Finite Group Databasebeta

← #49133239

Subgroups — #49133239

Order 36224.

394 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827161C211yesmaximal, characteristic, complemented
2#31827120C211yesmaximal, characteristic, complemented
3#31826834C211yesmaximal, characteristic, complemented
4#31826807C211yesmaximal, characteristic, complemented
5#31826796C211yesmaximal, characteristic, complemented
6#31826766C211yesmaximal, characteristic, complemented
7#31826711C211yesmaximal, characteristic, complemented
8#31826694C211yesmaximal, characteristic, complemented
9#31826671C211yesmaximal, characteristic, complemented
10#31826612C211yesmaximal, characteristic, complemented
11#31826612C211yesmaximal, characteristic, complemented
12#31826578C211yesmaximal, characteristic, complemented
13#31826467C211yesmaximal, characteristic, complemented
14#31826462C211yesmaximal, characteristic, complemented
15#435×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C2×#17985392C2211yescharacteristic
18C2×#17985381C2211yescharacteristic
19C2×#17985381C2211yescharacteristic
20C2×D2264C2211yescharacteristic
21#22583610C2211yescharacteristic
22#22583605—21no—
23#22583602C2211yescharacteristic
24#22583592—21no—
25#22583592—21no—
26#22583592—21no—
27#22583589C2211yescharacteristic
28#22583589C2211yescharacteristic
29#22583584C2211yescharacteristic
30#22583584C2211yescharacteristic
31#22583582—21no—
32#22583581—21no—
33C4×D1132C2211yescharacteristic
34C4×D1132C2211yescharacteristic
35(C22⋊D283)⋊C4—21no—
36#22583569C2211yescharacteristic
37C2×C4⋊Dic283C2211yescharacteristic
38C4⋊C4×D283—21no—
39#22583544C2211yescharacteristic
40#22583542C2211yescharacteristic
41#22583542C2211yescharacteristic
42#22583535C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583535C2211yescharacteristic
45#22583535C2211yescharacteristic
46#22583535C2211yescharacteristic
47#22583535C2211yescharacteristic
48#22583532C2211yescharacteristic
49#22583532C2211yescharacteristic
50#22583532C2211yescharacteristic
51#22583532C2211yescharacteristic
52C2×M16×C283C2211yescharacteristic
53C22×C8×C283C2211yescharacteristic
54C4×D4×C283C2211yescharacteristic
55C4⋊C8×C283C2211yescharacteristic
56C22⋊C8×C283C2211yescharacteristic
57C22⋊C8×C283C2211yescharacteristic
58#97×C283C2211yescharacteristic
59#17985392—22no—
60#17985392—22no—
61#17985392—41no—
62#17985392—41no—
63C2×Dic566C2311yescharacteristic
64C2×Dic566C2311yescharacteristic
65C2×D1132C2311yescharacteristic
66C2×D1132C2311yescharacteristic
67C2×C22⋊D283—21no—
68C2×C22⋊D283—21no—
69C2×C22⋊D283—21no—
70C2×C22⋊D283—21no—
71C22×Dic283—21no—
72C2×C4×D283—21no—
73C2×C4×D283—21no—
74C2×C4×D283—21no—
75C2×C4×D283—21no—
76#17985381—41no—
77#17985381—41no—
78D2264—22no—
79C4⋊Dic283—21no—
80C4⋊Dic283—21no—
81C4⋊Dic283—21no—
82C4⋊Dic283C2311yescharacteristic
83C4⋊Dic283C2311yescharacteristic
84C4⋊Dic283C2311yescharacteristic
85C4⋊Dic283C2311yescharacteristic
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88Dic283⋊C4—21no—
89Dic283⋊C4—21no—
90C22⋊Dic283—21no—
91C22⋊Dic283—21no—
