Finite Group Databasebeta

← C2×#22563805 #31023845

Subgroups — C2×#22563805 #31023845

Order 17152.

3246 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524042C211yesmaximal, characteristic, complemented
2C22×#14524020C211yesmaximal, characteristic
3C22×#14524020C211yesmaximal, characteristic
4C22×C4×Dic134C211yesmaximal, characteristic, complemented
5#22563805C2116yesmaximal, direct product factor
6C2×#16863329C211yesmaximal, characteristic, complemented
7C2×#16863328C211yesmaximal, characteristic, complemented
8C2×#16863319C211yesmaximal, characteristic
9C2×#16863319C211yesmaximal, characteristic
10C2×#16863300C211yesmaximal, characteristic, complemented
11C2×#16863294C211yesmaximal, characteristic, complemented
12C2×#16863293C211yesmaximal, characteristic, complemented
13C2×#16863293C211yesmaximal, characteristic, complemented
14C2×#16863289C211yesmaximal, characteristic
15C2×C22⋊C4×Dic67C211yesmaximal, characteristic
16C2×#388×C67C211yesmaximal, characteristic
17C23×Dic134C2211yescharacteristic
18C23×Dic134C2211yescharacteristic
19C24×Dic67C2211yescharacteristic
20C2×#14524042—28no—
21C2×#14524042C2218yescomplemented
22C2×#14524020—28no—
23C2×#14524020—28no—
24C2×#14524020C2218yes—
25C2×#14524020C2218yes—
26C2×C4×Dic134—28no—
27C2×C4×Dic134C2218yescomplemented
28C22×C4⋊Dic67C2211yescharacteristic
29C22×C4⋊Dic67C2211yescharacteristic
30C22×C4⋊Dic67C2211yescharacteristic
31C22×C4⋊Dic67C2211yescharacteristic
32C22×C4⋊Dic67C2211yescharacteristic
33C22×Dic67⋊C4C2211yescharacteristic
34C22×Dic67⋊C4C2211yescharacteristic
35C22×Dic67⋊C4C2211yescharacteristic
36C22×Dic67⋊C4C2211yescharacteristic
37C22×Dic67⋊C4C2211yescharacteristic
38C22×Dic67⋊C4C2211yescharacteristic
39C22×Dic67⋊C4C2211yescharacteristic
40C22×Dic67⋊C4C2211yescharacteristic
41C22×C22⋊Dic67C2211yescharacteristic
42C22×C22⋊Dic67C2211yescharacteristic
43C22×C22⋊Dic67C2211yescharacteristic
44C22×C4×Dic67C2211yescharacteristic
45C22×C4×Dic67C2211yescharacteristic
46C22×C4×Dic67C2211yescharacteristic
47#16863329C2218yescomplemented
48#16863328C2218yescomplemented
49#16863319C2218yes—
50#16863319C2218yes—
51#16863300C2218yescomplemented
52#16863294C2218yescomplemented
53#16863293C2218yescomplemented
54#16863293C2218yescomplemented
55#16863289C2218yes—
56C22⋊C4×Dic67C2218yes—
57C2×C67⋊#95C2211yescharacteristic
58C2×C67⋊#95C2211yescharacteristic
59C2×C67⋊#95C2211yescharacteristic
60C2×C67⋊#95C2211yescharacteristic
61C2×C67⋊#95C2211yescharacteristic
62C2×C67⋊#95C2211yescharacteristic
63C22×C4⋊C4×C67C2211yescharacteristic
