Finite Group Databasebeta

← #24993956

Subgroups — #24993956

Order 11008.

486 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143675C211yesmaximal, characteristic
2#19139803C211yesmaximal, characteristic
3#19134588C211yesmaximal, characteristic
4#19133277C211yesmaximal, characteristic
5#19133275C211yesmaximal, characteristic
6#19132498C211yesmaximal, characteristic
7C43×#1303C211yesmaximal, characteristic
8C2×#13063325C2211yescharacteristic
9C2×C4×Dic86C2211yescharacteristic
10C8×Dic86—22no—
11#14583023—22no—
12#14582952C2211yescharacteristic
13#14582949—22no—
14#14582923C2211yescharacteristic
15C2×#13063243—21no—
16#14582820C414yes—
17#14582805—21no—
18#14582798—22no—
19#14582769—21no—
20#14582667—21no—
21#14582647—22no—
22#14582647—22no—
23C43×#431C2211yescharacteristic
24C43×#423C2211yescharacteristic
25C4×C4⋊C4×C43C2211yescharacteristic
26C22×Dic86C2×C412yes—
27C22×Dic86D411yescharacteristic
28C2×#10621877—21no—
29#13063325—21no—
30#13063325—21no—
31#13063325—21no—
32#13063325—21no—
33C4×Dic86—21no—
34C4×Dic86—21no—
35C4×Dic86—21no—
36C4×Dic86—21no—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43—24no—
40C2×C4⋊Dic43D411yescharacteristic
41C2×Dic43⋊C4C2×C412yes—
42C2×C4×Dic43D412yes—
43C4⋊(C43⋊C8)—21no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)D412yes—
46Dic43⋊C8—24no—
47#13063243—42no—
48C22⋊(C43⋊C8)—21no—
49C4×C43⋊C8—21no—
50C8×Dic43—24no—
51C43⋊#95—24no—
52C2×M16×C43—21no—
53C2×C4⋊C4×C43—21no—
54C2×C42×C43—21no—
55C2×C42×C43C2311yescharacteristic
56C4⋊C8×C43—21no—
57C4⋊C8×C43—21no—
58C4⋊C8×C43D412yes—
59C22⋊C8×C43—21no—
60C4×C8×C43—21no—
61#95×C43C2×C412yes—
62C22×C4×C43—22no—
63C22×C4×C43C22×C411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×Dic43—22no—
67C22×Dic43C22⋊C412yes—
68C22×Dic43C22⋊C412yes—
69C2×Dic86—21no—
70C2×Dic86—21no—
71C2×Dic86—21no—
72C2×Dic86—21no—
73C2×Dic86—22no—
74C2×Dic86—22no—
75C2×Dic86—82no—
76C2×Dic86SD1612yes—
77C2×Dic86Q1612yes—
78M16×C43—41no—
79M16×C43—41no—
80C2×C8×C43—22no—
81C2×C8×C43—41no—
82C4⋊C4×C43—24no—
83C42×C43—41no—
84C42×C43—41no—
85C42×C43C2×D411yescharacteristic
86C42×C43C2×D411yescharacteristic
87C42×C43#4111yescharacteristic
88C42×C43#4111yescharacteristic
89C4⋊Dic43—21no—
90C4⋊Dic43—21no—
91C4⋊Dic43—41no—
92C4⋊Dic43—41no—
93C4⋊Dic43—41no—
94C4⋊Dic43—41no—
95C4⋊Dic43—84no—
96Dic43⋊C4—22no—
97Dic43⋊C4—22no—
98C4×Dic43—22no—
99C4×Dic43—22no—
100#10621877—41no—
101#10621877—41no—
102C2×C43⋊C8—22no—
103C2×C43⋊C8—41no—
104C23×C43C2×C22⋊C411yescharacteristic
105C2×C4×C43—22no—
106C2×C4×C43—24no—
107C2×C4×C43—41no—
108C2×C4×C43—42no—
109C2×C4×C43—42no—
110C2×C4×C43C4×D411yescharacteristic
111C2×C4×C43C4×D411yescharacteristic
112C2×C4×C43#12011yescharacteristic
113C2×C4×C43#12111yescharacteristic
114C2×C4×C43#12111yescharacteristic
115C2×C4×C43#12311yescharacteristic
116C2×C4×C43C2×SD1611yescharacteristic
117C2×C4×C43C2×Q1611yescharacteristic
118C2×C4×C43#13511yescharacteristic
119C2×C4×C43#13511yescharacteristic
120C2×Dic43—22no—
121C2×Dic43—22no—
122C2×Dic43—22no—
123C2×Dic43—42no—
124C2×Dic43—44no—
125C2×Dic43—42no—
126C2×Dic43#10314yes—
127Dic86—22no—
128Dic86—22no—
129Dic86—22no—
130Dic86—22no—
131Dic86—82no—
132Dic86—82no—
133C8×C43—42no—
134C8×C43—81no—
135C43⋊C8—42no—
136C43⋊C8—81no—
137#9392—431nomaximal, Sylow
138C22×C43—21no—
139C22×C43—21no—
140C22×C43#38611yescharacteristic
141C22×C43C2×#10311yescharacteristic
142C22×C43#41611yescharacteristic
143C4×C43—21no—
144C4×C43—21no—
145C4×C43—21no—
146C4×C43—44no—
147C4×C43#45612yes—
148C4×C43#46511yescharacteristic
149C4×C43#46511yescharacteristic
150C4×C43#46711yescharacteristic
151C4×C43#46711yescharacteristic
152Dic43—24no—
153Dic43—42no—
154Dic43—82no—
155#2982—431no—
156#2567—431no—
