Finite Group Databasebeta

← #24994241

Subgroups — #24994241

Order 11008.

474 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 99 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#19139044C211yesmaximal, characteristic
2#19134672C211yesmaximal, characteristic
3#19133129C212yesmaximal
4#19132449C212yesmaximal
5C43×#2921C211yesmaximal, characteristic
6C2×#13063304C2211yescharacteristic
7#14582827—21no—
8#14582827—21no—
9#14582804C411yescharacteristic, complemented
10#14582804C411yescharacteristic, complemented
11#14582783—21no—
12#14582783—21no—
13#14582768C411yescharacteristic, complemented
14#14582764C411yescharacteristic, complemented
15#14582762C2212yes—
16C4×C22⋊Dic43C2211yescharacteristic
17#14582666—21no—
18#14582666—21no—
19#14582637—24no—
20C2×#117×C43C2211yescharacteristic
21C43×#433—24no—
22C43×#423—21no—
23C43×#407C2212yes—
24C4×M16×C43—21no—
25C22×Dic86C2×C411yescharacteristic
26#13063304—22no—
27#13063304—22no—
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×C22⋊Dic43—21no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—22no—
35C2×C4×Dic43C2×C411yescharacteristic
36C2×C4×Dic43C2×C411yescharacteristic
37C43⋊#95—21no—
38C43⋊#95—21no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—22no—
45C43⋊#95—22no—
46C23×C4×C43C2311yescharacteristic
47C2×M16×C43—22no—
48#117×C43—22no—
49#117×C43—22no—
50C2×C4⋊C4×C43C2×C411yescharacteristic
51C2×C4⋊C4×C43C2×C411yescharacteristic
52C2×C22⋊C4×C43D411yescharacteristic
53C2×C22⋊C4×C43D411yescharacteristic
54C2×C42×C43D411yescharacteristic
55C2×C42×C43D411yescharacteristic
56C4⋊C8×C43—24no—
57C22⋊C8×C43—22no—
58C22⋊C8×C43D414yes—
59#97×C43—22no—
60C4×C8×C43—22no—
61C24×C43C2×D411yescharacteristic
62C22×C4×C43—41no—
63C22×C4×C43—41no—
64C22×C4×C43C22⋊C411yescharacteristic
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22×C411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43C2×D412yes—
71C22×C4×C43#4112yes—
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—42no—
77C2×Dic86—22no—
78C2×Dic86—41no—
79C2×Dic86—41no—
80M16×C43—42no—
81M16×C43—42no—
82C2×C8×C43—24no—
83C4⋊C4×C43—22no—
84C4⋊C4×C43—22no—
85C22⋊C4×C43—22no—
86C22⋊C4×C43—22no—
87C42×C43—21no—
88C42×C43—21no—
89C42×C43—21no—
90C42×C43—21no—
91C22⋊Dic43—42no—
92C22⋊Dic43—42no—
93C22⋊Dic43—42no—
94C22⋊Dic43—42no—
95C4⋊Dic43—22no—
96Dic43⋊C4—42no—
97Dic43⋊C4—42no—
98Dic43⋊C4—41no—
99Dic43⋊C4—41no—
100C4×Dic43—41no—
101C4×Dic43—41no—
102C23×C43—21no—
103C23×C43—21no—
104C23×C43—41no—
105C23×C43—41no—
106C23×C43C2×C22⋊C411yescharacteristic
107C23×C43#12112yes—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—42no—
117C2×C4×C43—42no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43C4×D412yes—
123C2×C4×C43#12011yescharacteristic
124C2×C4×C43#12311yescharacteristic
125C2×Dic43—22no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—82no—
138C2×Dic43—82no—
139C2×Dic43—82no—
140Dic86—82no—
141C8×C43—44no—
142#9444—431nomaximal, Sylow
143C22×C43—21no—
144C22×C43—21no—
145C22×C43—22no—
146C22×C43—22no—
147C22×C43—22no—
148C22×C43—81no—
149C22×C43—81no—
150C22×C43#38611yescharacteristic
151C22×C43#41011yescharacteristic
152C22×C43#41011yescharacteristic
153C4×C43—21no—
154C4×C43—22no—
155C4×C43—21no—
156C4×C43—41no—
157C4×C43—41no—
158C4×C43—41no—
159C4×C43—41no—
160Dic43—42no—
161Dic43—81no—
162Dic43—81no—
163Dic43—81no—
164Dic43—162no—
165#2921D4311yescharacteristic
166#2499—431no—
167#1820—431no—
168#1511—432no—
169#1284—432no—
170C2×C43—21no—
171C2×C43—21no—
172C2×C43—42no—
173C2×C43#188411yescharacteristic
174C2×C43#189911yescharacteristic
