Finite Group Databasebeta

← C2×#22624402 #33993613

Subgroups — C2×#22624402 #33993613

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#22624402C2132yesmaximal, direct product factor
2C2×#17989333C214yesmaximal, complemented
3C2×#17989322C212yesmaximal, complemented
4C2×#17989322C211yesmaximal, characteristic, complemented
5C2×#17989315C211yesmaximal, characteristic, complemented
6C2×#17989297C212yesmaximal, complemented
7C2×#17989259C211yesmaximal, characteristic, complemented
8C2×Q8×D292C211yesmaximal, characteristic, complemented
9C2×#17989247C212yesmaximal, complemented
10C2×#17989239C212yesmaximal, complemented
11C2×#17989211C212yesmaximal, complemented
12C2×#17989208C212yesmaximal, complemented
13C2×#17989192C212yesmaximal, complemented
14C2×#17989185C214yesmaximal, complemented
15C2×#17989162C212yesmaximal, complemented
16C2×#17989137C211yesmaximal, characteristic, complemented
17C2×#17989121C211yesmaximal, characteristic, complemented
18C2×#533×C73C211yesmaximal, characteristic, complemented
19C22×#11924029C2212yes—
20C22×#11924028C2212yes—
21C22×Q8×D73C2212yes—
22#17989333C22164yescomplemented
23#17989322C22116yescomplemented
24#17989322C22132yescomplemented
25#17989315C22116yescomplemented
26#17989297C22132yescomplemented
27#17989259C22116yescomplemented
28Q8×D292C22116yescomplemented
29#17989247C22132yescomplemented
30#17989239C22132yescomplemented
31#17989211C22132yescomplemented
32#17989208C22132yescomplemented
33#17989192C22132yescomplemented
34#17989185C22164yescomplemented
35#17989162C22132yescomplemented
36#17989137C22116yescomplemented
37C2×#14556591C2211yescharacteristic
38C2×#14556591C2212yes—
39C2×#14556589C2212yes—
40C2×#14556588C2212yes—
41C2×#14556588C2211yescharacteristic
42#17989121C22116yescomplemented
43C2×#14556586C2214yes—
44C2×#14556585C2212yes—
45C2×#14556583C2212yes—
46C2×#14556583C2211yescharacteristic
47C2×#14556581C2214yes—
48C2×#14556580C2212yes—
49C2×#14556580C2214yes—
50C2×#14556579C2212yes—
51C2×#14556579C2212yes—
52C2×#14556579C2211yescharacteristic
53C2×#14556577C2214yes—
54C2×#14556576C2214yes—
55C2×#14556576C2214yes—
56C2×#14556576C2214yes—
57C2×#14556576C2214yes—
58C2×#14556576C2214yes—
59C2×#14556574C2212yes—
60C2×#14556573C2214yes—
61C2×#14556571C2214yes—
62C2×#14556571C2212yes—
63C2×#14556570C2211yescharacteristic
64C2×#14556569C2214yes—
65C2×#14556569C2214yes—
66C2×#14556569C2214yes—
67C2×#14556567C2214yes—
68C2×#14556566C2214yes—
69C2×#14556566C2212yes—
70C2×#14556565C2212yes—
71C2×#14556565C2211yescharacteristic
72C2×#14556565C2212yes—
73C2×#14556564C2214yes—
74C2×#14556564C2214yes—
