Finite Group Databasebeta

← #21456052

Subgroups — #21456052

Order 7808.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840384C211yesmaximal, characteristic
2#16840238C211yesmaximal, characteristic, complemented
3#16840102C211yesmaximal, characteristic, complemented
4#16840088C211yesmaximal, characteristic
5#16840055C211yesmaximal, characteristic, complemented
6#16840046C211yesmaximal, characteristic, complemented
7#16839987C211yesmaximal, characteristic, complemented
8#16839986C211yesmaximal, characteristic, complemented
9#16839916C211yesmaximal, characteristic, complemented
10#16839902C211yesmaximal, characteristic
11#16839864C211yesmaximal, characteristic, complemented
12C4×#11758202C211yesmaximal, characteristic, complemented
13C4×#11758201C211yesmaximal, characteristic, complemented
14#16839824C211yesmaximal, characteristic, complemented
15C61×#441C211yesmaximal, characteristic, complemented
16C2×Q8×D61C2211yescharacteristic
17C2×#11758202C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19C2×#11758201C2211yescharacteristic
20#14519776C2211yescharacteristic
21#14519771—21no—
22#14519766C2211yescharacteristic
23#14519765—21no—
24#14519762—21no—
25#14519755—21no—
26#14519753C2211yescharacteristic
27#14519752C2211yescharacteristic
28Q8×Dic61C2211yescharacteristic
29C4×Dic122—21no—
30C4×Dic122C2211yescharacteristic
31#14519742—21no—
32#14519742C2211yescharacteristic
33C4×D244C2211yescharacteristic
34#14519735—21no—
35#14519735C2211yescharacteristic
36#14519734—21no—
37#14519734C2211yescharacteristic
38#14519711C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519708C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51C4×#92418C2211yescharacteristic
52C2×Q16×C61C2211yescharacteristic
53C4×Q8×C61C2211yescharacteristic
54C4×Q8×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×Q8×C61C2311yescharacteristic
61Q8×D61—22no—
62Q8×D61—22no—
63C2×D244—21no—
64C2×D244C2311yescharacteristic
65C2×C4×D61—21no—
66C2×C4×D61—21no—
67C2×C4×D61C2311yescharacteristic
68C2×Dic122—21no—
69C2×Dic122—21no—
70C2×Dic122C2311yescharacteristic
71Q16×C61—22no—
72C2×C8×C61C2311yescharacteristic
73C2×C8×C61C2311yescharacteristic
74C4⋊C4×C61—21no—
75C4⋊C4×C61—21no—
76C4⋊C4×C61C2311yescharacteristic
77C4⋊C4×C61C2311yescharacteristic
78C42×C61—21no—
79C42×C61—21no—
80C42×C61C2311yescharacteristic
81#11758202—22no—
82#11758201—22no—
83#11758198—21no—
84#11758198—21no—
85#11758198—21no—
86#11758198—21no—
87#11758198—21no—
88#11758198—21no—
89#11758198D411yescharacteristic
90#11758198D411yescharacteristic
91C4⋊Dic61—21no—
92C4⋊Dic61C2311yescharacteristic
93C4⋊Dic61C2311yescharacteristic
94#11758196—21no—
95#11758196—21no—
96#11758196—21no—
97#11758196—21no—
98#11758196D411yescharacteristic
99#11758196D411yescharacteristic
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107#11758190—22no—
108C22×D61—21no—
109C22×D61C2×D411yescharacteristic
110Q8×C61—21no—
111Q8×C61—21no—
112Q8×C61—21no—
113Q8×C61#4112yes—
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×C61C2411yescharacteristic
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61C2×D411yescharacteristic
125C2×Dic61C2×D411yescharacteristic
126C2×Dic61C2×D411yescharacteristic
127D244—21no—
128D244—21no—
129D244—81no—
130C4×D61—24no—
131C4×D61—21no—
132C4×D61—21no—
133C4×D61—81no—
134Dic122—24no—
135Dic122—21no—
136Dic122—81no—
137Dic122#4112yes—
138C8×C61—21no—
139C8×C61—21no—
140#92418—21no—
141#92418—21no—
142C22×C61C22×D411yescharacteristic
143C2×D61—21no—
144C2×D61—21no—
145C2×D61—21no—
146C2×D61—41no—
147C2×D61—41no—
148C2×D61—41no—
149C4×C61—22no—
150C4×C61—21no—
151C4×C61—21no—
152C4×C61—41no—
153C4×C61—41no—
154C4×C61—41no—
155C4×C61C2×#4111yescharacteristic
