Finite Group Databasebeta

← #22569277

Subgroups — #22569277

Order 8576.

394 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16863943C211yesmaximal, characteristic
2#16863470C211yesmaximal, characteristic, complemented
3#16863469C211yesmaximal, characteristic, complemented
4#16863468C211yesmaximal, characteristic, complemented
5#16863467C211yesmaximal, characteristic, complemented
6#16863466C211yesmaximal, characteristic, complemented
7#16863465C211yesmaximal, characteristic, complemented
8#16863464C211yesmaximal, characteristic, complemented
9#16863452C211yesmaximal, characteristic, complemented
10#16863451C211yesmaximal, characteristic, complemented
11#16863364C211yesmaximal, characteristic, complemented
12#16863362C211yesmaximal, characteristic, complemented
13#16863361C211yesmaximal, characteristic, complemented
14#16863361C211yesmaximal, characteristic, complemented
15#435×C67C211yesmaximal, characteristic, complemented
16C2×#11761628C2211yescharacteristic
17C2×#11761628C2211yescharacteristic
18C2×#11761612C2211yescharacteristic
19C2×#11761611C2211yescharacteristic
20C2×#11761611C2211yescharacteristic
21C22×C67⋊C8C2211yescharacteristic
22C2×C8×D67C2211yescharacteristic
23C2×C8×D67C2211yescharacteristic
24#14524042C411yescharacteristic
25#14524039C411yescharacteristic
26#14524029C411yescharacteristic
27#14524029C411yescharacteristic
28#14524018C411yescharacteristic
29#14524016C411yescharacteristic
30#14524016C411yescharacteristic
31#14524014C411yescharacteristic
32C4×D268C2211yescharacteristic
33C4×C22⋊D67C2211yescharacteristic
34C4×C22⋊D67C2211yescharacteristic
35C42×D67C2211yescharacteristic
36C4⋊(C67⋊C8)C2211yescharacteristic
37Dic67⋊C8C2211yescharacteristic
38Dic67⋊C8C2211yescharacteristic
39C22⋊(C67⋊C8)C2211yescharacteristic
40C22⋊(C67⋊C8)C2211yescharacteristic
41(C2×D67)⋊C8C2211yescharacteristic
42(C2×D67)⋊C8C2211yescharacteristic
43(C2×D67)⋊C8C2211yescharacteristic
44(C2×D67)⋊C8C2211yescharacteristic
45(C2×D67)⋊C8C2211yescharacteristic
46(C2×D67)⋊C8C2211yescharacteristic
47(C2×D67)⋊C8C2211yescharacteristic
48(C2×D67)⋊C8C2211yescharacteristic
49#14523954C2211yescharacteristic
50#14523953C2211yescharacteristic
51#14523953C2211yescharacteristic
52C2×M16×C67C2211yescharacteristic
53C22×C8×C67C2211yescharacteristic
54C4×D4×C67C2211yescharacteristic
55C4⋊C8×C67C2211yescharacteristic
56C22⋊C8×C67C2211yescharacteristic
57C22⋊C8×C67C2211yescharacteristic
58#97×C67C2211yescharacteristic
59#11761628—41no—
60#11761628—41no—
61#11761628—41no—
62#11761628—41no—
63C2×Dic134C2×C411yescharacteristic
64C2×Dic134C2×C411yescharacteristic
65C2×D268C2×C411yescharacteristic
66C2×D268C2×C411yescharacteristic
67C2×D268C2×C411yescharacteristic
68C2×C22⋊D67C2×C411yescharacteristic
69C2×C22⋊D67C2×C411yescharacteristic
70C2×C22⋊D67C2×C411yescharacteristic
71C2×C22⋊D67C2×C411yescharacteristic
72C2×C22⋊D67C2×C411yescharacteristic
73C2×C22⋊D67C2×C411yescharacteristic
74C2×C4×D67C2×C411yescharacteristic
75C2×C4×D67C2×C411yescharacteristic
76C2×C4×D67C2311yescharacteristic
77C2×C4×D67C2311yescharacteristic
78C2×C4×D67C2311yescharacteristic
79#11761612—41no—
80#11761611—41no—
81#11761611—41no—
82C2×C67⋊C8—41no—
83C2×C67⋊C8C2311yescharacteristic
84C2×C67⋊C8C2311yescharacteristic
85C2×C67⋊C8C2311yescharacteristic
86C2×C67⋊C8C2311yescharacteristic
87C8×D67—41no—
88C8×D67—41no—
89C4⋊Dic67C2×C411yescharacteristic
90Dic67⋊C4C2×C411yescharacteristic
