Finite Group Databasebeta

← #49175292

Subgroups — #49175292

Order 37504.

532 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34037078C212yesmaximal, complemented
2#34037078C212yesmaximal, complemented
3#34037076C212yesmaximal
4#34037074C211yesmaximal, characteristic, complemented
5#34037073C211yesmaximal, characteristic, complemented
6#34037072C211yesmaximal, characteristic
7C4×C4⋊#11924078C211yesmaximal, characteristic, complemented
8C22⋊C4×#11924078C212yesmaximal
9#34037065C211yesmaximal, characteristic, complemented
10C2×(C2×#11924078)⋊C4C211yesmaximal, characteristic
11#117×D293C211yesmaximal, characteristic
12C23×#11924078C2212yes—
13C2×C4⋊#11924078C2212yes—
14C2×C4⋊#11924078C2212yes—
15C2×C22⋊#11924078C2212yes—
16C2×C4×#11924078C2212yes—
17C2×C4×#11924078C2212yes—
18(C2×#11924078)⋊C4C2211yescharacteristic
19(C2×#11924078)⋊C4C2211yescharacteristic
20(C2×#11924078)⋊C4C2212yes—
21(C2×#11924078)⋊C4C2211yescharacteristic
22(C2×#11924078)⋊C4C2212yes—
23(C2×#11924078)⋊C4C2212yes—
24(C2×#11924078)⋊C4C2212yes—
25(C2×#11924078)⋊C4C2211yescharacteristic
26(C2×#11924078)⋊C4C2212yes—
27(C2×#11924078)⋊C4C2212yes—
28C22×C4×D293C2211yescharacteristic
29#22627583C411yescharacteristic, complemented
30#22627582C411yescharacteristic, complemented
31#22627582C411yescharacteristic, complemented
32#22627581C411yescharacteristic, complemented
33#22627581C411yescharacteristic, complemented
34#22627580C411yescharacteristic, complemented
35#22627580C411yescharacteristic, complemented
36C4⋊C4×D293C2211yescharacteristic
37C4⋊C4×D293C2211yescharacteristic
38C22⋊C4×D293C2211yescharacteristic
39C22⋊C4×D293C2211yescharacteristic
40C42×D293C2211yescharacteristic
41C42×D293C2211yescharacteristic
42#117×C293C411yescharacteristic, complemented
43C22×#11924078—24no—
44C22×#11924078—24no—
45C22×#11924078—42no—
46C22×#11924078C2312yes—
47C22×#11924078C2312yes—
48C22×#11924078C2312yes—
49C22×#11924078C2312yes—
50C4⋊#11924078—24no—
51C4⋊#11924078—42no—
52C22⋊#11924078—24no—
53C4×#11924078—24no—
54C4×#11924078—42no—
55C23×D293C2311yescharacteristic
56C22×Dic293C2×C411yescharacteristic
57C2×C4×D293—24no—
58C2×C4×D293C2×C411yescharacteristic
59C2×C4×D293C2×C411yescharacteristic
60C2×C4×D293C2311yescharacteristic
61C2×C4×D293C2311yescharacteristic
62C2×C4×D293C2311yescharacteristic
63C2×C4×D293C2311yescharacteristic
64C2×C4×D293C2311yescharacteristic
65C2×C4×D293C2311yescharacteristic
66C4⋊Dic293C2×C411yescharacteristic, complemented
67C4⋊Dic293C2×C411yescharacteristic, complemented
68#17989781C2×C411yescharacteristic, complemented
69#17989781C2×C411yescharacteristic, complemented
70#17989781C2×C411yescharacteristic, complemented
71#17989781C2×C411yescharacteristic, complemented
72C22⋊Dic293C2×C411yescharacteristic
73C22⋊Dic293C2×C411yescharacteristic
74#17989779C2×C411yescharacteristic
75#17989779C2×C411yescharacteristic
76#17989779C2×C411yescharacteristic
77#17989779C2×C411yescharacteristic
78C4×Dic293C2×C411yescharacteristic, complemented
79C4×Dic293C2×C411yescharacteristic, complemented
80C4×Dic293C2×C411yescharacteristic, complemented
81C4×Dic293C2×C411yescharacteristic, complemented
82C4×Dic293C2×C411yescharacteristic, complemented
83C4×Dic293C2×C411yescharacteristic, complemented
84C22×C4×C293C2×C411yescharacteristic
85C4⋊C4×C293C2×C411yescharacteristic, complemented
86C4⋊C4×C293C2×C411yescharacteristic, complemented
87C22⋊C4×C293C2×C411yescharacteristic
