Finite Group Databasebeta

← #49131494

Subgroups — #49131494

Order 36224.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827087C211yesmaximal, characteristic
2#31826941C211yesmaximal, characteristic, complemented
3#31826805C211yesmaximal, characteristic, complemented
4#31826791C211yesmaximal, characteristic
5#31826758C211yesmaximal, characteristic, complemented
6#31826749C211yesmaximal, characteristic, complemented
7#31826690C211yesmaximal, characteristic, complemented
8#31826689C211yesmaximal, characteristic, complemented
9#31826619C211yesmaximal, characteristic, complemented
10#31826605C211yesmaximal, characteristic
11#31826567C211yesmaximal, characteristic, complemented
12C4×#17985382C211yesmaximal, characteristic, complemented
13C4×#17985379C211yesmaximal, characteristic, complemented
14#31826527C211yesmaximal, characteristic, complemented
15#441×C283C211yesmaximal, characteristic, complemented
16C2×Q8×D283C2211yescharacteristic
17C2×#17985382C2211yescharacteristic
18C2×#17985381C2211yescharacteristic
19C2×#17985379C2211yescharacteristic
20#22583609C2211yescharacteristic
21#22583604—21no—
22#22583599C2211yescharacteristic
23#22583598—21no—
24#22583595—21no—
25#22583588—21no—
26#22583586C2211yescharacteristic
27#22583585C2211yescharacteristic
28Q8×Dic283C2211yescharacteristic
29C4×Dic566—21no—
30C4×Dic566C2211yescharacteristic
31#22583575—21no—
32#22583575C2211yescharacteristic
33C4×D1132C2211yescharacteristic
34#22583568—21no—
35#22583568C2211yescharacteristic
36#22583567—21no—
37#22583567C2211yescharacteristic
38#22583544C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583541C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583534C2211yescharacteristic
45#22583534C2211yescharacteristic
46#22583533C2211yescharacteristic
47#22583532C2211yescharacteristic
48#22583530C2211yescharacteristic
49(C2×D283)⋊C8C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51C4×C283⋊C8C2211yescharacteristic
52C2×Q16×C283C2211yescharacteristic
53C4×Q8×C283C2211yescharacteristic
54C4×Q8×C283C2211yescharacteristic
55#106×C283C2211yescharacteristic
56#103×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#97×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×Dic566—21no—
61C2×Dic566C2311yescharacteristic
62Q8×D283—22no—
63Q8×D283—22no—
64C2×D1132—21no—
65C2×D1132C2311yescharacteristic
66C2×C4×D283—21no—
67C2×C4×D283—21no—
68C2×C4×D283C2311yescharacteristic
69#17985382—22no—
70#17985381—22no—
71#17985379—22no—
72C2×C283⋊C8C2311yescharacteristic
73C2×C283⋊C8C2311yescharacteristic
74C4⋊Dic283—21no—
75C4⋊Dic283C2311yescharacteristic
76C4⋊Dic283C2311yescharacteristic
77Dic283⋊C4—21no—
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4D411yescharacteristic
82Dic283⋊C4D411yescharacteristic
83(C2×D283)⋊C4—21no—
84(C2×D283)⋊C4—21no—
85(C2×D283)⋊C4—21no—
86(C2×D283)⋊C4—21no—
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4D411yescharacteristic
90(C2×D283)⋊C4D411yescharacteristic
91C4×Dic283—21no—
92C4×Dic283—21no—
93C4×Dic283—21no—
94C4×Dic283—21no—
95C4×Dic283C2311yescharacteristic
96C2×Q8×C283C2311yescharacteristic
97C2×Q8×C283C2311yescharacteristic
98Q16×C283—22no—
99C2×C8×C283C2311yescharacteristic
100C2×C8×C283C2311yescharacteristic
101C4⋊C4×C283—21no—
102C4⋊C4×C283—21no—
103C4⋊C4×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C42×C283—21no—
106C42×C283—21no—
107C42×C283C2311yescharacteristic
108C22×D283—21no—
109C22×D283C2×D411yescharacteristic
110Dic566—24no—
111Dic566—21no—
112Dic566—81no—
113Dic566#4112yes—
114D1132—21no—
115D1132—21no—
116D1132—81no—
117C2×Dic283—21no—
118C2×Dic283—21no—
119C2×Dic283—21no—
120C2×Dic283C2×D411yescharacteristic
121C2×Dic283C2×D411yescharacteristic
122C2×Dic283C2×D411yescharacteristic
123C4×D283—24no—
124C4×D283—21no—
125C4×D283—21no—
126C4×D283—81no—
127C283⋊C8—21no—
128C283⋊C8—21no—
129Q8×C283—21no—
130Q8×C283—21no—
131Q8×C283—21no—
132Q8×C283#4112yes—
133C2×C4×C283—21no—
134C2×C4×C283—21no—
135C2×C4×C283—21no—
136C2×C4×C283—21no—
137C2×C4×C283C2×D411yescharacteristic
138C2×C4×C283C2×D411yescharacteristic
139C2×C4×C283C2411yescharacteristic
140C8×C283—21no—
141C8×C283—21no—
142C22×C283C22×D411yescharacteristic
143C2×D283—21no—
144C2×D283—21no—
145C2×D283—21no—
146C2×D283—41no—
147C2×D283—41no—
148C2×D283—41no—
149C4×C283—22no—
150C4×C283—21no—
151C4×C283—21no—
152C4×C283—41no—
153C4×C283—41no—
