Finite Group Databasebeta

← #49132767

Subgroups — #49132767

Order 36224.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583640C211yesmaximal, characteristic, complemented
2C22×#17985380C211yesmaximal, characteristic, complemented
3D4×Dic566C211yesmaximal, characteristic, complemented
4#31826860C211yesmaximal, characteristic, complemented
5#31826709C211yesmaximal, characteristic, complemented
6#31826704C211yesmaximal, characteristic, complemented
7#31826684C211yesmaximal, characteristic, complemented
8#31826670C211yesmaximal, characteristic, complemented
9#31826627C211yesmaximal, characteristic, complemented
10#31826620C211yesmaximal, characteristic, complemented
11#31826616C211yesmaximal, characteristic, complemented
12#31826603C211yesmaximal, characteristic, complemented
13#31826565C211yesmaximal, characteristic, complemented
14#31826537C211yesmaximal, characteristic, complemented
15#546×C283C211yesmaximal, characteristic
16C22×Dic566C2211yescharacteristic
17C22×Dic566C2211yescharacteristic, complemented
18#22583640—24no—
19C2×#17985382C2211yescharacteristic, complemented
20C2×#17985382C2211yescharacteristic, complemented
21C2×#17985382C2211yescharacteristic, complemented
22C2×#17985380—24no—
23C2×#17985380C2211yescharacteristic
24C2×#17985380C2211yescharacteristic
25C2×#17985380C2211yescharacteristic
26C2×#17985380C2211yescharacteristic
27C2×#17985380C2211yescharacteristic
28C2×#17985380C2211yescharacteristic
29C2×#17985376C2211yescharacteristic, complemented
30C22×C283⋊C8C2211yescharacteristic
31#22583610C2211yescharacteristic, complemented
32#22583609—21no—
33#22583589C2211yescharacteristic
34#22583589C2211yescharacteristic, complemented
35#22583587—21no—
36#22583587—21no—
37C4×Dic566C2211yescharacteristic, complemented
38D4×Dic283—21no—
39#22583543C2211yescharacteristic, complemented
40C4⋊(C283⋊C8)C2211yescharacteristic, complemented
41#22583534C2211yescharacteristic, complemented
42#22583533C2211yescharacteristic, complemented
43#22583533C2211yescharacteristic, complemented
44#22583533C2211yescharacteristic, complemented
45#22583531C2211yescharacteristic
46#22583531C2211yescharacteristic
47C22⋊(C283⋊C8)C2211yescharacteristic
48C22⋊(C283⋊C8)C2211yescharacteristic, complemented
49#22583521C2211yescharacteristic, complemented
50C2×#41×C283C2211yescharacteristic
51C22×D4×C283C2211yescharacteristic
52#124×C283C2211yescharacteristic
53#123×C283—21no—
54C22⋊Q8×C283C2211yescharacteristic
55#121×C283—21no—
56#121×C283C2211yescharacteristic
57#120×C283—21no—
58C4×D4×C283C2211yescharacteristic
59C4×D4×C283C2211yescharacteristic
60C2×C22⋊C4×C283—21no—
61C2×Dic566—22no—
62C2×Dic566—22no—
63C2×Dic566—21no—
64C2×Dic566—21no—
65C2×Dic566—41no—
66C2×Dic566—41no—
67C2×Dic566C2311yescharacteristic
68C2×Dic566C2311yescharacteristic
69C2×Dic566C2311yescharacteristic
70C22×Dic283—21no—
71C22×Dic283—21no—
72#17985382—22no—
73#17985382—22no—
74#17985382—41no—
75#17985380—22no—
76#17985380—22no—
77#17985380—22no—
78#17985380—22no—
79#17985380—41no—
80#17985380D414yescomplemented
81#17985376—22no—
82C2×C283⋊C8—22no—
83C2×C283⋊C8C2311yescharacteristic
84C2×C283⋊C8C2311yescharacteristic
85C2×C283⋊C8C2311yescharacteristic
86C2×C283⋊C8C2311yescharacteristic
87C4⋊Dic283—21no—
88C4⋊Dic283—21no—
89C4⋊Dic283C2311yescharacteristic
90Dic283⋊C4—21no—
91Dic283⋊C4—21no—
92Dic283⋊C4—21no—
93C22⋊Dic283—21no—
94C22⋊Dic283—21no—
95C4×Dic283—21no—
96C24×C283—21no—
97#41×C283—22no—
98#41×C283—41no—
99C2×Q8×C283C2311yescharacteristic
100C2×D4×C283—22no—
101C2×D4×C283—21no—
102C2×D4×C283—21no—
103C2×D4×C283—21no—
104C2×D4×C283—41no—
105C2×D4×C283D411yescharacteristic
106C2×D4×C283C2311yescharacteristic
