Finite Group Databasebeta

← #21445774

Subgroups — #21445774

Order 7808.

620 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 101 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×#14519823C211yesmaximal, characteristic
2C2×#14519705C211yesmaximal, characteristic, complemented
3#16839764C211yesmaximal, characteristic, complemented
4#16839763C211yesmaximal, characteristic, complemented
5C2×#14519693C211yesmaximal, characteristic, complemented
6#16839664C211yesmaximal, characteristic, complemented
7C2×#104×C61C211yesmaximal, characteristic, complemented
8#14519823—22no—
9#14519823—22no—
10#14519823—22no—
11#14519823C414yescomplemented
12C2×#11758226—21no—
13C2×#11758222—21no—
14C2×#11758222C2211yescharacteristic
15C22×D244—21no—
16C22×D244C2211yescharacteristic
17C2×D4×D61—22no—
18C2×D4×D61—21no—
19C2×#11758194C2211yescharacteristic, complemented
20C2×C4⋊Dic61C2211yescharacteristic, complemented
21C2×#11758198—22no—
22#14519705—22no—
23#14519702—21no—
24#14519701—21no—
25#14519699—21no—
26#14519698—21no—
27#14519693—22no—
28C2×#41×C61C2211yescharacteristic
29C2×M16×C61C2211yescharacteristic, complemented
30C2×C42×C61C2211yescharacteristic, complemented
31#104×C61—22no—
32C23×D61—22no—
33C23×D61D412yes—
34#41×C61—21no—
35#41×C61—21no—
36#41×C61C2×C412yes—
37#41×C61D412yes—
38C2×Q8×C61D411yescharacteristic
39C2×D4×C61—21no—
40C2×D4×C61D411yescharacteristic
41C22×C4×C61—21no—
42C22×C4×C61—21no—
43C22×C4×C61C2311yescharacteristic
44C2×C22⋊D61—22no—
45C2×C22⋊D61—21no—
46C22×Dic61—21no—
47#11758226—24no—
48#11758226—24no—
49D4×D61—28no—
50D4×D61—24no—
51D4×D61—28no—
52D4×D61—24no—
53#11758222—24no—
54#11758222—21no—
55#11758222—21no—
56#11758222—24no—
57#11758222C2×C412yes—
58#11758222D412yes—
59C2×D244—22no—
60C2×D244—24no—
61C2×D244—21no—
62C2×D244—21no—
63C2×D244—21no—
64C2×D244—21no—
65C2×D244—24no—
66C2×D244C2×C412yes—
67C2×D244D412yes—
68C2×D244D411yescharacteristic
69C2×C4×D61—22no—
70C2×C4×D61—21no—
71C2×Dic122D411yescharacteristic
72M16×C61—21no—
73M16×C61—21no—
74C2×C8×C61—21no—
75C42×C61—21no—
76C42×C61—21no—
77#11758198—44no—
78C4⋊Dic61—21no—
79C4⋊Dic61—21no—
80#11758194—21no—
81#11758194—21no—
82C2×#92418—21no—
83C23×C61—21no—
84C23×C61C2×D411yescharacteristic
85C22×D61—22no—
86C22×D61—21no—
87C22×D61—28no—
88C22×D61—22no—
89C22×D61—42no—
90C22×D61—42no—
91C22×D61—82no—
92C22×D61—82no—
93C22×D61C22⋊C414yes—
94Q8×C61—21no—
95Q8×C61C22⋊C412yescomplemented
96D4×C61—22no—
97D4×C61—22no—
98D4×C61—21no—
99D4×C61C22⋊C412yescomplemented
100C2×C4×C61—21no—
101C2×C4×C61—22no—
102C2×C4×C61—22no—
103C2×C4×C61—22no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61C22×C411yescharacteristic
107C2×C4×C61C2×D411yescharacteristic
108C2×C4×C61C2×D411yescharacteristic
109C2×C4×C61C2×D411yescharacteristic
110C2×C4×C61C2×D411yescharacteristic
111C2×C4×C61C2×D411yescharacteristic
112C22⋊D61—28no—
113C22⋊D61—22no—
114C22⋊D61—22no—
115C2×Dic61—21no—
116C2×Dic61—42no—
117C2×Dic61—41no—
118D244—28no—
119D244—22no—
120D244—22no—
121D244—22no—
122D244—21no—
123D244—22no—
124D244C22⋊C412yescomplemented
125C4×D61—28no—
126C4×D61—22no—
127C4×D61—22no—
128Dic122—21no—
129Dic122C22⋊C412yescomplemented
130C8×C61—41no—
131#92418—41no—
132C22×C61—21no—
133C22×C61—21no—
134C22×C61—22no—
135C22×C61—41no—
136C22×C61—41no—
137C22×C61C2×C22⋊C411yescharacteristic
138C22×C61#12011yescharacteristic
139C22×C61#12011yescharacteristic
140C2×D61—24no—
141C2×D61—22no—
142C2×D61—42no—
143C2×D61—41no—
144C2×D61—42no—
145C2×D61—41no—
146C2×D61—44no—
147C2×D61—82no—
148C2×D61—88no—
149C4×C61—22no—
150C4×C61—42no—
151C4×C61C2×C22⋊C411yescharacteristic
152C4×C61C2×C22⋊C411yescharacteristic
153C4×C61#12011yescharacteristic
154C4×C61#12011yescharacteristic
155Dic61—22no—
156Dic61—81no—
157#1792—611nomaximal, Sylow
158C2×C61—21no—
159C2×C61—21no—
160C2×C61—42no—
161C2×C61#37911yescharacteristic
162C2×C61#45311yescharacteristic
