Finite Group Databasebeta

← C2×#22574110 #31764198

Subgroups — C2×#22574110 #31764198

Order 17152.

7758 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574110C2132yesmaximal, direct product factor
2C2×#16864115C212yesmaximal, complemented
3C2×#16864110C212yesmaximal, complemented
4C2×#16864105C212yesmaximal, complemented
5C2×#16864096C212yesmaximal, complemented
6C2×#16864093C212yesmaximal, complemented
7C2×#16864054C212yesmaximal, complemented
8C2×#16864053C212yesmaximal, complemented
9C2×#16864045C212yesmaximal, complemented
10C2×#16864013C212yesmaximal, complemented
11C2×#16864011C212yesmaximal, complemented
12C2×#16863975C212yesmaximal, complemented
13C2×#16863953C211yesmaximal, characteristic, complemented
14C2×#16863951C211yesmaximal, characteristic, complemented
15C2×#16863944C211yesmaximal, characteristic, complemented
16C2×#16863944C211yesmaximal, characteristic, complemented
17C2×C4⋊Q8×D67C211yesmaximal, characteristic, complemented
18C2×#16863875C212yesmaximal, complemented
19C2×C4×#11761628C211yesmaximal, characteristic, complemented
20C2×#532×C67C211yesmaximal, characteristic, complemented
21C22×#11761628C2211yescharacteristic
22C22×#11761627C2212yes—
23C22×#11761627C2212yes—
24C22×Q8×D67C2212yes—
25#16864115C22132yescomplemented
26#16864110C22132yescomplemented
27#16864105C22132yescomplemented
28#16864096C22132yescomplemented
29#16864093C22132yescomplemented
30#16864054C22132yescomplemented
31#16864053C22132yescomplemented
32#16864045C22132yescomplemented
33#16864013C22132yescomplemented
34#16864011C22132yescomplemented
35#16863975C22132yescomplemented
36#16863953C22116yescomplemented
37#16863951C22116yescomplemented
38#16863944C22116yescomplemented
39#16863944C22116yescomplemented
40C2×#14524043C2211yescharacteristic
41C2×#14524043C2211yescharacteristic
42C2×#14524042C2212yes—
43C2×#14524042C2212yes—
44C2×#14524041C2212yes—
45C4⋊Q8×D67C22116yescomplemented
46C2×#14524036C2214yes—
47C2×#14524036C2214yes—
48C2×#14524035C2212yes—
49C2×#14524034C2212yes—
50C2×#14524030C2212yes—
51C2×#14524030C2214yes—
52C2×#14524030C2212yes—
53C2×#14524029C2214yes—
54C2×#14524026C2214yes—
55C2×#14524024C2214yes—
56C2×#14524023C2212yes—
57C2×#14524022C2214yes—
58C2×#14524022C2212yes—
59C2×#14524022C2212yes—
60C2×#14524020C2214yes—
61C2×#14524020C2214yes—
62C2×#14524019C2212yes—
63C2×#14524016C2214yes—
64C2×#14524015C2214yes—
65C2×#14524014C2212yes—
66C2×#14524014C2212yes—
67C2×#14524014C2214yes—
68C2×#14524014C2212yes—
69C2×#14524014C2212yes—
70#16863875C22132yescomplemented
71C4×#11761628C22116yescomplemented
72C2×Q8×Dic67C2212yes—
73C2×C4×Dic134C2212yes—
74C2×C4×Dic134C2211yescharacteristic
75C2×C4×Dic134C2211yescharacteristic
76C2×C4×Dic134C2212yes—
77C2×#14524008C2212yes—
78C2×C4×D268C2211yescharacteristic
79C2×C4×D268C2211yescharacteristic
80C2×D4×Dic67C2212yes—
81C2×D4×Dic67C2212yes—
82C2×D4×Dic67C2212yes—
83C2×D4×Dic67C2212yes—
84C2×C4×C22⋊D67C2211yescharacteristic
85C2×C4×C22⋊D67C2211yescharacteristic
