Finite Group Databasebeta

← #21458732

Subgroups — #21458732

Order 7808.

340 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×Dic122C211yesmaximal, characteristic, complemented
2#16840468C211yesmaximal, characteristic
3#16840172C211yesmaximal, characteristic, complemented
4#16840169C211yesmaximal, characteristic, complemented
5#16840166C211yesmaximal, characteristic, complemented
6#16840071C211yesmaximal, characteristic, complemented
7#16840055C211yesmaximal, characteristic, complemented
8#16840051C211yesmaximal, characteristic
9#16840043C211yesmaximal, characteristic
10#16840041C211yesmaximal, characteristic
11#16839891C211yesmaximal, characteristic, complemented
12#16839865C211yesmaximal, characteristic
13#16839860C211yesmaximal, characteristic
14#16839847C211yesmaximal, characteristic
15C61×#479C211yesmaximal, characteristic, complemented
16C2×#11758201C2211yescharacteristic
17#14519777—21no—
18#14519777C2211yescharacteristic
19#14519776—21no—
20#14519776—21no—
21#14519776C2211yescharacteristic
22#14519776C2211yescharacteristic
23#14519776C2211yescharacteristic
24#14519768C2211yescharacteristic
25#14519757—21no—
26#14519755—21no—
27#14519755—21no—
28Q8×Dic61C2211yescharacteristic
29Q8×Dic61C2211yescharacteristic
30C4×Dic122—21no—
31C4×Dic122C2211yescharacteristic
32C4×D244C2211yescharacteristic
33#14519739C2211yescharacteristic
34#14519739C2211yescharacteristic
35C4⋊C4×D61—21no—
36#14519711C2211yescharacteristic
37#14519711C2211yescharacteristic
38#14519710C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519710C2211yescharacteristic
41#14519708C2211yescharacteristic
42#14519708C2211yescharacteristic
43#14519706C2211yescharacteristic
44#14519706C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519688C2211yescharacteristic
50#14519687C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52#125×C61C2211yescharacteristic
53C4×Q8×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56C4⋊C8×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#103×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D244C2311yescharacteristic
61C2×C4×D61—21no—
62C2×C4×D61—21no—
63C2×C4×D61—21no—
64C2×Dic122—21no—
65C2×Dic122—21no—
66C2×Dic122—21no—
67C2×Dic122—21no—
68C2×Dic122D411yescharacteristic
69C2×C8×C61C2311yescharacteristic
70C2×C8×C61C2311yescharacteristic
71C4⋊C4×C61—21no—
72C4⋊C4×C61—21no—
73C4⋊C4×C61—21no—
74C4⋊C4×C61C2311yescharacteristic
75C4⋊C4×C61C2311yescharacteristic
76C4⋊C4×C61C2311yescharacteristic
77C42×C61—21no—
78C42×C61C2311yescharacteristic
79#11758201Q814yescomplemented
80#11758198—21no—
81#11758198—21no—
82#11758198—21no—
83C4⋊Dic61—21no—
84C4⋊Dic61—21no—
85C4⋊Dic61—21no—
86C4⋊Dic61—21no—
87C4⋊Dic61D411yescharacteristic
88C4⋊Dic61C2311yescharacteristic
89C4⋊Dic61C2311yescharacteristic
90C4⋊Dic61C2311yescharacteristic
91#11758196—21no—
92#11758196—21no—
93#11758196—21no—
94#11758196—21no—
95#11758196D411yescharacteristic
96#11758196D411yescharacteristic
97C4×Dic61—21no—
98C4×Dic61—21no—
99C4×Dic61C2311yescharacteristic
100C4×Dic61C2311yescharacteristic
101C2×#92418C2311yescharacteristic
102C2×#92418C2311yescharacteristic
103C22×D61—21no—
104Q8×C61—21no—
105Q8×C61C2×Q812yes—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61C2×D411yescharacteristic
111C2×C4×C61C2×D411yescharacteristic
112C2×C4×C61C2411yescharacteristic
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61C2×D411yescharacteristic
117C2×Dic61C2×D411yescharacteristic
118C2×Dic61C2×D411yescharacteristic
119C2×Dic61C2×D411yescharacteristic
120D244—21no—
121D244C2×Q812yes—
122C4×D61—42no—
123C4×D61—81no—
124C4×D61—81no—
125Dic122—22no—
126Dic122—81no—
127Dic122—81no—
128Dic122—81no—
129Dic122—81no—
130C8×C61—21no—
131C8×C61—21no—
132#92418—21no—
133#92418C2×Q812yes—
134C22×C61C22×D411yescharacteristic
