Finite Group Databasebeta

← #46783197

Subgroups — #46783197

Order 33664.

598 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22554438C211yesmaximal, characteristic
2C2×C22⋊C4×D263C211yesmaximal, characteristic, complemented
3C2×#22554385C211yesmaximal, characteristic, complemented
4#30681793C211yesmaximal, characteristic, complemented
5#30681704C211yesmaximal, characteristic, complemented
6#30681704C211yesmaximal, characteristic, complemented
7C2×#99×C263C211yesmaximal, characteristic, complemented
8C24×D263C2211yescharacteristic
9C22×C22⋊D263C412yescomplemented
10C22×C4×D263—21no—
11#22554438—21no—
12#22554438—22no—
13#22554438—21no—
14C2×C22⋊Dic263C2211yescharacteristic
15C2×C22⋊Dic263C2211yescharacteristic
16C2×C22⋊Dic263C2211yescharacteristic
17C2×(C2×D263)⋊C4—21no—
18C2×(C2×D263)⋊C4—22no—
19C2×(C2×D263)⋊C4C412yescomplemented
20C22⋊C4×D263—22no—
21C22⋊C4×D263—22no—
22#22554385—22no—
23C22×D4×C263C2211yescharacteristic
24C2×C22⋊C4×C263C2211yescharacteristic
25C2×C22⋊C4×C263C2211yescharacteristic
26#99×C263—22no—
27C23×D263—21no—
28C23×D263—21no—
29C23×D263—21no—
30C23×D263—21no—
31C23×D263—44no—
32C23×D263C2×C412yes—
33C23×D263D411yescharacteristic
34C23×D263D412yes—
35C23×D263D411yescharacteristic
36C2×C22⋊D263—22no—
37C2×C22⋊D263—22no—
38C2×C22⋊D263—44no—
39C22×Dic263—21no—
40C22×Dic263—21no—
41C22×Dic263C2×C412yescomplemented
42C2×C4×D263—24no—
43C2×C4×D263—44no—
44C22⋊Dic263—21no—
45C22⋊Dic263—21no—
46C22⋊Dic263—21no—
47C22⋊Dic263—21no—
48C22⋊Dic263—21no—
49C22⋊Dic263D412yescomplemented
50(C2×D263)⋊C4—24no—
51(C2×D263)⋊C4—22no—
52(C2×D263)⋊C4—22no—
53(C2×D263)⋊C4—44no—
54C24×C263C2×C411yescharacteristic, complemented
55C24×C263C2311yescharacteristic
56C2×D4×C263—21no—
57C2×D4×C263—21no—
58C2×D4×C263—21no—
59C2×D4×C263—21no—
60C2×D4×C263—21no—
61C2×D4×C263—21no—
62C22×C4×C263—21no—
63C22×C4×C263—21no—
64C22×C4×C263C2×C411yescharacteristic, complemented
65C22⋊C4×C263—21no—
66C22⋊C4×C263—21no—
67C22⋊C4×C263—21no—
68C22⋊C4×C263D412yescomplemented
69C22×D263—21no—
70C22×D263—21no—
71C22×D263—24no—
72C22×D263—22no—
73C22×D263—22no—
74C22×D263—21no—
75C22×D263—22no—
76C22×D263—22no—
77C22×D263—21no—
78C22×D263—24no—
79C22×D263—24no—
80C22×D263—42no—
81C22×D263—42no—
82C22×D263—42no—
83C22×D263—44no—
84C22×D263—44no—
85C22×D263—44no—
86C22×D263—44no—
87C22×D263C22⋊C412yes—
88C22×D263C22⋊C412yes—
89C22⋊D263—44no—
90C22⋊D263—44no—
91C2×Dic263—22no—
92C2×Dic263—22no—
93C2×Dic263—42no—
94C2×Dic263—42no—
95C2×Dic263—42no—
96C2×Dic263—41no—
97C4×D263—48no—
98C23×C263—21no—
99C23×C263—21no—
100C23×C263—21no—
101C23×C263—42no—
102C23×C263—42no—
103C23×C263C22×C411yescharacteristic
104C23×C263C2×D411yescharacteristic
105C23×C263C2×D411yescharacteristic
106C23×C263C2×D411yescharacteristic
