Finite Group Databasebeta

← #49132667

Subgroups — #49132667

Order 36224.

358 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#31827088C211yesmaximal, characteristic, complemented
2#31827068C211yesmaximal, characteristic, complemented
3#31826770C211yesmaximal, characteristic, complemented
4#31826768C211yesmaximal, characteristic, complemented
5#31826753C211yesmaximal, characteristic, complemented
6#31826744C211yesmaximal, characteristic, complemented
7#31826718C211yesmaximal, characteristic, complemented
8#31826699C211yesmaximal, characteristic, complemented
9#31826696C211yesmaximal, characteristic, complemented
10#31826683C211yesmaximal, characteristic, complemented
11#31826682C211yesmaximal, characteristic, complemented
12#31826663C211yesmaximal, characteristic, complemented
13#31826659C211yesmaximal, characteristic, complemented
14#31826493C211yesmaximal, characteristic, complemented
15#468×C283C211yesmaximal, characteristic, complemented
16C2×#17985379C2211yescharacteristic
17C2×D2264C2211yescharacteristic
18C2×#17985377C2211yescharacteristic
19C22×C283⋊C8C2211yescharacteristic
20#22583609C2211yescharacteristic
21#22583606C2211yescharacteristic
22#22583605—21no—
23#22583601C2211yescharacteristic
24#22583599C2211yescharacteristic
25#22583596—21no—
26#22583594—21no—
27#22583592—21no—
28#22583592—21no—
29#22583590—21no—
30#22583584C2211yescharacteristic
31#22583584C2211yescharacteristic
32#22583582—21no—
33#22583581—21no—
34Q8×Dic283C2211yescharacteristic
35D4×Dic283C2211yescharacteristic
36#22583572C2211yescharacteristic
37#22583572C2211yescharacteristic
38#22583569C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583542C2211yescharacteristic
41#22583541C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43Dic283⋊C8C2211yescharacteristic
44Dic283⋊C8C2211yescharacteristic
45Dic283⋊C8C2211yescharacteristic
46#22583534C2211yescharacteristic
47#22583532C2211yescharacteristic
48#22583532C2211yescharacteristic
49#22583531C2211yescharacteristic
50#22583530C2211yescharacteristic
51#22583530C2211yescharacteristic
52C2×SD16×C283C2211yescharacteristic
53C2×M16×C283C2211yescharacteristic
54C22⋊Q8×C283C2211yescharacteristic
55#121×C283C2211yescharacteristic
56#107×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#102×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×D1132C2311yescharacteristic
61C2×D1132C2311yescharacteristic
62C2×C22⋊D283—21no—
63C2×C22⋊D283—21no—
64C2×C22⋊D283—21no—
65C2×C22⋊D283—21no—
66C22×Dic283—21no—
67C2×C4×D283—21no—
68C2×C4×D283—21no—
69#17985379—41no—
70D2264—41no—
71#17985377—41no—
72C2×C283⋊C8—41no—
73C2×C283⋊C8C2311yescharacteristic
74C2×C283⋊C8C2311yescharacteristic
75C4⋊Dic283—21no—
76C4⋊Dic283—21no—
77C4⋊Dic283D411yescharacteristic
78C4⋊Dic283D411yescharacteristic
79C4⋊Dic283C2311yescharacteristic
80C4⋊Dic283C2311yescharacteristic
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83C22⋊Dic283—21no—
84C22⋊Dic283D411yescharacteristic
85C22⋊Dic283D411yescharacteristic
86(C2×D283)⋊C4—21no—
