Finite Group Databasebeta

← C2×#22570121 #31723597

Subgroups — C2×#22570121 #31723597

Order 17152.

2378 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16863906C211yesmaximal, characteristic
2C2×#117×D67C211yesmaximal, characteristic, complemented
3#22570121C2116yesmaximal, direct product factor
4C2×#16863733C211yesmaximal, characteristic, complemented
5C2×#16863713C211yesmaximal, characteristic, complemented
6C2×#16863738C211yesmaximal, characteristic, complemented
7C2×#16863737C211yesmaximal, characteristic, complemented
8C2×#16863717C211yesmaximal, characteristic, complemented
9C2×#16863728C211yesmaximal, characteristic, complemented
10C2×#16863708C211yesmaximal, characteristic, complemented
11C2×#16863433C211yesmaximal, characteristic, complemented
12C2×#16863431C211yesmaximal, characteristic, complemented
13C2×#16863389C211yesmaximal, characteristic, complemented
14C2×#16863389C211yesmaximal, characteristic, complemented
15C2×C22⋊C8×D67C211yesmaximal, characteristic, complemented
16C2×#482×C67C211yesmaximal, characteristic, complemented
17C22×#11761627C2211yescharacteristic
18C23×C4×D67C2211yescharacteristic
19C22×C8×D67C2211yescharacteristic
20C22×C8×D67C2211yescharacteristic
21#16863906—24no—
22#16863906C2218yes—
23C2×#14524025—21no—
24C2×#14524023C2211yescharacteristic
25C2×#14524022C2211yescharacteristic
26C2×#14524014C2211yescharacteristic
27C2×#14524011—21no—
28C2×D4×Dic67—21no—
29C2×(C22⋊D67)⋊C4—21no—
30C2×#14524002C2211yescharacteristic
31C2×#14524001C2211yescharacteristic
32C2×#14524001C2211yescharacteristic
33C2×#14524001C2211yescharacteristic
34C2×#14524000—21no—
35C2×#14523999—21no—
36#117×D67—24no—
37#117×D67C2218yescomplemented
38C2×C4⋊C4×D67C2211yescharacteristic
39C2×C4⋊C4×D67C2211yescharacteristic
40C2×C22⋊C4×D67—21no—
41C2×C42×D67—21no—
42#16863738C2218yescomplemented
43#16863737C2218yescomplemented
44#16863733C2218yescomplemented
45#16863728C2218yescomplemented
46#16863717C2218yescomplemented
47#16863713C2218yescomplemented
48#16863708C2218yescomplemented
49#16863433C2218yescomplemented
50#16863431C2218yescomplemented
51C2×#14523977C2211yescharacteristic, complemented
52C2×#14523976C2211yescharacteristic, complemented
53C2×#14523976C2211yescharacteristic, complemented
54C2×#14523975C2211yescharacteristic, complemented
55C2×#14523974C2211yescharacteristic, complemented
56C2×#14523974C2211yescharacteristic, complemented
57#16863389C2218yescomplemented
58#16863389C2218yescomplemented
59C2×#14523968C2211yescharacteristic, complemented
60C2×#14523968C2211yescharacteristic, complemented
61C2×#14523966C2211yescharacteristic, complemented
62C2×#14523966C2211yescharacteristic, complemented
63C2×#14523964C2211yescharacteristic, complemented
64C2×#14523964C2211yescharacteristic, complemented
65C2×C22⋊(C67⋊C8)C2211yescharacteristic
66C2×(C2×D67)⋊C8C2211yescharacteristic
67C2×(C2×D67)⋊C8C2211yescharacteristic
