Finite Group Databasebeta

← C2×#22563198 #31015331

Subgroups — C2×#22563198 #31015331

Order 17152.

3830 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524025C211yesmaximal, characteristic
2C22×(C22⋊D67)⋊C4C211yesmaximal, characteristic
3C22×#14524000C211yesmaximal, characteristic, complemented
4#22563198C2116yesmaximal, direct product factor
5C2×#16863292C211yesmaximal, characteristic, complemented
6C2×#16863290C211yesmaximal, characteristic, complemented
7C2×#16863281C211yesmaximal, characteristic, complemented
8C2×#16863278C211yesmaximal, characteristic, complemented
9C2×#16863272C211yesmaximal, characteristic
10C2×#16863268C211yesmaximal, characteristic, complemented
11C2×#16863267C211yesmaximal, characteristic, complemented
12C2×C4×Dic67⋊C4C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic67C211yesmaximal, characteristic, complemented
14C2×#16863243C211yesmaximal, characteristic, complemented
15C2×#95×D67C211yesmaximal, characteristic, complemented
16C2×#388×C67C211yesmaximal, characteristic, complemented
17C23×C22⋊D67C2211yescharacteristic
18C24×Dic67C2211yescharacteristic
19C23×C4×D67C2211yescharacteristic
20C23×C4×D67C2211yescharacteristic
21C23×C4×D67C2211yescharacteristic
22C2×#14524025C4116yescomplemented
23C2×#14524025C2218yes—
24C2×(C22⋊D67)⋊C4—28no—
25C2×(C22⋊D67)⋊C4C2218yes—
26C2×#14524000—28no—
27C2×#14524000C2218yescomplemented
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×C4×Dic67C2211yescharacteristic
40C22×C4×Dic67C2211yescharacteristic
41C22×C4×Dic67C2211yescharacteristic
42C22×C4×Dic67C2211yescharacteristic
43#16863292C2218yescomplemented
44#16863290C2218yescomplemented
45#16863281C2218yescomplemented
46#16863278C2218yescomplemented
47#16863272C2218yes—
48#16863268C2218yescomplemented
49#16863267C2218yescomplemented
50C4×Dic67⋊C4C2218yescomplemented
51C22⋊C4×Dic67C2218yescomplemented
52#16863243C2218yescomplemented
53C2×C67⋊#95C2211yescharacteristic
54C2×C67⋊#95C2211yescharacteristic
55C2×C67⋊#95C2211yescharacteristic
56C2×C67⋊#95C2211yescharacteristic
57C2×C67⋊#95C2211yescharacteristic
58C2×C67⋊#95C2211yescharacteristic
59C2×C67⋊#95C2211yescharacteristic
60C2×C67⋊#95C2211yescharacteristic
61#95×D67C2218yescomplemented
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×C22⋊D67—24no—
72C22×C22⋊D67—24no—
73C22×C22⋊D67C2×C418yes—
74C22×C22⋊D67C2314yes—
75C23×Dic67—24no—
76C23×Dic67—24no—
77C23×Dic67—42no—
78C23×Dic67C2311yescharacteristic
79C23×Dic67C2314yes—
80C23×Dic67C2311yescharacteristic
81C23×Dic67C2311yescharacteristic
82C23×Dic67C2311yescharacteristic
83C23×Dic67C2311yescharacteristic
84C23×Dic67C2311yescharacteristic
85C23×Dic67C2311yescharacteristic
86C22×C4×D67—24no—
87C22×C4×D67—24no—
88C22×C4×D67—24no—
89C22×C4×D67—24no—
90C22×C4×D67—24no—
91C22×C4×D67—24no—
92C22×C4×D67—42no—
93C22×C4×D67—42no—