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92C4×Dic283—21no—
93C4×Dic283C2311yescharacteristic
94C4×Dic283C2311yescharacteristic
95C2×Q8×C283C2311yescharacteristic
96C2×D4×C283—21no—
97C2×D4×C283C2311yescharacteristic
98C22×C4×C283C2311yescharacteristic
99SD16×C283—41no—
100M16×C283—41no—
101C2×C8×C283C2311yescharacteristic
102C2×C8×C283C2311yescharacteristic
103C4⋊C4×C283—21no—
104C4⋊C4×C283C2311yescharacteristic
105C4⋊C4×C283C2311yescharacteristic
106C22⋊C4×C283—21no—
107C22⋊C4×C283—21no—
108C22×D283—21no—
109C22×D283—21no—
110Dic566—81no—
111D1132—21no—
112D1132—21no—
113D1132—21no—
114D1132—21no—
115C22⋊D283—81no—
116C22⋊D283—81no—
117C22⋊D283—81no—
118C22⋊D283—81no—
119C2×Dic283—21no—
120C2×Dic283—21no—
121C2×Dic283—81no—
122C2×Dic283C2×D411yescharacteristic
123C2×Dic283C2×D411yescharacteristic
124C2×Dic283C2×D411yescharacteristic
125C2×Dic283C2×D411yescharacteristic
126C4×D283—81no—
127C4×D283—81no—
128C283⋊C8—21no—
129C283⋊C8—21no—
130C23×C283—21no—
131C23×C283C2×D411yescharacteristic
132Q8×C283—21no—
133Q8×C283—21no—
134D4×C283—21no—
135D4×C283—21no—
136D4×C283—81no—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283C2×D411yescharacteristic
143C2×C4×C283C2411yescharacteristic
144C8×C283—21no—
145C8×C283—21no—
146C22×C283—21no—
147C22×C283—21no—
148C22×C283—21no—
149C22×C283—41no—
150C22×C283—41no—
151C22×C283—41no—
152C22×C283C22×D411yescharacteristic
153C2×D283—41no—
154C2×D283—41no—
155C2×D283—41no—
156C2×D283—41no—
157C2×D283—41no—
158C2×D283—41no—
159C4×C283—21no—
160C4×C283—41no—
161C4×C283—41no—
162C4×C283—41no—
163C4×C283H(5,𝔽2)11yescharacteristic
164C4×C2832−1+411yescharacteristic
165Dic283—21no—
166Dic283—21no—
167Dic283—21no—
168Dic283—21no—
169Dic283—41no—
170Dic283—41no—
171C2×C283—41no—
172C2×C283—81no—
173C2×C283#53711yescharacteristic
174C2×C283#57611yescharacteristic
175C2×C283#57711yescharacteristic
176D283—81no—
177D283—81no—
178C283#325711yescharacteristic, complemented, Sylow
179#3257—2831nomaximal, Sylow
180#542—2831no—
181#540—2831no—
182#479—2831no—
183#478—2831no—
184#476—2831no—
185#474—2831no—
186#469—2831no—
187#468D28311yescharacteristic, complemented
188#466—2831no—
189#465—2831no—
190#463—2831no—
191#463—2831no—
192#460—2831no—
193#459—2831no—
194#424—2831no—
195C2×SD16—2831no—
196C2×SD16C2×D28311yescharacteristic
197C2×D8—2831no—
198C2×D8—2831no—
199C2×M16C2×D28311yescharacteristic
200C22×C8—2831no—
201C4⋊Q8—2831no—
202#127—2831no—
203#126—5661no—
204#125—2831no—
205#124—2831no—
206#124—5661no—
207#123—5661no—
208#123—5661no—
209#123—5661no—
210C22⋊Q8—5661no—
211C22⋊Q8C2×D28311yescharacteristic
212#121—2831no—
213#121—2831no—
214#121—5661no—
215#121—5661no—
216#121C2×D28311yescharacteristic
217C4×Q8—2831no—
218C4×D4—2831no—
219C4×D4—2831no—
220C4×D4—2831no—
221#117—2831no—
222#107—2831no—
223#107C2×D28311yescharacteristic
224#106—2831no—
225#106—2831no—
226C4⋊C8—2831no—
227C4⋊C8—2831no—
228C4⋊C8—2831no—
229C4⋊C8—2831no—
230#103—2831no—
231#103C2×D28311yescharacteristic
232#102—2831no—
233#102—2831no—