75C2×C4×Dic146C2212yes—
76C2×C4×Dic146C2211yescharacteristic
77C2×#14556556C2212yes—
78C2×C4×D292C2212yes—
79C2×C4×D292C2212yes—
80C2×C4×D292C2212yes—
81C2×C4×D292C2212yes—
82C2×C4×D292C2212yes—
83C2×C4×D292C2211yescharacteristic
84C2×#14556553C2214yes—
85C2×#14556553C2212yes—
86C2×C4×C22⋊D73C2212yes—
87C2×#14556548C2212yes—
88C2×C4⋊C4×D73C2214yes—
89#533×C73C22116yescomplemented
90C2×C4⋊Q8×C73C2211yescharacteristic
91C2×C4⋊Q8×C73C2211yescharacteristic
92C2×#125×C73C2212yes—
93C2×C22⋊Q8×C73C2212yes—
94C2×C22⋊Q8×C73C2211yescharacteristic
95C2×C22⋊Q8×C73C2211yescharacteristic
96C2×C4×Q8×C73C2211yescharacteristic
97C2×C4×Q8×C73C2211yescharacteristic
98C2×C4×Q8×C73C2212yes—
99C2×#117×C73C2212yes—
100C22×C42×C73C2211yescharacteristic
101C2×#11924029—48no—
102C2×#11924029C23116yes—
103C2×#11924028—48no—
104C2×#11924028C23116yes—
105C22×Dic146C2312yes—
106C22×Dic146C2311yescharacteristic
107C22×Dic146C2314yes—
108C2×Q8×D73—48no—
109C2×Q8×D73C23116yes—
110C22×D292C2311yescharacteristic
111C22×D292C2312yes—
112C22×D292C2312yes—
113C22×D292C2314yes—
114C22×D292C2314yes—
115C22×D292C2312yes—
116C22×C22⋊D73C2314yes—
117C22×C22⋊D73C2312yes—
118C22×C4×D73C2312yes—
119C22×C4×D73C2314yes—
120C22×C4×D73C2314yes—
121C22×C4×D73C2314yes—
122C22×C4×D73C2314yes—
123#14556591C2318yes—
124#14556591C23116yes—
125#14556589C23116yes—
126#14556588C2318yes—
127#14556588C23116yes—
128#14556586C23132yes—
129#14556585C23116yes—
130#14556583C2318yes—
131#14556583C23116yes—
132#14556581C23132yes—
133#14556580C23116yes—
134#14556580C23132yes—
135#14556579C2318yes—
136#14556579C23116yes—
137#14556579C23116yes—
138#14556577C23132yes—
139#14556576C23132yes—
140#14556576C23132yes—
141#14556576C23132yes—
142#14556576C23132yes—
143#14556576C23132yes—
144#14556574C23116yes—
145#14556573C23132yes—
146#14556571C23132yes—
147#14556571C23116yes—
148#14556570C2318yes—
149#14556569C23132yes—
150#14556569C23132yes—
151#14556569C23132yes—
152#14556567C23132yes—
153#14556566C23132yes—
154#14556566C23116yes—
155#14556565C2318yes—
156#14556565C23116yes—
157#14556565C23116yes—
158#14556564C23132yes—
159#14556564C23132yes—
160C4×Dic146C2318yes—
161C4×Dic146C23116yes—
162#14556556C23116yes—
163C4×D292C2318yes—
164C4×D292C23116yes—
165C4×D292C23116yes—
166C4×D292C23116yes—
167C4×D292C23116yes—
168C4×D292C23116yes—
169#14556553C23132yes—
170#14556553C23116yes—
171C4×C22⋊D73C23116yes—
172#14556548C23116yes—
173C2×C4⋊Dic73C2311yescharacteristic
174C2×C4⋊Dic73C2312yes—
175C2×C4⋊Dic73C2314yes—
176C2×C4⋊Dic73C2312yes—
177C2×C4⋊Dic73C2311yescharacteristic
178C2×#11924007C2314yes—
