Finite Group Databasebeta

← #21456496

Subgroups — #21456496

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#16840367C211yesmaximal, characteristic, complemented
2#16840168C211yesmaximal, characteristic, complemented
3#16840152C211yesmaximal, characteristic, complemented
4#16840116C211yesmaximal, characteristic, complemented
5#16840110C211yesmaximal, characteristic, complemented
6#16840013C211yesmaximal, characteristic, complemented
7#16840010C211yesmaximal, characteristic, complemented
8#16839996C211yesmaximal, characteristic, complemented
9#16839993C211yesmaximal, characteristic, complemented
10#16839872C211yesmaximal, characteristic, complemented
11#16839860C211yesmaximal, characteristic, complemented
12C4×#11758201C211yesmaximal, characteristic, complemented
13C4×#11758199C211yesmaximal, characteristic, complemented
14#16839718C211yesmaximal, characteristic, complemented
15C61×#542C211yesmaximal, characteristic, complemented
16C2×#11758201C2211yescharacteristic
17C2×#11758201C2211yescharacteristic
18C2×#11758199C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20C2×#11758194C2211yescharacteristic
21C22×#92418C2211yescharacteristic
22#14519774C2211yescharacteristic
23#14519769C2211yescharacteristic
24#14519762—21no—
25#14519762—21no—
26#14519751C2211yescharacteristic
27#14519751C2211yescharacteristic
28#14519750—21no—
29#14519750—21no—
30C4×D244C2211yescharacteristic
31C4×D244C2211yescharacteristic
32#14519710C2211yescharacteristic
33#14519710C2211yescharacteristic
34#14519708C2211yescharacteristic
35#14519708C2211yescharacteristic
36#14519701C2211yescharacteristic
37#14519701C2211yescharacteristic
38#14519698C2211yescharacteristic
39#14519698C2211yescharacteristic
40#14519697C2211yescharacteristic
41#14519697C2211yescharacteristic
42#14519697C2211yescharacteristic
43#14519697C2211yescharacteristic
44#14519688C2211yescharacteristic
45#14519688C2211yescharacteristic
46C4×#92418C2211yescharacteristic
47C4×#92418C2211yescharacteristic
48C4⋊Q8×C61C2211yescharacteristic
49#126×C61—21no—
50#124×C61—21no—
51#124×C61C2211yescharacteristic
52#123×C61—21no—
53C22⋊Q8×C61—21no—
54C22⋊Q8×C61C2211yescharacteristic
55#121×C61C2211yescharacteristic
56C4×Q8×C61C2211yescharacteristic
57C4×D4×C61C2211yescharacteristic
58#117×C61C2211yescharacteristic
59C2×Q8×C61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×D4×C61—21no—
62C2×D4×C61C2311yescharacteristic
63C22×C4×C61—21no—
64C22×C4×C61C2311yescharacteristic
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×D244—21no—
68C2×D244—21no—
69C2×D244C2311yescharacteristic
70C2×D244C2311yescharacteristic
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C4⋊C4×C61—21no—
74C4⋊C4×C61—21no—
75C4⋊C4×C61—21no—
76C4⋊C4×C61D411yescharacteristic
77C4⋊C4×C61D411yescharacteristic
78C4⋊C4×C61C2311yescharacteristic
79C4⋊C4×C61C2311yescharacteristic
80C22⋊C4×C61—21no—
81C22⋊C4×C61—21no—
82C22⋊C4×C61—21no—
83C22⋊C4×C61—21no—
84C22⋊C4×C61—21no—
85C22⋊C4×C61D411yescharacteristic
86C22⋊C4×C61D411yescharacteristic
87C42×C61—21no—
88C42×C61C2311yescharacteristic
89C42×C61C2311yescharacteristic
90#11758201—22no—
91#11758201—22no—
92#11758199—22no—
93#11758199—22no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98C4⋊Dic61C2311yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100#11758196—21no—
101#11758196—21no—
102#11758194—22no—
103C2×#92418—22no—
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108C23×C61—21no—
109C23×C61C2×D411yescharacteristic
110C22×D61—21no—
111C22×D61—21no—
112Q8×C61—21no—
113Q8×C61—21no—
114Q8×C61—81no—
115D4×C61—21no—
