Finite Group Databasebeta

← C2×#22562918 #31014616

Subgroups — C2×#22562918 #31014616

Order 17152.

3566 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524029C211yesmaximal, characteristic
2C22×C4×Dic134C211yesmaximal, characteristic, complemented
3C22×(C22⋊D67)⋊C4C211yesmaximal, characteristic
4#22562918C2116yesmaximal, direct product factor
5C2×#16863300C211yesmaximal, characteristic, complemented
6C2×#16863296C211yesmaximal, characteristic
7C2×#16863288C211yesmaximal, characteristic, complemented
8C2×#16863287C211yesmaximal, characteristic, complemented
9C2×#16863284C211yesmaximal, characteristic, complemented
10C2×#16863271C211yesmaximal, characteristic, complemented
11C2×#16863270C211yesmaximal, characteristic, complemented
12C2×#16863268C211yesmaximal, characteristic, complemented
13C2×#16863267C211yesmaximal, characteristic, complemented
14C2×#16863265C211yesmaximal, characteristic, complemented
15C2×#16863241C211yesmaximal, characteristic, complemented
16C2×#388×C67C211yesmaximal, characteristic, complemented
17C23×Dic134C2211yescharacteristic
18C23×C22⋊D67C2211yescharacteristic
19C24×Dic67C2211yescharacteristic
20C23×C4×D67C2211yescharacteristic
21C2×#14524029C4116yescomplemented
22C2×#14524029C2218yes—
23C2×C4×Dic134—28no—
24C2×C4×Dic134C2218yescomplemented
25C2×(C22⋊D67)⋊C4—28no—
26C2×(C22⋊D67)⋊C4C2218yes—
27C22×C4⋊Dic67C2211yescharacteristic
28C22×C4⋊Dic67C2211yescharacteristic
29C22×Dic67⋊C4C2211yescharacteristic
30C22×Dic67⋊C4C2211yescharacteristic
31C22×Dic67⋊C4C2211yescharacteristic
32C22×Dic67⋊C4C2211yescharacteristic
33C22×Dic67⋊C4C2211yescharacteristic
34C22×C22⋊Dic67C2211yescharacteristic
35C22×C22⋊Dic67C2211yescharacteristic
36C22×(C2×D67)⋊C4C2211yescharacteristic
37C22×(C2×D67)⋊C4C2211yescharacteristic
38C22×(C2×D67)⋊C4C2211yescharacteristic
39C22×(C2×D67)⋊C4C2211yescharacteristic
40C22×(C2×D67)⋊C4C2211yescharacteristic
41C22×C4×Dic67C2211yescharacteristic
42C22×C4×Dic67C2211yescharacteristic
43C22×C4×Dic67C2211yescharacteristic
44C22×C4×Dic67C2211yescharacteristic
45#16863300C2218yescomplemented
46#16863296C2218yes—
47#16863288C2218yescomplemented
48#16863287C2218yescomplemented
49#16863284C2218yescomplemented
50#16863271C2218yescomplemented
51#16863270C2218yescomplemented
52#16863268C2218yescomplemented
53#16863267C2218yescomplemented
54#16863265C2218yescomplemented
55#16863241C2218yescomplemented
56C2×C67⋊#95C2211yescharacteristic
57C2×C67⋊#95C2211yescharacteristic
58C2×C67⋊#95C2211yescharacteristic
59C2×C67⋊#95C2211yescharacteristic
60C2×C67⋊#95C2211yescharacteristic
61C2×C67⋊#95C2211yescharacteristic
62C22×C4⋊C4×C67C2211yescharacteristic
63C22×C22⋊C4×C67C2211yescharacteristic
64C22×C22⋊C4×C67C2211yescharacteristic
