Finite Group Databasebeta

← C2×#22571635 #31728757

Subgroups — C2×#22571635 #31728757

Order 17152.

1818 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864008C211yesmaximal, characteristic, complemented
2#22571635C2116yesmaximal, direct product factor
3C2×#16863703C211yesmaximal, characteristic, complemented
4C2×#16863688C211yesmaximal, characteristic, complemented
5C2×#16863678C211yesmaximal, characteristic, complemented
6C2×#16863696C211yesmaximal, characteristic, complemented
7C2×#16863652C211yesmaximal, characteristic, complemented
8C2×#16863640C211yesmaximal, characteristic
9C2×#16863635C211yesmaximal, characteristic, complemented
10C2×#16863623C211yesmaximal, characteristic
11C2×#16863615C211yesmaximal, characteristic, complemented
12C2×#16863615C211yesmaximal, characteristic, complemented
13C2×#16863606C211yesmaximal, characteristic, complemented
14C2×#16863601C211yesmaximal, characteristic, complemented
15C2×#16863423C211yesmaximal, characteristic, complemented
16C2×#542×C67C211yesmaximal, characteristic
17C22×#11761618C2211yescharacteristic
18C22×#11761618C2211yescharacteristic
19C22×#11761616C2211yescharacteristic
20C22×#11761616C2211yescharacteristic
21C22×#11761612C2211yescharacteristic
22C23×C67⋊C8C2211yescharacteristic
23#16864008—24no—
24#16864008C2218yescomplemented
25C2×#14524043C2211yescharacteristic
26C2×#14524036—21no—
27C2×#14524036—21no—
28C2×#14524035C2211yescharacteristic
29C2×#14524033—21no—
30C2×#14524033—21no—
31C2×#14524022C2211yescharacteristic
32C2×#14524022C2211yescharacteristic
33C2×C4×Dic134C2211yescharacteristic
34C2×C4×Dic134C2211yescharacteristic
35#16863703C2218yescomplemented
36#16863696C2218yescomplemented
37#16863688C2218yescomplemented
38#16863678C2218yescomplemented
39#16863652C2218yescomplemented
40#16863640C2218yes—
41#16863635C2218yescomplemented
42#16863623C2218yes—
43#16863615C2218yescomplemented
44#16863615C2218yescomplemented
45#16863606C2218yescomplemented
46#16863601C2218yescomplemented
47C2×#14523976C2211yescharacteristic
48C2×#14523976C2211yescharacteristic
49C2×#14523974C2211yescharacteristic
50C2×#14523974C2211yescharacteristic
51#16863423C2218yescomplemented
52C2×C4⋊(C67⋊C8)C2211yescharacteristic
53C2×C4⋊(C67⋊C8)C2211yescharacteristic
54C2×C4⋊(C67⋊C8)C2211yescharacteristic
55C2×C4⋊(C67⋊C8)C2211yescharacteristic
56C2×#14523967C2211yescharacteristic
57C2×#14523967C2211yescharacteristic
58C2×#14523966C2211yescharacteristic
59C2×#14523966C2211yescharacteristic
60C2×#14523966C2211yescharacteristic
61C2×#14523966C2211yescharacteristic
62C2×#14523964C2211yescharacteristic
63C2×#14523964C2211yescharacteristic
64#542×C67—24no—
65#542×C67C2218yes—
66C2×C4⋊Q8×C67C2211yescharacteristic
67C2×#126×C67—21no—
68C2×#124×C67—21no—
69C2×#124×C67C2211yescharacteristic
70C2×#123×C67—21no—
71C2×C22⋊Q8×C67—21no—
72C2×C22⋊Q8×C67C2211yescharacteristic
