Finite Group Databasebeta

← C2×#22574740 #31763200

Subgroups — C2×#22574740 #31763200

Order 17152.

7194 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574740C2132yesmaximal, direct product factor
2C2×#16864150C212yesmaximal, complemented
3C2×#16864140C212yesmaximal, complemented
4C2×#16864106C212yesmaximal, complemented
5C2×#16864092C212yesmaximal, complemented
6C2×#16864092C212yesmaximal, complemented
7C2×#16864050C212yesmaximal, complemented
8C2×#16864044C214yesmaximal, complemented
9C2×#16864024C212yesmaximal, complemented
10C2×#16864001C212yesmaximal, complemented
11C2×#16863995C212yesmaximal, complemented
12C2×#16863987C214yesmaximal, complemented
13C2×#16863973C212yesmaximal, complemented
14C2×#16863946C211yesmaximal, characteristic, complemented
15C22×#14524035C211yesmaximal, characteristic, complemented
16C2×#529×C67C211yesmaximal, characteristic, complemented
17C22×#11761628C2212yes—
18C22×#11761627C2214yes—
19#16864150C22132yescomplemented
20#16864140C22132yescomplemented
21#16864106C22132yescomplemented
22#16864092C22132yescomplemented
23#16864092C22132yescomplemented
24#16864050C22132yescomplemented
25#16864044C22164yescomplemented
26#16864024C22132yescomplemented
27#16864001C22132yescomplemented
28#16863995C22132yescomplemented
29#16863987C22164yescomplemented
30#16863973C22132yescomplemented
31#16863946C22116yescomplemented
32C2×#14524043C2211yescharacteristic
33C2×#14524043C2212yes—
34C2×#14524042C2214yes—
35C2×#14524040C2211yescharacteristic
36C2×#14524038C2214yes—
37C2×#14524038C2214yes—
38C2×#14524035C2212yes—
39C2×#14524035C2212yes—
40C2×#14524035C2212yes—
41C2×#14524035C2212yes—
42C2×#14524035C2212yes—
43C2×#14524035C22116yescomplemented
44C2×#14524034C2214yes—
45C2×#14524031C2212yes—
46C2×#14524028C2214yes—
47C2×#14524028C2214yes—
48C2×#14524027C2214yes—
49C2×#14524027C2214yes—
50C2×#14524025C2214yes—
51C2×#14524025C2214yes—
52C2×#14524023C2214yes—
53C2×#14524021C2214yes—
54C2×#14524021C2214yes—
55C2×#14524020C2214yes—
56C2×#14524020C2214yes—
57C2×#14524019C2214yes—
58C2×#14524017C2212yes—
59C2×#14524017C2212yes—
60C2×#14524017C2212yes—
61C2×#14524017C2212yes—
62C2×#14524016C2214yes—
63C2×#14524016C2214yes—
64C2×#14524015C2214yes—
65C2×#14524015C2214yes—
66C2×C4×D268C2212yes—
67C2×C4×D268C2212yes—
68C2×C4×D268C2212yes—
69C2×C4×D268C2212yes—
70C2×(C22⋊D67)⋊C4C2214yes—
71C2×(C22⋊D67)⋊C4C2214yes—
72C2×#14524002C2212yes—
