Finite Group Databasebeta

← #49161905

Subgroups — #49161905

Order 37504.

496 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22627618C211yesmaximal, characteristic
2#34036026C211yesmaximal, characteristic, complemented
3#34036021C211yesmaximal, characteristic
4#34036020C211yesmaximal, characteristic
5#34036018C211yesmaximal, characteristic
6#34036016C211yesmaximal, characteristic, complemented
7#34036013C211yesmaximal, characteristic, complemented
8#34036011C211yesmaximal, characteristic, complemented
9#34036003C211yesmaximal, characteristic
10C4×#17989781C211yesmaximal, characteristic, complemented
11C4×C4⋊Dic293C211yesmaximal, characteristic, complemented
12#34035980C211yesmaximal, characteristic, complemented
13C4×#17989779C211yesmaximal, characteristic
14#34035976C211yesmaximal, characteristic
15#376×C293C211yesmaximal, characteristic, complemented
16C22×C4×D293C2211yescharacteristic
17#22627618C418yescomplemented
18C2×C4⋊Dic293C2211yescharacteristic
19C2×C4⋊Dic293C2211yescharacteristic
20C2×#17989781C2211yescharacteristic
21C2×#17989781C2211yescharacteristic
22C2×#17989781C2211yescharacteristic
23C2×#17989781C2211yescharacteristic
24C2×#17989781C2211yescharacteristic
25C2×#17989781C2211yescharacteristic
26C2×#17989779C2211yescharacteristic
27C2×#17989779C2211yescharacteristic
28C2×#17989779C2211yescharacteristic
29C2×#17989779C2211yescharacteristic
30C2×#17989779C2211yescharacteristic
31C2×#17989779C2211yescharacteristic
32C2×C4×Dic293C2211yescharacteristic
33C2×C4×Dic293C2211yescharacteristic
34C2×C4×Dic293C2211yescharacteristic
35C2×C4×Dic293C2211yescharacteristic
36C2×C4×Dic293C2211yescharacteristic
37#22627531C2211yescharacteristic
38#22627531C2211yescharacteristic
39#22627531C2211yescharacteristic
40#22627531C2211yescharacteristic
41#22627531C2211yescharacteristic
42#22627531C2211yescharacteristic
43#22627531C2211yescharacteristic
44#22627531C2211yescharacteristic
45C2×C42×C293C2211yescharacteristic
46C2×C42×C293C2211yescharacteristic
47C2×C42×C293C2211yescharacteristic
48#95×C293C2211yescharacteristic
49#95×C293C2211yescharacteristic
50#95×C293C2211yescharacteristic
51#95×C293C2211yescharacteristic
52C23×D293C2311yescharacteristic
53C22×Dic293C2311yescharacteristic
54C22×Dic293C2311yescharacteristic
55C22×Dic293C2311yescharacteristic
56C22×Dic293C2311yescharacteristic
57C22×Dic293C2311yescharacteristic
58C22×Dic293C2311yescharacteristic
59C22×Dic293C2311yescharacteristic
60C2×C4×D293—22no—
61C2×C4×D293—22no—
62C2×C4×D293—41no—
63C4⋊Dic293—22no—
64C4⋊Dic293—22no—
65#17989781—22no—
66#17989781—22no—
67#17989781—41no—
68#17989781C2×C414yescomplemented
69#17989781C2×C414yescomplemented
70#17989781C2×C414yescomplemented
71#17989779—22no—
72#17989779—22no—
73#17989779—41no—
74#17989779C2×C414yes—
75#17989779C2×C414yes—
76#17989779C2×C414yes—
77C4×Dic293—22no—
78C4×Dic293—22no—
79C4×Dic293—41no—
80C4×Dic293—41no—
81C4×Dic293—41no—
82C22×C4×C293C2311yescharacteristic
83C22×C4×C293C2311yescharacteristic
84C22×C4×C293C2311yescharacteristic
85C22×C4×C293C2311yescharacteristic
86C22×C4×C293C2311yescharacteristic
87C22×C4×C293C2311yescharacteristic
88C22×C4×C293C2311yescharacteristic