154C4×C283—41no—
155C4×C283C2×#4111yescharacteristic
156C4×C283C2×#4111yescharacteristic
157Dic283—22no—
158Dic283—21no—
159Dic283—21no—
160Dic283—21no—
161Dic283—41no—
162Dic283—41no—
163C2×C283#52511yescharacteristic
164C2×C283#57711yescharacteristic
165C2×C283#57811yescharacteristic
166D283—41no—
167D283—81no—
168C283#312111yescharacteristic, complemented, Sylow
169#3121—2831nomaximal, Sylow
170#542—2831no—
171#519—2831no—
172#485—2831no—
173#482—2831no—
174#477—2831no—
175#475—2831no—
176#464—2831no—
177#464—2831no—
178#451—2831no—
179#448—2831no—
180#441D28311yescharacteristic, complemented
181#440—2831no—
182C4×Q16—2831no—
183C4×SD16—2831no—
184#433—2831no—
185C22×Q8—2831no—
186C2×Q16—2831no—
187C2×Q16C2×D28311yescharacteristic
188C2×SD16—2831no—
189C2×SD16—2831no—
190C4⋊Q8—2831no—
191#126—5661no—
192#124—2831no—
193#124—5661no—
194#123—5661no—
195C22⋊Q8—2831no—
196C22⋊Q8—5661no—
197#121—2831no—
198C4×Q8—2831no—
199C4×Q8—2831no—
200C4×Q8—2831no—
201C4×Q8—5661no—
202C4×Q8—5661no—
203C4×Q8C2×D28311yescharacteristic
204C4×Q8C2×D28311yescharacteristic
205C4×D4—2831no—
206#117—2831no—
207#117—2831no—
208#117—5661no—
209#117—5661no—
210#107—2831no—
211#107—2831no—
212#106—2831no—
213#106C2×D28311yescharacteristic
214C4⋊C8—2831no—
215C4⋊C8—2831no—
216#103—2831no—
217#103—2831no—
218#103—2831no—
219#103—2831no—
220#103C2×D28311yescharacteristic
221#103C2×D28311yescharacteristic
222#102—2831no—
223#102—2831no—
224C22⋊C8—2831no—
225C22⋊C8—2831no—
226#97C2×D28311yescharacteristic
227C4×C8—2831no—
228C2×Q8—2831no—
229C2×Q8—5661no—
230C2×Q8—5661no—
231C2×Q8—5662no—
232C2×Q8—5662no—
233C2×Q8C22×D28311yescharacteristic
234C2×Q8C22×D28311yescharacteristic
235C2×D4—2831no—
236C2×D4—5661no—
237C22×C4—2831no—
238C22×C4—5661no—
239C22×C4—5661no—
240Q16—22no—
241Q16—5662no—
242SD16—5662no—
243SD16—5662no—
244C2×C8—2831no—
245C2×C8—2831no—
246C2×C8C22×D28311yescharacteristic
247C2×C8C22×D28311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—2831no—
251C4⋊C4—2831no—
252C4⋊C4—2831no—
253C4⋊C4—2831no—
254C4⋊C4—5661no—
255C4⋊C4—5661no—
256C4⋊C4—5661no—
257C4⋊C4—5661no—
258C4⋊C4—5661no—
259C4⋊C4C22×D28311yescharacteristic
260C4⋊C4C22×D28311yescharacteristic
261C22⋊C4—2831no—
262C22⋊C4—2831no—
263C22⋊C4—5661no—
264C22⋊C4—5661no—
265C22⋊C4—5661no—
266C22⋊C4—5661no—
267C22⋊C4—5661no—
268C22⋊C4—5661no—
269C42—21no—
270C42—21no—
271C42—2831no—
272C42—5661no—
273C42—5661no—
274C42—5661no—
275C42—5661no—
276C42C22×D28311yescharacteristic
277C23—2831no—
278C23—5661no—
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—2832no—
283Q8—5664no—
284Q8—5661no—
285Q8—22641no—
286Q8#1798539212yes—
287D4—5661no—
288D4—5661no—
289D4—22641no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—2831no—
295C2×C4—2831no—
296C2×C4—2831no—
297C2×C4—5664no—
298C2×C4—5661no—
299C2×C4—5661no—
300C2×C4—5661no—
301C2×C4—5661no—
302C2×C4—5661no—
303C2×C4—22641no—
304C2×C4D4×D28311yescharacteristic
305C2×C4D4×D28311yescharacteristic
306C2×C4C23×D28311yescharacteristic
307C8—21no—
308C8—21no—
309C8—5661no—
310C8—5661no—
311C22—5661no—
312C22—5661no—
313C22—5661no—
314C22—11321no—
315C22—11321no—
316C22—11321no—
317C22C2×D4×D28311yescharacteristic
318C4—22no—
319C4—21no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—5661no—
325C4—5662no—
326C4—5661no—
327C4—5661no—
328C4—11321no—
329C4—11321no—
330C4#41×D28311yescharacteristic
331C4C2×#1798539211yescharacteristic
332C2—11321no—
333C2—22641no—
334C2#3182697411yescharacteristic
335C2#3182727411yescharacteristic
336C2#3182728111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#441×C283C2
socleC22×C283C22×D4
prime radical#22583585C22
hypercenter#441D283
hypocenterC283#3121
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
2. #31826941C2semidirect
3. #31826805C2semidirect
5. #31826758C2semidirect
6. #31826749C2semidirect
7. #31826690C2semidirect
8. #31826689C2semidirect
9. #31826619C2semidirect
11. #31826567C2semidirect
12. C4×#17985382C2semidirect
13. C4×#17985379C2semidirect
14. #31826527C2semidirect
15. #441×C283C2semidirect
168. C283#3121semidirect
180. #441D283semidirect

Maximal subgroups

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

subgroupindex
#318270872
#318269412
#318268052
#318267912
#318267582
#318267492
#318266902
#318266892
#318266192
#318266052
#318265672
C4×#179853822
C4×#179853792
#318265272
#441×C2832
#3121283