Finite Group Databasebeta

← #49175267

Subgroups — #49175267

Order 37504.

568 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34037079C212yesmaximal, complemented
2#34037078C212yesmaximal, complemented
3#34037077C212yesmaximal
4#34037076C212yesmaximal, complemented
5#34037074C211yesmaximal, characteristic, complemented
6#34037073C211yesmaximal, characteristic, complemented
7#34037072C211yesmaximal, characteristic, complemented
8#34037071C211yesmaximal, characteristic, complemented
9C4×C22⋊#11924078C211yesmaximal, characteristic, complemented
10C2×(C2×#11924078)⋊C4C211yesmaximal, characteristic, complemented
11C4×D4×D293C211yesmaximal, characteristic
12C23×#11924078C2212yes—
13C2×C4⋊#11924078C2212yes—
14C2×C4⋊#11924078C2212yes—
15C2×C22⋊#11924078C2212yes—
16C2×C22⋊#11924078C2212yes—
17C2×C22⋊#11924078C2212yes—
18C2×C4×#11924078C2212yes—
19(C2×#11924078)⋊C4C2211yescharacteristic
20(C2×#11924078)⋊C4C2211yescharacteristic
21(C2×#11924078)⋊C4C2212yes—
22(C2×#11924078)⋊C4C2211yescharacteristic
23(C2×#11924078)⋊C4C2211yescharacteristic
24(C2×#11924078)⋊C4C2212yes—
25(C2×#11924078)⋊C4C2212yes—
26(C2×#11924078)⋊C4C2212yes—
27(C2×#11924078)⋊C4C2212yes—
28C2×D4×D293C2211yescharacteristic
29C22×C4×D293C2211yescharacteristic
30C22×C4×D293C2211yescharacteristic
31C4×D1172C411yescharacteristic, complemented
32D4×Dic293C411yescharacteristic, complemented
33#22627586C411yescharacteristic, complemented
34C4×C22⋊D293C411yescharacteristic, complemented
35C4×C22⋊D293C411yescharacteristic, complemented
36#22627584C411yescharacteristic, complemented
37#22627584C411yescharacteristic, complemented
38C4⋊C4×D293C2211yescharacteristic
39C22⋊C4×D293C2211yescharacteristic
40C22⋊C4×D293C2211yescharacteristic
41C42×D293C2211yescharacteristic
42C4×D4×C293C411yescharacteristic, complemented
43C22×#11924078—24no—
44C22×#11924078—42no—
45C22×#11924078—42no—
46C22×#11924078C2312yes—
47C22×#11924078C2312yes—
48C22×#11924078C2312yes—
49C22×#11924078C2312yes—
50C4⋊#11924078—42no—
51C4⋊#11924078—42no—
52C22⋊#11924078—24no—
53C22⋊#11924078—42no—
54C22⋊#11924078—42no—
55C4×#11924078—42no—
56C23×D293C2311yescharacteristic
57C23×D293C2311yescharacteristic
58C2×D1172C2×C411yescharacteristic
59C2×C22⋊D293C2×C411yescharacteristic
60C2×C22⋊D293C2×C411yescharacteristic
61D4×D293—24no—
62C22×Dic293C2×C411yescharacteristic
63C22×Dic293C2×C411yescharacteristic, complemented
64C2×C4×D293—42no—
65C2×C4×D293—42no—
66C2×C4×D293C2×C411yescharacteristic
67C2×C4×D293C2×C411yescharacteristic
68C2×C4×D293C2×C411yescharacteristic, complemented
69C2×C4×D293C2×C411yescharacteristic, complemented
70C2×C4×D293C2311yescharacteristic
71C2×C4×D293C2311yescharacteristic
72C2×C4×D293C2311yescharacteristic
73C2×C4×D293C2311yescharacteristic
74C2×C4×D293C2311yescharacteristic
