Finite Group Databasebeta

← #21458161

Subgroups — #21458161

Order 7808.

420 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#16840413C211yesmaximal, characteristic, complemented
2#16840412C211yesmaximal, characteristic, complemented
3#16840166C211yesmaximal, characteristic, complemented
4#16840077C211yesmaximal, characteristic, complemented
5#16840076C211yesmaximal, characteristic, complemented
6#16840074C211yesmaximal, characteristic, complemented
7#16840041C211yesmaximal, characteristic, complemented
8#16840040C211yesmaximal, characteristic, complemented
9#16839997C211yesmaximal, characteristic, complemented
10#16839996C211yesmaximal, characteristic, complemented
11#16839842C211yesmaximal, characteristic, complemented
12#16839825C211yesmaximal, characteristic, complemented
13C2×#14519710C211yesmaximal, characteristic, complemented
14#107×D61C211yesmaximal, characteristic, complemented
15C61×#480C211yesmaximal, characteristic, complemented
16C2×#11758222—21no—
17C2×#11758224—21no—
18C2×#11758199C2211yescharacteristic
19C22×#92418C2211yescharacteristic
20C2×C8×D61C2211yescharacteristic
21#14519776C2211yescharacteristic
22#14519776C2211yescharacteristic
23#14519762—21no—
24#14519760—21no—
25#14519759—21no—
26#14519758—21no—
27#14519755—21no—
28#14519754—21no—
29#14519752C2211yescharacteristic
30#14519751C2211yescharacteristic
31#14519748C2211yescharacteristic
32D4×Dic61C2211yescharacteristic
33#14519739C2211yescharacteristic
34C4×C22⋊D61C2211yescharacteristic
35C2×C4⋊Dic61C2211yescharacteristic
36C4⋊C4×D61C2211yescharacteristic
37C4⋊C4×D61C2211yescharacteristic
38#14519711C2211yescharacteristic
39#14519711C2211yescharacteristic
40#14519710C2211yescharacteristic
41#14519710C2211yescharacteristic
42#14519710C2211yescharacteristic
43#14519710C2211yescharacteristic
44#14519710C2211yescharacteristic
45#14519706C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519689C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52#121×C61C2211yescharacteristic
53C2×C4⋊C4×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#107×C61C2211yescharacteristic
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C2×D4×C61—21no—
60C2×D4×C61C2311yescharacteristic
61C22×C4×C61—21no—
62C22×C4×C61C2311yescharacteristic
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61D411yescharacteristic
66C22×Dic61—21no—
67C22×Dic61—21no—
68#11758224—44no—
69#11758222—44no—
70C2×D244—21no—
71C2×D244C2311yescharacteristic
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61C2311yescharacteristic
76C2×Dic122—21no—
77C2×Dic122—21no—
78C2×C8×C61C2311yescharacteristic
79C2×C8×C61C2311yescharacteristic
80C4⋊C4×C61—21no—
81C4⋊C4×C61C2311yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C22⋊C4×C61—21no—
85C22⋊Dic61—21no—
86C22⋊Dic61—21no—
87C22⋊Dic61D411yescharacteristic
88#11758199—22no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198D411yescharacteristic
93C4⋊Dic61—21no—
94C4⋊Dic61C2311yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101#11758196D411yescharacteristic
102C4×Dic61C2311yescharacteristic
103C2×#92418—22no—
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106C8×D61—22no—
107C23×C61—21no—
108C23×C61C2×D411yescharacteristic
109C22×D61—21no—
110C22×D61C2×D411yescharacteristic
111D4×C61—21no—
112D4×C61—21no—
113D4×C61—42no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—42no—
120C2×C4×C61C2×D411yescharacteristic
121C2×C4×C61C2411yescharacteristic
122C22⋊D61—42no—
123C22⋊D61—42no—
124C22⋊D61D814yescomplemented
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—42no—
129C2×Dic61—42no—
130C2×Dic61C2×D411yescharacteristic
131C2×Dic61C2×D411yescharacteristic
132C2×Dic61C2×D411yescharacteristic
133D244—21no—
134D244—21no—
135D244—42no—
136C4×D61—21no—
137C4×D61—21no—
138C4×D61—42no—
139C4×D61—42no—
140C4×D61—42no—
141Dic122—42no—
142Dic122—42no—
143C8×C61—21no—
144C8×C61—21no—
145#92418—21no—
146#92418#4112yescomplemented
147C22×C61—21no—
148C22×C61—21no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61C2×D812yes—
153C22×C61C22×D411yescharacteristic
154C2×D61—21no—
155C2×D61—21no—
