Finite Group Databasebeta

← #22620139

Subgroups — #22620139

Order 9344.

372 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#17989067C211yesmaximal, characteristic
2#17988920C211yesmaximal, characteristic, complemented
3#17988915C211yesmaximal, characteristic, complemented
4#17988891C211yesmaximal, characteristic, complemented
5#17988884C211yesmaximal, characteristic, complemented
6#17988794C211yesmaximal, characteristic, complemented
7#17988789C211yesmaximal, characteristic, complemented
8#17988747C211yesmaximal, characteristic
9#17988747C211yesmaximal, characteristic
10#17988692C211yesmaximal, characteristic, complemented
11#17988685C211yesmaximal, characteristic, complemented
12C4×#11924018C211yesmaximal, characteristic, complemented
13C4×#11924015C211yesmaximal, characteristic, complemented
14#17988648C211yesmaximal, characteristic, complemented
15#541×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C2×#11924018C2211yescharacteristic
18C2×#11924018C2211yescharacteristic
19C2×#11924015C2211yescharacteristic
20C2×#11924015C2211yescharacteristic
21C4×Dic146C2211yescharacteristic
22C4×Dic146C2211yescharacteristic
23C4×D292C2211yescharacteristic
24C4×D292C2211yescharacteristic
25#14556551—21no—
26#14556551—21no—
27#14556549—21no—
28C2×C4⋊Dic73C2211yescharacteristic
29C4⋊C4×D73—21no—
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
48C4⋊Q8×C73C2211yescharacteristic
49#126×C73—21no—
50#126×C73—21no—
51#125×C73—21no—
52#125×C73—21no—
53#125×C73C2211yescharacteristic
54C22⋊Q8×C73C2211yescharacteristic
55C22⋊Q8×C73C2211yescharacteristic
56C4×Q8×C73C2211yescharacteristic
57C4×Q8×C73C2211yescharacteristic
58#117×C73C2211yescharacteristic
59#11924028—22no—
60#11924028—22no—
61C2×Dic146C2311yescharacteristic
62C2×D292C2311yescharacteristic
63C2×C22⋊D73—21no—
64C22×Dic73—21no—
65C2×C4×D73—21no—
66C2×C4×D73—21no—
67C2×C4×D73—21no—
68#11924018—22no—
69#11924018—22no—
70#11924015—22no—
71#11924015—22no—
72C2×#10596831C2311yescharacteristic
73C2×#10596831C2311yescharacteristic
74C2×#10596831C2311yescharacteristic
75C2×#10596831C2311yescharacteristic
76C4⋊Dic73—21no—
77C4⋊Dic73C2311yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79#11924007—21no—
80#11924007—21no—
81#11924005—21no—
82#11924005—21no—
83C4×Dic73—21no—
84C4×Dic73—21no—
85C2×Q8×C73C2311yescharacteristic
86C2×Q8×C73C2311yescharacteristic
87C22×C4×C73C2311yescharacteristic
88C4⋊C4×C73—21no—
89C4⋊C4×C73—21no—
90C4⋊C4×C73—21no—
91C4⋊C4×C73—21no—
92C4⋊C4×C73—21no—
93C4⋊C4×C73—21no—
94C4⋊C4×C73—21no—
95C4⋊C4×C73—21no—
96C4⋊C4×C73D411yescharacteristic
97C4⋊C4×C73D411yescharacteristic
98C4⋊C4×C73C2311yescharacteristic
99C4⋊C4×C73C2311yescharacteristic
100C22⋊C4×C73—21no—
101C22⋊C4×C73—21no—
102C22⋊C4×C73D411yescharacteristic
103C22⋊C4×C73D411yescharacteristic
104C42×C73—21no—
105C42×C73—21no—
106C42×C73C2311yescharacteristic
107C42×C73C2311yescharacteristic
108C23×C73C2×D411yescharacteristic
109C22×D73—21no—
110Q8×C73—21no—
111Q8×C73—21no—
112Q8×C73—21no—
113Q8×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73C2×D411yescharacteristic
121C2×C4×C73C2×D411yescharacteristic
122C2×C4×C73C2×D411yescharacteristic
123C2×C4×C73C2×D411yescharacteristic
124C2×C4×C73C2×D411yescharacteristic
125C2×C4×C73C2411yescharacteristic
126C22⋊D73—24no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73—21no—
130C2×Dic73—81no—
131D292—21no—
132D292#4112yes—
133C4×D73—24no—
134C4×D73—81no—
