Finite Group Databasebeta

← #49171533

Subgroups — #49171533

Order 37504.

358 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036865C211yesmaximal, characteristic, complemented
2#34036835C211yesmaximal, characteristic, complemented
3#34036487C211yesmaximal, characteristic, complemented
4#34036482C211yesmaximal, characteristic, complemented
5#34036433C211yesmaximal, characteristic, complemented
6#34036427C211yesmaximal, characteristic, complemented
7#34036407C211yesmaximal, characteristic, complemented
8#34036343C211yesmaximal, characteristic, complemented
9#34036343C211yesmaximal, characteristic, complemented
10#34036321C211yesmaximal, characteristic
11#34036257C211yesmaximal, characteristic, complemented
12#34036238C211yesmaximal, characteristic, complemented
13#34036231C211yesmaximal, characteristic, complemented
14#34036209C211yesmaximal, characteristic, complemented
15#490×C293C211yesmaximal, characteristic, complemented
16C2×#17989791C2211yescharacteristic
17C2×#17989787C2211yescharacteristic
18C2×#17989787C2211yescharacteristic
19#22627623C2211yescharacteristic
20#22627615C2211yescharacteristic
21#22627611—21no—
22#22627611C2211yescharacteristic
23#22627611C2211yescharacteristic
24#22627605—21no—
25#22627605—21no—
26#22627604—21no—
27#22627602—21no—
28#22627602—21no—
29C4×Dic586C2211yescharacteristic
30C4×Dic586C2211yescharacteristic
31C4×D1172C2211yescharacteristic
32D4×Dic293—21no—
33D4×Dic293C2211yescharacteristic
34D4×Dic293C2211yescharacteristic
35#22627586C2211yescharacteristic
36#22627586C2211yescharacteristic
37C4⋊C4×D293—21no—
38#22627558C2211yescharacteristic
39#22627557C2211yescharacteristic
40#22627555C2211yescharacteristic
41C4⋊#14556873C2211yescharacteristic
42#22627553C2211yescharacteristic
43#22627553C2211yescharacteristic
44#22627549C2211yescharacteristic
45#22627547C2211yescharacteristic
46#22627547C2211yescharacteristic
47#22627546C2211yescharacteristic
48#22627545C2211yescharacteristic
49#22627545C2211yescharacteristic
50#22627534C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52#127×C293C2211yescharacteristic
53#125×C293C2211yescharacteristic
54#102×C293C2211yescharacteristic
55#102×C293C2211yescharacteristic
56#102×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58#97×C293C2211yescharacteristic
59C2×Dic586—21no—
60C2×Dic586D411yescharacteristic
61C2×Dic586C2311yescharacteristic
62C2×D1172C2311yescharacteristic
63C22×Dic293—21no—
64C22×Dic293—21no—
65C2×C4×D293—21no—
66C2×C4×D293—21no—
67C2×C4×D293—21no—
68#17989791—22no—
69#17989787—22no—
70#17989787—22no—
71C2×#14556873C2311yescharacteristic
72C2×#14556873C2311yescharacteristic
73C4⋊Dic293—21no—
74C4⋊Dic293D411yescharacteristic
75C4⋊Dic293C2311yescharacteristic
76C4⋊Dic293C2311yescharacteristic
77#17989781—21no—
78#17989781—21no—
79#17989781—21no—
80#17989781D411yescharacteristic
81#17989781D411yescharacteristic
82C22⋊Dic293—21no—
83C22⋊Dic293—21no—
84C22⋊Dic293—21no—
85C22⋊Dic293—21no—
86C22⋊Dic293—21no—
