Finite Group Databasebeta

← #21445781

Subgroups — #21445781

Order 7808.

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

normal subgroups only

This group has 548 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
1#16840598C211yesmaximal, characteristic
2#16839778C211yesmaximal, characteristic, complemented
3#16839758C211yesmaximal, characteristic, complemented
4#16839756C211yesmaximal, characteristic, complemented
5#16839735C211yesmaximal, characteristic, complemented
6#16839730C211yesmaximal, characteristic, complemented
7C61×#421C211yesmaximal, characteristic, complemented
8#14519825—21no—
9#14519824—21no—
10#14519824C412yescomplemented
11#14519823—21no—
12#14519823C412yescomplemented
13#14519822—21no—
14#14519822—22no—
15C2×#11758222—22no—
16C2×#11758222C2211yescharacteristic
17C2×#11758222C2211yescharacteristic
18#41×D61—22no—
19#41×D61—22no—
20C22×#92418C2211yescharacteristic, complemented
21#14519736C2211yescharacteristic, complemented
22#14519703—22no—
23#14519701—21no—
24#14519700—21no—
25#14519698—21no—
26#14519697—21no—
27#14519691—22no—
28#14519689—22no—
29C2×#41×C61C2211yescharacteristic
30C2×M16×C61C2211yescharacteristic, complemented
31#117×C61C2211yescharacteristic, complemented
32#104×C61—22no—
33#41×C61—21no—
34#41×C61—21no—
35#41×C61C2×C412yes—
36#41×C61D412yes—
37C2×Q8×C61D411yescharacteristic
38C2×D4×C61—21no—
39C2×D4×C61D411yescharacteristic
40C22×C4×C61—21no—
41C22×C4×C61C2311yescharacteristic
42C2×C22⋊D61—24no—
43C2×C22⋊D61—21no—
44C2×C22⋊D61D412yes—
45#11758226—22no—
46#11758226—22no—
47Q8×D61—22no—
48Q8×D61—22no—
49#11758224—24no—
50#11758224—22no—
51#11758224—22no—
52#11758224—24no—
53D4×D61—24no—
54D4×D61—22no—
55D4×D61—24no—
56D4×D61—22no—
57#11758222—24no—
58#11758222—24no—
59#11758222—21no—
60#11758222—21no—
61#11758222—21no—
62#11758222—21no—
63#11758222—21no—
64#11758222—21no—
65#11758222—22no—
66#11758222—22no—
67#11758222C2×C412yes—
68#11758222D412yes—
69C2×D244—22no—
70C2×D244C2×C411yescharacteristic
71C2×D244D411yescharacteristic
72C2×C4×D61—24no—
73C2×C4×D61—21no—
74C2×C4×D61D412yes—
75C2×Dic122—22no—
76C2×Dic122C2×C411yescharacteristic
77C2×Dic122D411yescharacteristic
78M16×C61—21no—
79M16×C61—21no—
80C2×C8×C61—21no—
81C4⋊C4×C61—21no—
82C22⋊C4×C61—21no—
83C42×C61—21no—
84C22⋊Dic61—21no—
85C4⋊Dic61—21no—
86C4×Dic61—21no—
87C2×#92418—21no—
88C2×#92418—21no—
89C2×#92418—21no—
90C23×C61—21no—
91C23×C61C2×D411yescharacteristic
92C22×D61—24no—
93C22×D61—21no—
94C22×D61C22⋊C412yes—
95Q8×C61—21no—
96Q8×C61C22⋊C412yes—
97D4×C61—22no—
98D4×C61—22no—
99D4×C61—21no—
100D4×C61C22⋊C412yes—
101C2×C4×C61—21no—
102C2×C4×C61—22no—
103C2×C4×C61—22no—
104C2×C4×C61—41no—
105C2×C4×C61C22×C411yescharacteristic
106C2×C4×C61C2×D411yescharacteristic
107C2×C4×C61C2×D411yescharacteristic
108C2×C4×C61C2×D411yescharacteristic
109C2×C4×C61C2×D411yescharacteristic
110C2×C4×C61C2×D411yescharacteristic
111C22⋊D61—24no—
112C22⋊D61—24no—
113C22⋊D61—22no—
114C22⋊D61—22no—
115C22⋊D61—22no—
116C22⋊D61—22no—
117C2×Dic61—24no—
118C2×Dic61—21no—
119C2×Dic61—41no—
120C2×Dic61C22⋊C412yes—
121D244—24no—
122D244—21no—
123D244—21no—
124D244—21no—
125D244C22⋊C412yes—
126C4×D61—24no—
127C4×D61—24no—
128C4×D61—22no—
129C4×D61—22no—
130C4×D61—22no—
131C4×D61—22no—
132Dic122—24no—
133Dic122—21no—
134Dic122—21no—
135Dic122—21no—
136Dic122C22⋊C412yes—
137C8×C61—41no—
138#92418—41no—
139C22×C61—22no—
140C22×C61—41no—
141C22×C61—81no—
142C22×C61C2×C22⋊C411yescharacteristic
143C22×C61#12011yescharacteristic
144C22×C61#12011yescharacteristic
145C2×D61—22no—
146C2×D61—22no—
147C2×D61—42no—
148C2×D61—81no—
149C2×D61—84no—
150C4×C61—22no—
151C4×C61—81no—
152C4×C61C2×C22⋊C411yescharacteristic
153C4×C61C2×C22⋊C411yescharacteristic
154C4×C61#12011yescharacteristic
155C4×C61#12011yescharacteristic
156Dic61—22no—
157Dic61—22no—
158Dic61—81no—
