Finite Group Databasebeta

← #49168882

Subgroups — #49168882

Order 37504.

444 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036683C211yesmaximal, characteristic, complemented
2C4×D4×D293C211yesmaximal, characteristic
3#34036466C211yesmaximal, characteristic, complemented
4#34036463C211yesmaximal, characteristic, complemented
5#34036408C211yesmaximal, characteristic, complemented
6#34036407C211yesmaximal, characteristic, complemented
7#34036333C211yesmaximal, characteristic, complemented
8#34036332C211yesmaximal, characteristic, complemented
9#34036281C211yesmaximal, characteristic
10#34036278C211yesmaximal, characteristic
11#34036231C211yesmaximal, characteristic, complemented
12#34036229C211yesmaximal, characteristic, complemented
13#34036227C211yesmaximal, characteristic, complemented
14#34036184C211yesmaximal, characteristic, complemented
15#440×C293C211yesmaximal, characteristic, complemented
16C2×D4×D293C2211yescharacteristic
17C22×C4×D293—21no—
18C2×#17989791C2211yescharacteristic
19C2×#17989790C2211yescharacteristic
20C2×#17989789C2211yescharacteristic
21#22627623C2211yescharacteristic, complemented
22#22627622C2211yescharacteristic, complemented
23#22627614—21no—
24#22627604C2211yescharacteristic
25#22627602—21no—
26#22627600C2211yescharacteristic
27C4×Dic586—21no—
28C4×Dic586C2211yescharacteristic, complemented
29C4×D1172C2211yescharacteristic
30D4×Dic293C2211yescharacteristic
31#22627586C2211yescharacteristic
32C4×C22⋊D293—21no—
33#22627584—21no—
34#22627581—21no—
35C4⋊C4×D293C2211yescharacteristic
36C22⋊C4×D293—21no—
37C42×D293C2211yescharacteristic
38#22627558C2211yescharacteristic, complemented
39#22627557C2211yescharacteristic, complemented
40#22627557C2211yescharacteristic, complemented
41#22627553C2211yescharacteristic, complemented
42#22627553C2211yescharacteristic, complemented
43#22627549C2211yescharacteristic, complemented
44#22627548C2211yescharacteristic, complemented
45#22627547C2211yescharacteristic, complemented
46#22627546C2211yescharacteristic
47#22627545C2211yescharacteristic
48#22627544C2211yescharacteristic
49#22627536C2211yescharacteristic
50#22627536C2211yescharacteristic
51#22627535C2211yescharacteristic, complemented
52C2×SD16×C293C2211yescharacteristic
53C4×Q8×C293C2211yescharacteristic, complemented
54C4×D4×C293C2211yescharacteristic
55#107×C293C2211yescharacteristic, complemented
56#103×C293C2211yescharacteristic, complemented
57#102×C293C2211yescharacteristic
58#97×C293C2211yescharacteristic, complemented
59C23×D293—21no—
60C2×Dic586—21no—
61C2×Dic586C2311yescharacteristic
62C2×D1172C2311yescharacteristic
63C2×C22⋊D293—21no—
64D4×D293—22no—
65D4×D293—22no—
66C22×Dic293—21no—
67C2×C4×D293—21no—
68C2×C4×D293—21no—
69C2×C4×D293—21no—
70C2×C4×D293—44no—
71C2×C4×D293D411yescharacteristic
72C2×C4×D293D411yescharacteristic
73C2×C4×D293C2311yescharacteristic
74#17989791—22no—
75#17989790—22no—
76#17989789—22no—
77C2×#14556873C2311yescharacteristic
78C2×#14556873C2311yescharacteristic
79C4⋊Dic293—21no—
80C4⋊Dic293C2311yescharacteristic
81C4⋊Dic293C2311yescharacteristic
82#17989781—21no—
83#17989781—21no—
84#17989781—21no—
85#17989781—21no—
86#17989781—21no—
87#17989781—21no—
88C22⋊Dic293—21no—
89#17989779—21no—
90#17989779—21no—
91#17989779—21no—
92#17989779—21no—
93C4×Dic293—21no—
