Finite Group Databasebeta

← C2×#22572596 #31734287

Subgroups — C2×#22572596 #31734287

Order 17152.

1942 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864104C211yesmaximal, characteristic
2C2×#16864101C211yesmaximal, characteristic
3#22572596C2116yesmaximal, direct product factor
4C2×#16863800C211yesmaximal, characteristic, complemented
5C2×#16863733C211yesmaximal, characteristic, complemented
6C2×#16863732C211yesmaximal, characteristic, complemented
7C2×#16863730C211yesmaximal, characteristic, complemented
8C2×#16863690C211yesmaximal, characteristic, complemented
9C2×#16863689C211yesmaximal, characteristic, complemented
10C2×#16863636C211yesmaximal, characteristic, complemented
11C2×#16863635C211yesmaximal, characteristic, complemented
12C2×#16863488C211yesmaximal, characteristic, complemented
13C2×(C22⋊D67)⋊C8C211yesmaximal, characteristic
14C22×#14523976C211yesmaximal, characteristic, complemented
15C2×#107×D67C211yesmaximal, characteristic, complemented
16C2×#484×C67C211yesmaximal, characteristic, complemented
17C22×#11761618C2211yescharacteristic
18C23×C67⋊C8C2211yescharacteristic
19C22×C8×D67C2211yescharacteristic
20#16864104—24no—
21#16864104C2218yes—
22#16864101—24no—
23#16864101C2218yes—
24C2×#14524042C2211yescharacteristic
25C2×#14524042C2211yescharacteristic
26C2×#14524033—21no—
27C2×#14524033—21no—
28C2×#14524023—21no—
29C2×#14524023C2211yescharacteristic
30C2×#14524022—21no—
31C2×#14524022C2211yescharacteristic
32C2×#14524021—21no—
33C2×#14524020—21no—
34C2×#14524019C2211yescharacteristic
35C2×Q8×Dic67C2211yescharacteristic
36C2×#14524008C2211yescharacteristic
37C2×C4×C22⋊D67—21no—
38C2×C4×C22⋊D67C2211yescharacteristic
39C2×(C22⋊D67)⋊C4—21no—
40C22×C4⋊Dic67C2211yescharacteristic
41C2×C4⋊C4×D67C2211yescharacteristic
42C2×C4⋊C4×D67C2211yescharacteristic
43#16863800C2218yescomplemented
44#16863733C2218yescomplemented
45#16863732C2218yescomplemented
46#16863730C2218yescomplemented
47#16863690C2218yescomplemented
48#16863689C2218yescomplemented
49#16863636C2218yescomplemented
50#16863635C2218yescomplemented
51#16863488C2218yescomplemented
52(C22⋊D67)⋊C8C2218yes—
53C2×#14523977C2211yescharacteristic
54C2×#14523977C2211yescharacteristic
55C2×#14523976C2211yescharacteristic
56C2×#14523976C2211yescharacteristic
57C2×#14523976C2211yescharacteristic
58C2×#14523976C2211yescharacteristic
59C2×#14523976C2211yescharacteristic
60C2×#14523976C2218yescomplemented
61#107×D67C2218yescomplemented
62C2×Dic67⋊C8C2211yescharacteristic