107C2×D4×C283C2311yescharacteristic
108C22×C4×C283—21no—
109C22×C4×C283—21no—
110C22×C4×C283C2311yescharacteristic
111C22×C4×C283C2311yescharacteristic
112C4⋊C4×C283—21no—
113C4⋊C4×C283D411yescharacteristic
114C4⋊C4×C283C2311yescharacteristic
115C22⋊C4×C283—21no—
116C22⋊C4×C283—21no—
117C22⋊C4×C283—21no—
118C22⋊C4×C283—21no—
119C22⋊C4×C283—21no—
120C22⋊C4×C283D411yescharacteristic
121C22⋊C4×C283D411yescharacteristic
122C42×C283C2311yescharacteristic
123Dic566—21no—
124Dic566—21no—
125Dic566—21no—
126Dic566—21no—
127Dic566—21no—
128Dic566—42no—
129Dic566—42no—
130Dic566C2×D412yes—
131C2×Dic283—21no—
132C2×Dic283—21no—
133C2×Dic283—21no—
134C2×Dic283—21no—
135C2×Dic283—42no—
136C2×Dic283—42no—
137C283⋊C8—21no—
138C283⋊C8—21no—
139C283⋊C8—21no—
140C283⋊C8C2×D412yes—
141C23×C283—21no—
142C23×C283—21no—
143C23×C283—42no—
144C23×C283—42no—
145C23×C283—81no—
146C23×C283C2×D411yescharacteristic
147C23×C283C2×D411yescharacteristic
148Q8×C283—21no—
149Q8×C283—21no—
150D4×C283—22no—
151D4×C283—21no—
152D4×C283—21no—
153D4×C283—21no—
154D4×C283—42no—
155D4×C283—42no—
156D4×C283—81no—
157D4×C283C2×D412yes—
158C2×C4×C283—21no—
159C2×C4×C283—21no—
160C2×C4×C283—21no—
161C2×C4×C283—21no—
162C2×C4×C283—21no—
163C2×C4×C283—21no—
164C2×C4×C283—42no—
165C2×C4×C283—81no—
166C2×C4×C283C2×D411yescharacteristic
167C2×C4×C283C2×D411yescharacteristic
168C2×C4×C283C2×D411yescharacteristic
169C2×C4×C283C2×D411yescharacteristic
170C2×C4×C283C2411yescharacteristic
171C22×C283—21no—
172C22×C283—21no—
173C22×C283—21no—
174C22×C283—22no—
175C22×C283—21no—
176C22×C283—21no—
177C22×C283—41no—
178C22×C283—41no—
179C22×C283—41no—
180C22×C283—41no—
181C22×C283—41no—
182C22×C283—84no—
183C22×C283#13712yescomplemented
184C22×C283C22×D411yescharacteristic
185C4×C283—21no—
186C4×C283—21no—
187C4×C283—21no—
188C4×C283—21no—
189C4×C283—41no—
190C4×C283—41no—
191C4×C283C22×D411yescharacteristic
192C4×C283H(5,𝔽2)11yescharacteristic
193Dic283—22no—
194Dic283—41no—
195Dic283—41no—
196Dic283—41no—
197C2×C283—22no—
198C2×C283—41no—
199C2×C283—42no—
200C2×C283—81no—
201C2×C283D4211yescharacteristic
202C2×C283C2×#13711yescharacteristic
203C2×C283#57711yescharacteristic
204C283#326611yescharacteristic, complemented, Sylow
205#3266—2831nomaximal, Sylow
206C2×#137—2831no—
207C22×SD16—2831no—
208D4×Q8—2831no—
209#546D28311yescharacteristic
210#497—2831no—
211#468—2831no—
212#467—2831no—
213#464—2831no—
214#461—2831no—
215#452—2831no—
216#451—2831no—
217#450—2831no—
218#448—2831no—
219#440—2831no—
220#435—2831no—
221C2×#41C2×D28311yescharacteristic
222C22×Q8—2831no—
223C22×Q8—2831no—
224C22×D4C2×D28311yescharacteristic
225#137—5664no—
226C2×Q16—2831no—
227C2×Q16—2831no—
228C2×Q16—2831no—
229C2×SD16—2831no—
230C2×SD16—2831no—
231C2×SD16—2831no—
232C2×SD16—2831no—
233C2×SD16—2831no—
234C2×SD16—2831no—
235C2×SD16—5664no—
236C2×M16—2831no—
237C22×C8—2831no—
238C4⋊Q8—2831no—
239C4⋊Q8—5661no—
240#124C2×D28311yescharacteristic
241#123—21no—
242C22⋊Q8—2831no—
243C22⋊Q8—2831no—
244C22⋊Q8—5661no—
245C22⋊Q8—5661no—
246C22⋊Q8C2×D28311yescharacteristic
247#121—21no—
248#121C2×D28311yescharacteristic
249#120—21no—
250C4×Q8—2831no—
251C4×D4—5661no—
252C4×D4C2×D28311yescharacteristic
253C4×D4C2×D28311yescharacteristic
254C2×C22⋊C4—21no—
255#107—2831no—
256C4⋊C8—2831no—
257#103—2831no—
258#103—2831no—
259#103—2831no—
260#103—2831no—
261#102—2831no—
262#102—2831no—
263C22⋊C8—2831no—
264C22⋊C8—2831no—
265#97—2831no—
266C24—21no—
267#41—22no—
268#41—41no—
269C2×Q8—2831no—
270C2×Q8—2831no—
271C2×Q8—2831no—
272C2×Q8—5662no—
273C2×Q8—5662no—
274C2×Q8—5661no—
275C2×Q8—5661no—
276C2×Q8—11321no—
277C2×Q8—11321no—
278C2×Q8C22×D28311yescharacteristic
