Finite Group Databasebeta

← #22569031

Subgroups — #22569031

Order 8576.

484 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14524072C211yesmaximal, characteristic
2C4×#11761627C211yesmaximal, characteristic
3C4×Q8×D67C211yesmaximal, characteristic, complemented
4#16863504C211yesmaximal, characteristic, complemented
5#16863501C211yesmaximal, characteristic, complemented
6#16863496C211yesmaximal, characteristic, complemented
7#16863490C211yesmaximal, characteristic, complemented
8#16863488C211yesmaximal, characteristic, complemented
9#16863487C211yesmaximal, characteristic, complemented
10SD16×Dic67C211yesmaximal, characteristic, complemented
11#16863437C211yesmaximal, characteristic, complemented
12#16863403C211yesmaximal, characteristic, complemented
13#16863394C211yesmaximal, characteristic
14#16863348C211yesmaximal, characteristic, complemented
15#440×C67C211yesmaximal, characteristic, complemented
16C2×#11761627C2211yescharacteristic
17C2×Q8×D67C2211yescharacteristic
18#14524072C418yescomplemented
19C2×Dic268C2211yescharacteristic
20C2×#11761618C2211yescharacteristic
21C2×#11761616C2211yescharacteristic
22C2×#11761611C2211yescharacteristic
23C2×#11761611C2211yescharacteristic
24Q8×Dic67C2211yescharacteristic
25C4×Dic134—21no—
26C4×Dic134C2211yescharacteristic
27C4×Dic134C2211yescharacteristic
28#14524008—21no—
29#14524008C2211yescharacteristic
30#14524008C2211yescharacteristic
31D4×Dic67C2211yescharacteristic
32C4×C22⋊D67—21no—
33(C22⋊D67)⋊C4—21no—
34#14524001C2211yescharacteristic
35#14523999—21no—
36C4⋊C4×D67—21no—
37C4⋊C4×D67C2211yescharacteristic
38C2×C4×Dic67—21no—
39C42×D67—21no—
40C42×D67C2211yescharacteristic
41#14523976C2211yescharacteristic
42#14523975C2211yescharacteristic
43#14523974C2211yescharacteristic
44#14523968C2211yescharacteristic
45#14523968C2211yescharacteristic
46#14523967C2211yescharacteristic
47#14523966C2211yescharacteristic
48#14523966C2211yescharacteristic
49#14523964C2211yescharacteristic
50#14523954C2211yescharacteristic
51C8×Dic67C2211yescharacteristic
52C8×Dic67C2211yescharacteristic
53C2×SD16×C67C2211yescharacteristic
54C4×Q8×C67C2211yescharacteristic
55C4×D4×C67C2211yescharacteristic
56#107×C67C2211yescharacteristic
57#103×C67C2211yescharacteristic
58#102×C67C2211yescharacteristic
59#97×C67C2211yescharacteristic
60#11761627—22no—
61#11761627C2×C414yes—
62C2×Dic134—21no—
63C2×Dic134C2311yescharacteristic
64C2×Dic134C2311yescharacteristic
65Q8×D67—22no—
66Q8×D67C2×C414yescomplemented
67C2×C22⋊D67—21no—
68C22×Dic67—21no—
69C22×Dic67—21no—
70C2×C4×D67—21no—
71C2×C4×D67—21no—
72C2×C4×D67D411yescharacteristic
73C2×C4×D67D411yescharacteristic
74C2×C4×D67C2311yescharacteristic
75Dic268C2×C414yescomplemented
76#11761618C2×C414yescomplemented
77#11761616C2×C414yescomplemented
78#11761611—22no—
79#11761611C2×C414yescomplemented
80C2×C67⋊C8C2311yescharacteristic
81C2×C67⋊C8C2311yescharacteristic
82C4⋊Dic67—21no—
83C4⋊Dic67C2311yescharacteristic
84C4⋊Dic67C2311yescharacteristic
85Dic67⋊C4—21no—
86Dic67⋊C4—21no—
87Dic67⋊C4—21no—
88Dic67⋊C4—21no—
89Dic67⋊C4—21no—
