Finite Group Databasebeta

← #49134336

Subgroups — #49134336

Order 36224.

356 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827188C211yesmaximal, characteristic, complemented
2#31826860C211yesmaximal, characteristic, complemented
3#31826857C211yesmaximal, characteristic, complemented
4#31826847C211yesmaximal, characteristic
5#31826687C211yesmaximal, characteristic, complemented
6#31826684C211yesmaximal, characteristic, complemented
7#31826680C211yesmaximal, characteristic
8#31826677C211yesmaximal, characteristic
9#31826675C211yesmaximal, characteristic, complemented
10#31826672C211yesmaximal, characteristic, complemented
11#31826596C211yesmaximal, characteristic, complemented
12#31826565C211yesmaximal, characteristic, complemented
13#31826563C211yesmaximal, characteristic, complemented
14C4×#17985382C211yesmaximal, characteristic, complemented
15#556×C283C211yesmaximal, characteristic, complemented
16C2×#17985382C2211yescharacteristic
17C2×#17985382C2211yescharacteristic
18C2×#17985382C2211yescharacteristic
19C2×#17985382C2211yescharacteristic
20C2×#17985380C2211yescharacteristic
21C2×#17985380C2211yescharacteristic
22C2×#17985379C2211yescharacteristic
23C2×#17985379C2211yescharacteristic
24C2×#17985377C2211yescharacteristic
25#22583610C2211yescharacteristic
26#22583605—21no—
27#22583605—21no—
28#22583598C2211yescharacteristic
29#22583598C2211yescharacteristic
30#22583586—21no—
31C4×Dic566C2211yescharacteristic
32C4×Dic566C2211yescharacteristic
33C4×D1132C2211yescharacteristic
34#22583568—21no—
35#22583543C2211yescharacteristic
36C4⋊(C283⋊C8)C2211yescharacteristic
37C4⋊(C283⋊C8)C2211yescharacteristic
38C4⋊(C283⋊C8)C2211yescharacteristic
39#22583534C2211yescharacteristic
40#22583534C2211yescharacteristic
41#22583533C2211yescharacteristic
42#22583533C2211yescharacteristic
43#22583531C2211yescharacteristic
44#22583530C2211yescharacteristic
45#22583521C2211yescharacteristic
46#22583521C2211yescharacteristic
47C4×C283⋊C8C2211yescharacteristic
48C4⋊Q8×C283C2211yescharacteristic
49#126×C283—21no—
50#126×C283—21no—
51#124×C283C2211yescharacteristic
52#124×C283C2211yescharacteristic
53C22⋊Q8×C283—21no—
54C4×Q8×C283C2211yescharacteristic
55C4×Q8×C283C2211yescharacteristic
56C4×Q8×C283C2211yescharacteristic
57C4×D4×C283C2211yescharacteristic
58#117×C283—21no—
59C2×Dic566C2311yescharacteristic
60C2×Dic566C2311yescharacteristic
61C2×D1132C2311yescharacteristic
62C2×C4×D283—21no—
63#17985382—22no—
64#17985382—41no—
65#17985382—41no—
66#17985382—41no—
67#17985380—22no—
68#17985380—41no—
69#17985379—22no—
70#17985379—41no—
71#17985377—41no—
72C2×C283⋊C8C2311yescharacteristic
73C2×C283⋊C8C2311yescharacteristic
74C2×C283⋊C8C2311yescharacteristic
75C2×C283⋊C8C2311yescharacteristic
76C4⋊Dic283—21no—
77C4⋊Dic283—21no—
78C4⋊Dic283C2311yescharacteristic
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81(C2×D283)⋊C4—21no—
82(C2×D283)⋊C4—21no—
83(C2×D283)⋊C4—21no—
