Finite Group Databasebeta

← #21457995

Subgroups — #21457995

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#16840462C211yesmaximal, characteristic
2Q8×D244C211yesmaximal, characteristic, complemented
3#16840131C211yesmaximal, characteristic, complemented
4#16840105C211yesmaximal, characteristic, complemented
5#16840099C211yesmaximal, characteristic, complemented
6#16840069C211yesmaximal, characteristic, complemented
7#16840007C211yesmaximal, characteristic, complemented
8#16839990C211yesmaximal, characteristic, complemented
9#16839967C211yesmaximal, characteristic, complemented
10#16839899C211yesmaximal, characteristic, complemented
11#16839899C211yesmaximal, characteristic, complemented
12#16839835C211yesmaximal, characteristic, complemented
13#16839769C211yesmaximal, characteristic, complemented
14#103×D61C211yesmaximal, characteristic, complemented
15C61×#440C211yesmaximal, characteristic, complemented
16C2×Q8×D61C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×#11758200C2211yescharacteristic
20C2×#11758189C2211yescharacteristic
21C2×C8×D61C2211yescharacteristic
22#14519777—21no—
23#14519777C2211yescharacteristic
24#14519770—21no—
25#14519769C2211yescharacteristic
26#14519760—21no—
27#14519757—21no—
28#14519757—21no—
29#14519757C2211yescharacteristic
30#14519757C2211yescharacteristic
31#14519750—21no—
32#14519748C2211yescharacteristic
33#14519748C2211yescharacteristic
34C4×D244—21no—
35C4×D244C2211yescharacteristic
36C4×C22⋊D61—21no—
37#14519735C2211yescharacteristic
38C4⋊C4×D61C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519708C2211yescharacteristic
41C4⋊#92418C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519702C2211yescharacteristic
46#14519701C2211yescharacteristic
47#14519701C2211yescharacteristic
48#14519700C2211yescharacteristic
49#14519700C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519689C2211yescharacteristic
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—
64Q8×D61—22no—
65Q8×D61—22no—
66Q8×D61—41no—
67Q8×D61—41no—
68C2×D244D411yescharacteristic
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61C2311yescharacteristic
73C2×C4×D61C2311yescharacteristic
74C2×Dic122—21no—
75C2×Dic122—21no—
76C2×Dic122C2311yescharacteristic
77C2×Dic122C2311yescharacteristic
78SD16×C61—22no—
79C2×C8×C61C2311yescharacteristic
80C2×C8×C61C2311yescharacteristic
81C4⋊C4×C61—21no—
82C4⋊C4×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C22⋊C4×C61—21no—
85C42×C61—21no—
86C42×C61C2311yescharacteristic
87C22⋊Dic61—21no—
88C22⋊Dic61—21no—
89#11758200—41no—
90#11758200—41no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198D411yescharacteristic
95#11758198D411yescharacteristic
96C4⋊Dic61—21no—
97C4⋊Dic61—21no—
98C4⋊Dic61—21no—
99C4⋊Dic61—21no—
100C4⋊Dic61D411yescharacteristic
101C4⋊Dic61C2311yescharacteristic
102C4⋊Dic61C2311yescharacteristic
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106C4×Dic61—21no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109#11758189—41no—
110C8×D61—41no—
111C23×C61—21no—
112C22×D61C2×D411yescharacteristic
113C22×D61C2×D411yescharacteristic
114Q8×C61—21no—
115Q8×C61#4112yes—
116D4×C61—21no—
117D4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—81no—
122C2×C4×C61C2×D411yescharacteristic
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2411yescharacteristic
125C22⋊D61—42no—
126C22⋊D61—81no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61C2×D411yescharacteristic
132C2×Dic61C2×D411yescharacteristic
133D244—22no—
134C4×D61—21no—
135C4×D61—21no—
136C4×D61—21no—
137C4×D61—21no—
138C4×D61—42no—
139C4×D61—42no—
140C4×D61—81no—
141Dic122—21no—
142Dic122—21no—
143Dic122—21no—
144Dic122—21no—
145Dic122—42no—
146Dic122—42no—
147C8×C61—21no—
148C8×C61—21no—
149#92418—21no—
150#92418—21no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61C22×D411yescharacteristic