68C22⋊C8×D67C2218yescomplemented
69C2×#121×C67C2211yescharacteristic
70C2×#117×C67C2211yescharacteristic
71#482×C67C2218yescomplemented
72C2×#107×C67C2211yescharacteristic, complemented
73C2×#106×C67C2211yescharacteristic, complemented
74C2×#102×C67C2211yescharacteristic, complemented
75C2×#102×C67C2211yescharacteristic, complemented
76C2×C22⋊C8×C67C2211yescharacteristic
77C24×D67D411yescharacteristic
78C2×#11761627—22no—
79C2×#11761627—24no—
80C2×#11761627—24no—
81C2×#11761627C2314yes—
82C22×Dic134C2311yescharacteristic
83C22×C22⋊D67—21no—
84C22×C22⋊D67—21no—
85C23×Dic67—21no—
86C23×Dic67D411yescharacteristic
87C22×C4×D67—24no—
88C22×C4×D67—24no—
89C22×C4×D67—21no—
90C22×C4×D67—21no—
91C22×C4×D67D411yescharacteristic
92C22×C4×D67D414yes—
93C22×C4×D67D411yescharacteristic
94C22×C4×D67C2311yescharacteristic
95C22×C4×D67C2314yes—
96C22×C4×D67C2311yescharacteristic
97C22×C67⋊C8C2311yescharacteristic
98C22×C67⋊C8C2311yescharacteristic
99C2×C8×D67—24no—
100C2×C8×D67—24no—
101C2×C8×D67C2314yes—
102C2×C8×D67C2314yes—
103#14524025—28no—
104#14524023—22no—
105#14524023C2314yes—
106#14524022—22no—
107#14524022C2314yes—
108#14524014—22no—
109#14524014C2314yes—
110#14524011—28no—
111D4×Dic67—28no—
112(C22⋊D67)⋊C4—28no—
113#14524002—22no—
114#14524002C2314yes—
115#14524001—22no—
116#14524001—22no—
117#14524001—22no—
118#14524001C2314yes—
119#14524001C2314yes—
120#14524001C2314yes—
121#14524000—28no—
122#14523999—28no—
123C2×C4⋊Dic67—21no—
124C2×C4⋊Dic67C2311yescharacteristic
125C2×C4⋊Dic67C2311yescharacteristic
126C2×C4⋊Dic67C2311yescharacteristic
127C2×Dic67⋊C4—21no—
128C2×Dic67⋊C4—21no—
129C2×Dic67⋊C4—21no—
130C4⋊C4×D67—22no—
131C4⋊C4×D67—22no—
132C4⋊C4×D67C2314yes—
133C4⋊C4×D67C2314yes—
134C2×C22⋊Dic67—21no—
135C2×C22⋊Dic67—21no—
136C2×C22⋊Dic67—21no—
137C2×(C2×D67)⋊C4—21no—
138C2×(C2×D67)⋊C4—21no—
139C2×(C2×D67)⋊C4—21no—
140C2×(C2×D67)⋊C4—21no—
141C22⋊C4×D67—28no—
142C2×C4×Dic67—21no—
143C2×C4×Dic67—21no—
144C2×C4×Dic67—21no—
145C2×C4×Dic67—21no—
146C42×D67—28no—
147#14523977C2314yescomplemented
148#14523976C2314yescomplemented
149#14523976C2314yescomplemented
150#14523975C2314yescomplemented
151#14523974C2314yescomplemented
152#14523974C2314yescomplemented
153#14523968C2314yescomplemented
154#14523968C2314yescomplemented
155#14523966C2314yescomplemented
156#14523966C2314yescomplemented
157#14523964C2314yescomplemented
158#14523964C2314yescomplemented
159C22⋊(C67⋊C8)C2314yes—
160(C2×D67)⋊C8C2314yes—
161(C2×D67)⋊C8C2314yes—
162C22×D4×C67—21no—
163C22×D4×C67C2311yescharacteristic
164C23×C4×C67C2311yescharacteristic
165C22×C8×C67C2311yescharacteristic
166C22×C8×C67C2311yescharacteristic
167#121×C67—22no—
168#121×C67C2314yes—
169#117×C67—22no—
170#117×C67C2314yes—
171C2×C4⋊C4×C67C2311yescharacteristic
172C2×C4⋊C4×C67C2311yescharacteristic
173C2×C4⋊C4×C67C2311yescharacteristic
174C2×C22⋊C4×C67—21no—
175C2×C22⋊C4×C67—21no—
176C2×C42×C67—21no—