63C2×#14523968C2211yescharacteristic
64C2×#14523968C2211yescharacteristic
65C2×#14523967C2211yescharacteristic
66C2×#14523966C2211yescharacteristic
67C2×(C2×D67)⋊C8C2211yescharacteristic
68C2×C8×Dic67C2211yescharacteristic
69C2×C22⋊Q8×C67C2211yescharacteristic
70C22×C4⋊C4×C67C2211yescharacteristic
71#484×C67C2218yescomplemented
72C2×#107×C67C2211yescharacteristic
73C2×#107×C67C2211yescharacteristic
74C2×#103×C67C2211yescharacteristic
75C2×#103×C67C2211yescharacteristic
76C2×C22⋊C8×C67C2211yescharacteristic
77C22×Dic134—21no—
78C22×Dic134—21no—
79C22×Dic134C2311yescharacteristic
80C22×C22⋊D67D411yescharacteristic
81C23×Dic67—21no—
82C22×C4×D67—21no—
83C22×C4×D67—21no—
84C22×C4×D67C2311yescharacteristic
85C2×#11761618—24no—
86C2×#11761618C2314yes—
87C22×C67⋊C8—24no—
88C22×C67⋊C8C2311yescharacteristic
89C22×C67⋊C8C2314yes—
90C22×C67⋊C8C2311yescharacteristic
91C2×C8×D67—24no—
92C2×C8×D67C2314yes—
93#14524042—22no—
94#14524042—22no—
95#14524042C2314yes—
96#14524042C2314yes—
97#14524033—28no—
98#14524033—28no—
99#14524023—22no—
100#14524023—28no—
101#14524023C2314yes—
102#14524022—28no—
103#14524022—22no—
104#14524022C2314yes—
105#14524021—28no—
106#14524020—28no—
107#14524019—22no—
108#14524019C2314yes—
109Q8×Dic67—22no—
110Q8×Dic67C2314yes—
111#14524008—22no—
112#14524008C2314yes—
113C4×C22⋊D67—28no—
114C4×C22⋊D67D414yes—
115C4×C22⋊D67C2314yes—
116(C22⋊D67)⋊C4—28no—
117C2×C4⋊Dic67—21no—
118C2×C4⋊Dic67—21no—
119C2×C4⋊Dic67—22no—
120C2×C4⋊Dic67—21no—
121C2×C4⋊Dic67C2311yescharacteristic
122C2×C4⋊Dic67C2311yescharacteristic
123C2×C4⋊Dic67C2314yes—
124C2×C4⋊Dic67C2311yescharacteristic
125C2×Dic67⋊C4—21no—
126C2×Dic67⋊C4—21no—
127C2×Dic67⋊C4—21no—
128C2×Dic67⋊C4—21no—
129C2×Dic67⋊C4—21no—
130C2×Dic67⋊C4—21no—
131C2×Dic67⋊C4—21no—
132C2×Dic67⋊C4D411yescharacteristic
133C4⋊C4×D67—22no—
134C4⋊C4×D67—22no—
135C4⋊C4×D67C2314yes—
136C4⋊C4×D67C2314yes—
137C2×C22⋊Dic67—21no—
138C2×C22⋊Dic67D411yescharacteristic
139C2×(C2×D67)⋊C4—21no—
140C2×(C2×D67)⋊C4—21no—
141C2×(C2×D67)⋊C4D411yescharacteristic
142C2×C4×Dic67—21no—
143C2×C4×Dic67—21no—
144C2×C4×Dic67C2311yescharacteristic
145#14523977C2314yes—
146#14523977C2314yes—
147#14523976C2314yes—
148#14523976C2314yes—
149#14523976C2314yes—
150#14523976C2314yes—
151#14523976C2314yes—
152Dic67⋊C8C2314yes—
153#14523968C2314yes—
154#14523968C2314yes—
155#14523967C2314yes—
156#14523966C2314yes—
157(C2×D67)⋊C8C2314yes—
158C8×Dic67C2314yes—
159C22×Q8×C67C2311yescharacteristic
160C23×C4×C67—21no—
