Finite Group Databasebeta

← C2×#22572809 #31734553

Subgroups — C2×#22572809 #31734553

Order 17152.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864092C211yesmaximal, characteristic, complemented
2#22572809C2116yesmaximal, direct product factor
3C2×#16863795C211yesmaximal, characteristic, complemented
4C2×#16863720C211yesmaximal, characteristic, complemented
5C2×#16863717C211yesmaximal, characteristic, complemented
6C2×#16863709C211yesmaximal, characteristic, complemented
7C2×#16863707C211yesmaximal, characteristic, complemented
8C2×#16863696C211yesmaximal, characteristic, complemented
9C2×#16863693C211yesmaximal, characteristic, complemented
10C2×#16863647C211yesmaximal, characteristic, complemented
11C2×#16863647C211yesmaximal, characteristic, complemented
12C2×C4×#11761613C211yesmaximal, characteristic, complemented
13C2×#16863474C211yesmaximal, characteristic, complemented
14C2×#16863439C211yesmaximal, characteristic, complemented
15C2×#16863436C211yesmaximal, characteristic, complemented
16C2×#553×C67C211yesmaximal, characteristic, complemented
17C22×#11761613C2211yescharacteristic
18C22×#11761612C2211yescharacteristic
19C22×#11761612C2211yescharacteristic
20#16864092—24no—
21#16864092C2218yescomplemented
22C2×#14524038—21no—
23C2×#14524035C2211yescharacteristic
24C2×#14524025—21no—
25C2×#14524017C2211yescharacteristic
26C2×#14524017C2211yescharacteristic
27C2×#14524015—21no—
28C2×C4×D268C2211yescharacteristic
29C2×(C22⋊D67)⋊C4—21no—
30C2×#14524002C2211yescharacteristic
31C22×C4⋊Dic67C2211yescharacteristic
32#16863795C2218yescomplemented
33#16863720C2218yescomplemented
34#16863717C2218yescomplemented
35#16863709C2218yescomplemented
36#16863707C2218yescomplemented
37#16863696C2218yescomplemented
38#16863693C2218yescomplemented
39#16863647C2218yescomplemented
40#16863647C2218yescomplemented
41C4×#11761613C2218yescomplemented
42#16863474C2218yescomplemented
43#16863439C2218yescomplemented
44#16863436C2218yescomplemented
45C2×#14523976C2211yescharacteristic
46C2×#14523976C2211yescharacteristic
47C2×#14523976C2211yescharacteristic
48C2×#14523976C2211yescharacteristic
49C2×#14523976C2211yescharacteristic
50C2×#14523974C2211yescharacteristic
51C2×#14523974C2211yescharacteristic
52C2×#14523974C2211yescharacteristic
53C2×#14523974C2211yescharacteristic
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×C4×C67⋊C8C2211yescharacteristic
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
77C22×D268C2311yescharacteristic
78C22×C22⋊D67—21no—
79C22×C22⋊D67—21no—
80C23×Dic67—21no—
81C22×C4×D67—21no—
82C2×#11761613—24no—
83C2×#11761613C2314yes—
84C2×#11761612—24no—
85C2×#11761612—24no—
86C2×#11761612C2314yes—
87C2×#11761612C2314yes—
88C22×C67⋊C8C2311yescharacteristic
89C22×C67⋊C8C2311yescharacteristic
90C22×C67⋊C8C2311yescharacteristic
