Finite Group Databasebeta

← #49169395

Subgroups — #49169395

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#34036752C211yesmaximal, characteristic, complemented
2#34036746C211yesmaximal, characteristic, complemented
3#34036526C211yesmaximal, characteristic, complemented
4#34036510C211yesmaximal, characteristic, complemented
5#34036490C211yesmaximal, characteristic, complemented
6#34036487C211yesmaximal, characteristic, complemented
7#34036385C211yesmaximal, characteristic, complemented
8#34036380C211yesmaximal, characteristic
9#34036358C211yesmaximal, characteristic, complemented
10#34036238C211yesmaximal, characteristic, complemented
11#34036233C211yesmaximal, characteristic, complemented
12SD16×Dic293C211yesmaximal, characteristic, complemented
13#34036216C211yesmaximal, characteristic, complemented
14#34036084C211yesmaximal, characteristic, complemented
15#465×C293C211yesmaximal, characteristic, complemented
16C2×#17989792C2211yescharacteristic
17C2×#17989791C2211yescharacteristic
18C2×#17989787C2211yescharacteristic
19C2×#17989786C2211yescharacteristic
20#22627623C2211yescharacteristic
21#22627623C2211yescharacteristic
22#22627619—21no—
23#22627617—21no—
24#22627613C2211yescharacteristic
25#22627611—21no—
26#22627611C2211yescharacteristic
27#22627610—21no—
28#22627606—21no—
29#22627605—21no—
30#22627604—21no—
31#22627603C2211yescharacteristic
32#22627601—21no—
33#22627598C2211yescharacteristic
34Q8×Dic293C2211yescharacteristic
35#22627589C2211yescharacteristic
36D4×Dic293C2211yescharacteristic
37#22627586C2211yescharacteristic
38#22627583C2211yescharacteristic
39#22627556C2211yescharacteristic
40#22627555C2211yescharacteristic
41#22627555C2211yescharacteristic
42#22627549C2211yescharacteristic
43#22627548C2211yescharacteristic
44#22627547C2211yescharacteristic
45#22627546C2211yescharacteristic
46#22627545C2211yescharacteristic
47#22627544C2211yescharacteristic
48#22627534C2211yescharacteristic
49#22627534C2211yescharacteristic
50C8×Dic293C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52C2×SD16×C293C2211yescharacteristic
53C22×C8×C293C2211yescharacteristic
54C22⋊Q8×C293C2211yescharacteristic
55#121×C293C2211yescharacteristic
56#106×C293C2211yescharacteristic
57#103×C293C2211yescharacteristic
58#102×C293C2211yescharacteristic
59C2×Dic586—21no—
60C2×Dic586—21no—
61C2×Dic586C2311yescharacteristic
62C2×D1172C2311yescharacteristic
63C2×C22⋊D293—21no—
64C22×Dic293—21no—
65C2×C4×D293—21no—
66#17989792—22no—
67#17989791—22no—
68#17989787—22no—
69#17989786—22no—
70C2×#14556873C2311yescharacteristic
71C2×#14556873C2311yescharacteristic
72C4⋊Dic293—21no—
73C4⋊Dic293D411yescharacteristic
74C4⋊Dic293D411yescharacteristic
75C4⋊Dic293C2311yescharacteristic
76C4⋊Dic293C2311yescharacteristic
77#17989781—21no—
78#17989781—21no—
79#17989781—21no—
80#17989781—21no—
81C22⋊Dic293—21no—
82C22⋊Dic293—21no—
83C22⋊Dic293—21no—
84C22⋊Dic293—21no—
85C22⋊Dic293D411yescharacteristic
86C22⋊Dic293D411yescharacteristic
87#17989779—21no—
88#17989779—21no—
89#17989779—21no—
90#17989779—21no—
91C4×Dic293—21no—
92C4×Dic293—21no—
93C4×Dic293C2311yescharacteristic
94C4×Dic293C2311yescharacteristic
95C2×Q8×C293C2311yescharacteristic
96C2×D4×C293—21no—
97C2×D4×C293C2311yescharacteristic
98C22×C4×C293C2311yescharacteristic
99SD16×C293—22no—
100C2×C8×C293—22no—
101C2×C8×C293C2311yescharacteristic
102C2×C8×C293C2311yescharacteristic
103C4⋊C4×C293—21no—
104C4⋊C4×C293C2311yescharacteristic
105C4⋊C4×C293C2311yescharacteristic
106C22⋊C4×C293—21no—
107C22⋊C4×C293—21no—
108C22×D293—21no—
109Dic586—21no—
110Dic586—21no—
111Dic586—81no—
112Dic586—81no—
113D1172—21no—
114D1172—21no—
115C22⋊D293—81no—
116C2×Dic293—21no—
117C2×Dic293—21no—
118C2×Dic293—21no—
119C2×Dic293—81no—
120C2×Dic293C2×D411yescharacteristic
121C2×Dic293C2×D411yescharacteristic
122C2×Dic293C2×D411yescharacteristic
123C2×Dic293C2×D411yescharacteristic
124C4×D293—81no—
125#14556873—21no—
126#14556873#4112yes—
127C23×C293—21no—
128C23×C293C2×D411yescharacteristic
129Q8×C293—21no—
130Q8×C293—21no—
131D4×C293—21no—
132D4×C293—21no—
133D4×C293—81no—
134C2×C4×C293—21no—
135C2×C4×C293—21no—