94C4×Dic293D411yescharacteristic
95C4×Dic293D411yescharacteristic
96C4×Dic293C2311yescharacteristic
97C2×Q8×C293C2311yescharacteristic
98C2×D4×C293C2311yescharacteristic
99C22×C4×C293—21no—
100SD16×C293—22no—
101C2×C8×C293C2311yescharacteristic
102C2×C8×C293C2311yescharacteristic
103C4⋊C4×C293—21no—
104C4⋊C4×C293C2311yescharacteristic
105C4⋊C4×C293C2311yescharacteristic
106C22⋊C4×C293—21no—
107C42×C293—21no—
108C42×C293C2311yescharacteristic
109C22×D293—24no—
110C22×D293—21no—
111C22×D293—42no—
112C22×D293—42no—
113C22×D293C2×D411yescharacteristic
114Dic586—21no—
115Dic586—21no—
116Dic586—42no—
117D1172—21no—
118D1172#4112yes—
119C22⋊D293—24no—
120C2×Dic293—21no—
121C2×Dic293—21no—
122C2×Dic293—21no—
123C2×Dic293—42no—
124C2×Dic293C2×D411yescharacteristic
125C2×Dic293C2×D411yescharacteristic
126C2×Dic293C2×D411yescharacteristic
127C4×D293—22no—
128C4×D293—21no—
129C4×D293—21no—
130C4×D293—22no—
131C4×D293—42no—
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#4112yes—
141C2×C4×C293—21no—
142C2×C4×C293—21no—
143C2×C4×C293—21no—
144C2×C4×C293—42no—
145C2×C4×C293C2×D411yescharacteristic
146C2×C4×C293C2×D411yescharacteristic
147C2×C4×C293C2411yescharacteristic
148C8×C293—21no—
149C8×C293—21no—
150C22×C293—22no—
151C22×C293—41no—
152C22×C293—41no—
153C22×C293C22×D411yescharacteristic
154C2×D293—21no—
155C2×D293—21no—
156C2×D293—22no—
157C2×D293—48no—
158C2×D293—41no—
159C2×D293—41no—
160C2×D293#13712yes—
161C4×C293—21no—
162C4×C293—21no—
163C4×C293—41no—
164C4×C293—41no—
165C4×C293—41no—
166C4×C293C2×#4111yescharacteristic
167C4×C293C2×#4111yescharacteristic
168Dic293—21no—
169Dic293—21no—
170Dic293—41no—
171Dic293—41no—
172Dic293—41no—
173Dic293AGL(1,ℤ/8)12yes—
174C2×C293—42no—
175C2×C293#52511yescharacteristic
176C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
177C2×C293C2×#13711yescharacteristic
178D293—22no—
179D293—42no—
180C293#311011yescharacteristic, complemented, Sylow
181#3110—2931nomaximal, Sylow
182#533—2931no—
183C2×C4×D4—2931no—
184#484—2931no—
185#484—2931no—
186#474—2931no—
187#474—2931no—
188#461—2931no—
189#461—2931no—
190#450—2931no—
191#450—2931no—
192#440—2931no—
193#440—2931no—
194#440—2931no—
195#440D29311yescharacteristic, complemented
196#432—2931no—
197C22×D4—2931no—
198C23×C4—5861no—
199C2×SD16—2931no—
200C2×SD16—2931no—
201C2×SD16—2931no—
202C2×SD16C2×D29311yescharacteristic
203C4⋊Q8—2931no—
204C4⋊Q8—2931no—
205#125—5861no—
206C22⋊Q8—2931no—
207C22⋊Q8—2931no—
208C22⋊Q8—5861no—
209C4×Q8—2931no—
210C4×Q8—5861no—
211C4×Q8C2×D29311yescharacteristic, complemented
212C4×D4—2931no—
213C4×D4—2931no—
214C4×D4—2931no—
215C4×D4—5861no—
216C4×D4—5861no—
217C4×D4C2×D29311yescharacteristic
218#117—5861no—
219C2×C4⋊C4—2931no—
220C2×C22⋊C4—5861no—
221C2×C42—2931no—
222#107—2931no—
223#107—2931no—
224#107—2931no—
225#107C2×D29311yescharacteristic, complemented
226C4⋊C8—2931no—
227C4⋊C8—2931no—
228#103—2931no—
229#103—2931no—
230#103—2931no—
231#103C2×D29311yescharacteristic, complemented
232#102—2931no—
233#102—2931no—
234#102—2931no—
235#102C2×D29311yescharacteristic
236C22⋊C8—2931no—
237C22⋊C8—2931no—
238#97—2931no—
239#97C2×D29311yescharacteristic, complemented
240C24—5861no—
241C2×Q8—2931no—
242C2×Q8—5861no—
243C2×Q8C22×D29311yescharacteristic
244C2×D4—2931no—
245C2×D4—5861no—
246C2×D4—5862no—
247C2×D4—5862no—
