Finite Group Databasebeta

← C2×#22569145 #31720199

Subgroups — C2×#22569145 #31720199

Order 17152.

1894 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16863950C211yesmaximal, characteristic
2#22569145C2116yesmaximal, direct product factor
3C2×#16863527C211yesmaximal, characteristic, complemented
4C2×#16863526C211yesmaximal, characteristic, complemented
5C2×#16863525C211yesmaximal, characteristic, complemented
6C2×#16863525C211yesmaximal, characteristic, complemented
7C2×#16863524C211yesmaximal, characteristic, complemented
8C2×#16863524C211yesmaximal, characteristic, complemented
9C2×#16863523C211yesmaximal, characteristic, complemented
10C2×#16863421C211yesmaximal, characteristic
11C2×#16863421C211yesmaximal, characteristic
12C2×#16863418C211yesmaximal, characteristic
13C2×#16863353C211yesmaximal, characteristic
14C2×#16863350C211yesmaximal, characteristic
15C2×#97×D67C211yesmaximal, characteristic
16C2×#446×C67C211yesmaximal, characteristic, complemented
17C22×#11761611C2211yescharacteristic
18C22×#11761611C2211yescharacteristic
19C22×C8×D67C2211yescharacteristic
20C22×C8×D67C2211yescharacteristic
21#16863950C418yes—
22#16863950C2218yes—
23C2×#14524042C411yescharacteristic
24C2×#14524041C411yescharacteristic
25C2×#14524033C411yescharacteristic
26C2×#14524033C411yescharacteristic
27C2×#14524023C411yescharacteristic
28C2×#14524021C411yescharacteristic
29C2×#14524021C411yescharacteristic
30C2×#14524019C411yescharacteristic
31C2×C4×Dic134C2211yescharacteristic
32C2×C4×Dic134C2211yescharacteristic
33C2×C4×Dic134C2211yescharacteristic
34C2×#14524000C2211yescharacteristic
35C2×#14524000C2211yescharacteristic
36C2×C42×D67C2211yescharacteristic
37#16863527C2218yescomplemented
38#16863526C2218yescomplemented
39#16863525C2218yescomplemented
40#16863525C2218yescomplemented
41#16863524C2218yescomplemented
42#16863524C2218yescomplemented
43#16863523C2218yescomplemented
44#16863421C2218yes—
45#16863421C2218yes—
46#16863418C2218yes—
47C2×C4⋊(C67⋊C8)C2211yescharacteristic
48C2×C4⋊(C67⋊C8)C2211yescharacteristic
49C2×C4⋊(C67⋊C8)C2211yescharacteristic
50C2×Dic67⋊C8C2211yescharacteristic
51C2×Dic67⋊C8C2211yescharacteristic
52C2×Dic67⋊C8C2211yescharacteristic
53C2×Dic67⋊C8C2211yescharacteristic
54C2×Dic67⋊C8C2211yescharacteristic
55C2×Dic67⋊C8C2211yescharacteristic
56#16863353C2218yes—
57#16863350C2218yes—
58C2×#14523954C2211yescharacteristic
59C2×#14523954C2211yescharacteristic
60C2×#14523953C2211yescharacteristic
61C2×#14523953C2211yescharacteristic
