Finite Group Databasebeta

← C2×#22563137 #31015157

Subgroups — C2×#22563137 #31015157

Order 17152.

3894 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×(C22⋊D67)⋊C4C211yesmaximal, characteristic
2C22×#14523999C211yesmaximal, characteristic, complemented
3C22×C4⋊C4×D67C211yesmaximal, characteristic, complemented
4#22563137C2116yesmaximal, direct product factor
5C2×#16863289C211yesmaximal, characteristic, complemented
6C2×#16863283C211yesmaximal, characteristic, complemented
7C2×#16863277C211yesmaximal, characteristic, complemented
8C2×#16863272C211yesmaximal, characteristic
9C2×#16863272C211yesmaximal, characteristic
10C2×#16863260C211yesmaximal, characteristic, complemented
11C2×#16863255C211yesmaximal, characteristic, complemented
12C2×#16863254C211yesmaximal, characteristic, complemented
13C2×C4×Dic67⋊C4C211yesmaximal, characteristic, complemented
14C2×C4×(C2×D67)⋊C4C211yesmaximal, characteristic, complemented
15C2×#16863243C211yesmaximal, characteristic, complemented
16C2×#388×C67C211yesmaximal, characteristic, complemented
17C23×C22⋊D67C2211yescharacteristic
18C24×Dic67C2211yescharacteristic
19C23×C4×D67C2211yescharacteristic
20C23×C4×D67C2211yescharacteristic
21C23×C4×D67C2211yescharacteristic
22C2×(C22⋊D67)⋊C4C4116yescomplemented
23C2×(C22⋊D67)⋊C4C2218yes—
24C2×#14523999—28no—
25C2×#14523999C2218yescomplemented
26C22×C4⋊Dic67C2211yescharacteristic
27C22×Dic67⋊C4C2211yescharacteristic
28C22×Dic67⋊C4C2211yescharacteristic
29C22×Dic67⋊C4C2211yescharacteristic
30C22×Dic67⋊C4C2211yescharacteristic
31C22×Dic67⋊C4C2211yescharacteristic
32C2×C4⋊C4×D67—28no—
33C2×C4⋊C4×D67C2218yescomplemented
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#16863289C2218yescomplemented
44#16863283C2218yescomplemented
45#16863277C2218yescomplemented
46#16863272C2218yes—
47#16863272C2218yes—
48#16863260C2218yescomplemented
49#16863255C2218yescomplemented
50#16863254C2218yescomplemented
51C4×Dic67⋊C4C2218yescomplemented
52C4×(C2×D67)⋊C4C2218yescomplemented
53#16863243C2218yescomplemented
54C2×C67⋊#95C2211yescharacteristic
55C2×C67⋊#95C2211yescharacteristic
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×C22⋊D67—24no—
72C22×C22⋊D67—24no—
73C22×C22⋊D67C2×C418yes—
74C22×C22⋊D67C2314yes—
75C23×Dic67—24no—
76C23×Dic67—24no—
77C23×Dic67C2×C418yescomplemented
78C23×Dic67C2311yescharacteristic
79C23×Dic67C2311yescharacteristic
80C23×Dic67C2311yescharacteristic
81C23×Dic67C2311yescharacteristic
82C23×Dic67C2311yescharacteristic
83C23×Dic67C2314yes—
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×C418yes—
95C22×C4×D67C2314yes—
96C22×C4×D67C2314yes—
97C22×C4×D67C2314yes—
98(C22⋊D67)⋊C4C2×C4164yescomplemented
99#14523999—232no—
100C2×C4⋊Dic67—24no—
101C2×C4⋊Dic67C2314yes—
102C2×Dic67⋊C4—24no—
103C2×Dic67⋊C4—24no—
104C2×Dic67⋊C4—24no—
105C2×Dic67⋊C4C2×C418yescomplemented
106C2×Dic67⋊C4D418yescomplemented
107C2×Dic67⋊C4C2314yes—
108C2×Dic67⋊C4C2314yes—
109C2×Dic67⋊C4C2314yes—
110C2×Dic67⋊C4C2314yes—
