Finite Group Databasebeta

← #21457864

Subgroups — #21457864

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
1D4×Dic122C211yesmaximal, characteristic
2#16840132C211yesmaximal, characteristic, complemented
3#16840103C211yesmaximal, characteristic, complemented
4#16840092C211yesmaximal, characteristic, complemented
5#16840066C211yesmaximal, characteristic, complemented
6#16840018C211yesmaximal, characteristic, complemented
7#16840001C211yesmaximal, characteristic, complemented
8#16839972C211yesmaximal, characteristic, complemented
9#16839917C211yesmaximal, characteristic, complemented
10#16839917C211yesmaximal, characteristic, complemented
11#16839867C211yesmaximal, characteristic, complemented
12#16839834C211yesmaximal, characteristic
13#16839770C211yesmaximal, characteristic, complemented
14C2×#14519700C211yesmaximal, characteristic, complemented
15C61×#552C211yesmaximal, characteristic
16C22×Dic122C2211yescharacteristic
17C22×Dic122C2211yescharacteristic
18C2×#11758202C2211yescharacteristic
19C2×#11758202C2211yescharacteristic
20C2×#11758202C2211yescharacteristic
21C2×#11758194C2211yescharacteristic
22C22×#92418C2211yescharacteristic
23#14519777C2211yescharacteristic
24#14519776—21no—
25#14519756C2211yescharacteristic
26#14519756C2211yescharacteristic
27#14519754—21no—
28#14519754—21no—
29C4×Dic122C2211yescharacteristic
30D4×Dic61—21no—
31#14519710C2211yescharacteristic
32#14519708C2211yescharacteristic
33#14519708C2211yescharacteristic
34C4⋊#92418C2211yescharacteristic
35#14519701C2211yescharacteristic
36#14519700C2211yescharacteristic
37#14519700C2211yescharacteristic
38#14519700C2211yescharacteristic
39#14519700C2211yescharacteristic
40#14519700C2211yescharacteristic
41#14519700C2211yescharacteristic
42#14519700C2211yescharacteristic
43#14519700C2211yescharacteristic
44#14519700C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46C22⋊#92418C2211yescharacteristic
47#14519688C2211yescharacteristic
48#126×C61—21no—
49#125×C61—21no—
50#125×C61C2211yescharacteristic
51#123×C61—21no—
52C22⋊Q8×C61C2211yescharacteristic
53C22⋊Q8×C61C2211yescharacteristic
54C4×Q8×C61C2211yescharacteristic
55C4×D4×C61C2211yescharacteristic
56#117×C61—21no—
57#117×C61C2211yescharacteristic
58C2×C4⋊C4×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D4×C61D411yescharacteristic
61C22×C4×C61—21no—
62C22×C4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C22×Dic61—21no—
65C22×Dic61—21no—
66C2×Dic122—22no—
67C2×Dic122—22no—
68C2×Dic122—21no—
69C2×Dic122—21no—
70C2×Dic122—41no—
71C2×Dic122—41no—
72C2×Dic122C2311yescharacteristic
73C2×Dic122C2311yescharacteristic
74C2×Dic122C2311yescharacteristic
75C4⋊C4×C61—21no—
76C4⋊C4×C61—21no—
77C4⋊C4×C61—21no—
78C4⋊C4×C61—21no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61D411yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C22⋊C4×C61—21no—
86C22⋊C4×C61—21no—
87C22⋊C4×C61—21no—
88C22⋊C4×C61D411yescharacteristic
89C22⋊C4×C61D411yescharacteristic
90C42×C61—21no—
91C42×C61—21no—
92C42×C61C2311yescharacteristic
93C22⋊Dic61—21no—
94C22⋊Dic61—21no—
95#11758202—22no—
96#11758202—41no—
97#11758202—41no—
98C4⋊Dic61—21no—
99C4⋊Dic61—21no—
100C4⋊Dic61C2311yescharacteristic
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104C4×Dic61—21no—
105#11758194—41no—
106C2×#92418—41no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C23×C61C2×D411yescharacteristic
112C23×C61C2×D411yescharacteristic
113Q8×C61—21no—
114Q8×C61—21no—
115D4×C61—22no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—42no—
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2×D411yescharacteristic
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2411yescharacteristic
