Finite Group Databasebeta

← C2×#22574020 #31764155

Subgroups — C2×#22574020 #31764155

Order 17152.

7478 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574020C2132yesmaximal, direct product factor
2C2×#16864126C212yesmaximal, complemented
3C2×#16864124C211yesmaximal, characteristic, complemented
4C2×#16864121C211yesmaximal, characteristic, complemented
5C2×#16864105C212yesmaximal, complemented
6C2×#16864100C214yesmaximal, complemented
7C2×D4×Dic134C211yesmaximal, characteristic, complemented
8C2×Q8×C22⋊D67C212yesmaximal, complemented
9C2×#16864059C212yesmaximal, complemented
10C2×#16864025C214yesmaximal, complemented
11C2×#16864023C212yesmaximal, complemented
12C2×#16863950C211yesmaximal, characteristic, complemented
13C2×#16863948C212yesmaximal, complemented
14C22×#14524041C212yesmaximal, complemented
15C2×C4⋊Q8×D67C211yesmaximal, characteristic, complemented
16C2×#16863875C212yesmaximal
17C2×C4×#11761627C211yesmaximal, characteristic
18C2×D4×Q8×C67C211yesmaximal, characteristic, complemented
19C22×#11761627C2211yescharacteristic
20C23×Dic134C2212yes—
21C22×Q8×D67C2212yes—
22#16864126C22132yescomplemented
23#16864124C22116yescomplemented
24#16864121C22116yescomplemented
25#16864105C22132yescomplemented
26#16864100C22164yescomplemented
27D4×Dic134C22116yescomplemented
28Q8×C22⋊D67C22132yescomplemented
29#16864059C22132yescomplemented
30#16864025C22164yescomplemented
31#16864023C22132yescomplemented
32#16863950C22116yescomplemented
33#16863948C22132yescomplemented
34C2×#14524043C2211yescharacteristic
35C2×#14524042C2212yes—
36C2×#14524042C2212yes—
37C2×#14524042C2214yes—
38C2×#14524042C2212yes—
39C2×#14524042C2211yescharacteristic
40C2×#14524041C2214yes—
41C2×#14524041C2214yes—
42C2×#14524041C2212yes—
43C2×#14524041C2212yes—
44C2×#14524041C2214yes—
45C2×#14524041C2212yes—
46C2×#14524041C2211yescharacteristic
47C2×#14524041C22132yescomplemented
48C4⋊Q8×D67C22116yescomplemented
49C2×#14524035C2212yes—
50C2×#14524034C2212yes—
51C2×#14524033C2214yes—
52C2×#14524033C2212yes—
53C2×#14524033C2214yes—
54C2×#14524033C2214yes—
55C2×#14524023C2211yescharacteristic
56C2×#14524022C2214yes—
57C2×#14524022C2212yes—
58C2×#14524021C2214yes—
59C2×#14524021C2212yes—
60C2×#14524020C2214yes—
61C2×#14524020C2214yes—
62C2×#14524020C2214yes—
63C2×#14524019C2214yes—
64C2×#14524019C2211yescharacteristic
65#16863875C22132yes—
66C4×#11761627C22116yes—
67C2×Q8×Dic67C2212yes—
68C2×C4×Dic134C2211yescharacteristic
69C2×C4×Dic134C2212yes—
70C2×C4×Dic134C2211yescharacteristic
71C2×C4×Dic134C2212yes—
72C2×#14524008C2211yescharacteristic
73C2×#14524008C2212yes—
74C2×#14524008C2212yes—
75C2×#14524008C2214yes—
76C2×D4×Dic67C2211yescharacteristic