179C2×#11924007C2314yes—
180C2×#11924007C2312yes—
181C2×#11924007C2312yes—
182C2×#11924007C2312yes—
183C2×#11924007C2314yes—
184C2×#11924007C2312yes—
185C4⋊C4×D73C23132yes—
186C2×C22⋊Dic73C2312yes—
187C2×#11924005C2312yes—
188C2×#11924005C2312yes—
189C2×#11924005C2312yes—
190C2×#11924005C2314yes—
191C2×#11924005C2314yes—
192C2×#11924005C2314yes—
193C2×#11924005C2314yes—
194C2×#11924005C2314yes—
195C2×#11924005C2314yes—
196C2×#11924005C2314yes—
197C2×#11924005C2312yes—
198C2×C4×Dic73C2312yes—
199C2×C4×Dic73C2314yes—
200C22×Q8×C73C2311yescharacteristic
201C22×Q8×C73C2311yescharacteristic
202C22×Q8×C73C2312yes—
203C23×C4×C73C2311yescharacteristic
204C23×C4×C73C2311yescharacteristic
205C23×C4×C73C2311yescharacteristic
206C4⋊Q8×C73C2318yes—
207C4⋊Q8×C73C2318yes—
208#125×C73C23116yes—
209C22⋊Q8×C73C2318yes—
210C22⋊Q8×C73C2318yes—
211C22⋊Q8×C73C23116yes—
212C4×Q8×C73C2318yes—
213C4×Q8×C73C2318yes—
214C4×Q8×C73C23116yes—
215#117×C73C23116yes—
216C2×C4⋊C4×C73C2312yes—
217C2×C4⋊C4×C73C2312yes—
218C2×C4⋊C4×C73C2312yes—
219C2×C4⋊C4×C73C2312yes—
220C2×C4⋊C4×C73C2312yes—
221C2×C4⋊C4×C73C2312yes—
222C2×C4⋊C4×C73C2311yescharacteristic
223C2×C4⋊C4×C73C2311yescharacteristic
224C2×C4⋊C4×C73C2312yes—
225C2×C22⋊C4×C73C2312yes—
226C2×C22⋊C4×C73C2312yes—
227C2×C42×C73C2318yes—
228C2×C42×C73C2311yescharacteristic
229C2×C42×C73C2312yes—
230C2×C42×C73C2312yes—
231C2×C42×C73C2311yescharacteristic
232C2×C42×C73C2311yescharacteristic
233C2×C42×C73C2311yescharacteristic
234C23×D73C2412yes—
235C23×D73C2414yes—
236#11924029—432no—
237#11924028—432no—
238C2×Dic146—28no—
239C2×Dic146—24no—
240C2×Dic146—48no—
241C2×Dic146C2418yes—
242C2×Dic146C2414yes—
243C2×Dic146C24116yes—
244Q8×D73—432no—
245C2×D292—28no—
246C2×D292—24no—
247C2×D292—28no—
248C2×D292—44no—
249C2×D292—48no—
250C2×D292—48no—
251C2×D292C2418yes—
252C2×D292C2414yes—
253C2×D292C2418yes—
254C2×D292C24116yes—
255C2×D292C2418yes—
256C2×D292C24116yes—
257C2×C22⋊D73—44no—
258C2×C22⋊D73—48no—
259C2×C22⋊D73C2418yes—
260C2×C22⋊D73C24116yes—
261C22×Dic73C2412yes—
262C22×Dic73C2412yes—
263C22×Dic73C2414yes—
264C22×Dic73C2412yes—
265C2×C4×D73—28no—
266C2×C4×D73—48no—
267C2×C4×D73—48no—
268C2×C4×D73—48no—
269C2×C4×D73—48no—
270C2×C4×D73C2418yes—
271C2×C4×D73C24116yes—
272C2×C4×D73C24116yes—
273C2×C4×D73C24116yes—
274C2×C4×D73C24116yes—
275C4⋊Dic73C24116yes—
276C4⋊Dic73C2414yes—
277C4⋊Dic73C2414yes—
278C4⋊Dic73C2418yes—
279C4⋊Dic73C2418yes—
280#11924007C2418yes—
281#11924007C24116yes—
282#11924007C2418yes—
283#11924007C2418yes—
284#11924007C24116yes—
285#11924007C24116yes—
286#11924007C2418yes—
287C22⋊Dic73C2418yes—
