Finite Group Databasebeta

← #49134345

Subgroups — #49134345

Order 36224.

380 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827200C211yesmaximal, characteristic, complemented
2#31826855C211yesmaximal, characteristic, complemented
3#31826852C211yesmaximal, characteristic, complemented
4#31826847C211yesmaximal, characteristic, complemented
5#31826687C211yesmaximal, characteristic, complemented
6#31826684C211yesmaximal, characteristic, complemented
7#31826680C211yesmaximal, characteristic, complemented
8#31826677C211yesmaximal, characteristic, complemented
9#31826660C211yesmaximal, characteristic, complemented
10#31826657C211yesmaximal, characteristic, complemented
11#31826596C211yesmaximal, characteristic, complemented
12#31826565C211yesmaximal, characteristic, complemented
13#31826563C211yesmaximal, characteristic, complemented
14C4×#17985377C211yesmaximal, characteristic, complemented
15#559×C283C211yesmaximal, characteristic, complemented
16C2×#17985382C2211yescharacteristic
17C2×#17985380C2211yescharacteristic
18C2×#17985380C2211yescharacteristic
19C2×#17985379C2211yescharacteristic
20C2×#17985379C2211yescharacteristic
21C2×#17985377C2211yescharacteristic
22C2×#17985377C2211yescharacteristic
23C2×#17985377C2211yescharacteristic
24C2×#17985377C2211yescharacteristic
25#22583607C2211yescharacteristic
26#22583599—21no—
27#22583598C2211yescharacteristic
28#22583598C2211yescharacteristic
29#22583595—21no—
30#22583595—21no—
31C4×Dic566C2211yescharacteristic
32C4×D1132C2211yescharacteristic
33C4×D1132C2211yescharacteristic
34#22583572—21no—
35#22583543C2211yescharacteristic
36C4⋊(C283⋊C8)C2211yescharacteristic
37C4⋊(C283⋊C8)C2211yescharacteristic
38C4⋊(C283⋊C8)C2211yescharacteristic
39#22583534C2211yescharacteristic
40#22583533C2211yescharacteristic
41#22583531C2211yescharacteristic
42#22583531C2211yescharacteristic
43#22583530C2211yescharacteristic
44#22583530C2211yescharacteristic
45#22583521C2211yescharacteristic
46#22583521C2211yescharacteristic
47C4×C283⋊C8C2211yescharacteristic
48#127×C283C2211yescharacteristic
49#124×C283—21no—
50#124×C283C2211yescharacteristic
51#124×C283C2211yescharacteristic
52#123×C283—21no—
53#123×C283—21no—
54C4×Q8×C283C2211yescharacteristic
55C4×Q8×C283C2211yescharacteristic
56C4×D4×C283—21no—
57C4×D4×C283C2211yescharacteristic
58C4×D4×C283C2211yescharacteristic
59C2×Dic566C2311yescharacteristic
60C2×D1132—21no—
61C2×D1132—21no—
62C2×D1132C2311yescharacteristic
63C2×D1132C2311yescharacteristic
64C2×C4×D283—21no—
65C2×C4×D283—21no—
66#17985382—41no—
67#17985380—22no—
68#17985380—41no—
69#17985379—22no—
70#17985379—41no—
71#17985377—22no—
72#17985377—41no—
73#17985377—41no—
74#17985377—41no—
75C2×C283⋊C8C2311yescharacteristic
76C2×C283⋊C8C2311yescharacteristic
77C2×C283⋊C8C2311yescharacteristic
78C2×C283⋊C8C2311yescharacteristic
79C4⋊Dic283C2311yescharacteristic
80Dic283⋊C4—21no—
81(C2×D283)⋊C4—21no—
82(C2×D283)⋊C4—21no—
83(C2×D283)⋊C4—21no—
84(C2×D283)⋊C4—21no—
85(C2×D283)⋊C4—21no—
86(C2×D283)⋊C4—21no—
87C4×Dic283—21no—
88C2×Q8×C283D411yescharacteristic
89C2×Q8×C283C2311yescharacteristic
90C2×D4×C283—21no—
91C2×D4×C283—21no—
