Finite Group Databasebeta

← #21456497

Subgroups — #21456497

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#16840385C211yesmaximal, characteristic, complemented
2#16840365C211yesmaximal, characteristic, complemented
3#16840169C211yesmaximal, characteristic, complemented
4#16840148C211yesmaximal, characteristic, complemented
5#16840118C211yesmaximal, characteristic, complemented
6#16840107C211yesmaximal, characteristic, complemented
7#16840013C211yesmaximal, characteristic, complemented
8#16840010C211yesmaximal, characteristic, complemented
9#16839998C211yesmaximal, characteristic, complemented
10#16839873C211yesmaximal, characteristic, complemented
11#16839863C211yesmaximal, characteristic, complemented
12#16839847C211yesmaximal, characteristic, complemented
13#16839842C211yesmaximal, characteristic, complemented
14#16839717C211yesmaximal, characteristic, complemented
15C61×#465C211yesmaximal, characteristic, complemented
16C2×#11758201C2211yescharacteristic
17C2×D488C2211yescharacteristic
18C2×#11758199C2211yescharacteristic
19C2×#11758194C2211yescharacteristic
20#14519776C2211yescharacteristic
21#14519773C2211yescharacteristic
22#14519772—21no—
23#14519768C2211yescharacteristic
24#14519766C2211yescharacteristic
25#14519763—21no—
26#14519761—21no—
27#14519759—21no—
28#14519759—21no—
29#14519757—21no—
30#14519751C2211yescharacteristic
31#14519751C2211yescharacteristic
32#14519749—21no—
33#14519748—21no—
34Q8×Dic61C2211yescharacteristic
35D4×Dic61C2211yescharacteristic
36#14519739C2211yescharacteristic
37#14519739C2211yescharacteristic
38#14519736C2211yescharacteristic
39#14519711C2211yescharacteristic
40#14519710C2211yescharacteristic
41#14519708C2211yescharacteristic
42#14519701C2211yescharacteristic
43#14519699C2211yescharacteristic
44#14519699C2211yescharacteristic
45#14519698C2211yescharacteristic
46#14519697C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519687C2211yescharacteristic
49#14519687C2211yescharacteristic
50C8×Dic61C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×SD16×C61C2211yescharacteristic
53C22×C8×C61C2211yescharacteristic
54C22⋊Q8×C61C2211yescharacteristic
55#121×C61C2211yescharacteristic
56#106×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⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C22×Dic61—21no—
68C2×D244C2311yescharacteristic
69C2×D244C2311yescharacteristic
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×Dic122—21no—
73SD16×C61—22no—
74C2×C8×C61—22no—
75C2×C8×C61C2311yescharacteristic
76C2×C8×C61C2311yescharacteristic
77C4⋊C4×C61—21no—
78C4⋊C4×C61C2311yescharacteristic
79C4⋊C4×C61C2311yescharacteristic
80C22⋊C4×C61—21no—
81C22⋊C4×C61—21no—
82C22⋊Dic61—21no—
83C22⋊Dic61D411yescharacteristic
84C22⋊Dic61D411yescharacteristic
85#11758201—22no—
86#11758199—22no—
87#11758198—21no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61—21no—
95C4⋊Dic61D411yescharacteristic
96C4⋊Dic61D411yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99#11758196—21no—
100#11758196—21no—
101C4×Dic61—21no—
102C4×Dic61C2311yescharacteristic
103C4×Dic61C2311yescharacteristic
104#11758194—22no—
105C2×#92418C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107D488—22no—
108C23×C61—21no—
109C23×C61C2×D411yescharacteristic
110C22×D61—21no—
111C22×D61—21no—
112Q8×C61—21no—
113Q8×C61—21no—
114D4×C61—21no—
115D4×C61—21no—
116D4×C61—81no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61C2×D411yescharacteristic
123C2×C4×C61C2411yescharacteristic
124C22⋊D61—81no—
125C22⋊D61—81no—
126C22⋊D61—81no—
127C22⋊D61—81no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—81no—
131C2×Dic61C2×D411yescharacteristic
132C2×Dic61C2×D411yescharacteristic
133C2×Dic61C2×D411yescharacteristic
134C2×Dic61C2×D411yescharacteristic
135D244—21no—
136D244—21no—
137D244—21no—
138D244—21no—
139C4×D61—81no—
140C4×D61—81no—
141Dic122—81no—
142C8×C61—21no—
143C8×C61#4112yes—
144#92418—21no—
145#92418#4112yes—
146C22×C61—21no—
147C22×C61—21no—
