Finite Group Databasebeta

← C2×#22572673 #31734388

Subgroups — C2×#22572673 #31734388

Order 17152.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864050C211yesmaximal, characteristic, complemented
2#22572673C2116yesmaximal, direct product factor
3C2×#16863806C211yesmaximal, characteristic, complemented
4C2×#16863714C211yesmaximal, characteristic, complemented
5C2×#16863712C211yesmaximal, characteristic, complemented
6C2×#16863720C211yesmaximal, characteristic, complemented
7C2×#16863707C211yesmaximal, characteristic, complemented
8C2×#16863693C211yesmaximal, characteristic, complemented
9C2×#16863686C211yesmaximal, characteristic, complemented
10C2×#16863647C211yesmaximal, characteristic, complemented
11C2×#16863630C211yesmaximal, characteristic, complemented
12C2×#16863506C211yesmaximal, characteristic, complemented
13C2×#16863468C211yesmaximal, characteristic, complemented
14C2×#16863439C211yesmaximal, characteristic, complemented
15C22×#14523974C211yesmaximal, characteristic, complemented
16C2×#553×C67C211yesmaximal, characteristic, complemented
17C22×#11761627—21no—
18C22×#11761613C2211yescharacteristic
19C22×#11761612C2211yescharacteristic
20C23×C67⋊C8C2211yescharacteristic
21#16864050—24no—
22#16864050C2218yescomplemented
23C2×#14524043C2211yescharacteristic
24C2×#14524027—21no—
25C2×#14524027—21no—
26C2×#14524023—21no—
27C2×#14524017C2211yescharacteristic
28C2×#14524017C2211yescharacteristic
29C2×C4×D268C2211yescharacteristic
30C22×C4⋊Dic67C2211yescharacteristic
31C22×C4⋊Dic67C2211yescharacteristic
32#16863806C2218yescomplemented
33#16863720C2218yescomplemented
34#16863714C2218yescomplemented
35#16863712C2218yescomplemented
36#16863707C2218yescomplemented
37#16863693C2218yescomplemented
38#16863686C2218yescomplemented
39#16863647C2218yescomplemented
40#16863630C2218yescomplemented
41#16863506C2218yescomplemented
42#16863468C2218yescomplemented
43#16863439C2218yescomplemented
44C2×#14523976C2211yescharacteristic
45C2×#14523976C2211yescharacteristic
46C2×#14523976C2211yescharacteristic
47C2×#14523974C2211yescharacteristic
48C2×#14523974C2211yescharacteristic
49C2×#14523974C2211yescharacteristic
50C2×#14523974C2211yescharacteristic
51C2×#14523974C2211yescharacteristic
52C2×#14523974C2211yescharacteristic
53C2×#14523974C2218yescomplemented
54C2×C4⋊(C67⋊C8)C2211yescharacteristic
55C2×#14523964C2211yescharacteristic
56C2×#14523964C2211yescharacteristic
57C2×#14523964C2211yescharacteristic
58C2×#14523963C2211yescharacteristic
59C2×#14523963C2211yescharacteristic
60C2×#14523963C2211yescharacteristic
61C2×C22⋊(C67⋊C8)C2211yescharacteristic
62C2×C22⋊(C67⋊C8)C2211yescharacteristic
63C2×#14523954C2211yescharacteristic
64#553×C67—24no—
65#553×C67C2218yescomplemented
66C2×#126×C67—21no—
67C2×#125×C67C2211yescharacteristic
68C2×#123×C67—21no—
69C2×#121×C67—21no—
70C2×#121×C67C2211yescharacteristic
71C2×#121×C67C2211yescharacteristic
72C2×C4×D4×C67—21no—
73C2×C4×D4×C67C2211yescharacteristic
74C2×C4×D4×C67C2211yescharacteristic