288#11924005C2418yes—
289#11924005C2418yes—
290#11924005C2418yes—
291#11924005C24116yes—
292#11924005C24116yes—
293#11924005C24116yes—
294#11924005C24116yes—
295#11924005C24116yes—
296#11924005C24116yes—
297#11924005C24116yes—
298#11924005C2418yes—
299C4×Dic73C2418yes—
300C4×Dic73C24116yes—
301C24×C73C2411yescharacteristic
302C2×Q8×C73—24no—
303C2×Q8×C73—24no—
304C2×Q8×C73—44no—
305C2×Q8×C73C2414yes—
306C2×Q8×C73C2414yes—
307C2×Q8×C73C2418yes—
308C22×C4×C73—24no—
309C22×C4×C73—24no—
310C22×C4×C73—42no—
311C22×C4×C73C2411yescharacteristic
312C22×C4×C73C2411yescharacteristic
313C22×C4×C73C2411yescharacteristic
314C22×C4×C73C2411yescharacteristic
315C22×C4×C73C2414yes—
316C22×C4×C73C2414yes—
317C22×C4×C73C2412yes—
318C22×C4×C73C2412yes—
319C22×C4×C73C2412yes—
320C22×C4×C73C2412yes—
321C22×C4×C73C2414yes—
322C22×C4×C73C2411yescharacteristic
323C22×C4×C73C2411yescharacteristic
324C4⋊C4×C73C2418yes—
325C4⋊C4×C73C2418yes—
326C4⋊C4×C73C2418yes—
327C4⋊C4×C73C2418yes—
328C4⋊C4×C73C2418yes—
329C4⋊C4×C73C2418yes—
330C4⋊C4×C73C2414yes—
331C4⋊C4×C73C2414yes—
332C4⋊C4×C73C2418yes—
333C22⋊C4×C73C2418yes—
334C22⋊C4×C73C2418yes—
335C42×C73C2414yes—
336C42×C73C2414yes—
337C42×C73C2414yes—
338C42×C73C2414yes—
339C42×C73C2418yes—
340C42×C73C2418yes—
341C23×C73—22no—
342C23×C73—22no—
343C23×C73—22no—
344C23×C73C2512yes—
345C23×C73C2511yescharacteristic
346C22×D73—24no—
347C22×D73—28no—
348C22×D73—24no—
349C22×D73—28no—
350C22×D73—28no—
351C22×D73—24no—
352C22×D73C2514yes—
353C22×D73C2518yes—
354Q8×C73—28no—
355Q8×C73—28no—
356Q8×C73—48no—
357C2×C4×C73—22no—
358C2×C4×C73—24no—
359C2×C4×C73—24no—
360C2×C4×C73—22no—
361C2×C4×C73—22no—
362C2×C4×C73—22no—
363C2×C4×C73—24no—
364C2×C4×C73—24no—
365C2×C4×C73—28no—
366C2×C4×C73—28no—
367C2×C4×C73—44no—
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×C73C2514yes—
375C2×C4×C73C2514yes—
376C2×C4×C73C2514yes—
377C2×C4×C73C2514yes—
378C2×C4×C73C2512yes—
379C2×C4×C73C2512yes—
380C22⋊D73—48no—
381C22⋊D73—416no—
382C2×Dic73—24no—
383C2×Dic73—28no—
384C2×Dic73—24no—
385C2×Dic73—24no—
386C2×Dic73C2514yes—
387C2×Dic73C2514yes—
388C2×Dic73C2518yes—
389C2×Dic73C2514yes—
390D292—216no—
391D292—28no—
392D292—216no—
393D292—48no—
394D292—416no—
395D292—416no—
396C4×D73—216no—
397C4×D73—416no—
398C4×D73—416no—
399C4×D73—416no—
400C4×D73—416no—
401Dic146—216no—
402Dic146—28no—
403Dic146—416no—
404C22×C73—22no—
405C22×C73—22no—
406C22×C73—22no—
407C22×C73—44no—
408C22×C73C2×H(5,𝔽2)12yes—
409C22×C73C2×2−1+412yes—
410C22×C73#58512yes—
411C22×C73C2611yescharacteristic
412C2×D73—24no—
413C2×D73—28no—
414C2×D73—24no—
415C2×D73—28no—