92C22⋊Dic283—21no—
93(C2×D283)⋊C4—21no—
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4—21no—
96(C2×D283)⋊C4—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
111C22×D283—21no—
112C22×D283—21no—
113Dic566—21no—
114Dic566—21no—
115Dic566—21no—
116Dic566—21no—
117D1132—21no—
118D1132—21no—
119D1132—21no—
120D1132#4112yes—
121C22⋊D283—42no—
122C22⋊D283—42no—
123C22⋊D283—42no—
124C22⋊D283—81no—
125C2×Dic283—21no—
126C2×Dic283—21no—
127C2×Dic283—21no—
128C2×Dic283—21no—
129C2×Dic283—21no—
130C2×Dic283—21no—
131C2×Dic283—81no—
132C4×D283—42no—
133C4×D283—42no—
134C4×D283—42no—
135C4×D283—81no—
136C23×C283C2×D411yescharacteristic
137C23×C283C2×D411yescharacteristic
138D4×C283—41no—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283—21no—
143C2×C4×C283C2×D411yescharacteristic
144C2×C4×C283C2×D411yescharacteristic
145C2×C4×C283C2×D411yescharacteristic
146C2×C4×C283C2×D411yescharacteristic
147C2×C4×C283C2411yescharacteristic
148C8×C283—21no—
149C8×C283—21no—
150C8×C283—21no—
151C8×C283—21no—
152C22×C283—21no—
153C22×C283—21no—
154C22×C283—21no—
155C22×C283—21no—
156C22×C283—21no—
157C22×C283—21no—
158C22×C283C22×D411yescharacteristic
159C2×D283—22no—
160C2×D283—41no—
161C2×D283—41no—
162C2×D283—41no—
163C2×D283—41no—
164C2×D283—41no—
165C4×C283—21no—
166C4×C283—21no—
167C4×C283—21no—
168C4×C283—21no—
169C4×C283C2×#4111yescharacteristic
170C4×C283H(5,𝔽2)11yescharacteristic
171Dic283—41no—
172Dic283—41no—
173Dic283—41no—
174Dic283—41no—
175Dic283—41no—
176Dic283—41no—
177C2×C283—41no—
178C2×C283—41no—
179C2×C283#54611yescharacteristic
180C2×C283#57511yescharacteristic
181C2×C283#57711yescharacteristic
182D283—42no—
183D283—81no—
184C283#330711yescharacteristic, complemented, Sylow
185#3307—2831nomaximal, Sylow
186#553—2831no—
187#547—2831no—
188#491—2831no—
189#485—2831no—
190#483—2831no—
191#478—2831no—
192#468—2831no—
193#465—2831no—
194#461—2831no—
195#449—2831no—
196#449—2831no—
197#442—2831no—
198#435D28311yescharacteristic, complemented
199#417—2831no—
200#416—2831no—
201C2×#41—2831no—
202C2×#41—2831no—
203C2×SD16—2831no—
204C2×SD16—2831no—
205C2×D8—2831no—
206C2×M16C2×D28311yescharacteristic
207C22×C8C2×D28311yescharacteristic
208C4⋊Q8—2831no—
209#126—5661no—
210#125—2831no—
211#123—5661no—
212#123—5661no—
213#123—5661no—
214C22⋊Q8—2831no—
215C22⋊Q8—2831no—
216#121—2831no—
217#121—2831no—
218#121—5661no—
219#121—5661no—
220C4×D4—2831no—
221C4×D4—2831no—
222C4×D4—5661no—
223C4×D4C2×D28311yescharacteristic
224#117—2831no—
225C2×C4⋊C4—2831no—
226C2×C4⋊C4—5661no—
227#107—2831no—
228#106—2831no—
229#106—2831no—
230C4⋊C8C2×D28311yescharacteristic
231#103—2831no—
232#103—2831no—
233#103—2831no—
234#103—2831no—
235#103—2831no—
236#103—2831no—
237#102—2831no—
238#102—2831no—
239#102—2831no—
240#102—2831no—
241C22⋊C8C2×D28311yescharacteristic
242C22⋊C8C2×D28311yescharacteristic
243#97C2×D28311yescharacteristic
244#41—5662no—
245#41—5662no—
246#41—11321no—
247#41—11321no—
248C2×Q8—2831no—
249C2×Q8—2831no—
250C2×D4—2831no—
251C2×D4—2831no—
252C2×D4—5661no—
253C2×D4—5661no—