73C2×#121×C67C2211yescharacteristic
74C2×C4×Q8×C67C2211yescharacteristic
75C2×C4×D4×C67C2211yescharacteristic
76C2×#117×C67C2211yescharacteristic
77C22×Dic134C2311yescharacteristic
78C22×Dic134C2311yescharacteristic
79C2×#11761618—42no—
80C2×#11761618—42no—
81C2×#11761618C2314yes—
82C2×#11761618C2314yes—
83C2×#11761616—42no—
84C2×#11761616—42no—
85C2×#11761616C2314yes—
86C2×#11761616C2314yes—
87C2×#11761612—42no—
88C2×#11761612C2314yes—
89C22×C67⋊C8—42no—
90C22×C67⋊C8C2311yescharacteristic
91C22×C67⋊C8C2311yescharacteristic
92C22×C67⋊C8C2311yescharacteristic
93C22×C67⋊C8C2311yescharacteristic
94C22×C67⋊C8C2314yes—
95#14524043—22no—
96#14524043C2314yes—
97#14524036—28no—
98#14524036—28no—
99#14524035—22no—
100#14524035C2314yes—
101#14524033—28no—
102#14524033—28no—
103#14524022—22no—
104#14524022—22no—
105#14524022C2314yes—
106#14524022C2314yes—
107C4×Dic134—22no—
108C4×Dic134—22no—
109C4×Dic134C2314yes—
110C4×Dic134C2314yes—
111C2×C4⋊Dic67—21no—
112C2×C4⋊Dic67—21no—
113C2×C4⋊Dic67C2311yescharacteristic
114C2×C4⋊Dic67C2311yescharacteristic
115C2×Dic67⋊C4—21no—
116C2×Dic67⋊C4—21no—
117C2×Dic67⋊C4—21no—
118C2×Dic67⋊C4—21no—
119C2×Dic67⋊C4—21no—
120C2×Dic67⋊C4—21no—
121C2×C22⋊Dic67—21no—
122C2×C22⋊Dic67—21no—
123C2×C4×Dic67—21no—
124C2×C4×Dic67—21no—
125#14523976C2314yes—
126#14523976C2314yes—
127#14523974C2314yes—
128#14523974C2314yes—
129C4⋊(C67⋊C8)C2314yes—
130C4⋊(C67⋊C8)C2314yes—
131C4⋊(C67⋊C8)C2314yes—
132C4⋊(C67⋊C8)C2314yes—
133#14523967C2314yes—
134#14523967C2314yes—
135#14523966C2314yes—
136#14523966C2314yes—
137#14523966C2314yes—
138#14523966C2314yes—
139#14523964C2314yes—
140#14523964C2314yes—
141C22×Q8×C67—21no—
142C22×Q8×C67C2311yescharacteristic
143C22×D4×C67—21no—
144C22×D4×C67C2311yescharacteristic
145C23×C4×C67—21no—
146C23×C4×C67C2311yescharacteristic
147C4⋊Q8×C67—22no—
148C4⋊Q8×C67C2314yes—
149#126×C67—28no—
150#124×C67—28no—
151#124×C67—22no—
152#124×C67C2314yes—
153#123×C67—28no—
154C22⋊Q8×C67—22no—
155C22⋊Q8×C67—28no—
156C22⋊Q8×C67C2314yes—
157#121×C67—22no—
158#121×C67C2314yes—
159C4×Q8×C67—22no—
160C4×Q8×C67C2314yes—
161C4×D4×C67—22no—
162C4×D4×C67C2314yes—
163#117×C67D414yes—
164#117×C67C2314yes—
165C2×C4⋊C4×C67—21no—
166C2×C4⋊C4×C67—21no—
167C2×C4⋊C4×C67—21no—
168C2×C4⋊C4×C67D411yescharacteristic
169C2×C4⋊C4×C67D411yescharacteristic
170C2×C4⋊C4×C67C2311yescharacteristic
171C2×C4⋊C4×C67C2311yescharacteristic
172C2×C22⋊C4×C67—21no—
173C2×C22⋊C4×C67—21no—
174C2×C22⋊C4×C67—21no—
175C2×C22⋊C4×C67—21no—
176C2×C22⋊C4×C67—21no—
177C2×C22⋊C4×C67D411yescharacteristic
178C2×C22⋊C4×C67D411yescharacteristic
179C2×C42×C67—21no—
180C2×C42×C67C2311yescharacteristic
181C2×C42×C67C2311yescharacteristic
182C2×Dic134—22no—
183C2×Dic134—22no—
184C2×Dic134—22no—
185C2×Dic134—22no—
186C2×Dic134—21no—
187C2×Dic134—21no—
188C2×Dic134C2412yes—
189C2×Dic134C2412yes—
