Finite Group Databasebeta

← #25007752

Subgroups — #25007752

Order 11008.

372 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 95 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#19139957C211yesmaximal, characteristic
2#19134591C211yesmaximal, characteristic
3#19132626C212yesmaximal
4#19132623C212yesmaximal
5C43×#1461C211yesmaximal, characteristic
6C2×C4×Dic86C411yescharacteristic
7#14582923—21no—
8C2×#13063244—21no—
9#14582838C411yescharacteristic
10#14582838C2211yescharacteristic
11#14582819C411yescharacteristic
12#14582819C2211yescharacteristic
13#14582806—21no—
14#14582795—21no—
15#14582783—21no—
16#14582783—21no—
17#14582765C411yescharacteristic
18#14582668C2212yes—
19C2×C4×Q8×C43C2211yescharacteristic
20C43×#431—21no—
21C43×#324—21no—
22C43×#324C2212yes—
23C22×Dic86C2×C411yescharacteristic
24C2×#10621877—22no—
25C4×Dic86—41no—
26C4×Dic86—41no—
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×C4×Dic43—21no—
33C4⋊(C43⋊C8)—41no—
34C4⋊(C43⋊C8)—41no—
35#13063244—42no—
36C43⋊#95—21no—
37C43⋊#95—21no—
38C43⋊#95—21no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95C2×C411yescharacteristic
44C43⋊#95C2×C411yescharacteristic
45C22×Q8×C43D411yescharacteristic
46C4×Q8×C43—41no—
47C4×Q8×C43—41no—
48C2×C4⋊C4×C43C2×C411yescharacteristic
49C2×C4⋊C4×C43D411yescharacteristic
50C2×C4⋊C4×C43C2311yescharacteristic
51C2×C42×C43C2×C411yescharacteristic
52C2×C42×C43D411yescharacteristic
53C2×C42×C43D411yescharacteristic
54C4⋊C8×C43—41no—
55C22⋊C8×C43—22no—
56C4×C8×C43—41no—
57C2×Q8×C43—41no—
58C2×Q8×C43—41no—
59C2×Q8×C43SD1612yes—
60C2×Q8×C43Q1612yes—
61C22×C4×C43C22⋊C411yescharacteristic
62C22×C4×C43C22⋊C411yescharacteristic
63C22×C4×C43C22⋊C411yescharacteristic
64C22×C4×C43C22⋊C411yescharacteristic
65C22×C4×C43C22×C411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—21no—
72C2×Dic86—41no—
73C2×Dic86—42no—
74C2×C8×C43—42no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77C4⋊C4×C43—41no—
78C42×C43—21no—
79C42×C43—21no—
80C42×C43—21no—
81C42×C43—21no—
82C42×C43—21no—
83C42×C43—21no—
84C4⋊Dic43—42no—
85C4⋊Dic43—41no—
86Dic43⋊C4—42no—
87Dic43⋊C4—42no—
88Dic43⋊C4—41no—
89Dic43⋊C4—41no—
90C4×Dic43—42no—
91#10621877—42no—
92#10621877—42no—
93C2×C43⋊C8—42no—
94C23×C43C2×C22⋊C411yescharacteristic
95Q8×C43—42no—
96Q8×C43—42no—
97C2×C4×C43—21no—
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43#9911yescharacteristic
111C2×C4×C43#9911yescharacteristic
112C2×C4×C43#10312yes—
113C2×C4×C43#10312yes—
114C2×C4×C43C2×SD1611yescharacteristic
115C2×C4×C43C2×Q1611yescharacteristic
116C2×Dic43—22no—
117C2×Dic43—41no—
118C2×Dic43—41no—
119C2×Dic43—41no—
120C2×Dic43—41no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—42no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127Dic86—42no—
128Dic86—42no—
129C8×C43—82no—
130C43⋊C8—82no—
131#11905—431nomaximal, Sylow
132C22×C43—21no—
133C22×C43—21no—
134C22×C43C2×#9911yescharacteristic
135C22×C43C2×#10311yescharacteristic
136C22×C43#42111yescharacteristic
137C4×C43—21no—
138C4×C43—21no—
139C4×C43—21no—
140C4×C43—22no—
141C4×C43—22no—
142C4×C43—21no—
143C4×C43—41no—
144C4×C43—41no—
145C4×C43—41no—
146Dic43—42no—
147Dic43—81no—
148Dic43—81no—
149Dic43—81no—
150#2581—431no—
151#1801—431no—
152#1461D4311yescharacteristic
153#1354—432no—