65C22×C22⋊C4×C67C2211yescharacteristic
66C22×C42×C67C2211yescharacteristic
67#388×C67C2218yescomplemented
68C2×#95×C67C2211yescharacteristic
69C2×#95×C67C2211yescharacteristic
70C24×D67C2311yescharacteristic
71C22×Dic134—24no—
72C22×Dic134—24no—
73C22×Dic134C2×C418yescomplemented
74C22×Dic134C2314yes—
75C22×C22⋊D67—24no—
76C22×C22⋊D67—24no—
77C22×C22⋊D67C2×C418yes—
78C22×C22⋊D67C2314yes—
79C23×Dic67—24no—
80C23×Dic67—42no—
81C23×Dic67—42no—
82C23×Dic67C2311yescharacteristic
83C23×Dic67C2311yescharacteristic
84C23×Dic67C2311yescharacteristic
85C23×Dic67C2311yescharacteristic
86C23×Dic67C2311yescharacteristic
87C23×Dic67C2311yescharacteristic
88C23×Dic67C2314yes—
89C23×Dic67C2311yescharacteristic
90C22×C4×D67—24no—
91C22×C4×D67—42no—
92C22×C4×D67—42no—
93C22×C4×D67C2314yes—
94#14524029C2×C4164yescomplemented
95C4×Dic134—232no—
96(C22⋊D67)⋊C4—232no—
97C2×C4⋊Dic67—24no—
98C2×C4⋊Dic67—42no—
99C2×C4⋊Dic67C2314yes—
100C2×C4⋊Dic67C2314yes—
101C2×Dic67⋊C4—24no—
102C2×Dic67⋊C4—24no—
103C2×Dic67⋊C4—24no—
104C2×Dic67⋊C4—42no—
105C2×Dic67⋊C4—42no—
106C2×Dic67⋊C4C2314yes—
107C2×Dic67⋊C4C2314yes—
108C2×Dic67⋊C4C2314yes—
109C2×Dic67⋊C4C2314yes—
110C2×Dic67⋊C4C2314yes—
111C2×C22⋊Dic67—42no—
112C2×C22⋊Dic67C2×C418yescomplemented
113C2×C22⋊Dic67C2314yes—
114C2×C22⋊Dic67C2314yes—
115C2×(C2×D67)⋊C4—24no—
116C2×(C2×D67)⋊C4—42no—
117C2×(C2×D67)⋊C4—42no—
118C2×(C2×D67)⋊C4C2×C418yescomplemented
119C2×(C2×D67)⋊C4C2×C418yescomplemented
120C2×(C2×D67)⋊C4C2314yes—
121C2×(C2×D67)⋊C4C2314yes—
122C2×(C2×D67)⋊C4C2314yes—
123C2×(C2×D67)⋊C4C2314yes—
124C2×(C2×D67)⋊C4C2314yes—
125C2×C4×Dic67—24no—
126C2×C4×Dic67—24no—
127C2×C4×Dic67C2×C418yescomplemented
128C2×C4×Dic67D418yes—
129C2×C4×Dic67C2314yes—
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—42no—
147C2×C4⋊C4×C67C2314yes—
148C2×C22⋊C4×C67—24no—
149C2×C22⋊C4×C67—42no—
150C2×C22⋊C4×C67C2×C418yescomplemented
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—
158C23×D67—22no—
159C23×D67—22no—
160C23×D67—22no—
161C23×D67—22no—
162C23×D67—22no—
163C23×D67—22no—
164C23×D67C22×C414yes—
165C23×D67C2412yes—
166C2×Dic134—232no—
167C2×Dic134—28no—
168C2×Dic134—28no—
169C2×Dic134C22×C4116yescomplemented
170C2×C22⋊D67—232no—
171C2×C22⋊D67—28no—
172C2×C22⋊D67—28no—
173C2×C22⋊D67C22×C4116yes—
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—22no—
185C22×Dic67—22no—
186C22×Dic67—22no—
187C22×Dic67—22no—
188C22×Dic67—22no—
189C22×Dic67—28no—
190C22×Dic67—44no—
191C22×Dic67—44no—
192C22×Dic67—416no—
193C22×Dic67C22×C414yes—
194C22×Dic67C22×C414yes—
195C22×Dic67C22×C414yes—
196C22×Dic67C2×D414yes—
197C22×Dic67C2×D414yes—
198C22×Dic67#4114yes—
199C22×Dic67C2412yes—
200C22×Dic67C2412yes—
201C22×Dic67C2412yes—
