Finite Group Databasebeta

← #49168999

Subgroups — #49168999

Order 37504.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036741C211yesmaximal, characteristic, complemented
2#34036464C211yesmaximal, characteristic, complemented
3#34036459C211yesmaximal, characteristic, complemented
4#34036436C211yesmaximal, characteristic, complemented
5#34036429C211yesmaximal, characteristic, complemented
6#34036339C211yesmaximal, characteristic, complemented
7#34036334C211yesmaximal, characteristic, complemented
8#34036291C211yesmaximal, characteristic
9#34036291C211yesmaximal, characteristic
10#34036234C211yesmaximal, characteristic, complemented
11#34036229C211yesmaximal, characteristic, complemented
12C4×#17989792C211yesmaximal, characteristic, complemented
13C4×#17989790C211yesmaximal, characteristic, complemented
14#34036190C211yesmaximal, characteristic, complemented
15#520×C293C211yesmaximal, characteristic
16C2×#17989792C2211yescharacteristic
17C2×#17989792C2211yescharacteristic
18C2×#17989790C2211yescharacteristic
19C2×#17989790C2211yescharacteristic
20#22627624C2211yescharacteristic
21#22627617—21no—
22#22627617—21no—
23#22627616C2211yescharacteristic
24#22627614—21no—
25#22627614—21no—
26#22627603C2211yescharacteristic
27#22627603C2211yescharacteristic
28C4×Dic586C2211yescharacteristic
29C4×Dic586C2211yescharacteristic
30#22627557C2211yescharacteristic
31#22627557C2211yescharacteristic
32#22627555C2211yescharacteristic
33#22627555C2211yescharacteristic
34C4⋊#14556873C2211yescharacteristic
35C4⋊#14556873C2211yescharacteristic
36#22627548C2211yescharacteristic
37#22627548C2211yescharacteristic
38#22627547C2211yescharacteristic
39#22627547C2211yescharacteristic
40#22627547C2211yescharacteristic
41#22627547C2211yescharacteristic
42#22627545C2211yescharacteristic
43#22627545C2211yescharacteristic
44C22⋊#14556873C2211yescharacteristic
45C22⋊#14556873C2211yescharacteristic
46#22627535C2211yescharacteristic
47C4×#14556873C2211yescharacteristic
48C2×#41×C293C2211yescharacteristic
49C4×Q8×C293C2211yescharacteristic
50C4×Q8×C293C2211yescharacteristic
51C4×D4×C293—21no—
52C4×D4×C293—21no—
53C4×D4×C293C2211yescharacteristic
54C4×D4×C293C2211yescharacteristic
55#117×C293—21no—
56#117×C293C2211yescharacteristic
57C2×C4⋊C4×C293—21no—
58C2×C4⋊C4×C293C2211yescharacteristic
59C2×Dic586C2311yescharacteristic
60C2×Dic586C2311yescharacteristic
61#17989792—22no—
62#17989792—22no—
63#17989790—22no—
64#17989790—22no—
65C2×#14556873C2311yescharacteristic
66C2×#14556873C2311yescharacteristic
67C2×#14556873C2311yescharacteristic
68C2×#14556873C2311yescharacteristic
69C4⋊Dic293—21no—
70C4⋊Dic293—21no—
71C4⋊Dic293C2311yescharacteristic
72C4⋊Dic293C2311yescharacteristic
73#17989781—21no—
74#17989781—21no—
75#17989781—21no—
76#17989781—21no—
77#17989781—21no—
78#17989781—21no—
79C22⋊Dic293—21no—
80C22⋊Dic293—21no—
81C4×Dic293—21no—
82C4×Dic293—21no—
83#41×C293—22no—
84#41×C293—22no—
85C2×Q8×C293C2311yescharacteristic
