Finite Group Databasebeta

← #22569049

Subgroups — #22569049

Order 8576.

470 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14524072C211yesmaximal, characteristic
2#16863875C211yesmaximal, characteristic
3#16863872C211yesmaximal, characteristic, complemented
4#16863504C211yesmaximal, characteristic, complemented
5#16863500C211yesmaximal, characteristic, complemented
6#16863493C211yesmaximal, characteristic, complemented
7#16863490C211yesmaximal, characteristic, complemented
8C4×#11761618C211yesmaximal, characteristic, complemented
9SD16×Dic67C211yesmaximal, characteristic, complemented
10C4×#11761616C211yesmaximal, characteristic, complemented
11#16863437C211yesmaximal, characteristic, complemented
12#16863389C211yesmaximal, characteristic
13#103×D67C211yesmaximal, characteristic, complemented
14#16863353C211yesmaximal, characteristic, complemented
15#440×C67C211yesmaximal, characteristic, complemented
16C2×#11761627C2211yescharacteristic
17C2×Q8×D67C2211yescharacteristic
18#14524072C418yescomplemented
19C2×Dic268C2211yescharacteristic
20C2×#11761618C2211yescharacteristic
21C2×#11761616C2211yescharacteristic
22C2×#11761611C2211yescharacteristic
23C2×C8×D67C2211yescharacteristic
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#14524001—21no—
35#14524001C2211yescharacteristic
36#14524000—21no—
37#14524000C2211yescharacteristic
38#14523999—21no—
39C2×Dic67⋊C4—21no—
40C4⋊C4×D67C2211yescharacteristic
41#14523976C2211yescharacteristic
42#14523975C2211yescharacteristic
43#14523974C2211yescharacteristic
44#14523968C2211yescharacteristic
45#14523968C2211yescharacteristic
46#14523967C2211yescharacteristic
47#14523966C2211yescharacteristic
48#14523966C2211yescharacteristic
49#14523964C2211yescharacteristic
50#14523953C2211yescharacteristic
51C4×C67⋊C8C2211yescharacteristic
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×D67C2311yescharacteristic
73Dic268C2×C414yescomplemented
74#11761618C2×C414yescomplemented
75#11761616C2×C414yescomplemented
76#11761611C2×C414yescomplemented
77C2×C67⋊C8C2311yescharacteristic
78C2×C67⋊C8C2311yescharacteristic
79C8×D67—22no—
80C4⋊Dic67—21no—
81C4⋊Dic67C2311yescharacteristic
82C4⋊Dic67C2311yescharacteristic
83Dic67⋊C4—21no—
84Dic67⋊C4—21no—
85Dic67⋊C4—21no—
86Dic67⋊C4—21no—
87Dic67⋊C4—21no—
88Dic67⋊C4D411yescharacteristic
89Dic67⋊C4D411yescharacteristic
90C22⋊Dic67—21no—
91(C2×D67)⋊C4—21no—
92(C2×D67)⋊C4D411yescharacteristic
93(C2×D67)⋊C4D411yescharacteristic
94C4×Dic67—21no—
95C4×Dic67—21no—
96C4×Dic67—21no—
97C4×Dic67—21no—
98C4×Dic67—21no—
99C4×Dic67—21no—
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—81no—
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—81no—
133C2×Dic67C2×D411yescharacteristic
134C2×Dic67C2×D411yescharacteristic
135C2×Dic67C2×D411yescharacteristic
136C4×D67—24no—
137C4×D67—81no—
138C4×D67C22×C412yes—
139C4×D67#4112yes—
140Dic134—21no—
141Dic134—21no—
142Dic134—24no—
143Dic134C22×C412yes—
144Dic134C22×C412yes—
145C8×C67—21no—
146C8×C67C22×C412yes—
147C67⋊C8—21no—
148C67⋊C8C22×C412yes—
149C22×C67—22no—
150C22×C67—41no—
151C22×C67—41no—
152C22×C67C22×D411yescharacteristic
153C2×D67—21no—
154C2×D67—21no—
155C2×D67C4×D412yes—
156C4×C67—22no—
157C4×C67—21no—
158C4×C67—21no—
159C4×C67—41no—
160C4×C67—41no—
161C4×C67C23×C411yescharacteristic
162C4×C67C2×#4111yescharacteristic
163Dic67—22no—
164Dic67—22no—
165Dic67—21no—
166Dic67—21no—
167Dic67—41no—
168Dic67—41no—
169Dic67C4×D412yes—
170C2×C67—42no—
171C2×C67C2×C4×D411yescharacteristic
172C2×C67#57711yescharacteristic
173C2×C67#57811yescharacteristic
174D67—22no—
175#2947—671nomaximal, Sylow
176C67#294711yescharacteristic, complemented, Sylow
177C2×#137—671no—
178#520—671no—
179#519—671no—
180#441—671no—
181#441—671no—
182#440—671no—
183#440D6711yescharacteristic, complemented
184C4×Q16—671no—
185C4×Q16—671no—
186C4×SD16—671no—
