Finite Group Databasebeta

← #49171547

Subgroups — #49171547

Order 37504.

344 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036857C211yesmaximal, characteristic, complemented
2#34036493C211yesmaximal, characteristic
3#34036488C211yesmaximal, characteristic, complemented
4#34036483C211yesmaximal, characteristic, complemented
5#34036436C211yesmaximal, characteristic, complemented
6#34036429C211yesmaximal, characteristic, complemented
7#34036419C211yesmaximal, characteristic, complemented
8#34036348C211yesmaximal, characteristic, complemented
9#34036348C211yesmaximal, characteristic, complemented
10#34036326C211yesmaximal, characteristic
11#34036260C211yesmaximal, characteristic, complemented
12#34036234C211yesmaximal, characteristic, complemented
13#34036229C211yesmaximal, characteristic, complemented
14C4×#17989790C211yesmaximal, characteristic, complemented
15#559×C293C211yesmaximal, characteristic
16C2×#17989792C2211yescharacteristic
17C2×#17989790C2211yescharacteristic
18C2×#17989790C2211yescharacteristic
19#22627624C2211yescharacteristic
20#22627622—21no—
21#22627616C2211yescharacteristic
22#22627616C2211yescharacteristic
23#22627614—21no—
24#22627614—21no—
25C4×Dic586C2211yescharacteristic
26C4×Dic586C2211yescharacteristic
27C4×Dic586C2211yescharacteristic
28#22627589—21no—
29#22627557C2211yescharacteristic
30#22627555C2211yescharacteristic
31#22627555C2211yescharacteristic
32C4⋊#14556873C2211yescharacteristic
33C4⋊#14556873C2211yescharacteristic
34C4⋊#14556873C2211yescharacteristic
35#22627548C2211yescharacteristic
36#22627548C2211yescharacteristic
37#22627548C2211yescharacteristic
38#22627547C2211yescharacteristic
39#22627545C2211yescharacteristic
40#22627545C2211yescharacteristic
41#22627545C2211yescharacteristic
42#22627545C2211yescharacteristic
43#22627545C2211yescharacteristic
44#22627545C2211yescharacteristic
45#22627535C2211yescharacteristic
46#22627535C2211yescharacteristic
47C4×#14556873C2211yescharacteristic
48#127×C293C2211yescharacteristic
49#124×C293—21no—
50#124×C293C2211yescharacteristic
51#124×C293C2211yescharacteristic
52#123×C293—21no—
53#123×C293—21no—
54C4×Q8×C293C2211yescharacteristic
55C4×Q8×C293C2211yescharacteristic
56C4×D4×C293—21no—
57C4×D4×C293C2211yescharacteristic
58C4×D4×C293C2211yescharacteristic
59C2×Dic586—21no—
60C2×Dic586C2311yescharacteristic
61#17989792—22no—
62#17989790—22no—
63#17989790—22no—
64C2×#14556873C2311yescharacteristic
65C2×#14556873C2311yescharacteristic
66C2×#14556873C2311yescharacteristic
67C2×#14556873C2311yescharacteristic
68C4⋊Dic293—21no—
69C4⋊Dic293C2311yescharacteristic
70C4⋊Dic293C2311yescharacteristic
71C4⋊Dic293C2311yescharacteristic
72#17989781—21no—
73#17989781—21no—
74#17989781—21no—
75#17989781—21no—
76#17989781—21no—
77#17989781—21no—
78#17989781—21no—
79C4×Dic293—21no—
80C4×Dic293—21no—
81C4×Dic293—21no—
82C2×Q8×C293D411yescharacteristic
