Finite Group Databasebeta

← #49133314

Subgroups — #49133314

Order 36224.

376 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827155C211yesmaximal, characteristic
2D4×Dic566C211yesmaximal, characteristic
3#31826834C211yesmaximal, characteristic, complemented
4#31826807C211yesmaximal, characteristic, complemented
5#31826796C211yesmaximal, characteristic, complemented
6#31826773C211yesmaximal, characteristic, complemented
7#31826723C211yesmaximal, characteristic, complemented
8#31826706C211yesmaximal, characteristic, complemented
9#31826676C211yesmaximal, characteristic, complemented
10#31826623C211yesmaximal, characteristic, complemented
11#31826623C211yesmaximal, characteristic, complemented
12#31826573C211yesmaximal, characteristic, complemented
13#31826475C211yesmaximal, characteristic, complemented
14C2×#22583535C211yesmaximal, characteristic, complemented
15#435×C283C211yesmaximal, characteristic
16C22×Dic566C2211yescharacteristic
17C22×Dic566C2211yescharacteristic
18C2×Dic1132C2211yescharacteristic
19C2×Dic1132C2211yescharacteristic
20C2×Dic1132C2211yescharacteristic
21#22583610C2211yescharacteristic
22#22583609—21no—
23#22583603—21no—
24#22583602C2211yescharacteristic
25#22583600—21no—
26#22583591—21no—
27#22583589C2211yescharacteristic
28#22583589C2211yescharacteristic
29#22583589C2211yescharacteristic
30#22583589C2211yescharacteristic
31#22583587—21no—
32#22583587—21no—
33C4×Dic566C2211yescharacteristic
34C4×Dic566C2211yescharacteristic
35D4×Dic283—21no—
36#22583569C2211yescharacteristic
37#22583566—21no—
38C2×C4⋊Dic283C2211yescharacteristic
39#22583544C2211yescharacteristic
40#22583542C2211yescharacteristic
41#22583542C2211yescharacteristic
42#22583535C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583535C2211yescharacteristic
45#22583535C2211yescharacteristic
46#22583535C2211yescharacteristic
47#22583535C2211yescharacteristic
48#22583535C2211yescharacteristic
49#22583535C2211yescharacteristic
50#22583535C2211yescharacteristic
51#22583535C2211yescharacteristic
52C2×M16×C283C2211yescharacteristic
53C22×C8×C283C2211yescharacteristic
54C4×D4×C283C2211yescharacteristic
55C4⋊C8×C283C2211yescharacteristic
56C22⋊C8×C283C2211yescharacteristic
57C22⋊C8×C283C2211yescharacteristic
58#97×C283C2211yescharacteristic
59C2×Dic566—22no—
60C2×Dic566—22no—
61C2×Dic566—21no—
62C2×Dic566—21no—
63C2×Dic566—41no—
64C2×Dic566—41no—
65C2×Dic566C2311yescharacteristic
66C2×Dic566C2311yescharacteristic
67C2×Dic566C2311yescharacteristic
68C2×Dic566C2311yescharacteristic
69C22×Dic283—21no—
70C22×Dic283—21no—
71C22×Dic283—21no—
72Dic1132—22no—
73Dic1132—41no—
74Dic1132—41no—
75C4⋊Dic283—21no—
76C4⋊Dic283—21no—
77C4⋊Dic283—21no—
78C4⋊Dic283C2311yescharacteristic
79C4⋊Dic283C2311yescharacteristic
80C4⋊Dic283C2311yescharacteristic
81C4⋊Dic283C2311yescharacteristic
82Dic283⋊C4—21no—
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88Dic283⋊C4—21no—
89Dic283⋊C4—21no—
90C22⋊Dic283—21no—
91C22⋊Dic283—21no—
92C22⋊Dic283—21no—
93C22⋊Dic283—21no—
94C22⋊Dic283—21no—