177#107×C67C2314yescomplemented
178#106×C67C2314yescomplemented
179#102×C67C2314yescomplemented
180#102×C67C2314yescomplemented
181C22⋊C8×C67C2314yes—
182C23×D67—24no—
183C23×D67—24no—
184C23×D67—42no—
185C23×D67C2×D414yes—
186C23×D67C2×D411yescharacteristic
187C23×D67C2×D411yescharacteristic
188#11761627—28no—
189#11761627—28no—
190#11761627—48no—
191C2×Dic134—22no—
192C2×Dic134—22no—
193C2×Dic134—21no—
194C2×Dic134C2412yes—
195C2×C22⋊D67—24no—
196C2×C22⋊D67—24no—
197C2×C22⋊D67—44no—
198C2×C22⋊D67—44no—
199C22×Dic67—24no—
200C22×Dic67—21no—
201C22×Dic67—21no—
202C22×Dic67—21no—
203C22×Dic67—21no—
204C22×Dic67—24no—
205C22×Dic67—44no—
206C22×Dic67C2×D411yescharacteristic
207C22×Dic67C2×D414yes—
208C22×Dic67C2×D411yescharacteristic
209C2×C4×D67—24no—
210C2×C4×D67—22no—
211C2×C4×D67—22no—
212C2×C4×D67—24no—
213C2×C4×D67—216no—
214C2×C4×D67—28no—
215C2×C4×D67—28no—
216C2×C4×D67—24no—
217C2×C4×D67—24no—
218C2×C4×D67—44no—
219C2×C4×D67—44no—
220C2×C4×D67C2×D414yes—
221C2×C4×D67C2×D412yes—
222C2×C4×D67C2×D414yes—
223C2×C4×D67C2×D412yes—
224C2×C4×D67#4114yes—
225C2×C4×D67#4114yes—
226C2×C4×D67C2412yes—
227C2×C4×D67C2412yes—
228C2×C67⋊C8—22no—
229C2×C67⋊C8—22no—
230C2×C67⋊C8C2412yes—
231C2×C67⋊C8C2412yes—
232C8×D67—28no—
233C8×D67—28no—
234C4⋊Dic67—21no—
235C4⋊Dic67—21no—
236C4⋊Dic67—21no—
237C4⋊Dic67—24no—
238C4⋊Dic67C2412yes—
239C4⋊Dic67C2412yes—
240C4⋊Dic67C2412yes—
241Dic67⋊C4—24no—
242Dic67⋊C4—24no—
243Dic67⋊C4—24no—
244C22⋊Dic67—24no—
245C22⋊Dic67—24no—
246C22⋊Dic67—24no—
247(C2×D67)⋊C4—24no—
248(C2×D67)⋊C4—24no—
249(C2×D67)⋊C4—24no—
250(C2×D67)⋊C4—24no—
251C4×Dic67—24no—
252C4×Dic67—24no—
253C4×Dic67—24no—
254C4×Dic67—24no—
255C24×C67—21no—
256C24×C67C2×D411yescharacteristic
257C2×D4×C67—24no—
258C2×D4×C67—21no—
259C2×D4×C67—22no—
260C2×D4×C67—22no—
261C2×D4×C67—44no—
262C2×D4×C67C2412yes—
263C22×C4×C67—22no—
264C22×C4×C67—22no—
265C22×C4×C67—21no—
266C22×C4×C67—21no—
267C22×C4×C67—21no—
268C22×C4×C67C2×D411yescharacteristic
269C22×C4×C67C2×D412yes—
270C22×C4×C67C2412yes—
271C22×C4×C67C2411yescharacteristic
272C2×C8×C67—22no—
273C2×C8×C67—22no—
274C2×C8×C67C2412yes—
275C2×C8×C67C2412yes—
276C4⋊C4×C67—21no—
277C4⋊C4×C67—21no—
278C4⋊C4×C67—21no—
279C4⋊C4×C67C2412yes—
280C4⋊C4×C67C2412yes—
281C4⋊C4×C67C2412yes—
282C22⋊C4×C67—24no—
283C22⋊C4×C67—24no—
284C42×C67—24no—
285C23×C67—22no—
286C23×C67—22no—
287C23×C67—22no—
288C23×C67—22no—
289C23×C67—42no—
290C23×C67—42no—
291C23×C67—42no—
292C23×C67C22×D412yes—
293C23×C67C22×D411yescharacteristic
294C22×D67—22no—
295C22×D67—22no—
296C22×D67—22no—
297C22×D67—22no—
298C22×D67—28no—
299C22×D67—28no—
300C22×D67—44no—
301C22×D67—416no—
302C22×D67#12314yes—
303C22×D67#13514yes—
304C22×D67C22×D412yes—
305C22×D67C22×D412yes—
306D4×C67—22no—
307D4×C67—22no—
308D4×C67—48no—
309D4×C67—42no—
310C2×C4×C67—22no—
311C2×C4×C67—24no—
312C2×C4×C67—22no—
313C2×C4×C67—22no—
314C2×C4×C67—22no—
315C2×C4×C67—22no—
316C2×C4×C67—22no—
