Finite Group Databasebeta

← #49130103

Subgroups — #49130103

Order 36224.

470 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583642C211yesmaximal, characteristic
2#31826947C211yesmaximal, characteristic
3#31826941C211yesmaximal, characteristic, complemented
4#31826569C211yesmaximal, characteristic, complemented
5#31826568C211yesmaximal, characteristic, complemented
6#31826567C211yesmaximal, characteristic, complemented
7Q16×Dic283C211yesmaximal, characteristic, complemented
8C4×#17985382C211yesmaximal, characteristic, complemented
9C4×#17985379C211yesmaximal, characteristic, complemented
10#31826552C211yesmaximal, characteristic, complemented
11#31826504C211yesmaximal, characteristic, complemented
12#31826460C211yesmaximal, characteristic
13#103×D283C211yesmaximal, characteristic, complemented
14#31826422C211yesmaximal, characteristic, complemented
15#441×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×Q8×D283C2211yescharacteristic
18#22583642C418yescomplemented
19C2×#17985382C2211yescharacteristic
20C2×#17985381C2211yescharacteristic
21C2×#17985379C2211yescharacteristic
22C2×#17985375C2211yescharacteristic
23C2×C8×D283C2211yescharacteristic
24Q8×Dic283C2211yescharacteristic
25Q8×Dic283C2211yescharacteristic
26C4×Dic566—21no—
27C4×Dic566C2211yescharacteristic
28#22583575—21no—
29#22583575C2211yescharacteristic
30C4×D1132—21no—
31C4×D1132C2211yescharacteristic
32#22583572—21no—
33#22583572C2211yescharacteristic
34#22583568—21no—
35#22583568C2211yescharacteristic
36#22583567—21no—
37#22583567—21no—
38#22583567C2211yescharacteristic
39C4⋊C4×D283—21no—
40C4⋊C4×D283C2211yescharacteristic
41#22583544C2211yescharacteristic
42#22583543C2211yescharacteristic
43#22583541C2211yescharacteristic
44#22583535C2211yescharacteristic
45#22583534C2211yescharacteristic
46#22583534C2211yescharacteristic
47#22583533C2211yescharacteristic
48#22583532C2211yescharacteristic
49#22583530C2211yescharacteristic
50#22583520C2211yescharacteristic
51C4×C283⋊C8C2211yescharacteristic
52C8×Dic283C2211yescharacteristic
53C2×Q16×C283C2211yescharacteristic
54C4×Q8×C283C2211yescharacteristic
55C4×Q8×C283C2211yescharacteristic
56#106×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#103×C283C2211yescharacteristic
59#97×C283C2211yescharacteristic
60#17985393—22no—
61#17985393C2×C414yes—
62C2×Dic566—21no—
63C2×Dic566C2311yescharacteristic
64Q8×D283—22no—
65Q8×D283C2×C414yescomplemented
66C2×D1132—21no—
67C2×D1132C2311yescharacteristic
68C2×C4×D283—21no—
69C2×C4×D283—21no—
70C2×C4×D283—21no—
71C2×C4×D283—21no—
72C2×C4×D283—21no—
73C2×C4×D283C2311yescharacteristic
74#17985382C2×C414yescomplemented
75#17985381C2×C414yescomplemented
76#17985379C2×C414yescomplemented
77#17985375C2×C414yescomplemented
78C2×C283⋊C8C2311yescharacteristic
79C2×C283⋊C8C2311yescharacteristic
80C8×D283—22no—
81C4⋊Dic283—21no—
82C4⋊Dic283—21no—
83C4⋊Dic283C2311yescharacteristic
84C4⋊Dic283C2311yescharacteristic
85Dic283⋊C4—21no—
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88Dic283⋊C4D411yescharacteristic
89Dic283⋊C4D411yescharacteristic
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4D411yescharacteristic
