Finite Group Databasebeta

← #49170674

Subgroups — #49170674

Order 37504.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036819C211yesmaximal, characteristic, complemented
2#34036788C211yesmaximal, characteristic
3#34036484C211yesmaximal, characteristic, complemented
4#34036471C211yesmaximal, characteristic, complemented
5#34036443C211yesmaximal, characteristic, complemented
6#34036437C211yesmaximal, characteristic, complemented
7#34036370C211yesmaximal, characteristic, complemented
8#34036358C211yesmaximal, characteristic, complemented
9#34036352C211yesmaximal, characteristic, complemented
10#34036293C211yesmaximal, characteristic, complemented
11#34036287C211yesmaximal, characteristic, complemented
12C4×Dic1172C211yesmaximal, characteristic, complemented
13#34036126C211yesmaximal, characteristic, complemented
14C2×#22627549C211yesmaximal, characteristic, complemented
15C8×D4×C293C211yesmaximal, characteristic, complemented
16C2×#17989802C2211yescharacteristic
17C22×Dic586C2211yescharacteristic
18C2×Dic1172C2211yescharacteristic
19C2×Dic1172C2211yescharacteristic
20C2×#17989791C2211yescharacteristic
21#22627617—21no—
22#22627616C2211yescharacteristic
23#22627614—21no—
24#22627612C2211yescharacteristic
25#22627610—21no—
26#22627605—21no—
27#22627603C2211yescharacteristic
28#22627603C2211yescharacteristic
29#22627603C2211yescharacteristic
30#22627602—21no—
31#22627598C2211yescharacteristic
32#22627596—21no—
33C4×Dic586C2211yescharacteristic
34C4×Dic586C2211yescharacteristic
35#22627584—21no—
36#22627583C2211yescharacteristic
37#22627580—21no—
38C2×C4⋊Dic293C2211yescharacteristic
39#22627558C2211yescharacteristic
40#22627558C2211yescharacteristic
41#22627556C2211yescharacteristic
42#22627549C2211yescharacteristic
43#22627549C2211yescharacteristic
44#22627549C2211yescharacteristic
45#22627549C2211yescharacteristic
46#22627549C2211yescharacteristic
47#22627549C2211yescharacteristic
48#22627549C2211yescharacteristic
49#22627546C2211yescharacteristic
50#22627546C2211yescharacteristic
51#22627546C2211yescharacteristic
52C22×C8×C293C2211yescharacteristic
53C22×C8×C293C2211yescharacteristic
54C4×D4×C293C2211yescharacteristic
55C4⋊C8×C293C2211yescharacteristic
56C22⋊C8×C293C2211yescharacteristic
57C22⋊C8×C293C2211yescharacteristic
58C4×C8×C293C2211yescharacteristic
59#17989802—22no—
60#17989802—41no—
61C2×Dic586—22no—
62C2×Dic586—21no—
63C2×Dic586—41no—
64C2×Dic586C2311yescharacteristic
65C2×Dic586C2311yescharacteristic
66C2×Dic586C2311yescharacteristic
67C2×D1172C2311yescharacteristic
68C2×C22⋊D293—21no—
69C2×C22⋊D293—21no—
70C22×Dic293—21no—
71C22×Dic293—21no—
72C2×C4×D293—21no—
73Dic1172—22no—
74Dic1172—41no—
75#17989791—41no—
76C4⋊Dic293—21no—
77C4⋊Dic293C2311yescharacteristic
78C4⋊Dic293C2311yescharacteristic
79C4⋊Dic293C2311yescharacteristic
80C4⋊Dic293C2311yescharacteristic
81#17989781—21no—
82#17989781—21no—
83#17989781—21no—
84#17989781—21no—
85#17989781—21no—
86#17989781—21no—
87#17989781—21no—
88C22⋊Dic293—21no—
89C22⋊Dic293—21no—
90C22⋊Dic293—21no—
91C22⋊Dic293—21no—
92#17989779—21no—
93#17989779—21no—
94#17989779—21no—
95C4×Dic293—21no—
96C4×Dic293—21no—
