Finite Group Databasebeta

← #21455848

Subgroups — #21455848

Order 7808.

428 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840309C211yesmaximal, characteristic
2C4×Q8×D61C211yesmaximal, characteristic, complemented
3#16840082C211yesmaximal, characteristic, complemented
4#16840079C211yesmaximal, characteristic, complemented
5#16840046C211yesmaximal, characteristic, complemented
6#16840045C211yesmaximal, characteristic, complemented
7#16839961C211yesmaximal, characteristic, complemented
8#16839960C211yesmaximal, characteristic, complemented
9#16839902C211yesmaximal, characteristic, complemented
10#16839899C211yesmaximal, characteristic, complemented
11C4×#11758190C211yesmaximal, characteristic, complemented
12C4×#11758201C211yesmaximal, characteristic, complemented
13C4×#11758200C211yesmaximal, characteristic, complemented
14#16839813C211yesmaximal, characteristic, complemented
15C4×SD16×C61C211yesmaximal, characteristic, complemented
16C2×#11758222—21no—
17C2×Q8×D61C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19C2×#11758200C2211yescharacteristic
20C2×#11758201C2211yescharacteristic
21#14519776C2211yescharacteristic
22#14519773C2211yescharacteristic
23#14519763—21no—
24#14519752C2211yescharacteristic
25#14519750—21no—
26#14519748C2211yescharacteristic
27Q8×Dic61C2211yescharacteristic
28C4×Dic122—21no—
29C4×Dic122C2211yescharacteristic
30#14519742—21no—
31#14519742C2211yescharacteristic
32C4×D244C2211yescharacteristic
33C4×C22⋊D61—21no—
34C4⋊C4×D61—21no—
35C4⋊C4×D61C2211yescharacteristic
36C42×D61—21no—
37C42×D61C2211yescharacteristic
38#14519709C2211yescharacteristic
39#14519708C2211yescharacteristic
40#14519708C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519700C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51C4×#92418C2211yescharacteristic
52C2×SD16×C61C2211yescharacteristic
53C4×Q8×C61C2211yescharacteristic
54C4×D4×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C4×C8×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D4×C61C2311yescharacteristic
61C22×C4×C61—21no—
62C2×C22⋊D61—21no—
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65Q8×D61—22no—
66Q8×D61—22no—
67#11758222—44no—
68C2×D244—21no—
69C2×D244C2311yescharacteristic
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61D411yescharacteristic
74C2×C4×D61D411yescharacteristic
75C2×C4×D61C2311yescharacteristic
76C2×Dic122—21no—
77C2×Dic122—21no—
78C2×Dic122C2311yescharacteristic
79SD16×C61—22no—
80C2×C8×C61C2311yescharacteristic
81C2×C8×C61C2311yescharacteristic
82C4⋊C4×C61—21no—
83C4⋊C4×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C22⋊C4×C61—21no—
86C42×C61—21no—
87C42×C61C2311yescharacteristic
88C22⋊Dic61—21no—
89#11758201—22no—
90#11758200—22no—
91#11758198—21no—
92#11758198—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61C2311yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96#11758196—21no—
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61D411yescharacteristic
104C4×Dic61D411yescharacteristic
105C4×Dic61C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108#11758190—22no—
109C23×C61—21no—
110C22×D61—21no—
111C22×D61C2×D411yescharacteristic
112Q8×C61—21no—
113Q8×C61#4112yescomplemented
114D4×C61—21no—
115D4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—42no—
120C2×C4×C61C2×D411yescharacteristic
121C2×C4×C61C2×D411yescharacteristic
122C2×C4×C61C2411yescharacteristic
123C22⋊D61—42no—
124C22⋊D61—42no—
125C22⋊D61—42no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61C2×D411yescharacteristic
130C2×Dic61C2×D411yescharacteristic
131C2×Dic61C2×D411yescharacteristic
132D244—21no—
133D244—21no—
134D244—42no—
135C4×D61—24no—
136C4×D61—21no—
137C4×D61—21no—
138C4×D61—41no—
139C4×D61—42no—
140C4×D61—42no—
141C4×D61SD1614yescomplemented
142Dic122—24no—
143Dic122—21no—
144Dic122—42no—
145Dic122#4112yescomplemented
146C8×C61—21no—
147C8×C61—21no—
148#92418—21no—
149#92418—21no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61C22×D411yescharacteristic
154C2×D61—21no—
155C2×D61—21no—
156C2×D61—41no—
157C2×D61—41no—
158C2×D61—41no—
159C2×D61C2×SD1612yes—
160C4×C61—22no—
161C4×C61—21no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61C2×SD1612yes—
165C4×C61C2×#4111yescharacteristic
