Finite Group Databasebeta

← #22619772

Subgroups — #22619772

Order 9344.

362 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989217C211yesmaximal, characteristic
2#17989063C211yesmaximal, characteristic
3#17988896C211yesmaximal, characteristic, complemented
4#17988893C211yesmaximal, characteristic, complemented
5#17988891C211yesmaximal, characteristic, complemented
6#17988883C211yesmaximal, characteristic, complemented
7#17988880C211yesmaximal, characteristic, complemented
8#17988872C211yesmaximal, characteristic, complemented
9#17988871C211yesmaximal, characteristic, complemented
10#17988626C211yesmaximal, characteristic
11#17988624C211yesmaximal, characteristic
12#17988612C211yesmaximal, characteristic
13#17988594C211yesmaximal, characteristic
14#103×D73C211yesmaximal, characteristic
15#479×C73C211yesmaximal, characteristic, complemented
16C2×Q8×D73C2211yescharacteristic
17C2×#11924011C2211yescharacteristic
18C2×C8×D73C2211yescharacteristic
19#14556591C2211yescharacteristic
20#14556590—21no—
21#14556590C2211yescharacteristic
22#14556582C2211yescharacteristic
23#14556581—21no—
24#14556571—21no—
25#14556569—21no—
26Q8×Dic73C2211yescharacteristic
27C4×Dic146—21no—
28C4×Dic146C2211yescharacteristic
29#14556556—21no—
30#14556556C2211yescharacteristic
31#14556549—21no—
32#14556549C2211yescharacteristic
33#14556549C2211yescharacteristic
34#14556548—21no—
35#14556548C2211yescharacteristic
36C4⋊C4×D73C2211yescharacteristic
37#14556525C2211yescharacteristic
38#14556525C2211yescharacteristic
39#14556524C2211yescharacteristic
40#14556522C2211yescharacteristic
41#14556522C2211yescharacteristic
42#14556522C2211yescharacteristic
43C4⋊#10596831C2211yescharacteristic
44#14556520C2211yescharacteristic
45#14556520C2211yescharacteristic
46#14556516C2211yescharacteristic
47#14556516C2211yescharacteristic
48#14556515C2211yescharacteristic
49#14556515C2211yescharacteristic
50#14556514C2211yescharacteristic
51#14556514C2211yescharacteristic
52#125×C73C2211yescharacteristic
53C4×Q8×C73C2211yescharacteristic
54#107×C73C2211yescharacteristic
55#106×C73C2211yescharacteristic
56C4⋊C8×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58#103×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146—21no—
61C2×Dic146—21no—
62C2×Dic146C2311yescharacteristic
63Q8×D73—22no—
64Q8×D73Q814yescomplemented
65C2×C4×D73—21no—
66C2×C4×D73—21no—
67C2×C4×D73C2311yescharacteristic
68#11924011—22no—
69C2×#10596831C2311yescharacteristic
70C2×#10596831C2311yescharacteristic
71C8×D73—22no—
72C4⋊Dic73—21no—
73C4⋊Dic73—21no—
74C4⋊Dic73—21no—
75C4⋊Dic73C2311yescharacteristic
76C4⋊Dic73C2311yescharacteristic
77C4⋊Dic73C2311yescharacteristic
78#11924007—21no—
79#11924007—21no—
80#11924007—21no—
81#11924007—21no—
82#11924007—21no—
83#11924007D411yescharacteristic
84#11924007D411yescharacteristic
85#11924005—21no—
86#11924005—21no—
87#11924005D411yescharacteristic
88#11924005D411yescharacteristic
89C4×Dic73—21no—
90C4×Dic73—21no—
91C4×Dic73—21no—
92C4×Dic73—21no—
93C4×Dic73—21no—
94C4×Dic73C2311yescharacteristic
95C2×Q8×C73C2311yescharacteristic
96C2×C8×C73C2311yescharacteristic
97C2×C8×C73C2311yescharacteristic
98C4⋊C4×C73—21no—
99C4⋊C4×C73—21no—
100C4⋊C4×C73—21no—
101C4⋊C4×C73C2311yescharacteristic
102C4⋊C4×C73C2311yescharacteristic
103C4⋊C4×C73C2311yescharacteristic
104C42×C73—21no—
105C42×C73C2311yescharacteristic
106C22×D73C2×D411yescharacteristic
107Q8×C73—21no—
108Q8×C73C2×Q812yes—
109C2×C4×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73C2×D411yescharacteristic
114C2×C4×C73C2×D411yescharacteristic
115C2×C4×C73C2411yescharacteristic
116C2×Dic73—21no—
117C2×Dic73—21no—
118C2×Dic73—21no—
119C2×Dic73—21no—
120C2×Dic73C2×D411yescharacteristic
121C2×Dic73C2×D411yescharacteristic
122C2×Dic73C2×D411yescharacteristic
123C4×D73—24no—
124C4×D73—81no—
125C4×D73C2×Q812yes—
126C4×D73#4112yes—
127Dic146—21no—
128Dic146—24no—
129Dic146—81no—
130Dic146—81no—
131Dic146C2×Q812yes—
132C8×C73—21no—