62C2×#14523953C2211yescharacteristic
63C2×#14523953C2211yescharacteristic
64#97×D67C2218yes—
65C2×C4×C67⋊C8C2211yescharacteristic
66C2×C8×Dic67C2211yescharacteristic
67C2×C8×Dic67C2211yescharacteristic
68C2×C4×Q8×C67C2211yescharacteristic
69#446×C67C2218yescomplemented
70C2×C4⋊C8×C67C2211yescharacteristic
71C2×C4⋊C8×C67C2211yescharacteristic
72C2×C4⋊C8×C67C2211yescharacteristic
73C2×#97×C67C2211yescharacteristic
74C2×#97×C67C2211yescharacteristic
75C2×C4×C8×C67C2211yescharacteristic
76C22×Dic134C2×C411yescharacteristic
77C22×Dic134C2×C411yescharacteristic
78C22×Dic134C2×C411yescharacteristic
79C22×C4×D67C2×C411yescharacteristic
80C22×C4×D67C2×C411yescharacteristic
81C22×C4×D67C2311yescharacteristic
82C2×#11761611—24no—
83C2×#11761611—24no—
84C2×#11761611C2314yes—
85C2×#11761611C2314yes—
86C22×C67⋊C8C2311yescharacteristic
87C22×C67⋊C8C2311yescharacteristic
88C22×C67⋊C8C2311yescharacteristic
89C22×C67⋊C8C2311yescharacteristic
90C2×C8×D67—24no—
91C2×C8×D67Q818yescomplemented
92C2×C8×D67C2314yes—
93C2×C8×D67C2314yes—
94#14524042C2×C418yes—
95#14524041C2×C418yes—
96#14524033C2×C418yes—
97#14524033C2×C418yes—
98#14524023C2×C418yes—
99#14524021C2×C418yes—
100#14524021C2×C418yes—
101#14524019C2×C418yes—
102C4×Dic134C2×C414yes—
103C4×Dic134C2×C414yes—
104C4×Dic134C2×C414yes—
105C4×Dic134C2314yes—
106C4×Dic134C2314yes—
107C4×Dic134C2314yes—
108#14524000C2×C414yes—
109#14524000C2×C414yes—
110#14524000C2314yes—
111#14524000C2314yes—
112C2×C4⋊Dic67C2×C411yescharacteristic
113C2×C4⋊Dic67C2×C411yescharacteristic
114C2×C4⋊Dic67C2×C411yescharacteristic
115C2×Dic67⋊C4C2×C411yescharacteristic
116C2×Dic67⋊C4C2×C411yescharacteristic
117C2×Dic67⋊C4C2×C411yescharacteristic
118C2×Dic67⋊C4C2×C411yescharacteristic
119C2×Dic67⋊C4C2×C411yescharacteristic
120C2×Dic67⋊C4C2×C411yescharacteristic
121C2×Dic67⋊C4C2×C411yescharacteristic
122C2×Dic67⋊C4C2×C411yescharacteristic
123C2×Dic67⋊C4C2×C411yescharacteristic
124C2×Dic67⋊C4C2×C411yescharacteristic
125C2×(C2×D67)⋊C4C2×C411yescharacteristic
126C2×(C2×D67)⋊C4C2×C411yescharacteristic
127C2×(C2×D67)⋊C4C2×C411yescharacteristic
128C2×(C2×D67)⋊C4C2×C411yescharacteristic
129C2×C4×Dic67C2×C411yescharacteristic
130C2×C4×Dic67C2×C411yescharacteristic
131C2×C4×Dic67C2311yescharacteristic
132C2×C4×Dic67C2311yescharacteristic
133C2×C4×Dic67C2311yescharacteristic
134C42×D67C2×C414yes—
135C42×D67C2314yes—
136C4⋊(C67⋊C8)C2314yes—
137C4⋊(C67⋊C8)C2314yes—
138C4⋊(C67⋊C8)C2314yes—
139Dic67⋊C8C2314yes—
140Dic67⋊C8C2314yes—
141Dic67⋊C8C2314yes—
