Finite Group Databasebeta

← #49131521

Subgroups — #49131521

Order 36224.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827080C211yesmaximal, characteristic, complemented
2#31826947C211yesmaximal, characteristic, complemented
3#31826802C211yesmaximal, characteristic, complemented
4#31826777C211yesmaximal, characteristic, complemented
5#31826758C211yesmaximal, characteristic, complemented
6#31826744C211yesmaximal, characteristic, complemented
7#31826685C211yesmaximal, characteristic, complemented
8#31826679C211yesmaximal, characteristic, complemented
9#31826630C211yesmaximal, characteristic, complemented
10#31826609C211yesmaximal, characteristic
11#31826567C211yesmaximal, characteristic, complemented
12C4×#17985382C211yesmaximal, characteristic, complemented
13C4×#17985377C211yesmaximal, characteristic, complemented
14#31826527C211yesmaximal, characteristic, complemented
15#440×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×#17985382C2211yescharacteristic
18C2×#17985381C2211yescharacteristic
19C2×#17985377C2211yescharacteristic
20#22583609C2211yescharacteristic
21#22583603—21no—
22#22583597C2211yescharacteristic
23#22583596—21no—
24#22583593—21no—
25#22583590C2211yescharacteristic
26#22583589—21no—
27#22583581C2211yescharacteristic
28Q8×Dic283C2211yescharacteristic
29C4×Dic566C2211yescharacteristic
30C4×D1132—21no—
31C4×D1132C2211yescharacteristic
32#22583572—21no—
33#22583572C2211yescharacteristic
34#22583567—21no—
35#22583567C2211yescharacteristic
36C4⋊C4×D283—21no—
37C4⋊C4×D283C2211yescharacteristic
38#22583544C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583543C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583534C2211yescharacteristic
45#22583533C2211yescharacteristic
46#22583532C2211yescharacteristic
47#22583531C2211yescharacteristic
48#22583530C2211yescharacteristic
49(C2×D283)⋊C8C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51C4×C283⋊C8C2211yescharacteristic
52C2×SD16×C283C2211yescharacteristic
53C4×Q8×C283C2211yescharacteristic
54C4×D4×C283C2211yescharacteristic
55#107×C283C2211yescharacteristic
56#103×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58#97×C283C2211yescharacteristic
59#17985393—22no—
60#17985393—22no—
61C2×Dic566—21no—
62C2×Dic566C2311yescharacteristic
63C2×D1132—21no—
64C2×D1132C2311yescharacteristic
65C2×C22⋊D283—21no—
66C2×C4×D283—21no—
67C2×C4×D283—21no—
68C2×C4×D283—21no—
69C2×C4×D283—21no—
70C2×C4×D283C2311yescharacteristic
71#17985382—22no—
72#17985381—22no—
73#17985377—22no—
74C2×C283⋊C8C2311yescharacteristic
75C2×C283⋊C8C2311yescharacteristic
76C4⋊Dic283—21no—
77C4⋊Dic283—21no—
78C4⋊Dic283C2311yescharacteristic
79C4⋊Dic283C2311yescharacteristic
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4D411yescharacteristic
84Dic283⋊C4D411yescharacteristic
85C22⋊Dic283—21no—
86C22⋊Dic283—21no—
87C22⋊Dic283—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4D411yescharacteristic
92(C2×D283)⋊C4D411yescharacteristic
93C4×Dic283—21no—
94C4×Dic283—21no—
