Finite Group Databasebeta

← #49169009

Subgroups — #49169009

Order 37504.

370 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#34036746C211yesmaximal, characteristic
2#34036606C211yesmaximal, characteristic, complemented
3#34036470C211yesmaximal, characteristic, complemented
4#34036423C211yesmaximal, characteristic, complemented
5#34036413C211yesmaximal, characteristic, complemented
6#34036350C211yesmaximal, characteristic, complemented
7#34036350C211yesmaximal, characteristic, complemented
8#34036287C211yesmaximal, characteristic, complemented
9#34036267C211yesmaximal, characteristic
10#34036235C211yesmaximal, characteristic, complemented
11#34036226C211yesmaximal, characteristic, complemented
12#34036223C211yesmaximal, characteristic, complemented
13#34036220C211yesmaximal, characteristic, complemented
14#34036187C211yesmaximal, characteristic, complemented
15#482×C293C211yesmaximal, characteristic
16C22×Dic586C2211yescharacteristic
17C2×Dic1172C2211yescharacteristic
18C2×Dic1172C2211yescharacteristic
19C2×#17989790C2211yescharacteristic
20C2×#17989790C2211yescharacteristic
21#22627623C2211yescharacteristic
22#22627617—21no—
23#22627611—21no—
24#22627611C2211yescharacteristic
25#22627605—21no—
26#22627603C2211yescharacteristic
27#22627601—21no—
28C4×Dic586—21no—
29C4×Dic586—21no—
30#22627589C2211yescharacteristic
31#22627589C2211yescharacteristic
32#22627589C2211yescharacteristic
33#22627589C2211yescharacteristic
34#22627589C2211yescharacteristic
35D4×Dic293C2211yescharacteristic
36#22627583C2211yescharacteristic
37#22627580—21no—
38#22627580—21no—
39#22627557C2211yescharacteristic
40#22627555C2211yescharacteristic
41#22627553C2211yescharacteristic
42#22627553C2211yescharacteristic
43#22627549C2211yescharacteristic
44#22627549C2211yescharacteristic
45#22627547C2211yescharacteristic
46#22627547C2211yescharacteristic
47#22627547C2211yescharacteristic
48#22627547C2211yescharacteristic
49C22⋊#14556873C2211yescharacteristic
50#22627534C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52#121×C293C2211yescharacteristic
53#117×C293C2211yescharacteristic
54#107×C293C2211yescharacteristic
55#106×C293C2211yescharacteristic
56#102×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58C22⋊C8×C293C2211yescharacteristic
59C2×Dic586—22no—
60C2×Dic586—22no—
61C2×Dic586—21no—
62C2×Dic586—21no—
63C2×Dic586C2311yescharacteristic
64C2×Dic586C2311yescharacteristic
65C2×Dic586C2311yescharacteristic
66C22×Dic293—21no—
67C22×Dic293—21no—
68Dic1172—22no—
69Dic1172—22no—
70#17989790—22no—
71#17989790—22no—
72C2×#14556873C2311yescharacteristic
73C2×#14556873C2311yescharacteristic
74C4⋊Dic293D411yescharacteristic
75C4⋊Dic293D411yescharacteristic
76C4⋊Dic293C2311yescharacteristic
77#17989781—21no—
78#17989781—21no—
79#17989781—21no—
80#17989781—21no—
81#17989781—21no—
82#17989781—21no—
83#17989781—21no—
84C22⋊Dic293—21no—
85C22⋊Dic293—21no—