86C2×C4×C22⋊D67C2211yescharacteristic
87C2×C4×C22⋊D67C2211yescharacteristic
88C2×C4×C22⋊D67C2214yes—
89C2×(C22⋊D67)⋊C4C2214yes—
90C2×#14524002C2211yescharacteristic
91C2×#14524002C2212yes—
92C2×#14524001C2212yes—
93C2×#14524000C2211yescharacteristic
94C2×#14524000C2211yescharacteristic
95C2×#14523999C2214yes—
96C22×Dic67⋊C4C2214yes—
97C2×C4⋊C4×D67C2212yes—
98C2×C4⋊C4×D67C2212yes—
99C2×C42×D67C2211yescharacteristic
100C2×C42×D67C2211yescharacteristic
101C22×#41×C67C2212yes—
102#532×C67C22116yescomplemented
103C2×C4⋊Q8×C67C2211yescharacteristic
104C2×#127×C67C2211yescharacteristic
105C2×#124×C67C2212yes—
106C2×#121×C67C2212yes—
107C2×#121×C67C2212yes—
108C2×C4×D4×C67C2212yes—
109C2×C4×D4×C67C2212yes—
110C22×C42×C67C2211yescharacteristic
111C2×#11761628—28no—
112C2×#11761628C2318yes—
113C2×#11761627—216no—
114C2×#11761627—48no—
115C2×#11761627C23116yes—
116C2×#11761627C23116yes—
117C22×Dic134C2312yes—
118C22×Dic134C2311yescharacteristic
119C22×Dic134C2312yes—
120C22×Dic134C2314yes—
121C2×Q8×D67—48no—
122C2×Q8×D67C23116yes—
123C22×D268C2311yescharacteristic
124C22×C22⋊D67C2314yes—
125C22×C22⋊D67C2311yescharacteristic
126C22×C22⋊D67C2311yescharacteristic
127C22×C22⋊D67C2314yes—
128C23×Dic67C2314yes—
129C23×Dic67C2314yes—
130C22×C4×D67C2311yescharacteristic
131C22×C4×D67C2311yescharacteristic
132C22×C4×D67C2311yescharacteristic
133C22×C4×D67C2311yescharacteristic
134C22×C4×D67C2311yescharacteristic
135C22×C4×D67C2314yes—
136C22×C4×D67C2311yescharacteristic
137#14524043C2318yes—
138#14524043C2318yes—
139#14524042C23116yes—
140#14524042C23116yes—
141#14524041C23116yes—
142#14524036C23132yes—
143#14524036C23132yes—
144#14524035C23116yes—
145#14524034C23116yes—
146#14524030C23116yes—
147#14524030C23132yes—
148#14524030C23116yes—
149#14524029C23132yes—
150#14524026C23132yes—
151#14524024C23132yes—
152#14524023C23116yes—
153#14524022C23132yes—
154#14524022C23116yes—
155#14524022C23116yes—
156#14524020C23132yes—
157#14524020C23132yes—
158#14524019C23116yes—
159#14524016C23132yes—
160#14524015C23132yes—
161#14524014C23116yes—
162#14524014C23116yes—
163#14524014C23132yes—
164#14524014C23116yes—
165#14524014C23116yes—
166Q8×Dic67C23116yes—
167C4×Dic134C23116yes—
168C4×Dic134C23116yes—
169C4×Dic134C2318yes—
170C4×Dic134C2318yes—
171#14524008C23116yes—
172C4×D268C2318yes—
173C4×D268C2318yes—
174D4×Dic67C23116yes—
175D4×Dic67C23116yes—
176D4×Dic67C23116yes—
177D4×Dic67C23116yes—
178C4×C22⋊D67C2318yes—
179C4×C22⋊D67C2318yes—
180C4×C22⋊D67C23132yes—
181C4×C22⋊D67C2318yes—
182C4×C22⋊D67C2318yes—
183(C22⋊D67)⋊C4C23132yes—
184#14524002C2318yes—
185#14524002C23116yes—
186#14524001C23116yes—
187#14524000C2318yes—
188#14524000C2318yes—
189#14523999C23132yes—
190C2×C4⋊Dic67C2312yes—
191C2×C4⋊Dic67C2312yes—
192C2×C4⋊Dic67C2312yes—
193C2×C4⋊Dic67C2311yescharacteristic
194C2×C4⋊Dic67C2311yescharacteristic
195C2×C4⋊Dic67C2312yes—
196C2×C4⋊Dic67C2314yes—
197C2×Dic67⋊C4C23132yes—
198C2×Dic67⋊C4C2314yes—
199C2×Dic67⋊C4C2314yes—
200C2×Dic67⋊C4C2311yescharacteristic
