Finite Group Databasebeta

← C2×#22570395 #31724064

Subgroups — C2×#22570395 #31724064

Order 17152.

2274 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864017C211yesmaximal, characteristic, complemented
2C2×#16863870C211yesmaximal, characteristic, complemented
3#22570395C2116yesmaximal, direct product factor
4C2×#16863738C211yesmaximal, characteristic, complemented
5C2×#16863721C211yesmaximal, characteristic, complemented
6C2×#16863687C211yesmaximal, characteristic, complemented
7C2×#16863677C211yesmaximal, characteristic, complemented
8C2×#16863612C211yesmaximal, characteristic, complemented
9C2×#16863612C211yesmaximal, characteristic, complemented
10C2×#16863549C211yesmaximal, characteristic, complemented
11C2×#16863532C211yesmaximal, characteristic
12C2×#16863509C211yesmaximal, characteristic, complemented
13C2×#16863498C211yesmaximal, characteristic, complemented
14C2×C4×#11761617C211yesmaximal, characteristic, complemented
15C2×C4×D536C211yesmaximal, characteristic, complemented
16C2×#433×C67C211yesmaximal, characteristic, complemented
17C23×D268C2211yescharacteristic
18C22×#11761617C2211yescharacteristic
19C22×#11761617C2211yescharacteristic
20C22×D536C2211yescharacteristic
21C22×D536C2211yescharacteristic
22#16864017—24no—
23#16864017C2218yescomplemented
24C2×#14524043C2211yescharacteristic, complemented
25C2×#14524038—21no—
26C2×#14524031C2211yescharacteristic, complemented
27C2×#14524029—21no—
28C2×#14524025—21no—
29C2×#14524022C2211yescharacteristic
30C2×#14524021—21no—
31C2×#14524017C2211yescharacteristic
32#16863870—24no—
33#16863870C2218yescomplemented
34C2×C4×Dic134C2211yescharacteristic, complemented
35C2×C4×D268C2211yescharacteristic
36C2×C4×D268C2211yescharacteristic
37C2×C4×D268C2211yescharacteristic
38C2×C4×D268C2211yescharacteristic
39C2×C4×D268C2211yescharacteristic, complemented
40C2×#14524005—21no—
41C2×#14524005—21no—
42C2×#14524002C2211yescharacteristic
43C2×C22⋊C4×D67—21no—
44C2×C22⋊C4×D67—21no—
45#16863738C2218yescomplemented
46#16863721C2218yescomplemented
47#16863687C2218yescomplemented
48#16863677C2218yescomplemented
49#16863612C2218yescomplemented
50#16863612C2218yescomplemented
51#16863549C2218yescomplemented
52#16863532C2218yes—
53#16863509C2218yescomplemented
54#16863498C2218yescomplemented
55C4×#11761617C2218yescomplemented
56C4×D536C2218yescomplemented
57C2×#14523977C2211yescharacteristic, complemented
58C2×#14523977C2211yescharacteristic, complemented
59C2×#14523975C2211yescharacteristic, complemented
60C2×#14523975C2211yescharacteristic, complemented
61C2×#14523968C2211yescharacteristic, complemented
62C2×#14523968C2211yescharacteristic, complemented
63C2×#14523965C2211yescharacteristic
64C2×#14523965C2211yescharacteristic
65C2×#14523965C2211yescharacteristic
66C2×#14523965C2211yescharacteristic
67C2×#14523965C2211yescharacteristic, complemented
68C2×#14523965C2211yescharacteristic, complemented
