Finite Group Databasebeta

← #49169401

Subgroups — #49169401

Order 37504.

362 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036753C211yesmaximal, characteristic, complemented
2#34036748C211yesmaximal, characteristic, complemented
3#34036525C211yesmaximal, characteristic, complemented
4#34036511C211yesmaximal, characteristic, complemented
5#34036489C211yesmaximal, characteristic, complemented
6#34036386C211yesmaximal, characteristic, complemented
7#34036381C211yesmaximal, characteristic
8#34036361C211yesmaximal, characteristic, complemented
9#34036357C211yesmaximal, characteristic, complemented
10#34036238C211yesmaximal, characteristic, complemented
11#34036233C211yesmaximal, characteristic, complemented
12#34036220C211yesmaximal, characteristic, complemented
13#34036214C211yesmaximal, characteristic, complemented
14#34036086C211yesmaximal, characteristic, complemented
15#489×C293C211yesmaximal, characteristic, complemented
16C2×#17989792C2211yescharacteristic
17C2×#17989790C2211yescharacteristic
18C2×#17989789C2211yescharacteristic
19C2×#17989787C2211yescharacteristic
20C2×#17989785C2211yescharacteristic
21C2×C8×D293C2211yescharacteristic
22#22627624C2211yescharacteristic
23#22627619—21no—
24#22627617—21no—
25#22627613—21no—
26#22627612C2211yescharacteristic
27#22627610—21no—
28#22627609—21no—
29#22627608—21no—
30#22627604C2211yescharacteristic
31#22627601—21no—
32#22627600—21no—
33#22627600C2211yescharacteristic
34#22627599C2211yescharacteristic
35#22627595C2211yescharacteristic
36Q8×Dic293C2211yescharacteristic
37#22627589C2211yescharacteristic
38D4×Dic293C2211yescharacteristic
39#22627586C2211yescharacteristic
40#22627581C2211yescharacteristic
41#22627555C2211yescharacteristic
42#22627555C2211yescharacteristic
43#22627555C2211yescharacteristic
44#22627555C2211yescharacteristic
45#22627549C2211yescharacteristic
46#22627549C2211yescharacteristic
47#22627546C2211yescharacteristic
48#22627546C2211yescharacteristic
49#22627534C2211yescharacteristic
50C4×#14556873C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52C4⋊Q8×C293C2211yescharacteristic
53#124×C293C2211yescharacteristic
54#103×C293C2211yescharacteristic
55#103×C293C2211yescharacteristic
56#102×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58#97×C293C2211yescharacteristic
59C2×Dic586—21no—
60C2×Dic586C2311yescharacteristic
61C2×D1172—21no—
62C2×D1172C2311yescharacteristic
63C2×C22⋊D293—21no—
64C22×Dic293—21no—
65C2×C4×D293—21no—
66C2×C4×D293C2311yescharacteristic
67#17989792—22no—
68#17989790—22no—
69#17989789—22no—
70#17989787—22no—
71#17989785—22no—
72C2×#14556873C2311yescharacteristic
73C2×#14556873C2311yescharacteristic
74C8×D293—22no—
75C4⋊Dic293—21no—
76C4⋊Dic293—21no—
77C4⋊Dic293—21no—
78C4⋊Dic293C2311yescharacteristic
79C4⋊Dic293C2311yescharacteristic
80#17989781—21no—
81#17989781—21no—
82#17989781D411yescharacteristic
83#17989781D411yescharacteristic
84C22⋊Dic293—21no—
85C22⋊Dic293—21no—
86#17989779—21no—
87#17989779—21no—
88#17989779—21no—