201C2×Dic67⋊C4C2314yes—
202C2×Dic67⋊C4C2314yes—
203C2×Dic67⋊C4C2311yescharacteristic
204C2×Dic67⋊C4C2311yescharacteristic
205C2×Dic67⋊C4C2311yescharacteristic
206C2×Dic67⋊C4C2314yes—
207C4⋊C4×D67C23116yes—
208C4⋊C4×D67C23116yes—
209C2×C22⋊Dic67C2314yes—
210C2×C22⋊Dic67C2311yescharacteristic
211C2×C22⋊Dic67C2311yescharacteristic
212C2×C22⋊Dic67C2314yes—
213C2×C22⋊Dic67C2314yes—
214C2×C22⋊Dic67C2314yes—
215C2×C22⋊Dic67C2314yes—
216C2×(C2×D67)⋊C4C2311yescharacteristic
217C2×(C2×D67)⋊C4C2311yescharacteristic
218C2×(C2×D67)⋊C4C2311yescharacteristic
219C2×(C2×D67)⋊C4C2311yescharacteristic
220C2×(C2×D67)⋊C4C2314yes—
221C2×C4×Dic67C2311yescharacteristic
222C2×C4×Dic67C2311yescharacteristic
223C2×C4×Dic67C2311yescharacteristic
224C2×C4×Dic67C2311yescharacteristic
225C2×C4×Dic67C2311yescharacteristic
226C2×C4×Dic67C2311yescharacteristic
227C2×C4×Dic67C2314yes—
228C2×C4×Dic67C2314yes—
229C42×D67C2318yes—
230C42×D67C2318yes—
231C2×#41×C67—48no—
232C2×#41×C67C23116yes—
233C22×Q8×C67C2312yes—
234C22×D4×C67C2312yes—
235C22×D4×C67C2312yes—
236C22×D4×C67C2312yes—
237C22×D4×C67C2314yes—
238C23×C4×C67C2311yescharacteristic
239C23×C4×C67C2311yescharacteristic
240C23×C4×C67C2311yescharacteristic
241C23×C4×C67C2314yes—
242C4⋊Q8×C67C2318yes—
243#127×C67C2318yes—
244#124×C67C23116yes—
245#121×C67C23116yes—
246#121×C67C23116yes—
247C4×D4×C67C23116yes—
248C4×D4×C67C23116yes—
249C2×C4⋊C4×C67C2312yes—
250C2×C4⋊C4×C67C2312yes—
251C2×C22⋊C4×C67C2314yes—
252C2×C22⋊C4×C67C2314yes—
253C2×C42×C67C2311yescharacteristic
254C2×C42×C67C2311yescharacteristic
255C2×C42×C67C2311yescharacteristic
256C2×C42×C67C2311yescharacteristic
257C2×C42×C67C2318yes—
258C23×D67C2411yescharacteristic
259C23×D67C2411yescharacteristic
260#11761628—232no—
261#11761627—264no—
262#11761627—432no—
263C2×Dic134—28no—
264C2×Dic134—28no—
265C2×Dic134—24no—
266C2×Dic134—48no—
267C2×Dic134C2418yes—
268C2×Dic134C2414yes—
269C2×Dic134C2418yes—
270C2×Dic134C24116yes—
271Q8×D67—432no—
272C2×D268—24no—
273C2×D268C2414yes—
274C2×C22⋊D67—216no—
275C2×C22⋊D67—24no—
276C2×C22⋊D67—24no—
277C2×C22⋊D67—48no—
278C2×C22⋊D67C24116yes—
279C2×C22⋊D67C2414yes—
280C2×C22⋊D67C2414yes—
281C2×C22⋊D67C24116yes—
282C22×Dic67—216no—
283C22×Dic67—48no—
284C22×Dic67C2411yescharacteristic
285C22×Dic67C2411yescharacteristic
286C22×Dic67C2411yescharacteristic
287C22×Dic67C2414yes—
288C22×Dic67C2411yescharacteristic
289C22×Dic67C2411yescharacteristic
290C22×Dic67C2414yes—
291C22×Dic67C24116yes—
292C22×Dic67C24116yes—
293C22×Dic67C2411yescharacteristic
294C2×C4×D67—24no—
295C2×C4×D67—24no—
296C2×C4×D67—24no—
297C2×C4×D67—24no—
298C2×C4×D67—24no—
299C2×C4×D67—48no—
300C2×C4×D67#4118yescomplemented
301C2×C4×D67C2414yes—
302C2×C4×D67C2414yes—
303C2×C4×D67C2414yes—
304C2×C4×D67C2414yes—
305C2×C4×D67C2414yes—
306C2×C4×D67C24116yes—
307C2×C4×D67C2414yes—
308C4⋊Dic67C2418yes—
309C4⋊Dic67C2418yes—
310C4⋊Dic67C2418yes—
311C4⋊Dic67C2414yes—
312C4⋊Dic67C2414yes—
313C4⋊Dic67C2418yes—
314C4⋊Dic67C24116yes—