90C22⋊Dic67—21no—
91(C2×D67)⋊C4—21no—
92C4×Dic67—21no—
93C4×Dic67—21no—
94C4×Dic67—21no—
95C4×Dic67—21no—
96C4×Dic67—21no—
97C4×Dic67—21no—
98C4×Dic67D411yescharacteristic
99C4×Dic67D411yescharacteristic
100C4×Dic67C2311yescharacteristic
101C2×Q8×C67C2311yescharacteristic
102C2×D4×C67C2311yescharacteristic
103C22×C4×C67—21no—
104SD16×C67C2×C414yescomplemented
105C2×C8×C67C2311yescharacteristic
106C2×C8×C67C2311yescharacteristic
107C4⋊C4×C67—21no—
108C4⋊C4×C67C2311yescharacteristic
109C4⋊C4×C67C2311yescharacteristic
110C22⋊C4×C67—21no—
111C42×C67—21no—
112C42×C67C2311yescharacteristic
113C23×C67—21no—
114C22×D67C2×D411yescharacteristic
115Q8×C67—21no—
116Q8×C67C22×C412yes—
117D4×C67—21no—
118D4×C67C22×C412yes—
119C2×C4×C67—21no—
120C2×C4×C67—21no—
121C2×C4×C67—21no—
122C2×C4×C67—42no—
123C2×C4×C67C2×D411yescharacteristic
124C2×C4×C67C2×D411yescharacteristic
125C2×C4×C67C2411yescharacteristic
126C22⋊D67—24no—
127C2×Dic67—21no—
128C2×Dic67—21no—
129C2×Dic67—24no—
130C2×Dic67—21no—
131C2×Dic67—21no—
132C2×Dic67—42no—
133C2×Dic67C2×D411yescharacteristic
134C2×Dic67C2×D411yescharacteristic
135C2×Dic67C2×D411yescharacteristic
136C4×D67—24no—
137C4×D67—22no—
138C4×D67—41no—
139C4×D67—42no—
140C4×D67C22×C412yes—
141C4×D67#4112yes—
142Dic134—21no—
143Dic134—21no—
144Dic134—24no—
145Dic134C22×C412yes—
146Dic134C22×C412yes—
147C8×C67—21no—
148C8×C67C22×C412yes—
149C67⋊C8—21no—
150C67⋊C8C22×C412yes—
151C22×C67—22no—
152C22×C67—41no—
153C22×C67—41no—
154C22×C67C22×D411yescharacteristic
155C2×D67—21no—
156C2×D67—21no—
157C2×D67C4×D412yes—
158C4×C67—22no—
159C4×C67—21no—
160C4×C67—21no—
161C4×C67—41no—
162C4×C67—41no—
163C4×C67C23×C411yescharacteristic
164C4×C67C2×#4111yescharacteristic
165Dic67—22no—
166Dic67—22no—
167Dic67—21no—
168Dic67—41no—
169Dic67—41no—
170Dic67C4×D412yes—
171Dic67#13712yescomplemented
172C2×C67—42no—
173C2×C67C2×C4×D411yescharacteristic
174C2×C67C2×#13711yescharacteristic
175C2×C67#57511yescharacteristic
176D67—22no—
177C4×#137—671nomaximal, Sylow
178C67C4×#13711yescharacteristic, complemented, Sylow
179C2×#137—671no—
180C4×#41—671no—
181C2×C4×Q8—671no—
182#441—671no—
183#441—671no—
184#440—671no—
185#440D6711yescharacteristic, complemented
186C4×Q16—671no—
187C4×Q16—671no—
188C4×SD16—671no—
189C4×SD16—671no—
190#428—671no—
191#419—671no—
192#417—671no—
193C4×M16—671no—
194C2×#41—671no—
195C22×Q8—671no—
196#137—678no—
197C2×Q16—671no—
198C2×Q16—671no—
199C2×SD16—671no—
200C2×SD16C2×D6711yescharacteristic
201C2×M16—671no—
202C2×M16—671no—
203C4×Q8—671no—
204C4×Q8—671no—
205C4×Q8—671no—
206C4×Q8—671no—
207C4×Q8—671no—
208C4×Q8—1341no—
209C4×Q8—1341no—
210C4×Q8C2×D6711yescharacteristic
211C4×D4—671no—
212C4×D4—1341no—
213C4×D4—1341no—
214C4×D4C2×D6711yescharacteristic
215#117—671no—
216#117—1341no—
217C2×C4⋊C4—671no—
218C2×C4⋊C4—1341no—
219C2×C42—671no—
220C2×C42—1341no—
221C2×C42—1341no—
222#107—671no—
223#107C2×D6711yescharacteristic
224#106—671no—
225#106—671no—
226#103—671no—
227#103—671no—
228#103—671no—
229#103—671no—
230#103—671no—
231#103C2×D6711yescharacteristic
232#102—671no—