142Dic67⋊C8C2314yes—
143Dic67⋊C8C2314yes—
144Dic67⋊C8C2314yes—
145#14523954C2314yes—
146#14523954C2314yes—
147#14523953C2314yes—
148#14523953C2314yes—
149#14523953C2314yes—
150#14523953C2314yes—
151C4×C67⋊C8C2314yes—
152C8×Dic67C2314yes—
153C8×Dic67C2314yes—
154C22×Q8×C67C2×C411yescharacteristic
155C22×C8×C67C2311yescharacteristic
156C22×C8×C67C2311yescharacteristic
157C22×C8×C67C2311yescharacteristic
158C22×C8×C67C2311yescharacteristic
159C4×Q8×C67C2×C414yes—
160C4×Q8×C67C2314yes—
161C2×C4⋊C4×C67C2×C411yescharacteristic
162C2×C4⋊C4×C67C2×C411yescharacteristic
163C2×C4⋊C4×C67C2×C411yescharacteristic
164C2×C42×C67C2311yescharacteristic
165C2×C42×C67C2311yescharacteristic
166C2×C42×C67C2311yescharacteristic
167C4⋊C8×C67C2314yes—
168C4⋊C8×C67C2314yes—
169C4⋊C8×C67C2314yes—
170#97×C67C2314yes—
171#97×C67C2314yes—
172C4×C8×C67C2314yes—
173C23×D67C22×C411yescharacteristic
174C2×Dic134—42no—
175C2×Dic134—42no—
176C2×Dic134—42no—
177C2×Dic134C22×C414yes—
178C2×Dic134C22×C414yes—
179C2×Dic134C22×C414yes—
180C22×Dic67C22×C411yescharacteristic
181C22×Dic67C22×C411yescharacteristic
182C22×Dic67C22×C411yescharacteristic
183C22×Dic67C22×C411yescharacteristic
184C22×Dic67C22×C411yescharacteristic
185C22×Dic67C22×C411yescharacteristic
186C22×Dic67C22×C411yescharacteristic
187C2×C4×D67—42no—
188C2×C4×D67—42no—
189C2×C4×D67C22×C414yes—
190C2×C4×D67C22×C414yes—
191C2×C4×D67C22×C412yes—
192C2×C4×D67C2×Q814yes—
193C2×C4×D67#4114yes—
194C2×C4×D67C2412yes—
195#11761611—28no—
196#11761611—28no—
197C2×C67⋊C8—22no—
198C2×C67⋊C8—22no—
199C2×C67⋊C8—22no—
200C2×C67⋊C8C2×Q814yes—
201C2×C67⋊C8C2412yes—
202C2×C67⋊C8C2412yes—
203C2×C67⋊C8C2412yes—
204C2×C67⋊C8C2412yes—
205C8×D67—28no—
206C8×D67C2×Q8116yescomplemented
207C4⋊Dic67C22×C414yes—
208C4⋊Dic67C22×C414yes—
209C4⋊Dic67C22×C414yes—
210Dic67⋊C4C22×C414yes—
211Dic67⋊C4C22×C414yes—
212Dic67⋊C4C22×C414yes—
213Dic67⋊C4C22×C414yes—
214Dic67⋊C4C22×C414yes—
215Dic67⋊C4C22×C414yes—
216Dic67⋊C4C22×C414yes—
217Dic67⋊C4C22×C414yes—
218Dic67⋊C4C22×C414yes—
219Dic67⋊C4C22×C414yes—
220(C2×D67)⋊C4C22×C414yes—
221(C2×D67)⋊C4C22×C414yes—
222(C2×D67)⋊C4C22×C414yes—
223(C2×D67)⋊C4C22×C414yes—
224C4×Dic67C22×C412yes—
225C4×Dic67C22×C414yes—
226C4×Dic67C22×C414yes—
227C4×Dic67C22×C412yes—
228C4×Dic67C22×C412yes—
229C4×Dic67C2412yes—
230C4×Dic67C2412yes—
231C4×Dic67C2412yes—
232C2×Q8×C67—42no—
233C2×Q8×C67C22×C414yes—
234C22×C4×C67C22×C411yescharacteristic
235C22×C4×C67C22×C411yescharacteristic
236C22×C4×C67C22×C411yescharacteristic
