Finite Group Databasebeta

← #49132665

Subgroups — #49132665

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#31827082C211yesmaximal, characteristic, complemented
2#31827068C211yesmaximal, characteristic, complemented
3#31826771C211yesmaximal, characteristic, complemented
4#31826767C211yesmaximal, characteristic, complemented
5#31826753C211yesmaximal, characteristic, complemented
6#31826744C211yesmaximal, characteristic, complemented
7#31826716C211yesmaximal, characteristic, complemented
8#31826709C211yesmaximal, characteristic, complemented
9#31826694C211yesmaximal, characteristic, complemented
10#31826679C211yesmaximal, characteristic, complemented
11#31826678C211yesmaximal, characteristic, complemented
12#31826664C211yesmaximal, characteristic, complemented
13#31826658C211yesmaximal, characteristic, complemented
14#31826491C211yesmaximal, characteristic, complemented
15#466×C283C211yesmaximal, characteristic, complemented
16C2×#17985381C2211yescharacteristic
17C2×#17985380C2211yescharacteristic
18C2×#17985377C2211yescharacteristic
19C2×#17985376C2211yescharacteristic
20#22583609C2211yescharacteristic
21#22583606C2211yescharacteristic
22#22583603—21no—
23#22583601C2211yescharacteristic
24#22583597—21no—
25#22583597C2211yescharacteristic
26#22583594—21no—
27#22583592—21no—
28#22583591—21no—
29#22583589C2211yescharacteristic
30#22583587—21no—
31#22583584C2211yescharacteristic
32#22583582—21no—
33#22583581—21no—
34#22583575C2211yescharacteristic
35D4×Dic283C2211yescharacteristic
36D4×Dic283C2211yescharacteristic
37#22583572C2211yescharacteristic
38#22583569C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583542C2211yescharacteristic
41#22583541C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43Dic283⋊C8C2211yescharacteristic
44Dic283⋊C8C2211yescharacteristic
45Dic283⋊C8C2211yescharacteristic
46#22583535C2211yescharacteristic
47#22583533C2211yescharacteristic
48#22583532C2211yescharacteristic
49#22583531C2211yescharacteristic
50#22583531C2211yescharacteristic
51#22583530C2211yescharacteristic
52C2×D8×C283C2211yescharacteristic
53C22×C8×C283C2211yescharacteristic
54#121×C283C2211yescharacteristic
55#121×C283C2211yescharacteristic
56#107×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58#102×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×Dic566C2311yescharacteristic
61C2×D1132C2311yescharacteristic
62C2×C22⋊D283—21no—
63C2×C22⋊D283—21no—
64C2×C22⋊D283—21no—
65C22×Dic283—21no—
66C22×Dic283—21no—
67C2×C4×D283—21no—
68#17985381—41no—
69#17985380—41no—
70#17985377—41no—
71#17985376—41no—
72C2×C283⋊C8C2311yescharacteristic
73C2×C283⋊C8C2311yescharacteristic
74C4⋊Dic283—21no—
75C4⋊Dic283D411yescharacteristic
76C4⋊Dic283D411yescharacteristic
77C4⋊Dic283C2311yescharacteristic
78C4⋊Dic283C2311yescharacteristic
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83C22⋊Dic283—21no—
84C22⋊Dic283—21no—
85C22⋊Dic283—21no—
86C22⋊Dic283—21no—
87C22⋊Dic283—21no—
88C22⋊Dic283D411yescharacteristic
89C22⋊Dic283D411yescharacteristic
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92C4×Dic283—21no—
93C4×Dic283C2311yescharacteristic
94C4×Dic283C2311yescharacteristic
95C2×D4×C283—21no—
96C2×D4×C283—21no—
97C2×D4×C283C2311yescharacteristic
98C2×D4×C283C2311yescharacteristic
99C22×C4×C283C2311yescharacteristic
100D8×C283—41no—
101C2×C8×C283—41no—
102C2×C8×C283C2311yescharacteristic
103C2×C8×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C4⋊C4×C283C2311yescharacteristic
106C22⋊C4×C283—21no—
107C22⋊C4×C283—21no—
108C22×D283—21no—
109Dic566—21no—
110Dic566—21no—
111Dic566—81no—
112D1132—21no—
113D1132—21no—
114C22⋊D283—81no—
115C22⋊D283—81no—
116C22⋊D283—81no—
117C2×Dic283—21no—
118C2×Dic283—21no—
119C2×Dic283—21no—
120C2×Dic283—81no—
121C2×Dic283—81no—
122C2×Dic283C2×D411yescharacteristic
123C2×Dic283C2×D411yescharacteristic
124C2×Dic283C2×D411yescharacteristic
125C2×Dic283C2×D411yescharacteristic
126C4×D283—81no—