77C2×D4×Dic67C2212yes—
78C2×C4×C22⋊D67C2212yes—
79C2×C4×C22⋊D67C2214yes—
80C2×(C22⋊D67)⋊C4C2212yes—
81C2×(C22⋊D67)⋊C4C2214yes—
82C2×#14524001C2211yescharacteristic
83C2×#14524000C2212yes—
84C2×#14523999C2212yes—
85C2×#14523999C2214yes—
86C22×Dic67⋊C4C2214yes—
87C22×Dic67⋊C4C2214yes—
88C2×C4⋊C4×D67C2212yes—
89C2×C4⋊C4×D67C2212yes—
90C22×C4×Dic67C2212yes—
91C2×C42×D67C2211yescharacteristic
92C23×Q8×C67C2212yes—
93D4×Q8×C67C22116yescomplemented
94C2×C4⋊Q8×C67C2212yes—
95C2×C4⋊Q8×C67C2211yescharacteristic
96C2×C22⋊Q8×C67C2214yes—
97C2×C22⋊Q8×C67C2212yes—
98C2×C4×Q8×C67C2211yescharacteristic
99C2×C4×D4×C67C2211yescharacteristic
100C2×C4×D4×C67C2212yes—
101C2×#11761627Q8116yescomplemented
102C2×#11761627C2318yes—
103C22×Dic134—48no—
104C22×Dic134C2312yes—
105C22×Dic134C2312yes—
106C22×Dic134C2311yescharacteristic
107C22×Dic134C23116yes—
108C22×Dic134C2314yes—
109C22×Dic134C2314yes—
110C22×Dic134C2311yescharacteristic
111C2×Q8×D67—48no—
112C2×Q8×D67C23116yes—
113C22×C22⋊D67C2312yes—
114C23×Dic67C2312yes—
115C23×Dic67C2314yes—
116C23×Dic67C2312yes—
117C22×C4×D67C2311yescharacteristic
118C22×C4×D67C2311yescharacteristic
119C22×C4×D67C2314yes—
120C22×C4×D67C2311yescharacteristic
121#14524043C2318yes—
122#14524042C23116yes—
123#14524042C23116yes—
124#14524042C23132yes—
125#14524042C23116yes—
126#14524042C2318yes—
127#14524041C23132yes—
128#14524041C23132yes—
129#14524041C23116yes—
130#14524041C23116yes—
131#14524041C23132yes—
132#14524041C23116yes—
133#14524041C2318yes—
134#14524035C23116yes—
135#14524034C23116yes—
136#14524033C23132yes—
137#14524033C23116yes—
138#14524033C23132yes—
139#14524033C23132yes—
140#14524023C2318yes—
141#14524022C23132yes—
142#14524022C23116yes—
143#14524021C23132yes—
144#14524021C23116yes—
145#14524020C23132yes—
146#14524020C23132yes—
147#14524020C23132yes—
148#14524019C23132yes—
149#14524019C2318yes—
150Q8×Dic67C23116yes—
151C4×Dic134C2318yes—
152C4×Dic134C23116yes—
153C4×Dic134C2318yes—
154C4×Dic134C23116yes—
155#14524008C23116yes—
156#14524008C23132yes—
157#14524008C2318yes—
158#14524008C23116yes—
159D4×Dic67C23116yes—
160D4×Dic67C2318yes—
161C4×C22⋊D67C23116yes—
162C4×C22⋊D67C23132yes—
163(C22⋊D67)⋊C4C23132yes—
164(C22⋊D67)⋊C4C23116yes—
165#14524001C2318yes—
166#14524000C23116yes—
167#14523999C23116yes—
168#14523999C23132yes—
169C2×C4⋊Dic67C2312yes—
170C2×C4⋊Dic67C2312yes—
171C2×C4⋊Dic67C2311yescharacteristic
172C2×C4⋊Dic67C2311yescharacteristic
173C2×C4⋊Dic67C2312yes—
174C2×C4⋊Dic67C2314yes—
175C2×Dic67⋊C4C23132yes—
176C2×Dic67⋊C4C23132yes—
177C2×Dic67⋊C4C2314yes—
178C2×Dic67⋊C4C2314yes—
179C2×Dic67⋊C4C2312yes—
180C2×Dic67⋊C4C2312yes—
181C2×Dic67⋊C4C2314yes—
182C2×Dic67⋊C4C2314yes—