86C2×D4×C293—21no—
87C2×D4×C293C2311yescharacteristic
88C22×C4×C293—21no—
89C22×C4×C293—21no—
90C22×C4×C293—21no—
91C22×C4×C293—21no—
92C22×C4×C293C2311yescharacteristic
93C4⋊C4×C293—21no—
94C4⋊C4×C293—21no—
95C4⋊C4×C293—21no—
96C4⋊C4×C293D411yescharacteristic
97C4⋊C4×C293D411yescharacteristic
98C4⋊C4×C293C2311yescharacteristic
99C4⋊C4×C293C2311yescharacteristic
100C22⋊C4×C293—21no—
101C22⋊C4×C293—21no—
102C22⋊C4×C293D411yescharacteristic
103C22⋊C4×C293D411yescharacteristic
104C42×C293—21no—
105C42×C293—21no—
106C42×C293C2311yescharacteristic
107C42×C293C2311yescharacteristic
108Dic586—21no—
109Dic586—21no—
110Dic586—21no—
111Dic586—21no—
112C2×Dic293—21no—
113C2×Dic293—21no—
114C2×Dic293—21no—
115C2×Dic293—21no—
116#14556873—21no—
117#14556873—21no—
118#14556873—21no—
119#14556873—21no—
120C23×C293—21no—
121C23×C293C2×D411yescharacteristic
122Q8×C293—21no—
123Q8×C293#4112yes—
124D4×C293—24no—
125D4×C293—21no—
126D4×C293#4112yes—
127C2×C4×C293—24no—
128C2×C4×C293—21no—
129C2×C4×C293—21no—
130C2×C4×C293—21no—
131C2×C4×C293—21no—
132C2×C4×C293—21no—
133C2×C4×C293—81no—
134C2×C4×C293—81no—
135C2×C4×C293—81no—
136C2×C4×C293C2×D411yescharacteristic
137C2×C4×C293C2×D411yescharacteristic
138C2×C4×C293C2×D411yescharacteristic
139C2×C4×C293C2×D411yescharacteristic
140C2×C4×C293C2×D411yescharacteristic
141C2×C4×C293C2411yescharacteristic
142C22×C293—21no—
143C22×C293—22no—
144C22×C293—21no—
145C22×C293—21no—
146C22×C293—41no—
147C22×C293—41no—
148C22×C293C22×D411yescharacteristic
149C4×C293—21no—
150C4×C293—22no—
151C4×C293—21no—
152C4×C293—21no—
153C4×C293—21no—
154C4×C293—21no—
155C4×C293—41no—
156C4×C293—41no—
157C4×C293C2×#4111yescharacteristic
158C4×C293C2×#4111yescharacteristic
159Dic293—41no—
160Dic293—41no—
161Dic293—41no—
162Dic293—41no—
163C2×C293—41no—
164C2×C293—42no—
165C2×C293#52511yescharacteristic
166C2×C293#57711yescharacteristic
167C2×C293#57811yescharacteristic
168C293#312011yescharacteristic, complemented, Sylow
169#3120—2931nomaximal, Sylow
170#541—2931no—
171#520D29311yescharacteristic
172#484—2931no—
173#483—2931no—
174#479—2931no—
175#478—2931no—
176#462—2931no—
177#461—2931no—
178#452—2931no—
179#452—2931no—
180#441—2931no—
181#440—2931no—
182C4×Q16—2931no—
183C4×SD16—2931no—
184#433—2931no—
185C2×#41C2×D29311yescharacteristic
186C2×Q16—2931no—
187C2×Q16—2931no—
188C2×SD16—2931no—
189C2×SD16—2931no—
190C4⋊Q8—2931no—
191#126—5861no—
192#126—5861no—
193#125—2931no—
194#125—5861no—
195#125—5861no—
196C22⋊Q8—2931no—
197C22⋊Q8—2931no—
198C4×Q8—2931no—
199C4×Q8—2931no—
200C4×Q8C2×D29311yescharacteristic
201C4×Q8C2×D29311yescharacteristic
202C4×D4—21no—
203C4×D4—21no—
204C4×D4C2×D29311yescharacteristic
205C4×D4C2×D29311yescharacteristic
206#117—21no—
207#117C2×D29311yescharacteristic
208C2×C4⋊C4—21no—
209C2×C4⋊C4C2×D29311yescharacteristic
210#107—2931no—
211#107—2931no—
212#106—2931no—
213#106—2931no—
214C4⋊C8—2931no—
215C4⋊C8—2931no—
216#103—2931no—
217#103—2931no—
218#103—2931no—
