Finite Group Databasebeta

← #49168620

Subgroups — #49168620

Order 37504.

362 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036756C211yesmaximal, characteristic
2#34036605C211yesmaximal, characteristic
3#34036439C211yesmaximal, characteristic, complemented
4#34036437C211yesmaximal, characteristic, complemented
5#34036436C211yesmaximal, characteristic, complemented
6#34036434C211yesmaximal, characteristic, complemented
7#34036422C211yesmaximal, characteristic, complemented
8#34036421C211yesmaximal, characteristic, complemented
9#34036413C211yesmaximal, characteristic, complemented
10#34036168C211yesmaximal, characteristic
11#34036164C211yesmaximal, characteristic
12#34036154C211yesmaximal, characteristic
13#34036136C211yesmaximal, characteristic
14#103×D293C211yesmaximal, characteristic
15#475×C293C211yesmaximal, characteristic, complemented
16C2×Q8×D293C2211yescharacteristic
17C2×#17989785C2211yescharacteristic
18C2×C8×D293C2211yescharacteristic
19#22627623C2211yescharacteristic
20#22627622—21no—
21#22627616C2211yescharacteristic
22#22627615C2211yescharacteristic
23#22627614—21no—
24#22627602—21no—
25#22627600—21no—
26Q8×Dic293C2211yescharacteristic
27C4×Dic586—21no—
28C4×Dic586C2211yescharacteristic
29#22627589—21no—
30#22627589C2211yescharacteristic
31#22627582—21no—
32#22627582C2211yescharacteristic
33#22627582C2211yescharacteristic
34#22627581—21no—
35#22627581C2211yescharacteristic
36C4⋊C4×D293C2211yescharacteristic
37#22627558C2211yescharacteristic
38#22627557C2211yescharacteristic
39#22627557C2211yescharacteristic
40#22627557C2211yescharacteristic
41#22627556C2211yescharacteristic
42#22627555C2211yescharacteristic
43C4⋊#14556873C2211yescharacteristic
44#22627553C2211yescharacteristic
45#22627553C2211yescharacteristic
46#22627549C2211yescharacteristic
47#22627549C2211yescharacteristic
48#22627548C2211yescharacteristic
49#22627548C2211yescharacteristic
50#22627547C2211yescharacteristic
51#22627547C2211yescharacteristic
52C4⋊Q8×C293C2211yescharacteristic
53C4×Q8×C293C2211yescharacteristic
54#106×C293C2211yescharacteristic
55#106×C293C2211yescharacteristic
56C4⋊C8×C293C2211yescharacteristic
57#103×C293C2211yescharacteristic
58#103×C293C2211yescharacteristic
59C2×Dic586—21no—
60C2×Dic586—21no—
61C2×Dic586C2311yescharacteristic
62Q8×D293—22no—
63Q8×D293Q814yescomplemented
64C2×C4×D293—21no—
65C2×C4×D293—21no—
66C2×C4×D293C2311yescharacteristic
67#17989785—22no—
68C2×#14556873C2311yescharacteristic
69C2×#14556873C2311yescharacteristic
70C8×D293—22no—
71C4⋊Dic293—21no—
72C4⋊Dic293—21no—
73C4⋊Dic293C2311yescharacteristic
74C4⋊Dic293C2311yescharacteristic
75C4⋊Dic293C2311yescharacteristic
76#17989781—21no—
77#17989781—21no—
78#17989781—21no—
79#17989781—21no—
80#17989781—21no—
81#17989781—21no—
82#17989781—21no—
83#17989781D411yescharacteristic
84#17989781D411yescharacteristic
85#17989779—21no—
86#17989779—21no—
87#17989779D411yescharacteristic
88#17989779D411yescharacteristic
89C4×Dic293—21no—
90C4×Dic293—21no—
91C4×Dic293—21no—
92C4×Dic293—21no—
93C4×Dic293—21no—
94C4×Dic293C2311yescharacteristic
95C2×Q8×C293—21no—
96C2×Q8×C293C2311yescharacteristic
97C2×C8×C293C2311yescharacteristic
98C2×C8×C293C2311yescharacteristic
99C4⋊C4×C293—21no—
100C4⋊C4×C293—21no—
101C4⋊C4×C293C2311yescharacteristic
102C4⋊C4×C293C2311yescharacteristic
103C4⋊C4×C293C2311yescharacteristic
104C42×C293—21no—
105C42×C293C2311yescharacteristic
106C22×D293C2×D411yescharacteristic
107Dic586—21no—
108Dic586—24no—
109Dic586—81no—
110Dic586C2×Q812yes—
111C2×Dic293—21no—
112C2×Dic293—21no—
113C2×Dic293—21no—
114C2×Dic293—21no—
115C2×Dic293C2×D411yescharacteristic
116C2×Dic293C2×D411yescharacteristic
117C2×Dic293C2×D411yescharacteristic
118C4×D293—24no—
119C4×D293—81no—
120C4×D293C2×Q812yes—
121C4×D293#4112yes—
122#14556873—21no—
123#14556873—21no—
124Q8×C293—21no—
125Q8×C293—81no—
126Q8×C293C2×Q812yes—
127C2×C4×C293—21no—
128C2×C4×C293—21no—
129C2×C4×C293—21no—
130C2×C4×C293—21no—
131C2×C4×C293C2×D411yescharacteristic
132C2×C4×C293C2×D411yescharacteristic
133C2×C4×C293C2411yescharacteristic
134C8×C293—21no—
