Finite Group Databasebeta

← C2×#22624372 #33993591

Subgroups — C2×#22624372 #33993591

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#22624372C2132yesmaximal, direct product factor
2C2×#17989336C214yesmaximal, complemented
3C2×#17989312C211yesmaximal, characteristic, complemented
4C2×#17989311C211yesmaximal, characteristic, complemented
5C2×#17989292C212yesmaximal, complemented
6C2×#17989285C212yesmaximal, complemented
7C2×#17989252C211yesmaximal, characteristic, complemented
8C2×Q8×C22⋊D73C212yesmaximal, complemented
9C2×#17989248C212yesmaximal, complemented
10C2×#17989240C211yesmaximal, characteristic, complemented
11C2×#17989214C212yesmaximal, complemented
12C2×#17989211C212yesmaximal, complemented
13C2×#17989198C212yesmaximal, complemented
14C2×#17989184C214yesmaximal, complemented
15C2×#17989162C212yesmaximal, complemented
16C2×#17989121C211yesmaximal, characteristic, complemented
17C2×#17989121C211yesmaximal, characteristic, complemented
18C22×C4⋊Q8×C73C211yesmaximal, characteristic, complemented
19C22×#11924029C2212yes—
20C22×Q8×D73C2212yes—
21#17989336C22164yescomplemented
22#17989312C22116yescomplemented
23#17989311C22116yescomplemented
24#17989292C22132yescomplemented
25#17989285C22132yescomplemented
26#17989252C22116yescomplemented
27Q8×C22⋊D73C22132yescomplemented
28#17989248C22132yescomplemented
29#17989240C22116yescomplemented
30#17989214C22132yescomplemented
31#17989211C22132yescomplemented
32#17989198C22132yescomplemented
33#17989184C22164yescomplemented
34#17989162C22132yescomplemented
35C2×#14556590C2212yes—
36C2×#14556589C2212yes—
37C2×#14556589C2214yes—
38#17989121C22116yescomplemented
39#17989121C22116yescomplemented
40C2×#14556586C2214yes—
41C2×#14556586C2214yes—
42C2×#14556586C2214yes—
43C2×#14556585C2212yes—
44C2×#14556585C2212yes—
45C2×#14556583C2211yescharacteristic
46C2×#14556583C2211yescharacteristic
47C2×#14556582C2212yes—
48C2×#14556581C2214yes—
49C2×#14556581C2214yes—
50C2×#14556581C2214yes—
51C2×#14556580C2212yes—
52C2×#14556580C2214yes—
53C2×#14556579C2211yescharacteristic
54C2×#14556579C2211yescharacteristic
55C2×#14556576C2214yes—
56C2×#14556576C2214yes—
57C2×#14556576C2214yes—
58C2×#14556574C2212yes—
59C2×#14556574C2212yes—
60C2×#14556571C2212yes—
61C2×#14556570C2214yes—
62C2×#14556570C2211yescharacteristic
63C2×#14556570C2211yescharacteristic
64C2×#14556569C2214yes—
65C2×#14556569C2214yes—
66C2×#14556569C2214yes—
67C2×#14556567C2214yes—
68C2×#14556567C2214yes—
69C2×#14556567C2212yes—
70C2×#14556567C2212yes—
71C2×#14556566C2212yes—
72C2×#14556565C2214yes—