416C2×D73—28no—
417C2×D73—24no—
418C2×D73—48no—
419C2×D73—416no—
420C4×C73—24no—
421C4×C73—22no—
422C4×C73—24no—
423C4×C73—22no—
424C4×C73—24no—
425C4×C73—22no—
426C4×C73—24no—
427C4×C73—22no—
428C4×C73C2×H(5,𝔽2)14yes—
429C4×C73C2×2−1+414yes—
430Dic73—28no—
431Dic73—24no—
432Dic73—24no—
433Dic73—24no—
434C2×#3554—731nomaximal, Sylow
435C2×C73—42no—
436C2×C73#355414yescomplemented
437C2×C73C22×H(5,𝔽2)11yescharacteristic
438C2×C73C22×2−1+411yescharacteristic
439C2×C73C2×#58511yescharacteristic
440D73—44no—
441D73—48no—
442#3554—7332no—
443C2×#562—734no—
444C2×#559—732no—
445C2×#559—731no—
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×#533D7311yescharacteristic, complemented
458C2×#532—731no—
459C2×#529—731no—
460C73C2×#355411yescharacteristic, complemented, Sylow
461C22×#41—732no—
462C22×#41—732no—
463C23×Q8—732no—
464#562—7364no—
465#559—7332no—
466#559—7316no—
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#533C2×D73116yescomplemented
479#532—7316no—
480C2×C4⋊Q8—732no—
481C2×C4⋊Q8—731no—
482C2×C4⋊Q8—732no—
483C2×C4⋊Q8C2×D7311yescharacteristic
484C2×C4⋊Q8C2×D7311yescharacteristic
485C2×#127—731no—
486C2×#127—732no—
487#529—7316no—
488C2×#126—734no—
489C2×#126—732no—
490C2×#125—734no—
491C2×#125—731no—
492C2×#125—732no—
493C2×#125C2×D7312yes—
494C2×#124—732no—
495C2×#124—734no—
496C2×#124—734no—
497C2×#124—731no—
498C2×#124—732no—
499C2×#124—732no—
500C2×#123—732no—
501C2×#123—734no—
502C2×#123—734no—
503C2×#123—734no—
504C2×#123—734no—
505C2×#123—734no—
506C2×#123—734no—
507C2×C22⋊Q8—734no—
508C2×C22⋊Q8—731no—
509C2×C22⋊Q8—734no—
510C2×C22⋊Q8—734no—
511C2×C22⋊Q8—734no—
512C2×C22⋊Q8—734no—
513C2×C22⋊Q8—732no—
514C2×C22⋊Q8C2×D7311yescharacteristic
515C2×C22⋊Q8C2×D7311yescharacteristic
516C2×C22⋊Q8C2×D7312yes—
517C2×#121—731no—
518C2×#121—732no—
519C2×#121—732no—
520C2×#121—734no—
521C2×#121—732no—
522C2×#121—734no—
523C2×#121—734no—
524C2×C4×Q8—732no—
525C2×C4×Q8—731no—
526C2×C4×Q8—732no—
527C2×C4×Q8C2×D7311yescharacteristic
528C2×C4×Q8C2×D7311yescharacteristic
529C2×C4×Q8C2×D7312yes—
530C2×C4×D4—732no—
531C2×C4×D4—734no—
532C2×C4×D4—732no—
533C2×C4×D4—731no—
534C2×C4×D4—732no—
535C2×C4×D4—732no—
536C2×C4×D4—732no—
537C2×C4×D4—732no—
538C2×C4×D4—732no—
539C2×#117—732no—
540C2×#117C2×D7312yes—
541C22×C4⋊C4—734no—
542C22×C42C2×D7311yescharacteristic
543C2×#41—2928no—
544C2×#41—2928no—
545C2×#41—7316no—
546C2×#41—7316no—
547C22×Q8—2928no—
548C22×Q8—7316no—
549C22×Q8—734no—
550C22×Q8—731no—
551C22×Q8—732no—
552C22×Q8C22×D7311yescharacteristic
553C22×Q8C22×D7311yescharacteristic
554C22×Q8C22×D7312yes—
555C22×D4—732no—
