Finite Group Databasebeta

← #21457992

Subgroups — #21457992

Order 7808.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840458C211yesmaximal, characteristic
2D4×Dic122C211yesmaximal, characteristic, complemented
3#16840131C211yesmaximal, characteristic, complemented
4#16840104C211yesmaximal, characteristic, complemented
5#16840098C211yesmaximal, characteristic, complemented
6#16840070C211yesmaximal, characteristic, complemented
7#16840008C211yesmaximal, characteristic, complemented
8#16839991C211yesmaximal, characteristic, complemented
9#16839968C211yesmaximal, characteristic, complemented
10#16839903C211yesmaximal, characteristic, complemented
11#16839903C211yesmaximal, characteristic, complemented
12#16839864C211yesmaximal, characteristic, complemented
13#16839772C211yesmaximal, characteristic, complemented
14C2×#14519702C211yesmaximal, characteristic, complemented
15C61×#435C211yesmaximal, characteristic, complemented
16C22×Dic122C2211yescharacteristic
17C22×Dic122C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19C2×#11758190C2211yescharacteristic
20C2×#11758190C2211yescharacteristic
21#14519777C2211yescharacteristic
22#14519776—21no—
23#14519772—21no—
24#14519769C2211yescharacteristic
25#14519759—21no—
26#14519756C2211yescharacteristic
27#14519756C2211yescharacteristic
28#14519754—21no—
29#14519754—21no—
30#14519751C2211yescharacteristic
31#14519751C2211yescharacteristic
32#14519749—21no—
33C4×Dic122C2211yescharacteristic
34C4×D244C2211yescharacteristic
35D4×Dic61—21no—
36#14519737—21no—
37#14519736C2211yescharacteristic
38C2×C4⋊Dic61C2211yescharacteristic
39#14519711C2211yescharacteristic
40#14519711C2211yescharacteristic
41#14519709C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519702C2211yescharacteristic
46#14519702C2211yescharacteristic
47#14519702C2211yescharacteristic
48#14519702C2211yescharacteristic
49#14519702C2211yescharacteristic
50#14519702C2211yescharacteristic
51#14519699C2211yescharacteristic
52C2×M16×C61C2211yescharacteristic
53C22×C8×C61C2211yescharacteristic
54C4×D4×C61C2211yescharacteristic
55C4⋊C8×C61C2211yescharacteristic
56C22⋊C8×C61C2211yescharacteristic
57C22⋊C8×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×D4×C61D411yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C2×C22⋊D61—21no—
63C2×C22⋊D61—21no—
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61—21no—
67C2×D244C2311yescharacteristic
68C2×C4×D61—21no—
69C2×Dic122—22no—
70C2×Dic122—22no—
71C2×Dic122—21no—
72C2×Dic122—21no—
73C2×Dic122—41no—
74C2×Dic122—41no—
75C2×Dic122C2311yescharacteristic
76C2×Dic122C2311yescharacteristic
77C2×Dic122C2311yescharacteristic
78M16×C61—41no—
79C2×C8×C61—41no—
80C2×C8×C61C2311yescharacteristic
81C2×C8×C61C2311yescharacteristic
82C2×C8×C61C2311yescharacteristic
83C2×C8×C61C2311yescharacteristic
84C4⋊C4×C61D411yescharacteristic
85C22⋊C4×C61D411yescharacteristic
86C22⋊C4×C61D411yescharacteristic
87C42×C61C2311yescharacteristic
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90C22⋊Dic61—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94C4⋊Dic61—21no—
95C4⋊Dic61—21no—
96C4⋊Dic61—21no—
97C4⋊Dic61C2311yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100C4⋊Dic61C2311yescharacteristic
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108#11758190—22no—
109#11758190—41no—
110#11758190—41no—
111C23×C61C2×D411yescharacteristic
112C23×C61C2×D411yescharacteristic
113C22×D61—21no—
114D4×C61—22no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61C2×D411yescharacteristic
120C2×C4×C61C2×D411yescharacteristic
121C2×C4×C61C2×D411yescharacteristic
122C2×C4×C61C2×D411yescharacteristic
123C2×C4×C61C2411yescharacteristic
124C22⋊D61—42no—
125C22⋊D61—81no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—42no—
134C2×Dic61—42no—
135C2×Dic61—81no—
136D244—21no—
137D244—21no—
138C4×D61—81no—
139Dic122—21no—
140Dic122—21no—
141Dic122—21no—
142Dic122—21no—
143Dic122—21no—
144Dic122—42no—
145Dic122—42no—
146Dic122#4112yes—
147C8×C61—21no—
148C8×C61—21no—
149C8×C61—21no—
150C8×C61—21no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61#13712yes—
157C22×C61C22×D411yescharacteristic