111C2×Dic67⋊C4C2314yes—
112C4⋊C4×D67—232no—
113C2×C22⋊Dic67—24no—
114C2×C22⋊Dic67—42no—
115C2×C22⋊Dic67C2314yes—
116C2×C22⋊Dic67C2314yes—
117C2×(C2×D67)⋊C4—24no—
118C2×(C2×D67)⋊C4—24no—
119C2×(C2×D67)⋊C4C2×C418yes—
120C2×(C2×D67)⋊C4C2314yes—
121C2×(C2×D67)⋊C4C2314yes—
122C2×(C2×D67)⋊C4C2314yes—
123C2×C4×Dic67—24no—
124C2×C4×Dic67—24no—
125C2×C4×Dic67—42no—
126C2×C4×Dic67C2×C418yescomplemented
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—24no—
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—42no—
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×D67#4114yes—
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—232no—
177C22×Dic67—28no—
178C22×Dic67—28no—
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×Dic67C22×C414yes—
189C22×Dic67C22×C414yes—
190C22×Dic67C22×C414yes—
191C22×Dic67C22×C4116yescomplemented
192C22×Dic67C2×D414yes—
193C22×Dic67C2×D414yes—
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×C4116yes—
214C4⋊Dic67—28no—
215Dic67⋊C4—28no—
216Dic67⋊C4—28no—
217Dic67⋊C4—28no—
218Dic67⋊C4C22×C4116yescomplemented
219Dic67⋊C4C2×D4116yescomplemented
220C22⋊Dic67—28no—
221C22⋊Dic67—44no—
222(C2×D67)⋊C4—28no—
223(C2×D67)⋊C4—28no—
224(C2×D67)⋊C4C22×C4116yes—
225C4×Dic67—28no—
226C4×Dic67—28no—
227C4×Dic67—44no—
228C4×Dic67C22×C4116yescomplemented
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—28no—
263C22⋊C4×C67—28no—
264C22⋊C4×C67—44no—
265C22⋊C4×C67C22×C4116yescomplemented
266C42×C67—44no—
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×D67#117116yescomplemented
300C22×D67C23×C414yes—
301C22×D67C2×#4114yes—
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—22no—
332C2×Dic67—22no—
333C2×Dic67—22no—
334C2×Dic67—22no—
335C2×Dic67—22no—
336C2×Dic67—22no—
337C2×Dic67—232no—
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—44no—
348C2×Dic67—44no—
349C2×Dic67—44no—
350C2×Dic67C4×D4116yes—
351C2×Dic67C23×C414yes—
352C2×Dic67C23×C414yes—
353C2×Dic67C23×C414yes—
354C2×Dic67C22×D414yes—
355C2×Dic67C22×D414yes—
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×#11714yes—
369C22×C67C2×C4×D414yes—
370C22×C67#52014yes—
371C22×C67#54614yes—
372C22×C67#54814yes—
373C22×C67#55214yes—
374C22×C67#55314yes—
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×#11718yescomplemented
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—42no—
400Dic67—42no—
401Dic67—42no—
402Dic67C2×C4×D418yes—
403C2×#2352—671nomaximal, Sylow
404C2×C67—44no—
405C2×C67#235218yescomplemented
406C2×C67C22×#11711yescharacteristic
407C2×C67C22×C4×D411yescharacteristic
408C2×C67C2×#52011yescharacteristic
409C2×C67C2×#54611yescharacteristic
410C2×C67C2×#54811yescharacteristic
411C2×C67C2×#55211yescharacteristic
412C2×C67C2×#55311yescharacteristic
413D67—28no—
414C22×C4×D4—671no—
415C22×#117—671no—
416C23×C4⋊C4—671no—
417#2352—6716no—
418C2×#388—671no—
419C2×#388D6711yescharacteristic, complemented
420C2×#387—671no—
421C2×#387—671no—
422C2×#386—671no—
423C2×#386—671no—
