Finite Group Databasebeta

← #21455856

Subgroups — #21455856

Order 7808.

384 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840316C211yesmaximal, characteristic
2C4×Q8×D61C211yesmaximal, characteristic
3#16840099C211yesmaximal, characteristic
4#16840096C211yesmaximal, characteristic
5#16840056C211yesmaximal, characteristic, complemented
6#16840055C211yesmaximal, characteristic, complemented
7#16839971C211yesmaximal, characteristic, complemented
8#16839970C211yesmaximal, characteristic, complemented
9#16839919C211yesmaximal, characteristic
10#16839916C211yesmaximal, characteristic
11C4×Dic244C211yesmaximal, characteristic, complemented
12C4×#11758202C211yesmaximal, characteristic, complemented
13C4×#11758202C211yesmaximal, characteristic, complemented
14#16839813C211yesmaximal, characteristic
15C4×Q16×C61C211yesmaximal, characteristic, complemented
16C2×Q8×D61C2211yescharacteristic
17C2×Dic244C2211yescharacteristic
18C2×#11758202C2211yescharacteristic
19C2×#11758202C2211yescharacteristic
20#14519776C2211yescharacteristic
21#14519775C2211yescharacteristic
22#14519767—21no—
23#14519757C2211yescharacteristic
24#14519755—21no—
25#14519753C2211yescharacteristic
26Q8×Dic61C2211yescharacteristic
27C4×Dic122—21no—
28C4×Dic122—21no—
29C4×Dic122C2211yescharacteristic
30C4×Dic122C2211yescharacteristic
31#14519742—21no—
32#14519742C2211yescharacteristic
33#14519734—21no—
34C4⋊C4×D61—21no—
35C4⋊C4×D61C2211yescharacteristic
36C42×D61—21no—
37C42×D61C2211yescharacteristic
38#14519711C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519710C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519701C2211yescharacteristic
47#14519700C2211yescharacteristic
48#14519700C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51C4×#92418C2211yescharacteristic
52C2×Q16×C61C2211yescharacteristic
53C4×Q8×C61C2211yescharacteristic
54C4×Q8×C61C2211yescharacteristic
55#107×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58C4×C8×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×Q8×C61C2311yescharacteristic
61Q8×D61—22no—
62Q8×D61—22no—
63C2×C4×D61—21no—
64C2×C4×D61—21no—
65C2×C4×D61D411yescharacteristic
66C2×C4×D61D411yescharacteristic
67C2×C4×D61C2311yescharacteristic
68C2×Dic122—21no—
69C2×Dic122—21no—
70C2×Dic122C2311yescharacteristic
71C2×Dic122C2311yescharacteristic
72Q16×C61—22no—
73C2×C8×C61C2311yescharacteristic
74C2×C8×C61C2311yescharacteristic
75C4⋊C4×C61—21no—
76C4⋊C4×C61—21no—
77C4⋊C4×C61C2311yescharacteristic
78C4⋊C4×C61C2311yescharacteristic
79C42×C61—21no—
80C42×C61—21no—
81C42×C61C2311yescharacteristic
82#11758202—22no—
83#11758202—22no—
84#11758198—21no—
85#11758198—21no—
86C4⋊Dic61—21no—
87C4⋊Dic61—21no—
88C4⋊Dic61C2311yescharacteristic
89C4⋊Dic61C2311yescharacteristic
90#11758196—21no—
91#11758196—21no—
92#11758196—21no—
93#11758196—21no—
94#11758196—21no—
95#11758196—21no—
96#11758196—21no—
97#11758196—21no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61D411yescharacteristic
103C4×Dic61D411yescharacteristic
104C4×Dic61C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107Dic244—22no—
108C22×D61C2×D411yescharacteristic
109Q8×C61—21no—
110Q8×C61—21no—
111Q8×C61—21no—
112Q8×C61#4112yes—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61C2×D411yescharacteristic
118C2×C4×C61C2×D411yescharacteristic
119C2×C4×C61C2411yescharacteristic
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61C2×D411yescharacteristic
125C2×Dic61C2×D411yescharacteristic
126C2×Dic61C2×D411yescharacteristic
127C4×D61—24no—
128C4×D61—21no—
129C4×D61—21no—
130C4×D61—41no—
131C4×D61—42no—
132C4×D61Q1614yescomplemented
133Dic122—24no—
134Dic122—21no—
135Dic122—21no—
136Dic122—21no—
137Dic122—42no—
138Dic122#4112yes—
139C8×C61—21no—
140C8×C61—21no—
141#92418—21no—
142#92418—21no—
143C22×C61C22×D411yescharacteristic
144C2×D61—21no—
145C2×D61—21no—
146C2×D61C2×Q1612yes—
147C4×C61—22no—
148C4×C61—21no—
149C4×C61—41no—