135C8×C293—21no—
136C22×C293C22×D411yescharacteristic
137C2×D293—21no—
138C2×D293—21no—
139C2×D293C22⋊Q812yes—
140C4×C293—22no—
141C4×C293—21no—
142C4×C293—21no—
143C4×C293—41no—
144C4×C293—41no—
145C4×C293—41no—
146C4×C293C22×Q811yescharacteristic
147C4×C293C2×#4111yescharacteristic
148Dic293—22no—
149Dic293—21no—
150Dic293—21no—
151Dic293—41no—
152Dic293—41no—
153Dic293—41no—
154Dic293C22⋊Q812yes—
155C2×C293C2×C22⋊Q811yescharacteristic
156C2×C293#57711yescharacteristic
157C2×C293#57811yescharacteristic
158D293—22no—
159C293#308211yescharacteristic, complemented, Sylow
160#3082—2931nomaximal, Sylow
161#544—2931no—
162#519—2931no—
163#479—2931no—
164#479—2931no—
165#479—2931no—
166#479—2931no—
167#477—2931no—
168#477—2931no—
169#475—2931no—
170#475D29311yescharacteristic, complemented
171#428—2931no—
172#427—2931no—
173#424—2931no—
174#419—2931no—
175C2×#103—2931no—
176C22×Q8—2931no—
177C2×M16—2931no—
178C22×C8—2931no—
179C4⋊Q8—2931no—
180C4⋊Q8—5861no—
181C4⋊Q8C2×D29311yescharacteristic
182#125—2931no—
183#125—2931no—
184#125—5861no—
185C22⋊Q8—5861no—
186C22⋊Q8—5861no—
187C4×Q8—2931no—
188C4×Q8—2931no—
189C4×Q8—2931no—
190C4×Q8—5861no—
191C4×Q8—5861no—
192C4×Q8C2×D29311yescharacteristic
193#117—2931no—
194#117—2931no—
195#117—2931no—
196#117—5861no—
197#117—5861no—
198C2×C4⋊C4—2931no—
199#107—2931no—
200#107—2931no—
201#107—2931no—
202#107—2931no—
203#106—2931no—
204#106—2931no—
205#106C2×D29311yescharacteristic
206#106C2×D29311yescharacteristic
207C4⋊C8—2931no—
208C4⋊C8—2931no—
209C4⋊C8—2931no—
210C4⋊C8C2×D29311yescharacteristic
211#103—2931no—
212#103—2931no—
213#103—2931no—
214#103—2931no—
215#103—2931no—
216#103—2931no—
217#103C2×D29311yescharacteristic
218#103C2×D29311yescharacteristic
219C2×Q8—21no—
220C2×Q8—2934no—
221C2×Q8—2931no—
222C2×Q8—5861no—
223C2×Q8—5861no—
224C2×Q8—5862no—
225C2×Q8C22×D29311yescharacteristic
226C22×C4—2931no—
227C22×C4—5861no—
228C22×C4—5861no—
229M16—5862no—
230C2×C8—2931no—
231C2×C8—2931no—
232C2×C8—5862no—
233C2×C8C22×D29311yescharacteristic
234C2×C8C22×D29311yescharacteristic
235C4⋊C4—21no—
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
253C4⋊C4C22×D29311yescharacteristic
254C22⋊C4—2931no—
255C22⋊C4—2931no—
256C22⋊C4—5861no—
257C22⋊C4—5861no—
258C42—21no—
259C42—2931no—
260C42—5861no—
261C42—5861no—
262C42—5861no—
263C42—5861no—
264C42—5861no—
265C42C22×D29311yescharacteristic
266C23—2931no—
267Q8—21no—
268Q8—81no—
269Q8—2932no—
270Q8—23441no—
271Q8—5864no—
272Q8—5861no—
273Q8Q8×D29312yes—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—2931no—
279C2×C4—2932no—
280C2×C4—2932no—
281C2×C4—2931no—
282C2×C4—2931no—
283C2×C4—23441no—
284C2×C4—5864no—
285C2×C4—5861no—
286C2×C4—5861no—
287C2×C4—5861no—
288C2×C4—5861no—
289C2×C4D4×D29311yescharacteristic
290C2×C4D4×D29311yescharacteristic
291C2×C4C23×D29311yescharacteristic
292C8—21no—
293C8—21no—
294C8—5861no—
295C8—5861no—
296C22—2932no—
297C22—5861no—
298C22—5861no—
299C22C2×D4×D29311yescharacteristic
300C4—22no—
301C4—21no—
302C4—21no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—2932no—
307C4—5862no—
308C4—5861no—
309C4—5861no—
310C4—11721no—
311C4—11721no—
312C4—11721no—
313C4C2×Q8×D29311yescharacteristic
314C4#41×D29311yescharacteristic
315C2—5862no—
316C2C22⋊Q8×D29311yescharacteristic
317C2#3403693511yescharacteristic
318C2#3403694511yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#475×C293C2
socleC22×C293C22×D4
prime radicalC22×D293C2×D4
hypercenter#475D293
hypocenterC293#3082
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
3. #34036439C2semidirect
4. #34036437C2semidirect
5. #34036436C2semidirect
6. #34036434C2semidirect
7. #34036422C2semidirect
8. #34036421C2semidirect
9. #34036413C2semidirect
15. #475×C293C2semidirect
63. Q8×D293Q8semidirect
159. C293#3082semidirect
170. #475D293semidirect

Maximal subgroups

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

subgroupindex
#340367562
#340366052
#340364392
#340364372
#340364362
#340364342
#340364222
#340364212
#340364132
#340361682
#340361642
#340361542
#340361362
#103×D2932
#475×C2932
#3082293