Finite Group Databasebeta

← #49171471

Subgroups — #49171471

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#34036855C211yesmaximal, characteristic, complemented
2#34036851C211yesmaximal, characteristic
3#34036485C211yesmaximal, characteristic
4#34036484C211yesmaximal, characteristic
5#34036478C211yesmaximal, characteristic, complemented
6#34036436C211yesmaximal, characteristic, complemented
7#34036435C211yesmaximal, characteristic, complemented
8#34036408C211yesmaximal, characteristic
9#34036353C211yesmaximal, characteristic
10#34036351C211yesmaximal, characteristic
11#34036337C211yesmaximal, characteristic, complemented
12C8×Dic586C211yesmaximal, characteristic, complemented
13#34036221C211yesmaximal, characteristic, complemented
14#34036214C211yesmaximal, characteristic
15C4×Q16×C293C211yesmaximal, characteristic, complemented
16C2×#17989792C2211yescharacteristic
17C2×#17989789C2211yescharacteristic
18#22627623—21no—
19#22627623C2211yescharacteristic
20#22627622C2211yescharacteristic
21#22627619—21no—
22#22627618—21no—
23#22627616—21no—
24#22627616C2211yescharacteristic
25#22627615—21no—
26#22627615C2211yescharacteristic
27#22627613C2211yescharacteristic
28#22627612C2211yescharacteristic
29#22627602—21no—
30Q8×Dic293C2211yescharacteristic
31Q8×Dic293C2211yescharacteristic
32C4×Dic586—21no—
33C4×Dic586C2211yescharacteristic
34#22627589C2211yescharacteristic
35#22627586C2211yescharacteristic
36#22627581—21no—
37#22627557C2211yescharacteristic
38#22627555C2211yescharacteristic
39C4⋊#14556873C2211yescharacteristic
40#22627553C2211yescharacteristic
41#22627553C2211yescharacteristic
42#22627549C2211yescharacteristic
43#22627549C2211yescharacteristic
44#22627548C2211yescharacteristic
45#22627548C2211yescharacteristic
46#22627547C2211yescharacteristic
47#22627546C2211yescharacteristic
48#22627546C2211yescharacteristic
49#22627544C2211yescharacteristic
50C8×Dic293C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52C2×Q16×C293C2211yescharacteristic
53C4×Q8×C293C2211yescharacteristic
54C4×Q8×C293C2211yescharacteristic
55#107×C293C2211yescharacteristic
56#103×C293C2211yescharacteristic
57#103×C293C2211yescharacteristic
58C4×C8×C293C2211yescharacteristic
59C2×Dic586—21no—
60C2×Dic586D411yescharacteristic
61C2×Dic586C2311yescharacteristic
62C2×D1172C2311yescharacteristic
63C2×C4×D293—21no—
64#17989792—22no—
65#17989789—22no—
66C2×#14556873C2311yescharacteristic
67C2×#14556873C2311yescharacteristic
68C4⋊Dic293—21no—
69C4⋊Dic293—21no—
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#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×Dic293C2311yescharacteristic
92C4×Dic293C2311yescharacteristic
93C2×Q8×C293C2311yescharacteristic
94C2×Q8×C293C2311yescharacteristic
95Q16×C293—22no—
96C2×C8×C293C2311yescharacteristic
97C2×C8×C293C2311yescharacteristic
98C4⋊C4×C293—21no—
99C4⋊C4×C293—21no—
100C4⋊C4×C293C2311yescharacteristic
101C4⋊C4×C293C2311yescharacteristic
102C42×C293—21no—
103C42×C293—21no—
104C42×C293C2311yescharacteristic
105C22×D293—21no—
106Dic586—22no—
107Dic586—21no—
108Dic586—21no—
109Dic586—42no—
110D1172—21no—
111D1172—21no—
112C2×Dic293—21no—
113C2×Dic293—21no—
114C2×Dic293—21no—
115C2×Dic293C2×D411yescharacteristic
116C2×Dic293C2×D411yescharacteristic
117C2×Dic293C2×D411yescharacteristic
118C2×Dic293C2×D411yescharacteristic
