Finite Group Databasebeta

← C2×#22569051 #31719939

Subgroups — C2×#22569051 #31719939

Order 17152.

2730 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524075C211yesmaximal, characteristic
2C2×#16863878C211yesmaximal, characteristic
3C2×#16863872C211yesmaximal, characteristic, complemented
4#22569051C2116yesmaximal, direct product factor
5C2×#16863500C211yesmaximal, characteristic, complemented
6C2×#16863499C211yesmaximal, characteristic, complemented
7C2×#16863498C211yesmaximal, characteristic, complemented
8C2×Q16×Dic67C211yesmaximal, characteristic, complemented
9C2×C4×#11761618C211yesmaximal, characteristic, complemented
10C2×C4×#11761615C211yesmaximal, characteristic, complemented
11C2×#16863483C211yesmaximal, characteristic, complemented
12C2×#16863435C211yesmaximal, characteristic, complemented
13C2×#16863391C211yesmaximal, characteristic
14C2×#103×D67C211yesmaximal, characteristic, complemented
15C2×#16863353C211yesmaximal, characteristic, complemented
16C2×#441×C67C211yesmaximal, characteristic, complemented
17C22×#11761629C2211yescharacteristic
18C22×Q8×D67C2211yescharacteristic
19C2×#14524075C4116yescomplemented
20C2×#14524075C2218yes—
21C22×#11761618C2211yescharacteristic
22C22×#11761617C2211yescharacteristic
23C22×#11761615C2211yescharacteristic
24C22×#11761611C2211yescharacteristic
25C22×C8×D67C2211yescharacteristic
26#16863878—24no—
27#16863878C2218yes—
28#16863872—24no—
29#16863872C2218yescomplemented
30C2×Q8×Dic67C2211yescharacteristic
31C2×Q8×Dic67C2211yescharacteristic
32C2×C4×Dic134—21no—
33C2×C4×Dic134C2211yescharacteristic
34C2×#14524008—21no—
35C2×#14524008C2211yescharacteristic
36C2×C4×D268—21no—
37C2×C4×D268C2211yescharacteristic
38C2×#14524005—21no—
39C2×#14524005C2211yescharacteristic
40C2×#14524001—21no—
41C2×#14524001C2211yescharacteristic
42C2×#14524000—21no—
43C2×#14524000—21no—
44C2×#14524000C2211yescharacteristic
45C2×C4⋊C4×D67—21no—
46C2×C4⋊C4×D67C2211yescharacteristic
47#16863500C2218yescomplemented
48#16863499C2218yescomplemented
49#16863498C2218yescomplemented
50Q16×Dic67C2218yescomplemented
51C4×#11761618C2218yescomplemented
52C4×#11761615C2218yescomplemented
53#16863483C2218yescomplemented
54#16863435C2218yescomplemented
55C2×#14523977C2211yescharacteristic
56C2×#14523976C2211yescharacteristic
57C2×#14523974C2211yescharacteristic
58#16863391C2218yes—
59C2×#14523968C2211yescharacteristic
60C2×#14523967C2211yescharacteristic
61C2×#14523967C2211yescharacteristic
62C2×#14523966C2211yescharacteristic
63#103×D67C2218yescomplemented
64C2×#14523965C2211yescharacteristic
65C2×#14523963C2211yescharacteristic
66#16863353C2218yescomplemented
67C2×#14523953C2211yescharacteristic
68C2×C4×C67⋊C8C2211yescharacteristic