94C22×C4×D67C2×C418yescomplemented
95C22×C4×D67C2314yes—
96C22×C4×D67C2314yes—
97C22×C4×D67C2314yes—
98#14524025C2×C4164yescomplemented
99(C22⋊D67)⋊C4—232no—
100#14524000—232no—
101C2×C4⋊Dic67C2×C418yescomplemented
102C2×C4⋊Dic67C2314yes—
103C2×Dic67⋊C4—24no—
104C2×Dic67⋊C4—24no—
105C2×Dic67⋊C4—24no—
106C2×Dic67⋊C4—24no—
107C2×Dic67⋊C4C2×C418yescomplemented
108C2×Dic67⋊C4C2314yes—
109C2×Dic67⋊C4C2314yes—
110C2×Dic67⋊C4C2314yes—
111C2×Dic67⋊C4C2314yes—
112C2×Dic67⋊C4C2314yes—
113C2×C22⋊Dic67—24no—
114C2×C22⋊Dic67C2×C418yescomplemented
115C2×C22⋊Dic67C2314yes—
116C2×C22⋊Dic67C2314yes—
117C2×(C2×D67)⋊C4—24no—
118C2×(C2×D67)⋊C4C2×C418yescomplemented
119C2×(C2×D67)⋊C4D418yes—
120C2×(C2×D67)⋊C4C2314yes—
121C2×(C2×D67)⋊C4C2314yes—
122C2×(C2×D67)⋊C4C2314yes—
123C2×C4×Dic67—24no—
124C2×C4×Dic67—24no—
125C2×C4×Dic67—24no—
126C2×C4×Dic67—42no—
127C2×C4×Dic67C2314yes—
128C2×C4×Dic67C2314yes—
129C2×C4×Dic67C2314yes—
130C2×C4×Dic67C2314yes—
131C67⋊#95C2314yes—
132C67⋊#95C2314yes—
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×D67C22×C414yes—
163C23×D67C2×D414yes—
164C23×D67#4114yes—
165C23×D67C2412yes—
166C2×C22⋊D67—232no—
167C2×C22⋊D67—28no—
168C2×C22⋊D67—28no—
169C2×C22⋊D67C22×C4116yes—
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—22no—
185C22×Dic67—28no—
186C22×Dic67—28no—
187C22×Dic67—44no—
188C22×Dic67—416no—
189C22×Dic67C22×C414yes—
190C22×Dic67C22×C414yes—
191C22×Dic67C22×C414yes—
192C22×Dic67C2×D414yes—
193C22×Dic67#4114yes—
194C22×Dic67#4114yes—
195C22×Dic67C2412yes—
196C22×Dic67C2412yes—
197C22×Dic67C2412yes—
198C22×Dic67C2412yes—
199C22×Dic67C2412yes—
200C22×Dic67C2412yes—
201C22×Dic67C2412yes—
202C2×C4×D67—232no—
203C2×C4×D67—28no—
204C2×C4×D67—28no—
205C2×C4×D67—28no—
206C2×C4×D67—28no—
207C2×C4×D67—28no—
208C2×C4×D67—28no—
209C2×C4×D67—44no—
210C2×C4×D67—44no—
211C2×C4×D67—416no—
212C2×C4×D67—416no—
213C2×C4×D67C22×C4116yescomplemented
214C4⋊Dic67C22×C4116yescomplemented
215Dic67⋊C4—28no—
216Dic67⋊C4—28no—
217Dic67⋊C4—28no—
218Dic67⋊C4—28no—
219Dic67⋊C4C22×C4116yescomplemented
220C22⋊Dic67—28no—
221C22⋊Dic67C22×C4116yescomplemented
222(C2×D67)⋊C4—28no—
223(C2×D67)⋊C4C22×C4116yescomplemented
224(C2×D67)⋊C4C2×D4116yes—
225C4×Dic67—28no—
226C4×Dic67—28no—
227C4×Dic67—28no—
228C4×Dic67—44no—
229C24×C67—22no—
230C24×C67—22no—
231C24×C67—22no—
232C24×C67—22no—
233C24×C67—22no—
234C24×C67—22no—
235C24×C67C22×C414yes—
236C24×C67C2412yes—
237C24×C67C2411yescharacteristic
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×C67—22no—
253C22×C4×C67C22×C414yes—
254C22×C4×C67C22×C414yes—
255C22×C4×C67C2×D414yes—
256C22×C4×C67C2412yes—
257C22×C4×C67C2412yes—
258C22×C4×C67C2412yes—
259C22×C4×C67C2412yes—
260C22×C4×C67C2412yes—
261C22×C4×C67C2412yes—
262C4⋊C4×C67—44no—
263C22⋊C4×C67—28no—
264C22⋊C4×C67—44no—
265C22⋊C4×C67C22×C4116yescomplemented
266C42×C67—28no—