75C2×#117×C67C2211yescharacteristic
76C22×C4⋊C4×C67C2211yescharacteristic
77C2×#11761627—28no—
78C2×#11761627—48no—
79C22×Dic134—21no—
80C22×D268C2311yescharacteristic
81C22×C22⋊D67—21no—
82C22×C22⋊D67—21no—
83C23×Dic67—21no—
84C23×Dic67—21no—
85C22×C4×D67—21no—
86C2×#11761613—24no—
87C2×#11761613C2314yes—
88C2×#11761612—24no—
89C2×#11761612C2314yes—
90C22×C67⋊C8—24no—
91C22×C67⋊C8C2311yescharacteristic
92C22×C67⋊C8C2311yescharacteristic
93C22×C67⋊C8C2311yescharacteristic
94C22×C67⋊C8C2314yes—
95C22×C67⋊C8C2311yescharacteristic
96#14524043—22no—
97#14524043C2314yes—
98#14524027—28no—
99#14524027—28no—
100#14524023—28no—
101#14524017—22no—
102#14524017—22no—
103#14524017C2314yes—
104#14524017C2314yes—
105C4×D268—22no—
106C4×D268C2314yes—
107C2×C4⋊Dic67—22no—
108C2×C4⋊Dic67—22no—
109C2×C4⋊Dic67—21no—
110C2×C4⋊Dic67—21no—
111C2×C4⋊Dic67—21no—
112C2×C4⋊Dic67C2314yes—
113C2×C4⋊Dic67C2314yes—
114C2×C4⋊Dic67C2311yescharacteristic
115C2×C4⋊Dic67C2311yescharacteristic
116C2×C4⋊Dic67C2311yescharacteristic
117C2×(C2×D67)⋊C4—21no—
118C2×(C2×D67)⋊C4—21no—
119C2×(C2×D67)⋊C4—21no—
120#14523976C2314yes—
121#14523976C2314yes—
122#14523976C2314yes—
123#14523974C2314yes—
124#14523974C2314yes—
125#14523974C2314yes—
126#14523974C2314yes—
127#14523974C2314yes—
128#14523974C2314yes—
129C4⋊(C67⋊C8)C2314yes—
130#14523964C2314yes—
131#14523964C2314yes—
132#14523964C2314yes—
133#14523963C2314yes—
134#14523963C2314yes—
135#14523963C2314yes—
136C22⋊(C67⋊C8)C2314yes—
137C22⋊(C67⋊C8)C2314yes—
138#14523954C2314yes—
139C22×D4×C67—21no—
140C22×D4×C67—21no—
141C22×D4×C67D411yescharacteristic
142C22×D4×C67C2311yescharacteristic
143C23×C4×C67—21no—
144C23×C4×C67—21no—
145C23×C4×C67C2311yescharacteristic
146C23×C4×C67C2311yescharacteristic
147#126×C67—28no—
148#125×C67—22no—
149#125×C67C2314yes—
150#123×C67—28no—
151#121×C67—28no—
152#121×C67—22no—
153#121×C67—22no—
154#121×C67C2314yes—
155#121×C67C2314yes—
156C4×D4×C67—28no—
157C4×D4×C67—22no—
158C4×D4×C67D414yes—
159C4×D4×C67C2314yes—
160C4×D4×C67C2314yes—
161#117×C67—22no—
162#117×C67C2314yes—
163C2×C4⋊C4×C67—21no—
164C2×C4⋊C4×C67—22no—
165C2×C4⋊C4×C67—21no—
166C2×C4⋊C4×C67—21no—
167C2×C4⋊C4×C67D411yescharacteristic
168C2×C4⋊C4×C67C2311yescharacteristic
169C2×C4⋊C4×C67C2311yescharacteristic
170C2×C4⋊C4×C67C2314yes—
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×C67D411yescharacteristic
177C2×C22⋊C4×C67D411yescharacteristic
178C2×C42×C67—21no—
179C2×C42×C67C2311yescharacteristic
180C23×D67—21no—
181#11761627—432no—
182C2×Dic134—24no—
183C2×Dic134—44no—
184C2×D268—22no—
185C2×D268—22no—
186C2×D268—21no—
187C2×D268C2412yes—
188C2×C22⋊D67—24no—
189C2×C22⋊D67—24no—
190C2×C22⋊D67—44no—
191C2×C22⋊D67—44no—
192C22×Dic67—21no—
193C22×Dic67—21no—
194C22×Dic67—21no—
195C22×Dic67—24no—
196C22×Dic67—24no—
197C22×Dic67—44no—
198C22×Dic67—44no—
199C2×C4×D67—24no—
200C2×C4×D67—44no—
201#11761613—28no—
202#11761612—28no—
203C2×C67⋊C8—22no—
204C2×C67⋊C8—22no—
205C2×C67⋊C8—22no—
206C2×C67⋊C8—28no—
