Finite Group Databasebeta

← #49123721

Subgroups — #49123721

Order 36224.

652 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×(C22⋊D283)⋊C4C211yesmaximal, characteristic
2C2×#22583568C211yesmaximal, characteristic, complemented
3C2×#22583566C211yesmaximal, characteristic, complemented
4#31826365C211yesmaximal, characteristic
5#31826365C211yesmaximal, characteristic
6#31826362C211yesmaximal, characteristic, complemented
7#31826360C211yesmaximal, characteristic, complemented
8#31826358C211yesmaximal, characteristic, complemented
9#31826356C211yesmaximal, characteristic, complemented
10#31826354C211yesmaximal, characteristic, complemented
11#31826316C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic283C211yesmaximal, characteristic, complemented
13#31826312C211yesmaximal, characteristic, complemented
14C42×Dic283C211yesmaximal, characteristic, complemented
15#388×C283C211yesmaximal, characteristic, complemented
16C22×C22⋊D283C2211yescharacteristic
17C23×Dic283C2211yescharacteristic
18C22×C4×D283C2211yescharacteristic
19(C22⋊D283)⋊C4C418yescomplemented
20#22583568—24no—
21#22583566—24no—
22C2×C4⋊Dic283C2211yescharacteristic
23C2×Dic283⋊C4C2211yescharacteristic
24C2×Dic283⋊C4C2211yescharacteristic
25C2×Dic283⋊C4C2211yescharacteristic
26C2×Dic283⋊C4C2211yescharacteristic
27C2×Dic283⋊C4C2211yescharacteristic
28C2×C22⋊Dic283C2211yescharacteristic
29C2×C22⋊Dic283C2211yescharacteristic
30C2×(C2×D283)⋊C4C2211yescharacteristic
31C2×(C2×D283)⋊C4C2211yescharacteristic
32C2×(C2×D283)⋊C4C2211yescharacteristic
33C2×(C2×D283)⋊C4C2211yescharacteristic
34C2×(C2×D283)⋊C4C2211yescharacteristic
35C2×C4×Dic283C2211yescharacteristic
36C2×C4×Dic283C2211yescharacteristic
37C2×C4×Dic283C2211yescharacteristic
38C2×C4×Dic283C2211yescharacteristic
39C2×C4×Dic283C2211yescharacteristic
40C2×C4×Dic283C2211yescharacteristic
41C2×C4×Dic283C2211yescharacteristic
42C2×C4×Dic283C2211yescharacteristic
43C283⋊#95C2211yescharacteristic
44C283⋊#95C2211yescharacteristic
45C283⋊#95C2211yescharacteristic
46C283⋊#95C2211yescharacteristic
47C2×C4⋊C4×C283C2211yescharacteristic
48C2×C22⋊C4×C283C2211yescharacteristic
49C2×C22⋊C4×C283C2211yescharacteristic
50C2×C22⋊C4×C283C2211yescharacteristic
51C2×C42×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×Dic283C2×C414yes—
61C22×Dic283C2311yescharacteristic
62C22×Dic283C2311yescharacteristic
63C22×Dic283C2311yescharacteristic
64C22×Dic283C2311yescharacteristic
65C22×Dic283C2311yescharacteristic
66C22×Dic283C2311yescharacteristic
67C22×Dic283C2311yescharacteristic
68C2×C4×D283—22no—
69C2×C4×D283—22no—
70C2×C4×D283C2×C414yes—
71C4⋊Dic283—22no—
72Dic283⋊C4—22no—
73Dic283⋊C4—22no—
74Dic283⋊C4—22no—
75Dic283⋊C4—22no—
76Dic283⋊C4C2×C414yes—
77C22⋊Dic283—22no—
78C22⋊Dic283—22no—
79(C2×D283)⋊C4—22no—
80(C2×D283)⋊C4—22no—
81(C2×D283)⋊C4—22no—
82(C2×D283)⋊C4—22no—
83(C2×D283)⋊C4C2×C414yes—
84C4×Dic283—22no—
85C4×Dic283—22no—
86C4×Dic283—22no—
87C4×Dic283—22no—
88C4×Dic283—22no—
89C4×Dic283—22no—
90C4×Dic283C2×C414yes—
91C4×Dic283D414yescomplemented
92C24×C283C2311yescharacteristic
93C22×C4×C283C2311yescharacteristic
94C22×C4×C283C2311yescharacteristic
95C22×C4×C283C2311yescharacteristic
96C22×C4×C283C2311yescharacteristic
97C22×C4×C283C2311yescharacteristic
98C22×C4×C283C2311yescharacteristic