161C23×C4×C67C2311yescharacteristic
162C22×C8×C67C2311yescharacteristic
163C22×C8×C67C2311yescharacteristic
164C22⋊Q8×C67—22no—
165C22⋊Q8×C67C2314yes—
166C2×C4⋊C4×C67—22no—
167C2×C4⋊C4×C67—21no—
168C2×C4⋊C4×C67—21no—
169C2×C4⋊C4×C67C2314yes—
170C2×C4⋊C4×C67C2311yescharacteristic
171C2×C4⋊C4×C67C2311yescharacteristic
172C2×C4⋊C4×C67C2311yescharacteristic
173C2×C22⋊C4×C67—21no—
174#107×C67C2314yes—
175#107×C67C2314yes—
176#103×C67C2314yes—
177#103×C67C2314yes—
178C22⋊C8×C67C2314yes—
179C23×D67C2×D411yescharacteristic
180C2×Dic134—22no—
181C2×Dic134—22no—
182C2×Dic134—21no—
183C2×Dic134—24no—
184C2×Dic134—24no—
185C2×Dic134—82no—
186C2×Dic134—82no—
187C2×Dic134C2412yes—
188C2×C22⋊D67Q1618yescomplemented
189C2×C22⋊D67C2×D414yes—
190C22×Dic67—21no—
191C22×Dic67—21no—
192C22×Dic67—21no—
193C22×Dic67—21no—
194C22×Dic67—24no—
195C22×Dic67—82no—
196C22×Dic67C2×D411yescharacteristic
197C22×Dic67C2×D411yescharacteristic
198C22×Dic67C2×D411yescharacteristic
199C2×C4×D67—22no—
200C2×C4×D67—22no—
201C2×C4×D67—24no—
202C2×C4×D67—24no—
203C2×C4×D67—82no—
204C2×C4×D67—82no—
205C2×C4×D67C2×D412yes—
206C2×C4×D67C2412yes—
207#11761618—28no—
208C2×C67⋊C8—22no—
209C2×C67⋊C8—28no—
210C2×C67⋊C8#4114yes—
211C2×C67⋊C8C2412yes—
212C2×C67⋊C8C2412yes—
213C8×D67—28no—
214C4⋊Dic67—21no—
215C4⋊Dic67—21no—
216C4⋊Dic67—21no—
217C4⋊Dic67—24no—
218C4⋊Dic67—24no—
219C4⋊Dic67—24no—
220C4⋊Dic67C2412yes—
221C4⋊Dic67C2412yes—
222C4⋊Dic67C2412yes—
223Dic67⋊C4—24no—
224Dic67⋊C4—24no—
225Dic67⋊C4—24no—
226Dic67⋊C4—24no—
227Dic67⋊C4—24no—
228Dic67⋊C4—24no—
229Dic67⋊C4—24no—
230Dic67⋊C4C2×D414yes—
231C22⋊Dic67—24no—
232C22⋊Dic67C2×D414yes—
233(C2×D67)⋊C4—24no—
234(C2×D67)⋊C4—24no—
235(C2×D67)⋊C4C2×D414yes—
236C4×Dic67—24no—
237C4×Dic67—24no—
238C4×Dic67C2×D412yes—
239C4×Dic67C2412yes—
240C24×C67C2×D411yescharacteristic
241C2×Q8×C67—21no—
242C2×Q8×C67—22no—
243C2×Q8×C67—22no—
244C2×Q8×C67C2412yes—
245C22×C4×C67—22no—
246C22×C4×C67—22no—
247C22×C4×C67—21no—
248C22×C4×C67—21no—
249C22×C4×C67—21no—
250C22×C4×C67—21no—
251C22×C4×C67—24no—
252C22×C4×C67—82no—
253C22×C4×C67C2×D411yescharacteristic
254C22×C4×C67C2×D412yes—
255C22×C4×C67C2412yes—
256C22×C4×C67C2411yescharacteristic
257C2×C8×C67—22no—
258C2×C8×C67—22no—
259C2×C8×C67C2412yes—
260C2×C8×C67C2412yes—
261C4⋊C4×C67—21no—
262C4⋊C4×C67—24no—
263C4⋊C4×C67—21no—
264C4⋊C4×C67—24no—
265C4⋊C4×C67—21no—
266C4⋊C4×C67C2412yes—
267C4⋊C4×C67C2412yes—
268C4⋊C4×C67C2412yes—
269C22⋊C4×C67—24no—
270C23×C67—22no—
271C23×C67—22no—
272C23×C67C2×Q1614yes—