133C8×C73—21no—
134#10596831—21no—
135#10596831—21no—
136C22×C73C22×D411yescharacteristic
137C2×D73—21no—
138C2×D73—21no—
139C2×D73C22⋊Q812yes—
140C4×C73—22no—
141C4×C73—21no—
142C4×C73—21no—
143C4×C73—41no—
144C4×C73—41no—
145C4×C73—41no—
146C4×C73C22×Q811yescharacteristic
147C4×C73C2×#4111yescharacteristic
148Dic73—22no—
149Dic73—21no—
150Dic73—21no—
151Dic73—41no—
152Dic73—41no—
153Dic73—41no—
154Dic73C22⋊Q812yes—
155C2×C73C2×C22⋊Q811yescharacteristic
156C2×C73#57711yescharacteristic
157C2×C73#57811yescharacteristic
158D73—22no—
159#3082—731nomaximal, Sylow
160C73#308211yescharacteristic, complemented, Sylow
161#544—731no—
162#519—731no—
163#479—731no—
164#479—731no—
165#479—731no—
166#479D7311yescharacteristic, complemented
167#477—731no—
168#477—731no—
169#475—731no—
170#475—731no—
171#428—731no—
172#427—731no—
173#424—731no—
174#419—731no—
175C2×#103—731no—
176C22×Q8—731no—
177C2×M16—731no—
178C22×C8—731no—
179C4⋊Q8—731no—
180C4⋊Q8—731no—
181C4⋊Q8—1461no—
182#125—731no—
183#125—1461no—
184#125C2×D7311yescharacteristic
185C22⋊Q8—1461no—
186C22⋊Q8—1461no—
187C4×Q8—731no—
188C4×Q8—731no—
189C4×Q8—731no—
190C4×Q8—1461no—
191C4×Q8—1461no—
192C4×Q8C2×D7311yescharacteristic
193#117—731no—
194#117—731no—
195#117—731no—
196#117—1461no—
197#117—1461no—
198C2×C4⋊C4—731no—
199#107—731no—
200#107—731no—
201#107—731no—
202#107C2×D7311yescharacteristic
203#106—731no—
204#106—731no—
205#106—731no—
206#106C2×D7311yescharacteristic
207C4⋊C8—731no—
208C4⋊C8—731no—
209C4⋊C8—731no—
210C4⋊C8C2×D7311yescharacteristic
211#103—731no—
212#103—731no—
213#103—731no—
214#103—731no—
215#103—731no—
216#103—731no—
217#103C2×D7311yescharacteristic
218#103C2×D7311yescharacteristic
219C2×Q8—734no—
220C2×Q8—731no—
221C2×Q8—1461no—
222C2×Q8—1461no—
223C2×Q8—1462no—
224C2×Q8—1461no—
225C2×Q8C22×D7311yescharacteristic
226C22×C4—731no—
227C22×C4—1461no—
228C22×C4—1461no—
229M16—1462no—
230C2×C8—731no—
231C2×C8—731no—
232C2×C8—1462no—
233C2×C8C22×D7311yescharacteristic
234C2×C8C22×D7311yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—731no—
239C4⋊C4—731no—
240C4⋊C4—731no—
241C4⋊C4—731no—
242C4⋊C4—731no—
243C4⋊C4—1461no—
244C4⋊C4—1461no—
245C4⋊C4—1461no—
246C4⋊C4—1461no—
247C4⋊C4—1461no—
248C4⋊C4—1461no—
249C4⋊C4—1461no—
250C4⋊C4—1461no—
251C4⋊C4C22×D7311yescharacteristic
252C4⋊C4C22×D7311yescharacteristic
253C4⋊C4C22×D7311yescharacteristic
254C22⋊C4—731no—
255C22⋊C4—731no—
256C22⋊C4—1461no—
257C22⋊C4—1461no—
258C42—21no—
259C42—731no—
260C42—1461no—
261C42—1461no—
262C42—1461no—
263C42—1461no—
264C42—1461no—
265C42C22×D7311yescharacteristic
266C23—731no—
267Q8—21no—
268Q8—5841no—
269Q8—5841no—
270Q8—732no—
271Q8—1464no—
272Q8—1461no—
273Q8Q8×D7312yes—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—5841no—
279C2×C4—731no—
280C2×C4—732no—
281C2×C4—732no—
282C2×C4—731no—
283C2×C4—731no—
284C2×C4—1464no—
285C2×C4—1461no—
286C2×C4—1461no—
287C2×C4—1461no—
288C2×C4—1461no—
289C2×C4D4×D7311yescharacteristic
290C2×C4D4×D7311yescharacteristic
291C2×C4C23×D7311yescharacteristic
292C8—21no—
293C8—21no—
294C8—1461no—
295C8—1461no—
296C22—732no—
297C22—1461no—
298C22—1461no—
299C22C2×D4×D7311yescharacteristic
300C4—21no—
301C4—21no—
302C4—22no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—2921no—
307C4—2921no—
308C4—2921no—
309C4—732no—
310C4—1461no—
311C4—1461no—
312C4—1462no—
313C4C2×Q8×D7311yescharacteristic
314C4#41×D7311yescharacteristic
315C2—1462no—
316C2C22⋊Q8×D7311yescharacteristic
317C2#1798939611yescharacteristic
318C2#1798940111yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#479×C73C2
socleC22×C73C22×D4
hypercenter#479D73
hypocenterC73#3082
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
3. #17988896C2semidirect
4. #17988893C2semidirect
5. #17988891C2semidirect
6. #17988883C2semidirect
7. #17988880C2semidirect
8. #17988872C2semidirect
9. #17988871C2semidirect
15. #479×C73C2semidirect
64. Q8×D73Q8semidirect
160. C73#3082semidirect
166. #479D73semidirect