73C2×#14556565C2211yescharacteristic
74C2×#14556565C2211yescharacteristic
75C2×Q8×Dic73C2212yes—
76C2×Q8×Dic73C2212yes—
77C2×C4×Dic146C2211yescharacteristic
78C2×C4×Dic146C2211yescharacteristic
79C2×#14556556C2212yes—
80C2×C4×D292C2211yescharacteristic
81C2×C4×D292C2211yescharacteristic
82C2×#14556553C2212yes—
83C2×C4×C22⋊D73C2214yes—
84C2×C4×C22⋊D73C2214yes—
85C2×C4×C22⋊D73C2212yes—
86C2×C4×C22⋊D73C2212yes—
87C2×#14556549C2212yes—
88C2×#14556548C2212yes—
89C2×#14556548C2212yes—
90C2×C4⋊C4×D73C2212yes—
91C23×Q8×C73C2212yes—
92C2×C4⋊Q8×C73C2211yescharacteristic
93C2×C4⋊Q8×C73C2212yes—
94C2×C4⋊Q8×C73C2212yes—
95C2×C4⋊Q8×C73C2212yes—
96C2×C4⋊Q8×C73C2211yescharacteristic
97C2×C4⋊Q8×C73C22116yescomplemented
98C22×C4⋊C4×C73C2212yes—
99C22×C4⋊C4×C73C2212yes—
100C22×C42×C73C2211yescharacteristic
101C2×#11924029—48no—
102C2×#11924029C23116yes—
103C22×Dic146C2311yescharacteristic
104C22×Dic146C2311yescharacteristic
105C22×Dic146C2314yes—
106C2×Q8×D73—48no—
107C2×Q8×D73C23116yes—
108C22×D292C2311yescharacteristic
109C22×D292C2311yescharacteristic
110C22×D292C2314yes—
111C22×C22⋊D73C2312yes—
112C22×C22⋊D73C2312yes—
113C22×C4×D73C2312yes—
114C22×C4×D73C2312yes—
115C22×C4×D73C2314yes—
116C22×C4×D73C2314yes—
117#14556590C23116yes—
118#14556589C23116yes—
119#14556589C23132yes—
120#14556586C23132yes—
121#14556586C23132yes—
122#14556586C23132yes—
123#14556585C23116yes—
124#14556585C23116yes—
125#14556583C2318yes—
126#14556583C2318yes—
127#14556582C23116yes—
128#14556581C23132yes—
129#14556581C23132yes—
130#14556581C23132yes—
131#14556580C23116yes—
132#14556580C23132yes—
133#14556579C2318yes—
134#14556579C2318yes—
135#14556576C23132yes—
136#14556576C23132yes—
137#14556576C23132yes—
138#14556574C23116yes—
139#14556574C23116yes—
140#14556571C23116yes—
141#14556570C2318yes—
142#14556570C2318yes—
143#14556570C23132yes—
144#14556569C23132yes—
145#14556569C23132yes—
146#14556569C23132yes—
147#14556567C23116yes—
148#14556567C23116yes—
149#14556567C23132yes—
150#14556567C23132yes—
151#14556566C23116yes—
152#14556565C2318yes—
153#14556565C2318yes—
154#14556565C23132yes—
155Q8×Dic73C23116yes—
156Q8×Dic73C23116yes—
157C4×Dic146C2318yes—
158C4×Dic146C2318yes—
159#14556556C23116yes—
160C4×D292C2318yes—
161C4×D292C2318yes—
162#14556553C23116yes—
163C4×C22⋊D73C23116yes—
164C4×C22⋊D73C23116yes—
165C4×C22⋊D73C23132yes—
166C4×C22⋊D73C23132yes—
167#14556549C23116yes—
168#14556548C23116yes—
169#14556548C23116yes—
170C2×C4⋊Dic73C2311yescharacteristic
171C2×C4⋊Dic73C2311yescharacteristic
172C2×C4⋊Dic73C2311yescharacteristic
173C2×C4⋊Dic73C2311yescharacteristic
