Finite Group Databasebeta

← #49168954

Subgroups — #49168954

Order 37504.

386 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#34036661C211yesmaximal, characteristic
2C4×Q8×D293C211yesmaximal, characteristic, complemented
3#34036466C211yesmaximal, characteristic, complemented
4#34036446C211yesmaximal, characteristic
5#34036435C211yesmaximal, characteristic, complemented
6#34036434C211yesmaximal, characteristic, complemented
7#34036350C211yesmaximal, characteristic, complemented
8#34036349C211yesmaximal, characteristic, complemented
9#34036286C211yesmaximal, characteristic, complemented
10#34036266C211yesmaximal, characteristic
11#34036237C211yesmaximal, characteristic, complemented
12#34036234C211yesmaximal, characteristic, complemented
13#34036229C211yesmaximal, characteristic, complemented
14#34036184C211yesmaximal, characteristic, complemented
15#440×C293C211yesmaximal, characteristic, complemented
16C2×Q8×D293C2211yescharacteristic
17C2×Dic1172C2211yescharacteristic
18C2×#17989792C2211yescharacteristic
19C2×#17989790C2211yescharacteristic
20#22627617—21no—
21#22627615C2211yescharacteristic
22#22627611C2211yescharacteristic
23#22627606—21no—
24#22627604C2211yescharacteristic
25#22627595C2211yescharacteristic
26Q8×Dic293C2211yescharacteristic
27C4×Dic586—21no—
28C4×Dic586C2211yescharacteristic
29C4×Dic586C2211yescharacteristic
30#22627589—21no—
31#22627589C2211yescharacteristic
32C4×C22⋊D293—21no—
33#22627583—21no—
34C4⋊C4×D293—21no—
35C4⋊C4×D293C2211yescharacteristic
36C42×D293—21no—
37C42×D293C2211yescharacteristic
38#22627557C2211yescharacteristic
39#22627556C2211yescharacteristic
40#22627555C2211yescharacteristic
41#22627553C2211yescharacteristic
42#22627553C2211yescharacteristic
43#22627549C2211yescharacteristic
44#22627549C2211yescharacteristic
45#22627548C2211yescharacteristic
46#22627547C2211yescharacteristic
47#22627547C2211yescharacteristic
48#22627545C2211yescharacteristic
49#22627536C2211yescharacteristic
50#22627536C2211yescharacteristic
51#22627535C2211yescharacteristic
52C2×SD16×C293C2211yescharacteristic
53C4×Q8×C293C2211yescharacteristic
54C4×D4×C293C2211yescharacteristic
55#107×C293C2211yescharacteristic
56#103×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58#97×C293C2211yescharacteristic
59C2×Dic586—21no—
60C2×Dic586C2311yescharacteristic
61C2×Dic586C2311yescharacteristic
62Q8×D293—22no—
63Q8×D293—22no—
64C2×C22⋊D293—21no—
65C2×C4×D293—21no—
66C2×C4×D293—21no—
67C2×C4×D293D411yescharacteristic
68C2×C4×D293D411yescharacteristic
69C2×C4×D293C2311yescharacteristic
70Dic1172—22no—
71#17989792—22no—
72#17989790—22no—
73C2×#14556873C2311yescharacteristic
74C2×#14556873C2311yescharacteristic
75C4⋊Dic293—21no—
76C4⋊Dic293—21no—
77C4⋊Dic293—21no—
78C4⋊Dic293C2311yescharacteristic
79C4⋊Dic293C2311yescharacteristic
80#17989781—21no—
81#17989781—21no—
82#17989781—21no—
83#17989781—21no—
84#17989781—21no—
85C22⋊Dic293—21no—
