Finite Group Databasebeta

← #49161644

Subgroups — #49161644

Order 37504.

532 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22627582C211yesmaximal, characteristic
2#34036015C211yesmaximal, characteristic, complemented
3#34036014C211yesmaximal, characteristic, complemented
4#34036012C211yesmaximal, characteristic, complemented
5#34036003C211yesmaximal, characteristic
6#34036000C211yesmaximal, characteristic
7#34035996C211yesmaximal, characteristic, complemented
8#34035994C211yesmaximal, characteristic, complemented
9#34035991C211yesmaximal, characteristic
10C4×#17989781C211yesmaximal, characteristic, complemented
11C4×#17989779C211yesmaximal, characteristic
12#34035976C211yesmaximal, characteristic
13#34035974C211yesmaximal, characteristic, complemented
14#95×D293C211yesmaximal, characteristic
15#387×C293C211yesmaximal, characteristic, complemented
16C22×C4×D293C2211yescharacteristic
17C22×C4×D293C2211yescharacteristic
18C22×C4×D293C2211yescharacteristic
19#22627582C418yescomplemented
20C2×C4⋊Dic293C2211yescharacteristic
21C2×C4⋊Dic293C2211yescharacteristic
22C2×#17989781C2211yescharacteristic
23C2×#17989781C2211yescharacteristic
24C2×#17989779C2211yescharacteristic
25C2×#17989779C2211yescharacteristic
26C2×#17989779C2211yescharacteristic
27C2×#17989779C2211yescharacteristic
28C2×C4×Dic293C2211yescharacteristic
29C2×C4×Dic293C2211yescharacteristic
30C2×C4×Dic293C2211yescharacteristic
31C2×C4×Dic293C2211yescharacteristic
32C2×C4×Dic293C2211yescharacteristic
33#22627531C2211yescharacteristic
34#22627531C2211yescharacteristic
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
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—22no—
63C2×C4×D293—22no—
64C2×C4×D293—22no—
65C2×C4×D293—22no—
66C2×C4×D293—41no—
67C2×C4×D293—41no—
68C2×C4×D293C2×C414yes—
69C4⋊Dic293—41no—
70C4⋊Dic293C2×C414yescomplemented
71#17989781—22no—
72#17989781—22no—
73#17989779—22no—
74#17989779—22no—
75#17989779C2×C414yes—
76#17989779C2×C414yes—
77C4×Dic293—22no—
78C4×Dic293—22no—
79C4×Dic293—41no—
80C4×Dic293C2×C414yescomplemented
81C4×Dic293C2×C414yescomplemented
82C22×C4×C293C2311yescharacteristic
83C22×C4×C293C2311yescharacteristic
84C22×C4×C293C2311yescharacteristic
85C22×C4×C293C2311yescharacteristic
86C22×C4×C293C2311yescharacteristic
87C22×C4×C293C2311yescharacteristic
88C22×C4×C293C2311yescharacteristic
89C4⋊C4×C293—41no—
90C4⋊C4×C293C2×C414yescomplemented
91C42×C293—41no—
92C22×D293—21no—
93C22×D293—21no—
94C22×D293—21no—
95C22×D293—21no—
96C22×D293C22×C412yes—
97C22×D293#4112yes—
98C22×D293#4112yes—
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×Dic293—21no—
116C2×Dic293C22×C412yes—
117C2×Dic293C22×C412yes—
118C2×Dic293C22×C412yes—
119C2×Dic293#4112yes—
120C4×D293—28no—
121C4×D293—44no—
122C4×D293—44no—
123C23×C293C2411yescharacteristic
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×C293—21no—
139C2×C4×C293—21no—
140C2×C4×C293—21no—
141C2×C4×C293C22×C412yes—
142C2×C4×C293C22×C412yes—
143C2×C4×C293C22×C412yes—
144C2×C4×C293#4112yes—
145C22×C293C23×C411yescharacteristic
146C22×C293C2×#4111yescharacteristic
147C22×C293C2×#4111yescharacteristic
148C22×C293C2×#4111yescharacteristic
149C22×C293C2×#4111yescharacteristic
150C22×C293H(5,𝔽2)11yescharacteristic
151C22×C2932−1+411yescharacteristic
152C2×D293—22no—
153C2×D293—22no—
154C2×D293—22no—
155C2×D293—22no—
156C2×D293—22no—
157C2×D293—22no—
158C2×D293#11714yes—
159C4×C293—22no—
160C4×C293—22no—
161C4×C293—22no—
162C4×C293—22no—
163C4×C293—41no—
164C4×C293—41no—
165C4×C293—41no—
166Dic293—22no—
167Dic293—22no—
168Dic293—22no—
169Dic293—22no—
170Dic293—41no—
171Dic293—41no—
172Dic293—41no—
173C2×C293C2×#11711yescharacteristic
174C2×C293C4×#4111yescharacteristic
175C2×C293#52011yescharacteristic
176C2×C293#55111yescharacteristic
177C2×C293#55111yescharacteristic
178C2×C293#55211yescharacteristic
179C2×C293#55211yescharacteristic
180D293—24no—
181C293#234311yescharacteristic, complemented, Sylow
182#2343—2931nomaximal, Sylow