97C4×Dic293—21no—
98C2×D4×C293D411yescharacteristic
99C22×C4×C293C2311yescharacteristic
100C22×C4×C293C2311yescharacteristic
101C2×C8×C293—41no—
102C2×C8×C293—41no—
103C2×C8×C293C2311yescharacteristic
104C2×C8×C293C2311yescharacteristic
105C2×C8×C293C2311yescharacteristic
106C2×C8×C293C2311yescharacteristic
107C4⋊C4×C293D411yescharacteristic
108C22⋊C4×C293D411yescharacteristic
109C22⋊C4×C293D411yescharacteristic
110C42×C293C2311yescharacteristic
111C22×D293—21no—
112Dic586—21no—
113Dic586—21no—
114Dic586—21no—
115Dic586—21no—
116Dic586—21no—
117Dic586—42no—
118Dic586#4112yes—
119D1172—21no—
120D1172—21no—
121C22⋊D293—42no—
122C22⋊D293—42no—
123C2×Dic293—21no—
124C2×Dic293—21no—
125C2×Dic293—21no—
126C2×Dic293—21no—
127C2×Dic293—21no—
128C2×Dic293—21no—
129C2×Dic293—21no—
130C2×Dic293—42no—
131C2×Dic293—42no—
132C4×D293—42no—
133C23×C293C2×D411yescharacteristic
134C23×C293C2×D411yescharacteristic
135D4×C293—22no—
136C2×C4×C293—21no—
137C2×C4×C293—21no—
138C2×C4×C293—21no—
139C2×C4×C293—21no—
140C2×C4×C293C2×D411yescharacteristic
141C2×C4×C293C2×D411yescharacteristic
142C2×C4×C293C2×D411yescharacteristic
143C2×C4×C293C2×D411yescharacteristic
144C2×C4×C293C2411yescharacteristic
145C8×C293—21no—
146C8×C293—21no—
147C8×C293—21no—
148C8×C293—21no—
149C22×C293—21no—
150C22×C293—21no—
151C22×C293—21no—
152C22×C293—21no—
153C22×C293—21no—
154C22×C293#13512yes—
155C22×C293C22×D411yescharacteristic
156C2×D293—41no—
157C2×D293—41no—
158C2×D293—41no—
159C4×C293—21no—
160C4×C293—21no—
161C4×C293—21no—
162C4×C293—21no—
163C4×C293C2×#4111yescharacteristic
164C4×C293H(5,𝔽2)11yescharacteristic
165Dic293—22no—
166Dic293—41no—
167Dic293—41no—
168Dic293—41no—
169Dic293—41no—
170Dic293—41no—
171Dic293—41no—
172C2×C293—22no—
173C2×C293—41no—
174C2×C293#54611yescharacteristic
175C2×C293C2×#13511yescharacteristic
176C2×C293#57811yescharacteristic
177D293—81no—
178C293#330011yescharacteristic, complemented, Sylow
179#3300—2931nomaximal, Sylow
180#552—2931no—
181#548—2931no—
182#488—2931no—
183#485—2931no—
184#480—2931no—
185#479—2931no—
186#467—2931no—
187#465—2931no—
188#464—2931no—
189#452—2931no—
190#451—2931no—
191C4×Q16—2931no—
192C8×D4D29311yescharacteristic, complemented
193#416—2931no—
194C2×#103—2931no—
195C2×#41—2931no—
196C22×Q8—2931no—
197C2×Q16—2931no—
198C2×Q16—2931no—
199C2×SD16—2931no—
200C22×C8C2×D29311yescharacteristic
201C22×C8C2×D29311yescharacteristic
202#126—5861no—
203#125—2931no—
204#125—5861no—
205#124—2931no—
206#124—5861no—
207#123—5861no—
208C22⋊Q8—2931no—
209C22⋊Q8—2931no—
210C22⋊Q8—2931no—
211C22⋊Q8—5861no—
212#121—2931no—
213#121—5861no—
214C4×Q8—2931no—
215C4×Q8—2931no—
216C4×D4—5861no—
217C4×D4C2×D29311yescharacteristic
218#117—2931no—
219#117—5861no—
220C2×C4⋊C4—2931no—
221#107—2931no—
222#107—2931no—
223#106—2931no—
224C4⋊C8C2×D29311yescharacteristic
225#103—2931no—
226#103—2931no—
227#103—2931no—
228#103—2931no—
229#103—2931no—
230#103—2931no—
231#103—2931no—
232#102—2931no—
233#102—2931no—
234#102—2931no—
235C22⋊C8C2×D29311yescharacteristic
236C22⋊C8C2×D29311yescharacteristic
237C4×C8C2×D29311yescharacteristic
238#41—5862no—
239#41—11721no—
240C2×Q8—2931no—
241C2×Q8—2931no—
