Finite Group Databasebeta

← C2×#22571556 #31728648

Subgroups — C2×#22571556 #31728648

Order 17152.

1962 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×#16863930C211yesmaximal, characteristic, complemented
2#22571556C2116yesmaximal, direct product factor
3C2×#16863703C211yesmaximal, characteristic, complemented
4C2×#16863700C211yesmaximal, characteristic, complemented
5C2×#16863696C211yesmaximal, characteristic, complemented
6C2×#16863693C211yesmaximal, characteristic, complemented
7C2×#16863635C211yesmaximal, characteristic, complemented
8C2×#16863630C211yesmaximal, 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
15C22×C4⋊(C67⋊C8)C211yesmaximal, characteristic, complemented
16C2×#529×C67C211yesmaximal, characteristic, complemented
17C22×#11761618C2211yescharacteristic
18C22×#11761616C2211yescharacteristic
19C22×#11761615C2211yescharacteristic
20C22×#11761613C2211yescharacteristic
21C23×C67⋊C8C2211yescharacteristic
22C23×C67⋊C8C2211yescharacteristic
23#16863930—24no—
24#16863930C2218yescomplemented
25C2×#14524037—21no—
26C2×#14524035C2211yescharacteristic
27C2×#14524031C2211yescharacteristic
28C2×#14524026—21no—
29C2×#14524022C2211yescharacteristic
30C2×#14524017C2211yescharacteristic
31C2×C4×Dic134C2211yescharacteristic
32C2×C4×D268C2211yescharacteristic
33C2×C4×C22⋊D67—21no—
34C2×#14524000—21no—
35#16863703C2218yescomplemented
36#16863700C2218yescomplemented
37#16863696C2218yescomplemented
38#16863693C2218yescomplemented
39#16863635C2218yescomplemented
40#16863630C2218yes—
41#16863627C2218yescomplemented
42#16863623C2218yescomplemented
43#16863618C2218yescomplemented
44#16863615C2218yescomplemented
45#16863611C2218yescomplemented
46#16863608C2218yescomplemented
47C2×#14523976C2211yescharacteristic
48C2×#14523976C2211yescharacteristic
49C2×#14523974C2211yescharacteristic
50C2×#14523974C2211yescharacteristic
51C2×C4⋊(C67⋊C8)C2211yescharacteristic
52C2×C4⋊(C67⋊C8)C2211yescharacteristic
53C2×C4⋊(C67⋊C8)C2211yescharacteristic
54C2×C4⋊(C67⋊C8)C2211yescharacteristic
55C2×C4⋊(C67⋊C8)C2218yescomplemented
56C2×#14523967C2211yescharacteristic
57C2×#14523967C2211yescharacteristic
58C2×#14523966C2211yescharacteristic
59C2×#14523966C2211yescharacteristic
60C2×#14523964C2211yescharacteristic
61C2×#14523964C2211yescharacteristic
62C2×#14523963C2211yescharacteristic
63C2×#14523963C2211yescharacteristic
64#529×C67—24no—
65#529×C67C2218yescomplemented
66C2×#126×C67—21no—
67C2×#125×C67C2211yescharacteristic
68C2×#124×C67C2211yescharacteristic
69C2×#123×C67—21no—
70C2×C22⋊Q8×C67C2211yescharacteristic
71C2×#121×C67C2211yescharacteristic
72C2×C4×Q8×C67C2211yescharacteristic
73C2×C4×D4×C67—21no—
74C2×C4×D4×C67C2211yescharacteristic
75C2×#117×C67—21no—
76C22×C42×C67C2211yescharacteristic
77C22×Dic134C2311yescharacteristic
78C22×D268C2311yescharacteristic
79C22×C22⋊D67—21no—
80C22×C4×D67—21no—
81C2×#11761618—42no—
82C2×#11761618C2314yes—
83C2×#11761616—42no—
84C2×#11761616C2314yes—
85C2×#11761615—42no—
86C2×#11761615C2314yes—
87C2×#11761613—42no—
88C2×#11761613C2314yes—
89C22×C67⋊C8—42no—
