Finite Group Databasebeta

← #49161739

Subgroups — #49161739

Order 37504.

480 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22627589C211yesmaximal, characteristic
2#34036033C211yesmaximal, characteristic
3#34036033C211yesmaximal, characteristic
4#34036016C211yesmaximal, characteristic
5#34036015C211yesmaximal, characteristic
6#34036010C211yesmaximal, characteristic
7#34035998C211yesmaximal, characteristic
8#34035993C211yesmaximal, characteristic
9#34035993C211yesmaximal, characteristic
10C4×#17989781C211yesmaximal, characteristic
11C4×#17989781C211yesmaximal, characteristic
12#34035980C211yesmaximal, characteristic
13#34035980C211yesmaximal, characteristic
14#34035980C211yesmaximal, characteristic
15#387×C293C211yesmaximal, characteristic
16C22×Dic586C2211yescharacteristic
17#22627589C418yescomplemented
18C2×C4⋊Dic293C2211yescharacteristic
19C2×#17989781C2211yescharacteristic
20C2×#17989781C2211yescharacteristic
21C2×#17989781C2211yescharacteristic
22C2×#17989781C2211yescharacteristic
23C2×#17989781C2211yescharacteristic
24C2×#17989781C2211yescharacteristic
25C2×#17989781C2211yescharacteristic
26C2×#17989781C2211yescharacteristic
27C2×C4×Dic293C2211yescharacteristic
28C2×C4×Dic293C2211yescharacteristic
29C2×C4×Dic293C2211yescharacteristic
30C2×C4×Dic293C2211yescharacteristic
31C2×C4×Dic293C2211yescharacteristic
32C2×C4×Dic293C2211yescharacteristic
33C2×C4×Dic293C2211yescharacteristic
34C2×C4×Dic293C2211yescharacteristic
35#22627531C2211yescharacteristic
36#22627531C2211yescharacteristic
37#22627531C2211yescharacteristic
38#22627531C2211yescharacteristic
39#22627531C2211yescharacteristic
40#22627531C2211yescharacteristic
41#22627531C2211yescharacteristic
42#22627531C2211yescharacteristic
43#22627531C2211yescharacteristic
44#22627531C2211yescharacteristic
45C2×C4⋊C4×C293C2211yescharacteristic
46C2×C4⋊C4×C293C2211yescharacteristic
47C2×C42×C293C2211yescharacteristic
48#95×C293C2211yescharacteristic
49#95×C293C2211yescharacteristic
50#95×C293C2211yescharacteristic
51#95×C293C2211yescharacteristic
52C2×Dic586—22no—
53C2×Dic586—22no—
54C2×Dic586C2×C414yes—
55C22×Dic293C2311yescharacteristic
56C22×Dic293C2311yescharacteristic
57C22×Dic293C2311yescharacteristic
58C22×Dic293C2311yescharacteristic
59C22×Dic293C2311yescharacteristic
60C22×Dic293C2311yescharacteristic
61C22×Dic293C2311yescharacteristic
62C22×Dic293C2311yescharacteristic
63C4⋊Dic293—41no—
64#17989781—22no—
65#17989781—22no—
66#17989781—22no—
67#17989781—22no—
68#17989781—22no—
69#17989781C2×C414yes—
70#17989781C2×C414yes—
71#17989781Q814yescomplemented
72C4×Dic293—22no—
73C4×Dic293—22no—
74C4×Dic293—41no—
75C4×Dic293—41no—
76C4×Dic293—41no—
77C4×Dic293C2×C414yes—
78C4×Dic293C2×C414yes—
79C4×Dic293C2×C414yes—
80C22×C4×C293C2311yescharacteristic
81C22×C4×C293C2311yescharacteristic
82C22×C4×C293C2311yescharacteristic