64C22×C22⋊C4×C67C2211yescharacteristic
65C22×C22⋊C4×C67C2211yescharacteristic
66C22×C22⋊C4×C67C2211yescharacteristic
67C22×C42×C67C2211yescharacteristic
68#388×C67C2218yes—
69C2×#95×C67C2211yescharacteristic
70C2×#95×C67C2211yescharacteristic
71C22×Dic134—24no—
72C22×Dic134—24no—
73C22×Dic134—24no—
74C22×Dic134—24no—
75C22×Dic134—24no—
76C22×Dic134D418yes—
77C22×Dic134C2314yes—
78C22×Dic134C2314yes—
79C23×Dic67—24no—
80C23×Dic67—24no—
81C23×Dic67—24no—
82C23×Dic67C2311yescharacteristic
83C23×Dic67C2311yescharacteristic
84C23×Dic67C2311yescharacteristic
85C23×Dic67C2311yescharacteristic
86C23×Dic67C2314yes—
87C23×Dic67C2311yescharacteristic
88C23×Dic67C2311yescharacteristic
89C23×Dic67C2311yescharacteristic
90C23×Dic67C2311yescharacteristic
91#14524042—232no—
92#14524020—232no—
93#14524020—232no—
94C4×Dic134—232no—
95C2×C4⋊Dic67—24no—
96C2×C4⋊Dic67—24no—
97C2×C4⋊Dic67—24no—
98C2×C4⋊Dic67—24no—
99C2×C4⋊Dic67—24no—
100C2×C4⋊Dic67C2314yes—
101C2×C4⋊Dic67C2314yes—
102C2×C4⋊Dic67C2314yes—
103C2×C4⋊Dic67C2314yes—
104C2×C4⋊Dic67C2314yes—
105C2×Dic67⋊C4—24no—
106C2×Dic67⋊C4—24no—
107C2×Dic67⋊C4—24no—
108C2×Dic67⋊C4—24no—
109C2×Dic67⋊C4—24no—
110C2×Dic67⋊C4—24no—
111C2×Dic67⋊C4—24no—
112C2×Dic67⋊C4D418yes—
113C2×Dic67⋊C4C2314yes—
114C2×Dic67⋊C4C2314yes—
115C2×Dic67⋊C4C2314yes—
116C2×Dic67⋊C4C2314yes—
117C2×Dic67⋊C4C2314yes—
118C2×Dic67⋊C4C2314yes—
119C2×Dic67⋊C4C2314yes—
120C2×Dic67⋊C4C2314yes—
121C2×C22⋊Dic67—24no—
122C2×C22⋊Dic67—24no—
123C2×C22⋊Dic67—24no—
124C2×C22⋊Dic67C2314yes—
125C2×C22⋊Dic67C2314yes—
126C2×C22⋊Dic67C2314yes—
127C2×C4×Dic67—24no—
128C2×C4×Dic67—24no—
129C2×C4×Dic67—24no—
130C2×C4×Dic67C2314yes—
131C2×C4×Dic67C2314yes—
132C2×C4×Dic67C2314yes—
133C67⋊#95C2314yes—
134C67⋊#95C2314yes—
135C67⋊#95C2314yes—
136C67⋊#95C2314yes—
137C67⋊#95C2314yes—
138C67⋊#95C2314yes—
139C25×C67C2311yescharacteristic
140C23×C4×C67C2311yescharacteristic
141C23×C4×C67C2311yescharacteristic
142C23×C4×C67C2311yescharacteristic
143C23×C4×C67C2311yescharacteristic
144C23×C4×C67C2311yescharacteristic
145C23×C4×C67C2311yescharacteristic
146C2×C4⋊C4×C67—24no—
147C2×C4⋊C4×C67C2314yes—
148C2×C22⋊C4×C67—24no—
149C2×C22⋊C4×C67—24no—
150C2×C22⋊C4×C67Q818yescomplemented
151C2×C22⋊C4×C67C2314yes—
152C2×C22⋊C4×C67C2314yes—
153C2×C22⋊C4×C67C2314yes—
154C2×C42×C67—24no—
155C2×C42×C67C2314yes—
156#95×C67C2314yes—
157#95×C67C2314yes—
158C2×Dic134—232no—
159C2×Dic134—28no—
160C2×Dic134—28no—
161C2×Dic134—28no—
162C2×Dic134—28no—
163C2×Dic134—28no—
164C2×Dic134—416no—
165C2×Dic134C2×D4116yes—
166C22×Dic67—22no—
