Finite Group Databasebeta

← #49124251

Subgroups — #49124251

Order 36224.

652 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583594C211yesmaximal, characteristic
2C2×C4×C22⋊D283C211yesmaximal, characteristic
3C2×#22583566C211yesmaximal, characteristic, complemented
4#31826361C211yesmaximal, characteristic, complemented
5#31826355C211yesmaximal, characteristic, complemented
6#31826354C211yesmaximal, characteristic, complemented
7#31826348C211yesmaximal, characteristic, complemented
8#31826348C211yesmaximal, characteristic, complemented
9#31826342C211yesmaximal, characteristic
10#31826336C211yesmaximal, characteristic, complemented
11C4⋊C4×Dic283C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic283C211yesmaximal, characteristic, complemented
13#31826312C211yesmaximal, characteristic, complemented
14C2×C283⋊#95C211yesmaximal, characteristic, complemented
15#385×C283C211yesmaximal, characteristic, complemented
16C22×C22⋊D283C2211yescharacteristic
17C23×Dic283C2211yescharacteristic
18C23×Dic283C2211yescharacteristic
19C22×C4×D283C2211yescharacteristic
20#22583594C418yescomplemented
21C4×C22⋊D283—24no—
22#22583566—24no—
23C2×C4⋊Dic283C2211yescharacteristic
24C2×C4⋊Dic283C2211yescharacteristic
25C2×Dic283⋊C4C2211yescharacteristic
26C2×Dic283⋊C4C2211yescharacteristic
27C2×Dic283⋊C4C2211yescharacteristic
28C2×C22⋊Dic283C2211yescharacteristic
29C2×(C2×D283)⋊C4C2211yescharacteristic
30C2×(C2×D283)⋊C4C2211yescharacteristic
31C2×(C2×D283)⋊C4C2211yescharacteristic
32C2×(C2×D283)⋊C4C2211yescharacteristic
33C2×(C2×D283)⋊C4C2211yescharacteristic
34C2×C4×Dic283C2211yescharacteristic
35C2×C4×Dic283C2211yescharacteristic
36C2×C4×Dic283C2211yescharacteristic
37C2×C4×Dic283C2211yescharacteristic
38C2×C4×Dic283C2211yescharacteristic
39C283⋊#95C2211yescharacteristic
40C283⋊#95C2211yescharacteristic
41C283⋊#95C2211yescharacteristic
42C283⋊#95C2211yescharacteristic
43C283⋊#95C2211yescharacteristic
44C283⋊#95C2211yescharacteristic
45C283⋊#95C2211yescharacteristic
46C283⋊#95C2211yescharacteristic
47C23×C4×C283C2211yescharacteristic
48C2×C4⋊C4×C283C2211yescharacteristic
49C2×C4⋊C4×C283C2211yescharacteristic
50C2×C22⋊C4×C283C2211yescharacteristic
51C2×C22⋊C4×C283C2211yescharacteristic
52#95×C283C2211yescharacteristic
53#95×C283C2211yescharacteristic
54C23×D283C2311yescharacteristic
55C2×C22⋊D283—22no—
56C2×C22⋊D283—22no—
57C2×C22⋊D283C2×C414yes—
58C22×Dic283—22no—
59C22×Dic283—22no—
60C22×Dic283—22no—
61C22×Dic283—22no—
62C22×Dic283—41no—
63C22×Dic283C2×C414yescomplemented
64C22×Dic283C2311yescharacteristic
65C22×Dic283C2311yescharacteristic
66C22×Dic283C2311yescharacteristic
67C22×Dic283C2311yescharacteristic
68C22×Dic283C2311yescharacteristic