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—42no—
135C2×Dic61—42no—
136Dic122—21no—
137Dic122—21no—
138Dic122—21no—
139Dic122—21no—
140Dic122—21no—
141Dic122—42no—
142Dic122—42no—
143Dic122#4112yes—
144#92418—21no—
145#92418—21no—
146#92418—21no—
147#92418—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×C61—41no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61C2×#4111yescharacteristic
164C4×C61H(5,𝔽2)11yescharacteristic
165Dic61—22no—
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#552D6111yescharacteristic
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#435—611no—
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×M16—611no—
197C22×C8—611no—
198C4⋊Q8—611no—
199C4⋊Q8—1221no—
200#126—21no—
201#125—21no—
202#125C2×D6111yescharacteristic
203#123—21no—
204C22⋊Q8—611no—
205C22⋊Q8—611no—
206C22⋊Q8—1221no—
207C22⋊Q8—1221no—
208C22⋊Q8C2×D6111yescharacteristic
209C22⋊Q8C2×D6111yescharacteristic
210C4×Q8—611no—
211C4×Q8C2×D6111yescharacteristic
212C4×D4—1221no—
213C4×D4C2×D6111yescharacteristic
214#117—21no—
215#117C2×D6111yescharacteristic
216C2×C4⋊C4C2×D6111yescharacteristic
217#107—611no—
218#106—611no—
219#106—611no—
220C4⋊C8—611no—
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⋊C8—611no—
232C22⋊C8—611no—
233#97—611no—
234C2×Q8—611no—
235C2×Q8—611no—
236C2×Q8—611no—
237C2×Q8—1222no—
238C2×Q8—1222no—
239C2×Q8—1221no—
240C2×Q8—1221no—
241C2×Q8—2441no—
242C2×Q8—2441no—
243C2×Q8C22×D6111yescharacteristic
244C2×D4C22⋊D6111yescharacteristic
245C22×C4—21no—
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4C22×D6111yescharacteristic
249C22×C4C22×D6111yescharacteristic
250Q16—1222no—
251Q16—2441no—
252Q16—2441no—
253M16—2441no—
254C2×C8—611no—
255C2×C8—611no—
256C2×C8—611no—
257C2×C8—611no—
258C2×C8—2441no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—611no—
266C4⋊C4—1221no—
267C4⋊C4—1221no—
268C4⋊C4—1221no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4C22⋊D6111yescharacteristic
272C4⋊C4C22×D6111yescharacteristic
273C4⋊C4C22×D6111yescharacteristic
274C4⋊C4C22×D6111yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4C22⋊D6111yescharacteristic
281C22⋊C4C22⋊D6111yescharacteristic
282C42—21no—
283C42—21no—
284C42—1221no—
285C42C22×D6111yescharacteristic
286C23C2×C22⋊D6111yescharacteristic
287C23C2×C22⋊D6111yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—612no—
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—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—2442no—
313C2×C4—2442no—
314C2×C4C2×C22⋊D6111yescharacteristic
315C2×C4C2×C22⋊D6111yescharacteristic
316C2×C4C2×C22⋊D6111yescharacteristic
317C2×C4C2×C22⋊D6111yescharacteristic
318C2×C4C23×D6111yescharacteristic
319C8—1221no—
320C8—1221no—
321C8—1221no—
322C8—1221no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22#1451980712yes—
329C22C22×C22⋊D6111yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—1222no—
339C4—2441no—
340C4—2441no—
341C4—2441no—
342C4#41×D6111yescharacteristic
343C4#1451982311yescharacteristic
344C2—22no—
345C2—41no—
346C2#1684040011yescharacteristic
347C2C2×#1451980711yescharacteristic
348C2#1684057711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#552C2
socleC22×C61C22×D4
hypercenter#552D61
hypocenterC61#3312
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #16840132C2semidirect
3. #16840103C2semidirect
4. #16840092C2semidirect
5. #16840066C2semidirect
6. #16840018C2semidirect
7. #16840001C2semidirect
8. #16839972C2semidirect
9. #16839917C2semidirect
10. #16839917C2semidirect
11. #16839867C2semidirect
13. #16839770C2semidirect
14. C2×#14519700C2semidirect
190. C61#3312semidirect