237C22×C4×C67C22×C411yescharacteristic
238C22×C4×C67C22×C411yescharacteristic
239C22×C4×C67C22×C411yescharacteristic
240C22×C4×C67C2411yescharacteristic
241C2×C8×C67—22no—
242C2×C8×C67—22no—
243C2×C8×C67—22no—
244C2×C8×C67C2×Q814yes—
245C2×C8×C67C2412yes—
246C2×C8×C67C2412yes—
247C2×C8×C67C2412yes—
248C2×C8×C67C2412yes—
249C4⋊C4×C67C22×C414yes—
250C4⋊C4×C67C22×C414yes—
251C4⋊C4×C67C22×C414yes—
252C42×C67C22×C412yes—
253C42×C67C22×C412yes—
254C42×C67C22×C412yes—
255C42×C67C2412yes—
256C42×C67C2412yes—
257C42×C67C2412yes—
258C23×C67C23×C411yescharacteristic
259C22×D67—22no—
260C22×D67—22no—
261C22×D67C4×Q814yes—
262C22×D67C23×C412yes—
263Q8×C67—44no—
264C2×C4×C67—22no—
265C2×C4×C67—22no—
266C2×C4×C67—22no—
267C2×C4×C67—22no—
268C2×C4×C67—22no—
269C2×C4×C67—22no—
270C2×C4×C67C23×C412yes—
271C2×C4×C67C23×C412yes—
272C2×C4×C67C23×C412yes—
273C2×C4×C67C23×C412yes—
274C2×C4×C67C23×C412yes—
275C2×C4×C67C23×C412yes—
276C2×C4×C67C23×C411yescharacteristic
277C2×C4×C67C22×Q812yes—
278C2×C4×C67C2×#4112yes—
279C2×C4×C67C2511yescharacteristic
280C2×Dic67—22no—
281C2×Dic67—22no—
282C2×Dic67—22no—
283C2×Dic67—22no—
284C2×Dic67—22no—
285C2×Dic67—22no—
286C2×Dic67C4×Q814yes—
287C2×Dic67C23×C412yes—
288C2×Dic67C23×C412yes—
289C2×Dic67C23×C412yes—
290C2×Dic67C23×C412yes—
291C2×Dic67C23×C412yes—
292C2×Dic67C23×C412yes—
293C2×Dic67C23×C412yes—
294C4×D67—44no—
295C4×D67—44no—
296C4×D67C4×Q818yes—
297C4×D67C22×Q814yes—
298C4×D67C2×#4114yes—
299Dic134—44no—
300Dic134—44no—
301Dic134—44no—
302C8×C67—22no—
303C8×C67—22no—
304C8×C67—22no—
305C8×C67C22×Q814yes—
306C67⋊C8—22no—
307C67⋊C8—22no—
308C67⋊C8—22no—
309C67⋊C8C22×Q814yes—
310C22×C67C2×C4×Q812yes—
311C22×C67#56812yes—
312C22×C67#56812yes—
313C22×C67C24×C411yescharacteristic
314C2×D67—28no—
315C2×D67—22no—
316C2×D67—22no—
317C2×D67C2×C4×Q814yes—
318C4×C67—22no—
319C4×C67—22no—
320C4×C67—22no—
321C4×C67—22no—
322C4×C67—22no—
323C4×C67—22no—
324C4×C67C2×C4×Q812yes—
325C4×C67C23×Q811yescharacteristic
326C4×C67C22×#4111yescharacteristic
327Dic67—22no—
328Dic67—22no—
329Dic67—22no—
330Dic67—22no—
331Dic67—22no—
332Dic67—22no—
333Dic67C2×C4×Q814yes—
334C2×#2961—671nomaximal, Sylow
335C2×C67#296114yescomplemented
336C2×C67C22×C4×Q811yescharacteristic
337C2×C67C2×#56811yescharacteristic
338C2×C67C2×#56811yescharacteristic
339D67—24no—
340C2×#533—671no—
341#2961—6716no—
342C2×#446—671no—
343C2×#446—671no—
344C2×#446—671no—
345C2×#446—671no—
346C2×#446—671no—
347C2×#446—671no—
348C2×#446—671no—
349C2×#446D6711yescharacteristic, complemented