136C2×C4×C293—21no—
137C2×C4×C293—21no—
138C2×C4×C293—21no—
139C2×C4×C293C2×D411yescharacteristic
140C2×C4×C293C2411yescharacteristic
141C8×C293—21no—
142C8×C293#4112yes—
143C22×C293—21no—
144C22×C293—21no—
145C22×C293—21no—
146C22×C293—41no—
147C22×C293—41no—
148C22×C293—41no—
149C22×C293C22×D411yescharacteristic
150C2×D293—41no—
151C2×D293—41no—
152C2×D293—41no—
153C4×C293—21no—
154C4×C293—41no—
155C4×C293—41no—
156C4×C293—41no—
157C4×C293C2×#4111yescharacteristic
158C4×C293C2×#4111yescharacteristic
159Dic293—21no—
160Dic293—21no—
161Dic293—21no—
162Dic293—21no—
163Dic293—41no—
164Dic293—41no—
165Dic293—41no—
166C2×C293—41no—
167C2×C293—81no—
168C2×C293#53211yescharacteristic
169C2×C293#57711yescharacteristic
170C2×C293#57711yescharacteristic
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#489—2931no—
180#470—2931no—
181#469—2931no—
182#465—2931no—
183#465D29311yescharacteristic, complemented
184#442—2931no—
185#441—2931no—
186C4×SD16—2931no—
187C4×SD16—2931no—
188#405—2931no—
189C2×Q16—2931no—
190C2×SD16—2931no—
191C2×SD16C2×D29311yescharacteristic
192C2×D8—2931no—
193C2×M16—2931no—
194C22×C8C2×D29311yescharacteristic
195C4⋊Q8—2931no—
196C4⋊Q8—2931no—
197#126—5861no—
198#126—5861no—
199#124—2931no—
200#124—2931no—
201#124—5861no—
202#124—5861no—
203#123—5861no—
204#123—5861no—
205C22⋊Q8—2931no—
206C22⋊Q8—5861no—
207C22⋊Q8—5861no—
208C22⋊Q8C2×D29311yescharacteristic
209#121—2931no—
210#121C2×D29311yescharacteristic
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#106C2×D29311yescharacteristic
220#103—2931no—
221#103—2931no—
222#103—2931no—
223#103C2×D29311yescharacteristic
224#102—2931no—
225#102—2931no—
226#102—2931no—
227#102C2×D29311yescharacteristic
228#97—2931no—
229#97—2931no—
230C4×C8—2931no—
231C4×C8—2931no—
232C2×Q8—2931no—
233C2×Q8—5861no—
234C2×Q8—5861no—
235C2×Q8C22×D29311yescharacteristic
236C2×D4—21no—
237C2×D4—2931no—
238C2×D4—5861no—
239C2×D4C22×D29311yescharacteristic
240C22×C4—5861no—
241C22×C4—5861no—
242C22×C4C22×D29311yescharacteristic
243Q16—5862no—
244SD16—22no—
245SD16—5862no—
246D8—5862no—
247M16—5862no—
248C2×C8—22no—
249C2×C8—2931no—
250C2×C8—2931no—
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—2931no—
279C42—5861no—
280C42—5861no—
281C23—21no—
282C23—5861no—
283C23D4×D29311yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—23441no—
287Q8—23441no—
288Q8—5861no—
289Q8—5861no—
290D4—21no—
291D4—21no—
292D4—81no—
293D4—23441no—
294D4—5861no—
295D4—5861no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—2931no—
302C2×C4—2931no—
303C2×C4—2931no—
304C2×C4—2931no—
305C2×C4—23441no—
306C2×C4—23441no—
307C2×C4—5861no—
308C2×C4—5861no—
309C2×C4—5861no—
310C2×C4D4×D29311yescharacteristic
311C2×C4C23×D29311yescharacteristic
312C8—21no—
313C8—2932no—
314C8—5861no—
315C8#1798980112yes—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—11721no—
323C22—11721no—
324C22—11721no—
325C22C2×D4×D29311yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—5861no—
331C4—5861no—
332C4—5861no—
333C4—5861no—
334C4—11721no—
335C4—11721no—
336C4—11721no—
337C4#41×D29311yescharacteristic
338C4C2×#1798980111yescharacteristic
339C2—41no—
340C2—81no—
341C2—23441no—
342C2#3403667411yescharacteristic
343C2#3403693511yescharacteristic
344C2#3403693611yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#465×C293C2
socleC22×C293C22×D4
prime radical#34036380C2
hypercenter#465D293
hypocenterC293#3173
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #34036752C2semidirect
2. #34036746C2semidirect
3. #34036526C2semidirect
4. #34036510C2semidirect
5. #34036490C2semidirect
6. #34036487C2semidirect
7. #34036385C2semidirect
9. #34036358C2semidirect
10. #34036238C2semidirect
11. #34036233C2semidirect
12. SD16×Dic293C2semidirect
13. #34036216C2semidirect
14. #34036084C2semidirect
15. #465×C293C2semidirect
172. C293#3173semidirect
183. #465D293semidirect

Maximal subgroups

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

subgroupindex
#340367522
#340367462
#340365262
#340365102
#340364902
#340364872
#340363852
#340363802
#340363582
#340362382
#340362332
SD16×Dic2932
#340362162
#340360842
#465×C2932
#3173293