83C2×Q8×C293C2311yescharacteristic
84C2×D4×C293—21no—
85C2×D4×C293—21no—
86C2×D4×C293C2311yescharacteristic
87C2×D4×C293C2311yescharacteristic
88C22×C4×C293—21no—
89C22×C4×C293—21no—
90C4⋊C4×C293—21no—
91C4⋊C4×C293D411yescharacteristic
92C4⋊C4×C293D411yescharacteristic
93C4⋊C4×C293D411yescharacteristic
94C4⋊C4×C293C2311yescharacteristic
95C22⋊C4×C293—21no—
96C22⋊C4×C293—21no—
97C22⋊C4×C293—21no—
98C22⋊C4×C293—21no—
99C22⋊C4×C293—21no—
100C22⋊C4×C293—21no—
101C42×C293—21no—
102C42×C293C2311yescharacteristic
103C42×C293C2311yescharacteristic
104C42×C293C2311yescharacteristic
105Dic586—21no—
106Dic586—42no—
107Dic586#4112yes—
108C2×Dic293—21no—
109C2×Dic293—21no—
110C2×Dic293—21no—
111C2×Dic293—21no—
112#14556873—21no—
113#14556873—21no—
114#14556873—21no—
115#14556873—21no—
116C23×C293—21no—
117C23×C293—21no—
118Q8×C293—21no—
119Q8×C293—21no—
120Q8×C293—41no—
121D4×C293—21no—
122D4×C293—21no—
123D4×C293—21no—
124D4×C293—21no—
125D4×C293—42no—
126D4×C293—81no—
127C2×C4×C293—21no—
128C2×C4×C293—21no—
129C2×C4×C293—81no—
130C2×C4×C293—81no—
131C2×C4×C293C2×D411yescharacteristic
132C2×C4×C293C2×D411yescharacteristic
133C2×C4×C293C2×D411yescharacteristic
134C2×C4×C293C2×D411yescharacteristic
135C2×C4×C293C2×D411yescharacteristic
136C2×C4×C293C2×D411yescharacteristic
137C2×C4×C293C2411yescharacteristic
138C22×C293—41no—
139C22×C293—41no—
140C22×C293—41no—
141C22×C293—41no—
142C22×C293—41no—
143C22×C293—41no—
144C22×C293C22×D411yescharacteristic
145C4×C293—21no—
146C4×C293—21no—
147C4×C293—21no—
148C4×C293—21no—
149C4×C293—21no—
150C4×C293—21no—
151C4×C293—41no—
152C4×C293—41no—
153C4×C293C2×#4111yescharacteristic
154C4×C2932−1+411yescharacteristic
155Dic293—22no—
156Dic293—41no—
157Dic293—41no—
158Dic293—41no—
159C2×C293—81no—
160C2×C293—81no—
161C2×C293#54811yescharacteristic
162C2×C293#57511yescharacteristic
163C2×C293#57711yescharacteristic
164C293#337111yescharacteristic, complemented, Sylow
165#3371—2931nomaximal, Sylow
166#559D29311yescharacteristic
167#557—2931no—
168#490—2931no—
169#489—2931no—
170#488—2931no—
171#479—2931no—
172#478—2931no—
173#476—2931no—
174#464—2931no—
175#464—2931no—
176#460—2931no—
177#446—2931no—
178#441—2931no—
179#440—2931no—
180C4×SD16—2931no—
181C2×Q16—2931no—
182C2×SD16—2931no—
183C2×SD16—2931no—
184C4⋊Q8—2931no—
185C4⋊Q8—5861no—
186#127C2×D29311yescharacteristic
187#125—2931no—
188#125—2931no—
189#125—5861no—
190#125—5861no—
191#124—21no—
192#124C2×D29311yescharacteristic
193#124C2×D29311yescharacteristic
194#123—21no—
195#123—21no—
196C4×Q8—2931no—
197C4×Q8—2931no—
198C4×Q8—2931no—
199C4×Q8—5861no—
200C4×Q8C2×D29311yescharacteristic
201C4×Q8C2×D29311yescharacteristic
202C4×D4—21no—
203C4×D4C2×D29311yescharacteristic
204C4×D4C2×D29311yescharacteristic
205#107—2931no—
206#106—2931no—
207#106—2931no—
208C4⋊C8—2931no—
209C4⋊C8—2931no—
210C4⋊C8—2931no—
211#103—2931no—
