Finite Group Databasebeta

← #21457713

Subgroups — #21457713

Order 7808.

386 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#16840453C211yesmaximal, characteristic, complemented
2#16840420C211yesmaximal, characteristic
3#16840116C211yesmaximal, characteristic, complemented
4#16840101C211yesmaximal, characteristic, complemented
5#16840074C211yesmaximal, characteristic, complemented
6#16840070C211yesmaximal, characteristic, complemented
7#16840000C211yesmaximal, characteristic, complemented
8#16839988C211yesmaximal, characteristic, complemented
9#16839921C211yesmaximal, characteristic, complemented
10#16839916C211yesmaximal, characteristic, complemented
11C4×#11758202C211yesmaximal, characteristic, complemented
12#16839827C211yesmaximal, characteristic, complemented
13#16839755C211yesmaximal, characteristic, complemented
14#103×D61C211yesmaximal, characteristic, complemented
15C61×#464C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18C2×#11758202C2211yescharacteristic
19C2×C8×D61C2211yescharacteristic
20C2×C8×D61C2211yescharacteristic
21#14519771—21no—
22#14519769C2211yescharacteristic
23#14519767—21no—
24#14519763—21no—
25#14519762—21no—
26#14519754—21no—
27#14519753C2211yescharacteristic
28#14519753C2211yescharacteristic
29#14519753C2211yescharacteristic
30#14519750—21no—
31#14519748C2211yescharacteristic
32C4×Dic122C2211yescharacteristic
33C4×D244C2211yescharacteristic
34#14519737—21no—
35#14519735C2211yescharacteristic
36#14519734—21no—
37C4⋊C4×D61C2211yescharacteristic
38#14519711C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519709C2211yescharacteristic
41#14519702C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51C4×#92418C2211yescharacteristic
52C2×Q16×C61C2211yescharacteristic
53C2×SD16×C61C2211yescharacteristic
54#124×C61C2211yescharacteristic
55C4×Q8×C61C2211yescharacteristic
56C4⋊C8×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×Q8×C61C2311yescharacteristic
61C2×D4×C61C2311yescharacteristic
62C2×C22⋊D61—21no—
63C2×C22⋊D61—21no—
64C22×Dic61—21no—
65Q8×D61—22no—
66Q8×D61—41no—
67#11758224—22no—
68#11758224—41no—
69C2×D244D411yescharacteristic
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61C2311yescharacteristic
73C2×C4×D61C2311yescharacteristic
74C2×Dic122—21no—
75C2×Dic122C2311yescharacteristic
76Q16×C61—41no—
77SD16×C61—41no—
78C2×C8×C61C2311yescharacteristic
79C2×C8×C61C2311yescharacteristic
80C4⋊C4×C61—21no—
81C4⋊C4×C61C2311yescharacteristic
82C22⋊C4×C61—21no—
83C22⋊C4×C61—21no—
84C42×C61—21no—
85C42×C61C2311yescharacteristic
86C22⋊Dic61—21no—
87#11758202—22no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198D411yescharacteristic
93#11758198D411yescharacteristic
94C4⋊Dic61D411yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104#11758196—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C8×D61—41no—
110C8×D61—41no—
111C23×C61—21no—
112C22×D61C2×D411yescharacteristic
113C22×D61C2×D411yescharacteristic
114Q8×C61—21no—
115Q8×C61—21no—
116Q8×C61—21no—
117Q8×C61—21no—
118D4×C61—21no—
119D4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2411yescharacteristic
126C22⋊D61—42no—
127C22⋊D61—42no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—42no—
133C2×Dic61C2×D411yescharacteristic
134C2×Dic61C2×D411yescharacteristic
135D244—22no—
136C4×D61—21no—
137C4×D61—21no—
138C4×D61—21no—
139C4×D61—21no—
140C4×D61—42no—
141C4×D61—42no—
142Dic122—21no—
143Dic122—42no—
144Dic122#4112yes—
145C8×C61—21no—
146C8×C61—21no—
147#92418—21no—
148#92418—21no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61C22×D411yescharacteristic
153C2×D61—21no—
154C2×D61—21no—
155C2×D61—21no—
156C2×D61—21no—
157C2×D61—21no—
