Finite Group Databasebeta

← #22620160

Subgroups — #22620160

Order 9344.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989208C211yesmaximal, characteristic
2#17988928C211yesmaximal, characteristic, complemented
3#17988911C211yesmaximal, characteristic
4#17988882C211yesmaximal, characteristic, complemented
5#17988872C211yesmaximal, characteristic, complemented
6#17988809C211yesmaximal, characteristic, complemented
7#17988809C211yesmaximal, characteristic, complemented
8#17988743C211yesmaximal, characteristic, complemented
9#17988726C211yesmaximal, characteristic
10#17988692C211yesmaximal, characteristic, complemented
11#17988685C211yesmaximal, characteristic, complemented
12C4×#11924018C211yesmaximal, characteristic, complemented
13C4×#11924015C211yesmaximal, characteristic, complemented
14#17988648C211yesmaximal, characteristic, complemented
15#519×C73C211yesmaximal, characteristic, complemented
16C2×#11924018C2211yescharacteristic
17C2×#11924018C2211yescharacteristic
18C2×#11924015C2211yescharacteristic
19C2×#11924015C2211yescharacteristic
20#14556591C2211yescharacteristic
21#14556586—21no—
22#14556579C2211yescharacteristic
23#14556577—21no—
24#14556573—21no—
25#14556570C2211yescharacteristic
26#14556569—21no—
27#14556565C2211yescharacteristic
28C4×Dic146C2211yescharacteristic
29C4×D292C2211yescharacteristic
30#14556524C2211yescharacteristic
31#14556524C2211yescharacteristic
32#14556522C2211yescharacteristic
33#14556522C2211yescharacteristic
34C4⋊#10596831C2211yescharacteristic
35C4⋊#10596831C2211yescharacteristic
36#14556515C2211yescharacteristic
37#14556515C2211yescharacteristic
38#14556515C2211yescharacteristic
39#14556515C2211yescharacteristic
40#14556514C2211yescharacteristic
41#14556514C2211yescharacteristic
42#14556511C2211yescharacteristic
43#14556511C2211yescharacteristic
44C22⋊#10596831C2211yescharacteristic
45C22⋊#10596831C2211yescharacteristic
46#14556502C2211yescharacteristic
47C4×#10596831C2211yescharacteristic
48C22×Q8×C73C2211yescharacteristic
49C4×Q8×C73—21no—
50C4×Q8×C73—21no—
51C4×Q8×C73C2211yescharacteristic
52C4×Q8×C73C2211yescharacteristic
53C4×Q8×C73C2211yescharacteristic
54C4×Q8×C73C2211yescharacteristic
55#117×C73—21no—
56#117×C73—21no—
57#117×C73C2211yescharacteristic
58#117×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146C2311yescharacteristic
61C2×D292C2311yescharacteristic
62C2×C22⋊D73—21no—
63C2×C4×D73—21no—
64#11924018—22no—
65#11924018—22no—
66#11924015—22no—
67#11924015—22no—
68C2×#10596831C2311yescharacteristic
69C2×#10596831C2311yescharacteristic
70C2×#10596831C2311yescharacteristic
71C2×#10596831C2311yescharacteristic
72C4⋊Dic73—21no—
73C4⋊Dic73C2311yescharacteristic
74C4⋊Dic73C2311yescharacteristic
75#11924007—21no—
76#11924007—21no—
77C22⋊Dic73—21no—
78#11924005—21no—
79#11924005—21no—
80#11924005—21no—
81#11924005—21no—
82C4×Dic73—21no—
83C2×Q8×C73—22no—
84C2×Q8×C73—22no—
85C2×Q8×C73—21no—
86C2×Q8×C73C2311yescharacteristic
87C2×Q8×C73C2311yescharacteristic
88C22×C4×C73—21no—
89C22×C4×C73C2311yescharacteristic
90C4⋊C4×C73—21no—
91C4⋊C4×C73—21no—
92C4⋊C4×C73—21no—
93C4⋊C4×C73—21no—
94C4⋊C4×C73D411yescharacteristic
95C4⋊C4×C73D411yescharacteristic
96C4⋊C4×C73C2311yescharacteristic
97C4⋊C4×C73C2311yescharacteristic
98C22⋊C4×C73—21no—
99C22⋊C4×C73D411yescharacteristic
100C22⋊C4×C73D411yescharacteristic
101C42×C73—21no—
102C42×C73—21no—
103C42×C73—21no—
104C42×C73—21no—
105C42×C73—21no—
106C42×C73C2311yescharacteristic
107C42×C73C2311yescharacteristic
108C23×C73C2×D411yescharacteristic
109C22×D73—21no—
110Q8×C73—24no—
111Q8×C73—21no—
112Q8×C73—21no—
113Q8×C73#4112yes—
114Q8×C73#4112yes—
115C2×C4×C73—24no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73C2×D411yescharacteristic
123C2×C4×C73C2×D411yescharacteristic
124C2×C4×C73C2×D411yescharacteristic
125C2×C4×C73C2×D411yescharacteristic
126C2×C4×C73C2×D411yescharacteristic
127C2×C4×C73C2411yescharacteristic
128C22⋊D73—81no—
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132D292—21no—
133D292—21no—
134C4×D73—81no—
135Dic146—21no—
136Dic146—21no—
137Dic146—81no—
138#10596831—21no—
139#10596831—21no—
140#10596831—21no—
141#10596831—21no—
142C22×C73—21no—
143C22×C73—21no—
144C22×C73—21no—