556C22×D4—734no—
557C22×D4—732no—
558C22×D4—734no—
559C22×D4—734no—
560C22×D4—731no—
561C22×D4—732no—
562C22×D4—732no—
563C23×C4—734no—
564C23×C4—734no—
565C23×C4—734no—
566C23×C4—734no—
567C23×C4—732no—
568C23×C4C22×D7311yescharacteristic
569C23×C4C22×D7311yescharacteristic
570C23×C4C22×D7311yescharacteristic
571C4⋊Q8—7316no—
572C4⋊Q8—738no—
573C4⋊Q8—7316no—
574C4⋊Q8C22×D7318yes—
575C4⋊Q8C22×D7318yes—
576#127—738no—
577#127—7316no—
578#126—7332no—
579#126—7316no—
580#125—7332no—
581#125—738no—
582#125—7316no—
583#125C22×D73116yes—
584#124—7316no—
585#124—7332no—
586#124—7332no—
587#124—738no—
588#124—7316no—
589#124—7316no—
590#123—7316no—
591#123—7332no—
592#123—7332no—
593#123—7332no—
594#123—7332no—
595#123—7332no—
596#123—7332no—
597C22⋊Q8—7332no—
598C22⋊Q8—738no—
599C22⋊Q8—7332no—
600C22⋊Q8—7332no—
601C22⋊Q8—7332no—
602C22⋊Q8—7332no—
603C22⋊Q8—7316no—
604C22⋊Q8C22×D7318yes—
605C22⋊Q8C22×D7318yes—
606C22⋊Q8C22×D73116yes—
607#121—738no—
608#121—7316no—
609#121—7316no—
610#121—7332no—
611#121—7316no—
612#121—7332no—
613#121—7332no—
614C4×Q8—7316no—
615C4×Q8—738no—
616C4×Q8—7316no—
617C4×Q8C22×D7318yes—
618C4×Q8C22×D7318yes—
619C4×Q8C22×D73116yes—
620C4×D4—7316no—
621C4×D4—7332no—
622C4×D4—7316no—
623C4×D4—738no—
624C4×D4—7316no—
625C4×D4—7316no—
626C4×D4—7316no—
627C4×D4—7316no—
628C4×D4—7316no—
629#117—7316no—
630#117C22×D73116yes—
631C2×C4⋊C4—732no—
632C2×C4⋊C4—734no—
633C2×C4⋊C4—734no—
634C2×C4⋊C4—732no—
635C2×C4⋊C4—732no—
636C2×C4⋊C4—731no—
637C2×C4⋊C4—731no—
638C2×C4⋊C4—732no—
639C2×C4⋊C4—732no—
640C2×C4⋊C4—734no—
641C2×C4⋊C4—734no—
642C2×C4⋊C4—732no—
643C2×C4⋊C4—7332no—
644C2×C4⋊C4C22×D7312yes—
645C2×C4⋊C4C22×D7312yes—
646C2×C4⋊C4C22×D7312yes—
647C2×C4⋊C4C22×D7312yes—
648C2×C4⋊C4C22×D7311yescharacteristic
649C2×C4⋊C4C22×D7311yescharacteristic
650C2×C4⋊C4C22×D7312yes—
651C2×C4⋊C4C22×D7312yes—
652C2×C4⋊C4C22×D7312yes—
653C2×C22⋊C4—732no—
654C2×C22⋊C4—732no—
655C2×C22⋊C4—732no—
656C2×C22⋊C4—732no—
657C2×C22⋊C4—732no—
658C2×C22⋊C4—734no—
659C2×C22⋊C4—734no—
660C2×C22⋊C4—734no—
661C2×C22⋊C4—734no—
662C2×C22⋊C4—734no—
663C2×C22⋊C4—734no—
664C2×C22⋊C4—734no—
665C2×C22⋊C4C22×D7312yes—
666C2×C22⋊C4C22×D7312yes—
667C2×C42—732no—
668C2×C42—734no—
669C2×C42C22×D7311yescharacteristic
670C2×C42C22×D7312yes—
671C2×C42C22×D7312yes—
672C2×C42C22×D7311yescharacteristic
673C2×C42C22×D7311yescharacteristic
674C2×C42C22×D7311yescharacteristic
675C2×C42C22×D7318yes—
676C24—732no—
677C24—734no—
678C24C23×D7311yescharacteristic
679#41—29232no—
680#41—29232no—
681C2×Q8—24no—
682C2×Q8—24no—
683C2×Q8—44no—
684C2×Q8—2928no—
685C2×Q8—29232no—
686C2×Q8—7316no—
