Finite Group Databasebeta

← #25005987

Subgroups — #25005987

Order 11008.

670 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 87 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#19137175C211yesmaximal, characteristic
2#19132929C211yesmaximal, characteristic, complemented
3#19132526C214yesmaximal, complemented
4C43×#1464C211yesmaximal, characteristic, complemented
5C23×D172C411yescharacteristic
6C2×#13063284C411yescharacteristic
7#14582956—21no—
8#14582801—21no—
9#14582801—21no—
10#14582800C412yes—
11#14582800C2212yes—
12#14582754—21no—
13#14582754—21no—
14#14582625C2212yescomplemented
15#14582623—21no—
16C2×#117×C43C2211yescharacteristic
17C43×#432—21no—
18C43×#324C2212yescomplemented
19C43×#323—21no—
20C24×D43—21no—
21C22×D172—21no—
22C22×D172—24no—
23C22×D172—42no—
24C22×D172—41no—
25C22×D172—41no—
26C22×D172C2×C412yes—
27#13063284—42no—
28C2×C4⋊Dic43—21no—
29C2×C22⋊Dic43—21no—
30C2×(C2×D43)⋊C4—22no—
31C2×(C2×D43)⋊C4—22no—
32C2×(C2×D43)⋊C4—22no—
33C2×(C2×D43)⋊C4—22no—
34C2×C4×Dic43C2×C412yes—
35C4⋊(C43⋊C8)—41no—
36C22⋊(C43⋊C8)—22no—
37#13063236—41no—
38C23×C4×C43C2×C411yescharacteristic
39#117×C43—41no—
40#117×C43—41no—
41C2×C4⋊C4×C43C2×C411yescharacteristic
42C2×C4⋊C4×C43C2311yescharacteristic
43C2×C22⋊C4×C43D411yescharacteristic
44C2×C22⋊C4×C43D411yescharacteristic
45C2×C42×C43D411yescharacteristic
46C2×C42×C43D411yescharacteristic
47C4⋊C8×C43—41no—
48C22⋊C8×C43—22no—
49#97×C43—41no—
50C24×C43C22⋊C411yescharacteristic
51C23×D43—22no—
52C23×D43—24no—
53C23×D43—42no—
54C23×D43—42no—
55C23×D43—82no—
56C23×D43—82no—
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—22no—
60C22×C4×C43—22no—
61C22×C4×C43C22⋊C411yescharacteristic
62C22×C4×C43C22⋊C411yescharacteristic
63C22×C4×C43C22⋊C411yescharacteristic
64C22×C4×C43C22×C411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×Dic43—22no—
68C2×D172—24no—
69C2×D172—22no—
70C2×D172—48no—
71C2×D172—48no—
72C2×D172—42no—
73C2×D172—41no—
74C2×D172—41no—
75C2×D172—42no—
76C2×D172—42no—
77C2×D172M1614yes—
78C2×C8×C43—42no—
79C4⋊C4×C43—41no—
80C4⋊C4×C43—41no—
81C22⋊C4×C43—41no—
82C22⋊C4×C43—41no—
83C42×C43—21no—
84C42×C43—21no—
85C42×C43—21no—
86C42×C43—21no—
87C22⋊Dic43—42no—
88(C2×D43)⋊C4—82no—
89(C2×D43)⋊C4—82no—
90(C2×D43)⋊C4—82no—
91(C2×D43)⋊C4—82no—
92C4⋊Dic43—42no—
93C4×Dic43—42no—
94C2×C43⋊C8—42no—
95C23×C43—21no—
96C23×C43—21no—
97C23×C43—41no—
98C23×C43—41no—
99C23×C43#10012yes—
100C23×C43C2×C22⋊C411yescharacteristic
101C22×D43—24no—
102C22×D43—42no—
103C22×D43—42no—
104C22×D43—42no—
105C22×D43—42no—
106C22×D43—48no—
107C22×D43—42no—
108C22×D43—42no—
109C22×D43—88no—
110C22×D43—88no—
111C22×D43—84no—
112C22×D43—84no—
113C2×C4×C43—24no—
114C2×C4×C43—24no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43#9911yescharacteristic
128C2×C4×C43#9911yescharacteristic
129C2×C4×C43C2×M1612yes—
130C2×Dic43—42no—
131C2×Dic43—42no—
132C2×Dic43—42no—
133D172—44no—
134D172—44no—
135D172—44no—
136D172—44no—
137C8×C43—82no—
138C43⋊C8—82no—
139#11509—431nomaximal, Sylow
140C22×C43—21no—
141C22×C43—21no—
142C22×C43—22no—
143C22×C43—42no—
144C22×C43—42no—
145C22×C43—41no—
146C22×C43—41no—
147C22×C43#40711yescharacteristic
148C22×C43C2×#9911yescharacteristic
149C22×C43C2×#10011yescharacteristic
150C2×D43—44no—
151C2×D43—44no—
152C2×D43—44no—
153C2×D43—82no—
154C2×D43—82no—
155C2×D43—816no—
156C2×D43—82no—
157C2×D43—82no—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—22no—
161C4×C43—41no—
162C4×C43—41no—
163C4×C43—41no—
164C4×C43—41no—
165Dic43—82no—
166#2309—431no—
167#1464—431no—
168#1464D4311yescharacteristic, complemented
169#1318—434no—
170C2×C43—21no—
171C2×C43—21no—
172C2×C43—42no—
173C2×C43#146211yescharacteristic