234#102—2831no—
235#102—2831no—
236#102—2831no—
237#102C2×D28311yescharacteristic
238C2×Q8—5661no—
239C2×Q8C22×D28311yescharacteristic
240C2×D4—21no—
241C2×D4—2831no—
242C2×D4—2831no—
243C2×D4—5661no—
244C2×D4—5661no—
245C2×D4—5661no—
246C2×D4—5661no—
247C2×D4C22×D28311yescharacteristic
248C22×C4—5661no—
249C22×C4—5661no—
250C22×C4—5661no—
251C22×C4C22×D28311yescharacteristic
252SD16—41no—
253SD16—11321no—
254D8—11321no—
255D8—11321no—
256M16—41no—
257C2×C8—2831no—
258C2×C8—2831no—
259C2×C8—11321no—
260C2×C8C22×D28311yescharacteristic
261C2×C8C22×D28311yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—2831no—
264C4⋊C4—2831no—
265C4⋊C4—2831no—
266C4⋊C4—2831no—
267C4⋊C4—5661no—
268C4⋊C4—5661no—
269C4⋊C4—5661no—
270C4⋊C4—5661no—
271C4⋊C4C22×D28311yescharacteristic
272C4⋊C4C22×D28311yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—2831no—
276C22⋊C4—2831no—
277C22⋊C4—5661no—
278C22⋊C4—5661no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C22⋊C4—5661no—
284C42—2831no—
285C42—2831no—
286C42—5661no—
287C23—21no—
288C23—5661no—
289C23—5661no—
290C23D4×D28311yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—22641no—
294D4—21no—
295D4—21no—
296D4—81no—
297D4—5661no—
298D4—5661no—
299D4—5661no—
300D4—5661no—
301D4—22641no—
302D4—22641no—
303D4—22641no—
304D4—22641no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—2831no—
311C2×C4—2831no—
312C2×C4—2831no—
313C2×C4—2831no—
314C2×C4—5661no—
315C2×C4—5661no—
316C2×C4—22641no—
317C2×C4—22641no—
318C2×C4—22641no—
319C2×C4D4×D28311yescharacteristic
320C2×C4C23×D28311yescharacteristic
321C8—21no—
322C8—21no—
323C8—5661no—
324C8—5661no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—11321no—
332C22—11321no—
333C22—11321no—
334C22—11321no—
335C22—11321no—
336C22—11321no—
337C22C2×D4×D28311yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—5661no—
343C4—5661no—
344C4—5661no—
345C4—5661no—
346C4—11321no—
347C4—11321no—
348C4#2258365511yescharacteristic
349C4#2258365711yescharacteristic
350C2—41no—
351C2—81no—
352C2—22641no—
353C2—22641no—
354C2#3182704211yescharacteristic
355C2#3182726911yescharacteristic
356C2#3182727411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#468×C283C2
socleC22×C283C22×D4
hypercenter#468D283
hypocenterC283#3257
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #31827088C2semidirect
2. #31827068C2semidirect
3. #31826770C2semidirect
4. #31826768C2semidirect
5. #31826753C2semidirect
6. #31826744C2semidirect
7. #31826718C2semidirect
8. #31826699C2semidirect
9. #31826696C2semidirect
10. #31826683C2semidirect
11. #31826682C2semidirect
12. #31826663C2semidirect
13. #31826659C2semidirect
14. #31826493C2semidirect
15. #468×C283C2semidirect
178. C283#3257semidirect
187. #468D283semidirect

Maximal subgroups

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

subgroupindex
#318270882
#318270682
#318267702
#318267682
#318267532
#318267442
#318267182
#318266992
#318266962
#318266832
#318266822
#318266632
#318266592
#318264932
#468×C2832
#3257283