91C22×C67⋊C8C2311yescharacteristic
92#14524038—28no—
93#14524035—22no—
94#14524035C2314yes—
95#14524025—28no—
96#14524017—22no—
97#14524017—22no—
98#14524017C2314yes—
99#14524017C2314yes—
100#14524015—28no—
101C4×D268—22no—
102C4×D268C2314yes—
103(C22⋊D67)⋊C4—28no—
104#14524002—22no—
105#14524002C2314yes—
106C2×C4⋊Dic67—22no—
107C2×C4⋊Dic67—21no—
108C2×C4⋊Dic67C2314yes—
109C2×C4⋊Dic67C2311yescharacteristic
110C2×C4⋊Dic67C2311yescharacteristic
111C2×C4⋊Dic67C2311yescharacteristic
112C2×Dic67⋊C4—21no—
113C2×Dic67⋊C4—21no—
114C2×C22⋊Dic67—21no—
115C2×(C2×D67)⋊C4—21no—
116C2×(C2×D67)⋊C4—21no—
117C2×(C2×D67)⋊C4—21no—
118C2×C4×Dic67—21no—
119#14523976C2314yes—
120#14523976C2314yes—
121#14523976C2314yes—
122#14523976C2314yes—
123#14523976C2314yes—
124#14523974C2314yes—
125#14523974C2314yes—
126#14523974C2314yes—
127#14523974C2314yes—
128C4⋊(C67⋊C8)C2314yes—
129#14523964C2314yes—
130#14523964C2314yes—
131#14523964C2314yes—
132#14523963C2314yes—
133#14523963C2314yes—
134#14523963C2314yes—
135C22⋊(C67⋊C8)C2314yes—
136C22⋊(C67⋊C8)C2314yes—
137C4×C67⋊C8C2314yes—
138C22×D4×C67—21no—
139C22×D4×C67—21no—
140C22×D4×C67D411yescharacteristic
141C22×D4×C67C2311yescharacteristic
142C23×C4×C67—21no—
143C23×C4×C67—21no—
144C23×C4×C67C2311yescharacteristic
145C23×C4×C67C2311yescharacteristic
146#126×C67—28no—
147#125×C67—22no—
148#125×C67C2314yes—
149#123×C67—28no—
150#121×C67—28no—
151#121×C67—22no—
152#121×C67—22no—
153#121×C67C2314yes—
154#121×C67C2314yes—
155C4×D4×C67—28no—
156C4×D4×C67—22no—
157C4×D4×C67D414yes—
158C4×D4×C67C2314yes—
159C4×D4×C67C2314yes—
160#117×C67—22no—
161#117×C67C2314yes—
162C2×C4⋊C4×C67—21no—
163C2×C4⋊C4×C67—22no—
164C2×C4⋊C4×C67—21no—
165C2×C4⋊C4×C67—21no—
166C2×C4⋊C4×C67D411yescharacteristic
167C2×C4⋊C4×C67C2311yescharacteristic
168C2×C4⋊C4×C67C2311yescharacteristic
169C2×C4⋊C4×C67C2314yes—
170C2×C4⋊C4×C67C2311yescharacteristic
171C2×C22⋊C4×C67—21no—
172C2×C22⋊C4×C67—21no—
173C2×C22⋊C4×C67—21no—
174C2×C22⋊C4×C67—21no—
175C2×C22⋊C4×C67D411yescharacteristic
176C2×C22⋊C4×C67D411yescharacteristic
177C2×C42×C67—21no—
178C2×C42×C67C2311yescharacteristic
179C23×D67—21no—
180C2×D268—22no—
181C2×D268—22no—
182C2×D268—21no—
183C2×D268C2412yes—
184C2×C22⋊D67—24no—
185C2×C22⋊D67—24no—
186C2×C22⋊D67—44no—
187C2×C22⋊D67—82no—
188C22×Dic67—21no—
189C22×Dic67—21no—
190C22×Dic67—21no—
191C22×Dic67—24no—
192C22×Dic67—82no—
193C2×C4×D67—24no—
194C2×C4×D67—82no—
195#11761613—28no—
196#11761612—28no—
197#11761612—28no—
198C2×C67⋊C8—22no—
199C2×C67⋊C8—22no—
200C2×C67⋊C8—22no—
201C2×C67⋊C8#4114yes—
202C2×C67⋊C8C2412yes—
203C2×C67⋊C8C2412yes—
204C2×C67⋊C8C2412yes—
205C2×C67⋊C8C2412yes—
206C4⋊Dic67—21no—
207C4⋊Dic67—21no—
208C4⋊Dic67—24no—
209C4⋊Dic67—21no—
210C4⋊Dic67C2412yes—
211C4⋊Dic67C2412yes—
212C4⋊Dic67C2412yes—
213Dic67⋊C4—24no—
214Dic67⋊C4—24no—
215C22⋊Dic67—24no—