73C22×C4⋊Dic67C2212yes—
74C22×C4⋊Dic67C2211yescharacteristic
75C22×C4⋊Dic67C2211yescharacteristic
76C22×Dic67⋊C4C2212yes—
77C22×Dic67⋊C4C2212yes—
78C2×C4⋊C4×D67C2214yes—
79#529×C67C22116yescomplemented
80C2×#126×C67C2212yes—
81C2×#125×C67C2211yescharacteristic
82C2×#124×C67C2211yescharacteristic
83C2×#123×C67C2212yes—
84C2×C22⋊Q8×C67C2211yescharacteristic
85C2×#121×C67C2211yescharacteristic
86C2×C4×Q8×C67C2211yescharacteristic
87C2×C4×D4×C67C2212yes—
88C2×C4×D4×C67C2211yescharacteristic
89C2×#117×C67C2212yes—
90C22×C42×C67C2211yescharacteristic
91C2×#11761628—48no—
92C2×#11761628C23116yes—
93C2×#11761627—416no—
94C2×#11761627C23132yes—
95C22×Dic134C2312yes—
96C22×Dic134C2314yes—
97C22×D268C2312yes—
98C22×D268C2312yes—
99C22×D268C2312yes—
100C22×C22⋊D67C2314yes—
101C22×C22⋊D67C2314yes—
102C22×C22⋊D67C2314yes—
103C23×Dic67C2312yes—
104C23×Dic67C2312yes—
105C23×Dic67C2314yes—
106C22×C4×D67C2314yes—
107C22×C4×D67C2314yes—
108C22×C4×D67C2314yes—
109#14524043C2318yes—
110#14524043C23116yes—
111#14524042C23132yes—
112#14524040C2318yes—
113#14524038C23132yes—
114#14524038C23132yes—
115#14524035C23116yes—
116#14524035C23116yes—
117#14524035C23116yes—
118#14524035C23116yes—
119#14524035C23116yes—
120#14524034C23132yes—
121#14524031C23116yes—
122#14524028C23132yes—
123#14524028C23132yes—
124#14524027C23132yes—
125#14524027C23132yes—
126#14524025C23132yes—
127#14524025C23132yes—
128#14524023C23132yes—
129#14524021C23132yes—
130#14524021C23132yes—
131#14524020C23132yes—
132#14524020C23132yes—
133#14524019C23132yes—
134#14524017C23116yes—
135#14524017C23116yes—
136#14524017C23116yes—
137#14524017C23116yes—
138#14524016C23132yes—
139#14524016C23132yes—
140#14524015C23132yes—
141#14524015C23132yes—
142C4×D268C23116yes—
143C4×D268C23116yes—
144C4×D268C23116yes—
145C4×D268C23116yes—
146(C22⋊D67)⋊C4C23132yes—
147(C22⋊D67)⋊C4C23132yes—
148#14524002C23116yes—
149C2×C4⋊Dic67C23116yes—
150C2×C4⋊Dic67C2318yes—
151C2×C4⋊Dic67C2318yes—
152C2×C4⋊Dic67C2314yes—
153C2×C4⋊Dic67C2312yes—
154C2×C4⋊Dic67C2312yes—
155C2×C4⋊Dic67C2312yes—
156C2×C4⋊Dic67C2312yes—
157C2×C4⋊Dic67C2314yes—
158C2×C4⋊Dic67C2312yes—
159C2×C4⋊Dic67C2312yes—
160C2×Dic67⋊C4C23116yes—
161C2×Dic67⋊C4C2314yes—
162C2×Dic67⋊C4C2314yes—
163C2×Dic67⋊C4C2314yes—
164C2×Dic67⋊C4C2314yes—
165C2×Dic67⋊C4C2314yes—
166C2×Dic67⋊C4C23116yes—
167C2×Dic67⋊C4C2314yes—
168C4⋊C4×D67C23132yes—
169C2×C22⋊Dic67C2314yes—
170C2×(C2×D67)⋊C4C2314yes—
