Finite Group Databasebeta

← #49133153

Subgroups — #49133153

Order 36224.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827156C211yesmaximal, characteristic, complemented
2#31827127C211yesmaximal, characteristic
3#31826820C211yesmaximal, characteristic, complemented
4#31826808C211yesmaximal, characteristic, complemented
5#31826780C211yesmaximal, characteristic, complemented
6#31826772C211yesmaximal, characteristic, complemented
7#31826705C211yesmaximal, characteristic, complemented
8#31826697C211yesmaximal, characteristic, complemented
9#31826687C211yesmaximal, characteristic, complemented
10#31826626C211yesmaximal, characteristic, complemented
11#31826619C211yesmaximal, characteristic, complemented
12C8×D1132C211yesmaximal, characteristic, complemented
13#31826460C211yesmaximal, characteristic, complemented
14#103×D283C211yesmaximal, characteristic, complemented
15C4×Q16×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×Q8×D283C2211yescharacteristic
18C2×#17985382C2211yescharacteristic
19C2×#17985379C2211yescharacteristic
20C2×C8×D283C2211yescharacteristic
21C2×C8×D283C2211yescharacteristic
22#22583604—21no—
23#22583602C2211yescharacteristic
24#22583600—21no—
25#22583598—21no—
26#22583598C2211yescharacteristic
27#22583595—21no—
28#22583590—21no—
29#22583590C2211yescharacteristic
30#22583586C2211yescharacteristic
31#22583586C2211yescharacteristic
32#22583585—21no—
33#22583585C2211yescharacteristic
34C4×D1132—21no—
35C4×D1132C2211yescharacteristic
36#22583568C2211yescharacteristic
37#22583567—21no—
38C4⋊C4×D283C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583541C2211yescharacteristic
41C4⋊(C283⋊C8)C2211yescharacteristic
42#22583535C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583534C2211yescharacteristic
45#22583534C2211yescharacteristic
46#22583533C2211yescharacteristic
47#22583532C2211yescharacteristic
48#22583532C2211yescharacteristic
49#22583530C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51(C2×D283)⋊C8C2211yescharacteristic
52C2×Q16×C283C2211yescharacteristic
53C4×Q8×C283C2211yescharacteristic
54C4×Q8×C283C2211yescharacteristic
55#107×C283C2211yescharacteristic
56#103×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58C4×C8×C283C2211yescharacteristic
59#17985393—22no—
60#17985393—41no—
61C2×Dic566—21no—
62C2×Dic566C2311yescharacteristic
63Q8×D283—22no—
64Q8×D283—41no—
65C2×D1132—21no—
66C2×D1132—21no—
67C2×D1132D411yescharacteristic
68C2×D1132C2311yescharacteristic
69C2×C4×D283—21no—
70C2×C4×D283—21no—
71C2×C4×D283—21no—
72C2×C4×D283C2311yescharacteristic
73C2×C4×D283C2311yescharacteristic
74#17985382—41no—
75#17985379—41no—
76C2×C283⋊C8C2311yescharacteristic
77C2×C283⋊C8C2311yescharacteristic
78C8×D283—41no—
79C8×D283—41no—
80C4⋊Dic283—21no—
81C4⋊Dic283D411yescharacteristic
82C4⋊Dic283C2311yescharacteristic
83C4⋊Dic283C2311yescharacteristic
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88Dic283⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4—21no—
96(C2×D283)⋊C4D411yescharacteristic
