Finite Group Databasebeta

← #21457984

Subgroups — #21457984

Order 7808.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×Dic122C211yesmaximal, characteristic, complemented
2#16840132C211yesmaximal, characteristic, complemented
3#16840103C211yesmaximal, characteristic, complemented
4#16840097C211yesmaximal, characteristic, complemented
5#16840066C211yesmaximal, characteristic, complemented
6#16840006C211yesmaximal, characteristic, complemented
7#16839989C211yesmaximal, characteristic, complemented
8#16839967C211yesmaximal, characteristic, complemented
9#16839900C211yesmaximal, characteristic, complemented
10#16839900C211yesmaximal, characteristic, complemented
11#16839862C211yesmaximal, characteristic, complemented
12#16839834C211yesmaximal, characteristic, complemented
13#16839770C211yesmaximal, characteristic, complemented
14C2×#14519700C211yesmaximal, characteristic, complemented
15C61×#553C211yesmaximal, characteristic
16C22×Dic122C2211yescharacteristic
17C22×Dic122C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×#11758200C2211yescharacteristic
20C2×#11758200C2211yescharacteristic
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#14519710C2211yescharacteristic
33#14519708C2211yescharacteristic
34C4⋊#92418C2211yescharacteristic
35#14519700C2211yescharacteristic
36#14519700C2211yescharacteristic
37#14519700C2211yescharacteristic
38#14519700C2211yescharacteristic
39#14519700C2211yescharacteristic
40#14519700C2211yescharacteristic
41#14519700C2211yescharacteristic
42#14519700C2211yescharacteristic
43#14519700C2211yescharacteristic
44#14519698C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46C22⋊#92418C2211yescharacteristic
47#14519688C2211yescharacteristic
48#126×C61—21no—
49#125×C61C2211yescharacteristic
50#123×C61—21no—
51#121×C61—21no—
52#121×C61C2211yescharacteristic
53#121×C61C2211yescharacteristic
54C4×D4×C61—21no—
55C4×D4×C61C2211yescharacteristic
56C4×D4×C61C2211yescharacteristic
57#117×C61C2211yescharacteristic
58C2×C4⋊C4×C61C2211yescharacteristic
59C2×D4×C61—21no—
60C2×D4×C61—21no—
61C2×D4×C61D411yescharacteristic
62C2×D4×C61C2311yescharacteristic
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C22×Dic61—21no—
68C22×Dic61—21no—
69C2×Dic122—22no—
70C2×Dic122—22no—
71C2×Dic122—21no—
72C2×Dic122—21no—
73C2×Dic122—41no—
74C2×Dic122—41no—
75C2×Dic122C2311yescharacteristic
76C2×Dic122C2311yescharacteristic
77C2×Dic122C2311yescharacteristic
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×C61—21no—
89C22⋊C4×C61D411yescharacteristic
90C22⋊C4×C61D411yescharacteristic
91C42×C61—21no—
92C42×C61C2311yescharacteristic
93C22⋊Dic61—21no—
94C22⋊Dic61—21no—
95#11758200—22no—
96#11758200—41no—
97#11758200—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×C61—21no—
112C23×C61C2×D411yescharacteristic
113C23×C61C2×D411yescharacteristic
114D4×C61—22no—
115D4×C61—21no—
116D4×C61—21no—
117D4×C61—42no—
118D4×C61—81no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—81no—
127C2×C4×C61—81no—
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2×D411yescharacteristic
131C2×C4×C61C2×D411yescharacteristic
132C2×C4×C61C2411yescharacteristic
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—42no—
138C2×Dic61—42no—
139Dic122—21no—
140Dic122—21no—
141Dic122—21no—
142Dic122—21no—
143Dic122—21no—
144Dic122—42no—
145Dic122—42no—
146Dic122#4112yes—
147#92418—21no—
148#92418—21no—
149#92418—21no—
150#92418—21no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61#13712yes—
160C22×C61C22×D411yescharacteristic
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61C2×#4111yescharacteristic
169C4×C61H(5,𝔽2)11yescharacteristic
170Dic61—22no—
171Dic61—41no—
172Dic61—41no—
173Dic61—41no—
174#3320—611nomaximal, Sylow
