Finite Group Databasebeta

← C2×#22574743 #31763198

Subgroups — C2×#22574743 #31763198

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#22574743C2132yesmaximal, direct product factor
2C2×#16864150C212yesmaximal, complemented
3C2×#16864144C212yesmaximal, complemented
4C2×#16864102C212yesmaximal, complemented
5C2×#16864099C212yesmaximal, complemented
6C2×#16864094C212yesmaximal, complemented
7C2×#16864047C212yesmaximal, complemented
8C2×#16864047C214yesmaximal, complemented
9C2×#16864026C212yesmaximal, complemented
10C2×#16864002C212yesmaximal, complemented
11C2×#16863994C214yesmaximal, complemented
12C2×#16863993C212yesmaximal, complemented
13C2×#16863977C212yesmaximal, complemented
14C2×#16863946C211yesmaximal, characteristic, complemented
15C2×#16863930C211yesmaximal, characteristic, complemented
16C22×#125×C67C211yesmaximal, characteristic, complemented
17C22×#11761628C2212yes—
18C22×#11761628C2214yes—
19#16864150C22132yescomplemented
20#16864144C22132yescomplemented
21#16864102C22132yescomplemented
22#16864099C22132yescomplemented
23#16864094C22132yescomplemented
24#16864047C22132yescomplemented
25#16864047C22164yescomplemented
26#16864026C22132yescomplemented
27#16864002C22132yescomplemented
28#16863994C22164yescomplemented
29#16863993C22132yescomplemented
30#16863977C22132yescomplemented
31#16863946C22116yescomplemented
32C2×#14524043C2211yescharacteristic
33C2×#14524042C2214yes—
34C2×#14524042C2212yes—
35C2×#14524040C2211yescharacteristic
36#16863930C22116yescomplemented
37C2×#14524038C2214yes—
38C2×#14524038C2214yes—
39C2×#14524037C2212yes—
40C2×#14524035C2211yescharacteristic
41C2×#14524034C2212yes—
42C2×#14524033C2214yes—
43C2×#14524031C2211yescharacteristic
44C2×#14524031C2212yes—
45C2×#14524028C2214yes—
46C2×#14524028C2214yes—
47C2×#14524028C2214yes—
48C2×#14524028C2214yes—
49C2×#14524028C2214yes—
50C2×#14524026C2212yes—
51C2×#14524026C2214yes—
52C2×#14524023C2214yes—
53C2×#14524023C2214yes—
54C2×#14524022C2211yescharacteristic
55C2×#14524021C2214yes—
56C2×#14524021C2214yes—
57C2×#14524021C2214yes—
58C2×#14524021C2214yes—
59C2×#14524018C2214yes—
60C2×#14524018C2214yes—
61C2×#14524018C2212yes—
62C2×#14524018C2212yes—
63C2×#14524018C2214yes—
64C2×#14524017C2212yes—
65C2×#14524017C2214yes—
66C2×#14524017C2211yescharacteristic
67C2×#14524017C2212yes—
68C2×C4×Dic134C2211yescharacteristic
69C2×C4×D268C2211yescharacteristic
70C2×C4×D268C2212yes—
71C2×C4×D268C2212yes—
72C2×#14524005C2212yes—
73C2×#14524005C2212yes—
74C2×#14524005C2214yes—
75C2×C4×C22⋊D67C2212yes—
76C2×C4×C22⋊D67C2214yes—
77C2×#14524001C2212yes—
78C2×#14524000C2212yes—
79C2×C4⋊C4×D67C2212yes—
80C2×C4⋊C4×D67C2214yes—
81C2×#125×C67C2212yes—