350C2×#424—671no—
351C2×#424—671no—
352C2×#423—671no—
353C2×#405—671no—
354C2×#405—671no—
355C22×#97—671no—
356C67C2×#296111yescharacteristic, complemented, Sylow
357C22×M16—671no—
358C22×M16—671no—
359C23×C8—671no—
360C23×C8—671no—
361#533—678no—
362#533—678no—
363C2×C4⋊Q8—671no—
364C2×C4⋊Q8—671no—
365C2×#125—671no—
366C2×#125—671no—
367C2×C22⋊Q8—671no—
368C2×C22⋊Q8—671no—
369C2×C22⋊Q8—671no—
370C2×C22⋊Q8—671no—
371C2×C4×Q8—671no—
372C2×C4×Q8—671no—
373C2×C4×Q8—671no—
374C2×C4×Q8C2×D6711yescharacteristic
375C2×#117—671no—
376C2×#117—671no—
377C22×C42—671no—
378#446—678no—
379#446—678no—
380#446—678no—
381#446—678no—
382#446—678no—
383#446—678no—
384#446—678no—
385#446C2×D6718yescomplemented
386#424—678no—
387#424—678no—
388#423—678no—
389C2×C4⋊C8—671no—
390C2×C4⋊C8—671no—
391C2×C4⋊C8—671no—
392C2×C4⋊C8—671no—
393C2×C4⋊C8—671no—
394C2×C4⋊C8—671no—
395C2×C4⋊C8—671no—
396C2×C4⋊C8—671no—
397C2×C4⋊C8—671no—
398C2×C4⋊C8C2×D6711yescharacteristic
399C2×C4⋊C8C2×D6711yescharacteristic
400C2×C4⋊C8C2×D6711yescharacteristic
401#405—678no—
402#405—678no—
403C2×#97—671no—
404C2×#97—671no—
405C2×#97—671no—
406C2×#97—671no—
407C2×#97—671no—
408C2×#97—671no—
409C2×#97—678no—
410C2×#97C2×D6711yescharacteristic
411C2×#97C2×D6711yescharacteristic
412C2×C4×C8—671no—
413C2×C4×C8—671no—
414C2×C4×C8—671no—
415C2×C4×C8C2×D6711yescharacteristic
416C22×Q8—671no—
417C22×Q8—671no—
418C22×Q8—671no—
419C22×Q8C4×D6711yescharacteristic
420C23×C4—671no—
421C23×C4—671no—
422C23×C4—671no—
423C2×M16—674no—
424C2×M16—674no—
425C2×M16—1344no—
426C2×M16—1344no—
427C22×C8—671no—
428C22×C8—678no—
429C22×C8—674no—
430C22×C8—671no—
431C22×C8—671no—
432C22×C8—671no—
433C22×C8—674no—
434C22×C8—1344no—
435C22×C8C22×D6711yescharacteristic
436C22×C8C22×D6711yescharacteristic
437C22×C8C22×D6711yescharacteristic
438C22×C8C22×D6711yescharacteristic
439C4⋊Q8—678no—
440C4⋊Q8—678no—
441#125—678no—
442#125—678no—
443C22⋊Q8—678no—
444C22⋊Q8—678no—
445C22⋊Q8—678no—
446C22⋊Q8—678no—
447C4×Q8—674no—
448C4×Q8—674no—
449C4×Q8—674no—
450C4×Q8—674no—
451C4×Q8—674no—
452C4×Q8—674no—
453C4×Q8C4×D6714yes—
454C4×Q8C22×D6714yes—
455#117—674no—
456#117—674no—
457#117—674no—
458#117—674no—
459C2×C4⋊C4—671no—
460C2×C4⋊C4—671no—
461C2×C4⋊C4—671no—
462C2×C4⋊C4—671no—
463C2×C4⋊C4—671no—
464C2×C4⋊C4—671no—
465C2×C4⋊C4—671no—
466C2×C4⋊C4—671no—
467C2×C4⋊C4—671no—
468C2×C4⋊C4—671no—
469C2×C4⋊C4—671no—
470C2×C4⋊C4—671no—
471C2×C4⋊C4—671no—
472C2×C4⋊C4C4×D6711yescharacteristic
473C2×C4⋊C4C4×D6711yescharacteristic