69C22×Dic283C2311yescharacteristic
70C22×Dic283C2311yescharacteristic
71C2×C4×D283—22no—
72C2×C4×D283—22no—
73C2×C4×D283—41no—
74C4⋊Dic283C2×C414yescomplemented
75C4⋊Dic283C2×C414yescomplemented
76Dic283⋊C4—22no—
77Dic283⋊C4—22no—
78Dic283⋊C4—22no—
79C22⋊Dic283D414yes—
80(C2×D283)⋊C4—22no—
81(C2×D283)⋊C4—22no—
82(C2×D283)⋊C4—41no—
83(C2×D283)⋊C4C2×C414yescomplemented
84(C2×D283)⋊C4C2×C414yescomplemented
85C4×Dic283—22no—
86C4×Dic283—22no—
87C4×Dic283—22no—
88C4×Dic283—22no—
89C4×Dic283—41no—
90C24×C283C2311yescharacteristic
91C22×C4×C283—22no—
92C22×C4×C283—22no—
93C22×C4×C283—41no—
94C22×C4×C283C2311yescharacteristic
95C22×C4×C283C2311yescharacteristic
96C22×C4×C283C2311yescharacteristic
97C22×C4×C283C2311yescharacteristic
98C22×C4×C283C2311yescharacteristic
99C22×C4×C283C2311yescharacteristic
100C4⋊C4×C283—22no—
101C4⋊C4×C283—41no—
102C22⋊C4×C283—22no—
103C22⋊C4×C283C2×C414yescomplemented
104C22×D283—21no—
105C22×D283—21no—
106C22×D283—21no—
107C22×D283—21no—
108C22×D283—21no—
109C22×D283—21no—
110C22×D283C22×C412yes—
111C22⋊D283—28no—
112C2×Dic283—28no—
113C2×Dic283—21no—
114C2×Dic283—21no—
115C2×Dic283—21no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C2×Dic283—21no—
119C2×Dic283—21no—
120C2×Dic283—21no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283—21no—
124C2×Dic283—21no—
125C2×Dic283—21no—
126C2×Dic283—21no—
127C2×Dic283—21no—
128C2×Dic283—44no—
129C2×Dic283C22×C412yes—
130C2×Dic283C22×C412yes—
131C2×Dic283C22×C412yes—
132C2×Dic283C2×D412yes—
133C2×Dic283C2×D412yes—
134C2×Dic283#4112yes—
135C4×D283—44no—
136C23×C283—21no—
137C23×C283—21no—
138C23×C283—21no—
139C23×C283—21no—
140C23×C283C22×C412yes—
141C23×C283C2×D412yes—
142C23×C283#4112yes—
143C23×C283C2411yescharacteristic
144C2×C4×C283—21no—
145C2×C4×C283—21no—
146C2×C4×C283—21no—
147C2×C4×C283—21no—
148C2×C4×C283—21no—
149C2×C4×C283—21no—
150C2×C4×C283—21no—
151C2×C4×C283—21no—
152C2×C4×C283—21no—
153C2×C4×C283—21no—
154C2×C4×C283—21no—
155C2×C4×C283—21no—
156C2×C4×C283—21no—
157C2×C4×C283—21no—
158C2×C4×C283—21no—
159C2×C4×C283—44no—
160C2×C4×C283C22×C412yes—
161C2×C4×C283C22×C412yes—
162C2×C4×C283#4112yes—
163C22×C283—22no—
164C22×C283—22no—
165C22×C283—22no—
166C22×C283—22no—
167C22×C283—22no—
168C22×C283—22no—
169C22×C283C4×D414yes—
170C22×C283C23×C411yescharacteristic
171C22×C283C22×D411yescharacteristic
172C22×C283C2×#4111yescharacteristic
173C22×C283C2×#4111yescharacteristic
174C22×C283C2×#4111yescharacteristic
175C22×C283H(5,𝔽2)11yescharacteristic
176C22×C2832−1+411yescharacteristic
177C2×D283—22no—
178C2×D283—22no—
179C2×D283—22no—
180C2×D283—41no—
181C2×D283—41no—
182C2×D283—41no—
183C2×D283—41no—
184C4×C283—22no—
185C4×C283—22no—
186C4×C283—22no—