89C42×C293—22no—
90C42×C293—22no—
91C42×C293C2×C414yescomplemented
92C22×D293—21no—
93C22×D293—21no—
94C22×D293—21no—
95C22×D293—21no—
96C22×D293—21no—
97C22×D293—21no—
98C22×D293C22×C412yes—
99C2×Dic293—21no—
100C2×Dic293—21no—
101C2×Dic293—21no—
102C2×Dic293—21no—
103C2×Dic293—21no—
104C2×Dic293—21no—
105C2×Dic293—21no—
106C2×Dic293—21no—
107C2×Dic293—21no—
108C2×Dic293—21no—
109C2×Dic293—21no—
110C2×Dic293—21no—
111C2×Dic293—21no—
112C2×Dic293—21no—
113C2×Dic293—21no—
114C2×Dic293—21no—
115C2×Dic293C22×C412yes—
116C2×Dic293C22×C412yes—
117C2×Dic293C22×C412yes—
118C2×Dic293#4112yes—
119C2×Dic293#4112yes—
120C4×D293—44no—
121C23×C293C2411yescharacteristic
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×C293—21no—
134C2×C4×C293—21no—
135C2×C4×C293—21no—
136C2×C4×C293—21no—
137C2×C4×C293—21no—
138C2×C4×C293C22×C412yes—
139C2×C4×C293C22×C412yes—
140C2×C4×C293C22×C412yes—
141C2×C4×C293#4112yes—
142C2×C4×C293#4112yes—
143C22×C293C23×C411yescharacteristic
144C22×C293C2×#4111yescharacteristic
145C22×C293C2×#4111yescharacteristic
146C22×C293C2×#4111yescharacteristic
147C22×C293C2×#4111yescharacteristic
148C22×C293H(5,𝔽2)11yescharacteristic
149C22×C2932−1+411yescharacteristic
150C2×D293—22no—
151C2×D293—22no—
152C2×D293—22no—
153C2×D293—41no—
154C2×D293—41no—
155C2×D293—41no—
156C2×D293—41no—
157C4×C293—22no—
158C4×C293—22no—
159C4×C293—22no—
160C4×C293—22no—
161C4×C293—22no—
162C4×C293—41no—
163C4×C293—41no—
164Dic293—22no—
165Dic293—22no—
166Dic293—22no—
167Dic293—22no—
168Dic293—22no—
169Dic293—41no—
170Dic293—41no—
171C2×C293C4×#4111yescharacteristic
172C2×C293C4×#4111yescharacteristic
173C2×C293#52011yescharacteristic
174C2×C293#55111yescharacteristic
175C2×C293#55211yescharacteristic
176C2×C293#55311yescharacteristic
177C2×C293#55611yescharacteristic
178D293—42no—
179C293#237311yescharacteristic, complemented, Sylow
180#2373—2931nomaximal, Sylow
181C2×#126—2931no—
182#389—2931no—
183#388—2931no—
184#388—2931no—
185#388—2931no—
186#387—2931no—
187#387—2931no—
188#387—2931no—
189#385—2931no—
190C4×C4⋊C4—2931no—
191C4×C4⋊C4—2931no—
192C4×C4⋊C4—2931no—
193C4×C22⋊C4—2931no—
194C4×C22⋊C4—2931no—
195#376D29311yescharacteristic, complemented
196C23×C4—2931no—
197#126—2938no—
198C2×C4⋊C4—2931no—
199C2×C4⋊C4—2931no—
200C2×C4⋊C4—2931no—
201C2×C4⋊C4—2931no—
202C2×C4⋊C4—2931no—
203C2×C4⋊C4—2931no—
204C2×C4⋊C4—2931no—
205C2×C4⋊C4—2931no—
206C2×C22⋊C4—2931no—
207C2×C22⋊C4—2931no—
208C2×C22⋊C4—2931no—
209C2×C22⋊C4—2931no—
210C2×C22⋊C4—2931no—
211C2×C22⋊C4—2931no—
212C2×C42—2931no—
213C2×C42—2931no—
214C2×C42—2931no—
215C2×C42—2931no—
216C2×C42—2931no—
217C2×C42C2×D29311yescharacteristic
218C2×C42C2×D29311yescharacteristic
219C2×C42C2×D29311yescharacteristic
220#95—2931no—
221#95—2931no—
222#95—2931no—
223#95—2931no—
224#95—2931no—
225#95—2931no—
226#95—2931no—
227#95—2931no—
228#95C2×D29311yescharacteristic
229#95C2×D29311yescharacteristic
230#95C2×D29311yescharacteristic
231#95C2×D29311yescharacteristic
232C24—2931no—
233C22×C4—2931no—
234C22×C4—2931no—
235C22×C4—2931no—
236C22×C4—2931no—
237C22×C4—2931no—
238C22×C4—2931no—
239C22×C4—2931no—
240C22×C4—5862no—
241C22×C4—5862no—