154#1353—432no—
155C2×C43—21no—
156C2×C43—21no—
157C2×C43#152011yescharacteristic
158C2×C43#212011yescharacteristic
159C2×C43#213311yescharacteristic
160C2×C4×Q8—431no—
161C2×C4×Q8C2×D4311yescharacteristic
162#431—21no—
163#423—861no—
164C2×#101—861no—
165#400—431no—
166#400—431no—
167#395—431no—
168#395—431no—
169#391—861no—
170#389—861no—
171#387—861no—
172#387—861no—
173#382—431no—
174#343—432no—
175#324—21no—
176#324C2×D4312yes—
177C43#1190511yescharacteristic, complemented, Sylow
178C22×Q8—431no—
179C22×Q8D17211yescharacteristic
180C2×M16—862no—
181C4×Q8—41no—
182C4×Q8—41no—
183C4×Q8—1721no—
184C4×Q8—1721no—
185C2×C4⋊C4—431no—
186C2×C4⋊C4—861no—
187C2×C4⋊C4—861no—
188C2×C4⋊C4—861no—
189C2×C4⋊C4—861no—
190C2×C4⋊C4C4×D4311yescharacteristic
191C2×C4⋊C4C22⋊D4311yescharacteristic
192C2×C4⋊C4C22×D4311yescharacteristic
193C2×C42—861no—
194C2×C42C4×D4311yescharacteristic
195C2×C42D17211yescharacteristic
196C2×C42C22⋊D4311yescharacteristic
197C4⋊C8—41no—
198C4⋊C8—1721no—
199C4⋊C8—1721no—
200#101—1722no—
201C22⋊C8—22no—
202C4×C8—41no—
203#95—431no—
204#95—431no—
205#95—861no—
206#95—861no—
207#95—861no—
208#95—861no—
209#95—861no—
210#95—861no—
211#95—861no—
212C2×Q8—41no—
213C2×Q8—41no—
214C2×Q8—1721no—
215C2×Q8—1722no—
216C2×Q8#1062187312yes—
217C2×Q8Dic17212yes—
218C22×C4—861no—
219C22×C4—861no—
220C22×C4—861no—
221C22×C4—861no—
222C22×C4(C2×D43)⋊C411yescharacteristic
223C22×C4(C2×D43)⋊C411yescharacteristic
224C22×C4(C2×D43)⋊C411yescharacteristic
225C22×C4(C2×D43)⋊C411yescharacteristic
226C22×C4C2×C4×D4311yescharacteristic
227C22×C4C2×D17211yescharacteristic
228C22×C4C2×C22⋊D4311yescharacteristic
229M16—1722no—
230M16—1722no—
231C2×C8—42no—
232C2×C8—1722no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—1721no—
237C4⋊C4—1722no—
238C4⋊C4—1722no—
239C4⋊C4—1722no—
240C4⋊C4—1721no—
241C4⋊C4—1721no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—1722no—
249C23C2×(C2×D43)⋊C411yescharacteristic
250Q8—42no—
251Q8—42no—
252Q8—1722no—
253Q8—1722no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—862no—
268C2×C4—1721no—
269C2×C4—1721no—
270C2×C4—1721no—
271C2×C4—1721no—
272C2×C4—1722no—
273C2×C4—1721no—
274C2×C4—1721no—
275C2×C4—1721no—
276C2×C4—1721no—
277C2×C4—1721no—
278C2×C4#1306323911yescharacteristic
279C2×C4#1306323911yescharacteristic
280C2×C4#1306325012yes—
281C2×C4#1306325012yes—
282C2×C4C2×#1062187311yescharacteristic
283C2×C4C2×Dic17211yescharacteristic
284C8—82no—
285C8—3442no—
286C22—21no—
287C22—21no—
288C22C2×#1306323911yescharacteristic
289C22C2×#1306325011yescharacteristic
290C22#1458291511yescharacteristic
291C4—21no—
292C4—21no—
293C4—21no—
294C4—22no—
295C4—22no—
296C4—21no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—3441no—
301C4—3441no—
302C4—3441no—
303C4—1722no—
304C2—21no—
305C2—21no—
306C2#1913316811yescharacteristic
307C2#1913623411yescharacteristic
308C2#1913628211yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1461C2
socleC22×C43C2×#99
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1461D43
hypocenterC43#11905
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
177. C43#11905semidirect

Maximal subgroups

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

subgroupindex
#191399572
#191345912
#191326262
#191326232
C43×#14612
#1190543