95C4×Dic283—21no—
96C4×Dic283—21no—
97C4×Dic283—21no—
98C2×D4×C283D411yescharacteristic
99C22×C4×C283C2311yescharacteristic
100C22×C4×C283C2311yescharacteristic
101M16×C283—41no—
102C2×C8×C283—41no—
103C2×C8×C283C2311yescharacteristic
104C2×C8×C283C2311yescharacteristic
105C2×C8×C283C2311yescharacteristic
106C2×C8×C283C2311yescharacteristic
107C4⋊C4×C283D411yescharacteristic
108C22⋊C4×C283D411yescharacteristic
109C22⋊C4×C283D411yescharacteristic
110C42×C283C2311yescharacteristic
111Dic566—21no—
112Dic566—21no—
113Dic566—21no—
114Dic566—21no—
115Dic566—21no—
116Dic566—21no—
117Dic566—21no—
118Dic566—42no—
119Dic566—42no—
120Dic566#4112yes—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283—21no—
124C2×Dic283—21no—
125C2×Dic283—21no—
126C2×Dic283—21no—
127C2×Dic283—21no—
128C2×Dic283—21no—
129C2×Dic283—42no—
130C2×Dic283—42no—
131C2×Dic283—42no—
132C23×C283C2×D411yescharacteristic
133C23×C283C2×D411yescharacteristic
134D4×C283—22no—
135C2×C4×C283—21no—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283C2×D411yescharacteristic
140C2×C4×C283C2×D411yescharacteristic
141C2×C4×C283C2×D411yescharacteristic
142C2×C4×C283C2×D411yescharacteristic
143C2×C4×C283C2411yescharacteristic
144C8×C283—21no—
145C8×C283—21no—
146C8×C283—21no—
147C8×C283—21no—
148C22×C283—21no—
149C22×C283—21no—
150C22×C283—21no—
151C22×C283—21no—
152C22×C283—21no—
153C22×C283#13712yes—
154C22×C283C22×D411yescharacteristic
155C4×C283—21no—
156C4×C283—21no—
157C4×C283—21no—
158C4×C283—21no—
159C4×C283C2×#4111yescharacteristic
160C4×C283H(5,𝔽2)11yescharacteristic
161Dic283—22no—
162Dic283—41no—
163Dic283—41no—
164Dic283—41no—
165Dic283—41no—
166Dic283—41no—
167Dic283—41no—
168Dic283—41no—
169C2×C283—22no—
170C2×C283—41no—
171C2×C283#54611yescharacteristic
172C2×C283C2×#13711yescharacteristic
173C2×C283#57811yescharacteristic
174C283#331211yescharacteristic, complemented, Sylow
175#3312—2831nomaximal, Sylow
176#552—2831no—
177D4×Q8—2831no—
178#491—2831no—
179#485—2831no—
180#483—2831no—
181#479—2831no—
182#470—2831no—
183#467—2831no—
184#462—2831no—
185#451—2831no—
186#451—2831no—
187#441—2831no—
188#435D28311yescharacteristic
189#419—2831no—
190C2×#103—2831no—
191C22×Q8—2831no—
192C22×Q8—2831no—
193C2×Q16—2831no—
194C2×Q16—2831no—
195C2×Q16—2831no—
196C2×M16C2×D28311yescharacteristic
197C22×C8C2×D28311yescharacteristic
198C4⋊Q8—2831no—
199C4⋊Q8—5661no—
200#126—5661no—
201#125—2831no—
202#125—5661no—
203#123—5661no—
204C22⋊Q8—2831no—
205C22⋊Q8—2831no—
206C22⋊Q8—2831no—
207C22⋊Q8—2831no—
208C22⋊Q8—5661no—
209C22⋊Q8—5661no—
210C4×Q8—2831no—
211C4×Q8—2831no—
212C4×D4—5661no—
213C4×D4C2×D28311yescharacteristic
214#117—2831no—
215#117—5661no—
216C2×C4⋊C4—2831no—
217#107—2831no—
218#106—2831no—
219#106—2831no—
220C4⋊C8C2×D28311yescharacteristic
221#103—2831no—
222#103—2831no—
223#103—2831no—
224#103—2831no—
225#103—2831no—
226#103—2831no—
227#103—2831no—
228#103—2831no—
229#103—2831no—
230#103—2831no—
231C22⋊C8C2×D28311yescharacteristic
232C22⋊C8C2×D28311yescharacteristic