155C2×D61—21no—
156C2×D61—21no—
157C2×D61—21no—
158C2×D61—21no—
159C2×D61—21no—
160C2×D61#13712yes—
161C4×C61—22no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61C2×#4111yescharacteristic
167C4×C61H(5,𝔽2)11yescharacteristic
168Dic61—21no—
169Dic61—21no—
170Dic61—41no—
171Dic61—41no—
172Dic61—41no—
173Dic61—41no—
174#3320—611nomaximal, Sylow
175C2×C61—81no—
176C2×C61#54611yescharacteristic
177C2×C61C2×#13711yescharacteristic
178C2×C61#57711yescharacteristic
179D61—22no—
180D61—41no—
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#440D6111yescharacteristic, complemented
193#435—611no—
194#419—611no—
195C2×#103—611no—
196C61#332011yescharacteristic, complemented, Sylow
197C22×Q8—611no—
198C22×Q8—611no—
199C2×SD16—611no—
200C2×SD16—611no—
201C2×SD16C2×D6111yescharacteristic
202C2×M16—611no—
203C22×C8—611no—
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×Q8C2×D6111yescharacteristic
217C4×D4—611no—
218C4×D4—1221no—
219C4×D4—1221no—
220C4×D4C2×D6111yescharacteristic
221#117—611no—
222C2×C4⋊C4—611no—
223#107—611no—
224#107C2×D6111yescharacteristic
225#106—611no—
226C4⋊C8—611no—
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#103C2×D6111yescharacteristic
236#102C2×D6111yescharacteristic
237C22⋊C8—611no—
238C22⋊C8—611no—
239#97C2×D6111yescharacteristic
240C2×Q8—611no—
241C2×Q8—611no—
242C2×Q8—1221no—
243C2×Q8—1221no—
244C2×Q8—1222no—
245C2×Q8—1222no—
246C2×Q8—2441no—
247C2×Q8—2441no—
248C2×Q8C22×D6111yescharacteristic
249C2×D4—611no—
250C2×D4—1221no—
251C2×D4—1221no—
252C2×D4C22×D6111yescharacteristic
253C22×C4—21no—
254C22×C4—611no—
255C22×C4—611no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—1221no—
259SD16—22no—
260SD16—2441no—
261SD16—2441no—
262M16—2441no—
263C2×C8—611no—
264C2×C8—611no—
265C2×C8—2441no—
266C2×C8C22×D6111yescharacteristic
267C2×C8C22×D6111yescharacteristic
268C4⋊C4—21no—
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⋊C4C22×D6111yescharacteristic
280C4⋊C4C22×D6111yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—611no—
283C22⋊C4—611no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C42—21no—
290C42—1221no—
291C42C22×D6111yescharacteristic
292C23—21no—
293C23—611no—
294C23—611no—
295Q8—21no—
296Q8—1221no—
297Q8—1221no—
298Q8—1221no—
299Q8—1221no—
300Q8—2442no—
301Q8—2442no—
302Q8#1175822212yes—
303D4—21no—
304D4—21no—
305D4—1222no—
306D4—4881no—
307D4—2442no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—611no—
313C2×C4—611no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—4881no—
323C2×C4—2442no—
324C2×C4—2442no—
325C2×C4D4×D6111yescharacteristic
326C2×C4D4×D6111yescharacteristic
327C2×C4C23×D6111yescharacteristic
328C8—21no—
329C8—21no—
330C8—1221no—
331C8—1221no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—612no—
336C22—1221no—
337C22—1221no—
338C22—1221no—
339C22—1221no—
340C22—1221no—
341C22C2×D4×D6111yescharacteristic
342C4—21no—
343C4—21no—
344C4—22no—
345C4—41no—
346C4—41no—
347C4—1221no—
348C4—1221no—
349C4—2441no—
350C4—2441no—
351C4—2441no—
352C4—2441no—
353C4C2×#1175822211yescharacteristic
354C4#1451982311yescharacteristic
355C2—81no—
356C2—1222no—
357C2—2441no—
358C2#1684040811yescharacteristic
359C2#137×D6111yescharacteristic
360C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#440C2
socleC22×C61C22×D4
hypercenter#440D61
hypocenterC61#3320
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
2. Q8×D244C2semidirect
3. #16840131C2semidirect
4. #16840105C2semidirect
5. #16840099C2semidirect
6. #16840069C2semidirect
7. #16840007C2semidirect
8. #16839990C2semidirect
9. #16839967C2semidirect
10. #16839899C2semidirect
11. #16839899C2semidirect
12. #16839835C2semidirect
13. #16839769C2semidirect
14. #103×D61C2semidirect
15. C61×#440C2semidirect
192. #440D61semidirect
196. C61#3320semidirect