Finite Group Databasebeta

← #49123793

Subgroups — #49123793

Order 36224.

656 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583587C211yesmaximal, characteristic
2C2×#22583575C211yesmaximal, characteristic, complemented
3C22×C4×Dic283C211yesmaximal, characteristic
4#31826369C211yesmaximal, characteristic, complemented
5#31826360C211yesmaximal, characteristic, complemented
6#31826350C211yesmaximal, characteristic, complemented
7#31826346C211yesmaximal, characteristic, complemented
8#31826338C211yesmaximal, characteristic
9#31826323C211yesmaximal, characteristic
10C4⋊C4×Dic283C211yesmaximal, characteristic, complemented
11#31826316C211yesmaximal, characteristic, complemented
12#31826316C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic283C211yesmaximal, characteristic
14C22⋊C4×Dic283C211yesmaximal, characteristic
15#385×C283C211yesmaximal, characteristic
16C22×Dic566C2211yescharacteristic
17C23×Dic283C2211yescharacteristic
18C23×Dic283C2211yescharacteristic
19#22583587C418yescomplemented
20#22583575—24no—
21C2×C4⋊Dic283C2211yescharacteristic
22C2×Dic283⋊C4C2211yescharacteristic
23C2×Dic283⋊C4C2211yescharacteristic
24C2×Dic283⋊C4C2211yescharacteristic
25C2×Dic283⋊C4C2211yescharacteristic
26C2×Dic283⋊C4C2211yescharacteristic
27C2×Dic283⋊C4C2211yescharacteristic
28C2×C22⋊Dic283C2211yescharacteristic
29C2×C22⋊Dic283C2211yescharacteristic
30C2×C4×Dic283—24no—
31C2×C4×Dic283C2211yescharacteristic
32C2×C4×Dic283C2211yescharacteristic
33C2×C4×Dic283C2211yescharacteristic
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
54C2×Dic566—22no—
55C2×Dic566—22no—
56C2×Dic566C2×C414yescomplemented
57C22×Dic283—22no—
58C22×Dic283—22no—
59C22×Dic283—22no—
60C22×Dic283—22no—
61C22×Dic283C2×C414yes—
62C22×Dic283Q814yescomplemented
63C22×Dic283C2311yescharacteristic
64C22×Dic283C2311yescharacteristic
65C22×Dic283C2311yescharacteristic
66C22×Dic283C2311yescharacteristic
67C22×Dic283C2311yescharacteristic
68C22×Dic283C2311yescharacteristic
69C22×Dic283C2311yescharacteristic
70C22×Dic283C2311yescharacteristic
71C4⋊Dic283C2×C414yescomplemented
72Dic283⋊C4—22no—
73Dic283⋊C4—22no—
74Dic283⋊C4—22no—
75Dic283⋊C4—22no—
76Dic283⋊C4C2×C414yescomplemented
77Dic283⋊C4C2×C414yescomplemented
78C22⋊Dic283—22no—
79C22⋊Dic283C2×C414yes—
80C4×Dic283—22no—
81C4×Dic283—22no—
82C4×Dic283—22no—
83C4×Dic283—22no—
84C4×Dic283—22no—
85C4×Dic283—22no—
86C4×Dic283—22no—
87C4×Dic283D414yes—
88C24×C283C2311yescharacteristic
89C22×C4×C283—22no—
90C22×C4×C283—22no—
91C22×C4×C283—22no—
92C22×C4×C283C2311yescharacteristic
93C22×C4×C283C2311yescharacteristic
94C22×C4×C283C2311yescharacteristic
95C22×C4×C283C2311yescharacteristic
96C22×C4×C283C2311yescharacteristic
97C22×C4×C283C2311yescharacteristic
98C4⋊C4×C283—22no—
99C4⋊C4×C283—22no—
100C22⋊C4×C283—22no—
101C22⋊C4×C283C2×C414yes—
102Dic566—28no—
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—28no—
112C2×Dic283—28no—
113C2×Dic283—21no—
114C2×Dic283—21no—
115C2×Dic283—21no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C2×Dic283—21no—
119C2×Dic283C22×C412yes—
120C2×Dic283C22×C412yes—
121C2×Dic283C22×C412yes—
