Finite Group Databasebeta

← #49124115

Subgroups — #49124115

Order 36224.

532 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583566C211yesmaximal, characteristic
2#31826349C211yesmaximal, characteristic, complemented
3#31826349C211yesmaximal, characteristic, complemented
4#31826347C211yesmaximal, characteristic, complemented
5#31826347C211yesmaximal, characteristic, complemented
6#31826338C211yesmaximal, characteristic
7#31826337C211yesmaximal, characteristic
8#31826332C211yesmaximal, characteristic, complemented
9#31826329C211yesmaximal, characteristic, complemented
10#31826326C211yesmaximal, characteristic
11C4×Dic283⋊C4C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic283C211yesmaximal, characteristic
13#31826311C211yesmaximal, characteristic, complemented
14C2×C283⋊#95C211yesmaximal, characteristic
15C4×C22⋊C4×C283C211yesmaximal, characteristic
16C23×Dic283C2211yescharacteristic
17C23×Dic283C2211yescharacteristic
18#22583566C418yescomplemented
19C2×Dic283⋊C4C2211yescharacteristic
20C2×Dic283⋊C4C2211yescharacteristic
21C2×Dic283⋊C4C2211yescharacteristic
22C2×Dic283⋊C4C2211yescharacteristic
23C2×Dic283⋊C4C2211yescharacteristic
24C2×Dic283⋊C4C2211yescharacteristic
25C2×C22⋊Dic283C2211yescharacteristic
26C2×C22⋊Dic283C2211yescharacteristic
27C2×C4×Dic283C2211yescharacteristic
28C2×C4×Dic283C2211yescharacteristic
29C2×C4×Dic283C2211yescharacteristic
30C2×C4×Dic283C2211yescharacteristic
31C283⋊#95C2211yescharacteristic
32C283⋊#95C2211yescharacteristic
33C283⋊#95C2211yescharacteristic
34C283⋊#95C2211yescharacteristic
35C283⋊#95C2211yescharacteristic
36C283⋊#95C2211yescharacteristic
37C283⋊#95C2211yescharacteristic
38C283⋊#95C2211yescharacteristic
39C283⋊#95C2211yescharacteristic
40C283⋊#95C2211yescharacteristic
41C283⋊#95C2211yescharacteristic
42C283⋊#95C2211yescharacteristic
43C283⋊#95C2211yescharacteristic
44C283⋊#95C2211yescharacteristic
45C23×C4×C283C2211yescharacteristic
46C2×C22⋊C4×C283C2211yescharacteristic
47C2×C22⋊C4×C283C2211yescharacteristic
48C2×C42×C283C2211yescharacteristic
49C2×C42×C283C2211yescharacteristic
50#95×C283C2211yescharacteristic
51#95×C283C2211yescharacteristic
52C22×Dic283—22no—
53C22×Dic283—22no—
54C22×Dic283—22no—
55C22×Dic283—22no—
56C22×Dic283—41no—
57C22×Dic283C2×C414yes—
58C22×Dic283C2311yescharacteristic
59C22×Dic283C2311yescharacteristic
60C22×Dic283C2311yescharacteristic
61C22×Dic283C2311yescharacteristic
62C22×Dic283C2311yescharacteristic
63C22×Dic283C2311yescharacteristic
64C22×Dic283C2311yescharacteristic
65C22×Dic283C2311yescharacteristic
66Dic283⋊C4—22no—
67Dic283⋊C4—22no—
68Dic283⋊C4—41no—
69Dic283⋊C4—41no—
70Dic283⋊C4C2×C414yescomplemented
71Dic283⋊C4C2×C414yescomplemented
72C22⋊Dic283—22no—
73C22⋊Dic283C2×C414yes—
74C4×Dic283—22no—
75C4×Dic283—41no—
76C4×Dic283C2×C414yescomplemented
77C4×Dic283C2×C414yescomplemented
78C24×C283C2311yescharacteristic
79C22×C4×C283—22no—
80C22×C4×C283—22no—
81C22×C4×C283—41no—
82C22×C4×C283C2311yescharacteristic
83C22×C4×C283C2311yescharacteristic
84C22×C4×C283C2311yescharacteristic
85C22×C4×C283C2311yescharacteristic
86C22×C4×C283C2311yescharacteristic
87C22×C4×C283C2311yescharacteristic
