Finite Group Databasebeta

← #49170671

Subgroups — #49170671

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#34036817C211yesmaximal, characteristic, complemented
2#34036787C211yesmaximal, characteristic
3#34036469C211yesmaximal, characteristic, complemented
4#34036441C211yesmaximal, characteristic, complemented
5#34036433C211yesmaximal, characteristic, complemented
6#34036369C211yesmaximal, characteristic, complemented
7#34036357C211yesmaximal, characteristic, complemented
8#34036348C211yesmaximal, characteristic, complemented
9#34036292C211yesmaximal, characteristic, complemented
10#34036286C211yesmaximal, characteristic, complemented
11C4×Dic1172C211yesmaximal, characteristic, complemented
12C8×D1172C211yesmaximal, characteristic, complemented
13#34036122C211yesmaximal, characteristic, complemented
14#103×D293C211yesmaximal, characteristic, complemented
15#488×C293C211yesmaximal, characteristic, complemented
16C2×#17989801C2211yescharacteristic
17C2×Q8×D293C2211yescharacteristic
18C2×Dic1172C2211yescharacteristic
19C2×#17989792C2211yescharacteristic
20C2×#17989790C2211yescharacteristic
21C2×C8×D293C2211yescharacteristic
22C2×C8×D293C2211yescharacteristic
23#22627619—21no—
24#22627615—21no—
25#22627610—21no—
26#22627609—21no—
27#22627604C2211yescharacteristic
28#22627604C2211yescharacteristic
29#22627601—21no—
30#22627600C2211yescharacteristic
31#22627597—21no—
32#22627595C2211yescharacteristic
33C4×Dic586C2211yescharacteristic
34C4×Dic586C2211yescharacteristic
35C4×D1172C2211yescharacteristic
36#22627584—21no—
37#22627582—21no—
38#22627582C2211yescharacteristic
39C4⋊C4×D293C2211yescharacteristic
40#22627558C2211yescharacteristic
41#22627557C2211yescharacteristic
42#22627555C2211yescharacteristic
43C4⋊#14556873C2211yescharacteristic
44#22627549C2211yescharacteristic
45#22627549C2211yescharacteristic
46#22627548C2211yescharacteristic
47#22627547C2211yescharacteristic
48#22627547C2211yescharacteristic
49#22627545C2211yescharacteristic
50#22627536C2211yescharacteristic
51#22627536C2211yescharacteristic
52#125×C293C2211yescharacteristic
53#124×C293C2211yescharacteristic
54#103×C293C2211yescharacteristic
55#103×C293C2211yescharacteristic
56#102×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58C4×C8×C293C2211yescharacteristic
59#17989801—22no—
60#17989801—41no—
61C2×Dic586—21no—
62C2×Dic586C2311yescharacteristic
63C2×Dic586C2311yescharacteristic
64Q8×D293—22no—
65Q8×D293—41no—
66C2×D1172D411yescharacteristic
67C2×C22⋊D293—21no—
68C2×C22⋊D293—21no—
69C22×Dic293—21no—
70C2×C4×D293—21no—
71C2×C4×D293—21no—
72C2×C4×D293C2311yescharacteristic
73C2×C4×D293C2311yescharacteristic
74Dic1172—22no—
75#17989792—41no—
76#17989790—41no—
77C2×#14556873C2311yescharacteristic
78C2×#14556873C2311yescharacteristic
79C8×D293—41no—
80C8×D293—41no—
81C4⋊Dic293—21no—
82C4⋊Dic293—21no—
83C4⋊Dic293D411yescharacteristic
84C4⋊Dic293C2311yescharacteristic
85C4⋊Dic293C2311yescharacteristic
86#17989781—21no—
87#17989781—21no—
88#17989781—21no—