187C4×SD16—671no—
188#428—671no—
189#416—671no—
190C2×#103—671no—
191#405—671no—
192C2×#41—671no—
193C22×Q8—671no—
194#137—678no—
195C2×Q16—671no—
196C2×Q16—671no—
197C2×SD16—671no—
198C2×SD16C2×D6711yescharacteristic
199C2×M16—671no—
200C22×C8—671no—
201C4×Q8—671no—
202C4×Q8—671no—
203C4×Q8—671no—
204C4×Q8—671no—
205C4×Q8—671no—
206C4×Q8—1341no—
207C4×Q8—1341no—
208C4×Q8C2×D6711yescharacteristic
209C4×D4—671no—
210C4×D4—1341no—
211C4×D4—1341no—
212C4×D4C2×D6711yescharacteristic
213#117—671no—
214#117—671no—
215#117—1341no—
216#117—1341no—
217#117—1341no—
218C2×C4⋊C4—671no—
219C2×C4⋊C4—1341no—
220#107—671no—
221#107C2×D6711yescharacteristic
222#106—671no—
223#106—671no—
224#103—671no—
225#103—671no—
226#103—671no—
227#103—671no—
228#103—671no—
229#103C2×D6711yescharacteristic
230#102—671no—
231#102C2×D6711yescharacteristic
232#97—671no—
233#97C2×D6711yescharacteristic
234C4×C8—671no—
235C4×C8—671no—
236#41—674no—
237#41—1342no—
238C2×Q8—674no—
239C2×Q8—671no—
240C2×Q8—671no—
241C2×Q8—1341no—
242C2×Q8—1342no—
243C2×Q8C22×D6711yescharacteristic
244C2×D4—1341no—
245C2×D4C22×D6711yescharacteristic
246C22×C4—21no—
247C22×C4—671no—
248C22×C4—1341no—
249C22×C4—1341no—
250C22×C4—1341no—
251C22×C4—1341no—
252Q16—674no—
253Q16—674no—
254SD16—674no—
255SD16C4×D6714yescomplemented
256M16—674no—
257C2×C8—671no—
258C2×C8—671no—
259C2×C8—1342no—
260C2×C8C22×D6711yescharacteristic
261C2×C8C22×D6711yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—671no—
264C4⋊C4—671no—
265C4⋊C4—671no—
266C4⋊C4—671no—
267C4⋊C4—1341no—
268C4⋊C4—1341no—
269C4⋊C4—1341no—
270C4⋊C4—1341no—
271C4⋊C4—1341no—
272C4⋊C4—1341no—
273C4⋊C4C22×D6711yescharacteristic
274C4⋊C4C22×D6711yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—671no—
277C22⋊C4—671no—
278C22⋊C4—1341no—
279C22⋊C4—1341no—
280C42—21no—
281C42—671no—
282C42—1341no—
283C42—1341no—
284C42—1341no—
285C42—1341no—
286C42—1341no—
287C42—1341no—
288C42C22×D6711yescharacteristic
289C23—21no—
290C23—671no—
291Q8—21no—
292Q8—672no—
293Q8—672no—
294Q8—1344no—
295Q8—1341no—
296Q8—1341no—
297Q8C2×C4×D6712yes—
298D4—21no—
299D4—1344no—
300D4C2×C4×D6712yes—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—81no—
305C2×C4—5361no—
306C2×C4—5361no—
307C2×C4—671no—
308C2×C4—672no—
309C2×C4—672no—
310C2×C4—671no—
311C2×C4—671no—
312C2×C4—1344no—
313C2×C4—1341no—
314C2×C4—1341no—
315C2×C4—1344no—
316C2×C4—1341no—
317C2×C4—1341no—
318C2×C4D4×D6711yescharacteristic
319C2×C4D4×D6711yescharacteristic
320C2×C4C23×D6711yescharacteristic
321C8—21no—
322C8—672no—
323C8—1341no—
324C8C2×C4×D6712yes—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—672no—
329C22—1341no—
330C22—1341no—
331C22C2×D4×D6711yescharacteristic
332C4—22no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—2681no—
338C4—2681no—
339C4—672no—
340C4—1342no—
341C4—1342no—
342C4—1341no—
343C4—1341no—
344C4C22×C4×D6711yescharacteristic
345C4#41×D6711yescharacteristic
346C2—42no—
347C2—1342no—
348C2C4×D4×D6711yescharacteristic
349C2#1686420611yescharacteristic
350C2#1686421211yescharacteristic
subgroupG/H
centerC22C2×D4×D67
commutatorC4×C67C23×C4
FrattiniC2×C4C23×D67
Fitting#440×C67C2
socleC22×C67C22×D4
hypercenter#440D67
hypocenterC67#2947
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. #16863872C2semidirect
4. #16863504C2semidirect
5. #16863500C2semidirect
6. #16863493C2semidirect
7. #16863490C2semidirect
8. C4×#11761618C2semidirect
9. SD16×Dic67C2semidirect
10. C4×#11761616C2semidirect
11. #16863437C2semidirect
13. #103×D67C2semidirect
14. #16863353C2semidirect
15. #440×C67C2semidirect
18. #14524072C4semidirect
66. Q8×D67C2×C4semidirect
73. Dic268C2×C4semidirect
74. #11761618C2×C4semidirect
75. #11761616C2×C4semidirect
76. #11761611C2×C4semidirect
104. SD16×C67C2×C4semidirect
176. C67#2947semidirect
183. #440D67semidirect
255. SD16C4×D67semidirect