424C2×#382—671no—
425C2×#380—671no—
426C2×#380—671no—
427C2×C4×C4⋊C4—671no—
428C2×C4×C22⋊C4—671no—
429C2×C4×C22⋊C4—671no—
430C67C2×#235211yescharacteristic, complemented, Sylow
431C23×D4—671no—
432C24×C4—671no—
433C24×C4—671no—
434C24×C4—671no—
435C24×C4—671no—
436C2×C4×D4—6716no—
437C2×C4×D4—678no—
438C2×#117—678no—
439C2×#117—1348no—
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⋊C4—678no—
447C22×C4⋊C4—1348no—
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#388—678no—
463#388C2×D6718yescomplemented
464#387—678no—
465#387—678no—
466#386—678no—
467#386—678no—
468#382—678no—
469#380—678no—
470#380—678no—
471C4×C4⋊C4—678no—
472C4×C22⋊C4—678no—
473C4×C22⋊C4—678no—
474C2×#95—671no—
475C2×#95—671no—
476C2×#95—671no—
477C2×#95—671no—
478C2×#95—671no—
479C2×#95—671no—
480C2×#95—671no—
481C2×#95—671no—
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—674no—
493C23×C4—674no—
494C23×C4—671no—
495C23×C4—678no—
496C23×C4—674no—
497C23×C4—671no—
498C23×C4—671no—
499C23×C4—671no—
500C23×C4—678no—
501C23×C4—674no—
502C23×C4—671no—
503C23×C4—671no—
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
519C4×D4—6764no—
520#117—13432no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4—678no—
523C2×C4⋊C4—678no—
524C2×C4⋊C4—674no—
525C2×C4⋊C4—674no—
526C2×C4⋊C4—674no—
527C2×C4⋊C4—674no—
528C2×C4⋊C4—674no—
529C2×C4⋊C4—674no—
530C2×C4⋊C4—13432no—
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—2682no—
539C2×C22⋊C4—674no—
540C2×C22⋊C4—678no—
541C2×C22⋊C4—674no—
542C2×C22⋊C4—674no—
543C2×C22⋊C4—674no—
544C2×C22⋊C4—674no—
545C2×C22⋊C4—1344no—
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—42no—
553C2×C42—2682no—
554C2×C42—674no—
555C2×C42—678no—
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#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—13432no—
591C2×D4—1348no—
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—26816no—
609C22×C4—2684no—
610C22×C4—2684no—
611C22×C4—26816no—
612C22×C4—674no—
613C22×C4—674no—
614C22×C4—674no—
615C22×C4—672no—
616C22×C4—674no—
617C22×C4—674no—
618C22×C4—6716no—
619C22×C4—674no—
620C22×C4—672no—
621C22×C4—672no—
622C22×C4—672no—
623C22×C4—6716no—
624C22×C4—672no—
625C22×C4—672no—
626C22×C4—672no—
627C22×C4—1348no—
628C22×C4—1348no—
629C22×C4—1348no—
630C22×C4—1348no—
631C22×C4—13432no—
632C22×C4—1348no—
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—1348no—
643C22×C4—1348no—
644C22×C4—13432no—
645C22×C4—1348no—
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—28no—
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—2684no—
671C22⋊C4—6716no—
672C22⋊C4—1348no—
673C22⋊C4—1348no—
674C22⋊C4—1348no—
675C22⋊C4C2×C4×D67116yescomplemented
676C42—44no—
677C42—2684no—
678C42—6716no—
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—2684no—
743C2×C4—2684no—
744C2×C4—6716no—
745C2×C4—674no—
746C2×C4—674no—
747C2×C4—674no—
748C2×C4—674no—
749C2×C4—674no—
750C2×C4—674no—
751C2×C4—13432no—
752C2×C4—1342no—
753C2×C4—1342no—