167C22×Dic67—22no—
168C22×Dic67—22no—
169C22×Dic67—22no—
170C22×Dic67—22no—
171C22×Dic67—22no—
172C22×Dic67—22no—
173C22×Dic67—22no—
174C22×Dic67—22no—
175C22×Dic67—22no—
176C22×Dic67—22no—
177C22×Dic67—22no—
178C22×Dic67—22no—
179C22×Dic67—22no—
180C22×Dic67—22no—
181C22×Dic67—22no—
182C22×Dic67—22no—
183C22×Dic67—22no—
184C22×Dic67—28no—
185C22×Dic67—28no—
186C22×Dic67—28no—
187C22×Dic67—416no—
188C22×Dic67C2×D414yes—
189C22×Dic67C2×D414yes—
190C22×Dic67C2×D414yes—
191C22×Dic67C2×D414yes—
192C22×Dic67#4114yes—
193C22×Dic67#4114yes—
194C22×Dic67C2412yes—
195C22×Dic67C2412yes—
196C22×Dic67C2412yes—
197C22×Dic67C2412yes—
198C22×Dic67C2412yes—
199C22×Dic67C2412yes—
200C22×Dic67C2412yes—
201C22×Dic67C2412yes—
202C4⋊Dic67—28no—
203C4⋊Dic67—28no—
204C4⋊Dic67—28no—
205C4⋊Dic67—28no—
206C4⋊Dic67—28no—
207Dic67⋊C4—28no—
208Dic67⋊C4—28no—
209Dic67⋊C4—28no—
210Dic67⋊C4—28no—
211Dic67⋊C4—28no—
212Dic67⋊C4—28no—
213Dic67⋊C4—28no—
214Dic67⋊C4C2×D4116yes—
215C22⋊Dic67—28no—
216C22⋊Dic67—28no—
217C22⋊Dic67—28no—
218C4×Dic67—28no—
219C4×Dic67—28no—
220C4×Dic67—28no—
221C24×C67—22no—
222C24×C67—22no—
223C24×C67—22no—
224C24×C67—22no—
225C24×C67—22no—
226C24×C67—22no—
227C24×C67C2×Q814yes—
228C24×C67C2412yes—
229C24×C67C2411yescharacteristic
230C22×C4×C67—22no—
231C22×C4×C67—22no—
232C22×C4×C67—22no—
233C22×C4×C67—22no—
234C22×C4×C67—22no—
235C22×C4×C67—22no—
236C22×C4×C67—22no—
237C22×C4×C67—22no—
238C22×C4×C67—22no—
239C22×C4×C67—22no—
240C22×C4×C67—22no—
241C22×C4×C67—22no—
242C22×C4×C67—22no—
243C22×C4×C67—22no—
244C22×C4×C67C2×D414yes—
245C22×C4×C67C2×D414yes—
246C22×C4×C67C2×Q814yes—
247C22×C4×C67C2×Q814yes—
248C22×C4×C67C2412yes—
249C22×C4×C67C2412yes—
250C22×C4×C67C2412yes—
251C22×C4×C67C2412yes—
252C22×C4×C67C2412yes—
253C22×C4×C67C2412yes—
254C4⋊C4×C67—28no—
255C22⋊C4×C67—28no—
256C22⋊C4×C67—28no—
257C22⋊C4×C67C2×Q8116yescomplemented
258C42×C67—28no—
259C23×C67—28no—
260C23×C67—28no—
261C23×C67—28no—
262C23×C67—22no—
263C23×C67—22no—
264C23×C67—22no—
265C23×C67—22no—
266C23×C67—22no—
267C23×C67—22no—
268C23×C67—44no—
269C23×C67—44no—
270C23×C67—44no—
271C23×C67—44no—
272C23×C67C22×D412yes—
273C23×C67C22×D412yes—
274C23×C67C22×Q814yes—
275C23×C67C22×Q812yes—
276C23×C67C2×#4112yes—
277C23×C67C2×#4112yes—
278C23×C672−1+412yes—
279C23×C672−1+412yes—
280C23×C67C2511yescharacteristic
281C2×C4×C67—28no—
282C2×C4×C67—28no—
283C2×C4×C67—28no—
284C2×C4×C67—28no—
285C2×C4×C67—22no—
286C2×C4×C67—22no—
287C2×C4×C67—22no—
288C2×C4×C67—22no—
289C2×C4×C67—22no—
290C2×C4×C67—22no—
291C2×C4×C67—22no—
