Finite Group Databasebeta

← #21458108

Subgroups — #21458108

Order 7808.

386 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#16840476C211yesmaximal, characteristic
2#16840425C211yesmaximal, characteristic, complemented
3#16840111C211yesmaximal, characteristic, complemented
4#16840105C211yesmaximal, characteristic, complemented
5#16840100C211yesmaximal, characteristic, complemented
6#16840056C211yesmaximal, characteristic, complemented
7#16840007C211yesmaximal, characteristic, complemented
8#16839965C211yesmaximal, characteristic, complemented
9#16839900C211yesmaximal, characteristic, complemented
10#16839899C211yesmaximal, characteristic, complemented
11#16839853C211yesmaximal, characteristic, complemented
12#16839838C211yesmaximal, characteristic, complemented
13#16839772C211yesmaximal, characteristic, complemented
14#16839769C211yesmaximal, characteristic, complemented
15C61×#468C211yesmaximal, characteristic, complemented
16C22×Dic122C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×#11758200C2211yescharacteristic
20C2×#11758189C2211yescharacteristic
21#14519776—21no—
22#14519776C2211yescharacteristic
23#14519775C2211yescharacteristic
24#14519764—21no—
25#14519763—21no—
26#14519757C2211yescharacteristic
27#14519755—21no—
28#14519754—21no—
29#14519749—21no—
30#14519748C2211yescharacteristic
31#14519742C2211yescharacteristic
32D4×Dic61C2211yescharacteristic
33C4×C22⋊D61C2211yescharacteristic
34#14519737—21no—
35#14519736C2211yescharacteristic
36#14519735C2211yescharacteristic
37#14519733—21no—
38#14519710C2211yescharacteristic
39#14519708C2211yescharacteristic
40#14519706C2211yescharacteristic
41#14519702C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519701C2211yescharacteristic
47#14519700C2211yescharacteristic
48#14519700C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×SD16×C61C2211yescharacteristic
53C2×M16×C61C2211yescharacteristic
54C22⋊Q8×C61C2211yescharacteristic
55#121×C61C2211yescharacteristic
56#107×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D4×C61—21no—
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C2×C22⋊D61—21no—
64C2×C22⋊D61D411yescharacteristic
65C22×Dic61—21no—
66C22×Dic61—21no—
67Q8×D61—22no—
68Q8×D61—41no—
69C2×C4×D61—21no—
70C2×C4×D61C2311yescharacteristic
71C2×Dic122—22no—
72C2×Dic122—21no—
73C2×Dic122—21no—
74C2×Dic122—21no—
75C2×Dic122—41no—
76C2×Dic122C2311yescharacteristic
77C2×Dic122C2311yescharacteristic
78SD16×C61—41no—
79M16×C61—41no—
80C2×C8×C61C2311yescharacteristic
81C2×C8×C61C2311yescharacteristic
82C4⋊C4×C61—21no—
83C4⋊C4×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C22⋊C4×C61—21no—
86C22⋊C4×C61—21no—
87C22⋊Dic61—21no—
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90C22⋊Dic61D411yescharacteristic
91#11758200—22no—
92#11758200—41no—
93#11758198—21no—
94#11758198—21no—
95#11758198D411yescharacteristic
96C4⋊Dic61—21no—
97C4⋊Dic61C2311yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196D411yescharacteristic
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110#11758189—41no—
111C23×C61—21no—
112C23×C61C2×D411yescharacteristic
113C22×D61C2×D411yescharacteristic
114Q8×C61—21no—
115Q8×C61—21no—
116D4×C61—21no—
117D4×C61—21no—
118D4×C61—81no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2411yescharacteristic
126C22⋊D61—22no—
127C22⋊D61—81no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—42no—
133C2×Dic61—42no—
134C2×Dic61C2×D411yescharacteristic
135C2×Dic61C2×D411yescharacteristic
136C2×Dic61C2×D411yescharacteristic
137C4×D61—21no—
138C4×D61—21no—
139C4×D61—42no—
140Dic122—21no—
141Dic122—21no—
142Dic122—21no—
143Dic122—42no—
144Dic122—42no—
145Dic122—81no—
146Dic122#4112yes—
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—21no—