187C4×C283—41no—
188C4×C283—41no—
189C4×C283—41no—
190Dic283—22no—
191Dic283—22no—
192Dic283—22no—
193Dic283—22no—
194Dic283—22no—
195Dic283—22no—
196Dic283—41no—
197C2×C283—24no—
198C2×C283C2×C4×D411yescharacteristic
199C2×C283C4×#4111yescharacteristic
200C2×C283#52011yescharacteristic
201C2×C283#54611yescharacteristic
202C2×C283#54711yescharacteristic
203C2×C283#55111yescharacteristic
204C2×C283#55211yescharacteristic
205D283—42no—
206C283#235911yescharacteristic, complemented, Sylow
207#2359—2831nomaximal, Sylow
208C2×#123—2831no—
209C2×C4×D4—2831no—
210C2×#117—2831no—
211#389—2831no—
212#388—2831no—
213#388—2831no—
214#387—2831no—
215#387—2831no—
216#386—2831no—
217#385—2831no—
218#385D28311yescharacteristic, complemented
219C4×C4⋊C4—2831no—
220C4×C22⋊C4—2831no—
221C4×C22⋊C4—2831no—
222C2×#95—2831no—
223C22×D4—2831no—
224C23×C4—2831no—
225C23×C4—2831no—
226C23×C4—2831no—
227C23×C4C2×D28311yescharacteristic
228#123—2838no—
229C4×D4—5664no—
230#117—5664no—
231C2×C4⋊C4—2831no—
232C2×C4⋊C4—2831no—
233C2×C4⋊C4—2831no—
234C2×C4⋊C4—2831no—
235C2×C4⋊C4—2831no—
236C2×C4⋊C4C2×D28311yescharacteristic
237C2×C4⋊C4C2×D28311yescharacteristic
238C2×C22⋊C4—2831no—
239C2×C22⋊C4—2831no—
240C2×C22⋊C4—2831no—
241C2×C22⋊C4—2831no—
242C2×C22⋊C4—2831no—
243C2×C22⋊C4—2831no—
244C2×C22⋊C4C2×D28311yescharacteristic
245C2×C22⋊C4C2×D28311yescharacteristic
246C2×C42—2831no—
247C2×C42—2831no—
248C2×C42—2831no—
249C2×C42—2831no—
250C2×C42—2831no—
251#95—2831no—
252#95—2831no—
253#95—2831no—
254#95—2831no—
255#95—2831no—
256#95—2831no—
257#95—2831no—
258#95—2831no—
259#95C2×D28311yescharacteristic
260#95C2×D28311yescharacteristic
261C24—2831no—
262C24C22×D28311yescharacteristic
263C2×D4—2834no—
264C2×D4—5662no—
265C2×D4—5662no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—41no—
269C22×C4—2834no—
270C22×C4—2831no—
271C22×C4—2831no—
272C22×C4—2831no—
273C22×C4—2831no—
274C22×C4—2831no—
275C22×C4—2831no—
276C22×C4—2831no—
277C22×C4—5662no—
278C22×C4—5662no—
279C22×C4—5662no—
280C22×C4—5662no—
281C22×C4—5662no—
282C22×C4—5662no—
283C22×C4—11321no—
284C22×C4—11321no—
285C22×C4C22×D28311yescharacteristic
286C22×C4C22×D28311yescharacteristic
287C22×C4C22×D28311yescharacteristic
288C22×C4C22×D28311yescharacteristic
289C22×C4C22×D28311yescharacteristic
290C22×C4C22×D28311yescharacteristic
291C4⋊C4—22no—
292C4⋊C4—41no—
293C4⋊C4—2834no—
294C4⋊C4—2834no—
295C4⋊C4—5662no—
296C4⋊C4—5662no—
297C4⋊C4—5662no—
298C22⋊C4—22no—
299C22⋊C4—2834no—
300C22⋊C4—2834no—
301C22⋊C4—2834no—
302C22⋊C4—5662no—
303C22⋊C4—5662no—
304C22⋊C4—11321no—
305C22⋊C4C4×D28314yescomplemented
306C42—5662no—
307C42—5662no—
308C42—5662no—
309C42—5662no—
310C42—11321no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—2832no—