292C2×C4×C67—22no—
293C2×C4×C67—22no—
294C2×C4×C67—22no—
295C2×C4×C67—22no—
296C2×C4×C67—22no—
297C2×C4×C67—22no—
298C2×C4×C67—22no—
299C2×C4×C67—44no—
300C2×C4×C67—44no—
301C2×C4×C67C22×D414yes—
302C2×C4×C67C22×D414yes—
303C2×C4×C67C22×Q814yes—
304C2×C4×C67C22×Q814yes—
305C2×Dic67—28no—
306C2×Dic67—28no—
307C2×Dic67—28no—
308C2×Dic67—22no—
309C2×Dic67—22no—
310C2×Dic67—22no—
311C2×Dic67—22no—
312C2×Dic67—22no—
313C2×Dic67—22no—
314C2×Dic67—22no—
315C2×Dic67—22no—
316C2×Dic67—22no—
317C2×Dic67—22no—
318C2×Dic67—22no—
319C2×Dic67—22no—
320C2×Dic67—22no—
321C2×Dic67—22no—
322C2×Dic67—22no—
323C2×Dic67—22no—
324C2×Dic67—22no—
325C2×Dic67—22no—
326C2×Dic67—44no—
327C2×Dic67—44no—
328C2×Dic67—44no—
329C2×Dic67—44no—
330C2×Dic67—416no—
331C2×Dic67#121116yes—
332C2×Dic67C22×D414yes—
333C2×Dic67C22×D414yes—
334C2×Dic67C22×D414yes—
335C2×Dic67C22×D414yes—
336C2×Dic67C2×#4114yes—
337C2×Dic67C2×#4114yes—
338Dic134—232no—
339Dic134—416no—
340C22×C67—24no—
341C22×C67—24no—
342C22×C67—24no—
343C22×C67—42no—
344C22×C67—416no—
345C22×C67—42no—
346C22×C67—42no—
347C22×C67—42no—
348C22×C67C2×#12114yes—
349C22×C67#53314yes—
350C22×C67#54114yes—
351C22×C67#54714yes—
352C22×C67#54814yes—
353C22×C67D4×Q814yes—
354C22×C67D4×Q814yes—
355C22×C67C23×D411yescharacteristic
356C22×C67C23×D411yescharacteristic
357C22×C67C23×Q811yescharacteristic
358C22×C67C22×#4111yescharacteristic
359C22×C67C22×#4111yescharacteristic
360C22×C67C2×2−1+411yescharacteristic
361C22×C67C2×2−1+411yescharacteristic
362C4×C67—24no—
363C4×C67—24no—
364C4×C67—24no—
365C4×C67—24no—
366C4×C67—42no—
367C4×C67—42no—
368Dic67—24no—
369Dic67—24no—
370Dic67—24no—
371Dic67—42no—
372Dic67—42no—
373Dic67—42no—
374Dic67—42no—
375Dic67C2×#12118yes—
376C2×#2429—671nomaximal, Sylow
377C2×C67—44no—
378C2×C67#242918yescomplemented
379C2×C67C22×#12111yescharacteristic
380C2×C67C2×#53311yescharacteristic
381C2×C67C2×#54111yescharacteristic
382C2×C67C2×#54711yescharacteristic
383C2×C67C2×#54811yescharacteristic
384C2×C67C2×D4×Q811yescharacteristic
385C2×C67C2×D4×Q811yescharacteristic
386C22×C4⋊Q8—671no—
387C22×C22⋊Q8—671no—
388C22×C22⋊Q8—671no—
389C22×C4×Q8—671no—
390#2429—6716no—
391C2×#398—671no—
392C2×#398—671no—
393C2×#396—671no—
394C2×#396—671no—
395C2×#391—671no—
396C2×#389—671no—
397C2×#389—671no—
398C2×#389—671no—
399C2×#388—671no—
400C2×#388D6711yescharacteristic
401C2×C4×C22⋊C4—671no—
402C67C2×#242911yescharacteristic, complemented, Sylow
403C23×Q8—671no—
404C23×Q8—671no—
405C24×C4—671no—
406C2×C4⋊Q8—678no—
407C2×C4⋊Q8—1348no—
