Finite Group Databasebeta

← #21457872

Subgroups — #21457872

Order 7808.

376 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840452C211yesmaximal, characteristic
2D4×Dic122C211yesmaximal, characteristic
3#16840131C211yesmaximal, characteristic, complemented
4#16840104C211yesmaximal, characteristic, complemented
5#16840093C211yesmaximal, characteristic, complemented
6#16840070C211yesmaximal, characteristic, complemented
7#16840020C211yesmaximal, characteristic, complemented
8#16840003C211yesmaximal, characteristic, complemented
9#16839973C211yesmaximal, characteristic, complemented
10#16839920C211yesmaximal, characteristic, complemented
11#16839920C211yesmaximal, characteristic, complemented
12#16839870C211yesmaximal, characteristic, complemented
13#16839772C211yesmaximal, characteristic, complemented
14C2×#14519702C211yesmaximal, characteristic, complemented
15C61×#435C211yesmaximal, characteristic
16C22×Dic122C2211yescharacteristic
17C22×Dic122C2211yescharacteristic
18C2×Dic244C2211yescharacteristic
19C2×Dic244C2211yescharacteristic
20C2×Dic244C2211yescharacteristic
21#14519777C2211yescharacteristic
22#14519776—21no—
23#14519770—21no—
24#14519769C2211yescharacteristic
25#14519767—21no—
26#14519758—21no—
27#14519756C2211yescharacteristic
28#14519756C2211yescharacteristic
29#14519756C2211yescharacteristic
30#14519756C2211yescharacteristic
31#14519754—21no—
32#14519754—21no—
33C4×Dic122C2211yescharacteristic
34C4×Dic122C2211yescharacteristic
35D4×Dic61—21no—
36#14519736C2211yescharacteristic
37#14519733—21no—
38C2×C4⋊Dic61C2211yescharacteristic
39#14519711C2211yescharacteristic
40#14519709C2211yescharacteristic
41#14519709C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519702C2211yescharacteristic
46#14519702C2211yescharacteristic
47#14519702C2211yescharacteristic
48#14519702C2211yescharacteristic
49#14519702C2211yescharacteristic
50#14519702C2211yescharacteristic
51#14519702C2211yescharacteristic
52C2×M16×C61C2211yescharacteristic
53C22×C8×C61C2211yescharacteristic
54C4×D4×C61C2211yescharacteristic
55C4⋊C8×C61C2211yescharacteristic
56C22⋊C8×C61C2211yescharacteristic
57C22⋊C8×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×D4×C61D411yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C22×Dic61—21no—
63C22×Dic61—21no—
64C22×Dic61—21no—
65C2×Dic122—22no—
66C2×Dic122—22no—
67C2×Dic122—21no—
68C2×Dic122—21no—
69C2×Dic122—41no—
70C2×Dic122—41no—
71C2×Dic122C2311yescharacteristic
72C2×Dic122C2311yescharacteristic
73C2×Dic122C2311yescharacteristic
74C2×Dic122C2311yescharacteristic
75M16×C61—41no—
76C2×C8×C61—41no—
77C2×C8×C61C2311yescharacteristic
78C2×C8×C61C2311yescharacteristic
79C2×C8×C61C2311yescharacteristic
80C2×C8×C61C2311yescharacteristic
81C4⋊C4×C61D411yescharacteristic
82C22⋊C4×C61D411yescharacteristic
83C22⋊C4×C61D411yescharacteristic
84C42×C61C2311yescharacteristic
85C22⋊Dic61—21no—
86C22⋊Dic61—21no—
87C22⋊Dic61—21no—
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90C4⋊Dic61—21no—
91C4⋊Dic61—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61C2311yescharacteristic
94C4⋊Dic61C2311yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104#11758196—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108Dic244—22no—
109Dic244—41no—
110Dic244—41no—
111C23×C61C2×D411yescharacteristic
112C23×C61C2×D411yescharacteristic
113D4×C61—22no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61C2×D411yescharacteristic
119C2×C4×C61C2×D411yescharacteristic
120C2×C4×C61C2×D411yescharacteristic
121C2×C4×C61C2×D411yescharacteristic
122C2×C4×C61C2411yescharacteristic
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×Dic61—42no—
132C2×Dic61—42no—
133C2×Dic61—42no—
134Dic122—21no—
135Dic122—21no—
136Dic122—21no—
137Dic122—21no—
138Dic122—21no—
139Dic122—21no—
140Dic122—21no—
141Dic122—42no—
142Dic122—42no—
143Dic122#4112yes—
144C8×C61—21no—
145C8×C61—21no—
146C8×C61—21no—
147C8×C61—21no—
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61#13712yes—
154C22×C61C22×D411yescharacteristic
