Finite Group Databasebeta

← #49129961

Subgroups — #49129961

Order 36224.

492 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583618C211yesmaximal, characteristic, complemented
2C2×M16×D283C211yesmaximal, characteristic, complemented
3#31826974C211yesmaximal, characteristic
4#31826544C211yesmaximal, characteristic, complemented
5#31826541C211yesmaximal, characteristic, complemented
6#31826541C211yesmaximal, characteristic, complemented
7#31826539C211yesmaximal, characteristic, complemented
8#31826537C211yesmaximal, characteristic, complemented
9#31826535C211yesmaximal, characteristic, complemented
10#31826533C211yesmaximal, characteristic, complemented
11#31826490C211yesmaximal, characteristic, complemented
12#31826430C211yesmaximal, characteristic, complemented
13#31826427C211yesmaximal, characteristic, complemented
14#31826419C211yesmaximal, characteristic, complemented
15#436×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C22×C4×D283C2211yescharacteristic
18#22583618—24no—
19C2×#17985376C2211yescharacteristic
20C2×#17985375C2211yescharacteristic
21C2×#17985375C2211yescharacteristic
22C2×#17985375C2211yescharacteristic
23C2×#17985375C2211yescharacteristic
24C2×#17985375C2211yescharacteristic, complemented
25M16×D283—24no—
26C22×C283⋊C8C2211yescharacteristic, complemented
27C2×C8×D283C2211yescharacteristic
28C2×C8×D283C2211yescharacteristic
29C2×C8×D283C2211yescharacteristic, complemented
30#22583595C411yescharacteristic
31#22583592C411yescharacteristic
32#22583588C411yescharacteristic
33#22583587C411yescharacteristic
34#22583583C411yescharacteristic
35#22583582C411yescharacteristic
36#22583580C411yescharacteristic
37#22583578C411yescharacteristic
38C4×D1132C2211yescharacteristic
39C4×C22⋊D283C2211yescharacteristic
40C4×C22⋊D283C2211yescharacteristic
41#22583567C2211yescharacteristic
42C4⋊(C283⋊C8)C2211yescharacteristic, complemented
43Dic283⋊C8C2211yescharacteristic, complemented
44Dic283⋊C8C2211yescharacteristic, complemented
45C22⋊(C283⋊C8)C2211yescharacteristic
46C22⋊(C283⋊C8)C2211yescharacteristic, complemented
47(C2×D283)⋊C8C2211yescharacteristic
48(C2×D283)⋊C8C2211yescharacteristic
49(C2×D283)⋊C8C2211yescharacteristic, complemented
50(C2×D283)⋊C8C2211yescharacteristic, complemented
51#22583521C2211yescharacteristic, complemented
52#22583520C2211yescharacteristic, complemented
53C8×Dic283C2211yescharacteristic, complemented
54C2×M16×C283C2211yescharacteristic
55C2×M16×C283C2211yescharacteristic, complemented
56C4×D4×C283C2211yescharacteristic
57C4⋊C8×C283C2211yescharacteristic, complemented
58C22⋊C8×C283C2211yescharacteristic
59C22⋊C8×C283C2211yescharacteristic, complemented
60C4×C8×C283C2211yescharacteristic, complemented
61C23×D283C2×C411yescharacteristic
62#17985392—22no—
63#17985392—22no—
64C2×Dic566C2×C411yescharacteristic
65C2×D1132C2×C411yescharacteristic
66C2×D1132C2×C411yescharacteristic
67C2×C22⋊D283C2×C411yescharacteristic
68C2×C22⋊D283C2×C411yescharacteristic