94(C2×D283)⋊C4D411yescharacteristic
95C4×Dic283—21no—
96C4×Dic283—21no—
97C4×Dic283—21no—
98C4×Dic283—21no—
99C4×Dic283—21no—
100C4×Dic283C2311yescharacteristic
101C2×Q8×C283C2311yescharacteristic
102C2×Q8×C283C2311yescharacteristic
103Q16×C283C2×C414yescomplemented
104C2×C8×C283C2311yescharacteristic
105C2×C8×C283C2311yescharacteristic
106C4⋊C4×C283—21no—
107C4⋊C4×C283—21no—
108C4⋊C4×C283C2311yescharacteristic
109C4⋊C4×C283C2311yescharacteristic
110C42×C283—21no—
111C42×C283—21no—
112C42×C283C2311yescharacteristic
113C22×D283—21no—
114C22×D283C2×D411yescharacteristic
115Dic566—21no—
116Dic566—24no—
117Dic566C22×C412yes—
118D1132—24no—
119D1132—21no—
120D1132C22×C412yes—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283—21no—
124C2×Dic283C2×D411yescharacteristic
125C2×Dic283C2×D411yescharacteristic
126C2×Dic283C2×D411yescharacteristic
127C4×D283—24no—
128C4×D283—24no—
129C4×D283—81no—
130C4×D283—81no—
131C4×D283—81no—
132C4×D283C22×C412yes—
133C4×D283#4112yes—
134C283⋊C8—21no—
135C283⋊C8C22×C412yes—
136Q8×C283—21no—
137Q8×C283—21no—
138Q8×C283C22×C412yes—
139Q8×C283C22×C412yes—
140C2×C4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283C2×D411yescharacteristic
145C2×C4×C283C2×D411yescharacteristic
146C2×C4×C283C2411yescharacteristic
147C8×C283—21no—
148C8×C283C22×C412yes—
149C22×C283C22×D411yescharacteristic
150C2×D283—21no—
151C2×D283—21no—
152C2×D283—22no—
153C2×D283—41no—
154C2×D283—41no—
155C2×D283C4×D412yes—
156C4×C283—22no—
157C4×C283—22no—
158C4×C283—21no—
159C4×C283—21no—
160C4×C283—41no—
161C4×C283—41no—
162C4×C283C23×C411yescharacteristic
163C4×C283C2×#4111yescharacteristic
164Dic283—22no—
165Dic283—21no—
166Dic283—21no—
167Dic283—41no—
168Dic283—41no—
169Dic283C4×D412yes—
170C2×C283C2×C4×D411yescharacteristic
171C2×C283#57711yescharacteristic
172C2×C283#57811yescharacteristic
173D283—22no—
174D283—42no—
175C283#294711yescharacteristic, complemented, Sylow
176#2947—2831nomaximal, Sylow
177C2×#137—2831no—
178#520—2831no—
179#519—2831no—
180#441—2831no—
181#441D28311yescharacteristic, complemented
182#440—2831no—
183#440—2831no—
184C4×Q16—2831no—
185C4×Q16—2831no—
186C4×SD16—2831no—
187C4×SD16—2831no—
188#428—2831no—
189#416—2831no—
190C2×#103—2831no—
191#405—2831no—
192C2×#41—2831no—
193C22×Q8—2831no—
194#137—2838no—
195C2×Q16—2831no—
196C2×Q16C2×D28311yescharacteristic
197C2×SD16—2831no—
198C2×SD16—2831no—
199C2×M16—2831no—
200C22×C8—2831no—
201C4×Q8—2831no—
202C4×Q8—2831no—
203C4×Q8—2831no—
204C4×Q8—2831no—
205C4×Q8—5661no—
206C4×Q8—5661no—
207C4×Q8C2×D28311yescharacteristic
208C4×Q8C2×D28311yescharacteristic
209C4×D4—2831no—
210C4×D4—2831no—
211C4×D4—5661no—
212C4×D4—5661no—
213#117—2831no—
214#117—2831no—
215#117—5661no—
216#117—5661no—
217#117—5661no—
218C2×C4⋊C4—2831no—
219C2×C4⋊C4—5661no—
220#107—2831no—
221#107—2831no—
222#106—2831no—
223#106C2×D28311yescharacteristic
224#103—2831no—
225#103—2831no—
226#103—2831no—
227#103—2831no—
228#103C2×D28311yescharacteristic
229#103C2×D28311yescharacteristic
230#102—2831no—
231#102—2831no—
232#97—2831no—
233#97C2×D28311yescharacteristic
234C4×C8—2831no—
235C4×C8—2831no—
236#41—2834no—
237#41—5662no—
238C2×Q8—2834no—