84(C2×D283)⋊C4—21no—
85(C2×D283)⋊C4—21no—
86C4×Dic283—21no—
87C4×Dic283—21no—
88C2×Q8×C283D411yescharacteristic
89C2×Q8×C283C2311yescharacteristic
90C2×Q8×C283C2311yescharacteristic
91C2×D4×C283C2311yescharacteristic
92C22×C4×C283—21no—
93C4⋊C4×C283—21no—
94C4⋊C4×C283—21no—
95C4⋊C4×C283—21no—
96C4⋊C4×C283—21no—
97C4⋊C4×C283D411yescharacteristic
98C4⋊C4×C283D411yescharacteristic
99C4⋊C4×C283D411yescharacteristic
100C4⋊C4×C283C2311yescharacteristic
101C22⋊C4×C283—21no—
102C22⋊C4×C283—21no—
103C22⋊C4×C283—21no—
104C22⋊C4×C283—21no—
105C22⋊C4×C283—21no—
106C42×C283—21no—
107C42×C283—21no—
108C42×C283C2311yescharacteristic
109C42×C283C2311yescharacteristic
110C42×C283C2311yescharacteristic
111C22×D283—21no—
112Dic566—21no—
113Dic566—21no—
114Dic566—21no—
115Dic566—21no—
116D1132—21no—
117D1132—21no—
118C2×Dic283—21no—
119C2×Dic283—21no—
120C2×Dic283—21no—
121C4×D283—42no—
122C283⋊C8—21no—
123C283⋊C8—21no—
124C283⋊C8—21no—
125C283⋊C8#4112yes—
126C23×C283—21no—
127Q8×C283—21no—
128Q8×C283—21no—
129Q8×C283—21no—
130Q8×C283—21no—
131Q8×C283—41no—
132D4×C283—21no—
133D4×C283—21no—
134C2×C4×C283—21no—
135C2×C4×C283—21no—
136C2×C4×C283—21no—
137C2×C4×C283—42no—
138C2×C4×C283C2×D411yescharacteristic
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—41no—
146C22×C283—41no—
147C22×C283—41no—
148C22×C283C22×D411yescharacteristic
149C2×D283—41no—
150C2×D283—41no—
151C2×D283—41no—
152C4×C283—21no—
153C4×C283—21no—
154C4×C283—21no—
155C4×C283—21no—
156C4×C283—21no—
157C4×C283—21no—
158C4×C283—41no—
159C4×C283—41no—
160C4×C283—41no—
161C4×C283C2×#4111yescharacteristic
162C4×C283H(5,𝔽2)11yescharacteristic
163Dic283—41no—
164Dic283—41no—
165Dic283—41no—
166C2×C283—81no—
167C2×C283#55011yescharacteristic
168C2×C283#57511yescharacteristic
169C2×C283#57811yescharacteristic
170D283—81no—
171C283#340211yescharacteristic, complemented, Sylow
172#3402—2831nomaximal, Sylow
173#556—2831no—
174#556D28311yescharacteristic, complemented
175#497—2831no—
176#497—2831no—
177#495—2831no—
178#464—2831no—
179#464—2831no—
180#463—2831no—
181#463—2831no—
182#462—2831no—
183#462—2831no—
184#446—2831no—
185#440—2831no—
186#440—2831no—
187C4×Q16—2831no—
188C2×Q16—2831no—
189C2×Q16—2831no—
190C2×Q16—2831no—
191C2×Q16—2831no—
192C2×SD16—2831no—
193C2×SD16—2831no—
194C2×SD16—2831no—
195C2×SD16—2831no—
196C2×D8—2831no—
197C4⋊Q8—2831no—
198C4⋊Q8C2×D28311yescharacteristic
199#126—21no—
200#126—21no—
201#126—5661no—
202#126—5661no—
203#124—2831no—
204#124—2831no—
205#124C2×D28311yescharacteristic
206#124C2×D28311yescharacteristic
207C22⋊Q8—21no—
208C22⋊Q8—5661no—
209C4×Q8—2831no—
210C4×Q8—2831no—
211C4×Q8C2×D28311yescharacteristic
212C4×Q8C2×D28311yescharacteristic
213C4×Q8C2×D28311yescharacteristic
214C4×D4—2831no—
215C4×D4C2×D28311yescharacteristic
216#117—21no—
217#117—5661no—
218#107—2831no—
219C4⋊C8—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#97—2831no—
229#97—2831no—
230C4×C8—2831no—
231C2×Q8—2831no—