202C22×Dic67C2412yes—
203C22×Dic67C2412yes—
204C22×Dic67C2412yes—
205C22×Dic67C2412yes—
206C2×C4×D67—28no—
207C2×C4×D67—44no—
208C2×C4×D67—44no—
209C2×C4×D67—416no—
210C4⋊Dic67—28no—
211C4⋊Dic67—44no—
212Dic67⋊C4—28no—
213Dic67⋊C4—28no—
214Dic67⋊C4—28no—
215Dic67⋊C4—44no—
216Dic67⋊C4—44no—
217C22⋊Dic67—44no—
218C22⋊Dic67C22×C4116yescomplemented
219(C2×D67)⋊C4—28no—
220(C2×D67)⋊C4—44no—
221(C2×D67)⋊C4—44no—
222(C2×D67)⋊C4C22×C4116yescomplemented
223(C2×D67)⋊C4C22×C4116yescomplemented
224C4×Dic67—28no—
225C4×Dic67—28no—
226C4×Dic67C22×C4116yescomplemented
227C4×Dic67C2×D4116yes—
228C24×C67—22no—
229C24×C67—22no—
230C24×C67—22no—
231C24×C67—22no—
232C24×C67—22no—
233C24×C67—22no—
234C24×C67C22×C414yes—
235C24×C67C2412yes—
236C24×C67C2411yescharacteristic
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×C67—22no—
245C22×C4×C67—22no—
246C22×C4×C67—22no—
247C22×C4×C67—22no—
248C22×C4×C67—22no—
249C22×C4×C67—22no—
250C22×C4×C67—22no—
251C22×C4×C67—22no—
252C22×C4×C67C22×C414yes—
253C22×C4×C67C22×C414yes—
254C22×C4×C67C2×D414yes—
255C22×C4×C67C2412yes—
256C22×C4×C67C2412yes—
257C22×C4×C67C2412yes—
258C22×C4×C67C2412yes—
259C22×C4×C67C2412yes—
260C22×C4×C67C2412yes—
261C4⋊C4×C67—44no—
262C22⋊C4×C67—28no—
263C22⋊C4×C67—44no—
264C22⋊C4×C67C22×C4116yescomplemented
265C42×C67—28no—
266C23×C67—28no—
267C23×C67—28no—
268C23×C67—28no—
269C23×C67—22no—
270C23×C67—22no—
271C23×C67—22no—
272C23×C67—22no—
273C23×C67—22no—
274C23×C67—22no—
275C23×C67—44no—
276C23×C67—44no—
277C23×C67—44no—
278C23×C67—44no—
279C23×C67C23×C414yes—
280C23×C67C23×C412yes—
281C23×C67C22×D412yes—
282C23×C67C2×#4112yes—
283C23×C67H(5,𝔽2)12yes—
284C23×C67H(5,𝔽2)12yes—
285C23×C672−1+412yes—
286C23×C672−1+412yes—
287C23×C67C2511yescharacteristic
288C22×D67—28no—
289C22×D67—28no—
290C22×D67—28no—
291C22×D67—22no—
292C22×D67—22no—
293C22×D67—22no—
294C22×D67—22no—
295C22×D67—22no—
296C22×D67—22no—
297C22×D67—44no—
298C22×D67—44no—
299C22×D67—44no—
300C22×D67—44no—
301C22×D67C23×C414yes—
302C2×C4×C67—28no—
303C2×C4×C67—28no—
304C2×C4×C67—28no—
305C2×C4×C67—22no—
306C2×C4×C67—22no—
307C2×C4×C67—22no—
308C2×C4×C67—22no—
309C2×C4×C67—22no—
310C2×C4×C67—22no—
311C2×C4×C67—22no—
312C2×C4×C67—22no—
313C2×C4×C67—22no—
314C2×C4×C67—22no—
315C2×C4×C67—22no—
316C2×C4×C67—22no—
317C2×C4×C67—22no—
318C2×C4×C67—22no—
319C2×C4×C67—22no—
320C2×C4×C67—44no—
321C2×C4×C67—44no—
322C2×C4×C67—44no—
323C2×C4×C67C23×C414yes—
324C2×C4×C67C23×C414yes—
325C2×C4×C67C22×D414yes—
326C22⋊D67—232no—
327C2×Dic67—28no—
328C2×Dic67—28no—
329C2×Dic67—28no—
330C2×Dic67—22no—
331C2×Dic67—22no—
332C2×Dic67—22no—
333C2×Dic67—22no—
334C2×Dic67—22no—
335C2×Dic67—22no—
336C2×Dic67—22no—
337C2×Dic67—22no—
