Finite Group Databasebeta

← #22622709

Subgroups — #22622709

Order 9344.

340 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989312C211yesmaximal, characteristic, complemented
2#17989293C211yesmaximal, characteristic
3#17988954C211yesmaximal, characteristic, complemented
4#17988936C211yesmaximal, characteristic, complemented
5#17988896C211yesmaximal, characteristic, complemented
6#17988891C211yesmaximal, characteristic, complemented
7#17988880C211yesmaximal, characteristic, complemented
8#17988791C211yesmaximal, characteristic
9#17988791C211yesmaximal, characteristic
10#17988789C211yesmaximal, characteristic
11#17988715C211yesmaximal, characteristic, complemented
12#17988690C211yesmaximal, characteristic
13#17988689C211yesmaximal, characteristic
14#17988672C211yesmaximal, characteristic
15#491×C73C211yesmaximal, characteristic, complemented
16C2×#11924017C2211yescharacteristic
17C2×#11924015C2211yescharacteristic
18C2×#11924015C2211yescharacteristic
19#14556590C2211yescharacteristic
20#14556589C2211yescharacteristic
21#14556589C2211yescharacteristic
22#14556582—21no—
23#14556582C2211yescharacteristic
24#14556581—21no—
25#14556581—21no—
26#14556571—21no—
27#14556569—21no—
28#14556569—21no—
29Q8×Dic73C2211yescharacteristic
30Q8×Dic73C2211yescharacteristic
31C4×Dic146C2211yescharacteristic
32C4×Dic146C2211yescharacteristic
33#14556556—21no—
34C4×D292C2211yescharacteristic
35#14556553C2211yescharacteristic
36#14556553C2211yescharacteristic
37C4⋊C4×D73—21no—
38#14556525C2211yescharacteristic
39#14556524C2211yescharacteristic
40#14556522C2211yescharacteristic
41C4⋊#10596831C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556520C2211yescharacteristic
44#14556516C2211yescharacteristic
45#14556515C2211yescharacteristic
46#14556515C2211yescharacteristic
47#14556514C2211yescharacteristic
48#14556514C2211yescharacteristic
49#14556513C2211yescharacteristic
50#14556501C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C4⋊Q8×C73C2211yescharacteristic
53#125×C73C2211yescharacteristic
54#103×C73C2211yescharacteristic
55#103×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58#97×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146D411yescharacteristic
61C2×Dic146C2311yescharacteristic
62C2×D292C2311yescharacteristic
63C2×C4×D73—21no—
64C2×C4×D73—21no—
65C2×C4×D73—21no—
66#11924017—22no—
67#11924015—22no—
68#11924015—22no—
69C2×#10596831C2311yescharacteristic
70C2×#10596831C2311yescharacteristic
71C4⋊Dic73—21no—
72C4⋊Dic73—21no—
73C4⋊Dic73—21no—
74C4⋊Dic73D411yescharacteristic
75C4⋊Dic73C2311yescharacteristic
76C4⋊Dic73C2311yescharacteristic
77#11924007—21no—
78#11924007—21no—
79#11924007—21no—
80#11924007—21no—
81#11924007—21no—
82#11924007—21no—
83#11924007—21no—
84#11924007D411yescharacteristic
85#11924007D411yescharacteristic
86#11924005—21no—
87#11924005—21no—
88#11924005—21no—
89C4×Dic73—21no—
90C4×Dic73—21no—
91C4×Dic73—21no—
92C4×Dic73C2311yescharacteristic
93C4×Dic73C2311yescharacteristic
94C2×Q8×C73C2311yescharacteristic
95C2×Q8×C73C2311yescharacteristic
96C2×C8×C73C2311yescharacteristic
97C2×C8×C73C2311yescharacteristic
98C4⋊C4×C73—21no—
99C4⋊C4×C73—21no—
100C4⋊C4×C73—21no—
101C4⋊C4×C73—21no—
102C4⋊C4×C73C2311yescharacteristic
103C4⋊C4×C73C2311yescharacteristic
104C42×C73C2311yescharacteristic
105C22×D73—21no—
106Q8×C73—21no—
107Q8×C73—21no—
108Q8×C73—21no—
109Q8×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73C2×D411yescharacteristic
115C2×C4×C73C2×D411yescharacteristic
116C2×C4×C73C2411yescharacteristic
117C2×Dic73—21no—
118C2×Dic73—21no—
119C2×Dic73—21no—
120C2×Dic73C2×D411yescharacteristic
121C2×Dic73C2×D411yescharacteristic
122C2×Dic73C2×D411yescharacteristic
123C2×Dic73C2×D411yescharacteristic
124D292—21no—
125D292#4112yes—
126C4×D73—42no—
127C4×D73—81no—
128C4×D73—81no—
129Dic146—22no—
130Dic146—21no—
131Dic146—21no—
132Dic146—81no—
133C8×C73—21no—
