Finite Group Databasebeta

← C2×#22565595 #31027063

Subgroups — C2×#22565595 #31027063

Order 17152.

2574 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524033C211yesmaximal, characteristic
2C22×#14524008C211yesmaximal, characteristic
3#22565595C2116yesmaximal, direct product factor
4C2×#16863330C211yesmaximal, characteristic
5C2×#16863329C211yesmaximal, characteristic
6C2×#16863317C211yesmaximal, characteristic
7C2×#16863316C211yesmaximal, characteristic
8C2×#16863294C211yesmaximal, characteristic
9C2×#16863293C211yesmaximal, characteristic
10C2×#16863293C211yesmaximal, characteristic
11C2×#16863291C211yesmaximal, characteristic
12C2×#16863291C211yesmaximal, characteristic
13C2×#16863291C211yesmaximal, characteristic
14C2×#16863291C211yesmaximal, characteristic
15C2×C4×Dic67⋊C4C211yesmaximal, characteristic
16C2×#389×C67C211yesmaximal, characteristic
17C23×Dic134C2211yescharacteristic
18C2×#14524033—28no—
19C2×#14524033C2218yes—
20C2×#14524008—28no—
21C2×#14524008C2218yes—
22C22×C4⋊Dic67C2211yescharacteristic
23C22×C4⋊Dic67C2211yescharacteristic
24C22×C4⋊Dic67C2211yescharacteristic
25C22×Dic67⋊C4C2211yescharacteristic
26C22×Dic67⋊C4C2211yescharacteristic
27C22×Dic67⋊C4C2211yescharacteristic
28C22×Dic67⋊C4C2211yescharacteristic
29C22×Dic67⋊C4C2211yescharacteristic
30C22×Dic67⋊C4C2211yescharacteristic
31C22×Dic67⋊C4C2211yescharacteristic
32C22×Dic67⋊C4C2211yescharacteristic
33C22×Dic67⋊C4C2211yescharacteristic
34C22×Dic67⋊C4C2211yescharacteristic
35C22×Dic67⋊C4C2211yescharacteristic
36C22×Dic67⋊C4C2211yescharacteristic
37C22×C4×Dic67C2211yescharacteristic
38C22×C4×Dic67C2211yescharacteristic
39C22×C4×Dic67C2211yescharacteristic
40C22×C4×Dic67C2211yescharacteristic
41#16863330C2218yes—
42#16863329C2218yes—
43#16863317C2218yes—
44#16863316C2218yes—
45#16863294C2218yes—
46#16863293C2218yes—
47#16863293C2218yes—
48#16863291C2218yes—
49#16863291C2218yes—
50#16863291C2218yes—
51#16863291C2218yes—
52C4×Dic67⋊C4C2218yes—
53C2×C67⋊#95C2211yescharacteristic
54C2×C67⋊#95C2211yescharacteristic
55C2×C67⋊#95C2211yescharacteristic
56C2×C67⋊#95C2211yescharacteristic
57C2×C67⋊#95C2211yescharacteristic
58C2×C67⋊#95C2211yescharacteristic
59C2×C67⋊#95C2211yescharacteristic
60C2×C67⋊#95C2211yescharacteristic
61C22×C4⋊C4×C67C2211yescharacteristic
62C22×C4⋊C4×C67C2211yescharacteristic
63C22×C4⋊C4×C67C2211yescharacteristic
64C22×C4⋊C4×C67C2211yescharacteristic
65C22×C42×C67C2211yescharacteristic
66#389×C67C2218yes—
67C2×#95×C67C2211yescharacteristic
68C2×#95×C67C2211yescharacteristic
69C22×Dic134—24no—
70C22×Dic134—24no—
71C22×Dic134—24no—
72C22×Dic134C2314yes—