69C2×C8×Dic67C2211yescharacteristic
70C22×Q16×C67C2211yescharacteristic
71C2×C4×Q8×C67C2211yescharacteristic
72C2×C4×Q8×C67C2211yescharacteristic
73#441×C67C2218yescomplemented
74C2×#106×C67C2211yescharacteristic
75C2×#103×C67C2211yescharacteristic
76C2×#103×C67C2211yescharacteristic
77C2×#97×C67C2211yescharacteristic
78C2×#11761629—22no—
79C2×#11761629—24no—
80C2×#11761629C2×C418yes—
81C2×#11761629C2314yes—
82C22×Dic134—21no—
83C22×Dic134C2311yescharacteristic
84C2×Q8×D67—22no—
85C2×Q8×D67—24no—
86C2×Q8×D67C2×C418yescomplemented
87C2×Q8×D67C2314yes—
88C22×D268—21no—
89C22×D268C2311yescharacteristic
90C22×C4×D67—21no—
91C22×C4×D67—21no—
92C22×C4×D67—21no—
93C22×C4×D67—21no—
94C22×C4×D67—21no—
95C22×C4×D67C2311yescharacteristic
96#14524075C2×C4164yescomplemented
97C2×#11761618C2×C418yescomplemented
98C2×#11761618C2314yes—
99C2×#11761617C2×C418yescomplemented
100C2×#11761617C2314yes—
101C2×#11761615C2×C418yescomplemented
102C2×#11761615C2314yes—
103C2×#11761611C2×C418yescomplemented
104C2×#11761611C2314yes—
105C22×C67⋊C8C2311yescharacteristic
106C22×C67⋊C8C2311yescharacteristic
107C2×C8×D67—24no—
108C2×C8×D67C2314yes—
109Q8×Dic67—22no—
110Q8×Dic67—22no—
111Q8×Dic67C2314yes—
112Q8×Dic67C2314yes—
113C4×Dic134—28no—
114C4×Dic134—22no—
115C4×Dic134C2314yes—
116#14524008—28no—
117#14524008—22no—
118#14524008C2314yes—
119C4×D268—28no—
120C4×D268—22no—
121C4×D268C2314yes—
122#14524005—28no—
123#14524005—22no—
124#14524005C2314yes—
125#14524001—22no—
126#14524001—28no—
127#14524001C2314yes—
128#14524000—28no—
129#14524000—28no—
130#14524000D414yes—
131#14524000C2314yes—
132C2×C4⋊Dic67—21no—
133C2×C4⋊Dic67—21no—
134C2×C4⋊Dic67C2311yescharacteristic
135C2×C4⋊Dic67C2311yescharacteristic
136C2×Dic67⋊C4—21no—
137C2×Dic67⋊C4—21no—
138C2×Dic67⋊C4—21no—
139C2×Dic67⋊C4D411yescharacteristic
140C2×Dic67⋊C4D411yescharacteristic
141C4⋊C4×D67—22no—
142C4⋊C4×D67—28no—
143C4⋊C4×D67C2314yes—
144C2×(C2×D67)⋊C4—21no—
145C2×(C2×D67)⋊C4—21no—
146C2×(C2×D67)⋊C4—21no—
147C2×(C2×D67)⋊C4D411yescharacteristic
148C2×(C2×D67)⋊C4D411yescharacteristic
149C2×C4×Dic67—21no—
150C2×C4×Dic67—21no—
151C2×C4×Dic67—21no—
152C2×C4×Dic67—21no—
153C2×C4×Dic67—21no—
154C2×C4×Dic67C2311yescharacteristic
155#14523977C2314yes—
156#14523976C2314yes—
157#14523974C2314yes—
158#14523968C2314yes—
159#14523967C2314yes—
160#14523967C2314yes—
161#14523966C2314yes—
162#14523965C2314yes—
163#14523963C2314yes—
164#14523953C2314yes—
165C4×C67⋊C8C2314yes—
166C8×Dic67C2314yes—
167C22×Q8×C67C2311yescharacteristic
168C22×Q8×C67C2311yescharacteristic
169C2×Q16×C67C2×C418yescomplemented
170C2×Q16×C67C2314yes—
171C22×C8×C67C2311yescharacteristic
172C22×C8×C67C2311yescharacteristic
173C4×Q8×C67—22no—
174C4×Q8×C67—22no—
