Finite Group Databasebeta

← #25012582

Subgroups — #25012582

Order 11008.

544 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 103 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#124×Dic43C211yesmaximal, characteristic
2C2×#14582694C211yesmaximal, characteristic
3#19134581C212yesmaximal
4#19132719C212yesmaximal
5C2×C43×#354C211yesmaximal, characteristic
6C2×Q8×Dic43C411yescharacteristic, complemented
7C2×D4×Dic43C2211yescharacteristic
8C2×#13063240C2212yes—
9#14582806C411yescharacteristic, complemented
10#14582802C2211yescharacteristic
11#14582792—22no—
12#14582765C411yescharacteristic, complemented
13#14582757—22no—
14C22⋊C4×Dic43—22no—
15C42×Dic43C411yescharacteristic, complemented
16#14582694—22no—
17#14582665—22no—
18C2×#124×C43C2211yescharacteristic
19C2×#99×C43C2212yes—
20C43×#354—22no—
21C23×Dic43D412yes—
22Q8×Dic43—41no—
23Q8×Dic43—41no—
24D4×Dic43—41no—
25D4×Dic43—41no—
26C2×C4⋊Dic43—21no—
27C2×C4⋊Dic43C2×C411yescharacteristic
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×Dic43⋊C4—42no—
30C2×C22⋊Dic43—22no—
31C2×C22⋊Dic43—22no—
32C2×C22⋊Dic43D412yes—
33C2×C4×Dic43—21no—
34C2×C4×Dic43—21no—
35C2×C4×Dic43—21no—
36C2×C4×Dic43C2×C411yescharacteristic
37C2×C4×Dic43C2×C411yescharacteristic
38#13063240—22no—
39#13063240—22no—
40C43⋊#95—22no—
41C43⋊#95—22no—
42C43⋊#95—42no—
43C22×Q8×C43C2×C411yescharacteristic
44C22×D4×C43C2311yescharacteristic
45#124×C43—22no—
46#124×C43D412yes—
47#124×C43Q812yes—
48C2×C22⋊C4×C43—22no—
49C2×C22⋊C4×C43—22no—
50C2×C42×C43C2×C411yescharacteristic
51#99×C43—22no—
52#99×C43—22no—
53C24×C43C2×D412yes—
54C2×Q8×C43—21no—
55C2×Q8×C43—41no—
56C2×Q8×C43—41no—
57C2×Q8×C43C4⋊C412yescomplemented
58C2×D4×C43—41no—
59C2×D4×C43—41no—
60C2×D4×C43C2×D411yescharacteristic
61C2×D4×C43C2×Q811yescharacteristic
62C2×D4×C43#4112yes—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—42no—
66C22×C4×C43C22×C411yescharacteristic
67C22×Dic43—22no—
68C22×Dic43—22no—
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—42no—
72C22×Dic43—44no—
73C22×Dic43C22⋊C411yescharacteristic
74C22×Dic43C22⋊C412yes—
75C22×Dic43C22⋊C411yescharacteristic
76C22⋊C4×C43—24no—
77C22⋊C4×C43—24no—
78C22⋊C4×C43—42no—
79C22⋊C4×C43—42no—
80C42×C43—21no—
81C42×C43C4⋊C412yescomplemented
82C22⋊Dic43—42no—
83C22⋊Dic43—42no—
84C22⋊Dic43—44no—
85C22⋊Dic43—42no—
86C4⋊Dic43—41no—
87C4⋊Dic43—42no—
88C4⋊Dic43—41no—
89Dic43⋊C4—84no—
90C4×Dic43—21no—
91C4×Dic43—21no—
92C4×Dic43—42no—
93C4×Dic43—42no—
94C4×Dic43—41no—
95C4×Dic43—41no—
96C4×Dic43—41no—
97C23×C43—22no—
98C23×C43—22no—
99C23×C43—42no—
100C23×C43—42no—
101C23×C43C2×C22⋊C411yescharacteristic
102C23×C43#12112yes—
103C23×C43C22⋊Q812yes—
104Q8×C43—42no—
105Q8×C43—42no—
106D4×C43—41no—
107D4×C43—41no—
108D4×C43—42no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—22no—
112C2×C4×C43—22no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—82no—
118C2×C4×C43—82no—
119C2×C4×C43—82no—
120C2×C4×C43C2×C4⋊C411yescharacteristic
121C2×C4×C43#11711yescharacteristic
122C2×Dic43—22no—
123C2×Dic43—22no—
124C2×Dic43—21no—
125C2×Dic43—22no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—44no—
129C2×Dic43—41no—
130C2×Dic43—42no—
131C2×Dic43—42no—
132C2×Dic43—41no—
133C2×Dic43—82no—
134C2×Dic43—82no—
135C2×Dic43—82no—
136C2×Dic43—82no—
137C2×Dic43#9911yescharacteristic
138C2×Dic43#9911yescharacteristic
139#12798—431nomaximal, Sylow
140C22×C43—21no—
141C22×C43—21no—
142C22×C43—22no—
143C22×C43—22no—
144C22×C43—42no—
145C22×C43—42no—
146C22×C43—42no—
147C22×C43—42no—
148C22×C43—82no—
149C22×C43#38011yescharacteristic
150C22×C43C2×#9911yescharacteristic
151C22×C43#41011yescharacteristic
152C4×C43—21no—
153C4×C43—21no—
154C4×C43—42no—
155C4×C43—42no—
156C4×C43—162no—
157Dic43—21no—
158Dic43—42no—
159Dic43—42no—
160Dic43—41no—
161Dic43—81no—
162Dic43—162no—
163Dic43#35412yescomplemented
164C4×#124—431no—
165C2×#354—431no—
166C2×#354D4311yescharacteristic