242C22×C4—11721no—
243C22×C4C22×D29311yescharacteristic
244C22×C4C22×D29311yescharacteristic
245C22×C4C22×D29311yescharacteristic
246C22×C4C22×D29311yescharacteristic
247C22×C4C22×D29311yescharacteristic
248C22×C4C22×D29311yescharacteristic
249C22×C4C22×D29311yescharacteristic
250C4⋊C4—2934no—
251C4⋊C4—2934no—
252C4⋊C4—2934no—
253C4⋊C4—5862no—
254C4⋊C4—5862no—
255C4⋊C4—5862no—
256C4⋊C4—5862no—
257C4⋊C4—11721no—
258C22⋊C4—2934no—
259C22⋊C4—2934no—
260C22⋊C4—2934no—
261C22⋊C4—5862no—
262C22⋊C4—5862no—
263C22⋊C4—11721no—
264C42—22no—
265C42—22no—
266C42—5862no—
267C42—5862no—
268C42—11721no—
269C42—11721no—
270C42—11721no—
271C42C4×D29314yescomplemented
272C23—2932no—
273C23—5861no—
274C23—5861no—
275C23—5861no—
276C23—5861no—
277C23—5861no—
278C23—5861no—
279C23C23×D29311yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—2932no—
297C2×C4—2932no—
298C2×C4—2932no—
299C2×C4—2932no—
300C2×C4—2932no—
301C2×C4—5861no—
302C2×C4—5861no—
303C2×C4—5861no—
304C2×C4—5861no—
305C2×C4—5861no—
306C2×C4—5861no—
307C2×C4—5861no—
308C2×C4—5861no—
309C2×C4—5861no—
310C2×C4—5861no—
311C2×C4—5861no—
312C2×C4—5861no—
313C2×C4—5861no—
314C2×C4—5861no—
315C2×C4—5861no—
316C2×C4—5861no—
317C2×C4—11724no—
318C2×C4C2×C4×D29312yes—
319C2×C4C2×C4×D29312yes—
320C2×C4C2×C4×D29312yes—
321C2×C4#1798980212yes—
322C2×C4#1798980212yes—
323C22—5862no—
324C22—5862no—
325C22—5862no—
326C22—11721no—
327C22—11721no—
328C22—11721no—
329C22—11721no—
330C22C22×C4×D29311yescharacteristic
331C22#41×D29311yescharacteristic
332C22#41×D29311yescharacteristic
333C22C2×#1798980211yescharacteristic
334C22C2×#1798980211yescharacteristic
335C22#2262767011yescharacteristic
336C22#2262767111yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—22no—
341C4—22no—
342C4—41no—
343C4—41no—
344C4—5862no—
345C4—5862no—
346C4—5862no—
347C4—5862no—
348C4—5862no—
349C4—11721no—
350C4—11721no—
351C2—11722no—
352C2#3403659711yescharacteristic
353C2C4×#1798980211yescharacteristic
354C2#3403660911yescharacteristic
355C2#3403680311yescharacteristic
356C2#3403681211yescharacteristic
357C2#3403682311yescharacteristic
358C2#3403684711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D293
commutatorC22×C293C23×C4
Fitting#376×C293C2
socle, cosocleC23×C293C24
prime radicalC23×D293C23
hypercenter#376D293
hypocenterC293#2373
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C23 ◁ #376

Complements

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

NH ≅ G/Ntype
2. #34036026C2semidirect
6. #34036016C2semidirect
7. #34036013C2semidirect
8. #34036011C2semidirect
10. C4×#17989781C2semidirect
11. C4×C4⋊Dic293C2semidirect
12. #34035980C2semidirect
15. #376×C293C2semidirect
17. #22627618C4semidirect
68. #17989781C2×C4semidirect
69. #17989781C2×C4semidirect
70. #17989781C2×C4semidirect
91. C42×C293C2×C4semidirect
179. C293#2373semidirect
195. #376D293semidirect
271. C42C4×D293semidirect

Maximal subgroups

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

subgroupindex
C2×#226276182
#340360262
#340360212
#340360202
#340360182
#340360162
#340360132
#340360112
#340360032
C4×#179897812
C4×C4⋊Dic2932
#340359802
C4×#179897792
#340359762
#376×C2932
#2373293