Finite Group Databasebeta

← #49168874

Subgroups — #49168874

Order 37504.

488 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036676C211yesmaximal, characteristic, complemented
2C4×D4×D293C211yesmaximal, characteristic, complemented
3#34036449C211yesmaximal, characteristic, complemented
4#34036446C211yesmaximal, characteristic, complemented
5#34036418C211yesmaximal, characteristic, complemented
6#34036417C211yesmaximal, characteristic, complemented
7#34036323C211yesmaximal, characteristic, complemented
8#34036322C211yesmaximal, characteristic, complemented
9#34036264C211yesmaximal, characteristic, complemented
10#34036261C211yesmaximal, characteristic, complemented
11#34036242C211yesmaximal, characteristic, complemented
12#34036239C211yesmaximal, characteristic, complemented
13#34036239C211yesmaximal, characteristic, complemented
14#34036184C211yesmaximal, characteristic, complemented
15#442×C293C211yesmaximal, characteristic, complemented
16C2×#17989802—21no—
17C2×D4×D293C2211yescharacteristic
18C22×C4×D293—21no—
19C2×D2344C2211yescharacteristic
20C2×#17989787C2211yescharacteristic
21C2×#17989787C2211yescharacteristic
22#22627623C2211yescharacteristic, complemented
23#22627620C2211yescharacteristic, complemented
24#22627610—21no—
25#22627599C2211yescharacteristic
26#22627597—21no—
27#22627595C2211yescharacteristic
28C4×D1172C2211yescharacteristic
29C4×D1172C2211yescharacteristic, complemented
30D4×Dic293C2211yescharacteristic
31#22627586C2211yescharacteristic
32C4×C22⋊D293—21no—
33C4×C22⋊D293—21no—
34#22627584—21no—
35C4⋊C4×D293C2211yescharacteristic
36C22⋊C4×D293—21no—
37C42×D293C2211yescharacteristic
38#22627556C2211yescharacteristic, complemented
39#22627555C2211yescharacteristic, complemented
40#22627555C2211yescharacteristic, complemented
41#22627553C2211yescharacteristic, complemented
42#22627553C2211yescharacteristic, complemented
43#22627546C2211yescharacteristic
44#22627546C2211yescharacteristic, complemented
45#22627545C2211yescharacteristic
46#22627545C2211yescharacteristic, complemented
47#22627544C2211yescharacteristic
48#22627544C2211yescharacteristic, complemented
49#22627536C2211yescharacteristic
50#22627536C2211yescharacteristic
51#22627535C2211yescharacteristic, complemented
52C2×D8×C293C2211yescharacteristic
53C4×D4×C293C2211yescharacteristic
54C4×D4×C293C2211yescharacteristic, complemented
55#106×C293C2211yescharacteristic, complemented
56#102×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic, complemented
58#97×C293C2211yescharacteristic, complemented
59C23×D293—21no—
60#17989802—44no—
61C2×Dic586—21no—
62C2×D1172—21no—
63C2×D1172C2311yescharacteristic
64C2×D1172C2311yescharacteristic
65C2×C22⋊D293—21no—
66C2×C22⋊D293—21no—
67C2×C22⋊D293—21no—
68C2×C22⋊D293—21no—
69D4×D293—22no—
70D4×D293—22no—
71C22×Dic293—21no—
72C2×C4×D293—21no—
73C2×C4×D293—21no—
74C2×C4×D293—21no—
75C2×C4×D293—21no—
76C2×C4×D293—44no—
77C2×C4×D293D411yescharacteristic
78C2×C4×D293D411yescharacteristic
79C2×C4×D293C2311yescharacteristic
80D2344—22no—
81#17989787—22no—
82#17989787—22no—
83C2×#14556873C2311yescharacteristic
84C2×#14556873C2311yescharacteristic
85C4⋊Dic293C2311yescharacteristic
86C4⋊Dic293C2311yescharacteristic
87#17989781—21no—
88#17989781—21no—
89C22⋊Dic293—21no—
90C22⋊Dic293—21no—
91#17989779—21no—
92#17989779—21no—
93#17989779—21no—
94#17989779—21no—
95C4×Dic293D411yescharacteristic
96C4×Dic293D411yescharacteristic
97C4×Dic293C2311yescharacteristic
98C2×D4×C293C2311yescharacteristic
99C2×D4×C293C2311yescharacteristic
100C22×C4×C293—21no—
101C22×C4×C293—21no—
