Finite Group Databasebeta

← #49132721

Subgroups — #49132721

Order 36224.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827089C211yesmaximal, characteristic, complemented
2#31827080C211yesmaximal, characteristic, complemented
3#31826759C211yesmaximal, characteristic, complemented
4#31826757C211yesmaximal, characteristic, complemented
5#31826744C211yesmaximal, characteristic, complemented
6#31826712C211yesmaximal, characteristic, complemented
7#31826710C211yesmaximal, characteristic, complemented
8#31826707C211yesmaximal, characteristic, complemented
9#31826700C211yesmaximal, characteristic
10#31826688C211yesmaximal, characteristic, complemented
11#31826686C211yesmaximal, characteristic, complemented
12#31826680C211yesmaximal, characteristic, complemented
13#31826679C211yesmaximal, characteristic, complemented
14#31826490C211yesmaximal, characteristic, complemented
15#474×C283C211yesmaximal, characteristic, complemented
16C2×Dic1132C2211yescharacteristic
17C2×#17985381C2211yescharacteristic
18C2×#17985380C2211yescharacteristic
19C2×#17985377C2211yescharacteristic
20C2×#17985375C2211yescharacteristic
21C2×C8×D283C2211yescharacteristic
22#22583609C2211yescharacteristic
23#22583605—21no—
24#22583603—21no—
25#22583599—21no—
26#22583598C2211yescharacteristic
27#22583597C2211yescharacteristic
28#22583596—21no—
29#22583595—21no—
30#22583593—21no—
31#22583590C2211yescharacteristic
32#22583590C2211yescharacteristic
33#22583589—21no—
34#22583586—21no—
35#22583585C2211yescharacteristic
36#22583581C2211yescharacteristic
37C4×Dic566C2211yescharacteristic
38#22583575C2211yescharacteristic
39#22583572C2211yescharacteristic
40#22583567C2211yescharacteristic
41#22583543C2211yescharacteristic
42#22583543C2211yescharacteristic
43C4⋊(C283⋊C8)C2211yescharacteristic
44Dic283⋊C8C2211yescharacteristic
45Dic283⋊C8C2211yescharacteristic
46#22583535C2211yescharacteristic
47#22583533C2211yescharacteristic
48#22583533C2211yescharacteristic
49#22583533C2211yescharacteristic
50#22583532C2211yescharacteristic
51#22583530C2211yescharacteristic
52C4⋊Q8×C283C2211yescharacteristic
53C4×D4×C283C2211yescharacteristic
54#107×C283C2211yescharacteristic
55#107×C283C2211yescharacteristic
56C4⋊C8×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58#102×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×Dic566C2311yescharacteristic
61C2×Dic566C2311yescharacteristic
62C2×D1132—21no—
63C2×D1132C2311yescharacteristic
64C2×C22⋊D283—21no—
65C2×C4×D283—21no—
66C2×C4×D283C2311yescharacteristic
67Dic1132—41no—
68#17985381—41no—
69#17985380—41no—
70#17985377—41no—
71#17985375—41no—
72C2×C283⋊C8C2311yescharacteristic
73C2×C283⋊C8C2311yescharacteristic
74C8×D283—41no—
75C4⋊Dic283—21no—
76C4⋊Dic283—21no—
77C4⋊Dic283C2311yescharacteristic
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4D411yescharacteristic
82Dic283⋊C4D411yescharacteristic
83C22⋊Dic283—21no—
84C22⋊Dic283—21no—
85C22⋊Dic283—21no—
86(C2×D283)⋊C4—21no—