273C23×C67C22×D412yes—
274C23×C67C22×D411yescharacteristic
275C22×D67—22no—
276C22×D67—22no—
277C22×D67C2×Q1614yes—
278C22×D67C22×D412yes—
279Q8×C67—22no—
280Q8×C67—22no—
281Q8×C67—42no—
282C2×C4×C67—22no—
283C2×C4×C67—24no—
284C2×C4×C67—22no—
285C2×C4×C67—22no—
286C2×C4×C67—22no—
287C2×C4×C67—22no—
288C2×C4×C67—22no—
289C2×C4×C67—22no—
290C2×C4×C67—42no—
291C2×C4×C67—42no—
292C2×C4×C67—42no—
293C2×C4×C67—42no—
294C2×C4×C67—84no—
295C2×C4×C67C22×D412yes—
296C2×C4×C67C22×D411yescharacteristic
297C2×C4×C67C2×#4112yes—
298C2×C4×C672−1+412yes—
299C2×C4×C67C2511yescharacteristic
300C22⋊D67C2×Q16116yescomplemented
301C2×Dic67—22no—
302C2×Dic67—22no—
303C2×Dic67—22no—
304C2×Dic67—22no—
305C2×Dic67—22no—
306C2×Dic67—22no—
307C2×Dic67—42no—
308C2×Dic67—42no—
309C2×Dic67—42no—
310C2×Dic67—42no—
311C2×Dic67—84no—
312C2×Dic67C2×Q1614yes—
313C2×Dic67C22×D412yes—
314C2×Dic67C22×D412yes—
315C2×Dic67C22×D412yes—
316C4×D67—24no—
317C4×D67—22no—
318C4×D67—22no—
319C4×D67—84no—
320C4×D67—84no—
321Dic134—22no—
322Dic134—22no—
323Dic134—42no—
324Dic134—84no—
325Dic134—84no—
326C8×C67—22no—
327C8×C67—22no—
328C67⋊C8—22no—
329C67⋊C8C2×#4114yes—
330C22×C67—28no—
331C22×C67—22no—
332C22×C67—22no—
333C22×C67#54712yes—
334C22×C67C22×Q1614yes—
335C22×C67C22×Q1612yes—
336C22×C67#57612yes—
337C22×C67C23×D411yescharacteristic
338C2×D67—28no—
339C2×D67—22no—
340C2×D67—22no—
341C2×D67C22×Q1614yes—
342C4×C67—22no—
343C4×C67—42no—
344C4×C67—42no—
345C4×C67—42no—
346C4×C67—42no—
347C4×C67#54712yes—
348C4×C67C22×#4111yescharacteristic
349C4×C67C2×2−1+411yescharacteristic
350Dic67—22no—
351Dic67—22no—
352Dic67—42no—
353Dic67—42no—
354Dic67—42no—
355Dic67—42no—
356Dic67C22×Q1614yes—
357C2×#3338—671nomaximal, Sylow
358C2×C67—24no—
359C2×C67#333814yescomplemented
360C2×C67C2×#54711yescharacteristic
361C2×C67C23×Q1611yescharacteristic
362C2×C67C2×#57611yescharacteristic
363D67—24no—
364C2×#554—671no—
365C2×#554—671no—
366#3338—6716no—
367C2×#500—671no—
368C2×#484—671no—
369C2×#484—671no—
370C2×#484—671no—
371C2×#484D6711yescharacteristic, complemented
372C2×#477—671no—
373C2×#477—671no—
374C2×#467—671no—
375C2×#467—671no—
376C2×C4×Q16—671no—
377C2×C8×D4—671no—
378C22×#107—671no—
379C22×#107—671no—
380C67C2×#333811yescharacteristic, complemented, Sylow
381C22×Q16—671no—
382C23×C8—671no—
383C23×C8—671no—
384#554—678no—
385#554—678no—
386#554—1344no—
387#554—1344no—
388C2×C4⋊Q8—671no—
389C2×C4⋊Q8—671no—
390C2×#125—1341no—
391C2×#125—1341no—
392C2×C22⋊Q8—671no—
393C2×C22⋊Q8—671no—
