Finite Group Databasebeta

← #21456098

Subgroups — #21456098

Order 7808.

384 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#16840383C211yesmaximal, characteristic, complemented
2#16840242C211yesmaximal, characteristic, complemented
3#16840093C211yesmaximal, characteristic, complemented
4#16840081C211yesmaximal, characteristic, complemented
5#16840053C211yesmaximal, characteristic, complemented
6#16840048C211yesmaximal, characteristic, complemented
7#16839985C211yesmaximal, characteristic, complemented
8#16839978C211yesmaximal, characteristic, complemented
9#16839926C211yesmaximal, characteristic, complemented
10#16839909C211yesmaximal, characteristic
11#16839875C211yesmaximal, characteristic, complemented
12#16839870C211yesmaximal, characteristic, complemented
13C4×#11758190C211yesmaximal, characteristic, complemented
14C4×#11758190C211yesmaximal, characteristic, complemented
15C61×#433C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×Dic244C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19C2×#11758190C2211yescharacteristic
20C2×D488C2211yescharacteristic
21#14519777C2211yescharacteristic
22#14519772—21no—
23#14519765C2211yescharacteristic
24#14519763—21no—
25#14519759—21no—
26#14519756C2211yescharacteristic
27#14519755—21no—
28#14519751C2211yescharacteristic
29C4×Dic122C2211yescharacteristic
30C4×Dic122C2211yescharacteristic
31C4×Dic122C2211yescharacteristic
32C4×D244C2211yescharacteristic
33C4×D244C2211yescharacteristic
34C4×D244C2211yescharacteristic
35#14519737—21no—
36#14519737—21no—
37#14519735—21no—
38C2×C4⋊Dic61C2211yescharacteristic
39C4⋊C4×D61—21no—
40#14519709C2211yescharacteristic
41#14519709C2211yescharacteristic
42#14519709C2211yescharacteristic
43#14519709C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519702C2211yescharacteristic
46#14519702C2211yescharacteristic
47#14519702C2211yescharacteristic
48#14519699C2211yescharacteristic
49#14519699C2211yescharacteristic
50#14519699C2211yescharacteristic
51#14519699C2211yescharacteristic
52#117×C61C2211yescharacteristic
53C4⋊C8×C61C2211yescharacteristic
54C4⋊C8×C61C2211yescharacteristic
55C22⋊C8×C61C2211yescharacteristic
56C22⋊C8×C61C2211yescharacteristic
57#97×C61C2211yescharacteristic
58C4×C8×C61C2211yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C2×C22⋊D61—21no—
61C2×C22⋊D61—21no—
62C22×Dic61—21no—
63#11758222—22no—
64#11758222—22no—
65C2×D244C2311yescharacteristic
66C2×D244C2311yescharacteristic
67C2×C4×D61—21no—
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×Dic122—21no—
72C2×Dic122C2311yescharacteristic
73C2×Dic122C2311yescharacteristic
74C2×C8×C61C2311yescharacteristic
75C2×C8×C61C2311yescharacteristic
76C2×C8×C61C2311yescharacteristic
77C2×C8×C61C2311yescharacteristic
78C4⋊C4×C61D411yescharacteristic
79C4⋊C4×C61D411yescharacteristic
80C22⋊C4×C61D411yescharacteristic
81C22⋊C4×C61D411yescharacteristic
82C42×C61C2311yescharacteristic
83C42×C61C2311yescharacteristic
84C22⋊Dic61—21no—
85#11758198—21no—
86#11758198—21no—
87#11758198—21no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91C4⋊Dic61—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61C2311yescharacteristic
94C4⋊Dic61C2311yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104Dic244—22no—
105D488—22no—
106#11758190—22no—
107#11758190—22no—
108C23×C61C2×D411yescharacteristic
109C22×D61—21no—
110C22×D61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61C2×D411yescharacteristic
114C2×C4×C61C2×D411yescharacteristic
115C2×C4×C61C2×D411yescharacteristic
116C2×C4×C61C2×D411yescharacteristic
117C2×C4×C61C2×D411yescharacteristic
118C2×C4×C61C2411yescharacteristic
119C22⋊D61—24no—
120C22⋊D61—81no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—81no—
128D244—21no—
129D244—21no—
130D244—21no—
131D244#4112yes—
132C4×D61—24no—
133C4×D61—81no—
134C4×D61—81no—
135C4×D61—81no—
136Dic122—21no—
137Dic122—21no—
138Dic122—21no—
139Dic122—81no—
140Dic122#4112yes—
141C8×C61—21no—
142C8×C61—21no—
143C8×C61—21no—
144C8×C61—21no—
145C22×C61—21no—
146C22×C61—21no—
147C22×C61—21no—
148C22×C61C22×D411yescharacteristic
149C2×D61—22no—
150C2×D61—41no—
151C2×D61—41no—
152C2×D61—41no—
153C2×D61—41no—
154C2×D61—41no—
