Finite Group Databasebeta

← C2×#22569301 #31720784

Subgroups — C2×#22569301 #31720784

Order 17152.

1750 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16863949C211yesmaximal, characteristic
2#22569301C2116yesmaximal, direct product factor
3C2×#16863526C211yesmaximal, characteristic, complemented
4C2×#16863525C211yesmaximal, characteristic, complemented
5C2×#16863525C211yesmaximal, characteristic, complemented
6C2×#16863524C211yesmaximal, characteristic, complemented
7C2×#16863524C211yesmaximal, characteristic, complemented
8C2×#16863523C211yesmaximal, characteristic, complemented
9C2×C8×Dic134C211yesmaximal, characteristic, complemented
10C2×#16863520C211yesmaximal, characteristic, complemented
11C2×#16863457C211yesmaximal, characteristic
12C2×#16863454C211yesmaximal, characteristic
13C2×#16863454C211yesmaximal, characteristic
14C2×#16863450C211yesmaximal, characteristic
15C2×#16863446C211yesmaximal, characteristic
16C2×#433×C67C211yesmaximal, characteristic
17#16863949C418yes—
18#16863949C2218yes—
19C2×#14524042C411yescharacteristic
20C2×#14524042C411yescharacteristic
21C2×#14524034C411yescharacteristic
22C2×#14524034C411yescharacteristic
23C2×#14524020C411yescharacteristic
24C2×#14524020C411yescharacteristic
25C2×#14524020C411yescharacteristic
26C2×#14524020C411yescharacteristic
27C2×C4×Dic134C2211yescharacteristic
28C2×C4×Dic134C2211yescharacteristic
29C2×C4×Dic134C2211yescharacteristic
30C2×C4×Dic134C2211yescharacteristic
31C2×#14524002C2211yescharacteristic
32C22×C4×Dic67C2211yescharacteristic
33#16863526C2218yescomplemented
34#16863525C2218yescomplemented
35#16863525C2218yescomplemented
36#16863524C2218yescomplemented
37#16863524C2218yescomplemented
38#16863523C2218yescomplemented
39C8×Dic134C2218yescomplemented
40#16863520C2218yescomplemented
41#16863457C2218yes—
42#16863454C2218yes—
43#16863454C2218yes—
44#16863450C2218yes—
45#16863446C2218yes—
46C2×C4⋊(C67⋊C8)C2211yescharacteristic
47C2×C4⋊(C67⋊C8)C2211yescharacteristic
48C2×Dic67⋊C8C2211yescharacteristic
49C2×Dic67⋊C8C2211yescharacteristic
50C2×Dic67⋊C8C2211yescharacteristic
51C2×Dic67⋊C8C2211yescharacteristic
52C2×Dic67⋊C8C2211yescharacteristic
53C2×Dic67⋊C8C2211yescharacteristic
54C2×Dic67⋊C8C2211yescharacteristic
55C2×Dic67⋊C8C2211yescharacteristic
56C2×C22⋊(C67⋊C8)C2211yescharacteristic
57C2×C22⋊(C67⋊C8)C2211yescharacteristic
58C2×#14523954C2211yescharacteristic
59C2×#14523953C2211yescharacteristic
60C2×#14523953C2211yescharacteristic
61C2×#14523953C2211yescharacteristic
62C2×#14523953C2211yescharacteristic
63C2×C4×C67⋊C8C2211yescharacteristic
64C2×C8×Dic67C2211yescharacteristic
65C2×C8×Dic67C2211yescharacteristic
66C2×C8×Dic67C2211yescharacteristic
67C2×C8×Dic67C2211yescharacteristic
68C2×#117×C67C2211yescharacteristic
69#433×C67C2218yes—
70C2×C4⋊C8×C67C2211yescharacteristic
71C2×C4⋊C8×C67C2211yescharacteristic