394C2×C22⋊Q8—671no—
395C2×C22⋊Q8—1341no—
396C2×C22⋊Q8—1341no—
397C2×C22⋊Q8—1341no—
398C2×C22⋊Q8—1341no—
399C2×C22⋊Q8C2×D6711yescharacteristic
400C2×C4×Q8—671no—
401C2×C4×Q8—671no—
402C2×C4×D4—671no—
403C2×C4×D4—1341no—
404C2×C4×D4—1341no—
405C22×C4⋊C4—671no—
406C22×C4⋊C4—671no—
407C22×C4⋊C4—671no—
408C22×C4⋊C4C2×D6711yescharacteristic
409#500—678no—
410#484—678no—
411#484—678no—
412#484—678no—
413#484C2×D6718yescomplemented
414#477—678no—
415#477—678no—
416#467—678no—
417#467—678no—
418C4×Q16—678no—
419C8×D4—678no—
420C2×#107—671no—
421C2×#107—671no—
422C2×#107—671no—
423C2×#107—671no—
424C2×#107—678no—
425C2×#107—671no—
426C2×#107—671no—
427C2×#107—671no—
428C2×#107—678no—
429C2×#107C2×D6711yescharacteristic
430C2×#107C2×D6711yescharacteristic
431C2×C4⋊C8—671no—
432C2×#103—671no—
433C2×#103—671no—
434C2×#103—671no—
435C2×#103—671no—
436C2×#103C2×D6711yescharacteristic
437C2×#103C2×D6711yescharacteristic
438C2×C22⋊C8—671no—
439C2×C22⋊C8C2×D6711yescharacteristic
440C2×C4×C8—671no—
441C22×Q8—671no—
442C22×Q8—1341no—
443C22×Q8—1341no—
444C22×Q8C22×D6711yescharacteristic
445C22×D4—671no—
446C23×C4—21no—
447C23×C4—671no—
448C23×C4—1341no—
449C23×C4—1341no—
450C23×C4—1341no—
451C23×C4C22×D6711yescharacteristic
452C2×Q16—674no—
453C2×Q16—1344no—
454C22×C8—671no—
455C22×C8—671no—
456C22×C8—674no—
457C22×C8—674no—
458C22×C8—1344no—
459C22×C8—1344no—
460C22×C8C22×D6711yescharacteristic
461C22×C8C22×D6711yescharacteristic
462C4⋊Q8—674no—
463C4⋊Q8—674no—
464C4⋊Q8—1342no—
465C4⋊Q8—1342no—
466#125—1348no—
467#125—1348no—
468C22⋊Q8—22no—
469C22⋊Q8—674no—
470C22⋊Q8—674no—
471C22⋊Q8—674no—
472C22⋊Q8—1348no—
473C22⋊Q8—1348no—
474C22⋊Q8—1348no—
475C22⋊Q8—1348no—
476C22⋊Q8—1342no—
477C22⋊Q8—1342no—
478C22⋊Q8—1342no—
479C22⋊Q8C22×D6714yes—
480C4×Q8—674no—
481C4×Q8—674no—
482C4×Q8—1342no—
483C4×Q8—1342no—
484C4×D4—674no—
485C4×D4—674no—
486C4×D4—1348no—
487C4×D4—1348no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—671no—
492C2×C4⋊C4—671no—
493C2×C4⋊C4—671no—
494C2×C4⋊C4—671no—
495C2×C4⋊C4—674no—
496C2×C4⋊C4—674no—
497C2×C4⋊C4—674no—
498C2×C4⋊C4—1342no—
499C2×C4⋊C4—1342no—
500C2×C4⋊C4—1341no—
501C2×C4⋊C4—1341no—
502C2×C4⋊C4—1341no—
503C2×C4⋊C4—1341no—
504C2×C4⋊C4—1341no—
505C2×C4⋊C4—1341no—
506C2×C4⋊C4—1341no—
507C2×C4⋊C4—1341no—
508C2×C4⋊C4—1341no—
509C2×C4⋊C4—1342no—
510C2×C4⋊C4—1341no—
511C2×C4⋊C4C22×D6711yescharacteristic
512C2×C4⋊C4C22×D6711yescharacteristic
513C2×C4⋊C4C22×D6711yescharacteristic
514C2×C4⋊C4C22×D6714yes—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—671no—