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—41no—
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61C2×#4111yescharacteristic
166C4×C61H(5,𝔽2)11yescharacteristic
167Dic61—22no—
168Dic61—41no—
169Dic61—41no—
170Dic61—41no—
171Dic61—41no—
172Dic61—41no—
173Dic61—41no—
174#3320—611nomaximal, Sylow
175C2×C61—22no—
176C2×C61—41no—
177C2×C61#54611yescharacteristic
178C2×C61C2×#13711yescharacteristic
179C2×C61#57711yescharacteristic
180D61—81no—
181#553—611no—
182D4×Q8—611no—
183#491—611no—
184#485—611no—
185#484—611no—
186#479—611no—
187#468—611no—
188#465—611no—
189#461—611no—
190#448—611no—
191#448—611no—
192#440—611no—
193#435D6111yescharacteristic, complemented
194#419—611no—
195C2×#103—611no—
196C61#332011yescharacteristic, complemented, Sylow
197C22×Q8—611no—
198C22×Q8—611no—
199C2×SD16—611no—
200C2×SD16—611no—
201C2×SD16—611no—
202C2×M16C2×D6111yescharacteristic
203C22×C8C2×D6111yescharacteristic
204C4⋊Q8—611no—
205C4⋊Q8—1221no—
206#126—1221no—
207#125—611no—
208#123—1221no—
209C22⋊Q8—611no—
210C22⋊Q8—611no—
211C22⋊Q8—1221no—
212C22⋊Q8—1221no—
213#121—611no—
214#121—611no—
215#121—1221no—
216C4×Q8—611no—
217C4×D4—611no—
218C4×D4—1221no—
219C4×D4—1221no—
220C4×D4C2×D6111yescharacteristic
221#117—611no—
222C2×C4⋊C4—611no—
223#107—611no—
224#107—611no—
225#106—611no—
226C4⋊C8C2×D6111yescharacteristic
227#103—611no—
228#103—611no—
229#103—611no—
230#103—611no—
231#103—611no—
232#103—611no—
233#103—611no—
234#103—611no—
235#103—611no—
236#102—611no—
237C22⋊C8C2×D6111yescharacteristic
238C22⋊C8C2×D6111yescharacteristic
239#97C2×D6111yescharacteristic
240C2×Q8—611no—
241C2×Q8—611no—
242C2×Q8—611no—
243C2×Q8—1222no—
244C2×Q8—1222no—
245C2×Q8—1221no—
246C2×Q8—1221no—
247C2×Q8—2441no—
248C2×Q8—2441no—
249C2×D4—611no—
250C2×D4—1221no—
251C2×D4—1221no—
252C2×D4D24411yescharacteristic
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4C22×D6111yescharacteristic
258C22×C4C22×D6111yescharacteristic
259SD16—1222no—
260SD16—2441no—
261SD16—2441no—
262M16—41no—
263C2×C8—41no—
264C2×C8C22×D6111yescharacteristic
265C2×C8C22×D6111yescharacteristic
266C2×C8C22×D6111yescharacteristic
267C2×C8C22×D6111yescharacteristic
268C4⋊C4—611no—
269C4⋊C4—611no—
270C4⋊C4—611no—
271C4⋊C4—611no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4D24411yescharacteristic
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C22⋊C4D24411yescharacteristic
288C22⋊C4D24411yescharacteristic
289C42—1221no—
290C42—1221no—
291C42C22×D6111yescharacteristic
292C23—1221no—
293C23C2×D24411yescharacteristic
294C23C2×D24411yescharacteristic
295Q8—612no—
296Q8—1221no—
297Q8—1221no—
298Q8—1221no—
299Q8—1221no—
300Q8—1221no—
301Q8—2442no—
302Q8—2442no—
303D4—22no—
304D4—1221no—
305D4—1221no—
306D4—4881no—
307D4—2442no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—4881no—
320C2×C4—4881no—
321C2×C4—2442no—
322C2×C4—2442no—
323C2×C4C2×D24411yescharacteristic
324C2×C4C2×D24411yescharacteristic
325C2×C4C2×D24411yescharacteristic
326C2×C4C2×D24411yescharacteristic
327C2×C4C23×D6111yescharacteristic
328C8—21no—
329C8—21no—
330C8—21no—
331C8—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—2441no—
338C22—2441no—
339C22—2441no—
340C22#1451981012yes—
341C22C22×D24411yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—1222no—
347C4—2441no—
348C4—2441no—
349C4—2441no—
350C4—2441no—
351C4—2441no—
352C4—2441no—
353C4#41×D6111yescharacteristic
354C4#1451982211yescharacteristic
355C2—22no—
356C2—41no—
357C2—4881no—
358C2#1684040711yescharacteristic
359C2C2×#1451981011yescharacteristic
360C2#1684057411yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#435C2
socleC22×C61C22×D4
hypercenter#435D61
hypocenterC61#3320
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. D4×Dic122C2semidirect
3. #16840131C2semidirect
4. #16840104C2semidirect
5. #16840098C2semidirect
6. #16840070C2semidirect
7. #16840008C2semidirect
8. #16839991C2semidirect
9. #16839968C2semidirect
10. #16839903C2semidirect
11. #16839903C2semidirect
12. #16839864C2semidirect
13. #16839772C2semidirect
14. C2×#14519702C2semidirect
15. C61×#435C2semidirect
193. #435D61semidirect
196. C61#3320semidirect