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4D411yescharacteristic
93(C2×D283)⋊C4D411yescharacteristic
94C4×Dic283—21no—
95C4×Dic283—21no—
96C4×Dic283C2311yescharacteristic
97C2×Q8×C283—21no—
98C2×D4×C283C2311yescharacteristic
99C22×C4×C283—21no—
100C2×C8×C283C2311yescharacteristic
101C2×C8×C283C2311yescharacteristic
102C4⋊C4×C283—21no—
103C4⋊C4×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C4⋊C4×C283C2311yescharacteristic
106C22⋊C4×C283—21no—
107C42×C283C2311yescharacteristic
108C22×D283—21no—
109C22×D283C2×D411yescharacteristic
110Dic566—21no—
111Dic566—21no—
112Dic566—21no—
113Dic566—21no—
114Dic566—81no—
115D1132—21no—
116D1132—21no—
117D1132—81no—
118C22⋊D283—81no—
119C2×Dic283—21no—
120C2×Dic283—21no—
121C2×Dic283—21no—
122C2×Dic283C2×D411yescharacteristic
123C2×Dic283C2×D411yescharacteristic
124C2×Dic283C2×D411yescharacteristic
125C4×D283—21no—
126C4×D283—21no—
127C4×D283—81no—
128C283⋊C8—21no—
129C283⋊C8—21no—
130C23×C283—21no—
131Q8×C283—81no—
132D4×C283—21no—
133D4×C283—21no—
134C2×C4×C283—21no—
135C2×C4×C283—21no—
136C2×C4×C283—21no—
137C2×C4×C283—81no—
138C2×C4×C283C2×D411yescharacteristic
139C2×C4×C283C2×D411yescharacteristic
140C2×C4×C283C2411yescharacteristic
141C8×C283—21no—
142C8×C283—21no—
143C22×C283—41no—
144C22×C283—41no—
145C22×C283—41no—
146C22×C283C22×D411yescharacteristic
147C2×D283—21no—
148C2×D283—21no—
149C2×D283—21no—
150C2×D283—41no—
151C2×D283—41no—
152C2×D283—41no—
153C4×C283—21no—
154C4×C283—21no—
155C4×C283—41no—
156C4×C283—41no—
157C4×C283—41no—
158C4×C283H(5,𝔽2)11yescharacteristic
159C4×C2832−1+411yescharacteristic
160Dic283—21no—
161Dic283—21no—
162Dic283—21no—
163Dic283—41no—
164Dic283—41no—
165Dic283—41no—
166C2×C283—81no—
167C2×C283#53711yescharacteristic
168C2×C283#57611yescharacteristic
169C2×C283#57811yescharacteristic
170D283—41no—
171D283—81no—
172C283#326211yescharacteristic, complemented, Sylow
173#3262—2831nomaximal, Sylow
174#542—2831no—
175#542—2831no—
176#477—2831no—
177#477—2831no—
178#474—2831no—
179#474D28311yescharacteristic, complemented
180#468—2831no—
181#468—2831no—
182#467—2831no—
183#466—2831no—
184#464—2831no—
185#464—2831no—
186#463—2831no—
187#463—2831no—
188#424—2831no—
189C2×Q16—2831no—
190C2×SD16—2831no—
191C2×SD16—2831no—
192C2×D8—2831no—
193C2×M16—2831no—
194C22×C8—2831no—
195C4⋊Q8—2831no—
196C4⋊Q8C2×D28311yescharacteristic
197#126—5661no—
198#126—5661no—
199#124—2831no—
200#124—2831no—
201#124—5661no—
202#124—5661no—
203#123—5661no—
204#123—5661no—
205C22⋊Q8—2831no—
206C22⋊Q8—2831no—
207C22⋊Q8—5661no—
208C22⋊Q8—5661no—
209#121—2831no—
210#121—2831no—
211C4×Q8—2831no—
212C4×Q8—2831no—
213C4×D4—2831no—
214C4×D4C2×D28311yescharacteristic
215#117—2831no—
216#107—2831no—
217#107—2831no—
218#107C2×D28311yescharacteristic
219#107C2×D28311yescharacteristic
220C4⋊C8—2831no—
221C4⋊C8—2831no—
222C4⋊C8—2831no—
223C4⋊C8C2×D28311yescharacteristic
224#103—2831no—
225#103—2831no—
226#103—2831no—
227#103—2831no—
228#102—2831no—
229#102—2831no—
230#102C2×D28311yescharacteristic
