Finite Group Databasebeta

← #49171487

Subgroups — #49171487

Order 37504.

396 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036838C211yesmaximal, characteristic, complemented
2#34036799C211yesmaximal, characteristic, complemented
3#34036493C211yesmaximal, characteristic, complemented
4#34036492C211yesmaximal, characteristic, complemented
5#34036474C211yesmaximal, characteristic, complemented
6#34036430C211yesmaximal, characteristic, complemented
7#34036427C211yesmaximal, characteristic, complemented
8#34036417C211yesmaximal, characteristic, complemented
9#34036322C211yesmaximal, characteristic, complemented
10#34036322C211yesmaximal, characteristic, complemented
11#34036258C211yesmaximal, characteristic, complemented
12#34036241C211yesmaximal, characteristic, complemented
13#34036239C211yesmaximal, characteristic, complemented
14D8×Dic293C211yesmaximal, characteristic, complemented
15#459×C293C211yesmaximal, characteristic, complemented
16C2×#17989801—21no—
17C2×#17989787C2211yescharacteristic
18#22627623C2211yescharacteristic
19#22627620C2211yescharacteristic
20#22627620C2211yescharacteristic
21#22627616C2211yescharacteristic
22#22627615C2211yescharacteristic
23#22627603—21no—
24#22627601—21no—
25#22627601—21no—
26#22627596—21no—
27#22627596—21no—
28#22627595—21no—
29C4×Dic586C2211yescharacteristic
30C4×D1172C2211yescharacteristic
31D4×Dic293C2211yescharacteristic
32D4×Dic293C2211yescharacteristic
33D4×Dic293C2211yescharacteristic
34D4×Dic293C2211yescharacteristic
35C2×#17989781—21no—
36#22627558C2211yescharacteristic
37#22627556C2211yescharacteristic
38#22627555C2211yescharacteristic
39#22627553C2211yescharacteristic
40#22627553C2211yescharacteristic
41#22627546C2211yescharacteristic
42#22627546C2211yescharacteristic
43#22627545C2211yescharacteristic
44#22627545C2211yescharacteristic
45#22627545C2211yescharacteristic
46#22627545C2211yescharacteristic
47#22627545C2211yescharacteristic
48#22627544C2211yescharacteristic
49#22627535C2211yescharacteristic
50#22627534C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52C2×D8×C293C2211yescharacteristic
53C2×D8×C293C2211yescharacteristic
54#127×C293C2211yescharacteristic
55C4×D4×C293C2211yescharacteristic
56C4⋊C8×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58#102×C293C2211yescharacteristic
59#17989801—44no—
60C2×Dic586—21no—
61C2×Dic586D411yescharacteristic
62C2×D1172C2311yescharacteristic
63C2×C22⋊D293—21no—
64C2×C22⋊D293—21no—
65C2×C22⋊D293—21no—
66C2×C22⋊D293—21no—
67C22×Dic293—21no—
68C22×Dic293—21no—
69C22×Dic293—21no—
70C22×Dic293—21no—
71C2×C4×D293—21no—
72#17989787—22no—
73C2×#14556873C2311yescharacteristic
74C2×#14556873C2311yescharacteristic
75C4⋊Dic293—21no—
76C4⋊Dic293D411yescharacteristic
77C4⋊Dic293C2311yescharacteristic
78C4⋊Dic293C2311yescharacteristic
79C4⋊Dic293C2311yescharacteristic
80#17989781—21no—
81#17989781—21no—
82#17989781—21no—
83#17989781—21no—
84#17989781D411yescharacteristic
85#17989781D411yescharacteristic
86C22⋊Dic293—21no—
87C22⋊Dic293—21no—
88C22⋊Dic293—21no—
89C22⋊Dic293—21no—
90#17989779—21no—
91C4×Dic293C2311yescharacteristic