75C4⋊Dic293C2×C411yescharacteristic, complemented
76#17989781C2×C411yescharacteristic, complemented
77#17989781C2×C411yescharacteristic, complemented
78C22⋊Dic293C2×C411yescharacteristic
79C22⋊Dic293C2×C411yescharacteristic, complemented
80#17989779C2×C411yescharacteristic
81#17989779C2×C411yescharacteristic
82#17989779C2×C411yescharacteristic, complemented
83#17989779C2×C411yescharacteristic, complemented
84C4×Dic293C2×C411yescharacteristic, complemented
85C4×Dic293C2×C411yescharacteristic, complemented
86C4×Dic293C2×C411yescharacteristic, complemented
87C2×D4×C293C2×C411yescharacteristic
88C22×C4×C293C2×C411yescharacteristic
89C22×C4×C293C2×C411yescharacteristic, complemented
90C4⋊C4×C293C2×C411yescharacteristic, complemented
91C22⋊C4×C293C2×C411yescharacteristic
92C22⋊C4×C293C2×C411yescharacteristic, complemented
93C42×C293C2×C411yescharacteristic, complemented
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—22no—
103C2×#11924078—22no—
104C2×#11924078—22no—
105C2×#11924078—22no—
106C2×#11924078—48no—
107C22×D293—22no—
108C22×D293—21no—
109C22×D293—21no—
110C22×D293—22no—
111C22×D293—22no—
112C22×D293—21no—
113C22×D293—21no—
114C22×D293C22×C411yescharacteristic
115C22×D293C22×C411yescharacteristic
116C22×D293#4114yes—
117C22×D293C2411yescharacteristic
118D1172—22no—
119C22⋊D293—22no—
120C22⋊D293—22no—
121C2×Dic293—41no—
122C2×Dic293—41no—
123C2×Dic293C22×C411yescharacteristic
124C2×Dic293C22×C411yescharacteristic
125C2×Dic293C22×C411yescharacteristic
126C2×Dic293C22×C411yescharacteristic
127C2×Dic293C22×C411yescharacteristic
128C4×D293—22no—
129C4×D293—22no—
130C4×D293—22no—
131C4×D293—22no—
132C4×D293—21no—
133C4×D293—21no—
134C4×D293—41no—
135C4×D293—41no—
136C4×D293—41no—
137C4×D293—41no—
138C23×C293C22×C411yescharacteristic
139C23×C293C22×C411yescharacteristic
140D4×C293—22no—
141C2×C4×C293—41no—
142C2×C4×C293—41no—
143C2×C4×C293C22×C411yescharacteristic
144C2×C4×C293C22×C411yescharacteristic
145C2×C4×C293C22×C411yescharacteristic
146C2×C4×C293C22×C411yescharacteristic
147C2×C4×C293C22×C411yescharacteristic
148C22×C293—21no—
149C22×C293—21no—
150C22×C293—21no—
151C22×C293—21no—
152C22×C293—21no—
153C22×C293#11712yes—
154C22×C293C23×C411yescharacteristic
155C2×D293—21no—
156C2×D293—21no—
157C2×D293—24no—
158C2×D293—24no—
159C2×D293—21no—
160C2×D293—21no—
161C2×D293—21no—
162C2×D293—42no—
163C2×D293—42no—
164C2×D293#11712yes—
165C2×D293C2×#4112yes—
166C2×D293H(5,𝔽2)11yescharacteristic
167C2×D293H(5,𝔽2)12yes—
168C2×D2932−1+411yescharacteristic
169#11924078—42no—
170#11924078—42no—
171#11924078—42no—
172#11924078—42no—
173C4×C293—21no—
174C4×C293—21no—
175C4×C293—21no—
176C4×C293—21no—
177C4×C293—21no—
178Dic293—21no—
179Dic293—21no—
180Dic293—21no—
181Dic293—21no—