315Dic67⋊C4C24116yes—
316Dic67⋊C4C24116yes—
317Dic67⋊C4C2414yes—
318Dic67⋊C4C24116yes—
319Dic67⋊C4C24116yes—
320Dic67⋊C4C2414yes—
321Dic67⋊C4C2414yes—
322Dic67⋊C4C2414yes—
323Dic67⋊C4C24116yes—
324C22⋊Dic67C24116yes—
325C22⋊Dic67C2414yes—
326C22⋊Dic67C2414yes—
327C22⋊Dic67C24116yes—
328C22⋊Dic67C24116yes—
329C22⋊Dic67C24116yes—
330C22⋊Dic67C24116yes—
331(C2×D67)⋊C4C2414yes—
332(C2×D67)⋊C4C2414yes—
333(C2×D67)⋊C4C2414yes—
334(C2×D67)⋊C4C2414yes—
335(C2×D67)⋊C4C24116yes—
336C4×Dic67C2414yes—
337C4×Dic67C2414yes—
338C4×Dic67C2414yes—
339C4×Dic67C2414yes—
340C4×Dic67C2414yes—
341C4×Dic67C2414yes—
342C4×Dic67C24116yes—
343C4×Dic67C24116yes—
344C24×C67C2414yes—
345C24×C67C2411yescharacteristic
346#41×C67—432no—
347C2×Q8×C67—28no—
348C2×Q8×C67C2418yes—
349C2×D4×C67—28no—
350C2×D4×C67—28no—
351C2×D4×C67—28no—
352C2×D4×C67—48no—
353C2×D4×C67C2418yes—
354C2×D4×C67C2418yes—
355C2×D4×C67C2418yes—
356C2×D4×C67C24116yes—
357C22×C4×C67—24no—
358C22×C4×C67—24no—
359C22×C4×C67—24no—
360C22×C4×C67—48no—
361C22×C4×C67C2411yescharacteristic
362C22×C4×C67C2411yescharacteristic
363C22×C4×C67C2414yes—
364C22×C4×C67C2414yes—
365C22×C4×C67C2411yescharacteristic
366C22×C4×C67C2414yes—
367C22×C4×C67C2414yes—
368C22×C4×C67C24116yes—
369C22×C4×C67C2411yescharacteristic
370C22×C4×C67C2411yescharacteristic
371C22×C4×C67C2411yescharacteristic
372C4⋊C4×C67C2418yes—
373C4⋊C4×C67C2418yes—
374C22⋊C4×C67C24116yes—
375C22⋊C4×C67C24116yes—
376C42×C67C2414yes—
377C42×C67C2414yes—
378C42×C67C2414yes—
379C42×C67C2414yes—
380C23×C67—22no—
381C23×C67—28no—
382C23×C67—22no—
383C23×C67—28no—
384C23×C67—22no—
385C23×C67—28no—
386C23×C67C2518yes—
387C23×C67C2512yes—
388C23×C67C2511yescharacteristic
389C22×D67—22no—
390C22×D67—22no—
391C22×D67—22no—
392C22×D67—22no—
393C22×D67—22no—
394C22×D67C2×#4114yes—
395C22×D67C2512yes—
396C22×D67C2512yes—
397Q8×C67—216no—
398D4×C67—216no—
399D4×C67—216no—
400D4×C67—216no—
401D4×C67—416no—
402C2×C4×C67—22no—
403C2×C4×C67—22no—
404C2×C4×C67—28no—
405C2×C4×C67—22no—
406C2×C4×C67—28no—
407C2×C4×C67—28no—
408C2×C4×C67—28no—
409C2×C4×C67—416no—
410C2×C4×C67C2×#4114yes—
411C2×C4×C67H(5,𝔽2)14yes—
412C2×C4×C672−1+414yes—
413C2×C4×C67C2512yes—
414C2×C4×C67C2512yes—
415C2×C4×C67C2512yes—
416C2×C4×C67C2518yes—
417C2×C4×C67C2512yes—
418C2×C4×C67C2512yes—
419C2×C4×C67C2512yes—
420C22⋊D67—232no—
421C22⋊D67—28no—
422C22⋊D67—28no—
423C22⋊D67—416no—
424C2×Dic67—22no—
425C2×Dic67—28no—
426C2×Dic67—22no—
427C2×Dic67—22no—
428C2×Dic67—28no—
429C2×Dic67—22no—
430C2×Dic67—22no—
431C2×Dic67—232no—
432C2×Dic67—416no—
433C2×Dic67C2×#4114yes—
434C2×Dic67C2512yes—
435C2×Dic67C2512yes—
436C2×Dic67C2512yes—
437C2×Dic67C2518yes—
438C2×Dic67C2512yes—
439C2×Dic67C2512yes—
440C2×Dic67C2518yes—
441C2×Dic67C2512yes—
442D268—28no—
443C4×D67—28no—
444C4×D67—28no—
445C4×D67—28no—
446C4×D67—28no—
447C4×D67—28no—
448C4×D67—416no—
449C4×D67C2×#41116yescomplemented
450Dic134—216no—
451Dic134—216no—
452Dic134—28no—
453Dic134—416no—
454C22×C67—28no—
455C22×C67—22no—
456C22×C67—28no—