239C2×Q8—2831no—
240C2×Q8—5661no—
241C2×Q8—5662no—
242C2×Q8C22×D28311yescharacteristic
243C2×Q8C22×D28311yescharacteristic
244C2×D4—2831no—
245C2×D4—5661no—
246C22×C4—2831no—
247C22×C4—5661no—
248C22×C4—5661no—
249C22×C4—5661no—
250C22×C4—5661no—
251C22×C4—5661no—
252Q16—2834no—
253Q16C4×D28314yescomplemented
254SD16—2834no—
255SD16—2834no—
256M16—2834no—
257C2×C8—2831no—
258C2×C8—2831no—
259C2×C8—5662no—
260C2×C8C22×D28311yescharacteristic
261C2×C8C22×D28311yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—2831no—
265C4⋊C4—2831no—
266C4⋊C4—2831no—
267C4⋊C4—2831no—
268C4⋊C4—5661no—
269C4⋊C4—5661no—
270C4⋊C4—5661no—
271C4⋊C4—5661no—
272C4⋊C4—5661no—
273C4⋊C4C22×D28311yescharacteristic
274C4⋊C4C22×D28311yescharacteristic
275C22⋊C4—2831no—
276C22⋊C4—2831no—
277C22⋊C4—5661no—
278C22⋊C4—5661no—
279C22⋊C4—5661no—
280C42—21no—
281C42—21no—
282C42—2831no—
283C42—5661no—
284C42—5661no—
285C42—5661no—
286C42—5661no—
287C42—5661no—
288C42C22×D28311yescharacteristic
289C23—2831no—
290C23—5661no—
291Q8—21no—
292Q8—21no—
293Q8—2832no—
294Q8—5664no—
295Q8—5661no—
296Q8C2×C4×D28312yes—
297Q8C2×C4×D28312yes—
298D4—2832no—
299D4—5664no—
300D4—5661no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—2831no—
306C2×C4—2832no—
307C2×C4—2832no—
308C2×C4—2831no—
309C2×C4—2831no—
310C2×C4—5664no—
311C2×C4—5664no—
312C2×C4—5661no—
313C2×C4—5661no—
314C2×C4—5661no—
315C2×C4—22641no—
316C2×C4—22641no—
317C2×C4—22641no—
318C2×C4D4×D28311yescharacteristic
319C2×C4D4×D28311yescharacteristic
320C2×C4C23×D28311yescharacteristic
321C8—21no—
322C8—2832no—
323C8—5661no—
324C8C2×C4×D28312yes—
325C22—2832no—
326C22—5661no—
327C22—5661no—
328C22—5662no—
329C22—11321no—
330C22—11321no—
331C22C2×D4×D28311yescharacteristic
332C4—21no—
333C4—21no—
334C4—22no—
335C4—22no—
336C4—41no—
337C4—41no—
338C4—2832no—
339C4—5661no—
340C4—5661no—
341C4—5662no—
342C4—11321no—
343C4—11321no—
344C4C22×C4×D28311yescharacteristic
345C4#41×D28311yescharacteristic
346C2—5662no—
347C2—11322no—
348C2C4×D4×D28311yescharacteristic
349C2#3182727411yescharacteristic
350C2#3182728111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutatorC4×C283C23×C4
FrattiniC2×C4C23×D283
Fitting#441×C283C2
socleC22×C283C22×D4
prime radicalC2×#17985393C22
cosocleC2×C4×C283C24
hypercenter#441D283
hypocenterC283#2947
LCSG ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
3. #31826941C2semidirect
4. #31826569C2semidirect
5. #31826568C2semidirect
6. #31826567C2semidirect
7. Q16×Dic283C2semidirect
8. C4×#17985382C2semidirect
9. C4×#17985379C2semidirect
10. #31826552C2semidirect
11. #31826504C2semidirect
13. #103×D283C2semidirect
14. #31826422C2semidirect
15. #441×C283C2semidirect
18. #22583642C4semidirect
65. Q8×D283C2×C4semidirect
74. #17985382C2×C4semidirect
75. #17985381C2×C4semidirect
76. #17985379C2×C4semidirect
77. #17985375C2×C4semidirect
103. Q16×C283C2×C4semidirect
175. C283#2947semidirect
181. #441D283semidirect
253. Q16C4×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836422
#318269472
#318269412
#318265692
#318265682
#318265672
Q16×Dic2832
C4×#179853822
C4×#179853792
#318265522
#318265042
#318264602
#103×D2832
#318264222
#441×C2832
#2947283