89#17989779—21no—
90#17989779—21no—
91#17989779—21no—
92#17989779D411yescharacteristic
93#17989779D411yescharacteristic
94C4×Dic293—21no—
95C4×Dic293—21no—
96C4×Dic293C2311yescharacteristic
97C2×Q8×C293—21no—
98C2×Q8×C293C2311yescharacteristic
99C2×D4×C293C2311yescharacteristic
100C2×C8×C293C2311yescharacteristic
101C2×C8×C293C2311yescharacteristic
102C4⋊C4×C293—21no—
103C4⋊C4×C293C2311yescharacteristic
104C4⋊C4×C293C2311yescharacteristic
105C22⋊C4×C293—21no—
106C22⋊C4×C293—21no—
107C42×C293C2311yescharacteristic
108C22×D293—21no—
109C22×D293C2×D411yescharacteristic
110Dic586—21no—
111Dic586—21no—
112Dic586—81no—
113D1172—21no—
114D1172—21no—
115D1172—81no—
116C22⋊D293—81no—
117C2×Dic293—21no—
118C2×Dic293—21no—
119C2×Dic293—21no—
120C2×Dic293—81no—
121C2×Dic293C2×D411yescharacteristic
122C2×Dic293C2×D411yescharacteristic
123C2×Dic293C2×D411yescharacteristic
124C4×D293—21no—
125C4×D293—21no—
126C4×D293—81no—
127#14556873#4112yes—
128#14556873#4112yes—
129C23×C293—21no—
130Q8×C293—21no—
131Q8×C293—21no—
132Q8×C293—81no—
133D4×C293—21no—
134D4×C293—21no—
135C2×C4×C293—21no—
136C2×C4×C293—21no—
137C2×C4×C293—21no—
138C2×C4×C293C2×D411yescharacteristic
139C2×C4×C293C2×D411yescharacteristic
140C2×C4×C293C2411yescharacteristic
141C8×C293—21no—
142C8×C293—21no—
143C22×C293—41no—
144C22×C293—41no—
145C22×C293—41no—
146C22×C293C22×D411yescharacteristic
147C2×D293—21no—
148C2×D293—21no—
149C2×D293—21no—
150C2×D293—41no—
151C2×D293—41no—
152C2×D293—41no—
153C4×C293—21no—
154C4×C293—21no—
155C4×C293—41no—
156C4×C293—41no—
157C4×C293—41no—
158C4×C293C2×#4111yescharacteristic
159C4×C293C2×#4111yescharacteristic
160Dic293—21no—
161Dic293—21no—
162Dic293—21no—
163Dic293—41no—
164Dic293—41no—
165Dic293—41no—
166C2×C293—81no—
167C2×C293#53211yescharacteristic
168C2×C293#57711yescharacteristic
169C2×C293#57711yescharacteristic
170D293—41no—
171D293—81no—
172C293#317311yescharacteristic, complemented, Sylow
173#3173—2931nomaximal, Sylow
174#542—2931no—
175#542—2931no—
176#498—2931no—
177#495—2931no—
178#489—2931no—
179#489D29311yescharacteristic, complemented
180#470—2931no—
181#469—2931no—
182#465—2931no—
183#465—2931no—
184#442—2931no—
185#441—2931no—
186C4×SD16—2931no—
187C4×SD16—2931no—
188#405—2931no—
189C2×Q16—2931no—
190C2×SD16—2931no—
191C2×SD16—2931no—
192C2×D8—2931no—
193C2×M16—2931no—
194C22×C8—2931no—
195C4⋊Q8—2931no—
196C4⋊Q8C2×D29311yescharacteristic
197#126—5861no—
198#126—5861no—
199#124—2931no—
200#124—5861no—
201#124—5861no—
202#124C2×D29311yescharacteristic
203#123—5861no—
204#123—5861no—
205C22⋊Q8—2931no—
206C22⋊Q8—2931no—
207C22⋊Q8—5861no—
208C22⋊Q8—5861no—
209#121—2931no—
210#121—2931no—
211C4×Q8—2931no—
212C4×Q8—2931no—
213C4×D4—2931no—
214C4×D4—2931no—
215#117—2931no—
216#106—2931no—
217#106—2931no—
218#106—2931no—
219#106—2931no—
220#103—2931no—
221#103—2931no—
222#103C2×D29311yescharacteristic
223#103C2×D29311yescharacteristic
224#102—2931no—
225#102—2931no—
226#102C2×D29311yescharacteristic
227#102C2×D29311yescharacteristic