267C23×C67—28no—
268C23×C67—28no—
269C23×C67—28no—
270C23×C67—22no—
271C23×C67—22no—
272C23×C67—22no—
273C23×C67—22no—
274C23×C67—22no—
275C23×C67—22no—
276C23×C67—44no—
277C23×C67—44no—
278C23×C67—44no—
279C23×C67—44no—
280C23×C67C23×C414yes—
281C23×C67C23×C412yes—
282C23×C67C22×D412yes—
283C23×C67C2×#4112yes—
284C23×C67C2×#4112yes—
285C23×C67C2×#4112yes—
286C23×C67H(5,𝔽2)12yes—
287C23×C672−1+412yes—
288C23×C67C2511yescharacteristic
289C22×D67—28no—
290C22×D67—28no—
291C22×D67—28no—
292C22×D67—28no—
293C22×D67—28no—
294C22×D67—28no—
295C22×D67—22no—
296C22×D67—22no—
297C22×D67—22no—
298C22×D67—22no—
299C22×D67C4×D4116yes—
300C22×D67C23×C414yes—
301C22×D67C22×D414yes—
302C22×D67C2×#4114yes—
303C2×C4×C67—28no—
304C2×C4×C67—28no—
305C2×C4×C67—28no—
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—22no—
321C2×C4×C67—44no—
322C2×C4×C67—44no—
323C2×C4×C67—44no—
324C2×C4×C67C23×C414yes—
325C2×C4×C67C23×C414yes—
326C2×C4×C67C22×D414yes—
327C22⋊D67—232no—
328C2×Dic67—28no—
329C2×Dic67—28no—
330C2×Dic67—28no—
331C2×Dic67—28no—
332C2×Dic67—28no—
333C2×Dic67—28no—
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—22no—
346C2×Dic67—22no—
347C2×Dic67—22no—
348C2×Dic67—22no—
349C2×Dic67—416no—
350C2×Dic67—44no—
351C2×Dic67C23×C414yes—
352C2×Dic67C23×C414yes—
353C2×Dic67C23×C414yes—
354C2×Dic67C22×D414yes—
355C2×Dic67C2×#4114yes—
356C2×Dic67C2×#4114yes—
357C4×D67—232no—
358C4×D67—416no—
359C4×D67—416no—
360C22×C67—24no—
361C22×C67—24no—
362C22×C67—24no—
363C22×C67—416no—
364C22×C67—42no—
365C22×C67—42no—
366C22×C67—42no—
367C22×C67—42no—
368C22×C67C2×C4×D414yes—
369C22×C67C4×#4114yes—
370C22×C67#52014yes—
371C22×C67#54614yes—
372C22×C67#54714yes—
373C22×C67#55114yes—
374C22×C67#55214yes—
375C22×C67C24×C411yescharacteristic
376C22×C67C23×D411yescharacteristic
377C22×C67C22×#4111yescharacteristic
378C22×C67C22×#4111yescharacteristic
379C22×C67C22×#4111yescharacteristic
380C22×C67C2×H(5,𝔽2)11yescharacteristic
381C22×C67C2×2−1+411yescharacteristic
382C2×D67—232no—
383C2×D67—24no—
384C2×D67—24no—
385C2×D67—24no—
386C2×D67—24no—
387C2×D67—24no—
388C2×D67—24no—
389C2×D67C2×C4×D418yes—
390C4×C67—24no—
391C4×C67—24no—
392C4×C67—24no—
393C4×C67—42no—
394C4×C67—42no—
395C4×C67—42no—
396Dic67—24no—
397Dic67—24no—
398Dic67—24no—
399Dic67—24no—
400Dic67—24no—
401Dic67—24no—
402Dic67—42no—
403C2×#2359—671nomaximal, Sylow
404C2×C67—44no—
405C2×C67#235918yescomplemented
406C2×C67C22×C4×D411yescharacteristic
407C2×C67C2×C4×#4111yescharacteristic
408C2×C67C2×#52011yescharacteristic
409C2×C67C2×#54611yescharacteristic
410C2×C67C2×#54711yescharacteristic
411C2×C67C2×#55111yescharacteristic
412C2×C67C2×#55211yescharacteristic
413D67—28no—
414C22×#123—671no—
415C22×C4×D4—671no—
416C22×#117—671no—
417#2359—6716no—
418C2×#389—671no—
419C2×#388—671no—
420C2×#388D6711yescharacteristic, complemented