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—21no—
158C4×C61—21no—
159C4×C61C2×#4111yescharacteristic
160C4×C61H(5,𝔽2)11yescharacteristic
161Dic61—22no—
162Dic61—41no—
163Dic61—41no—
164Dic61—41no—
165Dic61—41no—
166Dic61—41no—
167Dic61—41no—
168Dic61—41no—
169#3312—611nomaximal, Sylow
170C2×C61—22no—
171C2×C61—41no—
172C2×C61#54611yescharacteristic
173C2×C61C2×#13711yescharacteristic
174C2×C61#57811yescharacteristic
175#552—611no—
176D4×Q8—611no—
177#491—611no—
178#485—611no—
179#483—611no—
180#479—611no—
181#470—611no—
182#467—611no—
183#462—611no—
184#451—611no—
185#451—611no—
186#441—611no—
187#435D6111yescharacteristic
188#419—611no—
189C2×#103—611no—
190C61#331211yescharacteristic, complemented, Sylow
191C22×Q8—611no—
192C22×Q8—611no—
193C2×Q16—611no—
194C2×Q16—611no—
195C2×Q16—611no—
196C2×M16C2×D6111yescharacteristic
197C22×C8C2×D6111yescharacteristic
198C4⋊Q8—611no—
199C4⋊Q8—1221no—
200#126—1221no—
201#125—611no—
202#125—1221no—
203#123—1221no—
204C22⋊Q8—611no—
205C22⋊Q8—611no—
206C22⋊Q8—611no—
207C22⋊Q8—611no—
208C22⋊Q8—1221no—
209C22⋊Q8—1221no—
210C4×Q8—611no—
211C4×Q8—611no—
212C4×D4—1221no—
213C4×D4C2×D6111yescharacteristic
214#117—611no—
215#117—1221no—
216C2×C4⋊C4—611no—
217#107—611no—
218#106—611no—
219#106—611no—
220C4⋊C8C2×D6111yescharacteristic
221#103—611no—
222#103—611no—
223#103—611no—
224#103—611no—
225#103—611no—
226#103—611no—
227#103—611no—
228#103—611no—
229#103—611no—
230#103—611no—
231C22⋊C8C2×D6111yescharacteristic
232C22⋊C8C2×D6111yescharacteristic
233#97C2×D6111yescharacteristic
234C2×Q8—611no—
235C2×Q8—611no—
236C2×Q8—611no—
237C2×Q8—611no—
238C2×Q8—1222no—
239C2×Q8—1222no—
240C2×Q8—1221no—
241C2×Q8—1221no—
242C2×Q8—2441no—
243C2×Q8—2441no—
244C2×D4D24411yescharacteristic
245C22×C4—1221no—
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4C22×D6111yescharacteristic
249C22×C4C22×D6111yescharacteristic
250Q16—1222no—
251Q16—2441no—
252Q16—2441no—
253M16—41no—
254C2×C8—41no—
255C2×C8C22×D6111yescharacteristic
256C2×C8C22×D6111yescharacteristic
257C2×C8C22×D6111yescharacteristic
258C2×C8C22×D6111yescharacteristic
259C4⋊C4—611no—
260C4⋊C4—611no—
261C4⋊C4—611no—
262C4⋊C4—611no—
263C4⋊C4—1221no—
264C4⋊C4—1221no—
265C4⋊C4—1221no—
266C4⋊C4—1221no—
267C4⋊C4—1221no—
268C4⋊C4—1221no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4D24411yescharacteristic
275C22⋊C4—1221no—
276C22⋊C4—1221no—
277C22⋊C4—1221no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4D24411yescharacteristic
281C22⋊C4D24411yescharacteristic
282C42—1221no—
283C42—1221no—
284C42—1221no—
285C42C22×D6111yescharacteristic
286C23C2×D24411yescharacteristic
287C23C2×D24411yescharacteristic
288Q8—612no—
289Q8—1221no—
290Q8—1221no—
291Q8—1221no—
292Q8—1221no—
293Q8—1221no—
294Q8—1221no—
295Q8—1221no—
296Q8—2442no—
297Q8—2442no—
298D4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—2442no—
312C2×C4—2442no—
313C2×C4—2442no—
314C2×C4C2×D24411yescharacteristic
315C2×C4C2×D24411yescharacteristic
316C2×C4C2×D24411yescharacteristic
317C2×C4C2×D24411yescharacteristic
318C2×C4C23×D6111yescharacteristic
319C8—21no—
320C8—21no—
321C8—21no—
322C8—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22#1451981012yes—
329C22C22×D24411yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—1222no—
335C4—2441no—
336C4—2441no—
337C4—2441no—
338C4—2441no—
339C4—2441no—
340C4—2441no—
341C4—2441no—
342C4#41×D6111yescharacteristic
343C4#1451982211yescharacteristic
344C2—22no—
345C2—41no—
346C2#1684040711yescharacteristic
347C2C2×#1451981011yescharacteristic
348C2#1684057911yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#435C2
socleC22×C61C22×D4
hypercenter#435D61
hypocenterC61#3312
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
3. #16840131C2semidirect
4. #16840104C2semidirect
5. #16840093C2semidirect
6. #16840070C2semidirect
7. #16840020C2semidirect
8. #16840003C2semidirect
9. #16839973C2semidirect
10. #16839920C2semidirect
11. #16839920C2semidirect
12. #16839870C2semidirect
13. #16839772C2semidirect
14. C2×#14519702C2semidirect
190. C61#3312semidirect