122C2×Dic283C22×C412yes—
123C2×Dic283C2×D412yes—
124C2×Dic283C2×D412yes—
125C2×Dic283C2×Q812yes—
126C2×Dic283C2×Q812yes—
127C2×Dic283#4112yes—
128C2×Dic283#4112yes—
129C23×C283—21no—
130C23×C283—21no—
131C23×C283—21no—
132C23×C283—21no—
133C23×C283C22×C412yes—
134C23×C283C2×Q812yes—
135C23×C283#4112yes—
136C23×C283C2411yescharacteristic
137C2×C4×C283—28no—
138C2×C4×C283—21no—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283—21no—
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×C283C22×C412yes—
153C2×C4×C283C22×C412yes—
154C2×C4×C283C2×D412yes—
155C2×C4×C283#4112yes—
156C22×C283—22no—
157C22×C283—22no—
158C22×C283—22no—
159C22×C283—22no—
160C22×C283—22no—
161C22×C283—22no—
162C22×C283C4×Q814yescomplemented
163C22×C283C23×C411yescharacteristic
164C22×C283C22×D411yescharacteristic
165C22×C283C22×Q811yescharacteristic
166C22×C283C2×#4111yescharacteristic
167C22×C283C2×#4111yescharacteristic
168C22×C283C2×#4111yescharacteristic
169C22×C283C2×#4111yescharacteristic
170C4×C283—22no—
171C4×C283—22no—
172C4×C283—22no—
173C4×C283—22no—
174C4×C283—41no—
175C4×C283—41no—
176Dic283—22no—
177Dic283—22no—
178Dic283—22no—
179Dic283—22no—
180Dic283—41no—
181Dic283—41no—
182Dic283C4×D414yes—
183Dic283C22⋊Q814yescomplemented
184C2×C283—24no—
185C2×C283C2×C4×D411yescharacteristic
186C2×C283C2×C4×Q811yescharacteristic
187C2×C283C4×#4111yescharacteristic
188C2×C283C2×C22⋊Q811yescharacteristic
189C2×C283#52511yescharacteristic
190C2×C283#52911yescharacteristic
191C2×C283#53311yescharacteristic
192C283C4×C22⋊Q811yescharacteristic, complemented, Sylow
193C4×C22⋊Q8—2831nomaximal, Sylow
194C2×C22⋊Q8—2831no—
195C2×C4×Q8—2831no—
196C22×C42—2831no—
197#391—2831no—
198#389—2831no—
199#387—2831no—
200#387—2831no—
201#385—2831no—
202#385D28311yescharacteristic
203#380—2831no—
204C4×C4⋊C4—2831no—
205C4×C4⋊C4—2831no—
206C4×C4⋊C4—2831no—
207C4×C22⋊C4—2831no—
208C4×C22⋊C4—2831no—
209C22×Q8—2831no—
210C23×C4—2831no—
211C23×C4—2831no—
212C23×C4C2×D28311yescharacteristic
213C22⋊Q8—2838no—
214C4×Q8—5664no—
215C2×C4⋊C4—2831no—
216C2×C4⋊C4—2831no—
217C2×C4⋊C4—2831no—
218C2×C4⋊C4—2831no—
219C2×C4⋊C4—2831no—
220C2×C4⋊C4—2831no—
221C2×C4⋊C4—2831no—
222C2×C4⋊C4C2×D28311yescharacteristic
223C2×C4⋊C4C2×D28311yescharacteristic
224C2×C22⋊C4—2831no—
225C2×C22⋊C4—2831no—
226C2×C22⋊C4C2×D28311yescharacteristic
227C2×C22⋊C4C2×D28311yescharacteristic
228C2×C42—2831no—
229C2×C42—2831no—
230C2×C42—2831no—
231C2×C42—2831no—
232C2×C42—2831no—
233C2×C42—2831no—
234C2×C42—2831no—
235C2×C42—2831no—
236C2×C42—5664no—
237#95—2831no—
238#95—2831no—
239#95—2831no—
240#95—2831no—
241#95—2831no—
242#95—2831no—
243#95—2831no—
244#95—2831no—
245#95C2×D28311yescharacteristic
246#95C2×D28311yescharacteristic
247C24C22×D28311yescharacteristic
248C2×Q8—2834no—
249C2×Q8—5662no—
250C2×Q8—5662no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—2831no—
255C22×C4—2831no—
256C22×C4—2834no—
257C22×C4—2834no—
258C22×C4—2831no—
259C22×C4—2831no—
260C22×C4—2831no—
261C22×C4—2831no—
262C22×C4—2831no—
263C22×C4—2831no—
264C22×C4—5662no—
265C22×C4—5662no—
266C22×C4—5662no—
267C22×C4—5662no—
