Finite Group Databasebeta

← #49098639

Subgroups — #49098639

Order 35968.

864 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 864 conjugacy classes of subgroups — too many to draw. Only its 159 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
1C22×#17985139C211yesmaximal, characteristic
2C2×#22582864C212yesmaximal, complemented
3C2×C4⋊C4×D281C211yesmaximal, characteristic, complemented
4#31823382C211yesmaximal, characteristic, complemented
5#31823381C211yesmaximal, characteristic, complemented
6#31823380C211yesmaximal, characteristic, complemented
7#31823341C212yesmaximal, complemented
8#31823337C212yesmaximal, complemented
9#31823334C212yesmaximal, complemented
10#31823325C211yesmaximal, characteristic, complemented
11#395×C281C211yesmaximal, characteristic, complemented
12C2×#17985139—28no—
13C2×#17985139—24no—
14C22×D1124C2211yescharacteristic
15C22×D1124C2212yes—
16C22×C4×D281C2211yescharacteristic
17C22×C4×D281C2211yescharacteristic
18C22×C4×D281C2212yes—
19C22×C4×D281C2211yescharacteristic
20#22582864—28no—
21C2×C4⋊Dic281C2211yescharacteristic
22C2×#17985117C2211yescharacteristic
23C2×#17985117C2212yes—
24C2×#17985117C2211yescharacteristic
25C4⋊C4×D281—24no—
26C2×#17985115C2212yes—
27C2×#17985115C2212yes—
28C2×#17985115C2212yes—
29C2×#17985115C2212yes—
30C2×#17985115C2212yes—
31#22582786C2211yescharacteristic
32#22582786C2212yes—
33#22582786C2212yes—
34C22×Q8×C281C2211yescharacteristic
35C2×C4⋊C4×C281C2211yescharacteristic
36C2×C4⋊C4×C281C2212yes—
37#95×C281C2211yescharacteristic
38#95×C281C2212yes—
39C23×D281C2312yes—
40C23×D281C2311yescharacteristic
41#17985139—232no—
42C2×D1124—24no—
43C2×D1124—24no—
44C2×D1124—24no—
45C2×D1124—22no—
46C2×D1124D418yes—
47C22×Dic281C2312yes—
48C22×Dic281C2311yescharacteristic
49C22×Dic281C2311yescharacteristic
50C22×Dic281C2311yescharacteristic
51C2×C4×D281—22no—
52C2×C4×D281—24no—
53C2×C4×D281—24no—
54C2×C4×D281—24no—
55C2×C4×D281—22no—
56C2×C4×D281—22no—
57C2×C4×D281—24no—
58C2×C4×D281—24no—
59C2×C4×D281—22no—
60C2×C4×D281D414yes—
61C4⋊Dic281—22no—
62#17985117—22no—
63#17985117—22no—
64#17985117—24no—
65#17985115—24no—
66#17985115—24no—
67#17985115—24no—
68#17985115—24no—
69#17985115—24no—
70C2×Q8×C281—24no—
71C2×Q8×C281—22no—
72C22×C4×C281C2312yes—
73C22×C4×C281C2311yescharacteristic
74C22×C4×C281C2312yes—
75C22×C4×C281C2311yescharacteristic
76C22×C4×C281C2311yescharacteristic
77C4⋊C4×C281—22no—
78C4⋊C4×C281—24no—
79C22×D281—21no—
80C22×D281—21no—
81C22×D281—22no—
82C22×D281—22no—
83C22×D281—22no—
84C22×D281—22no—
85C22×D281—22no—
86C22×D281—22no—
87C22×D281—22no—
88C22×D281C2×D414yes—
89C22×D281C2×D414yes—
90C22×D281C2×D412yes—
91D1124—28no—
92D1124—216no—
93C2×Dic281—21no—
94C2×Dic281—22no—
95C2×Dic281—21no—
96C2×Dic281—22no—
97C2×Dic281—22no—
98C2×Dic281—21no—
99C2×Dic281—22no—
100C2×Dic281—22no—
101C2×Dic281C2×D412yes—
102C2×Dic281#4112yescomplemented
103C4×D281—28no—
104C4×D281—216no—
105C4×D281—28no—
106C4×D281—44no—
107C23×C281C2411yescharacteristic
108Q8×C281—28no—
109C2×C4×C281—21no—
110C2×C4×C281—22no—
111C2×C4×C281—22no—
112C2×C4×C281—22no—
113C2×C4×C281—21no—
114C2×C4×C281—22no—
115C2×C4×C281—22no—
116C2×C4×C281—21no—
117C2×C4×C281—22no—
118C2×C4×C281—22no—
119C2×C4×C281C2×D414yes—
120C2×C4×C281C2×D412yes—
121C2×C4×C281#4112yescomplemented
122C22×C281C22×D411yescharacteristic
123C22×C281C22×D412yes—
124C22×C281C2×#4111yescharacteristic
125C22×C281C2×#4111yescharacteristic
126C22×C2812−1+412yes—
127C2×D281—22no—
128C2×D281—22no—
129C2×D281—24no—
130C2×D281—24no—
131C2×D281—24no—
132C2×D281—24no—
133C2×D281—24no—
134C2×D281—42no—
135C2×D281—42no—
136C2×D281—42no—
137C2×D281—42no—
138C2×D281#12014yes—
139C4×C281—24no—
140C4×C281—22no—
141C4×C281—22no—
142C4×C281—41no—
143C4×C281—42no—
144Dic281—22no—
145Dic281—22no—
146Dic281—41no—
147Dic281—42no—
148C2×C281C2×#12011yescharacteristic
149C2×C281#52511yescharacteristic