183C2×Dic67⋊C4C2314yes—
184C2×Dic67⋊C4C2314yes—
185C2×Dic67⋊C4C2312yes—
186C2×Dic67⋊C4C2312yes—
187C2×Dic67⋊C4C2312yes—
188C2×Dic67⋊C4C2314yes—
189C2×Dic67⋊C4C2314yes—
190C2×Dic67⋊C4C2312yes—
191C2×Dic67⋊C4C2312yes—
192C4⋊C4×D67C23116yes—
193C4⋊C4×D67C23116yes—
194C2×C22⋊Dic67C2314yes—
195C2×C22⋊Dic67C2312yes—
196C2×(C2×D67)⋊C4C2312yes—
197C2×(C2×D67)⋊C4C2312yes—
198C2×(C2×D67)⋊C4C2312yes—
199C2×C4×Dic67C2311yescharacteristic
200C2×C4×Dic67C2311yescharacteristic
201C2×C4×Dic67C2311yescharacteristic
202C2×C4×Dic67C2312yes—
203C2×C4×Dic67C2312yes—
204C2×C4×Dic67C2312yes—
205C2×C4×Dic67C23116yes—
206C2×C4×Dic67C2314yes—
207C2×C4×Dic67C2314yes—
208C2×C4×Dic67C2312yes—
209C42×D67C2318yes—
210C22×Q8×C67—48no—
211C22×Q8×C67C2311yescharacteristic
212C22×Q8×C67C2312yes—
213C22×Q8×C67C23116yes—
214C22×Q8×C67C2314yes—
215C22×D4×C67C2311yescharacteristic
216C23×C4×C67C2312yes—
217C23×C4×C67C2314yes—
218C4⋊Q8×C67C23116yes—
219C4⋊Q8×C67C2318yes—
220C22⋊Q8×C67C23132yes—
221C22⋊Q8×C67C23116yes—
222C4×Q8×C67C2318yes—
223C4×D4×C67C2318yes—
224C4×D4×C67C23116yes—
225C2×C4⋊C4×C67C2312yes—
226C2×C4⋊C4×C67C2311yescharacteristic
227C2×C4⋊C4×C67C2311yescharacteristic
228C2×C4⋊C4×C67C2312yes—
229C2×C4⋊C4×C67C2312yes—
230C2×C4⋊C4×C67C2314yes—
231C2×C22⋊C4×C67C2314yes—
232C2×C22⋊C4×C67C2312yes—
233C2×C42×C67C2311yescharacteristic
234C2×C42×C67C2312yes—
235C23×D67C2411yescharacteristic
236#11761627C2×Q8164yescomplemented
237C2×Dic134—28no—
238C2×Dic134—24no—
239C2×Dic134—28no—
240C2×Dic134—432no—
241C2×Dic134—48no—
242C2×Dic134—48no—
243C2×Dic134C2×Q818yescomplemented
244C2×Dic134C2418yes—
245C2×Dic134C2418yes—
246C2×Dic134C2414yes—
247C2×Dic134C24116yes—
248C2×Dic134C24116yes—
249C2×Dic134C2414yes—
250Q8×D67—432no—
251C2×C22⋊D67C2×Q8116yescomplemented
252C2×C22⋊D67C2418yes—
253C22×Dic67—28no—
254C22×Dic67—48no—
255C22×Dic67C2×Q8116yescomplemented
256C22×Dic67C2412yes—
257C22×Dic67C2412yes—
258C22×Dic67C2411yescharacteristic
259C22×Dic67C2418yes—
260C22×Dic67C2412yes—
261C22×Dic67C2414yes—
262C22×Dic67C24116yes—
263C22×Dic67C2412yes—
264C22×Dic67C2411yescharacteristic
265C22×Dic67C2418yes—
266C22×Dic67C2411yescharacteristic
267C2×C4×D67—24no—
268C2×C4×D67—24no—
269C2×C4×D67—48no—
270C2×C4×D67C2×Q818yescomplemented
271C2×C4×D67C2414yes—
272C2×C4×D67C2414yes—
273C2×C4×D67C24116yes—
274C2×C4×D67C2414yes—
275C4⋊Dic67C2418yes—
276C4⋊Dic67C2418yes—
277C4⋊Dic67C2414yes—
278C4⋊Dic67C2414yes—
279C4⋊Dic67C2418yes—
280C4⋊Dic67C24116yes—
281Dic67⋊C4C24116yes—
282Dic67⋊C4C24116yes—
283Dic67⋊C4C2418yes—
284Dic67⋊C4C2418yes—
285Dic67⋊C4C24116yes—
286Dic67⋊C4C24116yes—
287Dic67⋊C4C24116yes—
288Dic67⋊C4C24116yes—
289Dic67⋊C4C2418yes—
290Dic67⋊C4C2418yes—