171C2×(C2×D67)⋊C4C2314yes—
172C2×(C2×D67)⋊C4C2314yes—
173C2×(C2×D67)⋊C4C2314yes—
174C2×(C2×D67)⋊C4C2314yes—
175C2×(C2×D67)⋊C4C2314yes—
176C2×C4×Dic67C2314yes—
177C22×Q8×C67C2311yescharacteristic
178C22×D4×C67C2312yes—
179C22×D4×C67C2311yescharacteristic
180C23×C4×C67C2311yescharacteristic
181C23×C4×C67C2311yescharacteristic
182C23×C4×C67C2312yes—
183C23×C4×C67C2311yescharacteristic
184#126×C67C23116yes—
185#125×C67C2318yes—
186#124×C67C2318yes—
187#123×C67C23116yes—
188C22⋊Q8×C67C2318yes—
189#121×C67C2318yes—
190C4×Q8×C67C2318yes—
191C4×D4×C67C23116yes—
192C4×D4×C67C2318yes—
193#117×C67C23116yes—
194C2×C4⋊C4×C67C2312yes—
195C2×C4⋊C4×C67C2312yes—
196C2×C4⋊C4×C67C2311yescharacteristic
197C2×C4⋊C4×C67C2312yes—
198C2×C4⋊C4×C67C2311yescharacteristic
199C2×C4⋊C4×C67C2312yes—
200C2×C22⋊C4×C67C2312yes—
201C2×C22⋊C4×C67C2312yes—
202C2×C22⋊C4×C67C2312yes—
203C2×C22⋊C4×C67C2312yes—
204C2×C22⋊C4×C67C2312yes—
205C2×C42×C67C2311yescharacteristic
206C2×C42×C67C2311yescharacteristic
207C2×C42×C67C2311yescharacteristic
208C2×C42×C67C2311yescharacteristic
209C2×C42×C67C2318yes—
210C2×C42×C67C2312yes—
211C23×D67C2414yes—
212#11761628—432no—
213#11761627—464no—
214C2×Dic134—48no—
215C2×Dic134—44no—
216C2×Dic134C2418yes—
217C2×Dic134C24116yes—
218C2×D268—28no—
219C2×D268—44no—
220C2×D268—44no—
221C2×D268C2418yes—
222C2×D268C2418yes—
223C2×D268C2418yes—
224C2×C22⋊D67—216no—
225C2×C22⋊D67—48no—
226C2×C22⋊D67—48no—
227C2×C22⋊D67C24116yes—
228C2×C22⋊D67C24116yes—
229C2×C22⋊D67C24116yes—
230C22×Dic67—28no—
231C22×Dic67—44no—
232C22×Dic67—48no—
233C22×Dic67C2414yes—
234C22×Dic67C2414yes—
235C22×Dic67C2414yes—
236C22×Dic67C2418yes—
237C22×Dic67C2418yes—
238C22×Dic67C24116yes—
239C2×C4×D67—48no—
240C2×C4×D67—48no—
241C2×C4×D67—48no—
242C2×C4×D67C24116yes—
243C2×C4×D67C24116yes—
244C2×C4×D67C24116yes—
245C4⋊Dic67C24116yes—
246C4⋊Dic67C2418yes—
247C4⋊Dic67C2418yes—
248C4⋊Dic67C2418yes—
249C4⋊Dic67C2418yes—
250C4⋊Dic67C24116yes—
251C4⋊Dic67C2418yes—
252C4⋊Dic67C2418yes—
253Dic67⋊C4C24116yes—
254Dic67⋊C4C24116yes—
255Dic67⋊C4C24116yes—
256Dic67⋊C4C24116yes—
257Dic67⋊C4C24116yes—
258Dic67⋊C4C24116yes—
259C22⋊Dic67C24116yes—
260(C2×D67)⋊C4C24116yes—
261(C2×D67)⋊C4C24116yes—
262(C2×D67)⋊C4C24116yes—
263(C2×D67)⋊C4C24116yes—
264(C2×D67)⋊C4C24116yes—
265(C2×D67)⋊C4C24116yes—
266C4×Dic67C24116yes—
267C24×C67C2412yes—
268C24×C67C2411yescharacteristic
269C2×Q8×C67—42no—
270C2×Q8×C67C2414yes—
271C2×D4×C67—28no—