175C4×Q8×C67C2314yes—
176C4×Q8×C67C2314yes—
177C2×C4⋊C4×C67—21no—
178C2×C4⋊C4×C67—21no—
179C2×C4⋊C4×C67C2311yescharacteristic
180C2×C4⋊C4×C67C2311yescharacteristic
181C2×C42×C67—21no—
182C2×C42×C67—21no—
183C2×C42×C67C2311yescharacteristic
184#106×C67C2314yes—
185#103×C67C2314yes—
186#103×C67C2314yes—
187#97×C67C2314yes—
188C23×D67—21no—
189C23×D67C2×D411yescharacteristic
190#11761629—216no—
191#11761629—28no—
192#11761629C22×C4116yes—
193C2×Dic134—21no—
194C2×Dic134—22no—
195C2×Dic134—28no—
196C2×Dic134—24no—
197C2×Dic134C22×C414yes—
198C2×Dic134C2412yes—
199Q8×D67—216no—
200Q8×D67—28no—
201Q8×D67C22×C4116yescomplemented
202C2×D268—28no—
203C2×D268—24no—
204C2×D268—21no—
205C2×D268—22no—
206C2×D268C22×C414yes—
207C2×D268C2412yes—
208C22×Dic67—21no—
209C22×Dic67—21no—
210C22×Dic67—21no—
211C22×Dic67C2×D411yescharacteristic
212C22×Dic67C2×D411yescharacteristic
213C22×Dic67C2×D411yescharacteristic
214C2×C4×D67—28no—
215C2×C4×D67—24no—
216C2×C4×D67—28no—
217C2×C4×D67—24no—
218C2×C4×D67—24no—
219C2×C4×D67—24no—
220C2×C4×D67—24no—
221C2×C4×D67—82no—
222C2×C4×D67—82no—
223C2×C4×D67—82no—
224C2×C4×D67C22×C414yes—
225C2×C4×D67C2×D412yes—
226C2×C4×D67#4114yes—
227C2×C4×D67C2412yes—
228#11761618C22×C4116yescomplemented
229#11761617C22×C4116yescomplemented
230#11761615C22×C4116yescomplemented
231#11761611C22×C4116yescomplemented
232C2×C67⋊C8—22no—
233C2×C67⋊C8C22×C414yes—
234C2×C67⋊C8C2412yes—
235C2×C67⋊C8C2412yes—
236C8×D67—28no—
237C4⋊Dic67—21no—
238C4⋊Dic67—21no—
239C4⋊Dic67—24no—
240C4⋊Dic67—24no—
241C4⋊Dic67C2412yes—
242C4⋊Dic67C2412yes—
243Dic67⋊C4—24no—
244Dic67⋊C4—24no—
245Dic67⋊C4—24no—
246Dic67⋊C4C2×D414yes—
247Dic67⋊C4C2×D414yes—
248(C2×D67)⋊C4—24no—
249(C2×D67)⋊C4—24no—
250(C2×D67)⋊C4—24no—
251(C2×D67)⋊C4C2×D414yes—
252(C2×D67)⋊C4C2×D414yes—
253C4×Dic67—24no—
254C4×Dic67—24no—
255C4×Dic67—24no—
256C4×Dic67—24no—
257C4×Dic67—24no—
258C4×Dic67C2×D412yes—
259C4×Dic67C2412yes—
260C2×Q8×C67—21no—
261C2×Q8×C67—21no—
262C2×Q8×C67—22no—
263C2×Q8×C67—22no—
264C2×Q8×C67C22×C414yes—
265C2×Q8×C67C22×C414yes—
266C2×Q8×C67C2412yes—
267C2×Q8×C67C2412yes—
268C22×C4×C67—21no—
269C22×C4×C67—21no—
270C22×C4×C67—21no—
271C22×C4×C67—21no—
272C22×C4×C67C2×D411yescharacteristic
273C22×C4×C67C2×D411yescharacteristic
274C22×C4×C67C2411yescharacteristic
275Q16×C67C22×C4116yescomplemented
276C2×C8×C67—22no—
277C2×C8×C67C22×C414yes—
278C2×C8×C67C2412yes—
279C2×C8×C67C2412yes—
280C4⋊C4×C67—24no—
281C4⋊C4×C67—24no—
282C4⋊C4×C67—21no—
283C4⋊C4×C67—21no—
284C4⋊C4×C67C2412yes—
285C4⋊C4×C67C2412yes—
286C42×C67—24no—
287C42×C67—24no—
288C42×C67C2×D412yes—
289C42×C67C2412yes—
290C23×C67C22×D411yescharacteristic
291C22×D67—22no—
292C22×D67—22no—
293C22×D67—24no—
294C22×D67—22no—
