Finite Group Databasebeta

← #21458300

Subgroups — #21458300

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#16840467C211yesmaximal, characteristic, complemented
2#16840460C211yesmaximal, characteristic
3#16840170C211yesmaximal, characteristic, complemented
4#16840105C211yesmaximal, characteristic, complemented
5#16840097C211yesmaximal, characteristic, complemented
6#16840080C211yesmaximal, characteristic, complemented
7#16840077C211yesmaximal, characteristic, complemented
8#16840068C211yesmaximal, characteristic, complemented
9#16840041C211yesmaximal, characteristic, complemented
10#16840009C211yesmaximal, characteristic, complemented
11#16839991C211yesmaximal, characteristic, complemented
12#16839861C211yesmaximal, characteristic, complemented
13#16839833C211yesmaximal, characteristic, complemented
14#16839803C211yesmaximal, characteristic, complemented
15C2×#107×C61C211yesmaximal, characteristic, complemented
16C2×#11758190C2211yescharacteristic
17C2×#11758189C2211yescharacteristic
18#14519776C2211yescharacteristic
19#14519772—21no—
20#14519768C2211yescharacteristic
21#14519767—21no—
22#14519762—21no—
23#14519757C2211yescharacteristic
24#14519756—21no—
25#14519756C2211yescharacteristic
26#14519755—21no—
27#14519752C2211yescharacteristic
28#14519751—21no—
29#14519751C2211yescharacteristic
30#14519742C2211yescharacteristic
31#14519739C2211yescharacteristic
32C4×C22⋊D61—21no—
33C4×C22⋊D61—21no—
34C4×C22⋊D61C2211yescharacteristic
35#14519735C2211yescharacteristic
36C4⋊C4×D61C2211yescharacteristic
37#14519710C2211yescharacteristic
38#14519710C2211yescharacteristic
39#14519709C2211yescharacteristic
40#14519708C2211yescharacteristic
41#14519708C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519700C2211yescharacteristic
45#14519700C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519687C2211yescharacteristic
52C22×C8×C61C2211yescharacteristic
53C2×C4⋊C4×C61C2211yescharacteristic
54C2×C4⋊C4×C61C2211yescharacteristic
55#107×C61C2211yescharacteristic
56#107×C61C2211yescharacteristic
57#107×C61C2211yescharacteristic
58#107×C61C2211yescharacteristic
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61C2311yescharacteristic
62C2×C22⋊D61—21no—
63C2×C22⋊D61D411yescharacteristic
64C2×D244—21no—
65C2×D244C2311yescharacteristic
66C2×C4×D61—21no—
67C2×C4×D61—21no—
68C2×C4×D61C2311yescharacteristic
69C2×Dic122—21no—
70C2×Dic122C2311yescharacteristic
71C2×C8×C61—22no—
72C2×C8×C61C2311yescharacteristic
73C2×C8×C61C2311yescharacteristic
74C4⋊C4×C61—21no—
75C4⋊C4×C61—21no—
76C4⋊C4×C61C2311yescharacteristic
77C4⋊C4×C61C2311yescharacteristic
78C4⋊C4×C61C2311yescharacteristic
79C4⋊C4×C61C2311yescharacteristic
80C22⋊Dic61—21no—
81C22⋊Dic61D411yescharacteristic
82#11758198—21no—
83#11758198—21no—
84#11758198—21no—
85#11758198—21no—
86#11758198—21no—
87#11758198D411yescharacteristic
88C4⋊Dic61—21no—
89C4⋊Dic61—21no—
90C4⋊Dic61C2311yescharacteristic
91C4⋊Dic61C2311yescharacteristic
92#11758196—21no—
93#11758196—21no—
94#11758196—21no—
95#11758196—21no—
96#11758196—21no—
97#11758196D411yescharacteristic
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61C2311yescharacteristic
101C2×#92418C2311yescharacteristic
102C2×#92418C2311yescharacteristic
103#11758190—22no—
104#11758189—22no—
105C23×C61C2×D411yescharacteristic
106C22×D61—21no—
107C22×D61C2×D411yescharacteristic
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—81no—
115C2×C4×C61—81no—
116C2×C4×C61C2×D411yescharacteristic
117C2×C4×C61C2411yescharacteristic
118C22⋊D61—22no—
119C22⋊D61—42no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61C2×D411yescharacteristic
124C2×Dic61C2×D411yescharacteristic
125C2×Dic61C2×D411yescharacteristic
126D244—21no—
127D244—21no—
128D244—81no—
129C4×D61—21no—
130C4×D61—21no—
131C4×D61—81no—
132C4×D61—81no—
133Dic122—21no—
134Dic122—21no—
135Dic122—81no—
136C8×C61—21no—
137C8×C61#4112yes—
138#92418—21no—
