Finite Group Databasebeta

← #21448534

Subgroups — #21448534

Order 7808.

516 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519776C211yesmaximal, characteristic
2C2×C4×Dic122C211yesmaximal, characteristic
3C2×#14519742C211yesmaximal, characteristic
4#16839666C211yesmaximal, characteristic
5#16839666C211yesmaximal, characteristic
6#16839649C211yesmaximal, characteristic
7#16839648C211yesmaximal, characteristic
8#16839647C211yesmaximal, characteristic
9#16839646C211yesmaximal, characteristic
10#16839645C211yesmaximal, characteristic
11#16839644C211yesmaximal, characteristic
12#16839643C211yesmaximal, characteristic
13#16839626C211yesmaximal, characteristic
14#16839607C211yesmaximal, characteristic
15C61×#387C211yesmaximal, characteristic
16C22×Dic122C2211yescharacteristic
17C22×Dic122C2211yescharacteristic
18#14519776C418yescomplemented
19C4×Dic122—24no—
20#14519742—24no—
21C2×C4⋊Dic61C2211yescharacteristic
22C2×C4⋊Dic61C2211yescharacteristic
23C2×#11758196C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×#11758196C2211yescharacteristic
29C2×C4×Dic61C2211yescharacteristic
30C2×C4×Dic61C2211yescharacteristic
31C2×C4×Dic61C2211yescharacteristic
32C2×C4×Dic61C2211yescharacteristic
33C2×C4×Dic61C2211yescharacteristic
34C2×C4×Dic61C2211yescharacteristic
35#14519684C2211yescharacteristic
36#14519684C2211yescharacteristic
37#14519684C2211yescharacteristic
38#14519684C2211yescharacteristic
39#14519684C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46#14519684C2211yescharacteristic
47C2×C4⋊C4×C61C2211yescharacteristic
48C2×C4⋊C4×C61C2211yescharacteristic
49C2×C42×C61C2211yescharacteristic
50#95×C61C2211yescharacteristic
51#95×C61C2211yescharacteristic
52#95×C61C2211yescharacteristic
53#95×C61C2211yescharacteristic
54C22×C4×C61C2311yescharacteristic
55C22×C4×C61C2311yescharacteristic
56C22×C4×C61C2311yescharacteristic
57C22×C4×C61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C22×Dic61C2311yescharacteristic
62C22×Dic61C2311yescharacteristic
63C22×Dic61C2311yescharacteristic
64C22×Dic61C2311yescharacteristic
65C22×Dic61C2311yescharacteristic
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C22×Dic61C2311yescharacteristic
69C2×Dic122—22no—
70C2×Dic122—22no—
71C2×Dic122—22no—
72C2×Dic122—22no—
73C2×Dic122C2×C414yes—
74C2×Dic122C2×C414yes—
75C4⋊C4×C61—22no—
76C4⋊C4×C61C2×C414yes—
77C42×C61—22no—
78C4⋊Dic61—22no—
79C4⋊Dic61C2×C414yes—
80#11758196—22no—
81#11758196—22no—
82#11758196—22no—
83#11758196—22no—
84#11758196C2×C414yes—
85#11758196C2×C414yes—
86C4×Dic61—22no—
87C4×Dic61—22no—
88C4×Dic61—22no—
89C4×Dic61—22no—
90C4×Dic61C2×C414yes—
91C4×Dic61D414yes—
92C23×C61C2411yescharacteristic
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61C22×C412yes—
111C2×C4×C61C22×C412yes—
112C2×C4×C61C22×C412yes—
113C2×C4×C61C2×D412yes—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61C22×C412yes—
132C2×Dic61C22×C412yes—
133C2×Dic61C22×C412yes—
134C2×Dic61C22×C412yes—
135C2×Dic61C2×D412yes—
136C2×Dic61C2×D412yes—
137C2×Dic61#4112yes—
138Dic122—28no—
139Dic122—28no—
140C22×C61C23×C411yescharacteristic
141C22×C61C22×D411yescharacteristic
142C22×C61C2×#4111yescharacteristic
143C22×C612−1+411yescharacteristic
144C22×C612−1+411yescharacteristic
145C22×C612−1+411yescharacteristic
146C22×C612−1+411yescharacteristic
147C4×C61—22no—
148C4×C61—22no—
149C4×C61—22no—
150C4×C61—22no—
151C4×C61—41no—
152C4×C61—41no—
153C4×C61—41no—
154Dic61—22no—
155Dic61—22no—
