Finite Group Databasebeta

← #49130083

Subgroups — #49130083

Order 36224.

484 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
1C2×#22583639C211yesmaximal, characteristic
2C4×#17985391C211yesmaximal, characteristic
3C4×Q8×D283C211yesmaximal, characteristic, complemented
4#31826573C211yesmaximal, characteristic, complemented
5#31826570C211yesmaximal, characteristic, complemented
6#31826565C211yesmaximal, characteristic, complemented
7#31826559C211yesmaximal, characteristic, complemented
8#31826557C211yesmaximal, characteristic, complemented
9#31826556C211yesmaximal, characteristic, complemented
10SD16×Dic283C211yesmaximal, characteristic, complemented
11#31826506C211yesmaximal, characteristic, complemented
12#31826472C211yesmaximal, characteristic, complemented
13#31826463C211yesmaximal, characteristic
14#31826417C211yesmaximal, characteristic, complemented
15#440×C283C211yesmaximal, characteristic, complemented
16C2×#17985391C2211yescharacteristic
17C2×Q8×D283C2211yescharacteristic
18#22583639C418yescomplemented
19C2×Dic1132C2211yescharacteristic
20C2×#17985382C2211yescharacteristic
21C2×#17985380C2211yescharacteristic
22C2×#17985375C2211yescharacteristic
23C2×#17985375C2211yescharacteristic
24Q8×Dic283C2211yescharacteristic
25C4×Dic566—21no—
26C4×Dic566C2211yescharacteristic
27C4×Dic566C2211yescharacteristic
28#22583575—21no—
29#22583575C2211yescharacteristic
30#22583575C2211yescharacteristic
31D4×Dic283C2211yescharacteristic
32C4×C22⋊D283—21no—
33(C22⋊D283)⋊C4—21no—
34#22583568C2211yescharacteristic
35#22583566—21no—
36C4⋊C4×D283—21no—
37C4⋊C4×D283C2211yescharacteristic
38C2×C4×Dic283—21no—
39C42×D283—21no—
40C42×D283C2211yescharacteristic
41#22583543C2211yescharacteristic
42#22583542C2211yescharacteristic
43#22583541C2211yescharacteristic
44#22583535C2211yescharacteristic
45#22583535C2211yescharacteristic
46#22583534C2211yescharacteristic
47#22583533C2211yescharacteristic
48#22583533C2211yescharacteristic
49#22583531C2211yescharacteristic
50#22583521C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52C8×Dic283C2211yescharacteristic
53C2×SD16×C283C2211yescharacteristic
54C4×Q8×C283C2211yescharacteristic
55C4×D4×C283C2211yescharacteristic
56#107×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#102×C283C2211yescharacteristic
59#97×C283C2211yescharacteristic
60#17985391—22no—
61#17985391C2×C414yes—
62C2×Dic566—21no—
63C2×Dic566C2311yescharacteristic
64C2×Dic566C2311yescharacteristic
65Q8×D283—22no—
66Q8×D283C2×C414yescomplemented
67C2×C22⋊D283—21no—
68C22×Dic283—21no—
69C22×Dic283—21no—
70C2×C4×D283—21no—
71C2×C4×D283—21no—
72C2×C4×D283D411yescharacteristic
73C2×C4×D283D411yescharacteristic
74C2×C4×D283C2311yescharacteristic
75Dic1132C2×C414yescomplemented
76#17985382C2×C414yescomplemented
77#17985380C2×C414yescomplemented
78#17985375—22no—
79#17985375C2×C414yescomplemented
80C2×C283⋊C8C2311yescharacteristic
81C2×C283⋊C8C2311yescharacteristic
82C4⋊Dic283—21no—
83C4⋊Dic283C2311yescharacteristic
84C4⋊Dic283C2311yescharacteristic
85Dic283⋊C4—21no—
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88Dic283⋊C4—21no—
89Dic283⋊C4—21no—
90C22⋊Dic283—21no—
91(C2×D283)⋊C4—21no—
92C4×Dic283—21no—
93C4×Dic283—21no—
94C4×Dic283—21no—
95C4×Dic283—21no—