82C2×#125×C67C2212yes—
83C2×#125×C67C2212yes—
84C2×#125×C67C2212yes—
85C2×#125×C67C22116yescomplemented
86C22×C4⋊C4×C67C2211yescharacteristic
87C22×C4⋊C4×C67C2212yes—
88C22×C4⋊C4×C67C2211yescharacteristic
89C22×C4⋊C4×C67C2212yes—
90C22×C42×C67C2211yescharacteristic
91C2×#11761628—48no—
92C2×#11761628—416no—
93C2×#11761628C23116yes—
94C2×#11761628C23132yes—
95C22×Dic134C2311yescharacteristic
96C22×Dic134C2314yes—
97C22×Dic134C2312yes—
98C22×D268C2312yes—
99C22×D268C2314yes—
100C22×D268C2311yescharacteristic
101C22×D268C2312yes—
102C22×D268C2314yes—
103C22×D268C2312yes—
104C22×C22⋊D67C2312yes—
105C22×C22⋊D67C2314yes—
106C22×C4×D67C2312yes—
107C22×C4×D67C2314yes—
108C22×C4×D67C2314yes—
109C22×C4×D67C2314yes—
110C22×C4×D67C2314yes—
111#14524043C2318yes—
112#14524042C23116yes—
113#14524042C23132yes—
114#14524040C2318yes—
115#14524038C23132yes—
116#14524038C23132yes—
117#14524037C23116yes—
118#14524035C2318yes—
119#14524034C23116yes—
120#14524033C23132yes—
121#14524031C2318yes—
122#14524031C23116yes—
123#14524028C23132yes—
124#14524028C23132yes—
125#14524028C23132yes—
126#14524028C23132yes—
127#14524028C23132yes—
128#14524026C23116yes—
129#14524026C23132yes—
130#14524023C23132yes—
131#14524023C23132yes—
132#14524022C2318yes—
133#14524021C23132yes—
134#14524021C23132yes—
135#14524021C23132yes—
136#14524021C23132yes—
137#14524018C23116yes—
138#14524018C23132yes—
139#14524018C23116yes—
140#14524018C23132yes—
141#14524018C23132yes—
142#14524017C23116yes—
143#14524017C23132yes—
144#14524017C2318yes—
145#14524017C23116yes—
146C4×Dic134C2318yes—
147C4×D268C2318yes—
148C4×D268C23116yes—
149C4×D268C23116yes—
150#14524005C23116yes—
151#14524005C23116yes—
152#14524005C23132yes—
153C4×C22⋊D67C23116yes—
154C4×C22⋊D67C23132yes—
155#14524001C23116yes—
156#14524000C23116yes—
157C2×C4⋊Dic67C2312yes—
158C2×C4⋊Dic67C2314yes—
159C2×C4⋊Dic67C2312yes—
160C2×C4⋊Dic67C2311yescharacteristic
161C2×C4⋊Dic67C2311yescharacteristic
162C2×Dic67⋊C4C2312yes—
163C2×Dic67⋊C4C2314yes—
164C2×Dic67⋊C4C2314yes—
165C2×Dic67⋊C4C2312yes—
166C2×Dic67⋊C4C2312yes—
167C2×Dic67⋊C4C2314yes—
168C2×Dic67⋊C4C2312yes—
169C4⋊C4×D67C23116yes—
170C4⋊C4×D67C23132yes—
171C2×C22⋊Dic67C2312yes—
172C2×(C2×D67)⋊C4C2312yes—
173C2×(C2×D67)⋊C4C2312yes—
174C2×(C2×D67)⋊C4C2314yes—
175C2×(C2×D67)⋊C4C2314yes—
176C2×(C2×D67)⋊C4C2312yes—
177C2×(C2×D67)⋊C4C2312yes—
178C2×(C2×D67)⋊C4C2314yes—
179C2×(C2×D67)⋊C4C2314yes—
180C2×(C2×D67)⋊C4C2314yes—
181C2×(C2×D67)⋊C4C2314yes—
182C2×(C2×D67)⋊C4C2314yes—
183C2×C4×Dic67C2312yes—
184C2×C4×Dic67C2314yes—
185C23×C4×C67C2311yescharacteristic
186C23×C4×C67C2311yescharacteristic
187C23×C4×C67C2312yes—
188C23×C4×C67C2311yescharacteristic
189C23×C4×C67C2312yes—