457C22×C67—22no—
458C22×C67—22no—
459C22×C67—28no—
460C22×C67—44no—
461C22×C67—416no—
462C22×C67C22×#4112yes—
463C22×C67C2×H(5,𝔽2)12yes—
464C22×C67C2×2−1+412yes—
465C22×C67C2611yescharacteristic
466C2×D67—22no—
467C2×D67—22no—
468C2×D67—28no—
469C2×D67—22no—
470C2×D67—22no—
471C2×D67—22no—
472C2×D67—44no—
473C2×D67C22×#4114yes—
474C4×C67—22no—
475C4×C67—28no—
476C4×C67—22no—
477C4×C67—22no—
478C4×C67C22×#4114yes—
479C4×C67C2×H(5,𝔽2)14yes—
480C4×C67C2×2−1+414yes—
481Dic67—22no—
482Dic67—28no—
483Dic67—28no—
484Dic67—22no—
485Dic67—22no—
486Dic67—22no—
487Dic67—22no—
488Dic67C22×#4114yes—
489C2×#3511—671nomaximal, Sylow
490C2×C67—48no—
491C2×C67—42no—
492C2×C67#351114yescomplemented
493C2×C67C23×#4111yescharacteristic
494C2×C67C22×H(5,𝔽2)11yescharacteristic
495C2×C67C22×2−1+411yescharacteristic
496D67—24no—
497D67—42no—
498#3511—6732no—
499C2×#556—672no—
500C2×#555—672no—
501C2×#554—672no—
502C2×#553—672no—
503C2×#553—672no—
504C2×#548—672no—
505C2×#548—672no—
506C2×#547—672no—
507C2×#542—672no—
508C2×#542—672no—
509C2×#537—672no—
510C2×#533—671no—
511C2×#533—671no—
512C2×#532—671no—
513C2×#532—671no—
514C2×#532D6711yescharacteristic, complemented
515C22×C4⋊Q8—671no—
516C2×#520—672no—
517C2×C4×#41—671no—
518C67C2×#351111yescharacteristic, complemented, Sylow
519C22×#41—672no—
520C22×#41—672no—
521C22×#41—671no—
522C22×#41C2×D6712yes—
523C23×Q8—672no—
524#556—6732no—
525#555—6732no—
526#554—6732no—
527#553—6732no—
528#553—6732no—
529#548—6732no—
530#548—6732no—
531#547—6732no—
532#542—6732no—
533#542—6732no—
534#537—6732no—
535#533—6716no—
536#533—6716no—
537#532—6716no—
538#532—6716no—
539#532C2×D67116yescomplemented
540C2×C4⋊Q8—672no—
541C2×C4⋊Q8—6716no—
542C2×C4⋊Q8—672no—
543C2×C4⋊Q8—672no—
544C2×C4⋊Q8—671no—
545C2×C4⋊Q8—671no—
546C2×C4⋊Q8C2×D6711yescharacteristic
547C2×#127C2×D6711yescharacteristic
548C2×#126—674no—
549C2×#126—674no—
550C2×#125—672no—
551C2×#125—672no—
552C2×#124—672no—
553C2×#124—672no—
554C2×#124—674no—
555C2×#124—674no—
556C2×#124C2×D6712yes—
557C2×#123—674no—
558C2×#123—674no—
559C2×C22⋊Q8—672no—
560C2×C22⋊Q8—672no—
561C2×C22⋊Q8—672no—
562C2×C22⋊Q8—674no—
563C2×C22⋊Q8—672no—
564C2×C22⋊Q8—674no—
565C2×C22⋊Q8—674no—
566C2×#121—672no—
567C2×#121—672no—
568C2×#121—672no—
569C2×#121—672no—
570C2×#121—674no—
571C2×#121—674no—
572C2×#121—674no—
573C2×#121C2×D6712yes—
574C2×#121C2×D6712yes—
575#520—6732no—
576C4×#41—6716no—
577C2×C4×Q8—672no—
578C2×C4×Q8—672no—
579C2×C4×Q8—671no—
580C2×C4×Q8—671no—
581C2×C4×Q8—672no—
582C2×C4×Q8—672no—
583C2×C4×D4—672no—
584C2×C4×D4—672no—
585C2×C4×D4—672no—
586C2×C4×D4—672no—
587C2×C4×D4—671no—
588C2×C4×D4—671no—
589C2×C4×D4—671no—
590C2×C4×D4—671no—
591C2×C4×D4—674no—
592C2×C4×D4—674no—
593C2×C4×D4—671no—
594C2×C4×D4—671no—
595C2×C4×D4C2×D6712yes—
596C2×C4×D4C2×D6712yes—
597C2×#117—671no—
598C2×#117—672no—
599C2×#117—672no—
600C2×#117—674no—
601C2×#117—671no—
602C2×#117—671no—
603C22×C4⋊C4—674no—
604C22×C4⋊C4—672no—
605C22×C4⋊C4—672no—
606C22×C42—671no—
607C22×C42—671no—