687C2×Q8—734no—
688C2×Q8—738no—
689C2×Q8—1468no—
690C2×Q8—1464no—
691C2×Q8C23×D7314yes—
692C2×Q8C23×D7314yes—
693C2×Q8C23×D7318yes—
694C2×D4—2924no—
695C2×D4—2928no—
696C2×D4—2928no—
697C2×D4—2924no—
698C2×D4—2928no—
699C2×D4—738no—
700C2×D4—7316no—
701C2×D4—738no—
702C2×D4—7316no—
703C2×D4—7316no—
704C2×D4—734no—
705C2×D4—738no—
706C2×D4—738no—
707C2×D4—1468no—
708C2×D4—1464no—
709C2×D4—1468no—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—42no—
713C22×C4—2928no—
714C22×C4—2928no—
715C22×C4—2928no—
716C22×C4—2928no—
717C22×C4—7316no—
718C22×C4—7316no—
719C22×C4—7316no—
720C22×C4—7316no—
721C22×C4—732no—
722C22×C4—732no—
723C22×C4—734no—
724C22×C4—732no—
725C22×C4—738no—
726C22×C4—1468no—
727C22×C4C23×D7314yes—
728C22×C4C23×D7314yes—
729C22×C4C23×D7312yes—
730C22×C4C23×D7311yescharacteristic
731C22×C4C23×D7311yescharacteristic
732C22×C4C23×D7311yescharacteristic
733C22×C4C23×D7311yescharacteristic
734C22×C4C23×D7312yes—
735C22×C4C23×D7312yes—
736C22×C4C23×D7312yes—
737C22×C4C23×D7314yes—
738C22×C4C23×D7311yescharacteristic
739C22×C4C23×D7311yescharacteristic
740C4⋊C4—738no—
741C4⋊C4—7316no—
742C4⋊C4—738no—
743C4⋊C4—738no—
744C4⋊C4—7316no—
745C4⋊C4—7316no—
746C4⋊C4—738no—
747C4⋊C4—7316no—
748C4⋊C4—734no—
749C4⋊C4—734no—
750C4⋊C4—738no—
751C4⋊C4—738no—
752C4⋊C4C23×D7318yes—
753C4⋊C4C23×D7318yes—
754C4⋊C4C23×D7318yes—
755C4⋊C4C23×D7318yes—
756C4⋊C4C23×D7314yes—
757C4⋊C4C23×D7314yes—
758C4⋊C4C23×D7318yes—
759C4⋊C4C23×D7318yes—
760C4⋊C4C23×D7318yes—
761C22⋊C4—738no—
762C22⋊C4—738no—
763C22⋊C4—738no—
764C22⋊C4—738no—
765C22⋊C4—738no—
766C22⋊C4—7316no—
767C22⋊C4—7316no—
768C22⋊C4—7316no—
769C22⋊C4—7316no—
770C22⋊C4—7316no—
771C22⋊C4—7316no—
772C22⋊C4—7316no—
773C22⋊C4C23×D7318yes—
774C22⋊C4C23×D7318yes—
775C42—738no—
776C42—7316no—
777C42C23×D7314yes—
778C42C23×D7314yes—
779C42C23×D7314yes—
780C42C23×D7314yes—
781C42C23×D7318yes—
782C42C23×D7318yes—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—734no—
787C23—738no—
788C23—1464no—
789C23—1468no—
790C23—1464no—
791C23—1468no—
792C23—1468no—
793C23—1464no—
794C23C24×D7312yes—
795C23C24×D7311yescharacteristic
796Q8—28no—
797Q8—28no—
798Q8—48no—
799Q8—29216no—
800Q8—14616no—
801Q8—1468no—
802D4—29216no—
803D4—2928no—
804D4—29216no—
805D4—29216no—
806D4—2928no—
807D4—14616no—
808D4—1468no—
809D4—14616no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—28no—
819C2×C4—28no—
820C2×C4—44no—
821C2×C4—29216no—
822C2×C4—29216no—
823C2×C4—29216no—
824C2×C4—29216no—
825C2×C4—734no—
826C2×C4—734no—
827C2×C4—738no—
828C2×C4—734no—
829C2×C4—1464no—
830C2×C4—1468no—
831C2×C4—1464no—