190#125×C67C23116yes—
191#125×C67C23116yes—
192#125×C67C23116yes—
193#125×C67C23116yes—
194C2×C4⋊C4×C67C2318yes—
195C2×C4⋊C4×C67C23116yes—
196C2×C4⋊C4×C67C2312yes—
197C2×C4⋊C4×C67C2314yes—
198C2×C4⋊C4×C67C2312yes—
199C2×C4⋊C4×C67C2314yes—
200C2×C4⋊C4×C67C2314yes—
201C2×C4⋊C4×C67C2314yes—
202C2×C4⋊C4×C67C2312yes—
203C2×C4⋊C4×C67C2312yes—
204C2×C4⋊C4×C67C2318yes—
205C2×C4⋊C4×C67C23116yes—
206C2×C42×C67C2311yescharacteristic
207C2×C42×C67C2311yescharacteristic
208C2×C42×C67C2311yescharacteristic
209C2×C42×C67C2311yescharacteristic
210C2×C42×C67C2318yes—
211C23×D67C2412yes—
212C23×D67C2414yes—
213#11761628—432no—
214#11761628—464no—
215C2×Dic134—42no—
216C2×Dic134—48no—
217C2×Dic134—44no—
218C2×Dic134C2414yes—
219C2×Dic134C24116yes—
220C2×Dic134C2418yes—
221C2×D268—28no—
222C2×D268—48no—
223C2×D268—44no—
224C2×D268—42no—
225C2×D268—48no—
226C2×D268—44no—
227C2×D268C2418yes—
228C2×D268C24116yes—
229C2×D268C2414yes—
230C2×D268C2418yes—
231C2×D268C24116yes—
232C2×D268C2418yes—
233C2×C22⋊D67—28no—
234C2×C22⋊D67—216no—
235C2×C22⋊D67C2418yes—
236C2×C22⋊D67C24116yes—
237C22×Dic67C2412yes—
238C22×Dic67C2412yes—
239C22×Dic67C2412yes—
240C22×Dic67C2414yes—
241C2×C4×D67—28no—
242C2×C4×D67—48no—
243C2×C4×D67—48no—
244C2×C4×D67—48no—
245C2×C4×D67—48no—
246C2×C4×D67C2418yes—
247C2×C4×D67C24116yes—
248C2×C4×D67C24116yes—
249C2×C4×D67C24116yes—
250C2×C4×D67C24116yes—
251C4⋊Dic67C2418yes—
252C4⋊Dic67C24116yes—
253C4⋊Dic67C2418yes—
254C4⋊Dic67C2414yes—
255C4⋊Dic67C2414yes—
256Dic67⋊C4C2418yes—
257Dic67⋊C4C24116yes—
258Dic67⋊C4C24116yes—
259Dic67⋊C4C2418yes—
260Dic67⋊C4C2418yes—
261Dic67⋊C4C24116yes—
262Dic67⋊C4C2418yes—
263C22⋊Dic67C2418yes—
264(C2×D67)⋊C4C2418yes—
265(C2×D67)⋊C4C2418yes—
266(C2×D67)⋊C4C24116yes—
267(C2×D67)⋊C4C24116yes—
268(C2×D67)⋊C4C2418yes—
269(C2×D67)⋊C4C2418yes—
270(C2×D67)⋊C4C24116yes—
271(C2×D67)⋊C4C24116yes—
272(C2×D67)⋊C4C24116yes—
273(C2×D67)⋊C4C24116yes—
274(C2×D67)⋊C4C24116yes—
275C4×Dic67C2418yes—
276C4×Dic67C24116yes—
277C24×C67C2411yescharacteristic
278C22×C4×C67—24no—
279C22×C4×C67—28no—
280C22×C4×C67—24no—
281C22×C4×C67—44no—
282C22×C4×C67—42no—
283C22×C4×C67C2411yescharacteristic
284C22×C4×C67C2411yescharacteristic
285C22×C4×C67C2411yescharacteristic
286C22×C4×C67C2411yescharacteristic
287C22×C4×C67C2411yescharacteristic
288C22×C4×C67C2414yes—
289C22×C4×C67C2414yes—
290C22×C4×C67C2414yes—
291C22×C4×C67C2414yes—
292C22×C4×C67C2418yes—
293C22×C4×C67C2414yes—
294C22×C4×C67C2418yes—
295C22×C4×C67C2411yescharacteristic
296C4⋊C4×C67C2418yes—
297C4⋊C4×C67C24116yes—
298C4⋊C4×C67C2418yes—
299C4⋊C4×C67C24116yes—
300C4⋊C4×C67C24116yes—
301C4⋊C4×C67C24116yes—
302C4⋊C4×C67C2418yes—
303C4⋊C4×C67C2418yes—
304C42×C67C2414yes—