135C2×D61—22no—
136C2×D61—41no—
137C2×D61—41no—
138C4×C61—22no—
139C4×C61—21no—
140C4×C61—21no—
141C4×C61—41no—
142C4×C61—41no—
143C4×C61—41no—
144C4×C61C22×Q811yescharacteristic
145C4×C612−1+411yescharacteristic
146Dic61—21no—
147Dic61—21no—
148Dic61—21no—
149Dic61—41no—
150Dic61—41no—
151Dic61—41no—
152Dic61#13712yes—
153#3385—611nomaximal, Sylow
154C2×C61D4×Q811yescharacteristic
155C2×C61C2×#13711yescharacteristic
156C2×C61#57611yescharacteristic
157D61—42no—
158Q82—611no—
159#554—611no—
160#501—611no—
161#501—611no—
162#500—611no—
163#479—611no—
164#479D6111yescharacteristic, complemented
165#477—611no—
166#476—611no—
167#474—611no—
168#474—611no—
169#446—611no—
170#440—611no—
171#440—611no—
172C4×SD16—611no—
173C61#338511yescharacteristic, complemented, Sylow
174C2×SD16—611no—
175C4⋊Q8—611no—
176C4⋊Q8—611no—
177C4⋊Q8—611no—
178C4⋊Q8—611no—
179C4⋊Q8—1221no—
180C4⋊Q8—1221no—
181C4⋊Q8—1221no—
182#125—611no—
183#125C2×D6111yescharacteristic
184C22⋊Q8—1221no—
185C22⋊Q8—1221no—
186C22⋊Q8—1221no—
187C4×Q8—611no—
188C4×Q8—611no—
189C4×Q8—611no—
190C4×Q8—1221no—
191C4×Q8C2×D6111yescharacteristic
192C4×D4—611no—
193C4×D4—611no—
194C4×D4—611no—
195C2×C4⋊C4—1221no—
196#107—611no—
197#107—611no—
198#107—611no—
199#107—611no—
200#107—611no—
201#107C2×D6111yescharacteristic
202#106—611no—
203#106—611no—
204#106C2×D6111yescharacteristic
205C4⋊C8—611no—
206C4⋊C8—611no—
207C4⋊C8C2×D6111yescharacteristic
208#103—611no—
209#103C2×D6111yescharacteristic
210#103C2×D6111yescharacteristic
211#102—611no—
212#102—611no—
213#102—611no—
214#97—611no—
215#97—611no—
216C4×C8—611no—
217C2×Q8—611no—
218C2×Q8—1221no—
219C2×Q8—1221no—
220C2×Q8—1221no—
221C2×Q8—1221no—
222C2×Q8C22×D6111yescharacteristic
223C2×D4—611no—
224C22×C4—1221no—
225C22×C4—1221no—
226C22×C4—1221no—
227SD16—614no—
228C2×C8—611no—
229C2×C8—611no—
230C2×C8C22×D6111yescharacteristic
231C2×C8C22×D6111yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—611no—
236C4⋊C4—611no—
237C4⋊C4—611no—
238C4⋊C4—611no—
239C4⋊C4—611no—
240C4⋊C4—611no—
241C4⋊C4—1221no—
242C4⋊C4—1221no—
243C4⋊C4—1221no—
244C4⋊C4—1221no—
245C4⋊C4—1221no—
246C4⋊C4—1221no—
247C4⋊C4—1221no—
248C4⋊C4—1221no—
249C4⋊C4C22×D6111yescharacteristic
250C4⋊C4C22×D6111yescharacteristic
251C4⋊C4C22×D6111yescharacteristic
252C22⋊C4—1221no—
253C22⋊C4—1221no—
254C22⋊C4—1221no—
255C42—21no—
256C42—611no—
257C42—611no—
258C42—1221no—
259C42—1221no—
260C42C22×D6111yescharacteristic
261C23—1221no—
262Q8—21no—
263Q8—1222no—
264Q8—4881no—
265Q8—4881no—
266Q8—4881no—
267Q8—4881no—
268Q8Q8×D6112yes—
269D4—612no—
270D4—1221no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—611no—
276C2×C4—611no—
277C2×C4—611no—
278C2×C4—611no—
279C2×C4—1221no—
280C2×C4—1221no—
281C2×C4—1221no—
282C2×C4—4881no—
283C2×C4—4881no—
284C2×C4—2442no—
285C2×C4D4×D6111yescharacteristic
286C2×C4D4×D6111yescharacteristic
287C2×C4C23×D6111yescharacteristic
288C8—21no—
289C8—21no—
290C8—612no—
291C8—1221no—
292C22—1222no—
293C22—2441no—
294C22—2441no—
295C22C2×D4×D6111yescharacteristic
296C4—21no—
297C4—21no—
298C4—22no—
299C4—41no—
300C4—41no—
301C4—41no—
302C4—612no—
303C4—1221no—
304C4—1221no—
305C4—1221no—
306C4—2441no—
307C4—2441no—
308C4—2441no—
309C4C2×Q8×D6111yescharacteristic
310C4#1451982411yescharacteristic
311C2—2442no—
312C2#1684042511yescharacteristic
313C2#137×D6111yescharacteristic
314C2#1684056411yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#479C2
socleC22×C61C22×D4
hypercenter#479D61
hypocenterC61#3385
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. Q8×Dic122C2semidirect
3. #16840172C2semidirect
4. #16840169C2semidirect
5. #16840166C2semidirect
6. #16840071C2semidirect
7. #16840055C2semidirect
11. #16839891C2semidirect
15. C61×#479C2semidirect
79. #11758201Q8semidirect
164. #479D61semidirect
173. C61#3385semidirect