Finite Group Databasebeta

← #49171522

Subgroups — #49171522

Order 37504.

338 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#34036859C211yesmaximal, characteristic, complemented
2#34036848C211yesmaximal, characteristic
3#34036487C211yesmaximal, characteristic
4#34036478C211yesmaximal, characteristic, complemented
5#34036417C211yesmaximal, characteristic
6#34036412C211yesmaximal, characteristic, complemented
7#34036411C211yesmaximal, characteristic, complemented
8#34036350C211yesmaximal, characteristic
9#34036348C211yesmaximal, characteristic
10#34036338C211yesmaximal, characteristic, complemented
11#34036257C211yesmaximal, characteristic, complemented
12#34036237C211yesmaximal, characteristic, complemented
13#34036233C211yesmaximal, characteristic, complemented
14#34036220C211yesmaximal, characteristic
15#489×C293C211yesmaximal, characteristic
16C2×Dic1172C2211yescharacteristic
17C2×#17989792C2211yescharacteristic
18C2×#17989790C2211yescharacteristic
19#22627623—21no—
20#22627623C2211yescharacteristic
21#22627623C2211yescharacteristic
22#22627622—21no—
23#22627622—21no—
24#22627622C2211yescharacteristic
25#22627617—21no—
26#22627617—21no—
27#22627611C2211yescharacteristic
28#22627601—21no—
29Q8×Dic293C2211yescharacteristic
30C4×Dic586C2211yescharacteristic
31C4×Dic586C2211yescharacteristic
32C4×Dic586C2211yescharacteristic
33#22627589—21no—
34#22627589C2211yescharacteristic
35#22627589C2211yescharacteristic
36D4×Dic293C2211yescharacteristic
37#22627580—21no—
38#22627556C2211yescharacteristic
39#22627555C2211yescharacteristic
40#22627555C2211yescharacteristic
41C4⋊#14556873C2211yescharacteristic
42#22627553C2211yescharacteristic
43#22627553C2211yescharacteristic
44#22627549C2211yescharacteristic
45#22627549C2211yescharacteristic
46#22627548C2211yescharacteristic
47#22627547C2211yescharacteristic
48#22627547C2211yescharacteristic
49#22627545C2211yescharacteristic
50#22627534C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52C4⋊Q8×C293C2211yescharacteristic
53#124×C293C2211yescharacteristic
54#103×C293C2211yescharacteristic
55#103×C293C2211yescharacteristic
56#102×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58#97×C293C2211yescharacteristic
59C2×Dic586—21no—
60C2×Dic586—21no—
61C2×Dic586D411yescharacteristic
62C2×Dic586C2311yescharacteristic
63C2×Dic586C2311yescharacteristic
64C22×Dic293—21no—
65Dic1172—22no—
66#17989792—22no—
67#17989790—22no—
68C2×#14556873C2311yescharacteristic
69C2×#14556873C2311yescharacteristic
70C4⋊Dic293—21no—
71C4⋊Dic293D411yescharacteristic
72C4⋊Dic293C2311yescharacteristic
73C4⋊Dic293C2311yescharacteristic
74#17989781—21no—
75#17989781—21no—
76#17989781—21no—
77#17989781—21no—
78#17989781—21no—
79#17989781—21no—
80#17989781—21no—
81#17989781—21no—
82#17989781D411yescharacteristic
83#17989781D411yescharacteristic
84C22⋊Dic293—21no—
85C22⋊Dic293—21no—
86C22⋊Dic293—21no—
87C4×Dic293—21no—
88C4×Dic293—21no—
89C4×Dic293—21no—
90C4×Dic293—21no—
91C4×Dic293—21no—
92C4×Dic293C2311yescharacteristic
93C4×Dic293C2311yescharacteristic
94C2×Q8×C293—21no—
95C2×Q8×C293C2311yescharacteristic
96C2×D4×C293C2311yescharacteristic
97C2×C8×C293C2311yescharacteristic
98C2×C8×C293C2311yescharacteristic
99C4⋊C4×C293—21no—
100C4⋊C4×C293C2311yescharacteristic
101C4⋊C4×C293C2311yescharacteristic
102C22⋊C4×C293—21no—
103C22⋊C4×C293—21no—
104C42×C293C2311yescharacteristic
105Dic586—21no—
106Dic586—22no—
107Dic586—21no—
108Dic586—21no—
109Dic586—81no—
110Dic586—81no—
111Dic586#4112yes—
112C2×Dic293—21no—
113C2×Dic293—21no—
114C2×Dic293—21no—
115C2×Dic293—21no—
116C2×Dic293—42no—
117C2×Dic293C2×D411yescharacteristic
118C2×Dic293C2×D411yescharacteristic
119C2×Dic293C2×D411yescharacteristic
120C2×Dic293C2×D411yescharacteristic
121#14556873—21no—
122#14556873—21no—
123C23×C293—21no—
124Q8×C293—21no—
125Q8×C293—21no—
126Q8×C293—81no—
127D4×C293—21no—
128D4×C293—21no—
129C2×C4×C293—21no—
130C2×C4×C293—21no—
131C2×C4×C293—21no—
132C2×C4×C293C2×D411yescharacteristic
133C2×C4×C293C2×D411yescharacteristic
134C2×C4×C293C2411yescharacteristic
135C8×C293—21no—
136C8×C293—21no—
137C22×C293—41no—
138C22×C293—41no—
139C22×C293—41no—
