Finite Group Databasebeta

← C2×#22571674 #31728801

Subgroups — C2×#22571674 #31728801

Order 17152.

1882 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864017C211yesmaximal, characteristic, complemented
2#22571674C2116yesmaximal, direct product factor
3C2×#16863681C211yesmaximal, characteristic, complemented
4C2×#16863678C211yesmaximal, characteristic, complemented
5C2×#16863686C211yesmaximal, characteristic, complemented
6C2×#16863683C211yesmaximal, characteristic, complemented
7C2×#16863652C211yesmaximal, characteristic, complemented
8C2×#16863647C211yesmaximal, characteristic
9C2×#16863627C211yesmaximal, characteristic, complemented
10C2×#16863623C211yesmaximal, characteristic, complemented
11C2×#16863618C211yesmaximal, characteristic, complemented
12C2×#16863615C211yesmaximal, characteristic, complemented
13C2×#16863611C211yesmaximal, characteristic, complemented
14C2×#16863608C211yesmaximal, characteristic, complemented
15C2×#16863423C211yesmaximal, characteristic, complemented
16C2×#542×C67C211yesmaximal, characteristic, complemented
17C22×#11761618C2211yescharacteristic
18C22×#11761616C2211yescharacteristic
19C22×#11761615C2211yescharacteristic
20C22×#11761613C2211yescharacteristic
21C22×#11761612C2211yescharacteristic
22C23×C67⋊C8C2211yescharacteristic
23#16864017—24no—
24#16864017C2218yescomplemented
25C2×#14524043C2211yescharacteristic
26C2×#14524038—21no—
27C2×#14524031C2211yescharacteristic
28C2×#14524029—21no—
29C2×#14524025—21no—
30C2×#14524022C2211yescharacteristic
31C2×#14524021—21no—
32C2×#14524017C2211yescharacteristic
33C2×C4×Dic134C2211yescharacteristic
34C2×C4×D268C2211yescharacteristic
35#16863686C2218yescomplemented
36#16863683C2218yescomplemented
37#16863681C2218yescomplemented
38#16863678C2218yescomplemented
39#16863652C2218yescomplemented
40#16863647C2218yes—
41#16863627C2218yescomplemented
42#16863623C2218yescomplemented
43#16863618C2218yescomplemented
44#16863615C2218yescomplemented
45#16863611C2218yescomplemented
46#16863608C2218yescomplemented
47C2×#14523974C2211yescharacteristic
48C2×#14523974C2211yescharacteristic
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×#14523964C2211yescharacteristic
61C2×#14523964C2211yescharacteristic
62C2×#14523963C2211yescharacteristic
63C2×#14523963C2211yescharacteristic
64#542×C67—24no—
65#542×C67C2218yescomplemented
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×Dic134—21no—
78C22×Dic134C2311yescharacteristic
79C22×D268C2311yescharacteristic
80C22×C22⋊D67—21no—
81C22×C4×D67—21no—
82C2×#11761618—42no—
83C2×#11761618C2314yes—
84C2×#11761616—42no—
85C2×#11761616C2314yes—
86C2×#11761615—42no—
87C2×#11761615C2314yes—
