Finite Group Databasebeta

← #21457916

Subgroups — #21457916

Order 7808.

382 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840447C211yesmaximal, characteristic, complemented
2#16840411C211yesmaximal, characteristic
3#16840129C211yesmaximal, characteristic, complemented
4#16840101C211yesmaximal, characteristic, complemented
5#16840097C211yesmaximal, characteristic, complemented
6#16840064C211yesmaximal, characteristic, complemented
7#16840020C211yesmaximal, characteristic, complemented
8#16840002C211yesmaximal, characteristic, complemented
9#16839971C211yesmaximal, characteristic, complemented
10#16839925C211yesmaximal, characteristic, complemented
11#16839924C211yesmaximal, characteristic, complemented
12#16839859C211yesmaximal, characteristic, complemented
13#16839831C211yesmaximal, characteristic, complemented
14#16839755C211yesmaximal, characteristic, complemented
15C61×#417C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17C2×Dic244C2211yescharacteristic
18C2×#11758202C2211yescharacteristic
19C2×#11758200C2211yescharacteristic
20C2×C8×D61C2211yescharacteristic
21#14519775C2211yescharacteristic
22#14519772—21no—
23#14519768C2211yescharacteristic
24#14519767—21no—
25#14519760—21no—
26#14519760—21no—
27#14519758—21no—
28#14519757C2211yescharacteristic
29#14519756C2211yescharacteristic
30#14519756C2211yescharacteristic
31#14519753C2211yescharacteristic
32#14519749—21no—
33#14519742C2211yescharacteristic
34D4×Dic61C2211yescharacteristic
35C4×C22⋊D61C2211yescharacteristic
36#14519736—21no—
37#14519735C2211yescharacteristic
38C2×#11758196—21no—
39#14519710C2211yescharacteristic
40#14519710C2211yescharacteristic
41#14519709C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519700C2211yescharacteristic
48#14519698C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519687C2211yescharacteristic
52C2×#41×C61C2211yescharacteristic
53C2×M16×C61C2211yescharacteristic
54C2×C4⋊C4×C61C2211yescharacteristic
55#103×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59#41×C61—22no—
60#41×C61—41no—
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61—21no—
63C2×D4×C61C2311yescharacteristic
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61D411yescharacteristic
69C22×Dic61—21no—
70C22×Dic61—21no—
71#11758224—22no—
72#11758224—41no—
73C2×C4×D61C2311yescharacteristic
74C2×Dic122C2311yescharacteristic
75C2×Dic122C2311yescharacteristic
76M16×C61—41no—
77C2×C8×C61C2311yescharacteristic
78C2×C8×C61C2311yescharacteristic
79C4⋊C4×C61—21no—
80C4⋊C4×C61C2311yescharacteristic
81C4⋊C4×C61C2311yescharacteristic
82C22⋊Dic61—21no—
83C22⋊Dic61—21no—
84C22⋊Dic61—21no—
85C22⋊Dic61D411yescharacteristic
86#11758202—41no—
87#11758200—22no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198D411yescharacteristic
92C4⋊Dic61—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61C2311yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96#11758196—21no—
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196D411yescharacteristic
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109Dic244—41no—
110C8×D61—41no—
111C23×C61—21no—
112C23×C61C2×D411yescharacteristic
113C22×D61C2×D411yescharacteristic
114Q8×C61—21no—
115Q8×C61—21no—
116D4×C61—21no—
117D4×C61—42no—
118D4×C61#4112yes—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—42no—
125C2×C4×C61—42no—
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2411yescharacteristic
128C22⋊D61—41no—
129C22⋊D61—42no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—42no—
135C2×Dic61—42no—
136C2×Dic61C2×D411yescharacteristic
137C2×Dic61C2×D411yescharacteristic
138C2×Dic61C2×D411yescharacteristic
139C4×D61—21no—
140C4×D61—21no—
141Dic122—21no—
142Dic122—21no—
143Dic122—21no—
144Dic122—21no—
145C8×C61—21no—
146C8×C61—21no—
147#92418—21no—
148#92418—21no—
149C22×C61—22no—
150C22×C61—21no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61C22×D411yescharacteristic
156C2×D61—21no—
157C2×D61—21no—
158C2×D61—21no—
