C4⋊C4—734no—
755C4⋊C4—734no—
756C4⋊C4—734no—
757C4⋊C4—7316no—
758C4⋊C4—738no—
759C4⋊C4C23×D7318yes—
760C4⋊C4C23×D7318yes—
761C22⋊C4—738no—
762C22⋊C4—738no—
763C22⋊C4—7316no—
764C22⋊C4—7316no—
765C22⋊C4—738no—
766C22⋊C4—7316no—
767C22⋊C4—7316no—
768C22⋊C4—738no—
769C22⋊C4—738no—
770C22⋊C4—738no—
771C22⋊C4—738no—
772C22⋊C4—7316no—
773C22⋊C4C23×D73116yes—
774C22⋊C4C23×D73116yes—
775C42—738no—
776C42—738no—
777C42—738no—
778C42—7316no—
779C42C23×D7314yes—
780C42C23×D7314yes—
781C42C23×D7314yes—
782C42C23×D7314yes—
783C23—22no—
784C23—28no—
785C23—22no—
786C23—28no—
787C23—22no—
788C23—28no—
789C23—734no—
790C23—1464no—
791C23—1464no—
792C23—1464no—
793C23C24×D7312yes—
794C23C24×D7318yes—
795C23C24×D7311yescharacteristic
796Q8—216no—
797Q8—29216no—
798Q8—2928no—
799Q8—1468no—
800Q8—1468no—
801Q8—1468no—
802D4—216no—
803D4—216no—
804D4—416no—
805D4—48no—
806D4—29216no—
807D4—2928no—
808D4—29216no—
809D4—1468no—
810C2×C4—22no—
811C2×C4—28no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—28no—
816C2×C4—28no—
817C2×C4—416no—
818C2×C4—44no—
819C2×C4—29216no—
820C2×C4—29216no—
821C2×C4—29216no—
822C2×C4—734no—
823C2×C4—734no—
824C2×C4—734no—
825C2×C4—734no—
826C2×C4—734no—
827C2×C4—734no—
828C2×C4—734no—
829C2×C4—1464no—
830C2×C4—1464no—
831C2×C4—1464no—
832C2×C4—1464no—
833C2×C4—1464no—
834C2×C4—1464no—
835C2×C4—1464no—
836C2×C4—14616no—
837C2×C4#1455663614yes—
838C2×C4#1455663814yes—
839C2×C4C24×D7318yes—
840C2×C4C24×D7312yes—
841C2×C4C24×D7312yes—
842C2×C4C24×D7312yes—
843C2×C4C24×D7312yes—
844C2×C4C24×D7312yes—
845C2×C4C24×D7312yes—
846C22—22no—
847C22—28no—
848C22—22no—
849C22—28no—
850C22—22no—
851C22—28no—
852C22—44no—
853C22—416no—
854C22—2928no—
855C22—1464no—
856C22—1464no—
857C22—1464no—
858C22C2×#1455663612yes—
859C22C2×#1455663812yes—
860C22#1798942312yes—
861C22C25×D7311yescharacteristic
862C4—22no—
863C4—28no—
864C4—22no—
865C4—22no—
866C4—22no—
867C4—1464no—
868C4—1464no—
869C4—1464no—
870C4—1464no—
871C4—1464no—
872C4—1464no—
873C4—1464no—
874C4C2×#1455663614yes—
875C4C2×#1455663814yes—
876C2—42no—
877C2—48no—
878C2—2924no—
879C2#2262439614yesdirect product factor
880C2C22×#1455663611yescharacteristic
881C2C22×#1455663811yescharacteristic
882C2C2×#1798942311yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#532×C73C2
socleC23×C73C25
hypercenterC2×#532D73
hypocenterC73C2×#3554
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #22624396C2direct (N × H)
2. C2×#17989332C2semidirect
3. C2×#17989323C2semidirect
4. C2×#17989320C2semidirect
5. C2×#17989312C2semidirect
6. C2×#17989296C2semidirect
7. C2×#17989257C2semidirect
8. C2×#17989252C2semidirect
9. C2×#17989244C2semidirect
10. C2×#17989236C2semidirect
11. C2×#17989206C2semidirect
12. C2×#17989204C2semidirect
13. C2×#17989190C2semidirect
14. C2×#17989179C2semidirect
15. C2×#17989157C2semidirect
16. C2×#17989144C2semidirect
17. C2×#17989121C2semidirect
18. C2×#532×C73C2semidirect
21. #17989332C22semidirect
22. #17989323C22semidirect
23. #17989320C22semidirect
24. #17989312C22semidirect
25. #17989296C22semidirect
26. #17989257C22semidirect
27. #17989252C22semidirect
28. #17989244C22semidirect
29. #17989236C22semidirect
30. #17989206C22semidirect
31. #17989204C22semidirect
32. #17989190C22semidirect
33. #17989179C22semidirect
34. #17989157C22semidirect
35. #17989144C22semidirect
41. #17989121C22semidirect
92. #532×C73C22semidirect
437. C2×C73#3554semidirect
458. C2×#532D73semidirect
460. C73C2×#3554semidirect
479. #532C2×D73semidirect
879. C2#22624396direct (N × H)

Maximal subgroups

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

subgroupindex
#226243962
C2×#179893322
C2×#179893232
C2×#179893202
C2×#179893122
C2×#179892962
C2×#179892572
C2×#179892522
C2×#179892442
C2×#179892362
C2×#179892062
C2×#179892042
C2×#179891902
C2×#179891792
C2×#179891572
C2×#179891442
C2×#179891212
C2×#532×C732
C2×#355473