216(C2×D67)⋊C4—24no—
217(C2×D67)⋊C4—24no—
218(C2×D67)⋊C4—24no—
219C4×Dic67—24no—
220C24×C67—21no—
221C24×C67C2×D411yescharacteristic
222C24×C67C2×D411yescharacteristic
223C2×D4×C67—24no—
224C2×D4×C67—24no—
225C2×D4×C67—21no—
226C2×D4×C67—22no—
227C2×D4×C67—22no—
228C2×D4×C67—42no—
229C2×D4×C67—44no—
230C2×D4×C67—82no—
231C2×D4×C67C2×D414yes—
232C2×D4×C67C2412yes—
233C22×C4×C67—22no—
234C22×C4×C67—22no—
235C22×C4×C67—22no—
236C22×C4×C67—22no—
237C22×C4×C67—21no—
238C22×C4×C67—21no—
239C22×C4×C67—21no—
240C22×C4×C67—24no—
241C22×C4×C67—24no—
242C22×C4×C67—82no—
243C22×C4×C67—82no—
244C22×C4×C67C2×D411yescharacteristic
245C22×C4×C67C2×D411yescharacteristic
246C22×C4×C67C2×D411yescharacteristic
247C22×C4×C67C2×D411yescharacteristic
248C22×C4×C67C2×D412yes—
249C22×C4×C67C2×D412yes—
250C22×C4×C67C2412yes—
251C22×C4×C67C2412yes—
252C22×C4×C67C2411yescharacteristic
253C4⋊C4×C67—21no—
254C4⋊C4×C67—21no—
255C4⋊C4×C67—24no—
256C4⋊C4×C67—24no—
257C4⋊C4×C67—24no—
258C4⋊C4×C67—21no—
259C4⋊C4×C67C2×D414yes—
260C4⋊C4×C67C2412yes—
261C4⋊C4×C67C2412yes—
262C4⋊C4×C67C2412yes—
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×C67C2412yes—
272C23×C67—22no—
273C23×C67—22no—
274C23×C67—22no—
275C23×C67—22no—
276C23×C67—22no—
277C23×C67—22no—
278C23×C67—22no—
279C23×C67—42no—
280C23×C67—42no—
281C23×C67—42no—
282C23×C67C22×D412yes—
283C23×C67C22×D412yes—
284C23×C67C22×D411yescharacteristic
285C22×D67—22no—
286C22×D67—42no—
287C22×D67—42no—
288C22×D67—42no—
289D4×C67—22no—
290D4×C67—22no—
291D4×C67—44no—
292D4×C67—48no—
293D4×C67—42no—
294D4×C67—84no—
295C2×C4×C67—22no—
296C2×C4×C67—22no—
297C2×C4×C67—22no—
298C2×C4×C67—22no—
299C2×C4×C67—24no—
300C2×C4×C67—24no—
301C2×C4×C67—22no—
302C2×C4×C67—22no—
303C2×C4×C67—22no—
304C2×C4×C67—22no—
305C2×C4×C67—22no—
306C2×C4×C67—22no—
307C2×C4×C67—22no—
308C2×C4×C67—42no—
309C2×C4×C67—42no—
310C2×C4×C67—42no—
311C2×C4×C67—84no—
312C2×C4×C67—84no—
313C2×C4×C67C22×D412yes—
314C2×C4×C67C22×D412yes—
315C2×C4×C67C22×D412yes—
316C2×C4×C67C22×D412yes—
317C2×C4×C67C22×D411yescharacteristic
318C2×C4×C67C2×#4112yes—
319C2×C4×C672−1+412yes—
320C2×C4×C67C2511yescharacteristic
321C22⋊D67—48no—
322C22⋊D67—84no—
323C2×Dic67—22no—
324C2×Dic67—22no—
325C2×Dic67—22no—
326C2×Dic67—42no—
327C2×Dic67—42no—
328C2×Dic67—42no—
329C2×Dic67—84no—
330D268—22no—
331D268—22no—
332D268—42no—
333C4×D67—84no—
334C67⋊C8—22no—
335C67⋊C8—22no—
336C67⋊C8—22no—
337C67⋊C8C2×#4114yes—
338C22×C67—22no—
339C22×C67—22no—
340C22×C67—22no—
341C22×C67—22no—
342C22×C67—22no—
343C22×C67—22no—
344C22×C67—44no—
345C22×C67—44no—
346C22×C67—42no—
347C22×C67—42no—
348C22×C67—42no—
349C22×C67—84no—
350C22×C67#54712yes—
351C22×C67#57512yes—
352C22×C67#57612yes—
353C22×C67C23×D411yescharacteristic
354C2×D67—42no—
355C2×D67—42no—
356C2×D67—42no—
357C2×D67—84no—
358C4×C67—22no—
359C4×C67—22no—