102D8×C293—22no—
103C2×C8×C293C2311yescharacteristic
104C2×C8×C293C2311yescharacteristic
105C4⋊C4×C293C2311yescharacteristic
106C4⋊C4×C293C2311yescharacteristic
107C22⋊C4×C293—21no—
108C22⋊C4×C293—21no—
109C42×C293C2311yescharacteristic
110C22×D293—24no—
111C22×D293—21no—
112C22×D293—21no—
113C22×D293—42no—
114C22×D293—42no—
115C22×D293C2×D411yescharacteristic
116Dic586—42no—
117D1172—21no—
118D1172—21no—
119D1172—21no—
120D1172—42no—
121D1172#4112yescomplemented
122C22⋊D293—24no—
123C22⋊D293—42no—
124C22⋊D293—42no—
125C22⋊D293—42no—
126C2×Dic293—21no—
127C2×Dic293—21no—
128C2×Dic293—42no—
129C2×Dic293C2×D411yescharacteristic
130C2×Dic293C2×D411yescharacteristic
131C2×Dic293C2×D411yescharacteristic
132C4×D293—22no—
133C4×D293—21no—
134C4×D293—21no—
135C4×D293—22no—
136C4×D293—42no—
137C4×D293—42no—
138C4×D293—42no—
139C4×D293—42no—
140#14556873—21no—
141#14556873—21no—
142C23×C293—21no—
143C23×C293—21no—
144D4×C293—21no—
145D4×C293—21no—
146D4×C293—21no—
147D4×C293#4112yescomplemented
148C2×C4×C293—21no—
149C2×C4×C293—21no—
150C2×C4×C293—42no—
151C2×C4×C293—42no—
152C2×C4×C293C2×D411yescharacteristic
153C2×C4×C293C2×D411yescharacteristic
154C2×C4×C293C2411yescharacteristic
155C8×C293—21no—
156C8×C293—21no—
157C22×C293—22no—
158C22×C293—41no—
159C22×C293—41no—
160C22×C293—41no—
161C22×C293—41no—
162C22×C293—41no—
163C22×C293C22×D411yescharacteristic
164C2×D293—21no—
165C2×D293—21no—
166C2×D293—22no—
167C2×D293—48no—
168C2×D293—41no—
169C2×D293—41no—
170C2×D293—41no—
171C2×D293—41no—
172C2×D293—41no—
173C2×D293AGL(1,ℤ/8)12yes—
174C4×C293—21no—
175C4×C293—21no—
176C4×C293—41no—
177C4×C293—41no—
178C4×C293C2×#4111yescharacteristic
179C4×C293C2×#4111yescharacteristic
180Dic293—21no—
181Dic293—21no—
182Dic293—41no—
183Dic293—41no—
184Dic293AGL(1,ℤ/8)12yes—
185C2×C293—42no—
186C2×C293—81no—
187C2×C293#52511yescharacteristic
188C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
189C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
190D293—22no—
191D293—42no—
192D293—81no—
193C293#310911yescharacteristic, complemented, Sylow
194#3109—2931nomaximal, Sylow
195#532—2931no—
196C2×C4×D4—2931no—
197#481—2931no—
198#481—2931no—
199#476—2931no—
200#476—2931no—
201#459—2931no—
202#459—2931no—
203#447—2931no—
204#447—2931no—
205#442—2931no—
206#442—2931no—
207#442—2931no—
208#442D29311yescharacteristic, complemented
209#432—2931no—
210C2×#41—5861no—
211C22×D4—2931no—
212C23×C4—5861no—
213C2×D8—2931no—
214C2×D8—2931no—
215C2×D8—2931no—
216C2×D8C2×D29311yescharacteristic
217C4⋊Q8—2931no—
218#127—2931no—
219#124—5861no—
220#121—2931no—
221#121—2931no—
222#121—5861no—
223C4×D4—2931no—
224C4×D4—2931no—
225C4×D4—2931no—
226C4×D4—2931no—
227C4×D4—5861no—
228C4×D4—5861no—
229C4×D4—5861no—
230C4×D4C2×D29311yescharacteristic
231C4×D4C2×D29311yescharacteristic, complemented
232C2×C4⋊C4—2931no—
233C2×C22⋊C4—5861no—
234C2×C42—2931no—
235#106—2931no—
236#106—2931no—
237#106—2931no—
238#106C2×D29311yescharacteristic, complemented
239C4⋊C8—2931no—
240C4⋊C8—2931no—
241#102—2931no—
242#102—2931no—
243#102—2931no—
244#102—2931no—
245#102—2931no—
246#102—2931no—
247#102C2×D29311yescharacteristic
248#102C2×D29311yescharacteristic, complemented
249C22⋊C8—2931no—
250C22⋊C8—2931no—
251#97—2931no—
252#97C2×D29311yescharacteristic, complemented
253C24—5861no—
254#41—11724no—
255C2×Q8—5861no—
256C2×D4—2931no—
257C2×D4—2931no—
258C2×D4—5861no—
259C2×D4—5861no—
260C2×D4—5861no—
261C2×D4—5861no—
262C2×D4—5862no—
263C2×D4—5862no—
264C2×D4—5861no—
265C2×D4C22×D29311yescharacteristic
266C2×D4C22×D29311yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—2931no—