279C2×D4—22no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—41no—
284C2×D4C22⋊D28311yescharacteristic
285C2×D4C22×D28311yescharacteristic
286C2×D4C22×D28311yescharacteristic
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—5661no—
290C22×C4—5661no—
291C22×C4C22×D28311yescharacteristic
292C22×C4C22×D28311yescharacteristic
293Q16—5662no—
294Q16—5662no—
295Q16—11321no—
296SD16—2834no—
297SD16—5662no—
298SD16—5662no—
299SD16—5662no—
300SD16—5662no—
301SD16—11321no—
302M16—5662no—
303C2×C8—2831no—
304C2×C8—2831no—
305C2×C8—2831no—
306C2×C8—2831no—
307C2×C8—5662no—
308C4⋊C4—21no—
309C4⋊C4—2831no—
310C4⋊C4—5661no—
311C4⋊C4—5661no—
312C4⋊C4—5661no—
313C4⋊C4—5661no—
314C4⋊C4—5661no—
315C4⋊C4C22⋊D28311yescharacteristic
316C4⋊C4C22×D28311yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—5661no—
323C22⋊C4—5661no—
324C22⋊C4C22⋊D28311yescharacteristic
325C22⋊C4C22⋊D28311yescharacteristic
326C42—5661no—
327C42C22×D28311yescharacteristic
328C23—21no—
329C23—21no—
330C23—42no—
331C23—42no—
332C23—81no—
333C23C2×C22⋊D28311yescharacteristic
334C23C2×C22⋊D28311yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—2832no—
338Q8—5661no—
339Q8—5661no—
340Q8—5661no—
341Q8—5661no—
342Q8—5661no—
343Q8—11322no—
344Q8—11322no—
345D4—22no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—42no—
350D4—42no—
351D4—81no—
352D4D4×D28312yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—42no—
360C2×C4—81no—
361C2×C4—5661no—
362C2×C4—5661no—
363C2×C4—5661no—
364C2×C4—5661no—
365C2×C4—11322no—
366C2×C4—11322no—
367C2×C4C2×C22⋊D28311yescharacteristic
368C2×C4C2×C22⋊D28311yescharacteristic
369C2×C4C2×C22⋊D28311yescharacteristic
370C2×C4C2×C22⋊D28311yescharacteristic
371C2×C4C23×D28311yescharacteristic
372C8—2832no—
373C8—5661no—
374C8—5661no—
375C8—5661no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—22no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—84no—
388C22#2258364012yescomplemented
389C22C22×C22⋊D28311yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—41no—
395C4—41no—
396C4—5662no—
397C4—11321no—
398C4—11321no—
399C4—11321no—
400C4C2×D4×D28311yescharacteristic
401C4#2258365511yescharacteristic
402C2—22no—
403C2—41no—
404C2—42no—
405C2—81no—
406C2D4×C22⋊D28311yescharacteristic
407C2C2×#2258364011yescharacteristic
408C2#3182727611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting, prime radical#546×C283C2
socleC22×C283C22×D4
hypercenter#546D283
hypocenterC283#3266
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#22583640C2semidirect
2. C22×#17985380C2semidirect
3. D4×Dic566C2semidirect
4. #31826860C2semidirect
5. #31826709C2semidirect
6. #31826704C2semidirect
7. #31826684C2semidirect
8. #31826670C2semidirect
9. #31826627C2semidirect
10. #31826620C2semidirect
11. #31826616C2semidirect
12. #31826603C2semidirect
13. #31826565C2semidirect
14. #31826537C2semidirect
17. C22×Dic566C22semidirect
19. C2×#17985382C22semidirect
20. C2×#17985382C22semidirect
21. C2×#17985382C22semidirect
29. C2×#17985376C22semidirect
31. #22583610C22semidirect
34. #22583589C22semidirect
37. C4×Dic566C22semidirect
39. #22583543C22semidirect
40. C4⋊(C283⋊C8)C22semidirect
41. #22583534C22semidirect
42. #22583533C22semidirect
43. #22583533C22semidirect
44. #22583533C22semidirect
48. C22⋊(C283⋊C8)C22semidirect
49. #22583521C22semidirect
80. #17985380D4semidirect
183. C22×C283#137semidirect
204. C283#3266semidirect
388. C22#22583640semidirect

Maximal subgroups

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

subgroupindex
C2×#225836402
C22×#179853802
D4×Dic5662
#318268602
#318267092
#318267042
#318266842
#318266702
#318266272
#318266202
#318266162
#318266032
#318265652
#318265372
#546×C2832
#3266283