291Dic67⋊C4C2418yes—
292Dic67⋊C4C24116yes—
293Dic67⋊C4C24116yes—
294Dic67⋊C4C2418yes—
295Dic67⋊C4C2418yes—
296C22⋊Dic67C24116yes—
297C22⋊Dic67C2418yes—
298(C2×D67)⋊C4C2418yes—
299(C2×D67)⋊C4C2418yes—
300(C2×D67)⋊C4C2418yes—
301C4×Dic67C2414yes—
302C4×Dic67C2414yes—
303C4×Dic67C2414yes—
304C4×Dic67C2418yes—
305C4×Dic67C2418yes—
306C4×Dic67C2418yes—
307C4×Dic67C24116yes—
308C4×Dic67C24116yes—
309C4×Dic67C2418yes—
310C24×C67C2412yes—
311C2×Q8×C67—24no—
312C2×Q8×C67—28no—
313C2×Q8×C67—48no—
314C2×Q8×C67—432no—
315C2×Q8×C67C2414yes—
316C2×Q8×C67C2418yes—
317C2×Q8×C67C24116yes—
318C2×D4×C67C2×Q818yescomplemented
319C2×D4×C67C2414yes—
320C22×C4×C67—28no—
321C22×C4×C67—48no—
322C22×C4×C67C2412yes—
323C22×C4×C67C2411yescharacteristic
324C22×C4×C67C2412yes—
325C22×C4×C67C2412yes—
326C22×C4×C67C2414yes—
327C22×C4×C67C2418yes—
328C22×C4×C67C24116yes—
329C22×C4×C67C2411yescharacteristic
330C22×C4×C67C2411yescharacteristic
331C4⋊C4×C67C2418yes—
332C4⋊C4×C67C2414yes—
333C4⋊C4×C67C2414yes—
334C4⋊C4×C67C2418yes—
335C4⋊C4×C67C2418yes—
336C4⋊C4×C67C24116yes—
337C22⋊C4×C67C24116yes—
338C22⋊C4×C67C2418yes—
339C42×C67C2414yes—
340C42×C67C2418yes—
341C23×C67—24no—
342C23×C67—24no—
343C23×C67C22×Q818yes—
344C23×C67C2514yes—
345C23×C67C2511yescharacteristic
346C22×D67—22no—
347C22×D67—22no—
348C22×D67C22×Q814yes—
349C22×D67C2512yes—
350Q8×C67—28no—
351Q8×C67—216no—
352Q8×C67—416no—
353D4×C67C22×Q8116yescomplemented
354C2×C4×C67—24no—
355C2×C4×C67—24no—
356C2×C4×C67—28no—
357C2×C4×C67—22no—
358C2×C4×C67—24no—
359C2×C4×C67—216no—
360C2×C4×C67—416no—
361C2×C4×C67C22×Q814yes—
362C2×C4×C67H(5,𝔽2)14yes—
363C2×C4×C67C2514yes—
364C2×C4×C67C2512yes—
365C2×C4×C67C2514yes—
366C2×C4×C67C2514yes—
367C2×C4×C67C2518yes—
368C2×C4×C67C2512yes—
369C2×C4×C67C2512yes—
370C22⋊D67C22×Q8132yescomplemented
371C2×Dic67—22no—
372C2×Dic67—28no—
373C2×Dic67—24no—
374C2×Dic67—24no—
375C2×Dic67—24no—
376C2×Dic67—216no—
377C2×Dic67—416no—
378C2×Dic67C22×Q814yes—
379C2×Dic67C22×Q818yes—
380C2×Dic67C22×Q8132yescomplemented
381C2×Dic672−1+414yes—
382C2×Dic67C2514yes—
383C2×Dic67C2514yes—
384C2×Dic67C2512yes—
385C2×Dic67C2514yes—
386C2×Dic67C2518yes—
387C2×Dic67C2514yes—
388C2×Dic67C2512yes—
389C2×Dic67C2512yes—
390C4×D67—28no—
391C4×D67—28no—
392C4×D67—416no—
393C4×D67C22×Q8116yescomplemented
394Dic134—216no—
395Dic134—28no—
396Dic134—216no—
397Dic134—416no—
398Dic134—416no—
399Dic134C22×Q8116yescomplemented
400C22×C67—24no—
401C22×C67—24no—
402C22×C67—216no—
403C22×C67C23×Q818yes—
404C22×C67C23×Q812yes—
405C22×C67C2×H(5,𝔽2)12yes—
406C22×C67C2×2−1+412yes—
407C22×C67C2611yescharacteristic
408C2×D67—22no—
409C2×D67—22no—
410C2×D67—28no—
411C2×D67C23×Q814yes—
412C4×C67—24no—