272C2×D4×C67—42no—
273C2×D4×C67C2418yes—
274C2×D4×C67C2414yes—
275C22×C4×C67—24no—
276C22×C4×C67—24no—
277C22×C4×C67—28no—
278C22×C4×C67—42no—
279C22×C4×C67C2411yescharacteristic
280C22×C4×C67C2411yescharacteristic
281C22×C4×C67C2411yescharacteristic
282C22×C4×C67C2411yescharacteristic
283C22×C4×C67C2411yescharacteristic
284C22×C4×C67C2414yes—
285C22×C4×C67C2414yes—
286C22×C4×C67C2412yes—
287C22×C4×C67C2412yes—
288C22×C4×C67C2412yes—
289C22×C4×C67C2418yes—
290C22×C4×C67C2414yes—
291C22×C4×C67C2411yescharacteristic
292C4⋊C4×C67C2418yes—
293C4⋊C4×C67C2418yes—
294C4⋊C4×C67C2414yes—
295C4⋊C4×C67C2418yes—
296C4⋊C4×C67C2414yes—
297C4⋊C4×C67C2418yes—
298C22⋊C4×C67C2418yes—
299C22⋊C4×C67C2418yes—
300C22⋊C4×C67C2418yes—
301C22⋊C4×C67C2418yes—
302C22⋊C4×C67C2418yes—
303C42×C67C2414yes—
304C42×C67C2414yes—
305C42×C67C2414yes—
306C42×C67C2414yes—
307C42×C67C2418yes—
308C23×C67—22no—
309C23×C67—22no—
310C23×C67—24no—
311C23×C67—24no—
312C23×C67—24no—
313C23×C67H(5,𝔽2)14yes—
314C23×C67C2514yes—
315C23×C67C2512yes—
316C23×C67C2511yescharacteristic
317C22×D67—28no—
318C22×D67—28no—
319C22×D67—28no—
320C22×D67C2518yes—
321Q8×C67—44no—
322D4×C67—216no—
323D4×C67—44no—
324C2×C4×C67—22no—
325C2×C4×C67—22no—
326C2×C4×C67—28no—
327C2×C4×C67—24no—
328C2×C4×C67—22no—
329C2×C4×C67—24no—
330C2×C4×C67—22no—
331C2×C4×C67—22no—
332C2×C4×C67—24no—
333C2×C4×C67—28no—
334C2×C4×C67—216no—
335C2×C4×C67—44no—
336C2×C4×C672−1+414yes—
337C2×C4×C67C2512yes—
338C2×C4×C67C2512yes—
339C2×C4×C67C2512yes—
340C2×C4×C67C2512yes—
341C2×C4×C67C2512yes—
342C2×C4×C67C2514yes—
343C2×C4×C67C2514yes—
344C2×C4×C67C2514yes—
345C2×C4×C67C2512yes—
346C22⋊D67—232no—
347C22⋊D67—416no—
348C22⋊D67—416no—
349C2×Dic67—28no—
350C2×Dic67—28no—
351C2×Dic67—216no—
352C2×Dic67—28no—
353C2×Dic67—48no—
354C2×Dic67—416no—
355C2×Dic67C2518yes—
356C2×Dic67C2518yes—
357C2×Dic67C2518yes—
358D268—216no—
359D268—48no—
360D268—48no—
361C4×D67—416no—
362C4×D67—416no—
363C4×D67—416no—
364Dic134—416no—
365Dic134—48no—
366C22×C67—22no—
367C22×C67—22no—
368C22×C67—28no—
369C22×C67—24no—
370C22×C67—24no—
371C22×C67—24no—
372C22×C67—48no—
373C22×C67C2×H(5,𝔽2)14yes—
374C22×C67C2×H(5,𝔽2)12yes—
375C22×C67C2×2−1+412yes—
376C22×C67#58512yes—
377C22×C67C2611yescharacteristic
378C2×D67—28no—
379C2×D67—28no—
380C2×D67—28no—
381C2×D67—416no—
382C4×C67—24no—
383C4×C67—22no—
384C4×C67—22no—
385C4×C67—22no—
386C4×C67—24no—
387C4×C67—24no—
