Finite Group Databasebeta

← #49171473

Subgroups — #49171473

Order 37504.

336 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036856C211yesmaximal, characteristic, complemented
2#34036851C211yesmaximal, characteristic
3#34036486C211yesmaximal, characteristic
4#34036485C211yesmaximal, characteristic
5#34036478C211yesmaximal, characteristic, complemented
6#34036439C211yesmaximal, characteristic, complemented
7#34036408C211yesmaximal, characteristic
8#34036354C211yesmaximal, characteristic
9#34036352C211yesmaximal, characteristic
10#34036338C211yesmaximal, characteristic, complemented
11#34036253C211yesmaximal, characteristic, complemented
12#34036223C211yesmaximal, characteristic, complemented
13C4×#17989792C211yesmaximal, characteristic, complemented
14#34036216C211yesmaximal, characteristic
15#479×C293C211yesmaximal, characteristic, complemented
16C2×Dic1172C2211yescharacteristic
17C2×#17989792C2211yescharacteristic
18C2×#17989791C2211yescharacteristic
19#22627623—21no—
20#22627623C2211yescharacteristic
21#22627622C2211yescharacteristic
22#22627619—21no—
23#22627618—21no—
24#22627615C2211yescharacteristic
25#22627614—21no—
26#22627614—21no—
27#22627613C2211yescharacteristic
28#22627612C2211yescharacteristic
29#22627602—21no—
30C4×Dic586C2211yescharacteristic
31C4×Dic586C2211yescharacteristic
32#22627589—21no—
33#22627589C2211yescharacteristic
34#22627589C2211yescharacteristic
35#22627589C2211yescharacteristic
36#22627586C2211yescharacteristic
37#22627581—21no—
38#22627557C2211yescharacteristic
39#22627553C2211yescharacteristic
40#22627553C2211yescharacteristic
41#22627549C2211yescharacteristic
42#22627548C2211yescharacteristic
43#22627547C2211yescharacteristic
44#22627547C2211yescharacteristic
45#22627547C2211yescharacteristic
46#22627546C2211yescharacteristic
47#22627544C2211yescharacteristic
48#22627544C2211yescharacteristic
49C4×#14556873C2211yescharacteristic
50C8×Dic293C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52#125×C293C2211yescharacteristic
53C4×Q8×C293C2211yescharacteristic
54#107×C293C2211yescharacteristic
55#106×C293C2211yescharacteristic
56C4⋊C8×C293C2211yescharacteristic
57#103×C293C2211yescharacteristic
58#103×C293C2211yescharacteristic
59C2×Dic586—21no—
60C2×Dic586D411yescharacteristic
61C2×Dic586C2311yescharacteristic
62C2×Dic586C2311yescharacteristic
63C2×D1172C2311yescharacteristic
64C2×C4×D293—21no—
65Dic1172—22no—
66#17989792—22no—
67#17989791—22no—
68C2×#14556873C2311yescharacteristic
69C2×#14556873C2311yescharacteristic
70C4⋊Dic293—21no—
71C4⋊Dic293D411yescharacteristic
72C4⋊Dic293C2311yescharacteristic
73#17989781—21no—
74#17989781—21no—
75#17989781—21no—
76#17989781—21no—
77#17989781—21no—
78#17989781—21no—
79#17989781—21no—
80#17989781—21no—
81#17989781D411yescharacteristic
82#17989781D411yescharacteristic
83#17989779—21no—
84#17989779—21no—
85#17989779—21no—
86#17989779—21no—
87#17989779—21no—
88C4×Dic293—21no—
89C4×Dic293—21no—
90C4×Dic293—21no—
91C4×Dic293—21no—
92C4×Dic293C2311yescharacteristic
93C4×Dic293C2311yescharacteristic
94C2×Q8×C293C2311yescharacteristic
95C2×C8×C293C2311yescharacteristic
96C2×C8×C293C2311yescharacteristic
97C4⋊C4×C293—21no—
98C4⋊C4×C293—21no—
99C4⋊C4×C293—21no—
100C4⋊C4×C293C2311yescharacteristic
101C4⋊C4×C293C2311yescharacteristic
102C4⋊C4×C293C2311yescharacteristic
103C42×C293—21no—
104C42×C293C2311yescharacteristic
105C22×D293—21no—
106Dic586—21no—
107Dic586—22no—
108Dic586—21no—
109Dic586—21no—
110Dic586—42no—
111Dic586#4112yes—
112D1172—21no—
113D1172—21no—
114C2×Dic293—21no—
115C2×Dic293—21no—
116C2×Dic293—21no—
117C2×Dic293C2×D411yescharacteristic
118C2×Dic293C2×D411yescharacteristic
119C2×Dic293C2×D411yescharacteristic
120C2×Dic293C2×D411yescharacteristic
121C4×D293—42no—
122#14556873—21no—
123#14556873—21no—
124Q8×C293—21no—
125Q8×C293—21no—
126C2×C4×C293—21no—
127C2×C4×C293—21no—
128C2×C4×C293—21no—
129C2×C4×C293—21no—
130C2×C4×C293C2×D411yescharacteristic
131C2×C4×C293C2×D411yescharacteristic
132C2×C4×C293C2411yescharacteristic
133C8×C293—21no—
134C8×C293—21no—
135C22×C293C22×D411yescharacteristic
136C2×D293—41no—
137C2×D293—41no—