83C22×C4×C293C2311yescharacteristic
84C22×C4×C293C2311yescharacteristic
85C22×C4×C293C2311yescharacteristic
86C22×C4×C293C2311yescharacteristic
87C4⋊C4×C293—41no—
88C4⋊C4×C293C2×C414yes—
89C42×C293—41no—
90Dic586—28no—
91C2×Dic293—21no—
92C2×Dic293—21no—
93C2×Dic293—21no—
94C2×Dic293—21no—
95C2×Dic293—21no—
96C2×Dic293—21no—
97C2×Dic293—21no—
98C2×Dic293—21no—
99C2×Dic293—21no—
100C2×Dic293—21no—
101C2×Dic293—21no—
102C2×Dic293—21no—
103C2×Dic293—21no—
104C2×Dic293—21no—
105C2×Dic293—21no—
106C2×Dic293C22×C412yes—
107C2×Dic293C22×C412yes—
108C2×Dic293C22×C412yes—
109C2×Dic293C22×C412yes—
110C2×Dic293C2×Q812yes—
111C2×Dic293C2×Q812yes—
112C2×Dic293#4112yes—
113C2×Dic293#4112yes—
114C2×Dic293#4112yes—
115C23×C293C2411yescharacteristic
116C2×C4×C293—21no—
117C2×C4×C293—21no—
118C2×C4×C293—21no—
119C2×C4×C293—21no—
120C2×C4×C293—21no—
121C2×C4×C293—21no—
122C2×C4×C293—21no—
123C2×C4×C293—21no—
124C2×C4×C293—21no—
125C2×C4×C293—21no—
126C2×C4×C293—21no—
127C2×C4×C293—21no—
128C2×C4×C293—21no—
129C2×C4×C293—21no—
130C2×C4×C293—21no—
131C2×C4×C293—21no—
132C2×C4×C293—21no—
133C2×C4×C293C22×C412yes—
134C2×C4×C293C22×C412yes—
135C2×C4×C293C22×C412yes—
136C2×C4×C293C2×Q812yes—
137C22×C293C23×C411yescharacteristic
138C22×C293C22×Q811yescharacteristic
139C22×C293C2×#4111yescharacteristic
140C22×C293C2×#4111yescharacteristic
141C22×C293C2×#4111yescharacteristic
142C22×C293H(5,𝔽2)11yescharacteristic
143C22×C2932−1+411yescharacteristic
144C4×C293—22no—
145C4×C293—22no—
146C4×C293—22no—
147C4×C293—22no—
148C4×C293—41no—
149C4×C293—41no—
150C4×C293—41no—
151Dic293—22no—
152Dic293—22no—
153Dic293—22no—
154Dic293—41no—
155Dic293—41no—
156Dic293—41no—
157Dic293#11714yes—
158Dic293C4×Q814yes—
159C2×C293C2×#11711yescharacteristic
160C2×C293C2×C4×Q811yescharacteristic
161C2×C293#52011yescharacteristic
162C2×C293#55411yescharacteristic
163C2×C293#55611yescharacteristic
164C2×C293#55711yescharacteristic
165C2×C293#55911yescharacteristic
166C293#235511yescharacteristic, complemented, Sylow
167#2355—2931nomaximal, Sylow
168C2×C4×Q8—2931no—
169#391—2931no—
170#391—2931no—
171#387—2931no—
172#387—2931no—
173#387—2931no—
174#387D29311yescharacteristic
175#384—2931no—
176#382—2931no—
177#382—2931no—
178C4×C4⋊C4—2931no—
179C4×C4⋊C4—2931no—
180C4×C4⋊C4—2931no—
181C4×C4⋊C4—2931no—
182C4×C4⋊C4—2931no—
183C22×Q8—2931no—
184C4×Q8—2938no—
185C2×C4⋊C4—2931no—
186C2×C4⋊C4—2931no—
187C2×C4⋊C4—2931no—
188C2×C4⋊C4—2931no—
189C2×C4⋊C4—2931no—
190C2×C4⋊C4—2931no—
191C2×C4⋊C4—2931no—
192C2×C4⋊C4—2931no—
193C2×C4⋊C4—2931no—
194C2×C4⋊C4C2×D29311yescharacteristic
195C2×C4⋊C4C2×D29311yescharacteristic
196C2×C42—2931no—
197C2×C42—2931no—
198C2×C42—2931no—
199C2×C42—2931no—
200C2×C42—2931no—
201C2×C42—2931no—
202C2×C42—2931no—
203C2×C42—2931no—
204C2×C42C2×D29311yescharacteristic
205#95—2931no—
206#95—2931no—
207#95—2931no—