107C23×C263C2×D411yescharacteristic
108C23×C263#4111yescharacteristic
109C23×C263#4111yescharacteristic
110D4×C263—41no—
111D4×C263—41no—
112D4×C263—41no—
113D4×C263—41no—
114C2×C4×C263—21no—
115C2×C4×C263—21no—
116C2×C4×C263—21no—
117C2×C4×C263—22no—
118C2×C4×C263—42no—
119C2×C4×C263—42no—
120C2×C4×C263—41no—
121C22×C263—22no—
122C22×C263—22no—
123C22×C263—22no—
124C22×C263—41no—
125C22×C263—41no—
126C22×C263—41no—
127C22×C263—41no—
128C22×C263—41no—
129C22×C263—42no—
130C22×C263—81no—
131C22×C263—81no—
132C22×C263C2×C22⋊C411yescharacteristic
133C22×C263C4×D411yescharacteristic
134C22×C263C4×D411yescharacteristic
135C22×C263#12011yescharacteristic
136C22×C263#12111yescharacteristic
137C22×C263#12111yescharacteristic
138C22×C263#12311yescharacteristic
139C2×D263—24no—
140C2×D263—24no—
141C2×D263—22no—
142C2×D263—22no—
143C2×D263—22no—
144C2×D263—22no—
145C2×D263—22no—
146C2×D263—44no—
147C2×D263—44no—
148C2×D263—44no—
149C2×D263—44no—
150C2×D263—42no—
151C2×D263—42no—
152C2×D263#9914yescomplemented
153C4×C263—42no—
154C4×C263—41no—
155C4×C263—81no—
156Dic263—42no—
157Dic263—42no—
158Dic263—81no—
159C2×C263—21no—
160C2×C263—21no—
161C2×C263—21no—
162C2×C263—21no—
163C2×C263—21no—
164C2×C263—21no—
165C2×C263—81no—
166C2×C263#38611yescharacteristic
167C2×C263C2×#9912yes—
168D263—24no—
169D263—42no—
170C263#189811yescharacteristic, complemented, Sylow
171#1898—2631nomaximal, Sylow
172C2×#120—2631no—
173C22×C22⋊C4—2631no—
174C2×#99—2631no—
175C2×#99D26311yescharacteristic, complemented
176#379—2631no—
177#342—2631no—
178#342—2631no—
179C25—2631no—
180C22×D4—2632no—
181C22×D4C2×D26311yescharacteristic
182C23×C4—5261no—
183#120—5261no—
184#120—5262no—
185#120—5261no—
186C2×C22⋊C4—2631no—
187C2×C22⋊C4—2631no—
188C2×C22⋊C4—2632no—
189C2×C22⋊C4—2631no—
190C2×C22⋊C4—5262no—
191C2×C22⋊C4—5261no—
192C2×C22⋊C4—5262no—
193C2×C22⋊C4—5262no—
194C2×C22⋊C4C2×D26311yescharacteristic
195C2×C22⋊C4C2×D26311yescharacteristic
196#99—22no—
197#99—5262no—
198C24—2631no—
199C24—2632no—
200C24—2632no—
201C24—2631no—
202C24—5261no—
203C24—5261no—
204C24—5261no—
205C24—5261no—
206C24—10524no—
207C24C4×D26311yescharacteristic, complemented
208C24C22×D26311yescharacteristic
209C2×D4—21no—
210C2×D4—21no—
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—21no—
214C2×D4—21no—
215C2×D4—5262no—
216C2×D4—5262no—
217C2×D4—10524no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—2632no—
221C22×C4—5264no—
222C22×C4—5261no—
223C22×C4—5261no—
224C22×C4—10524no—
225C22×C4C4×D26311yescharacteristic, complemented
226C22⋊C4—21no—
227C22⋊C4—21no—
228C22⋊C4—21no—
229C22⋊C4—2632no—
230C22⋊C4—5262no—
231C22⋊C4—5262no—
232C22⋊C4—5264no—
233C22⋊C4—5261no—
234C22⋊C4—5261no—
235C22⋊C4—5261no—
236C22⋊C4—5261no—
237C22⋊C4—5261no—
238C22⋊C4—10524no—
