Finite Group Databasebeta

← #21456507

Subgroups — #21456507

Order 7808.

374 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#16840386C211yesmaximal, characteristic, complemented
2#16840368C211yesmaximal, characteristic, complemented
3#16840151C211yesmaximal, characteristic, complemented
4#16840119C211yesmaximal, characteristic, complemented
5#16840110C211yesmaximal, characteristic, complemented
6#16840016C211yesmaximal, characteristic, complemented
7#16840009C211yesmaximal, characteristic, complemented
8#16839999C211yesmaximal, characteristic, complemented
9#16839992C211yesmaximal, characteristic, complemented
10#16839873C211yesmaximal, characteristic, complemented
11#16839861C211yesmaximal, characteristic, complemented
12#16839849C211yesmaximal, characteristic, complemented
13#16839844C211yesmaximal, characteristic, complemented
14#16839719C211yesmaximal, characteristic, complemented
15C61×#501C211yesmaximal, characteristic, complemented
16C2×#11758190C2211yescharacteristic
17C2×#11758190C2211yescharacteristic
18C2×D488C2211yescharacteristic
19C2×D488C2211yescharacteristic
20C2×#11758189C2211yescharacteristic
21C2×C8×D61C2211yescharacteristic
22#14519774C2211yescharacteristic
23#14519772—21no—
24#14519766—21no—
25#14519765C2211yescharacteristic
26#14519762—21no—
27#14519762—21no—
28#14519762—21no—
29#14519757C2211yescharacteristic
30#14519753—21no—
31#14519752—21no—
32#14519752—21no—
33#14519752C2211yescharacteristic
34#14519752C2211yescharacteristic
35#14519752C2211yescharacteristic
36#14519742C2211yescharacteristic
37#14519739C2211yescharacteristic
38#14519739C2211yescharacteristic
39#14519739C2211yescharacteristic
40#14519734C2211yescharacteristic
41#14519700C2211yescharacteristic
42#14519700C2211yescharacteristic
43#14519697C2211yescharacteristic
44#14519697C2211yescharacteristic
45#14519697C2211yescharacteristic
46#14519697C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519687C2211yescharacteristic
50C4×#92418C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C4⋊Q8×C61C2211yescharacteristic
53#125×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#107×C61C2211yescharacteristic
56#106×C61C2211yescharacteristic
57#106×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×Q8×C61—21no—
60C2×D244—21no—
61C2×D244—21no—
62C2×D244—21no—
63C2×D244—21no—
64C2×D244—21no—
65C2×D244C2311yescharacteristic
66C2×D244C2311yescharacteristic
67C2×D244C2311yescharacteristic
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61C2311yescharacteristic
72C2×Dic122C2311yescharacteristic
73C2×C8×C61C2311yescharacteristic
74C2×C8×C61C2311yescharacteristic
75C4⋊C4×C61—21no—
76C4⋊C4×C61—21no—
77C4⋊C4×C61—21no—
78C4⋊C4×C61C2311yescharacteristic
79C4⋊C4×C61C2311yescharacteristic
80C4⋊C4×C61C2311yescharacteristic
81C4⋊C4×C61C2311yescharacteristic
82C42×C61C2311yescharacteristic
83#11758198—21no—
84#11758198—21no—
85#11758198—21no—
86#11758198—21no—
87#11758198—21no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198D411yescharacteristic
93#11758198D411yescharacteristic
94C4⋊Dic61—21no—
95#11758196—21no—
96#11758196D411yescharacteristic
97#11758196D411yescharacteristic
98C4×Dic61—21no—
99C4×Dic61C2311yescharacteristic
100C2×#92418C2311yescharacteristic
101C2×#92418C2311yescharacteristic
102D488—22no—
103D488—22no—
104#11758190—22no—
105#11758190—22no—
106#11758189—22no—
107C8×D61—22no—
108C22×D61—21no—
109C22×D61—21no—
110C22×D61—21no—
111C22×D61C2×D411yescharacteristic
112Q8×C61—81no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61C2×D411yescharacteristic
118C2×C4×C61C2×D411yescharacteristic
119C2×C4×C61C2411yescharacteristic
120C2×Dic61—21no—
121C2×Dic61C2×D411yescharacteristic
122C2×Dic61C2×D411yescharacteristic
123C2×Dic61C2×D411yescharacteristic
124D244—21no—
125D244—21no—
126D244—21no—
127D244—21no—
128D244—21no—
129D244—21no—
130D244—81no—
131D244—81no—
132D244—81no—
133D244—81no—
134D244—81no—
135C4×D61—21no—
136C4×D61—21no—
137C4×D61—81no—
138C4×D61—81no—
139C4×D61—81no—
140Dic122—21no—
141Dic122—21no—
142C8×C61#4112yes—
143C8×C61#4112yes—
144#92418—21no—
145#92418—21no—
146C22×C61C22×D411yescharacteristic
147C2×D61—21no—
148C2×D61—21no—
149C2×D61—21no—
150C2×D61—41no—
151C2×D61—41no—