87C22⋊Dic293—21no—
88#17989779—21no—
89#17989779—21no—
90#17989779—21no—
91C4×Dic293—21no—
92C4×Dic293C2311yescharacteristic
93C4×Dic293C2311yescharacteristic
94C2×D4×C293—21no—
95C2×D4×C293—21no—
96C2×D4×C293C2311yescharacteristic
97C2×D4×C293C2311yescharacteristic
98C2×C8×C293C2311yescharacteristic
99C2×C8×C293C2311yescharacteristic
100C4⋊C4×C293—21no—
101C4⋊C4×C293—21no—
102C4⋊C4×C293C2311yescharacteristic
103C4⋊C4×C293C2311yescharacteristic
104C42×C293C2311yescharacteristic
105C22×D293—21no—
106Dic586—21no—
107Dic586—21no—
108Dic586—41no—
109Dic586—81no—
110D1172—21no—
111D1172#4112yes—
112C2×Dic293—21no—
113C2×Dic293—21no—
114C2×Dic293—21no—
115C2×Dic293—81no—
116C2×Dic293—81no—
117C2×Dic293C2×D411yescharacteristic
118C2×Dic293C2×D411yescharacteristic
119C2×Dic293C2×D411yescharacteristic
120C2×Dic293C2×D411yescharacteristic
121C4×D293—42no—
122C4×D293—81no—
123C4×D293—81no—
124#14556873—21no—
125#14556873—21no—
126C23×C293—21no—
127C23×C293—21no—
128D4×C293—21no—
129D4×C293—21no—
130D4×C293—21no—
131D4×C293—21no—
132D4×C293—42no—
133D4×C293—81no—
134C2×C4×C293—21no—
135C2×C4×C293—21no—
136C2×C4×C293C2×D411yescharacteristic
137C2×C4×C293C2×D411yescharacteristic
138C2×C4×C293C2411yescharacteristic
139C8×C293—21no—
140C8×C293—21no—
141C22×C293—41no—
142C22×C293—41no—
143C22×C293—41no—
144C22×C293—41no—
145C22×C293—41no—
146C22×C293—41no—
147C22×C293C22×D411yescharacteristic
148C2×D293—22no—
149C2×D293—41no—
150C2×D293—41no—
151C4×C293—21no—
152C4×C293—21no—
153C4×C293—41no—
154C4×C293—41no—
155C4×C293C2×#4111yescharacteristic
156C4×C2932−1+411yescharacteristic
157Dic293—21no—
158Dic293—21no—
159Dic293—21no—
160Dic293—21no—
161Dic293—41no—
162Dic293—41no—
163Dic293—41no—
164C2×C293—81no—
165C2×C293—81no—
166C2×C293#54811yescharacteristic
167C2×C293#57511yescharacteristic
168C2×C293#57611yescharacteristic
169D293—42no—
170C293#337011yescharacteristic, complemented, Sylow
171#3370—2931nomaximal, Sylow
172#559—2931no—
173#554—2931no—
174#490D29311yescharacteristic, complemented
175#489—2931no—
176#488—2931no—
177#479—2931no—
178#478—2931no—
179#474—2931no—
180#463—2931no—
181#463—2931no—
182#459—2931no—
183#446—2931no—
184#442—2931no—
185#440—2931no—
186C4×D8—2931no—
187C2×SD16—2931no—
188C2×D8—2931no—
189C2×D8—2931no—
190C4⋊Q8—2931no—
191#127C2×D29311yescharacteristic
192#125—2931no—
193#125C2×D29311yescharacteristic
194#124—2931no—
195#124—2931no—
196#124—5861no—
197#123—5861no—
198#123—5861no—
199C22⋊Q8—5861no—
200C22⋊Q8—5861no—
201C22⋊Q8—5861no—
202C4×Q8—2931no—
203C4×Q8—2931no—
204C4×D4—2931no—
205C4×D4—2931no—
206C4×D4—2931no—
207C4×D4—2931no—
208C4×D4—2931no—
209C4×D4—5861no—
210C2×C4⋊C4—5861no—
211#107—2931no—
212#107—2931no—
213#106—2931no—
214C4⋊C8—2931no—
215C4⋊C8—2931no—
216C4⋊C8—2931no—
217#103—2931no—
218#103—2931no—
219#103—2931no—
220#102—2931no—
221#102—2931no—
222#102—2931no—
223#102C2×D29311yescharacteristic
224#102C2×D29311yescharacteristic
225#102C2×D29311yescharacteristic
