Finite Group Databasebeta

← #21456534

Subgroups — #21456534

Order 7808.

402 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#16840316C211yesmaximal, characteristic, complemented
2#16840309C211yesmaximal, characteristic
3#16840166C211yesmaximal, characteristic, complemented
4#16840133C211yesmaximal, characteristic, complemented
5#16840111C211yesmaximal, characteristic, complemented
6#16840107C211yesmaximal, characteristic, complemented
7#16840011C211yesmaximal, characteristic, complemented
8#16840009C211yesmaximal, characteristic, complemented
9#16840007C211yesmaximal, characteristic, complemented
10#16840005C211yesmaximal, characteristic, complemented
11#16839864C211yesmaximal, characteristic, complemented
12#16839862C211yesmaximal, characteristic, complemented
13#16839860C211yesmaximal, characteristic, complemented
14#16839714C211yesmaximal, characteristic, complemented
15C61×#440C211yesmaximal, characteristic, complemented
16C2×#11758222—21no—
17C2×#11758190C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×#11758201C2211yescharacteristic
20C2×#11758189C2211yescharacteristic
21C2×#11758189C2211yescharacteristic
22#14519776C2211yescharacteristic
23#14519776C2211yescharacteristic
24#14519775C2211yescharacteristic
25#14519773C2211yescharacteristic
26#14519767—21no—
27#14519763—21no—
28#14519757C2211yescharacteristic
29#14519755—21no—
30#14519753C2211yescharacteristic
31#14519752C2211yescharacteristic
32#14519750—21no—
33#14519748C2211yescharacteristic
34C4×Dic122—21no—
35C4×Dic122C2211yescharacteristic
36C4×D244C2211yescharacteristic
37C4×C22⋊D61—21no—
38#14519734—21no—
39C42×D61C2211yescharacteristic
40#14519711C2211yescharacteristic
41#14519710C2211yescharacteristic
42#14519710C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519700C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519688C2211yescharacteristic
50C8×Dic61C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×SD16×C61C2211yescharacteristic
53C4×Q8×C61C2211yescharacteristic
54C4×D4×C61C2211yescharacteristic
55#107×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D4×C61C2311yescharacteristic
61C22×C4×C61—21no—
62C2×C22⋊D61—21no—
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65#11758222—44no—
66C2×D244—21no—
67C2×D244C2311yescharacteristic
68C2×C4×D61—21no—
69C2×C4×D61D411yescharacteristic
70C2×C4×D61D411yescharacteristic
71C2×C4×D61C2311yescharacteristic
72C2×Dic122—21no—
73C2×Dic122—21no—
74C2×Dic122C2311yescharacteristic
75SD16×C61—22no—
76C2×C8×C61C2311yescharacteristic
77C2×C8×C61C2311yescharacteristic
78C4⋊C4×C61—21no—
79C4⋊C4×C61C2311yescharacteristic
80C4⋊C4×C61C2311yescharacteristic
81C22⋊C4×C61—21no—
82C42×C61—21no—
83C42×C61C2311yescharacteristic
84C22⋊Dic61—21no—
85#11758201—22no—
86#11758200—22no—
87#11758198—21no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91C4⋊Dic61—21no—
92C4⋊Dic61C2311yescharacteristic
93C4⋊Dic61C2311yescharacteristic
94#11758196—21no—
95#11758196—21no—
96#11758196—21no—
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100C4×Dic61—21no—
101C4×Dic61D411yescharacteristic
102C4×Dic61D411yescharacteristic
103C4×Dic61C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106#11758190—22no—
107#11758189—22no—
108#11758189—22no—
109C23×C61—21no—
110C22×D61—21no—
111C22×D61C2×D411yescharacteristic
112Q8×C61—21no—
113Q8×C61—21no—
114D4×C61—21no—
115D4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—42no—
120C2×C4×C61C2×D411yescharacteristic
121C2×C4×C61C2×D411yescharacteristic
122C2×C4×C61C2411yescharacteristic
123C22⋊D61—42no—
124C22⋊D61—42no—
125C22⋊D61—42no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61C2×D411yescharacteristic
130C2×Dic61C2×D411yescharacteristic
131C2×Dic61C2×D411yescharacteristic
132D244—21no—
133D244—21no—
134D244—42no—
135C4×D61—21no—
136C4×D61—21no—
137C4×D61—22no—
138C4×D61—22no—
139C4×D61—42no—
140Dic122—21no—
141Dic122—21no—
142Dic122—42no—
143Dic122—42no—
144C8×C61—21no—
145C8×C61#4112yescomplemented
146#92418—21no—
147#92418#4112yescomplemented
148C22×C61—41no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61C22×D411yescharacteristic
152C2×D61—21no—
153C2×D61—21no—
154C2×D61—21no—