207C2×C67⋊C8#4114yescomplemented
208C2×C67⋊C8C2412yes—
209C2×C67⋊C8C2412yes—
210C2×C67⋊C8C2412yes—
211C2×C67⋊C8C2412yes—
212C4⋊Dic67—21no—
213C4⋊Dic67—21no—
214C4⋊Dic67—21no—
215C4⋊Dic67—24no—
216C4⋊Dic67—24no—
217C4⋊Dic67—24no—
218C4⋊Dic67C2412yes—
219C4⋊Dic67C2412yes—
220C4⋊Dic67C2412yes—
221(C2×D67)⋊C4—24no—
222(C2×D67)⋊C4—24no—
223(C2×D67)⋊C4—24no—
224C24×C67—21no—
225C24×C67C2×D411yescharacteristic
226C24×C67C2×D411yescharacteristic
227C2×D4×C67—24no—
228C2×D4×C67—24no—
229C2×D4×C67—24no—
230C2×D4×C67—21no—
231C2×D4×C67—22no—
232C2×D4×C67—22no—
233C2×D4×C67—44no—
234C2×D4×C67—82no—
235C2×D4×C67C2×D414yes—
236C2×D4×C67C2412yes—
237C22×C4×C67—22no—
238C22×C4×C67—22no—
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—24no—
246C22×C4×C67—82no—
247C22×C4×C67—82no—
248C22×C4×C67C2×D411yescharacteristic
249C22×C4×C67C2×D411yescharacteristic
250C22×C4×C67C2×D411yescharacteristic
251C22×C4×C67C2×D411yescharacteristic
252C22×C4×C67C2×D412yes—
253C22×C4×C67C2×D412yes—
254C22×C4×C67C2412yes—
255C22×C4×C67C2412yes—
256C22×C4×C67C2411yescharacteristic
257C4⋊C4×C67—21no—
258C4⋊C4×C67—21no—
259C4⋊C4×C67—24no—
260C4⋊C4×C67—24no—
261C4⋊C4×C67—24no—
262C4⋊C4×C67—21no—
263C4⋊C4×C67C2×D414yes—
264C4⋊C4×C67C2412yes—
265C4⋊C4×C67C2412yes—
266C4⋊C4×C67C2412yes—
267C22⋊C4×C67—24no—
268C22⋊C4×C67—24no—
269C22⋊C4×C67—24no—
270C22⋊C4×C67—24no—
271C22⋊C4×C67C2×D414yes—
272C22⋊C4×C67C2×D414yes—
273C42×C67—24no—
274C42×C67C2×D412yes—
275C42×C67C2412yes—
276C23×C67—22no—
277C23×C67—22no—
278C23×C67—22no—
279C23×C67—22no—
280C23×C67—22no—
281C23×C67—22no—
282C23×C67—42no—
283C23×C67—42no—
284C23×C67—42no—
285C23×C67AGL(1,ℤ/8)14yes—
286C23×C67C22×D412yes—
287C23×C67C22×D412yes—
288C23×C67C22×D411yescharacteristic
289C22×D67—22no—
290C22×D67—42no—
291C22×D67—42no—
292C22×D67—42no—
293D4×C67—28no—
294D4×C67—22no—
295D4×C67—22no—
296D4×C67—48no—
297D4×C67—42no—
298D4×C67—84no—
299C2×C4×C67—22no—
300C2×C4×C67—22no—
301C2×C4×C67—22no—
302C2×C4×C67—22no—
303C2×C4×C67—24no—
304C2×C4×C67—24no—
305C2×C4×C67—22no—
306C2×C4×C67—22no—
307C2×C4×C67—22no—
308C2×C4×C67—22no—
309C2×C4×C67—22no—
310C2×C4×C67—22no—
311C2×C4×C67—22no—
312C2×C4×C67—42no—
313C2×C4×C67—42no—
314C2×C4×C67—42no—
315C2×C4×C67—84no—
316C2×C4×C67—84no—
317C2×C4×C67C22×D412yes—
318C2×C4×C67C22×D412yes—
319C2×C4×C67C22×D412yes—
320C2×C4×C67C22×D412yes—
321C2×C4×C67C22×D411yescharacteristic
322C2×C4×C67C2×#4112yes—
323C2×C4×C672−1+412yes—
324C2×C4×C67C2511yescharacteristic
325C22⋊D67—48no—
326C22⋊D67—48no—
327C2×Dic67—22no—
328C2×Dic67—22no—
329C2×Dic67—22no—
330C2×Dic67—48no—
331C2×Dic67—42no—
332C2×Dic67—42no—
333C2×Dic67—42no—
334C2×Dic67—48no—
335D268—22no—
336D268—22no—
337D268—42no—
338C4×D67—48no—
339Dic134—48no—
340C67⋊C8—22no—
341C67⋊C8—22no—
342C67⋊C8—22no—
343C67⋊C8C2×#4114yescomplemented
344C22×C67—28no—
345C22×C67—22no—
346C22×C67—22no—
347C22×C67—22no—
348C22×C67—22no—
349C22×C67—22no—
350C22×C67—44no—
351C22×C67—42no—
352C22×C67—42no—
353C22×C67—42no—
354C22×C67—84no—