212#103—2931no—
213#103—2931no—
214#103—2931no—
215#102—2931no—
216#102—2931no—
217#102—2931no—
218#102—2931no—
219#102—2931no—
220#102—2931no—
221#97—2931no—
222#97—2931no—
223C4×C8—2931no—
224C2×Q8—2931no—
225C2×Q8—5861no—
226C2×Q8C22⋊D29311yescharacteristic
227C2×Q8C22×D29311yescharacteristic
228C2×D4—21no—
229C2×D4—21no—
230C2×D4C22×D29311yescharacteristic
231C2×D4C22×D29311yescharacteristic
232C22×C4—21no—
233C22×C4—21no—
234Q16—5862no—
235SD16—5862no—
236SD16—5862no—
237C2×C8—2931no—
238C2×C8—2931no—
239C2×C8—2931no—
240C2×C8—2931no—
241C4⋊C4—21no—
242C4⋊C4—2931no—
243C4⋊C4—2931no—
244C4⋊C4—2931no—
245C4⋊C4—5861no—
246C4⋊C4—5861no—
247C4⋊C4—5861no—
248C4⋊C4—5861no—
249C4⋊C4—5861no—
250C4⋊C4—5861no—
251C4⋊C4—5861no—
252C4⋊C4—5861no—
253C4⋊C4C22⋊D29311yescharacteristic
254C4⋊C4C22⋊D29311yescharacteristic
255C4⋊C4C22⋊D29311yescharacteristic
256C4⋊C4C22×D29311yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—21no—
263C42—21no—
264C42—5861no—
265C42—5861no—
266C42—5861no—
267C42C22×D29311yescharacteristic
268C42C22×D29311yescharacteristic
269C42C22×D29311yescharacteristic
270C23—21no—
271C23—21no—
272Q8—21no—
273Q8—21no—
274Q8—41no—
275Q8—2932no—
276Q8—5861no—
277Q8—11722no—
278D4—21no—
279D4—21no—
280D4—21no—
281D4—21no—
282D4—42no—
283D4—81no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—5861no—
289C2×C4—5861no—
290C2×C4—5861no—
291C2×C4—5861no—
292C2×C4C2×C22⋊D29311yescharacteristic
293C2×C4C2×C22⋊D29311yescharacteristic
294C2×C4C2×C22⋊D29311yescharacteristic
295C2×C4C2×C22⋊D29311yescharacteristic
296C2×C4C2×C22⋊D29311yescharacteristic
297C2×C4C2×C22⋊D29311yescharacteristic
298C2×C4C23×D29311yescharacteristic
299C8—5861no—
300C8—5861no—
301C8—5861no—
302C8—5861no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22C22×C22⋊D29311yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—5862no—
319C4—11721no—
320C4—11721no—
321C4—11721no—
322C4#41×D29311yescharacteristic
323C4#2262767111yescharacteristic
324C2—81no—
325C2—81no—
326C2#3403678611yescharacteristic
327C2#3403692711yescharacteristic
328C2#3403694011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#559×C293C2
socleC22×C293C22×D4
prime radical#127×C293C22
hypercenter#559D293
hypocenterC293#3371
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #34036857C2semidirect
3. #34036488C2semidirect
4. #34036483C2semidirect
5. #34036436C2semidirect
6. #34036429C2semidirect
7. #34036419C2semidirect
8. #34036348C2semidirect
9. #34036348C2semidirect
11. #34036260C2semidirect
12. #34036234C2semidirect
13. #34036229C2semidirect
14. C4×#17989790C2semidirect
164. C293#3371semidirect

Maximal subgroups

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

subgroupindex
#340368572
#340364932
#340364882
#340364832
#340364362
#340364292
#340364192
#340363482
#340363262
#340362602
#340362342
#340362292
C4×#179897902
#559×C2932
#3371293