Finite Group Databasebeta

← #25017011

Subgroups — #25017011

Order 11008.

316 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 67 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#19145656C211yesmaximal, characteristic
2#19136290C211yesmaximal, characteristic, complemented
3#19132767C212yesmaximal, complemented
4#19132761C212yesmaximal, complemented
5C43×#2133C211yesmaximal, characteristic, complemented
6#14583504C411yescharacteristic
7#14583289C411yescharacteristic
8#14583273C2211yescharacteristic
9#14583267C2211yescharacteristic
10#14583253C411yescharacteristic
11#14583111—21no—
12#14583101—21no—
13#14583044—21no—
14#14583038—21no—
15#14582960C411yescharacteristic
16#14582883—21no—
17#14582698—21no—
18#14582698C2212yes—
19C43×#536C2211yescharacteristic
20C2×#101×C43—21no—
21C43×#356C2212yes—
22C43×#355—21no—
23C2×#10621884—21no—
24C2×#10621884—21no—
25C2×#10621884—21no—
26C2×#10621882—21no—
27C2×#10621877—41no—
28#13063322C2×C411yescharacteristic
29#13063317C2×C411yescharacteristic
30#13063310—41no—
31#13063299—21no—
32#13063298—41no—
33C4×D172—21no—
34C4⋊(C43⋊C8)—21no—
35#13063249—21no—
36#13063249—21no—
37#13063249—21no—
38#13063246—21no—
39#13063244—22no—
40#13063242—41no—
41C22⋊(C43⋊C8)—21no—
42#13063236C2×C411yescharacteristic
43C4×C43⋊C8C2×C411yescharacteristic
44C2×#41×C43D411yescharacteristic
45C22×Q8×C43D411yescharacteristic
46C2×M16×C43—41no—
47C4⋊Q8×C43D411yescharacteristic
48C4⋊Q8×C43C2311yescharacteristic
49#124×C43C2×C411yescharacteristic
50#124×C43D411yescharacteristic
51#123×C43—41no—
52C22⋊Q8×C43—41no—
53#117×C43C2×C411yescharacteristic
54#101×C43—22no—
55#101×C43—41no—
56#41×C43—81no—
57C2×Q8×C43—21no—
58C2×Q8×C43—81no—
59C2×Q8×C43C22⋊C411yescharacteristic
60C2×Q8×C43C2×D411yescharacteristic
61C2×Q8×C43C2×D411yescharacteristic
62C2×D4×C43—21no—
63C2×D4×C43C22⋊C411yescharacteristic
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43C22⋊C411yescharacteristic
67C2×C22⋊D43—41no—
68C2×D172—21no—
69C2×D172—41no—
70C2×C4×D43—41no—
71M16×C43—42no—
72M16×C43—81no—
73C2×C8×C43—81no—
74C4⋊C4×C43—21no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77C22⋊C4×C43—21no—
78C22⋊C4×C43—41no—
79C22⋊C4×C43—41no—
80C42×C43C22⋊C411yescharacteristic
81C42×C43C22×C411yescharacteristic
82#10621884—81no—
83#10621884—81no—
84#10621884—81no—
85#10621882—81no—
86(C2×D43)⋊C4—41no—
87(C2×D43)⋊C4—41no—
88C4⋊Dic43—21no—
89Dic43⋊C4—41no—
90#10621877—42no—
91#10621877—81no—
92C2×C43⋊C8—21no—
93C2×C43⋊C8—21no—
94C2×C43⋊C8—81no—
95C23×C43—21no—
96C23×C43#9911yescharacteristic
97C22×D43—41no—
98Q8×C43—41no—
99Q8×C43—41no—
100Q8×C43—41no—
101Q8×C43—81no—
102D4×C43—41no—
103D4×C43—81no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43#9911yescharacteristic
115C2×C4×C43C2×C22⋊C411yescharacteristic
116C22⋊D43—161no—
117C2×Dic43—41no—
118D172—41no—
119D172—41no—
120D172—161no—
121C4×D43—161no—
122C8×C43—82no—
123C43⋊C8—41no—
124C43⋊C8—41no—
125C43⋊C8—82no—
126#13611—431nomaximal, Sylow
127C22×C43—21no—
128C22×C43—41no—
129C22×C43—41no—
130C22×C43—81no—
131C22×C43C2×#9911yescharacteristic
132C2×D43—81no—
133C2×D43—81no—
134C2×D43—81no—
135C4×C43—21no—
136C4×C43—21no—
137C4×C43—41no—
138C4×C43—41no—
139C4×C43—41no—
140C4×C43—41no—
141C4×C43—41no—
142Dic43—81no—
143#3221—431no—
144#2135—431no—
145#2133D4311yescharacteristic, complemented