295C22×D67—42no—
296C22×D67—42no—
297C22×D67C4×D414yes—
298C22×D67C22×D412yes—
299Q8×C67—24no—
300Q8×C67—24no—
301Q8×C67—22no—
302Q8×C67—22no—
303Q8×C67C23×C414yes—
304Q8×C67C23×C414yes—
305C2×C4×C67—24no—
306C2×C4×C67—24no—
307C2×C4×C67—22no—
308C2×C4×C67—22no—
309C2×C4×C67—22no—
310C2×C4×C67—22no—
311C2×C4×C67—22no—
312C2×C4×C67—22no—
313C2×C4×C67—42no—
314C2×C4×C67—42no—
315C2×C4×C67C23×C412yes—
316C2×C4×C67C22×D412yes—
317C2×C4×C67C22×D412yes—
318C2×C4×C67C22×D411yescharacteristic
319C2×C4×C67C2×#4112yes—
320C2×C4×C67C2511yescharacteristic
321C2×Dic67—24no—
322C2×Dic67—22no—
323C2×Dic67—22no—
324C2×Dic67—22no—
325C2×Dic67—22no—
326C2×Dic67—22no—
327C2×Dic67—42no—
328C2×Dic67—42no—
329C2×Dic67C4×D414yes—
330C2×Dic67C22×D412yes—
331C2×Dic67C22×D412yes—
332C2×Dic67C22×D412yes—
333D268—216no—
334D268—24no—
335D268—22no—
336D268C23×C414yes—
337C4×D67—216no—
338C4×D67—216no—
339C4×D67—84no—
340C4×D67—84no—
341C4×D67—84no—
342C4×D67C4×D418yes—
343C4×D67C23×C414yes—
344C4×D67C2×#4114yes—
345Dic134—24no—
346Dic134—22no—
347Dic134—216no—
348Dic134C23×C414yes—
349C8×C67—22no—
350C8×C67C23×C414yes—
351C67⋊C8—22no—
352C67⋊C8C23×C414yes—
353C22×C67C2×C4×D412yes—
354C22×C67#57712yes—
355C22×C67#57812yes—
356C22×C67C23×D411yescharacteristic
357C2×D67—28no—
358C2×D67—22no—
359C2×D67—22no—
360C2×D67—24no—
361C2×D67—48no—
362C2×D67—42no—
363C2×D67—42no—
364C2×D67C2×C4×D414yes—
365C4×C67—24no—
366C4×C67—24no—
367C4×C67—22no—
368C4×C67—22no—
369C4×C67—42no—
370C4×C67—42no—
371C4×C67C2×C4×D412yes—
372C4×C67C24×C411yescharacteristic
373C4×C67C22×#4111yescharacteristic
374Dic67—24no—
375Dic67—22no—
376Dic67—22no—
377Dic67—42no—
378Dic67—42no—
379Dic67C2×C4×D414yes—
380C2×#2947—671nomaximal, Sylow
381C2×C67#294714yescomplemented
382C2×C67C22×C4×D411yescharacteristic
383C2×C67C2×#57711yescharacteristic
384C2×C67C2×#57811yescharacteristic
385D67—24no—
386D67—44no—
387C22×#137—671no—
388C2×#520—671no—
389C2×#519—671no—
390#2947—6716no—
391C2×#441—671no—
392C2×#441D6711yescharacteristic, complemented
393C2×#440—671no—
394C2×#440—671no—
395C2×C4×Q16—671no—
396C2×C4×Q16—671no—
397C2×C4×SD16—671no—
398C2×C4×SD16—671no—
399C2×#428—671no—
400C2×#416—671no—
401C22×#103—671no—
402C2×#405—671no—
403C67C2×#294711yescharacteristic, complemented, Sylow
404C22×#41—671no—
405C23×Q8—671no—
406C2×#137—6716no—
407C2×#137—678no—
408C22×Q16—671no—
409C22×Q16C2×D6711yescharacteristic
410C22×SD16—671no—
411C22×SD16—671no—
412C22×M16—671no—
413C23×C8—671no—
414#520—678no—
415#520—1344no—
416#519—678no—
417#519—1344no—
418C2×C4×Q8—671no—
419C2×C4×Q8—671no—
420C2×C4×Q8—671no—
421C2×C4×Q8—671no—
422C2×C4×Q8—1341no—
423C2×C4×Q8—1341no—
424C2×C4×Q8C2×D6711yescharacteristic
425C2×C4×Q8C2×D6711yescharacteristic