166C4×C61C2×#4111yescharacteristic
167Dic61—21no—
168Dic61—22no—
169Dic61—21no—
170Dic61—41no—
171Dic61—41no—
172Dic61C2×SD1612yes—
173#3103—611nomaximal, Sylow
174C2×C61—81no—
175C2×C61#52511yescharacteristic
176C2×C61C22×SD1611yescharacteristic
177C2×C61#57511yescharacteristic
178D61—22no—
179D61—81no—
180#532—611no—
181C2×C4×Q8—611no—
182#481—611no—
183#481—611no—
184#475—611no—
185#475—611no—
186#460—611no—
187#460—611no—
188#448—611no—
189#448—611no—
190C4×SD16—611no—
191C4×SD16—611no—
192C4×SD16—611no—
193C4×SD16D6111yescharacteristic, complemented
194#431—611no—
195C61#310311yescharacteristic, complemented, Sylow
196C2×#41—1221no—
197C22×Q8—611no—
198C2×SD16—611no—
199C2×SD16—611no—
200C2×SD16—611no—
201C2×SD16C2×D6111yescharacteristic
202C4⋊Q8—611no—
203#127—611no—
204#124—1221no—
205#121—611no—
206#121—611no—
207#121—1221no—
208C4×Q8—611no—
209C4×Q8—611no—
210C4×Q8—611no—
211C4×Q8—1221no—
212C4×Q8—1221no—
213C4×Q8C2×D6111yescharacteristic
214C4×D4—611no—
215C4×D4—1221no—
216C4×D4C2×D6111yescharacteristic
217C2×C4⋊C4—611no—
218C2×C4⋊C4—1221no—
219C2×C42—611no—
220C2×C42—1221no—
221#106—611no—
222#106—611no—
223#106—611no—
224#106C2×D6111yescharacteristic
225C4⋊C8—611no—
226C4⋊C8—611no—
227#103—611no—
228#103—611no—
229#103—611no—
230#103C2×D6111yescharacteristic
231#102—611no—
232#102—611no—
233#102—611no—
234#102C2×D6111yescharacteristic
235C22⋊C8—611no—
236C22⋊C8—611no—
237C4×C8—611no—
238C4×C8C2×D6111yescharacteristic
239#41—2444no—
240C2×Q8—611no—
241C2×Q8—1221no—
242C2×Q8—1221no—
243C2×Q8—1222no—
244C2×Q8—1222no—
245C2×Q8C22×D6111yescharacteristic
246C2×D4—611no—
247C2×D4—1221no—
248C2×D4—1221no—
249C2×D4—1221no—
250C2×D4—1221no—
251C2×D4C22×D6111yescharacteristic
252C22×C4—21no—
253C22×C4—611no—
254C22×C4—611no—
255C22×C4—611no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—1221no—
259SD16—22no—
260SD16—1222no—
261SD16—1222no—
262SD16—1222no—
263C2×C8—611no—
264C2×C8—611no—
265C2×C8C22×D6111yescharacteristic
266C2×C8C22×D6111yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—611no—
269C4⋊C4—611no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4C22×D6111yescharacteristic
276C4⋊C4C22×D6111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C42—21no—
282C42—611no—
283C42—611no—
284C42—611no—
285C42—1221no—
286C42—1221no—
287C42—1221no—
288C42C22×D6111yescharacteristic
289C23—21no—
290C23—611no—
291C23—1221no—
292Q8—21no—
293Q8—612no—
294Q8—1224no—
295Q8—1221no—
296Q8—2442no—
297Q8#1175822212yescomplemented
298D4—21no—
299D4—21no—
300D4—1221no—
301D4—1221no—
302D4—2442no—
303D4—2442no—
304D4—2442no—
305D4—2442no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—611no—
311C2×C4—614no—
312C2×C4—611no—
313C2×C4—611no—
314C2×C4—1224no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—2441no—
321C2×C4—2442no—
322C2×C4—2442no—
323C2×C4D4×D6111yescharacteristic
324C2×C4D4×D6111yescharacteristic
325C2×C4C23×D6111yescharacteristic
326C8—21no—
327C8—21no—
328C8—1221no—
329C8—1221no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—612no—
334C22—1221no—
335C22—1221no—
336C22—2441no—
337C22—2441no—
338C22—2441no—
339C22C2×D4×D6111yescharacteristic
340C4—22no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—612no—
345C4—1221no—
346C4—1222no—
347C4—1221no—
348C4—2441no—
349C4—2441no—
350C4SD16×D6112yes—
351C4#41×D6111yescharacteristic
352C4C2×#1175822211yescharacteristic
353C2—81no—
354C2—1222no—
355C2—4881no—
356C2#1684027111yescharacteristic
357C2C2×SD16×D6111yescharacteristic
358C2#1684055911yescharacteristic
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC4×SD16×C61C2
socleC22×C61C22×D4
hypercenterC4×SD16D61
hypocenterC61#3103
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D61C2semidirect
3. #16840082C2semidirect
4. #16840079C2semidirect
5. #16840046C2semidirect
6. #16840045C2semidirect
7. #16839961C2semidirect
8. #16839960C2semidirect
9. #16839902C2semidirect
10. #16839899C2semidirect
11. C4×#11758190C2semidirect
12. C4×#11758201C2semidirect
13. C4×#11758200C2semidirect
14. #16839813C2semidirect
15. C4×SD16×C61C2semidirect
113. Q8×C61#41semidirect
141. C4×D61SD16semidirect
145. Dic122#41semidirect
193. C4×SD16D61semidirect
195. C61#3103semidirect
297. Q8#11758222semidirect