69C2×#117×C67C2211yescharacteristic
70#433×C67C2218yescomplemented
71C2×C4⋊C8×C67C2211yescharacteristic, complemented
72C2×C4⋊C8×C67C2211yescharacteristic, complemented
73C2×C22⋊C8×C67C2211yescharacteristic
74C2×C22⋊C8×C67C2211yescharacteristic
75C2×#97×C67C2211yescharacteristic, complemented
76C2×C4×C8×C67C2211yescharacteristic, complemented
77C24×D67—21no—
78C22×Dic134—21no—
79C22×Dic134C2311yescharacteristic
80C22×D268—24no—
81C22×D268—24no—
82C22×D268—21no—
83C22×D268—22no—
84C22×D268C2314yes—
85C22×D268C2311yescharacteristic
86C22×D268C2311yescharacteristic
87C22×D268C2311yescharacteristic
88C22×C22⋊D67—21no—
89C22×C4×D67—21no—
90C22×C4×D67—21no—
91C22×C4×D67—21no—
92C22×C4×D67—21no—
93C22×C4×D67—21no—
94C2×#11761617—24no—
95C2×#11761617—24no—
96C2×#11761617C2314yes—
97C2×#11761617C2314yes—
98C2×D536—24no—
99C2×D536—24no—
100C2×D536C2314yes—
101C2×D536C2314yes—
102#14524043—22no—
103#14524043C2314yescomplemented
104#14524038—28no—
105#14524031—22no—
106#14524031C2314yescomplemented
107#14524029—28no—
108#14524025—28no—
109#14524022—22no—
110#14524022C2314yes—
111#14524021—28no—
112#14524017—22no—
113#14524017C2314yes—
114C4×Dic134—22no—
115C4×Dic134C2314yescomplemented
116C4×D268—22no—
117C4×D268—22no—
118C4×D268—22no—
119C4×D268—22no—
120C4×D268—22no—
121C4×D268C2314yes—
122C4×D268C2314yes—
123C4×D268C2314yes—
124C4×D268C2314yes—
125C4×D268C2314yescomplemented
126#14524005—28no—
127#14524005—28no—
128#14524002—22no—
129#14524002C2314yes—
130C2×C4⋊Dic67—21no—
131C2×C4⋊Dic67C2311yescharacteristic
132C2×C4⋊Dic67C2311yescharacteristic
133C2×C4⋊Dic67C2311yescharacteristic
134C2×C4⋊Dic67C2311yescharacteristic
135C2×Dic67⋊C4—21no—
136C2×Dic67⋊C4—21no—
137C2×C22⋊Dic67—21no—
138C2×C22⋊Dic67—21no—
139C2×(C2×D67)⋊C4—21no—
140C2×(C2×D67)⋊C4—21no—
141C2×(C2×D67)⋊C4—21no—
142C2×(C2×D67)⋊C4—21no—
143C2×(C2×D67)⋊C4—21no—
144C2×(C2×D67)⋊C4—21no—
145C2×(C2×D67)⋊C4—21no—
146C2×(C2×D67)⋊C4—21no—
147C22⋊C4×D67—28no—
148C22⋊C4×D67—28no—
149C2×C4×Dic67—21no—
150C2×C4×Dic67—21no—
151#14523977C2314yescomplemented
152#14523977C2314yescomplemented
153#14523975C2314yescomplemented
154#14523975C2314yescomplemented
155#14523968C2314yescomplemented
156#14523968C2314yescomplemented
157#14523965C2314yes—
158#14523965C2314yes—
159#14523965C2314yes—
160#14523965C2314yes—
161#14523965C2314yescomplemented
162#14523965C2314yescomplemented
163C23×C4×C67C2311yescharacteristic
164C22×C8×C67C2311yescharacteristic
165C22×C8×C67C2311yescharacteristic
166C22×C8×C67C2311yescharacteristic
167C22×C8×C67C2311yescharacteristic
168#117×C67D414yes—
169#117×C67C2314yes—
170C2×C4⋊C4×C67D411yescharacteristic
171C2×C4⋊C4×C67D411yescharacteristic
172C2×C22⋊C4×C67D411yescharacteristic
173C2×C22⋊C4×C67D411yescharacteristic
174C2×C42×C67C2311yescharacteristic
175C2×C42×C67C2311yescharacteristic
176C4⋊C8×C67C2314yescomplemented
177C4⋊C8×C67C2314yescomplemented