338C2×Dic67—22no—
339C2×Dic67—22no—
340C2×Dic67—22no—
341C2×Dic67—22no—
342C2×Dic67—22no—
343C2×Dic67—22no—
344C2×Dic67—22no—
345C2×Dic67—416no—
346C2×Dic67—44no—
347C2×Dic67—44no—
348C2×Dic67—44no—
349C2×Dic67C4×D4116yes—
350C2×Dic67C23×C414yes—
351C2×Dic67C23×C414yes—
352C2×Dic67C23×C414yes—
353C2×Dic67C22×D414yes—
354C2×Dic67C22×D414yes—
355C2×Dic67C2×#4114yes—
356C4×D67—416no—
357Dic134—232no—
358C22×C67—24no—
359C22×C67—24no—
360C22×C67—24no—
361C22×C67—416no—
362C22×C67—42no—
363C22×C67—42no—
364C22×C67—42no—
365C22×C67—42no—
366C22×C67C2×C4×D414yes—
367C22×C67#52014yes—
368C22×C67#52014yes—
369C22×C67#53514yes—
370C22×C67#53614yes—
371C22×C67#54214yes—
372C22×C67#54214yes—
373C22×C67C24×C411yescharacteristic
374C22×C67C23×D411yescharacteristic
375C22×C67C22×#4111yescharacteristic
376C22×C67C2×H(5,𝔽2)11yescharacteristic
377C22×C67C2×H(5,𝔽2)11yescharacteristic
378C22×C67C2×2−1+411yescharacteristic
379C22×C67C2×2−1+411yescharacteristic
380C2×D67—24no—
381C2×D67—24no—
382C2×D67—24no—
383C2×D67—416no—
384C2×D67—42no—
385C2×D67—42no—
386C2×D67—42no—
387C2×D67—42no—
388C4×C67—24no—
389C4×C67—24no—
390C4×C67—24no—
391C4×C67—42no—
392C4×C67—42no—
393C4×C67—42no—
394Dic67—24no—
395Dic67—24no—
396Dic67—24no—
397Dic67—42no—
398Dic67—42no—
399Dic67—42no—
400Dic67C2×C4×D418yes—
401C2×#2326—671nomaximal, Sylow
402C2×C67—44no—
403C2×C67#232618yescomplemented
404C2×C67C22×C4×D411yescharacteristic
405C2×C67C2×#52011yescharacteristic
406C2×C67C2×#52011yescharacteristic
407C2×C67C2×#53511yescharacteristic
408C2×C67C2×#53611yescharacteristic
409C2×C67C2×#54211yescharacteristic
410C2×C67C2×#54211yescharacteristic
411D67—44no—
412C22×#124—671no—
413C22×C4×Q8—671no—
414C22×C4×D4—671no—
415#2326—6716no—
416C2×#391—671no—
417C2×#390—671no—
418C2×#388—671no—
419C2×#388—671no—
420C2×#388—671no—
421C2×#388D6711yescharacteristic, complemented
422C2×#385—671no—
423C2×#385—671no—
424C2×#385—671no—
425C2×#385—671no—
426C2×#384—671no—
427C2×#376—671no—
428C67C2×#232611yescharacteristic, complemented, Sylow
429C23×Q8—671no—
430C23×D4—671no—
431C24×C4—671no—
432C24×C4—671no—
433C2×#124—6716no—
434C2×#124—678no—
435C2×C4×Q8—678no—
436C2×C4×Q8—1348no—
437C2×C4×D4—678no—
438C2×C4×D4—1348no—
439C22×C4⋊C4—671no—
440C22×C4⋊C4—671no—
441C22×C4⋊C4—671no—
442C22×C4⋊C4—671no—
443C22×C4⋊C4—671no—
444C22×C4⋊C4—671no—
445C22×C4⋊C4—671no—
446C22×C4⋊C4C2×D6711yescharacteristic
447C22×C22⋊C4—671no—
448C22×C22⋊C4—671no—
449C22×C22⋊C4—671no—
450C22×C22⋊C4—671no—
451C22×C22⋊C4—671no—
452C22×C22⋊C4—671no—
453C22×C22⋊C4—671no—
454C22×C22⋊C4C2×D6711yescharacteristic
455C22×C22⋊C4C2×D6711yescharacteristic
456C22×C22⋊C4C2×D6711yescharacteristic
457C22×C42—671no—
458C22×C42—671no—