219#103—2931no—
220#103—2931no—
221#103—2931no—
222#102—2931no—
223#102—2931no—
224C22⋊C8—2931no—
225C22⋊C8—2931no—
226#97—2931no—
227C4×C8—2931no—
228#41—22no—
229#41—22no—
230C2×Q8—2931no—
231C2×Q8—2931no—
232C2×Q8C22×D29311yescharacteristic
233C2×D4—21no—
234C2×D4C22×D29311yescharacteristic
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4C22×D29311yescharacteristic
240Q16—5862no—
241Q16—5862no—
242SD16—5862no—
243SD16—5862no—
244C2×C8—2931no—
245C2×C8—2931no—
246C2×C8—2931no—
247C2×C8—2931no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—2931no—
252C4⋊C4—2931no—
253C4⋊C4—5861no—
254C4⋊C4—5861no—
255C4⋊C4—5861no—
256C4⋊C4—5861no—
257C4⋊C4—5861no—
258C4⋊C4—5861no—
259C4⋊C4—5861no—
260C4⋊C4—5861no—
261C4⋊C4C22⋊D29311yescharacteristic
262C4⋊C4C22⋊D29311yescharacteristic
263C4⋊C4C22×D29311yescharacteristic
264C4⋊C4C22×D29311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—5861no—
268C22⋊C4—5861no—
269C22⋊C4C22⋊D29311yescharacteristic
270C22⋊C4C22⋊D29311yescharacteristic
271C42—21no—
272C42—21no—
273C42—5861no—
274C42—5861no—
275C42C22×D29311yescharacteristic
276C42C22×D29311yescharacteristic
277C23—21no—
278C23C2×C22⋊D29311yescharacteristic
279Q8—21no—
280Q8—5861no—
281Q8—5861no—
282Q8—5861no—
283Q8—5861no—
284Q8#1798980212yes—
285D4—24no—
286D4—21no—
287D4#1798980212yes—
288C2×C4—24no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—5861no—
298C2×C4—5861no—
299C2×C4—5861no—
300C2×C4—5861no—
301C2×C4C2×C22⋊D29311yescharacteristic
302C2×C4C2×C22⋊D29311yescharacteristic
303C2×C4C2×C22⋊D29311yescharacteristic
304C2×C4C2×C22⋊D29311yescharacteristic
305C2×C4C2×C22⋊D29311yescharacteristic
306C2×C4C23×D29311yescharacteristic
307C8—5861no—
308C8—5861no—
309C8—5861no—
310C8—5861no—
311C22—21no—
312C22—22no—
313C22—21no—
314C22—21no—
315C22—41no—
316C22—41no—
317C22C22×C22⋊D29311yescharacteristic
318C4—21no—
319C4—22no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—11721no—
327C4—11721no—
328C4—11721no—
329C4—11721no—
330C4C2×#1798980211yescharacteristic
331C4C2×#1798980211yescharacteristic
332C2—41no—
333C2—42no—
334C2#3403664011yescharacteristic
335C2#3403694011yescharacteristic
336C2#3403694411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#520×C293C2
socleC22×C293C22×D4
prime radicalC2×#41×C293C22
hypercenter#520D293
hypocenterC293#3120
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #34036741C2semidirect
2. #34036464C2semidirect
3. #34036459C2semidirect
4. #34036436C2semidirect
5. #34036429C2semidirect
6. #34036339C2semidirect
7. #34036334C2semidirect
10. #34036234C2semidirect
11. #34036229C2semidirect
12. C4×#17989792C2semidirect
13. C4×#17989790C2semidirect
14. #34036190C2semidirect
168. C293#3120semidirect

Maximal subgroups

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

subgroupindex
#340367412
#340364642
#340364592
#340364362
#340364292
#340363392
#340363342
#340362912
#340362342
#340362292
C4×#179897922
C4×#179897902
#340361902
#520×C2932
#3120293