178C22⋊C8×C67C2314yes—
179C22⋊C8×C67C2314yes—
180#97×C67C2314yescomplemented
181C4×C8×C67C2314yescomplemented
182C23×D67—21no—
183C23×D67—21no—
184C23×D67—28no—
185C23×D67—24no—
186C23×D67—21no—
187C23×D67—82no—
188C23×D67—82no—
189C2×Dic134—22no—
190C2×Dic134—22no—
191C2×Dic134—21no—
192C2×Dic134—24no—
193C2×Dic134—82no—
194C2×Dic134C2412yes—
195C2×D268—28no—
196C2×D268—216no—
197C2×D268—24no—
198C2×D268—21no—
199C2×D268—21no—
200C2×D268—22no—
201C2×D268—22no—
202C2×D268—28no—
203C2×D268—28no—
204C2×D268—22no—
205C2×D268—22no—
206C2×D268—21no—
207C2×D268#4114yes—
208C2×D268#4114yes—
209C2×D268C2412yes—
210C2×D268C2412yes—
211C2×D268C2412yes—
212C2×C22⋊D67—24no—
213C2×C22⋊D67—82no—
214C22×Dic67—21no—
215C22×Dic67—21no—
216C22×Dic67—21no—
217C22×Dic67—21no—
218C22×Dic67—21no—
219C2×C4×D67—24no—
220C2×C4×D67—24no—
221C2×C4×D67—24no—
222C2×C4×D67—24no—
223C2×C4×D67—24no—
224C2×C4×D67—82no—
225C2×C4×D67—82no—
226C2×C4×D67—82no—
227C2×C4×D67—82no—
228C2×C4×D67—82no—
229#11761617—28no—
230#11761617—28no—
231D536—28no—
232D536—28no—
233C4⋊Dic67—24no—
234C4⋊Dic67—21no—
235C4⋊Dic67—21no—
236C4⋊Dic67—21no—
237C4⋊Dic67—21no—
238C4⋊Dic67C2412yes—
239C4⋊Dic67C2412yes—
240C4⋊Dic67C2412yes—
241C4⋊Dic67C2412yes—
242Dic67⋊C4—24no—
243Dic67⋊C4—24no—
244C22⋊Dic67—24no—
245C22⋊Dic67—24no—
246(C2×D67)⋊C4—24no—
247(C2×D67)⋊C4—24no—
248(C2×D67)⋊C4—24no—
249(C2×D67)⋊C4—24no—
250(C2×D67)⋊C4—24no—
251(C2×D67)⋊C4—24no—
252(C2×D67)⋊C4—24no—
253(C2×D67)⋊C4—24no—
254C4×Dic67—24no—
255C4×Dic67—24no—
256C24×C67C2×D411yescharacteristic
257C22×C4×C67—22no—
258C22×C4×C67—22no—
259C22×C4×C67C2×D411yescharacteristic
260C22×C4×C67C2×D411yescharacteristic
261C22×C4×C67C2×D411yescharacteristic
262C22×C4×C67C2×D411yescharacteristic
263C22×C4×C67C2×D411yescharacteristic
264C22×C4×C67C2×D412yes—
265C22×C4×C67C2412yes—
266C22×C4×C67C2411yescharacteristic
267C2×C8×C67—22no—
268C2×C8×C67—22no—
269C2×C8×C67—22no—
270C2×C8×C67—22no—
271C2×C8×C67C2412yes—
272C2×C8×C67C2412yes—
273C2×C8×C67C2412yes—
274C2×C8×C67C2412yes—
275C4⋊C4×C67C2×D414yes—
276C4⋊C4×C67C2×D414yes—
277C22⋊C4×C67C2×D414yes—
278C22⋊C4×C67C2×D414yes—
279C42×C67C2×D412yes—
280C42×C67C2×D412yes—
281C42×C67C2412yes—
282C42×C67C2412yes—
283C23×C67—22no—
284C23×C67—22no—
285C23×C67—22no—
286C23×C67C22×D412yes—
287C23×C67C22×D411yescharacteristic
288C22×D67—24no—
289C22×D67—24no—
290C22×D67—22no—
291C22×D67—22no—
292C22×D67—216no—
293C22×D67—22no—
294C22×D67—42no—
295C22×D67—42no—
296C22×D67—42no—
297C22×D67—42no—
298C22×D67—42no—
299C22×D67—42no—
300C22×D67—42no—
301C22×D67—84no—
302C22×D67—84no—
303C22×D67—816no—
304C2×C4×C67—22no—
305C2×C4×C67—22no—
306C2×C4×C67—22no—
307C2×C4×C67—22no—
308C2×C4×C67—22no—
309C2×C4×C67—24no—
310C2×C4×C67—22no—
311C2×C4×C67—22no—
312C2×C4×C67C22×D412yes—
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×C67C2×#4112yes—
320C2×C4×C67C2511yescharacteristic
