Finite Group Databasebeta

← #21456532

Subgroups — #21456532

Order 7808.

402 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
1#16840314C211yesmaximal, characteristic, complemented
2#16840307C211yesmaximal, characteristic
3#16840166C211yesmaximal, characteristic, complemented
4#16840133C211yesmaximal, characteristic, complemented
5#16840111C211yesmaximal, characteristic, complemented
6#16840107C211yesmaximal, characteristic, complemented
7#16840010C211yesmaximal, characteristic, complemented
8#16840008C211yesmaximal, characteristic, complemented
9#16840006C211yesmaximal, characteristic, complemented
10#16839865C211yesmaximal, characteristic, complemented
11#16839863C211yesmaximal, characteristic, complemented
12#16839861C211yesmaximal, characteristic, complemented
13#16839859C211yesmaximal, characteristic, complemented
14M16×Dic61C211yesmaximal, characteristic, complemented
15C61×#468C211yesmaximal, characteristic, complemented
16C2×#11758224—21no—
17C2×#11758190C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×#11758201C2211yescharacteristic
20C2×#11758194C2211yescharacteristic
21#14519776C2211yescharacteristic
22#14519776C2211yescharacteristic
23#14519775C2211yescharacteristic
24#14519773C2211yescharacteristic
25#14519767—21no—
26#14519763—21no—
27#14519756C2211yescharacteristic
28#14519754—21no—
29#14519751C2211yescharacteristic
30#14519749—21no—
31Q8×Dic61C2211yescharacteristic
32#14519742—21no—
33#14519742C2211yescharacteristic
34D4×Dic61C2211yescharacteristic
35#14519739C2211yescharacteristic
36#14519737—21no—
37#14519733—21no—
38C2×C4×Dic61C2211yescharacteristic
39#14519711C2211yescharacteristic
40#14519710C2211yescharacteristic
41#14519710C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519700C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519687C2211yescharacteristic
49#14519687C2211yescharacteristic
50C8×Dic61C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×SD16×C61C2211yescharacteristic
53C2×M16×C61C2211yescharacteristic
54C22⋊Q8×C61C2211yescharacteristic
55#121×C61C2211yescharacteristic
56#107×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D4×C61—21no—
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C22×Dic61—21no—
67C22×Dic61D411yescharacteristic
68C22×Dic61D411yescharacteristic
69#11758224—44no—
70C2×D244C2311yescharacteristic
71C2×C4×D61—21no—
72C2×Dic122—21no—
73C2×Dic122—21no—
74C2×Dic122C2311yescharacteristic
75SD16×C61—22no—
76M16×C61—22no—
77C2×C8×C61C2311yescharacteristic
78C2×C8×C61C2311yescharacteristic
79C4⋊C4×C61—21no—
80C4⋊C4×C61C2311yescharacteristic
81C4⋊C4×C61C2311yescharacteristic
82C22⋊C4×C61—21no—
83C22⋊C4×C61—21no—
84C22⋊Dic61—21no—
85C22⋊Dic61—21no—
86#11758201—22no—
87#11758200—22no—
88#11758198—21no—
89#11758198—21no—
90C4⋊Dic61—21no—
91C4⋊Dic61C2311yescharacteristic
92C4⋊Dic61C2311yescharacteristic
93#11758196—21no—
94#11758196—21no—
95#11758196—21no—
96#11758196—21no—
97#11758196—21no—
98#11758196—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61D411yescharacteristic
102C4×Dic61D411yescharacteristic
103C4×Dic61C2311yescharacteristic
104C4×Dic61C2311yescharacteristic
105#11758194—22no—
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108#11758190—22no—
109C23×C61—21no—
110C23×C61C2×D411yescharacteristic
111C22×D61—21no—
112Q8×C61—21no—
113Q8×C61—21no—
114D4×C61—21no—
115D4×C61—21no—
116D4×C61—42no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61C2×D411yescharacteristic
123C2×C4×C61C2411yescharacteristic
124C22⋊D61—42no—
125C22⋊D61—42no—
126C22⋊D61—42no—
127C2×Dic61—22no—
128C2×Dic61—22no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—42no—
133C2×Dic61C2×D411yescharacteristic
134C2×Dic61C2×D411yescharacteristic
135C2×Dic61C2×D411yescharacteristic
136C2×Dic61C2×D411yescharacteristic
137D244—21no—
138D244—21no—
139C4×D61—42no—
140Dic122—21no—
141Dic122—21no—
142Dic122—42no—
143Dic122—42no—
144C8×C61—21no—
145C8×C61#4112yescomplemented
146#92418—21no—
147#92418#4112yescomplemented
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61C22×D411yescharacteristic
155C2×D61—41no—
156C2×D61—41no—
157C2×D61—41no—
158C4×C61—21no—