96C4×Dic283—21no—
97C4×Dic283—21no—
98C4×Dic283D411yescharacteristic
99C4×Dic283D411yescharacteristic
100C4×Dic283C2311yescharacteristic
101C2×Q8×C283C2311yescharacteristic
102C2×D4×C283C2311yescharacteristic
103C22×C4×C283—21no—
104SD16×C283C2×C414yescomplemented
105C2×C8×C283C2311yescharacteristic
106C2×C8×C283C2311yescharacteristic
107C4⋊C4×C283—21no—
108C4⋊C4×C283C2311yescharacteristic
109C4⋊C4×C283C2311yescharacteristic
110C22⋊C4×C283—21no—
111C42×C283—21no—
112C42×C283C2311yescharacteristic
113C22×D283C2×D411yescharacteristic
114Dic566—21no—
115Dic566—21no—
116Dic566—24no—
117Dic566C22×C412yes—
118Dic566C22×C412yes—
119C22⋊D283—24no—
120C2×Dic283—21no—
121C2×Dic283—21no—
122C2×Dic283—24no—
123C2×Dic283—21no—
124C2×Dic283—21no—
125C2×Dic283—42no—
126C2×Dic283C2×D411yescharacteristic
127C2×Dic283C2×D411yescharacteristic
128C2×Dic283C2×D411yescharacteristic
129C4×D283—24no—
130C4×D283—22no—
131C4×D283—41no—
132C4×D283—42no—
133C4×D283C22×C412yes—
134C4×D283#4112yes—
135C283⋊C8—21no—
136C283⋊C8C22×C412yes—
137C23×C283—21no—
138Q8×C283—21no—
139Q8×C283C22×C412yes—
140D4×C283—21no—
141D4×C283C22×C412yes—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—42no—
146C2×C4×C283C2×D411yescharacteristic
147C2×C4×C283C2×D411yescharacteristic
148C2×C4×C283C2411yescharacteristic
149C8×C283—21no—
150C8×C283C22×C412yes—
151C22×C283—22no—
152C22×C283—41no—
153C22×C283—41no—
154C22×C283C22×D411yescharacteristic
155C2×D283—21no—
156C2×D283—21no—
157C2×D283C4×D412yes—
158C4×C283—22no—
159C4×C283—21no—
160C4×C283—21no—
161C4×C283—41no—
162C4×C283—41no—
163C4×C283C23×C411yescharacteristic
164C4×C283C2×#4111yescharacteristic
165Dic283—22no—
166Dic283—22no—
167Dic283—21no—
168Dic283—41no—
169Dic283—41no—
170Dic283C4×D412yes—
171Dic283#13712yescomplemented
172C2×C283—42no—
173C2×C283C2×C4×D411yescharacteristic
174C2×C283C2×#13711yescharacteristic
175C2×C283#57511yescharacteristic
176D283—22no—
177C283C4×#13711yescharacteristic, complemented, Sylow
178C4×#137—2831nomaximal, Sylow
179C2×#137—2831no—
180C4×#41—2831no—
181C2×C4×Q8—2831no—
182#441—2831no—
183#441—2831no—
184#440—2831no—
185#440D28311yescharacteristic, complemented
186C4×Q16—2831no—
187C4×Q16—2831no—
188C4×SD16—2831no—
189C4×SD16—2831no—
190#428—2831no—
191#419—2831no—
192#417—2831no—
193C4×M16—2831no—
194C2×#41—2831no—
195C22×Q8—2831no—
196#137—2838no—
197C2×Q16—2831no—
198C2×Q16—2831no—
199C2×SD16—2831no—
200C2×SD16C2×D28311yescharacteristic
201C2×M16—2831no—
202C2×M16—2831no—
203C4×Q8—2831no—
204C4×Q8—2831no—
205C4×Q8—2831no—
206C4×Q8—2831no—
207C4×Q8—2831no—
208C4×Q8—5661no—
209C4×Q8—5661no—
210C4×Q8C2×D28311yescharacteristic
211C4×D4—2831no—
212C4×D4—5661no—
213C4×D4—5661no—
214C4×D4C2×D28311yescharacteristic
215#117—2831no—
216#117—5661no—
217C2×C4⋊C4—2831no—
218C2×C4⋊C4—5661no—
219C2×C42—2831no—
220C2×C42—5661no—
221C2×C42—5661no—
222#107—2831no—
223#107C2×D28311yescharacteristic
224#106—2831no—
225#106—2831no—
226#103—2831no—
227#103—2831no—
228#103—2831no—
229#103—2831no—
230#103—2831no—
231#103C2×D28311yescharacteristic
232#102—2831no—
233#102C2×D28311yescharacteristic
234#97—2831no—
235#97C2×D28311yescharacteristic
236C4×C8—2831no—
237C4×C8—2831no—
238#41—2834no—
239#41—5662no—
240C2×Q8—2834no—
241C2×Q8—2831no—
