Finite Group Databasebeta

← #49169145

Subgroups — #49169145

Order 37504.

372 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#34036756C211yesmaximal, characteristic, complemented
2#34036704C211yesmaximal, characteristic
3#34036497C211yesmaximal, characteristic, complemented
4#34036496C211yesmaximal, characteristic, complemented
5#34036491C211yesmaximal, characteristic, complemented
6#34036490C211yesmaximal, characteristic, complemented
7#34036485C211yesmaximal, characteristic, complemented
8#34036484C211yesmaximal, characteristic, complemented
9#34036478C211yesmaximal, characteristic, complemented
10#34036136C211yesmaximal, characteristic, complemented
11#34036129C211yesmaximal, characteristic
12#34036124C211yesmaximal, characteristic
13#103×D293C211yesmaximal, characteristic, complemented
14#34036083C211yesmaximal, characteristic, complemented
15#487×C293C211yesmaximal, characteristic, complemented
16C2×#17989803C2211yescharacteristic
17C2×Q8×D293C2211yescharacteristic
18C2×#17989785C2211yescharacteristic
19C2×C8×D293C2211yescharacteristic
20#22627623C2211yescharacteristic
21#22627622—21no—
22#22627622C2211yescharacteristic
23#22627616C2211yescharacteristic
24#22627615C2211yescharacteristic
25#22627614—21no—
26#22627613C2211yescharacteristic
27#22627612C2211yescharacteristic
28#22627609—21no—
29#22627609—21no—
30#22627602—21no—
31#22627602—21no—
32#22627602—21no—
33#22627600—21no—
34#22627582C2211yescharacteristic
35#22627581C2211yescharacteristic
36C4⋊C4×D293C2211yescharacteristic
37#22627549C2211yescharacteristic
38#22627549C2211yescharacteristic
39#22627548C2211yescharacteristic
40#22627548C2211yescharacteristic
41#22627548C2211yescharacteristic
42#22627548C2211yescharacteristic
43#22627547C2211yescharacteristic
44#22627547C2211yescharacteristic
45#22627546C2211yescharacteristic
46#22627546C2211yescharacteristic
47#22627544C2211yescharacteristic
48#22627544C2211yescharacteristic
49#22627535C2211yescharacteristic
50#22627534C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52C4⋊Q8×C293C2211yescharacteristic
53C4⋊Q8×C293C2211yescharacteristic
54#103×C293C2211yescharacteristic
55#103×C293C2211yescharacteristic
56#103×C293C2211yescharacteristic
57#103×C293C2211yescharacteristic
58C4×C8×C293C2211yescharacteristic
59#17989803—22no—
60#17989803—22no—
61C2×Dic586—21no—
62C2×Dic586—21no—
63C2×Dic586C2311yescharacteristic
64Q8×D293—22no—
65Q8×D293—22no—
66C2×D1172—21no—
67C2×D1172C2311yescharacteristic
68C2×C4×D293—21no—
69C2×C4×D293—21no—
70C2×C4×D293—21no—
71C2×C4×D293C2311yescharacteristic
72#17989785—22no—
73C2×#14556873C2311yescharacteristic
74C2×#14556873C2311yescharacteristic
75C8×D293—22no—
76C4⋊Dic293—21no—
77C4⋊Dic293C2311yescharacteristic
78C4⋊Dic293C2311yescharacteristic
79#17989781—21no—
80#17989781—21no—
81#17989781—21no—
82#17989781—21no—
83#17989781—21no—
84#17989781—21no—
85#17989781—21no—
86#17989781D411yescharacteristic
87#17989781D411yescharacteristic