86C22⋊Dic293—21no—
87C22⋊Dic293—21no—
88C22⋊Dic293D411yescharacteristic
89C22⋊Dic293D411yescharacteristic
90C4×Dic293—21no—
91C4×Dic293—21no—
92C4×Dic293—21no—
93C4×Dic293—21no—
94C4×Dic293—21no—
95C4×Dic293C2311yescharacteristic
96C4×Dic293C2311yescharacteristic
97C2×D4×C293—21no—
98C2×D4×C293C2311yescharacteristic
99C22×C4×C293C2311yescharacteristic
100C2×C8×C293C2311yescharacteristic
101C2×C8×C293C2311yescharacteristic
102C4⋊C4×C293C2311yescharacteristic
103C4⋊C4×C293C2311yescharacteristic
104C4⋊C4×C293C2311yescharacteristic
105C22⋊C4×C293—21no—
106C22⋊C4×C293—21no—
107C42×C293—21no—
108Dic586—24no—
109Dic586—21no—
110Dic586—21no—
111Dic586—21no—
112Dic586—21no—
113Dic586—81no—
114Dic586#4112yes—
115Dic586#4112yes—
116C2×Dic293—24no—
117C2×Dic293—21no—
118C2×Dic293—21no—
119C2×Dic293—21no—
120C2×Dic293—21no—
121C2×Dic293—81no—
122C2×Dic293C2×D411yescharacteristic
123C2×Dic293C2×D411yescharacteristic
124C2×Dic293C2×D411yescharacteristic
125C2×Dic293C2×D411yescharacteristic
126#14556873—21no—
127#14556873—21no—
128C23×C293—21no—
129C23×C293C2×D411yescharacteristic
130D4×C293—21no—
131D4×C293—21no—
132D4×C293—81no—
133C2×C4×C293—21no—
134C2×C4×C293—21no—
135C2×C4×C293—21no—
136C2×C4×C293—21no—
137C2×C4×C293—21no—
138C2×C4×C293C2×D411yescharacteristic
139C2×C4×C293C2411yescharacteristic
140C8×C293—21no—
141C8×C293—21no—
142C22×C293—21no—
143C22×C293—21no—
144C22×C293—21no—
145C22×C293—41no—
146C22×C293—41no—
147C22×C293—41no—
148C22×C293C22×D411yescharacteristic
149C4×C293—21no—
150C4×C293—41no—
151C4×C293—41no—
152C4×C293—41no—
153C4×C293C2×#4111yescharacteristic
154C4×C293C2×#4111yescharacteristic
155Dic293—22no—
156Dic293—22no—
157Dic293—21no—
158Dic293—21no—
159Dic293—21no—
160Dic293—21no—
161Dic293—41no—
162Dic293—41no—
163C2×C293—41no—
164C2×C293—81no—
165C2×C293#52511yescharacteristic
166C2×C293#57711yescharacteristic
167C2×C293#57811yescharacteristic
168C293#312111yescharacteristic, complemented, Sylow
169#3121—2931nomaximal, Sylow
170#542—2931no—
171#519—2931no—
172#485—2931no—
173#482D29311yescharacteristic
174#477—2931no—
175#475—2931no—
176#464—2931no—
177#464—2931no—
178#451—2931no—
179#448—2931no—
180#441—2931no—
181#440—2931no—
182C4×Q16—2931no—
183C4×SD16—2931no—
184#433—2931no—
185C22×Q8—2931no—
186C2×Q16—2931no—
187C2×Q16—2931no—
188C2×SD16—2931no—
189C2×SD16—2931no—
190C4⋊Q8—2931no—
191#126—5861no—
192#124—2931no—
193#124—5861no—
194#123—5861no—
195C22⋊Q8—2931no—
196C22⋊Q8—5861no—
197#121C2×D29311yescharacteristic
198C4×Q8—2931no—
199C4×Q8—2931no—
200C4×Q8—2931no—
201C4×Q8—2931no—
202C4×Q8—2931no—
203C4×Q8—5861no—
204C4×Q8—5861no—
205C4×D4—2931no—
206#117—2931no—
207#117—5861no—
208#117—5861no—
209#117C2×D29311yescharacteristic
210#107—2931no—
211#107C2×D29311yescharacteristic
212#106—2931no—
213#106C2×D29311yescharacteristic
214C4⋊C8—2931no—
215C4⋊C8—2931no—
216#103—2931no—
217#103—2931no—
