Finite Group Databasebeta

← #22619734

Subgroups — #22619734

Order 9344.

376 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989143C211yesmaximal, characteristic
2C4×Q8×D73C211yesmaximal, characteristic
3#17988895C211yesmaximal, characteristic, complemented
4#17988894C211yesmaximal, characteristic, complemented
5#17988891C211yesmaximal, characteristic, complemented
6#17988881C211yesmaximal, characteristic, complemented
7#17988880C211yesmaximal, characteristic, complemented
8#17988871C211yesmaximal, characteristic, complemented
9#17988870C211yesmaximal, characteristic, complemented
10#17988628C211yesmaximal, characteristic
11#17988626C211yesmaximal, characteristic
12#17988609C211yesmaximal, characteristic
13#17988594C211yesmaximal, characteristic
14#17988594C211yesmaximal, characteristic
15#479×C73C211yesmaximal, characteristic, complemented
16C2×Q8×D73C2211yescharacteristic
17C2×#11924011C2211yescharacteristic
18C2×#11924011C2211yescharacteristic
19#14556590C2211yescharacteristic
20#14556590C2211yescharacteristic
21#14556583C2211yescharacteristic
22#14556569—21no—
23#14556569—21no—
24Q8×Dic73C2211yescharacteristic
25C4×Dic146—21no—
26C4×Dic146C2211yescharacteristic
27#14556556—21no—
28#14556556—21no—
29#14556556—21no—
30#14556556C2211yescharacteristic
31#14556549C2211yescharacteristic
32#14556549C2211yescharacteristic
33C4⋊C4×D73—21no—
34C4⋊C4×D73C2211yescharacteristic
35C42×D73—21no—
36C42×D73C2211yescharacteristic
37#14556525C2211yescharacteristic
38#14556524C2211yescharacteristic
39#14556524C2211yescharacteristic
40#14556523C2211yescharacteristic
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×D73D411yescharacteristic
68C2×C4×D73D411yescharacteristic
69C2×C4×D73C2311yescharacteristic
70#11924011—22no—
71#11924011—22no—
72C2×#10596831C2311yescharacteristic
73C2×#10596831C2311yescharacteristic
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#11924007—21no—
84#11924007—21no—
85#11924005—21no—
86#11924005—21no—
87C4×Dic73—21no—
88C4×Dic73—21no—
89C4×Dic73—21no—
90C4×Dic73—21no—
91C4×Dic73—21no—
92C4×Dic73D411yescharacteristic
93C4×Dic73D411yescharacteristic
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—22no—
125C4×D73—41no—
126C4×D73—42no—
127C4×D73C2×Q812yes—
128C4×D73#4112yes—
129Dic146—21no—
130Dic146—24no—
131Dic146—42no—
132Dic146—42no—
133Dic146C2×Q812yes—
134C8×C73—21no—
135C8×C73—21no—
136#10596831—21no—
137#10596831—21no—
138C22×C73C22×D411yescharacteristic
139C2×D73—21no—
140C2×D73—21no—
141C2×D73C22⋊Q812yes—
142C4×C73—22no—
143C4×C73—21no—
144C4×C73—21no—
145C4×C73—41no—
146C4×C73—41no—
147C4×C73—41no—
148C4×C73C22×Q811yescharacteristic
149C4×C73C2×#4111yescharacteristic
150Dic73—22no—
151Dic73—21no—
152Dic73—41no—
153Dic73—41no—
154Dic73—41no—
155Dic73C22⋊Q812yes—
156Dic73#13712yes—
157C2×C73C2×C22⋊Q811yescharacteristic
158C2×C73C2×#13711yescharacteristic
159C2×C73#57511yescharacteristic
160D73—22no—
161#3078—731nomaximal, Sylow
162C73#307811yescharacteristic, complemented, Sylow
163#533—731no—
164C2×C4×Q8—731no—
165#479—731no—
166#479—731no—