88C2×#11761613—42no—
89C2×#11761613C2314yes—
90C2×#11761612—42no—
91C2×#11761612C2314yes—
92C22×C67⋊C8—42no—
93C22×C67⋊C8C2311yescharacteristic
94C22×C67⋊C8C2311yescharacteristic
95C22×C67⋊C8C2311yescharacteristic
96C22×C67⋊C8C2311yescharacteristic
97C22×C67⋊C8C2314yes—
98#14524043—22no—
99#14524043C2314yes—
100#14524038—28no—
101#14524031—22no—
102#14524031C2314yes—
103#14524029—28no—
104#14524025—28no—
105#14524022—22no—
106#14524022C2314yes—
107#14524021—28no—
108#14524017—22no—
109#14524017C2314yes—
110C4×Dic134—22no—
111C4×Dic134C2314yes—
112C4×D268—22no—
113C4×D268C2314yes—
114C2×C4⋊Dic67—21no—
115C2×C4⋊Dic67C2311yescharacteristic
116C2×C4⋊Dic67C2311yescharacteristic
117C2×Dic67⋊C4—21no—
118C2×Dic67⋊C4—21no—
119C2×C22⋊Dic67—21no—
120C2×(C2×D67)⋊C4—21no—
121C2×(C2×D67)⋊C4—21no—
122C2×(C2×D67)⋊C4—21no—
123C2×(C2×D67)⋊C4—21no—
124C2×C4×Dic67—21no—
125#14523974C2314yes—
126#14523974C2314yes—
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#14523964C2314yes—
138#14523964C2314yes—
139#14523963C2314yes—
140#14523963C2314yes—
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
182C23×D67—21no—
183C2×Dic134—22no—
184C2×Dic134—22no—
185C2×Dic134—21no—
186C2×Dic134—24no—
187C2×Dic134—82no—
188C2×Dic134C2412yes—
189C2×D268—22no—
190C2×D268—22no—
191C2×D268—21no—
192C2×D268C2412yes—
193C2×C22⋊D67—24no—
194C2×C22⋊D67—82no—
195C22×Dic67—21no—
196C22×Dic67—21no—
197C22×Dic67—21no—
198C2×C4×D67—24no—
199C2×C4×D67—82no—
200#11761618—44no—
201#11761616—44no—
202#11761615—44no—
203#11761613—44no—
204#11761612—44no—
205C2×C67⋊C8—22no—
206C2×C67⋊C8—22no—
207C2×C67⋊C8—22no—
208C2×C67⋊C8—22no—
209C2×C67⋊C8—44no—
210C2×C67⋊C8C2412yes—
211C2×C67⋊C8C2412yes—
212C2×C67⋊C8C2412yes—
213C2×C67⋊C8C2412yes—
214C4⋊Dic67—24no—
215C4⋊Dic67—21no—
216C4⋊Dic67—21no—
217C4⋊Dic67C2412yes—
218C4⋊Dic67C2412yes—
219Dic67⋊C4—24no—
220Dic67⋊C4—24no—
221C22⋊Dic67—24no—
222(C2×D67)⋊C4—24no—
223(C2×D67)⋊C4—24no—
224(C2×D67)⋊C4—24no—
225(C2×D67)⋊C4—24no—
226C4×Dic67—24no—
227C24×C67—21no—
228C24×C67C2×D411yescharacteristic
229C2×Q8×C67—21no—
230C2×Q8×C67—24no—
231C2×Q8×C67—22no—
232C2×Q8×C67—22no—
233C2×Q8×C67—82no—
234C2×Q8×C67C2412yes—
235C2×D4×C67—24no—
236C2×D4×C67—21no—
237C2×D4×C67—22no—
238C2×D4×C67—22no—
239C2×D4×C67—82no—
240C2×D4×C67C2412yes—
241C22×C4×C67—22no—
242C22×C4×C67—22no—
243C22×C4×C67—21no—
244C22×C4×C67—21no—
245C22×C4×C67—21no—
246C22×C4×C67—24no—
247C22×C4×C67—82no—
248C22×C4×C67C2×D411yescharacteristic
249C22×C4×C67C2×D411yescharacteristic
250C22×C4×C67C2×D411yescharacteristic
251C22×C4×C67C2×D411yescharacteristic
252C22×C4×C67C2×D411yescharacteristic
253C22×C4×C67C2×D412yes—
254C22×C4×C67C2412yes—
255C22×C4×C67C2411yescharacteristic