92C2×D4×C283C2311yescharacteristic
93C2×D4×C283C2311yescharacteristic
94C22×C4×C283—21no—
95C22×C4×C283—21no—
96C4⋊C4×C283—21no—
97C4⋊C4×C283D411yescharacteristic
98C4⋊C4×C283D411yescharacteristic
99C4⋊C4×C283D411yescharacteristic
100C4⋊C4×C283C2311yescharacteristic
101C22⋊C4×C283—21no—
102C22⋊C4×C283—21no—
103C22⋊C4×C283—21no—
104C22⋊C4×C283—21no—
105C22⋊C4×C283—21no—
106C22⋊C4×C283—21no—
107C42×C283—21no—
108C42×C283C2311yescharacteristic
109C42×C283C2311yescharacteristic
110C42×C283C2311yescharacteristic
111C22×D283—21no—
112C22×D283—21no—
113Dic566—21no—
114Dic566—21no—
115D1132—21no—
116D1132—21no—
117D1132—21no—
118D1132—21no—
119D1132—42no—
120D1132—81no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C4×D283—81no—
124C4×D283—81no—
125C283⋊C8—21no—
126C283⋊C8—21no—
127C283⋊C8—21no—
128C283⋊C8#4112yes—
129C23×C283—21no—
130C23×C283—21no—
131Q8×C283—21no—
132Q8×C283—21no—
133Q8×C283—41no—
134D4×C283—21no—
135D4×C283—21no—
136D4×C283—21no—
137D4×C283—21no—
138D4×C283—42no—
139D4×C283—81no—
140C2×C4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283—81no—
143C2×C4×C283—81no—
144C2×C4×C283C2×D411yescharacteristic
145C2×C4×C283C2×D411yescharacteristic
146C2×C4×C283C2×D411yescharacteristic
147C2×C4×C283C2×D411yescharacteristic
148C2×C4×C283C2×D411yescharacteristic
149C2×C4×C283C2×D411yescharacteristic
150C2×C4×C283C2411yescharacteristic
151C22×C283—41no—
152C22×C283—41no—
153C22×C283—41no—
154C22×C283—41no—
155C22×C283—41no—
156C22×C283—41no—
157C22×C283C22×D411yescharacteristic
158C2×D283—41no—
159C2×D283—41no—
160C2×D283—41no—
161C2×D283—41no—
162C2×D283—41no—
163C2×D283—41no—
164C4×C283—21no—
165C4×C283—21no—
166C4×C283—21no—
167C4×C283—21no—
168C4×C283—21no—
169C4×C283—21no—
170C4×C283—41no—
171C4×C283—41no—
172C4×C283C2×#4111yescharacteristic
173C4×C283H(5,𝔽2)11yescharacteristic
174Dic283—41no—
175Dic283—41no—
176C2×C283—81no—
177C2×C283—81no—
178C2×C283#55011yescharacteristic
179C2×C283#57511yescharacteristic
180C2×C283#57611yescharacteristic
181D283—81no—
182D283—81no—
183C283#340311yescharacteristic, complemented, Sylow
184#3403—2831nomaximal, Sylow
185#559—2831no—
186#559D28311yescharacteristic, complemented
187#496—2831no—
188#496—2831no—
189#495—2831no—
190#464—2831no—
191#464—2831no—
192#463—2831no—
193#463—2831no—
194#459—2831no—
195#459—2831no—
196#446—2831no—
197#440—2831no—
198#440—2831no—
199C4×D8—2831no—
200C2×Q16—2831no—
201C2×SD16—2831no—
202C2×SD16—2831no—
203C2×SD16—2831no—
204C2×SD16—2831no—
205C2×D8—2831no—
206C2×D8—2831no—
207C2×D8—2831no—
208C2×D8—2831no—
209#127—2831no—
210#127C2×D28311yescharacteristic
211#124—21no—
212#124—2831no—
213#124—2831no—
214#124—5661no—
215#124C2×D28311yescharacteristic
216#124C2×D28311yescharacteristic
217#123—21no—
218#123—21no—
219#123—5661no—
220#123—5661no—
221C4×Q8—2831no—
222C4×Q8C2×D28311yescharacteristic
223C4×Q8C2×D28311yescharacteristic
224C4×D4—21no—
225C4×D4—2831no—
226C4×D4—2831no—
227C4×D4—5661no—
228C4×D4C2×D28311yescharacteristic
229C4×D4C2×D28311yescharacteristic
230#107—2831no—
231C4⋊C8—2831no—
232C4⋊C8—2831no—
233C4⋊C8—2831no—
234#103—2831no—
235#103—2831no—
236#102—2831no—