231#102C2×D28311yescharacteristic
232C2×Q8—21no—
233C2×Q8—2831no—
234C2×Q8—2831no—
235C2×Q8—5661no—
236C2×D4—2831no—
237C2×D4—5661no—
238C2×D4—5661no—
239C2×D4C22×D28311yescharacteristic
240C22×C4—21no—
241C22×C4—2831no—
242C22×C4—5661no—
243Q16—11321no—
244SD16—11321no—
245SD16—11321no—
246D8—11321no—
247M16—11321no—
248C2×C8—2831no—
249C2×C8—2831no—
250C2×C8—11321no—
251C2×C8C22×D28311yescharacteristic
252C2×C8C22×D28311yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—2831no—
255C4⋊C4—2831no—
256C4⋊C4—2831no—
257C4⋊C4—5661no—
258C4⋊C4—5661no—
259C4⋊C4—5661no—
260C4⋊C4—5661no—
261C4⋊C4—5661no—
262C4⋊C4C22×D28311yescharacteristic
263C4⋊C4C22×D28311yescharacteristic
264C4⋊C4C22×D28311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—2831no—
267C22⋊C4—2831no—
268C22⋊C4—5661no—
269C22⋊C4—5661no—
270C22⋊C4—5661no—
271C22⋊C4—5661no—
272C22⋊C4—5661no—
273C22⋊C4—5661no—
274C22⋊C4—5661no—
275C22⋊C4—5661no—
276C22⋊C4—5661no—
277C42—2831no—
278C42—5661no—
279C42—5661no—
280C42C22×D28311yescharacteristic
281C23—21no—
282C23—2831no—
283C23—5661no—
284Q8—81no—
285Q8—5661no—
286Q8—5661no—
287Q8—5661no—
288Q8—5661no—
289Q8—22641no—
290D4—21no—
291D4—21no—
292D4—5661no—
293D4—5661no—
294D4—22641no—
295D4—22641no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—81no—
300C2×C4—2831no—
301C2×C4—2831no—
302C2×C4—2831no—
303C2×C4—5661no—
304C2×C4—5661no—
305C2×C4—5661no—
306C2×C4—5661no—
307C2×C4—5661no—
308C2×C4—22641no—
309C2×C4D4×D28311yescharacteristic
310C2×C4D4×D28311yescharacteristic
311C2×C4C23×D28311yescharacteristic
312C8—21no—
313C8—21no—
314C8—5661no—
315C8—5661no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—5661no—
320C22—5661no—
321C22—5661no—
322C22—11321no—
323C22—11321no—
324C22—11321no—
325C22C2×D4×D28311yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—5661no—
332C4—5661no—
333C4—5661no—
334C4—11321no—
335C4—11321no—
336C4—11321no—
337C4#2258365611yescharacteristic
338C4#2258365811yescharacteristic
339C2—81no—
340C2—11321no—
341C2—22641no—
342C2#3182704511yescharacteristic
343C2#3182726611yescharacteristic
344C2#3182728111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#474×C283C2
socleC22×C283C22×D4
prime radical#31826700C2
hypercenter#474D283
hypocenterC283#3262
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #31827089C2semidirect
2. #31827080C2semidirect
3. #31826759C2semidirect
4. #31826757C2semidirect
5. #31826744C2semidirect
6. #31826712C2semidirect
7. #31826710C2semidirect
8. #31826707C2semidirect
10. #31826688C2semidirect
11. #31826686C2semidirect
12. #31826680C2semidirect
13. #31826679C2semidirect
14. #31826490C2semidirect
15. #474×C283C2semidirect
172. C283#3262semidirect
179. #474D283semidirect

Maximal subgroups

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

subgroupindex
#318270892
#318270802
#318267592
#318267572
#318267442
#318267122
#318267102
#318267072
#318267002
#318266882
#318266862
#318266802
#318266792
#318264902
#474×C2832
#3262283