388C4×C67—22no—
389C4×C67—22no—
390C4×C67C2×2−1+414yes—
391Dic67—28no—
392Dic67—28no—
393Dic67—28no—
394C2×#3559—671nomaximal, Sylow
395C2×C67—24no—
396C2×C67—44no—
397C2×C67#355914yescomplemented
398C2×C67C22×H(5,𝔽2)11yescharacteristic
399C2×C67C22×2−1+411yescharacteristic
400C2×C67C2×#58511yescharacteristic
401D67—48no—
402#3559—6732no—
403C2×#563—672no—
404C2×#562—672no—
405C2×#554—672no—
406C2×#553—672no—
407C2×#553—672no—
408C2×#547—674no—
409C2×#547—672no—
410C2×#544—672no—
411C2×#540—672no—
412C2×#539—674no—
413C2×#539—672no—
414C2×#537—672no—
415C2×#532—671no—
416C2×#529D6711yescharacteristic, complemented
417C22×#125—671no—
418C67C2×#355911yescharacteristic, complemented, Sylow
419C22×#41—674no—
420C22×#41—672no—
421#563—6732no—
422#562—6732no—
423#554—6732no—
424#553—6732no—
425#553—6732no—
426#547—6764no—
427#547—6732no—
428#544—6732no—
429#540—6732no—
430#539—6764no—
431#539—6732no—
432#537—6732no—
433#532—6716no—
434C2×C4⋊Q8—674no—
435C2×C4⋊Q8—671no—
436C2×C4⋊Q8—672no—
437C2×#127—671no—
438#529C2×D67116yescomplemented
439C2×#126—674no—
440C2×#126—674no—
441C2×#126C2×D6712yes—
442C2×#125—674no—
443C2×#125—672no—
444C2×#125—672no—
445C2×#125—672no—
446C2×#125—672no—
447C2×#125—6716no—
448C2×#125—672no—
449C2×#125C2×D6711yescharacteristic
450C2×#124—672no—
451C2×#124C2×D6711yescharacteristic
452C2×#123—674no—
453C2×#123—674no—
454C2×#123—674no—
455C2×#123—674no—
456C2×#123—674no—
457C2×#123—674no—
458C2×#123C2×D6712yes—
459C2×C22⋊Q8—674no—
460C2×C22⋊Q8—674no—
461C2×C22⋊Q8—674no—
462C2×C22⋊Q8—674no—
463C2×C22⋊Q8—674no—
464C2×C22⋊Q8—674no—
465C2×C22⋊Q8C2×D6711yescharacteristic
466C2×#121—674no—
467C2×#121—674no—
468C2×#121—672no—
469C2×#121—672no—
470C2×#121—672no—
471C2×#121—672no—
472C2×#121—674no—
473C2×#121—674no—
474C2×#121C2×D6711yescharacteristic
475C2×C4×Q8C2×D6711yescharacteristic
476C2×C4×D4—674no—
477C2×C4×D4—674no—
478C2×C4×D4—672no—
479C2×C4×D4—672no—
480C2×C4×D4—672no—
481C2×C4×D4—672no—
482C2×C4×D4C2×D6712yes—
483C2×C4×D4C2×D6711yescharacteristic
484C2×#117—672no—
485C2×#117C2×D6712yes—
486C22×C4⋊C4—672no—
487C22×C4⋊C4—672no—
488C22×C4⋊C4—671no—
489C22×C4⋊C4—671no—
490C22×C4⋊C4—672no—
491C22×C4⋊C4—674no—
492C22×C42C2×D6711yescharacteristic
493C2×#41—2688no—
494C2×#41—26816no—
495C2×#41—6732no—
496C2×#41—6716no—
497C22×Q8—674no—
498C22×Q8—672no—
499C22×Q8C22×D6711yescharacteristic
500C22×D4—674no—
501C22×D4—674no—
502C22×D4—674no—
503C22×D4—672no—