150C4×C61—41no—
151C4×C61—41no—
152C4×C61C2×Q1612yes—
153C4×C61C2×#4111yescharacteristic
154C4×C61C2×#4111yescharacteristic
155Dic61—21no—
156Dic61—22no—
157Dic61—21no—
158Dic61—41no—
159Dic61—41no—
160Dic61—41no—
161Dic61C2×Q1612yes—
162#3104—611nomaximal, Sylow
163C2×C61#52511yescharacteristic
164C2×C61C22×Q1611yescharacteristic
165C2×C61#57511yescharacteristic
166D61—22no—
167#533—611no—
168C2×C4×Q8—611no—
169#484—611no—
170#484—611no—
171#477—611no—
172#477—611no—
173#462—611no—
174#462—611no—
175#451—611no—
176#451—611no—
177C4×Q16—611no—
178C4×Q16—611no—
179C4×Q16—611no—
180C4×Q16D6111yescharacteristic, complemented
181#431—611no—
182C61#310411yescharacteristic, complemented, Sylow
183C22×Q8—611no—
184C2×Q16—611no—
185C2×Q16—611no—
186C2×Q16—611no—
187C2×Q16C2×D6111yescharacteristic
188C4⋊Q8—611no—
189C4⋊Q8—611no—
190#125—1221no—
191C22⋊Q8—611no—
192C22⋊Q8—611no—
193C22⋊Q8—1221no—
194C4×Q8—611no—
195C4×Q8—611no—
196C4×Q8—611no—
197C4×Q8—611no—
198C4×Q8—1221no—
199C4×Q8—1221no—
200C4×Q8—1221no—
201C4×Q8C2×D6111yescharacteristic
202C4×Q8C2×D6111yescharacteristic
203#117—1221no—
204C2×C4⋊C4—611no—
205C2×C4⋊C4—1221no—
206C2×C42—611no—
207C2×C42—1221no—
208#107—611no—
209#107—611no—
210#107—611no—
211#107C2×D6111yescharacteristic
212C4⋊C8—611no—
213C4⋊C8—611no—
214#103—611no—
215#103—611no—
216#103—611no—
217#103—611no—
218#103—611no—
219#103—611no—
220#103C2×D6111yescharacteristic
221#103C2×D6111yescharacteristic
222C22⋊C8—611no—
223C22⋊C8—611no—
224C4×C8—611no—
225C4×C8C2×D6111yescharacteristic
226C2×Q8—611no—
227C2×Q8—611no—
228C2×Q8—1221no—
229C2×Q8—1221no—
230C2×Q8—1222no—
231C2×Q8—1222no—
232C2×Q8C22×D6111yescharacteristic
233C2×Q8C22×D6111yescharacteristic
234C22×C4—611no—
235C22×C4—611no—
236C22×C4—611no—
237C22×C4—1221no—
238C22×C4—1221no—
239Q16—22no—
240Q16—1222no—
241Q16—1222no—
242Q16—1222no—
243C2×C8—611no—
244C2×C8—611no—
245C2×C8C22×D6111yescharacteristic
246C2×C8C22×D6111yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—611no—
250C4⋊C4—611no—
251C4⋊C4—1221no—
252C4⋊C4—1221no—
253C4⋊C4—1221no—
254C4⋊C4—1221no—
255C4⋊C4—1221no—
256C4⋊C4—1221no—
257C4⋊C4—1221no—
258C4⋊C4—1221no—
259C4⋊C4—1221no—
260C4⋊C4—1221no—
261C4⋊C4C22×D6111yescharacteristic
262C4⋊C4C22×D6111yescharacteristic
263C22⋊C4—1221no—
264C22⋊C4—1221no—
265C42—21no—
266C42—21no—
267C42—611no—
268C42—611no—
269C42—611no—
270C42—1221no—
271C42—1221no—
272C42—1221no—
273C42—1221no—
274C42C22×D6111yescharacteristic
275C23—611no—
276Q8—21no—
277Q8—21no—
278Q8—21no—
279Q8—612no—
280Q8—1224no—
281Q8—1221no—
282Q8—1221no—
283Q8—1221no—
284Q8—2442no—
285Q8#1175822212yes—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—611no—
291C2×C4—614no—
292C2×C4—611no—
293C2×C4—611no—
294C2×C4—1224no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—1221no—
301C2×C4—2441no—
302C2×C4—2442no—
303C2×C4D4×D6111yescharacteristic
304C2×C4D4×D6111yescharacteristic
305C2×C4C23×D6111yescharacteristic
306C8—21no—
307C8—21no—
308C8—1221no—
309C8—1221no—
310C22—612no—
311C22—1221no—
312C22—1221no—
313C22C2×D4×D6111yescharacteristic
314C4—22no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—612no—
320C4—1221no—
321C4—1222no—
322C4—1221no—
323C4—2441no—
324C4—2441no—
325C4—2441no—
326C4Q16×D6112yes—
327C4#41×D6111yescharacteristic
328C4C2×#1175822211yescharacteristic
329C2—1222no—
330C2#1684027111yescharacteristic
331C2C2×Q16×D6111yescharacteristic
332C2#1684055911yescharacteristic
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC4×Q16×C61C2
socleC22×C61C22×D4
hypercenterC4×Q16D61
hypocenterC61#3104
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
5. #16840056C2semidirect
6. #16840055C2semidirect
7. #16839971C2semidirect
8. #16839970C2semidirect
11. C4×Dic244C2semidirect
12. C4×#11758202C2semidirect
13. C4×#11758202C2semidirect
15. C4×Q16×C61C2semidirect
132. C4×D61Q16semidirect
180. C4×Q16D61semidirect
182. C61#3104semidirect