Finite Group Databasebeta

← #21458091

Subgroups — #21458091

Order 7808.

380 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#16840446C211yesmaximal, characteristic, complemented
2#16840423C211yesmaximal, characteristic
3#16840118C211yesmaximal, characteristic, complemented
4#16840096C211yesmaximal, characteristic, complemented
5#16840087C211yesmaximal, characteristic, complemented
6#16840067C211yesmaximal, characteristic, complemented
7#16840017C211yesmaximal, characteristic, complemented
8#16840010C211yesmaximal, characteristic, complemented
9#16839986C211yesmaximal, characteristic, complemented
10#16839923C211yesmaximal, characteristic, complemented
11Q16×Dic61C211yesmaximal, characteristic, complemented
12#16839837C211yesmaximal, characteristic, complemented
13#16839771C211yesmaximal, characteristic, complemented
14#16839762C211yesmaximal, characteristic, complemented
15C61×#451C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758201C2211yescharacteristic
18C2×#11758194C2211yescharacteristic
19C2×#11758189C2211yescharacteristic
20#14519770—21no—
21#14519768C2211yescharacteristic
22#14519767—21no—
23#14519766—21no—
24#14519766C2211yescharacteristic
25#14519759—21no—
26#14519753—21no—
27#14519753C2211yescharacteristic
28#14519753C2211yescharacteristic
29#14519751—21no—
30#14519751C2211yescharacteristic
31Q8×Dic61C2211yescharacteristic
32Q8×Dic61C2211yescharacteristic
33C4×C22⋊D61—21no—
34C4×C22⋊D61C2211yescharacteristic
35#14519736C2211yescharacteristic
36#14519735—21no—
37C4⋊C4×D61C2211yescharacteristic
38#14519711C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519709C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519701C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519701C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519699C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519689C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C22×Q8×C61C2211yescharacteristic
53C2×Q16×C61C2211yescharacteristic
54C2×Q16×C61C2211yescharacteristic
55C22⋊Q8×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C2×Q8×C61—21no—
60C2×Q8×C61—22no—
61C2×Q8×C61—41no—
62C2×Q8×C61C2311yescharacteristic
63C2×Q8×C61C2311yescharacteristic
64C2×Q8×C61C2311yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61D411yescharacteristic
69#11758226—22no—
70#11758226—41no—
71C2×D244—21no—
72C2×D244C2311yescharacteristic
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61C2311yescharacteristic
76Q16×C61—22no—
77Q16×C61—41no—
78C2×C8×C61C2311yescharacteristic
79C2×C8×C61C2311yescharacteristic
80C4⋊C4×C61—21no—
81C4⋊C4×C61C2311yescharacteristic
82C22⋊C4×C61—21no—
83C22⋊Dic61—21no—
84C22⋊Dic61D411yescharacteristic
85#11758201—41no—
86#11758198—21no—
87#11758198—21no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198D411yescharacteristic
92C4⋊Dic61—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61—21no—
95C4⋊Dic61C2311yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196D411yescharacteristic
103C4×Dic61—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61C2311yescharacteristic
107#11758194—41no—
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110#11758189—41no—
111C23×C61C2×D411yescharacteristic
112C22×D61—21no—
113C22×D61C2×D411yescharacteristic
114Q8×C61—21no—
115Q8×C61—21no—
116Q8×C61—21no—
117Q8×C61—21no—
118Q8×C61—21no—
119Q8×C61—42no—
120Q8×C61#4112yes—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—42no—
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2411yescharacteristic
130C22⋊D61—41no—
131C22⋊D61—42no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61C2×D411yescharacteristic
136C2×Dic61C2×D411yescharacteristic
137C2×Dic61C2×D411yescharacteristic
138D244—21no—
139D244—21no—
140D244—42no—
141C4×D61—21no—
142C4×D61—21no—
143C4×D61—42no—
144C4×D61—42no—
145C8×C61—21no—
146C8×C61—21no—