504C22×D4—672no—
505C22×D4—672no—
506C22×D4C22×D6712yes—
507C22×D4C22×D6711yescharacteristic
508C23×C4—672no—
509C23×C4—674no—
510C23×C4—674no—
511C23×C4—674no—
512C23×C4—674no—
513C23×C4—672no—
514C23×C4C22×D6711yescharacteristic
515C23×C4C22×D6711yescharacteristic
516C23×C4C22×D6712yes—
517C23×C4C22×D6711yescharacteristic
518C4⋊Q8—6732no—
519C4⋊Q8—678no—
520C4⋊Q8—6716no—
521#127—678no—
522#126—6732no—
523#126—6732no—
524#126C22×D67116yes—
525#125—6732no—
526#125—6716no—
527#125—6716no—
528#125—6716no—
529#125—6716no—
530#125—6716no—
531#125C22×D6718yes—
532#124—6716no—
533#124C22×D6718yes—
534#123—6732no—
535#123—6732no—
536#123—6732no—
537#123—6732no—
538#123—6732no—
539#123—6732no—
540#123C22×D67116yes—
541C22⋊Q8—6732no—
542C22⋊Q8—6732no—
543C22⋊Q8—6732no—
544C22⋊Q8—6732no—
545C22⋊Q8—6732no—
546C22⋊Q8—6732no—
547C22⋊Q8C22×D6718yes—
548#121—6732no—
549#121—6732no—
550#121—6716no—
551#121—6716no—
552#121—6716no—
553#121—6716no—
554#121—6732no—
555#121—6732no—
556#121C22×D6718yes—
557C4×Q8C22×D6718yes—
558C4×D4—6732no—
559C4×D4—6732no—
560C4×D4—6716no—
561C4×D4—6716no—
562C4×D4—6716no—
563C4×D4—6716no—
564C4×D4C22×D67116yes—
565C4×D4C22×D6718yes—
566#117—6716no—
567#117C22×D67116yes—
568C2×C4⋊C4—672no—
569C2×C4⋊C4—674no—
570C2×C4⋊C4—672no—
571C2×C4⋊C4—672no—
572C2×C4⋊C4—674no—
573C2×C4⋊C4—674no—
574C2×C4⋊C4—674no—
575C2×C4⋊C4—674no—
576C2×C4⋊C4—672no—
577C2×C4⋊C4—674no—
578C2×C4⋊C4—674no—
579C2×C4⋊C4—672no—
580C2×C4⋊C4—6716no—
581C2×C4⋊C4—6716no—
582C2×C4⋊C4—678no—
583C2×C4⋊C4—678no—
584C2×C4⋊C4—6716no—
585C2×C4⋊C4—672no—
586C2×C4⋊C4—674no—
587C2×C4⋊C4—6732no—
588C2×C4⋊C4C22×D6712yes—
589C2×C4⋊C4C22×D6712yes—
590C2×C4⋊C4C22×D6712yes—
591C2×C4⋊C4C22×D6712yes—
592C2×C4⋊C4C22×D6711yescharacteristic
593C2×C4⋊C4C22×D6711yescharacteristic
594C2×C22⋊C4—674no—
595C2×C22⋊C4—674no—
596C2×C22⋊C4—674no—
597C2×C22⋊C4—674no—
598C2×C22⋊C4—674no—
599C2×C22⋊C4—674no—
600C2×C22⋊C4—674no—
601C2×C22⋊C4C22×D6712yes—
602C2×C22⋊C4C22×D6712yes—
603C2×C22⋊C4C22×D6712yes—
604C2×C22⋊C4C22×D6712yes—
605C2×C22⋊C4C22×D6712yes—
606C2×C42—674no—
607C2×C42C22×D6711yescharacteristic
608C2×C42C22×D6712yes—
609C2×C42C22×D6711yescharacteristic
610C2×C42C22×D6711yescharacteristic
611C2×C42C22×D6711yescharacteristic
612C2×C42C22×D6718yes—
613C24—674no—
614C24C23×D6712yes—
615C24C23×D6711yescharacteristic
616#41—26832no—
617#41—26864no—
618C2×Q8—42no—
619C2×Q8—2684no—
620C2×Q8—2688no—