256C4⋊C4×C67—24no—
257C4⋊C4×C67—24no—
258C4⋊C4×C67—24no—
259C4⋊C4×C67—21no—
260C4⋊C4×C67—21no—
261C4⋊C4×C67C2×D414yes—
262C4⋊C4×C67C2×D414yes—
263C4⋊C4×C67C2412yes—
264C4⋊C4×C67C2412yes—
265C22⋊C4×C67—24no—
266C22⋊C4×C67—24no—
267C22⋊C4×C67—24no—
268C22⋊C4×C67—24no—
269C22⋊C4×C67—24no—
270C22⋊C4×C67C2×D414yes—
271C22⋊C4×C67C2×D414yes—
272C42×C67—24no—
273C42×C67C2×D412yes—
274C42×C67C2×D412yes—
275C42×C67C2412yes—
276C42×C67C2412yes—
277C23×C67—22no—
278C23×C67—22no—
279C23×C67—22no—
280C23×C67—22no—
281C23×C67—42no—
282C23×C67—42no—
283C23×C67—42no—
284C23×C67C22×D412yes—
285C23×C67C22×D411yescharacteristic
286C22×D67—22no—
287C22×D67—42no—
288C22×D67—42no—
289C22×D67—42no—
290Q8×C67—22no—
291Q8×C67—22no—
292Q8×C67—42no—
293Q8×C67—84no—
294D4×C67—22no—
295D4×C67—22no—
296D4×C67—42no—
297D4×C67—84no—
298C2×C4×C67—22no—
299C2×C4×C67—22no—
300C2×C4×C67—22no—
301C2×C4×C67—22no—
302C2×C4×C67—22no—
303C2×C4×C67—24no—
304C2×C4×C67—22no—
305C2×C4×C67—22no—
306C2×C4×C67—22no—
307C2×C4×C67—22no—
308C2×C4×C67—22no—
309C2×C4×C67—42no—
310C2×C4×C67—42no—
311C2×C4×C67—42no—
312C2×C4×C67—84no—
313C2×C4×C67C22×D412yes—
314C2×C4×C67C22×D412yes—
315C2×C4×C67C22×D412yes—
316C2×C4×C67C22×D412yes—
317C2×C4×C67C22×D412yes—
318C2×C4×C67C22×D411yescharacteristic
319C2×C4×C67H(5,𝔽2)12yes—
320C2×C4×C672−1+412yes—
321C2×C4×C67C2511yescharacteristic
322C22⋊D67—84no—
323C2×Dic67—22no—
324C2×Dic67—22no—
325C2×Dic67—22no—
326C2×Dic67—42no—
327C2×Dic67—42no—
328C2×Dic67—42no—
329D268—22no—
330D268—22no—
331D268—42no—
332C4×D67—84no—
333Dic134—22no—
334Dic134—22no—
335Dic134—42no—
336Dic134—84no—
337C67⋊C8—22no—
338C67⋊C8—22no—
339C67⋊C8—22no—
340C67⋊C8—22no—
341C22×C67—22no—
342C22×C67—22no—
343C22×C67—22no—
344C22×C67—44no—
345C22×C67—42no—
346C22×C67—42no—
347C22×C67—42no—
348C22×C67—84no—
349C22×C67#53712yes—
350C22×C67#57712yes—
351C22×C67#57712yes—
352C22×C67C23×D411yescharacteristic
353C2×D67—42no—
354C2×D67—42no—
355C2×D67—42no—
356C2×D67—84no—
357C4×C67—22no—
358C4×C67—22no—
359C4×C67—22no—
360C4×C67—22no—
361C4×C67—22no—
362C4×C67—42no—
363C4×C67—42no—
364C4×C67—42no—
365C4×C67#53712yes—
366C4×C67C2×H(5,𝔽2)11yescharacteristic
367C4×C67C2×2−1+411yescharacteristic
368Dic67—42no—
369Dic67—42no—
370Dic67—42no—
371C2×#3263—671nomaximal, Sylow
372C2×C67—42no—
373C2×C67—82no—
374C2×C67#326314yescomplemented
375C2×C67C2×#53711yescharacteristic
376C2×C67C2×#57711yescharacteristic
377C2×C67C2×#57711yescharacteristic
378D67—82no—
379C2×#542—671no—
380C2×#542D6711yescharacteristic, complemented
381#3263—6716no—
382C2×#475—671no—
383C2×#475—671no—
384C2×#476—671no—
385C2×#476—671no—
386C2×#470—671no—
387C2×#469—671no—