88C22⋊C4×C293C2×C411yescharacteristic
89C42×C293C2×C411yescharacteristic, complemented
90C42×C293C2×C411yescharacteristic, complemented
91C2×#11924078—22no—
92C2×#11924078—22no—
93C2×#11924078—22no—
94C2×#11924078—22no—
95C2×#11924078—22no—
96C2×#11924078—22no—
97C2×#11924078—22no—
98C2×#11924078—22no—
99C2×#11924078—22no—
100C2×#11924078—22no—
101C2×#11924078—22no—
102C2×#11924078—48no—
103C2×#11924078#4114yes—
104C22×D293—22no—
105C22×D293—21no—
106C22×D293—21no—
107C22×D293C22×C411yescharacteristic
108C22×D293#4114yes—
109C22×D293C2411yescharacteristic
110C2×Dic293—22no—
111C2×Dic293C22×C411yescharacteristic
112C2×Dic293C22×C411yescharacteristic
113C2×Dic293C22×C411yescharacteristic
114C2×Dic293C22×C411yescharacteristic
115C2×Dic293C22×C411yescharacteristic
116C2×Dic293C22×C411yescharacteristic
117C4×D293—22no—
118C4×D293—22no—
119C4×D293—22no—
120C4×D293—22no—
121C4×D293—22no—
122C4×D293—22no—
123C4×D293—21no—
124C4×D293—21no—
125C4×D293—21no—
126C4×D293—21no—
127C23×C293C22×C411yescharacteristic
128C2×C4×C293—22no—
129C2×C4×C293C22×C411yescharacteristic
130C2×C4×C293C22×C411yescharacteristic
131C2×C4×C293C22×C411yescharacteristic
132C2×C4×C293C22×C411yescharacteristic
133C2×C4×C293C22×C411yescharacteristic
134C2×C4×C293C22×C411yescharacteristic
135C22×C293—21no—
136C22×C293—21no—
137C22×C293#11712yes—
138C22×C293C23×C411yescharacteristic
139C2×D293—21no—
140C2×D293—21no—
141C2×D293—24no—
142C2×D293—24no—
143C2×D293#11712yes—
144C2×D293C2×#4112yes—
145C2×D293C2×#4112yes—
146C2×D293H(5,𝔽2)11yescharacteristic
147C2×D2932−1+411yescharacteristic
148#11924078—24no—
149#11924078—42no—
150#11924078—42no—
151#11924078—42no—
152C4×C293—21no—
153C4×C293—21no—
154C4×C293—21no—
155C4×C293—21no—
156C4×C293—21no—
157C4×C293—21no—
158Dic293—21no—
159Dic293—21no—
160Dic293—21no—
161Dic293—21no—
162Dic293—21no—
163Dic293—21no—
164C2×C293—22no—
165C2×C293C2×#11711yescharacteristic
166C2×C293C4×#4111yescharacteristic
167C2×C293#52011yescharacteristic
168D293—22no—
169D293#55112yes—
170D293#55212yes—
171C293#234311yescharacteristic, complemented, Sylow
172#2343—2931nomaximal, Sylow
173C2×#117—2931no—
174#387—2932no—
175#387—2932no—
176#385—2932no—
177#383—2931no—
178#382—2931no—
179#381—2931no—
180C4×C4⋊C4—2931no—
181C4×C22⋊C4—2932no—
182#376—2931no—
183C2×#95—2931no—
184C23×C4—2931no—
185C23×C4—2932no—
186#117—2931no—
187#117—2931no—
188#117—2931no—
189#117—2931no—
190#117—2931no—
191#117—2931no—
192#117—2931no—
193#117#1192407811yescharacteristic, complemented
194C2×C4⋊C4—2931no—
195C2×C4⋊C4—2931no—
196C2×C4⋊C4—2932no—
197C2×C4⋊C4—2932no—
198C2×C22⋊C4—2931no—
199C2×C22⋊C4—2931no—
200C2×C22⋊C4—2932no—
201C2×C42—2931no—
202C2×C42—2931no—
203C2×C42—2932no—
204C2×C42—2932no—
205#95—2931no—
206#95—2931no—
207#95—2932no—
208#95—2931no—
209#95—2932no—
210#95—2932no—
211#95—2932no—
212#95—2931no—
213#95—2932no—
214#95—2932no—
215C24—2931no—
216C22×C4—2932no—
217C22×C4—2931no—
218C22×C4—2931no—
219C22×C4—2931no—
220C22×C4—2931no—
221C22×C4—2931no—
222C22×C4—2931no—
223C22×C4—2931no—
224C22×C4—2931no—
225C22×C4—2931no—
226C22×C4—2932no—
227C22×C4—2932no—
228C22×C4—2932no—
229C22×C4—5864no—
230C22×C4—5864no—
231C22×C4—5864no—
232C22×C4—11722no—
233C22×C4C2×#1192407811yescharacteristic
234C4⋊C4—2931no—
235C4⋊C4—2931no—
236C4⋊C4—2931no—
237C4⋊C4—2931no—
238C4⋊C4—2931no—
239C4⋊C4—2931no—
240C4⋊C4—5864no—
241C4⋊C4—11722no—
242C4⋊C4C2×#1192407811yescharacteristic, complemented
