Finite Group Databasebeta

← #21456104

Subgroups — #21456104

Order 7808.

382 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840365C211yesmaximal, characteristic
2#16840240C211yesmaximal, characteristic, complemented
3#16840087C211yesmaximal, characteristic, complemented
4#16840083C211yesmaximal, characteristic, complemented
5#16840071C211yesmaximal, characteristic, complemented
6#16840067C211yesmaximal, characteristic, complemented
7#16839960C211yesmaximal, characteristic, complemented
8#16839960C211yesmaximal, characteristic, complemented
9#16839901C211yesmaximal, characteristic, complemented
10#16839865C211yesmaximal, characteristic, complemented
11#16839863C211yesmaximal, characteristic, complemented
12SD16×Dic61C211yesmaximal, characteristic, complemented
13#16839847C211yesmaximal, characteristic, complemented
14#16839820C211yesmaximal, characteristic, complemented
15C61×#448C211yesmaximal, characteristic, complemented
16C2×#11758201C2211yescharacteristic
17C2×#11758201C2211yescharacteristic
18#14519773C2211yescharacteristic
19#14519768C2211yescharacteristic
20#14519761—21no—
21#14519759—21no—
22#14519751C2211yescharacteristic
23#14519749—21no—
24#14519748—21no—
25Q8×Dic61—21no—
26Q8×Dic61—21no—
27Q8×Dic61C2211yescharacteristic
28Q8×Dic61C2211yescharacteristic
29Q8×Dic61C2211yescharacteristic
30Q8×Dic61C2211yescharacteristic
31D4×Dic61C2211yescharacteristic
32#14519739C2211yescharacteristic
33#14519736—21no—
34#14519736—21no—
35#14519736C2211yescharacteristic
36#14519736C2211yescharacteristic
37#14519711C2211yescharacteristic
38#14519710C2211yescharacteristic
39#14519709C2211yescharacteristic
40#14519708C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519687C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C22×Q8×C61C2211yescharacteristic
53C2×SD16×C61C2211yescharacteristic
54C2×SD16×C61C2211yescharacteristic
55#121×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C2×Q8×C61—22no—
60C2×Q8×C61—22no—
61C2×Q8×C61—21no—
62C2×Q8×C61C2311yescharacteristic
63C2×Q8×C61C2311yescharacteristic
64C2×D4×C61—21no—
65C2×D4×C61C2311yescharacteristic
66C22×C4×C61—21no—
67C22×C4×C61C2311yescharacteristic
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C22×Dic61—21no—
72C2×D244C2311yescharacteristic
73C2×C4×D61—21no—
74SD16×C61—22no—
75SD16×C61—22no—
76C2×C8×C61C2311yescharacteristic
77C2×C8×C61C2311yescharacteristic
78C4⋊C4×C61C2311yescharacteristic
79C22⋊C4×C61—21no—
80C22⋊Dic61—21no—
81C22⋊Dic61—21no—
82C22⋊Dic61D411yescharacteristic
83C22⋊Dic61D411yescharacteristic
84#11758201—22no—
85#11758201—22no—
86#11758198—21no—
87#11758198—21no—
88C4⋊Dic61—21no—
89C4⋊Dic61—21no—
90C4⋊Dic61—21no—
91C4⋊Dic61—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61D411yescharacteristic
94C4⋊Dic61D411yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98#11758196—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61C2311yescharacteristic
105C4×Dic61C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108C23×C61—21no—
109C23×C61C2×D411yescharacteristic
110C22×D61—21no—
111Q8×C61—24no—
112Q8×C61—21no—
113Q8×C61—21no—
114Q8×C61#4112yes—
115Q8×C61#4112yes—
116D4×C61—21no—
117D4×C61—21no—
118D4×C61—81no—
119C2×C4×C61—24no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2411yescharacteristic
127C22⋊D61—81no—
128C22⋊D61—81no—
129C22⋊D61—81no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—81no—
134C2×Dic61C2×D411yescharacteristic
135C2×Dic61C2×D411yescharacteristic
136C2×Dic61C2×D411yescharacteristic
137C2×Dic61C2×D411yescharacteristic
138D244—21no—
139D244—21no—
140C4×D61—81no—
141C8×C61—21no—
142C8×C61—21no—
143#92418—21no—
144#92418—21no—
145C22×C61—21no—
146C22×C61—21no—
147C22×C61—21no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61C22×D411yescharacteristic
152C2×D61—41no—
153C2×D61—41no—
154C2×D61—41no—
155C4×C61—22no—
156C4×C61—22no—
157C4×C61—21no—
158C4×C61—41no—
159C4×C61C2×#4111yescharacteristic
160C4×C61C2×#4111yescharacteristic
161Dic61—21no—