208#95—2931no—
209#95—2931no—
210#95—2931no—
211#95—2931no—
212#95—2931no—
213#95—2931no—
214#95—2931no—
215#95C2×D29311yescharacteristic
216#95C2×D29311yescharacteristic
217#95C2×D29311yescharacteristic
218#95C2×D29311yescharacteristic
219C2×Q8—2934no—
220C2×Q8—5862no—
221C2×Q8—5862no—
222C22×C4—2931no—
223C22×C4—2931no—
224C22×C4—2931no—
225C22×C4—2931no—
226C22×C4—2931no—
227C22×C4—2931no—
228C22×C4—2931no—
229C22×C4—2931no—
230C22×C4C22×D29311yescharacteristic
231C22×C4C22×D29311yescharacteristic
232C22×C4C22×D29311yescharacteristic
233C22×C4C22×D29311yescharacteristic
234C22×C4C22×D29311yescharacteristic
235C22×C4C22×D29311yescharacteristic
236C22×C4C22×D29311yescharacteristic
237C4⋊C4—41no—
238C4⋊C4—2934no—
239C4⋊C4—2934no—
240C4⋊C4—2934no—
241C4⋊C4—5862no—
242C4⋊C4—5862no—
243C4⋊C4—5862no—
244C4⋊C4—5862no—
245C4⋊C4—5862no—
246C4⋊C4—11721no—
247C4⋊C4C4×D29314yes—
248C42—41no—
249C42—2934no—
250C42—2934no—
251C42—2934no—
252C42—5862no—
253C42—5862no—
254C42—11721no—
255C42—11721no—
256C42—11721no—
257C23C23×D29311yescharacteristic
258Q8—5868no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—2932no—
277C2×C4—2932no—
278C2×C4—2932no—
279C2×C4—2932no—
280C2×C4—2932no—
281C2×C4—2932no—
282C2×C4—2932no—
283C2×C4—2932no—
284C2×C4—2932no—
285C2×C4—5861no—
286C2×C4—5861no—
287C2×C4—5861no—
288C2×C4—5861no—
289C2×C4—5861no—
290C2×C4—5861no—
291C2×C4—5861no—
292C2×C4—5861no—
293C2×C4—5861no—
294C2×C4—5861no—
295C2×C4—5861no—
296C2×C4—5861no—
297C2×C4—5861no—
298C2×C4—5861no—
299C2×C4—5861no—
300C2×C4C2×C4×D29312yes—
301C2×C4C2×C4×D29312yes—
302C2×C4C2×C4×D29312yes—
303C2×C4Q8×D29312yes—
304C22C22×C4×D29311yescharacteristic
305C22C2×Q8×D29311yescharacteristic
306C22#41×D29311yescharacteristic
307C22#41×D29311yescharacteristic
308C22#41×D29311yescharacteristic
309C22#2262766911yescharacteristic
310C22#2262767111yescharacteristic
311C4—22no—
312C4—22no—
313C4—22no—
314C4—22no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—2934no—
319C4—2934no—
320C4—5862no—
321C4—5862no—
322C4—5862no—
323C4—11721no—
324C4—11721no—
325C4—11721no—
326C2#117×D29311yescharacteristic
327C2C4×Q8×D29311yescharacteristic
328C2#3403660811yescharacteristic
329C2#3403683311yescharacteristic
330C2#3403684611yescharacteristic
331C2#3403685611yescharacteristic
332C2#3403686311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D293
commutatorC22×C293C23×C4
Fitting#387×C293C2
socle, prime radical, cosocleC23×C293C24
hypercenter#387D293
hypocenterC293#2355
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
17. #22627589C4semidirect
71. #17989781Q8semidirect
166. C293#2355semidirect

Maximal subgroups

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

subgroupindex
C2×#226275892
#340360332
#340360162
#340360152
#340360102
#340359982
#340359932
C4×#179897812
#340359802
#387×C2932
#2355293