242C2×Q8—2931no—
243C2×Q8—5862no—
244C2×Q8—5861no—
245C2×Q8—11721no—
246C2×D4—2931no—
247C2×D4—5861no—
248C2×D4—5861no—
249C2×D4D117211yescharacteristic
250C22×C4—5861no—
251C22×C4—5861no—
252C22×C4—5861no—
253C22×C4C22×D29311yescharacteristic
254C22×C4C22×D29311yescharacteristic
255Q16—5862no—
256Q16—11721no—
257SD16—11721no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8C22×D29311yescharacteristic
261C2×C8C22×D29311yescharacteristic
262C2×C8C22×D29311yescharacteristic
263C2×C8C22×D29311yescharacteristic
264C4⋊C4—2931no—
265C4⋊C4—2931no—
266C4⋊C4—2931no—
267C4⋊C4—2931no—
268C4⋊C4—5861no—
269C4⋊C4—5861no—
270C4⋊C4—5861no—
271C4⋊C4—5861no—
272C4⋊C4—5861no—
273C4⋊C4—5861no—
274C4⋊C4—5861no—
275C4⋊C4—5861no—
276C4⋊C4D117211yescharacteristic
277C22⋊C4—5861no—
278C22⋊C4—5861no—
279C22⋊C4—5861no—
280C22⋊C4—5861no—
281C22⋊C4—5861no—
282C22⋊C4—5861no—
283C22⋊C4—5861no—
284C22⋊C4D117211yescharacteristic
285C22⋊C4D117211yescharacteristic
286C42—5861no—
287C42—5861no—
288C42—5861no—
289C42C22×D29311yescharacteristic
290C23—5861no—
291C23C2×D117211yescharacteristic
292C23C2×D117211yescharacteristic
293Q8—2932no—
294Q8—5861no—
295Q8—5861no—
296Q8—5861no—
297Q8—5861no—
298Q8—5861no—
299Q8—11722no—
300D4—22no—
301D4—5861no—
302D4—5861no—
303D4—11722no—
304D4—11722no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—5861no—
310C2×C4—5861no—
311C2×C4—5861no—
312C2×C4—5861no—
313C2×C4—5861no—
314C2×C4—5861no—
315C2×C4—5861no—
316C2×C4—11722no—
317C2×C4—11722no—
318C2×C4—11722no—
319C2×C4C2×D117211yescharacteristic
320C2×C4C2×D117211yescharacteristic
321C2×C4C2×D117211yescharacteristic
322C2×C4C2×D117211yescharacteristic
323C2×C4C23×D29311yescharacteristic
324C8—21no—
325C8—21no—
326C8—21no—
327C8—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—11721no—
334C22—11721no—
335C22—11721no—
336C22#2262764612yes—
337C22C22×D117211yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—5862no—
343C4—11721no—
344C4—11721no—
345C4—11721no—
346C4—11721no—
347C4—11721no—
348C4—11721no—
349C4#41×D29311yescharacteristic
350C4#2262766911yescharacteristic
351C2—22no—
352C2—41no—
353C2—23441no—
354C2#3403677411yescharacteristic
355C2C2×#2262764611yescharacteristic
356C2#3403694611yescharacteristic
subgroupG/H
centerC22C22×D1172
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC8×D4×C293C2
socleC22×C293C22×D4
prime radical#34036788C2
hypercenterC8×D4D293
hypocenterC293#3300
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #34036819C2semidirect
3. #34036484C2semidirect
4. #34036471C2semidirect
5. #34036443C2semidirect
6. #34036437C2semidirect
7. #34036370C2semidirect
8. #34036358C2semidirect
9. #34036352C2semidirect
10. #34036293C2semidirect
11. #34036287C2semidirect
12. C4×Dic1172C2semidirect
13. #34036126C2semidirect
14. C2×#22627549C2semidirect
15. C8×D4×C293C2semidirect
178. C293#3300semidirect
192. C8×D4D293semidirect

Maximal subgroups

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

subgroupindex
#340368192
#340367882
#340364842
#340364712
#340364432
#340364372
#340363702
#340363582
#340363522
#340362932
#340362872
C4×Dic11722
#340361262
C2×#226275492
C8×D4×C2932
#3300293