Finite Group Databasebeta

← #49131517

Subgroups — #49131517

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#31826945C211yesmaximal, characteristic, complemented
2#31826798C211yesmaximal, characteristic, complemented
3#31826776C211yesmaximal, characteristic, complemented
4#31826757C211yesmaximal, characteristic, complemented
5#31826742C211yesmaximal, characteristic, complemented
6#31826684C211yesmaximal, characteristic, complemented
7#31826677C211yesmaximal, characteristic, complemented
8#31826625C211yesmaximal, characteristic, complemented
9#31826608C211yesmaximal, characteristic
10#31826565C211yesmaximal, characteristic, complemented
11#31826563C211yesmaximal, characteristic, complemented
12C4×#17985382C211yesmaximal, characteristic, complemented
13C4×#17985377C211yesmaximal, characteristic, complemented
14#31826526C211yesmaximal, characteristic, complemented
15#542×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C2×#17985382C2211yescharacteristic
18C2×#17985380C2211yescharacteristic
19C2×#17985379C2211yescharacteristic
20C2×#17985377C2211yescharacteristic
21C4×Dic566C2211yescharacteristic
22C4×Dic566C2211yescharacteristic
23C4×D1132C2211yescharacteristic
24C4×D1132C2211yescharacteristic
25(C22⋊D283)⋊C4—21no—
26(C22⋊D283)⋊C4—21no—
27#22583568—21no—
28C2×C4⋊Dic283C2211yescharacteristic
29C4⋊C4×D283—21no—
30#22583543C2211yescharacteristic
31#22583543C2211yescharacteristic
32#22583543C2211yescharacteristic
33#22583543C2211yescharacteristic
34C4⋊(C283⋊C8)C2211yescharacteristic
35C4⋊(C283⋊C8)C2211yescharacteristic
36#22583534C2211yescharacteristic
37#22583534C2211yescharacteristic
38#22583533C2211yescharacteristic
39#22583533C2211yescharacteristic
40#22583531C2211yescharacteristic
41#22583531C2211yescharacteristic
42#22583530C2211yescharacteristic
43#22583530C2211yescharacteristic
44C22⋊(C283⋊C8)C2211yescharacteristic
45C22⋊(C283⋊C8)C2211yescharacteristic
46#22583521C2211yescharacteristic
47C4×C283⋊C8C2211yescharacteristic
48C4⋊Q8×C283C2211yescharacteristic
49#126×C283—21no—
50#124×C283—21no—
51#124×C283C2211yescharacteristic
52#123×C283—21no—
53C22⋊Q8×C283—21no—
54C22⋊Q8×C283C2211yescharacteristic
55#121×C283C2211yescharacteristic
56C4×Q8×C283C2211yescharacteristic
57C4×D4×C283C2211yescharacteristic
58#117×C283C2211yescharacteristic
59#17985392—22no—
60#17985392—22no—
61C2×Dic566C2311yescharacteristic
62C2×D1132C2311yescharacteristic
63C2×C22⋊D283—21no—
64C22×Dic283—21no—
65C2×C4×D283—21no—
66C2×C4×D283—21no—
67C2×C4×D283—21no—
68#17985382—22no—
69#17985380—22no—
70#17985379—22no—
71#17985377—22no—
72C2×C283⋊C8C2311yescharacteristic
73C2×C283⋊C8C2311yescharacteristic
74C2×C283⋊C8C2311yescharacteristic
75C2×C283⋊C8C2311yescharacteristic
76C4⋊Dic283—21no—
77C4⋊Dic283C2311yescharacteristic
78C4⋊Dic283C2311yescharacteristic
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81(C2×D283)⋊C4—21no—
82(C2×D283)⋊C4—21no—
83C4×Dic283—21no—
84C4×Dic283—21no—
85C2×Q8×C283—21no—