174C2×C4⋊Dic73C2314yes—
175C2×C4⋊Dic73C2314yes—
176C2×#11924007C2312yes—
177C2×#11924007C2312yes—
178C2×#11924007C2314yes—
179C2×#11924007C2314yes—
180C2×#11924007C2314yes—
181C2×#11924007C2314yes—
182C2×#11924007C2312yes—
183C2×#11924007C2312yes—
184C2×#11924007C2312yes—
185C2×#11924007C2312yes—
186C2×#11924007C2312yes—
187C2×#11924007C2312yes—
188C4⋊C4×D73C23116yes—
189C2×C22⋊Dic73C2312yes—
190C2×C22⋊Dic73C2312yes—
191C2×#11924005C2312yes—
192C2×#11924005C2312yes—
193C2×#11924005C2312yes—
194C2×#11924005C2312yes—
195C2×#11924005C2314yes—
196C2×#11924005C2314yes—
197C2×#11924005C2312yes—
198C2×#11924005C2312yes—
199C2×#11924005C2314yes—
200C2×#11924005C2314yes—
201C2×#11924005C2312yes—
202C2×#11924005C2312yes—
203C2×C4×Dic73C2312yes—
204C2×C4×Dic73C2314yes—
205C2×C4×Dic73C2312yes—
206C2×C4×Dic73C2314yes—
207C22×Q8×C73—48no—
208C22×Q8×C73C2312yes—
209C22×Q8×C73C2312yes—
210C22×Q8×C73C2314yes—
211C22×Q8×C73C23116yes—
212C23×C4×C73C2311yescharacteristic
213C23×C4×C73C2311yescharacteristic
214C23×C4×C73C2311yescharacteristic
215C23×C4×C73C2314yes—
216C4⋊Q8×C73C23116yes—
217C4⋊Q8×C73C23116yes—
218C4⋊Q8×C73C2318yes—
219C4⋊Q8×C73C2318yes—
220C4⋊Q8×C73C23116yes—
221C2×C4⋊C4×C73C2312yes—
222C2×C4⋊C4×C73C23116yes—
223C2×C4⋊C4×C73C2312yes—
224C2×C4⋊C4×C73C2312yes—
225C2×C4⋊C4×C73C2314yes—
226C2×C4⋊C4×C73C2314yes—
227C2×C4⋊C4×C73C2312yes—
228C2×C4⋊C4×C73C23116yes—
229C2×C42×C73C2318yes—
230C2×C42×C73C2311yescharacteristic
231C2×C42×C73C2311yescharacteristic
232C2×C42×C73C2311yescharacteristic
233C2×C42×C73C2311yescharacteristic
234C23×D73C2412yes—
235C23×D73C2412yes—
236#11924029—432no—
237C2×Dic146—24no—
238C2×Dic146—24no—
239C2×Dic146—48no—
240C2×Dic146C2414yes—
241C2×Dic146C2414yes—
242C2×Dic146C24116yes—
243Q8×D73—432no—
244C2×D292—24no—
245C2×D292—24no—
246C2×D292—48no—
247C2×D292C2414yes—
248C2×D292C2414yes—
249C2×D292C24116yes—
250C2×C22⋊D73—28no—
251C2×C22⋊D73—28no—
252C2×C22⋊D73C2418yes—
253C2×C22⋊D73C2418yes—
254C22×Dic73C2412yes—
255C22×Dic73C2412yes—
256C22×Dic73C2412yes—
257C22×Dic73C2412yes—
258C22×Dic73C2412yes—
259C22×Dic73C2412yes—
260C2×C4×D73—28no—
261C2×C4×D73—28no—
262C2×C4×D73—48no—
263C2×C4×D73—48no—
264C2×C4×D73C2418yes—
265C2×C4×D73C2418yes—
266C2×C4×D73C24116yes—
267C2×C4×D73C24116yes—
268C4⋊Dic73C2414yes—
269C4⋊Dic73C2414yes—
270C4⋊Dic73C2414yes—
271C4⋊Dic73C2414yes—
272C4⋊Dic73C24116yes—
273C4⋊Dic73C24116yes—
274#11924007C24116yes—
275#11924007C2418yes—
276#11924007C2418yes—
277#11924007C2418yes—
278#11924007C2418yes—
279#11924007C24116yes—
280#11924007C2418yes—
281#11924007C24116yes—