159C4×C61—41no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61C2×#4111yescharacteristic
163C4×C61C2×#4111yescharacteristic
164Dic61—21no—
165Dic61—21no—
166Dic61—41no—
167Dic61—41no—
168Dic61—41no—
169Dic61AGL(1,ℤ/8)12yes—
170Dic61#13712yes—
171#3182—611nomaximal, Sylow
172C2×C61—41no—
173C2×C61—81no—
174C2×C61#53211yescharacteristic
175C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
176C2×C61C2×#13711yescharacteristic
177D61—81no—
178#533—611no—
179#532—611no—
180#500—611no—
181#492—611no—
182#487—611no—
183#486—611no—
184#468—611no—
185#468—611no—
186#468—611no—
187#468D6111yescharacteristic, complemented
188#440—611no—
189#440—611no—
190#440—611no—
191#440—611no—
192C4×M16—611no—
193C61#318211yescharacteristic, complemented, Sylow
194C2×#41—1221no—
195C2×SD16—611no—
196C2×SD16—611no—
197C2×SD16—611no—
198C2×SD16C2×D6111yescharacteristic
199C2×M16—611no—
200C2×M16C2×D6111yescharacteristic
201C4⋊Q8—611no—
202C4⋊Q8—611no—
203C4⋊Q8—611no—
204#127—611no—
205#125—1221no—
206#124—1221no—
207C22⋊Q8—611no—
208C22⋊Q8—1221no—
209C22⋊Q8C2×D6111yescharacteristic
210#121—611no—
211#121—1221no—
212#121C2×D6111yescharacteristic
213C4×Q8—611no—
214C4×Q8—611no—
215C4×Q8—1221no—
216C4×D4—611no—
217C4×D4—611no—
218C4×D4—1221no—
219#117—1221no—
220C2×C42—611no—
221#107—611no—
222#107—611no—
223#107—611no—
224#107C2×D6111yescharacteristic
225#103—611no—
226#103—611no—
227#103—611no—
228#103C2×D6111yescharacteristic
229#102—611no—
230#102—611no—
231#102—611no—
232#102C2×D6111yescharacteristic
233#97—611no—
234#97—611no—
235C4×C8—611no—
236C4×C8—611no—
237#41—2444no—
238C2×Q8—611no—
239C2×Q8—1221no—
240C2×Q8—1221no—
241C2×Q8C22×D6111yescharacteristic
242C2×D4—21no—
243C2×D4—611no—
244C2×D4—1221no—
245C2×D4—1221no—
246C2×D4—1221no—
247C2×D4C22×D6111yescharacteristic
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4C22×D6111yescharacteristic
253SD16—22no—
254SD16—1222no—
255SD16—1222no—
256SD16—1222no—
257M16—22no—
258M16—1222no—
259C2×C8—611no—
260C2×C8—611no—
261C2×C8C22×D6111yescharacteristic
262C2×C8C22×D6111yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—611no—
265C4⋊C4—611no—
266C4⋊C4—1221no—
267C4⋊C4—1221no—
268C4⋊C4—1221no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4C22×D6111yescharacteristic
274C4⋊C4C22×D6111yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—1221no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C42—611no—
282C42—611no—
283C42—611no—
284C42—611no—
285C42—1221no—
286C42—1221no—
287C23—21no—
288C23—1221no—
289C23D4×D6111yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—1221no—
293Q8—1221no—
294Q8—2442no—
295Q8—2442no—
296D4—21no—
297D4—21no—
298D4—42no—
299D4—1221no—
300D4—1221no—
301D4—2442no—
302D4—2442no—
303D4—2442no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—611no—
310C2×C4—611no—
311C2×C4—611no—
312C2×C4—611no—
313C2×C4—1222no—
314C2×C4—1222no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—2442no—
319C2×C4—2442no—
320C2×C4D4×D6111yescharacteristic
321C2×C4C23×D6111yescharacteristic
322C8—21no—
323C8—612no—
324C8—1221no—
325C8#1175822412yescomplemented
326C22—21no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—2441no—
333C22—2441no—
334C22—2441no—
335C22C2×D4×D6111yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—612no—
341C4—612no—
342C4—1221no—
343C4—1221no—
344C4—2441no—
345C4—2441no—
346C4—2441no—
347C4#41×D6111yescharacteristic
348C4C2×#1175822411yescharacteristic
349C2—41no—
350C2—81no—
351C2—4881no—
352C2#1684030711yescharacteristic
353C2AGL(1,ℤ/8)×D6111yescharacteristic
354C2#137×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#468C2
socleC22×C61C22×D4
hypercenter#468D61
hypocenterC61#3182
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #16840314C2semidirect
3. #16840166C2semidirect
4. #16840133C2semidirect
5. #16840111C2semidirect
6. #16840107C2semidirect
7. #16840010C2semidirect
8. #16840008C2semidirect
9. #16840006C2semidirect
10. #16839865C2semidirect
11. #16839863C2semidirect
12. #16839861C2semidirect
13. #16839859C2semidirect
14. M16×Dic61C2semidirect
15. C61×#468C2semidirect
145. C8×C61#41semidirect
147. #92418#41semidirect
187. #468D61semidirect
193. C61#3182semidirect
325. C8#11758224semidirect