Finite Group Databasebeta

← #21445756

Subgroups — #21445756

Order 7808.

612 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C22×#11758224C211yesmaximal, characteristic
2C2×#14519702C211yesmaximal, characteristic, complemented
3C2×#14519700C211yesmaximal, characteristic, complemented
4C2×#14519698C211yesmaximal, characteristic, complemented
5C2×#14519689C211yesmaximal, characteristic, complemented
6#16839619C211yesmaximal, characteristic, complemented
7C2×#102×C61C211yesmaximal, characteristic, complemented
8C2×#11758224—22no—
9C2×#11758224—22no—
10C2×#11758224—22no—
11C2×#11758224—22no—
12C2×#11758224—22no—
13C2×#11758224C414yescomplemented
14C22×Dic122C2211yescharacteristic
15C22×C22⋊D61—21no—
16C23×Dic61—21no—
17C22×C4×D61C2211yescharacteristic
18C22×#92418C2211yescharacteristic
19C2×C4⋊Dic61C2211yescharacteristic
20C2×#11758198—21no—
21#14519702—22no—
22#14519700—22no—
23#14519698—22no—
24#14519689—22no—
25#14519684—21no—
26C22×D4×C61C2211yescharacteristic
27C22×C8×C61C2211yescharacteristic
28C2×C4⋊C4×C61C2211yescharacteristic
29#102×C61—22no—
30C24×C61—21no—
31C23×D61D411yescharacteristic
32C2×D4×C61—21no—
33C2×D4×C61—21no—
34C2×D4×C61—21no—
35C2×D4×C61C2×C412yes—
36C2×D4×C61D412yes—
37C2×D4×C61D412yes—
38C22×C4×C61—21no—
39C22×C4×C61C2311yescharacteristic
40C2×C22⋊D61—24no—
41C2×C22⋊D61—24no—
42C2×C22⋊D61—24no—
43C22×Dic61—24no—
44C22×Dic61—24no—
45C22×Dic61—21no—
46C22×Dic61—24no—
47C22×Dic61—21no—
48C22×Dic61D411yescharacteristic
49#11758224—28no—
50#11758224—28no—
51#11758224—28no—
52#11758224—28no—
53C2×C4×D61—21no—
54C2×C4×D61—21no—
55C2×C4×D61—21no—
56C2×C4×D61—21no—
57C2×C4×D61C2×C412yes—
58C2×C4×D61D412yes—
59C2×Dic122—21no—
60C2×Dic122—21no—
61C2×Dic122—21no—
62C2×Dic122C2×C412yes—
63C2×Dic122D412yes—
64C2×Dic122D412yes—
65C2×C8×C61—21no—
66C2×C8×C61—21no—
67C2×C8×C61—21no—
68C4⋊C4×C61—21no—
69C4⋊C4×C61—21no—
70#11758198—42no—
71C4⋊Dic61—21no—
72C4⋊Dic61—21no—
73C2×#92418—21no—
74C2×#92418—21no—
75C2×#92418—21no—
76C23×C61—22no—
77C23×C61—22no—
78C23×C61—22no—
79C23×C61—41no—
80C23×C61—41no—
81C23×C61—41no—
82C23×C61—41no—
83C23×C61C2×D411yescharacteristic
84C22×D61—21no—
85C22×D61—21no—
86C22×D61—21no—
87C22×D61—21no—
88C22×D61—21no—
89C22×D61—21no—
90C22×D61C22⋊C412yes—
91D4×C61—22no—
92D4×C61—22no—
93D4×C61—22no—
94D4×C61C22⋊C414yescomplemented
95C2×C4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61C22×C411yescharacteristic
99C2×C4×C61C2×D411yescharacteristic
100C2×C4×C61C2×D411yescharacteristic
101C2×C4×C61C2×D411yescharacteristic
102C2×C4×C61C2×D411yescharacteristic
103C2×C4×C61C2×D411yescharacteristic
104C22⋊D61—216no—
105C2×Dic61—216no—
106C2×Dic61—22no—
107C2×Dic61—22no—
108C2×Dic61—22no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61—41no—
114C2×Dic61C22⋊C412yes—
115C4×D61—22no—
116C4×D61—22no—
117C4×D61—22no—
118C4×D61—22no—
119Dic122—22no—
120Dic122—22no—
121Dic122—22no—
122Dic122C22⋊C414yescomplemented
123C8×C61—41no—
124#92418—41no—
125C22×C61—24no—
126C22×C61—42no—
127C22×C61—42no—
128C22×C61—42no—
129C22×C61—42no—
130C22×C61—42no—
131C22×C61—42no—
132C22×C61C2×C22⋊C411yescharacteristic
133C22×C61#12011yescharacteristic
134C22×C61#12011yescharacteristic
135C22×C61#13511yescharacteristic
136C22×C61#13511yescharacteristic
137C22×C61AGL(1,ℤ/8)11yescharacteristic
138C22×C61#13711yescharacteristic
139C2×D61—22no—
140C2×D61—22no—
141C2×D61—22no—
142C2×D61—41no—
143C2×D61—41no—
144C2×D61—41no—
145C2×D61—41no—
146C4×C61—81no—
147C4×C61C2×C22⋊C411yescharacteristic
148C4×C61C2×C22⋊C411yescharacteristic
149C4×C61#12011yescharacteristic
150C4×C61#12011yescharacteristic
151Dic61—24no—
152Dic61—22no—
153Dic61—81no—
154#1788—611nomaximal, Sylow
155C2×C61—44no—
156C2×C61#37911yescharacteristic
157C2×C61#41611yescharacteristic
158C2×C61#41711yescharacteristic
159C2×C61#44911yescharacteristic