72C2×C22⋊C8×C67C2211yescharacteristic
73C2×C22⋊C8×C67C2211yescharacteristic
74C2×#97×C67C2211yescharacteristic
75C2×C4×C8×C67C2211yescharacteristic
76C22×Dic134C2×C411yescharacteristic
77C22×Dic134C2×C411yescharacteristic
78C22×Dic134C2×C411yescharacteristic
79C22×Dic134C2×C411yescharacteristic
80C23×Dic67C2×C411yescharacteristic
81C23×Dic67C2×C411yescharacteristic
82C22×C67⋊C8C2311yescharacteristic
83C22×C67⋊C8C2311yescharacteristic
84C22×C67⋊C8C2311yescharacteristic
85C22×C67⋊C8C2311yescharacteristic
86#14524042C2×C418yes—
87#14524042C2×C418yes—
88#14524034C2×C418yes—
89#14524034C2×C418yes—
90#14524020C2×C418yes—
91#14524020C2×C418yes—
92#14524020C2×C418yes—
93#14524020C2×C418yes—
94C4×Dic134C2×C414yes—
95C4×Dic134C2×C414yes—
96C4×Dic134C2×C414yes—
97C4×Dic134C2×C414yes—
98C4×Dic134C2314yes—
99C4×Dic134C2314yes—
100C4×Dic134C2314yes—
101C4×Dic134C2314yes—
102#14524002C2×C414yes—
103#14524002C2314yes—
104C2×C4⋊Dic67C2×C411yescharacteristic
105C2×C4⋊Dic67C2×C411yescharacteristic
106C2×C4⋊Dic67C2×C411yescharacteristic
107C2×C4⋊Dic67C2×C411yescharacteristic
108C2×C4⋊Dic67C2×C411yescharacteristic
109C2×C4⋊Dic67C2×C411yescharacteristic
110C2×Dic67⋊C4C2×C411yescharacteristic
111C2×Dic67⋊C4C2×C411yescharacteristic
112C2×Dic67⋊C4C2×C411yescharacteristic
113C2×Dic67⋊C4C2×C411yescharacteristic
114C2×Dic67⋊C4C2×C411yescharacteristic
115C2×Dic67⋊C4C2×C411yescharacteristic
116C2×Dic67⋊C4C2×C411yescharacteristic
117C2×Dic67⋊C4C2×C411yescharacteristic
118C2×C22⋊Dic67C2×C411yescharacteristic
119C2×C22⋊Dic67C2×C411yescharacteristic
120C2×C4×Dic67C2×C411yescharacteristic
121C2×C4×Dic67C2×C411yescharacteristic
122C2×C4×Dic67C2×C414yes—
123C2×C4×Dic67C2311yescharacteristic
124C2×C4×Dic67C2311yescharacteristic
125C2×C4×Dic67C2314yes—
126C2×C4×Dic67C2311yescharacteristic
127C2×C4×Dic67C2311yescharacteristic
128C4⋊(C67⋊C8)C2314yes—
129C4⋊(C67⋊C8)C2314yes—
130Dic67⋊C8C2314yes—
131Dic67⋊C8C2314yes—
132Dic67⋊C8C2314yes—
133Dic67⋊C8C2314yes—
134Dic67⋊C8C2314yes—
135Dic67⋊C8C2314yes—
136Dic67⋊C8C2314yes—
137Dic67⋊C8C2314yes—
138C22⋊(C67⋊C8)C2314yes—
139C22⋊(C67⋊C8)C2314yes—
140#14523954C2314yes—
141#14523953C2314yes—
142#14523953C2314yes—
143#14523953C2314yes—
144#14523953C2314yes—
145C4×C67⋊C8C2314yes—
146C8×Dic67C2314yes—
147C8×Dic67C2314yes—
148C8×Dic67C2314yes—
149C8×Dic67C2314yes—
150C23×C4×C67C2311yescharacteristic
151C22×C8×C67C2311yescharacteristic
152C22×C8×C67C2311yescharacteristic
153C22×C8×C67C2311yescharacteristic
154C22×C8×C67C2311yescharacteristic
155#117×C67C2×C414yes—
156#117×C67C2314yes—
157C2×C4⋊C4×C67C2×C411yescharacteristic
158C2×C4⋊C4×C67C2×C411yescharacteristic
159C2×C22⋊C4×C67C2×C411yescharacteristic
160C2×C22⋊C4×C67C2×C411yescharacteristic
161C2×C42×C67C2311yescharacteristic
162C2×C42×C67C2311yescharacteristic
163C4⋊C8×C67C2314yes—
164C4⋊C8×C67C2314yes—