408C2×C22⋊Q8—678no—
409C2×C22⋊Q8—678no—
410C2×C22⋊Q8—1348no—
411C2×C22⋊Q8—1348no—
412C2×C4×Q8—678no—
413C2×C4×Q8—1348no—
414C22×C4⋊C4—671no—
415C22×C4⋊C4—671no—
416C22×C4⋊C4—671no—
417C22×C4⋊C4—671no—
418C22×C4⋊C4—671no—
419C22×C4⋊C4—671no—
420C22×C4⋊C4—671no—
421C22×C4⋊C4—671no—
422C22×C4⋊C4—671no—
423C22×C4⋊C4—671no—
424C22×C4⋊C4—671no—
425C22×C4⋊C4—671no—
426C22×C4⋊C4—671no—
427C22×C4⋊C4C2×D6711yescharacteristic
428C22×C22⋊C4—671no—
429C22×C22⋊C4—671no—
430C22×C22⋊C4—671no—
431C22×C22⋊C4C2×D6711yescharacteristic
432C22×C22⋊C4C2×D6711yescharacteristic
433C22×C22⋊C4C2×D6711yescharacteristic
434C22×C42—671no—
435C22×C42—671no—
436C22×C42—671no—
437C22×C42C2×D6711yescharacteristic
438#398—678no—
439#398—678no—
440#396—678no—
441#396—678no—
442#391—678no—
443#389—678no—
444#389—678no—
445#389—678no—
446#388—678no—
447#388C2×D6718yes—
448C4×C22⋊C4—678no—
449C2×#95—671no—
450C2×#95—671no—
451C2×#95—671no—
452C2×#95—671no—
453C2×#95—671no—
454C2×#95—671no—
455C2×#95C2×D6711yescharacteristic
456C2×#95C2×D6711yescharacteristic
457C25C22×D6711yescharacteristic
458C22×Q8—678no—
459C22×Q8—674no—
460C22×Q8—674no—
461C22×Q8—1344no—
462C22×Q8—1344no—
463C22×Q8—1344no—
464C22×Q8—1344no—
465C22×Q8—1344no—
466C23×C4—671no—
467C23×C4—671no—
468C23×C4—671no—
469C23×C4—671no—
470C23×C4—674no—
471C23×C4—671no—
472C23×C4—671no—
473C23×C4—671no—
474C23×C4—671no—
475C23×C4—1344no—
476C23×C4—1344no—
477C23×C4—1344no—
478C23×C4C22×D6711yescharacteristic
479C23×C4C22×D6711yescharacteristic
480C23×C4C22×D6711yescharacteristic
481C23×C4C22×D6711yescharacteristic
482C23×C4C22×D6711yescharacteristic
483C23×C4C22×D6711yescharacteristic
484C4⋊Q8—13432no—
485C22⋊Q8—13432no—
486C22⋊Q8—13432no—
487C4×Q8—13432no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—678no—
490C2×C4⋊C4—674no—
491C2×C4⋊C4—674no—
492C2×C4⋊C4—674no—
493C2×C4⋊C4—674no—
494C2×C4⋊C4—674no—
495C2×C4⋊C4—674no—
496C2×C4⋊C4—674no—
497C2×C4⋊C4—674no—
498C2×C4⋊C4—674no—
499C2×C4⋊C4—674no—
500C2×C4⋊C4—674no—
501C2×C4⋊C4—674no—
502C2×C4⋊C4—674no—
503C2×C4⋊C4—1344no—
504C2×C4⋊C4—1344no—
505C2×C4⋊C4—1344no—
506C2×C4⋊C4—1344no—
507C2×C4⋊C4—1344no—
508C2×C4⋊C4—1344no—
509C2×C4⋊C4—1344no—
510C2×C4⋊C4—1344no—
511C2×C4⋊C4—1344no—
512C2×C4⋊C4—1344no—
513C2×C4⋊C4—1344no—
514C2×C4⋊C4—1344no—
515C2×C4⋊C4C22×D6714yes—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—674no—
519C2×C22⋊C4—674no—
520C2×C22⋊C4—674no—
521C2×C22⋊C4—1344no—
522C2×C22⋊C4—1344no—
523C2×C22⋊C4—1344no—
524C2×C22⋊C4Dic13418yescomplemented
525C2×C22⋊C4C22×D6714yes—
526C2×C22⋊C4C22×D6714yes—