355C22×C67#54712yes—
356C22×C67C2×AGL(1,ℤ/8)14yes—
357C22×C67C2×AGL(1,ℤ/8)12yes—
358C22×C67#57712yes—
359C22×C67C23×D411yescharacteristic
360C2×D67—42no—
361C2×D67—42no—
362C2×D67—42no—
363C2×D67—84no—
364C4×C67—22no—
365C4×C67—22no—
366C4×C67—22no—
367C4×C67—22no—
368C4×C67—42no—
369C4×C67—42no—
370C4×C67—42no—
371C4×C67#54712yes—
372C4×C67C22×#4111yescharacteristic
373C4×C67C2×2−1+411yescharacteristic
374Dic67—42no—
375Dic67—42no—
376Dic67—42no—
377C2×#3345—671nomaximal, Sylow
378C2×C67—24no—
379C2×C67—42no—
380C2×C67—82no—
381C2×C67#334514yescomplemented
382C2×C67C2×#54711yescharacteristic
383C2×C67C22×AGL(1,ℤ/8)11yescharacteristic
384C2×C67C2×#57711yescharacteristic
385D67—82no—
386C2×#553D6711yescharacteristic, complemented
387C2×#547—671no—
388#3345—6716no—
389C2×#501—671no—
390C2×#481—671no—
391C2×#481—671no—
392C2×#482—671no—
393C2×#480—671no—
394C2×#478—671no—
395C2×#476—671no—
396C2×#469—671no—
397C2×#466—671no—
398C2×#442—671no—
399C2×#435—671no—
400C2×#428—671no—
401C22×#106—671no—
402C67C2×#334511yescharacteristic, complemented, Sylow
403C22×#41—1341no—
404C22×D8—671no—
405C22×M16—671no—
406C23×C8—671no—
407#553—24no—
408#553C2×D6718yescomplemented
409#547—678no—
410#547—1344no—
411C2×C4⋊Q8—671no—
412C2×#126—21no—
413C2×#125C2×D6711yescharacteristic
414C2×#123—21no—
415C2×#123—1341no—
416C2×#123—1341no—
417C2×C22⋊Q8—1341no—
418C2×#121—21no—
419C2×#121—671no—
420C2×#121—671no—
421C2×#121C2×D6711yescharacteristic
422C2×#121C2×D6711yescharacteristic
423C2×C4×D4—21no—
424C2×C4×D4—671no—
425C2×C4×D4C2×D6711yescharacteristic
426C2×C4×D4C2×D6711yescharacteristic
427C2×#117C2×D6711yescharacteristic
428C22×C4⋊C4—671no—
429C22×C4⋊C4—671no—
430C22×C4⋊C4C2×D6711yescharacteristic
431#501—678no—
432#482—678no—
433#481—678no—
434#481—678no—
435#480—678no—
436#478—678no—
437#476—678no—
438#469—678no—
439#466—678no—
440#442—678no—
441#435—678no—
442#428—678no—
443C2×#107—671no—
444C2×#107—671no—
445C2×#107—671no—
446C2×#106—671no—
447C2×#106—671no—
448C2×#106—671no—
449C2×#106—671no—
450C2×#106—678no—
451C2×#106—671no—
452C2×#106—671no—
453C2×C4⋊C8—671no—
454C2×#102—671no—
455C2×#102—671no—
456C2×#102—671no—
457C2×#102—671no—
458C2×#102—671no—
459C2×#102—671no—
460C2×C22⋊C8—671no—
461C2×C22⋊C8—671no—
462C2×#97—671no—
463C2×#41—2688no—
464C2×#41—1348no—
465C22×Q8—1341no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4—671no—
469C22×D4—1341no—
470C22×D4—1341no—
471C22×D4C22⋊D6711yescharacteristic
472C22×D4C22×D6711yescharacteristic
473C23×C4—21no—
474C23×C4—21no—
475C23×C4—1341no—
476C23×C4—1341no—
477C23×C4—1341no—
478C23×C4C22×D6711yescharacteristic
479C23×C4C22×D6711yescharacteristic
480C2×D8—674no—
481C2×D8—1344no—
482C2×M16—674no—
483C2×M16—1344no—
484C22×C8—671no—
485C22×C8—671no—
486C22×C8—674no—
487C22×C8—671no—
488C22×C8—671no—
489C22×C8—1344no—
490C4⋊Q8—674no—
491C4⋊Q8—1342no—
492#126—28no—
493#125—22no—
494#125C22×D6714yes—
495#123—28no—
496#123—1348no—
497#123—1348no—
498C22⋊Q8—1348no—
499#121—28no—