165C22⋊C8×C67C2314yes—
166C22⋊C8×C67C2314yes—
167#97×C67C2314yes—
168C4×C8×C67C2314yes—
169C2×Dic134—24no—
170C2×Dic134—24no—
171C2×Dic134—42no—
172C2×Dic134—42no—
173C2×Dic134C22×C414yes—
174C2×Dic134C22×C414yes—
175C2×Dic134C22×C414yes—
176C2×Dic134C22×C414yes—
177C22×Dic67—24no—
178C22×Dic67—42no—
179C22×Dic67C22×C411yescharacteristic
180C22×Dic67C22×C411yescharacteristic
181C22×Dic67C22×C411yescharacteristic
182C22×Dic67C22×C414yes—
183C22×Dic67C22×C411yescharacteristic
184C22×Dic67C22×C411yescharacteristic
185C22×Dic67C22×C411yescharacteristic
186C22×Dic67C22×C411yescharacteristic
187C22×Dic67C22×C414yes—
188C22×Dic67C22×C411yescharacteristic
189C2×C67⋊C8—22no—
190C2×C67⋊C8—22no—
191C2×C67⋊C8—22no—
192C2×C67⋊C8—22no—
193C2×C67⋊C8C2412yes—
194C2×C67⋊C8C2412yes—
195C2×C67⋊C8C2412yes—
196C2×C67⋊C8C2412yes—
197C4⋊Dic67C22×C414yes—
198C4⋊Dic67C22×C414yes—
199C4⋊Dic67C22×C414yes—
200C4⋊Dic67C22×C414yes—
201C4⋊Dic67C22×C414yes—
202C4⋊Dic67C22×C414yes—
203Dic67⋊C4C22×C414yes—
204Dic67⋊C4C22×C414yes—
205Dic67⋊C4C22×C414yes—
206Dic67⋊C4C22×C414yes—
207Dic67⋊C4C22×C414yes—
208Dic67⋊C4C22×C414yes—
209Dic67⋊C4C22×C414yes—
210Dic67⋊C4C22×C414yes—
211C22⋊Dic67C22×C414yes—
212C22⋊Dic67C22×C414yes—
213C4×Dic67C22×C412yes—
214C4×Dic67C22×C412yes—
215C4×Dic67C22×C414yes—
216C4×Dic67C22×C414yes—
217C4×Dic67C22×C412yes—
218C4×Dic67C22×C412yes—
219C4×Dic67C2412yes—
220C4×Dic67C2412yes—
221C4×Dic67C2412yes—
222C4×Dic67C2412yes—
223C24×C67C22×C411yescharacteristic
224C22×C4×C67—22no—
225C22×C4×C67—22no—
226C22×C4×C67C22×C411yescharacteristic
227C22×C4×C67C22×C411yescharacteristic
228C22×C4×C67C22×C411yescharacteristic
229C22×C4×C67C22×C411yescharacteristic
230C22×C4×C67C22×C411yescharacteristic
231C22×C4×C67C22×C412yes—
232C22×C4×C67C2412yes—
233C22×C4×C67C2411yescharacteristic
234C2×C8×C67—22no—
235C2×C8×C67—22no—
236C2×C8×C67—22no—
237C2×C8×C67—22no—
238C2×C8×C67C2412yes—
239C2×C8×C67C2412yes—
240C2×C8×C67C2412yes—
241C2×C8×C67C2412yes—
242C4⋊C4×C67C22×C414yes—
243C4⋊C4×C67C22×C414yes—
244C22⋊C4×C67C22×C414yes—
245C22⋊C4×C67C22×C414yes—
246C42×C67C22×C412yes—
247C42×C67C22×C412yes—
248C42×C67C2412yes—
249C42×C67C2412yes—
250C23×C67—22no—
251C23×C67—22no—
252C23×C67—22no—
253C23×C67C23×C412yes—
254C23×C67C23×C411yescharacteristic
255C2×C4×C67—22no—
256C2×C4×C67—22no—
257C2×C4×C67—22no—
258C2×C4×C67—22no—
259C2×C4×C67—22no—
260C2×C4×C67—24no—
261C2×C4×C67—22no—
262C2×C4×C67—22no—
263C2×C4×C67C23×C412yes—
264C2×C4×C67C23×C412yes—
265C2×C4×C67C23×C412yes—
266C2×C4×C67C23×C412yes—
267C2×C4×C67C23×C412yes—
268C2×C4×C67C23×C411yescharacteristic
269C2×C4×C672−1+412yes—
270C2×C4×C672−1+412yes—
271C2×C4×C67C2511yescharacteristic
272C2×Dic67—22no—
273C2×Dic67—22no—
274C2×Dic67—22no—
275C2×Dic67—22no—
276C2×Dic67—22no—
277C2×Dic67—22no—
278C2×Dic67—22no—
279C2×Dic67—28no—
280C2×Dic67—44no—
281C2×Dic67#13114yes—