248C2×D4C22×D29311yescharacteristic
249C22×C4—21no—
250C22×C4—2931no—
251C22×C4—2931no—
252C22×C4—2931no—
253C22×C4—5861no—
254C22×C4—5861no—
255C22×C4—5861no—
256C22×C4—5861no—
257C22×C4—11724no—
258SD16—22no—
259SD16—5862no—
260SD16—5862no—
261SD16—5862no—
262C2×C8—2931no—
263C2×C8—2931no—
264C2×C8C22×D29311yescharacteristic
265C2×C8C22×D29311yescharacteristic
266C4⋊C4—21no—
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⋊C4—5861no—
276C4⋊C4C22×D29311yescharacteristic
277C4⋊C4C22×D29311yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—5861no—
280C22⋊C4—5861no—
281C22⋊C4—5861no—
282C22⋊C4—5861no—
283C22⋊C4—5861no—
284C42—21no—
285C42—2931no—
286C42—2931no—
287C42—2931no—
288C42—5861no—
289C42C22×D29311yescharacteristic
290C23—21no—
291C23—2931no—
292C23—5864no—
293C23—5861no—
294C23—11722no—
295C23—11722no—
296Q8—21no—
297Q8—21no—
298Q8—5861no—
299Q8—5861no—
300Q8—11722no—
301D4—21no—
302D4—2932no—
303D4—5864no—
304D4—5861no—
305D4#1798980212yes—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—2931no—
311C2×C4—2931no—
312C2×C4—2931no—
313C2×C4—5862no—
314C2×C4—5862no—
315C2×C4—5861no—
316C2×C4—5861no—
317C2×C4—5861no—
318C2×C4—5861no—
319C2×C4—5861no—
320C2×C4—11722no—
321C2×C4—11722no—
322C2×C4—11722no—
323C2×C4—11722no—
324C2×C4D4×D29311yescharacteristic
325C2×C4D4×D29311yescharacteristic
326C2×C4C23×D29311yescharacteristic
327C8—21no—
328C8—21no—
329C8—5861no—
330C8—5861no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—2932no—
335C22—5861no—
336C22—5861no—
337C22—5862no—
338C22—11728no—
339C22—11721no—
340C22—11721no—
341C22C2×D4×D29311yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—2932no—
348C4—5861no—
349C4—5861no—
350C4—11721no—
351C4—11721no—
352C4—11721no—
353C4#41×D29311yescharacteristic
354C4C2×#1798980211yescharacteristic
355C2—42no—
356C2—5862no—
357C2—11722no—
358C2#3403663811yescharacteristic
359C2AGL(1,ℤ/8)×D29311yescharacteristic
360C2#137×D29311yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#440×C293C2
socleC22×C293C22×D4
prime radicalC2×D4×D293C22
hypercenter#440D293
hypocenterC293#3110
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
1. #34036683C2semidirect
3. #34036466C2semidirect
4. #34036463C2semidirect
5. #34036408C2semidirect
6. #34036407C2semidirect
7. #34036333C2semidirect
8. #34036332C2semidirect
11. #34036231C2semidirect
12. #34036229C2semidirect
13. #34036227C2semidirect
14. #34036184C2semidirect
15. #440×C293C2semidirect
21. #22627623C22semidirect
22. #22627622C22semidirect
28. C4×Dic586C22semidirect
38. #22627558C22semidirect
39. #22627557C22semidirect
40. #22627557C22semidirect
41. #22627553C22semidirect
42. #22627553C22semidirect
43. #22627549C22semidirect
44. #22627548C22semidirect
45. #22627547C22semidirect
51. #22627535C22semidirect
53. C4×Q8×C293C22semidirect
55. #107×C293C22semidirect
56. #103×C293C22semidirect
58. #97×C293C22semidirect
180. C293#3110semidirect
195. #440D293semidirect
211. C4×Q8C2×D293semidirect
225. #107C2×D293semidirect
231. #103C2×D293semidirect
239. #97C2×D293semidirect

Maximal subgroups

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

subgroupindex
#340366832
C4×D4×D2932
#340364662
#340364632
#340364082
#340364072
#340363332
#340363322
#340362812
#340362782
#340362312
#340362292
#340362272
#340361842
#440×C2932
#3110293