360C4×C67—22no—
361C4×C67—22no—
362C4×C67—42no—
363C4×C67—42no—
364C4×C67—42no—
365C4×C67#54712yes—
366C4×C67C22×#4111yescharacteristic
367C4×C67C2×2−1+411yescharacteristic
368Dic67—42no—
369Dic67—42no—
370Dic67—42no—
371C2×#3355—671nomaximal, Sylow
372C2×C67—42no—
373C2×C67—42no—
374C2×C67—82no—
375C2×C67#335514yescomplemented
376C2×C67C2×#54711yescharacteristic
377C2×C67C2×#57511yescharacteristic
378C2×C67C2×#57611yescharacteristic
379D67—82no—
380C2×#553—671no—
381C2×#553D6711yescharacteristic, complemented
382#3355—6716no—
383C2×#499—671no—
384C2×#482—671no—
385C2×#482—671no—
386C2×#480—671no—
387C2×#480—671no—
388C2×#478—671no—
389C2×#478—671no—
390C2×#469—671no—
391C2×#469—671no—
392C2×C4×D8—671no—
393C2×#436—671no—
394C2×#428—671no—
395C2×#428—671no—
396C67C2×#335511yescharacteristic, complemented, Sylow
397C22×D8—671no—
398C22×M16—671no—
399C22×M16—671no—
400#553—24no—
401#553—678no—
402#553—1344no—
403#553C2×D6718yescomplemented
404C2×#126—21no—
405C2×#126—1341no—
406C2×#125—671no—
407C2×#125C2×D6711yescharacteristic
408C2×#123—21no—
409C2×#123—1341no—
410C2×#121—21no—
411C2×#121—671no—
412C2×#121—671no—
413C2×#121—1341no—
414C2×#121C2×D6711yescharacteristic
415C2×#121C2×D6711yescharacteristic
416C2×C4×D4—21no—
417C2×C4×D4—671no—
418C2×C4×D4—1341no—
419C2×C4×D4C2×D6711yescharacteristic
420C2×C4×D4C2×D6711yescharacteristic
421C2×#117—671no—
422C2×#117C2×D6711yescharacteristic
423C22×C4⋊C4—671no—
424C22×C4⋊C4C2×D6711yescharacteristic
425#499—678no—
426#482—678no—
427#482—678no—
428#480—678no—
429#480—678no—
430#478—678no—
431#478—678no—
432#469—678no—
433#469—678no—
434C4×D8—678no—
435#436—678no—
436#428—678no—
437#428—678no—
438C2×#107—671no—
439C2×#107—671no—
440C2×#107—671no—
441C2×#107—671no—
442C2×#107—671no—
443C2×#106—671no—
444C2×#106—671no—
445C2×#106—671no—
446C2×#106—671no—
447C2×C4⋊C8—671no—
448C2×#102—671no—
449C2×#102—671no—
450C2×#102—671no—
451C2×#102—671no—
452C2×#102—671no—
453C2×#102—671no—
454C2×C22⋊C8—671no—
455C2×C22⋊C8—671no—
456C2×C4×C8—671no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—671no—
460C22×D4—1341no—
461C22×D4—1341no—
462C22×D4C22⋊D6711yescharacteristic
463C22×D4C22×D6711yescharacteristic
464C23×C4—21no—
465C23×C4—21no—
466C23×C4—1341no—
467C23×C4—1341no—
468C23×C4C22×D6711yescharacteristic
469C23×C4C22×D6711yescharacteristic
470C2×D8—674no—
471C2×D8—1344no—
472C2×M16—674no—
473C2×M16—674no—
474C2×M16—1344no—
475C2×M16—1344no—
476C22×C8—671no—
477C22×C8—671no—
478C22×C8—671no—
479C22×C8—671no—
480#126—28no—
481#126—1348no—
482#125—22no—
483#125—674no—
484#125—1342no—
485#125C22×D6714yes—
486#123—28no—
487#123—1348no—
488#121—28no—
489#121—22no—
490#121—22no—
491#121—674no—
492#121—674no—
493#121—1348no—
494#121—1342no—
495#121—1342no—
496#121C22×D6714yes—
497#121C22×D6714yes—
498C4×D4—28no—
499C4×D4—22no—