832C2×C4—1464no—
833C2×C4—14616no—
834C2×C4#1455663714yes—
835C2×C4#1455663914yes—
836C2×C4C24×D7314yes—
837C2×C4C24×D7312yes—
838C2×C4C24×D7312yes—
839C2×C4C24×D7312yes—
840C2×C4C24×D7312yes—
841C2×C4C24×D7314yes—
842C2×C4C24×D7314yes—
843C2×C4C24×D7314yes—
844C2×C4C24×D7312yes—
845C2×C4C24×D7312yes—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—44no—
850C22—2928no—
851C22—29216no—
852C22—1464no—
853C22—1468no—
854C22—1464no—
855C22—1468no—
856C22—1468no—
857C22—1464no—
858C22C2×#1455663712yes—
859C22C2×#1455663912yes—
860C22#1798942312yes—
861C22C25×D7311yescharacteristic
862C4—22no—
863C4—24no—
864C4—24no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—24no—
869C4—24no—
870C4—1464no—
871C4—1468no—
872C4—1464no—
873C4—1464no—
874C4C2×#1455663714yes—
875C4C2×#1455663914yes—
876C2—42no—
877C2—2924no—
878C2—2928no—
879C2#2262440214yesdirect product factor
880C2C22×#1455663711yescharacteristic
881C2C22×#1455663911yescharacteristic
882C2C2×#1798942311yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#533×C73C2
socleC23×C73C25
hypercenterC2×#533D73
hypocenterC73C2×#3554
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #22624402C2direct (N × H)
2. C2×#17989333C2semidirect
3. C2×#17989322C2semidirect
4. C2×#17989322C2semidirect
5. C2×#17989315C2semidirect
6. C2×#17989297C2semidirect
7. C2×#17989259C2semidirect
8. C2×Q8×D292C2semidirect
9. C2×#17989247C2semidirect
10. C2×#17989239C2semidirect
11. C2×#17989211C2semidirect
12. C2×#17989208C2semidirect
13. C2×#17989192C2semidirect
14. C2×#17989185C2semidirect
15. C2×#17989162C2semidirect
16. C2×#17989137C2semidirect
17. C2×#17989121C2semidirect
18. C2×#533×C73C2semidirect
22. #17989333C22semidirect
23. #17989322C22semidirect
24. #17989322C22semidirect
25. #17989315C22semidirect
26. #17989297C22semidirect
27. #17989259C22semidirect
28. Q8×D292C22semidirect
29. #17989247C22semidirect
30. #17989239C22semidirect
31. #17989211C22semidirect
32. #17989208C22semidirect
33. #17989192C22semidirect
34. #17989185C22semidirect
35. #17989162C22semidirect
36. #17989137C22semidirect
42. #17989121C22semidirect
89. #533×C73C22semidirect
436. C2×C73#3554semidirect
457. C2×#533D73semidirect
460. C73C2×#3554semidirect
478. #533C2×D73semidirect
879. C2#22624402direct (N × H)

Maximal subgroups

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

subgroupindex
#226244022
C2×#179893332
C2×#179893222
C2×#179893152
C2×#179892972
C2×#179892592
C2×Q8×D2922
C2×#179892472
C2×#179892392
C2×#179892112
C2×#179892082
C2×#179891922
C2×#179891852
C2×#179891622
C2×#179891372
C2×#179891212
C2×#533×C732
C2×#355473