73C23×Dic67C2311yescharacteristic
74C23×Dic67C2311yescharacteristic
75C23×Dic67C2311yescharacteristic
76C23×Dic67C2311yescharacteristic
77C23×Dic67C2311yescharacteristic
78C23×Dic67C2311yescharacteristic
79C23×Dic67C2311yescharacteristic
80C23×Dic67C2311yescharacteristic
81#14524033—232no—
82#14524008—232no—
83C2×C4⋊Dic67—24no—
84C2×C4⋊Dic67—24no—
85C2×C4⋊Dic67—42no—
86C2×C4⋊Dic67C2314yes—
87C2×C4⋊Dic67C2314yes—
88C2×C4⋊Dic67C2314yes—
89C2×Dic67⋊C4—24no—
90C2×Dic67⋊C4—24no—
91C2×Dic67⋊C4—24no—
92C2×Dic67⋊C4—24no—
93C2×Dic67⋊C4—24no—
94C2×Dic67⋊C4—24no—
95C2×Dic67⋊C4—24no—
96C2×Dic67⋊C4—24no—
97C2×Dic67⋊C4—42no—
98C2×Dic67⋊C4—42no—
99C2×Dic67⋊C4Q818yescomplemented
100C2×Dic67⋊C4Q818yescomplemented
101C2×Dic67⋊C4C2314yes—
102C2×Dic67⋊C4C2314yes—
103C2×Dic67⋊C4C2314yes—
104C2×Dic67⋊C4C2314yes—
105C2×Dic67⋊C4C2314yes—
106C2×Dic67⋊C4C2314yes—
107C2×Dic67⋊C4C2314yes—
108C2×Dic67⋊C4C2314yes—
109C2×Dic67⋊C4C2314yes—
110C2×Dic67⋊C4C2314yes—
111C2×Dic67⋊C4C2314yes—
112C2×Dic67⋊C4C2314yes—
113C2×C4×Dic67—24no—
114C2×C4×Dic67—24no—
115C2×C4×Dic67—42no—
116C2×C4×Dic67D418yes—
117C2×C4×Dic67C2314yes—
118C2×C4×Dic67C2314yes—
119C2×C4×Dic67C2314yes—
120C2×C4×Dic67C2314yes—
121C67⋊#95C2314yes—
122C67⋊#95C2314yes—
123C67⋊#95C2314yes—
124C67⋊#95C2314yes—
125C67⋊#95C2314yes—
126C67⋊#95C2314yes—
127C67⋊#95C2314yes—
128C67⋊#95C2314yes—
129C23×C4×C67C2311yescharacteristic
130C23×C4×C67C2311yescharacteristic
131C23×C4×C67C2311yescharacteristic
132C23×C4×C67C2311yescharacteristic
133C23×C4×C67C2311yescharacteristic
134C23×C4×C67C2311yescharacteristic
135C23×C4×C67C2311yescharacteristic
136C2×C4⋊C4×C67—24no—
137C2×C4⋊C4×C67—24no—
138C2×C4⋊C4×C67—24no—
139C2×C4⋊C4×C67—42no—
140C2×C4⋊C4×C67C2314yes—
141C2×C4⋊C4×C67C2314yes—
142C2×C4⋊C4×C67C2314yes—
143C2×C4⋊C4×C67C2314yes—
144C2×C42×C67—42no—
145C2×C42×C67C2314yes—
146#95×C67C2314yes—
147#95×C67C2314yes—
148C2×Dic134—232no—
149C2×Dic134—28no—
150C2×Dic134—28no—
151C2×Dic134—28no—
152C22×Dic67—22no—
153C22×Dic67—22no—
154C22×Dic67—22no—
155C22×Dic67—22no—
156C22×Dic67—22no—
157C22×Dic67—22no—
158C22×Dic67—22no—
159C22×Dic67—22no—
160C22×Dic67—22no—
161C22×Dic67—22no—
162C22×Dic67—22no—
163C22×Dic67—22no—
164C22×Dic67—22no—
165C22×Dic67—22no—
166C22×Dic67—22no—
167C22×Dic67—22no—
168C22×Dic67—22no—
169C22×Dic67C2×D414yes—
170C22×Dic67C2×D414yes—
171C22×Dic67C2×Q814yes—
172C22×Dic67C2×Q814yes—
173C22×Dic67C2×Q814yes—
174C22×Dic67C2×Q814yes—
175C22×Dic67#4114yes—
176C22×Dic67C2412yes—
177C22×Dic67C2412yes—
178C22×Dic67C2412yes—
179C22×Dic67C2412yes—
180C22×Dic67C2412yes—
181C22×Dic67C2412yes—
182C22×Dic67C2412yes—
183C22×Dic67C2412yes—
184C4⋊Dic67—28no—