152C2×D61—41no—
153C2×D61—41no—
154C2×D61—41no—
155C2×D61—41no—
156C2×D61—41no—
157C2×D61—41no—
158C2×D61—41no—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61—41no—
165C4×C61C2×#4111yescharacteristic
166C4×C61C2×#4111yescharacteristic
167Dic61—21no—
168Dic61—21no—
169Dic61—21no—
170Dic61—41no—
171#3179—611nomaximal, Sylow
172C2×C61#53211yescharacteristic
173C2×C61#57611yescharacteristic
174C2×C61#57711yescharacteristic
175D61—41no—
176D61—81no—
177D61—81no—
178D61—81no—
179#542—611no—
180#540—611no—
181#501D6111yescharacteristic, complemented
182#496—611no—
183#488—611no—
184#486—611no—
185#469—611no—
186#468—611no—
187#466—611no—
188#465—611no—
189#442—611no—
190#440—611no—
191C4×SD16—611no—
192C4×D8—611no—
193#405—611no—
194C61#317911yescharacteristic, complemented, Sylow
195C2×SD16—611no—
196C2×SD16—611no—
197C2×D8—611no—
198C2×D8—611no—
199C2×M16—611no—
200C22×C8—611no—
201C4⋊Q8C2×D6111yescharacteristic
202#127—611no—
203#126—1221no—
204#125C2×D6111yescharacteristic
205#124—611no—
206#124—1221no—
207#123—1221no—
208#123—1221no—
209#123—1221no—
210C22⋊Q8—611no—
211C22⋊Q8—1221no—
212#121—611no—
213#121—611no—
214#121—611no—
215#121—1221no—
216#121—1221no—
217C4×Q8—611no—
218C4×D4—611no—
219C4×D4—611no—
220C4×D4—611no—
221#117—611no—
222#107C2×D6111yescharacteristic
223#107C2×D6111yescharacteristic
224#106C2×D6111yescharacteristic
225#106C2×D6111yescharacteristic
226#103—611no—
227#103—611no—
228#102—611no—
229#102—611no—
230#102—611no—
231#102—611no—
232#102—611no—
233#102—611no—
234#97—611no—
235#97C2×D6111yescharacteristic
236C4×C8—611no—
237C4×C8—611no—
238C2×Q8—21no—
239C2×Q8—611no—
240C2×D4—611no—
241C2×D4—611no—
242C2×D4—611no—
243C2×D4—1221no—
244C2×D4—1221no—
245C2×D4—1221no—
246C2×D4—1221no—
247C2×D4—1221no—
248C22×C4—611no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—1221no—
252SD16—1222no—
253SD16—1222no—
254D8—1222no—
255D8—1222no—
256M16—1222no—
257C2×C8—611no—
258C2×C8—611no—
259C2×C8—1222no—
260C2×C8C22×D6111yescharacteristic
261C2×C8C22×D6111yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—611no—
266C4⋊C4—611no—
267C4⋊C4—1221no—
268C4⋊C4—1221no—
269C4⋊C4C22×D6111yescharacteristic
270C4⋊C4C22×D6111yescharacteristic
271C4⋊C4C22×D6111yescharacteristic
272C4⋊C4C22×D6111yescharacteristic
273C22⋊C4—611no—
274C22⋊C4—611no—
275C22⋊C4—1221no—
276C22⋊C4—1221no—
277C22⋊C4—1221no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C42—611no—
285C42—1221no—
286C42C22×D6111yescharacteristic
287C23—611no—
288C23—1221no—
289C23—1221no—
290C23—1221no—
291Q8—81no—
292Q8—1221no—
293Q8—1221no—
294D4—1221no—
295D4—1221no—
296D4—1221no—
297D4—1221no—
298D4—1221no—
299D4—1221no—
300D4—4881no—
301D4—4881no—
302D4—4881no—
303D4—4881no—
304D4—4881no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—611no—
310C2×C4—611no—
311C2×C4—611no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—4881no—
316C2×C4—4881no—
317C2×C4—4881no—
318C2×C4D4×D6111yescharacteristic
319C2×C4D4×D6111yescharacteristic
320C2×C4C23×D6111yescharacteristic
321C8—1221no—
322C8—1221no—
323C8#1175822612yes—
324C8#1175822612yes—
325C22—1221no—
326C22—1221no—
327C22—1221no—
328C22—2441no—
329C22—2441no—
330C22—2441no—
331C22—2441no—
332C22—2441no—
333C22—2441no—
334C22—2441no—
335C22—2441no—
336C22—2441no—
337C22C2×D4×D6111yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—1221no—
345C4—1221no—
346C4—1221no—
347C4—2441no—
348C4C2×#1175822611yescharacteristic
349C4C2×#1175822611yescharacteristic
350C2—4881no—
351C2—4881no—
352C2—4881no—
353C2—2441no—
354C2#1684031311yescharacteristic
355C2#1684056611yescharacteristic
356C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#501C2
socleC22×C61C22×D4
hypercenter#501D61
hypocenterC61#3179
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #16840386C2semidirect
2. #16840368C2semidirect
3. #16840151C2semidirect
4. #16840119C2semidirect
5. #16840110C2semidirect
6. #16840016C2semidirect
7. #16840009C2semidirect
8. #16839999C2semidirect
9. #16839992C2semidirect
10. #16839873C2semidirect
11. #16839861C2semidirect
12. #16839849C2semidirect
13. #16839844C2semidirect
14. #16839719C2semidirect
15. C61×#501C2semidirect
181. #501D61semidirect
194. C61#3179semidirect