161C4×C61—21no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61—41no—
165C4×C61C2×#4111yescharacteristic
166C4×C61H(5,𝔽2)11yescharacteristic
167Dic61—22no—
168Dic61—21no—
169Dic61—21no—
170Dic61—41no—
171Dic61—41no—
172Dic61—41no—
173Dic61#13712yes—
174#3329—611nomaximal, Sylow
175C2×C61—41no—
176C2×C61—81no—
177C2×C61#54611yescharacteristic
178C2×C61C2×#13711yescharacteristic
179C2×C61#57711yescharacteristic
180D61—41no—
181#555—611no—
182D4×Q8—611no—
183#487—611no—
184#485—611no—
185#485—611no—
186#477—611no—
187#468—611no—
188#468D6111yescharacteristic, complemented
189#461—611no—
190#448—611no—
191#448—611no—
192C4×SD16—611no—
193#436—611no—
194#419—611no—
195#419—611no—
196C61#332911yescharacteristic, complemented, Sylow
197C22×Q8—611no—
198C22×Q8—611no—
199C2×SD16—611no—
200C2×SD16—611no—
201C2×SD16C2×D6111yescharacteristic
202C2×M16—611no—
203C2×M16C2×D6111yescharacteristic
204C4⋊Q8—611no—
205C4⋊Q8—611no—
206C4⋊Q8—1221no—
207#124—1221no—
208#124—1221no—
209C22⋊Q8—611no—
210C22⋊Q8—1221no—
211C22⋊Q8—1221no—
212C22⋊Q8C2×D6111yescharacteristic
213#121—611no—
214#121—1221no—
215#121C2×D6111yescharacteristic
216C4×Q8—611no—
217C4×D4—611no—
218C4×D4—611no—
219C4×D4—1221no—
220#117—611no—
221#117—611no—
222#117—1221no—
223#107—611no—
224#107C2×D6111yescharacteristic
225#106—611no—
226C4⋊C8—611no—
227#103—611no—
228#103—611no—
229#103—611no—
230#103—611no—
231#103—611no—
232#103—611no—
233#103—611no—
234#103—611no—
235#103C2×D6111yescharacteristic
236#102C2×D6111yescharacteristic
237C22⋊C8—611no—
238C22⋊C8—611no—
239C4×C8—611no—
240C2×Q8—611no—
241C2×Q8—611no—
242C2×Q8—1221no—
243C2×Q8—1221no—
244C2×Q8—1222no—
245C2×Q8—1221no—
246C2×Q8—1222no—
247C2×Q8—2441no—
248C2×Q8—2441no—
249C2×Q8C22×D6111yescharacteristic
250C2×D4—21no—
251C2×D4—611no—
252C2×D4—1221no—
253C2×D4C22×D6111yescharacteristic
254C22×C4—611no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4C22×D6111yescharacteristic
259SD16—41no—
260SD16—1222no—
261SD16—2441no—
262M16—41no—
263M16—2441no—
264C2×C8—611no—
265C2×C8—611no—
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⋊C4C22×D6111yescharacteristic
278C4⋊C4C22×D6111yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—611no—
282C22⋊C4—611no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C42—611no—
289C42—1221no—
290C42—1221no—
291C42—1221no—
292C23—21no—
293C23—611no—
294C23D4×D6111yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—612no—
298Q8—1221no—
299Q8—1221no—
300Q8—1221no—
301Q8—4881no—
302Q8—2442no—
303Q8—2442no—
304D4—21no—
305D4—21no—
306D4—81no—
307D4—1222no—
308D4—4881no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—611no—
315C2×C4—611no—
316C2×C4—611no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—2442no—
324C2×C4—2442no—
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—1221no—
339C22—1221no—
340C22—1221no—
341C22C2×D4×D6111yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—612no—
347C4—1221no—
348C4—1221no—
349C4—1222no—
350C4—2441no—
351C4—2441no—
352C4—2441no—
353C4#41×D6111yescharacteristic
354C4#1451982211yescharacteristic
355C2—41no—
356C2—81no—
357C2—2441no—
358C2#1684040111yescharacteristic
359C2#137×D6111yescharacteristic
360C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#468C2
socleC22×C61C22×D4
hypercenter#468D61
hypocenterC61#3329
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
2. #16840425C2semidirect
3. #16840111C2semidirect
4. #16840105C2semidirect
5. #16840100C2semidirect
6. #16840056C2semidirect
7. #16840007C2semidirect
8. #16839965C2semidirect
9. #16839900C2semidirect
10. #16839899C2semidirect
11. #16839853C2semidirect
12. #16839838C2semidirect
13. #16839772C2semidirect
14. #16839769C2semidirect
15. C61×#468C2semidirect
188. #468D61semidirect
196. C61#3329semidirect