156C4×C61C2×#4111yescharacteristic
157Dic61—21no—
158Dic61—22no—
159Dic61—21no—
160Dic61—21no—
161Dic61—41no—
162Dic61—41no—
163#3121—611nomaximal, Sylow
164C2×C61#52511yescharacteristic
165C2×C61#57711yescharacteristic
166C2×C61#57811yescharacteristic
167D61—41no—
168D61—81no—
169#542—611no—
170#519—611no—
171#485—611no—
172#482—611no—
173#477—611no—
174#475—611no—
175#464—611no—
176#464—611no—
177#451—611no—
178#448—611no—
179#441D6111yescharacteristic, complemented
180#440—611no—
181C4×Q16—611no—
182C4×SD16—611no—
183#433—611no—
184C61#312111yescharacteristic, complemented, Sylow
185C22×Q8—611no—
186C2×Q16—611no—
187C2×Q16C2×D6111yescharacteristic
188C2×SD16—611no—
189C2×SD16—611no—
190C4⋊Q8—611no—
191#126—1221no—
192#124—611no—
193#124—1221no—
194#123—1221no—
195C22⋊Q8—611no—
196C22⋊Q8—1221no—
197#121—611no—
198C4×Q8—611no—
199C4×Q8—611no—
200C4×Q8—611no—
201C4×Q8—1221no—
202C4×Q8—1221no—
203C4×Q8C2×D6111yescharacteristic
204C4×Q8C2×D6111yescharacteristic
205C4×D4—611no—
206#117—611no—
207#117—611no—
208#117—1221no—
209#117—1221no—
210#107—611no—
211#107—611no—
212#106—611no—
213#106C2×D6111yescharacteristic
214C4⋊C8—611no—
215C4⋊C8—611no—
216#103—611no—
217#103—611no—
218#103—611no—
219#103—611no—
220#103C2×D6111yescharacteristic
221#103C2×D6111yescharacteristic
222#102—611no—
223#102—611no—
224C22⋊C8—611no—
225C22⋊C8—611no—
226#97C2×D6111yescharacteristic
227C4×C8—611no—
228C2×Q8—611no—
229C2×Q8—1221no—
230C2×Q8—1221no—
231C2×Q8—1222no—
232C2×Q8—1222no—
233C2×Q8C22×D6111yescharacteristic
234C2×Q8C22×D6111yescharacteristic
235C2×D4—611no—
236C2×D4—1221no—
237C22×C4—611no—
238C22×C4—1221no—
239C22×C4—1221no—
240Q16—22no—
241Q16—1222no—
242SD16—1222no—
243SD16—1222no—
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—611no—
254C4⋊C4—1221no—
255C4⋊C4—1221no—
256C4⋊C4—1221no—
257C4⋊C4—1221no—
258C4⋊C4—1221no—
259C4⋊C4C22×D6111yescharacteristic
260C4⋊C4C22×D6111yescharacteristic
261C22⋊C4—611no—
262C22⋊C4—611no—
263C22⋊C4—1221no—
264C22⋊C4—1221no—
265C22⋊C4—1221no—
266C22⋊C4—1221no—
267C22⋊C4—1221no—
268C22⋊C4—1221no—
269C42—21no—
270C42—21no—
271C42—611no—
272C42—1221no—
273C42—1221no—
274C42—1221no—
275C42—1221no—
276C42C22×D6111yescharacteristic
277C23—611no—
278C23—1221no—
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—612no—
283Q8—1224no—
284Q8—1221no—
285Q8—4881no—
286Q8#1175822212yes—
287D4—1221no—
288D4—1221no—
289D4—4881no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—611no—
295C2×C4—611no—
296C2×C4—611no—
297C2×C4—1224no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—4881no—
304C2×C4D4×D6111yescharacteristic
305C2×C4D4×D6111yescharacteristic
306C2×C4C23×D6111yescharacteristic
307C8—21no—
308C8—21no—
309C8—1221no—
310C8—1221no—
311C22—1221no—
312C22—1221no—
313C22—1221no—
314C22—2441no—
315C22—2441no—
316C22—2441no—
317C22C2×D4×D6111yescharacteristic
318C4—22no—
319C4—21no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—1221no—
325C4—1222no—
326C4—1221no—
327C4—1221no—
328C4—2441no—
329C4—2441no—
330C4#41×D6111yescharacteristic
331C4C2×#1175822211yescharacteristic
332C2—4881no—
333C2—2441no—
334C2#1684027111yescharacteristic
335C2#1684057111yescharacteristic
336C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#441C2
socleC22×C61C22×D4
hypercenter#441D61
hypocenterC61#3121
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
2. #16840238C2semidirect
3. #16840102C2semidirect
5. #16840055C2semidirect
6. #16840046C2semidirect
7. #16839987C2semidirect
8. #16839986C2semidirect
9. #16839916C2semidirect
11. #16839864C2semidirect
12. C4×#11758202C2semidirect
13. C4×#11758201C2semidirect
14. #16839824C2semidirect
15. C61×#441C2semidirect
179. #441D61semidirect
184. C61#3121semidirect