116D4×C61—21no—
117D4×C61—81no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—81no—
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2×D411yescharacteristic
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2411yescharacteristic
130C22⋊D61—81no—
131C22⋊D61—81no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134D244—21no—
135D244—21no—
136D244—21no—
137D244—21no—
138D244—81no—
139D244—81no—
140C4×D61—81no—
141C4×D61—81no—
142#92418—21no—
143#92418—21no—
144#92418#4112yes—
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—21no—
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61C2×#4111yescharacteristic
168C4×C61C2×#4111yescharacteristic
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#542D6111yescharacteristic, complemented
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#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—21no—
204#125—611no—
205#124—21no—
206#124C2×D6111yescharacteristic
207#123—21no—
208#123—1221no—
209#123—1221no—
210C22⋊Q8—21no—
211C22⋊Q8C2×D6111yescharacteristic
212#121—611no—
213#121—611no—
214#121—1221no—
215#121—1221no—
216#121C2×D6111yescharacteristic
217C4×Q8C2×D6111yescharacteristic
218C4×D4—611no—
219C4×D4—611no—
220C4×D4C2×D6111yescharacteristic
221#117C2×D6111yescharacteristic
222#107—611no—
223#107—611no—
224#106—611no—
225#106—611no—
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#97—611no—
236C4×C8—611no—
237C4×C8—611no—
238C2×Q8—21no—
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—21no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4C22×D6111yescharacteristic
252SD16—1222no—
253SD16—1222no—
254D8—1222no—
255D8—1222no—
256M16—1222no—
257C2×C8—611no—
258C2×C8—611no—
259C2×C8—611no—
260C2×C8—611no—
261C2×C8—1222no—
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—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4C22⋊D6111yescharacteristic
283C22⋊C4C22⋊D6111yescharacteristic
284C42—21no—
285C42C22×D6111yescharacteristic
286C42C22×D6111yescharacteristic
287C23—21no—
288C23—1221no—
289C23—1221no—
290C23C2×C22⋊D6111yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—81no—
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—81no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—4881no—
314C2×C4—4881no—
315C2×C4C2×C22⋊D6111yescharacteristic
316C2×C4C2×C22⋊D6111yescharacteristic
317C2×C4C2×C22⋊D6111yescharacteristic
318C2×C4C2×C22⋊D6111yescharacteristic
319C2×C4C2×C22⋊D6111yescharacteristic
320C2×C4C23×D6111yescharacteristic
321C8—612no—
322C8—612no—
323C8—1221no—
324C8—1221no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—2441no—
332C22—2441no—
333C22—2441no—
334C22—2441no—
335C22—2441no—
336C22—2441no—
337C22C22×C22⋊D6111yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—2441no—
347C4—2441no—
348C4#41×D6111yescharacteristic
349C4#41×D6111yescharacteristic
350C2—41no—
351C2—81no—
352C2—4881no—
353C2—4881no—
354C2#1684030811yescharacteristic
355C2#1684056511yescharacteristic
356C2#1684057011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#542C2
socleC22×C61C22×D4
hypercenter#542D61
hypocenterC61#3179
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #16840367C2semidirect
2. #16840168C2semidirect
3. #16840152C2semidirect
4. #16840116C2semidirect
5. #16840110C2semidirect
6. #16840013C2semidirect
7. #16840010C2semidirect
8. #16839996C2semidirect
9. #16839993C2semidirect
10. #16839872C2semidirect
11. #16839860C2semidirect
12. C4×#11758201C2semidirect
13. C4×#11758199C2semidirect
14. #16839718C2semidirect
15. C61×#542C2semidirect
179. #542D61semidirect
194. C61#3179semidirect