426C2×C4×D4—671no—
427C2×C4×D4—671no—
428C2×C4×D4—1341no—
429C2×C4×D4—1341no—
430C2×#117—671no—
431C2×#117—671no—
432C2×#117—1341no—
433C2×#117—1341no—
434C2×#117—1341no—
435C22×C4⋊C4—671no—
436C22×C4⋊C4—1341no—
437#441—678no—
438#441C2×D6718yescomplemented
439#440—678no—
440#440—678no—
441C4×Q16—678no—
442C4×Q16—678no—
443C4×SD16—678no—
444C4×SD16—678no—
445#428—678no—
446C2×#107—671no—
447C2×#107—671no—
448C2×#106—671no—
449C2×#106C2×D6711yescharacteristic
450#416—678no—
451C2×#103—671no—
452C2×#103—671no—
453C2×#103—671no—
454C2×#103—671no—
455C2×#103—678no—
456C2×#103C2×D6711yescharacteristic
457C2×#103C2×D6711yescharacteristic
458C2×#102—671no—
459C2×#102—671no—
460#405—678no—
461C2×#97—671no—
462C2×#97C2×D6711yescharacteristic
463C2×C4×C8—671no—
464C2×C4×C8—671no—
465C2×#41—678no—
466C2×#41—674no—
467C2×#41—1342no—
468C2×#41—1344no—
469C22×Q8—678no—
470C22×Q8—674no—
471C22×Q8—671no—
472C22×Q8—1341no—
473C22×Q8—1342no—
474C22×Q8—1344no—
475C22×Q8C22×D6711yescharacteristic
476C22×Q8C22×D6711yescharacteristic
477C22×D4—671no—
478C22×D4—1341no—
479C23×C4—671no—
480C23×C4—1341no—
481C23×C4—1341no—
482C23×C4—1341no—
483C23×C4—1341no—
484C23×C4—1341no—
485#137—6764no—
486C2×Q16—678no—
487C2×Q16—674no—
488C2×Q16C4×D6718yescomplemented
489C2×Q16C22×D6714yes—
490C2×SD16—678no—
491C2×SD16—674no—
492C2×SD16—678no—
493C2×SD16—674no—
494C2×M16—678no—
495C2×M16—674no—
496C22×C8—671no—
497C22×C8—671no—
498C22×C8—674no—
499C22×C8—1344no—
500C22×C8C22×D6711yescharacteristic
501C22×C8C22×D6711yescharacteristic
502C4×Q8—22no—
503C4×Q8—22no—
504C4×Q8—674no—
505C4×Q8—674no—
506C4×Q8—674no—
507C4×Q8—674no—
508C4×Q8—1348no—
509C4×Q8—1342no—
510C4×Q8—1342no—
511C4×Q8—1342no—
512C4×Q8—1348no—
513C4×Q8—1342no—
514C4×Q8C22×D6714yes—
515C4×Q8C22×D6714yes—
516C4×D4—674no—
517C4×D4—674no—
518C4×D4—1348no—
519C4×D4—1342no—
520C4×D4—1348no—
521C4×D4—1342no—
522#117—674no—
523#117—674no—
524#117—674no—
525#117—1348no—
526#117—1348no—
527#117—1348no—
528#117—1342no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—671no—
532C2×C4⋊C4—671no—
533C2×C4⋊C4—671no—
534C2×C4⋊C4—671no—
535C2×C4⋊C4—674no—
536C2×C4⋊C4—1348no—
537C2×C4⋊C4—1342no—
538C2×C4⋊C4—1341no—
539C2×C4⋊C4—1341no—
540C2×C4⋊C4—1341no—
541C2×C4⋊C4—1341no—
542C2×C4⋊C4—1341no—
543C2×C4⋊C4C22×D6711yescharacteristic
544C2×C4⋊C4C22×D6711yescharacteristic
545C2×C22⋊C4—671no—
546C2×C22⋊C4—671no—
547C2×C22⋊C4—1341no—
548C2×C22⋊C4—1341no—
549C2×C22⋊C4—1341no—
550C2×C42—21no—
551C2×C42—21no—
552C2×C42—671no—
553C2×C42—1341no—
554C2×C42—1341no—
555C2×C42—1341no—
556C2×C42—1341no—
557C2×C42—1341no—
558C2×C42C22×D6711yescharacteristic
559#107—674no—
560#107—674no—
561#106—674no—
562#106C22×D6714yes—
563#103—674no—
564#103—674no—