459C22×C42—671no—
460C22×C42—671no—
461C22×C42C2×D6711yescharacteristic
462#391—678no—
463#390—678no—
464#388—678no—
465#388—678no—
466#388—678no—
467#388C2×D6718yescomplemented
468#385—678no—
469#385—678no—
470#385—678no—
471#385—678no—
472#384—678no—
473#376—678no—
474C2×#95—671no—
475C2×#95—671no—
476C2×#95—671no—
477C2×#95—671no—
478C2×#95—671no—
479C2×#95—671no—
480C2×#95C2×D6711yescharacteristic
481C2×#95C2×D6711yescharacteristic
482C25—671no—
483C25C22×D6711yescharacteristic
484C22×Q8—678no—
485C22×Q8—674no—
486C22×Q8—1344no—
487C22×Q8—1344no—
488C22×D4—678no—
489C22×D4—674no—
490C22×D4—1344no—
491C22×D4—1344no—
492C23×C4—2682no—
493C23×C4—2682no—
494C23×C4—2682no—
495C23×C4—2682no—
496C23×C4—674no—
497C23×C4—674no—
498C23×C4—671no—
499C23×C4—671no—
500C23×C4—671no—
501C23×C4—671no—
502C23×C4—671no—
503C23×C4—671no—
504C23×C4—671no—
505C23×C4—1344no—
506C23×C4—1344no—
507C23×C4C22×D6711yescharacteristic
508C23×C4C22×D6711yescharacteristic
509C23×C4C22×D6711yescharacteristic
510C23×C4C22×D6711yescharacteristic
511C23×C4C22×D6711yescharacteristic
512C23×C4C22×D6711yescharacteristic
513#124—6764no—
514C4×Q8—13432no—
515C4×D4—13432no—
516C2×C4⋊C4—42no—
517C2×C4⋊C4—2682no—
518C2×C4⋊C4—2682no—
519C2×C4⋊C4—2682no—
520C2×C4⋊C4—674no—
521C2×C4⋊C4—674no—
522C2×C4⋊C4—674no—
523C2×C4⋊C4—674no—
524C2×C4⋊C4—674no—
525C2×C4⋊C4—674no—
526C2×C4⋊C4—674no—
527C2×C4⋊C4—1344no—
528C2×C4⋊C4—1344no—
529C2×C4⋊C4—1344no—
530C2×C4⋊C4—1344no—
531C2×C4⋊C4C22×D6714yes—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—2682no—
535C2×C22⋊C4—2682no—
536C2×C22⋊C4—2682no—
537C2×C22⋊C4—674no—
538C2×C22⋊C4—674no—
539C2×C22⋊C4—674no—
540C2×C22⋊C4—678no—
541C2×C22⋊C4—674no—
542C2×C22⋊C4—678no—
543C2×C22⋊C4—678no—
544C2×C22⋊C4—674no—
545C2×C22⋊C4—674no—
546C2×C22⋊C4—674no—
547C2×C22⋊C4—1344no—
548C2×C22⋊C4C4×D6718yescomplemented
549C2×C22⋊C4C22×D6714yes—
550C2×C22⋊C4C22×D6714yes—
551C2×C22⋊C4C22×D6714yes—
552C2×C42—24no—
553C2×C42—678no—
554C2×C42—678no—
555C2×C42—674no—
556C2×C42—674no—
557C2×C42—674no—
558C2×C42—674no—
559C2×C42—1344no—
560C2×C42—1344no—
561C2×C42C22×D6714yes—
562#95—674no—
563#95—674no—
564#95—674no—
565#95—674no—
566#95—674no—
567#95—674no—
568#95C22×D6714yes—
569#95C22×D6714yes—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—674no—
577C24—672no—
578C24—1342no—
579C24—1342no—
580C24—1342no—
581C24—1342no—
582C24—1342no—
583C24—1342no—
584C24C2×C4×D6714yes—
585C24C23×D6712yes—
586C24C23×D6711yescharacteristic
587C2×Q8—6716no—
588C2×Q8—1348no—
589C2×Q8—13432no—
590C2×Q8—1348no—
591C2×D4—6716no—
592C2×D4—1348no—
593C2×D4—13432no—
594C2×D4—1348no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—2684no—
611C22×C4—2684no—
612C22×C4—26816no—