474C2×C4⋊C4C4×D6711yescharacteristic
475C2×C22⋊C4—671no—
476C2×C22⋊C4—671no—
477C2×C22⋊C4—671no—
478C2×C22⋊C4—671no—
479C2×C42—671no—
480C2×C42—671no—
481C2×C42—671no—
482C2×C42—671no—
483C2×C42—671no—
484C2×C42—674no—
485C2×C42—674no—
486C2×C42C22×D6711yescharacteristic
487C2×C42C22×D6711yescharacteristic
488C2×C42C22×D6711yescharacteristic
489C4⋊C8—674no—
490C4⋊C8—674no—
491C4⋊C8—674no—
492C4⋊C8—674no—
493C4⋊C8—674no—
494C4⋊C8—674no—
495C4⋊C8—674no—
496C4⋊C8—674no—
497C4⋊C8—674no—
498C4⋊C8C22×D6714yes—
499C4⋊C8C22×D6714yes—
500C4⋊C8C22×D6714yes—
501#97—674no—
502#97—674no—
503#97—674no—
504#97—674no—
505#97—674no—
506#97—674no—
507#97C22×D6714yes—
508#97C22×D6714yes—
509C4×C8—674no—
510C4×C8—674no—
511C4×C8—674no—
512C4×C8C22×D6714yes—
513C24—671no—
514C2×Q8—42no—
515C2×Q8—2682no—
516C2×Q8—2682no—
517C2×Q8—2682no—
518C2×Q8—674no—
519C2×Q8—674no—
520C2×Q8—674no—
521C2×Q8C2×C4×D6714yes—
522C22×C4—2682no—
523C22×C4—2682no—
524C22×C4—674no—
525C22×C4—674no—
526C22×C4—671no—
527C22×C4—672no—
528C22×C4—674no—
529C22×C4—674no—
530C22×C4—672no—
531C22×C4—671no—
532C22×C4—671no—
533C22×C4—671no—
534C22×C4—671no—
535C22×C4—671no—
536C22×C4—671no—
537C22×C4C2×C4×D6711yescharacteristic
538C22×C4C2×C4×D6711yescharacteristic
539C22×C4C2×C4×D6711yescharacteristic
540C22×C4C2×C4×D6711yescharacteristic
541C22×C4C2×C4×D6711yescharacteristic
542C22×C4C2×C4×D6711yescharacteristic
543C22×C4C23×D6711yescharacteristic
544M16—1348no—
545M16—1348no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—674no—
550C2×C8—672no—
551C2×C8—6716no—
552C2×C8—672no—
553C2×C8—672no—
554C2×C8—672no—
555C2×C8—1348no—
556C2×C8—1342no—
557C2×C8—1342no—
558C2×C8—1342no—
559C2×C8Q8×D6714yes—
560C2×C8C23×D6712yes—
561C2×C8C23×D6712yes—
562C2×C8C23×D6712yes—
563C2×C8C23×D6712yes—
564C4⋊C4—674no—
565C4⋊C4—674no—
566C4⋊C4—674no—
567C4⋊C4—674no—
568C4⋊C4—674no—
569C4⋊C4—674no—
570C4⋊C4—674no—
571C4⋊C4—674no—
572C4⋊C4—674no—
573C4⋊C4—674no—
574C4⋊C4—674no—
575C4⋊C4—674no—
576C4⋊C4—674no—
577C4⋊C4C2×C4×D6714yes—
578C4⋊C4C2×C4×D6714yes—
579C4⋊C4C2×C4×D6714yes—
580C22⋊C4—674no—
581C22⋊C4—674no—
582C22⋊C4—674no—
583C22⋊C4—674no—
584C42—672no—
585C42—674no—
586C42—674no—
587C42—672no—
588C42—672no—
589C42—672no—
590C42—672no—
591C42—672no—
592C42C2×C4×D6712yes—
593C42C2×C4×D6712yes—
594C42C2×C4×D6712yes—
595C42C23×D6712yes—
596C42C23×D6712yes—
597C42C23×D6712yes—
598C23—674no—
599C23—672no—
600C23—1342no—
601C23—1342no—
602C23C22×C4×D6711yescharacteristic
603Q8—44no—
604Q8—2684no—
605Q8—2684no—