237#102—2831no—
238#102—2831no—
239#102—2831no—
240#97—2831no—
241#97—2831no—
242C4×C8—2831no—
243C2×Q8—2831no—
244C2×Q8C22⋊D28311yescharacteristic
245C2×Q8C22×D28311yescharacteristic
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—2831no—
249C2×D4—2831no—
250C2×D4—5661no—
251C2×D4—5661no—
252C2×D4C22×D28311yescharacteristic
253C2×D4C22×D28311yescharacteristic
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—5661no—
257C22×C4—5661no—
258Q16—11321no—
259SD16—5662no—
260SD16—5662no—
261SD16—11321no—
262SD16—11321no—
263D8—5662no—
264D8—11321no—
265D8—11321no—
266D8—11321no—
267C2×C8—2831no—
268C2×C8—2831no—
269C2×C8—2831no—
270C2×C8—2831no—
271C4⋊C4—21no—
272C4⋊C4—2831no—
273C4⋊C4—5661no—
274C4⋊C4C22⋊D28311yescharacteristic
275C4⋊C4C22⋊D28311yescharacteristic
276C4⋊C4C22⋊D28311yescharacteristic
277C4⋊C4C22×D28311yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—5661no—
285C22⋊C4—5661no—
286C22⋊C4—5661no—
287C22⋊C4—5661no—
288C22⋊C4—5661no—
289C22⋊C4—5661no—
290C42—21no—
291C42—5661no—
292C42C22×D28311yescharacteristic
293C42C22×D28311yescharacteristic
294C42C22×D28311yescharacteristic
295C23—21no—
296C23—21no—
297C23—5661no—
298C23—5661no—
299Q8—21no—
300Q8—21no—
301Q8—41no—
302Q8—5661no—
303Q8—5661no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—5661no—
311D4—5661no—
312D4—5661no—
313D4—5661no—
314D4—11322no—
315D4—22641no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—5661no—
321C2×C4—5661no—
322C2×C4—22641no—
323C2×C4—22641no—
324C2×C4C2×C22⋊D28311yescharacteristic
325C2×C4C2×C22⋊D28311yescharacteristic
326C2×C4C2×C22⋊D28311yescharacteristic
327C2×C4C2×C22⋊D28311yescharacteristic
328C2×C4C2×C22⋊D28311yescharacteristic
329C2×C4C2×C22⋊D28311yescharacteristic
330C2×C4C23×D28311yescharacteristic
331C8—2832no—
332C8—5661no—
333C8—5661no—
334C8—5661no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—11321no—
342C22—11321no—
343C22—11321no—
344C22—11321no—
345C22—11321no—
346C22—11321no—
347C22C22×C22⋊D28311yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—11321no—
357C4—11321no—
358C4#41×D28311yescharacteristic
359C4#2258365611yescharacteristic
360C2—81no—
361C2—81no—
362C2—22641no—
363C2—22641no—
364C2#3182713411yescharacteristic
365C2#3182726311yescharacteristic
366C2#3182726811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#559×C283C2
socleC22×C283C22×D4
hypercenter#559D283
hypocenterC283#3403
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #31827200C2semidirect
2. #31826855C2semidirect
3. #31826852C2semidirect
4. #31826847C2semidirect
5. #31826687C2semidirect
6. #31826684C2semidirect
7. #31826680C2semidirect
8. #31826677C2semidirect
9. #31826660C2semidirect
10. #31826657C2semidirect
11. #31826596C2semidirect
12. #31826565C2semidirect
13. #31826563C2semidirect
14. C4×#17985377C2semidirect
15. #559×C283C2semidirect
183. C283#3403semidirect
186. #559D283semidirect

Maximal subgroups

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

subgroupindex
#318272002
#318268552
#318268522
#318268472
#318266872
#318266842
#318266802
#318266772
#318266602
#318266572
#318265962
#318265652
#318265632
C4×#179853772
#559×C2832
#3403283