163C2×C61#45511yescharacteristic
164D61—44no—
165D61—42no—
166C2×H(5,𝔽2)—611no—
167C2×#104—611no—
168C2×#104D6111yescharacteristic, complemented
169#417—611no—
170#417—611no—
171C2×#100—611no—
172#390—611no—
173C61#179211yescharacteristic, complemented, Sylow
174H(5,𝔽2)—614no—
175H(5,𝔽2)—1222no—
176H(5,𝔽2)—1222no—
177H(5,𝔽2)—1222no—
178C2×#41—611no—
179C2×#41—1221no—
180C2×#41—1221no—
181C2×#41C2×D6111yescharacteristic
182C22×D4—611no—
183C22×D4—1221no—
184C22×D4—1222no—
185C22×D4—1221no—
186C2×M16—611no—
187C2×M16C2×D6111yescharacteristic, complemented
188C2×C4⋊C4—611no—
189C2×C22⋊C4—1222no—
190C2×C42C2×D6111yescharacteristic, complemented
191#104—22no—
192#104—1222no—
193#103—1221no—
194#103—1221no—
195#102—1221no—
196#102—1221no—
197#100—1222no—
198C24—612no—
199C24—1222no—
200#41—21no—
201#41—21no—
202#41—612no—
203#41—612no—
204#41—1224no—
205#41—1224no—
206#41—1224no—
207#41—1224no—
208#41—1221no—
209#41—1221no—
210#41C4×D6112yes—
211#41C22⋊D6112yes—
212C2×Q8—611no—
213C2×Q8D24411yescharacteristic
214C2×D4—21no—
215C2×D4—612no—
216C2×D4—611no—
217C2×D4—612no—
218C2×D4—1224no—
219C2×D4—1222no—
220C2×D4—1224no—
221C2×D4—1228no—
222C2×D4—1228no—
223C2×D4—1224no—
224C2×D4—1222no—
225C2×D4—1221no—
226C2×D4—1224no—
227C2×D4—1221no—
228C2×D4—1221no—
229C2×D4—1221no—
230C2×D4—1221no—
231C2×D4D24411yescharacteristic
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—1222no—
235C22×C4—1221no—
236C22×C4—1221no—
237C22×C4C22×D6111yescharacteristic
238M16—21no—
239M16—21no—
240M16—1221no—
241M16—1221no—
242C2×C8—21no—
243C2×C8—1221no—
244C4⋊C4—1221no—
245C4⋊C4—1221no—
246C22⋊C4—2444no—
247C42—21no—
248C42—21no—
249C23—21no—
250C23—614no—
251C23—1228no—
252C23—1222no—
253C23—1221no—
254C23—1222no—
255C23—4882no—
256C23—4882no—
257C23—2442no—
258C23—2442no—
259C23D4×D6111yescharacteristic
260Q8—21no—
261Q8—612no—
262Q8—1221no—
263Q8#1175819812yescomplemented
264D4—22no—
265D4—22no—
266D4—21no—
267D4—612no—
268D4—1228no—
269D4—1228no—
270D4—1222no—
271D4—1222no—
272D4—1222no—
273D4—1222no—
274D4—1221no—
275D4—1222no—
276D4—1222no—
277D4#1175819812yescomplemented
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—1228no—
285C2×C4—1221no—
286C2×C4—1222no—
287C2×C4—1222no—
288C2×C4—2442no—
289C2×C4—2441no—
290C2×C4C2×C4×D6111yescharacteristic
291C2×C4C2×D24411yescharacteristic
292C2×C4D4×D6111yescharacteristic
293C2×C4D4×D6111yescharacteristic
294C2×C4D4×D6111yescharacteristic
295C2×C4C2×C22⋊D6111yescharacteristic
296C8—41no—
297C8—2441no—
298C22—21no—
299C22—21no—
300C22—22no—
301C22—41no—
302C22—41no—
303C22—1222no—
304C22—1224no—
305C22—4882no—
306C22—4888no—
307C22—2444no—
308C22—2441no—
309C22—2442no—
310C22—2441no—
311C22—2442no—
312C22C22⋊C4×D6111yescharacteristic
313C22#1451974511yescharacteristic
314C22#1451974711yescharacteristic
315C4—22no—
316C4—42no—
317C4—1222no—
318C4—4881no—
319C4C22⋊C4×D6111yescharacteristic
320C4C2×#1175819811yescharacteristic
321C4#1451974511yescharacteristic
322C4#1451974711yescharacteristic
323C2—21no—
324C2—21no—
325C2—42no—
326C2—2442no—
327C2—2444no—
328C2#1683961711yescharacteristic
329C2#1683993111yescharacteristic
330C2#1683994111yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#104×C61C2
socleC22×C61#120
hypercenterC2×#104D61
hypocenterC61#1792
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#14519705C2semidirect
3. #16839764C2semidirect
4. #16839763C2semidirect
5. C2×#14519693C2semidirect
6. #16839664C2semidirect
7. C2×#104×C61C2semidirect
11. #14519823C4semidirect
19. C2×#11758194C22semidirect
20. C2×C4⋊Dic61C22semidirect
29. C2×M16×C61C22semidirect
30. C2×C42×C61C22semidirect
95. Q8×C61C22⋊C4semidirect
99. D4×C61C22⋊C4semidirect
124. D244C22⋊C4semidirect
129. Dic122C22⋊C4semidirect
168. C2×#104D61semidirect
173. C61#1792semidirect
187. C2×M16C2×D61semidirect
190. C2×C42C2×D61semidirect
263. Q8#11758198semidirect
277. D4#11758198semidirect