99C4⋊C4×C283—22no—
100C22⋊C4×C283—22no—
101C22⋊C4×C283—22no—
102C22⋊C4×C283C2×C414yes—
103C42×C283—22no—
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—21no—
113C2×Dic283—21no—
114C2×Dic283—21no—
115C2×Dic283—21no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C2×Dic283—28no—
119C2×Dic283—21no—
120C2×Dic283—21no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283—21no—
124C2×Dic283—21no—
125C2×Dic283C22×C412yes—
126C2×Dic283C22×C412yes—
127C2×Dic283C22×C412yes—
128C2×Dic283C2×D412yes—
129C2×Dic283C2×D412yes—
130C2×Dic283#4112yes—
131C2×Dic283#4112yes—
132C2×Dic283#4112yes—
133C2×Dic283#4112yes—
134C4×D283—28no—
135C23×C283—21no—
136C23×C283—21no—
137C23×C283—21no—
138C23×C283—21no—
139C23×C283—21no—
140C23×C283—21no—
141C23×C283C22×C412yes—
142C23×C283C2411yescharacteristic
143C2×C4×C283—21no—
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×C283C22×C412yes—
158C2×C4×C283C22×C412yes—
159C2×C4×C283C2×D412yes—
160C2×C4×C283#4112yes—
161C22×C283—22no—
162C22×C283—22no—
163C22×C283—22no—
164C22×C283—41no—
165C22×C283—41no—
166C22×C283—41no—
167C22×C283—41no—
168C22×C283C23×C411yescharacteristic
169C22×C283C22×D411yescharacteristic
170C22×C283C2×#4111yescharacteristic
171C22×C283C2×#4111yescharacteristic
172C22×C283C2×#4111yescharacteristic
173C22×C283C2×#4111yescharacteristic
174C22×C283C2×#4111yescharacteristic
175C2×D283—22no—
176C2×D283—22no—
177C2×D283—22no—
178C2×D283—41no—
179C2×D283—41no—
180C2×D283—41no—
181C2×D283—41no—
182C4×C283—22no—
183C4×C283—22no—
184C4×C283—22no—
185C4×C283—22no—
186C4×C283—41no—
187C4×C283—41no—
188Dic283—22no—
189Dic283—22no—
190Dic283—22no—
191Dic283—41no—
192Dic283—41no—
193Dic283#11714yescomplemented
194Dic283C4×D414yes—
195C2×C283—42no—
196C2×C283C2×#11711yescharacteristic
197C2×C283C2×C4×D411yescharacteristic
198C2×C283C4×#4111yescharacteristic
199C2×C283#52911yescharacteristic
200C2×C283#52911yescharacteristic
201C2×C283#53211yescharacteristic
202C2×C283#53211yescharacteristic
203D283—42no—
204C283#229311yescharacteristic, complemented, Sylow
205#2293—2831nomaximal, Sylow
206C2×C4×D4—2831no—
207C2×#117—2831no—
208C2×#117—2831no—
209#390—2831no—
210#390—2831no—
211#389—2831no—
212#389—2831no—
213#388—2831no—
214#388—2831no—
215#388—2831no—
216#388D28311yescharacteristic, complemented
217C4×C4⋊C4—2831no—
218C4×C22⋊C4—2831no—
219C4×C22⋊C4—2831no—
220C43—2831no—
221C22×D4—2831no—
222C23×C4—2831no—
223C23×C4—2831no—
224C4×D4—2838no—
225#117—5664no—
226#117—5664no—
227C2×C4⋊C4—2831no—
228C2×C4⋊C4—2831no—
229C2×C4⋊C4—2831no—
230C2×C4⋊C4—2831no—
231C2×C4⋊C4—2831no—
232C2×C4⋊C4—2831no—
233C2×C4⋊C4C2×D28311yescharacteristic
234C2×C22⋊C4—2831no—
235C2×C22⋊C4—2831no—
236C2×C22⋊C4—2831no—
237C2×C22⋊C4—2831no—
238C2×C22⋊C4—2831no—
239C2×C22⋊C4—2831no—
240C2×C22⋊C4—2831no—
241C2×C22⋊C4C2×D28311yescharacteristic
242C2×C22⋊C4C2×D28311yescharacteristic
243C2×C22⋊C4C2×D28311yescharacteristic
244C2×C42—2831no—
245C2×C42—2831no—
246C2×C42—2831no—
247C2×C42—2831no—
248C2×C42—2831no—
249C2×C42—2831no—
250C2×C42—2831no—
251C2×C42—2831no—
252C2×C42C2×D28311yescharacteristic
253#95—2831no—
254#95—2831no—
255#95—2831no—
256#95—2831no—
257#95C2×D28311yescharacteristic
258#95C2×D28311yescharacteristic
259C24—2831no—
260C24C22×D28311yescharacteristic
