Finite Group Databasebeta

← #21458888

Subgroups — #21458888

Order 7808.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840497C211yesmaximal, characteristic, complemented
2#16840481C211yesmaximal, characteristic, complemented
3#16840155C211yesmaximal, characteristic, complemented
4#16840152C211yesmaximal, characteristic
5#16840143C211yesmaximal, characteristic, complemented
6#16839986C211yesmaximal, characteristic, complemented
7#16839979C211yesmaximal, characteristic, complemented
8#16839976C211yesmaximal, characteristic, complemented
9#16839966C211yesmaximal, characteristic, complemented
10#16839963C211yesmaximal, characteristic, complemented
11#16839891C211yesmaximal, characteristic, complemented
12#16839871C211yesmaximal, characteristic, complemented
13#16839867C211yesmaximal, characteristic, complemented
14#16839847C211yesmaximal, characteristic, complemented
15C61×#464C211yesmaximal, characteristic, complemented
16C2×#11758202C2211yescharacteristic
17C2×#11758190C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19C2×#11758201C2211yescharacteristic
20C2×#11758201C2211yescharacteristic
21C2×#11758199C2211yescharacteristic
22C2×#11758199C2211yescharacteristic
23#14519775C2211yescharacteristic
24#14519774C2211yescharacteristic
25#14519770—21no—
26#14519770—21no—
27#14519766C2211yescharacteristic
28#14519766C2211yescharacteristic
29#14519765—21no—
30#14519764C2211yescharacteristic
31#14519762—21no—
32#14519762—21no—
33#14519754—21no—
34Q8×Dic61C2211yescharacteristic
35C4×Dic122C2211yescharacteristic
36C4×Dic122C2211yescharacteristic
37C4×D244—21no—
38D4×Dic61C2211yescharacteristic
39#14519739C2211yescharacteristic
40#14519739C2211yescharacteristic
41#14519733—21no—
42#14519708C2211yescharacteristic
43#14519706C2211yescharacteristic
44#14519706C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519699C2211yescharacteristic
49#14519688C2211yescharacteristic
50#14519687C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
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
62C22×Dic61—21no—
63C2×D244—21no—
64C2×D244—21no—
65C2×D244C2311yescharacteristic
66C2×D244C2311yescharacteristic
67C2×C4×D61—21no—
68C2×C4×D61—21no—
69C2×Dic122D411yescharacteristic
70C2×Dic122C2311yescharacteristic
71Q16×C61—41no—
72SD16×C61—41no—
73C2×C8×C61C2311yescharacteristic
74C2×C8×C61C2311yescharacteristic
75C4⋊C4×C61—21no—
76C4⋊C4×C61C2311yescharacteristic
77C22⋊C4×C61—21no—
78C22⋊C4×C61—21no—
79C42×C61—21no—
80C42×C61C2311yescharacteristic
81C22⋊Dic61—21no—
82C22⋊Dic61—21no—
83C22⋊Dic61—21no—
84#11758202—22no—
85#11758201—22no—
86#11758201—41no—
87#11758199—22no—
88#11758199—41no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95C4⋊Dic61—21no—
96C4⋊Dic61D411yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101#11758196D411yescharacteristic
102#11758196D411yescharacteristic
103C4×Dic61—21no—
104C4×Dic61—21no—
105C4×Dic61C2311yescharacteristic
106C4×Dic61C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109#11758190—41no—
110#11758190—41no—
111C23×C61—21no—
112C22×D61—21no—
113C22×D61—21no—
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
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—42no—
129C2×Dic61C2×D411yescharacteristic
130C2×Dic61C2×D411yescharacteristic
131C2×Dic61C2×D411yescharacteristic
132C2×Dic61C2×D411yescharacteristic
133D244—21no—
134D244—21no—
135D244—21no—
136D244—21no—
137D244—42no—
138D244—81no—
139C4×D61—81no—
140C4×D61—81no—
141Dic122—21no—
142Dic122—21no—
143Dic122—41no—
144C8×C61—21no—
145C8×C61—21no—
146#92418—21no—
147#92418#4112yes—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61C22×D411yescharacteristic
152C2×D61—41no—
153C2×D61—41no—
154C2×D61—41no—
155C2×D61—41no—
156C2×D61—41no—
157C2×D61—41no—
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61C2×#4111yescharacteristic
164C4×C61H(5,𝔽2)11yescharacteristic
165Dic61—21no—
166Dic61—21no—
167Dic61—21no—
168Dic61—21no—
169Dic61—41no—