421C2×#387—671no—
422C2×#387—671no—
423C2×#386—671no—
424C2×#385—671no—
425C2×#385—671no—
426C2×C4×C4⋊C4—671no—
427C2×C4×C22⋊C4—671no—
428C2×C4×C22⋊C4—671no—
429C22×#95—671no—
430C67C2×#235911yescharacteristic, complemented, Sylow
431C23×D4—671no—
432C24×C4—671no—
433C24×C4—671no—
434C24×C4—671no—
435C24×C4—671no—
436C2×#123—6716no—
437C2×#123—678no—
438C2×C4×D4—678no—
439C2×C4×D4—1348no—
440C2×#117—678no—
441C2×#117—1348no—
442C22×C4⋊C4—671no—
443C22×C4⋊C4—671no—
444C22×C4⋊C4—671no—
445C22×C4⋊C4—671no—
446C22×C4⋊C4—671no—
447C22×C4⋊C4—671no—
448C22×C4⋊C4C2×D6711yescharacteristic
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#389—678no—
463#388—678no—
464#388C2×D6718yescomplemented
465#387—678no—
466#387—678no—
467#386—678no—
468#385—678no—
469#385—678no—
470C4×C4⋊C4—678no—
471C4×C22⋊C4—678no—
472C4×C22⋊C4—678no—
473C2×#95—671no—
474C2×#95—671no—
475C2×#95—671no—
476C2×#95—671no—
477C2×#95—671no—
478C2×#95—671no—
479C2×#95—671no—
480C2×#95—671no—
481C2×#95—678no—
482C2×#95C2×D6711yescharacteristic
483C2×#95C2×D6711yescharacteristic
484C25—671no—
485C25C22×D6711yescharacteristic
486C22×D4—678no—
487C22×D4—674no—
488C22×D4—1344no—
489C22×D4—1344no—
490C23×C4—2682no—
491C23×C4—2682no—
492C23×C4—2682no—
493C23×C4—674no—
494C23×C4—674no—
495C23×C4—674no—
496C23×C4—671no—
497C23×C4—671no—
498C23×C4—671no—
499C23×C4—671no—
500C23×C4—671no—
501C23×C4—671no—
502C23×C4—678no—
503C23×C4—674no—
504C23×C4—671no—
505C23×C4—1344no—
506C23×C4—1344no—
507C23×C4—1344no—
508C23×C4—1344no—
509C23×C4—1344no—
510C23×C4—1344no—
511C23×C4—1344no—
512C23×C4—1344no—
513C23×C4C22×D6711yescharacteristic
514C23×C4C22×D6711yescharacteristic
515C23×C4C22×D6711yescharacteristic
516C23×C4C22×D6711yescharacteristic
517C23×C4C22×D6711yescharacteristic
518C23×C4C22×D6711yescharacteristic
519#123—6764no—
520C4×D4—13432no—
521#117—13432no—
522C2×C4⋊C4—42no—
523C2×C4⋊C4—678no—
524C2×C4⋊C4—678no—
525C2×C4⋊C4—674no—
526C2×C4⋊C4—674no—
527C2×C4⋊C4—674no—
528C2×C4⋊C4—674no—
529C2×C4⋊C4—674no—
530C2×C4⋊C4—674no—
531C2×C4⋊C4—1344no—
532C2×C4⋊C4—1344no—
533C2×C4⋊C4—1344no—
534C2×C4⋊C4—1344no—
535C2×C4⋊C4C22×D6714yes—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—678no—
539C2×C22⋊C4—674no—
540C2×C22⋊C4—678no—
541C2×C22⋊C4—678no—
542C2×C22⋊C4—674no—
543C2×C22⋊C4—674no—
544C2×C22⋊C4—674no—
545C2×C22⋊C4—674no—
546C2×C22⋊C4—1344no—
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—2682no—
554C2×C42—674no—
555C2×C42—674no—
556C2×C42—674no—
557C2×C42—674no—
558C2×C42—1344no—
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#95—674no—
569#95—674no—
570#95C22×D6714yes—
571#95C22×D6714yes—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—674no—
579C24—674no—
580C24—674no—
581C24—672no—
582C24—1342no—
583C24—1342no—
584C24—1342no—
585C24—1342no—
586C24C2×C4×D6714yes—