305C42×C67C2414yes—
306C42×C67C2414yes—
307C42×C67C2414yes—
308C23×C67—22no—
309C23×C67—22no—
310C23×C67H(5,𝔽2)14yes—
311C23×C67C2512yes—
312C23×C67C2511yescharacteristic
313C22×D67—24no—
314C22×D67—28no—
315C22×D67—24no—
316C22×D67—28no—
317C22×D67—28no—
318C22×D67—24no—
319C22×D67C2514yes—
320C22×D67C2518yes—
321C2×C4×C67—22no—
322C2×C4×C67—28no—
323C2×C4×C67—22no—
324C2×C4×C67—28no—
325C2×C4×C67—216no—
326C2×C4×C67—22no—
327C2×C4×C67—28no—
328C2×C4×C67—22no—
329C2×C4×C67—22no—
330C2×C4×C67—28no—
331C2×C4×C67—44no—
332C2×C4×C67—48no—
333C2×C4×C672−1+414yes—
334C2×C4×C67C2512yes—
335C2×C4×C67C2512yes—
336C2×C4×C67C2512yes—
337C2×C4×C67C2512yes—
338C2×C4×C67C2512yes—
339C2×C4×C67C2518yes—
340C2×C4×C67C2518yes—
341C2×C4×C67C2512yes—
342C22⋊D67—216no—
343C22⋊D67—232no—
344C2×Dic67—28no—
345C2×Dic67—24no—
346C2×Dic67—24no—
347C2×Dic67—24no—
348C2×Dic67C2514yes—
349C2×Dic67C2514yes—
350C2×Dic67C2514yes—
351C2×Dic67C2518yes—
352D268—216no—
353D268—44no—
354D268—416no—
355D268—48no—
356D268—48no—
357D268—416no—
358C4×D67—216no—
359C4×D67—416no—
360C4×D67—416no—
361C4×D67—416no—
362C4×D67—416no—
363Dic134—44no—
364Dic134—48no—
365Dic134—416no—
366C22×C67—22no—
367C22×C67—22no—
368C22×C67—28no—
369C22×C67C2×H(5,𝔽2)14yes—
370C22×C67C2×H(5,𝔽2)12yes—
371C22×C67C2×2−1+412yes—
372C22×C67#58512yes—
373C22×C67C2611yescharacteristic
374C2×D67—24no—
375C2×D67—28no—
376C2×D67—24no—
377C2×D67—28no—
378C2×D67—28no—
379C2×D67—24no—
380C2×D67—48no—
381C2×D67—416no—
382C4×C67—22no—
383C4×C67—28no—
384C4×C67—22no—
385C4×C67—22no—
386C4×C67—22no—
387C4×C67—28no—
388C4×C67—22no—
389C4×C67C2×2−1+414yes—
390Dic67—28no—
391Dic67—24no—
392Dic67—24no—
393Dic67—24no—
394C2×#3559—671nomaximal, Sylow
395C2×C67—24no—
396C2×C67#355914yescomplemented
397C2×C67C22×H(5,𝔽2)11yescharacteristic
398C2×C67C22×2−1+411yescharacteristic
399C2×C67C2×#58511yescharacteristic
400D67—44no—
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×#529—671no—
417C22×#125D6711yescharacteristic, complemented
418C67C2×#355911yescharacteristic, complemented, Sylow
419C22×#41—672no—
420C22×#41—674no—
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—672no—
435C2×C4⋊Q8—674no—
436C2×C4⋊Q8—671no—
437C2×#127—671no—
438#529—6716no—
439C2×#126—674no—
440C2×#126—674no—
441C2×#126—672no—
442C2×#125—674no—
443C2×#125—672no—
444C2×#125—671no—
445C2×#125C2×D6712yes—
446C2×#125C2×D6712yes—
447C2×#125C2×D6712yes—
448C2×#125C2×D6712yes—
449C2×#125C2×D67116yescomplemented
450C2×#124—671no—
451C2×#124—672no—
452C2×#123—672no—
453C2×#123—674no—
454C2×#123—674no—
455C2×#123—674no—
456C2×#123—674no—
457C2×#123—674no—
458C2×#123—674no—
459C2×C22⋊Q8—671no—
460C2×C22⋊Q8—674no—