321C22⋊D67—84no—
322C2×Dic67—22no—
323C2×Dic67—22no—
324C2×Dic67—22no—
325C2×Dic67—22no—
326C2×Dic67—22no—
327C2×Dic67—42no—
328C2×Dic67—42no—
329C2×Dic67—42no—
330C2×Dic67—42no—
331C2×Dic67—42no—
332D268—216no—
333D268—24no—
334D268—24no—
335D268—22no—
336D268—22no—
337D268—22no—
338D268—22no—
339D268—42no—
340D268C2×#4114yes—
341D268C2×#4114yes—
342C4×D67—84no—
343C4×D67—84no—
344C4×D67—84no—
345C4×D67—84no—
346C4×D67—84no—
347Dic134—22no—
348Dic134—22no—
349Dic134—42no—
350Dic134—84no—
351C8×C67—22no—
352C8×C67—22no—
353C8×C67—22no—
354C8×C67—22no—
355C22×C67—22no—
356C22×C67—22no—
357C22×C67—22no—
358C22×C67—44no—
359C22×C67#52512yes—
360C22×C67#57612yes—
361C22×C67#57712yes—
362C22×C67C23×D411yescharacteristic
363C2×D67—24no—
364C2×D67—24no—
365C2×D67—48no—
366C2×D67—48no—
367C2×D67—42no—
368C2×D67—42no—
369C2×D67—42no—
370C2×D67—42no—
371C2×D67—42no—
372C2×D67—42no—
373C2×D67—42no—
374C2×D67—816no—
375C2×D67—84no—
376C4×C67—22no—
377C4×C67—22no—
378C4×C67—22no—
379C4×C67—22no—
380C4×C67—22no—
381C4×C67#52512yes—
382C4×C67C22×#4111yescharacteristic
383C4×C67C22×#4111yescharacteristic
384Dic67—42no—
385Dic67—42no—
386Dic67—42no—
387Dic67—42no—
388Dic67—42no—
389C2×#3118—671nomaximal, Sylow
390C2×C67—42no—
391C2×C67#311814yescomplemented
392C2×C67C2×#52511yescharacteristic
393C2×C67C2×#57611yescharacteristic
394C2×C67C2×#57711yescharacteristic
395D67—44no—
396D67—44no—
397D67—82no—
398C2×#542—671no—
399C2×#518—671no—
400#3118—6716no—
401C2×#485—671no—
402C2×#482—671no—
403C2×#476—671no—
404C2×#474—671no—
405C2×#463—671no—
406C2×#463—671no—
407C2×#450—671no—
408C2×#447—671no—
409C2×#442—671no—
410C2×#440—671no—
411C2×C4×SD16—671no—
412C2×C4×D8—671no—
413C2×#433D6711yescharacteristic, complemented
414C67C2×#311811yescharacteristic, complemented, Sylow
415C23×D4—671no—
416C22×SD16—671no—
417C22×SD16—671no—
418C22×D8—671no—
419C22×D8—671no—
420#542—678no—
421#542—1344no—
422C2×C4⋊Q8—671no—
423C2×#126—1341no—
424C2×#124—671no—
425C2×#124—1341no—
426C2×#123—1341no—
427C2×C22⋊Q8—671no—
428C2×C22⋊Q8—1341no—
429C2×#121—671no—
430#518—678no—
431#518—1344no—
432C2×C4×Q8—671no—
433C2×C4×D4—671no—
434C2×C4×D4—671no—
435C2×C4×D4—671no—
436C2×C4×D4—671no—
437C2×C4×D4—671no—
438C2×C4×D4—1341no—
439C2×C4×D4—1341no—
440C2×#117—671no—
441C2×#117C2×D6711yescharacteristic
442C22×C22⋊C4—1341no—
443C22×C22⋊C4—1341no—
444#485—678no—
445#482—678no—
446#476—678no—
447#474—678no—
448#463—678no—
449#463—678no—
450#450—678no—
451#447—678no—
452#442—678no—
453#440—678no—
454C4×SD16—678no—
455C4×D8—678no—
456#433C2×D6718yescomplemented
457C2×#107—671no—
458C2×#107—671no—
459C2×#106—671no—
460C2×#106—671no—
461C2×C4⋊C8C2×D6711yescharacteristic, complemented
462C2×C4⋊C8C2×D6711yescharacteristic, complemented
463C2×#103—671no—
464C2×#103—671no—
465C2×#102—671no—
466C2×#102—671no—
467C2×#102—671no—
468C2×#102—671no—
469C2×#102—671no—
470C2×#102—671no—