608C22×C42C2×D6711yescharacteristic
609C2×#41—48no—
610C2×#41—2688no—
611C2×#41—6716no—
612C2×#41—6716no—
613C2×#41—678no—
614C2×#41—1348no—
615C2×#41—13416no—
616C2×#41C22×D67116yes—
617C22×Q8—2688no—
618C22×Q8—6716no—
619C22×Q8—674no—
620C22×Q8—671no—
621C22×Q8—672no—
622C22×Q8—672no—
623C22×Q8C22×D6712yes—
624C22×D4—674no—
625C22×D4—671no—
626C22×D4—671no—
627C22×D4—674no—
628C22×D4—671no—
629C22×D4C22×D6712yes—
630C22×D4C22×D6712yes—
631C22×D4C22×D6712yes—
632C22×D4C22×D6714yes—
633C23×C4—674no—
634C23×C4—674no—
635C23×C4—671no—
636C23×C4—674no—
637C23×C4—671no—
638C23×C4—671no—
639C23×C4—671no—
640C23×C4—671no—
641C23×C4—671no—
642C23×C4C22×D6711yescharacteristic
643C23×C4C22×D6711yescharacteristic
644C23×C4C22×D6711yescharacteristic
645C23×C4C22×D6714yes—
646C4⋊Q8—6716no—
647C4⋊Q8—6716no—
648C4⋊Q8—6716no—
649C4⋊Q8—678no—
650C4⋊Q8—678no—
651C4⋊Q8C22×D6718yes—
652#127C22×D6718yes—
653#126—6732no—
654#126—6732no—
655#125—6716no—
656#125—6716no—
657#124—6716no—
658#124—6716no—
659#124—6732no—
660#124—6732no—
661#124C22×D67116yes—
662#123—6732no—
663#123—6732no—
664C22⋊Q8—6716no—
665C22⋊Q8—6716no—
666C22⋊Q8—6716no—
667C22⋊Q8—6732no—
668C22⋊Q8—6716no—
669C22⋊Q8—6732no—
670C22⋊Q8—6732no—
671#121—6716no—
672#121—6716no—
673#121—6716no—
674#121—6716no—
675#121—6732no—
676#121—6732no—
677#121—6732no—
678#121C22×D67116yes—
679#121C22×D67116yes—
680C4×Q8—6716no—
681C4×Q8—6716no—
682C4×Q8—678no—
683C4×Q8—678no—
684C4×Q8—6716no—
685C4×Q8—6716no—
686C4×D4—6716no—
687C4×D4—6716no—
688C4×D4—6716no—
689C4×D4—6716no—
690C4×D4—678no—
691C4×D4—678no—
692C4×D4—678no—
693C4×D4—678no—
694C4×D4—6732no—
695C4×D4—6732no—
696C4×D4—678no—
697C4×D4—678no—
698C4×D4C22×D67116yes—
699C4×D4C22×D67116yes—
700#117—678no—
701#117—6716no—
702#117—6716no—
703#117—6732no—
704#117—678no—
705#117—678no—
706C2×C4⋊C4—671no—
707C2×C4⋊C4—674no—
708C2×C4⋊C4—672no—
709C2×C4⋊C4—672no—
710C2×C4⋊C4—674no—
711C2×C4⋊C4—674no—
712C2×C4⋊C4—6732no—
713C2×C4⋊C4—674no—
714C2×C4⋊C4—671no—
715C2×C4⋊C4—672no—
716C2×C4⋊C4—671no—
717C2×C4⋊C4—671no—
718C2×C4⋊C4—671no—
719C2×C4⋊C4—671no—
720C2×C4⋊C4—672no—
721C2×C4⋊C4—674no—
722C2×C4⋊C4—674no—
723C2×C4⋊C4—6716no—
724C2×C4⋊C4—6716no—
725C2×C4⋊C4C22×D6712yes—
726C2×C4⋊C4C22×D6712yes—
727C2×C22⋊C4—674no—
728C2×C22⋊C4—671no—
729C2×C22⋊C4—671no—
730C2×C22⋊C4—674no—
731C2×C22⋊C4—674no—
732C2×C22⋊C4—674no—
733C2×C22⋊C4—674no—
734C2×C22⋊C4—671no—
735C2×C22⋊C4—671no—
736C2×C22⋊C4—671no—
737C2×C22⋊C4—671no—
738C2×C22⋊C4—674no—
739C2×C22⋊C4C22×D6714yes—
740C2×C22⋊C4C22×D6714yes—
741C2×C42—671no—
742C2×C42—674no—
743C2×C42—674no—
744C2×C42—671no—
745C2×C42—671no—
746C2×C42—671no—
747C2×C42—671no—
748C2×C42—671no—
749C2×C42—678no—
750C2×C42—678no—
751C2×C42C22×D6711yescharacteristic
752C2×C42C22×D6711yescharacteristic
753C2×C42C22×D6711yescharacteristic
754C2×C42C22×D6718yes—
755C2×C42C22×D6711yescharacteristic
756C24—671no—
757C24—671no—
758C24C23×D6711yescharacteristic
759C24C23×D6714yes—
760#41—432no—
761#41—26832no—
762#41—13432no—