92C4×Dic293C2311yescharacteristic
93C2×D4×C293—21no—
94C2×D4×C293—21no—
95C2×D4×C293C2311yescharacteristic
96C2×D4×C293C2311yescharacteristic
97C2×D4×C293C2311yescharacteristic
98C22×C4×C293—21no—
99D8×C293—22no—
100D8×C293—22no—
101C2×C8×C293C2311yescharacteristic
102C2×C8×C293C2311yescharacteristic
103C4⋊C4×C293C2311yescharacteristic
104C22⋊C4×C293—21no—
105C42×C293C2311yescharacteristic
106C22×D293—21no—
107Dic586—22no—
108Dic586—81no—
109D1172—21no—
110D1172—21no—
111C22⋊D293—42no—
112C22⋊D293—42no—
113C22⋊D293—81no—
114C22⋊D293—81no—
115C2×Dic293—21no—
116C2×Dic293—21no—
117C2×Dic293—21no—
118C2×Dic293—42no—
119C2×Dic293—42no—
120C2×Dic293—42no—
121C2×Dic293—81no—
122C2×Dic293C2×D411yescharacteristic
123C2×Dic293C2×D411yescharacteristic
124C2×Dic293C2×D411yescharacteristic
125C2×Dic293C2×D411yescharacteristic
126C4×D293—42no—
127#14556873—21no—
128#14556873—21no—
129C23×C293—21no—
130C23×C293—21no—
131C23×C293—21no—
132D4×C293—21no—
133D4×C293—21no—
134D4×C293—21no—
135D4×C293—21no—
136D4×C293—21no—
137D4×C293—42no—
138D4×C293—81no—
139D4×C293#4112yescomplemented
140C2×C4×C293—21no—
141C2×C4×C293—81no—
142C2×C4×C293C2×D411yescharacteristic
143C2×C4×C293C2×D411yescharacteristic
144C2×C4×C293C2411yescharacteristic
145C8×C293—21no—
146C8×C293—21no—
147C22×C293—22no—
148C22×C293—41no—
149C22×C293—41no—
150C22×C293—41no—
151C22×C293—41no—
152C22×C293—41no—
153C22×C293—41no—
154C22×C293—41no—
155C22×C293—41no—
156C22×C293C22×D411yescharacteristic
157C2×D293—41no—
158C2×D293—41no—
159C2×D293—41no—
160C4×C293—21no—
161C4×C293—21no—
162C4×C293—41no—
163C4×C293C2×#4111yescharacteristic
164C4×C2932−1+411yescharacteristic
165Dic293—21no—
166Dic293—21no—
167Dic293—21no—
168Dic293—41no—
169Dic293—41no—
170Dic293—41no—
171Dic293AGL(1,ℤ/8)12yes—
172C2×C293—42no—
173C2×C293—81no—
174C2×C293—81no—
175C2×C293#54811yescharacteristic
176C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
177C2×C293#57611yescharacteristic
178D293—81no—
179C293#336611yescharacteristic, complemented, Sylow
180#3366—2931nomaximal, Sylow
181#554—2931no—
182#550—2931no—
183#490—2931no—
184#490—2931no—
185#486—2931no—
186#478—2931no—
187#478—2931no—
188#476—2931no—
189#459—2931no—
190#459—2931no—
191#459D29311yescharacteristic, complemented
192#446—2931no—
193#442—2931no—
194#442—2931no—
195C4×D8—2931no—
196C2×#41—5861no—
197C2×D8—2931no—
198C2×D8C2×D29311yescharacteristic
199C2×D8C2×D29311yescharacteristic
200C4⋊Q8—2931no—
201#127—2931no—
202#127—2931no—
203#127C2×D29311yescharacteristic
204#125—2931no—
205#125—2931no—
206C22⋊Q8—5861no—
207C22⋊Q8—5861no—
208C22⋊Q8—5861no—
209#121—5861no—
210#121—5861no—
211#121—5861no—
212C4×Q8—2931no—
213C4×D4—2931no—
214C4×D4—2931no—
215C4×D4—2931no—
216C4×D4—2931no—
217C4×D4—2931no—
218C4×D4C2×D29311yescharacteristic
219C2×C4⋊C4—5861no—
220#107—2931no—
221#106—2931no—
222#106—2931no—
223C4⋊C8—2931no—
224C4⋊C8—2931no—
225C4⋊C8C2×D29311yescharacteristic
226#102—2931no—
227#102—2931no—
228#102—2931no—
229#102—2931no—
230#102—2931no—
231#102—2931no—
232#102—2931no—
233#102—2931no—
234#102C2×D29311yescharacteristic