517C2×C22⋊C4—671no—
518C2×C22⋊C4—1341no—
519C2×C22⋊C4—1341no—
520C2×C22⋊C4—1341no—
521C2×C42—671no—
522C2×C42—1341no—
523C2×C42—1341no—
524#107—674no—
525#107—674no—
526#107—674no—
527#107—674no—
528#107—674no—
529#107—674no—
530#107—674no—
531#107C22×D6714yes—
532#107C22×D6714yes—
533C4⋊C8—674no—
534#103—674no—
535#103—674no—
536#103—674no—
537#103—674no—
538#103C22×D6714yes—
539#103C22×D6714yes—
540C22⋊C8—674no—
541C22⋊C8C22×D6714yes—
542C4×C8—674no—
543C24—671no—
544C24D4×D6711yescharacteristic
545C2×Q8—21no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—5362no—
549C2×Q8—5362no—
550C2×Q8—672no—
551C2×Q8—1344no—
552C2×Q8—1344no—
553C2×Q8—1342no—
554C2×Q8—1342no—
555C2×Q8—1341no—
556C2×Q8C23×D6712yes—
557C2×D4—678no—
558C2×D4—674no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—24no—
566C22×C4—82no—
567C22×C4—5362no—
568C22×C4—5362no—
569C22×C4—5362no—
570C22×C4—671no—
571C22×C4—671no—
572C22×C4—671no—
573C22×C4—672no—
574C22×C4—672no—
575C22×C4—1344no—
576C22×C4—1344no—
577C22×C4—1341no—
578C22×C4—1341no—
579C22×C4—1341no—
580C22×C4—1341no—
581C22×C4—1344no—
582C22×C4—1342no—
583C22×C4—1342no—
584C22×C4D4×D6712yes—
585C22×C4D4×D6711yescharacteristic
586C22×C4C23×D6712yes—
587C22×C4C23×D6711yescharacteristic
588Q16—1348no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—674no—
592C2×C8—672no—
593C2×C8—672no—
594C2×C8—1348no—
595C2×C8—1348no—
596C2×C8—1342no—
597C2×C8C23×D6712yes—
598C2×C8C23×D6712yes—
599C4⋊C4—21no—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—674no—
605C4⋊C4—672no—
606C4⋊C4—672no—
607C4⋊C4—672no—
608C4⋊C4—1344no—
609C4⋊C4—1344no—
610C4⋊C4—1344no—
611C4⋊C4—1344no—
612C4⋊C4—1344no—
613C4⋊C4—1344no—
614C4⋊C4—1344no—
615C4⋊C4—1344no—
616C4⋊C4—1341no—
617C4⋊C4—1344no—
618C4⋊C4—1341no—
619C4⋊C4—1341no—
620C4⋊C4—1344no—
621C4⋊C4C23×D6712yes—
622C4⋊C4C23×D6712yes—
623C4⋊C4C23×D6712yes—
624C22⋊C4—24no—
625C22⋊C4—674no—
626C22⋊C4—674no—
627C22⋊C4—1344no—
628C22⋊C4—1344no—
629C22⋊C4—1344no—
630C42—672no—
631C42—672no—
632C42—1344no—
633C42—1344no—
634C23—22no—
635C23—22no—
636C23—674no—
637C23—672no—
638C23—1342no—
639C23—1342no—
640C23Q16×D6714yes—
641C23C2×D4×D6712yes—
642C23C2×D4×D6711yescharacteristic
643Q8—22no—
644Q8—22no—
645Q8—42no—
646Q8—2682no—
647Q8—5364no—
648Q8—5364no—
649Q8—1342no—
650Q8—1342no—
651D4—6716no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—84no—
665C2×C4—2682no—
666C2×C4—2682no—
667C2×C4—2682no—
668C2×C4—2682no—
669C2×C4—5364no—
670C2×C4—5364no—