190C22×Dic67—21no—
191C22×Dic67—21no—
192C22×Dic67—21no—
193C22×Dic67—21no—
194#11761618—44no—
195#11761618—44no—
196#11761616—44no—
197#11761616—44no—
198#11761612—44no—
199C2×C67⋊C8—22no—
200C2×C67⋊C8—22no—
201C2×C67⋊C8—22no—
202C2×C67⋊C8—22no—
203C2×C67⋊C8—44no—
204C2×C67⋊C8C2412yes—
205C2×C67⋊C8C2412yes—
206C2×C67⋊C8C2412yes—
207C2×C67⋊C8C2412yes—
208C4⋊Dic67—24no—
209C4⋊Dic67—24no—
210C4⋊Dic67—21no—
211C4⋊Dic67—21no—
212C4⋊Dic67C2412yes—
213C4⋊Dic67C2412yes—
214Dic67⋊C4—24no—
215Dic67⋊C4—24no—
216Dic67⋊C4—24no—
217Dic67⋊C4—24no—
218Dic67⋊C4—24no—
219Dic67⋊C4—24no—
220C22⋊Dic67—24no—
221C22⋊Dic67—24no—
222C4×Dic67—24no—
223C4×Dic67—24no—
224C24×C67—21no—
225C24×C67C2×D411yescharacteristic
226C2×Q8×C67—21no—
227C2×Q8×C67—24no—
228C2×Q8×C67—22no—
229C2×Q8×C67—22no—
230C2×Q8×C67—82no—
231C2×Q8×C67C2412yes—
232C2×D4×C67—24no—
233C2×D4×C67—21no—
234C2×D4×C67—22no—
235C2×D4×C67—22no—
236C2×D4×C67—82no—
237C2×D4×C67C2412yes—
238C22×C4×C67—22no—
239C22×C4×C67—22no—
240C22×C4×C67—21no—
241C22×C4×C67—21no—
242C22×C4×C67—21no—
243C22×C4×C67—24no—
244C22×C4×C67—82no—
245C22×C4×C67C2×D411yescharacteristic
246C22×C4×C67C2×D411yescharacteristic
247C22×C4×C67C2×D411yescharacteristic
248C22×C4×C67C2×D411yescharacteristic
249C22×C4×C67C2×D411yescharacteristic
250C22×C4×C67C2×D412yes—
251C22×C4×C67C2412yes—
252C22×C4×C67C2411yescharacteristic
253C4⋊C4×C67—24no—
254C4⋊C4×C67—24no—
255C4⋊C4×C67—24no—
256C4⋊C4×C67—21no—
257C4⋊C4×C67—21no—
258C4⋊C4×C67C2×D414yes—
259C4⋊C4×C67C2×D414yes—
260C4⋊C4×C67C2412yes—
261C4⋊C4×C67C2412yes—
262C22⋊C4×C67—24no—
263C22⋊C4×C67—24no—
264C22⋊C4×C67—24no—
265C22⋊C4×C67—24no—
266C22⋊C4×C67—24no—
267C22⋊C4×C67C2×D414yes—
268C22⋊C4×C67C2×D414yes—
269C42×C67—24no—
270C42×C67C2×D412yes—
271C42×C67C2×D412yes—
272C42×C67C2412yes—
273C42×C67C2412yes—
274C23×C67—22no—
275C23×C67—22no—
276C23×C67—22no—
277C23×C67—22no—
278C23×C67—42no—
279C23×C67—42no—
280C23×C67—42no—
281C23×C67C22×D412yes—
282C23×C67C22×D411yescharacteristic
283Q8×C67—22no—
284Q8×C67—22no—
285Q8×C67—42no—
286Q8×C67—84no—
287D4×C67—22no—
288D4×C67—22no—
289D4×C67—42no—
290D4×C67—84no—
291C2×C4×C67—22no—
292C2×C4×C67—22no—
293C2×C4×C67—22no—
294C2×C4×C67—22no—
295C2×C4×C67—22no—
296C2×C4×C67—24no—
297C2×C4×C67—22no—
298C2×C4×C67—22no—
299C2×C4×C67—22no—
300C2×C4×C67—22no—
301C2×C4×C67—22no—
302C2×C4×C67—42no—
303C2×C4×C67—42no—
304C2×C4×C67—42no—
305C2×C4×C67—84no—
306C2×C4×C67C22×D412yes—
307C2×C4×C67C22×D412yes—
308C2×C4×C67C22×D412yes—
309C2×C4×C67C22×D412yes—
310C2×C4×C67C22×D412yes—
311C2×C4×C67C22×D411yescharacteristic
312C2×C4×C67H(5,𝔽2)12yes—
313C2×C4×C672−1+412yes—
314C2×C4×C67C2511yescharacteristic
315C2×Dic67—22no—
316C2×Dic67—22no—
317C2×Dic67—22no—
318C2×Dic67—22no—
319C2×Dic67—42no—
320C2×Dic67—42no—
321C2×Dic67—42no—
322C2×Dic67—42no—
323Dic134—22no—
324Dic134—22no—
325Dic134—22no—
326Dic134—22no—