175C2×C61—22no—
176C2×C61—41no—
177C2×C61—81no—
178C2×C61#54611yescharacteristic
179C2×C61C2×#13711yescharacteristic
180C2×C61#57711yescharacteristic
181#553D6111yescharacteristic
182D4×Q8—611no—
183#491—611no—
184#485—611no—
185#484—611no—
186#479—611no—
187#468—611no—
188#465—611no—
189#461—611no—
190#448—611no—
191#448—611no—
192#440—611no—
193#435—611no—
194#419—611no—
195C2×#103—611no—
196C61#332011yescharacteristic, complemented, Sylow
197C22×Q8—611no—
198C22×Q8—611no—
199C2×SD16—611no—
200C2×SD16—611no—
201C2×SD16—611no—
202C2×M16—611no—
203C22×C8—611no—
204C4⋊Q8—611no—
205C4⋊Q8—1221no—
206#126—21no—
207#125C2×D6111yescharacteristic
208#123—21no—
209C22⋊Q8—611no—
210C22⋊Q8—611no—
211C22⋊Q8—1221no—
212C22⋊Q8—1221no—
213#121—21no—
214#121C2×D6111yescharacteristic
215#121C2×D6111yescharacteristic
216C4×Q8—611no—
217C4×D4—21no—
218C4×D4—1221no—
219C4×D4C2×D6111yescharacteristic
220C4×D4C2×D6111yescharacteristic
221#117C2×D6111yescharacteristic
222C2×C4⋊C4C2×D6111yescharacteristic
223#107—611no—
224#107—611no—
225#106—611no—
226C4⋊C8—611no—
227#103—611no—
228#103—611no—
229#103—611no—
230#103—611no—
231#103—611no—
232#103—611no—
233#103—611no—
234#103—611no—
235#103—611no—
236#102—611no—
237C22⋊C8—611no—
238C22⋊C8—611no—
239#97—611no—
240C2×Q8—611no—
241C2×Q8—611no—
242C2×Q8—611no—
243C2×Q8—1222no—
244C2×Q8—1222no—
245C2×Q8—1221no—
246C2×Q8—1221no—
247C2×Q8—2441no—
248C2×Q8—2441no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4C22⋊D6111yescharacteristic
252C2×D4C22×D6111yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4C22×D6111yescharacteristic
258C22×C4C22×D6111yescharacteristic
259SD16—1222no—
260SD16—2441no—
261SD16—2441no—
262M16—2441no—
263C2×C8—611no—
264C2×C8—611no—
265C2×C8—611no—
266C2×C8—611no—
267C2×C8—2441no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—611no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4C22⋊D6111yescharacteristic
278C4⋊C4C22×D6111yescharacteristic
279C4⋊C4C22×D6111yescharacteristic
280C4⋊C4C22×D6111yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C22⋊C4C22⋊D6111yescharacteristic
288C22⋊C4C22⋊D6111yescharacteristic
289C42—21no—
290C42—1221no—
291C42C22×D6111yescharacteristic
292C23—21no—
293C23C2×C22⋊D6111yescharacteristic
294C23C2×C22⋊D6111yescharacteristic
295Q8—612no—
296Q8—1221no—
297Q8—1221no—
298Q8—1221no—
299Q8—1221no—
300Q8—1221no—
301Q8—2442no—
302Q8—2442no—
303D4—22no—
304D4—21no—
305D4—21no—
306D4—42no—
307D4—81no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—2442no—
322C2×C4—2442no—
323C2×C4C2×C22⋊D6111yescharacteristic
324C2×C4C2×C22⋊D6111yescharacteristic
325C2×C4C2×C22⋊D6111yescharacteristic
326C2×C4C2×C22⋊D6111yescharacteristic
327C2×C4C23×D6111yescharacteristic
328C8—1221no—
329C8—1221no—
330C8—1221no—
331C8—1221no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22#1451980712yes—
341C22C22×C22⋊D6111yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—1222no—
350C4—2441no—
351C4—2441no—
352C4—2441no—
353C4#41×D6111yescharacteristic
354C4#1451982311yescharacteristic
355C2—22no—
356C2—41no—
357C2—81no—
358C2#1684040011yescharacteristic
359C2C2×#1451980711yescharacteristic
360C2#1684057311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#553C2
socleC22×C61C22×D4
hypercenter#553D61
hypocenterC61#3320
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. D4×Dic122C2semidirect
2. #16840132C2semidirect
3. #16840103C2semidirect
4. #16840097C2semidirect
5. #16840066C2semidirect
6. #16840006C2semidirect
7. #16839989C2semidirect
8. #16839967C2semidirect
9. #16839900C2semidirect
10. #16839900C2semidirect
11. #16839862C2semidirect
12. #16839834C2semidirect
13. #16839770C2semidirect
14. C2×#14519700C2semidirect
196. C61#3320semidirect