763#41—13464no—
764C2×Q8—28no—
765C2×Q8—2688no—
766C2×Q8—26832no—
767C2×Q8—6716no—
768C2×Q8—674no—
769C2×Q8—678no—
770C2×Q8—678no—
771C2×Q8—1344no—
772C2×Q8—1348no—
773C2×Q8—1348no—
774C2×Q8C23×D6718yes—
775C2×D4—28no—
776C2×D4—28no—
777C2×D4—28no—
778C2×D4—48no—
779C2×D4—2688no—
780C2×D4—6716no—
781C2×D4—674no—
782C2×D4—674no—
783C2×D4—6716no—
784C2×D4—674no—
785C2×D4—1344no—
786C2×D4—1344no—
787C2×D4—1344no—
788C2×D4—13416no—
789C2×D4C23×D6718yes—
790C2×D4C23×D6718yes—
791C2×D4C23×D6718yes—
792C2×D4C23×D67116yes—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—48no—
797C22×C4—2688no—
798C22×C4—2688no—
799C22×C4—6716no—
800C22×C4—6716no—
801C22×C4—671no—
802C22×C4—678no—
803C22×C4—674no—
804C22×C4—6716no—
805C22×C4—671no—
806C22×C4—671no—
807C22×C4—671no—
808C22×C4—674no—
809C22×C4—671no—
810C22×C4—671no—
811C22×C4—674no—
812C22×C4—674no—
813C22×C4—674no—
814C22×C4—674no—
815C22×C4—674no—
816C22×C4—674no—
817C22×C4—13416no—
818C22×C4—1344no—
819C22×C4—1344no—
820C22×C4—1344no—
821C22×C4—1344no—
822C22×C4—1344no—
823C22×C4C23×D6714yes—
824C22×C4C23×D6714yes—
825C22×C4C23×D6714yes—
826C22×C4C23×D6711yescharacteristic
827C22×C4C23×D6714yes—
828C22×C4C23×D6711yescharacteristic
829C22×C4C23×D6711yescharacteristic
830C22×C4C23×D67116yes—
831C22×C4C23×D6711yescharacteristic
832C22×C4C23×D6711yescharacteristic
833C22×C4C23×D6711yescharacteristic
834C4⋊C4—674no—
835C4⋊C4—6716no—
836C4⋊C4—678no—
837C4⋊C4—678no—
838C4⋊C4—6716no—
839C4⋊C4—6716no—
840C4⋊C4—6716no—
841C4⋊C4—674no—
842C4⋊C4—678no—
843C4⋊C4—674no—
844C4⋊C4—674no—
845C4⋊C4—674no—
846C4⋊C4—674no—
847C4⋊C4—678no—
848C4⋊C4—6716no—
849C4⋊C4—6716no—
850C4⋊C4C23×D6718yes—
851C4⋊C4C23×D6718yes—
852C22⋊C4—6716no—
853C22⋊C4—674no—
854C22⋊C4—674no—
855C22⋊C4—6716no—
856C22⋊C4—6716no—
857C22⋊C4—6716no—
858C22⋊C4—6716no—
859C22⋊C4—674no—
860C22⋊C4—674no—
861C22⋊C4—674no—
862C22⋊C4—674no—
863C22⋊C4—6716no—
864C22⋊C4C23×D67116yes—
865C22⋊C4C23×D67116yes—
866C42—674no—
867C42—674no—
868C42—674no—
869C42—674no—
870C42—674no—
871C42—674no—
872C42—6716no—
873C42—6716no—
874C42C23×D6714yes—
875C42C23×D6714yes—
876C42C23×D6714yes—
877C42C23×D6714yes—
878C23—22no—
879C23—28no—
880C23—22no—
881C23—28no—
882C23—22no—
883C23—28no—
884C23—674no—
885C23—672no—
886C23—672no—
887C23—1342no—
888C23—1342no—
889C23—1342no—
890C23—1342no—
891C23—1342no—
892C23C24×D6712yes—
893C23C24×D6718yes—
894C23C24×D6711yescharacteristic
895Q8—216no—
896Q8—26816no—
897Q8—1348no—
898Q8—13416no—
899Q8—13416no—
900D4—216no—
901D4—216no—
902D4—216no—
903D4—416no—
904D4—26816no—
905D4—1348no—
906D4—1348no—
907D4—1348no—
908D4—13432no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—28no—
912C2×C4—22no—
913C2×C4—28no—
914C2×C4—28no—
915C2×C4—28no—
916C2×C4—416no—
917C2×C4—26816no—
918C2×C4—26816no—
919C2×C4—674no—
920C2×C4—672no—
921C2×C4—6716no—
922C2×C4—672no—
923C2×C4—672no—
924C2×C4—672no—
925C2×C4—672no—
926C2×C4—678no—
927C2×C4—672no—
928C2×C4—678no—
929C2×C4—13432no—
930C2×C4—1348no—
931C2×C4—1342no—
