Finite Group Databasebeta

← #21445786

Subgroups — #21445786

Order 7808.

588 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#14519822C211yesmaximal, characteristic
2#16839780C211yesmaximal, characteristic, complemented
3#16839778C211yesmaximal, characteristic, complemented
4#16839767C211yesmaximal, characteristic, complemented
5#16839744C211yesmaximal, characteristic, complemented
6#16839735C211yesmaximal, characteristic, complemented
7C61×#418C211yesmaximal, characteristic, complemented
8#14519822—22no—
9#14519822—22no—
10#14519822—22no—
11#14519822—22no—
12C2×#11758222C2211yescharacteristic
13C2×#11758222C2211yescharacteristic
14C2×#11758224—21no—
15C2×#11758224C412yescomplemented
16C22×C22⋊D61—22no—
17C2×D4×D61—21no—
18C2×D4×D61C412yescomplemented
19C2×#11758194C2211yescharacteristic, complemented
20#14519736C2211yescharacteristic, complemented
21#14519705—22no—
22#14519703—22no—
23#14519698—22no—
24#14519695—21no—
25#14519693—21no—
26#14519691—22no—
27C22×D4×C61C2211yescharacteristic
28C2×M16×C61C2211yescharacteristic, complemented
29#117×C61C2211yescharacteristic, complemented
30#102×C61—22no—
31C24×C61—21no—
32C23×D61—22no—
33C2×D4×C61—21no—
34C2×D4×C61—21no—
35C2×D4×C61—21no—
36C2×D4×C61C2×C412yes—
37C2×D4×C61D412yes—
38C2×D4×C61D412yes—
39C22×C4×C61C2311yescharacteristic
40C2×C22⋊D61—28no—
41C2×C22⋊D61—28no—
42C2×C22⋊D61—21no—
43C2×C22⋊D61—22no—
44C2×C22⋊D61—22no—
45C2×C22⋊D61D412yes—
46C22×Dic61—22no—
47#11758224—24no—
48#11758224—24no—
49#11758224—24no—
50#11758224—24no—
51D4×D61—24no—
52D4×D61—24no—
53D4×D61—24no—
54D4×D61—24no—
55#11758222—21no—
56#11758222—21no—
57#11758222—21no—
58#11758222—21no—
59#11758222—21no—
60#11758222—21no—
61#11758222D412yes—
62#11758222D412yes—
63C2×D244C2×C411yescharacteristic
64C2×D244D411yescharacteristic
65C2×C4×D61—21no—
66C2×C4×D61C2×C412yes—
67C2×Dic122C2×C411yescharacteristic
68C2×Dic122D411yescharacteristic
69M16×C61—21no—
70M16×C61—21no—
71C2×C8×C61—21no—
72C4⋊C4×C61—21no—
73C22⋊C4×C61—21no—
74C42×C61—21no—
75C22⋊Dic61—21no—
76C4⋊Dic61—21no—
77C4×Dic61—21no—
78#11758194—21no—
79#11758194—21no—
80C2×#92418—21no—
81C23×C61—22no—
82C23×C61—22no—
83C23×C61—22no—
84C23×C61—82no—
85C23×C61C2×D411yescharacteristic
86C22×D61—21no—
87C22×D61—28no—
88C22×D61—84no—
89C22×D61C22⋊C412yes—
90D4×C61—22no—
91D4×C61—22no—
92D4×C61—22no—
93D4×C61C22⋊C414yes—
94C2×C4×C61—41no—
95C2×C4×C61C22×C411yescharacteristic
96C2×C4×C61C2×D411yescharacteristic
97C2×C4×C61C2×D411yescharacteristic
98C2×C4×C61C2×D411yescharacteristic
99C2×C4×C61C2×D411yescharacteristic
100C2×C4×C61C2×D411yescharacteristic
101C22⋊D61—28no—
102C22⋊D61—28no—
103C22⋊D61—22no—
104C22⋊D61—22no—
105C22⋊D61—22no—
106C22⋊D61—22no—
107C2×Dic61—28no—
108C2×Dic61—21no—
109C2×Dic61—41no—
110C2×Dic61C22⋊C412yes—
111D244—21no—
112D244—21no—
113D244—21no—
114D244C22⋊C412yes—
115C4×D61—22no—
116C4×D61—22no—
117C4×D61—22no—
118C4×D61—22no—
119Dic122—21no—
120Dic122—21no—
121Dic122—21no—
122Dic122C22⋊C412yes—
123C8×C61—41no—
124#92418—41no—
125C22×C61—24no—
126C22×C61—41no—
127C22×C61—44no—
128C22×C61—82no—
129C22×C61—82no—
130C22×C61C2×C22⋊C411yescharacteristic
131C22×C61#12011yescharacteristic
132C22×C61#12011yescharacteristic
133C2×D61—22no—
134C2×D61—22no—
135C2×D61—42no—
136C2×D61—42no—
137C2×D61—88no—
138C4×C61—81no—
139C4×C61C2×C22⋊C411yescharacteristic
140C4×C61C2×C22⋊C411yescharacteristic
141C4×C61#12011yescharacteristic
142C4×C61#12011yescharacteristic
143Dic61—22no—
144Dic61—22no—
145Dic61—81no—
146#1795—611nomaximal, Sylow
147C2×C61—21no—
148C2×C61—21no—