86C2×Q8×C283C2311yescharacteristic
87C2×D4×C283—21no—
88C2×D4×C283C2311yescharacteristic
89C22×C4×C283—21no—
90C22×C4×C283C2311yescharacteristic
91C4⋊C4×C283—21no—
92C4⋊C4×C283—21no—
93C4⋊C4×C283—21no—
94C4⋊C4×C283D411yescharacteristic
95C4⋊C4×C283D411yescharacteristic
96C4⋊C4×C283C2311yescharacteristic
97C4⋊C4×C283C2311yescharacteristic
98C22⋊C4×C283—21no—
99C22⋊C4×C283—21no—
100C22⋊C4×C283—21no—
101C22⋊C4×C283—21no—
102C22⋊C4×C283—21no—
103C22⋊C4×C283D411yescharacteristic
104C22⋊C4×C283D411yescharacteristic
105C42×C283—21no—
106C42×C283C2311yescharacteristic
107C42×C283C2311yescharacteristic
108C22×D283—21no—
109Dic566—21no—
110Dic566#4112yes—
111D1132—21no—
112D1132#4112yes—
113C22⋊D283—24no—
114C2×Dic283—21no—
115C2×Dic283—21no—
116C2×Dic283—21no—
117C2×Dic283—81no—
118C4×D283—24no—
119C4×D283—81no—
120C4×D283—81no—
121C283⋊C8—21no—
122C283⋊C8—21no—
123C283⋊C8—21no—
124C283⋊C8—21no—
125C23×C283—21no—
126C23×C283C2×D411yescharacteristic
127Q8×C283—21no—
128Q8×C283—21no—
129Q8×C283—81no—
130D4×C283—21no—
131D4×C283—21no—
132D4×C283—81no—
133C2×C4×C283—21no—
134C2×C4×C283—21no—
135C2×C4×C283—21no—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283—81no—
139C2×C4×C283C2×D411yescharacteristic
140C2×C4×C283C2×D411yescharacteristic
141C2×C4×C283C2×D411yescharacteristic
142C2×C4×C283C2×D411yescharacteristic
143C2×C4×C283C2×D411yescharacteristic
144C2×C4×C283C2411yescharacteristic
145C22×C283—21no—
146C22×C283—21no—
147C22×C283—21no—
148C22×C283—41no—
149C22×C283—41no—
150C22×C283—41no—
151C22×C283C22×D411yescharacteristic
152C2×D283—22no—
153C2×D283—41no—
154C2×D283—41no—
155C4×C283—21no—
156C4×C283—21no—
157C4×C283—21no—
158C4×C283—21no—
159C4×C283—21no—
160C4×C283—41no—
161C4×C283—41no—
162C4×C283—41no—
163C4×C283C2×#4111yescharacteristic
164C4×C283C2×#4111yescharacteristic
165Dic283—22no—
166Dic283—41no—
167Dic283—41no—
168C2×C283—41no—
169C2×C283—81no—
170C2×C283#52511yescharacteristic
171C2×C283#57611yescharacteristic
172C2×C283#57811yescharacteristic
173D283—42no—
174C283#312411yescharacteristic, complemented, Sylow
175#3124—2831nomaximal, Sylow
176#542D28311yescharacteristic, complemented
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#440—2831no—
188C4×Q16—2831no—
189C4×D8—2831no—
190#433—2831no—
191C2×#41—2831no—
192C2×Q16—2831no—
193C2×SD16—2831no—
194C2×SD16—2831no—
195C2×D8—2831no—
196C4⋊Q8C2×D28311yescharacteristic
197#126—21no—
198#124—21no—
199#124C2×D28311yescharacteristic
200#123—21no—
201C22⋊Q8—21no—
202C22⋊Q8C2×D28311yescharacteristic
203#121C2×D28311yescharacteristic
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—5661no—
213#117C2×D28311yescharacteristic
214C2×C4⋊C4—2831no—
215C2×C4⋊C4—5661no—
216#107—2831no—
217#107—2831no—
218#107—2831no—
219#107—2831no—
220C4⋊C8—2831no—
221C4⋊C8—2831no—
222#103—2831no—
223#103—2831no—
224#103—2831no—
225#103—2831no—
226#102—2831no—
227#102—2831no—
228#102—2831no—
229#102—2831no—
230C22⋊C8—2831no—
231C22⋊C8—2831no—