232C2×Q8—2831no—
233C2×Q8C22⋊D28311yescharacteristic
234C2×Q8C22×D28311yescharacteristic
235C2×Q8C22×D28311yescharacteristic
236C2×D4—2831no—
237C2×D4C22×D28311yescharacteristic
238C22×C4—21no—
239C22×C4—5661no—
240Q16—5662no—
241Q16—11321no—
242Q16—11321no—
243Q16—11321no—
244SD16—5662no—
245SD16—5662no—
246SD16—11321no—
247SD16—11321no—
248D8—11321no—
249C2×C8—2831no—
250C2×C8—2831no—
251C2×C8—2831no—
252C2×C8—2831no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—2831no—
258C4⋊C4—5661no—
259C4⋊C4—5661no—
260C4⋊C4—5661no—
261C4⋊C4—5661no—
262C4⋊C4C22⋊D28311yescharacteristic
263C4⋊C4C22⋊D28311yescharacteristic
264C4⋊C4C22⋊D28311yescharacteristic
265C4⋊C4C22×D28311yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—5661no—
272C22⋊C4—5661no—
273C22⋊C4—5661no—
274C22⋊C4—5661no—
275C22⋊C4—5661no—
276C42—21no—
277C42—21no—
278C42—5661no—
279C42—5661no—
280C42C22×D28311yescharacteristic
281C42C22×D28311yescharacteristic
282C42C22×D28311yescharacteristic
283C23—21no—
284C23—5661no—
285Q8—21no—
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—41no—
290Q8—5661no—
291Q8—5661no—
292Q8—5661no—
293Q8—5661no—
294D4—21no—
295D4—21no—
296D4—5661no—
297D4—5661no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—5661no—
303C2×C4—5661no—
304C2×C4—5661no—
305C2×C4—11322no—
306C2×C4C2×C22⋊D28311yescharacteristic
307C2×C4C2×C22⋊D28311yescharacteristic
308C2×C4C2×C22⋊D28311yescharacteristic
309C2×C4C2×C22⋊D28311yescharacteristic
310C2×C4C2×C22⋊D28311yescharacteristic
311C2×C4C2×C22⋊D28311yescharacteristic
312C2×C4C23×D28311yescharacteristic
313C8—2832no—
314C8—5661no—
315C8—5661no—
316C8—5661no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—11321no—
321C22—11321no—
322C22—11321no—
323C22C22×C22⋊D28311yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—11321no—
334C4—11321no—
335C4—11321no—
336C4#41×D28311yescharacteristic
337C4#2258365611yescharacteristic
338C2—81no—
339C2—22641no—
340C2#3182713411yescharacteristic
341C2#3182726311yescharacteristic
342C2#3182728011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#556×C283C2
socleC22×C283C22×D4
prime radicalC2×#17985377C22
hypercenter#556D283
hypocenterC283#3402
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

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

NH ≅ G/Ntype
1. #31827188C2semidirect
2. #31826860C2semidirect
3. #31826857C2semidirect
5. #31826687C2semidirect
6. #31826684C2semidirect
9. #31826675C2semidirect
10. #31826672C2semidirect
11. #31826596C2semidirect
12. #31826565C2semidirect
13. #31826563C2semidirect
14. C4×#17985382C2semidirect
15. #556×C283C2semidirect
171. C283#3402semidirect
174. #556D283semidirect

Maximal subgroups

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

subgroupindex
#318271882
#318268602
#318268572
#318268472
#318266872
#318266842
#318266802
#318266772
#318266752
#318266722
#318265962
#318265652
#318265632
C4×#179853822
#556×C2832
#3402283