621C2×Q8—6716no—
622C2×Q8—678no—
623C2×Q8C23×D6714yes—
624C2×D4—28no—
625C2×D4—42no—
626C2×D4—2684no—
627C2×D4—2684no—
628C2×D4—2688no—
629C2×D4—2688no—
630C2×D4—6716no—
631C2×D4—6716no—
632C2×D4—6716no—
633C2×D4—678no—
634C2×D4—678no—
635C2×D4—678no—
636C2×D4—13416no—
637C2×D4—1348no—
638C2×D4C23×D6718yes—
639C2×D4C23×D6714yes—
640C22×C4—24no—
641C22×C4—24no—
642C22×C4—28no—
643C22×C4—42no—
644C22×C4—2688no—
645C22×C4—2688no—
646C22×C4—2688no—
647C22×C4—2688no—
648C22×C4—2684no—
649C22×C4—678no—
650C22×C4—6716no—
651C22×C4—6716no—
652C22×C4—6716no—
653C22×C4—6716no—
654C22×C4—678no—
655C22×C4—674no—
656C22×C4—674no—
657C22×C4—674no—
658C22×C4—1348no—
659C22×C4C23×D6714yes—
660C22×C4C23×D6714yes—
661C22×C4C23×D6718yes—
662C22×C4C23×D6712yes—
663C22×C4C23×D6711yescharacteristic
664C22×C4C23×D6711yescharacteristic
665C22×C4C23×D6711yescharacteristic
666C22×C4C23×D6711yescharacteristic
667C22×C4C23×D6711yescharacteristic
668C22×C4C23×D6712yes—
669C22×C4C23×D6712yes—
670C22×C4C23×D6714yes—
671C22×C4C23×D6711yescharacteristic
672C4⋊C4—678no—
673C4⋊C4—6716no—
674C4⋊C4—678no—
675C4⋊C4—678no—
676C4⋊C4—6716no—
677C4⋊C4—6716no—
678C4⋊C4—6716no—
679C4⋊C4—6716no—
680C4⋊C4—678no—
681C4⋊C4—6716no—
682C4⋊C4—6716no—
683C4⋊C4—678no—
684C4⋊C4—678no—
685C4⋊C4—6716no—
686C4⋊C4C23×D6718yes—
687C4⋊C4C23×D6718yes—
688C4⋊C4C23×D6718yes—
689C4⋊C4C23×D6718yes—
690C4⋊C4C23×D6714yes—
691C4⋊C4C23×D6714yes—
692C22⋊C4—6716no—
693C22⋊C4—6716no—
694C22⋊C4—6716no—
695C22⋊C4—6716no—
696C22⋊C4—6716no—
697C22⋊C4—6716no—
698C22⋊C4—6716no—
699C22⋊C4C23×D6718yes—
700C22⋊C4C23×D6718yes—
701C22⋊C4C23×D6718yes—
702C22⋊C4C23×D6718yes—
703C22⋊C4C23×D6718yes—
704C42—6716no—
705C42C23×D6714yes—
706C42C23×D6714yes—
707C42C23×D6714yes—
708C42C23×D6714yes—
709C42C23×D6718yes—
710C23—22no—
711C23—22no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—678no—
716C23—1348no—
717C23—1348no—
718C23—1348no—
719C23#1452408914yes—
720C23C24×D6714yes—
721C23C24×D6712yes—
722C23C24×D6711yescharacteristic
723Q8—44no—
724Q8—2688no—
725Q8—26816no—
726D4—216no—
727D4—44no—
728D4—2688no—
729D4—2688no—
730D4—26816no—
731D4—26816no—
732D4—13432no—
733D4—13416no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—28no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—28no—
744C2×C4—216no—
745C2×C4—44no—
746C2×C4—26816no—
747C2×C4—26816no—
748C2×C4—26816no—
749C2×C4—26816no—
750C2×C4—2688no—
751C2×C4—678no—
752C2×C4—678no—