170Dic61—41no—
171#3401—611nomaximal, Sylow
172C2×C61—81no—
173C2×C61#55011yescharacteristic
174C2×C61#57511yescharacteristic
175C2×C61#57711yescharacteristic
176D61—81no—
177D61—81no—
178#559—611no—
179#556—611no—
180#497—611no—
181#496—611no—
182#495—611no—
183#464—611no—
184#464D6111yescharacteristic, complemented
185#463—611no—
186#463—611no—
187#461—611no—
188#460—611no—
189#446—611no—
190#442—611no—
191#441—611no—
192C4×SD16—611no—
193C61#340111yescharacteristic, complemented, Sylow
194C2×Q16—611no—
195C2×Q16C2×D6111yescharacteristic
196C2×SD16—611no—
197C2×SD16—611no—
198C2×SD16—611no—
199C2×SD16—611no—
200C2×SD16C2×D6111yescharacteristic
201C2×D8—611no—
202C2×D8—611no—
203C4⋊Q8—611no—
204#127—611no—
205#126—1221no—
206#126—1221no—
207#124—611no—
208#124—611no—
209#124—611no—
210#124—1221no—
211#124C2×D6111yescharacteristic
212#123—1221no—
213#123—1221no—
214C22⋊Q8—1221no—
215C4×Q8—611no—
216C4×Q8—611no—
217C4×Q8—611no—
218C4×Q8C2×D6111yescharacteristic
219C4×D4—611no—
220C4×D4—611no—
221C4×D4—611no—
222C4×D4—1221no—
223#117—1221no—
224#106—611no—
225C4⋊C8—611no—
226C4⋊C8—611no—
227C4⋊C8C2×D6111yescharacteristic
228#103—611no—
229#103—611no—
230#103C2×D6111yescharacteristic
231#102—611no—
232#102—611no—
233#102C2×D6111yescharacteristic
234#97—611no—
235#97—611no—
236C4×C8—611no—
237C2×Q8—611no—
238C2×Q8—611no—
239C2×Q8C22×D6111yescharacteristic
240C2×Q8C22×D6111yescharacteristic
241C2×D4—611no—
242C2×D4—611no—
243C2×D4—1221no—
244C2×D4—1221no—
245C2×D4C22×D6111yescharacteristic
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4—1221no—
249Q16—41no—
250Q16—1222no—
251SD16—41no—
252SD16—1222no—
253SD16—2441no—
254SD16—2441no—
255SD16—2441no—
256D8—1222no—
257D8—2441no—
258C2×C8—611no—
259C2×C8—611no—
260C2×C8C22×D6111yescharacteristic
261C2×C8C22×D6111yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—611no—
264C4⋊C4—611no—
265C4⋊C4—611no—
266C4⋊C4—611no—
267C4⋊C4—1221no—
268C4⋊C4—1221no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4C22×D6111yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—1221no—
275C22⋊C4—1221no—
276C22⋊C4—1221no—
277C22⋊C4—1221no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C42—21no—
284C42—611no—
285C42—611no—
286C42—1221no—
287C42—1221no—
288C42C22×D6111yescharacteristic
289C23—21no—
290C23—1221no—
291C23—1221no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—1221no—
297Q8—1221no—
298Q8—2441no—
299D4—21no—
300D4—21no—
301D4—1221no—
302D4—1221no—
303D4—1221no—
304D4—1221no—
305D4—4881no—
306D4—2442no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—611no—
311C2×C4—611no—
312C2×C4—611no—
313C2×C4—611no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—4881no—
317C2×C4—4881no—
318C2×C4—2442no—
319C2×C4D4×D6111yescharacteristic
320C2×C4D4×D6111yescharacteristic
321C2×C4C23×D6111yescharacteristic
322C8—21no—
323C8—21no—
324C8—612no—
325C8—1221no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—2441no—
330C22—2441no—
331C22—2441no—
332C22—2441no—
333C22—2441no—
334C22—2441no—
335C22C2×D4×D6111yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—1221no—
342C4—1221no—
343C4—1221no—
344C4—1221no—
345C4—2441no—
346C4—2441no—
347C4#41×D6111yescharacteristic
348C4#1451982211yescharacteristic
349C2—81no—
350C2—4881no—
351C2—4881no—
352C2#1684043011yescharacteristic
353C2#1684056111yescharacteristic
354C2#1684056911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#464C2
socleC22×C61C22×D4
hypercenter#464D61
hypocenterC61#3401
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. #16840497C2semidirect
2. #16840481C2semidirect
3. #16840155C2semidirect
5. #16840143C2semidirect
6. #16839986C2semidirect
7. #16839979C2semidirect
8. #16839976C2semidirect
9. #16839966C2semidirect
10. #16839963C2semidirect
11. #16839891C2semidirect
12. #16839871C2semidirect
13. #16839867C2semidirect
14. #16839847C2semidirect
15. C61×#464C2semidirect
184. #464D61semidirect
193. C61#3401semidirect