182Dic293—21no—
183C2×C293—22no—
184C2×C293—41no—
185C2×C293C2×#11711yescharacteristic
186C2×C293#51811yescharacteristic
187C2×C293#52011yescharacteristic
188D293—22no—
189D293—41no—
190D293#53812yes—
191D293#53912yes—
192C293#231811yescharacteristic, complemented, Sylow
193#2318—2931nomaximal, Sylow
194C2×C4×D4—2931no—
195#388—2932no—
196#387—2932no—
197#386—2932no—
198#385—2932no—
199#383—2931no—
200#382—2931no—
201#381—2931no—
202#380—2931no—
203C4×C22⋊C4—2931no—
204C2×#95—2931no—
205C22×D4—2931no—
206C23×C4—2931no—
207C23×C4—2931no—
208C23×C4—2932no—
209C4×D4—2931no—
210C4×D4—2931no—
211C4×D4—2931no—
212C4×D4—2931no—
213C4×D4—2931no—
214C4×D4—2931no—
215C4×D4—2931no—
216C4×D4#1192407811yescharacteristic, complemented
217C2×C4⋊C4—2931no—
218C2×C4⋊C4—2932no—
219C2×C4⋊C4—2932no—
220C2×C22⋊C4—2931no—
221C2×C22⋊C4—2931no—
222C2×C22⋊C4—2932no—
223C2×C22⋊C4—2932no—
224C2×C22⋊C4—2932no—
225C2×C42—2931no—
226C2×C42—2932no—
227#95—2931no—
228#95—2931no—
229#95—2932no—
230#95—2931no—
231#95—2931no—
232#95—2932no—
233#95—2932no—
234#95—2932no—
235#95—2932no—
236C24—2931no—
237C24—2931no—
238C2×D4—2931no—
239C2×D4—2931no—
240C2×D4—2931no—
241C2×D4—5864no—
242C2×D4C2×#1192407811yescharacteristic
243C22×C4—2931no—
244C22×C4—2931no—
245C22×C4—2931no—
246C22×C4—2931no—
247C22×C4—2931no—
248C22×C4—2931no—
249C22×C4—2931no—
250C22×C4—2931no—
251C22×C4—2931no—
252C22×C4—2931no—
253C22×C4—2931no—
254C22×C4—2932no—
255C22×C4—2932no—
256C22×C4—2932no—
257C22×C4—2932no—
258C22×C4—5864no—
259C22×C4—11722no—
260C22×C4—11722no—
261C22×C4—11722no—
262C22×C4—11722no—
263C22×C4C2×#1192407811yescharacteristic
264C22×C4C2×#1192407811yescharacteristic, complemented
265C4⋊C4—2931no—
266C4⋊C4—2931no—
267C4⋊C4—2931no—
268C4⋊C4—11722no—
269C4⋊C4—11722no—
270C4⋊C4C2×#1192407811yescharacteristic, complemented
271C22⋊C4—2931no—
272C22⋊C4—2931no—
273C22⋊C4—2931no—
274C22⋊C4—2931no—
275C22⋊C4—2931no—
276C22⋊C4—2931no—
277C22⋊C4—5864no—
278C22⋊C4—11722no—
279C22⋊C4—11722no—
280C22⋊C4C2×#1192407811yescharacteristic
281C22⋊C4C2×#1192407811yescharacteristic, complemented
282C42—2931no—
283C42—2931no—
284C42—2931no—
285C42—11722no—
286C42C2×#1192407811yescharacteristic, complemented
287C23—2931no—
288C23—2934no—
289C23—2931no—
290C23—2931no—
291C23—5862no—
292C23—5861no—
293C23—5861no—
294C23—5861no—
295C23—5862no—
296C23—5862no—
297C23—5861no—
298C23C22×#1192407811yescharacteristic
299C23C22×#1192407811yescharacteristic
300D4—22no—
301D4—5862no—
302D4—5862no—
303D4—5862no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—2931no—
307C2×C4—2931no—
308C2×C4—2931no—
309C2×C4—2931no—
310C2×C4—2931no—
311C2×C4—5862no—
312C2×C4—5861no—
313C2×C4—5862no—
314C2×C4—5862no—
315C2×C4—5862no—
316C2×C4—5861no—
317C2×C4—5862no—
318C2×C4—5862no—
319C2×C4—5862no—