233#97C2×D28311yescharacteristic
234C2×Q8—2831no—
235C2×Q8—2831no—
236C2×Q8—2831no—
237C2×Q8—2831no—
238C2×Q8—5662no—
239C2×Q8—5662no—
240C2×Q8—5661no—
241C2×Q8—5661no—
242C2×Q8—11321no—
243C2×Q8—11321no—
244C2×D4D113211yescharacteristic
245C22×C4—5661no—
246C22×C4—5661no—
247C22×C4—5661no—
248C22×C4C22×D28311yescharacteristic
249C22×C4C22×D28311yescharacteristic
250Q16—5662no—
251Q16—11321no—
252Q16—11321no—
253M16—41no—
254C2×C8—41no—
255C2×C8C22×D28311yescharacteristic
256C2×C8C22×D28311yescharacteristic
257C2×C8C22×D28311yescharacteristic
258C2×C8C22×D28311yescharacteristic
259C4⋊C4—2831no—
260C4⋊C4—2831no—
261C4⋊C4—2831no—
262C4⋊C4—2831no—
263C4⋊C4—5661no—
264C4⋊C4—5661no—
265C4⋊C4—5661no—
266C4⋊C4—5661no—
267C4⋊C4—5661no—
268C4⋊C4—5661no—
269C4⋊C4—5661no—
270C4⋊C4—5661no—
271C4⋊C4—5661no—
272C4⋊C4—5661no—
273C4⋊C4—5661no—
274C4⋊C4D113211yescharacteristic
275C22⋊C4—5661no—
276C22⋊C4—5661no—
277C22⋊C4—5661no—
278C22⋊C4—5661no—
279C22⋊C4—5661no—
280C22⋊C4D113211yescharacteristic
281C22⋊C4D113211yescharacteristic
282C42—5661no—
283C42—5661no—
284C42—5661no—
285C42C22×D28311yescharacteristic
286C23C2×D113211yescharacteristic
287C23C2×D113211yescharacteristic
288Q8—2832no—
289Q8—5661no—
290Q8—5661no—
291Q8—5661no—
292Q8—5661no—
293Q8—5661no—
294Q8—5661no—
295Q8—5661no—
296Q8—11322no—
297Q8—11322no—
298D4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—5661no—
304C2×C4—5661no—
305C2×C4—5661no—
306C2×C4—5661no—
307C2×C4—5661no—
308C2×C4—5661no—
309C2×C4—5661no—
310C2×C4—5661no—
311C2×C4—11322no—
312C2×C4—11322no—
313C2×C4—11322no—
314C2×C4C2×D113211yescharacteristic
315C2×C4C2×D113211yescharacteristic
316C2×C4C2×D113211yescharacteristic
317C2×C4C2×D113211yescharacteristic
318C2×C4C23×D28311yescharacteristic
319C8—21no—
320C8—21no—
321C8—21no—
322C8—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22#2258364312yes—
329C22C22×D113211yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—5662no—
335C4—11321no—
336C4—11321no—
337C4—11321no—
338C4—11321no—
339C4—11321no—
340C4—11321no—
341C4—11321no—
342C4#41×D28311yescharacteristic
343C4#2258365511yescharacteristic
344C2—22no—
345C2—41no—
346C2#3182711011yescharacteristic
347C2C2×#2258364311yescharacteristic
348C2#3182728211yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#435×C283C2
socleC22×C283C22×D4
prime radicalC2×D4×C283D4
hypercenter#435D283
hypocenterC283#3312
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
3. #31826834C2semidirect
4. #31826807C2semidirect
5. #31826796C2semidirect
6. #31826773C2semidirect
7. #31826723C2semidirect
8. #31826706C2semidirect
9. #31826676C2semidirect
10. #31826623C2semidirect
11. #31826623C2semidirect
12. #31826573C2semidirect
13. #31826475C2semidirect
14. C2×#22583535C2semidirect
174. C283#3312semidirect

Maximal subgroups

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

subgroupindex
#318271552
D4×Dic5662
#318268342
#318268072
#318267962
#318267732
#318267232
#318267062
#318266762
#318266232
#318265732
#318264752
C2×#225835352
#435×C2832
#3312283