156Dic61—22no—
157Dic61—22no—
158Dic61—41no—
159Dic61—41no—
160Dic61—41no—
161Dic61C4×D414yes—
162#2327—611nomaximal, Sylow
163C2×C61C2×C4×D411yescharacteristic
164C2×C61#51911yescharacteristic
165C2×C61#51911yescharacteristic
166C2×C61#53611yescharacteristic
167C2×C61#53611yescharacteristic
168C2×C61#54111yescharacteristic
169C2×C61#54111yescharacteristic
170C2×C4⋊Q8—611no—
171C2×C4×Q8—611no—
172C2×C4×Q8—611no—
173#391—611no—
174#391—611no—
175#387—611no—
176#387—611no—
177#387—611no—
178#387—611no—
179#387—611no—
180#387—611no—
181#387—611no—
182#387D6111yescharacteristic
183#382—611no—
184#376—611no—
185C61#232711yescharacteristic, complemented, Sylow
186C22×Q8—611no—
187C22×Q8—611no—
188C4⋊Q8—618no—
189C4×Q8—1224no—
190C4×Q8—1224no—
191C2×C4⋊C4—611no—
192C2×C4⋊C4—611no—
193C2×C4⋊C4—611no—
194C2×C4⋊C4—611no—
195C2×C4⋊C4—611no—
196C2×C4⋊C4—611no—
197C2×C4⋊C4—611no—
198C2×C4⋊C4—611no—
199C2×C4⋊C4C2×D6111yescharacteristic
200C2×C4⋊C4C2×D6111yescharacteristic
201C2×C42—611no—
202C2×C42—611no—
203C2×C42—611no—
204C2×C42—611no—
205C2×C42—611no—
206C2×C42—611no—
207C2×C42C2×D6111yescharacteristic
208#95—611no—
209#95—611no—
210#95—611no—
211#95—611no—
212#95—611no—
213#95—611no—
214#95—611no—
215#95—611no—
216#95—611no—
217#95—611no—
218#95—611no—
219#95—611no—
220#95C2×D6111yescharacteristic
221#95C2×D6111yescharacteristic
222#95C2×D6111yescharacteristic
223#95C2×D6111yescharacteristic
224C2×Q8—614no—
225C2×Q8—614no—
226C2×Q8—1222no—
227C2×Q8—1222no—
228C2×Q8—1222no—
229C2×Q8—1222no—
230C22×C4—611no—
231C22×C4—611no—
232C22×C4—611no—
233C22×C4—611no—
234C22×C4—611no—
235C22×C4—611no—
236C22×C4—611no—
237C22×C4—611no—
238C22×C4C22×D6111yescharacteristic
239C22×C4C22×D6111yescharacteristic
240C22×C4C22×D6111yescharacteristic
241C22×C4C22×D6111yescharacteristic
242C22×C4C22×D6111yescharacteristic
243C22×C4C22×D6111yescharacteristic
244C22×C4C22×D6111yescharacteristic
245C4⋊C4—22no—
246C4⋊C4—614no—
247C4⋊C4—614no—
248C4⋊C4—614no—
249C4⋊C4—1222no—
250C4⋊C4—1222no—
251C4⋊C4—1222no—
252C4⋊C4—1222no—
253C4⋊C4—1222no—
254C4⋊C4C4×D6114yes—
255C42—22no—
256C42—614no—
257C42—614no—
258C42—1222no—
259C42—1222no—
260C42—1222no—
261C42—1222no—
262C23C23×D6111yescharacteristic
263Q8—1228no—
264Q8—1228no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—612no—
283C2×C4—612no—
284C2×C4—612no—
285C2×C4—612no—
286C2×C4—612no—
287C2×C4—612no—
288C2×C4—612no—
289C2×C4—1221no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4C2×C4×D6112yes—
307C2×C4C2×C4×D6112yes—
308C2×C4C2×C4×D6112yes—
309C2×C4D4×D6112yes—
310C22C22×C4×D6111yescharacteristic
311C22C2×D4×D6111yescharacteristic
312C22#41×D6111yescharacteristic
313C22#1451982411yescharacteristic
314C22#1451982411yescharacteristic
315C22#1451982411yescharacteristic
316C22#1451982511yescharacteristic
317C4—22no—
318C4—22no—
319C4—22no—
320C4—22no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—614no—
325C4—1222no—
326C4—1222no—
327C4—1222no—
328C4—1222no—
329C4—2441no—
330C4—2441no—
331C4—2441no—
332C2C4×D4×D6111yescharacteristic
333C2#1684023811yescharacteristic
334C2#1684023911yescharacteristic
335C2#1684033411yescharacteristic
336C2#1684033511yescharacteristic
337C2#1684036911yescharacteristic
338C2#1684037111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC61×#387C2
socleC23×C61C24
hypercenter#387D61
hypocenterC61#2327
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
18. #14519776C4semidirect
185. C61#2327semidirect