90C22×C67⋊C8—42no—
91C22×C67⋊C8C2311yescharacteristic
92C22×C67⋊C8C2311yescharacteristic
93C22×C67⋊C8C2311yescharacteristic
94C22×C67⋊C8C2311yescharacteristic
95C22×C67⋊C8C2314yes—
96C22×C67⋊C8C2314yes—
97#14524037—28no—
98#14524035—22no—
99#14524035C2314yes—
100#14524031—22no—
101#14524031C2314yes—
102#14524026—28no—
103#14524022—22no—
104#14524022C2314yes—
105#14524017—22no—
106#14524017C2314yes—
107C4×Dic134—22no—
108C4×Dic134C2314yes—
109C4×D268—22no—
110C4×D268C2314yes—
111C4×C22⋊D67—28no—
112#14524000—28no—
113C2×C4⋊Dic67C2311yescharacteristic
114C2×C4⋊Dic67C2311yescharacteristic
115C2×Dic67⋊C4—21no—
116C2×Dic67⋊C4—21no—
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#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#14523964C2314yes—
138#14523964C2314yes—
139#14523963C2314yes—
140#14523963C2314yes—
141C22×Q8×C67C2311yescharacteristic
142C22×D4×C67—21no—
143C22×D4×C67C2311yescharacteristic
144C23×C4×C67—21no—
145C23×C4×C67D411yescharacteristic
146C23×C4×C67D411yescharacteristic
147C23×C4×C67C2311yescharacteristic
148#126×C67—28no—
149#125×C67—22no—
150#125×C67C2314yes—
151#124×C67—22no—
152#124×C67C2314yes—
153#123×C67—28no—
154C22⋊Q8×C67—22no—
155C22⋊Q8×C67C2314yes—
156#121×C67—22no—
157#121×C67C2314yes—
158C4×Q8×C67—22no—
159C4×Q8×C67C2314yes—
160C4×D4×C67—28no—
161C4×D4×C67—22no—
162C4×D4×C67C2314yes—
163#117×C67—28no—
164C2×C4⋊C4×C67—21no—
165C2×C4⋊C4×C67—21no—
166C2×C4⋊C4×C67—21no—
167C2×C4⋊C4×C67—21no—
168C2×C4⋊C4×C67C2311yescharacteristic
169C2×C4⋊C4×C67C2311yescharacteristic
170C2×C22⋊C4×C67—21no—
171C2×C22⋊C4×C67—21no—
172C2×C22⋊C4×C67—21no—
173C2×C22⋊C4×C67—21no—
174C2×C22⋊C4×C67—21no—
175C2×C42×C67—21no—
176C2×C42×C67D411yescharacteristic
177C2×C42×C67D411yescharacteristic
178C2×C42×C67D414yes—
179C2×C42×C67C2311yescharacteristic
180C2×C42×C67C2311yescharacteristic
181C2×C42×C67C2314yes—
182C23×D67—21no—
183C2×Dic134—22no—
184C2×Dic134—22no—
185C2×Dic134—21no—
186C2×Dic134C2412yes—
187C2×D268—22no—
188C2×D268—22no—
189C2×D268—21no—
190C2×D268C2412yes—
191C2×C22⋊D67—24no—
192C2×C22⋊D67—44no—
193C22×Dic67—21no—
194C22×Dic67—21no—
195C22×Dic67—21no—
196C2×C4×D67—24no—
197C2×C4×D67—44no—
198#11761618—44no—
199#11761616—44no—
200#11761615—44no—
201#11761613—44no—
202C2×C67⋊C8—22no—
203C2×C67⋊C8—22no—
204C2×C67⋊C8—22no—
205C2×C67⋊C8—22no—
206C2×C67⋊C8—44no—
207C2×C67⋊C8—44no—
208C2×C67⋊C8C2412yes—
209C2×C67⋊C8C2412yes—
210C2×C67⋊C8C2412yes—
211C2×C67⋊C8C2412yes—
212C4⋊Dic67—21no—
213C4⋊Dic67—21no—
214C4⋊Dic67C2412yes—
215C4⋊Dic67C2412yes—
216Dic67⋊C4—24no—
217Dic67⋊C4—24no—
218Dic67⋊C4—24no—
219Dic67⋊C4—24no—
220C22⋊Dic67—24no—
221(C2×D67)⋊C4—24no—
222(C2×D67)⋊C4—24no—
223(C2×D67)⋊C4—24no—
224(C2×D67)⋊C4—24no—
225C4×Dic67—24no—
226C24×C67—21no—
227C24×C67C2×D411yescharacteristic
228C2×Q8×C67—21no—
229C2×Q8×C67—22no—
230C2×Q8×C67—22no—
231C2×Q8×C67C2412yes—
232C2×D4×C67—24no—
233C2×D4×C67—21no—
234C2×D4×C67—22no—
235C2×D4×C67—22no—
236C2×D4×C67—44no—
237C2×D4×C67C2412yes—
238C22×C4×C67—24no—
239C22×C4×C67—22no—
240C22×C4×C67—22no—
241C22×C4×C67—21no—
242C22×C4×C67—21no—