613C22×C4—26816no—
614C22×C4—2684no—
615C22×C4—2684no—
616C22×C4—674no—
617C22×C4—674no—
618C22×C4—674no—
619C22×C4—672no—
620C22×C4—674no—
621C22×C4—674no—
622C22×C4—674no—
623C22×C4—672no—
624C22×C4—672no—
625C22×C4—672no—
626C22×C4—672no—
627C22×C4—672no—
628C22×C4—672no—
629C22×C4—1348no—
630C22×C4—1348no—
631C22×C4—1342no—
632C22×C4—1342no—
633C22×C4—1342no—
634C22×C4—1342no—
635C22×C4—1342no—
636C22×C4—1342no—
637C22×C4—1342no—
638C22×C4—1342no—
639C22×C4—1342no—
640C22×C4—1342no—
641C22×C4—1342no—
642C22×C4—1342no—
643C22×C4—1342no—
644C22×C4—1342no—
645C22×C4—1342no—
646C22×C4C2×C4×D6714yes—
647C22×C4C2×C4×D6714yes—
648C22×C4D4×D6714yes—
649C22×C4C23×D6712yes—
650C22×C4C23×D6712yes—
651C22×C4C23×D6712yes—
652C22×C4C23×D6712yes—
653C22×C4C23×D6712yes—
654C22×C4C23×D6712yes—
655C4⋊C4—44no—
656C4⋊C4—2684no—
657C4⋊C4—2684no—
658C4⋊C4—2684no—
659C4⋊C4—1348no—
660C4⋊C4—1348no—
661C4⋊C4—1348no—
662C4⋊C4—1348no—
663C22⋊C4—28no—
664C22⋊C4—44no—
665C22⋊C4—2684no—
666C22⋊C4—2684no—
667C22⋊C4—2684no—
668C22⋊C4—6716no—
669C22⋊C4—6716no—
670C22⋊C4—6716no—
671C22⋊C4—1348no—
672C22⋊C4C2×C4×D67116yescomplemented
673C42—28no—
674C42—6716no—
675C42—6716no—
676C42—1348no—
677C42—1348no—
678C23—28no—
679C23—28no—
680C23—28no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—2684no—
692C23—2684no—
693C23—2684no—
694C23—2684no—
695C23—674no—
696C23—1348no—
697C23—1348no—
698C23—1348no—
699C23—1342no—
700C23—1342no—
701C23—1342no—
702C23—1342no—
703C23—1342no—
704C23—1342no—
705C23C22×C4×D6714yes—
706C23C22×C4×D6712yes—
707C23C2×D4×D6712yes—
708C23#41×D6712yes—
709C23#1452408812yes—
710C23#1452408912yes—
711C23#1452409012yes—
712C23#1452409012yes—
713C23C24×D6711yescharacteristic
714Q8—13432no—
715D4—13432no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—28no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—26816no—
738C2×C4—2684no—
739C2×C4—2684no—
740C2×C4—2684no—
741C2×C4—26816no—
742C2×C4—6716no—
743C2×C4—674no—
744C2×C4—674no—
745C2×C4—674no—
746C2×C4—674no—
747C2×C4—674no—
748C2×C4—674no—
749C2×C4—1342no—
750C2×C4—1342no—
751C2×C4—1342no—
752C2×C4—1342no—
753C2×C4—1342no—
754C2×C4—1342no—
755C2×C4—1342no—
756C2×C4—1342no—
757C2×C4—1342no—
758C2×C4—1348no—
759C2×C4—1348no—
760C2×C4—1342no—
761C2×C4—1348no—
762C2×C4—1342no—
763C2×C4—1342no—
764C2×C4—1342no—
765C2×C4—1342no—
766C2×C4—1342no—
767C2×C4C22×C4×D6714yes—
768C2×C4C22×C4×D6714yes—
769C2×C4C2×D4×D6714yes—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—42no—
774C22—42no—
775C22—416no—
776C22—42no—
777C22—42no—
778C22—2682no—
779C22—2682no—
780C22—26816no—
781C22—2682no—
782C22—2682no—
783C22—1344no—
784C22—1344no—
785C22—1344no—
786C22C4×D4×D6714yes—
787C22#1686387514yes—