138C2×D293—41no—
139C4×C293—21no—
140C4×C293—21no—
141C4×C293—41no—
142C4×C293—41no—
143C4×C293—41no—
144C4×C293—41no—
145C4×C293C2×#4111yescharacteristic
146C4×C2932−1+411yescharacteristic
147Dic293—22no—
148Dic293—21no—
149Dic293—21no—
150Dic293—21no—
151Dic293—41no—
152Dic293—41no—
153Dic293#13512yes—
154C2×C293#54811yescharacteristic
155C2×C293C2×#13511yescharacteristic
156C2×C293#57811yescharacteristic
157D293—81no—
158C293#336411yescharacteristic, complemented, Sylow
159#3364—2931nomaximal, Sylow
160#557—2931no—
161#556—2931no—
162#488—2931no—
163#488—2931no—
164#487—2931no—
165#479—2931no—
166#479D29311yescharacteristic, complemented
167#474—2931no—
168#464—2931no—
169#464—2931no—
170#462—2931no—
171C8×Q8—2931no—
172C4×Q16—2931no—
173C4×Q16—2931no—
174C4×SD16—2931no—
175C2×Q16—2931no—
176C2×Q16—2931no—
177C2×SD16—2931no—
178C4⋊Q8—2931no—
179C4⋊Q8—2931no—
180C4⋊Q8—5861no—
181#126—5861no—
182#126—5861no—
183#125—2931no—
184#125—5861no—
185#125—5861no—
186#125C2×D29311yescharacteristic
187#124—2931no—
188#124—2931no—
189C22⋊Q8—5861no—
190C4×Q8—2931no—
191C4×Q8—2931no—
192C4×Q8—2931no—
193C4×Q8—2931no—
194C4×Q8—2931no—
195C4×Q8—5861no—
196C4×Q8C2×D29311yescharacteristic
197C4×D4—2931no—
198#117—5861no—
199#107—2931no—
200#107C2×D29311yescharacteristic
201#106C2×D29311yescharacteristic
202C4⋊C8—2931no—
203C4⋊C8—2931no—
204C4⋊C8C2×D29311yescharacteristic
205#103—2931no—
206#103—2931no—
207#103—2931no—
208#103—2931no—
209#103—2931no—
210#103C2×D29311yescharacteristic
211#103C2×D29311yescharacteristic
212#102—2931no—
213#102—2931no—
214#102—2931no—
215C4×C8—2931no—
216C4×C8—2931no—
217C4×C8—2931no—
218C2×Q8—2931no—
219C2×Q8—2931no—
220C2×Q8—2931no—
221C2×Q8—5861no—
222C2×Q8C22×D29311yescharacteristic
223C2×D4—2931no—
224C22×C4—5861no—
225Q16—5862no—
226Q16—5862no—
227SD16—5862no—
228C2×C8—2931no—
229C2×C8—2931no—
230C2×C8C22×D29311yescharacteristic
231C2×C8C22×D29311yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—2931no—
236C4⋊C4—2931no—
237C4⋊C4—2931no—
238C4⋊C4—2931no—
239C4⋊C4—5861no—
240C4⋊C4—5861no—
241C4⋊C4—5861no—
242C4⋊C4—5861no—
243C4⋊C4—5861no—
244C4⋊C4—5861no—
245C4⋊C4—5861no—
246C4⋊C4—5861no—
247C4⋊C4—5861no—
248C4⋊C4C22×D29311yescharacteristic
249C4⋊C4C22×D29311yescharacteristic
250C4⋊C4C22×D29311yescharacteristic
251C22⋊C4—5861no—
252C22⋊C4—5861no—
253C22⋊C4—5861no—
254C22⋊C4—5861no—
255C22⋊C4—5861no—
256C42—21no—
257C42—2931no—
258C42—2931no—
259C42—5861no—
260C42—5861no—
261C42—5861no—
262C42—5861no—
263C42C22×D29311yescharacteristic
264C23—5861no—
265Q8—21no—
266Q8—21no—
267Q8—2932no—
268Q8—5862no—
269Q8—5861no—
270Q8—5861no—
271Q8—5861no—
272Q8—11722no—
273D4—5861no—
274D4—5861no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—2931no—
280C2×C4—2931no—
281C2×C4—2931no—
282C2×C4—2931no—
283C2×C4—5861no—
284C2×C4—5861no—
285C2×C4—5861no—
286C2×C4—11722no—
287C2×C4D4×D29311yescharacteristic
288C2×C4D4×D29311yescharacteristic
289C2×C4C23×D29311yescharacteristic
290C8—21no—
291C8—21no—
292C8—5861no—
293C8—5861no—
294C22—11721no—
295C22—11721no—
296C22—11721no—
297C22C2×D4×D29311yescharacteristic
298C4—21no—
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—2932no—
305C4—5862no—
306C4—5861no—
307C4—5861no—
308C4—5861no—
309C4—11721no—
310C4—11721no—
311C4#41×D29311yescharacteristic
312C4#2262767211yescharacteristic
313C2—23441no—
314C2#3403678911yescharacteristic
315C2#135×D29311yescharacteristic
316C2#3403694511yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#479×C293C2
socleC22×C293C22×D4
prime radicalC2×D1172C23
hypercenter#479D293
hypocenterC293#3364
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #34036856C2semidirect
5. #34036478C2semidirect
6. #34036439C2semidirect
10. #34036338C2semidirect
11. #34036253C2semidirect
12. #34036223C2semidirect
13. C4×#17989792C2semidirect
15. #479×C293C2semidirect
158. C293#3364semidirect
166. #479D293semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#340368562
#340368512
#340364862
#340364852
#340364782
#340364392
#340364082
#340363542
#340363522
#340363382
#340362532
#340362232
C4×#179897922
#340362162
#479×C2932
#3364293