243C22×C4×C67—21no—
244C22×C4×C67—24no—
245C22×C4×C67—42no—
246C22×C4×C67—44no—
247C22×C4×C67C2×D411yescharacteristic
248C22×C4×C67C2×D411yescharacteristic
249C22×C4×C67C2×D412yes—
250C22×C4×C67C2×D411yescharacteristic
251C22×C4×C67C2×D411yescharacteristic
252C22×C4×C67C2×D411yescharacteristic
253C22×C4×C67C2×D414yes—
254C22×C4×C67C2×D414yes—
255C22×C4×C67C2412yes—
256C22×C4×C67C2411yescharacteristic
257C4⋊C4×C67—24no—
258C4⋊C4×C67—24no—
259C4⋊C4×C67—24no—
260C4⋊C4×C67—24no—
261C4⋊C4×C67—21no—
262C4⋊C4×C67—21no—
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—
270C42×C67—24no—
271C42×C67C2×D414yes—
272C42×C67C2×D412yes—
273C42×C67C2×D412yes—
274C42×C67C2×D414yes—
275C42×C67C2412yes—
276C42×C67C2412yes—
277C23×C67—22no—
278C23×C67—22no—
279C23×C67—22no—
280C23×C67—42no—
281C23×C67—42no—
282C23×C67—42no—
283C23×C67#13514yes—
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—
293D4×C67—22no—
294D4×C67—22no—
295D4×C67—48no—
296D4×C67—42no—
297C2×C4×C67—22no—
298C2×C4×C67—28no—
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—44no—
310C2×C4×C67—48no—
311C2×C4×C67—42no—
312C2×C4×C67—42no—
313C2×C4×C67—42no—
314C2×C4×C67C22×D412yes—
315C2×C4×C67C22×D412yes—
316C2×C4×C67C22×D412yes—
317C2×C4×C67C22×D412yes—
318C2×C4×C67C22×D412yes—
319C2×C4×C67C22×D411yescharacteristic
320C2×C4×C67H(5,𝔽2)12yes—
321C2×C4×C672−1+412yes—
322C2×C4×C67C2511yescharacteristic
323C22⋊D67—48no—
324C2×Dic67—22no—
325C2×Dic67—22no—
326C2×Dic67—22no—
327C2×Dic67—42no—
328C2×Dic67—42no—
329C2×Dic67—42no—
330D268—22no—
331D268—22no—
332D268—42no—
333C4×D67—48no—
334Dic134—22no—
335Dic134—22no—
336Dic134—42no—
337C67⋊C8—22no—
338C67⋊C8—22no—
339C67⋊C8—22no—
340C67⋊C8—22no—
341C22×C67—22no—
342C22×C67—28no—
343C22×C67—22no—
344C22×C67—42no—
345C22×C67—42no—
346C22×C67—42no—
347C22×C67—84no—
348C22×C67#53712yes—
349C22×C67C2×#13514yes—
350C22×C67C2×#13512yes—
351C22×C67#57512yes—
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×#3250—671nomaximal, Sylow
372C2×C67—24no—
373C2×C67—82no—
374C2×C67#325014yescomplemented
375C2×C67C2×#53711yescharacteristic
376C2×C67C22×#13511yescharacteristic
377C2×C67C2×#57511yescharacteristic
378D67—82no—
379C2×#529—671no—
380C2×#529D6711yescharacteristic, complemented
381#3250—6716no—
382C2×#479—671no—
383C2×#479—671no—
384C2×#478—671no—
385C2×#478—671no—
386C2×#467—671no—
387C2×#466—671no—
388C2×#465—671no—
389C2×#465—671no—
390C2×#464—671no—
391C2×#464—671no—
392C2×#463—671no—
393C2×#463—671no—
394C22×C4⋊C8—671no—
395C67C2×#325011yescharacteristic, complemented, Sylow
396C22×Q16—671no—
397C22×SD16—671no—
398C22×SD16—671no—
399C22×D8—671no—
400C23×C8—671no—
401C23×C8—671no—
402#529—24no—
403#529—678no—
404#529—1344no—
405#529C2×D6718yescomplemented
406C2×#126—21no—
407C2×#126—1341no—
408C2×#125—671no—
409C2×#125C2×D6711yescharacteristic
410C2×#124—671no—
411C2×#124C2×D6711yescharacteristic
412C2×#123—21no—
413C2×#123—1341no—
414C2×C22⋊Q8—671no—
415C2×C22⋊Q8C2×D6711yescharacteristic
416C2×#121—671no—
417C2×#121C2×D6711yescharacteristic
418C2×C4×Q8—671no—
419C2×C4×Q8C2×D6711yescharacteristic