91Dic67⋊C4C2×C411yescharacteristic
92C22⋊Dic67C2×C411yescharacteristic
93C22⋊Dic67C2×C411yescharacteristic
94(C2×D67)⋊C4C2×C411yescharacteristic
95(C2×D67)⋊C4C2×C411yescharacteristic
96(C2×D67)⋊C4C2×C411yescharacteristic
97(C2×D67)⋊C4C2×C411yescharacteristic
98C4×Dic67C2×C411yescharacteristic
99C4×Dic67C2×C411yescharacteristic
100C4×Dic67C2311yescharacteristic
101C2×D4×C67C2×C411yescharacteristic
102C22×C4×C67C2311yescharacteristic
103C22×C4×C67C2311yescharacteristic
104M16×C67—41no—
105C2×C8×C67—41no—
106C2×C8×C67C2311yescharacteristic
107C2×C8×C67C2311yescharacteristic
108C2×C8×C67C2311yescharacteristic
109C2×C8×C67C2311yescharacteristic
110C4⋊C4×C67C2×C411yescharacteristic
111C22⋊C4×C67C2×C411yescharacteristic
112C22⋊C4×C67C2×C411yescharacteristic
113C42×C67C2311yescharacteristic
114C23×C67C22×C411yescharacteristic
115C23×C67C22×C411yescharacteristic
116C22×D67C22×C411yescharacteristic
117C22×D67C22×C411yescharacteristic
118C22×D67C22×C411yescharacteristic
119D4×C67—41no—
120C2×C4×C67—21no—
121C2×C4×C67—21no—
122C2×C4×C67—21no—
123C2×C4×C67—21no—
124C2×C4×C67C22×C411yescharacteristic
125C2×C4×C67C22×C411yescharacteristic
126C2×C4×C67C22×C411yescharacteristic
127C2×C4×C67C22×C411yescharacteristic
128C2×C4×C67C2411yescharacteristic
129C22⋊D67—41no—
130C22⋊D67—41no—
131C22⋊D67—41no—
132C22⋊D67—41no—
133C22⋊D67—41no—
134C22⋊D67—41no—
135C2×Dic67C22×C411yescharacteristic
136C2×Dic67C22×C411yescharacteristic
137C2×Dic67C22×C411yescharacteristic
138C2×Dic67C22×C411yescharacteristic
139C2×Dic67C22×C411yescharacteristic
140D268—41no—
141D268—41no—
142D268—41no—
143C4×D67—21no—
144C4×D67—21no—
145C4×D67—21no—
146C4×D67—21no—
147C4×D67—21no—
148C4×D67—21no—
149C4×D67—41no—
150C4×D67—41no—
151Dic134—41no—
152Dic134—41no—
153C8×C67—21no—
154C8×C67—21no—
155C8×C67—21no—
156C8×C67—21no—
157C67⋊C8—21no—
158C67⋊C8—21no—
159C67⋊C8—21no—
160C67⋊C8—21no—
161C22×C67—21no—
162C22×C67—21no—
163C22×C67—21no—
164C22×C67—21no—
165C22×C67—21no—
166C22×C67—21no—
167C22×C67C23×C411yescharacteristic
168C2×D67—21no—
169C2×D67—21no—
170C2×D67—21no—
171C2×D67—21no—
172C2×D67—21no—
173C2×D67—21no—
174C2×D67—21no—
175C2×D67—21no—
176C2×D67—21no—
177C4×C67—21no—
178C4×C67—21no—
179C4×C67—21no—
180C4×C67—21no—
181C4×C67H(5,𝔽2)11yescharacteristic
182C4×C67H(5,𝔽2)11yescharacteristic
183Dic67—21no—
184Dic67—21no—
185Dic67—21no—
186Dic67—21no—
187Dic67—21no—
188C2×C67—41no—
189C2×C67—41no—
190C2×C67#51811yescharacteristic
191C2×C67#56811yescharacteristic
192C2×C67#56811yescharacteristic
193D67—41no—
194D67—41no—
195D67—41no—
196#2980—671nomaximal, Sylow
197C67#298011yescharacteristic, complemented, Sylow
198#532—671no—
199#435—671no—
200#435—671no—
201#435—671no—
202#435—671no—
203#435—671no—
204#435—671no—
205#435—671no—
206#435D6711yescharacteristic, complemented
207#432—671no—
208#432—671no—
209#408—671no—
210#408—671no—
211#408—671no—
212#408—671no—
213C2×#41—671no—
214C2×#41—671no—
215C2×M16—671no—
216C2×M16—671no—
217C2×M16—671no—
218C2×M16C2×D6711yescharacteristic
219C22×C8—671no—
220C22×C8—671no—
221C22×C8—671no—
222C22×C8C2×D6711yescharacteristic
223C4⋊Q8—671no—
224#127—671no—
225#124—671no—
226#124—671no—
227#121—671no—
228#121—671no—
229#121—671no—
230#121—671no—
231C4×D4—671no—
232C4×D4—671no—
233C4×D4—671no—
234C4×D4C2×D6711yescharacteristic
235C2×C42—671no—
236C4⋊C8—671no—
237C4⋊C8—671no—
238C4⋊C8—671no—