148C22×C61—21no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61C22×D411yescharacteristic
153C2×D61—41no—
154C2×D61—41no—
155C2×D61—41no—
156C2×D61—41no—
157C2×D61—41no—
158C2×D61—41no—
159C4×C61—21no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61C2×#4111yescharacteristic
164C4×C61C2×#4111yescharacteristic
165Dic61—21no—
166Dic61—21no—
167Dic61—21no—
168Dic61—21no—
169Dic61—41no—
170Dic61—41no—
171#3179—611nomaximal, Sylow
172C2×C61—41no—
173C2×C61—81no—
174C2×C61#53211yescharacteristic
175C2×C61#57611yescharacteristic
176C2×C61#57711yescharacteristic
177D61—81no—
178D61—81no—
179#542—611no—
180#540—611no—
181#501—611no—
182#496—611no—
183#488—611no—
184#486—611no—
185#469—611no—
186#468—611no—
187#466—611no—
188#465D6111yescharacteristic, complemented
189#442—611no—
190#440—611no—
191C4×SD16—611no—
192C4×D8—611no—
193#405—611no—
194C61#317911yescharacteristic, complemented, Sylow
195C2×SD16—611no—
196C2×SD16C2×D6111yescharacteristic
197C2×D8—611no—
198C2×D8—611no—
199C2×M16—611no—
200C22×C8C2×D6111yescharacteristic
201C4⋊Q8—611no—
202#127—611no—
203#126—1221no—
204#125—611no—
205#124—611no—
206#124—1221no—
207#123—1221no—
208#123—1221no—
209#123—1221no—
210C22⋊Q8—1221no—
211C22⋊Q8C2×D6111yescharacteristic
212#121—611no—
213#121—611no—
214#121—1221no—
215#121—1221no—
216#121C2×D6111yescharacteristic
217C4×Q8—611no—
218C4×D4—611no—
219C4×D4—611no—
220C4×D4—611no—
221#117—611no—
222#107—611no—
223#107—611no—
224#106—611no—
225#106C2×D6111yescharacteristic
226#103—611no—
227#103C2×D6111yescharacteristic
228#102—611no—
229#102—611no—
230#102—611no—
231#102—611no—
232#102—611no—
233#102C2×D6111yescharacteristic
234#97—611no—
235#97—611no—
236C4×C8—611no—
237C4×C8—611no—
238C2×Q8—1221no—
239C2×Q8C22×D6111yescharacteristic
240C2×D4—21no—
241C2×D4—611no—
242C2×D4—611no—
243C2×D4—1221no—
244C2×D4—1221no—
245C2×D4—1221no—
246C2×D4—1221no—
247C2×D4C22×D6111yescharacteristic
248C22×C4—1221no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4C22×D6111yescharacteristic
252SD16—22no—
253SD16—1222no—
254D8—1222no—
255D8—1222no—
256M16—1222no—
257C2×C8—22no—
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
272C4⋊C4C22×D6111yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—611no—
276C22⋊C4—611no—
277C22⋊C4—1221no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C42—611no—
285C42—611no—
286C42—1221no—
287C23—21no—
288C23—1221no—
289C23—1221no—
290C23D4×D6111yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—4881no—
294D4—21no—
295D4—21no—
296D4—81no—
297D4—1221no—
298D4—1221no—
299D4—1221no—
300D4—1221no—
301D4—4881no—
302D4—4881no—
303D4—4881no—
304D4—4881no—
305C2×C4—21no—
306C2×C4—21no—
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—4881no—
319C2×C4D4×D6111yescharacteristic
320C2×C4C23×D6111yescharacteristic
321C8—21no—
322C8—612no—
323C8—1221no—
324C8#1175822412yes—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—2441no—
332C22—2441no—
333C22—2441no—
334C22—2441no—
335C22—2441no—
336C22—2441no—
337C22C2×D4×D6111yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—1221no—
343C4—1221no—
344C4—1221no—
345C4—1221no—
346C4—2441no—
347C4—2441no—
348C4#41×D6111yescharacteristic
349C4C2×#1175822411yescharacteristic
350C2—41no—
351C2—81no—
352C2—4881no—
353C2—4881no—
354C2#1684030711yescharacteristic
355C2#1684056411yescharacteristic
356C2#1684056811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#465C2
socleC22×C61C22×D4
hypercenter#465D61
hypocenterC61#3179
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #16840385C2semidirect
2. #16840365C2semidirect
3. #16840169C2semidirect
4. #16840148C2semidirect
5. #16840118C2semidirect
6. #16840107C2semidirect
7. #16840013C2semidirect
8. #16840010C2semidirect
9. #16839998C2semidirect
10. #16839873C2semidirect
11. #16839863C2semidirect
12. #16839847C2semidirect
13. #16839842C2semidirect
14. #16839717C2semidirect
15. C61×#465C2semidirect
188. #465D61semidirect
194. C61#3179semidirect