282#11924007C2418yes—
283#11924007C24116yes—
284#11924007C2418yes—
285#11924007C2418yes—
286C22⋊Dic73C2418yes—
287C22⋊Dic73C2418yes—
288#11924005C2418yes—
289#11924005C2418yes—
290#11924005C2418yes—
291#11924005C2418yes—
292#11924005C24116yes—
293#11924005C24116yes—
294#11924005C2418yes—
295#11924005C2418yes—
296#11924005C24116yes—
297#11924005C24116yes—
298#11924005C2418yes—
299#11924005C2418yes—
300C4×Dic73C2418yes—
301C4×Dic73C2418yes—
302C4×Dic73C24116yes—
303C4×Dic73C24116yes—
304C24×C73C2411yescharacteristic
305C2×Q8×C73—28no—
306C2×Q8×C73—28no—
307C2×Q8×C73—48no—
308C2×Q8×C73—432no—
309C2×Q8×C73C2418yes—
310C2×Q8×C73C2418yes—
311C2×Q8×C73C24116yes—
312C22×C4×C73—24no—
313C22×C4×C73—24no—
314C22×C4×C73—24no—
315C22×C4×C73—48no—
316C22×C4×C73C2411yescharacteristic
317C22×C4×C73C2411yescharacteristic
318C22×C4×C73C2411yescharacteristic
319C22×C4×C73C2414yes—
320C22×C4×C73C2414yes—
321C22×C4×C73C2411yescharacteristic
322C22×C4×C73C2414yes—
323C22×C4×C73C2414yes—
324C22×C4×C73C2414yes—
325C22×C4×C73C24116yes—
326C22×C4×C73C2411yescharacteristic
327C22×C4×C73C2411yescharacteristic
328C4⋊C4×C73C2418yes—
329C4⋊C4×C73C2418yes—
330C4⋊C4×C73C2418yes—
331C4⋊C4×C73C24116yes—
332C4⋊C4×C73C24116yes—
333C4⋊C4×C73C2418yes—
334C42×C73C2414yes—
335C42×C73C2414yes—
336C42×C73C2414yes—
337C42×C73C2414yes—
338C23×C73—22no—
339C23×C73—22no—
340C23×C732−1+414yes—
341C23×C73C2512yes—
342C23×C73C2511yescharacteristic
343C22×D73—24no—
344C22×D73—24no—
345C22×D73—24no—
346C22×D73—24no—
347C22×D73—24no—
348C22×D73—24no—
349C22×D73C2514yes—
350C22×D73C2514yes—
351Q8×C73—216no—
352Q8×C73—216no—
353Q8×C73—416no—
354C2×C4×C73—22no—
355C2×C4×C73—28no—
356C2×C4×C73—28no—
357C2×C4×C73—28no—
358C2×C4×C73—22no—
359C2×C4×C73—22no—
360C2×C4×C73—22no—
361C2×C4×C73—28no—
362C2×C4×C73—28no—
363C2×C4×C73—416no—
364C2×C4×C73H(5,𝔽2)14yes—
365C2×C4×C732−1+414yes—
366C2×C4×C73C2512yes—
367C2×C4×C73C2512yes—
368C2×C4×C73C2512yes—
369C2×C4×C73C2512yes—
370C2×C4×C73C2518yes—
371C2×C4×C73C2518yes—
372C2×C4×C73C2512yes—
373C2×C4×C73C2512yes—
374C22⋊D73—216no—
375C22⋊D73—216no—
376C2×Dic73—24no—
377C2×Dic73—24no—
378C2×Dic73—24no—
379C2×Dic73—24no—
380C2×Dic73—24no—
381C2×Dic73—24no—
382C2×Dic73C2514yes—
383C2×Dic73C2514yes—
384C2×Dic73C2514yes—
385C2×Dic73C2514yes—
386C2×Dic73C2514yes—
387C2×Dic73C2514yes—
388D292—28no—
389D292—28no—
390D292—416no—
391C4×D73—216no—
392C4×D73—216no—
393C4×D73—416no—
394C4×D73—416no—
395Dic146—28no—
396Dic146—28no—
397Dic146—416no—
398C22×C73—22no—
399C22×C73—22no—
400C22×C73—28no—
401C22×C73C2×H(5,𝔽2)12yes—