788C22#1686387614yes—
789C22#1686396214yes—
790C22#1686396814yes—
791C22#1686401014yes—
792C22#1686401214yes—
793C22C23×C4×D6711yescharacteristic
794C22C22×D4×D6711yescharacteristic
795C22C2×#41×D6711yescharacteristic
796C22C2×#1452408811yescharacteristic
797C22C2×#1452408911yescharacteristic
798C22C2×#1452409011yescharacteristic
799C22C2×#1452409011yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—2682no—
807C4—2682no—
808C4—2682no—
809C4—678no—
810C4—1344no—
811C4—1344no—
812C4—1344no—
813C2—44no—
814C2—2684no—
815C2#2256291818yesdirect product factor
816C2C2×C4×D4×D6711yescharacteristic
817C2C2×#1686387511yescharacteristic
818C2C2×#1686387611yescharacteristic
819C2C2×#1686396211yescharacteristic
820C2C2×#1686396811yescharacteristic
821C2C2×#1686401011yescharacteristic
822C2C2×#1686401211yescharacteristic
subgroupG/H
centerC24C23×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC2×#388×C67C2
socleC24×C67C24
prime radicalC23×C22⋊D67C22
cosocleC23×C67C25
hypercenterC2×#388D67
hypocenterC67C2×#2326
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic134C2semidirect
4. #22562918C2direct (N × H)
5. C2×#16863300C2semidirect
7. C2×#16863288C2semidirect
8. C2×#16863287C2semidirect
9. C2×#16863284C2semidirect
10. C2×#16863271C2semidirect
11. C2×#16863270C2semidirect
12. C2×#16863268C2semidirect
13. C2×#16863267C2semidirect
14. C2×#16863265C2semidirect
15. C2×#16863241C2semidirect
16. C2×#388×C67C2semidirect
21. C2×#14524029C4semidirect
24. C2×C4×Dic134C22semidirect
45. #16863300C22semidirect
47. #16863288C22semidirect
48. #16863287C22semidirect
49. #16863284C22semidirect
50. #16863271C22semidirect
51. #16863270C22semidirect
52. #16863268C22semidirect
53. #16863267C22semidirect
54. #16863265C22semidirect
55. #16863241C22semidirect
67. #388×C67C22semidirect
73. C22×Dic134C2×C4semidirect
94. #14524029C2×C4semidirect
112. C2×C22⋊Dic67C2×C4semidirect
118. C2×(C2×D67)⋊C4C2×C4semidirect
119. C2×(C2×D67)⋊C4C2×C4semidirect
127. C2×C4×Dic67C2×C4semidirect
150. C2×C22⋊C4×C67C2×C4semidirect
169. C2×Dic134C22×C4semidirect
218. C22⋊Dic67C22×C4semidirect
222. (C2×D67)⋊C4C22×C4semidirect
223. (C2×D67)⋊C4C22×C4semidirect
226. C4×Dic67C22×C4semidirect
264. C22⋊C4×C67C22×C4semidirect
403. C2×C67#2326semidirect
421. C2×#388D67semidirect
428. C67C2×#2326semidirect
467. #388C2×D67semidirect
548. C2×C22⋊C4C4×D67semidirect
672. C22⋊C4C2×C4×D67semidirect
815. C2#22562918direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240292
C22×C4×Dic1342
C22×(C22⋊D67)⋊C42
#225629182
C2×#168633002
C2×#168632962
C2×#168632882
C2×#168632872
C2×#168632842
C2×#168632712
C2×#168632702
C2×#168632682
C2×#168632672
C2×#168632652
C2×#168632412
C2×#388×C672
C2×#232667