86C22⋊Dic293—21no—
87C22⋊Dic293—21no—
88#17989779—21no—
89C4×Dic293—21no—
90C4×Dic293—21no—
91C4×Dic293—21no—
92C4×Dic293—21no—
93C4×Dic293D411yescharacteristic
94C4×Dic293D411yescharacteristic
95C4×Dic293C2311yescharacteristic
96C2×Q8×C293C2311yescharacteristic
97C2×D4×C293C2311yescharacteristic
98C22×C4×C293—21no—
99SD16×C293—22no—
100C2×C8×C293C2311yescharacteristic
101C2×C8×C293C2311yescharacteristic
102C4⋊C4×C293—21no—
103C4⋊C4×C293C2311yescharacteristic
104C4⋊C4×C293C2311yescharacteristic
105C22⋊C4×C293—21no—
106C42×C293—21no—
107C42×C293C2311yescharacteristic
108C22×D293C2×D411yescharacteristic
109Dic586—24no—
110Dic586—21no—
111Dic586—21no—
112Dic586—21no—
113Dic586#4112yes—
114C22⋊D293—42no—
115C2×Dic293—21no—
116C2×Dic293—21no—
117C2×Dic293—21no—
118C2×Dic293—21no—
119C2×Dic293C2×D411yescharacteristic
120C2×Dic293C2×D411yescharacteristic
121C2×Dic293C2×D411yescharacteristic
122C4×D293—24no—
123C4×D293—22no—
124C4×D293—21no—
125C4×D293—21no—
126C4×D293—41no—
127C4×D293—42no—
128#14556873—21no—
129#14556873—21no—
130C23×C293—21no—
131Q8×C293—21no—
132Q8×C293#4112yes—
133D4×C293—21no—
134D4×C293—21no—
135C2×C4×C293—21no—
136C2×C4×C293—21no—
137C2×C4×C293—21no—
138C2×C4×C293—42no—
139C2×C4×C293C2×D411yescharacteristic
140C2×C4×C293C2×D411yescharacteristic
141C2×C4×C293C2411yescharacteristic
142C8×C293—21no—
143C8×C293—21no—
144C22×C293—41no—
145C22×C293—41no—
146C22×C293—41no—
147C22×C293C22×D411yescharacteristic
148C2×D293—21no—
149C2×D293—21no—
150C2×D293#13712yes—
151C4×C293—22no—
152C4×C293—21no—
153C4×C293—21no—
154C4×C293—41no—
155C4×C293—41no—
156C4×C293C2×#4111yescharacteristic
157C4×C293C2×#4111yescharacteristic
158Dic293—22no—
159Dic293—21no—
160Dic293—21no—
161Dic293—21no—
162Dic293—41no—
163Dic293—41no—
164Dic293—41no—
165C2×C293—81no—
166C2×C293#52511yescharacteristic
167C2×C293C2×#13711yescharacteristic
168C2×C293#57511yescharacteristic
169D293—22no—
170C293#311711yescharacteristic, complemented, Sylow
171#3117—2931nomaximal, Sylow
172#529—2931no—
173C2×C4×Q8—2931no—
174#484—2931no—
175#481—2931no—
176#479—2931no—
177#479—2931no—
178#464—2931no—
179#464—2931no—
180#451—2931no—
181#448—2931no—
182#441—2931no—
183#441—2931no—
184#440—2931no—
185#440D29311yescharacteristic, complemented
186#432—2931no—
187C22×Q8—2931no—
188C2×Q16—2931no—
189C2×Q16—2931no—
190C2×SD16—2931no—
191C2×SD16C2×D29311yescharacteristic
192#126—5861no—
193#125—2931no—
194#124—2931no—
195#123—5861no—
196C22⋊Q8—2931no—
197#121—2931no—
198C4×Q8—2931no—
199C4×Q8—2931no—
200C4×Q8—2931no—
201C4×Q8—2931no—
202C4×Q8—5861no—
203C4×Q8—5861no—
204C4×Q8C2×D29311yescharacteristic
205C4×D4—5861no—
206C4×D4C2×D29311yescharacteristic
207#117—5861no—
208C2×C4⋊C4—2931no—
209C2×C4⋊C4—5861no—
210C2×C42—2931no—
211C2×C42—5861no—
212#107—2931no—
213#107C2×D29311yescharacteristic
214#106—2931no—
215#106—2931no—
216C4⋊C8—2931no—
217C4⋊C8—2931no—
218#103—2931no—
219#103—2931no—
220#103—2931no—