671C2×C4—5364no—
672C2×C4—674no—
673C2×C4—672no—
674C2×C4—672no—
675C2×C4—672no—
676C2×C4—1342no—
677C2×C4—1342no—
678C2×C4—1342no—
679C2×C4—1342no—
680C2×C4—1342no—
681C2×C4—1342no—
682C2×C4—1344no—
683C2×C4—1342no—
684C2×C4—1342no—
685C2×C4C2×D4×D6712yes—
686C2×C4C2×D4×D6711yescharacteristic
687C2×C4#41×D6712yes—
688C2×C4#1452409012yes—
689C2×C4C24×D6711yescharacteristic
690C8—22no—
691C8—22no—
692C8—674no—
693C8—1342no—
694C22—28no—
695C22—22no—
696C22—22no—
697C22—674no—
698C22—1348no—
699C22—1342no—
700C22—1342no—
701C22#1686404412yes—
702C22C2×Q16×D6714yes—
703C22C2×Q16×D6712yes—
704C22#1686420012yes—
705C22C22×D4×D6711yescharacteristic
706C4—22no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—2682no—
712C4—2682no—
713C4—2682no—
714C4—2682no—
715C4—674no—
716C4—1342no—
717C4—1342no—
718C4#1686404412yes—
719C4C2×#41×D6711yescharacteristic
720C4C2×#1452409011yescharacteristic
721C2—24no—
722C2—1344no—
723C2#2257259614yesdirect product factor
724C2C2×#1686404411yescharacteristic
725C2C22×Q16×D6711yescharacteristic
726C2C2×#1686420011yescharacteristic
subgroupG/H
centerC23C2×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#484×C67C2
socleC23×C67C22×D4
prime radicalC22×C22⋊D67D4
hypercenterC2×#484D67
hypocenterC67C2×#3338
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
3. #22572596C2direct (N × H)
4. C2×#16863800C2semidirect
5. C2×#16863733C2semidirect
6. C2×#16863732C2semidirect
7. C2×#16863730C2semidirect
8. C2×#16863690C2semidirect
9. C2×#16863689C2semidirect
10. C2×#16863636C2semidirect
11. C2×#16863635C2semidirect
12. C2×#16863488C2semidirect
14. C22×#14523976C2semidirect
15. C2×#107×D67C2semidirect
16. C2×#484×C67C2semidirect
43. #16863800C22semidirect
44. #16863733C22semidirect
45. #16863732C22semidirect
46. #16863730C22semidirect
47. #16863690C22semidirect
48. #16863689C22semidirect
49. #16863636C22semidirect
50. #16863635C22semidirect
51. #16863488C22semidirect
60. C2×#14523976C22semidirect
61. #107×D67C22semidirect
71. #484×C67C22semidirect
188. C2×C22⋊D67Q16semidirect
300. C22⋊D67C2×Q16semidirect
359. C2×C67#3338semidirect
371. C2×#484D67semidirect
380. C67C2×#3338semidirect
413. #484C2×D67semidirect
723. C2#22572596direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168641042
C2×#168641012
#225725962
C2×#168638002
C2×#168637332
C2×#168637322
C2×#168637302
C2×#168636902
C2×#168636892
C2×#168636362
C2×#168636352
C2×#168634882
C2×(C22⋊D67)⋊C82
C22×#145239762
C2×#107×D672
C2×#484×C672
C2×#333867