175C2×C43#190911yescharacteristic
176C2×C22⋊Q8—431no—
177C2×#117C2×D4311yescharacteristic
178#433—24no—
179#423—21no—
180#407C2×D4312yes—
181C4×M16—21no—
182#397—861no—
183#397—861no—
184#391—431no—
185#391—431no—
186#387—861no—
187#387—861no—
188#384—431no—
189#382—431no—
190#381—432no—
191C4×C22⋊C4—431no—
192#342—861no—
193#342—861no—
194#328—864no—
195C43#944411yescharacteristic, complemented, Sylow
196C22×Q8—431no—
197C23×C4C22×D4311yescharacteristic
198C2×M16—22no—
199C22⋊Q8—862no—
200C22⋊Q8—862no—
201#117—22no—
202#117—22no—
203C2×C4⋊C4—431no—
204C2×C4⋊C4—861no—
205C2×C4⋊C4—861no—
206C2×C4⋊C4—861no—
207C2×C4⋊C4C4×D4311yescharacteristic
208C2×C4⋊C4C4×D4311yescharacteristic
209C2×C22⋊C4—861no—
210C2×C22⋊C4—861no—
211C2×C22⋊C4—862no—
212C2×C22⋊C4D17211yescharacteristic
213C2×C22⋊C4D17211yescharacteristic
214C2×C42—431no—
215C2×C42—431no—
216C2×C42C22⋊D4311yescharacteristic
217C2×C42C22⋊D4311yescharacteristic
218C4⋊C8—24no—
219C22⋊C8—22no—
220C22⋊C8C22⋊D4314yes—
221#97—22no—
222C4×C8—22no—
223#95—861no—
224#95—861no—
225#95—861no—
226#95—861no—
227#95—861no—
228#95—861no—
229#95—861no—
230#95—862no—
231#95—862no—
232C24C2×D17211yescharacteristic
233C2×Q8—862no—
234C2×Q8—1721no—
235C2×Q8—1721no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—861no—
239C22×C4—861no—
240C22×C4—861no—
241C22×C4—861no—
242C22×C4—1722no—
243C22×C4(C2×D43)⋊C411yescharacteristic
244C22×C4(C2×D43)⋊C411yescharacteristic
245C22×C4(C2×D43)⋊C411yescharacteristic
246C22×C4(C2×D43)⋊C411yescharacteristic
247C22×C4C2×C4×D4311yescharacteristic
248C22×C4#1062189812yes—
249C22×C4C2×C22⋊D4311yescharacteristic
250C22×C4C2×C22⋊D4312yes—
251M16—42no—
252M16—42no—
253C2×C8—24no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—862no—
257C4⋊C4—1722no—
258C4⋊C4—1722no—
259C4⋊C4—1721no—
260C4⋊C4—1721no—
261C22⋊C4—22no—
262C22⋊C4—22no—
263C22⋊C4—1722no—
264C22⋊C4—1722no—
265C22⋊C4—1722no—
266C22⋊C4—1722no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42—1721no—
272C42—1721no—
273C23—21no—
274C23—21no—
275C23—41no—
276C23—41no—
277C23C2×(C2×D43)⋊C411yescharacteristic
278C23#1306329912yes—
279Q8—3442no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—862no—
295C2×C4—3442no—
296C2×C4—3442no—
297C2×C4—3442no—
298C2×C4—1721no—
299C2×C4—1721no—
300C2×C4—1721no—
301C2×C4—1721no—
302C2×C4—1721no—
303C2×C4—1721no—
304C2×C4—1721no—
305C2×C4—1721no—
306C2×C4—1721no—
307C2×C4—1721no—
308C2×C4—1721no—
309C2×C4C4×C22⋊D4312yes—
310C2×C4#1306329411yescharacteristic
311C2×C4#1306330811yescharacteristic
312C8—44no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—22no—
317C22—22no—
318C22—81no—
319C22—81no—
320C22#1458277811yescharacteristic
321C22#1458287211yescharacteristic
322C22#1458287211yescharacteristic
323C4—21no—
324C4—22no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—3441no—
331C4—3441no—
332C4—3441no—
333C4—1722no—
334C4—6882no—
335C2—21no—
336C2—21no—
337C2—42no—
338C2#1913497811yescharacteristic
339C2#1913505311yescharacteristic
340C2#1913511711yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#2921C2
socleC22×C43#386
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenter#2921D43
hypocenterC43#9444
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2921

Complements

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

NH ≅ G/Ntype
9. #14582804C4semidirect
10. #14582804C4semidirect
13. #14582768C4semidirect
14. #14582764C4semidirect
195. C43#9444semidirect

Maximal subgroups

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

subgroupindex
#191390442
#191346722
#191331292
#191324492
C43×#29212
#944443