145C22×C73C22×D411yescharacteristic
146C2×D73—41no—
147C2×D73—41no—
148C2×D73—41no—
149C4×C73—22no—
150C4×C73—22no—
151C4×C73—21no—
152C4×C73—21no—
153C4×C73—21no—
154C4×C73—21no—
155C4×C73—21no—
156C4×C73—41no—
157C4×C73—41no—
158C4×C73C2×#4111yescharacteristic
159C4×C73C2×#4111yescharacteristic
160Dic73—41no—
161Dic73—41no—
162Dic73—41no—
163C2×C73—41no—
164C2×C73#52511yescharacteristic
165C2×C73#57711yescharacteristic
166C2×C73#57811yescharacteristic
167D73—81no—
168#3121—731nomaximal, Sylow
169C73#312111yescharacteristic, complemented, Sylow
170#542—731no—
171#519D7311yescharacteristic, complemented
172#485—731no—
173#482—731no—
174#477—731no—
175#475—731no—
176#464—731no—
177#464—731no—
178#451—731no—
179#448—731no—
180#441—731no—
181#440—731no—
182C4×Q16—731no—
183C4×SD16—731no—
184#433—731no—
185C22×Q8C2×D7311yescharacteristic
186C2×Q16—731no—
187C2×Q16—731no—
188C2×SD16—731no—
189C2×SD16—731no—
190C4⋊Q8—731no—
191#126—1461no—
192#124—731no—
193#124—1461no—
194#123—1461no—
195C22⋊Q8—731no—
196C22⋊Q8—1461no—
197#121—731no—
198C4×Q8—21no—
199C4×Q8—21no—
200C4×Q8—731no—
201C4×Q8C2×D7311yescharacteristic
202C4×Q8C2×D7311yescharacteristic
203C4×Q8C2×D7311yescharacteristic
204C4×Q8C2×D7311yescharacteristic
205C4×D4—731no—
206#117—21no—
207#117—21no—
208#117C2×D7311yescharacteristic
209#117C2×D7311yescharacteristic
210#107—731no—
211#107—731no—
212#106—731no—
213#106—731no—
214C4⋊C8—731no—
215C4⋊C8—731no—
216#103—731no—
217#103—731no—
218#103—731no—
219#103—731no—
220#103—731no—
221#103—731no—
222#102—731no—
223#102—731no—
224C22⋊C8—731no—
225C22⋊C8—731no—
226#97—731no—
227C4×C8—731no—
228C2×Q8—22no—
229C2×Q8—22no—
230C2×Q8—21no—
231C2×Q8—731no—
232C2×Q8—1461no—
233C2×Q8C22×D7311yescharacteristic
234C2×Q8C22×D7311yescharacteristic
235C2×D4—731no—
236C2×D4—1461no—
237C22×C4—21no—
238C22×C4—1461no—
239C22×C4C22×D7311yescharacteristic
240Q16—1462no—
241Q16—1462no—
242SD16—1462no—
243SD16—1462no—
244C2×C8—731no—
245C2×C8—731no—
246C2×C8—731no—
247C2×C8—731no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—731no—
253C4⋊C4—731no—
254C4⋊C4—1461no—
255C4⋊C4—1461no—
256C4⋊C4—1461no—
257C4⋊C4C22⋊D7311yescharacteristic
258C4⋊C4C22⋊D7311yescharacteristic
259C4⋊C4C22×D7311yescharacteristic
260C4⋊C4C22×D7311yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—1461no—
263C22⋊C4—1461no—
264C22⋊C4—1461no—
265C22⋊C4—1461no—
266C22⋊C4—1461no—
267C22⋊C4C22⋊D7311yescharacteristic
268C22⋊C4C22⋊D7311yescharacteristic
269C42—21no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42—1461no—
275C42C22×D7311yescharacteristic
276C42C22×D7311yescharacteristic
277C23—1461no—
278C23C2×C22⋊D7311yescharacteristic
279Q8—24no—
280Q8—21no—
281Q8—21no—
282Q8—5841no—
283Q8—1461no—
284Q8—1461no—
285Q8#1192402812yes—
286Q8#1192402812yes—
287D4—5841no—
288D4—1461no—
289D4—1461no—
290C2×C4—24no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—5841no—
298C2×C4—1461no—
299C2×C4—1461no—
300C2×C4—1461no—
301C2×C4C2×C22⋊D7311yescharacteristic
302C2×C4C2×C22⋊D7311yescharacteristic
303C2×C4C2×C22⋊D7311yescharacteristic
304C2×C4C2×C22⋊D7311yescharacteristic
305C2×C4C2×C22⋊D7311yescharacteristic
306C2×C4C23×D7311yescharacteristic
307C8—1461no—
308C8—1461no—
309C8—1461no—
310C8—1461no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—2921no—
315C22—2921no—
316C22—2921no—
317C22C22×C22⋊D7311yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—22no—
323C4—22no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—2921no—
328C4—2921no—
329C4—2921no—
330C4C2×#1192402811yescharacteristic
331C4C2×#1192402811yescharacteristic
332C2—41no—
333C2—5841no—
334C2#1798909811yescharacteristic
335C2#1798939511yescharacteristic
336C2#1798940211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#519×C73C2
socleC22×C73C22×D4
hypercenter#519D73
hypocenterC73#3121
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
2. #17988928C2semidirect
4. #17988882C2semidirect
5. #17988872C2semidirect
6. #17988809C2semidirect
7. #17988809C2semidirect
8. #17988743C2semidirect
10. #17988692C2semidirect
11. #17988685C2semidirect
12. C4×#11924018C2semidirect
13. C4×#11924015C2semidirect
14. #17988648C2semidirect
15. #519×C73C2semidirect
169. C73#3121semidirect
171. #519D73semidirect