327Dic134—42no—
328Dic134—42no—
329C67⋊C8—22no—
330C67⋊C8—22no—
331C67⋊C8—22no—
332C67⋊C8—22no—
333C22×C67—22no—
334C22×C67—22no—
335C22×C67—22no—
336C22×C67—44no—
337C22×C67—42no—
338C22×C67—42no—
339C22×C67—42no—
340C22×C67—84no—
341C22×C67#53712yes—
342C22×C67#57712yes—
343C22×C67#57812yes—
344C22×C67C23×D411yescharacteristic
345C4×C67—22no—
346C4×C67—22no—
347C4×C67—22no—
348C4×C67—22no—
349C4×C67—22no—
350C4×C67—42no—
351C4×C67—42no—
352C4×C67—42no—
353C4×C67#53712yes—
354C4×C67C2×H(5,𝔽2)11yescharacteristic
355C4×C67C2×2−1+411yescharacteristic
356Dic67—42no—
357Dic67—42no—
358Dic67—42no—
359Dic67—42no—
360C2×#3258—671nomaximal, Sylow
361C2×C67—42no—
362C2×C67—82no—
363C2×C67#325814yescomplemented
364C2×C67C2×#53711yescharacteristic
365C2×C67C2×#57711yescharacteristic
366C2×C67C2×#57811yescharacteristic
367C2×#542D6711yescharacteristic
368C2×#541—671no—
369#3258—6716no—
370C2×#479—671no—
371C2×#477—671no—
372C2×#475—671no—
373C2×#478—671no—
374C2×#470—671no—
375C2×#468—671no—
376C2×#467—671no—
377C2×#465—671no—
378C2×#464—671no—
379C2×#464—671no—
380C2×#462—671no—
381C2×#461—671no—
382C2×#424—671no—
383C67C2×#325811yescharacteristic, complemented, Sylow
384C22×Q16—671no—
385C22×Q16—671no—
386C22×SD16—671no—
387C22×SD16—671no—
388C22×M16—671no—
389C23×C8—671no—
390#542—24no—
391#542C2×D6718yes—
392#541—678no—
393#541—1344no—
394C2×C4⋊Q8—671no—
395C2×C4⋊Q8C2×D6711yescharacteristic
396C2×#126—21no—
397C2×#126—1341no—
398C2×#126—1341no—
399C2×#125—671no—
400C2×#125—1341no—
401C2×#125—1341no—
402C2×#124—21no—
403C2×#124C2×D6711yescharacteristic
404C2×#123—21no—
405C2×C22⋊Q8—21no—
406C2×C22⋊Q8—671no—
407C2×C22⋊Q8—671no—
408C2×C22⋊Q8C2×D6711yescharacteristic
409C2×#121C2×D6711yescharacteristic
410C2×C4×Q8—671no—
411C2×C4×Q8—671no—
412C2×C4×Q8C2×D6711yescharacteristic
413C2×C4×D4C2×D6711yescharacteristic
414C2×#117C2×D6711yescharacteristic
415#479—678no—
416#478—678no—
417#477—678no—
418#475—678no—
419#470—678no—
420#468—678no—
421#467—678no—
422#465—678no—
423#464—678no—
424#464—678no—
425#462—678no—
426#461—678no—
427C2×#107—671no—
428C2×#107—671no—
429C2×#106—671no—
430C2×#106—671no—
431#424—678no—
432C2×C4⋊C8—671no—
433C2×C4⋊C8—671no—
434C2×C4⋊C8—671no—
435C2×C4⋊C8—671no—
436C2×#103—671no—
437C2×#103—671no—
438C2×#103—671no—
439C2×#103—671no—
440C2×#103—671no—
441C2×#103—671no—
442C2×#102—671no—
443C2×#102—671no—
444C22×Q8—21no—
445C22×Q8—671no—
446C22×Q8—671no—
447C22×Q8C22×D6711yescharacteristic
448C22×D4—21no—
449C22×D4C22×D6711yescharacteristic
450C23×C4—21no—
451C23×C4C22×D6711yescharacteristic
452C2×Q16—2682no—
453C2×Q16—2682no—
454C2×Q16—674no—
455C2×Q16—674no—
456C2×SD16—2682no—
457C2×SD16—2682no—
458C2×SD16—674no—
459C2×SD16—674no—
460C2×M16—2682no—
461C2×M16—674no—
462C22×C8—2682no—
463C22×C8—674no—
464C22×C8—671no—
465C22×C8—671no—
466C22×C8—671no—
467C22×C8—671no—