119C4×D293—42no—
120#14556873—21no—
121#14556873—21no—
122Q8×C293—21no—
123Q8×C293—21no—
124Q8×C293—21no—
125Q8×C293#4112yes—
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—22no—
140C4×C293—21no—
141C4×C293—21no—
142C4×C293—41no—
143C4×C293—41no—
144C4×C293—41no—
145C4×C293C2×#4111yescharacteristic
146C4×C2932−1+411yescharacteristic
147Dic293—21no—
148Dic293—21no—
149Dic293—21no—
150Dic293—41no—
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#479—2931no—
167#474—2931no—
168#464—2931no—
169#464—2931no—
170#462—2931no—
171C8×Q8—2931no—
172C4×Q16—2931no—
173C4×Q16D29311yescharacteristic, complemented
174C4×SD16—2931no—
175C2×Q16—2931no—
176C2×Q16C2×D29311yescharacteristic
177C2×SD16—2931no—
178C4⋊Q8—2931no—
179C4⋊Q8—2931no—
180C4⋊Q8—5861no—
181#126—5861no—
182#126—5861no—
183#125—2931no—
184#125—2931no—
185#125—5861no—
186#125—5861no—
187#124—2931no—
188#124—2931no—
189C22⋊Q8—5861no—
190C4×Q8—2931no—
191C4×Q8—2931no—
192C4×Q8—2931no—
193C4×Q8—2931no—
194C4×Q8—5861no—
195C4×Q8C2×D29311yescharacteristic
196C4×Q8C2×D29311yescharacteristic
197C4×D4—2931no—
198#117—5861no—
199#107—2931no—
200#107C2×D29311yescharacteristic
201#106—2931no—
202C4⋊C8—2931no—
203C4⋊C8—2931no—
204C4⋊C8—2931no—
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×C8C2×D29311yescharacteristic
218C2×Q8—2931no—
219C2×Q8—2931no—
220C2×Q8—5861no—
221C2×Q8C22×D29311yescharacteristic
222C2×Q8C22×D29311yescharacteristic
223C2×D4—2931no—
224C22×C4—5861no—
225Q16—22no—
226Q16—5862no—
227SD16—5862no—
228C2×C8—2931no—
229C2×C8—2931no—
230C2×C8C22×D29311yescharacteristic
231C2×C8C22×D29311yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—2931no—
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⋊C4—5861no—
249C4⋊C4C22×D29311yescharacteristic
250C4⋊C4C22×D29311yescharacteristic
251C22⋊C4—5861no—
252C22⋊C4—5861no—
253C22⋊C4—5861no—
254C22⋊C4—5861no—
255C22⋊C4—5861no—
256C42—21no—
257C42—21no—
258C42—2931no—
259C42—2931no—
260C42—5861no—
261C42—5861no—
262C42—5861no—
263C42C22×D29311yescharacteristic
264C23—5861no—
265Q8—21no—
266Q8—21no—
267Q8—21no—
268Q8—5862no—
269Q8—5861no—
270Q8—5861no—
271Q8—11722no—
272Q8#1798980212yes—
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—22no—
299C4—21no—
300C4—21no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—2932no—
305C4—5861no—
306C4—5861no—
307C4—5861no—
308C4—11721no—
309C4—11721no—
310C4—11721no—
311C4C2×#1798980211yescharacteristic
312C4#2262767111yescharacteristic
313C2—23441no—
314C2#3403678811yescharacteristic
315C2#135×D29311yescharacteristic
316C2#3403694211yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC4×Q16×C293C2
socleC22×C293C22×D4
prime radicalC2×D1172C23
hypercenterC4×Q16D293
hypocenterC293#3364
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
1. #34036855C2semidirect
5. #34036478C2semidirect
6. #34036436C2semidirect
7. #34036435C2semidirect
11. #34036337C2semidirect
12. C8×Dic586C2semidirect
13. #34036221C2semidirect
15. C4×Q16×C293C2semidirect
158. C293#3364semidirect
173. C4×Q16D293semidirect

Maximal subgroups

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

subgroupindex
#340368552
#340368512
#340364852
#340364842
#340364782
#340364362
#340364352
#340364082
#340363532
#340363512
#340363372
C8×Dic5862
#340362212
#340362142
C4×Q16×C2932
#3364293