218#103—2931no—
219#103—2931no—
220#103—2931no—
221#103—2931no—
222#102C2×D29311yescharacteristic
223#102C2×D29311yescharacteristic
224C22⋊C8—2931no—
225C22⋊C8C2×D29311yescharacteristic
226#97—2931no—
227C4×C8—2931no—
228C2×Q8—2931no—
229C2×Q8—2931no—
230C2×Q8—2931no—
231C2×Q8—5861no—
232C2×Q8—5862no—
233C2×Q8—5862no—
234C2×Q8—5861no—
235C2×D4—21no—
236C2×D4C22×D29311yescharacteristic
237C22×C4—5861no—
238C22×C4—5861no—
239C22×C4C22×D29311yescharacteristic
240Q16—5862no—
241Q16—5862no—
242SD16—5862no—
243SD16—5862no—
244C2×C8—2931no—
245C2×C8—2931no—
246C2×C8C22×D29311yescharacteristic
247C2×C8C22×D29311yescharacteristic
248C4⋊C4—2931no—
249C4⋊C4—2931no—
250C4⋊C4—2931no—
251C4⋊C4—5861no—
252C4⋊C4—5861no—
253C4⋊C4—5861no—
254C4⋊C4—5861no—
255C4⋊C4—5861no—
256C4⋊C4—5861no—
257C4⋊C4—5861no—
258C4⋊C4C22×D29311yescharacteristic
259C4⋊C4C22×D29311yescharacteristic
260C4⋊C4C22×D29311yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—2931no—
264C22⋊C4—2931no—
265C22⋊C4—5861no—
266C22⋊C4—5861no—
267C22⋊C4—5861no—
268C22⋊C4—5861no—
269C42—21no—
270C42—2931no—
271C42—2931no—
272C42—5861no—
273C42—5861no—
274C42—5861no—
275C42—5861no—
276C42—5861no—
277C23—21no—
278C23D4×D29311yescharacteristic
279Q8—2932no—
280Q8—2932no—
281Q8—23441no—
282Q8—5864no—
283Q8—5861no—
284Q8—5861no—
285Q8—5861no—
286Q8—5861no—
287D4—21no—
288D4—21no—
289D4—81no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—2931no—
296C2×C4—2931no—
297C2×C4—2931no—
298C2×C4—2931no—
299C2×C4—23441no—
300C2×C4—5864no—
301C2×C4—5861no—
302C2×C4—5861no—
303C2×C4—5861no—
304C2×C4—5861no—
305C2×C4D4×D29311yescharacteristic
306C2×C4C23×D29311yescharacteristic
307C8—21no—
308C8—21no—
309C8—5861no—
310C8—5861no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22C2×D4×D29311yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—5862no—
323C4—5862no—
324C4—5861no—
325C4—5861no—
326C4—5861no—
327C4—5861no—
328C4—11721no—
329C4—11721no—
330C4#41×D29311yescharacteristic
331C4#41×D29311yescharacteristic
332C2—41no—
333C2—81no—
334C2#3403663711yescharacteristic
335C2#3403693911yescharacteristic
336C2#3403694311yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#482×C293C2
socleC22×C293C22×D4
prime radical#121×C293C22
hypercenter#482D293
hypocenterC293#3121
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #34036606C2semidirect
3. #34036470C2semidirect
4. #34036423C2semidirect
5. #34036413C2semidirect
6. #34036350C2semidirect
7. #34036350C2semidirect
8. #34036287C2semidirect
10. #34036235C2semidirect
11. #34036226C2semidirect
12. #34036223C2semidirect
13. #34036220C2semidirect
14. #34036187C2semidirect
168. C293#3121semidirect

Maximal subgroups

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

subgroupindex
#340367462
#340366062
#340364702
#340364232
#340364132
#340363502
#340362872
#340362672
#340362352
#340362262
#340362232
#340362202
#340361872
#482×C2932
#3121293