97(C2×D283)⋊C4D411yescharacteristic
98C4×Dic283—21no—
99C2×Q8×C283C2311yescharacteristic
100C2×Q8×C283C2311yescharacteristic
101Q16×C283—22no—
102C2×C8×C283C2311yescharacteristic
103C2×C8×C283C2311yescharacteristic
104C4⋊C4×C283—21no—
105C4⋊C4×C283—21no—
106C4⋊C4×C283C2311yescharacteristic
107C4⋊C4×C283C2311yescharacteristic
108C42×C283—21no—
109C42×C283—21no—
110C42×C283C2311yescharacteristic
111C22×D283—21no—
112C22×D283C2×D411yescharacteristic
113C22×D283C2×D411yescharacteristic
114Dic566—21no—
115Dic566—21no—
116Dic566—42no—
117D1132—22no—
118D1132—21no—
119D1132—21no—
120D1132—42no—
121D1132—42no—
122C2×Dic283—21no—
123C2×Dic283—21no—
124C2×Dic283—21no—
125C2×Dic283C2×D411yescharacteristic
126C2×Dic283C2×D411yescharacteristic
127C4×D283—21no—
128C4×D283—21no—
129C4×D283—21no—
130C4×D283—21no—
131C4×D283—42no—
132C4×D283—42no—
133C4×D283—42no—
134C283⋊C8—21no—
135C283⋊C8—21no—
136Q8×C283—21no—
137Q8×C283—21no—
138Q8×C283—21no—
139Q8×C283#4112yes—
140C2×C4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283C2×D411yescharacteristic
145C2×C4×C283C2×D411yescharacteristic
146C2×C4×C283C2411yescharacteristic
147C8×C283—21no—
148C8×C283—21no—
149C22×C283C22×D411yescharacteristic
150C2×D283—21no—
151C2×D283—21no—
152C2×D283—21no—
153C2×D283—21no—
154C2×D283—21no—
155C2×D283—41no—
156C2×D283—41no—
157C2×D283—41no—
158C2×D283#13512yes—
159C4×C283—22no—
160C4×C283—21no—
161C4×C283—21no—
162C4×C283—41no—
163C4×C283—41no—
164C4×C283—41no—
165C4×C283C2×#4111yescharacteristic
166C4×C283H(5,𝔽2)11yescharacteristic
167Dic283—21no—
168Dic283—21no—
169Dic283—41no—
170Dic283—41no—
171Dic283—41no—
172C2×C283#54611yescharacteristic
173C2×C283C2×#13511yescharacteristic
174C2×C283#57811yescharacteristic
175D283—22no—
176D283—41no—
177D283—81no—
178C283#330011yescharacteristic, complemented, Sylow
179#3300—2831nomaximal, Sylow
180#552—2831no—
181#548—2831no—
182#488—2831no—
183#485—2831no—
184#480—2831no—
185#479—2831no—
186#467—2831no—
187#465—2831no—
188#464—2831no—
189#452—2831no—
190#451—2831no—
191C4×Q16D28311yescharacteristic, complemented
192C8×D4—2831no—
193#416—2831no—
194C2×#103—2831no—
195C2×#41—2831no—
196C22×Q8—2831no—
197C2×Q16—2831no—
198C2×Q16C2×D28311yescharacteristic
199C2×SD16—2831no—
200C22×C8—2831no—
201C22×C8—2831no—
202#126—5661no—
203#125—2831no—
204#125—5661no—
205#124—2831no—
206#124—5661no—
207#123—5661no—
208C22⋊Q8—2831no—
209C22⋊Q8—2831no—
210C22⋊Q8—2831no—
211C22⋊Q8—5661no—
212#121—2831no—
213#121—5661no—
214C4×Q8C2×D28311yescharacteristic
215C4×Q8C2×D28311yescharacteristic
216C4×D4—2831no—
217C4×D4—5661no—
218#117—2831no—
219#117—5661no—
220C2×C4⋊C4—2831no—
221#107—2831no—
222#107C2×D28311yescharacteristic
223#106—2831no—
224C4⋊C8—2831no—
225#103—2831no—
226#103—2831no—
227#103—2831no—
228#103—2831no—
229#103—2831no—
230#103C2×D28311yescharacteristic
231#103C2×D28311yescharacteristic
232#102—2831no—
233#102—2831no—
234#102—2831no—
235C22⋊C8—2831no—
236C22⋊C8—2831no—
237C4×C8C2×D28311yescharacteristic
238#41—5662no—