69C2×C22⋊D283C2×C411yescharacteristic
70C2×C22⋊D283C2×C411yescharacteristic
71C22×Dic283C2×C411yescharacteristic
72C2×C4×D283—22no—
73C2×C4×D283—22no—
74C2×C4×D283C2×C411yescharacteristic
75C2×C4×D283C2×C411yescharacteristic
76C2×C4×D283C2311yescharacteristic
77C2×C4×D283C2311yescharacteristic
78C2×C4×D283C2311yescharacteristic
79#17985376—22no—
80#17985375—22no—
81#17985375—22no—
82#17985375—22no—
83#17985375—22no—
84#17985375—22no—
85C2×C283⋊C8—22no—
86C2×C283⋊C8C2311yescharacteristic
87C2×C283⋊C8C2311yescharacteristic
88C2×C283⋊C8C2311yescharacteristic
89C2×C283⋊C8C2311yescharacteristic
90C8×D283—22no—
91C8×D283—22no—
92C8×D283D414yescomplemented
93C4⋊Dic283C2×C411yescharacteristic
94Dic283⋊C4C2×C411yescharacteristic
95Dic283⋊C4C2×C411yescharacteristic
96Dic283⋊C4C2×C411yescharacteristic
97Dic283⋊C4C2×C411yescharacteristic
98C22⋊Dic283C2×C411yescharacteristic
99C22⋊Dic283C2×C411yescharacteristic
100(C2×D283)⋊C4C2×C411yescharacteristic
101(C2×D283)⋊C4C2×C411yescharacteristic
102(C2×D283)⋊C4C2×C411yescharacteristic
103(C2×D283)⋊C4C2×C411yescharacteristic
104(C2×D283)⋊C4C2×C411yescharacteristic
105(C2×D283)⋊C4C2×C411yescharacteristic
106C4×Dic283C2311yescharacteristic
107C2×D4×C283C2×C411yescharacteristic
108C22×C4×C283C2311yescharacteristic
109C22×C4×C283C2311yescharacteristic
110M16×C283—22no—
111M16×C283—22no—
112C2×C8×C283C2311yescharacteristic
113C2×C8×C283C2311yescharacteristic
114C2×C8×C283C2311yescharacteristic
115C2×C8×C283C2311yescharacteristic
116C4⋊C4×C283C2×C411yescharacteristic
117C22⋊C4×C283C2×C411yescharacteristic
118C22⋊C4×C283C2×C411yescharacteristic
119C42×C283C2311yescharacteristic
120C22×D283—22no—
121C22×D283—41no—
122C22×D283—41no—
123C22×D283C22×C411yescharacteristic
124C22×D283C22×C411yescharacteristic
125C22×D283C22×C411yescharacteristic
126Dic566—22no—
127D1132—22no—
128D1132—41no—
129C22⋊D283—22no—
130C22⋊D283—22no—
131C22⋊D283—41no—
132C22⋊D283—41no—
133C2×Dic283—22no—
134C2×Dic283C22×C411yescharacteristic
135C2×Dic283C22×C411yescharacteristic
136C2×Dic283C22×C411yescharacteristic
137C2×Dic283C22×C411yescharacteristic
138C2×Dic283C22×C411yescharacteristic
139C4×D283—22no—
140C4×D283—21no—
141C4×D283—21no—
142C4×D283—21no—
143C4×D283—21no—
144C4×D283—22no—
145C4×D283C2×D412yes—
146C4×D283#4112yes—
147C283⋊C8—21no—
148C283⋊C8—21no—
149C283⋊C8—21no—
150C283⋊C8C2×D412yes—
151C23×C283C22×C411yescharacteristic
152C23×C283C22×C411yescharacteristic
153D4×C283—41no—
154C2×C4×C283—21no—
155C2×C4×C283—21no—
156C2×C4×C283—21no—
157C2×C4×C283—21no—
158C2×C4×C283C22×C411yescharacteristic
159C2×C4×C283C22×C411yescharacteristic
160C2×C4×C283C22×C411yescharacteristic
161C2×C4×C283C22×C411yescharacteristic
162C2×C4×C283C2411yescharacteristic
163C8×C283—21no—
164C8×C283—21no—
165C8×C283—21no—
166C8×C283C2×D412yes—
167C22×C283—21no—
168C22×C283—21no—
169C22×C283—21no—
170C22×C283—21no—
171C22×C283—21no—
172C22×C283—21no—
173C22×C283C23×C411yescharacteristic
174C2×D283—21no—
175C2×D283—21no—
176C2×D283—21no—