388C2×#465—671no—
389C2×#465—671no—
390C2×#464—671no—
391C2×#464—671no—
392C2×#463—671no—
393C2×#463—671no—
394C2×#424—671no—
395C67C2×#326311yescharacteristic, complemented, Sylow
396C22×Q16—671no—
397C22×SD16—671no—
398C22×SD16—671no—
399C22×D8—671no—
400C22×M16—671no—
401C23×C8—671no—
402#542—24no—
403#542—678no—
404#542—1344no—
405#542C2×D6718yescomplemented
406C2×C4⋊Q8—671no—
407C2×C4⋊Q8C2×D6711yescharacteristic
408C2×#126—21no—
409C2×#126—1341no—
410C2×#124—21no—
411C2×#124—671no—
412C2×#124—1341no—
413C2×#124C2×D6711yescharacteristic
414C2×#123—21no—
415C2×#123—1341no—
416C2×C22⋊Q8—21no—
417C2×C22⋊Q8—671no—
418C2×C22⋊Q8—1341no—
419C2×C22⋊Q8C2×D6711yescharacteristic
420C2×#121—671no—
421C2×#121C2×D6711yescharacteristic
422C2×C4×Q8—671no—
423C2×C4×Q8C2×D6711yescharacteristic
424C2×C4×D4—671no—
425C2×C4×D4C2×D6711yescharacteristic
426C2×#117C2×D6711yescharacteristic
427#476—678no—
428#476—678no—
429#475—678no—
430#475—678no—
431#470—678no—
432#469—678no—
433#465—678no—
434#465—678no—
435#464—678no—
436#464—678no—
437#463—678no—
438#463—678no—
439C2×#106—671no—
440C2×#106—671no—
441C2×#106—671no—
442C2×#106—671no—
443#424—678no—
444C2×C4⋊C8—671no—
445C2×C4⋊C8—671no—
446C2×C4⋊C8—671no—
447C2×C4⋊C8—671no—
448C2×#103—671no—
449C2×#103—671no—
450C2×#103—671no—
451C2×#103—671no—
452C2×#102—671no—
453C2×#102—671no—
454C2×#102—671no—
455C2×#102—671no—
456C22×Q8—21no—
457C22×Q8—671no—
458C22×Q8—1341no—
459C22×Q8C22×D6711yescharacteristic
460C22×D4—21no—
461C22×D4—671no—
462C22×D4—1341no—
463C22×D4C22×D6711yescharacteristic
464C23×C4—21no—
465C23×C4—1341no—
466C23×C4C22×D6711yescharacteristic
467C2×Q16—2682no—
468C2×Q16—674no—
469C2×SD16—2682no—
470C2×SD16—2682no—
471C2×SD16—674no—
472C2×SD16—674no—
473C2×D8—2682no—
474C2×D8—674no—
475C2×M16—2682no—
476C2×M16—674no—
477C22×C8—2682no—
478C22×C8—674no—
479C22×C8—671no—
480C22×C8—671no—
481C22×C8—671no—
482C22×C8—671no—
483C4⋊Q8—22no—
484C4⋊Q8—674no—
485C4⋊Q8—1342no—
486C4⋊Q8C22×D6714yes—
487#126—28no—
488#126—1348no—
489#124—28no—
490#124—22no—
491#124—674no—
492#124—1348no—
493#124—1342no—
494#124C22×D6714yes—
495#123—28no—
496#123—1348no—
497C22⋊Q8—22no—
498C22⋊Q8—28no—
499C22⋊Q8—674no—
500C22⋊Q8—1342no—
501C22⋊Q8—1348no—
502C22⋊Q8C22×D6714yes—
503#121—22no—
504#121—674no—
505#121—1342no—
506#121C22×D6714yes—
507C4×Q8—22no—
508C4×Q8—674no—
509C4×Q8—1342no—
510C4×Q8C22×D6714yes—
511C4×D4—22no—
512C4×D4—674no—
513C4×D4—1342no—
514C4×D4C22×D6714yes—
515#117C22⋊D6714yes—
516#117C22×D6714yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—671no—
521C2×C4⋊C4—671no—
522C2×C4⋊C4—1341no—
523C2×C4⋊C4—1341no—
524C2×C4⋊C4—1341no—
525C2×C4⋊C4C22⋊D6711yescharacteristic