317C2×C4×C67—42no—
318C2×C4×C67—42no—
319C2×C4×C67—42no—
320C2×C4×C67C22×D412yes—
321C2×C4×C67C22×D411yescharacteristic
322C2×C4×C67C2×#4112yes—
323C2×C4×C67C2×#4112yes—
324C2×C4×C67C2511yescharacteristic
325C22⋊D67—48no—
326C22⋊D67—48no—
327C2×Dic67—22no—
328C2×Dic67—28no—
329C2×Dic67—22no—
330C2×Dic67—22no—
331C2×Dic67—22no—
332C2×Dic67—22no—
333C2×Dic67—42no—
334C2×Dic67—42no—
335C2×Dic67—42no—
336C2×Dic67—42no—
337C2×Dic67—48no—
338C2×Dic67#12314yes—
339C2×Dic67C22×D412yes—
340C2×Dic67C22×D412yes—
341C4×D67—28no—
342C4×D67—24no—
343C4×D67—22no—
344C4×D67—22no—
345C4×D67—28no—
346C4×D67—48no—
347C4×D67—48no—
348C4×D67#12318yes—
349C4×D67C2×#4114yes—
350C4×D67C2×#4114yes—
351Dic134—22no—
352Dic134—22no—
353Dic134—42no—
354C8×C67—22no—
355C8×C67—22no—
356C67⋊C8—22no—
357C67⋊C8—22no—
358C22×C67—22no—
359C22×C67—22no—
360C22×C67—22no—
361C22×C67—44no—
362C22×C67—42no—
363C22×C67—42no—
364C22×C67—42no—
365C22×C67—84no—
366C22×C67C2×#12312yes—
367C22×C67C2×#13512yes—
368C22×C67#57512yes—
369C22×C67C23×D411yescharacteristic
370C2×D67—28no—
371C2×D67—28no—
372C2×D67—22no—
373C2×D67—22no—
374C2×D67—22no—
375C2×D67—22no—
376C2×D67—416no—
377C2×D67C2×#12314yes—
378C2×D67C2×#13514yes—
379C4×C67—22no—
380C4×C67—42no—
381C4×C67—42no—
382C4×C67—42no—
383C4×C67C2×#12312yes—
384C4×C67C22×#4111yescharacteristic
385C4×C67C22×#4111yescharacteristic
386Dic67—22no—
387Dic67—42no—
388Dic67—42no—
389Dic67—42no—
390Dic67—42no—
391Dic67C2×#12314yes—
392C2×#3091—671nomaximal, Sylow
393C2×C67—42no—
394C2×C67—82no—
395C2×C67#309114yescomplemented
396C2×C67C22×#12311yescharacteristic
397C2×C67C22×#13511yescharacteristic
398C2×C67C2×#57511yescharacteristic
399D67—24no—
400D67—24no—
401C2×#525—671no—
402C22×#117—671no—
403#3091—6716no—
404C2×#484—671no—
405C2×#481—671no—
406C2×#485—671no—
407C2×#485—671no—
408C2×#482—671no—
409C2×#482D6711yescharacteristic, complemented
410C2×#483—671no—
411C2×#480—671no—
412C2×#427—671no—
413C2×#427—671no—
414C2×#416—671no—
415C2×#416—671no—
416C22×C22⋊C8—671no—
417C67C2×#309111yescharacteristic, complemented, Sylow
418C22×#41—671no—
419C24×C4—671no—
420C23×C8—671no—
421C23×C8—671no—
422#525—678no—
423#525—1344no—
424C2×#123—1341no—
425C2×C22⋊Q8—671no—
426C2×C22⋊Q8—671no—
427C2×#121—671no—
428C2×#121C2×D6711yescharacteristic
429C2×#120—1341no—
430C2×C4×D4—1341no—
431C2×C4×D4—1341no—
432C2×#117—671no—
433C2×#117—678no—
434C2×#117—671no—
435C2×#117—671no—
436C2×#117—671no—
437C2×#117—1341no—
438C2×#117—1341no—
439C2×#117—1344no—
440C2×#117C2×D6711yescharacteristic
441C22×C4⋊C4—671no—
442C22×C4⋊C4—671no—
443C22×C22⋊C4—1341no—
444C22×C42—1341no—
445#485—678no—
446#485—678no—
447#484—678no—
448#483—678no—
449#482—678no—
450#482C2×D6718yescomplemented
451#481—678no—
452#480—678no—
453#427—678no—
454#427—678no—
455C2×#107—671no—
456C2×#107—671no—
457C2×#107—671no—
458C2×#107C2×D6711yescharacteristic, complemented
459C2×#106—671no—