500#121—22no—
501#121—22no—
502#121—674no—
503#121—674no—
504#121—1342no—
505#121—1342no—
506#121C22×D6714yes—
507#121C22×D6714yes—
508C4×D4—28no—
509C4×D4—22no—
510C4×D4—674no—
511C4×D4—1342no—
512C4×D4C22⋊D6714yes—
513C4×D4C22×D6714yes—
514C4×D4C22×D6714yes—
515#117—22no—
516#117C22×D6714yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—671no—
522C2×C4⋊C4—671no—
523C2×C4⋊C4—671no—
524C2×C4⋊C4—674no—
525C2×C4⋊C4—674no—
526C2×C4⋊C4—1341no—
527C2×C4⋊C4—1341no—
528C2×C4⋊C4—1342no—
529C2×C4⋊C4—1342no—
530C2×C4⋊C4—1341no—
531C2×C4⋊C4C22⋊D6711yescharacteristic
532C2×C4⋊C4C22×D6711yescharacteristic
533C2×C4⋊C4C22×D6711yescharacteristic
534C2×C4⋊C4C22×D6714yes—
535C2×C4⋊C4C22×D6711yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—1341no—
541C2×C22⋊C4—1341no—
542C2×C22⋊C4—1341no—
543C2×C22⋊C4C22⋊D6711yescharacteristic
544C2×C22⋊C4C22⋊D6711yescharacteristic
545C2×C42—21no—
546C2×C42C22×D6711yescharacteristic
547#107—674no—
548#107—674no—
549#107—674no—
550#106—674no—
551#106—674no—
552#106—674no—
553#106—674no—
554#106—674no—
555#106—674no—
556C4⋊C8—674no—
557#102—674no—
558#102—674no—
559#102—674no—
560#102—674no—
561#102—674no—
562#102—674no—
563C22⋊C8—674no—
564C22⋊C8—674no—
565#97—674no—
566C24—21no—
567C24—1341no—
568C24C2×C22⋊D6711yescharacteristic
569C24C2×C22⋊D6711yescharacteristic
570#41—26832no—
571C2×Q8—2684no—
572C2×Q8—1344no—
573C2×D4—24no—
574C2×D4—24no—
575C2×D4—24no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—44no—
580C2×D4—82no—
581C2×D4—2684no—
582C2×D4—2684no—
583C2×D4—672no—
584C2×D4—1344no—
585C2×D4—1344no—
586C2×D4—1341no—
587C2×D4—1342no—
588C2×D4—1342no—
589C2×D4C2×C22⋊D6714yes—
590C2×D4C23×D6712yes—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—82no—
601C22×C4—82no—
602C22×C4—2684no—
603C22×C4—2684no—
604C22×C4—2684no—
605C22×C4—1344no—
606C22×C4—1344no—
607C22×C4—1341no—
608C22×C4—1341no—
609C22×C4—1341no—
610C22×C4—1344no—
611C22×C4C2×C22⋊D6712yes—
612C22×C4C2×C22⋊D6712yes—
613C22×C4C2×C22⋊D6711yescharacteristic
614C22×C4C2×C22⋊D6711yescharacteristic
615C22×C4C2×C22⋊D6711yescharacteristic
616C22×C4C2×C22⋊D6711yescharacteristic
617C22×C4C23×D6712yes—
618C22×C4C23×D6712yes—
619C22×C4C23×D6711yescharacteristic
620D8—1348no—
621M16—1348no—
622C2×C8—674no—
623C2×C8—672no—
624C2×C8—672no—
625C2×C8—672no—
626C2×C8—672no—
627C2×C8—1348no—
628C2×C8—1342no—
629C2×C8—1342no—
630C2×C8—1342no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—21no—
637C4⋊C4—672no—
638C4⋊C4—672no—
639C4⋊C4—672no—
640C4⋊C4—1341no—
641C4⋊C4—1341no—
642C4⋊C4—1341no—
643C4⋊C4—1344no—
644C4⋊C4—1344no—
645C4⋊C4—1344no—
646C4⋊C4C2×C22⋊D6714yes—
647C4⋊C4C23×D6712yes—
648C4⋊C4C23×D6712yes—
649C4⋊C4C23×D6712yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—1344no—
655C22⋊C4—1344no—
656C22⋊C4—1344no—
657C22⋊C4C2×C22⋊D6714yes—
658C22⋊C4C2×C22⋊D6714yes—
659C42—24no—
660C42C2×C22⋊D6712yes—
661C42C23×D6712yes—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—2682no—
672C23—2682no—
673C23—2682no—
674C23—1342no—