167#479—731no—
168#479D7311yescharacteristic, complemented
169#477—731no—
170#477—731no—
171#475—731no—
172#475—731no—
173#428—731no—
174#428—731no—
175#423—731no—
176#419—731no—
177#419—731no—
178C22×Q8—731no—
179C2×M16—731no—
180C2×M16—731no—
181C4⋊Q8—731no—
182C4⋊Q8—731no—
183#125—731no—
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×Q8—1461no—
193C4×Q8—1461no—
194C4×Q8C2×D7311yescharacteristic
195#117—731no—
196#117—731no—
197C2×C4⋊C4—731no—
198C2×C4⋊C4—1461no—
199C2×C42—731no—
200C2×C42—1461no—
201#107—731no—
202#107—731no—
203#107—731no—
204#107C2×D7311yescharacteristic
205#106—731no—
206#106—731no—
207#106—731no—
208#106C2×D7311yescharacteristic
209C4⋊C8—731no—
210C4⋊C8—731no—
211C4⋊C8—731no—
212C4⋊C8C2×D7311yescharacteristic
213#103—731no—
214#103—731no—
215#103—731no—
216#103—731no—
217#103—731no—
218#103—731no—
219#103C2×D7311yescharacteristic
220#103C2×D7311yescharacteristic
221C2×Q8—734no—
222C2×Q8—731no—
223C2×Q8—1461no—
224C2×Q8—1461no—
225C2×Q8—1461no—
226C2×Q8—1462no—
227C2×Q8C22×D7311yescharacteristic
228C22×C4—731no—
229C22×C4—731no—
230C22×C4—731no—
231C22×C4—1461no—
232C22×C4—1461no—
233M16—1462no—
234M16—1462no—
235C2×C8—731no—
236C2×C8—731no—
237C2×C8C22×D7311yescharacteristic
238C2×C8C22×D7311yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
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⋊C4C22×D7311yescharacteristic
254C4⋊C4C22×D7311yescharacteristic
255C4⋊C4C22×D7311yescharacteristic
256C22⋊C4—1461no—
257C22⋊C4—1461no—
258C42—21no—
259C42—731no—
260C42—731no—
261C42—731no—
262C42—1461no—
263C42—1461no—
264C42—1461no—
265C42—1461no—
266C42—1461no—
267C42C22×D7311yescharacteristic
268C23—731no—
269Q8—21no—
270Q8—2922no—
271Q8—2922no—
272Q8—732no—
273Q8—1464no—
274Q8—1461no—
275Q8Q8×D7312yes—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—2921no—
281C2×C4—2922no—
282C2×C4—731no—
283C2×C4—731no—
284C2×C4—732no—
285C2×C4—732no—
286C2×C4—731no—
287C2×C4—1462no—
288C2×C4—1464no—
289C2×C4—1461no—
290C2×C4—1461no—
291C2×C4—1461no—
292C2×C4—1461no—
293C2×C4D4×D7311yescharacteristic
294C2×C4D4×D7311yescharacteristic
295C2×C4C23×D7311yescharacteristic
296C8—21no—
297C8—21no—
298C8—1461no—
299C8—1461no—
300C22—732no—
301C22—1461no—
302C22—1461no—
303C22C2×D4×D7311yescharacteristic
304C4—21no—
305C4—21no—
306C4—22no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—2921no—
311C4—2921no—
312C4—2921no—
313C4—732no—
314C4—732no—
315C4—1461no—
316C4—1462no—
317C4C2×Q8×D7311yescharacteristic
318C4#41×D7311yescharacteristic
319C2—1462no—
320C2C22⋊Q8×D7311yescharacteristic
321C2#137×D7311yescharacteristic
322C2#1798938411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#479×C73C2
socleC22×C73C22×D4
hypercenter#479D73
hypocenterC73#3078
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. #17988895C2semidirect
4. #17988894C2semidirect
5. #17988891C2semidirect
6. #17988881C2semidirect
7. #17988880C2semidirect
8. #17988871C2semidirect
9. #17988870C2semidirect
15. #479×C73C2semidirect
64. Q8×D73Q8semidirect
162. C73#3078semidirect
168. #479D73semidirect