233#102C2×D6711yescharacteristic
234#97—671no—
235#97C2×D6711yescharacteristic
236C4×C8—671no—
237C4×C8—671no—
238#41—674no—
239#41—1342no—
240C2×Q8—674no—
241C2×Q8—671no—
242C2×Q8—671no—
243C2×Q8—1341no—
244C2×Q8—1342no—
245C2×Q8C22×D6711yescharacteristic
246C2×D4—1341no—
247C2×D4C22×D6711yescharacteristic
248C22×C4—21no—
249C22×C4—671no—
250C22×C4—671no—
251C22×C4—671no—
252C22×C4—1341no—
253C22×C4—1341no—
254C22×C4—1341no—
255C22×C4—1341no—
256Q16—674no—
257Q16—674no—
258SD16—674no—
259SD16C4×D6714yescomplemented
260M16—674no—
261M16—1342no—
262C2×C8—671no—
263C2×C8—671no—
264C2×C8C22×D6711yescharacteristic
265C2×C8C22×D6711yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—671no—
268C4⋊C4—671no—
269C4⋊C4—1341no—
270C4⋊C4—1341no—
271C4⋊C4—1341no—
272C4⋊C4—1341no—
273C4⋊C4—1341no—
274C4⋊C4—1341no—
275C4⋊C4C22×D6711yescharacteristic
276C4⋊C4C22×D6711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—1341no—
279C22⋊C4—1341no—
280C42—21no—
281C42—671no—
282C42—671no—
283C42—671no—
284C42—1341no—
285C42—1341no—
286C42—1341no—
287C42—1341no—
288C42—1341no—
289C42—1341no—
290C42C22×D6711yescharacteristic
291C23—21no—
292C23—671no—
293Q8—21no—
294Q8—672no—
295Q8—672no—
296Q8—1344no—
297Q8—1341no—
298Q8—1341no—
299Q8C2×C4×D6712yes—
300D4—21no—
301D4—1344no—
302D4C2×C4×D6712yes—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—42no—
307C2×C4—2681no—
308C2×C4—2682no—
309C2×C4—2682no—
310C2×C4—671no—
311C2×C4—671no—
312C2×C4—672no—
313C2×C4—672no—
314C2×C4—671no—
315C2×C4—1342no—
316C2×C4—1344no—
317C2×C4—1341no—
318C2×C4—1341no—
319C2×C4—1344no—
320C2×C4—1341no—
321C2×C4—1341no—
322C2×C4D4×D6711yescharacteristic
323C2×C4D4×D6711yescharacteristic
324C2×C4C23×D6711yescharacteristic
325C8—21no—
326C8—672no—
327C8—1341no—
328C8C2×C4×D6712yes—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—672no—
333C22—1341no—
334C22—1341no—
335C22C2×D4×D6711yescharacteristic
336C4—22no—
337C4—21no—
338C4—21no—
339C4—41no—
340C4—41no—
341C4—2681no—
342C4—2681no—
343C4—672no—
344C4—672no—
345C4—1342no—
346C4—1342no—
347C4—1341no—
348C4C22×C4×D6711yescharacteristic
349C4#41×D6711yescharacteristic
350C2—42no—
351C2—1342no—
352C2C4×D4×D6711yescharacteristic
353C2#137×D6711yescharacteristic
354C2#1686419211yescharacteristic
subgroupG/H
centerC22C2×D4×D67
commutatorC4×C67C23×C4
FrattiniC2×C4C23×D67
Fitting#440×C67C2
socleC22×C67C22×D4
hypercenter#440D67
hypocenterC67C4×#137
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
3. C4×Q8×D67C2semidirect
4. #16863504C2semidirect
5. #16863501C2semidirect
6. #16863496C2semidirect
7. #16863490C2semidirect
8. #16863488C2semidirect
9. #16863487C2semidirect
10. SD16×Dic67C2semidirect
11. #16863437C2semidirect
12. #16863403C2semidirect
14. #16863348C2semidirect
15. #440×C67C2semidirect
18. #14524072C4semidirect
66. Q8×D67C2×C4semidirect
75. Dic268C2×C4semidirect
76. #11761618C2×C4semidirect
77. #11761616C2×C4semidirect
79. #11761611C2×C4semidirect
104. SD16×C67C2×C4semidirect
171. Dic67#137semidirect
178. C67C4×#137semidirect
185. #440D67semidirect
259. SD16C4×D67semidirect