147#92418—21no—
148#92418—21no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—21no—
152C22×C61C22×D411yescharacteristic
153C2×D61—21no—
154C2×D61—21no—
155C2×D61—21no—
156C2×D61—41no—
157C2×D61—41no—
158C2×D61—41no—
159C4×C61—22no—
160C4×C61—21no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61C2×#4111yescharacteristic
165C4×C61H(5,𝔽2)11yescharacteristic
166Dic61—21no—
167Dic61—21no—
168Dic61—21no—
169Dic61—41no—
170Dic61—41no—
171Dic61—41no—
172#3327—611nomaximal, Sylow
173C2×C61—41no—
174C2×C61#54611yescharacteristic
175C2×C61#57511yescharacteristic
176C2×C61#57811yescharacteristic
177D61—41no—
178D61—81no—
179#552—611no—
180#548—611no—
181#488—611no—
182#484—611no—
183#482—611no—
184#479—611no—
185#470—611no—
186#468—611no—
187#464—611no—
188#452—611no—
189#451D6111yescharacteristic, complemented
190C4×Q16—611no—
191#436—611no—
192#419—611no—
193#417—611no—
194C61#332711yescharacteristic, complemented, Sylow
195C2×#41—611no—
196C22×Q8C2×D6111yescharacteristic
197C2×Q16C2×D6111yescharacteristic
198C2×Q16C2×D6111yescharacteristic
199C2×SD16—611no—
200C2×M16—611no—
201C2×M16—611no—
202#126—1221no—
203#125—611no—
204#125—1221no—
205#124—611no—
206#124—1221no—
207#123—1221no—
208C22⋊Q8—611no—
209C22⋊Q8—611no—
210C22⋊Q8—1221no—
211C22⋊Q8C2×D6111yescharacteristic
212#121—611no—
213#121—1221no—
214C4×Q8—611no—
215C4×Q8—611no—
216C4×D4—611no—
217C4×D4—1221no—
218#117—611no—
219#117—1221no—
220C2×C4⋊C4—611no—
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#102—611no—
234#102—611no—
235C22⋊C8—611no—
236C22⋊C8C2×D6111yescharacteristic
237C4×C8—611no—
238#41—1222no—
239#41—2441no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8C22×D6111yescharacteristic
244C2×Q8C22×D6111yescharacteristic
245C2×Q8C22×D6111yescharacteristic
246C2×D4—611no—
247C2×D4—611no—
248C2×D4—1221no—
249C2×D4—1221no—
250C22×C4—21no—
251C22×C4—611no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4C22×D6111yescharacteristic
255Q16—22no—
256Q16—41no—
257SD16—2441no—
258M16—2441no—
259M16—2441no—
260C2×C8—611no—
261C2×C8—611no—
262C2×C8C22×D6111yescharacteristic
263C2×C8C22×D6111yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—611no—
266C4⋊C4—611no—
267C4⋊C4—611no—
268C4⋊C4—611no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4C22×D6111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—611no—
279C22⋊C4—611no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C42—611no—
287C42—1221no—
288C42—1221no—
289C42—1221no—
290C23—611no—
291C23—1221no—
292C23D4×D6111yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—42no—
299Q8#1175822412yes—
300D4—1221no—
301D4—1221no—
302D4—2442no—
303D4—2441no—
304D4—2442no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—611no—
313C2×C4—611no—
314C2×C4—611no—
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—1221no—
332C22—1221no—
333C22—1221no—
334C22—2441no—
335C22—2441no—
336C22—2441no—
337C22C2×D4×D6111yescharacteristic
338C4—21no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—1221no—
344C4—1221no—
345C4—1221no—
346C4—2441no—
347C4—2441no—
348C4—2441no—
349C4C2×#1175822411yescharacteristic
350C4#1451982211yescharacteristic
351C2—41no—
352C2—4881no—
353C2—2441no—
354C2#1684039911yescharacteristic
355C2#1684056111yescharacteristic
356C2#1684057511yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#451C2
socleC22×C61C22×D4
hypercenter#451D61
hypocenterC61#3327
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. #16840446C2semidirect
3. #16840118C2semidirect
4. #16840096C2semidirect
5. #16840087C2semidirect
6. #16840067C2semidirect
7. #16840017C2semidirect
8. #16840010C2semidirect
9. #16839986C2semidirect
10. #16839923C2semidirect
11. Q16×Dic61C2semidirect
12. #16839837C2semidirect
13. #16839771C2semidirect
14. #16839762C2semidirect
15. C61×#451C2semidirect
189. #451D61semidirect
194. C61#3327semidirect