159#1794—611nomaximal, Sylow
160C2×C61—21no—
161C2×C61—21no—
162C2×C61—21no—
163C2×C61—42no—
164C2×C61#37911yescharacteristic
165D61—42no—
166D61—42no—
167#585—611no—
168#421—611no—
169#421D6111yescharacteristic, complemented
170#416—611no—
171#416—611no—
172#410—611no—
173#408—611no—
174C61#179411yescharacteristic, complemented, Sylow
1752−1+4—612no—
1762−1+4—1221no—
1772−1+4—1221no—
178H(5,𝔽2)—612no—
179H(5,𝔽2)—1222no—
180H(5,𝔽2)—1221no—
181H(5,𝔽2)—1221no—
182C2×#41—611no—
183C2×#41—611no—
184C2×#41—1222no—
185C2×#41—1222no—
186C2×#41—1222no—
187C2×#41C2×D6111yescharacteristic
188C2×M16C2×D6111yescharacteristic, complemented
189C22×C8—611no—
190#117—611no—
191#117C2×D6111yescharacteristic, complemented
192#104—22no—
193#104—1222no—
194#103—1221no—
195#103—1221no—
196#102—1221no—
197#102—1221no—
198#99—1222no—
199C22⋊C8—1222no—
200#41—21no—
201#41—21no—
202#41—612no—
203#41—612no—
204#41—1222no—
205#41—1222no—
206#41—1224no—
207#41—1224no—
208#41—1224no—
209#41—1224no—
210#41—1222no—
211#41—1222no—
212#41—1222no—
213#41—1222no—
214#41—1221no—
215#41—1221no—
216#41—1221no—
217#41—1221no—
218#41—1221no—
219#41—1221no—
220#41C4×D6112yes—
221#41C22⋊D6112yes—
222C2×Q8—611no—
223C2×Q8—611no—
224C2×Q8—1222no—
225C2×Q8—1222no—
226C2×Q8—1222no—
227C2×Q8D24411yescharacteristic
228C2×D4—21no—
229C2×D4—612no—
230C2×D4—611no—
231C2×D4—611no—
232C2×D4—1222no—
233C2×D4—1224no—
234C2×D4—1224no—
235C2×D4—1222no—
236C2×D4—1224no—
237C2×D4—1221no—
238C2×D4—1222no—
239C2×D4D24411yescharacteristic
240C22×C4—21no—
241C22×C4—612no—
242C22×C4—1224no—
243C22×C4—1221no—
244C22×C4C22×D6111yescharacteristic
245M16—21no—
246M16—21no—
247C2×C8—21no—
248C2×C8—1221no—
249C2×C8—1221no—
250C2×C8—1221no—
251C4⋊C4—21no—
252C4⋊C4—1221no—
253C22⋊C4—21no—
254C22⋊C4—1221no—
255C42—21no—
256C42—1221no—
257C23—21no—
258C23—612no—
259C23—1224no—
260C23—1221no—
261C23D4×D6111yescharacteristic
262Q8—21no—
263Q8—612no—
264Q8—1224no—
265Q8—1221no—
266Q8—1221no—
267Q8—1221no—
268Q8#1175819812yes—
269D4—22no—
270D4—22no—
271D4—21no—
272D4—612no—
273D4—1224no—
274D4—1224no—
275D4—1224no—
276D4—1222no—
277D4—1222no—
278D4—1222no—
279D4—1222no—
280D4—1221no—
281D4—1221no—
282D4—1221no—
283D4#1175819812yes—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—612no—
289C2×C4—1224no—
290C2×C4—1224no—
291C2×C4—1224no—
292C2×C4—1221no—
293C2×C4—1222no—
294C2×C4—1222no—
295C2×C4—1222no—
296C2×C4—1222no—
297C2×C4—2441no—
298C2×C4C2×C4×D6111yescharacteristic
299C2×C4C2×D24411yescharacteristic
300C2×C4D4×D6111yescharacteristic
301C2×C4D4×D6111yescharacteristic
302C2×C4D4×D6111yescharacteristic
303C2×C4C2×C22⋊D6111yescharacteristic
304C8—41no—
305C8—2441no—
306C22—22no—
307C22—41no—
308C22—81no—
309C22—1222no—
310C22—1222no—
311C22—4881no—
312C22—4884no—
313C22—2442no—
314C22C22⋊C4×D6111yescharacteristic
315C22#1451974511yescharacteristic
316C22#1451974711yescharacteristic
317C4—22no—
318C4—81no—
319C4—1222no—
320C4—1222no—
321C4—4881no—
322C4C22⋊C4×D6111yescharacteristic
323C4C2×#1175819811yescharacteristic
324C4#1451974511yescharacteristic
325C4#1451974711yescharacteristic
326C2—21no—
327C2—21no—
328C2—21no—
329C2—42no—
330C2—2442no—
331C2—2442no—
332C2#1683961711yescharacteristic
subgroupG/H
centerC4#14519745
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#421C2
socleC2×C61#379
hypercenter#421D61
hypocenterC61#1794
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #16839778C2semidirect
3. #16839758C2semidirect
4. #16839756C2semidirect
5. #16839735C2semidirect
6. #16839730C2semidirect
7. C61×#421C2semidirect
10. #14519824C4semidirect
12. #14519823C4semidirect
20. C22×#92418C22semidirect
21. #14519736C22semidirect
30. C2×M16×C61C22semidirect
31. #117×C61C22semidirect
169. #421D61semidirect
174. C61#1794semidirect
188. C2×M16C2×D61semidirect
191. #117C2×D61semidirect