134C8×C73—21no—
135#10596831—21no—
136#10596831—21no—
137C22×C73C22×D411yescharacteristic
138C2×D73—22no—
139C2×D73—41no—
140C2×D73—41no—
141C4×C73—21no—
142C4×C73—21no—
143C4×C73—41no—
144C4×C73—41no—
145C4×C73—41no—
146C4×C73—41no—
147C4×C73C2×#4111yescharacteristic
148C4×C732−1+411yescharacteristic
149Dic73—21no—
150Dic73—21no—
151Dic73—21no—
152Dic73—41no—
153Dic73—41no—
154Dic73—41no—
155Dic73#13712yes—
156C2×C73#54811yescharacteristic
157C2×C73C2×#13711yescharacteristic
158C2×C73#57711yescharacteristic
159D73—42no—
160#3372—731nomaximal, Sylow
161C73#337211yescharacteristic, complemented, Sylow
162#557—731no—
163#554—731no—
164#491—731no—
165#491D7311yescharacteristic, complemented
166#487—731no—
167#479—731no—
168#479—731no—
169#477—731no—
170#461—731no—
171#461—731no—
172#461—731no—
173#446—731no—
174#440—731no—
175#440—731no—
176C4×SD16—731no—
177C2×SD16—731no—
178C2×SD16—731no—
179C2×SD16—731no—
180C4⋊Q8—731no—
181C4⋊Q8—731no—
182C4⋊Q8—731no—
183C4⋊Q8C2×D7311yescharacteristic
184#125—731no—
185#125—1461no—
186#125—1461no—
187#125—1461no—
188#125C2×D7311yescharacteristic
189C22⋊Q8—1461no—
190C22⋊Q8—1461no—
191C22⋊Q8—1461no—
192C4×Q8—731no—
193C4×Q8—731no—
194C4×Q8—731no—
195C4×Q8—731no—
196C4×Q8—1461no—
197C4×D4—731no—
198C4×D4—731no—
199C4×D4—731no—
200C2×C4⋊C4—1461no—
201#107—731no—
202#107—731no—
203#106—731no—
204C4⋊C8—731no—
205C4⋊C8—731no—
206C4⋊C8—731no—
207#103—731no—
208#103—731no—
209#103—731no—
210#103—731no—
211#103—731no—
212#103C2×D7311yescharacteristic
213#103C2×D7311yescharacteristic
214#103C2×D7311yescharacteristic
215#103C2×D7311yescharacteristic
216#102—731no—
217#97—731no—
218#97C2×D7311yescharacteristic
219C4×C8—731no—
220C2×Q8—731no—
221C2×Q8—731no—
222C2×Q8—1461no—
223C2×Q8C22×D7311yescharacteristic
224C2×Q8C22×D7311yescharacteristic
225C2×D4—731no—
226C22×C4—1461no—
227C22×C4—1461no—
228C22×C4—1461no—
229SD16—1462no—
230SD16—1462no—
231SD16—1462no—
232C2×C8—731no—
233C2×C8—731no—
234C2×C8C22×D7311yescharacteristic
235C2×C8C22×D7311yescharacteristic
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—731no—
241C4⋊C4—731no—
242C4⋊C4—731no—
243C4⋊C4—731no—
244C4⋊C4—731no—
245C4⋊C4—1461no—
246C4⋊C4—1461no—
247C4⋊C4—1461no—
248C4⋊C4—1461no—
249C4⋊C4—1461no—
250C4⋊C4—1461no—
251C4⋊C4—1461no—
252C4⋊C4—1461no—
253C4⋊C4—1461no—
254C4⋊C4—1461no—
255C4⋊C4C22×D7311yescharacteristic
256C4⋊C4C22×D7311yescharacteristic
257C22⋊C4—1461no—
258C22⋊C4—1461no—
259C22⋊C4—1461no—
260C42—731no—
261C42—731no—
262C42—1461no—
263C42—1461no—
264C42—1461no—
265C42C22×D7311yescharacteristic
266C23—1461no—
267Q8—21no—
268Q8—21no—
269Q8—21no—
270Q8—21no—
271Q8—5841no—
272Q8—1462no—
273Q8—1461no—
274Q8—1461no—
275D4—732no—
276D4—1461no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—2922no—
282C2×C4—5841no—
283C2×C4—5841no—
284C2×C4—731no—
285C2×C4—731no—
286C2×C4—731no—
287C2×C4—731no—
288C2×C4—1461no—
289C2×C4—1461no—
290C2×C4—1461no—
291C2×C4D4×D7311yescharacteristic
292C2×C4D4×D7311yescharacteristic
293C2×C4C23×D7311yescharacteristic
294C8—21no—
295C8—21no—
296C8—1461no—
297C8—1461no—
298C22—2921no—
299C22—2921no—
300C22—1462no—
301C22C2×D4×D7311yescharacteristic
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—2921no—
309C4—2921no—
310C4—2921no—
311C4—732no—
312C4—1461no—
313C4—1461no—
314C4—1461no—
315C4#41×D7311yescharacteristic
316C4#1455663811yescharacteristic
317C2—2922no—
318C2#1798924511yescharacteristic
319C2#137×D7311yescharacteristic
320C2#1798939611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#491×C73C2
socleC22×C73C22×D4
hypercenter#491D73
hypocenterC73#3372
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
1. #17989312C2semidirect
3. #17988954C2semidirect
4. #17988936C2semidirect
5. #17988896C2semidirect
6. #17988891C2semidirect
7. #17988880C2semidirect
11. #17988715C2semidirect
15. #491×C73C2semidirect
161. C73#3372semidirect
165. #491D73semidirect