88#17989779—21no—
89#17989779—21no—
90#17989779—21no—
91#17989779—21no—
92#17989779—21no—
93#17989779D411yescharacteristic
94#17989779D411yescharacteristic
95C4×Dic293—21no—
96C4×Dic293C2311yescharacteristic
97C2×Q8×C293—21no—
98C2×Q8×C293C2311yescharacteristic
99C2×Q8×C293C2311yescharacteristic
100C2×C8×C293C2311yescharacteristic
101C2×C8×C293C2311yescharacteristic
102C4⋊C4×C293—21no—
103C4⋊C4×C293—21no—
104C4⋊C4×C293—21no—
105C4⋊C4×C293C2311yescharacteristic
106C4⋊C4×C293C2311yescharacteristic
107C42×C293C2311yescharacteristic
108C22×D293—21no—
109C22×D293C2×D411yescharacteristic
110Dic586—21no—
111Dic586—21no—
112Dic586—42no—
113Dic586—81no—
114D1172—21no—
115D1172—21no—
116D1172—42no—
117C2×Dic293—21no—
118C2×Dic293—21no—
119C2×Dic293—21no—
120C2×Dic293C2×D411yescharacteristic
121C2×Dic293C2×D411yescharacteristic
122C2×Dic293C2×D411yescharacteristic
123C4×D293—42no—
124C4×D293—42no—
125C4×D293—81no—
126C4×D293#4112yes—
127C4×D293#4112yes—
128#14556873—21no—
129#14556873—21no—
130Q8×C293—21no—
131Q8×C293—21no—
132Q8×C293—21no—
133Q8×C293—21no—
134Q8×C293—81no—
135C2×C4×C293—21no—
136C2×C4×C293—21no—
137C2×C4×C293—21no—
138C2×C4×C293—21no—
139C2×C4×C293C2×D411yescharacteristic
140C2×C4×C293C2×D411yescharacteristic
141C2×C4×C293C2411yescharacteristic
142C8×C293—21no—
143C8×C293—21no—
144C22×C293C22×D411yescharacteristic
145C2×D293—21no—
146C2×D293—21no—
147C2×D293—41no—
148C2×D293—41no—
149C2×D293—41no—
150C2×D293#12412yes—
151C4×C293—21no—
152C4×C293—21no—
153C4×C293—41no—
154C4×C293—41no—
155C4×C293—41no—
156C4×C293—41no—
157C4×C293C2×#4111yescharacteristic
158C4×C293C2×#4111yescharacteristic
159Dic293—21no—
160Dic293—21no—
161Dic293—41no—
162Dic293—41no—
163Dic293—41no—
164Dic293#12412yes—
165C2×C293C2×#12411yescharacteristic
166C2×C293#57711yescharacteristic
167C2×C293#57811yescharacteristic
168D293—22no—
169D293—81no—
170C293#313711yescharacteristic, complemented, Sylow
171#3137—2931nomaximal, Sylow
172#544—2931no—
173#536—2931no—
174#491—2931no—
175#491—2931no—
176#489—2931no—
177#489—2931no—
178#488—2931no—
179#488—2931no—
180#487—2931no—
181#487D29311yescharacteristic, complemented
182#419—2931no—
183#417—2931no—
184#416—2931no—
185C2×#103—2931no—
186#405—2931no—
187C2×#41—2931no—
188C22×Q8—2931no—
189C2×M16—2931no—
190C22×C8—2931no—
191C4⋊Q8—2931no—
192C4⋊Q8—2931no—
193C4⋊Q8—5861no—
194C4⋊Q8C2×D29311yescharacteristic
195C4⋊Q8C2×D29311yescharacteristic
196#125—2931no—
197#125—2931no—
198#125—5861no—
199#124—2931no—
200#124—2931no—
201#123—5861no—
202#123—5861no—
203C22⋊Q8—5861no—
204C22⋊Q8—5861no—
205C22⋊Q8—5861no—
206C22⋊Q8—5861no—
207#117—2931no—
208#117—2931no—
209C2×C4⋊C4—2931no—
210#103—2931no—
211#103—2931no—
212#103—2931no—
213#103—2931no—
214#103—2931no—
215#103—2931no—
216#103—2931no—
217#103—2931no—
218#103C2×D29311yescharacteristic
219#103C2×D29311yescharacteristic
220#103C2×D29311yescharacteristic
221#103C2×D29311yescharacteristic