261C2×D4—2834no—
262C2×D4—5662no—
263C2×D4—5662no—
264C22×C4—2831no—
265C22×C4—2831no—
266C22×C4—2834no—
267C22×C4—2831no—
268C22×C4—2831no—
269C22×C4—2831no—
270C22×C4—2834no—
271C22×C4—2831no—
272C22×C4—2831no—
273C22×C4—5662no—
274C22×C4—5662no—
275C22×C4—5662no—
276C22×C4—5662no—
277C22×C4C22×D28311yescharacteristic
278C22×C4C22×D28311yescharacteristic
279C22×C4C22×D28311yescharacteristic
280C22×C4C22×D28311yescharacteristic
281C22×C4C22×D28311yescharacteristic
282C22×C4C22×D28311yescharacteristic
283C4⋊C4—22no—
284C4⋊C4—2834no—
285C4⋊C4—5662no—
286C4⋊C4—5662no—
287C4⋊C4—5662no—
288C4⋊C4—5662no—
289C4⋊C4—5662no—
290C22⋊C4—22no—
291C22⋊C4—22no—
292C22⋊C4—2834no—
293C22⋊C4—5662no—
294C22⋊C4—5662no—
295C22⋊C4—5662no—
296C22⋊C4—5662no—
297C22⋊C4—5662no—
298C22⋊C4—5662no—
299C22⋊C4C4×D28314yes—
300C42—22no—
301C42—2834no—
302C42—2834no—
303C42—5662no—
304C42—5662no—
305C42—5662no—
306C42—5662no—
307C42—5662no—
308C42—5662no—
309C23—21no—
310C23—21no—
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—
323C23C23×D28311yescharacteristic
324D4—5668no—
325C2×C4—21no—
326C2×C4—21no—
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—2832no—
340C2×C4—2832no—
341C2×C4—2832no—
342C2×C4—2832no—
343C2×C4—2832no—
344C2×C4—2832no—
345C2×C4—2832no—
346C2×C4—2832no—
347C2×C4—2832no—
348C2×C4—5668no—
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×C4C2×C4×D28312yes—
363C2×C4C2×C4×D28312yes—
364C2×C4D4×D28312yes—
365C2×C4#1798539112yes—
366C22—22no—
367C22—22no—
368C22—22no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—5662no—
374C22—5662no—
375C22—5662no—
376C22—11321no—
377C22—11321no—
378C22—11321no—
379C22—11321no—
380C22C22×C4×D28311yescharacteristic
381C22C2×D4×D28311yescharacteristic
382C22#41×D28311yescharacteristic
383C22#41×D28311yescharacteristic
384C22#41×D28311yescharacteristic
385C22#41×D28311yescharacteristic
386C22C2×#1798539111yescharacteristic
387C4—22no—
388C4—22no—
389C4—22no—
390C4—22no—
391C4—41no—
392C4—41no—
393C4—2834no—
394C4—2834no—
395C4—5662no—
396C4—5662no—
397C4—5662no—
398C4—11321no—
399C4—11321no—
400C2—42no—
401C2—11322no—
402C2#117×D28311yescharacteristic
403C2C4×D4×D28311yescharacteristic
404C2C4×#1798539111yescharacteristic
405C2#3182699211yescharacteristic
406C2#3182699811yescharacteristic
407C2#3182701011yescharacteristic
408C2#3182701411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
Fitting#388×C283C2
socle, cosocleC23×C283C24
prime radicalC22×C22⋊D283C22
hypercenter#388D283
hypocenterC283#2293
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×#22583568C2semidirect
3. C2×#22583566C2semidirect
6. #31826362C2semidirect
7. #31826360C2semidirect
8. #31826358C2semidirect
9. #31826356C2semidirect
10. #31826354C2semidirect
11. #31826316C2semidirect
12. C22⋊C4×Dic283C2semidirect
13. #31826312C2semidirect
14. C42×Dic283C2semidirect
15. #388×C283C2semidirect
19. (C22⋊D283)⋊C4C4semidirect
91. C4×Dic283D4semidirect
193. Dic283#117semidirect
204. C283#2293semidirect
216. #388D283semidirect

Maximal subgroups

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

subgroupindex
C2×(C22⋊D283)⋊C42
C2×#225835682
C2×#225835662
#318263652
#318263622
#318263602
#318263582
#318263562
#318263542
#318263162
C22⋊C4×Dic2832
#318263122
C42×Dic2832
#388×C2832
#2293283