159C4×C61—21no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61C2×#4111yescharacteristic
164C4×C61H(5,𝔽2)11yescharacteristic
165Dic61—21no—
166Dic61—21no—
167Dic61—21no—
168Dic61—41no—
169Dic61—41no—
170Dic61—41no—
171Dic61—41no—
172#3315—611nomaximal, Sylow
173C2×C61—41no—
174C2×C61—42no—
175C2×C61#54611yescharacteristic
176C2×C61#57511yescharacteristic
177C2×C61#57811yescharacteristic
178D61—41no—
179#552—611no—
180#547—611no—
181#491—611no—
182#485—611no—
183#484—611no—
184#478—611no—
185#470—611no—
186#467—611no—
187#462—611no—
188#452—611no—
189#452—611no—
190#440—611no—
191#435—611no—
192#417D6111yescharacteristic, complemented
193#416—611no—
194C61#331511yescharacteristic, complemented, Sylow
195C2×#41—611no—
196C2×#41C2×D6111yescharacteristic
197C2×Q16—611no—
198C2×Q16—611no—
199C2×SD16—611no—
200C2×M16C2×D6111yescharacteristic
201C22×C8—611no—
202C4⋊Q8—611no—
203#126—1221no—
204#125—611no—
205#125—1221no—
206#123—1221no—
207#123—1221no—
208#123—1221no—
209C22⋊Q8—611no—
210C22⋊Q8—611no—
211C22⋊Q8—611no—
212C22⋊Q8—611no—
213#121—1221no—
214C4×Q8—611no—
215C4×D4—611no—
216C4×D4—611no—
217#117—611no—
218#117—1221no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4C2×D6111yescharacteristic
221#107—611no—
222#107—611no—
223#106—611no—
224C4⋊C8—611no—
225#103—611no—
226#103—611no—
227#103—611no—
228#103—611no—
229#103—611no—
230#103C2×D6111yescharacteristic
231#103C2×D6111yescharacteristic
232#102—611no—
233#102C2×D6111yescharacteristic
234#102C2×D6111yescharacteristic
235C22⋊C8—611no—
236C22⋊C8—611no—
237#97—611no—
238#41—22no—
239#41—41no—
240#41—1222no—
241#41—2441no—
242C2×Q8—611no—
243C2×Q8—611no—
244C2×Q8C22×D6111yescharacteristic
245C2×D4—21no—
246C2×D4—611no—
247C2×D4—1221no—
248C2×D4C22×D6111yescharacteristic
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—611no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4C22×D6111yescharacteristic
255Q16—2441no—
256Q16—2441no—
257SD16—1222no—
258M16—41no—
259C2×C8—611no—
260C2×C8—611no—
261C2×C8—2441no—
262C2×C8C22×D6111yescharacteristic
263C2×C8C22×D6111yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—611no—
266C4⋊C4—611no—
267C4⋊C4—611no—
268C4⋊C4—1221no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4C22×D6111yescharacteristic
278C4⋊C4C22×D6111yescharacteristic
279C22⋊C4—611no—
280C22⋊C4—611no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C42—611no—
288C42—1221no—
289C42—1221no—
290C23—21no—
291C23—611no—
292C23D4×D6111yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—1221no—
296Q8—1221no—
297Q8—1221no—
298Q8—1221no—
299D4—21no—
300D4—42no—
301D4—2441no—
302D4—2442no—
303D4#1175822212yes—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—611no—
312C2×C4—611no—
313C2×C4—611no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—2442no—
321C2×C4—2442no—
322C2×C4D4×D6111yescharacteristic
323C2×C4C23×D6111yescharacteristic
324C8—21no—
325C8—21no—
326C8—1221no—
327C8—1221no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—1221no—
335C22—1221no—
336C22—1221no—
337C22C2×D4×D6111yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—1221no—
343C4—1221no—
344C4—1221no—
345C4—2441no—
346C4—2441no—
347C4—2441no—
348C4—2441no—
349C4C2×#1175822211yescharacteristic
350C4#1451982211yescharacteristic
351C2—41no—
352C2—42no—
353C2—2441no—
354C2#1684040211yescharacteristic
355C2#1684055811yescharacteristic
356C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#417C2
socleC22×C61C22×D4
hypercenter#417D61
hypocenterC61#3315
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #16840447C2semidirect
3. #16840129C2semidirect
4. #16840101C2semidirect
5. #16840097C2semidirect
6. #16840064C2semidirect
7. #16840020C2semidirect
8. #16840002C2semidirect
9. #16839971C2semidirect
10. #16839925C2semidirect
11. #16839924C2semidirect
12. #16839859C2semidirect
13. #16839831C2semidirect
14. #16839755C2semidirect
15. C61×#417C2semidirect
192. #417D61semidirect
194. C61#3315semidirect