754C2×C4—1342no—
755C2×C4—1342no—
756C2×C4—1342no—
757C2×C4—1342no—
758C2×C4—1342no—
759C2×C4—1342no—
760C2×C4—1342no—
761C2×C4—13432no—
762C2×C4—1348no—
763C2×C4—1348no—
764C2×C4—1348no—
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—416no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—678no—
783C22—1344no—
784C22—13432no—
785C22—1344no—
786C22—1344no—
787C22—1344no—
788C22—1344no—
789C22—1344no—
790C22#117×D6714yes—
791C22C4×D4×D6714yes—
792C22#1686387514yes—
793C22#1686403514yes—
794C22#1686405414yes—
795C22#1686408214yes—
796C22#1686409114yes—
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—2682no—
812C4—2682no—
813C4—678no—
814C4—1344no—
815C4—1344no—
816C4—1344no—
817C2—44no—
818C2—1348no—
819C2#2256313718yesdirect product factor
820C2C2×#117×D6711yescharacteristic
821C2C2×C4×D4×D6711yescharacteristic
822C2C2×#1686387511yescharacteristic
823C2C2×#1686403511yescharacteristic
824C2C2×#1686405411yescharacteristic
825C2C2×#1686408211yescharacteristic
826C2C2×#1686409111yescharacteristic
subgroupG/H
centerC24C23×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC2×#388×C67C2
socleC24×C67C24
prime radicalC23×C22⋊D67C22
cosocleC23×C67C25
hypercenterC2×#388D67
hypocenterC67C2×#2352
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×#14523999C2semidirect
3. C22×C4⋊C4×D67C2semidirect
4. #22563137C2direct (N × H)
5. C2×#16863289C2semidirect
6. C2×#16863283C2semidirect
7. C2×#16863277C2semidirect
10. C2×#16863260C2semidirect
11. C2×#16863255C2semidirect
12. C2×#16863254C2semidirect
13. C2×C4×Dic67⋊C4C2semidirect
14. C2×C4×(C2×D67)⋊C4C2semidirect
15. C2×#16863243C2semidirect
16. C2×#388×C67C2semidirect
22. C2×(C22⋊D67)⋊C4C4semidirect
25. C2×#14523999C22semidirect
33. C2×C4⋊C4×D67C22semidirect
43. #16863289C22semidirect
44. #16863283C22semidirect
45. #16863277C22semidirect
48. #16863260C22semidirect
49. #16863255C22semidirect
50. #16863254C22semidirect
51. C4×Dic67⋊C4C22semidirect
52. C4×(C2×D67)⋊C4C22semidirect
53. #16863243C22semidirect
67. #388×C67C22semidirect
77. C23×Dic67C2×C4semidirect
98. (C22⋊D67)⋊C4C2×C4semidirect
105. C2×Dic67⋊C4C2×C4semidirect
106. C2×Dic67⋊C4D4semidirect
126. C2×C4×Dic67C2×C4semidirect
150. C2×C22⋊C4×C67C2×C4semidirect
191. C22×Dic67C22×C4semidirect
218. Dic67⋊C4C22×C4semidirect
219. Dic67⋊C4C2×D4semidirect
228. C4×Dic67C22×C4semidirect
265. C22⋊C4×C67C22×C4semidirect
299. C22×D67#117semidirect
389. C2×D67C2×#117semidirect
405. C2×C67#2352semidirect
419. C2×#388D67semidirect
430. C67C2×#2352semidirect
463. #388C2×D67semidirect
548. C2×C22⋊C4C4×D67semidirect
675. C22⋊C4C2×C4×D67semidirect
819. C2#22563137direct (N × H)

Maximal subgroups

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

subgroupindex
C22×(C22⋊D67)⋊C42
C22×#145239992
C22×C4⋊C4×D672
#225631372
C2×#168632892
C2×#168632832
C2×#168632772
C2×#168632722
C2×#168632602
C2×#168632552
C2×#168632542
C2×C4×Dic67⋊C42
C2×C4×(C2×D67)⋊C42
C2×#168632432
C2×#388×C672
C2×#235267