471C2×C22⋊C8C2×D6711yescharacteristic
472C2×C22⋊C8C2×D6711yescharacteristic
473C2×#97C2×D6711yescharacteristic, complemented
474C2×C4×C8C2×D6711yescharacteristic, complemented
475C25—1341no—
476C22×Q8—671no—
477C22×Q8—1341no—
478C22×D4—671no—
479C22×D4—671no—
480C22×D4—671no—
481C22×D4—674no—
482C22×D4—1344no—
483C22×D4—1344no—
484C22×D4—1341no—
485C22×D4—1341no—
486C22×D4—1342no—
487C23×C4—1341no—
488C23×C4—1341no—
489C23×C4—1341no—
490C23×C4—1341no—
491C23×C4—1341no—
492C23×C4C22×D6711yescharacteristic
493C2×SD16—674no—
494C2×SD16—674no—
495C2×SD16—1344no—
496C2×SD16—1344no—
497C2×D8—674no—
498C2×D8—674no—
499C2×D8—1344no—
500C2×D8—1344no—
501C22×C8C22×D6711yescharacteristic
502C22×C8C22×D6711yescharacteristic
503C22×C8C22×D6711yescharacteristic
504C22×C8C22×D6711yescharacteristic
505C4⋊Q8—674no—
506C4⋊Q8—1342no—
507#126—1348no—
508#124—674no—
509#124—1348no—
510#124—1342no—
511#123—1348no—
512C22⋊Q8—674no—
513C22⋊Q8—1342no—
514C22⋊Q8—1348no—
515#121—674no—
516#121—1342no—
517C4×Q8—674no—
518C4×Q8—1342no—
519C4×D4—674no—
520C4×D4—674no—
521C4×D4—674no—
522C4×D4—674no—
523C4×D4—674no—
524C4×D4—1348no—
525C4×D4—1348no—
526C4×D4—1342no—
527C4×D4—1342no—
528C4×D4—1342no—
529C4×D4—1342no—
530C4×D4—1342no—
531#117—674no—
532#117—1342no—
533#117D26814yes—
534#117C22×D6714yes—
535C2×C4⋊C4—671no—
536C2×C4⋊C4—671no—
537C2×C4⋊C4—671no—
538C2×C4⋊C4—671no—
539C2×C4⋊C4—1341no—
540C2×C4⋊C4—1341no—
541C2×C4⋊C4—1341no—
542C2×C4⋊C4D26811yescharacteristic
543C2×C4⋊C4D26811yescharacteristic
544C2×C22⋊C4—1341no—
545C2×C22⋊C4—1341no—
546C2×C22⋊C4—1341no—
547C2×C22⋊C4—1341no—
548C2×C22⋊C4—1341no—
549C2×C22⋊C4—1341no—
550C2×C22⋊C4—1341no—
551C2×C22⋊C4—1341no—
552C2×C22⋊C4—1341no—
553C2×C22⋊C4—1341no—
554C2×C22⋊C4—1348no—
555C2×C22⋊C4—1348no—
556C2×C22⋊C4D26811yescharacteristic
557C2×C22⋊C4D26811yescharacteristic
558C2×C42—1341no—
559C2×C42—1341no—
560C2×C42C22×D6711yescharacteristic
561C2×C42C22×D6711yescharacteristic
562#107—674no—
563#107—674no—
564#106—674no—
565#106—674no—
566C4⋊C8C22×D6714yescomplemented
567C4⋊C8C22×D6714yescomplemented
568#103—674no—
569#103—674no—
570#102—674no—
571#102—674no—
572#102—674no—
573#102—674no—
574#102—674no—
575#102—674no—
576C22⋊C8C22×D6714yes—
577C22⋊C8C22×D6714yes—
578#97C22×D6714yescomplemented
579C4×C8C22×D6714yescomplemented
580C24—5362no—
581C24—5362no—
582C24—1348no—
583C24—1341no—
584C24—1341no—
585C24—1341no—
586C24—1344no—
587C24C2×D26811yescharacteristic
588C2×Q8—5362no—
589C2×Q8—672no—
590C2×Q8—1342no—
591C2×Q8—1342no—
592C2×Q8—1341no—
593C2×Q8—1344no—
594C2×D4—5362no—
595C2×D4—674no—
596C2×D4—674no—
597C2×D4—672no—
598C2×D4—672no—
599C2×D4—672no—
600C2×D4—1348no—
601C2×D4—1348no—
602C2×D4—1348no—
603C2×D4—13416no—
604C2×D4—1344no—
605C2×D4—1341no—
606C2×D4—1344no—
607C2×D4—1341no—
608C2×D4—1341no—
609C2×D4—1342no—
610C2×D4—1342no—
611C2×D4—1342no—
612C2×D4—1342no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—5362no—