282C2×Dic67C23×C412yes—
283C2×Dic67C23×C412yes—
284C2×Dic67C23×C412yes—
285C2×Dic67C23×C412yes—
286C2×Dic67C23×C412yes—
287C2×Dic67C23×C412yes—
288C2×Dic67C23×C412yes—
289C2×Dic67C23×C412yes—
290Dic134—28no—
291Dic134—28no—
292Dic134—44no—
293Dic134—44no—
294C8×C67—22no—
295C8×C67—22no—
296C8×C67—22no—
297C8×C67—22no—
298C67⋊C8—22no—
299C67⋊C8—22no—
300C67⋊C8—22no—
301C67⋊C8—22no—
302C22×C67—22no—
303C22×C67—22no—
304C22×C67—22no—
305C22×C67—44no—
306C22×C67#51912yes—
307C22×C67C2×#13112yes—
308C22×C67#56812yes—
309C22×C67C24×C411yescharacteristic
310C4×C67—22no—
311C4×C67—22no—
312C4×C67—22no—
313C4×C67—22no—
314C4×C67—22no—
315C4×C67#51912yes—
316C4×C67C2×2−1+411yescharacteristic
317C4×C67C2×2−1+411yescharacteristic
318Dic67—22no—
319Dic67—22no—
320Dic67—22no—
321Dic67—22no—
322Dic67—22no—
323Dic67—22no—
324Dic67—22no—
325Dic67C2×#13114yes—
326C2×#2985—671nomaximal, Sylow
327C2×C67—42no—
328C2×C67#298514yescomplemented
329C2×C67C2×#51911yescharacteristic
330C2×C67C22×#13111yescharacteristic
331C2×C67C2×#56811yescharacteristic
332C2×#533—671no—
333#2985—6716no—
334C2×#446—671no—
335C2×#446—671no—
336C2×#446—671no—
337C2×#446—671no—
338C2×#446—671no—
339C2×#446—671no—
340C2×C8×Q8—671no—
341C2×C8×Q8—671no—
342C2×#433—671no—
343C2×#433—671no—
344C2×#433—671no—
345C2×#433D6711yescharacteristic
346C2×#432—671no—
347C2×#431—671no—
348C67C2×#298511yescharacteristic, complemented, Sylow
349#533—678no—
350#533—678no—
351C2×C4⋊Q8—671no—
352C2×C4⋊Q8—671no—
353C2×#125—671no—
354C2×#125—671no—
355C2×C22⋊Q8—671no—
356C2×C22⋊Q8—671no—
357C2×C22⋊Q8—671no—
358C2×C22⋊Q8—671no—
359C2×C4×Q8—671no—
360C2×C4×Q8—671no—
361C2×C4×Q8—671no—
362C2×C4×Q8—671no—
363C2×#117—671no—
364C2×#117C2×D6711yescharacteristic
365C22×C42—671no—
366#446—678no—
367#446—678no—
368#446—678no—
369#446—678no—
370#446—678no—
371#446—678no—
372C8×Q8—678no—
373C8×Q8—678no—
374#433—678no—
375#433—678no—
376#433—678no—
377#433C2×D6718yes—
378#432—678no—
379#431—678no—
380C2×C4⋊C8—671no—
381C2×C4⋊C8—671no—
382C2×C4⋊C8—671no—
383C2×C4⋊C8—671no—
384C2×C4⋊C8—671no—
385C2×C4⋊C8—671no—
386C2×C4⋊C8—671no—
387C2×C4⋊C8—671no—
388C2×C4⋊C8—671no—
389C2×C4⋊C8—671no—
390C2×C4⋊C8C2×D6711yescharacteristic
391C2×C4⋊C8C2×D6711yescharacteristic
392C2×C22⋊C8—671no—
393C2×C22⋊C8—671no—
394C2×C22⋊C8C2×D6711yescharacteristic
395C2×C22⋊C8C2×D6711yescharacteristic
396C2×#97—671no—
397C2×#97—671no—
398C2×#97—671no—
399C2×#97—671no—
400C2×#97—671no—
401C2×#97C2×D6711yescharacteristic
402C2×C4×C8—671no—
403C2×C4×C8—671no—
404C2×C4×C8—671no—
405C2×C4×C8—671no—
406C2×C4×C8—671no—
407C2×C4×C8C2×D6711yescharacteristic
408C22×Q8—671no—
409C22×Q8—671no—
410C22×Q8—671no—
411C22×Q8—671no—
412C23×C4—671no—
413C23×C4—671no—
414C23×C4C22×D6711yescharacteristic
415C22×C8—671no—
416C22×C8—671no—
417C22×C8—671no—
418C22×C8—671no—
419C22×C8C22×D6711yescharacteristic
