Finite Group Databasebeta

← #21457931

Subgroups — #21457931

Order 7808.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840467C211yesmaximal, characteristic, complemented
2#16840419C211yesmaximal, characteristic
3#16840120C211yesmaximal, characteristic, complemented
4#16840092C211yesmaximal, characteristic, complemented
5#16840079C211yesmaximal, characteristic, complemented
6#16840045C211yesmaximal, characteristic, complemented
7#16840020C211yesmaximal, characteristic, complemented
8#16839990C211yesmaximal, characteristic, complemented
9#16839983C211yesmaximal, characteristic, complemented
10#16839924C211yesmaximal, characteristic, complemented
11#16839919C211yesmaximal, characteristic, complemented
12#16839866C211yesmaximal, characteristic, complemented
13#16839831C211yesmaximal, characteristic, complemented
14#103×D61C211yesmaximal, characteristic, complemented
15C61×#417C211yesmaximal, characteristic, complemented
16C2×Q8×D61C2211yescharacteristic
17C2×Dic244C2211yescharacteristic
18C2×#11758202C2211yescharacteristic
19C2×#11758200C2211yescharacteristic
20C2×C8×D61C2211yescharacteristic
21#14519776C2211yescharacteristic
22#14519767—21no—
23#14519764—21no—
24#14519764C2211yescharacteristic
25#14519757C2211yescharacteristic
26#14519756—21no—
27#14519756—21no—
28#14519756C2211yescharacteristic
29#14519756C2211yescharacteristic
30#14519755—21no—
31#14519748—21no—
32#14519748C2211yescharacteristic
33Q8×Dic61C2211yescharacteristic
34#14519742C2211yescharacteristic
35C4×C22⋊D61—21no—
36C4×C22⋊D61—21no—
37C4×C22⋊D61C2211yescharacteristic
38C4⋊C4×D61C2211yescharacteristic
39#14519709C2211yescharacteristic
40#14519708C2211yescharacteristic
41#14519708C2211yescharacteristic
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
69Q8×D61—22no—
70Q8×D61—41no—
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61C2311yescharacteristic
74C2×Dic122—21no—
75C2×Dic122—21no—
76C2×Dic122C2311yescharacteristic
77C2×Dic122C2311yescharacteristic
78M16×C61—41no—
79C2×C8×C61C2311yescharacteristic
80C2×C8×C61C2311yescharacteristic
81C4⋊C4×C61—21no—
82C4⋊C4×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C22⋊Dic61—21no—
85C22⋊Dic61—21no—
86C22⋊Dic61—21no—
87C22⋊Dic61—21no—
88C22⋊Dic61—21no—
89C22⋊Dic61D411yescharacteristic
90#11758202—22no—
91#11758200—41no—
92#11758198—21no—
93#11758198D411yescharacteristic
94C4⋊Dic61—21no—
95C4⋊Dic61—21no—
96C4⋊Dic61C2311yescharacteristic
97C4⋊Dic61C2311yescharacteristic
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#4112yes—
116D4×C61—21no—
117D4×C61—21no—
118D4×C61—42no—
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—81no—
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2411yescharacteristic
128C22⋊D61—22no—
129C22⋊D61—42no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61C2×D411yescharacteristic
135C2×Dic61C2×D411yescharacteristic
136C2×Dic61C2×D411yescharacteristic
137C4×D61—21no—
138C4×D61—21no—
139C4×D61—42no—
140C4×D61—81no—
141Dic122—21no—
142Dic122—21no—
143Dic122—21no—
144Dic122—21no—
145Dic122—42no—
146Dic122—81no—
147C8×C61—21no—
148C8×C61—21no—
149#92418—21no—
150#92418—21no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61C22×D411yescharacteristic
158C2×D61—21no—
159C2×D61—21no—
160C2×D61#13712yes—
161C4×C61—22no—
162C4×C61—21no—
163C4×C61—41no—
164C4×C61—41no—
165C4×C61C2×#4111yescharacteristic
166C4×C61H(5,𝔽2)11yescharacteristic
167Dic61—21no—
168Dic61—21no—
169Dic61—21no—
170Dic61—41no—
171Dic61—41no—
172Dic61—41no—
173Dic61—41no—
174#3316—611nomaximal, Sylow
175C2×C61—41no—
176C2×C61—81no—
177C2×C61#54611yescharacteristic
178C2×C61C2×#13711yescharacteristic