158C2×D61#13512yes—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61C2×#4111yescharacteristic
165C4×C61H(5,𝔽2)11yescharacteristic
166Dic61—22no—
167Dic61—21no—
168Dic61—21no—
169Dic61—41no—
170Dic61—41no—
171Dic61—41no—
172#3300—611nomaximal, Sylow
173C2×C61—81no—
174C2×C61#54611yescharacteristic
175C2×C61C2×#13511yescharacteristic
176C2×C61#57811yescharacteristic
177D61—22no—
178D61—41no—
179#552—611no—
180#548—611no—
181#488—611no—
182#485—611no—
183#480—611no—
184#479—611no—
185#467—611no—
186#465—611no—
187#464D6111yescharacteristic, complemented
188#452—611no—
189#451—611no—
190C4×Q16—611no—
191C8×D4—611no—
192#416—611no—
193C2×#103—611no—
194C61#330011yescharacteristic, complemented, Sylow
195C2×#41—611no—
196C22×Q8—611no—
197C2×Q16—611no—
198C2×Q16C2×D6111yescharacteristic
199C2×SD16C2×D6111yescharacteristic
200C22×C8—611no—
201C22×C8—611no—
202#126—1221no—
203#125—611no—
204#125—1221no—
205#124—1221no—
206#124C2×D6111yescharacteristic
207#123—1221no—
208C22⋊Q8—611no—
209C22⋊Q8—611no—
210C22⋊Q8—611no—
211C22⋊Q8—1221no—
212#121—611no—
213#121—1221no—
214C4×Q8—611no—
215C4×Q8C2×D6111yescharacteristic
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⋊C8C2×D6111yescharacteristic
225#103—611no—
226#103—611no—
227#103—611no—
228#103—611no—
229#103—611no—
230#103—611no—
231#103C2×D6111yescharacteristic
232#102—611no—
233#102—611no—
234#102C2×D6111yescharacteristic
235C22⋊C8—611no—
236C22⋊C8—611no—
237C4×C8—611no—
238#41—1222no—
239#41—2441no—
240C2×Q8—611no—
241C2×Q8—1221no—
242C2×Q8—1222no—
243C2×Q8—2441no—
244C2×Q8C22×D6111yescharacteristic
245C2×Q8C22×D6111yescharacteristic
246C2×D4—611no—
247C2×D4—1221no—
248C2×D4—1221no—
249C2×D4C22×D6111yescharacteristic
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255Q16—41no—
256Q16—1222no—
257SD16—41no—
258C2×C8—611no—
259C2×C8—611no—
260C2×C8—2441no—
261C2×C8—2441no—
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—21no—
279C22⋊C4—611no—
280C22⋊C4—611no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C42—21no—
287C42—1221no—
288C42—1221no—
289C42C22×D6111yescharacteristic
290C23—21no—
291C23—611no—
292C23—611no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—612no—
298Q8—1221no—
299Q8—2442no—
300D4—21no—
301D4—21no—
302D4—1222no—
303D4—2442no—
304D4—2442no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—611no—
309C2×C4—611no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—2442no—
319C2×C4—2442no—
320C2×C4—2442no—
321C2×C4D4×D6111yescharacteristic
322C2×C4D4×D6111yescharacteristic
323C2×C4C23×D6111yescharacteristic
324C8—21no—
325C8—21no—
326C8—1221no—
327C8—1221no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—612no—
332C22—1221no—
333C22—1221no—
334C22—1221no—
335C22—1221no—
336C22—1221no—
337C22C2×D4×D6111yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—1221no—
344C4—1221no—
345C4—1222no—
346C4—2441no—
347C4—2441no—
348C4—2441no—
349C4#41×D6111yescharacteristic
350C4#1451982211yescharacteristic
351C2—81no—
352C2—1222no—
353C2—2441no—
354C2#1684040911yescharacteristic
355C2#135×D6111yescharacteristic
356C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#464C2
socleC22×C61C22×D4
hypercenter#464D61
hypocenterC61#3300
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #16840453C2semidirect
3. #16840116C2semidirect
4. #16840101C2semidirect
5. #16840074C2semidirect
6. #16840070C2semidirect
7. #16840000C2semidirect
8. #16839988C2semidirect
9. #16839921C2semidirect
10. #16839916C2semidirect
11. C4×#11758202C2semidirect
12. #16839827C2semidirect
13. #16839755C2semidirect
14. #103×D61C2semidirect
15. C61×#464C2semidirect
187. #464D61semidirect
194. C61#3300semidirect