139#92418—21no—
140C22×C61—21no—
141C22×C61—21no—
142C22×C61#13712yes—
143C22×C61C22×D411yescharacteristic
144C2×D61—21no—
145C2×D61—21no—
146C2×D61—21no—
147C2×D61—41no—
148C2×D61—41no—
149C2×D61—41no—
150C4×C61—21no—
151C4×C61—41no—
152C4×C61—41no—
153C4×C61—41no—
154C4×C61—41no—
155C4×C61C2×#4111yescharacteristic
156C4×C612−1+411yescharacteristic
157Dic61—21no—
158Dic61—21no—
159Dic61—21no—
160Dic61—41no—
161Dic61—41no—
162Dic61—41no—
163#3346—611nomaximal, Sylow
164C2×C61—22no—
165C2×C61#54711yescharacteristic
166C2×C61C2×#13711yescharacteristic
167C2×C61#57611yescharacteristic
168D61—41no—
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#435—611no—
183#428—611no—
184C2×#107D6111yescharacteristic, complemented
185C61#334611yescharacteristic, complemented, Sylow
186C2×SD16—611no—
187C2×M16—611no—
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—611no—
204C4×D4—1221no—
205C4×D4—1221no—
206#117—611no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4C2×D6111yescharacteristic
209C2×C4⋊C4C2×D6111yescharacteristic
210#107—611no—
211#107—611no—
212#107C2×D6111yescharacteristic
213#107C2×D6111yescharacteristic
214#107C2×D6111yescharacteristic
215#107C2×D6111yescharacteristic
216#106—611no—
217#106—611no—
218#106—611no—
219C4⋊C8—611no—
220#103—611no—
221#103—611no—
222#103—611no—
223#102—611no—
224#102—611no—
225#102—611no—
226C22⋊C8—611no—
227C22⋊C8—611no—
228#97—611no—
229C2×Q8—611no—
230C2×Q8—1221no—
231C2×D4—611no—
232C2×D4—611no—
233C2×D4—1221no—
234C2×D4—1221no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—611no—
238C22×C4—1221no—
239C22×C4—1221no—
240C22×C4C22×D6111yescharacteristic
241SD16—1222no—
242M16—1222no—
243C2×C8—22no—
244C2×C8—611no—
245C2×C8—611no—
246C2×C8C22×D6111yescharacteristic
247C2×C8C22×D6111yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—611no—
251C4⋊C4—611no—
252C4⋊C4—611no—
253C4⋊C4—1221no—
254C4⋊C4—1221no—
255C4⋊C4—1221no—
256C4⋊C4—1221no—
257C4⋊C4—1221no—
258C4⋊C4—1221no—
259C4⋊C4—1221no—
260C4⋊C4C22×D6111yescharacteristic
261C4⋊C4C22×D6111yescharacteristic
262C4⋊C4C22×D6111yescharacteristic
263C4⋊C4C22×D6111yescharacteristic
264C22⋊C4—611no—
265C22⋊C4—611no—
266C22⋊C4—1221no—
267C22⋊C4—1221no—
268C22⋊C4—1221no—
269C22⋊C4—1221no—
270C22⋊C4—1221no—
271C22⋊C4—1221no—
272C42—611no—
273C42—1221no—
274C42—1221no—
275C23—611no—
276C23—1221no—
277C23D4×D6111yescharacteristic
278Q8—1221no—
279Q8—1221no—
280Q8—4881no—
281D4—1222no—
282D4—1221no—
283D4—1221no—
284D4—4881no—
285D4—2442no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—611no—
295C2×C4—611no—
296C2×C4—611no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—4881no—
303C2×C4—4881no—
304C2×C4D4×D6111yescharacteristic
305C2×C4C23×D6111yescharacteristic
306C8—21no—
307C8—1221no—
308C8—1221no—
309C8#1175822212yes—
310C22—21no—
311C22—21no—
312C22—1221no—
313C22—1221no—
314C22—1221no—
315C22—2441no—
316C22—2441no—
317C22—2441no—
318C22#1451980912yes—
319C22C2×D4×D6111yescharacteristic
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—1221no—
326C4—1221no—
327C4—1221no—
328C4—2441no—
329C4—2441no—
330C4—2441no—
331C4C2×#1175822211yescharacteristic
332C4#1451982511yescharacteristic
333C2—22no—
334C2—4881no—
335C2—2441no—
336C2#1684041311yescharacteristic
337C2C2×#1451980911yescharacteristic
338C2#1684056311yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#107×C61C2
socleC22×C61C22×D4
hypercenterC2×#107D61
hypocenterC61#3346
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. #16840467C2semidirect
3. #16840170C2semidirect
4. #16840105C2semidirect
5. #16840097C2semidirect
6. #16840080C2semidirect
7. #16840077C2semidirect
8. #16840068C2semidirect
9. #16840041C2semidirect
10. #16840009C2semidirect
11. #16839991C2semidirect
12. #16839861C2semidirect
13. #16839833C2semidirect
14. #16839803C2semidirect
15. C2×#107×C61C2semidirect
184. C2×#107D61semidirect
185. C61#3346semidirect