88C22⋊C4×C283—22no—
89C22⋊C4×C283C2×C414yes—
90C42×C283—22no—
91C42×C283—41no—
92C2×Dic283—28no—
93C2×Dic283—21no—
94C2×Dic283—21no—
95C2×Dic283—21no—
96C2×Dic283—21no—
97C2×Dic283—21no—
98C2×Dic283—21no—
99C2×Dic283—21no—
100C2×Dic283—21no—
101C2×Dic283—21no—
102C2×Dic283—21no—
103C2×Dic283—21no—
104C2×Dic283—21no—
105C2×Dic283—21no—
106C2×Dic283—21no—
107C2×Dic283—21no—
108C2×Dic283—21no—
109C2×Dic283—21no—
110C2×Dic283—21no—
111C2×Dic283—21no—
112C2×Dic283—44no—
113C2×Dic283C22×C412yes—
114C2×Dic283C22×C412yes—
115C2×Dic283C22×C412yes—
116C2×Dic283C22×C412yes—
117C2×Dic283#4112yes—
118C23×C283—21no—
119C23×C283—21no—
120C23×C283—21no—
121C23×C283—21no—
122C23×C283C22×C412yes—
123C23×C283#4112yes—
124C23×C283#4112yes—
125C23×C283C2411yescharacteristic
126C2×C4×C283—21no—
127C2×C4×C283—21no—
128C2×C4×C283—21no—
129C2×C4×C283—21no—
130C2×C4×C283—21no—
131C2×C4×C283—21no—
132C2×C4×C283—21no—
133C2×C4×C283—21no—
134C2×C4×C283—21no—
135C2×C4×C283—21no—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283—44no—
142C2×C4×C283C22×C412yes—
143C2×C4×C283C22×C412yes—
144C2×C4×C283#4112yes—
145C22×C283—22no—
146C22×C283—22no—
147C22×C283—22no—
148C22×C283—22no—
149C22×C283—22no—
150C22×C283—22no—
151C22×C283#11714yes—
152C22×C283C23×C411yescharacteristic
153C22×C283C2×#4111yescharacteristic
154C22×C283C2×#4111yescharacteristic
155C22×C283C2×#4111yescharacteristic
156C22×C283C2×#4111yescharacteristic
157C22×C283H(5,𝔽2)11yescharacteristic
158C22×C2832−1+411yescharacteristic
159C4×C283—22no—
160C4×C283—22no—
161C4×C283—22no—
162C4×C283—41no—
163C4×C283—41no—
164C4×C283—41no—
165Dic283—22no—
166Dic283—22no—
167Dic283—22no—
168Dic283—22no—
169Dic283—22no—
170Dic283—41no—
171Dic283—41no—
172Dic283—41no—
173C2×C283—24no—
174C2×C283C2×#11711yescharacteristic
175C2×C283C4×#4111yescharacteristic
176C2×C283#52011yescharacteristic
177C2×C283#55111yescharacteristic
178C2×C283#55111yescharacteristic
179C2×C283#55211yescharacteristic
180C2×C283#55211yescharacteristic
181C283#234311yescharacteristic, complemented, Sylow
182#2343—2831nomaximal, Sylow
183C2×#117—2831no—
184#387—2831no—
185#387—2831no—
186#387—2831no—
187#387—2831no—
188#385—2831no—
189#385—2831no—
190#383—2831no—
191#382—2831no—
192#381—2831no—
193C4×C4⋊C4—2831no—
194C4×C22⋊C4—2831no—
195C4×C22⋊C4D28311yescharacteristic
196#376—2831no—
197C2×#95—2831no—
198C23×C4—2831no—
199C23×C4—2831no—
200C23×C4C2×D28311yescharacteristic
201#117—2838no—
202C2×C4⋊C4—2831no—
203C2×C4⋊C4—2831no—
204C2×C4⋊C4—2831no—
205C2×C4⋊C4—2831no—
206C2×C4⋊C4—2831no—
207C2×C4⋊C4—2831no—
208C2×C22⋊C4—2831no—
209C2×C22⋊C4—2831no—
210C2×C22⋊C4C2×D28311yescharacteristic
211C2×C22⋊C4C2×D28311yescharacteristic
212C2×C42—2831no—
213C2×C42—2831no—
214C2×C42—2831no—
215C2×C42—2831no—
216C2×C42C2×D28311yescharacteristic
217C2×C42C2×D28311yescharacteristic
218#95—2831no—
219#95—2831no—
220#95—2831no—
221#95—2831no—
222#95—2831no—
223#95—2831no—
224#95—2831no—
225#95—2831no—
226#95—2831no—
227#95—2831no—
228#95—2831no—
229#95—2831no—
230#95—2831no—
231#95—2831no—
232#95C2×D28311yescharacteristic
233#95C2×D28311yescharacteristic
234C24C22×D28311yescharacteristic
