Finite Group Databasebeta

← #21458306

Subgroups — #21458306

Order 7808.

356 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
1#16840469C211yesmaximal, characteristic, complemented
2#16840458C211yesmaximal, characteristic
3#16840171C211yesmaximal, characteristic, complemented
4#16840104C211yesmaximal, characteristic, complemented
5#16840098C211yesmaximal, characteristic, complemented
6#16840081C211yesmaximal, characteristic, complemented
7#16840076C211yesmaximal, characteristic, complemented
8#16840070C211yesmaximal, characteristic, complemented
9#16840043C211yesmaximal, characteristic, complemented
10#16840008C211yesmaximal, characteristic, complemented
11#16839991C211yesmaximal, characteristic, complemented
12#16839864C211yesmaximal, characteristic, complemented
13#16839804C211yesmaximal, characteristic, complemented
14C2×#14519711C211yesmaximal, characteristic, complemented
15C61×#435C211yesmaximal, characteristic, complemented
16C2×#11758190C2211yescharacteristic
17#14519777C2211yescharacteristic
18#14519772—21no—
19#14519769C2211yescharacteristic
20#14519768—21no—
21#14519759—21no—
22#14519756C2211yescharacteristic
23#14519756C2211yescharacteristic
24#14519754—21no—
25#14519754—21no—
26#14519751C2211yescharacteristic
27#14519751C2211yescharacteristic
28#14519749—21no—
29C4×Dic122C2211yescharacteristic
30C4×D244C2211yescharacteristic
31D4×Dic61—21no—
32#14519737—21no—
33#14519736C2211yescharacteristic
34C2×C4⋊Dic61C2211yescharacteristic
35C2×C4⋊Dic61C2211yescharacteristic
36C2×C4⋊Dic61C2211yescharacteristic
37#14519711C2211yescharacteristic
38#14519711C2211yescharacteristic
39#14519711C2211yescharacteristic
40#14519711C2211yescharacteristic
41#14519711C2211yescharacteristic
42#14519711C2211yescharacteristic
43#14519709C2211yescharacteristic
44#14519709C2211yescharacteristic
45#14519709C2211yescharacteristic
46#14519702C2211yescharacteristic
47#14519702C2211yescharacteristic
48#14519702C2211yescharacteristic
49#14519699C2211yescharacteristic
50#14519699C2211yescharacteristic
51#14519699C2211yescharacteristic
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
62C2×C22⋊D61—21no—
63C2×C22⋊D61—21no—
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61—21no—
67C2×D244C2311yescharacteristic
68C2×C4×D61—21no—
69C2×Dic122—21no—
70C2×Dic122C2311yescharacteristic
71M16×C61—22no—
72C2×C8×C61—22no—
73C2×C8×C61C2311yescharacteristic
74C2×C8×C61C2311yescharacteristic
75C2×C8×C61C2311yescharacteristic
76C2×C8×C61C2311yescharacteristic
77C4⋊C4×C61D411yescharacteristic
78C22⋊C4×C61D411yescharacteristic
79C22⋊C4×C61D411yescharacteristic
80C42×C61C2311yescharacteristic
81C22⋊Dic61—21no—
82C22⋊Dic61—21no—
83C22⋊Dic61—21no—
84#11758198—21no—
85#11758198—21no—
86#11758198—21no—
87C4⋊Dic61—21no—
88C4⋊Dic61—21no—
89C4⋊Dic61—21no—
90C4⋊Dic61—21no—
91C4⋊Dic61C2311yescharacteristic
92C4⋊Dic61C2311yescharacteristic
93C4⋊Dic61C2311yescharacteristic
94C4⋊Dic61C2311yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104#11758190—22no—
105C23×C61C2×D411yescharacteristic
106C23×C61C2×D411yescharacteristic
107C22×D61—21no—
108D4×C61—22no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61C2×D411yescharacteristic
114C2×C4×C61C2×D411yescharacteristic
115C2×C4×C61C2×D411yescharacteristic
116C2×C4×C61C2×D411yescharacteristic
117C2×C4×C61C2411yescharacteristic
118C22⋊D61—42no—
119C22⋊D61—81no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—81no—
128C2×Dic61—81no—
129C2×Dic61—81no—
130D244—21no—
131D244—21no—
132C4×D61—81no—
133Dic122—21no—
134Dic122—21no—
135Dic122—81no—
136C8×C61—21no—
137C8×C61—21no—
138C8×C61—21no—
139C8×C61#4112yes—
140C22×C61—21no—
141C22×C61—21no—
142C22×C61—21no—
143C22×C61—21no—
144C22×C61—21no—
145C22×C61#13712yes—
146C22×C61C22×D411yescharacteristic
147C2×D61—41no—
148C2×D61—41no—
149C2×D61—41no—
150C4×C61—21no—
151C4×C61—21no—
152C4×C61—21no—
153C4×C61—21no—
154C4×C61C2×#4111yescharacteristic
155C4×C612−1+411yescharacteristic
156Dic61—41no—
157Dic61—41no—