500C4×D4—674no—
501C4×D4—1348no—
502C4×D4—1342no—
503C4×D4C22⋊D6714yes—
504C4×D4C22×D6714yes—
505C4×D4C22×D6714yes—
506#117—22no—
507#117—674no—
508#117—1342no—
509#117C22×D6714yes—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—671no—
515C2×C4⋊C4—671no—
516C2×C4⋊C4—674no—
517C2×C4⋊C4—671no—
518C2×C4⋊C4—1341no—
519C2×C4⋊C4—1342no—
520C2×C4⋊C4—1341no—
521C2×C4⋊C4—1341no—
522C2×C4⋊C4C22⋊D6711yescharacteristic
523C2×C4⋊C4C22×D6711yescharacteristic
524C2×C4⋊C4C22×D6711yescharacteristic
525C2×C4⋊C4C22×D6714yes—
526C2×C4⋊C4C22×D6711yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—1341no—
532C2×C22⋊C4—1341no—
533C2×C22⋊C4—1341no—
534C2×C22⋊C4—1341no—
535C2×C22⋊C4C22⋊D6711yescharacteristic
536C2×C22⋊C4C22⋊D6711yescharacteristic
537C2×C42—21no—
538C2×C42—1341no—
539C2×C42C22×D6711yescharacteristic
540#107—674no—
541#107—674no—
542#107—674no—
543#107—674no—
544#107—674no—
545#106—674no—
546#106—674no—
547#106—674no—
548#106—674no—
549C4⋊C8—674no—
550#102—674no—
551#102—674no—
552#102—674no—
553#102—674no—
554#102—674no—
555#102—674no—
556C22⋊C8—674no—
557C22⋊C8—674no—
558C4×C8—674no—
559C24—21no—
560C24—1341no—
561C24C2×C22⋊D6711yescharacteristic
562C24C2×C22⋊D6711yescharacteristic
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—42no—
569C2×D4—44no—
570C2×D4—82no—
571C2×D4—2684no—
572C2×D4—5362no—
573C2×D4—672no—
574C2×D4—1344no—
575C2×D4—1344no—
576C2×D4—1341no—
577C2×D4—1342no—
578C2×D4—1342no—
579C2×D4C2×C22⋊D6714yes—
580C2×D4C23×D6712yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—82no—
591C22×C4—82no—
592C22×C4—5362no—
593C22×C4—5362no—
594C22×C4—1341no—
595C22×C4—1341no—
596C22×C4—1341no—
597C22×C4—1344no—
598C22×C4—1344no—
599C22×C4C2×C22⋊D6712yes—
600C22×C4C2×C22⋊D6712yes—
601C22×C4C2×C22⋊D6711yescharacteristic
602C22×C4C2×C22⋊D6711yescharacteristic
603C22×C4C2×C22⋊D6711yescharacteristic
604C22×C4C2×C22⋊D6711yescharacteristic
605C22×C4C23×D6712yes—
606C22×C4C23×D6712yes—
607C22×C4C23×D6711yescharacteristic
608D8—1348no—
609M16—1348no—
610M16—1348no—
611C2×C8—674no—
612C2×C8—672no—
613C2×C8—672no—
614C2×C8—672no—
615C2×C8—672no—
616C2×C8—1342no—
617C2×C8—1342no—
618C2×C8—1342no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—21no—
625C4⋊C4—672no—
626C4⋊C4—672no—
627C4⋊C4—672no—
628C4⋊C4—1341no—
629C4⋊C4—1341no—
630C4⋊C4—1344no—
631C4⋊C4—1341no—
632C4⋊C4—1344no—
633C4⋊C4—1344no—
634C4⋊C4C2×C22⋊D6714yes—
635C4⋊C4C23×D6712yes—
636C4⋊C4C23×D6712yes—
637C4⋊C4C23×D6712yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—1344no—
643C22⋊C4—1344no—
644C22⋊C4—1344no—
645C22⋊C4—1344no—
646C22⋊C4C2×C22⋊D6714yes—
647C22⋊C4C2×C22⋊D6714yes—
648C42—24no—
649C42—1344no—
650C42C2×C22⋊D6712yes—
651C42C23×D6712yes—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—2682no—
663C23—2682no—
664C23—2682no—
665C23—1342no—
666C23C22×C22⋊D6712yes—