616C22×C4—5362no—
617C22×C4—5362no—
618C22×C4—5362no—
619C22×C4—5362no—
620C22×C4—1341no—
621C22×C4—1341no—
622C22×C4—1341no—
623C22×C4—1341no—
624C22×C4—1341no—
625C22×C4—1344no—
626C22×C4—1344no—
627C22×C4—1344no—
628C22×C4—1344no—
629C22×C4—1344no—
630C22×C4C2×D26812yes—
631C22×C4C2×D26811yescharacteristic
632C22×C4C2×D26811yescharacteristic
633C22×C4C2×D26811yescharacteristic
634C22×C4C2×D26811yescharacteristic
635C22×C4C2×D26811yescharacteristic
636C22×C4C23×D6712yes—
637C22×C4C23×D6711yescharacteristic
638SD16—1348no—
639SD16—1348no—
640D8—1348no—
641D8—1348no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8C23×D6712yes—
647C2×C8C23×D6712yes—
648C2×C8C23×D6712yes—
649C2×C8C23×D6712yes—
650C4⋊C4—672no—
651C4⋊C4—672no—
652C4⋊C4—672no—
653C4⋊C4—672no—
654C4⋊C4—1341no—
655C4⋊C4—1341no—
656C4⋊C4—1341no—
657C4⋊C4—1341no—
658C4⋊C4—1344no—
659C4⋊C4—1344no—
660C4⋊C4—1344no—
661C4⋊C4C2×D26814yes—
662C4⋊C4C2×D26814yes—
663C22⋊C4—1344no—
664C22⋊C4—1344no—
665C22⋊C4—1344no—
666C22⋊C4—1344no—
667C22⋊C4—1344no—
668C22⋊C4—1344no—
669C22⋊C4—1344no—
670C22⋊C4—1344no—
671C22⋊C4—1344no—
672C22⋊C4—1344no—
673C22⋊C4C2×D26814yes—
674C22⋊C4C2×D26814yes—
675C42—1344no—
676C42—1344no—
677C42C2×D26812yes—
678C42C2×D26812yes—
679C42C23×D6712yes—
680C42C23×D6712yes—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—2682no—
685C23—2682no—
686C23—2682no—
687C23—2682no—
688C23—2682no—
689C23—2682no—
690C23—2682no—
691C23—5364no—
692C23—5364no—
693C23—53616no—
694C23—13416no—
695C23—1342no—
696C23—1344no—
697C23—1344no—
698C23—1342no—
699C23—1342no—
700C23C22×D26812yes—
701C23C22×D26811yescharacteristic
702Q8—2682no—
703Q8—5364no—
704Q8—1342no—
705Q8—1342no—
706D4—2682no—
707D4—5364no—
708D4—674no—
709D4—674no—
710D4—13416no—
711D4—1344no—
712D4—1344no—
713D4—1342no—
714D4—1342no—
715D4—1342no—
716D4—1342no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—2682no—
726C2×C4—2682no—
727C2×C4—2682no—
728C2×C4—2682no—
729C2×C4—2682no—
730C2×C4—5364no—
731C2×C4—5364no—
732C2×C4—5364no—
733C2×C4—5364no—
734C2×C4—5364no—
735C2×C4—1342no—
736C2×C4—1342no—
737C2×C4—1342no—
738C2×C4—1342no—
739C2×C4—1342no—
740C2×C4C22×D26812yes—
741C2×C4C22×D26812yes—
742C2×C4C22×D26812yes—
743C2×C4C22×D26812yes—
744C2×C4C22×D26812yes—
745C2×C4C22×D26811yescharacteristic
746C2×C4#41×D6712yes—
747C2×C4#41×D6712yes—
748C2×C4C24×D6711yescharacteristic
749C8—22no—
750C8—22no—
751C8—22no—
752C8—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—2682no—
758C22—2682no—
759C22—2682no—
760C22—2682no—
761C22—2688no—
762C22—2688no—
763C22—2682no—
764C22—2682no—
765C22—2682no—
766C22—53616no—
767C22—5364no—
768C22—1344no—
769C22—1344no—
770C22#1686390812yes—
771C22#1686420112yes—
772C22#1686420812yes—
773C22C23×D26811yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—2682no—
780C4—2682no—
781C4—2682no—
782C4—2682no—
783C4—2682no—