167#1799—432no—
168#1393—432no—
169C2×C43—21no—
170C2×C43—21no—
171C2×C43—42no—
172C2×C43—42no—
173C2×C43#179911yescharacteristic
174C2×C43C2×#35411yescharacteristic
175C2×C43#212611yescharacteristic
176C2×#124C2×D4311yescharacteristic
177C2×C4×Q8—431no—
178C2×C4×D4—431no—
179C2×#99—432no—
180C2×#99C2×D4312yes—
181#391—431no—
182#390—431no—
183#388—862no—
184#382—431no—
185#380—862no—
186C4×C22⋊C4—862no—
187C43—431no—
188#354—22no—
189#354—862no—
190#342—862no—
191C43#1279811yescharacteristic, complemented, Sylow
192C22×Q8C4×D4311yescharacteristic
193C22×D4C22×D4311yescharacteristic
194C23×C4—432no—
195#124—22no—
196#124Dic8612yes—
197#124C22⋊D4312yes—
198C4×Q8—1721no—
199C4×Q8—1721no—
200C4×D4—1721no—
201C4×D4—1721no—
202C2×C4⋊C4—431no—
203C2×C4⋊C4—431no—
204C2×C4⋊C4—861no—
205C2×C4⋊C4—1722no—
206C2×C22⋊C4—22no—
207C2×C22⋊C4—22no—
208C2×C22⋊C4—432no—
209C2×C22⋊C4—862no—
210C2×C22⋊C4—862no—
211C2×C42—431no—
212C2×C42—431no—
213C2×C42—861no—
214C2×C42—861no—
215C2×C42—861no—
216C2×C42C4×D4311yescharacteristic
217#99—22no—
218#99—22no—
219#99—862no—
220#99—862no—
221#95—862no—
222#95—862no—
223#95—1722no—
224C24D4×D4312yes—
225C2×Q8—21no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8Dic43⋊C412yescomplemented
229C2×D4—41no—
230C2×D4—41no—
231C2×D4C2×Dic8611yescharacteristic
232C2×D4#1062190012yes—
233C2×D4C2×C22⋊D4311yescharacteristic
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—42no—
237C22×C4—431no—
238C22×C4—432no—
239C22×C4—431no—
240C22×C4—862no—
241C22×C4—862no—
242C22×C4—861no—
243C22×C4—861no—
244C22×C4—1724no—
245C22×C4—1722no—
246C22×C4C2×C4×D4311yescharacteristic
247C4⋊C4—3444no—
248C4⋊C4—1721no—
249C4⋊C4—1721no—
250C4⋊C4—1722no—
251C22⋊C4—24no—
252C22⋊C4—24no—
253C22⋊C4—42no—
254C22⋊C4—42no—
255C22⋊C4—1722no—
256C22⋊C4—1724no—
257C22⋊C4—1722no—
258C22⋊C4—1722no—
259C42—21no—
260C42—861no—
261C42—861no—
262C42—1721no—
263C42—1721no—
264C42—1721no—
265C42—1722no—
266C42—1722no—
267C42Dic43⋊C412yescomplemented
268C23—22no—
269C23—22no—
270C23—42no—
271C23—42no—
272C23C22⋊C4×D4311yescharacteristic
273C23#1306329712yes—
274C23#1306330212yes—
275Q8—42no—
276Q8—42no—
277D4—41no—
278D4—42no—
279D4—41no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—82no—
289C2×C4—82no—
290C2×C4—82no—
291C2×C4—431no—
292C2×C4—431no—
293C2×C4—862no—
294C2×C4—862no—
295C2×C4—861no—
296C2×C4—862no—
297C2×C4—3442no—
298C2×C4—3442no—
299C2×C4—3442no—
300C2×C4—3442no—
301C2×C4—1724no—
302C2×C4—1722no—
303C2×C4—1721no—
304C2×C4—1721no—
305C2×C4—1721no—
306C2×C4—1721no—
307C2×C4—1722no—
308C2×C4C2×Dic43⋊C411yescharacteristic
309C2×C4#1306328111yescharacteristic
310C22—21no—
311C22—21no—
312C22—22no—
313C22—22no—
314C22—42no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22—82no—
319C22#1458275711yescharacteristic
320C22#99×D4311yescharacteristic
321C22#1458287111yescharacteristic
322C4—21no—
323C4—21no—
324C4—42no—
325C4—42no—
326C4—162no—
327C4—432no—
328C4—861no—
329C4—3441no—
330C4—1722no—
331C4—1721no—
332C4—1722no—
333C4—6882no—
334C2—21no—
335C2—21no—
336C2—42no—
337C2—42no—
338C2#1913458111yescharacteristic
339C2#354×D4311yescharacteristic
340C2#1913625911yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC22×D4C22×D43
FittingC2×C43×#354C2
socleC22×C43C2×#99
prime radical, cosocleC22×D4×C43C23
hypercenterC2×#354D43
hypocenterC43#12798
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#354

Complements

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

NH ≅ G/Ntype
6. C2×Q8×Dic43C4semidirect
9. #14582806C4semidirect
12. #14582765C4semidirect
15. C42×Dic43C4semidirect
57. C2×Q8×C43C4⋊C4semidirect
81. C42×C43C4⋊C4semidirect
163. Dic43#354semidirect
191. C43#12798semidirect
228. C2×Q8Dic43⋊C4semidirect
267. C42Dic43⋊C4semidirect

Maximal subgroups

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

subgroupindex
#124×Dic432
C2×#145826942
#191345812
#191327192
C2×C43×#3542
#1279843