89#17989781—21no—
90C22⋊Dic293—21no—
91#17989779—21no—
92#17989779—21no—
93#17989779—21no—
94#17989779—21no—
95#17989779D411yescharacteristic
96#17989779D411yescharacteristic
97C4×Dic293—21no—
98C4×Dic293—21no—
99C4×Dic293—21no—
100C2×Q8×C293C2311yescharacteristic
101C2×D4×C293C2311yescharacteristic
102C2×C8×C293C2311yescharacteristic
103C2×C8×C293C2311yescharacteristic
104C4⋊C4×C293—21no—
105C4⋊C4×C293—21no—
106C4⋊C4×C293C2311yescharacteristic
107C4⋊C4×C293C2311yescharacteristic
108C22⋊C4×C293—21no—
109C22⋊C4×C293—21no—
110C42×C293C2311yescharacteristic
111C22×D293C2×D411yescharacteristic
112C22×D293C2×D411yescharacteristic
113Dic586—21no—
114Dic586—21no—
115Dic586—21no—
116Dic586—42no—
117Dic586#4112yes—
118D1172—22no—
119C22⋊D293—42no—
120C22⋊D293—42no—
121C2×Dic293—21no—
122C2×Dic293—21no—
123C2×Dic293—21no—
124C2×Dic293—21no—
125C2×Dic293—42no—
126C2×Dic293C2×D411yescharacteristic
127C2×Dic293C2×D411yescharacteristic
128C4×D293—21no—
129C4×D293—21no—
130C4×D293—21no—
131C4×D293—21no—
132C4×D293—42no—
133C4×D293—42no—
134#14556873—21no—
135#14556873—21no—
136C23×C293—21no—
137Q8×C293—21no—
138Q8×C293—21no—
139D4×C293—21no—
140D4×C293—21no—
141C2×C4×C293—21no—
142C2×C4×C293—21no—
143C2×C4×C293—21no—
144C2×C4×C293C2×D411yescharacteristic
145C2×C4×C293C2×D411yescharacteristic
146C2×C4×C293C2411yescharacteristic
147C8×C293—21no—
148C8×C293—21no—
149C22×C293—41no—
150C22×C293—41no—
151C22×C293—41no—
152C22×C293C22×D411yescharacteristic
153C2×D293—21no—
154C2×D293—21no—
155C2×D293—21no—
156C2×D293—21no—
157C2×D293—21no—
158C2×D293#13512yes—
159C4×C293—21no—
160C4×C293—21no—
161C4×C293—41no—
162C4×C293—41no—
163C4×C293—41no—
164C4×C293C2×#4111yescharacteristic
165C4×C293H(5,𝔽2)11yescharacteristic
166Dic293—21no—
167Dic293—21no—
168Dic293—22no—
169Dic293—41no—
170Dic293—41no—
171Dic293—41no—
172C2×C293—81no—
173C2×C293#54611yescharacteristic
174C2×C293C2×#13511yescharacteristic
175C2×C293#57811yescharacteristic
176D293—22no—
177D293—41no—
178C293#330011yescharacteristic, complemented, Sylow
179#3300—2931nomaximal, Sylow
180#552—2931no—
181#548—2931no—
182#488D29311yescharacteristic, complemented
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×D4—2931no—
193#416—2931no—
194C2×#103—2931no—
195C2×#41—2931no—
196C22×Q8—2931no—
197C2×Q16—2931no—
198C2×Q16—2931no—
199C2×SD16—2931no—
200C22×C8—2931no—
201C22×C8—2931no—
202#126—5861no—
203#125—5861no—
204#125C2×D29311yescharacteristic
205#124—5861no—
206#124C2×D29311yescharacteristic
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—2931no—
217C4×D4—5861no—
218#117—2931no—
219#117—5861no—
220C2×C4⋊C4—2931no—
221#107—2931no—
222#107—2931no—
223#106—2931no—
224C4⋊C8—2931no—
225#103—2931no—
226#103—2931no—
227#103—2931no—
228#103—2931no—
229#103—2931no—
230#103C2×D29311yescharacteristic
231#103C2×D29311yescharacteristic
232#102—2931no—
233#102C2×D29311yescharacteristic
234#102C2×D29311yescharacteristic
235C22⋊C8—2931no—
236C22⋊C8—2931no—
237C4×C8C2×D29311yescharacteristic