228#97—2931no—
229#97C2×D29311yescharacteristic
230C4×C8—2931no—
231C4×C8—2931no—
232C2×Q8—21no—
233C2×Q8—2931no—
234C2×Q8—5861no—
235C2×Q8C22×D29311yescharacteristic
236C2×D4—2931no—
237C2×D4—5861no—
238C2×D4—5861no—
239C2×D4C22×D29311yescharacteristic
240C22×C4—2931no—
241C22×C4—5861no—
242C22×C4—5861no—
243Q16—5862no—
244SD16—5862no—
245SD16—5862no—
246D8—5862no—
247M16—5862no—
248C2×C8—2931no—
249C2×C8—2931no—
250C2×C8—5862no—
251C2×C8C22×D29311yescharacteristic
252C2×C8C22×D29311yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—2931no—
255C4⋊C4—2931no—
256C4⋊C4—2931no—
257C4⋊C4—2931no—
258C4⋊C4—5861no—
259C4⋊C4—5861no—
260C4⋊C4—5861no—
261C4⋊C4—5861no—
262C4⋊C4—5861no—
263C4⋊C4C22×D29311yescharacteristic
264C4⋊C4C22×D29311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—2931no—
268C22⋊C4—2931no—
269C22⋊C4—5861no—
270C22⋊C4—5861no—
271C22⋊C4—5861no—
272C22⋊C4—5861no—
273C22⋊C4—5861no—
274C22⋊C4—5861no—
275C22⋊C4—5861no—
276C22⋊C4—5861no—
277C42—2931no—
278C42—5861no—
279C42—5861no—
280C42C22×D29311yescharacteristic
281C23—21no—
282C23—2931no—
283C23—5861no—
284Q8—21no—
285Q8—21no—
286Q8—81no—
287Q8—23441no—
288Q8—5861no—
289Q8—5861no—
290D4—21no—
291D4—21no—
292D4—23441no—
293D4—23441no—
294D4—5861no—
295D4—5861no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—2931no—
300C2×C4—2931no—
301C2×C4—2931no—
302C2×C4—23441no—
303C2×C4—23441no—
304C2×C4—5861no—
305C2×C4—5861no—
306C2×C4—5861no—
307C2×C4—5861no—
308C2×C4—5861no—
309C2×C4D4×D29311yescharacteristic
310C2×C4D4×D29311yescharacteristic
311C2×C4C23×D29311yescharacteristic
312C8—21no—
313C8—21no—
314C8—2932no—
315C8—2932no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—5861no—
320C22—5861no—
321C22—5861no—
322C22—11721no—
323C22—11721no—
324C22—11721no—
325C22C2×D4×D29311yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—5861no—
332C4—5861no—
333C4—5861no—
334C4—11721no—
335C4—11721no—
336C4—11721no—
337C4#41×D29311yescharacteristic
338C4#41×D29311yescharacteristic
339C2—81no—
340C2—23441no—
341C2—11721no—
342C2#3403667811yescharacteristic
343C2#3403693811yescharacteristic
344C2#3403693911yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#489×C293C2
socleC22×C293C22×D4
prime radical#34036381C2
hypercenter#489D293
hypocenterC293#3173
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #34036753C2semidirect
2. #34036748C2semidirect
3. #34036525C2semidirect
4. #34036511C2semidirect
5. #34036489C2semidirect
6. #34036386C2semidirect
8. #34036361C2semidirect
9. #34036357C2semidirect
10. #34036238C2semidirect
11. #34036233C2semidirect
12. #34036220C2semidirect
13. #34036214C2semidirect
14. #34036086C2semidirect
15. #489×C293C2semidirect
172. C293#3173semidirect
179. #489D293semidirect

Maximal subgroups

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

subgroupindex
#340367532
#340367482
#340365252
#340365112
#340364892
#340363862
#340363812
#340363612
#340363572
#340362382
#340362332
#340362202
#340362142
#340360862
#489×C2932
#3173293