243C4⋊C4C2×#1192407811yescharacteristic, complemented
244C22⋊C4—2931no—
245C22⋊C4—2931no—
246C22⋊C4—2931no—
247C22⋊C4—2931no—
248C22⋊C4—2931no—
249C22⋊C4—2931no—
250C22⋊C4—5864no—
251C22⋊C4C2×#1192407811yescharacteristic
252C22⋊C4C2×#1192407811yescharacteristic
253C42—2931no—
254C42—2931no—
255C42—2931no—
256C42—2931no—
257C42—2931no—
258C42—2931no—
259C42—5864no—
260C42—11722no—
261C42C2×#1192407811yescharacteristic, complemented
262C42C2×#1192407811yescharacteristic, complemented
263C23—2931no—
264C23—2934no—
265C23—2931no—
266C23—5862no—
267C23—5861no—
268C23—5861no—
269C23C22×#1192407811yescharacteristic
270C2×C4—22no—
271C2×C4—2934no—
272C2×C4—2931no—
273C2×C4—2931no—
274C2×C4—2931no—
275C2×C4—2931no—
276C2×C4—2931no—
277C2×C4—2931no—
278C2×C4—5862no—
279C2×C4—5861no—
280C2×C4—5862no—
281C2×C4—5861no—
282C2×C4—5862no—
283C2×C4—5862no—
284C2×C4—5862no—
285C2×C4—5862no—
286C2×C4—5861no—
287C2×C4—5861no—
288C2×C4—5862no—
289C2×C4—5862no—
290C2×C4—5862no—
291C2×C4—5862no—
292C2×C4—5862no—
293C2×C4—5862no—
294C2×C4—5862no—
295C2×C4—5862no—
296C2×C4—5862no—
297C2×C4—5862no—
298C2×C4—5862no—
299C2×C4—5862no—
300C2×C4—11728no—
301C2×C4C22×#1192407811yescharacteristic
302C2×C4C22×#1192407811yescharacteristic
303C2×C4C22×#1192407811yescharacteristic
304C2×C4C22×#1192407811yescharacteristic
305C2×C4C22×#1192407811yescharacteristic
306C2×C4C22×#1192407811yescharacteristic
307C22—21no—
308C22—21no—
309C22—2932no—
310C22—2932no—
311C22—2931no—
312C22—2931no—
313C22—2932no—
314C22—5864no—
315C22—5864no—
316C22—5861no—
317C22—5861no—
318C22#2262770312yes—
319C22C23×#1192407811yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—5864no—
327C4—5861no—
328C4—5861no—
329C4—5861no—
330C4—5861no—
331C4—5861no—
332C4—5861no—
333C4—11722no—
334C4—11722no—
335C4—11722no—
336C2—22no—
337C2—2932no—
338C2—2932no—
339C2—5862no—
340C2C2×#2262770311yescharacteristic
341C2#41×#1192407811yescharacteristic
342C2#3403719811yescharacteristic
subgroupG/H
center, FrattiniC22C23×#11924078
commutator, socleC22×C293C23×C4
Fitting#117×C293C4
prime radicalC23×D293C23
cosocleC22×D293C24
hypercenter#117#11924078
hypocenterC293#2343
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #34037078C2semidirect
2. #34037078C2semidirect
4. #34037074C2semidirect
5. #34037073C2semidirect
7. C4×C4⋊#11924078C2semidirect
9. #34037065C2semidirect
29. #22627583C4semidirect
30. #22627582C4semidirect
31. #22627582C4semidirect
32. #22627581C4semidirect
33. #22627581C4semidirect
34. #22627580C4semidirect
35. #22627580C4semidirect
42. #117×C293C4semidirect
66. C4⋊Dic293C2×C4semidirect
67. C4⋊Dic293C2×C4semidirect
68. #17989781C2×C4semidirect
69. #17989781C2×C4semidirect
70. #17989781C2×C4semidirect
71. #17989781C2×C4semidirect
78. C4×Dic293C2×C4semidirect
79. C4×Dic293C2×C4semidirect
80. C4×Dic293C2×C4semidirect
81. C4×Dic293C2×C4semidirect
82. C4×Dic293C2×C4semidirect
83. C4×Dic293C2×C4semidirect
85. C4⋊C4×C293C2×C4semidirect
86. C4⋊C4×C293C2×C4semidirect
89. C42×C293C2×C4semidirect
90. C42×C293C2×C4semidirect
171. C293#2343semidirect
193. #117#11924078semidirect
242. C4⋊C4C2×#11924078semidirect
243. C4⋊C4C2×#11924078semidirect
261. C42C2×#11924078semidirect
262. C42C2×#11924078semidirect

Maximal subgroups

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

subgroupindex
#340370782
#340370762
#340370742
#340370732
#340370722
C4×C4⋊#119240782
C22⋊C4×#119240782
#340370652
C2×(C2×#11924078)⋊C42
#117×D2932
#2343293