Finite Group Databasebeta

← #21458010

Subgroups — #21458010

Order 7808.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840477C211yesmaximal, characteristic, complemented
2#16840424C211yesmaximal, characteristic, complemented
3#16840122C211yesmaximal, characteristic, complemented
4#16840105C211yesmaximal, characteristic, complemented
5#16840089C211yesmaximal, characteristic, complemented
6#16840047C211yesmaximal, characteristic, complemented
7#16840014C211yesmaximal, characteristic, complemented
8#16839990C211yesmaximal, characteristic, complemented
9#16839977C211yesmaximal, characteristic, complemented
10#16839906C211yesmaximal, characteristic, complemented
11#16839899C211yesmaximal, characteristic, complemented
12#16839835C211yesmaximal, characteristic, complemented
13#16839769C211yesmaximal, characteristic, complemented
14#16839757C211yesmaximal, characteristic, complemented
15C61×#440C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20C2×#11758189C2211yescharacteristic
21C2×C8×D61C2211yescharacteristic
22#14519777C2211yescharacteristic
23#14519765—21no—
24#14519765C2211yescharacteristic
25#14519763—21no—
26#14519763—21no—
27#14519757—21no—
28#14519757C2211yescharacteristic
29#14519752—21no—
30#14519752C2211yescharacteristic
31#14519751—21no—
32#14519748C2211yescharacteristic
33#14519748C2211yescharacteristic
34C4×D244—21no—
35C4×D244C2211yescharacteristic
36#14519736—21no—
37#14519735C2211yescharacteristic
38#14519735C2211yescharacteristic
39#14519708C2211yescharacteristic
40#14519708C2211yescharacteristic
41C4⋊#92418C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519699C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519689C2211yescharacteristic
52C2×SD16×C61C2211yescharacteristic
53C4×Q8×C61C2211yescharacteristic
54C4×D4×C61C2211yescharacteristic
55#107×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D4×C61C2311yescharacteristic
61C22×C4×C61—21no—
62C2×C22⋊D61—21no—
63C2×C22⋊D61—21no—
64#11758226—22no—
65#11758226—41no—
66Q8×D61—22no—
67Q8×D61—41no—
68C2×D244—21no—
69C2×D244—21no—
70C2×D244D411yescharacteristic
71C2×D244C2311yescharacteristic
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61C2311yescharacteristic
75C2×C4×D61C2311yescharacteristic
76C2×Dic122—21no—
77C2×Dic122—21no—
78C2×Dic122C2311yescharacteristic
79SD16×C61—22no—
80C2×C8×C61C2311yescharacteristic
81C2×C8×C61C2311yescharacteristic
82C4⋊C4×C61—21no—
83C4⋊C4×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C22⋊C4×C61—21no—
86C42×C61—21no—
87C42×C61C2311yescharacteristic
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90#11758200—41no—
91#11758199—41no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198D411yescharacteristic
99#11758198D411yescharacteristic
100C4⋊Dic61—21no—
101C4⋊Dic61—21no—
102C4⋊Dic61D411yescharacteristic
103C4⋊Dic61C2311yescharacteristic
104C4⋊Dic61C2311yescharacteristic
105C4×Dic61—21no—
106C4×Dic61—21no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109#11758189—41no—
110C8×D61—41no—
111C23×C61—21no—
112C22×D61—21no—
113C22×D61C2×D411yescharacteristic
114C22×D61C2×D411yescharacteristic
115Q8×C61—21no—
116Q8×C61#4112yes—
117D4×C61—21no—
118D4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—42no—
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2411yescharacteristic
126C22⋊D61—81no—
127C22⋊D61—81no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61C2×D411yescharacteristic
132C2×Dic61C2×D411yescharacteristic
133D244—21no—
134D244—21no—
135D244—41no—
136D244—42no—
137D244—42no—
138C4×D61—21no—
139C4×D61—21no—
140C4×D61—21no—
141C4×D61—21no—
142C4×D61—42no—
143C4×D61—42no—
144Dic122—21no—
145Dic122—21no—
146Dic122—42no—
147Dic122—81no—
148C8×C61—21no—
149C8×C61—21no—
150#92418—21no—
151#92418—21no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61C22×D411yescharacteristic
156C2×D61—21no—
157C2×D61—21no—
158C2×D61—21no—
159C2×D61—21no—
160C2×D61—21no—
161C2×D61—21no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—41no—
165C4×C61—22no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—41no—
169C4×C61—41no—
170C4×C61C2×#4111yescharacteristic