185C4⋊Dic67—28no—
186C4⋊Dic67—44no—
187Dic67⋊C4—28no—
188Dic67⋊C4—28no—
189Dic67⋊C4—28no—
190Dic67⋊C4—28no—
191Dic67⋊C4—28no—
192Dic67⋊C4—28no—
193Dic67⋊C4—28no—
194Dic67⋊C4—28no—
195Dic67⋊C4—44no—
196Dic67⋊C4—44no—
197Dic67⋊C4C2×Q8116yescomplemented
198Dic67⋊C4C2×Q8116yescomplemented
199C4×Dic67—28no—
200C4×Dic67—28no—
201C4×Dic67—44no—
202C4×Dic67C2×D4116yes—
203C24×C67C2411yescharacteristic
204C22×C4×C67—22no—
205C22×C4×C67—22no—
206C22×C4×C67—22no—
207C22×C4×C67—22no—
208C22×C4×C67—22no—
209C22×C4×C67—22no—
210C22×C4×C67—22no—
211C22×C4×C67—22no—
212C22×C4×C67—22no—
213C22×C4×C67—22no—
214C22×C4×C67—22no—
215C22×C4×C67—22no—
216C22×C4×C67—22no—
217C22×C4×C67—22no—
218C22×C4×C67—22no—
219C22×C4×C67—22no—
220C22×C4×C67—22no—
221C22×C4×C67C2×D414yes—
222C22×C4×C67C2×Q814yes—
223C22×C4×C67C2×Q814yes—
224C22×C4×C67#4114yes—
225C22×C4×C67C2412yes—
226C22×C4×C67C2412yes—
227C22×C4×C67C2412yes—
228C22×C4×C67C2412yes—
229C22×C4×C67C2412yes—
230C22×C4×C67C2412yes—
231C22×C4×C67C2412yes—
232C4⋊C4×C67—28no—
233C4⋊C4×C67—28no—
234C4⋊C4×C67—28no—
235C4⋊C4×C67—44no—
236C42×C67—44no—
237C23×C67C22×D412yes—
238C23×C67C22×Q812yes—
239C23×C67C22×Q812yes—
240C23×C67C2×#4112yes—
241C23×C67C2×#4112yes—
242C23×C67H(5,𝔽2)12yes—
243C23×C672−1+412yes—
244C23×C67C2511yescharacteristic
245C2×C4×C67—28no—
246C2×C4×C67—28no—
247C2×C4×C67—28no—
248C2×C4×C67—28no—
249C2×C4×C67—22no—
250C2×C4×C67—22no—
251C2×C4×C67—22no—
252C2×C4×C67—22no—
253C2×C4×C67—22no—
254C2×C4×C67—22no—
255C2×C4×C67—22no—
256C2×C4×C67—22no—
257C2×C4×C67—22no—
258C2×C4×C67—22no—
259C2×C4×C67—22no—
260C2×C4×C67—22no—
261C2×C4×C67—22no—
262C2×C4×C67—22no—
263C2×C4×C67—22no—
264C2×C4×C67—22no—
265C2×C4×C67—22no—
266C2×C4×C67—44no—
267C2×C4×C67—44no—
268C2×C4×C67—44no—
269C2×C4×C67C22×D414yes—
270C2×C4×C67C22×Q814yes—
271C2×C4×C67C22×Q814yes—
272C2×C4×C67C2×#4114yes—
273C2×Dic67—28no—
274C2×Dic67—28no—
275C2×Dic67—28no—
276C2×Dic67—28no—
277C2×Dic67—22no—
278C2×Dic67—22no—
279C2×Dic67—22no—
280C2×Dic67—22no—
281C2×Dic67—22no—
282C2×Dic67—22no—
283C2×Dic67—22no—
284C2×Dic67—22no—
285C2×Dic67—22no—
286C2×Dic67—22no—
287C2×Dic67—22no—
288C2×Dic67—22no—
289C2×Dic67—22no—
290C2×Dic67—22no—
291C2×Dic67—22no—
292C2×Dic67—22no—
293C2×Dic67—22no—
294C2×Dic67—44no—
295C2×Dic67—44no—
296C2×Dic67—44no—
297C2×Dic67C4⋊Q8116yes—
298C2×Dic67C22×D414yes—
299C2×Dic67C22×D414yes—
300C2×Dic67C22×Q814yes—
301C2×Dic67C22×Q814yes—
302C2×Dic67C22×Q814yes—
303C2×Dic67C22×Q814yes—
304C2×Dic67C2×#4114yes—
305Dic134—232no—
306C22×C67#52514yes—
307C22×C67C2×C4⋊Q814yes—
308C22×C67#53714yes—
309C22×C67#55414yes—
310C22×C67#55414yes—