420C22×C8C22×D6711yescharacteristic
421C22×C8C22×D6711yescharacteristic
422C22×C8C22×D6711yescharacteristic
423C4⋊Q8—678no—
424C4⋊Q8—678no—
425#125—678no—
426#125—678no—
427C22⋊Q8—678no—
428C22⋊Q8—678no—
429C22⋊Q8—678no—
430C22⋊Q8—678no—
431C4×Q8—674no—
432C4×Q8—674no—
433C4×Q8—674no—
434C4×Q8—674no—
435C4×Q8—674no—
436C4×Q8—674no—
437C4×Q8—674no—
438C4×Q8—674no—
439#117—674no—
440#117—674no—
441#117C4×D6714yes—
442#117C22×D6714yes—
443C2×C4⋊C4—671no—
444C2×C4⋊C4—671no—
445C2×C4⋊C4—671no—
446C2×C4⋊C4—671no—
447C2×C4⋊C4—671no—
448C2×C4⋊C4—671no—
449C2×C4⋊C4—671no—
450C2×C4⋊C4—671no—
451C2×C4⋊C4—671no—
452C2×C4⋊C4—671no—
453C2×C4⋊C4—671no—
454C2×C4⋊C4—671no—
455C2×C4⋊C4—671no—
456C2×C4⋊C4—671no—
457C2×C4⋊C4C4×D6711yescharacteristic
458C2×C4⋊C4C4×D6711yescharacteristic
459C2×C22⋊C4—671no—
460C2×C22⋊C4—671no—
461C2×C22⋊C4C4×D6711yescharacteristic
462C2×C22⋊C4C4×D6711yescharacteristic
463C2×C42—671no—
464C2×C42—671no—
465C2×C42—674no—
466C2×C42—674no—
467C2×C42—671no—
468C2×C42—671no—
469C2×C42—671no—
470C2×C42—671no—
471C2×C42C22×D6711yescharacteristic
472C2×C42C22×D6711yescharacteristic
473C4⋊C8—674no—
474C4⋊C8—674no—
475C4⋊C8—674no—
476C4⋊C8—674no—
477C4⋊C8—674no—
478C4⋊C8—674no—
479C4⋊C8—674no—
480C4⋊C8—674no—
481C4⋊C8—674no—
482C4⋊C8—674no—
483C4⋊C8C22×D6714yes—
484C4⋊C8C22×D6714yes—
485C22⋊C8—674no—
486C22⋊C8—674no—
487C22⋊C8C22×D6714yes—
488C22⋊C8C22×D6714yes—
489#97—674no—
490#97—674no—
491#97—674no—
492#97—674no—
493#97—674no—
494#97C22×D6714yes—
495C4×C8—674no—
496C4×C8—674no—
497C4×C8—674no—
498C4×C8—674no—
499C4×C8—674no—
500C4×C8C22×D6714yes—
501C24C2×C4×D6711yescharacteristic
502C2×Q8—2682no—
503C2×Q8—2682no—
504C2×Q8—674no—
505C2×Q8—674no—
506C2×Q8—674no—
507C2×Q8—674no—
508C2×Q8—1344no—
509C2×Q8—1344no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—2682no—
513C22×C4—674no—
514C22×C4—671no—
515C22×C4—671no—
516C22×C4—671no—
517C22×C4—671no—
518C22×C4—674no—
519C22×C4—671no—
520C22×C4—671no—
521C22×C4—671no—
522C22×C4—671no—
523C22×C4—1344no—
524C22×C4C2×C4×D6711yescharacteristic
525C22×C4C2×C4×D6712yes—
526C22×C4C2×C4×D6711yescharacteristic
527C22×C4C2×C4×D6711yescharacteristic
528C22×C4C2×C4×D6711yescharacteristic
529C22×C4C2×C4×D6711yescharacteristic
530C22×C4C23×D6712yes—
531C22×C4C23×D6711yescharacteristic
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—672no—
537C2×C8—672no—
538C2×C8—672no—
539C2×C8—672no—
540C2×C8—1342no—
541C2×C8—1342no—
542C2×C8—1342no—
543C2×C8—1342no—
544C2×C8C23×D6712yes—
545C2×C8C23×D6712yes—
546C2×C8C23×D6712yes—
547C2×C8C23×D6712yes—
548C4⋊C4—674no—
549C4⋊C4—674no—
550C4⋊C4—674no—
551C4⋊C4—674no—
552C4⋊C4—674no—
553C4⋊C4—674no—
554C4⋊C4—674no—
555C4⋊C4—674no—
556C4⋊C4—674no—
557C4⋊C4—674no—
558C4⋊C4—674no—
559C4⋊C4—674no—
560C4⋊C4—674no—
561C4⋊C4—674no—
562C4⋊C4C2×C4×D6714yes—
563C4⋊C4C2×C4×D6714yes—
564C22⋊C4—674no—