140C22×C293C22×D411yescharacteristic
141C4×C293—21no—
142C4×C293—21no—
143C4×C293—41no—
144C4×C293—41no—
145C4×C293—41no—
146C4×C293C2×#4111yescharacteristic
147C4×C2932−1+411yescharacteristic
148Dic293—22no—
149Dic293—21no—
150Dic293—21no—
151Dic293—21no—
152Dic293—41no—
153Dic293—41no—
154Dic293—41no—
155Dic293#13712yes—
156C2×C293—81no—
157C2×C293#54811yescharacteristic
158C2×C293C2×#13711yescharacteristic
159C2×C293#57711yescharacteristic
160C293#336911yescharacteristic, complemented, Sylow
161#3369—2931nomaximal, Sylow
162Q82—2931no—
163#556—2931no—
164#489—2931no—
165#489D29311yescharacteristic
166#487—2931no—
167#476—2931no—
168#475—2931no—
169#475—2931no—
170#464—2931no—
171#464—2931no—
172#462—2931no—
173#446—2931no—
174#441—2931no—
175#441—2931no—
176C4×SD16—2931no—
177C2×Q16—2931no—
178C2×Q16—2931no—
179C2×SD16—2931no—
180C4⋊Q8—2931no—
181C4⋊Q8—2931no—
182C4⋊Q8—2931no—
183C4⋊Q8—5861no—
184C4⋊Q8—5861no—
185C4⋊Q8—5861no—
186C4⋊Q8C2×D29311yescharacteristic
187#126—5861no—
188#126—5861no—
189#124—2931no—
190#124C2×D29311yescharacteristic
191C22⋊Q8—5861no—
192C4×Q8—2931no—
193C4×Q8—2931no—
194C4×Q8—2931no—
195C4×Q8—2931no—
196C4×Q8—2931no—
197C4×Q8—2931no—
198C4×Q8—5861no—
199C4×D4—2931no—
200#117—5861no—
201#106—2931no—
202#106—2931no—
203#106—2931no—
204C4⋊C8—2931no—
205C4⋊C8—2931no—
206C4⋊C8—2931no—
207#103—2931no—
208#103—2931no—
209#103—2931no—
210#103—2931no—
211#103—2931no—
212#103C2×D29311yescharacteristic
213#103C2×D29311yescharacteristic
214#102—2931no—
215#102C2×D29311yescharacteristic
216#102C2×D29311yescharacteristic
217#97—2931no—
218#97C2×D29311yescharacteristic
219C4×C8—2931no—
220C2×Q8—21no—
221C2×Q8—2931no—
222C2×Q8—2931no—
223C2×Q8—2931no—
224C2×Q8—5861no—
225C2×Q8—5861no—
226C2×Q8C22×D29311yescharacteristic
227C2×D4C22×D29311yescharacteristic
228C22×C4—5861no—
229Q16—5862no—
230Q16—5862no—
231SD16—5862no—
232C2×C8—2931no—
233C2×C8—2931no—
234C2×C8C22×D29311yescharacteristic
235C2×C8C22×D29311yescharacteristic
236C4⋊C4—21no—
237C4⋊C4—2931no—
238C4⋊C4—2931no—
239C4⋊C4—2931no—
240C4⋊C4—2931no—
241C4⋊C4—2931no—
242C4⋊C4—5861no—
243C4⋊C4—5861no—
244C4⋊C4—5861no—
245C4⋊C4—5861no—
246C4⋊C4—5861no—
247C4⋊C4—5861no—
248C4⋊C4—5861no—
249C4⋊C4—5861no—
250C4⋊C4—5861no—
251C4⋊C4C22×D29311yescharacteristic
252C4⋊C4C22×D29311yescharacteristic
253C22⋊C4—21no—
254C22⋊C4—21no—
255C22⋊C4—5861no—
256C22⋊C4—5861no—
257C22⋊C4—5861no—
258C42—2931no—
259C42—2931no—
260C42—5861no—
261C42—5861no—
262C42—5861no—
263C42—5861no—
264C42—5861no—
265C42C22×D29311yescharacteristic
266C23—21no—
267Q8—21no—
268Q8—21no—
269Q8—81no—
270Q8—2932no—
271Q8—23441no—
272Q8—23441no—
273Q8—5862no—
274Q8—5861no—
275Q8—5861no—
276Q8—5861no—
277D4—21no—
278D4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—2931no—
283C2×C4—2931no—
284C2×C4—2931no—
285C2×C4—2931no—
286C2×C4—5861no—
287C2×C4—5861no—
288C2×C4—5861no—
289C2×C4—5861no—
290C2×C4—11722no—
291C2×C4D4×D29311yescharacteristic
292C2×C4D4×D29311yescharacteristic
293C2×C4C23×D29311yescharacteristic
294C8—21no—
295C8—21no—
296C8—5861no—
297C8—5861no—
298C22—41no—
299C22—41no—
300C22—41no—
301C22C2×D4×D29311yescharacteristic
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—2932no—
308C4—5862no—
309C4—5861no—
310C4—5861no—
311C4—5861no—
312C4—11721no—
313C4—11721no—
314C4—11721no—
315C4#41×D29311yescharacteristic
316C4#2262767111yescharacteristic
317C2—81no—
318C2#3403678711yescharacteristic
319C2#137×D29311yescharacteristic
320C2#3403693911yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#489×C293C2
socleC22×C293C22×D4
prime radicalC2×D4×C293C23
hypercenter#489D293
hypocenterC293#3369
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #34036859C2semidirect
4. #34036478C2semidirect
6. #34036412C2semidirect
7. #34036411C2semidirect
10. #34036338C2semidirect
11. #34036257C2semidirect
12. #34036237C2semidirect
13. #34036233C2semidirect
160. C293#3369semidirect

Maximal subgroups

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

subgroupindex
#340368592
#340368482
#340364872
#340364782
#340364172
#340364122
#340364112
#340363502
#340363482
#340363382
#340362572
#340362372
#340362332
#340362202
#489×C2932
#3369293