461C2×C22⋊Q8—674no—
462C2×C22⋊Q8—674no—
463C2×C22⋊Q8—674no—
464C2×C22⋊Q8—674no—
465C2×C22⋊Q8—674no—
466C2×#121—671no—
467C2×#121—672no—
468C2×#121—672no—
469C2×#121—674no—
470C2×#121—674no—
471C2×#121—674no—
472C2×#121—672no—
473C2×#121—674no—
474C2×#121—672no—
475C2×C4×Q8—671no—
476C2×C4×D4—672no—
477C2×C4×D4—674no—
478C2×C4×D4—674no—
479C2×C4×D4—672no—
480C2×C4×D4—672no—
481C2×C4×D4—671no—
482C2×C4×D4—672no—
483C2×C4×D4—672no—
484C2×#117—672no—
485C2×#117—672no—
486C22×C4⋊C4—674no—
487C22×C4⋊C4—672no—
488C22×C4⋊C4C2×D6712yes—
489C22×C4⋊C4C2×D6711yescharacteristic
490C22×C4⋊C4C2×D6712yes—
491C22×C4⋊C4C2×D6711yescharacteristic
492C22×C42C2×D6711yescharacteristic
493C2×#41—2688no—
494C2×#41—26816no—
495C2×#41—6716no—
496C2×#41—6732no—
497C22×Q8—671no—
498C22×Q8—674no—
499C22×Q8—672no—
500C22×D4—672no—
501C22×D4—674no—
502C22×D4—674no—
503C22×D4—671no—
504C22×D4—672no—
505C22×D4—674no—
506C22×D4—672no—
507C22×D4—672no—
508C23×C4—674no—
509C23×C4—674no—
510C23×C4—674no—
511C23×C4—674no—
512C23×C4—672no—
513C23×C4C22×D6712yes—
514C23×C4C22×D6711yescharacteristic
515C23×C4C22×D6711yescharacteristic
516C23×C4C22×D6712yes—
517C23×C4C22×D6711yescharacteristic
518C4⋊Q8—6716no—
519C4⋊Q8—6732no—
520C4⋊Q8—678no—
521#127—678no—
522#126—6732no—
523#126—6732no—
524#126—6716no—
525#125—6732no—
526#125—6716no—
527#125—678no—
528#125C22×D67116yes—
529#125C22×D67116yes—
530#125C22×D67116yes—
531#125C22×D67116yes—
532#124—678no—
533#124—6716no—
534#123—6716no—
535#123—6732no—
536#123—6732no—
537#123—6732no—
538#123—6732no—
539#123—6732no—
540#123—6732no—
541C22⋊Q8—678no—
542C22⋊Q8—6732no—
543C22⋊Q8—6732no—
544C22⋊Q8—6732no—
545C22⋊Q8—6732no—
546C22⋊Q8—6732no—
547C22⋊Q8—6732no—
548#121—678no—
549#121—6716no—
550#121—6716no—
551#121—6732no—
552#121—6732no—
553#121—6732no—
554#121—6716no—
555#121—6732no—
556#121—6716no—
557C4×Q8—678no—
558C4×D4—6716no—
559C4×D4—6732no—
560C4×D4—6732no—
561C4×D4—6716no—
562C4×D4—6716no—
563C4×D4—678no—
564C4×D4—6716no—
565C4×D4—6716no—
566#117—6716no—
567#117—6716no—
568C2×C4⋊C4—672no—
569C2×C4⋊C4—672no—
570C2×C4⋊C4—674no—
571C2×C4⋊C4—674no—
572C2×C4⋊C4—674no—
573C2×C4⋊C4—672no—
574C2×C4⋊C4—672no—
575C2×C4⋊C4—672no—
576C2×C4⋊C4—674no—
577C2×C4⋊C4—672no—
578C2×C4⋊C4—671no—
579C2×C4⋊C4—671no—
580C2×C4⋊C4—6732no—
581C2×C4⋊C4—6716no—
582C2×C4⋊C4C22×D6712yes—
583C2×C4⋊C4C22×D6714yes—
584C2×C4⋊C4C22×D6712yes—
585C2×C4⋊C4C22×D6714yes—
586C2×C4⋊C4C22×D6714yes—
587C2×C4⋊C4C22×D6714yes—
588C2×C4⋊C4C22×D6712yes—
589C2×C4⋊C4C22×D6712yes—
590C2×C4⋊C4C22×D67116yes—
591C2×C4⋊C4C22×D6718yes—
592C2×C4⋊C4C22×D67116yes—
593C2×C4⋊C4C22×D6718yes—
594C2×C22⋊C4—672no—
595C2×C22⋊C4—672no—
596C2×C22⋊C4—674no—
597C2×C22⋊C4—672no—
598C2×C22⋊C4—672no—