135C4×D73—81no—
136Dic146—21no—
137Dic146#4112yes—
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—22no—
147C2×D73—41no—
148C2×D73—41no—
149C4×C73—21no—
150C4×C73—21no—
151C4×C73—21no—
152C4×C73—21no—
153C4×C73—21no—
154C4×C73—41no—
155C4×C73—41no—
156C4×C73—41no—
157C4×C73—41no—
158C4×C73C2×#4111yescharacteristic
159C4×C73C2×#4111yescharacteristic
160Dic73—22no—
161Dic73—41no—
162Dic73—41no—
163C2×C73—41no—
164C2×C73#52511yescharacteristic
165C2×C73#57711yescharacteristic
166C2×C73#57811yescharacteristic
167D73—42no—
168#3120—731nomaximal, Sylow
169C73#312011yescharacteristic, complemented, Sylow
170#541D7311yescharacteristic, complemented
171#520—731no—
172#484—731no—
173#483—731no—
174#479—731no—
175#478—731no—
176#462—731no—
177#461—731no—
178#452—731no—
179#452—731no—
180#441—731no—
181#440—731no—
182C4×Q16—731no—
183C4×SD16—731no—
184#433—731no—
185C2×#41—731no—
186C2×Q16—731no—
187C2×Q16—731no—
188C2×SD16—731no—
189C2×SD16—731no—
190C4⋊Q8C2×D7311yescharacteristic
191#126—21no—
192#126—21no—
193#125—21no—
194#125—21no—
195#125C2×D7311yescharacteristic
196C22⋊Q8C2×D7311yescharacteristic
197C22⋊Q8C2×D7311yescharacteristic
198C4×Q8—731no—
199C4×Q8—731no—
200C4×Q8C2×D7311yescharacteristic
201C4×Q8C2×D7311yescharacteristic
202C4×D4—731no—
203C4×D4—731no—
204C4×D4—1461no—
205C4×D4—1461no—
206#117—1461no—
207#117C2×D7311yescharacteristic
208C2×C4⋊C4—731no—
209C2×C4⋊C4—1461no—
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—
228#41—1462no—
229#41—1462no—
230C2×Q8—731no—
231C2×Q8C22×D7311yescharacteristic
232C2×Q8C22×D7311yescharacteristic
233C2×D4—731no—
234C2×D4—1461no—
235C22×C4—1461no—
236C22×C4—1461no—
237C22×C4—1461no—
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—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—731no—
257C4⋊C4—731no—
258C4⋊C4—1461no—
259C4⋊C4—1461no—
260C4⋊C4—1461no—
261C4⋊C4C22⋊D7311yescharacteristic
262C4⋊C4C22⋊D7311yescharacteristic
263C4⋊C4C22×D7311yescharacteristic
264C4⋊C4C22×D7311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—1461no—
268C22⋊C4—1461no—
269C22⋊C4C22⋊D7311yescharacteristic
270C22⋊C4C22⋊D7311yescharacteristic
271C42—21no—
272C42—21no—
273C42—1461no—
274C42—1461no—
275C42C22×D7311yescharacteristic
276C42C22×D7311yescharacteristic
277C23—1461no—
278C23C2×C22⋊D7311yescharacteristic
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—732no—
284Q8—1461no—
285D4—732no—
286D4—1464no—
287D4—1461no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—5841no—
295C2×C4—5841no—
296C2×C4—5841no—
297C2×C4—1464no—
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—1462no—
317C22C22×C22⋊D7311yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—2921no—
328C4—2921no—
329C4—1462no—
330C4#41×D7311yescharacteristic
331C4#41×D7311yescharacteristic
332C2—41no—
333C2—2922no—
334C2#1798909411yescharacteristic
335C2#1798939511yescharacteristic
336C2#1798940211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#541×C73C2
socleC22×C73C22×D4
hypercenter#541D73
hypocenterC73#3120
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #17988920C2semidirect
3. #17988915C2semidirect
4. #17988891C2semidirect
5. #17988884C2semidirect
6. #17988794C2semidirect
7. #17988789C2semidirect
10. #17988692C2semidirect
11. #17988685C2semidirect
12. C4×#11924018C2semidirect
13. C4×#11924015C2semidirect
14. #17988648C2semidirect
15. #541×C73C2semidirect
169. C73#3120semidirect
170. #541D73semidirect