420C2×C4×D4—21no—
421C2×C4×D4—671no—
422C2×C4×D4—1341no—
423C2×C4×D4C2×D6711yescharacteristic
424C2×#117—21no—
425C2×#117—1341no—
426C22×C42C2×D6711yescharacteristic
427#479—678no—
428#479—678no—
429#478—678no—
430#478—678no—
431#467—678no—
432#466—678no—
433#465—678no—
434#465—678no—
435#464—678no—
436#464—678no—
437#463—678no—
438#463—678no—
439C2×#107—671no—
440C2×#107—671no—
441C2×#106—671no—
442C2×#106—671no—
443C2×C4⋊C8—671no—
444C2×C4⋊C8—671no—
445C2×C4⋊C8—671no—
446C2×C4⋊C8—671no—
447C2×C4⋊C8—678no—
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—671no—
457C22×Q8C22×D6711yescharacteristic
458C22×D4—21no—
459C22×D4—671no—
460C22×D4—1341no—
461C22×D4C22×D6711yescharacteristic
462C23×C4—21no—
463C23×C4—1341no—
464C23×C4C22⋊D6711yescharacteristic
465C23×C4C22⋊D6711yescharacteristic
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—
475C22×C8—2682no—
476C22×C8—2682no—
477C22×C8—674no—
478C22×C8—674no—
479C22×C8—671no—
480C22×C8—671no—
481C22×C8—671no—
482C22×C8—671no—
483#126—28no—
484#126—1348no—
485#125—22no—
486#125—674no—
487#125—1342no—
488#125C22×D6714yes—
489#124—22no—
490#124—674no—
491#124—1342no—
492#124C22×D6714yes—
493#123—28no—
494#123—1348no—
495C22⋊Q8—22no—
496C22⋊Q8—674no—
497C22⋊Q8—1342no—
498C22⋊Q8C22×D6714yes—
499#121—22no—
500#121—674no—
501#121—1342no—
502#121C22×D6714yes—
503C4×Q8—22no—
504C4×Q8—674no—
505C4×Q8—1342no—
506C4×Q8C22×D6714yes—
507C4×D4—28no—
508C4×D4—22no—
509C4×D4—674no—
510C4×D4—1348no—
511C4×D4—1342no—
512C4×D4C22×D6714yes—
513#117—28no—
514#117—1348no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—671no—
520C2×C4⋊C4—671no—
521C2×C4⋊C4—1341no—
522C2×C4⋊C4—1341no—
523C2×C4⋊C4—1341no—
524C2×C4⋊C4—1341no—
525C2×C4⋊C4C22×D6711yescharacteristic
526C2×C4⋊C4C22×D6711yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—1341no—
533C2×C22⋊C4—1341no—
534C2×C22⋊C4—1341no—
535C2×C22⋊C4—1341no—
536C2×C22⋊C4—1341no—
537C2×C42—21no—
538C2×C42—1341no—
539C2×C42C22⋊D6711yescharacteristic
540C2×C42C22⋊D6711yescharacteristic
541C2×C42C22⋊D6714yes—
542C2×C42C22×D6711yescharacteristic
543C2×C42C22×D6711yescharacteristic
544C2×C42C22×D6714yes—
545#107—674no—
546#107—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—22no—
566C2×Q8—22no—
567C2×Q8—672no—
568C2×Q8—1342no—
569C2×Q8—1342no—
570C2×Q8—1341no—
571C2×Q8C23×D6712yes—
572C2×D4—24no—
573C2×D4—21no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—44no—
577C2×D4—2684no—
578C2×D4—672no—
579C2×D4—1344no—
580C2×D4—1341no—
581C2×D4—1342no—
582C2×D4—1342no—
583C2×D4C23×D6712yes—
584C22×C4—24no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—24no—
591C22×C4—42no—
592C22×C4—44no—
593C22×C4—2684no—
594C22×C4—1341no—
595C22×C4—1341no—
596C22×C4—1341no—
597C22×C4—1344no—
598C22×C4C2×C22⋊D6712yes—
599C22×C4C2×C22⋊D6714yes—
600C22×C4C2×C22⋊D6711yescharacteristic
601C22×C4C2×C22⋊D6711yescharacteristic
602C22×C4C2×C22⋊D6711yescharacteristic
603C22×C4C2×C22⋊D6711yescharacteristic
604C22×C4C2×C22⋊D6711yescharacteristic
605C22×C4C2×C22⋊D6714yes—
606C22×C4C23×D6712yes—
607C22×C4C23×D6711yescharacteristic