254C2×D4—5661no—
255C2×D4—5661no—
256C2×D4D113211yescharacteristic
257C22×C4—5661no—
258C22×C4—5661no—
259C22×C4—5661no—
260C22×C4—5661no—
261C22×C4—5661no—
262C22×C4C22×D28311yescharacteristic
263C22×C4C22×D28311yescharacteristic
264SD16—11321no—
265SD16—11321no—
266D8—5662no—
267M16—41no—
268C2×C8—41no—
269C2×C8C22×D28311yescharacteristic
270C2×C8C22×D28311yescharacteristic
271C2×C8C22×D28311yescharacteristic
272C2×C8C22×D28311yescharacteristic
273C4⋊C4—2831no—
274C4⋊C4—2831no—
275C4⋊C4—2831no—
276C4⋊C4—2831no—
277C4⋊C4—5661no—
278C4⋊C4—5661no—
279C4⋊C4—5661no—
280C4⋊C4—5661no—
281C4⋊C4—5661no—
282C4⋊C4—5661no—
283C4⋊C4—5661no—
284C4⋊C4D113211yescharacteristic
285C22⋊C4—5661no—
286C22⋊C4—5661no—
287C22⋊C4—5661no—
288C22⋊C4—5661no—
289C22⋊C4—5661no—
290C22⋊C4—5661no—
291C22⋊C4—5661no—
292C22⋊C4D113211yescharacteristic
293C22⋊C4D113211yescharacteristic
294C42—5661no—
295C42C22×D28311yescharacteristic
296C23—5661no—
297C23—5661no—
298C23C2×D113211yescharacteristic
299C23C2×D113211yescharacteristic
300Q8—5661no—
301Q8—5661no—
302Q8—5661no—
303Q8—5661no—
304D4—41no—
305D4—2832no—
306D4—5661no—
307D4—5661no—
308D4—5661no—
309D4—11322no—
310D4—11322no—
311D4—11322no—
312D4—22641no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—5661no—
318C2×C4—5661no—
319C2×C4—5661no—
320C2×C4—5661no—
321C2×C4—5661no—
322C2×C4—5661no—
323C2×C4—11322no—
324C2×C4—11322no—
325C2×C4—11322no—
326C2×C4—22641no—
327C2×C4—22641no—
328C2×C4C2×D113211yescharacteristic
329C2×C4C2×D113211yescharacteristic
330C2×C4C2×D113211yescharacteristic
331C2×C4C2×D113211yescharacteristic
332C2×C4C23×D28311yescharacteristic
333C8—21no—
334C8—21no—
335C8—21no—
336C8—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—5662no—
344C22—11321no—
345C22—11321no—
346C22—11321no—
347C22—11321no—
348C22—11321no—
349C22C22×D113211yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—11321no—
355C4—11321no—
356C4—11321no—
357C4—11321no—
358C4—11321no—
359C4—11321no—
360C4#41×D28311yescharacteristic
361C4#2258365511yescharacteristic
362C2—41no—
363C2—41no—
364C2—11322no—
365C2—22641no—
366C2#3182711011yescharacteristic
367C2#3182726511yescharacteristic
368C2#3182727711yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#435×C283C2
socleC22×C283C22×D4
hypercenter#435D283
hypocenterC283#3307
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
1. #31827161C2semidirect
2. #31827120C2semidirect
3. #31826834C2semidirect
4. #31826807C2semidirect
5. #31826796C2semidirect
6. #31826766C2semidirect
7. #31826711C2semidirect
8. #31826694C2semidirect
9. #31826671C2semidirect
10. #31826612C2semidirect
11. #31826612C2semidirect
12. #31826578C2semidirect
13. #31826467C2semidirect
14. #31826462C2semidirect
15. #435×C283C2semidirect
184. C283#3307semidirect
198. #435D283semidirect

Maximal subgroups

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

subgroupindex
#318271612
#318271202
#318268342
#318268072
#318267962
#318267662
#318267112
#318266942
#318266712
#318266122
#318265782
#318264672
#318264622
#435×C2832
#3307283