222#102—2931no—
223#102—2931no—
224#102—2931no—
225#102—2931no—
226#97—2931no—
227#97—2931no—
228C4×C8—2931no—
229C4×C8C2×D29311yescharacteristic
230#41—5862no—
231#41—5862no—
232C2×Q8—21no—
233C2×Q8—2931no—
234C2×Q8—5861no—
235C2×Q8—5861no—
236C2×Q8—5862no—
237C2×Q8—5862no—
238C2×Q8C22×D29311yescharacteristic
239C2×Q8C22×D29311yescharacteristic
240C2×D4—2931no—
241C2×D4—5861no—
242C22×C4—2931no—
243C22×C4—5861no—
244C22×C4—5861no—
245C22×C4—5861no—
246M16—5862no—
247C2×C8—2931no—
248C2×C8—2931no—
249C2×C8—5862no—
250C2×C8C22×D29311yescharacteristic
251C2×C8C22×D29311yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—2931no—
256C4⋊C4—2931no—
257C4⋊C4—2931no—
258C4⋊C4—2931no—
259C4⋊C4—5861no—
260C4⋊C4—5861no—
261C4⋊C4—5861no—
262C4⋊C4—5861no—
263C4⋊C4—5861no—
264C4⋊C4—5861no—
265C4⋊C4—5861no—
266C4⋊C4—5861no—
267C4⋊C4C22×D29311yescharacteristic
268C4⋊C4C22×D29311yescharacteristic
269C22⋊C4—2931no—
270C22⋊C4—2931no—
271C22⋊C4—5861no—
272C22⋊C4—5861no—
273C22⋊C4—5861no—
274C22⋊C4—5861no—
275C22⋊C4—5861no—
276C42—2931no—
277C42—5861no—
278C42C22×D29311yescharacteristic
279C23—2931no—
280C23—5861no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—21no—
285Q8—81no—
286Q8—23441no—
287Q8—5861no—
288Q8—5861no—
289Q8—11722no—
290D4—5861no—
291D4—5861no—
292D4—11722no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—2931no—
298C2×C4—2932no—
299C2×C4—2932no—
300C2×C4—2931no—
301C2×C4—2931no—
302C2×C4—23441no—
303C2×C4—5861no—
304C2×C4—5861no—
305C2×C4—5861no—
306C2×C4—11722no—
307C2×C4—11722no—
308C2×C4D4×D29311yescharacteristic
309C2×C4D4×D29311yescharacteristic
310C2×C4C23×D29311yescharacteristic
311C8—21no—
312C8—21no—
313C8—5861no—
314C8—5861no—
315C22—2932no—
316C22—5861no—
317C22—5861no—
318C22—11721no—
319C22—11721no—
320C22—11721no—
321C22C2×D4×D29311yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—2932no—
329C4—5861no—
330C4—5861no—
331C4—11721no—
332C4—11721no—
333C4—11721no—
334C4#41×D29311yescharacteristic
335C4#41×D29311yescharacteristic
336C2—23441no—
337C2—5862no—
338C2#124×D29311yescharacteristic
339C2#3403693511yescharacteristic
340C2#3403694211yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#487×C293C2
socleC22×C293C22×D4
prime radicalC2×#17989803C22
hypercenter#487D293
hypocenterC293#3137
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #34036756C2semidirect
3. #34036497C2semidirect
4. #34036496C2semidirect
5. #34036491C2semidirect
6. #34036490C2semidirect
7. #34036485C2semidirect
8. #34036484C2semidirect
9. #34036478C2semidirect
10. #34036136C2semidirect
13. #103×D293C2semidirect
14. #34036083C2semidirect
15. #487×C293C2semidirect
170. C293#3137semidirect
181. #487D293semidirect

Maximal subgroups

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

subgroupindex
#340367562
#340367042
#340364972
#340364962
#340364912
#340364902
#340364852
#340364842
#340364782
#340361362
#340361292
#340361242
#103×D2932
#340360832
#487×C2932
#3137293