162Dic61—21no—
163Dic61—21no—
164Dic61—21no—
165Dic61—41no—
166Dic61—41no—
167Dic61—41no—
168#3126—611nomaximal, Sylow
169C2×C61—41no—
170C2×C61—81no—
171C2×C61#52511yescharacteristic
172C2×C61#57711yescharacteristic
173C2×C61#57711yescharacteristic
174D61—81no—
175#540—611no—
176#519—611no—
177#482—611no—
178#482—611no—
179#479—611no—
180#479—611no—
181#460—611no—
182#460—611no—
183#448—611no—
184#448D6111yescharacteristic, complemented
185#440—611no—
186#440—611no—
187C4×SD16—611no—
188C4×SD16—611no—
189#433—611no—
190C61#312611yescharacteristic, complemented, Sylow
191C22×Q8C2×D6111yescharacteristic
192C2×SD16—611no—
193C2×SD16—611no—
194C2×SD16C2×D6111yescharacteristic
195C2×SD16C2×D6111yescharacteristic
196#127—611no—
197#125—611no—
198#123—1221no—
199#123—1221no—
200#121—611no—
201#121—1221no—
202#121—1221no—
203#121C2×D6111yescharacteristic
204C4×Q8—611no—
205C4×Q8—611no—
206C4×Q8—611no—
207C4×Q8—611no—
208C4×Q8—1221no—
209C4×Q8—1221no—
210C4×D4—611no—
211C4×D4—611no—
212#117—611no—
213#117—611no—
214#117—1221no—
215#117—1221no—
216#107—611no—
217#107—611no—
218#106—611no—
219#106—611no—
220C4⋊C8—611no—
221C4⋊C8—611no—
222#103—611no—
223#103—611no—
224#103C2×D6111yescharacteristic
225#103C2×D6111yescharacteristic
226#102—611no—
227#102—611no—
228#102—611no—
229#102—611no—
230C22⋊C8—611no—
231C22⋊C8C2×D6111yescharacteristic
232#97—611no—
233C4×C8—611no—
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8—21no—
237C2×Q8C22×D6111yescharacteristic
238C2×Q8C22×D6111yescharacteristic
239C2×D4—21no—
240C2×D4—611no—
241C2×D4—1221no—
242C2×D4—1221no—
243C2×D4—1221no—
244C2×D4C22×D6111yescharacteristic
245C22×C4—21no—
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4C22×D6111yescharacteristic
249SD16—22no—
250SD16—22no—
251SD16—1222no—
252SD16—1222no—
253C2×C8—611no—
254C2×C8—611no—
255C2×C8C22×D6111yescharacteristic
256C2×C8C22×D6111yescharacteristic
257C4⋊C4—611no—
258C4⋊C4—611no—
259C4⋊C4—611no—
260C4⋊C4—611no—
261C4⋊C4—611no—
262C4⋊C4—1221no—
263C4⋊C4—1221no—
264C4⋊C4—1221no—
265C4⋊C4—1221no—
266C4⋊C4—1221no—
267C4⋊C4—1221no—
268C4⋊C4C22×D6111yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—611no—
271C22⋊C4—611no—
272C22⋊C4—1221no—
273C22⋊C4—1221no—
274C22⋊C4—1221no—
275C22⋊C4—1221no—
276C42—611no—
277C42—611no—
278C42—1221no—
279C42—1221no—
280C42—1221no—
281C42—1221no—
282C42—1221no—
283C23—21no—
284C23—1221no—
285C23D4×D6111yescharacteristic
286Q8—24no—
287Q8—21no—
288Q8—21no—
289Q8#1175822412yes—
290Q8#1175822412yes—
291D4—21no—
292D4—21no—
293D4—81no—
294D4—1221no—
295D4—1221no—
296D4—4881no—
297D4—4881no—
298D4—4881no—
299C2×C4—24no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—611no—
306C2×C4—611no—
307C2×C4—611no—
308C2×C4—611no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—4881no—
313C2×C4—4881no—
314C2×C4D4×D6111yescharacteristic
315C2×C4C23×D6111yescharacteristic
316C8—21no—
317C8—21no—
318C8—1221no—
319C8—1221no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—2441no—
327C22—2441no—
328C22—2441no—
329C22C2×D4×D6111yescharacteristic
330C4—22no—
331C4—22no—
332C4—21no—
333C4—41no—
334C4—1221no—
335C4—1221no—
336C4—1221no—
337C4—1221no—
338C4—2441no—
339C4—2441no—
340C4—2441no—
341C4C2×#1175822411yescharacteristic
342C4C2×#1175822411yescharacteristic
343C2—41no—
344C2—81no—
345C2—4881no—
346C2#1684026811yescharacteristic
347C2#1684056811yescharacteristic
348C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#448C2
socleC22×C61C22×D4
hypercenter#448D61
hypocenterC61#3126
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
2. #16840240C2semidirect
3. #16840087C2semidirect
4. #16840083C2semidirect
5. #16840071C2semidirect
6. #16840067C2semidirect
7. #16839960C2semidirect
8. #16839960C2semidirect
9. #16839901C2semidirect
10. #16839865C2semidirect
11. #16839863C2semidirect
12. SD16×Dic61C2semidirect
13. #16839847C2semidirect
14. #16839820C2semidirect
15. C61×#448C2semidirect
184. #448D61semidirect
190. C61#3126semidirect