311C22×C67#55714yes—
312C22×C67#55714yes—
313C22×C67C23×D411yescharacteristic
314C22×C67C23×Q811yescharacteristic
315C22×C67C23×Q811yescharacteristic
316C22×C67C22×#4111yescharacteristic
317C22×C67C22×#4111yescharacteristic
318C22×C67C2×H(5,𝔽2)11yescharacteristic
319C22×C67C2×2−1+411yescharacteristic
320C4×C67—24no—
321C4×C67—24no—
322C4×C67—24no—
323C4×C67—24no—
324C4×C67—42no—
325C4×C67—42no—
326C4×C67—42no—
327Dic67—24no—
328Dic67—24no—
329Dic67—24no—
330Dic67—24no—
331Dic67—42no—
332Dic67—42no—
333Dic67—42no—
334Dic67C2×C4⋊Q818yes—
335C2×#2584—671nomaximal, Sylow
336C2×C67#258418yescomplemented
337C2×C67C2×#52511yescharacteristic
338C2×C67C22×C4⋊Q811yescharacteristic
339C2×C67C2×#53711yescharacteristic
340C2×C67C2×#55411yescharacteristic
341C2×C67C2×#55411yescharacteristic
342C2×C67C2×#55711yescharacteristic
343C2×C67C2×#55711yescharacteristic
344C22×#125—671no—
345C22×C4×Q8—671no—
346#2584—6716no—
347C2×#398—671no—
348C2×#398—671no—
349C2×#395—671no—
350C2×#395—671no—
351C2×#389—671no—
352C2×#389—671no—
353C2×#389—671no—
354C2×#389—671no—
355C2×#389—671no—
356C2×#389—671no—
357C2×#389—671no—
358C2×#389D6711yescharacteristic
359C2×C4×C4⋊C4—671no—
360C67C2×#258411yescharacteristic, complemented, Sylow
361C23×Q8—671no—
362C2×#125—678no—
363C2×#125—1348no—
364C2×C4×Q8—678no—
365C2×C4×Q8—1348no—
366C22×C4⋊C4—671no—
367C22×C4⋊C4—671no—
368C22×C4⋊C4—671no—
369C22×C4⋊C4—671no—
370C22×C4⋊C4—671no—
371C22×C4⋊C4—671no—
372C22×C4⋊C4—671no—
373C22×C4⋊C4—671no—
374C22×C4⋊C4—671no—
375C22×C4⋊C4—671no—
376C22×C4⋊C4—671no—
377C22×C4⋊C4—671no—
378C22×C4⋊C4—671no—
379C22×C4⋊C4—671no—
380C22×C4⋊C4—671no—
381C22×C4⋊C4C2×D6711yescharacteristic
382C22×C4⋊C4C2×D6711yescharacteristic
383C22×C4⋊C4C2×D6711yescharacteristic
384C22×C4⋊C4C2×D6711yescharacteristic
385C22×C42—671no—
386C22×C42—671no—
387C22×C42—671no—
388C22×C42—671no—
389C22×C42C2×D6711yescharacteristic
390#398—678no—
391#398—678no—
392#395—678no—
393#395—678no—
394#389—678no—
395#389—678no—
396#389—678no—
397#389—678no—
398#389—678no—
399#389—678no—
400#389—678no—
401#389C2×D6718yes—
402C4×C4⋊C4—678no—
403C2×#95—671no—
404C2×#95—671no—
405C2×#95—671no—
406C2×#95—671no—
407C2×#95—671no—
408C2×#95—671no—
409C2×#95—671no—
410C2×#95—671no—
411C2×#95C2×D6711yescharacteristic
412C2×#95C2×D6711yescharacteristic
413C22×Q8—674no—
414C22×Q8—1344no—
415C22×Q8—1344no—
416C22×Q8—1344no—
417C23×C4—671no—
418C23×C4—671no—
419C23×C4—671no—
420C23×C4—671no—
421C23×C4—671no—
422C23×C4—671no—
423C23×C4—671no—
424C23×C4—671no—
425C23×C4C22×D6711yescharacteristic
426C23×C4C22×D6711yescharacteristic
427C23×C4C22×D6711yescharacteristic