587C24C23×D6712yes—
588C24C23×D6711yescharacteristic
589C2×D4—6716no—
590C2×D4—1348no—
591C2×D4—13432no—
592C2×D4—1348no—
593C22×C4—22no—
594C22×C4—22no—
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—2684no—
609C22×C4—2684no—
610C22×C4—26816no—
611C22×C4—26816no—
612C22×C4—2684no—
613C22×C4—26816no—
614C22×C4—674no—
615C22×C4—674no—
616C22×C4—674no—
617C22×C4—674no—
618C22×C4—674no—
619C22×C4—674no—
620C22×C4—672no—
621C22×C4—672no—
622C22×C4—672no—
623C22×C4—672no—
624C22×C4—672no—
625C22×C4—672no—
626C22×C4—6716no—
627C22×C4—672no—
628C22×C4—1348no—
629C22×C4—1348no—
630C22×C4—1348no—
631C22×C4—1348no—
632C22×C4—1348no—
633C22×C4—13432no—
634C22×C4—1348no—
635C22×C4—1348no—
636C22×C4—1348no—
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×C4—1342no—
647C22×C4—1342no—
648C22×C4—1342no—
649C22×C4—1342no—
650C22×C4—1342no—
651C22×C4—1342no—
652C22×C4C2×C4×D6714yes—
653C22×C4C2×C4×D6714yes—
654C22×C4D4×D6714yes—
655C22×C4C23×D6712yes—
656C22×C4C23×D6712yes—
657C22×C4C23×D6712yes—
658C22×C4C23×D6712yes—
659C22×C4C23×D6712yes—
660C22×C4C23×D6712yes—
661C4⋊C4—44no—
662C4⋊C4—6716no—
663C4⋊C4—6716no—
664C4⋊C4—1348no—
665C4⋊C4—1348no—
666C4⋊C4—1348no—
667C4⋊C4—1348no—
668C22⋊C4—28no—
669C22⋊C4—44no—
670C22⋊C4—6716no—
671C22⋊C4—6716no—
672C22⋊C4—6716no—
673C22⋊C4—1348no—
674C22⋊C4—1348no—
675C22⋊C4C2×C4×D67116yescomplemented
676C42—28no—
677C42—2684no—
678C42—1348no—
679C42—1348no—
680C42—1348no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—6716no—
695C23—674no—
696C23—674no—
697C23—674no—
698C23—1348no—
699C23—1348no—
700C23—1348no—
701C23—1348no—
702C23—1348no—
703C23—1348no—
704C23—1342no—
705C23—1342no—
706C23—1342no—
707C23—1342no—
708C23C22×C4×D6714yes—
709C23C22×C4×D6712yes—
710C23C2×D4×D6712yes—
711C23#41×D6712yes—
712C23#41×D6712yes—
713C23#41×D6712yes—
714C23#1452408812yes—
715C23#1452409012yes—
716C23C24×D6711yescharacteristic
717D4—13432no—
718C2×C4—28no—
719C2×C4—28no—
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—22no—
735C2×C4—22no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—26816no—
740C2×C4—26816no—
741C2×C4—2684no—
742C2×C4—26816no—
743C2×C4—674no—
744C2×C4—674no—
745C2×C4—674no—
746C2×C4—674no—
747C2×C4—674no—
748C2×C4—674no—
749C2×C4—13432no—
750C2×C4—1342no—
751C2×C4—1342no—
752C2×C4—1342no—
753C2×C4—1348no—
754C2×C4—1348no—
755C2×C4—1348no—
756C2×C4—1348no—
757C2×C4—1348no—
758C2×C4—1348no—
759C2×C4—1342no—
760C2×C4—1342no—
761C2×C4—1342no—
762C2×C4—1342no—
763C2×C4—1342no—
764C2×C4—1342no—
765C2×C4—1342no—
766C2×C4—1342no—
767C2×C4—1342no—
768C2×C4—1342no—
769C2×C4—1342no—
770C2×C4—1342no—
771C2×C4C22×C4×D6714yes—
772C2×C4C22×C4×D6714yes—
773C2×C4C2×D4×D6714yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—42no—
778C22—42no—
779C22—416no—
780C22—42no—
781C22—42no—
782C22—678no—
783C22—1344no—
784C22—1344no—