468C4⋊Q8—22no—
469C4⋊Q8—674no—
470C4⋊Q8—1342no—
471C4⋊Q8C22×D6714yes—
472#126—28no—
473#126—1348no—
474#126—1348no—
475#125—674no—
476#125—1348no—
477#125—1348no—
478#125—1342no—
479#124—28no—
480#124—22no—
481#124C22×D6714yes—
482#123—28no—
483C22⋊Q8—22no—
484C22⋊Q8—28no—
485C22⋊Q8—674no—
486C22⋊Q8—674no—
487C22⋊Q8—1342no—
488C22⋊Q8—1342no—
489C22⋊Q8C22×D6714yes—
490#121—22no—
491#121C22×D6714yes—
492C4×Q8—22no—
493C4×Q8—674no—
494C4×Q8—674no—
495C4×Q8—1342no—
496C4×Q8—1342no—
497C4×Q8C22×D6714yes—
498C4×D4—22no—
499C4×D4C22×D6714yes—
500#117C22⋊D6714yes—
501#117C22×D6714yes—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—671no—
506C2×C4⋊C4—671no—
507C2×C4⋊C4—1341no—
508C2×C4⋊C4—1341no—
509C2×C4⋊C4—1341no—
510C2×C4⋊C4—1341no—
511C2×C4⋊C4—1341no—
512C2×C4⋊C4—1341no—
513C2×C4⋊C4—1341no—
514C2×C4⋊C4—1341no—
515C2×C4⋊C4C22⋊D6711yescharacteristic
516C2×C4⋊C4C22⋊D6711yescharacteristic
517C2×C4⋊C4C22×D6711yescharacteristic
518C2×C4⋊C4C22×D6711yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—1341no—
525C2×C22⋊C4—1341no—
526C2×C22⋊C4C22⋊D6711yescharacteristic
527C2×C22⋊C4C22⋊D6711yescharacteristic
528C2×C42—21no—
529C2×C42—1341no—
530C2×C42—1341no—
531C2×C42C22×D6711yescharacteristic
532C2×C42C22×D6711yescharacteristic
533#107—674no—
534#107—674no—
535#106—674no—
536#106—674no—
537C4⋊C8—674no—
538C4⋊C8—674no—
539C4⋊C8—674no—
540C4⋊C8—674no—
541#103—674no—
542#103—674no—
543#103—674no—
544#103—674no—
545#103—674no—
546#103—674no—
547#102—674no—
548#102—674no—
549C24—21no—
550C24C2×C22⋊D6711yescharacteristic
551C2×Q8—21no—
552C2×Q8—24no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—82no—
556C2×Q8—672no—
557C2×Q8—672no—
558C2×Q8—1342no—
559C2×Q8—1342no—
560C2×Q8—1342no—
561C2×Q8—1342no—
562C2×Q8—1341no—
563C2×Q8—1341no—
564C2×Q8C23×D6712yes—
565C2×D4—24no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—82no—
570C2×D4C23×D6712yes—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—24no—
577C22×C4—82no—
578C22×C4—1341no—
579C22×C4—1341no—
580C22×C4—1341no—
581C22×C4—1341no—
582C22×C4C2×C22⋊D6712yes—
583C22×C4C2×C22⋊D6711yescharacteristic
584C22×C4C2×C22⋊D6711yescharacteristic
585C22×C4C2×C22⋊D6711yescharacteristic
586C22×C4C2×C22⋊D6711yescharacteristic
587C22×C4C2×C22⋊D6711yescharacteristic
588C22×C4C23×D6712yes—
589C22×C4C23×D6711yescharacteristic
590Q16—2684no—
591Q16—2684no—
592SD16—2684no—
593SD16—2684no—
594M16—2684no—
595C2×C8—2684no—
596C2×C8—672no—
597C2×C8—672no—
598C2×C8—672no—
599C2×C8—672no—
600C2×C8—1342no—
601C2×C8—1342no—
602C2×C8—1342no—
603C2×C8—1342no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—672no—
610C4⋊C4—672no—
611C4⋊C4—1341no—
612C4⋊C4—1341no—
613C4⋊C4—1344no—
614C4⋊C4—1344no—
615C4⋊C4—1344no—
616C4⋊C4—1344no—
617C4⋊C4—1344no—
618C4⋊C4—1344no—
619C4⋊C4—1344no—
620C4⋊C4—1344no—
621C4⋊C4C2×C22⋊D6714yes—
622C4⋊C4C2×C22⋊D6714yes—