428C23×C4C22×D6711yescharacteristic
429C23×C4C22×D6711yescharacteristic
430C23×C4C22×D6711yescharacteristic
431C23×C4C22×D6711yescharacteristic
432#125—13432no—
433C4×Q8—13432no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—42no—
438C2×C4⋊C4—2682no—
439C2×C4⋊C4—2682no—
440C2×C4⋊C4—2682no—
441C2×C4⋊C4—674no—
442C2×C4⋊C4—674no—
443C2×C4⋊C4—674no—
444C2×C4⋊C4—678no—
445C2×C4⋊C4—678no—
446C2×C4⋊C4—674no—
447C2×C4⋊C4—674no—
448C2×C4⋊C4—674no—
449C2×C4⋊C4—674no—
450C2×C4⋊C4—674no—
451C2×C4⋊C4—674no—
452C2×C4⋊C4—674no—
453C2×C4⋊C4—674no—
454C2×C4⋊C4—674no—
455C2×C4⋊C4—674no—
456C2×C4⋊C4—674no—
457C2×C4⋊C4—674no—
458C2×C4⋊C4—1344no—
459C2×C4⋊C4—1344no—
460C2×C4⋊C4—1344no—
461C2×C4⋊C4—1344no—
462C2×C4⋊C4—1344no—
463C2×C4⋊C4—1344no—
464C2×C4⋊C4—1344no—
465C2×C4⋊C4—1344no—
466C2×C4⋊C4—1344no—
467C2×C4⋊C4—1344no—
468C2×C4⋊C4C22×D6714yes—
469C2×C4⋊C4C22×D6714yes—
470C2×C4⋊C4C22×D6714yes—
471C2×C4⋊C4C22×D6714yes—
472C2×C42—42no—
473C2×C42—2682no—
474C2×C42—674no—
475C2×C42—678no—
476C2×C42—674no—
477C2×C42—674no—
478C2×C42—674no—
479C2×C42—1344no—
480C2×C42—1344no—
481C2×C42C22×D6714yes—
482#95—674no—
483#95—674no—
484#95—674no—
485#95—674no—
486#95—674no—
487#95—674no—
488#95—674no—
489#95—674no—
490#95C22×D6714yes—
491#95C22×D6714yes—
492C24C23×D6711yescharacteristic
493C2×Q8—1348no—
494C2×Q8—1348no—
495C2×Q8—13432no—
496C2×Q8—1348no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—674no—
515C22×C4—674no—
516C22×C4—674no—
517C22×C4—672no—
518C22×C4—674no—
519C22×C4—674no—
520C22×C4—674no—
521C22×C4—674no—
522C22×C4—672no—
523C22×C4—672no—
524C22×C4—672no—
525C22×C4—672no—
526C22×C4—672no—
527C22×C4—672no—
528C22×C4—672no—
529C22×C4—1342no—
530C22×C4—1342no—
531C22×C4—1342no—
532C22×C4—1342no—
533C22×C4—1342no—
534C22×C4—1342no—
535C22×C4—1342no—
536C22×C4—1342no—
537C22×C4—1342no—
538C22×C4—1342no—
539C22×C4—1342no—
540C22×C4—1342no—
541C22×C4—1342no—
542C22×C4—1342no—
543C22×C4—1342no—
544C22×C4—1342no—
545C22×C4—1342no—
546C22×C4D4×D6714yes—
547C22×C4Q8×D6714yes—
548C22×C4Q8×D6714yes—
549C22×C4#1176162814yes—
550C22×C4C23×D6712yes—
551C22×C4C23×D6712yes—
552C22×C4C23×D6712yes—
553C22×C4C23×D6712yes—
554C22×C4C23×D6712yes—
555C22×C4C23×D6712yes—
556C22×C4C23×D6712yes—
557C4⋊C4—28no—
558C4⋊C4—28no—
559C4⋊C4—28no—
560C4⋊C4—44no—
561C4⋊C4—2684no—
562C4⋊C4—2684no—
563C4⋊C4—2684no—
564C4⋊C4—6716no—
565C4⋊C4—6716no—
566C4⋊C4—1348no—
567C4⋊C4—1348no—
568C4⋊C4—1348no—
569C4⋊C4—1348no—
570C4⋊C4—1348no—
571C4⋊C4—1348no—
572C4⋊C4—1348no—
573C4⋊C4—1348no—
574C4⋊C4—1348no—
575C4⋊C4—1348no—
576C42—44no—
577C42—2684no—
578C42—6716no—
579C42—1348no—
580C42—1348no—
581C23C2×D4×D6712yes—