413C4×C67—28no—
414C4×C67—24no—
415C4×C67—24no—
416C4×C67—22no—
417C4×C67C23×Q814yes—
418C4×C67C2×H(5,𝔽2)14yes—
419Dic67—28no—
420Dic67—24no—
421Dic67—22no—
422Dic67—24no—
423Dic67—24no—
424Dic67C23×Q818yes—
425Dic67C23×Q814yes—
426Dic67C2×2−1+414yes—
427C2×#3503—671nomaximal, Sylow
428C2×C67—28no—
429C2×C67#350314yescomplemented
430C2×C67C24×Q811yescharacteristic
431C2×C67C22×H(5,𝔽2)11yescharacteristic
432C2×C67C22×2−1+411yescharacteristic
433D67—24no—
434#3503—6732no—
435C2×Q82—672no—
436C2×#557—671no—
437C2×#557—671no—
438C2×#554—674no—
439C2×#554—672no—
440C2×D4×Q8—672no—
441C2×D4×Q8—672no—
442C2×D4×Q8—671no—
443C2×D4×Q8D6711yescharacteristic, complemented
444C2×#544—672no—
445C2×#544—674no—
446C2×#533—672no—
447C2×#533—671no—
448C22×C4⋊Q8—672no—
449C22×C4⋊Q8—671no—
450C2×#520—672no—
451C2×C4×#41—671no—
452C67C2×#350311yescharacteristic, complemented, Sylow
453C22×#41—671no—
454C23×Q8—672no—
455C23×Q8—672no—
456C23×Q8C2×D6712yes—
457Q82—6732no—
458#557—6716no—
459#557—6716no—
460#554—6764no—
461#554—6732no—
462D4×Q8—6732no—
463D4×Q8—6732no—
464D4×Q8—6716no—
465D4×Q8C2×D67116yescomplemented
466#544—6732no—
467#544—6764no—
468#533—6732no—
469#533—6716no—
470C2×C4⋊Q8—672no—
471C2×C4⋊Q8—671no—
472C2×C4⋊Q8—674no—
473C2×C4⋊Q8—672no—
474C2×C4⋊Q8—672no—
475C2×C4⋊Q8—674no—
476C2×C4⋊Q8—6732no—
477C2×C4⋊Q8—674no—
478C2×C4⋊Q8—6716no—
479C2×C4⋊Q8—672no—
480C2×C4⋊Q8—672no—
481C2×C4⋊Q8—671no—
482C2×C4⋊Q8—674no—
483C2×C4⋊Q8—672no—
484C2×C4⋊Q8—671no—
485C2×C4⋊Q8C2×D6711yescharacteristic
486C2×C4⋊Q8C2×D6712yes—
487C2×#125—674no—
488C2×#125—672no—
489C2×#125—674no—
490C2×#125—674no—
491C2×#125—672no—
492C2×#125—672no—
493C2×C22⋊Q8—671no—
494C2×C22⋊Q8—674no—
495C2×C22⋊Q8—672no—
496C2×C22⋊Q8—674no—
497C2×C22⋊Q8—671no—
498C2×C22⋊Q8—672no—
499C2×C22⋊Q8—674no—
500C2×C22⋊Q8—674no—
501C2×C22⋊Q8—674no—
502C2×C22⋊Q8—674no—
503C2×C22⋊Q8C2×D6712yes—
504C2×C22⋊Q8C2×D6714yes—
505#520—6732no—
506C4×#41—6716no—
507C2×C4×Q8—672no—
508C2×C4×Q8—671no—
509C2×C4×Q8—672no—
510C2×C4×Q8—672no—
511C2×C4×Q8—674no—
512C2×C4×Q8—671no—
513C2×C4×Q8—672no—
514C2×C4×Q8—671no—
515C2×C4×Q8—672no—
516C2×C4×Q8C2×D6711yescharacteristic
517C2×C4×D4—671no—
518C2×C4×D4—672no—
519C2×C4×D4—672no—
520C2×C4×D4—674no—
521C2×C4×D4—672no—
522C2×C4×D4—674no—
523C2×C4×D4C2×D6711yescharacteristic
524C2×C4×D4C2×D6712yes—
525C2×#117—671no—
526C2×#117—672no—
527C2×#117—674no—
528C2×#117—672no—
529C22×C4⋊C4—674no—
530C22×C4⋊C4—674no—
531C22×C4⋊C4—672no—
532C22×C4⋊C4—672no—
533C22×C42—672no—
534C22×C42—671no—
535C2×#41—6716no—
536C2×#41—678no—
537C22×Q8—48no—
538C22×Q8—2688no—
539C22×Q8—2688no—
540C22×Q8—6716no—
541C22×Q8—674no—
542C22×Q8—674no—
543C22×Q8—6716no—