171C4×C61H(5,𝔽2)11yescharacteristic
172Dic61—21no—
173Dic61—21no—
174Dic61—41no—
175Dic61—41no—
176Dic61—41no—
177#3321—611nomaximal, Sylow
178C2×C61—81no—
179C2×C61#54611yescharacteristic
180C2×C61#57511yescharacteristic
181C2×C61#57711yescharacteristic
182D61—41no—
183D61—41no—
184D61—81no—
185#555—611no—
186#548—611no—
187#489—611no—
188#485—611no—
189#482—611no—
190#475—611no—
191#469—611no—
192#465—611no—
193#463—611no—
194#449—611no—
195#448—611no—
196#440D6111yescharacteristic, complemented
197#435—611no—
198#419—611no—
199#416—611no—
200C61#332111yescharacteristic, complemented, Sylow
201C2×#41—611no—
202C22×Q8—611no—
203C2×SD16—611no—
204C2×SD16C2×D6111yescharacteristic
205C2×D8—611no—
206C2×M16—611no—
207C22×C8—611no—
208C4⋊Q8—611no—
209#124—611no—
210#124—1221no—
211#124—1221no—
212#124—1221no—
213C22⋊Q8—611no—
214C22⋊Q8—1221no—
215#121—611no—
216#121—611no—
217#121—611no—
218#121—1221no—
219#121—1221no—
220C4×Q8C2×D6111yescharacteristic
221C4×D4—611no—
222C4×D4—1221no—
223C4×D4C2×D6111yescharacteristic
224#117—611no—
225#117—611no—
226#117—1221no—
227#107C2×D6111yescharacteristic
228#106—611no—
229#106—611no—
230C4⋊C8—611no—
231#103—611no—
232#103—611no—
233#103—611no—
234#103—611no—
235#103—611no—
236#103C2×D6111yescharacteristic
237#102—611no—
238#102—611no—
239#102—611no—
240#102C2×D6111yescharacteristic
241C22⋊C8—611no—
242C22⋊C8—611no—
243#97C2×D6111yescharacteristic
244#41—1222no—
245#41—2441no—
246C2×Q8—611no—
247C2×Q8—1221no—
248C2×Q8—1221no—
249C2×Q8—1222no—
250C2×Q8—2441no—
251C2×Q8C22×D6111yescharacteristic
252C2×D4—611no—
253C2×D4—611no—
254C2×D4—1221no—
255C2×D4—1221no—
256C2×D4—1221no—
257C2×D4—1221no—
258C2×D4C22×D6111yescharacteristic
259C22×C4—21no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—1221no—
263C22×C4—1221no—
264SD16—22no—
265SD16—2441no—
266D8—2441no—
267M16—2441no—
268C2×C8—611no—
269C2×C8—611no—
270C2×C8—2441no—
271C2×C8C22×D6111yescharacteristic
272C2×C8C22×D6111yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—611no—
275C4⋊C4—611no—
276C4⋊C4—611no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4C22×D6111yescharacteristic
280C4⋊C4C22×D6111yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—611no—
283C22⋊C4—611no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C42—21no—
293C42—1221no—
294C42—1221no—
295C42C22×D6111yescharacteristic
296C23—21no—
297C23—611no—
298C23—611no—
299C23—1221no—
300Q8—21no—
301Q8—1221no—
302Q8—1221no—
303Q8—4881no—
304Q8—2442no—
305Q8#1175822212yes—
306D4—21no—
307D4—21no—
308D4—1221no—
309D4—1221no—
310D4—4881no—
311D4—4881no—
312D4—2441no—
313D4—2442no—
314D4—2442no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—611no—
320C2×C4—611no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—2442no—
329C2×C4—2442no—
330C2×C4D4×D6111yescharacteristic
331C2×C4D4×D6111yescharacteristic
332C2×C4C23×D6111yescharacteristic
333C8—21no—
334C8—21no—
335C8—1221no—
336C8—1221no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—1221no—
341C22—1221no—
342C22—1221no—
343C22—1221no—
344C22—1221no—
345C22—1221no—
346C22—2441no—
347C22—2441no—
348C22—2441no—
349C22C2×D4×D6111yescharacteristic
350C4—21no—
351C4—21no—
352C4—22no—
353C4—41no—
354C4—41no—
355C4—1221no—
356C4—1221no—
357C4—2441no—
358C4—2441no—
359C4—2441no—
360C4C2×#1175822211yescharacteristic
361C4#1451982311yescharacteristic
362C2—81no—
363C2—4881no—
364C2—2441no—
365C2—2441no—
366C2#1684040811yescharacteristic
367C2#1684055811yescharacteristic
368C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#440C2
socleC22×C61C22×D4
hypercenter#440D61
hypocenterC61#3321
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #16840477C2semidirect
2. #16840424C2semidirect
3. #16840122C2semidirect
4. #16840105C2semidirect
5. #16840089C2semidirect
6. #16840047C2semidirect
7. #16840014C2semidirect
8. #16839990C2semidirect
9. #16839977C2semidirect
10. #16839906C2semidirect
11. #16839899C2semidirect
12. #16839835C2semidirect
13. #16839769C2semidirect
14. #16839757C2semidirect
15. C61×#440C2semidirect
196. #440D61semidirect
200. C61#3321semidirect