Finite Group Databasebeta

← #21457621

Subgroups — #21457621

Order 7808.

444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840577C212yesmaximal, complemented
2#16840576C211yesmaximal, characteristic, complemented
3#16840140C211yesmaximal, characteristic, complemented
4#16840037C211yesmaximal, characteristic, complemented
5#16840035C212yesmaximal, complemented
6#16840034C211yesmaximal, characteristic, complemented
7#16839945C212yesmaximal, complemented
8#16839943C212yesmaximal, complemented
9#16839879C211yesmaximal, characteristic, complemented
10#16839877C211yesmaximal, characteristic, complemented
11C61×#578C211yesmaximal, characteristic, complemented
12#14519824C2212yes—
13#14519808—22no—
14#14519808C2212yes—
15#14519807—22no—
16#14519807C2212yes—
17#14519807C2212yes—
18#14519806—22no—
19#14519797—22no—
20#14519797C2211yescharacteristic
21#14519796—21no—
22C2×Dic244C2211yescharacteristic
23C2×#11758202—22no—
24C2×#11758202C2212yes—
25Q16×D61—21no—
26#14519784C2212yes—
27#14519783C2211yescharacteristic
28#14519775C2212yes—
29#14519713C2211yescharacteristic
30#14519712C2211yescharacteristic
31#14519704C2212yes—
32#14519704C2211yescharacteristic
33#14519703C2211yescharacteristic
34#14519696C2212yes—
35#14519695C2212yes—
36C8×Dic61C2211yescharacteristic
372−1+4×C61C2212yes—
38#137×C61—22no—
39#137×C61C2212yes—
40#135×C61—21no—
41#135×C61C2211yescharacteristic
42C2×Q16×C61—21no—
43C2×Q16×C61C2211yescharacteristic
44#131×C61C2211yescharacteristic
45#41×C61—22no—
46#41×C61—22no—
47#41×C61—42no—
48#41×C61C2312yes—
49#41×C61C2311yescharacteristic
50C2×Q8×C61—22no—
51C2×Q8×C61—22no—
52C2×Q8×C61C2312yes—
53Q8×D61—22no—
54#11758224—22no—
55#11758224—42no—
56#11758222—22no—
57#11758222C2311yescharacteristic
58C2×Dic122—22no—
59C2×Dic122C2312yes—
60Q16×C61—22no—
61Q16×C61—21no—
62Q16×C61—21no—
63Q16×C61D411yescharacteristic
64SD16×C61—22no—
65SD16×C61D412yes—
66D8×C61D411yescharacteristic
67M16×C61—21no—
68M16×C61C2311yescharacteristic
69C2×C8×C61—21no—
70C2×C8×C61C2311yescharacteristic
71#11758202—22no—
72#11758202—22no—
73#11758202—22no—
74#11758202—22no—
75#11758202—22no—
76#11758202D411yescharacteristic
77#11758201—22no—
78#11758201D411yescharacteristic
79#11758200—22no—
80#11758200—22no—
81#11758200D411yescharacteristic
82#11758199D411yescharacteristic
83#11758196—42no—
84C4×Dic61C2311yescharacteristic
85#11758194—22no—
86#11758194C2312yes—
87#11758194C2311yescharacteristic
88C2×#92418—22no—
89C2×#92418C2311yescharacteristic
90Dic244—21no—
91Dic244—21no—
92#11758189—21no—
93C8×D61—21no—
94Q8×C61—22no—
95Q8×C61—22no—
96Q8×C61—42no—
97Q8×C61C2×D411yescharacteristic
98Q8×C61C2×D412yes—
99D4×C61—22no—
100D4×C61—21no—
101D4×C61—42no—
102D4×C61C2×D411yescharacteristic
103D4×C61C2×D412yes—
104C2×C4×C61—22no—
105C2×C4×C61—21no—
106C2×C4×C61—22no—
107C2×C4×C61—42no—
108C2×C4×C61—42no—
109C2×C4×C61C2411yescharacteristic
110C22⋊D61—21no—
111C22⋊D61—42no—
112C2×Dic61—21no—
113C2×Dic61—22no—
114C2×Dic61—42no—
115D244C2×D411yescharacteristic
116C4×D61—21no—
117C4×D61—42no—
118Dic122—22no—
119Dic122—22no—
120Dic122—42no—
121Dic122C2×D411yescharacteristic
122C8×C61—21no—
123C8×C61C2×D411yescharacteristic
124C8×C61C2×D411yescharacteristic
125#92418—21no—
126#92418—22no—
127#92418C2×D411yescharacteristic
128#92418C2×D411yescharacteristic
129C22×C61—22no—
130C22×C61—21no—
131C22×C61H(5,𝔽2)11yescharacteristic
132C2×D61—21no—
133C4×C61—22no—
134C4×C61—21no—