177C2×D283—21no—
178C2×D283—21no—
179C2×D283—21no—
180C2×D283—21no—
181C2×D283—21no—
182C2×D283—44no—
183C2×D283C4×D412yes—
184C4×C283—21no—
185C4×C283—21no—
186C4×C283—21no—
187C4×C283—21no—
188C4×C283C22×D411yescharacteristic
189C4×C283C2×#4111yescharacteristic
190Dic283—21no—
191Dic283—21no—
192Dic283—21no—
193Dic283—21no—
194Dic283C4×D412yes—
195C2×C283—41no—
196C2×C283—41no—
197C2×C283C2×C4×D411yescharacteristic
198C2×C283#56811yescharacteristic
199C2×C283#56811yescharacteristic
200D283—22no—
201D283—41no—
202D283—41no—
203C283#293011yescharacteristic, complemented, Sylow
204#2930—2831nomaximal, Sylow
205C2×#131—2831no—
206C22×M16—2831no—
207#525—2831no—
208#436—2831no—
209#436—2831no—
210#436—2831no—
211#436D28311yescharacteristic, complemented
212#435—2831no—
213#435—2831no—
214#435—2831no—
215#435—2831no—
216#424—2831no—
217#408—2831no—
218#407—2831no—
219#405—2831no—
220C2×#41—2831no—
221C23×C4—2831no—
222#131—5664no—
223C2×M16—2831no—
224C2×M16—2831no—
225C2×M16—2831no—
226C2×M16—2831no—
227C2×M16—2831no—
228C2×M16—2831no—
229C2×M16—5664no—
230C2×M16C2×D28311yescharacteristic
231C2×M16C2×D28311yescharacteristic, complemented
232C22×C8—2831no—
233C22×C8—2831no—
234C22×C8—2831no—
235C22×C8—2831no—
236#123—2831no—
237#123—2831no—
238C22⋊Q8—2831no—
239C22⋊Q8—2831no—
240#121—2831no—
241#121—2831no—
242#120—2831no—
243#120—2831no—
244C4×D4—2831no—
245C4×D4—2831no—
246C4×D4—2831no—
247C4×D4C2×D28311yescharacteristic
248#117—2831no—
249C4⋊C8—2831no—
250C4⋊C8—2831no—
251C4⋊C8—2831no—
252C4⋊C8C2×D28311yescharacteristic, complemented
253C22⋊C8—2831no—
254C22⋊C8—2831no—
255C22⋊C8—2831no—
256C22⋊C8—2831no—
257C22⋊C8—2831no—
258C22⋊C8—2831no—
259C22⋊C8C2×D28311yescharacteristic
260C22⋊C8C2×D28311yescharacteristic, complemented
261#97—2831no—
262#97—2831no—
263C4×C8—2831no—
264C4×C8C2×D28311yescharacteristic, complemented
265C24—2831no—
266#41—5662no—
267#41—5662no—
268C2×Q8—2831no—
269C2×D4—2831no—
270C2×D4—2831no—
271C2×D4—2831no—
272C2×D4—2831no—
273C2×D4—2831no—
274C2×D4—2831no—
275C2×D4C4×D28311yescharacteristic
276C22×C4—2831no—
277C22×C4—2831no—
278C22×C4—2831no—
279C22×C4—2831no—
280C22×C4—2831no—
281C22×C4—2831no—
282C22×C4—5662no—
283C22×C4—5662no—
284C22×C4C22×D28311yescharacteristic
285C22×C4C22×D28311yescharacteristic
286M16—22no—
287M16—22no—
288M16—5662no—
289M16—5662no—
290M16—5662no—
291M16—5662no—
292M16—5662no—
293M16—5662no—
294C2×C8—2831no—
295C2×C8—2834no—
296C2×C8—2831no—
297C2×C8—2831no—
298C2×C8—2831no—
299C2×C8—5662no—
300C2×C8—5662no—
301C2×C8—5662no—
302C2×C8C22×D28311yescharacteristic
303C2×C8C22×D28311yescharacteristic
304C2×C8C22×D28311yescharacteristic
305C2×C8C22×D28311yescharacteristic
306C4⋊C4—2831no—
307C4⋊C4—2831no—
308C4⋊C4—2831no—
309C4⋊C4—2831no—
310C4⋊C4—2831no—
311C4⋊C4C4×D28311yescharacteristic
312C22⋊C4—2831no—
313C22⋊C4—2831no—
314C22⋊C4—2831no—
315C22⋊C4—2831no—
316C22⋊C4—2831no—
317C22⋊C4—2831no—
318C22⋊C4—2831no—
319C22⋊C4—2831no—
320C22⋊C4C4×D28311yescharacteristic