544C22×Q8—671no—
545C22×Q8—672no—
546C22×Q8—672no—
547C22×Q8—671no—
548C22×Q8C22×D6712yes—
549C22×Q8C22×D6711yescharacteristic
550C22×Q8C22×D6714yes—
551C22×Q8C22×D67116yes—
552C22×D4—672no—
553C22×D4C22×D6711yescharacteristic
554C23×C4—674no—
555C23×C4—674no—
556C23×C4—672no—
557C23×C4—671no—
558C23×C4—672no—
559C23×C4—671no—
560C23×C4—671no—
561C23×C4C22×D6712yes—
562C23×C4C22×D6714yes—
563C4⋊Q8—6716no—
564C4⋊Q8—678no—
565C4⋊Q8—6732no—
566C4⋊Q8—6716no—
567C4⋊Q8—6716no—
568C4⋊Q8—6732no—
569C4⋊Q8—6732no—
570C4⋊Q8—6716no—
571C4⋊Q8—6716no—
572C4⋊Q8—678no—
573C4⋊Q8—6732no—
574C4⋊Q8—6716no—
575C4⋊Q8—678no—
576C4⋊Q8C22×D6718yes—
577C4⋊Q8C22×D67116yes—
578#125—6732no—
579#125—6716no—
580#125—6732no—
581#125—6732no—
582#125—6716no—
583#125—6716no—
584C22⋊Q8—678no—
585C22⋊Q8—6732no—
586C22⋊Q8—6716no—
587C22⋊Q8—6732no—
588C22⋊Q8—678no—
589C22⋊Q8—6716no—
590C22⋊Q8—6732no—
591C22⋊Q8—6732no—
592C22⋊Q8—6732no—
593C22⋊Q8—6732no—
594C22⋊Q8C22×D67116yes—
595C22⋊Q8C22×D67132yes—
596C4×Q8—6716no—
597C4×Q8—678no—
598C4×Q8—6716no—
599C4×Q8—6716no—
600C4×Q8—6732no—
601C4×Q8—678no—
602C4×Q8—6716no—
603C4×Q8—678no—
604C4×Q8—6716no—
605C4×Q8C22×D6718yes—
606C4×D4—678no—
607C4×D4—6716no—
608C4×D4—6716no—
609C4×D4—6732no—
610C4×D4—6716no—
611C4×D4—6732no—
612C4×D4C22×D6718yes—
613C4×D4C22×D67116yes—
614#117—678no—
615#117—6716no—
616#117—6732no—
617#117—6716no—
618C2×C4⋊C4—674no—
619C2×C4⋊C4—672no—
620C2×C4⋊C4—674no—
621C2×C4⋊C4—672no—
622C2×C4⋊C4—674no—
623C2×C4⋊C4—674no—
624C2×C4⋊C4—672no—
625C2×C4⋊C4—6732no—
626C2×C4⋊C4—674no—
627C2×C4⋊C4—674no—
628C2×C4⋊C4—672no—
629C2×C4⋊C4—6732no—
630C2×C4⋊C4—672no—
631C2×C4⋊C4—672no—
632C2×C4⋊C4—671no—
633C2×C4⋊C4—672no—
634C2×C4⋊C4—671no—
635C2×C4⋊C4—672no—
636C2×C4⋊C4—674no—
637C2×C4⋊C4—674no—
638C2×C4⋊C4—672no—
639C2×C4⋊C4—674no—
640C2×C4⋊C4—672no—
641C2×C4⋊C4—6716no—
642C2×C4⋊C4—6716no—
643C2×C4⋊C4C22×D6712yes—
644C2×C4⋊C4C22×D6712yes—
645C2×C4⋊C4C22×D6711yescharacteristic
646C2×C4⋊C4C22×D6711yescharacteristic
647C2×C4⋊C4C22×D6714yes—
648C2×C4⋊C4C22×D6712yes—
649C2×C22⋊C4—674no—
650C2×C22⋊C4—672no—
651C2×C22⋊C4—672no—
652C2×C22⋊C4—672no—
653C2×C22⋊C4—672no—
654C2×C22⋊C4C22×D6714yes—
655C2×C22⋊C4C22×D6712yes—
656C2×C42—672no—
657C2×C42—671no—
658C2×C42—674no—
659C2×C42—674no—
660C2×C42—672no—
661C2×C42—672no—
662C2×C42—672no—
663C2×C42—671no—
664C2×C42—6716no—
665C2×C42—671no—
666C2×C42—678no—
667C2×C42C22×D6712yes—
668C2×C42C22×D6711yescharacteristic
669C24—671no—
670C24C23×D6712yes—
671#41—6764no—
672C2×Q8—24no—
673C2×Q8—28no—
674C2×Q8—48no—
675C2×Q8—432no—
676C2×Q8—26832no—
677C2×Q8—2688no—
678C2×Q8—2688no—
679C2×Q8—26832no—
680C2×Q8—678no—
681C2×Q8—6716no—
682C2×Q8—6716no—
683C2×Q8—674no—