527C2×C22⋊C4C22×D6714yes—
528C2×C42—24no—
529C2×C42—674no—
530C2×C42—674no—
531C2×C42—674no—
532C2×C42—1344no—
533C2×C42—1344no—
534C2×C42—1344no—
535C2×C42C22×D6714yes—
536#95—674no—
537#95—674no—
538#95—674no—
539#95—674no—
540#95—674no—
541#95—674no—
542#95C22×D6714yes—
543#95C22×D6714yes—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24C2×Dic13414yes—
551C24C23×D6712yes—
552C24C23×D6711yescharacteristic
553C2×Q8—26816no—
554C2×Q8—6716no—
555C2×Q8—1348no—
556C2×Q8—1348no—
557C2×Q8—1348no—
558C2×Q8—1348no—
559C2×Q8—13432no—
560C2×Q8—1348no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—26816no—
576C22×C4—674no—
577C22×C4—674no—
578C22×C4—674no—
579C22×C4—672no—
580C22×C4—674no—
581C22×C4—674no—
582C22×C4—674no—
583C22×C4—672no—
584C22×C4—672no—
585C22×C4—672no—
586C22×C4—672no—
587C22×C4—672no—
588C22×C4—672no—
589C22×C4—672no—
590C22×C4—1348no—
591C22×C4—1348no—
592C22×C4—1348no—
593C22×C4—1342no—
594C22×C4—1342no—
595C22×C4—1342no—
596C22×C4—1342no—
597C22×C4—1342no—
598C22×C4—1342no—
599C22×C4—1342no—
600C22×C4—1342no—
601C22×C4—1342no—
602C22×C4—1342no—
603C22×C4—1342no—
604C22×C4—1342no—
605C22×C4—1342no—
606C22×C4—1342no—
607C22×C4—1342no—
608C22×C4—1342no—
609C22×C4—1342no—
610C22×C4—1342no—
611C22×C4D4×D6714yes—
612C22×C4D4×D6714yes—
613C22×C4C2×Dic13414yes—
614C22×C4C2×Dic13414yes—
615C22×C4C23×D6712yes—
616C22×C4C23×D6712yes—
617C22×C4C23×D6712yes—
618C22×C4C23×D6712yes—
619C22×C4C23×D6712yes—
620C22×C4C23×D6712yes—
621C4⋊C4—28no—
622C4⋊C4—6716no—
623C4⋊C4—1348no—
624C4⋊C4—1348no—
625C4⋊C4—1348no—
626C4⋊C4—1348no—
627C4⋊C4—1348no—
628C4⋊C4—1348no—
629C4⋊C4—1348no—
630C4⋊C4—1348no—
631C4⋊C4—1348no—
632C4⋊C4—1348no—
633C4⋊C4—1348no—
634C4⋊C4—1348no—
635C22⋊C4—28no—
636C22⋊C4—28no—
637C22⋊C4—1348no—
638C22⋊C4—1348no—
639C22⋊C4—1348no—
640C22⋊C4C2×Dic134116yescomplemented
641C42—28no—
642C42—1348no—
643C42—1348no—
644C42—1348no—
645C23—28no—
646C23—28no—
647C23—28no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23C2×D4×D6712yes—
659C23C2×D4×D6712yes—
660C23C22×Dic13414yes—
661C23C22×Dic13412yes—
662C23#41×D6712yes—
663C23#41×D6712yes—
664C23#1452409012yes—
665C23#1452409012yes—
666C23C24×D6711yescharacteristic
667Q8—26816no—
668Q8—13432no—
669C2×C4—28no—
670C2×C4—28no—
671C2×C4—28no—
672C2×C4—28no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—2684no—
690C2×C4—2684no—
691C2×C4—2684no—
692C2×C4—2684no—
693C2×C4—26816no—
694C2×C4—6716no—
695C2×C4—674no—
696C2×C4—674no—
697C2×C4—674no—
698C2×C4—674no—
699C2×C4—674no—
700C2×C4—674no—
701C2×C4—1342no—