565C22⋊C4—674no—
566C22⋊C4C2×C4×D6714yes—
567C22⋊C4C2×C4×D6714yes—
568C42—672no—
569C42—672no—
570C42—674no—
571C42—674no—
572C42—672no—
573C42—672no—
574C42—672no—
575C42—672no—
576C42—672no—
577C42—672no—
578C42C2×C4×D6712yes—
579C42C2×C4×D6712yes—
580C42C23×D6712yes—
581C42C23×D6712yes—
582C23—22no—
583C23—22no—
584C23—22no—
585C23C22×C4×D6712yes—
586C23C22×C4×D6711yescharacteristic
587Q8—2684no—
588Q8—2684no—
589Q8—1348no—
590Q8—1348no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—24no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—2684no—
600C2×C4—674no—
601C2×C4—672no—
602C2×C4—672no—
603C2×C4—672no—
604C2×C4—672no—
605C2×C4—672no—
606C2×C4—672no—
607C2×C4—672no—
608C2×C4—672no—
609C2×C4—1348no—
610C2×C4—1342no—
611C2×C4—1342no—
612C2×C4—1342no—
613C2×C4—1342no—
614C2×C4—1342no—
615C2×C4—1342no—
616C2×C4—1342no—
617C2×C4C22×C4×D6712yes—
618C2×C4C22×C4×D6712yes—
619C2×C4C22×C4×D6712yes—
620C2×C4C22×C4×D6712yes—
621C2×C4C22×C4×D6712yes—
622C2×C4C22×C4×D6711yescharacteristic
623C2×C4#1452409012yes—
624C2×C4#1452409012yes—
625C2×C4C24×D6711yescharacteristic
626C8—22no—
627C8—22no—
628C8—22no—
629C8—22no—
630C8—1342no—
631C8—1342no—
632C8—1342no—
633C8—1342no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—44no—
638C22#1686387312yes—
639C22#131×D6712yes—
640C22#1686416112yes—
641C22C23×C4×D6711yescharacteristic
642C4—22no—
643C4—22no—
644C4—22no—
645C4—22no—
646C4—22no—
647C4—674no—
648C4—1342no—
649C4—1342no—
650C4—1342no—
651C4—1342no—
652C4—1342no—
653C4—1342no—
654C4—1342no—
655C4#1686387312yes—
656C4C2×#1452409011yescharacteristic
657C4C2×#1452409011yescharacteristic
658C2—42no—
659C2#2256930114yesdirect product factor
660C2C2×#1686387311yescharacteristic
661C2C2×#131×D6711yescharacteristic
662C2C2×#1686416111yescharacteristic
subgroupG/H
centerC22×C4C23×D67
commutatorC22×C67C24×C4
FrattiniC2×C4C24×D67
FittingC2×#433×C67C2
socleC23×C67C23×C4
prime radicalC24×C67C22×C4
cosocleC2×C4×C67C25
hypercenterC2×#433D67
hypocenterC67C2×#2985
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #22569301C2direct (N × H)
3. C2×#16863526C2semidirect
4. C2×#16863525C2semidirect
5. C2×#16863525C2semidirect
6. C2×#16863524C2semidirect
7. C2×#16863524C2semidirect
8. C2×#16863523C2semidirect
9. C2×C8×Dic134C2semidirect
10. C2×#16863520C2semidirect
33. #16863526C22semidirect
34. #16863525C22semidirect
35. #16863525C22semidirect
36. #16863524C22semidirect
37. #16863524C22semidirect
38. #16863523C22semidirect
39. C8×Dic134C22semidirect
40. #16863520C22semidirect
328. C2×C67#2985semidirect
348. C67C2×#2985semidirect
659. C2#22569301direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168639492
#225693012
C2×#168635262
C2×#168635252
C2×#168635242
C2×#168635232
C2×C8×Dic1342
C2×#168635202
C2×#168634572
C2×#168634542
C2×#168634502
C2×#168634462
C2×#433×C672
C2×#298567