565#103—674no—
566#103—674no—
567#103C22×D6714yes—
568#103C22×D6714yes—
569#102—674no—
570#102—674no—
571#97—674no—
572#97C22×D6714yes—
573C4×C8—674no—
574C4×C8—674no—
575C24—671no—
576C24—1341no—
577#41—6716no—
578#41—13416no—
579#41—1348no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—6716no—
585C2×Q8—674no—
586C2×Q8—672no—
587C2×Q8—1344no—
588C2×Q8—1348no—
589C2×Q8—13416no—
590C2×Q8—1348no—
591C2×Q8—1341no—
592C2×Q8—1342no—
593C2×Q8C2×C4×D6714yes—
594C2×Q8C2×C4×D6714yes—
595C2×Q8C23×D6712yes—
596C2×Q8C23×D6712yes—
597C2×D4—674no—
598C2×D4—672no—
599C2×D4—1344no—
600C2×D4—1348no—
601C2×D4—1341no—
602C2×D4—1342no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—5362no—
608C22×C4—5362no—
609C22×C4—5362no—
610C22×C4—671no—
611C22×C4—674no—
612C22×C4—672no—
613C22×C4—674no—
614C22×C4—672no—
615C22×C4—671no—
616C22×C4—671no—
617C22×C4—1344no—
618C22×C4—1344no—
619C22×C4—1344no—
620C22×C4—1348no—
621C22×C4—1344no—
622C22×C4—1348no—
623C22×C4—1341no—
624C22×C4—1341no—
625C22×C4—1344no—
626C22×C4—1341no—
627C22×C4D4×D6711yescharacteristic
628C22×C4D4×D6711yescharacteristic
629C22×C4C23×D6711yescharacteristic
630Q16—6716no—
631Q16C2×C4×D67116yescomplemented
632SD16—6716no—
633SD16—6716no—
634M16—6716no—
635C2×C8—22no—
636C2×C8—674no—
637C2×C8—672no—
638C2×C8—672no—
639C2×C8—1348no—
640C2×C8—1342no—
641C2×C8C2×C4×D6714yes—
642C2×C8C23×D6712yes—
643C2×C8C23×D6712yes—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—674no—
649C4⋊C4—674no—
650C4⋊C4—672no—
651C4⋊C4—672no—
652C4⋊C4—1344no—
653C4⋊C4—1344no—
654C4⋊C4—1344no—
655C4⋊C4—1344no—
656C4⋊C4—1341no—
657C4⋊C4—1341no—
658C4⋊C4—1344no—
659C4⋊C4C23×D6712yes—
660C4⋊C4C23×D6712yes—
661C22⋊C4—674no—
662C22⋊C4—674no—
663C22⋊C4—1344no—
664C22⋊C4—1344no—
665C22⋊C4—1344no—
666C42—24no—
667C42—24no—
668C42—672no—
669C42—672no—
670C42—1344no—
671C42—1344no—
672C42—1344no—
673C42—1344no—
674C42—1344no—
675C42D4×D6712yes—
676C42C23×D6712yes—
677C23—2682no—
678C23—2682no—
679C23—674no—
680C23—672no—
681C23—1344no—
682C23—1342no—
683C23—1342no—
684C23—1342no—
685C23C2×D4×D6711yescharacteristic
686Q8—24no—
687Q8—24no—
688Q8—22no—
689Q8—22no—
690Q8—674no—
691Q8—13416no—
692Q8—1344no—
693Q8—1342no—
694Q8C22×C4×D6714yes—
695Q8C22×C4×D6714yes—
696D4—674no—
697D4—13416no—
698D4—1344no—
699D4—1342no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—2682no—
711C2×C4—2682no—
712C2×C4—5364no—
713C2×C4—5364no—
714C2×C4—5364no—
715C2×C4—674no—
716C2×C4—672no—
717C2×C4—678no—
718C2×C4—674no—
719C2×C4—674no—
720C2×C4—672no—
721C2×C4—672no—
722C2×C4—13416no—
723C2×C4—13416no—
724C2×C4—1342no—
725C2×C4—1342no—
726C2×C4—1344no—
727C2×C4—1342no—
728C2×C4—1342no—
729C2×C4—1342no—
730C2×C4C22×C4×D6712yes—