684C2×Q8—678no—
685C2×Q8—678no—
686C2×Q8—674no—
687C2×Q8—1348no—
688C2×Q8—1344no—
689C2×Q8—1348no—
690C2×Q8C23×D6718yes—
691C2×Q8C23×D6714yes—
692C2×Q8C23×D67116yes—
693C2×D4—6716no—
694C2×D4—678no—
695C2×D4Q8×D6718yescomplemented
696C2×D4C23×D6714yes—
697C22×C4—28no—
698C22×C4—48no—
699C22×C4—2688no—
700C22×C4—2688no—
701C22×C4—6716no—
702C22×C4—6716no—
703C22×C4—6716no—
704C22×C4—678no—
705C22×C4—672no—
706C22×C4—671no—
707C22×C4—671no—
708C22×C4—678no—
709C22×C4—674no—
710C22×C4—678no—
711C22×C4—672no—
712C22×C4—672no—
713C22×C4—671no—
714C22×C4—674no—
715C22×C4—672no—
716C22×C4—674no—
717C22×C4—674no—
718C22×C4—1344no—
719C22×C4—1348no—
720C22×C4—1344no—
721C22×C4C23×D6718yes—
722C22×C4C23×D6712yes—
723C22×C4C23×D6712yes—
724C22×C4C23×D6711yescharacteristic
725C22×C4C23×D6714yes—
726C22×C4C23×D6712yes—
727C22×C4C23×D67116yes—
728C22×C4C23×D6711yescharacteristic
729C22×C4C23×D6711yescharacteristic
730C4⋊C4—6716no—
731C4⋊C4—678no—
732C4⋊C4—6716no—
733C4⋊C4—678no—
734C4⋊C4—6716no—
735C4⋊C4—6716no—
736C4⋊C4—678no—
737C4⋊C4—6716no—
738C4⋊C4—6716no—
739C4⋊C4—678no—
740C4⋊C4—678no—
741C4⋊C4—678no—
742C4⋊C4—674no—
743C4⋊C4—678no—
744C4⋊C4—674no—
745C4⋊C4—678no—
746C4⋊C4—6716no—
747C4⋊C4—6716no—
748C4⋊C4—678no—
749C4⋊C4—6716no—
750C4⋊C4—678no—
751C4⋊C4C23×D6718yes—
752C4⋊C4C23×D6718yes—
753C4⋊C4C23×D6714yes—
754C4⋊C4C23×D6714yes—
755C4⋊C4C23×D67116yes—
756C4⋊C4C23×D6718yes—
757C22⋊C4—6716no—
758C22⋊C4—678no—
759C22⋊C4—678no—
760C22⋊C4—678no—
761C22⋊C4—678no—
762C22⋊C4C23×D67116yes—
763C22⋊C4C23×D6718yes—
764C42—674no—
765C42—678no—
766C42—674no—
767C42—678no—
768C42—678no—
769C42—674no—
770C42—6716no—
771C42—6716no—
772C42—678no—
773C42C23×D6714yes—
774C42C23×D6718yes—
775C23—24no—
776C23—24no—
777C23—674no—
778C23—672no—
779C23—1342no—
780C23—1342no—
781C23C2×Q8×D6718yes—
782C23C24×D6714yes—
783C23C24×D6711yescharacteristic
784Q8—28no—
785Q8—216no—
786Q8—416no—
787Q8—26816no—
788Q8—26816no—
789Q8—6716no—
790Q8—13416no—
791Q8—1348no—
792Q8—13416no—
793D4—6732no—
794D4C2×Q8×D67116yescomplemented
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—28no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—216no—
801C2×C4—416no—
802C2×C4—26816no—
803C2×C4—26816no—
804C2×C4—674no—
805C2×C4—678no—
806C2×C4—6732no—
807C2×C4—674no—
808C2×C4—674no—
809C2×C4—672no—
810C2×C4—672no—
811C2×C4—6716no—
812C2×C4—674no—
813C2×C4—674no—
814C2×C4—672no—
815C2×C4—678no—
816C2×C4—674no—
817C2×C4—1348no—
818C2×C4—13416no—
819C2×C4—1348no—
820C2×C4—1344no—
821C2×C4—1342no—
822C2×C4—1344no—
823C2×C4—1344no—
824C2×C4—1348no—
825C2×C4C2×Q8×D6714yes—
826C2×C4#1452408814yes—
827C2×C4C24×D6714yes—
828C2×C4C24×D6714yes—
829C2×C4C24×D6712yes—