667C23C22×C22⋊D6712yes—
668C23C22×C22⋊D6711yescharacteristic
669D4—22no—
670D4—22no—
671D4—44no—
672D4—48no—
673D4—42no—
674D4—84no—
675D4—2688no—
676D4—2682no—
677D4—5364no—
678D4—1342no—
679D4—1342no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—84no—
697C2×C4—84no—
698C2×C4—2682no—
699C2×C4—2682no—
700C2×C4—2682no—
701C2×C4—5364no—
702C2×C4—5364no—
703C2×C4—1342no—
704C2×C4—1342no—
705C2×C4—1342no—
706C2×C4C22×C22⋊D6712yes—
707C2×C4C22×C22⋊D6712yes—
708C2×C4C22×C22⋊D6712yes—
709C2×C4C22×C22⋊D6712yes—
710C2×C4C22×C22⋊D6711yescharacteristic
711C2×C4#41×D6712yes—
712C2×C4#1452409012yes—
713C2×C4C24×D6711yescharacteristic
714C8—674no—
715C8—1342no—
716C8—1342no—
717C8—1342no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—44no—
725C22—44no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—84no—
730C22—2682no—
731C22—2682no—
732C22—2682no—
733C22—5364no—
734C22#1686404512yes—
735C22#1686419412yes—
736C22#1686419912yes—
737C22C23×C22⋊D6711yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—42no—
743C4—42no—
744C4—42no—
745C4—2682no—
746C4—2682no—
747C4—2682no—
748C4#1686404512yes—
749C4C2×#41×D6711yescharacteristic
750C4C2×#1452409011yescharacteristic
751C2—42no—
752C2—42no—
753C2—82no—
754C2—5362no—
755C2#2257280914yesdirect product factor
756C2C2×#1686404511yescharacteristic
757C2C2×#1686419411yescharacteristic
758C2C2×#1686419911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#553×C67C2
socleC23×C67C22×D4
hypercenterC2×#553D67
hypocenterC67C2×#3355
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×#16864092C2semidirect
2. #22572809C2direct (N × H)
3. C2×#16863795C2semidirect
4. C2×#16863720C2semidirect
5. C2×#16863717C2semidirect
6. C2×#16863709C2semidirect
7. C2×#16863707C2semidirect
8. C2×#16863696C2semidirect
9. C2×#16863693C2semidirect
10. C2×#16863647C2semidirect
11. C2×#16863647C2semidirect
12. C2×C4×#11761613C2semidirect
13. C2×#16863474C2semidirect
14. C2×#16863439C2semidirect
15. C2×#16863436C2semidirect
16. C2×#553×C67C2semidirect
21. #16864092C22semidirect
32. #16863795C22semidirect
33. #16863720C22semidirect
34. #16863717C22semidirect
35. #16863709C22semidirect
36. #16863707C22semidirect
37. #16863696C22semidirect
38. #16863693C22semidirect
39. #16863647C22semidirect
40. #16863647C22semidirect
41. C4×#11761613C22semidirect
42. #16863474C22semidirect
43. #16863439C22semidirect
44. #16863436C22semidirect
65. #553×C67C22semidirect
375. C2×C67#3355semidirect
381. C2×#553D67semidirect
396. C67C2×#3355semidirect
403. #553C2×D67semidirect
755. C2#22572809direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168640922
#225728092
C2×#168637952
C2×#168637202
C2×#168637172
C2×#168637092
C2×#168637072
C2×#168636962
C2×#168636932
C2×#168636472
C2×C4×#117616132
C2×#168634742
C2×#168634392
C2×#168634362
C2×#553×C672
C2×#335567