149C2×C61—21no—
150C2×C61—44no—
151C2×C61#37911yescharacteristic
152D61—42no—
153D61—42no—
154C2×H(5,𝔽2)—611no—
155#421—611no—
156#421—611no—
157#418—611no—
158#418D6111yescharacteristic, complemented
159#413—611no—
160#410—611no—
161C61#179511yescharacteristic, complemented, Sylow
162H(5,𝔽2)—1222no—
163H(5,𝔽2)—1222no—
164H(5,𝔽2)—1222no—
165H(5,𝔽2)—1222no—
166C2×#41—611no—
167C2×#41—612no—
168C2×#41—611no—
169C2×#41—1221no—
170C22×D4—612no—
171C22×D4—1221no—
172C22×D4—1222no—
173C22×D4C2×D6111yescharacteristic
174C2×M16—611no—
175C2×M16C2×D6111yescharacteristic, complemented
176#117—611no—
177#117C2×D6111yescharacteristic, complemented
178#104—1222no—
179#104—1222no—
180#102—22no—
181#102—1222no—
182#101—1221no—
183#100—1221no—
184#99—1222no—
185C24—21no—
186C24—1222no—
187#41—612no—
188#41—612no—
189#41—1224no—
190#41—1224no—
191#41—1224no—
192#41—1224no—
193#41—1221no—
194#41—1221no—
195#41—1221no—
196#41—1221no—
197#41—1221no—
198#41—1221no—
199C2×Q8—611no—
200C2×Q8—611no—
201C2×D4—21no—
202C2×D4—21no—
203C2×D4—21no—
204C2×D4—612no—
205C2×D4—611no—
206C2×D4—611no—
207C2×D4—1222no—
208C2×D4—1224no—
209C2×D4—1224no—
210C2×D4—1224no—
211C2×D4—1222no—
212C2×D4—1228no—
213C2×D4—1228no—
214C2×D4—1221no—
215C2×D4—1224no—
216C2×D4C4×D6112yes—
217C2×D4D24412yes—
218C2×D4C22⋊D6112yes—
219C22×C4—612no—
220C22×C4—1222no—
221C22×C4—1221no—
222C22×C4C22×D6111yescharacteristic
223M16—21no—
224M16—21no—
225M16—1221no—
226M16—1221no—
227C2×C8—21no—
228C2×C8—1221no—
229C4⋊C4—21no—
230C4⋊C4—1221no—
231C22⋊C4—21no—
232C22⋊C4—1221no—
233C42—21no—
234C42—1221no—
235C23—22no—
236C23—22no—
237C23—22no—
238C23—82no—
239C23—612no—
240C23—1228no—
241C23—1221no—
242C23—4884no—
243C23D4×D6111yescharacteristic
244Q8—612no—
245Q8—1221no—
246Q8—1221no—
247Q8—1221no—
248D4—22no—
249D4—22no—
250D4—22no—
251D4—612no—
252D4—1228no—
253D4—1228no—
254D4—1222no—
255D4—1222no—
256D4—1222no—
257D4—1222no—
258D4—1221no—
259D4—1221no—
260D4—1221no—
261D4#1175819814yes—
262C2×C4—41no—
263C2×C4—612no—
264C2×C4—1228no—
265C2×C4—1221no—
266C2×C4—1222no—
267C2×C4—1222no—
268C2×C4—1222no—
269C2×C4—1222no—
270C2×C4—2441no—
271C2×C4C2×C4×D6111yescharacteristic
272C2×C4C2×D24411yescharacteristic
273C2×C4D4×D6111yescharacteristic
274C2×C4D4×D6111yescharacteristic
275C2×C4D4×D6111yescharacteristic
276C2×C4C2×C22⋊D6111yescharacteristic
277C8—41no—
278C8—2441no—
279C22—24no—
280C22—41no—
281C22—44no—
282C22—82no—
283C22—82no—
284C22—1222no—
285C22—1222no—
286C22—4888no—
287C22—2442no—
288C22—2442no—
289C22C22⋊C4×D6111yescharacteristic
290C22#1451974511yescharacteristic
291C22#1451974711yescharacteristic
292C4—81no—
293C4—1222no—
294C4—1222no—
295C4—4881no—
296C4C22⋊C4×D6111yescharacteristic
297C4C2×#1175819811yescharacteristic
298C4#1451974511yescharacteristic
299C4#1451974711yescharacteristic
300C2—21no—
301C2—21no—
302C2—21no—
303C2—44no—
304C2—2442no—
305C2—2442no—
306C2#1683961711yescharacteristic
subgroupG/H
centerC2#16839617
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#418C2
socleC2×C61#379
hypercenter#418D61
hypocenterC61#1795
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. #16839780C2semidirect
3. #16839778C2semidirect
4. #16839767C2semidirect
5. #16839744C2semidirect
6. #16839735C2semidirect
7. C61×#418C2semidirect
15. C2×#11758224C4semidirect
18. C2×D4×D61C4semidirect
19. C2×#11758194C22semidirect
20. #14519736C22semidirect
28. C2×M16×C61C22semidirect
29. #117×C61C22semidirect
158. #418D61semidirect
161. C61#1795semidirect
175. C2×M16C2×D61semidirect
177. #117C2×D61semidirect