Finite Group Databasebeta

← #49134321

Subgroups — #49134321

Order 36224.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 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#31826852C211yesmaximal, characteristic
4#31826847C211yesmaximal, characteristic, complemented
5#31826687C211yesmaximal, characteristic, complemented
6#31826684C211yesmaximal, characteristic, complemented
7#31826680C211yesmaximal, characteristic, complemented
8#31826677C211yesmaximal, characteristic, complemented
9#31826670C211yesmaximal, characteristic, complemented
10#31826662C211yesmaximal, characteristic, complemented
11#31826596C211yesmaximal, characteristic, complemented
12#31826575C211yesmaximal, characteristic, complemented
13#31826570C211yesmaximal, characteristic, complemented
14C4×#17985380C211yesmaximal, characteristic, complemented
15#559×C283C211yesmaximal, characteristic, complemented
16C2×#17985382C2211yescharacteristic
17C2×#17985382C2211yescharacteristic
18C2×#17985380C2211yescharacteristic
19C2×#17985380C2211yescharacteristic
20C2×#17985380C2211yescharacteristic
21C2×#17985380C2211yescharacteristic
22C2×#17985379C2211yescharacteristic
23C2×#17985377C2211yescharacteristic
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#22583541C2211yescharacteristic
36C4⋊(C283⋊C8)C2211yescharacteristic
37C4⋊(C283⋊C8)C2211yescharacteristic
38C4⋊(C283⋊C8)C2211yescharacteristic
39#22583534C2211yescharacteristic
40#22583533C2211yescharacteristic
41#22583533C2211yescharacteristic
42#22583531C2211yescharacteristic
43#22583531C2211yescharacteristic
44#22583530C2211yescharacteristic
45#22583521C2211yescharacteristic
46#22583521C2211yescharacteristic
47C4×C283⋊C8C2211yescharacteristic
48#127×C283C2211yescharacteristic
49#124×C283—21no—
50#124×C283C2211yescharacteristic
51#124×C283C2211yescharacteristic
52#123×C283—21no—
53#123×C283—21no—
54C4×Q8×C283C2211yescharacteristic
55C4×Q8×C283C2211yescharacteristic
56C4×D4×C283—21no—
57C4×D4×C283C2211yescharacteristic
58C4×D4×C283C2211yescharacteristic
59C2×Dic566C2311yescharacteristic
60C2×Dic566C2311yescharacteristic
61C2×D1132C2311yescharacteristic
62C2×C4×D283—21no—
63#17985382—22no—
64#17985382—41no—
65#17985380—22no—
66#17985380—41no—
67#17985380—41no—
68#17985380—41no—
69#17985379—41no—
70#17985377—22no—
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×D4×C283—21no—
91C2×D4×C283—21no—
92C2×D4×C283C2311yescharacteristic
93C2×D4×C283C2311yescharacteristic
94C22×C4×C283—21no—
95C22×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—
106C22⋊C4×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—
127C23×C283—21no—
128Q8×C283—21no—
129Q8×C283—21no—
130Q8×C283—41no—
131D4×C283—21no—
132D4×C283—21no—
133D4×C283—21no—
134D4×C283—21no—
135D4×C283—42no—
136D4×C283—81no—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283—81no—
140C2×C4×C283—81no—
141C2×C4×C283C2×D411yescharacteristic
142C2×C4×C283C2×D411yescharacteristic
143C2×C4×C283C2×D411yescharacteristic
144C2×C4×C283C2×D411yescharacteristic
145C2×C4×C283C2×D411yescharacteristic
146C2×C4×C283C2×D411yescharacteristic
147C2×C4×C283C2411yescharacteristic
148C22×C283—41no—
149C22×C283—41no—
150C22×C283—41no—
151C22×C283—41no—
152C22×C283—41no—
153C22×C283—41no—
154C22×C283C22×D411yescharacteristic
155C2×D283—41no—
156C2×D283—41no—
157C2×D283—41no—
158C4×C283—21no—
159C4×C283—21no—
160C4×C283—21no—
161C4×C283—21no—
162C4×C283—21no—
163C4×C283—21no—
164C4×C283—41no—
165C4×C283—41no—
166C4×C283C2×#4111yescharacteristic
167C4×C283H(5,𝔽2)11yescharacteristic
168Dic283—41no—
169Dic283—41no—
170Dic283—41no—
171C2×C283—81no—
172C2×C283—81no—
173C2×C283#55011yescharacteristic
174C2×C283#57511yescharacteristic
175C2×C283#57711yescharacteristic
176D283—81no—
177C283#340111yescharacteristic, complemented, Sylow
178#3401—2831nomaximal, Sylow
179#559D28311yescharacteristic, complemented
180#556—2831no—
181#497—2831no—
182#496—2831no—
183#495—2831no—
184#464—2831no—
185#464—2831no—