127C283⋊C8—21no—
128C283⋊C8—21no—
129C23×C283—21no—
130C23×C283—21no—
131C23×C283C2×D411yescharacteristic
132D4×C283—21no—
133D4×C283—21no—
134D4×C283—21no—
135D4×C283—21no—
136D4×C283—81no—
137D4×C283—81no—
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×C283—41no—
153C22×C283—41no—
154C22×C283—41no—
155C22×C283C22×D411yescharacteristic
156C2×D283—41no—
157C2×D283—41no—
158C2×D283—41no—
159C4×C283—21no—
160C4×C283—41no—
161C4×C283—41no—
162C4×C283H(5,𝔽2)11yescharacteristic
163C4×C2832−1+411yescharacteristic
164Dic283—21no—
165Dic283—21no—
166Dic283—21no—
167Dic283—21no—
168Dic283—41no—
169Dic283—41no—
170Dic283—41no—
171C2×C283—41no—
172C2×C283—81no—
173C2×C283—81no—
174C2×C283#53711yescharacteristic
175C2×C283#57611yescharacteristic
176C2×C283#57711yescharacteristic
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#468—2831no—
188#466D28311yescharacteristic, complemented
189#465—2831no—
190#463—2831no—
191#463—2831no—
192#460—2831no—
193#459—2831no—
194#424—2831no—
195C2×SD16—2831no—
196C2×SD16—2831no—
197C2×D8—2831no—
198C2×D8C2×D28311yescharacteristic
199C2×M16—2831no—
200C22×C8C2×D28311yescharacteristic
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—2831no—
211C22⋊Q8—5661no—
212#121—2831no—
213#121—5661no—
214#121—5661no—
215#121C2×D28311yescharacteristic
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#103—2831no—
232#102—2831no—
233#102—2831no—
234#102—2831no—
235#102—2831no—
236#102C2×D28311yescharacteristic
237#102C2×D28311yescharacteristic
238C2×Q8—2831no—
239C2×Q8—5661no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—2831no—
243C2×D4—5661no—
244C2×D4—5661no—
245C2×D4—5661no—
246C2×D4C22×D28311yescharacteristic
247C2×D4C22×D28311yescharacteristic
248C22×C4—5661no—
249C22×C4—5661no—
250C22×C4—5661no—
251C22×C4C22×D28311yescharacteristic
252SD16—11321no—
253SD16—11321no—
254D8—41no—
255D8—11321no—
256M16—11321no—
257C2×C8—41no—
258C2×C8—2831no—
259C2×C8—2831no—
260C2×C8C22×D28311yescharacteristic
261C2×C8C22×D28311yescharacteristic
262C4⋊C4—2831no—
263C4⋊C4—2831no—
264C4⋊C4—2831no—
265C4⋊C4—2831no—
266C4⋊C4—5661no—
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—21no—
289C23—5661no—
290C23D4×D28311yescharacteristic
291Q8—5661no—
292Q8—5661no—
293Q8—22641no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—81no—
299D4—81no—
300D4—5661no—
301D4—5661no—
302D4—22641no—
303D4—22641no—
304D4—22641no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—2831no—
310C2×C4—2831no—
311C2×C4—2831no—
312C2×C4—2831no—
313C2×C4—5661no—
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—41no—
332C22—41no—
333C22—41no—
334C22—11321no—
335C22—11321no—
336C22—11321no—
337C22C2×D4×D28311yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—5661no—
342C4—5661no—
343C4—5661no—
344C4—5661no—
345C4—11321no—
346C4—11321no—
347C4—11321no—
348C4#2258365511yescharacteristic
349C4#2258365711yescharacteristic
350C2—41no—
351C2—81no—
352C2—81no—
353C2—22641no—
354C2#3182704211yescharacteristic
355C2#3182726611yescharacteristic
356C2#3182727211yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#466×C283C2
socleC22×C283C22×D4
hypercenter#466D283
hypocenterC283#3257
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #31827082C2semidirect
2. #31827068C2semidirect
3. #31826771C2semidirect
4. #31826767C2semidirect
5. #31826753C2semidirect
6. #31826744C2semidirect
7. #31826716C2semidirect
8. #31826709C2semidirect
9. #31826694C2semidirect
10. #31826679C2semidirect
11. #31826678C2semidirect
12. #31826664C2semidirect
13. #31826658C2semidirect
14. #31826491C2semidirect
15. #466×C283C2semidirect
178. C283#3257semidirect
188. #466D283semidirect

Maximal subgroups

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

subgroupindex
#318270822
#318270682
#318267712
#318267672
#318267532
#318267442
#318267162
#318267092
#318266942
#318266792
#318266782
#318266642
#318266582
#318264912
#466×C2832
#3257283