402C22×C73C2×2−1+414yes—
403C22×C73C2×2−1+412yes—
404C22×C73C2×2−1+412yes—
405C22×C73C2611yescharacteristic
406C2×D73—24no—
407C2×D73—24no—
408C2×D73—24no—
409C2×D73—24no—
410C2×D73—24no—
411C2×D73—24no—
412C2×D73—48no—
413C2×D73—48no—
414C4×C73—28no—
415C4×C73—28no—
416C4×C73—22no—
417C4×C73—22no—
418C4×C73—22no—
419C4×C73—22no—
420C4×C73C2×H(5,𝔽2)14yes—
421C4×C73C2×2−1+414yes—
422Dic73—24no—
423Dic73—24no—
424Dic73—24no—
425Dic73—24no—
426Dic73—24no—
427Dic73—24no—
428C2×#3552—731nomaximal, Sylow
429C2×C73—24no—
430C2×C73#355214yescomplemented
431C2×C73C22×H(5,𝔽2)11yescharacteristic
432C2×C73C22×2−1+411yescharacteristic
433C2×C73C22×2−1+411yescharacteristic
434D73—44no—
435D73—44no—
436#3552—7332no—
437C2×#563—734no—
438C2×#557—731no—
439C2×#556—731no—
440C2×#554—732no—
441C2×#553—732no—
442C2×D4×Q8—732no—
443C2×D4×Q8—731no—
444C2×#548—732no—
445C2×#547—731no—
446C2×#544—732no—
447C2×#542—732no—
448C2×#541—732no—
449C2×#539—734no—
450C2×#536—732no—
451C22×C4⋊Q8D7311yescharacteristic, complemented
452C2×#529—731no—
453C2×#529—731no—
454C73C2×#355211yescharacteristic, complemented, Sylow
455C22×#41—732no—
456C23×Q8—732no—
457C23×Q8C2×D7312yes—
458#563—7364no—
459#557—7316no—
460#556—7316no—
461#554—7332no—
462#553—7332no—
463D4×Q8—7332no—
464D4×Q8—7316no—
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—734no—
474C2×C4⋊Q8—732no—
475C2×C4⋊Q8C2×D7312yes—
476C2×C4⋊Q8C2×D7312yes—
477C2×C4⋊Q8C2×D7311yescharacteristic
478C2×C4⋊Q8C2×D7311yescharacteristic
479C2×C4⋊Q8C2×D7312yes—
480C2×C4⋊Q8C2×D73116yescomplemented
481#529—7316no—
482#529—7316no—
483C2×#126—734no—
484C2×#126—734no—
485C2×#126—734no—
486C2×#126—732no—
487C2×#126—732no—
488C2×#125—734no—
489C2×#125—734no—
490C2×#125—734no—
491C2×#125—732no—
492C2×#125—731no—
493C2×#125—731no—
494C2×#124—732no—
495C2×#124—734no—
496C2×#124—731no—
497C2×#124—731no—
498C2×#123—732no—
499C2×#123—732no—
500C2×#123—734no—
501C2×#123—734no—
502C2×#123—734no—
503C2×C22⋊Q8—732no—
504C2×C22⋊Q8—732no—
505C2×C22⋊Q8—734no—
506C2×C22⋊Q8—734no—
507C2×C22⋊Q8—731no—
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×#121—731no—
515C2×#121—731no—
516C2×#121—734no—
517C2×#121—732no—
518C2×C4×Q8—732no—
519C2×C4×Q8—732no—
520C2×C4×Q8—732no—
521C2×C4×Q8—731no—
522C2×C4×Q8—731no—
523C2×C4×D4—732no—
524C2×C4×D4—732no—
525C2×C4×D4—734no—
526C2×C4×D4—734no—
527C2×C4×D4—732no—
528C2×C4×D4—731no—
529C2×C4×D4—731no—
530C2×#117—732no—
531C2×#117—732no—
532C2×#117—732no—
533C22×C4⋊C4—732no—
534C22×C4⋊C4C2×D7312yes—
535C22×C4⋊C4C2×D7312yes—
536C22×C42C2×D7311yescharacteristic
537C2×#41—2928no—