830C2×C4C24×D6718yes—
831C2×C4C24×D6714yes—
832C2×C4C24×D6712yes—
833C2×C4C24×D6712yes—
834C22—24no—
835C22—24no—
836C22—216no—
837C22—674no—
838C22—1342no—
839C22—1342no—
840C22—1348no—
841C22C22×Q8×D6718yes—
842C22C22×Q8×D6712yes—
843C22C2×#1452408812yes—
844C222−1+4×D6712yes—
845C22C25×D6711yescharacteristic
846C4—24no—
847C4—24no—
848C4—28no—
849C4—22no—
850C4—24no—
851C4—674no—
852C4—678no—
853C4—674no—
854C4—1348no—
855C4—1344no—
856C4—1342no—
857C4—1344no—
858C4—1344no—
859C4C22×Q8×D6714yes—
860C4C2×#1452408814yes—
861C2—28no—
862C2—1344no—
863C2#2257402014yesdirect product factor
864C2C23×Q8×D6711yescharacteristic
865C2C22×#1452408811yescharacteristic
866C2C2×2−1+4×D6711yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×D4×Q8×C67C2
socleC23×C67C25
prime radicalC22×#11761627C22
hypercenterC2×D4×Q8D67
hypocenterC67C2×#3503
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #22574020C2direct (N × H)
2. C2×#16864126C2semidirect
3. C2×#16864124C2semidirect
4. C2×#16864121C2semidirect
5. C2×#16864105C2semidirect
6. C2×#16864100C2semidirect
7. C2×D4×Dic134C2semidirect
8. C2×Q8×C22⋊D67C2semidirect
9. C2×#16864059C2semidirect
10. C2×#16864025C2semidirect
11. C2×#16864023C2semidirect
12. C2×#16863950C2semidirect
13. C2×#16863948C2semidirect
14. C22×#14524041C2semidirect
15. C2×C4⋊Q8×D67C2semidirect
18. C2×D4×Q8×C67C2semidirect
22. #16864126C22semidirect
23. #16864124C22semidirect
24. #16864121C22semidirect
25. #16864105C22semidirect
26. #16864100C22semidirect
27. D4×Dic134C22semidirect
28. Q8×C22⋊D67C22semidirect
29. #16864059C22semidirect
30. #16864025C22semidirect
31. #16864023C22semidirect
32. #16863950C22semidirect
33. #16863948C22semidirect
47. C2×#14524041C22semidirect
48. C4⋊Q8×D67C22semidirect
93. D4×Q8×C67C22semidirect
101. C2×#11761627Q8semidirect
236. #11761627C2×Q8semidirect
243. C2×Dic134C2×Q8semidirect
251. C2×C22⋊D67C2×Q8semidirect
255. C22×Dic67C2×Q8semidirect
270. C2×C4×D67C2×Q8semidirect
318. C2×D4×C67C2×Q8semidirect
353. D4×C67C22×Q8semidirect
370. C22⋊D67C22×Q8semidirect
380. C2×Dic67C22×Q8semidirect
393. C4×D67C22×Q8semidirect
399. Dic134C22×Q8semidirect
429. C2×C67#3503semidirect
443. C2×D4×Q8D67semidirect
452. C67C2×#3503semidirect
465. D4×Q8C2×D67semidirect
695. C2×D4Q8×D67semidirect
794. D4C2×Q8×D67semidirect
863. C2#22574020direct (N × H)

Maximal subgroups

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

subgroupindex
#225740202
C2×#168641262
C2×#168641242
C2×#168641212
C2×#168641052
C2×#168641002
C2×D4×Dic1342
C2×Q8×C22⋊D672
C2×#168640592
C2×#168640252
C2×#168640232
C2×#168639502
C2×#168639482
C22×#145240412
C2×C4⋊Q8×D672
C2×#168638752
C2×C4×#117616272
C2×D4×Q8×C672
C2×#350367