731C2×C4C2×D4×D6712yes—
732C2×C4C2×D4×D6712yes—
733C2×C4C2×D4×D6711yescharacteristic
734C2×C4#41×D6712yes—
735C2×C4C24×D6711yescharacteristic
736C8—22no—
737C8—674no—
738C8—1342no—
739C8C22×C4×D6714yes—
740C22—2688no—
741C22—2682no—
742C22—2682no—
743C22—674no—
744C22—1344no—
745C22—1348no—
746C22—1342no—
747C22—1342no—
748C22C4×D4×D6712yes—
749C22#1686420512yes—
750C22#1686421212yes—
751C22C22×D4×D6711yescharacteristic
752C4—24no—
753C4—24no—
754C4—22no—
755C4—22no—
756C4—42no—
757C4—42no—
758C4—2682no—
759C4—2682no—
760C4—674no—
761C4—1344no—
762C4—1342no—
763C4—1342no—
764C4C4×D4×D6712yes—
765C4C23×C4×D6711yescharacteristic
766C4C2×#41×D6711yescharacteristic
767C2—2684no—
768C2—1344no—
769C2#2256905114yesdirect product factor
770C2C2×C4×D4×D6711yescharacteristic
771C2C2×#1686420511yescharacteristic
772C2C2×#1686421211yescharacteristic
subgroupG/H
centerC23C2×D4×D67
commutatorC4×C67C24×C4
FrattiniC2×C4C24×D67
FittingC2×#441×C67C2
socleC23×C67C22×D4
prime radicalC22×#11761629C22
cosocleC2×C4×C67C25
hypercenterC2×#441D67
hypocenterC67C2×#2947
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
3. C2×#16863872C2semidirect
4. #22569051C2direct (N × H)
5. C2×#16863500C2semidirect
6. C2×#16863499C2semidirect
7. C2×#16863498C2semidirect
8. C2×Q16×Dic67C2semidirect
9. C2×C4×#11761618C2semidirect
10. C2×C4×#11761615C2semidirect
11. C2×#16863483C2semidirect
12. C2×#16863435C2semidirect
14. C2×#103×D67C2semidirect
15. C2×#16863353C2semidirect
16. C2×#441×C67C2semidirect
19. C2×#14524075C4semidirect
29. #16863872C22semidirect
47. #16863500C22semidirect
48. #16863499C22semidirect
49. #16863498C22semidirect
50. Q16×Dic67C22semidirect
51. C4×#11761618C22semidirect
52. C4×#11761615C22semidirect
53. #16863483C22semidirect
54. #16863435C22semidirect
63. #103×D67C22semidirect
66. #16863353C22semidirect
73. #441×C67C22semidirect
86. C2×Q8×D67C2×C4semidirect
96. #14524075C2×C4semidirect
97. C2×#11761618C2×C4semidirect
99. C2×#11761617C2×C4semidirect
101. C2×#11761615C2×C4semidirect
103. C2×#11761611C2×C4semidirect
169. C2×Q16×C67C2×C4semidirect
201. Q8×D67C22×C4semidirect
228. #11761618C22×C4semidirect
229. #11761617C22×C4semidirect
230. #11761615C22×C4semidirect
231. #11761611C22×C4semidirect
275. Q16×C67C22×C4semidirect
381. C2×C67#2947semidirect
392. C2×#441D67semidirect
403. C67C2×#2947semidirect
438. #441C2×D67semidirect
488. C2×Q16C4×D67semidirect
631. Q16C2×C4×D67semidirect
769. C2#22569051direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240752
C2×#168638782
C2×#168638722
#225690512
C2×#168635002
C2×#168634992
C2×#168634982
C2×Q16×Dic672
C2×C4×#117616182
C2×C4×#117616152
C2×#168634832
C2×#168634352
C2×#168633912
C2×#103×D672
C2×#168633532
C2×#441×C672
C2×#294767