538C2×#41—7316no—
539C22×Q8—48no—
540C22×Q8—2928no—
541C22×Q8—7316no—
542C22×Q8—734no—
543C22×Q8—731no—
544C22×Q8—731no—
545C22×Q8C22×D7312yes—
546C22×Q8C22×D7312yes—
547C22×Q8C22×D7314yes—
548C22×Q8C22×D73116yes—
549C22×D4—732no—
550C22×D4—732no—
551C22×D4—734no—
552C22×D4—731no—
553C22×D4—731no—
554C23×C4—734no—
555C23×C4—734no—
556C23×C4—732no—
557C23×C4—732no—
558C23×C4C22×D7311yescharacteristic
559C23×C4C22×D7311yescharacteristic
560C23×C4C22×D7311yescharacteristic
561C23×C4C22×D7314yes—
562C4⋊Q8—7316no—
563C4⋊Q8—7332no—
564C4⋊Q8—7316no—
565C4⋊Q8C22×D73116yes—
566C4⋊Q8C22×D73116yes—
567C4⋊Q8C22×D7318yes—
568C4⋊Q8C22×D7318yes—
569C4⋊Q8C22×D73116yes—
570#126—7332no—
571#126—7332no—
572#126—7332no—
573#126—7316no—
574#126—7316no—
575#125—7332no—
576#125—7332no—
577#125—7332no—
578#125—7316no—
579#125—738no—
580#125—738no—
581#124—7316no—
582#124—7332no—
583#124—738no—
584#124—738no—
585#123—7316no—
586#123—7316no—
587#123—7332no—
588#123—7332no—
589#123—7332no—
590C22⋊Q8—7316no—
591C22⋊Q8—7316no—
592C22⋊Q8—7332no—
593C22⋊Q8—7332no—
594C22⋊Q8—738no—
595C22⋊Q8—738no—
596C22⋊Q8—7332no—
597C22⋊Q8—7332no—
598C22⋊Q8—7332no—
599C22⋊Q8—7332no—
600C22⋊Q8—7316no—
601#121—738no—
602#121—738no—
603#121—7332no—
604#121—7316no—
605C4×Q8—7316no—
606C4×Q8—7316no—
607C4×Q8—7316no—
608C4×Q8—738no—
609C4×Q8—738no—
610C4×D4—7316no—
611C4×D4—7316no—
612C4×D4—7332no—
613C4×D4—7332no—
614C4×D4—7316no—
615C4×D4—738no—
616C4×D4—738no—
617#117—7316no—
618#117—7316no—
619#117—7316no—
620C2×C4⋊C4—731no—
621C2×C4⋊C4—734no—
622C2×C4⋊C4—731no—
623C2×C4⋊C4—732no—
624C2×C4⋊C4—732no—
625C2×C4⋊C4—732no—
626C2×C4⋊C4—732no—
627C2×C4⋊C4—731no—
628C2×C4⋊C4—734no—
629C2×C4⋊C4—732no—
630C2×C4⋊C4—734no—
631C2×C4⋊C4—732no—
632C2×C4⋊C4—731no—
633C2×C4⋊C4—734no—
634C2×C4⋊C4—734no—
635C2×C4⋊C4—734no—
636C2×C4⋊C4—732no—
637C2×C4⋊C4—732no—
638C2×C4⋊C4—7316no—
639C2×C4⋊C4C22×D7312yes—
640C2×C4⋊C4C22×D7312yes—
641C2×C4⋊C4C22×D7312yes—
642C2×C4⋊C4C22×D7314yes—
643C2×C4⋊C4C22×D7314yes—
644C2×C4⋊C4C22×D7312yes—
645C2×C4⋊C4C22×D73116yes—
646C2×C4⋊C4C22×D73116yes—
647C2×C22⋊C4—732no—
648C2×C22⋊C4—732no—
649C2×C22⋊C4—734no—
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⋊C4—734no—
659C2×C22⋊C4—732no—
660C2×C22⋊C4—732no—
661C2×C42—732no—
662C2×C42—732no—
663C2×C42—734no—
664C2×C42—734no—
665C2×C42C22×D7311yescharacteristic
666C2×C42C22×D7311yescharacteristic
667C2×C42C22×D7311yescharacteristic
668C2×C42C22×D7311yescharacteristic
669C2×C42C22×D7318yes—
670C24—732no—
671C24—732no—
672C24C23×D7311yescharacteristic
673#41—29232no—
674C2×Q8—28no—