320C2×C4—5862no—
321C2×C4—5862no—
322C2×C4—5862no—
323C2×C4—5862no—
324C2×C4—5862no—
325C2×C4—5862no—
326C2×C4—5862no—
327C2×C4—5862no—
328C2×C4—5862no—
329C2×C4—11721no—
330C2×C4—11721no—
331C2×C4—11721no—
332C2×C4—11721no—
333C2×C4—11721no—
334C2×C4—11721no—
335C2×C4—11728no—
336C2×C4C22×#1192407811yescharacteristic
337C2×C4C22×#1192407811yescharacteristic
338C2×C4C22×#1192407811yescharacteristic
339C2×C4C22×#1192407811yescharacteristic
340C2×C4C22×#1192407811yescharacteristic
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—2932no—
347C22—2932no—
348C22—2931no—
349C22—2931no—
350C22—2932no—
351C22—5864no—
352C22—5864no—
353C22—5861no—
354C22—5861no—
355C22—5861no—
356C22—5861no—
357C22—5861no—
358C22—11722no—
359C22—11722no—
360C22#2262770312yes—
361C22C23×#1192407811yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—5861no—
368C4—5861no—
369C4—5861no—
370C4—5861no—
371C4—5861no—
372C4—11722no—
373C4—11722no—
374C4—11722no—
375C4—11722no—
376C2—22no—
377C2—41no—
378C2—2932no—
379C2—2932no—
380C2—5862no—
381C2—11721no—
382C2C2×#2262770311yescharacteristic
383C2#3403719611yescharacteristic
384C2#3403719811yescharacteristic
subgroupG/H
center, FrattiniC22C23×#11924078
commutator, socleC22×C293C23×C4
FittingC4×D4×C293C4
prime radicalC2×D4×D293C22
cosocleC22×D293C24
hypercenterC4×D4#11924078
hypocenterC293#2318
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #34037079C2semidirect
2. #34037078C2semidirect
4. #34037076C2semidirect
5. #34037074C2semidirect
6. #34037073C2semidirect
7. #34037072C2semidirect
8. #34037071C2semidirect
9. C4×C22⋊#11924078C2semidirect
10. C2×(C2×#11924078)⋊C4C2semidirect
31. C4×D1172C4semidirect
32. D4×Dic293C4semidirect
33. #22627586C4semidirect
34. C4×C22⋊D293C4semidirect
35. C4×C22⋊D293C4semidirect
36. #22627584C4semidirect
37. #22627584C4semidirect
42. C4×D4×C293C4semidirect
63. C22×Dic293C2×C4semidirect
68. C2×C4×D293C2×C4semidirect
69. C2×C4×D293C2×C4semidirect
75. C4⋊Dic293C2×C4semidirect
76. #17989781C2×C4semidirect
77. #17989781C2×C4semidirect
79. C22⋊Dic293C2×C4semidirect
82. #17989779C2×C4semidirect
83. #17989779C2×C4semidirect
84. C4×Dic293C2×C4semidirect
85. C4×Dic293C2×C4semidirect
86. C4×Dic293C2×C4semidirect
89. C22×C4×C293C2×C4semidirect
90. C4⋊C4×C293C2×C4semidirect
92. C22⋊C4×C293C2×C4semidirect
93. C42×C293C2×C4semidirect
192. C293#2318semidirect
216. C4×D4#11924078semidirect
264. C22×C4C2×#11924078semidirect
270. C4⋊C4C2×#11924078semidirect
281. C22⋊C4C2×#11924078semidirect
286. C42C2×#11924078semidirect

Maximal subgroups

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

subgroupindex
#340370792
#340370782
#340370772
#340370762
#340370742
#340370732
#340370722
#340370712
C4×C22⋊#119240782
C2×(C2×#11924078)⋊C42
C4×D4×D2932
#2318293