226#102C2×D29311yescharacteristic
227#97—2931no—
228#97C2×D29311yescharacteristic
229C4×C8—2931no—
230C2×Q8—2931no—
231C2×Q8—2931no—
232C2×Q8—5861no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—2931no—
236C2×D4C22×D29311yescharacteristic
237C2×D4C22×D29311yescharacteristic
238C22×C4—5861no—
239C22×C4—5861no—
240C22×C4—5861no—
241C22×C4—5861no—
242C22×C4—5861no—
243SD16—5862no—
244D8—5862no—
245D8—5862no—
246C2×C8—2931no—
247C2×C8—2931no—
248C2×C8C22×D29311yescharacteristic
249C2×C8C22×D29311yescharacteristic
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—2931no—
253C4⋊C4—2931no—
254C4⋊C4—2931no—
255C4⋊C4—2931no—
256C4⋊C4—2931no—
257C4⋊C4—5861no—
258C4⋊C4—5861no—
259C4⋊C4—5861no—
260C4⋊C4—5861no—
261C4⋊C4C22×D29311yescharacteristic
262C4⋊C4C22×D29311yescharacteristic
263C22⋊C4—5861no—
264C22⋊C4—5861no—
265C22⋊C4—5861no—
266C22⋊C4—5861no—
267C22⋊C4—5861no—
268C22⋊C4—5861no—
269C22⋊C4—5861no—
270C22⋊C4—5861no—
271C22⋊C4—5861no—
272C42—2931no—
273C42—2931no—
274C42—5861no—
275C42C22×D29311yescharacteristic
276C23—21no—
277C23—21no—
278C23—5861no—
279Q8—23441no—
280Q8—5861no—
281Q8—5861no—
282Q8—11721no—
283D4—21no—
284D4—21no—
285D4—21no—
286D4—21no—
287D4—42no—
288D4—81no—
289D4—2932no—
290D4—5861no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—2931no—
294C2×C4—2931no—
295C2×C4—2931no—
296C2×C4—2931no—
297C2×C4—23441no—
298C2×C4—23441no—
299C2×C4—23441no—
300C2×C4—23441no—
301C2×C4—5861no—
302C2×C4—5861no—
303C2×C4—5861no—
304C2×C4—11722no—
305C2×C4D4×D29311yescharacteristic
306C2×C4D4×D29311yescharacteristic
307C2×C4C23×D29311yescharacteristic
308C8—21no—
309C8—21no—
310C8—5861no—
311C8—5861no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—5862no—
319C22—11721no—
320C22—11721no—
321C22C2×D4×D29311yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—5861no—
327C4—5861no—
328C4—5861no—
329C4—5861no—
330C4—11721no—
331C4—11721no—
332C4—11721no—
333C4#41×D29311yescharacteristic
334C4#2262767111yescharacteristic
335C2—81no—
336C2—81no—
337C2—11722no—
338C2#3403678711yescharacteristic
339C2#3403692511yescharacteristic
340C2#3403693311yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#490×C293C2
socleC22×C293C22×D4
prime radical#34036321C2
hypercenter#490D293
hypocenterC293#3370
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #34036865C2semidirect
2. #34036835C2semidirect
3. #34036487C2semidirect
4. #34036482C2semidirect
5. #34036433C2semidirect
6. #34036427C2semidirect
7. #34036407C2semidirect
8. #34036343C2semidirect
9. #34036343C2semidirect
11. #34036257C2semidirect
12. #34036238C2semidirect
13. #34036231C2semidirect
14. #34036209C2semidirect
15. #490×C293C2semidirect
170. C293#3370semidirect
174. #490D293semidirect

Maximal subgroups

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

subgroupindex
#340368652
#340368352
#340364872
#340364822
#340364332
#340364272
#340364072
#340363432
#340363212
#340362572
#340362382
#340362312
#340362092
#490×C2932
#3370293