675C2×Q8—28no—
676C2×Q8—48no—
677C2×Q8—432no—
678C2×Q8—2928no—
679C2×Q8—29232no—
680C2×Q8—7316no—
681C2×Q8—734no—
682C2×Q8—734no—
683C2×Q8—1464no—
684C2×Q8—1464no—
685C2×Q8C23×D7318yes—
686C2×Q8C23×D7318yes—
687C2×Q8C23×D73116yes—
688C2×D4—2928no—
689C2×D4—738no—
690C2×D4—738no—
691C2×D4—7316no—
692C2×D4—734no—
693C2×D4—734no—
694C2×D4—1468no—
695C2×D4—1468no—
696C2×D4—1464no—
697C2×D4—1464no—
698C22×C4—24no—
699C22×C4—24no—
700C22×C4—24no—
701C22×C4—48no—
702C22×C4—2928no—
703C22×C4—2928no—
704C22×C4—7316no—
705C22×C4—7316no—
706C22×C4—732no—
707C22×C4—732no—
708C22×C4—732no—
709C22×C4—732no—
710C22×C4—732no—
711C22×C4—732no—
712C22×C4—738no—
713C22×C4—738no—
714C22×C4—1468no—
715C22×C4—1468no—
716C22×C4C23×D7314yes—
717C22×C4C23×D7314yes—
718C22×C4C23×D7314yes—
719C22×C4C23×D7314yes—
720C22×C4C23×D7314yes—
721C22×C4C23×D7311yescharacteristic
722C22×C4C23×D7311yescharacteristic
723C22×C4C23×D7311yescharacteristic
724C22×C4C23×D7311yescharacteristic
725C22×C4C23×D73116yes—
726C22×C4C23×D7311yescharacteristic
727C22×C4C23×D7311yescharacteristic
728C4⋊C4—7316no—
729C4⋊C4—738no—
730C4⋊C4—738no—
731C4⋊C4—738no—
732C4⋊C4—738no—
733C4⋊C4—7316no—
734C4⋊C4—738no—
735C4⋊C4—7316no—
736C4⋊C4—738no—
737C4⋊C4—7316no—
738C4⋊C4—738no—
739C4⋊C4—738no—
740C4⋊C4—734no—
741C4⋊C4—734no—
742C4⋊C4—734no—
743C4⋊C4—734no—
744C4⋊C4—7316no—
745C4⋊C4—7316no—
746C4⋊C4C23×D7318yes—
747C4⋊C4C23×D7318yes—
748C4⋊C4C23×D7318yes—
749C4⋊C4C23×D73116yes—
750C4⋊C4C23×D73116yes—
751C4⋊C4C23×D7318yes—
752C22⋊C4—738no—
753C22⋊C4—738no—
754C22⋊C4—7316no—
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⋊C4—7316no—
764C22⋊C4—738no—
765C22⋊C4—738no—
766C42—738no—
767C42—738no—
768C42—7316no—
769C42—7316no—
770C42C23×D7314yes—
771C42C23×D7314yes—
772C42C23×D7314yes—
773C42C23×D7314yes—
774C23—22no—
775C23—22no—
776C23—734no—
777C23—734no—
778C23—1464no—
779C23—1464no—
780C23—1464no—
781C23—1464no—
782C23—1464no—
783C23—1464no—
784C23#1455663914yes—
785C23C24×D7312yes—
786C23C24×D7311yescharacteristic
787Q8—216no—
788Q8—216no—
789Q8—416no—
790Q8—29216no—
791Q8—1468no—
792Q8—1468no—
793D4—29216no—
794D4—14616no—
795D4—14616no—
796D4—1468no—
797D4—1468no—
798C2×C4—22no—
799C2×C4—28no—
800C2×C4—28no—
801C2×C4—28no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—28no—
806C2×C4—28no—
807C2×C4—416no—
808C2×C4—29216no—
809C2×C4—29216no—
810C2×C4—734no—
811C2×C4—734no—
812C2×C4—734no—
813C2×C4—734no—
814C2×C4—734no—
815C2×C4—734no—
816C2×C4—1464no—
817C2×C4—1464no—
818C2×C4—1464no—
819C2×C4—1464no—
820C2×C4—1464no—
821C2×C4—1464no—
822C2×C4—14616no—