599C2×C22⋊C4—674no—
600C2×C22⋊C4—674no—
601C2×C22⋊C4—674no—
602C2×C22⋊C4—674no—
603C2×C22⋊C4—674no—
604C2×C22⋊C4—674no—
605C2×C22⋊C4—672no—
606C2×C42—672no—
607C2×C42—674no—
608C2×C42C22×D6711yescharacteristic
609C2×C42C22×D6711yescharacteristic
610C2×C42C22×D6711yescharacteristic
611C2×C42C22×D6711yescharacteristic
612C2×C42C22×D6718yes—
613C24—672no—
614C24—674no—
615C24C23×D6711yescharacteristic
616#41—26832no—
617#41—26864no—
618C2×Q8—2688no—
619C2×Q8—2684no—
620C2×Q8—2682no—
621C2×Q8—674no—
622C2×Q8—6716no—
623C2×Q8—678no—
624C2×D4—2688no—
625C2×D4—2684no—
626C2×D4—2688no—
627C2×D4—2684no—
628C2×D4—2682no—
629C2×D4—678no—
630C2×D4—6716no—
631C2×D4—6716no—
632C2×D4—674no—
633C2×D4—678no—
634C2×D4—6716no—
635C2×D4—678no—
636C2×D4—678no—
637C2×D4—1348no—
638C2×D4—13416no—
639C2×D4—1348no—
640C22×C4—24no—
641C22×C4—28no—
642C22×C4—24no—
643C22×C4—44no—
644C22×C4—42no—
645C22×C4—2688no—
646C22×C4—2688no—
647C22×C4—2688no—
648C22×C4—2688no—
649C22×C4—6716no—
650C22×C4—6716no—
651C22×C4—6716no—
652C22×C4—6716no—
653C22×C4—672no—
654C22×C4—672no—
655C22×C4—672no—
656C22×C4—674no—
657C22×C4—678no—
658C22×C4—1348no—
659C22×C4C23×D6714yes—
660C22×C4C23×D6714yes—
661C22×C4C23×D6718yes—
662C22×C4C23×D6714yes—
663C22×C4C23×D6711yescharacteristic
664C22×C4C23×D6711yescharacteristic
665C22×C4C23×D6711yescharacteristic
666C22×C4C23×D6711yescharacteristic
667C22×C4C23×D6711yescharacteristic
668C22×C4C23×D6714yes—
669C22×C4C23×D6714yes—
670C22×C4C23×D6718yes—
671C22×C4C23×D6711yescharacteristic
672C4⋊C4—678no—
673C4⋊C4—678no—
674C4⋊C4—6716no—
675C4⋊C4—6716no—
676C4⋊C4—6716no—
677C4⋊C4—678no—
678C4⋊C4—678no—
679C4⋊C4—678no—
680C4⋊C4—6716no—
681C4⋊C4—678no—
682C4⋊C4—674no—
683C4⋊C4—674no—
684C4⋊C4C23×D6718yes—
685C4⋊C4C23×D67116yes—
686C4⋊C4C23×D6718yes—
687C4⋊C4C23×D67116yes—
688C4⋊C4C23×D67116yes—
689C4⋊C4C23×D67116yes—
690C4⋊C4C23×D6718yes—
691C4⋊C4C23×D6718yes—
692C22⋊C4—678no—
693C22⋊C4—678no—
694C22⋊C4—6716no—
695C22⋊C4—678no—
696C22⋊C4—678no—
697C22⋊C4—6716no—
698C22⋊C4—6716no—
699C22⋊C4—6716no—
700C22⋊C4—6716no—
701C22⋊C4—6716no—
702C22⋊C4—6716no—
703C22⋊C4—678no—
704C42—678no—
705C42—6716no—
706C42C23×D6714yes—
707C42C23×D6714yes—
708C42C23×D6714yes—
709C42C23×D6714yes—
710C23—22no—
711C23—22no—
712C23—674no—
713C23—678no—
714C23—1344no—
715C23—1348no—
716C23—1344no—
717C23—1348no—
718C23—1348no—
719C23—1344no—
720C23#1452408914yes—
721C23C24×D6712yes—
722C23C24×D6711yescharacteristic
723Q8—26816no—
724Q8—2688no—
725Q8—2684no—
726D4—26816no—
727D4—2688no—
728D4—26816no—
729D4—2688no—
730D4—2684no—
731D4—13416no—
732D4—13432no—
733D4—13416no—
734C2×C4—22no—
735C2×C4—28no—
736C2×C4—22no—
737C2×C4—28no—
738C2×C4—216no—