932C2×C4—1342no—
933C2×C4—1348no—
934C2×C4—1342no—
935C2×C4—1342no—
936C2×C4—1342no—
937C2×C4—1348no—
938C2×C4—1348no—
939C2×C4—1348no—
940C2×C4—1348no—
941C2×C4—1348no—
942C2×C4#41×D6714yes—
943C2×C4#1452408814yes—
944C2×C4#1452409014yes—
945C2×C4C24×D6712yes—
946C2×C4C24×D6718yes—
947C2×C4C24×D6712yes—
948C2×C4C24×D6712yes—
949C2×C4C24×D6712yes—
950C2×C4C24×D6712yes—
951C2×C4C24×D6712yes—
952C22—22no—
953C22—28no—
954C22—22no—
955C22—28no—
956C22—22no—
957C22—28no—
958C22—44no—
959C22—416no—
960C22—2684no—
961C22—674no—
962C22—1342no—
963C22—1342no—
964C22—1342no—
965C22—1348no—
966C22—1342no—
967C22—1342no—
968C22C2×#41×D6712yes—
969C22C2×#1452408812yes—
970C22C2×#1452409012yes—
971C22C25×D6711yescharacteristic
972C4—22no—
973C4—22no—
974C4—28no—
975C4—22no—
976C4—674no—
977C4—1348no—
978C4—1342no—
979C4—1342no—
980C4—1348no—
981C4—1342no—
982C4—1342no—
983C4—1342no—
984C4C2×#41×D6714yes—
985C4C2×#1452408814yes—
986C4C2×#1452409014yes—
987C2—42no—
988C2—48no—
989C2—2682no—
990C2—1344no—
991C2#2257411014yesdirect product factor
992C2C22×#41×D6711yescharacteristic
993C2C22×#1452408811yescharacteristic
994C2C22×#1452409011yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#532×C67C2
socleC23×C67C25
hypercenterC2×#532D67
hypocenterC67C2×#3511
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #22574110C2direct (N × H)
2. C2×#16864115C2semidirect
3. C2×#16864110C2semidirect
4. C2×#16864105C2semidirect
5. C2×#16864096C2semidirect
6. C2×#16864093C2semidirect
7. C2×#16864054C2semidirect
8. C2×#16864053C2semidirect
9. C2×#16864045C2semidirect
10. C2×#16864013C2semidirect
11. C2×#16864011C2semidirect
12. C2×#16863975C2semidirect
13. C2×#16863953C2semidirect
14. C2×#16863951C2semidirect
15. C2×#16863944C2semidirect
16. C2×#16863944C2semidirect
17. C2×C4⋊Q8×D67C2semidirect
18. C2×#16863875C2semidirect
19. C2×C4×#11761628C2semidirect
20. C2×#532×C67C2semidirect
25. #16864115C22semidirect
26. #16864110C22semidirect
27. #16864105C22semidirect
28. #16864096C22semidirect
29. #16864093C22semidirect
30. #16864054C22semidirect
31. #16864053C22semidirect
32. #16864045C22semidirect
33. #16864013C22semidirect
34. #16864011C22semidirect
35. #16863975C22semidirect
36. #16863953C22semidirect
37. #16863951C22semidirect
38. #16863944C22semidirect
39. #16863944C22semidirect
45. C4⋊Q8×D67C22semidirect
70. #16863875C22semidirect
71. C4×#11761628C22semidirect
102. #532×C67C22semidirect
300. C2×C4×D67#41semidirect
449. C4×D67C2×#41semidirect
492. C2×C67#3511semidirect
514. C2×#532D67semidirect
518. C67C2×#3511semidirect
539. #532C2×D67semidirect
991. C2#22574110direct (N × H)

Maximal subgroups

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

subgroupindex
#225741102
C2×#168641152
C2×#168641102
C2×#168641052
C2×#168640962
C2×#168640932
C2×#168640542
C2×#168640532
C2×#168640452
C2×#168640132
C2×#168640112
C2×#168639752
C2×#168639532
C2×#168639512
C2×#168639442
C2×C4⋊Q8×D672
C2×#168638752
C2×C4×#117616282
C2×#532×C672
C2×#351167