702C2×C4—1342no—
703C2×C4—1342no—
704C2×C4—1342no—
705C2×C4—1342no—
706C2×C4—1342no—
707C2×C4—1342no—
708C2×C4—1342no—
709C2×C4—1342no—
710C2×C4—1342no—
711C2×C4—1342no—
712C2×C4—1342no—
713C2×C4—1348no—
714C2×C4—1348no—
715C2×C4—1348no—
716C2×C4—1342no—
717C2×C4—1342no—
718C2×C4—1342no—
719C2×C4—1342no—
720C2×C4—1342no—
721C2×C4—1342no—
722C2×C4C2×D4×D6714yes—
723C2×C4C2×D4×D6714yes—
724C2×C4C22×Dic13414yes—
725C2×C4C22×Dic13414yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—416no—
734C22#121×D6714yes—
735C22#1686394914yes—
736C22#1686400314yes—
737C22#1686404414yes—
738C22#1686405414yes—
739C22D4×Dic13414yes—
740C22D4×Dic13414yes—
741C22C22×D4×D6711yescharacteristic
742C22C22×D4×D6711yescharacteristic
743C22C23×Dic13411yescharacteristic
744C22C2×#41×D6711yescharacteristic
745C22C2×#41×D6711yescharacteristic
746C22C2×#1452409011yescharacteristic
747C22C2×#1452409011yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—2682no—
755C4—2682no—
756C4—2682no—
757C4—2682no—
758C4—678no—
759C4—1344no—
760C4—1344no—
761C4—1344no—
762C2—44no—
763C2#2256380518yesdirect product factor
764C2C2×#121×D6711yescharacteristic
765C2C2×#1686394911yescharacteristic
766C2C2×#1686400311yescharacteristic
767C2C2×#1686404411yescharacteristic
768C2C2×#1686405411yescharacteristic
769C2C2×D4×Dic13411yescharacteristic
770C2C2×D4×Dic13411yescharacteristic
subgroupG/H
centerC24C23×D67
commutator, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC2×#388×C67C2
socleC24×C67C24
prime radicalC25×C67C23
hypercenterC2×#388D67
hypocenterC67C2×#2429
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#14524042C2semidirect
4. C22×C4×Dic134C2semidirect
5. #22563805C2direct (N × H)
6. C2×#16863329C2semidirect
7. C2×#16863328C2semidirect
10. C2×#16863300C2semidirect
11. C2×#16863294C2semidirect
12. C2×#16863293C2semidirect
13. C2×#16863293C2semidirect
21. C2×#14524042C22semidirect
27. C2×C4×Dic134C22semidirect
47. #16863329C22semidirect
48. #16863328C22semidirect
51. #16863300C22semidirect
52. #16863294C22semidirect
53. #16863293C22semidirect
54. #16863293C22semidirect
150. C2×C22⋊C4×C67Q8semidirect
257. C22⋊C4×C67C2×Q8semidirect
378. C2×C67#2429semidirect
402. C67C2×#2429semidirect
524. C2×C22⋊C4Dic134semidirect
640. C22⋊C4C2×Dic134semidirect
763. C2#22563805direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240422
C22×#145240202
C22×C4×Dic1342
#225638052
C2×#168633292
C2×#168633282
C2×#168633192
C2×#168633002
C2×#168632942
C2×#168632932
C2×#168632892
C2×C22⋊C4×Dic672
C2×#388×C672
C2×#242967