526C2×C4⋊C4C22⋊D6711yescharacteristic
527C2×C4⋊C4C22×D6711yescharacteristic
528C2×C4⋊C4C22×D6711yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—1341no—
535C2×C22⋊C4—1341no—
536C2×C22⋊C4—1341no—
537C2×C22⋊C4—1341no—
538C2×C22⋊C4—1341no—
539C2×C22⋊C4C22⋊D6711yescharacteristic
540C2×C22⋊C4C22⋊D6711yescharacteristic
541C2×C42—21no—
542C2×C42—1341no—
543C2×C42C22×D6711yescharacteristic
544C2×C42C22×D6711yescharacteristic
545#106—674no—
546#106—674no—
547#106—674no—
548#106—674no—
549C4⋊C8—674no—
550C4⋊C8—674no—
551C4⋊C8—674no—
552C4⋊C8—674no—
553#103—674no—
554#103—674no—
555#103—674no—
556#103—674no—
557#102—674no—
558#102—674no—
559#102—674no—
560#102—674no—
561C24—21no—
562C24—1341no—
563C24C2×C22⋊D6711yescharacteristic
564C2×Q8—21no—
565C2×Q8—24no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—82no—
569C2×Q8—5362no—
570C2×Q8—672no—
571C2×Q8—1342no—
572C2×Q8—1342no—
573C2×Q8—1341no—
574C2×Q8—1344no—
575C2×Q8C23×D6712yes—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—82no—
581C2×D4—5362no—
582C2×D4—672no—
583C2×D4—1344no—
584C2×D4—1341no—
585C2×D4—1342no—
586C2×D4—1342no—
587C2×D4C23×D6712yes—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—24no—
594C22×C4—82no—
595C22×C4—5362no—
596C22×C4—1341no—
597C22×C4—1341no—
598C22×C4—1341no—
599C22×C4—1344no—
600C22×C4C2×C22⋊D6712yes—
601C22×C4C2×C22⋊D6711yescharacteristic
602C22×C4C2×C22⋊D6711yescharacteristic
603C22×C4C2×C22⋊D6711yescharacteristic
604C22×C4C2×C22⋊D6711yescharacteristic
605C22×C4C2×C22⋊D6711yescharacteristic
606C22×C4C23×D6712yes—
607C22×C4C23×D6711yescharacteristic
608Q16—2684no—
609SD16—2684no—
610SD16—2684no—
611D8—2684no—
612M16—2684no—
613C2×C8—2684no—
614C2×C8—672no—
615C2×C8—672no—
616C2×C8—672no—
617C2×C8—672no—
618C2×C8—1342no—
619C2×C8—1342no—
620C2×C8—1342no—
621C2×C8—1342no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—672no—
628C4⋊C4—672no—
629C4⋊C4—1341no—
630C4⋊C4—1341no—
631C4⋊C4—1344no—
632C4⋊C4—1344no—
633C4⋊C4—1344no—
634C4⋊C4C2×C22⋊D6714yes—
635C4⋊C4C2×C22⋊D6714yes—
636C4⋊C4C23×D6712yes—
637C4⋊C4C23×D6712yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—1344no—
644C22⋊C4—1344no—
645C22⋊C4—1344no—
646C22⋊C4—1344no—
647C22⋊C4—1344no—
648C22⋊C4C2×C22⋊D6714yes—
649C22⋊C4C2×C22⋊D6714yes—
650C42—24no—
651C42—1344no—
652C42C2×C22⋊D6712yes—
653C42C2×C22⋊D6712yes—
654C42C23×D6712yes—
655C42C23×D6712yes—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—2682no—
664C23—2682no—
665C23—2682no—
666C23—1342no—
667C23C22×C22⋊D6712yes—
668C23C22×C22⋊D6711yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—84no—
673Q8—2682no—
674Q8—5364no—
675Q8—1342no—
676Q8—1342no—
677D4—22no—
678D4—22no—
679D4—42no—
680D4—84no—