156C2×D61—41no—
157C2×D61—41no—
158C2×D61—41no—
159C2×D61C2×D812yes—
160C4×C61—21no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61C2×#4111yescharacteristic
165C4×C612−1+411yescharacteristic
166Dic61—21no—
167Dic61—21no—
168Dic61—41no—
169Dic61—41no—
170Dic61—41no—
171Dic61C2×D812yes—
172#3334—611nomaximal, Sylow
173C2×C61—22no—
174C2×C61—81no—
175C2×C61#54711yescharacteristic
176C2×C61C22×D811yescharacteristic
177C2×C61#57811yescharacteristic
178D61—22no—
179D61—81no—
180#547—611no—
181#547—611no—
182#500—611no—
183#480—611no—
184#480—611no—
185#480—611no—
186#480D6111yescharacteristic, complemented
187#474—611no—
188#474—611no—
189#466—611no—
190#466—611no—
191C4×D8—611no—
192C8×D4—611no—
193C2×#107—611no—
194C2×#107—611no—
195C61#333411yescharacteristic, complemented, Sylow
196C2×#41—1221no—
197C2×#41—1221no—
198C2×D8—611no—
199C22×C8—611no—
200C22×C8—611no—
201C4⋊Q8—611no—
202C4⋊Q8—611no—
203#123—1221no—
204#123—1221no—
205#123—1221no—
206#123—1221no—
207C22⋊Q8—1221no—
208C22⋊Q8—1221no—
209#121—611no—
210#121—611no—
211#121—611no—
212#121C2×D6111yescharacteristic
213C4×D4—611no—
214C4×D4—611no—
215C4×D4—611no—
216C2×C4⋊C4—611no—
217C2×C4⋊C4—611no—
218C2×C4⋊C4—611no—
219C2×C4⋊C4C2×D6111yescharacteristic
220#107—611no—
221#107—611no—
222#107—611no—
223#107—611no—
224#107—611no—
225#107—611no—
226#107—611no—
227#107C2×D6111yescharacteristic
228#107C2×D6111yescharacteristic
229C4⋊C8—611no—
230#102—611no—
231#102—611no—
232#102—611no—
233#102—611no—
234#102C2×D6111yescharacteristic
235#102C2×D6111yescharacteristic
236C22⋊C8—611no—
237C22⋊C8C2×D6111yescharacteristic
238C4×C8—611no—
239#41—2444no—
240#41—2444no—
241C2×Q8—1221no—
242C2×Q8—1221no—
243C2×D4—21no—
244C2×D4—611no—
245C2×D4—611no—
246C2×D4—1221no—
247C2×D4—1221no—
248C2×D4—1221no—
249C2×D4C22×D6111yescharacteristic
250C22×C4—21no—
251C22×C4—611no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4C22×D6111yescharacteristic
258D8—1222no—
259C2×C8—611no—
260C2×C8—611no—
261C2×C8—1222no—
262C2×C8—1222no—
263C2×C8C22×D6111yescharacteristic
264C2×C8C22×D6111yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—611no—
267C4⋊C4—611no—
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
277C4⋊C4C22×D6111yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—611no—
280C22⋊C4—611no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C42—611no—
287C23—21no—
288C23—611no—
289C23—1221no—
290C23D4×D6111yescharacteristic
291Q8—2442no—
292Q8—2442no—
293D4—21no—
294D4—21no—
295D4—42no—
296D4—614no—
297D4—1221no—
298D4—1221no—
299D4—2442no—
300D4—2442no—
301D4—2442no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—611no—
309C2×C4—611no—
310C2×C4—611no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—2442no—
317C2×C4—2442no—
318C2×C4—2442no—
319C2×C4—2442no—
320C2×C4—2442no—
321C2×C4D4×D6111yescharacteristic
322C2×C4C23×D6111yescharacteristic
323C8—21no—
324C8—21no—
325C8—612no—
326C8—1221no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—612no—
333C22—1221no—
334C22—1221no—
335C22—2441no—
336C22—2441no—
337C22—2441no—
338C22D8×D6112yes—
339C22C2×D4×D6111yescharacteristic
340C4—21no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—612no—
345C4—1221no—
346C4—1221no—
347C4—2441no—
348C4—2441no—
349C4—2441no—
350C4#41×D6111yescharacteristic
351C4#1451982411yescharacteristic
352C2—22no—
353C2—81no—
354C2—1222no—
355C2—4881no—
356C2#1684041011yescharacteristic
357C2C2×D8×D6111yescharacteristic
358C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#480C2
socleC22×C61C22×D4
hypercenter#480D61
hypocenterC61#3334
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #16840413C2semidirect
2. #16840412C2semidirect
3. #16840166C2semidirect
4. #16840077C2semidirect
5. #16840076C2semidirect
6. #16840074C2semidirect
7. #16840041C2semidirect
8. #16840040C2semidirect
9. #16839997C2semidirect
10. #16839996C2semidirect
11. #16839842C2semidirect
12. #16839825C2semidirect
13. C2×#14519710C2semidirect
14. #107×D61C2semidirect
15. C61×#480C2semidirect
124. C22⋊D61D8semidirect
146. #92418#41semidirect
186. #480D61semidirect
195. C61#3334semidirect