242C2×Q8—2831no—
243C2×Q8—5661no—
244C2×Q8—5662no—
245C2×Q8C22×D28311yescharacteristic
246C2×D4—5661no—
247C2×D4C22×D28311yescharacteristic
248C22×C4—21no—
249C22×C4—2831no—
250C22×C4—2831no—
251C22×C4—2831no—
252C22×C4—5661no—
253C22×C4—5661no—
254C22×C4—5661no—
255C22×C4—5661no—
256Q16—2834no—
257Q16—2834no—
258SD16—2834no—
259SD16C4×D28314yescomplemented
260M16—2834no—
261M16—5662no—
262C2×C8—2831no—
263C2×C8—2831no—
264C2×C8C22×D28311yescharacteristic
265C2×C8C22×D28311yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—2831no—
268C4⋊C4—2831no—
269C4⋊C4—5661no—
270C4⋊C4—5661no—
271C4⋊C4—5661no—
272C4⋊C4—5661no—
273C4⋊C4—5661no—
274C4⋊C4—5661no—
275C4⋊C4C22×D28311yescharacteristic
276C4⋊C4C22×D28311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—5661no—
279C22⋊C4—5661no—
280C42—21no—
281C42—2831no—
282C42—2831no—
283C42—2831no—
284C42—5661no—
285C42—5661no—
286C42—5661no—
287C42—5661no—
288C42—5661no—
289C42—5661no—
290C42C22×D28311yescharacteristic
291C23—21no—
292C23—2831no—
293Q8—21no—
294Q8—2832no—
295Q8—2832no—
296Q8—5664no—
297Q8—5661no—
298Q8—5661no—
299Q8C2×C4×D28312yes—
300D4—21no—
301D4—5664no—
302D4C2×C4×D28312yes—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—42no—
307C2×C4—2831no—
308C2×C4—2831no—
309C2×C4—2832no—
310C2×C4—2832no—
311C2×C4—2831no—
312C2×C4—5662no—
313C2×C4—5664no—
314C2×C4—5664no—
315C2×C4—5661no—
316C2×C4—5661no—
317C2×C4—5661no—
318C2×C4—5661no—
319C2×C4—11321no—
320C2×C4—11322no—
321C2×C4—11322no—
322C2×C4D4×D28311yescharacteristic
323C2×C4D4×D28311yescharacteristic
324C2×C4C23×D28311yescharacteristic
325C8—21no—
326C8—2832no—
327C8—5661no—
328C8C2×C4×D28312yes—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—2832no—
333C22—5661no—
334C22—5661no—
335C22C2×D4×D28311yescharacteristic
336C4—21no—
337C4—21no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—2832no—
342C4—2832no—
343C4—5661no—
344C4—5662no—
345C4—5662no—
346C4—11321no—
347C4—11321no—
348C4C22×C4×D28311yescharacteristic
349C4#41×D28311yescharacteristic
350C2—42no—
351C2—5662no—
352C2C4×D4×D28311yescharacteristic
353C2#137×D28311yescharacteristic
354C2#3182726111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutatorC4×C283C23×C4
FrattiniC2×C4C23×D283
Fitting#440×C283C2
socleC22×C283C22×D4
prime radicalC2×#17985391C22
cosocleC2×C4×C283C24
hypercenter#440D283
hypocenterC283C4×#137
LCSG ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
3. C4×Q8×D283C2semidirect
4. #31826573C2semidirect
5. #31826570C2semidirect
6. #31826565C2semidirect
7. #31826559C2semidirect
8. #31826557C2semidirect
9. #31826556C2semidirect
10. SD16×Dic283C2semidirect
11. #31826506C2semidirect
12. #31826472C2semidirect
14. #31826417C2semidirect
15. #440×C283C2semidirect
18. #22583639C4semidirect
66. Q8×D283C2×C4semidirect
75. Dic1132C2×C4semidirect
76. #17985382C2×C4semidirect
77. #17985380C2×C4semidirect
79. #17985375C2×C4semidirect
104. SD16×C283C2×C4semidirect
171. Dic283#137semidirect
177. C283C4×#137semidirect
185. #440D283semidirect
259. SD16C4×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836392
C4×#179853912
C4×Q8×D2832
#318265732
#318265702
#318265652
#318265592
#318265572
#318265562
SD16×Dic2832
#318265062
#318264722
#318264632
#318264172
#440×C2832
C4×#137283