784C4#1686390812yes—
785C4C2×#41×D6711yescharacteristic
786C4C2×#41×D6711yescharacteristic
787C2—42no—
788C2—2684no—
789C2—2684no—
790C2—5362no—
791C2#2257039514yesdirect product factor
792C2C2×#1686390811yescharacteristic
793C2C2×#1686420111yescharacteristic
794C2C2×#1686420811yescharacteristic
subgroupG/H
centerC23C22×D268
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#433×C67C2
socleC23×C67C22×D4
prime radicalC2×#16863532C2
hypercenterC2×#433D67
hypocenterC67C2×#3118
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#16864017C2semidirect
2. C2×#16863870C2semidirect
3. #22570395C2direct (N × H)
4. C2×#16863738C2semidirect
5. C2×#16863721C2semidirect
6. C2×#16863687C2semidirect
7. C2×#16863677C2semidirect
8. C2×#16863612C2semidirect
9. C2×#16863612C2semidirect
10. C2×#16863549C2semidirect
12. C2×#16863509C2semidirect
13. C2×#16863498C2semidirect
14. C2×C4×#11761617C2semidirect
15. C2×C4×D536C2semidirect
16. C2×#433×C67C2semidirect
23. #16864017C22semidirect
24. C2×#14524043C22semidirect
26. C2×#14524031C22semidirect
33. #16863870C22semidirect
34. C2×C4×Dic134C22semidirect
39. C2×C4×D268C22semidirect
45. #16863738C22semidirect
46. #16863721C22semidirect
47. #16863687C22semidirect
48. #16863677C22semidirect
49. #16863612C22semidirect
50. #16863612C22semidirect
51. #16863549C22semidirect
53. #16863509C22semidirect
54. #16863498C22semidirect
55. C4×#11761617C22semidirect
56. C4×D536C22semidirect
57. C2×#14523977C22semidirect
58. C2×#14523977C22semidirect
59. C2×#14523975C22semidirect
60. C2×#14523975C22semidirect
61. C2×#14523968C22semidirect
62. C2×#14523968C22semidirect
67. C2×#14523965C22semidirect
68. C2×#14523965C22semidirect
70. #433×C67C22semidirect
71. C2×C4⋊C8×C67C22semidirect
72. C2×C4⋊C8×C67C22semidirect
75. C2×#97×C67C22semidirect
76. C2×C4×C8×C67C22semidirect
103. #14524043C23semidirect
106. #14524031C23semidirect
115. C4×Dic134C23semidirect
125. C4×D268C23semidirect
151. #14523977C23semidirect
152. #14523977C23semidirect
153. #14523975C23semidirect
154. #14523975C23semidirect
155. #14523968C23semidirect
156. #14523968C23semidirect
161. #14523965C23semidirect
162. #14523965C23semidirect
176. C4⋊C8×C67C23semidirect
177. C4⋊C8×C67C23semidirect
180. #97×C67C23semidirect
181. C4×C8×C67C23semidirect
391. C2×C67#3118semidirect
413. C2×#433D67semidirect
414. C67C2×#3118semidirect
456. #433C2×D67semidirect
461. C2×C4⋊C8C2×D67semidirect
462. C2×C4⋊C8C2×D67semidirect
473. C2×#97C2×D67semidirect
474. C2×C4×C8C2×D67semidirect
566. C4⋊C8C22×D67semidirect
567. C4⋊C8C22×D67semidirect
578. #97C22×D67semidirect
579. C4×C8C22×D67semidirect
791. C2#22570395direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168640172
C2×#168638702
#225703952
C2×#168637382
C2×#168637212
C2×#168636872
C2×#168636772
C2×#168636122
C2×#168635492
C2×#168635322
C2×#168635092
C2×#168634982
C2×C4×#117616172
C2×C4×D5362
C2×#433×C672
C2×#311867