823C2×C4—14616no—
824C2×C4#1455663614yes—
825C2×C4#1455663914yes—
826C2×C4C24×D7318yes—
827C2×C4C24×D7318yes—
828C2×C4C24×D7312yes—
829C2×C4C24×D7312yes—
830C2×C4C24×D7312yes—
831C2×C4C24×D7312yes—
832C2×C4C24×D7312yes—
833C2×C4C24×D7312yes—
834C22—28no—
835C22—22no—
836C22—22no—
837C22—2928no—
838C22—2928no—
839C22—1464no—
840C22—1464no—
841C22—1464no—
842C22—1464no—
843C22—1464no—
844C22—1464no—
845C22C2×#1455663612yes—
846C22C2×#1455663914yes—
847C22C2×#1455663912yes—
848C22C2×#1455663912yes—
849C22C25×D7311yescharacteristic
850C4—22no—
851C4—28no—
852C4—28no—
853C4—22no—
854C4—22no—
855C4—22no—
856C4—1464no—
857C4—1464no—
858C4—1464no—
859C4—1464no—
860C4—1464no—
861C4—1464no—
862C4C2×#1455663614yes—
863C4C2×#1455663914yes—
864C2—24no—
865C2—2924no—
866C2—2924no—
867C2#2262437214yesdirect product factor
868C2C22×#1455663611yescharacteristic
869C2C22×#1455663911yescharacteristic
870C2C22×#1455663911yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC22×C4⋊Q8×C73C2
socleC23×C73C25
hypercenterC22×C4⋊Q8D73
hypocenterC73C2×#3552
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #22624372C2direct (N × H)
2. C2×#17989336C2semidirect
3. C2×#17989312C2semidirect
4. C2×#17989311C2semidirect
5. C2×#17989292C2semidirect
6. C2×#17989285C2semidirect
7. C2×#17989252C2semidirect
8. C2×Q8×C22⋊D73C2semidirect
9. C2×#17989248C2semidirect
10. C2×#17989240C2semidirect
11. C2×#17989214C2semidirect
12. C2×#17989211C2semidirect
13. C2×#17989198C2semidirect
14. C2×#17989184C2semidirect
15. C2×#17989162C2semidirect
16. C2×#17989121C2semidirect
17. C2×#17989121C2semidirect
18. C22×C4⋊Q8×C73C2semidirect
21. #17989336C22semidirect
22. #17989312C22semidirect
23. #17989311C22semidirect
24. #17989292C22semidirect
25. #17989285C22semidirect
26. #17989252C22semidirect
27. Q8×C22⋊D73C22semidirect
28. #17989248C22semidirect
29. #17989240C22semidirect
30. #17989214C22semidirect
31. #17989211C22semidirect
32. #17989198C22semidirect
33. #17989184C22semidirect
34. #17989162C22semidirect
38. #17989121C22semidirect
39. #17989121C22semidirect
97. C2×C4⋊Q8×C73C22semidirect
430. C2×C73#3552semidirect
451. C22×C4⋊Q8D73semidirect
454. C73C2×#3552semidirect
480. C2×C4⋊Q8C2×D73semidirect
867. C2#22624372direct (N × H)

Maximal subgroups

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

subgroupindex
#226243722
C2×#179893362
C2×#179893122
C2×#179893112
C2×#179892922
C2×#179892852
C2×#179892522
C2×Q8×C22⋊D732
C2×#179892482
C2×#179892402
C2×#179892142
C2×#179892112
C2×#179891982
C2×#179891842
C2×#179891622
C2×#179891212
C22×C4⋊Q8×C732
C2×#355273