183C2×#117—2931no—
184#387—2931no—
185#387—2931no—
186#387—2931no—
187#387D29311yescharacteristic, complemented
188#385—2931no—
189#385—2931no—
190#383—2931no—
191#382—2931no—
192#381—2931no—
193C4×C4⋊C4—2931no—
194C4×C22⋊C4—2931no—
195C4×C22⋊C4—2931no—
196#376—2931no—
197C2×#95—2931no—
198C23×C4—2931no—
199C23×C4—2931no—
200C23×C4—2931no—
201#117—2938no—
202C2×C4⋊C4—2931no—
203C2×C4⋊C4—2931no—
204C2×C4⋊C4—2931no—
205C2×C4⋊C4—2931no—
206C2×C4⋊C4C2×D29311yescharacteristic
207C2×C4⋊C4C2×D29311yescharacteristic
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
218#95—2931no—
219#95—2931no—
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#95—2931no—
229#95—2931no—
230#95C2×D29311yescharacteristic
231#95C2×D29311yescharacteristic
232#95C2×D29311yescharacteristic
233#95C2×D29311yescharacteristic
234C24—2931no—
235C22×C4—2931no—
236C22×C4—2931no—
237C22×C4—2931no—
238C22×C4—2931no—
239C22×C4—2934no—
240C22×C4—2931no—
241C22×C4—2931no—
242C22×C4—2931no—
243C22×C4—5862no—
244C22×C4—5862no—
245C22×C4—5862no—
246C22×C4—5862no—
247C22×C4—5862no—
248C22×C4—5862no—
249C22×C4—11721no—
250C22×C4—11721no—
251C22×C4C22×D29311yescharacteristic
252C22×C4C22×D29311yescharacteristic
253C22×C4C22×D29311yescharacteristic
254C22×C4C22×D29311yescharacteristic
255C22×C4C22×D29311yescharacteristic
256C22×C4C22×D29311yescharacteristic
257C22×C4C22×D29311yescharacteristic
258C4⋊C4—41no—
259C4⋊C4—2934no—
260C4⋊C4—5862no—
261C4⋊C4—5862no—
262C4⋊C4—11721no—
263C4⋊C4C4×D29314yescomplemented
264C22⋊C4—2934no—
265C22⋊C4—2934no—
266C22⋊C4—5862no—
267C22⋊C4—5862no—
268C42—41no—
269C42—2934no—
270C42—2934no—
271C42—5862no—
272C42—5862no—
273C42—11721no—
274C23—2932no—
275C23—2932no—
276C23—2932no—
277C23—5861no—
278C23—5861no—
279C23—5861no—
280C23—5861no—
281C23C23×D29311yescharacteristic
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—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—2932no—
300C2×C4—2932no—
301C2×C4—2932no—
302C2×C4—2932no—
303C2×C4—5868no—
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—5861no—
318C2×C4—5861no—
319C2×C4—5861no—
320C2×C4—5861no—
321C2×C4—11724no—
322C2×C4—11724no—
323C2×C4C2×C4×D29312yes—
324C2×C4C2×C4×D29312yes—
325C2×C4C2×C4×D29312yes—
326C2×C4#1798980312yes—
327C22—2934no—
328C22—5862no—
329C22—5862no—
330C22—5862no—
331C22—5862no—
332C22—5862no—
333C22—5862no—
334C22C22×C4×D29311yescharacteristic
335C22#41×D29311yescharacteristic
336C22#41×D29311yescharacteristic
337C22#41×D29311yescharacteristic
338C22C2×#1798980311yescharacteristic
339C22#2262766911yescharacteristic
340C22#2262767111yescharacteristic
341C4—22no—
342C4—22no—
343C4—22no—
344C4—22no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—5862no—
349C4—5862no—
350C4—5862no—
351C4—5862no—
352C4—11721no—
353C4—11721no—
354C4—11721no—
355C2—5864no—
356C2#117×D29311yescharacteristic
357C2C4×#1798980311yescharacteristic
358C2#3403660811yescharacteristic
359C2#3403680611yescharacteristic
360C2#3403680711yescharacteristic
361C2#3403681511yescharacteristic
362C2#3403681711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D293
commutatorC22×C293C23×C4
Fitting#387×C293C2
socle, cosocleC23×C293C24
prime radicalC23×D293C23
hypercenter#387D293
hypocenterC293#2343
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #34036015C2semidirect
3. #34036014C2semidirect
4. #34036012C2semidirect
7. #34035996C2semidirect
8. #34035994C2semidirect
10. C4×#17989781C2semidirect
13. #34035974C2semidirect
15. #387×C293C2semidirect
19. #22627582C4semidirect
70. C4⋊Dic293C2×C4semidirect
80. C4×Dic293C2×C4semidirect
81. C4×Dic293C2×C4semidirect
90. C4⋊C4×C293C2×C4semidirect
181. C293#2343semidirect
187. #387D293semidirect
263. C4⋊C4C4×D293semidirect

Maximal subgroups

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

subgroupindex
C2×#226275822
#340360152
#340360142
#340360122
#340360032
#340360002
#340359962
#340359942
#340359912
C4×#179897812
C4×#179897792
#340359762
#340359742
#95×D2932
#387×C2932
#2343293