95C4×Dic283C2311yescharacteristic
96C2×Q8×C283C2311yescharacteristic
97C2×D4×C283C2311yescharacteristic
98C22×C4×C283—21no—
99SD16×C283—22no—
100C2×C8×C283C2311yescharacteristic
101C2×C8×C283C2311yescharacteristic
102C4⋊C4×C283—21no—
103C4⋊C4×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C22⋊C4×C283—21no—
106C42×C283—21no—
107C42×C283C2311yescharacteristic
108C22×D283—21no—
109C22×D283C2×D411yescharacteristic
110Dic566—21no—
111Dic566—21no—
112Dic566—81no—
113D1132—24no—
114D1132—21no—
115D1132#4112yes—
116C22⋊D283—81no—
117C2×Dic283—21no—
118C2×Dic283—21no—
119C2×Dic283—21no—
120C2×Dic283C2×D411yescharacteristic
121C2×Dic283C2×D411yescharacteristic
122C2×Dic283C2×D411yescharacteristic
123C4×D283—24no—
124C4×D283—21no—
125C4×D283—21no—
126C4×D283—81no—
127C4×D283—81no—
128C4×D283—81no—
129C283⋊C8—21no—
130C283⋊C8—21no—
131C23×C283—21no—
132Q8×C283—21no—
133Q8×C283#4112yes—
134D4×C283—21no—
135D4×C283—21no—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283—81no—
140C2×C4×C283C2×D411yescharacteristic
141C2×C4×C283C2×D411yescharacteristic
142C2×C4×C283C2411yescharacteristic
143C8×C283—21no—
144C8×C283—21no—
145C22×C283—41no—
146C22×C283—41no—
147C22×C283—41no—
148C22×C283C22×D411yescharacteristic
149C2×D283—21no—
150C2×D283—22no—
151C2×D283—21no—
152C2×D283—21no—
153C2×D283—41no—
154C2×D283—41no—
155C4×C283—22no—
156C4×C283—21no—
157C4×C283—21no—
158C4×C283—41no—
159C4×C283—41no—
160C4×C283C2×#4111yescharacteristic
161C4×C283C2×#4111yescharacteristic
162Dic283—21no—
163Dic283—21no—
164Dic283—21no—
165Dic283—41no—
166Dic283—41no—
167Dic283—41no—
168C2×C283—81no—
169C2×C283#52511yescharacteristic
170C2×C283#57611yescharacteristic
171C2×C283#57811yescharacteristic
172D283—41no—
173D283—42no—
174C283#312411yescharacteristic, complemented, Sylow
175#3124—2831nomaximal, Sylow
176#542—2831no—
177#520—2831no—
178#484—2831no—
179#480—2831no—
180#477—2831no—
181#474—2831no—
182#464—2831no—
183#463—2831no—
184#452—2831no—
185#449—2831no—
186#440—2831no—
187#440D28311yescharacteristic, complemented
188C4×Q16—2831no—
189C4×D8—2831no—
190#433—2831no—
191C2×#41—2831no—
192C2×Q16—2831no—
193C2×SD16—2831no—
194C2×SD16C2×D28311yescharacteristic
195C2×D8—2831no—
196C4⋊Q8—2831no—
197#126—5661no—
198#124—2831no—
199#124—5661no—
200#123—5661no—
201C22⋊Q8—2831no—
202C22⋊Q8—5661no—
203#121—2831no—
204C4×Q8—2831no—
205C4×Q8—2831no—
206C4×Q8C2×D28311yescharacteristic
207C4×D4—2831no—
208C4×D4—2831no—
209C4×D4—5661no—
210C4×D4—5661no—
211C4×D4C2×D28311yescharacteristic
212#117—2831no—
213#117—5661no—
214C2×C4⋊C4—2831no—
215C2×C4⋊C4—5661no—
216#107—2831no—
217#107—2831no—
218#107—2831no—
219#107C2×D28311yescharacteristic
220C4⋊C8—2831no—
221C4⋊C8—2831no—
222#103—2831no—
223#103—2831no—
224#103—2831no—
225#103C2×D28311yescharacteristic
226#102—2831no—
227#102—2831no—
228#102—2831no—
229#102C2×D28311yescharacteristic
230C22⋊C8—2831no—
231C22⋊C8—2831no—
232#97C2×D28311yescharacteristic
233C4×C8—2831no—
234#41—5662no—
235#41—5662no—