232#97—2831no—
233C4×C8—2831no—
234#41—5662no—
235#41—5662no—
236C2×Q8—21no—
237C2×Q8—2831no—
238C2×Q8C22×D28311yescharacteristic
239C2×D4—21no—
240C2×D4—2831no—
241C2×D4—5661no—
242C2×D4C22×D28311yescharacteristic
243C22×C4—21no—
244C22×C4—5661no—
245C22×C4—5661no—
246C22×C4—5661no—
247C22×C4—5661no—
248C22×C4C22×D28311yescharacteristic
249Q16—5662no—
250SD16—5662no—
251SD16—5662no—
252D8—5662no—
253C2×C8—2831no—
254C2×C8—2831no—
255C2×C8—2831no—
256C2×C8—2831no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—2831no—
261C4⋊C4—2831no—
262C4⋊C4—5661no—
263C4⋊C4—5661no—
264C4⋊C4—5661no—
265C4⋊C4C22⋊D28311yescharacteristic
266C4⋊C4C22⋊D28311yescharacteristic
267C4⋊C4C22×D28311yescharacteristic
268C4⋊C4C22×D28311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—5661no—
275C22⋊C4—5661no—
276C22⋊C4C22⋊D28311yescharacteristic
277C22⋊C4C22⋊D28311yescharacteristic
278C42—21no—
279C42—5661no—
280C42—5661no—
281C42C22×D28311yescharacteristic
282C42C22×D28311yescharacteristic
283C23—21no—
284C23—5661no—
285C23C2×C22⋊D28311yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—81no—
289Q8—2832no—
290Q8—5661no—
291D4—21no—
292D4—21no—
293D4—81no—
294D4—2832no—
295D4—5664no—
296D4—5661no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—5664no—
304C2×C4—5661no—
305C2×C4—5661no—
306C2×C4—5661no—
307C2×C4—22641no—
308C2×C4—22641no—
309C2×C4—22641no—
310C2×C4C2×C22⋊D28311yescharacteristic
311C2×C4C2×C22⋊D28311yescharacteristic
312C2×C4C2×C22⋊D28311yescharacteristic
313C2×C4C2×C22⋊D28311yescharacteristic
314C2×C4C2×C22⋊D28311yescharacteristic
315C2×C4C23×D28311yescharacteristic
316C8—5661no—
317C8—5661no—
318C8—5661no—
319C8—5661no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—5662no—
327C22—11321no—
328C22—11321no—
329C22C22×C22⋊D28311yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—5662no—
339C4—11321no—
340C4—11321no—
341C4#41×D28311yescharacteristic
342C4#41×D28311yescharacteristic
343C2—41no—
344C2—81no—
345C2—11322no—
346C2#3182697211yescharacteristic
347C2#3182726811yescharacteristic
348C2#3182728011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#542×C283C2
socleC22×C283C22×D4
prime radical#31826608C2
hypercenter#542D283
hypocenterC283#3124
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #31826945C2semidirect
2. #31826798C2semidirect
3. #31826776C2semidirect
4. #31826757C2semidirect
5. #31826742C2semidirect
6. #31826684C2semidirect
7. #31826677C2semidirect
8. #31826625C2semidirect
10. #31826565C2semidirect
11. #31826563C2semidirect
12. C4×#17985382C2semidirect
13. C4×#17985377C2semidirect
14. #31826526C2semidirect
15. #542×C283C2semidirect
174. C283#3124semidirect
176. #542D283semidirect

Maximal subgroups

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

subgroupindex
#318269452
#318267982
#318267762
#318267572
#318267422
#318266842
#318266772
#318266252
#318266082
#318265652
#318265632
C4×#179853822
C4×#179853772
#318265262
#542×C2832
#3124283