239C4⋊C8C2×D6711yescharacteristic
240C22⋊C8—671no—
241C22⋊C8—671no—
242C22⋊C8—671no—
243C22⋊C8—671no—
244C22⋊C8—671no—
245C22⋊C8—671no—
246C22⋊C8—671no—
247C22⋊C8—671no—
248C22⋊C8—671no—
249C22⋊C8—671no—
250C22⋊C8C2×D6711yescharacteristic
251C22⋊C8C2×D6711yescharacteristic
252#97—671no—
253#97—671no—
254#97—671no—
255#97C2×D6711yescharacteristic
256#41—2681no—
257#41—2681no—
258#41—2681no—
259#41—2681no—
260C2×Q8—671no—
261C2×Q8—671no—
262C2×D4—671no—
263C2×D4—671no—
264C2×D4—671no—
265C2×D4—671no—
266C2×D4—671no—
267C2×D4—671no—
268C2×D4—671no—
269C2×D4—671no—
270C2×D4—671no—
271C2×D4C4×D6711yescharacteristic
272C22×C4—671no—
273C22×C4—671no—
274C22×C4—671no—
275C22×C4—671no—
276C22×C4—671no—
277C22×C4C22×D6711yescharacteristic
278C22×C4C22×D6711yescharacteristic
279M16—41no—
280M16—2681no—
281M16—2681no—
282M16—2681no—
283C2×C8—41no—
284C2×C8—2681no—
285C2×C8—2681no—
286C2×C8—2681no—
287C2×C8—671no—
288C2×C8—671no—
289C2×C8—671no—
290C2×C8—671no—
291C2×C8C22×D6711yescharacteristic
292C2×C8C22×D6711yescharacteristic
293C2×C8C22×D6711yescharacteristic
294C2×C8C22×D6711yescharacteristic
295C4⋊C4—671no—
296C4⋊C4—671no—
297C4⋊C4—671no—
298C4⋊C4C4×D6711yescharacteristic
299C22⋊C4—671no—
300C22⋊C4—671no—
301C22⋊C4—671no—
302C22⋊C4—671no—
303C22⋊C4—671no—
304C22⋊C4—671no—
305C22⋊C4C4×D6711yescharacteristic
306C22⋊C4C4×D6711yescharacteristic
307C42—671no—
308C42—671no—
309C42—671no—
310C42C22×D6711yescharacteristic
311C23—671no—
312C23—671no—
313C23—671no—
314C23C2×C4×D6711yescharacteristic
315C23C2×C4×D6711yescharacteristic
316Q8—2681no—
317Q8—2681no—
318D4—41no—
319D4—2681no—
320D4—2681no—
321D4—2681no—
322D4—2681no—
323D4—2681no—
324D4—2681no—
325D4—2681no—
326D4—2681no—
327D4—2681no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—2681no—
333C2×C4—2681no—
334C2×C4—671no—
335C2×C4—671no—
336C2×C4—671no—
337C2×C4—671no—
338C2×C4—671no—
339C2×C4—1341no—
340C2×C4—1341no—
341C2×C4—1341no—
342C2×C4—1341no—
343C2×C4—1341no—
344C2×C4—1341no—
345C2×C4C2×C4×D6711yescharacteristic
346C2×C4C2×C4×D6711yescharacteristic
347C2×C4C2×C4×D6711yescharacteristic
348C2×C4C2×C4×D6711yescharacteristic
349C2×C4C23×D6711yescharacteristic
350C8—21no—
351C8—21no—
352C8—21no—
353C8—21no—
354C8—1341no—
355C8—1341no—
356C8—1341no—
357C8—1341no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—1341no—
365C22—1341no—
366C22—1341no—
367C22—1341no—
368C22—1341no—
369C22—1341no—
370C22—1341no—
371C22—1341no—
372C22—1341no—
373C22C22×C4×D6711yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—1341no—
379C4—1341no—
380C4—1341no—
381C4—1341no—
382C4—1341no—
383C4#1452408811yescharacteristic
384C4#1452408911yescharacteristic
385C2—41no—
386C2—41no—
387C2—2681no—
388C2—2681no—
389C2—2681no—
390C2#1686386811yescharacteristic
391C2#1686416111yescharacteristic
392C2#1686416211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D67
commutator, socleC22×C67C23×C4
Fitting#435×C67C2
hypercenter#435D67
hypocenterC67#2980
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #16863470C2semidirect
3. #16863469C2semidirect
4. #16863468C2semidirect
5. #16863467C2semidirect
6. #16863466C2semidirect
7. #16863465C2semidirect
8. #16863464C2semidirect
9. #16863452C2semidirect
10. #16863451C2semidirect
11. #16863364C2semidirect
12. #16863362C2semidirect
13. #16863361C2semidirect
14. #16863361C2semidirect
15. #435×C67C2semidirect
197. C67#2980semidirect
206. #435D67semidirect