739C2×C4—22no—
740C2×C4—28no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—28no—
744C2×C4—48no—
745C2×C4—44no—
746C2×C4—26816no—
747C2×C4—26816no—
748C2×C4—26816no—
749C2×C4—26816no—
750C2×C4—674no—
751C2×C4—674no—
752C2×C4—674no—
753C2×C4—678no—
754C2×C4—1348no—
755C2×C4—1344no—
756C2×C4—1344no—
757C2×C4—1344no—
758C2×C4—13416no—
759C2×C4#1452409114yes—
760C2×C4C24×D6718yes—
761C2×C4C24×D6712yes—
762C2×C4C24×D6712yes—
763C2×C4C24×D6712yes—
764C2×C4C24×D6712yes—
765C2×C4C24×D6712yes—
766C2×C4C24×D6718yes—
767C2×C4C24×D6712yes—
768C22—28no—
769C22—22no—
770C22—22no—
771C22—2688no—
772C22—26816no—
773C22—1344no—
774C22—1348no—
775C22—1344no—
776C22—1348no—
777C22—1348no—
778C22—1344no—
779C22C2×#1452408914yes—
780C22C2×#1452408912yes—
781C22C2×#1452409112yes—
782C22#1686423212yes—
783C22C25×D6711yescharacteristic
784C4—22no—
785C4—28no—
786C4—22no—
787C4—22no—
788C4—28no—
789C4—22no—
790C4—22no—
791C4—1348no—
792C4—1344no—
793C4—1344no—
794C4—1344no—
795C4C2×#1452409114yes—
796C2—24no—
797C2—2684no—
798C2—2688no—
799C2#2257474314yesdirect product factor
800C2C22×#1452408911yescharacteristic
801C2C22×#1452409111yescharacteristic
802C2C2×#1686423211yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC22×#125×C67C2
socleC23×C67C25
hypercenterC22×#125D67
hypocenterC67C2×#3559
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
1. #22574743C2direct (N × H)
2. C2×#16864150C2semidirect
3. C2×#16864144C2semidirect
4. C2×#16864102C2semidirect
5. C2×#16864099C2semidirect
6. C2×#16864094C2semidirect
7. C2×#16864047C2semidirect
8. C2×#16864047C2semidirect
9. C2×#16864026C2semidirect
10. C2×#16864002C2semidirect
11. C2×#16863994C2semidirect
12. C2×#16863993C2semidirect
13. C2×#16863977C2semidirect
14. C2×#16863946C2semidirect
15. C2×#16863930C2semidirect
16. C22×#125×C67C2semidirect
19. #16864150C22semidirect
20. #16864144C22semidirect
21. #16864102C22semidirect
22. #16864099C22semidirect
23. #16864094C22semidirect
24. #16864047C22semidirect
25. #16864047C22semidirect
26. #16864026C22semidirect
27. #16864002C22semidirect
28. #16863994C22semidirect
29. #16863993C22semidirect
30. #16863977C22semidirect
31. #16863946C22semidirect
36. #16863930C22semidirect
85. C2×#125×C67C22semidirect
396. C2×C67#3559semidirect
417. C22×#125D67semidirect
418. C67C2×#3559semidirect
449. C2×#125C2×D67semidirect
799. C2#22574743direct (N × H)

Maximal subgroups

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

subgroupindex
#225747432
C2×#168641502
C2×#168641442
C2×#168641022
C2×#168640992
C2×#168640942
C2×#168640472
C2×#168640262
C2×#168640022
C2×#168639942
C2×#168639932
C2×#168639772
C2×#168639462
C2×#168639302
C22×#125×C672
C2×#355967