174C2×C43#212811yescharacteristic
175C2×C43#213411yescharacteristic
176D43—84no—
177C23×D4—431no—
178C2×#117—431no—
179C2×#117C2×D4311yescharacteristic
180#432—21no—
181#432—861no—
182#390—432no—
183#390—432no—
184#390—861no—
185#390—861no—
186#379—861no—
187#379—861no—
188#324—432no—
189#324C2×D4312yescomplemented
190#323—21no—
191#323—861no—
192C43#1150911yescharacteristic, complemented, Sylow
193C25—861no—
194C22×D4—432no—
195C22×D4—864no—
196C22×D4—861no—
197C22×D4—1722no—
198C22×D4—1721no—
199C22×D4—1721no—
200C23×C4C4×D4311yescharacteristic
201#117—41no—
202#117—41no—
203#117—1722no—
204C2×C4⋊C4—861no—
205C2×C4⋊C4C4×D4311yescharacteristic
206C2×C4⋊C4C22×D4311yescharacteristic
207C2×C22⋊C4—862no—
208C2×C22⋊C4—862no—
209C2×C22⋊C4—862no—
210C2×C22⋊C4—862no—
211C2×C22⋊C4—861no—
212C2×C22⋊C4D17211yescharacteristic
213C2×C22⋊C4C22⋊D4311yescharacteristic
214C2×C42—432no—
215C2×C42D17211yescharacteristic
216C2×C42C22⋊D4311yescharacteristic
217C4⋊C8—41no—
218C4⋊C8—1721no—
219C22⋊C8—22no—
220C22⋊C8—862no—
221#97—41no—
222#97—1721no—
223C24—864no—
224C24—862no—
225C24—3442no—
226C24—3442no—
227C24—1722no—
228C24—1722no—
229C24(C2×D43)⋊C411yescharacteristic
230C2×D4—434no—
231C2×D4—864no—
232C2×D4—862no—
233C2×D4—1722no—
234C2×D4—1722no—
235C2×D4—1728no—
236C2×D4—1728no—
237C2×D4—1722no—
238C2×D4—1721no—
239C2×D4—1721no—
240C22×C4—22no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—22no—
244C22×C4—862no—
245C22×C4(C2×D43)⋊C411yescharacteristic
246C22×C4(C2×D43)⋊C411yescharacteristic
247C22×C4(C2×D43)⋊C411yescharacteristic
248C22×C4C2×C4×D4311yescharacteristic
249C22×C4C2×D17211yescharacteristic
250C22×C4C2×C22⋊D4311yescharacteristic
251C2×C8—42no—
252C2×C8—1722no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—1722no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C22⋊C4—3442no—
259C22⋊C4—3442no—
260C22⋊C4—3442no—
261C22⋊C4—3442no—
262C22⋊C4—1722no—
263C42—21no—
264C42—21no—
265C42—21no—
266C42—21no—
267C42—1722no—
268C23—21no—
269C23—21no—
270C23—41no—
271C23—41no—
272C23—864no—
273C23—3448no—
274C23—3444no—
275C23—3444no—
276C23—3448no—
277C23—1722no—
278C23—1722no—
279C23—1722no—
280C23—1722no—
281C23—1728no—
282C23—1722no—
283C23—1722no—
284C23#1306324112yes—
285C23C2×(C2×D43)⋊C411yescharacteristic
286D4—1724no—
287D4—1724no—
288D4—1724no—
289D4—1724no—
290C2×C4—24no—
291C2×C4—24no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—1722no—
305C2×C4—1722no—
306C2×C4—1722no—
307C2×C4#1306323911yescharacteristic
308C2×C4#1306323911yescharacteristic
309C2×C4M16×D4312yes—
310C8—82no—
311C8—3442no—
312C22—21no—
313C22—21no—
314C22—22no—
315C22—42no—
316C22—42no—
317C22—41no—
318C22—41no—
319C22—3442no—
320C22—3442no—
321C22—34416no—
322C22—3442no—
323C22—3442no—
324C22—1724no—
325C22—1724no—
326C22—1724no—
327C22#1458286211yescharacteristic
328C22C2×#1306323911yescharacteristic
329C22C2×#1306324111yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—3442no—
338C2—21no—
339C2—21no—
340C2—42no—
341C2—3444no—
342C2#1913292111yescharacteristic
343C2#1913626611yescharacteristic
344C2#1913628611yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1464C2
socleC22×C43C2×#99
prime radicalC23×D172C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1464D43
hypocenterC43#11509
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
2. #19132929C2semidirect
3. #19132526C2semidirect
4. C43×#1464C2semidirect
14. #14582625C22semidirect
18. C43×#324C22semidirect
168. #1464D43semidirect
189. #324C2×D43semidirect
192. C43#11509semidirect

Maximal subgroups

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

subgroupindex
#191371752
#191329292
#191325262
C43×#14642
#1150943