608Q16—2684no—
609SD16—2684no—
610SD16—2684no—
611D8—2684no—
612C2×C8—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—24no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—672no—
629C4⋊C4—672no—
630C4⋊C4—1341no—
631C4⋊C4—1341no—
632C4⋊C4—1344no—
633C4⋊C4—1344no—
634C4⋊C4—1344no—
635C4⋊C4—1344no—
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—
648C42—24no—
649C42—1344no—
650C42C2×C22⋊D6714yes—
651C42C2×C22⋊D6714yes—
652C42C2×C22⋊D6712yes—
653C42C2×C22⋊D6712yes—
654C42C23×D6712yes—
655C42C23×D6712yes—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—2682no—
663C23—2682no—
664C23—2682no—
665C23—1342no—
666C23#1452406314yes—
667C23C22×C22⋊D6712yes—
668C23C22×C22⋊D6711yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—2682no—
673Q8—1342no—
674Q8—1342no—
675D4—22no—
676D4—22no—
677D4—48no—
678D4—42no—
679D4—2688no—
680D4—2682no—
681D4—1342no—
682D4—1342no—
683C2×C4—28no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—44no—
696C2×C4—48no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—2688no—
701C2×C4—2682no—
702C2×C4—2682no—
703C2×C4—2682no—
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—28no—
721C22—22no—
722C22—22no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—84no—
727C22—2682no—
728C22—2682no—
729C22—2682no—
730C22—5364no—
731C22#1686397412yes—
732C22C2×#1452406314yes—
733C22C2×#1452406312yes—
734C22#1686419412yes—
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—24no—
751C2—82no—
752C2—5362no—
753C2#2257155614yesdirect product factor
754C2C2×#1686397411yescharacteristic
755C2C22×#1452406311yescharacteristic
756C2C2×#1686419411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#529×C67C2
socleC23×C67C22×D4
prime radicalC2×#16863630C2
hypercenterC2×#529D67
hypocenterC67C2×#3250
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#16863930C2semidirect
2. #22571556C2direct (N × H)
3. C2×#16863703C2semidirect
4. C2×#16863700C2semidirect
5. C2×#16863696C2semidirect
6. C2×#16863693C2semidirect
7. C2×#16863635C2semidirect
9. C2×#16863627C2semidirect
10. C2×#16863623C2semidirect
11. C2×#16863618C2semidirect
12. C2×#16863615C2semidirect
13. C2×#16863611C2semidirect
14. C2×#16863608C2semidirect
15. C22×C4⋊(C67⋊C8)C2semidirect
16. C2×#529×C67C2semidirect
24. #16863930C22semidirect
35. #16863703C22semidirect
36. #16863700C22semidirect
37. #16863696C22semidirect
38. #16863693C22semidirect
39. #16863635C22semidirect
41. #16863627C22semidirect
42. #16863623C22semidirect
43. #16863618C22semidirect
44. #16863615C22semidirect
45. #16863611C22semidirect
46. #16863608C22semidirect
55. C2×C4⋊(C67⋊C8)C22semidirect
65. #529×C67C22semidirect
374. C2×C67#3250semidirect
380. C2×#529D67semidirect
395. C67C2×#3250semidirect
405. #529C2×D67semidirect
753. C2#22571556direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168639302
#225715562
C2×#168637032
C2×#168637002
C2×#168636962
C2×#168636932
C2×#168636352
C2×#168636302
C2×#168636272
C2×#168636232
C2×#168636182
C2×#168636152
C2×#168636112
C2×#168636082
C22×C4⋊(C67⋊C8)2
C2×#529×C672
C2×#325067