321C22⋊C4C4×D28311yescharacteristic
322C42—2831no—
323C42C22×D28311yescharacteristic
324C23—2831no—
325C23—2831no—
326C23—2831no—
327C23—5662no—
328C23—11321no—
329C23—11321no—
330C23C2×C4×D28311yescharacteristic
331C23C2×C4×D28311yescharacteristic
332Q8—5662no—
333D4—41no—
334D4—5662no—
335D4—5662no—
336D4—5662no—
337D4—11321no—
338D4—11321no—
339D4—11321no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—2831no—
345C2×C4—2832no—
346C2×C4—2832no—
347C2×C4—2831no—
348C2×C4—2831no—
349C2×C4—2831no—
350C2×C4—2831no—
351C2×C4—5662no—
352C2×C4—5662no—
353C2×C4—5662no—
354C2×C4—5661no—
355C2×C4—5661no—
356C2×C4—5661no—
357C2×C4—5661no—
358C2×C4C2×C4×D28311yescharacteristic
359C2×C4C2×C4×D28311yescharacteristic
360C2×C4C2×C4×D28311yescharacteristic
361C2×C4C2×C4×D28311yescharacteristic
362C2×C4C23×D28311yescharacteristic
363C8—21no—
364C8—21no—
365C8—21no—
366C8—2832no—
367C8—5661no—
368C8—5661no—
369C8—5661no—
370C8D4×D28312yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—2832no—
378C22—5661no—
379C22—5661no—
380C22—5661no—
381C22—5661no—
382C22—5661no—
383C22—5661no—
384C22—5661no—
385C22—5661no—
386C22—11324no—
387C22C22×C4×D28311yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—2832no—
393C4—5661no—
394C4—5661no—
395C4—5661no—
396C4—5661no—
397C4C2×D4×D28311yescharacteristic
398C4#41×D28311yescharacteristic
399C2—41no—
400C2—41no—
401C2—5662no—
402C2—11321no—
403C2—11321no—
404C2C4×D4×D28311yescharacteristic
405C2#3182723011yescharacteristic
406C2#3182723111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D283
commutator, socleC22×C283C23×C4
Fitting#436×C283C2
prime radical#31826974C2
cosocleC2×C4×C283C24
hypercenter#436D283
hypocenterC283#2930
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. C2×#22583618C2semidirect
2. C2×M16×D283C2semidirect
4. #31826544C2semidirect
5. #31826541C2semidirect
6. #31826541C2semidirect
7. #31826539C2semidirect
8. #31826537C2semidirect
9. #31826535C2semidirect
10. #31826533C2semidirect
11. #31826490C2semidirect
12. #31826430C2semidirect
13. #31826427C2semidirect
14. #31826419C2semidirect
15. #436×C283C2semidirect
24. C2×#17985375C22semidirect
26. C22×C283⋊C8C22semidirect
29. C2×C8×D283C22semidirect
42. C4⋊(C283⋊C8)C22semidirect
43. Dic283⋊C8C22semidirect
44. Dic283⋊C8C22semidirect
46. C22⋊(C283⋊C8)C22semidirect
49. (C2×D283)⋊C8C22semidirect
50. (C2×D283)⋊C8C22semidirect
51. #22583521C22semidirect
52. #22583520C22semidirect
53. C8×Dic283C22semidirect
55. C2×M16×C283C22semidirect
57. C4⋊C8×C283C22semidirect
59. C22⋊C8×C283C22semidirect
60. C4×C8×C283C22semidirect
92. C8×D283D4semidirect
203. C283#2930semidirect
211. #436D283semidirect
231. C2×M16C2×D283semidirect
252. C4⋊C8C2×D283semidirect
260. C22⋊C8C2×D283semidirect
264. C4×C8C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836182
C2×M16×D2832
#318269742
#318265442
#318265412
#318265392
#318265372
#318265352
#318265332
#318264902
#318264302
#318264272
#318264192
#436×C2832
#2930283