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×C61C2×#4111yescharacteristic
165Dic61—21no—
166Dic61—41no—
167Dic61—41no—
168Dic61—41no—
169Dic61AGL(1,ℤ/8)12yes—
170Dic61#13712yes—
171#3182—611nomaximal, Sylow
172C2×C61—81no—
173C2×C61#53211yescharacteristic
174C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
175C2×C61C2×#13711yescharacteristic
176D61—41no—
177D61—81no—
178#533—611no—
179#532—611no—
180#500—611no—
181#492—611no—
182#487—611no—
183#486—611no—
184#468—611no—
185#468—611no—
186#468—611no—
187#468—611no—
188#440—611no—
189#440—611no—
190#440—611no—
191#440D6111yescharacteristic, complemented
192C4×M16—611no—
193C61#318211yescharacteristic, complemented, Sylow
194C2×#41—1221no—
195C2×SD16—611no—
196C2×SD16—611no—
197C2×SD16—611no—
198C2×SD16C2×D6111yescharacteristic
199C2×M16—611no—
200C2×M16—611no—
201C4⋊Q8—611no—
202C4⋊Q8—611no—
203C4⋊Q8—611no—
204#127—611no—
205#125—1221no—
206#124—1221no—
207C22⋊Q8—611no—
208C22⋊Q8—611no—
209C22⋊Q8—1221no—
210#121—611no—
211#121—611no—
212#121—1221no—
213C4×Q8—611no—
214C4×Q8—1221no—
215C4×Q8C2×D6111yescharacteristic
216C4×D4—611no—
217C4×D4—1221no—
218C4×D4C2×D6111yescharacteristic
219#117—1221no—
220C2×C42—611no—
221#107—611no—
222#107—611no—
223#107—611no—
224#107C2×D6111yescharacteristic
225#103—611no—
226#103—611no—
227#103—611no—
228#103C2×D6111yescharacteristic
229#102—611no—
230#102—611no—
231#102—611no—
232#102C2×D6111yescharacteristic
233#97—611no—
234#97C2×D6111yescharacteristic
235C4×C8—611no—
236C4×C8—611no—
237#41—2444no—
238C2×Q8—611no—
239C2×Q8—1221no—
240C2×Q8—1221no—
241C2×Q8C22×D6111yescharacteristic
242C2×D4—611no—
243C2×D4—1221no—
244C2×D4—1221no—
245C2×D4—1221no—
246C2×D4—1221no—
247C2×D4C22×D6111yescharacteristic
248C22×C4—21no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—1221no—
253SD16—22no—
254SD16—1222no—
255SD16—1222no—
256SD16—1222no—
257M16—1222no—
258M16—1222no—
259C2×C8—611no—
260C2×C8—611no—
261C2×C8C22×D6111yescharacteristic
262C2×C8C22×D6111yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—611no—
265C4⋊C4—611no—
266C4⋊C4—1221no—
267C4⋊C4—1221no—
268C4⋊C4—1221no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4C22×D6111yescharacteristic
274C4⋊C4C22×D6111yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—1221no—
277C22⋊C4—1221no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C42—21no—
282C42—611no—
283C42—611no—
284C42—611no—
285C42—1221no—
286C42C22×D6111yescharacteristic
287C23—21no—
288C23—611no—
289C23—1221no—
290Q8—21no—
291Q8—21no—
292Q8—1221no—
293Q8—1221no—
294Q8—2442no—
295Q8—2442no—
296D4—21no—
297D4—21no—
298D4—1221no—
299D4—1221no—
300D4—2442no—
301D4—2442no—
302D4—2442no—
303D4—2442no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—611no—
309C2×C4—611no—
310C2×C4—611no—
311C2×C4—1222no—
312C2×C4—1222no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—2442no—
319C2×C4D4×D6111yescharacteristic
320C2×C4D4×D6111yescharacteristic
321C2×C4C23×D6111yescharacteristic
322C8—21no—
323C8—612no—
324C8—1221no—
325C8#1175822212yescomplemented
326C22—41no—
327C22—41no—
328C22—41no—
329C22—1221no—
330C22—1221no—
331C22—1221no—
332C22—2441no—
333C22—2441no—
334C22—2441no—
335C22C2×D4×D6111yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—612no—
342C4—612no—
343C4—1221no—
344C4—2441no—
345C4—2441no—
346C4—2441no—
347C4#41×D6111yescharacteristic
348C4C2×#1175822211yescharacteristic
349C2—81no—
350C2—4881no—
351C2—2441no—
352C2#1684030911yescharacteristic
353C2AGL(1,ℤ/8)×D6111yescharacteristic
354C2#137×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#440C2
socleC22×C61C22×D4
hypercenter#440D61
hypocenterC61#3182
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #16840316C2semidirect
3. #16840166C2semidirect
4. #16840133C2semidirect
5. #16840111C2semidirect
6. #16840107C2semidirect
7. #16840011C2semidirect
8. #16840009C2semidirect
9. #16840007C2semidirect
10. #16840005C2semidirect
11. #16839864C2semidirect
12. #16839862C2semidirect
13. #16839860C2semidirect
14. #16839714C2semidirect
15. C61×#440C2semidirect
145. C8×C61#41semidirect
147. #92418#41semidirect
191. #440D61semidirect
193. C61#3182semidirect
325. C8#11758222semidirect