238#41—5862no—
239#41—11721no—
240C2×Q8—2931no—
241C2×Q8—2931no—
242C2×Q8—5861no—
243C2×Q8—5862no—
244C2×Q8—11721no—
245C2×Q8C22×D29311yescharacteristic
246C2×D4—2931no—
247C2×D4—5861no—
248C2×D4—5861no—
249C2×D4C22×D29311yescharacteristic
250C22×C4—2931no—
251C22×C4—2931no—
252C22×C4—5861no—
253C22×C4—5861no—
254C22×C4—5861no—
255Q16—5862no—
256Q16—11721no—
257SD16—11721no—
258C2×C8—2931no—
259C2×C8—2931no—
260C2×C8—11721no—
261C2×C8—11721no—
262C2×C8C22×D29311yescharacteristic
263C2×C8C22×D29311yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—2931no—
267C4⋊C4—2931no—
268C4⋊C4—2931no—
269C4⋊C4—5861no—
270C4⋊C4—5861no—
271C4⋊C4—5861no—
272C4⋊C4—5861no—
273C4⋊C4—5861no—
274C4⋊C4—5861no—
275C4⋊C4C22×D29311yescharacteristic
276C4⋊C4C22×D29311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—2931no—
280C22⋊C4—2931no—
281C22⋊C4—5861no—
282C22⋊C4—5861no—
283C22⋊C4—5861no—
284C22⋊C4—5861no—
285C22⋊C4—5861no—
286C42—5861no—
287C42—5861no—
288C42—5861no—
289C42C22×D29311yescharacteristic
290C23—21no—
291C23—2931no—
292C23—2931no—
293Q8—21no—
294Q8—21no—
295Q8—2932no—
296Q8—5861no—
297Q8—5861no—
298Q8—5861no—
299Q8—11722no—
300D4—21no—
301D4—21no—
302D4—5862no—
303D4—11722no—
304D4—11722no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—2931no—
309C2×C4—2931no—
310C2×C4—5861no—
311C2×C4—5861no—
312C2×C4—5861no—
313C2×C4—5861no—
314C2×C4—5861no—
315C2×C4—5861no—
316C2×C4—5861no—
317C2×C4—5861no—
318C2×C4—11722no—
319C2×C4—11722no—
320C2×C4—11722no—
321C2×C4D4×D29311yescharacteristic
322C2×C4D4×D29311yescharacteristic
323C2×C4C23×D29311yescharacteristic
324C8—21no—
325C8—21no—
326C8—5861no—
327C8—5861no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—2932no—
332C22—5861no—
333C22—5861no—
334C22—5861no—
335C22—5861no—
336C22—5861no—
337C22C2×D4×D29311yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—5861no—
344C4—5861no—
345C4—5862no—
346C4—11721no—
347C4—11721no—
348C4—11721no—
349C4#41×D29311yescharacteristic
350C4#2262767011yescharacteristic
351C2—81no—
352C2—5862no—
353C2—11721no—
354C2#3403677211yescharacteristic
355C2#135×D29311yescharacteristic
356C2#3403694311yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#488×C293C2
socleC22×C293C22×D4
prime radical#34036787C2
hypercenter#488D293
hypocenterC293#3300
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #34036817C2semidirect
3. #34036469C2semidirect
4. #34036441C2semidirect
5. #34036433C2semidirect
6. #34036369C2semidirect
7. #34036357C2semidirect
8. #34036348C2semidirect
9. #34036292C2semidirect
10. #34036286C2semidirect
11. C4×Dic1172C2semidirect
12. C8×D1172C2semidirect
13. #34036122C2semidirect
14. #103×D293C2semidirect
15. #488×C293C2semidirect
178. C293#3300semidirect
182. #488D293semidirect

Maximal subgroups

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

subgroupindex
#340368172
#340367872
#340364692
#340364412
#340364332
#340363692
#340363572
#340363482
#340362922
#340362862
C4×Dic11722
C8×D11722
#340361222
#103×D2932
#488×C2932
#3300293