606Q8—2684no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—2684no—
614C2×C4—2684no—
615C2×C4—674no—
616C2×C4—672no—
617C2×C4—678no—
618C2×C4—674no—
619C2×C4—674no—
620C2×C4—672no—
621C2×C4—672no—
622C2×C4—672no—
623C2×C4—672no—
624C2×C4—672no—
625C2×C4—672no—
626C2×C4—1342no—
627C2×C4—1342no—
628C2×C4—1342no—
629C2×C4—1342no—
630C2×C4—1342no—
631C2×C4—1342no—
632C2×C4C22×C4×D6712yes—
633C2×C4C22×C4×D6712yes—
634C2×C4C22×C4×D6712yes—
635C2×C4C22×C4×D6712yes—
636C2×C4C22×C4×D6712yes—
637C2×C4C22×C4×D6712yes—
638C2×C4C22×C4×D6711yescharacteristic
639C2×C4C2×Q8×D6712yes—
640C2×C4#41×D6712yes—
641C2×C4C24×D6711yescharacteristic
642C8—22no—
643C8—22no—
644C8—22no—
645C8—674no—
646C8—1342no—
647C8—1342no—
648C8—1342no—
649C8C2×Q8×D6714yes—
650C22—674no—
651C22—1342no—
652C22—1342no—
653C22—1348no—
654C22C4×Q8×D6712yes—
655C22#1686416112yes—
656C22#1686416212yes—
657C22C23×C4×D6711yescharacteristic
658C4—22no—
659C4—22no—
660C4—22no—
661C4—22no—
662C4—22no—
663C4—22no—
664C4—674no—
665C4—1342no—
666C4—1342no—
667C4—1342no—
668C4—1342no—
669C4—1342no—
670C4—1342no—
671C4C4×Q8×D6712yes—
672C4C22×Q8×D6711yescharacteristic
673C4C2×#41×D6711yescharacteristic
674C2—1344no—
675C2#2256914514yesdirect product factor
676C2C2×C4×Q8×D6711yescharacteristic
677C2C2×#1686416111yescharacteristic
678C2C2×#1686416211yescharacteristic
subgroupG/H
centerC22×C4C23×D67
commutatorC22×C67C24×C4
FrattiniC2×C4C24×D67
FittingC2×#446×C67C2
socleC23×C67C23×C4
prime radicalC23×D67C22×C4
cosocleC2×C4×C67C25
hypercenterC2×#446D67
hypocenterC67C2×#2961
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. #22569145C2direct (N × H)
3. C2×#16863527C2semidirect
4. C2×#16863526C2semidirect
5. C2×#16863525C2semidirect
6. C2×#16863525C2semidirect
7. C2×#16863524C2semidirect
8. C2×#16863524C2semidirect
9. C2×#16863523C2semidirect
16. C2×#446×C67C2semidirect
37. #16863527C22semidirect
38. #16863526C22semidirect
39. #16863525C22semidirect
40. #16863525C22semidirect
41. #16863524C22semidirect
42. #16863524C22semidirect
43. #16863523C22semidirect
69. #446×C67C22semidirect
91. C2×C8×D67Q8semidirect
206. C8×D67C2×Q8semidirect
335. C2×C67#2961semidirect
349. C2×#446D67semidirect
356. C67C2×#2961semidirect
385. #446C2×D67semidirect
675. C2#22569145direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168639502
#225691452
C2×#168635272
C2×#168635262
C2×#168635252
C2×#168635242
C2×#168635232
C2×#168634212
C2×#168634182
C2×#168633532
C2×#168633502
C2×#97×D672
C2×#446×C672
C2×#296167