675C23#1452406814yes—
676C23C22×C22⋊D6712yes—
677C23C22×C22⋊D6712yes—
678C23C22×C22⋊D6711yescharacteristic
679Q8—2688no—
680D4—28no—
681D4—22no—
682D4—22no—
683D4—48no—
684D4—42no—
685D4—84no—
686D4—2688no—
687D4—2688no—
688D4—2682no—
689D4—1342no—
690D4—1342no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—84no—
708C2×C4—84no—
709C2×C4—2688no—
710C2×C4—2688no—
711C2×C4—2682no—
712C2×C4—2682no—
713C2×C4—2682no—
714C2×C4—2688no—
715C2×C4—1342no—
716C2×C4—1342no—
717C2×C4—1342no—
718C2×C4C22×C22⋊D6712yes—
719C2×C4C22×C22⋊D6712yes—
720C2×C4C22×C22⋊D6712yes—
721C2×C4C22×C22⋊D6712yes—
722C2×C4C22×C22⋊D6711yescharacteristic
723C2×C4#41×D6712yes—
724C2×C4#1452409012yes—
725C2×C4C24×D6711yescharacteristic
726C8—674no—
727C8—1342no—
728C8—1342no—
729C8—1342no—
730C22—22no—
731C22—22no—
732C22—28no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—44no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—84no—
741C22—2682no—
742C22—2682no—
743C22—2682no—
744C22—5364no—
745C22#1686404512yes—
746C22C2×#1452406814yes—
747C22C2×#1452406812yes—
748C22#1686420712yes—
749C22C23×C22⋊D6711yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—2682no—
758C4—2682no—
759C4—2682no—
760C4#1686404512yes—
761C4C2×#41×D6711yescharacteristic
762C4C2×#1452409011yescharacteristic
763C2—24no—
764C2—42no—
765C2—82no—
766C2—5362no—
767C2#2257267314yesdirect product factor
768C2C2×#1686404511yescharacteristic
769C2C22×#1452406811yescharacteristic
770C2C2×#1686420711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#553×C67C2
socleC23×C67C22×D4
hypercenterC2×#553D67
hypocenterC67C2×#3345
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#16864050C2semidirect
2. #22572673C2direct (N × H)
3. C2×#16863806C2semidirect
4. C2×#16863714C2semidirect
5. C2×#16863712C2semidirect
6. C2×#16863720C2semidirect
7. C2×#16863707C2semidirect
8. C2×#16863693C2semidirect
9. C2×#16863686C2semidirect
10. C2×#16863647C2semidirect
11. C2×#16863630C2semidirect
12. C2×#16863506C2semidirect
13. C2×#16863468C2semidirect
14. C2×#16863439C2semidirect
15. C22×#14523974C2semidirect
16. C2×#553×C67C2semidirect
22. #16864050C22semidirect
32. #16863806C22semidirect
33. #16863720C22semidirect
34. #16863714C22semidirect
35. #16863712C22semidirect
36. #16863707C22semidirect
37. #16863693C22semidirect
38. #16863686C22semidirect
39. #16863647C22semidirect
40. #16863630C22semidirect
41. #16863506C22semidirect
42. #16863468C22semidirect
43. #16863439C22semidirect
53. C2×#14523974C22semidirect
65. #553×C67C22semidirect
207. C2×C67⋊C8#41semidirect
343. C67⋊C8C2×#41semidirect
381. C2×C67#3345semidirect
386. C2×#553D67semidirect
402. C67C2×#3345semidirect
408. #553C2×D67semidirect
767. C2#22572673direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168640502
#225726732
C2×#168638062
C2×#168637142
C2×#168637122
C2×#168637202
C2×#168637072
C2×#168636932
C2×#168636862
C2×#168636472
C2×#168636302
C2×#168635062
C2×#168634682
C2×#168634392
C22×#145239742
C2×#553×C672
C2×#334567