268C22×C4C22×D28311yescharacteristic
269C22×C4C22×D28311yescharacteristic
270C22×C4C22×D28311yescharacteristic
271C22×C4C22×D28311yescharacteristic
272C22×C4C22×D28311yescharacteristic
273C22×C4C22×D28311yescharacteristic
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—2834no—
277C4⋊C4—2834no—
278C4⋊C4—2834no—
279C4⋊C4—5662no—
280C4⋊C4—5662no—
281C4⋊C4—5662no—
282C4⋊C4—5662no—
283C22⋊C4—22no—
284C22⋊C4—2834no—
285C22⋊C4—5662no—
286C22⋊C4C4×D28314yes—
287C42—2834no—
288C42—5662no—
289C42—5662no—
290C42—5662no—
291C42—5662no—
292C42—5662no—
293C42—5662no—
294C42—5662no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23C2×C4×D28312yes—
300C23Q8×D28312yes—
301C23#1798539112yes—
302C23C23×D28311yescharacteristic
303Q8—5668no—
304C2×C4—28no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—2832no—
320C2×C4—2832no—
321C2×C4—2832no—
322C2×C4—2832no—
323C2×C4—2832no—
324C2×C4—2832no—
325C2×C4—2832no—
326C2×C4—2832no—
327C2×C4—2832no—
328C2×C4—2832no—
329C2×C4—5668no—
330C2×C4—5668no—
331C2×C4—5661no—
332C2×C4—5661no—
333C2×C4—5661no—
334C2×C4—5661no—
335C2×C4—5661no—
336C2×C4—5661no—
337C2×C4—5661no—
338C2×C4—5661no—
339C2×C4—5661no—
340C2×C4—5661no—
341C2×C4—5661no—
342C2×C4—5661no—
343C2×C4—5661no—
344C2×C4—5661no—
345C2×C4C2×C4×D28312yes—
346C2×C4C2×C4×D28312yes—
347C2×C4D4×D28312yes—
348C2×C4#1798539112yes—
349C22—22no—
350C22—22no—
351C22—22no—
352C22—22no—
353C22—22no—
354C22—22no—
355C22#2258357514yescomplemented
356C22C22×C4×D28311yescharacteristic
357C22C2×D4×D28311yescharacteristic
358C22C2×Q8×D28311yescharacteristic
359C22#41×D28311yescharacteristic
360C22#41×D28311yescharacteristic
361C22C2×#1798539111yescharacteristic
362C22C2×#1798539111yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—22no—
367C4—41no—
368C4—41no—
369C4—2834no—
370C4—2834no—
371C4—5662no—
372C4—5662no—
373C4—5662no—
374C4—5662no—
375C4—11321no—
376C4—11321no—
377C2—24no—
378C2C4×D4×D28311yescharacteristic
379C2C2×#2258357511yescharacteristic
380C2C4×#1798539111yescharacteristic
381C2C22⋊Q8×D28311yescharacteristic
382C2#3182697111yescharacteristic
383C2#3182699211yescharacteristic
384C2#3182701711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
Fitting#385×C283C2
socle, cosocleC23×C283C24
prime radicalC24×C283C23
hypercenter#385D283
hypocenterC283C4×C22⋊Q8
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#22583575C2semidirect
4. #31826369C2semidirect
5. #31826360C2semidirect
6. #31826350C2semidirect
7. #31826346C2semidirect
10. C4⋊C4×Dic283C2semidirect
11. #31826316C2semidirect
12. #31826316C2semidirect
19. #22583587C4semidirect
56. C2×Dic566C2×C4semidirect
62. C22×Dic283Q8semidirect
71. C4⋊Dic283C2×C4semidirect
76. Dic283⋊C4C2×C4semidirect
77. Dic283⋊C4C2×C4semidirect
162. C22×C283C4×Q8semidirect
183. Dic283C22⋊Q8semidirect
192. C283C4×C22⋊Q8semidirect
355. C22#22583575semidirect

Maximal subgroups

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

subgroupindex
C2×#225835872
C2×#225835752
C22×C4×Dic2832
#318263692
#318263602
#318263502
#318263462
#318263382
#318263232
C4⋊C4×Dic2832
#318263162
C22⋊C4×Dic2832
#385×C2832
C4×C22⋊Q8283