135C4×C61—42no—
136C4×C61C22×D411yescharacteristic
137C4×C61C22×D411yescharacteristic
138Dic61—22no—
139Dic61—21no—
140Dic61—42no—
141#3293—611nomaximal, Sylow
142C2×C61—21no—
143C2×C61—42no—
144C2×C61—41no—
145C2×C61D4211yescharacteristic
146D61—41no—
147#578—612no—
148#578—611no—
149#578D6111yescharacteristic, complemented
150#494—611no—
151#473—612no—
152#473—611no—
153#473—611no—
154#456—612no—
155#456—612no—
156#443—611no—
157#443—611no—
158C61#329311yescharacteristic, complemented, Sylow
1592−1+4—612no—
1602−1+4C2×D6112yes—
161#137—22no—
162#137—612no—
163#137—612no—
164#137—612no—
165#137—1222no—
166#137—1222no—
167#137—1222no—
168#137C2×D6112yes—
169#135—21no—
170#135—611no—
171#135—1222no—
172#135—1221no—
173#135C2×D6111yescharacteristic
174C2×Q16—21no—
175C2×Q16—612no—
176C2×Q16—611no—
177C2×Q16—1222no—
178C2×Q16—1221no—
179C2×Q16C2×D6111yescharacteristic
180#131—612no—
181#131—611no—
182#131C2×D6111yescharacteristic
183C4⋊Q8—612no—
184#108—611no—
185#108—611no—
186#104—611no—
187#104—612no—
188#104—611no—
189#101—612no—
190#101—612no—
191C4×C8—611no—
192#41—22no—
193#41—22no—
194#41—42no—
195#41—611no—
196#41—1222no—
197#41—1222no—
198#41—2442no—
199#41C22×D6111yescharacteristic
200#41C22×D6112yes—
201C2×Q8—22no—
202C2×Q8—22no—
203C2×Q8—612no—
204C2×Q8—1222no—
205C2×Q8—1222no—
206C2×Q8C22×D6112yes—
207Q16—22no—
208Q16—21no—
209Q16—21no—
210Q16—611no—
211Q16—1222no—
212Q16—1222no—
213Q16—1222no—
214Q16—1222no—
215Q16—1222no—
216Q16—1221no—
217Q16—1221no—
218Q16C22⋊D6111yescharacteristic
219SD16—22no—
220SD16—611no—
221SD16—611no—
222SD16—1222no—
223SD16—1222no—
224SD16—1222no—
225SD16C22⋊D6112yes—
226D8—611no—
227D8C22⋊D6111yescharacteristic
228M16—21no—
229M16—612no—
230M16—611no—
231M16—1222no—
232M16—1221no—
233M16C22×D6111yescharacteristic
234C2×C8—21no—
235C2×C8—611no—
236C2×C8—1222no—
237C2×C8—1221no—
238C2×C8C22×D6111yescharacteristic
239C4⋊C4—2442no—
240C42—611no—
241Q8—22no—
242Q8—22no—
243Q8—42no—
244Q8—611no—
245Q8—1222no—
246Q8—1222no—
247Q8—2442no—
248Q8D4×D6111yescharacteristic
249Q8C2×C22⋊D6112yes—
250D4—21no—
251D4—22no—
252D4—42no—
253D4—611no—
254D4—1221no—
255D4—2442no—
256D4D4×D6111yescharacteristic
257D4C2×C22⋊D6112yes—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—1221no—
264C2×C4—1221no—
265C2×C4—1222no—
266C2×C4—2442no—
267C2×C4—2442no—
268C2×C4C23×D6111yescharacteristic
269C8—21no—
270C8—611no—
271C8—611no—
272C8—1222no—
273C8—1221no—
274C8C2×C22⋊D6111yescharacteristic
275C8C2×C22⋊D6111yescharacteristic
276C22—21no—
277C22—22no—
278C22—1221no—
279C22#1451982211yescharacteristic
280C4—21no—
281C4—22no—
282C4—42no—
283C4—1222no—
284C4—1221no—
285C4—2442no—
286C4C2×D4×D6111yescharacteristic
287C4C22×C22⋊D6111yescharacteristic
288C2—21no—
289C2—41no—
290C2—42no—
291C2—2441no—
292C2D4×C22⋊D6111yescharacteristic
subgroupG/H
centerC2D4×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#578C2
socleC2×C61D42
hypercenter#578D61
hypocenterC61#3293
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #578

Complements

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

NH ≅ G/Ntype
1. #16840577C2semidirect
2. #16840576C2semidirect
3. #16840140C2semidirect
4. #16840037C2semidirect
5. #16840035C2semidirect
6. #16840034C2semidirect
7. #16839945C2semidirect
8. #16839943C2semidirect
9. #16839879C2semidirect
10. #16839877C2semidirect
11. C61×#578C2semidirect
149. #578D61semidirect
158. C61#3293semidirect