681D4—2682no—
682D4—5364no—
683D4—1342no—
684D4—1342no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—84no—
700C2×C4—2682no—
701C2×C4—2682no—
702C2×C4—2682no—
703C2×C4—5364no—
704C2×C4—1342no—
705C2×C4—1342no—
706C2×C4—1342no—
707C2×C4C22×C22⋊D6712yes—
708C2×C4C22×C22⋊D6712yes—
709C2×C4C22×C22⋊D6712yes—
710C2×C4C22×C22⋊D6712yes—
711C2×C4C22×C22⋊D6712yes—
712C2×C4C22×C22⋊D6711yescharacteristic
713C2×C4#1452408912yes—
714C2×C4#1452409012yes—
715C2×C4C24×D6711yescharacteristic
716C8—1342no—
717C8—1342no—
718C8—1342no—
719C8—1342no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—44no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—84no—
728C22—2682no—
729C22—2682no—
730C22—2682no—
731C22—5364no—
732C22#1686397412yes—
733C22#1686420412yes—
734C22#1686420712yes—
735C22C23×C22⋊D6711yescharacteristic
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—22no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—2682no—
745C4—2682no—
746C4—2682no—
747C4#1686397412yes—
748C4C2×#1452408911yescharacteristic
749C4C2×#1452409011yescharacteristic
750C2—42no—
751C2—82no—
752C2—5362no—
753C2#2257167414yesdirect product factor
754C2C2×#1686397411yescharacteristic
755C2C2×#1686420411yescharacteristic
756C2C2×#1686420711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#542×C67C2
socleC23×C67C22×D4
prime radicalC2×#16863647C2
hypercenterC2×#542D67
hypocenterC67C2×#3263
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×#16864017C2semidirect
2. #22571674C2direct (N × H)
3. C2×#16863681C2semidirect
4. C2×#16863678C2semidirect
5. C2×#16863686C2semidirect
6. C2×#16863683C2semidirect
7. C2×#16863652C2semidirect
9. C2×#16863627C2semidirect
10. C2×#16863623C2semidirect
11. C2×#16863618C2semidirect
12. C2×#16863615C2semidirect
13. C2×#16863611C2semidirect
14. C2×#16863608C2semidirect
15. C2×#16863423C2semidirect
16. C2×#542×C67C2semidirect
24. #16864017C22semidirect
35. #16863686C22semidirect
36. #16863683C22semidirect
37. #16863681C22semidirect
38. #16863678C22semidirect
39. #16863652C22semidirect
41. #16863627C22semidirect
42. #16863623C22semidirect
43. #16863618C22semidirect
44. #16863615C22semidirect
45. #16863611C22semidirect
46. #16863608C22semidirect
51. #16863423C22semidirect
65. #542×C67C22semidirect
374. C2×C67#3263semidirect
380. C2×#542D67semidirect
395. C67C2×#3263semidirect
405. #542C2×D67semidirect
753. C2#22571674direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168640172
#225716742
C2×#168636812
C2×#168636782
C2×#168636862
C2×#168636832
C2×#168636522
C2×#168636472
C2×#168636272
C2×#168636232
C2×#168636182
C2×#168636152
C2×#168636112
C2×#168636082
C2×#168634232
C2×#542×C672
C2×#326367