460C2×#106—671no—
461C2×#106—671no—
462C2×#106C2×D6711yescharacteristic, complemented
463#416—678no—
464#416—678no—
465C2×#103—671no—
466C2×#103—671no—
467C2×#103—671no—
468C2×#103—671no—
469C2×#102—671no—
470C2×#102—671no—
471C2×#102C2×D6711yescharacteristic, complemented
472C2×#102C2×D6711yescharacteristic, complemented
473C2×C22⋊C8—671no—
474C2×C22⋊C8—671no—
475C2×C22⋊C8—671no—
476C2×C22⋊C8—678no—
477C2×C22⋊C8C2×D6711yescharacteristic
478C25—671no—
479C2×#41—674no—
480C2×#41—1344no—
481C2×#41—1344no—
482C2×#41—1342no—
483C22×Q8—671no—
484C22×D4—21no—
485C22×D4—1341no—
486C22×D4—1341no—
487C22×D4C22×D6711yescharacteristic
488C23×C4—671no—
489C23×C4—671no—
490C23×C4—671no—
491C23×C4—674no—
492C23×C4—671no—
493C23×C4—671no—
494C23×C4—674no—
495C23×C4—1341no—
496C23×C4—1341no—
497C23×C4—1344no—
498C23×C4—1344no—
499C23×C4—1341no—
500C23×C4C22×D6711yescharacteristic
501C22×C8—671no—
502C22×C8—671no—
503C22×C8—674no—
504C22×C8—674no—
505C22×C8—1344no—
506C22×C8—1344no—
507C22×C8C22×D6711yescharacteristic
508C22×C8C22×D6711yescharacteristic
509#123—1348no—
510C22⋊Q8—674no—
511C22⋊Q8—674no—
512C22⋊Q8—1342no—
513C22⋊Q8—1342no—
514#121—22no—
515#121—674no—
516#121—1342no—
517#121C22×D6714yes—
518#120—1348no—
519C4×D4—1348no—
520C4×D4—1348no—
521#117—22no—
522#117—674no—
523#117—674no—
524#117—674no—
525#117—674no—
526#117—1348no—
527#117—1348no—
528#117—1342no—
529#117—1342no—
530#117—1342no—
531#117—1342no—
532#117C22×D6714yes—
533C2×C4⋊C4—671no—
534C2×C4⋊C4—671no—
535C2×C4⋊C4—671no—
536C2×C4⋊C4—674no—
537C2×C4⋊C4—674no—
538C2×C4⋊C4—1342no—
539C2×C4⋊C4—1342no—
540C2×C4⋊C4—1341no—
541C2×C4⋊C4—1341no—
542C2×C4⋊C4—1341no—
543C2×C4⋊C4—1341no—
544C2×C4⋊C4C22×D6711yescharacteristic
545C2×C4⋊C4C22×D6711yescharacteristic
546C2×C4⋊C4C22×D6711yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—1348no—
550C2×C22⋊C4—1341no—
551C2×C22⋊C4—1341no—
552C2×C22⋊C4—1341no—
553C2×C22⋊C4—1341no—
554C2×C22⋊C4—1341no—
555C2×C22⋊C4—1341no—
556C2×C22⋊C4—1341no—
557C2×C42—21no—
558C2×C42—1348no—
559C2×C42—1341no—
560C2×C42—1341no—
561C2×C42—1341no—
562C2×C42—1341no—
563#107—674no—
564#107—674no—
565#107—674no—
566#107C22×D6714yescomplemented
567#106—674no—
568#106—674no—
569#106—674no—
570#106C22×D6714yescomplemented
571#103—674no—
572#103—674no—
573#103—674no—
574#103—674no—
575#102—674no—
576#102—674no—
577#102C22×D6714yescomplemented
578#102C22×D6714yescomplemented
579C22⋊C8—674no—
580C22⋊C8—674no—
581C22⋊C8—674no—
582C22⋊C8C22×D6714yes—
583C24—21no—
584C24—2682no—
585C24—674no—
586C24—671no—
587C24—671no—
588C24—1344no—
589C24—1344no—
590C24D4×D6711yescharacteristic
591#41—2688no—
592#41—1348no—
593#41—1348no—
594C2×Q8—672no—
595C2×Q8—1342no—
596C2×Q8—1342no—
597C2×Q8—1341no—
598C2×D4—24no—
599C2×D4—21no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—44no—
603C2×D4—2684no—
604C2×D4—2684no—
605C2×D4—1344no—
606C2×D4—1344no—