160C2×C61#44911yescharacteristic
161C2×C61#45211yescharacteristic
162C2×C61#45211yescharacteristic
163D61—42no—
164C22×#41—611no—
165C2×#103—611no—
166C2×#103—611no—
167C2×#102—611no—
168C2×#102D6111yescharacteristic, complemented
169C2×C22⋊C8—611no—
170#380—611no—
171C61#178811yescharacteristic, complemented, Sylow
172C2×#41—614no—
173C2×#41—1222no—
174C2×#41—1222no—
175C2×#41—1222no—
176C2×#41—1222no—
177C2×#41—1222no—
178C22×Q8—611no—
179C22×D4—1221no—
180C22×D4C2×D6111yescharacteristic
181C23×C4—611no—
182C23×C4—1221no—
183C22×C8—611no—
184C22×C8C2×D6111yescharacteristic
185C2×C4⋊C4—611no—
186C2×C4⋊C4C2×D6111yescharacteristic
187C2×C22⋊C4—1221no—
188#103—1222no—
189#103—1222no—
190#102—22no—
191#102—1222no—
192C22⋊C8—1222no—
193#95—1221no—
194C24—21no—
195C24—611no—
196#41—1228no—
197#41—1228no—
198#41—1228no—
199#41—1228no—
200C2×Q8—612no—
201C2×Q8—612no—
202C2×Q8—612no—
203C2×Q8—1221no—
204C2×Q8—1221no—
205C2×Q8—1221no—
206C2×D4—21no—
207C2×D4—21no—
208C2×D4—21no—
209C2×D4—1224no—
210C2×D4—1224no—
211C2×D4—1224no—
212C2×D4C4×D6112yes—
213C2×D4D24412yes—
214C2×D4C22⋊D6112yes—
215C22×C4—21no—
216C22×C4—611no—
217C22×C4—612no—
218C22×C4—612no—
219C22×C4—1224no—
220C22×C4—1224no—
221C22×C4—1224no—
222C22×C4—1221no—
223C22×C4—1221no—
224C22×C4—1221no—
225C22×C4—1221no—
226C22×C4—1221no—
227C22×C4—1221no—
228C22×C4C22×D6111yescharacteristic
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—1221no—
233C2×C8—1221no—
234C2×C8—1221no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—1221no—
238C4⋊C4—1221no—
239C22⋊C4—2442no—
240C23—22no—
241C23—22no—
242C23—22no—
243C23—41no—
244C23—41no—
245C23—41no—
246C23—41no—
247C23—612no—
248C23—1221no—
249C23—1221no—
250C23—1221no—
251C23—1221no—
252C23—1221no—
253C23—1221no—
254C23D4×D6111yescharacteristic
255Q8—614no—
256Q8—1222no—
257Q8—1222no—
258Q8—1222no—
259D4—22no—
260D4—22no—
261D4—22no—
262D4—12216no—
263D4#1175819814yescomplemented
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—612no—
268C2×C4—12216no—
269C2×C4—1222no—
270C2×C4—1221no—
271C2×C4—1222no—
272C2×C4—1221no—
273C2×C4—1222no—
274C2×C4—1222no—
275C2×C4—1222no—
276C2×C4—1222no—
277C2×C4—1222no—
278C2×C4—2441no—
279C2×C4—2441no—
280C2×C4—2441no—
281C2×C4C2×C4×D6111yescharacteristic
282C2×C4C2×D24411yescharacteristic
283C2×C4D4×D6111yescharacteristic
284C2×C4D4×D6111yescharacteristic
285C2×C4D4×D6111yescharacteristic
286C2×C4C2×C22⋊D6111yescharacteristic
287C8—41no—
288C8—2441no—
289C22—24no—
290C22—42no—
291C22—42no—
292C22—42no—
293C22—42no—
294C22—42no—
295C22—42no—
296C22—1222no—
297C22—1222no—
298C22—1222no—
299C22—2441no—
300C22—2441no—
301C22—2441no—
302C22—2441no—
303C22C22⋊C4×D6111yescharacteristic
304C22#1451974511yescharacteristic
305C22#1451974711yescharacteristic
306C22#1451979611yescharacteristic
307C22#1451979811yescharacteristic
308C22#1451980111yescharacteristic
309C22#1451980611yescharacteristic
310C4—81no—
311C4—1222no—
312C4—1224no—
313C4—4881no—
314C4C22⋊C4×D6111yescharacteristic
315C4C2×#1175819811yescharacteristic
316C4#1451974511yescharacteristic
317C4#1451974711yescharacteristic
318C2—44no—
319C2—2442no—
320C2#1683961711yescharacteristic
321C2#1683975511yescharacteristic
322C2#1683976011yescharacteristic
323C2#1683990411yescharacteristic
324C2#1683990811yescharacteristic
325C2#1683992111yescharacteristic
326C2#1683992511yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#102×C61C2
socleC23×C61C2×D4
hypercenterC2×#102D61
hypocenterC61#1788
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×#14519702C2semidirect
3. C2×#14519700C2semidirect
4. C2×#14519698C2semidirect
5. C2×#14519689C2semidirect
6. #16839619C2semidirect
7. C2×#102×C61C2semidirect
13. C2×#11758224C4semidirect
94. D4×C61C22⋊C4semidirect
122. Dic122C22⋊C4semidirect
168. C2×#102D61semidirect
171. C61#1788semidirect
263. D4#11758198semidirect