236C2×Q8—2831no—
237C2×Q8—5661no—
238C2×Q8C22×D28311yescharacteristic
239C2×D4—2831no—
240C2×D4—5661no—
241C2×D4—5661no—
242C2×D4C22×D28311yescharacteristic
243C22×C4—21no—
244C22×C4—2831no—
245C22×C4—5661no—
246C22×C4—5661no—
247C22×C4—5661no—
248C22×C4—5661no—
249Q16—5662no—
250SD16—22no—
251SD16—5662no—
252D8—5662no—
253C2×C8—2831no—
254C2×C8—2831no—
255C2×C8C22×D28311yescharacteristic
256C2×C8C22×D28311yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—2831no—
259C4⋊C4—2831no—
260C4⋊C4—2831no—
261C4⋊C4—2831no—
262C4⋊C4—5661no—
263C4⋊C4—5661no—
264C4⋊C4—5661no—
265C4⋊C4—5661no—
266C4⋊C4—5661no—
267C4⋊C4C22×D28311yescharacteristic
268C4⋊C4C22×D28311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—2831no—
271C22⋊C4—2831no—
272C22⋊C4—5661no—
273C22⋊C4—5661no—
274C22⋊C4—5661no—
275C22⋊C4—5661no—
276C22⋊C4—5661no—
277C22⋊C4—5661no—
278C42—21no—
279C42—2831no—
280C42—5661no—
281C42—5661no—
282C42C22×D28311yescharacteristic
283C23—21no—
284C23—2831no—
285C23—5661no—
286Q8—21no—
287Q8—5661no—
288Q8—5661no—
289Q8—22641no—
290Q8#1798539212yes—
291D4—21no—
292D4—21no—
293D4—2832no—
294D4—5664no—
295D4—5661no—
296D4—22641no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—81no—
301C2×C4—2831no—
302C2×C4—2831no—
303C2×C4—2831no—
304C2×C4—5664no—
305C2×C4—5661no—
306C2×C4—5661no—
307C2×C4—5661no—
308C2×C4—5661no—
309C2×C4—5661no—
310C2×C4—22641no—
311C2×C4—22641no—
312C2×C4—22641no—
313C2×C4D4×D28311yescharacteristic
314C2×C4D4×D28311yescharacteristic
315C2×C4C23×D28311yescharacteristic
316C8—21no—
317C8—21no—
318C8—5661no—
319C8—5661no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—5662no—
324C22—5661no—
325C22—5661no—
326C22—5661no—
327C22—11321no—
328C22—11321no—
329C22C2×D4×D28311yescharacteristic
330C4—22no—
331C4—21no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—5661no—
336C4—5661no—
337C4—5661no—
338C4—11321no—
339C4—11321no—
340C4—11321no—
341C4#41×D28311yescharacteristic
342C4C2×#1798539211yescharacteristic
343C2—81no—
344C2—11321no—
345C2—11322no—
346C2#3182697411yescharacteristic
347C2#3182726911yescharacteristic
348C2#3182728111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#440×C283C2
socleC22×C283C22×D4
prime radical#31826609C2
hypercenter#440D283
hypocenterC283#3124
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #31827080C2semidirect
2. #31826947C2semidirect
3. #31826802C2semidirect
4. #31826777C2semidirect
5. #31826758C2semidirect
6. #31826744C2semidirect
7. #31826685C2semidirect
8. #31826679C2semidirect
9. #31826630C2semidirect
11. #31826567C2semidirect
12. C4×#17985382C2semidirect
13. C4×#17985377C2semidirect
14. #31826527C2semidirect
15. #440×C283C2semidirect
174. C283#3124semidirect
187. #440D283semidirect

Maximal subgroups

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

subgroupindex
#318270802
#318269472
#318268022
#318267772
#318267582
#318267442
#318266852
#318266792
#318266302
#318266092
#318265672
C4×#179853822
C4×#179853772
#318265272
#440×C2832
#3124283