270C22×C4—2931no—
271C22×C4—2931no—
272C22×C4—5861no—
273C22×C4—5861no—
274C22×C4—5861no—
275C22×C4—5861no—
276C22×C4—5861no—
277C22×C4—11724no—
278D8—22no—
279D8—5862no—
280D8—5862no—
281D8—5862no—
282C2×C8—2931no—
283C2×C8—2931no—
284C2×C8C22×D29311yescharacteristic
285C2×C8C22×D29311yescharacteristic
286C4⋊C4—2931no—
287C4⋊C4—2931no—
288C4⋊C4—5861no—
289C4⋊C4—5861no—
290C4⋊C4C22×D29311yescharacteristic
291C4⋊C4C22×D29311yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—5861no—
295C22⋊C4—5861no—
296C22⋊C4—5861no—
297C22⋊C4—5861no—
298C22⋊C4—5861no—
299C22⋊C4—5861no—
300C42—2931no—
301C42—2931no—
302C42—2931no—
303C42C22×D29311yescharacteristic
304C23—21no—
305C23—21no—
306C23—2931no—
307C23—5864no—
308C23—5861no—
309C23—5861no—
310C23—11722no—
311C23—11722no—
312Q8—11722no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—2932no—
317D4—5864no—
318D4—5861no—
319D4—5861no—
320D4—5861no—
321D4—11722no—
322D4—11722no—
323D4—11722no—
324D4—11722no—
325D4#1798980212yescomplemented
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—2931no—
331C2×C4—2931no—
332C2×C4—2931no—
333C2×C4—5862no—
334C2×C4—5862no—
335C2×C4—5861no—
336C2×C4—5861no—
337C2×C4—5861no—
338C2×C4—5861no—
339C2×C4—11722no—
340C2×C4—11722no—
341C2×C4—11722no—
342C2×C4—11722no—
343C2×C4—11722no—
344C2×C4D4×D29311yescharacteristic
345C2×C4D4×D29311yescharacteristic
346C2×C4C23×D29311yescharacteristic
347C8—21no—
348C8—21no—
349C8—5861no—
350C8—5861no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—2932no—
358C22—5861no—
359C22—5861no—
360C22—5862no—
361C22—11728no—
362C22—11721no—
363C22—11721no—
364C22—11721no—
365C22—11721no—
366C22—11721no—
367C22C2×D4×D29311yescharacteristic
368C4—21no—
369C4—21no—
370C4—41no—
371C4—41no—
372C4—2932no—
373C4—5861no—
374C4—5861no—
375C4—11721no—
376C4—11721no—
377C4#41×D29311yescharacteristic
378C4C2×#1798980211yescharacteristic
379C2—42no—
380C2—81no—
381C2—23441no—
382C2—5862no—
383C2—11722no—
384C2#3403663811yescharacteristic
385C2AGL(1,ℤ/8)×D29311yescharacteristic
386C2AGL(1,ℤ/8)×D29311yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#442×C293C2
socleC22×C293C22×D4
hypercenter#442D293
hypocenterC293#3109
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #34036676C2semidirect
2. C4×D4×D293C2semidirect
3. #34036449C2semidirect
4. #34036446C2semidirect
5. #34036418C2semidirect
6. #34036417C2semidirect
7. #34036323C2semidirect
8. #34036322C2semidirect
9. #34036264C2semidirect
10. #34036261C2semidirect
11. #34036242C2semidirect
12. #34036239C2semidirect
13. #34036239C2semidirect
14. #34036184C2semidirect
15. #442×C293C2semidirect
22. #22627623C22semidirect
23. #22627620C22semidirect
29. C4×D1172C22semidirect
38. #22627556C22semidirect
39. #22627555C22semidirect
40. #22627555C22semidirect
41. #22627553C22semidirect
42. #22627553C22semidirect
44. #22627546C22semidirect
46. #22627545C22semidirect
48. #22627544C22semidirect
51. #22627535C22semidirect
54. C4×D4×C293C22semidirect
55. #106×C293C22semidirect
57. #102×C293C22semidirect
58. #97×C293C22semidirect
121. D1172#41semidirect
147. D4×C293#41semidirect
193. C293#3109semidirect
208. #442D293semidirect
231. C4×D4C2×D293semidirect
238. #106C2×D293semidirect
248. #102C2×D293semidirect
252. #97C2×D293semidirect
325. D4#17989802semidirect

Maximal subgroups

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

subgroupindex
#340366762
C4×D4×D2932
#340364492
#340364462
#340364182
#340364172
#340363232
#340363222
#340362642
#340362612
#340362422
#340362392
#340361842
#442×C2932
#3109293