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—21no—
160C4×C61C2×#4111yescharacteristic
161C4×C61C2×#4111yescharacteristic
162Dic61—22no—
163Dic61—41no—
164Dic61—41no—
165Dic61—41no—
166Dic61—41no—
167Dic61—41no—
168#3125—611nomaximal, Sylow
169C2×C61—41no—
170C2×C61#52511yescharacteristic
171C2×C61#57711yescharacteristic
172C2×C61#57711yescharacteristic
173D61—42no—
174D61—81no—
175#542—611no—
176#520—611no—
177#483—611no—
178#481—611no—
179#476—611no—
180#475—611no—
181#464—611no—
182#463—611no—
183#452—611no—
184#449—611no—
185#442—611no—
186#441—611no—
187C4×SD16—611no—
188C4×SD16—611no—
189#433D6111yescharacteristic, complemented
190C61#312511yescharacteristic, complemented, Sylow
191C2×#41—611no—
192C2×Q16—611no—
193C2×SD16—611no—
194C2×SD16—611no—
195C2×D8—611no—
196C4⋊Q8—611no—
197#126—1221no—
198#124—611no—
199#124—1221no—
200#123—1221no—
201C22⋊Q8—611no—
202C22⋊Q8—1221no—
203#121—611no—
204C4×Q8—611no—
205C4×Q8—611no—
206C4×Q8—611no—
207C4×D4—611no—
208C4×D4—611no—
209C4×D4—611no—
210C4×D4—1221no—
211C4×D4—1221no—
212#117—1221no—
213#117C2×D6111yescharacteristic
214C2×C4⋊C4—611no—
215C2×C4⋊C4—1221no—
216#106—611no—
217#106—611no—
218#106—611no—
219#106—611no—
220C4⋊C8C2×D6111yescharacteristic
221C4⋊C8C2×D6111yescharacteristic
222#103—611no—
223#103—611no—
224#103—611no—
225#103—611no—
226#102—611no—
227#102—611no—
228#102—611no—
229#102—611no—
230C22⋊C8C2×D6111yescharacteristic
231C22⋊C8C2×D6111yescharacteristic
232#97C2×D6111yescharacteristic
233C4×C8C2×D6111yescharacteristic
234#41—1222no—
235#41—1222no—
236C2×Q8—611no—
237C2×Q8—611no—
238C2×Q8—1221no—
239C2×D4—611no—
240C2×D4—611no—
241C2×D4—1221no—
242C2×D4—1221no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4—1221no—
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4C22×D6111yescharacteristic
249Q16—1222no—
250SD16—1222no—
251SD16—1222no—
252D8—1222no—
253C2×C8C22×D6111yescharacteristic
254C2×C8C22×D6111yescharacteristic
255C2×C8C22×D6111yescharacteristic
256C2×C8C22×D6111yescharacteristic
257C4⋊C4—611no—
258C4⋊C4—611no—
259C4⋊C4—611no—
260C4⋊C4—611no—
261C4⋊C4—1221no—
262C4⋊C4—1221no—
263C4⋊C4—1221no—
264C4⋊C4—1221no—
265C4⋊C4—1221no—
266C4⋊C4—1221no—
267C4⋊C4D24411yescharacteristic
268C4⋊C4D24411yescharacteristic
269C22⋊C4—1221no—
270C22⋊C4—1221no—
271C22⋊C4—1221no—
272C22⋊C4—1221no—
273C22⋊C4—1221no—
274C22⋊C4—1221no—
275C22⋊C4—1221no—
276C22⋊C4D24411yescharacteristic
277C22⋊C4D24411yescharacteristic
278C42—1221no—
279C42—1221no—
280C42—1221no—
281C42C22×D6111yescharacteristic
282C42C22×D6111yescharacteristic
283C23—1221no—
284C23—1221no—
285C23C2×D24411yescharacteristic
286Q8—612no—
287Q8—1221no—
288Q8—1221no—
289Q8—1221no—
290Q8—4881no—
291D4—612no—
292D4—1224no—
293D4—1221no—
294D4—1221no—
295D4—1221no—
296D4—4881no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—1224no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—4881no—
307C2×C4—4881no—
308C2×C4—4881no—
309C2×C4—4881no—
310C2×C4C2×D24411yescharacteristic
311C2×C4C2×D24411yescharacteristic
312C2×C4C2×D24411yescharacteristic
313C2×C4C2×D24411yescharacteristic
314C2×C4C2×D24411yescharacteristic
315C2×C4C23×D6111yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—1222no—
324C22—2441no—
325C22—2441no—
326C22—2441no—
327C22—2441no—
328C22—2441no—
329C22C22×D24411yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—1222no—
336C4—2441no—
337C4—2441no—
338C4—2441no—
339C4—2441no—
340C4—2441no—
341C4#41×D6111yescharacteristic
342C4#41×D6111yescharacteristic
343C2—41no—
344C2—4881no—
345C2—2442no—
346C2#1684027411yescharacteristic
347C2#1684057411yescharacteristic
348C2#1684057411yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#433C2
socleC22×C61C22×D4
hypercenter#433D61
hypocenterC61#3125
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #16840383C2semidirect
2. #16840242C2semidirect
3. #16840093C2semidirect
4. #16840081C2semidirect
5. #16840053C2semidirect
6. #16840048C2semidirect
7. #16839985C2semidirect
8. #16839978C2semidirect
9. #16839926C2semidirect
11. #16839875C2semidirect
12. #16839870C2semidirect
13. C4×#11758190C2semidirect
14. C4×#11758190C2semidirect
15. C61×#433C2semidirect
189. #433D61semidirect
190. C61#3125semidirect