221#103—2931no—
222#103—2931no—
223#103C2×D29311yescharacteristic
224#102—2931no—
225#102C2×D29311yescharacteristic
226C22⋊C8—2931no—
227C22⋊C8—2931no—
228#97—2931no—
229#97C2×D29311yescharacteristic
230C2×Q8—2931no—
231C2×Q8—2931no—
232C2×Q8—5861no—
233C2×Q8—5862no—
234C2×Q8—5862no—
235C2×Q8C22×D29311yescharacteristic
236C2×D4—5861no—
237C2×D4C22×D29311yescharacteristic
238C22×C4—21no—
239C22×C4—2931no—
240C22×C4—2931no—
241C22×C4—2931no—
242C22×C4—5861no—
243C22×C4—5861no—
244Q16—5862no—
245Q16—5862no—
246SD16—22no—
247SD16—5862no—
248C2×C8—2931no—
249C2×C8—2931no—
250C2×C8C22×D29311yescharacteristic
251C2×C8C22×D29311yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—2931no—
254C4⋊C4—2931no—
255C4⋊C4—5861no—
256C4⋊C4—5861no—
257C4⋊C4—5861no—
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—5861no—
267C22⋊C4—5861no—
268C22⋊C4—5861no—
269C22⋊C4—5861no—
270C42—21no—
271C42—2931no—
272C42—2931no—
273C42—2931no—
274C42—5861no—
275C42—5861no—
276C42—5861no—
277C42—5861no—
278C42C22×D29311yescharacteristic
279C23—21no—
280C23—2931no—
281Q8—21no—
282Q8—2932no—
283Q8—5864no—
284Q8—5861no—
285Q8—5861no—
286Q8—5861no—
287Q8#1798980212yes—
288D4—21no—
289D4—21no—
290D4—11722no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—2931no—
296C2×C4—2931no—
297C2×C4—2931no—
298C2×C4—5862no—
299C2×C4—5864no—
300C2×C4—5861no—
301C2×C4—5861no—
302C2×C4—5861no—
303C2×C4—5861no—
304C2×C4—5861no—
305C2×C4—5861no—
306C2×C4—11721no—
307C2×C4—11722no—
308C2×C4D4×D29311yescharacteristic
309C2×C4D4×D29311yescharacteristic
310C2×C4C23×D29311yescharacteristic
311C8—21no—
312C8—21no—
313C8—5861no—
314C8—5861no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—2932no—
319C22—5861no—
320C22—5861no—
321C22C2×D4×D29311yescharacteristic
322C4—22no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—5861no—
328C4—5862no—
329C4—5861no—
330C4—5861no—
331C4—11721no—
332C4—11721no—
333C4—11721no—
334C4#41×D29311yescharacteristic
335C4C2×#1798980211yescharacteristic
336C2—81no—
337C2—5862no—
338C2#3403663811yescharacteristic
339C2#137×D29311yescharacteristic
340C2#3403692511yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#440×C293C2
socleC22×C293C22×D4
prime radical#22627595C22
hypercenter#440D293
hypocenterC293#3117
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D293C2semidirect
3. #34036466C2semidirect
5. #34036435C2semidirect
6. #34036434C2semidirect
7. #34036350C2semidirect
8. #34036349C2semidirect
9. #34036286C2semidirect
11. #34036237C2semidirect
12. #34036234C2semidirect
13. #34036229C2semidirect
14. #34036184C2semidirect
15. #440×C293C2semidirect
170. C293#3117semidirect
185. #440D293semidirect

Maximal subgroups

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

subgroupindex
#340366612
C4×Q8×D2932
#340364662
#340364462
#340364352
#340364342
#340363502
#340363492
#340362862
#340362662
#340362372
#340362342
#340362292
#340361842
#440×C2932
#3117293