607C2×D4C23×D6712yes—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—2684no—
614C22×C4—2684no—
615C22×C4—2684no—
616C22×C4—671no—
617C22×C4—672no—
618C22×C4—674no—
619C22×C4—674no—
620C22×C4—672no—
621C22×C4—674no—
622C22×C4—671no—
623C22×C4—674no—
624C22×C4—672no—
625C22×C4—674no—
626C22×C4—672no—
627C22×C4—1344no—
628C22×C4—1344no—
629C22×C4—1344no—
630C22×C4—13416no—
631C22×C4—1348no—
632C22×C4—1348no—
633C22×C4—1344no—
634C22×C4—1344no—
635C22×C4—1341no—
636C22×C4—1341no—
637C22×C4—1341no—
638C22×C4—1341no—
639C22×C4—1344no—
640C22×C4—1342no—
641C22×C4—1342no—
642C22×C4D4×D6712yes—
643C22×C4D4×D6711yescharacteristic
644C22×C4C23×D6712yes—
645C22×C4C23×D6711yescharacteristic
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—672no—
649C2×C8—672no—
650C2×C8—1348no—
651C2×C8—1348no—
652C2×C8—1342no—
653C2×C8—1342no—
654C2×C8C23×D6712yes—
655C2×C8C23×D6712yes—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—672no—
660C4⋊C4—672no—
661C4⋊C4—672no—
662C4⋊C4—1344no—
663C4⋊C4—1344no—
664C4⋊C4—1344no—
665C4⋊C4—1341no—
666C4⋊C4—1341no—
667C4⋊C4—1341no—
668C4⋊C4—1344no—
669C4⋊C4C23×D6712yes—
670C4⋊C4C23×D6712yes—
671C4⋊C4C23×D6712yes—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—1344no—
675C22⋊C4—1344no—
676C22⋊C4—1344no—
677C22⋊C4—1344no—
678C22⋊C4—1344no—
679C22⋊C4—1344no—
680C22⋊C4—1344no—
681C42—24no—
682C42—1344no—
683C42—1344no—
684C42—1344no—
685C42—1344no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—2684no—
694C23—26816no—
695C23—674no—
696C23—674no—
697C23—672no—
698C23—672no—
699C23—1348no—
700C23—1348no—
701C23—1342no—
702C23—1342no—
703C23—1342no—
704C23—1342no—
705C23C2×D4×D6712yes—
706C23C2×D4×D6711yescharacteristic
707Q8—2682no—
708Q8—1342no—
709Q8—1342no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—42no—
714D4—2688no—
715D4—2688no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—2688no—
727C2×C4—2688no—
728C2×C4—2682no—
729C2×C4—2682no—
730C2×C4—2682no—
731C2×C4—2682no—
732C2×C4—2688no—
733C2×C4—674no—
734C2×C4—672no—
735C2×C4—678no—
736C2×C4—674no—
737C2×C4—674no—
738C2×C4—672no—
739C2×C4—1348no—
740C2×C4—1348no—
741C2×C4—1342no—
742C2×C4—1342no—
743C2×C4—1342no—
744C2×C4—1342no—
745C2×C4—1348no—
746C2×C4—1342no—
747C2×C4—1344no—
748C2×C4—1342no—
749C2×C4—1342no—
750C2×C4C2×D4×D6712yes—
751C2×C4C2×D4×D6711yescharacteristic
752C2×C4#41×D6712yes—
753C2×C4#41×D6712yes—
754C2×C4C24×D6711yescharacteristic
755C8—22no—
756C8—22no—
757C8—1342no—
758C8—1342no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—44no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—84no—
767C22—26816no—
768C22—674no—
769C22—674no—
770C22—1342no—
771C22—1342no—
772C22—1342no—
773C22—1342no—
774C22—1348no—
775C22—1348no—
776C22#123×D6712yes—
777C22#135×D6712yes—
778C22#1686419212yes—
779C22C22×D4×D6711yescharacteristic
780C4—22no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—2682no—
785C4—2682no—
786C4—2682no—
787C4—2682no—