179C2×C61#57711yescharacteristic
180D61—22no—
181#554—611no—
182#548—611no—
183#489—611no—
184#483—611no—
185#481—611no—
186#475—611no—
187#470—611no—
188#465—611no—
189#464—611no—
190#452—611no—
191#451—611no—
192#441—611no—
193#435—611no—
194#417D6111yescharacteristic, complemented
195C2×#103—611no—
196C61#331611yescharacteristic, complemented, Sylow
197C2×#41C2×D6111yescharacteristic
198C22×Q8—611no—
199C2×Q16—611no—
200C2×Q16—611no—
201C2×SD16—611no—
202C2×M16C2×D6111yescharacteristic
203C22×C8—611no—
204C4⋊Q8—611no—
205#125—1221no—
206#124—611no—
207#124—1221no—
208C22⋊Q8—611no—
209C22⋊Q8—611no—
210C22⋊Q8—611no—
211C22⋊Q8—1221no—
212C22⋊Q8—1221no—
213C22⋊Q8—1221no—
214#121—611no—
215#121—1221no—
216C4×Q8—611no—
217C4×Q8—611no—
218C4×D4—611no—
219C4×D4—1221no—
220C4×D4—1221no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4C2×D6111yescharacteristic
223#106—611no—
224#106—611no—
225#106—611no—
226C4⋊C8—611no—
227#103—611no—
228#103—611no—
229#103—611no—
230#103—611no—
231#103—611no—
232#103C2×D6111yescharacteristic
233#103C2×D6111yescharacteristic
234#102—611no—
235#102C2×D6111yescharacteristic
236#102C2×D6111yescharacteristic
237C22⋊C8—611no—
238C22⋊C8—611no—
239#97—611no—
240#41—22no—
241#41—41no—
242C2×Q8—611no—
243C2×Q8—611no—
244C2×Q8—1221no—
245C2×Q8—1221no—
246C2×Q8—1222no—
247C2×Q8—2441no—
248C2×Q8C22×D6111yescharacteristic
249C2×D4—21no—
250C2×D4—611no—
251C2×D4—1221no—
252C2×D4C22×D6111yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—611no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4C22×D6111yescharacteristic
259Q16—1222no—
260Q16—2441no—
261SD16—2441no—
262M16—41no—
263C2×C8—611no—
264C2×C8—611no—
265C2×C8—2441no—
266C2×C8C22×D6111yescharacteristic
267C2×C8C22×D6111yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—611no—
270C4⋊C4—611no—
271C4⋊C4—611no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4C22×D6111yescharacteristic
280C4⋊C4C22×D6111yescharacteristic
281C22⋊C4—611no—
282C22⋊C4—611no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C42—611no—
290C42—1221no—
291C42—1221no—
292C23—21no—
293C23—611no—
294C23D4×D6111yescharacteristic
295Q8—21no—
296Q8—1221no—
297Q8—1221no—
298Q8—1221no—
299Q8—1221no—
300Q8—4881no—
301Q8—2442no—
302Q8#1175822212yes—
303D4—21no—
304D4—21no—
305D4—42no—
306D4—1222no—
307D4—2442no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—81no—
315C2×C4—611no—
316C2×C4—611no—
317C2×C4—611no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—4881no—
325C2×C4—2442no—
326C2×C4D4×D6111yescharacteristic
327C2×C4C23×D6111yescharacteristic
328C8—21no—
329C8—21no—
330C8—1221no—
331C8—1221no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—612no—
339C22—1221no—
340C22—1221no—
341C22C2×D4×D6111yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—1221no—
347C4—1221no—
348C4—1221no—
349C4—2441no—
350C4—2441no—
351C4—2441no—
352C4—2441no—
353C4C2×#1175822211yescharacteristic
354C4#1451982211yescharacteristic
355C2—41no—
356C2—81no—
357C2—1222no—
358C2#1684040211yescharacteristic
359C2#137×D6111yescharacteristic
360C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#417C2
socleC22×C61C22×D4
hypercenter#417D61
hypocenterC61#3316
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. #16840467C2semidirect
3. #16840120C2semidirect
4. #16840092C2semidirect
5. #16840079C2semidirect
6. #16840045C2semidirect
7. #16840020C2semidirect
8. #16839990C2semidirect
9. #16839983C2semidirect
10. #16839924C2semidirect
11. #16839919C2semidirect
12. #16839866C2semidirect
13. #16839831C2semidirect
14. #103×D61C2semidirect
15. C61×#417C2semidirect
194. #417D61semidirect
196. C61#3316semidirect