785C22—1344no—
786C22—1344no—
787C22—13432no—
788C22—1344no—
789C22—1344no—
790C22C4×D4×D6714yes—
791C22#1686386414yes—
792C22#1686387514yes—
793C22#1686404314yes—
794C22#1686404414yes—
795C22#1686407614yes—
796C22#1686408214yes—
797C22C23×C4×D6711yescharacteristic
798C22C22×D4×D6711yescharacteristic
799C22C2×#41×D6711yescharacteristic
800C22C2×#41×D6711yescharacteristic
801C22C2×#41×D6711yescharacteristic
802C22C2×#1452408811yescharacteristic
803C22C2×#1452409011yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—2682no—
811C4—1344no—
812C4—1344no—
813C4—1344no—
814C4—1344no—
815C4—1344no—
816C4—1344no—
817C2—44no—
818C2—1348no—
819C2#2256319818yesdirect product factor
820C2C2×C4×D4×D6711yescharacteristic
821C2C2×#1686386411yescharacteristic
822C2C2×#1686387511yescharacteristic
823C2C2×#1686404311yescharacteristic
824C2C2×#1686404411yescharacteristic
825C2C2×#1686407611yescharacteristic
826C2C2×#1686408211yescharacteristic
subgroupG/H
centerC24C23×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC2×#388×C67C2
socleC24×C67C24
prime radicalC23×C22⋊D67C22
cosocleC23×C67C25
hypercenterC2×#388D67
hypocenterC67C2×#2359
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C22×#14524000C2semidirect
4. #22563198C2direct (N × H)
5. C2×#16863292C2semidirect
6. C2×#16863290C2semidirect
7. C2×#16863281C2semidirect
8. C2×#16863278C2semidirect
10. C2×#16863268C2semidirect
11. C2×#16863267C2semidirect
12. C2×C4×Dic67⋊C4C2semidirect
13. C2×C22⋊C4×Dic67C2semidirect
14. C2×#16863243C2semidirect
15. C2×#95×D67C2semidirect
16. C2×#388×C67C2semidirect
22. C2×#14524025C4semidirect
27. C2×#14524000C22semidirect
43. #16863292C22semidirect
44. #16863290C22semidirect
45. #16863281C22semidirect
46. #16863278C22semidirect
48. #16863268C22semidirect
49. #16863267C22semidirect
50. C4×Dic67⋊C4C22semidirect
51. C22⋊C4×Dic67C22semidirect
52. #16863243C22semidirect
61. #95×D67C22semidirect
67. #388×C67C22semidirect
94. C22×C4×D67C2×C4semidirect
98. #14524025C2×C4semidirect
101. C2×C4⋊Dic67C2×C4semidirect
107. C2×Dic67⋊C4C2×C4semidirect
114. C2×C22⋊Dic67C2×C4semidirect
118. C2×(C2×D67)⋊C4C2×C4semidirect
150. C2×C22⋊C4×C67C2×C4semidirect
213. C2×C4×D67C22×C4semidirect
214. C4⋊Dic67C22×C4semidirect
219. Dic67⋊C4C22×C4semidirect
221. C22⋊Dic67C22×C4semidirect
223. (C2×D67)⋊C4C22×C4semidirect
265. C22⋊C4×C67C22×C4semidirect
405. C2×C67#2359semidirect
420. C2×#388D67semidirect
430. C67C2×#2359semidirect
464. #388C2×D67semidirect
548. C2×C22⋊C4C4×D67semidirect
675. C22⋊C4C2×C4×D67semidirect
819. C2#22563198direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240252
C22×(C22⋊D67)⋊C42
C22×#145240002
#225631982
C2×#168632922
C2×#168632902
C2×#168632812
C2×#168632782
C2×#168632722
C2×#168632682
C2×#168632672
C2×C4×Dic67⋊C42
C2×C22⋊C4×Dic672
C2×#168632432
C2×#95×D672
C2×#388×C672
C2×#235967