788C4—674no—
789C4—1342no—
790C4#123×D6712yes—
791C4C2×#41×D6711yescharacteristic
792C4C2×#41×D6711yescharacteristic
793C2—42no—
794C2—82no—
795C2—1344no—
796C2—1344no—
797C2#2257012114yesdirect product factor
798C2C2×#123×D6711yescharacteristic
799C2C2×#135×D6711yescharacteristic
800C2C2×#1686419211yescharacteristic
subgroupG/H
centerC23C2×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#482×C67C2
socleC23×C67C22×D4
prime radicalC2×#16863906C2
hypercenterC2×#482D67
hypocenterC67C2×#3091
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
2. C2×#117×D67C2semidirect
3. #22570121C2direct (N × H)
4. C2×#16863733C2semidirect
5. C2×#16863713C2semidirect
6. C2×#16863738C2semidirect
7. C2×#16863737C2semidirect
8. C2×#16863717C2semidirect
9. C2×#16863728C2semidirect
10. C2×#16863708C2semidirect
11. C2×#16863433C2semidirect
12. C2×#16863431C2semidirect
13. C2×#16863389C2semidirect
14. C2×#16863389C2semidirect
15. C2×C22⋊C8×D67C2semidirect
16. C2×#482×C67C2semidirect
37. #117×D67C22semidirect
42. #16863738C22semidirect
43. #16863737C22semidirect
44. #16863733C22semidirect
45. #16863728C22semidirect
46. #16863717C22semidirect
47. #16863713C22semidirect
48. #16863708C22semidirect
49. #16863433C22semidirect
50. #16863431C22semidirect
51. C2×#14523977C22semidirect
52. C2×#14523976C22semidirect
53. C2×#14523976C22semidirect
54. C2×#14523975C22semidirect
55. C2×#14523974C22semidirect
56. C2×#14523974C22semidirect
57. #16863389C22semidirect
58. #16863389C22semidirect
59. C2×#14523968C22semidirect
60. C2×#14523968C22semidirect
61. C2×#14523966C22semidirect
62. C2×#14523966C22semidirect
63. C2×#14523964C22semidirect
64. C2×#14523964C22semidirect
68. C22⋊C8×D67C22semidirect
71. #482×C67C22semidirect
72. C2×#107×C67C22semidirect
73. C2×#106×C67C22semidirect
74. C2×#102×C67C22semidirect
75. C2×#102×C67C22semidirect
147. #14523977C23semidirect
148. #14523976C23semidirect
149. #14523976C23semidirect
150. #14523975C23semidirect
151. #14523974C23semidirect
152. #14523974C23semidirect
153. #14523968C23semidirect
154. #14523968C23semidirect
155. #14523966C23semidirect
156. #14523966C23semidirect
157. #14523964C23semidirect
158. #14523964C23semidirect
177. #107×C67C23semidirect
178. #106×C67C23semidirect
179. #102×C67C23semidirect
180. #102×C67C23semidirect
395. C2×C67#3091semidirect
409. C2×#482D67semidirect
417. C67C2×#3091semidirect
450. #482C2×D67semidirect
458. C2×#107C2×D67semidirect
462. C2×#106C2×D67semidirect
471. C2×#102C2×D67semidirect
472. C2×#102C2×D67semidirect
566. #107C22×D67semidirect
570. #106C22×D67semidirect
577. #102C22×D67semidirect
578. #102C22×D67semidirect
797. C2#22570121direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168639062
C2×#117×D672
#225701212
C2×#168637332
C2×#168637132
C2×#168637382
C2×#168637372
C2×#168637172
C2×#168637282
C2×#168637082
C2×#168634332
C2×#168634312
C2×#168633892
C2×C22⋊C8×D672
C2×#482×C672
C2×#309167