158Dic61—41no—
159Dic61—41no—
160Dic61—41no—
161Dic61—41no—
162Dic61—41no—
163#3346—611nomaximal, Sylow
164C2×C61—22no—
165C2×C61—41no—
166C2×C61#54711yescharacteristic
167C2×C61C2×#13711yescharacteristic
168C2×C61#57611yescharacteristic
169D61—81no—
170#554—611no—
171#553—611no—
172#501—611no—
173#485—611no—
174#484—611no—
175#481—611no—
176#480—611no—
177#479—611no—
178#474—611no—
179#468—611no—
180#465—611no—
181#440—611no—
182#435D6111yescharacteristic, complemented
183#428—611no—
184C2×#107—611no—
185C61#334611yescharacteristic, complemented, Sylow
186C2×SD16—611no—
187C2×M16C2×D6111yescharacteristic
188C22×C8C2×D6111yescharacteristic
189C4⋊Q8—611no—
190#126—1221no—
191#125—611no—
192#125—1221no—
193#123—1221no—
194C22⋊Q8—611no—
195C22⋊Q8—611no—
196C22⋊Q8—1221no—
197C22⋊Q8—1221no—
198#121—611no—
199#121—611no—
200#121—1221no—
201C4×Q8—611no—
202C4×D4—611no—
203C4×D4—1221no—
204C4×D4—1221no—
205C4×D4C2×D6111yescharacteristic
206#117—611no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4—611no—
209C2×C4⋊C4—611no—
210#107—611no—
211#107—611no—
212#107—611no—
213#107—611no—
214#107—611no—
215#107—611no—
216#106—611no—
217#106—611no—
218#106—611no—
219C4⋊C8C2×D6111yescharacteristic
220#103—611no—
221#103—611no—
222#103—611no—
223#102—611no—
224#102—611no—
225#102—611no—
226C22⋊C8C2×D6111yescharacteristic
227C22⋊C8C2×D6111yescharacteristic
228#97C2×D6111yescharacteristic
229C2×Q8—611no—
230C2×Q8—1221no—
231C2×D4—611no—
232C2×D4—1221no—
233C2×D4—1221no—
234C2×D4D24411yescharacteristic
235C22×C4—1221no—
236C22×C4—1221no—
237C22×C4—1221no—
238C22×C4—1221no—
239C22×C4C22×D6111yescharacteristic
240C22×C4C22×D6111yescharacteristic
241SD16—1222no—
242M16—22no—
243C2×C8—22no—
244C2×C8C22×D6111yescharacteristic
245C2×C8C22×D6111yescharacteristic
246C2×C8C22×D6111yescharacteristic
247C2×C8C22×D6111yescharacteristic
248C4⋊C4—611no—
249C4⋊C4—611no—
250C4⋊C4—611no—
251C4⋊C4—611no—
252C4⋊C4—611no—
253C4⋊C4—611no—
254C4⋊C4—1221no—
255C4⋊C4—1221no—
256C4⋊C4—1221no—
257C4⋊C4—1221no—
258C4⋊C4—1221no—
259C4⋊C4—1221no—
260C4⋊C4—1221no—
261C4⋊C4—1221no—
262C4⋊C4—1221no—
263C4⋊C4D24411yescharacteristic
264C22⋊C4—1221no—
265C22⋊C4—1221no—
266C22⋊C4—1221no—
267C22⋊C4—1221no—
268C22⋊C4—1221no—
269C22⋊C4—1221no—
270C22⋊C4D24411yescharacteristic
271C22⋊C4D24411yescharacteristic
272C42—1221no—
273C42—1221no—
274C42C22×D6111yescharacteristic
275C23—1221no—
276C23C2×D24411yescharacteristic
277C23C2×D24411yescharacteristic
278Q8—1221no—
279Q8—1221no—
280Q8—4881no—
281D4—22no—
282D4—1221no—
283D4—1221no—
284D4—4881no—
285D4—2442no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—4881no—
298C2×C4—4881no—
299C2×C4—4881no—
300C2×C4—4881no—
301C2×C4C2×D24411yescharacteristic
302C2×C4C2×D24411yescharacteristic
303C2×C4C2×D24411yescharacteristic
304C2×C4C2×D24411yescharacteristic
305C2×C4C23×D6111yescharacteristic
306C8—21no—
307C8—21no—
308C8—21no—
309C8#1175822412yes—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—2441no—
316C22—2441no—
317C22—2441no—
318C22#1451981012yes—
319C22C22×D24411yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—2441no—
325C4—2441no—
326C4—2441no—
327C4—2441no—
328C4—2441no—
329C4—2441no—
330C4—2441no—
331C4C2×#1175822411yescharacteristic
332C4#1451982411yescharacteristic
333C2—22no—
334C2—41no—
335C2—4881no—
336C2#1684041611yescharacteristic
337C2C2×#1451981011yescharacteristic
338C2#1684056711yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#435C2
socleC22×C61C22×D4
hypercenter#435D61
hypocenterC61#3346
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
1. #16840469C2semidirect
3. #16840171C2semidirect
4. #16840104C2semidirect
5. #16840098C2semidirect
6. #16840081C2semidirect
7. #16840076C2semidirect
8. #16840070C2semidirect
9. #16840043C2semidirect
10. #16840008C2semidirect
11. #16839991C2semidirect
12. #16839864C2semidirect
13. #16839804C2semidirect
14. C2×#14519711C2semidirect
15. C61×#435C2semidirect
182. #435D61semidirect
185. C61#3346semidirect