623C4⋊C4C23×D6712yes—
624C4⋊C4C23×D6712yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—1344no—
631C22⋊C4—1344no—
632C22⋊C4C2×C22⋊D6714yes—
633C22⋊C4C2×C22⋊D6714yes—
634C42—24no—
635C42—1344no—
636C42—1344no—
637C42C2×C22⋊D6712yes—
638C42C2×C22⋊D6712yes—
639C42C23×D6712yes—
640C42C23×D6712yes—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23C22×C22⋊D6712yes—
649C23C22×C22⋊D6711yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—84no—
654Q8—2682no—
655Q8—2682no—
656Q8—1342no—
657Q8—1342no—
658Q8—1342no—
659Q8—1342no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—84no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—84no—
679C2×C4—2682no—
680C2×C4—2682no—
681C2×C4—2682no—
682C2×C4—2682no—
683C2×C4—1342no—
684C2×C4—1342no—
685C2×C4—1342no—
686C2×C4—1342no—
687C2×C4C22×C22⋊D6712yes—
688C2×C4C22×C22⋊D6712yes—
689C2×C4C22×C22⋊D6712yes—
690C2×C4C22×C22⋊D6712yes—
691C2×C4C22×C22⋊D6712yes—
692C2×C4C22×C22⋊D6711yescharacteristic
693C2×C4#1452408912yes—
694C2×C4#1452409012yes—
695C2×C4C24×D6711yescharacteristic
696C8—1342no—
697C8—1342no—
698C8—1342no—
699C8—1342no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—84no—
708C22#1686397412yes—
709C22#1686420712yes—
710C22#1686421112yes—
711C22C23×C22⋊D6711yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—2682no—
721C4—2682no—
722C4—2682no—
723C4—2682no—
724C4#1686397412yes—
725C4C2×#1452408911yescharacteristic
726C4C2×#1452409011yescharacteristic
727C2—42no—
728C2—82no—
729C2#2257163514yesdirect product factor
730C2C2×#1686397411yescharacteristic
731C2C2×#1686420711yescharacteristic
732C2C2×#1686421111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#542×C67C2
socleC23×C67C22×D4
prime radicalC2×#121×C67C22
hypercenterC2×#542D67
hypocenterC67C2×#3258
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#16864008C2semidirect
2. #22571635C2direct (N × H)
3. C2×#16863703C2semidirect
4. C2×#16863688C2semidirect
5. C2×#16863678C2semidirect
6. C2×#16863696C2semidirect
7. C2×#16863652C2semidirect
9. C2×#16863635C2semidirect
11. C2×#16863615C2semidirect
12. C2×#16863615C2semidirect
13. C2×#16863606C2semidirect
14. C2×#16863601C2semidirect
15. C2×#16863423C2semidirect
24. #16864008C22semidirect
35. #16863703C22semidirect
36. #16863696C22semidirect
37. #16863688C22semidirect
38. #16863678C22semidirect
39. #16863652C22semidirect
41. #16863635C22semidirect
43. #16863615C22semidirect
44. #16863615C22semidirect
45. #16863606C22semidirect
46. #16863601C22semidirect
51. #16863423C22semidirect
363. C2×C67#3258semidirect
383. C67C2×#3258semidirect
729. C2#22571635direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168640082
#225716352
C2×#168637032
C2×#168636882
C2×#168636782
C2×#168636962
C2×#168636522
C2×#168636402
C2×#168636352
C2×#168636232
C2×#168636152
C2×#168636062
C2×#168636012
C2×#168634232
C2×#542×C672
C2×#325867