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—41no—
238C22×C4—2834no—
239C22×C4—2831no—
240C22×C4—2831no—
241C22×C4—2831no—
242C22×C4—2831no—
243C22×C4—2831no—
244C22×C4—2831no—
245C22×C4—2831no—
246C22×C4—2831no—
247C22×C4—5662no—
248C22×C4—5662no—
249C22×C4—5662no—
250C22×C4—5662no—
251C22×C4—11321no—
252C22×C4C22×D28311yescharacteristic
253C22×C4C22×D28311yescharacteristic
254C22×C4C22×D28311yescharacteristic
255C22×C4C22×D28311yescharacteristic
256C22×C4C22×D28311yescharacteristic
257C22×C4C22×D28311yescharacteristic
258C4⋊C4—2834no—
259C4⋊C4—2834no—
260C4⋊C4—5662no—
261C4⋊C4—5662no—
262C4⋊C4—11321no—
263C4⋊C4—11321no—
264C22⋊C4—22no—
265C22⋊C4—2834no—
266C22⋊C4—5662no—
267C22⋊C4C4×D28314yes—
268C42—22no—
269C42—41no—
270C42—2834no—
271C42—2834no—
272C42—5662no—
273C42—11321no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23C2×C4×D28312yes—
279C23#1798539212yes—
280C23#1798539212yes—
281C23C23×D28311yescharacteristic
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—44no—
298C2×C4—2832no—
299C2×C4—2832no—
300C2×C4—2832no—
301C2×C4—2832no—
302C2×C4—2832no—
303C2×C4—5668no—
304C2×C4—5661no—
305C2×C4—5661no—
306C2×C4—5661no—
307C2×C4—5661no—
308C2×C4—5661no—
309C2×C4—5661no—
310C2×C4—5661no—
311C2×C4—5661no—
312C2×C4—5661no—
313C2×C4—5661no—
314C2×C4—5661no—
315C2×C4—5661no—
316C2×C4—5661no—
317C2×C4—5661no—
318C2×C4—5661no—
319C2×C4—5661no—
320C2×C4—5661no—
321C2×C4—5661no—
322C2×C4—5661no—
323C2×C4—11324no—
324C2×C4C2×C4×D28312yes—
325C2×C4C2×C4×D28312yes—
326C2×C4#1798539112yes—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—22no—
331C22—22no—
332C22—22no—
333C22#2258356714yes—
334C22C22×C4×D28311yescharacteristic
335C22#41×D28311yescharacteristic
336C22C2×#1798539111yescharacteristic
337C22C2×#1798539211yescharacteristic
338C22C2×#1798539211yescharacteristic
339C22#2258365511yescharacteristic
340C22#2258365711yescharacteristic
341C4—22no—
342C4—22no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—5662no—
348C4—5662no—
349C4—5662no—
350C4—5662no—
351C4—5662no—
352C4—11321no—
353C4—11321no—
354C4—11321no—
355C2—24no—
356C2C2×#2258356711yescharacteristic
357C2C4×#1798539111yescharacteristic
358C2#3182694411yescharacteristic
359C2#3182714111yescharacteristic
360C2#3182714411yescharacteristic
361C2#3182714811yescharacteristic
362C2#3182715511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
FittingC4×C22⋊C4×C283C2
socle, cosocleC23×C283C24
prime radicalC24×C283C23
hypercenterC4×C22⋊C4D283
hypocenterC283#2343
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #31826349C2semidirect
3. #31826349C2semidirect
4. #31826347C2semidirect
5. #31826347C2semidirect
8. #31826332C2semidirect
9. #31826329C2semidirect
11. C4×Dic283⋊C4C2semidirect
13. #31826311C2semidirect
18. #22583566C4semidirect
70. Dic283⋊C4C2×C4semidirect
71. Dic283⋊C4C2×C4semidirect
76. C4×Dic283C2×C4semidirect
77. C4×Dic283C2×C4semidirect
181. C283#2343semidirect

Maximal subgroups

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

subgroupindex
C2×#225835662
#318263492
#318263472
#318263382
#318263372
#318263322
#318263292
#318263262
C4×Dic283⋊C42
C22⋊C4×Dic2832
#318263112
C2×C283⋊#952
C4×C22⋊C4×C2832
#2343283