186#463—2831no—
187#463—2831no—
188#461—2831no—
189#460—2831no—
190#446—2831no—
191#442—2831no—
192#441—2831no—
193C4×SD16—2831no—
194C2×Q16—2831no—
195C2×Q16—2831no—
196C2×SD16—2831no—
197C2×SD16—2831no—
198C2×SD16—2831no—
199C2×SD16—2831no—
200C2×SD16—2831no—
201C2×D8—2831no—
202C2×D8—2831no—
203C4⋊Q8—2831no—
204#127C2×D28311yescharacteristic
205#126—5661no—
206#126—5661no—
207#124—21no—
208#124—2831no—
209#124—2831no—
210#124C2×D28311yescharacteristic
211#124C2×D28311yescharacteristic
212#123—21no—
213#123—21no—
214C22⋊Q8—5661no—
215C4×Q8—2831no—
216C4×Q8—2831no—
217C4×Q8C2×D28311yescharacteristic
218C4×Q8C2×D28311yescharacteristic
219C4×D4—21no—
220C4×D4—2831no—
221C4×D4C2×D28311yescharacteristic
222C4×D4C2×D28311yescharacteristic
223#117—5661no—
224#106—2831no—
225C4⋊C8—2831no—
226C4⋊C8—2831no—
227C4⋊C8—2831no—
228#103—2831no—
229#103—2831no—
230#103—2831no—
231#102—2831no—
232#102—2831no—
233#102—2831no—
234#97—2831no—
235#97—2831no—
236C4×C8—2831no—
237C2×Q8—2831no—
238C2×Q8—2831no—
239C2×Q8C22⋊D28311yescharacteristic
240C2×Q8C22×D28311yescharacteristic
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—2831no—
244C2×D4C22×D28311yescharacteristic
245C2×D4C22×D28311yescharacteristic
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—5661no—
249Q16—5662no—
250Q16—11321no—
251SD16—5662no—
252SD16—11321no—
253SD16—11321no—
254SD16—11321no—
255SD16—11321no—
256D8—5662no—
257D8—11321no—
258C2×C8—2831no—
259C2×C8—2831no—
260C2×C8—2831no—
261C2×C8—2831no—
262C4⋊C4—21no—
263C4⋊C4—2831no—
264C4⋊C4—5661no—
265C4⋊C4—5661no—
266C4⋊C4—5661no—
267C4⋊C4—5661no—
268C4⋊C4C22⋊D28311yescharacteristic
269C4⋊C4C22⋊D28311yescharacteristic
270C4⋊C4C22⋊D28311yescharacteristic
271C4⋊C4C22×D28311yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—5661no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C42—21no—
284C42—5661no—
285C42—5661no—
286C42C22×D28311yescharacteristic
287C42C22×D28311yescharacteristic
288C42C22×D28311yescharacteristic
289C23—21no—
290C23—21no—
291C23—5661no—
292Q8—21no—
293Q8—21no—
294Q8—41no—
295Q8—5661no—
296Q8—5661no—
297Q8—5661no—
298Q8—5661no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—42no—
304D4—81no—
305D4—5661no—
306D4—5661no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—5661no—
312C2×C4—5661no—
313C2×C4—5661no—
314C2×C4—11322no—
315C2×C4C2×C22⋊D28311yescharacteristic
316C2×C4C2×C22⋊D28311yescharacteristic
317C2×C4C2×C22⋊D28311yescharacteristic
318C2×C4C2×C22⋊D28311yescharacteristic
319C2×C4C2×C22⋊D28311yescharacteristic
320C2×C4C2×C22⋊D28311yescharacteristic
321C2×C4C23×D28311yescharacteristic
322C8—2832no—
323C8—5661no—
324C8—5661no—
325C8—5661no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—11321no—
333C22—11321no—
334C22—11321no—
335C22C22×C22⋊D28311yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—11321no—
345C4—11321no—
346C4—11321no—
347C4#41×D28311yescharacteristic
348C4#2258365611yescharacteristic
349C2—81no—
350C2—81no—
351C2—22641no—
352C2#3182713411yescharacteristic
353C2#3182726311yescharacteristic
354C2#3182727611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#559×C283C2
socleC22×C283C22×D4
prime radical#31826852C2
hypercenter#559D283
hypocenterC283#3401
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #31827188C2semidirect
2. #31826860C2semidirect
4. #31826847C2semidirect
5. #31826687C2semidirect
6. #31826684C2semidirect
7. #31826680C2semidirect
8. #31826677C2semidirect
9. #31826670C2semidirect
10. #31826662C2semidirect
11. #31826596C2semidirect
12. #31826575C2semidirect
13. #31826570C2semidirect
14. C4×#17985380C2semidirect
15. #559×C283C2semidirect
177. C283#3401semidirect
179. #559D283semidirect

Maximal subgroups

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

subgroupindex
#318271882
#318268602
#318268522
#318268472
#318266872
#318266842
#318266802
#318266772
#318266702
#318266622
#318265962
#318265752
#318265702
C4×#179853802
#559×C2832
#3401283