239C22⋊C4C22⋊D26312yescomplemented
240C23—21no—
241C23—21no—
242C23—21no—
243C23—42no—
244C23—42no—
245C23—2632no—
246C23—2632no—
247C23—5264no—
248C23—5264no—
249C23—5264no—
250C23—5261no—
251C23—5261no—
252C23—5262no—
253C23—5262no—
254C23—5261no—
255C23—5262no—
256C23—5262no—
257C23—5261no—
258C23—10522no—
259C23—10522no—
260C23—10522no—
261C23—10524no—
262C23—10524no—
263C23—10524no—
264C23—10524no—
265C23C2×C4×D26311yescharacteristic
266C23D4×D26311yescharacteristic
267C23D4×D26311yescharacteristic
268C23D4×D26311yescharacteristic
269C23C2×C22⋊D26311yescharacteristic
270C23#1686237511yescharacteristic
271C23#1686237611yescharacteristic
272D4—41no—
273D4—41no—
274D4—41no—
275D4—41no—
276D4—10524no—
277D4—10524no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—41no—
285C2×C4—5262no—
286C2×C4—5262no—
287C2×C4—10528no—
288C2×C4—10522no—
289C2×C4—10522no—
290C2×C4—10522no—
291C2×C4—10521no—
292C22—22no—
293C22—22no—
294C22—22no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22—42no—
300C22—41no—
301C22—2634no—
302C22—81no—
303C22—81no—
304C22—5264no—
305C22—5264no—
306C22—5262no—
307C22—5262no—
308C22—5262no—
309C22—5262no—
310C22—5262no—
311C22—10524no—
312C22—10524no—
313C22—10524no—
314C22—10524no—
315C22—10522no—
316C22—10522no—
317C22C22⋊C4×D26311yescharacteristic
318C22(C22⋊D263)⋊C411yescharacteristic
319C22C4×C22⋊D26311yescharacteristic
320C22#2255443811yescharacteristic
321C22#2255444111yescharacteristic
322C22#2255444311yescharacteristic
323C22#2255445211yescharacteristic
324C4—42no—
325C4—41no—
326C4—81no—
327C4—10522no—
328C4—10522no—
329C4—21041no—
330C2—21no—
331C2—21no—
332C2—21no—
333C2—21no—
334C2—21no—
335C2—21no—
336C2—81no—
337C2—5264no—
338C2—10522no—
339C2#3068181411yescharacteristic
340C2#99×D26312yes—
subgroupG/H
centerC22C22⋊C4×D263
commutatorC23×C263C22×C4
FrattiniC24C22×D263
FittingC2×#99×C263C2
socleC22×C263C2×C22⋊C4
prime radicalC2×#22554438C2
cosocleC24×C263C23
hypercenterC2×#99D263
hypocenterC263#1898
LCSG ▷ C23×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C4×D263C2semidirect
3. C2×#22554385C2semidirect
4. #30681793C2semidirect
5. #30681704C2semidirect
6. #30681704C2semidirect
7. C2×#99×C263C2semidirect
9. C22×C22⋊D263C4semidirect
19. C2×(C2×D263)⋊C4C4semidirect
41. C22×Dic263C2×C4semidirect
49. C22⋊Dic263D4semidirect
54. C24×C263C2×C4semidirect
64. C22×C4×C263C2×C4semidirect
68. C22⋊C4×C263D4semidirect
152. C2×D263#99semidirect
170. C263#1898semidirect
175. C2×#99D263semidirect
207. C24C4×D263semidirect
225. C22×C4C4×D263semidirect
239. C22⋊C4C22⋊D263semidirect

Maximal subgroups

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

subgroupindex
C2×#225544382
C2×C22⋊C4×D2632
C2×#225543852
#306817932
#306817042
C2×#99×C2632
#1898263