239#41—11321no—
240C2×Q8—2831no—
241C2×Q8—5661no—
242C2×Q8—5662no—
243C2×Q8—11321no—
244C2×Q8C22×D28311yescharacteristic
245C2×Q8C22×D28311yescharacteristic
246C2×D4—2831no—
247C2×D4—2831no—
248C2×D4—5661no—
249C2×D4—5661no—
250C22×C4—2831no—
251C22×C4—2831no—
252C22×C4—5661no—
253C22×C4—5661no—
254C22×C4—5661no—
255Q16—22no—
256Q16—11321no—
257SD16—11321no—
258C2×C8—2831no—
259C2×C8—2831no—
260C2×C8—11321no—
261C2×C8—11321no—
262C2×C8C22×D28311yescharacteristic
263C2×C8C22×D28311yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—2831no—
267C4⋊C4—2831no—
268C4⋊C4—2831no—
269C4⋊C4—5661no—
270C4⋊C4—5661no—
271C4⋊C4—5661no—
272C4⋊C4—5661no—
273C4⋊C4—5661no—
274C4⋊C4—5661no—
275C4⋊C4C22×D28311yescharacteristic
276C4⋊C4C22×D28311yescharacteristic
277C22⋊C4—2831no—
278C22⋊C4—2831no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C22⋊C4—5661no—
284C22⋊C4—5661no—
285C22⋊C4—5661no—
286C42—21no—
287C42—21no—
288C42—5661no—
289C42C22×D28311yescharacteristic
290C23—2831no—
291C23—2831no—
292C23—5661no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—5661no—
297Q8—5661no—
298Q8—11322no—
299Q8#1798539212yes—
300D4—5662no—
301D4—5661no—
302D4—5661no—
303D4—11322no—
304D4—11322no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—2831no—
310C2×C4—2831no—
311C2×C4—5661no—
312C2×C4—5661no—
313C2×C4—5661no—
314C2×C4—5661no—
315C2×C4—5661no—
316C2×C4—5661no—
317C2×C4—5661no—
318C2×C4—11322no—
319C2×C4—11322no—
320C2×C4—11322no—
321C2×C4D4×D28311yescharacteristic
322C2×C4D4×D28311yescharacteristic
323C2×C4C23×D28311yescharacteristic
324C8—21no—
325C8—21no—
326C8—5661no—
327C8—5661no—
328C22—2832no—
329C22—5661no—
330C22—5661no—
331C22—5661no—
332C22—5661no—
333C22—5661no—
334C22—11321no—
335C22—11321no—
336C22—11321no—
337C22C2×D4×D28311yescharacteristic
338C4—21no—
339C4—21no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—5661no—
345C4—5661no—
346C4—11321no—
347C4—11321no—
348C4—11321no—
349C4C2×#1798539211yescharacteristic
350C4#2258365611yescharacteristic
351C2—5662no—
352C2—11321no—
353C2—22641no—
354C2#3182711111yescharacteristic
355C2#135×D28311yescharacteristic
356C2#3182727811yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC4×Q16×C283C2
socleC22×C283C22×D4
prime radical#31827127C2
hypercenterC4×Q16D283
hypocenterC283#3300
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
1. #31827156C2semidirect
3. #31826820C2semidirect
4. #31826808C2semidirect
5. #31826780C2semidirect
6. #31826772C2semidirect
7. #31826705C2semidirect
8. #31826697C2semidirect
9. #31826687C2semidirect
10. #31826626C2semidirect
11. #31826619C2semidirect
12. C8×D1132C2semidirect
13. #31826460C2semidirect
14. #103×D283C2semidirect
15. C4×Q16×C283C2semidirect
178. C283#3300semidirect
191. C4×Q16D283semidirect

Maximal subgroups

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

subgroupindex
#318271562
#318271272
#318268202
#318268082
#318267802
#318267722
#318267052
#318266972
#318266872
#318266262
#318266192
C8×D11322
#318264602
#103×D2832
C4×Q16×C2832
#3300283