753C2×C4—678no—
754C2×C4—1348no—
755C2×C4—1348no—
756C2×C4—13416no—
757C2×C4—1348no—
758C2×C4#1452409014yes—
759C2×C4C24×D6714yes—
760C2×C4C24×D6712yes—
761C2×C4C24×D6712yes—
762C2×C4C24×D6712yes—
763C2×C4C24×D6712yes—
764C2×C4C24×D6712yes—
765C2×C4C24×D6714yes—
766C2×C4C24×D6714yes—
767C2×C4C24×D6712yes—
768C22—28no—
769C22—22no—
770C22—22no—
771C22—24no—
772C22—24no—
773C22—24no—
774C22—48no—
775C22—26816no—
776C22—1348no—
777C22—1348no—
778C22—1348no—
779C22C2×#1452408914yes—
780C22C2×#1452408912yes—
781C22C2×#1452409012yes—
782C22#1686423212yes—
783C22C25×D6711yescharacteristic
784C4—22no—
785C4—22no—
786C4—24no—
787C4—24no—
788C4—22no—
789C4—22no—
790C4—22no—
791C4—24no—
792C4—1348no—
793C4—1348no—
794C4—1348no—
795C4C2×#1452409014yes—
796C2—24no—
797C2—44no—
798C2—2688no—
799C2#2257474014yesdirect product factor
800C2C22×#1452408911yescharacteristic
801C2C22×#1452409011yescharacteristic
802C2C2×#1686423211yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#529×C67C2
socleC23×C67C25
hypercenterC2×#529D67
hypocenterC67C2×#3559
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #22574740C2direct (N × H)
2. C2×#16864150C2semidirect
3. C2×#16864140C2semidirect
4. C2×#16864106C2semidirect
5. C2×#16864092C2semidirect
6. C2×#16864092C2semidirect
7. C2×#16864050C2semidirect
8. C2×#16864044C2semidirect
9. C2×#16864024C2semidirect
10. C2×#16864001C2semidirect
11. C2×#16863995C2semidirect
12. C2×#16863987C2semidirect
13. C2×#16863973C2semidirect
14. C2×#16863946C2semidirect
15. C22×#14524035C2semidirect
16. C2×#529×C67C2semidirect
19. #16864150C22semidirect
20. #16864140C22semidirect
21. #16864106C22semidirect
22. #16864092C22semidirect
23. #16864092C22semidirect
24. #16864050C22semidirect
25. #16864044C22semidirect
26. #16864024C22semidirect
27. #16864001C22semidirect
28. #16863995C22semidirect
29. #16863987C22semidirect
30. #16863973C22semidirect
31. #16863946C22semidirect
43. C2×#14524035C22semidirect
79. #529×C67C22semidirect
397. C2×C67#3559semidirect
416. C2×#529D67semidirect
418. C67C2×#3559semidirect
438. #529C2×D67semidirect
799. C2#22574740direct (N × H)

Maximal subgroups

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

subgroupindex
#225747402
C2×#168641502
C2×#168641402
C2×#168641062
C2×#168640922
C2×#168640502
C2×#168640442
C2×#168640242
C2×#168640012
C2×#168639952
C2×#168639872
C2×#168639732
C2×#168639462
C22×#145240352
C2×#529×C672
C2×#355967