582C23C2×Q8×D6712yes—
583C23C2×Q8×D6712yes—
584C23#41×D6712yes—
585C23C2×#1176162812yes—
586C23#1452408812yes—
587C23#1452409012yes—
588C23C24×D6711yescharacteristic
589Q8—13432no—
590C2×C4—28no—
591C2×C4—28no—
592C2×C4—28no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—28no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—44no—
612C2×C4—44no—
613C2×C4—44no—
614C2×C4—2684no—
615C2×C4—2684no—
616C2×C4—2684no—
617C2×C4—6716no—
618C2×C4—674no—
619C2×C4—674no—
620C2×C4—674no—
621C2×C4—674no—
622C2×C4—674no—
623C2×C4—674no—
624C2×C4—674no—
625C2×C4—1342no—
626C2×C4—1342no—
627C2×C4—1342no—
628C2×C4—1342no—
629C2×C4—1342no—
630C2×C4—1342no—
631C2×C4—1342no—
632C2×C4—1342no—
633C2×C4—1342no—
634C2×C4—1348no—
635C2×C4—1348no—
636C2×C4—1348no—
637C2×C4—1348no—
638C2×C4—1342no—
639C2×C4—1342no—
640C2×C4—1342no—
641C2×C4—1342no—
642C2×C4—1342no—
643C2×C4—1342no—
644C2×C4—1342no—
645C2×C4—1342no—
646C2×C4C2×D4×D6714yes—
647C2×C4C2×Q8×D6714yes—
648C2×C4C2×Q8×D6714yes—
649C2×C4C2×#1176162814yes—
650C22#1686390514yes—
651C22C4⋊Q8×D6714yes—
652C22#1686397314yes—
653C22#1686410014yes—
654C22#1686410114yes—
655C22#1686412314yes—
656C22#1686412414yes—
657C22C22×D4×D6711yescharacteristic
658C22C22×Q8×D6711yescharacteristic
659C22C22×Q8×D6711yescharacteristic
660C22C2×#41×D6711yescharacteristic
661C22C22×#1176162811yescharacteristic
662C22C2×#1452408811yescharacteristic
663C22C2×#1452409011yescharacteristic
664C4—24no—
665C4—24no—
666C4—24no—
667C4—24no—
668C4—42no—
669C4—42no—
670C4—42no—
671C4—2682no—
672C4—2682no—
673C4—2682no—
674C4—678no—
675C4—1344no—
676C4—1344no—
677C4—1344no—
678C4—1344no—
679C2#2256559518yesdirect product factor
680C2C2×#1686390511yescharacteristic
681C2C2×C4⋊Q8×D6711yescharacteristic
682C2C2×#1686397311yescharacteristic
683C2C2×#1686410011yescharacteristic
684C2C2×#1686410111yescharacteristic
685C2C2×#1686412311yescharacteristic
686C2C2×#1686412411yescharacteristic
subgroupG/H
centerC24C23×D67
commutator, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC2×#389×C67C2
socle, prime radicalC24×C67C24
hypercenterC2×#389D67
hypocenterC67C2×#2584
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. #22565595C2direct (N × H)
99. C2×Dic67⋊C4Q8semidirect
100. C2×Dic67⋊C4Q8semidirect
197. Dic67⋊C4C2×Q8semidirect
198. Dic67⋊C4C2×Q8semidirect
336. C2×C67#2584semidirect
360. C67C2×#2584semidirect
679. C2#22565595direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240332
C22×#145240082
#225655952
C2×#168633302
C2×#168633292
C2×#168633172
C2×#168633162
C2×#168632942
C2×#168632932
C2×#168632912
C2×C4×Dic67⋊C42
C2×#389×C672
C2×#258467