157#1801—431no—
158#1548—431no—
159#1548—431no—
160#1303—431no—
161#1303D4311yescharacteristic
162C2×C43—21no—
163C2×C43—21no—
164C2×C43#188611yescharacteristic
165C2×C43#189211yescharacteristic
166C2×C43#191411yescharacteristic
167C2×C4⋊Q8—431no—
168C2×C4×Q8—431no—
169C8×Q8—862no—
170C8×Q8—862no—
171#431—431no—
172#431—862no—
173#431C2×D4311yescharacteristic
174#423—431no—
175#423C2×D4311yescharacteristic
176C2×#101—861no—
177#395—434no—
178#391—861no—
179#389—862no—
180#384—861no—
181C4×C4⋊C4C2×D4311yescharacteristic
182#343—861no—
183#333—862no—
184#333—862no—
185C43#939211yescharacteristic, complemented, Sylow
186C22×Q8—431no—
187C22×Q8—432no—
188C2×M16—21no—
189C2×M16—861no—
190C4⋊Q8—861no—
191C4⋊Q8—861no—
192C4⋊Q8—861no—
193C4⋊Q8—861no—
194C4×Q8—861no—
195C4×Q8—861no—
196C4×Q8—861no—
197C4×Q8—861no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—432no—
200C2×C4⋊C4—431no—
201C2×C4⋊C4—864no—
202C2×C4⋊C4—861no—
203C2×C4⋊C4—861no—
204C2×C42—21no—
205C2×C42—432no—
206C2×C42C22×D4311yescharacteristic
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—432no—
210C4⋊C8—864no—
211C4⋊C8—861no—
212C4⋊C8—861no—
213C4⋊C8D17212yes—
214#101—1722no—
215C22⋊C8—21no—
216C22⋊C8—861no—
217C4×C8—21no—
218C4×C8—864no—
219C4×C8—861no—
220#95—864no—
221#95C4×D4312yes—
222C2×Q8—432no—
223C2×Q8—432no—
224C2×Q8—861no—
225C2×Q8—861no—
226C2×Q8—861no—
227C2×Q8—861no—
228C2×Q8—862no—
229C2×Q8—862no—
230C2×Q8—3442no—
231C22×C4—22no—
232C22×C4—432no—
233C22×C4—432no—
234C22×C4—862no—
235C22×C4C2×C4×D4311yescharacteristic
236C22×C4D4×D4311yescharacteristic
237C22×C4D4×D4311yescharacteristic
238M16—41no—
239M16—41no—
240M16—1721no—
241M16—1721no—
242C2×C8—22no—
243C2×C8—41no—
244C2×C8—862no—
245C2×C8—1721no—
246C4⋊C4—24no—
247C4⋊C4—862no—
248C4⋊C4—862no—
249C4⋊C4—861no—
250C4⋊C4—861no—
251C4⋊C4—3444no—
252C4⋊C4—1721no—
253C4⋊C4—1721no—
254C4⋊C4—1721no—
255C4⋊C4—1721no—
256C42—41no—
257C42—41no—
258C42—862no—
259C42—862no—
260C42C2×D17211yescharacteristic
261C42#1062189811yescharacteristic
262C42D4×D4311yescharacteristic
263C42#1062190211yescharacteristic
264C23C22⋊C4×D4311yescharacteristic
265Q8—862no—
266Q8—862no—
267Q8—862no—
268Q8—862no—
269Q8—3442no—
270Q8—3442no—
271C2×C4—22no—
272C2×C4—24no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—434no—
277C2×C4—862no—
278C2×C4—862no—
279C2×C4—862no—
280C2×C4—1724no—
281C2×C4—1722no—
282C2×C4—1722no—
283C2×C4#1306328711yescharacteristic
284C2×C4C4×D17211yescharacteristic
285C2×C4#1306329511yescharacteristic
286C2×C4#1306329811yescharacteristic
287C2×C4#1306330011yescharacteristic
288C2×C4#1306331011yescharacteristic
289C2×C4SD16×D4311yescharacteristic
290C2×C4Q16×D4311yescharacteristic
291C2×C4#1306334411yescharacteristic
292C2×C4#1306334611yescharacteristic
293C8—42no—
294C8—81no—
295C8—3441no—
296C8—1722no—
297C22—21no—
298C22—21no—
299C22#1458277711yescharacteristic
300C22#103×D4311yescharacteristic
301C22#1458289211yescharacteristic
302C4—21no—
303C4—21no—
304C4—21no—
305C4—44no—
306C4—864no—
307C4—3442no—
308C4—1722no—
309C4#1458308312yes—
310C4#1458312711yescharacteristic
311C4#1458312911yescharacteristic
312C4#1458313911yescharacteristic
313C4#1458314111yescharacteristic
314C2—21no—
315C2—21no—
316C2#1913498711yescharacteristic
317C2#1913501711yescharacteristic
318C2#1913514111yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1303C2
socleC22×C43#386
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1303D43
hypocenterC43#9392
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
185. C43#9392semidirect

Maximal subgroups

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

subgroupindex
#191436752
#191398032
#191345882
#191332772
#191332752
#191324982
C43×#13032
#939243