235#102C2×D29311yescharacteristic
236#97—2931no—
237#97—2931no—
238C4×C8—2931no—
239#41—11724no—
240C2×Q8—2931no—
241C2×Q8—5861no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—2931no—
245C2×D4—5861no—
246C2×D4—5861no—
247C2×D4—5861no—
248C2×D4—5861no—
249C2×D4C22×D29311yescharacteristic
250C2×D4C22×D29311yescharacteristic
251C2×D4C22×D29311yescharacteristic
252C22×C4—21no—
253C22×C4—5861no—
254C22×C4—5861no—
255C22×C4—5861no—
256C22×C4—5861no—
257C22×C4—5861no—
258D8—22no—
259D8—22no—
260D8—5862no—
261C2×C8—2931no—
262C2×C8—2931no—
263C2×C8C22×D29311yescharacteristic
264C2×C8C22×D29311yescharacteristic
265C4⋊C4—2931no—
266C4⋊C4—2931no—
267C4⋊C4—2931no—
268C4⋊C4—2931no—
269C4⋊C4—2931no—
270C4⋊C4—2931no—
271C4⋊C4—5861no—
272C4⋊C4—5861no—
273C4⋊C4—5861no—
274C4⋊C4—5861no—
275C4⋊C4—5861no—
276C4⋊C4C22×D29311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—5861no—
279C22⋊C4—5861no—
280C22⋊C4—5861no—
281C22⋊C4—5861no—
282C22⋊C4—5861no—
283C42—2931no—
284C42—2931no—
285C42C22×D29311yescharacteristic
286C23—21no—
287C23—21no—
288C23—21no—
289C23—5861no—
290Q8—23441no—
291Q8—5862no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—42no—
298D4—81no—
299D4—23441no—
300D4—23441no—
301D4—5861no—
302D4—5861no—
303D4—11722no—
304D4—11722no—
305D4#1798980112yescomplemented
306C2×C4—21no—
307C2×C4—81no—
308C2×C4—2931no—
309C2×C4—2931no—
310C2×C4—2931no—
311C2×C4—2931no—
312C2×C4—23441no—
313C2×C4—5861no—
314C2×C4—5861no—
315C2×C4—5861no—
316C2×C4—11722no—
317C2×C4—11722no—
318C2×C4—11722no—
319C2×C4—11722no—
320C2×C4D4×D29311yescharacteristic
321C2×C4D4×D29311yescharacteristic
322C2×C4C23×D29311yescharacteristic
323C8—21no—
324C8—21no—
325C8—5861no—
326C8—5861no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—11721no—
337C22—11721no—
338C22—11721no—
339C22C2×D4×D29311yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—2932no—
344C4—5861no—
345C4—5861no—
346C4—5861no—
347C4—11721no—
348C4—11721no—
349C4—11721no—
350C4C2×#1798980111yescharacteristic
351C4#2262767111yescharacteristic
352C2—42no—
353C2—81no—
354C2—81no—
355C2—23441no—
356C2#3403678511yescharacteristic
357C2AGL(1,ℤ/8)×D29311yescharacteristic
358C2#3403693011yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#459×C293C2
socleC22×C293C22×D4
hypercenter#459D293
hypocenterC293#3366
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #34036838C2semidirect
2. #34036799C2semidirect
3. #34036493C2semidirect
4. #34036492C2semidirect
5. #34036474C2semidirect
6. #34036430C2semidirect
7. #34036427C2semidirect
8. #34036417C2semidirect
9. #34036322C2semidirect
10. #34036322C2semidirect
11. #34036258C2semidirect
12. #34036241C2semidirect
13. #34036239C2semidirect
14. D8×Dic293C2semidirect
15. #459×C293C2semidirect
139. D4×C293#41semidirect
179. C293#3366semidirect
191. #459D293semidirect
305. D4#17989801semidirect

Maximal subgroups

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

subgroupindex
#340368382
#340367992
#340364932
#340364922
#340364742
#340364302
#340364272
#340364172
#340363222
#340362582
#340362412
#340362392
D8×Dic2932
#459×C2932
#3366293