316C23—5661no—
317C23—5661no—
318C23—5661no—
319C23—5661no—
320C23—5661no—
321C23—5661no—
322C23C2×C4×D28312yes—
323C23D4×D28312yes—
324C23#1798539312yes—
325C23C23×D28311yescharacteristic
326D4—5668no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—44no—
343C2×C4—2832no—
344C2×C4—2832no—
345C2×C4—2832no—
346C2×C4—2832no—
347C2×C4—2832no—
348C2×C4—2832no—
349C2×C4—5668no—
350C2×C4—5661no—
351C2×C4—5661no—
352C2×C4—5661no—
353C2×C4—5661no—
354C2×C4—5661no—
355C2×C4—5661no—
356C2×C4—5661no—
357C2×C4—5661no—
358C2×C4—5661no—
359C2×C4—5661no—
360C2×C4—5661no—
361C2×C4—5661no—
362C2×C4—5661no—
363C2×C4—5661no—
364C2×C4—5661no—
365C2×C4—11324no—
366C2×C4—11324no—
367C2×C4C2×C4×D28312yes—
368C2×C4C2×C4×D28312yes—
369C2×C4#1798539112yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—5662no—
377C22—5662no—
378C22—5662no—
379C22—11321no—
380C22—11321no—
381C22—11321no—
382C22—11321no—
383C22#2258357214yes—
384C22C22×C4×D28311yescharacteristic
385C22C2×D4×D28311yescharacteristic
386C22#41×D28311yescharacteristic
387C22C2×#1798539111yescharacteristic
388C22C2×#1798539311yescharacteristic
389C22#2258365511yescharacteristic
390C22#2258365711yescharacteristic
391C4—22no—
392C4—22no—
393C4—22no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—5662no—
398C4—5662no—
399C4—5662no—
400C4—5662no—
401C4—5662no—
402C4—5662no—
403C4—11321no—
404C2—24no—
405C2—11322no—
406C2C2×#2258357211yescharacteristic
407C2C4×#1798539111yescharacteristic
408C2#3182694411yescharacteristic
409C2#3182710211yescharacteristic
410C2#3182711311yescharacteristic
411C2#3182714211yescharacteristic
412C2#3182715711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
Fitting#385×C283C2
socle, cosocleC23×C283C24
prime radicalC22×C22⋊D283C22
hypercenter#385D283
hypocenterC283#2359
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
3. C2×#22583566C2semidirect
4. #31826361C2semidirect
5. #31826355C2semidirect
6. #31826354C2semidirect
7. #31826348C2semidirect
8. #31826348C2semidirect
10. #31826336C2semidirect
11. C4⋊C4×Dic283C2semidirect
12. C22⋊C4×Dic283C2semidirect
13. #31826312C2semidirect
14. C2×C283⋊#95C2semidirect
15. #385×C283C2semidirect
20. #22583594C4semidirect
63. C22×Dic283C2×C4semidirect
74. C4⋊Dic283C2×C4semidirect
75. C4⋊Dic283C2×C4semidirect
83. (C2×D283)⋊C4C2×C4semidirect
84. (C2×D283)⋊C4C2×C4semidirect
103. C22⋊C4×C283C2×C4semidirect
206. C283#2359semidirect
218. #385D283semidirect
305. C22⋊C4C4×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225835942
C2×C4×C22⋊D2832
C2×#225835662
#318263612
#318263552
#318263542
#318263482
#318263422
#318263362
C4⋊C4×Dic2832
C22⋊C4×Dic2832
#318263122
C2×C283⋊#952
#385×C2832
#2359283