150C2×C281#53611yescharacteristic
151C2×C281#54712yes—
152C2×C281#54712yes—
153D281—24no—
154D281—44no—
155C281#240611yescharacteristic, complemented, Sylow
156#2406—2811nomaximal, Sylow
157C22×#41—2811no—
158C2×#123—2812no—
159C22×C4⋊C4—2811no—
160#395—2811no—
161#395D28111yescharacteristic, complemented
162#394—2811no—
163#394—2811no—
164#386—2812no—
165#385—2812no—
166#385—2812no—
167#381—2811no—
168C2×#41—5624no—
169C2×#41—5628no—
170C22×Q8C2×D28111yescharacteristic
171C22×D4—2812no—
172C22×D4—2811no—
173C23×C4—2811no—
174C23×C4—2811no—
175C23×C4—2811no—
176C23×C4—2812no—
177#123—5628no—
178C2×C4⋊C4—2811no—
179C2×C4⋊C4—2811no—
180C2×C4⋊C4—2811no—
181C2×C4⋊C4—2812no—
182C2×C4⋊C4—5624no—
183C2×C4⋊C4C2×D28111yescharacteristic
184C2×C4⋊C4C2×D28112yes—
185C2×C22⋊C4—2812no—
186C2×C22⋊C4—2812no—
187C2×C22⋊C4—2812no—
188C2×C22⋊C4—2812no—
189C2×C22⋊C4—2812no—
190#95—2812no—
191#95—2811no—
192#95—2812no—
193#95C2×D28111yescharacteristic
194#95C2×D28112yes—
195C24—2811no—
196C24—2812no—
197#41—56232no—
198C2×Q8—22no—
199C2×Q8—24no—
200C2×D4—2818no—
201C2×D4—5624no—
202C2×D4—5624no—
203C2×D4—5624no—
204C2×D4—5622no—
205C22×C4—2811no—
206C22×C4—2811no—
207C22×C4—2814no—
208C22×C4—2812no—
209C22×C4—2811no—
210C22×C4—5622no—
211C22×C4—5624no—
212C22×C4—5622no—
213C22×C4—5624no—
214C22×C4—5624no—
215C22×C4—5622no—
216C22×C4—5624no—
217C22×C4—5624no—
218C22×C4—5622no—
219C22×C4C22×D28112yes—
220C22×C4C22×D28111yescharacteristic
221C22×C4C22×D28111yescharacteristic
222C22×C4C22×D28112yes—
223C22×C4C22×D28111yescharacteristic
224C4⋊C4—22no—
225C4⋊C4—24no—
226C4⋊C4—5622no—
227C4⋊C4—5622no—
228C4⋊C4—5622no—
229C4⋊C4—5624no—
230C22⋊C4—5624no—
231C22⋊C4—5624no—
232C22⋊C4—5624no—
233C22⋊C4—5624no—
234C22⋊C4—5624no—
235C23—2814no—
236C23—2812no—
237C23—2814no—
238C23—5621no—
239C23—5621no—
240C23—5622no—
241C23—5622no—
242C23—5622no—
243C23—5622no—
244C23—5622no—
245C23—5622no—
246C23—5622no—
247C23C23×D28111yescharacteristic
248Q8—28no—
249D4—56216no—
250D4—5628no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—2812no—
262C2×C4—2812no—
263C2×C4—5628no—
264C2×C4—56216no—
265C2×C4—5628no—
266C2×C4—5621no—
267C2×C4—5622no—
268C2×C4—5621no—
269C2×C4—5622no—
270C2×C4—5622no—
271C2×C4—5621no—
272C2×C4—5622no—
273C2×C4—5622no—
274C2×C4—11244no—
275C2×C4D4×D28112yes—
276C2×C4D4×D28114yes—
277C2×C4#1798513912yescomplemented
278C22—2814no—
279C22—5622no—
280C22—5622no—
281C22—5624no—
282C22—5624no—
283C22—5624no—
284C22—5624no—
285C22—5624no—
286C22—11242no—
287C22—11242no—
288C22—11242no—
289C22—11242no—
290C22C2×D4×D28111yescharacteristic
291C22C2×D4×D28112yes—
292C22#41×D28111yescharacteristic
293C22C2×#1798513911yescharacteristic
294C22#2258292712yes—
295C4—22no—
296C4—24no—
297C4—22no—
298C4—41no—
299C4—42no—
300C4—5622no—
301C4—5622no—
302C4—11241no—
303C4—11242no—
304C2—5624no—
305C2—11244no—
306C2#120×D28111yescharacteristic
307C2#3182397611yescharacteristic
308C2#3182403811yescharacteristic
309C2#3182411512yes—
310C2#3182411612yes—
subgroupG/H
center, FrattiniC23C23×D281
commutator, socle, cosocleC23×C281C24
Fitting#395×C281C2
prime radicalC22×#17985139C2
hypercenter#395D281
hypocenterC281#2406
LCSG ▷ C23×C281 ▷ C281
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
2. C2×#22582864C2semidirect
3. C2×C4⋊C4×D281C2semidirect
4. #31823382C2semidirect
5. #31823381C2semidirect
6. #31823380C2semidirect
7. #31823341C2semidirect
8. #31823337C2semidirect
9. #31823334C2semidirect
10. #31823325C2semidirect
11. #395×C281C2semidirect
102. C2×Dic281#41semidirect
121. C2×C4×C281#41semidirect
155. C281#2406semidirect
161. #395D281semidirect
277. C2×C4#17985139semidirect

Maximal subgroups

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

subgroupindex
C22×#179851392
C2×#225828642
C2×C4⋊C4×D2812
#318233822
#318233812
#318233802
#318233412
#318233372
#318233342
#318233252
#395×C2812
#2406281