146#1413—432no—
147#1410—432no—
148C2×C43—21no—
149C2×C43—41no—
150C2×C43—81no—
151C2×C43#212711yescharacteristic
152D43—161no—
153#540—431no—
154#536C2×D4311yescharacteristic
155#496—431no—
156#492—431no—
157#491—431no—
158#488—431no—
159#463—861no—
160#461—861no—
161#449—861no—
162#448—861no—
163#433—431no—
164#413—861no—
165C2×#101—21no—
166#356—432no—
167#356—861no—
168#356C2×D4312yes—
169#355—21no—
170C43#1361111yescharacteristic, complemented, Sylow
171C2×#41D17211yescharacteristic
172C22×Q8C22⋊D4311yescharacteristic
173C2×SD16—861no—
174C2×SD16—861no—
175C2×SD16—861no—
176C2×D8—861no—
177C2×M16—41no—
178C2×M16—1721no—
179C4⋊Q8D17211yescharacteristic
180C4⋊Q8C22×D4311yescharacteristic
181#127—431no—
182#125—431no—
183#124C4×D4311yescharacteristic
184#124C22⋊D4311yescharacteristic
185#123—41no—
186#123—1721no—
187C22⋊Q8—41no—
188#121—861no—
189#121—1721no—
190C4×D4—861no—
191#117C4×D4311yescharacteristic
192C4⋊C8—861no—
193#103—861no—
194#103—861no—
195#103—861no—
196#102—861no—
197#101—22no—
198#101—41no—
199#101—862no—
200#100—1721no—
201C22⋊C8—861no—
202#97—431no—
203C4×C8—431no—
204#41—81no—
205C2×Q8—21no—
206C2×Q8—81no—
207C2×Q8(C2×D43)⋊C411yescharacteristic
208C2×Q8C2×D17211yescharacteristic
209C2×Q8C2×C22⋊D4311yescharacteristic
210C2×D4—21no—
211C2×D4—861no—
212C2×D4—1721no—
213C2×D4—1721no—
214C2×D4(C2×D43)⋊C411yescharacteristic
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—1721no—
218C22×C4(C2×D43)⋊C411yescharacteristic
219SD16—3441no—
220SD16—3441no—
221SD16—3441no—
222D8—3441no—
223M16—42no—
224M16—81no—
225M16—3441no—
226M16—1722no—
227C2×C8—81no—
228C2×C8—861no—
229C2×C8—861no—
230C2×C8—3441no—
231C4⋊C4—21no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—861no—
235C4⋊C4—1721no—
236C22⋊C4—21no—
237C22⋊C4—41no—
238C22⋊C4—41no—
239C22⋊C4—1721no—
240C22⋊C4—1721no—
241C42(C2×D43)⋊C411yescharacteristic
242C42C2×C4×D4311yescharacteristic
243C23—21no—
244C23—1721no—
245C23#1306323911yescharacteristic
246Q8—41no—
247Q8—41no—
248Q8—41no—
249Q8—81no—
250D4—41no—
251D4—81no—
252D4—1721no—
253D4—1721no—
254D4—6881no—
255D4—6881no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—1721no—
267C2×C4—6881no—
268C2×C4#1306323911yescharacteristic
269C2×C4C2×(C2×D43)⋊C411yescharacteristic
270C8—82no—
271C8—3442no—
272C8—1721no—
273C8—1721no—
274C22—21no—
275C22—41no—
276C22—41no—
277C22—81no—
278C22—3441no—
279C22—3441no—
280C22—3441no—
281C22C2×#1306323911yescharacteristic
282C4—21no—
283C4—21no—
284C4—41no—
285C4—41no—
286C4—41no—
287C4—41no—
288C4—41no—
289C4—3441no—
290C2—21no—
291C2—41no—
292C2—81no—
293C2—6881no—
294C2#1913626211yescharacteristic
subgroupG/H
centerC2#19136262
commutatorC42×C43C22×C4
FrattiniC4⋊Q8C22×D43
FittingC43×#2133C2
socleC2×C43#2127
prime radical#19145656C2
cosocleC4⋊Q8×C43C23
hypercenter#2133D43
hypocenterC43#13611
LCSG ▷ C42×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C22×C4 ◁ #536 ◁ #2133

Complements

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

NH ≅ G/Ntype
2. #19136290C2semidirect
3. #19132767C2semidirect
4. #19132761C2semidirect
5. C43×#2133C2semidirect
145. #2133D43semidirect
170. C43#13611semidirect

Maximal subgroups

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

subgroupindex
#191456562
#191362902
#191327672
#191327612
C43×#21332
#1361143