Finite Group Databasebeta

← #24990235

Subgroups — #24990235

Order 11008.

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

normal subgroups only

This group has 466 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#19137568C211yesmaximal, characteristic
2C4×#13063240C211yesmaximal, characteristic
3#19132480C212yesmaximal, complemented
4#19132449C212yesmaximal, complemented
5C43×#1465C211yesmaximal, characteristic
6C2×#13063240—21no—
7#14582802—21no—
8#14582792—21no—
9#14582792—21no—
10#14582765C411yescharacteristic, complemented
11#14582762C411yescharacteristic, complemented
12#14582762C2211yescharacteristic
13C4⋊C4×Dic43—21no—
14C4×C4⋊Dic43C411yescharacteristic, complemented
15C4×C22⋊Dic43C411yescharacteristic, complemented
16C4×C22⋊Dic43C2212yes—
17C4×C22⋊Dic43C2211yescharacteristic
18#14582666—21no—
19C2×C4×D4×C43C2211yescharacteristic
20C43×#407C2212yes—
21C43×#324—21no—
22C43×#323—21no—
23C2×C4⋊Dic43—21no—
24C2×C4⋊Dic43—21no—
25C2×C22⋊Dic43—22no—
26C2×C22⋊Dic43—21no—
27C2×C22⋊Dic43—21no—
28C2×C22⋊Dic43—21no—
29C2×C22⋊Dic43—21no—
30C2×C4×Dic43—21no—
31C2×C4×Dic43—21no—
32C2×C4×Dic43—21no—
33C2×C4×Dic43—22no—
34#13063240—24no—
35C43⋊#95—21no—
36C43⋊#95—21no—
37C43⋊#95—21no—
38C43⋊#95—22no—
39C43⋊#95C2×C411yescharacteristic
40C43⋊#95C2×C411yescharacteristic
41C43⋊#95C2×C411yescharacteristic
42C43⋊#95C2×C411yescharacteristic
43C22×D4×C43D411yescharacteristic
44C23×C4×C43C2×C411yescharacteristic
45C23×C4×C43C2311yescharacteristic
46C2×M16×C43—22no—
47C4×D4×C43—22no—
48C4×D4×C43—22no—
49C2×C4⋊C4×C43D411yescharacteristic
50C2×C22⋊C4×C43D411yescharacteristic
51C2×C22⋊C4×C43D411yescharacteristic
52C2×C42×C43C2×C411yescharacteristic
53C22⋊C8×C43—22no—
54C22⋊C8×C43—22no—
55C24×C43C22⋊C411yescharacteristic
56C24×C43C2×D411yescharacteristic
57C2×D4×C43—22no—
58C2×D4×C43—22no—
59C2×D4×C43—41no—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—81no—
63C22×C4×C43—81no—
64C22×C4×C43C22⋊C411yescharacteristic
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43#4112yes—
70C22×C4×C43#4112yes—
71C22×Dic43—21no—
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—42no—
76M16×C43—82no—
77C2×C8×C43—42no—
78C4⋊C4×C43—22no—
79C22⋊C4×C43—22no—
80C22⋊C4×C43—22no—
81C42×C43—21no—
82C42×C43—21no—
83C22⋊Dic43—24no—
84C22⋊Dic43—42no—
85C22⋊Dic43—42no—
86C22⋊Dic43—42no—
87C22⋊Dic43—81no—
88C22⋊Dic43—81no—
89C4⋊Dic43—42no—
90C4⋊Dic43—42no—
91C4×Dic43—42no—
92C4×Dic43—81no—
93C4×Dic43—81no—
94C4×Dic43—82no—
95C23×C43—21no—
96C23×C43—21no—
97C23×C43—21no—
98C23×C43—21no—
99C23×C43—21no—
100C23×C43—41no—
101C23×C43—41no—
102C23×C43—41no—
103C23×C43—41no—
104C23×C43C2×C22⋊C411yescharacteristic
105C23×C43#12312yes—
106D4×C43—44no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—41no—
112C2×C4×C43—42no—
113C2×C4×C43—42no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—81no—
118C2×C4×C43—81no—
119C2×C4×C43#10412yes—
120C2×C4×C43#11711yescharacteristic
121C2×C4×C43#11711yescharacteristic
122C2×C4×C43#12312yes—
123C2×Dic43—22no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—44no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—82no—
137C2×Dic43—82no—
138C8×C43—82no—
139#8779—431nomaximal, Sylow
140C22×C43—21no—
141C22×C43—21no—
142C22×C43—22no—
143C22×C43—22no—
144C22×C43—22no—
145C22×C43—41no—
146C22×C43—41no—
147C22×C43—41no—
148C22×C43—81no—
149C22×C43—81no—
150C22×C43—81no—
151C22×C43—81no—
152C22×C43#38111yescharacteristic
153C22×C43C2×#10411yescharacteristic
154C22×C43#42111yescharacteristic
155C4×C43—22no—
156C4×C43—22no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—41no—
160C4×C43—41no—
161Dic43—42no—
162Dic43—81no—
163Dic43—81no—
164Dic43—81no—
165Dic43—84no—
166#2357—431no—
167C4×#99—431no—
168#1465D4311yescharacteristic
169#1297—432no—
170#1284—432no—
171C2×C43—21no—
172C2×C43—21no—
173C2×C43—42no—
174C2×C43—81no—
175C2×C43#182611yescharacteristic
176C2×C43#182711yescharacteristic
177C2×C43#182811yescharacteristic
178C2×C4×D4C2×D4311yescharacteristic
179C2×#99—861no—
180#407C2×D4312yes—
181#390—861no—
182#388—861no—
183#388—861no—
184#382—431no—
185#381—431no—
186#381—431no—
187C4×C4⋊C4—431no—
188C4×C4⋊C4—861no—
189C4×C22⋊C4—431no—
190C4×C22⋊C4—431no—
191C4×C22⋊C4—432no—
192#342—861no—
193#324—21no—
194#323—21no—
195C43#877911yescharacteristic, complemented, Sylow
196C22×D4D17211yescharacteristic
197C23×C4C4×D4311yescharacteristic
198C23×C4C22×D4311yescharacteristic
199C2×M16—22no—
200C4×D4—22no—
201C4×D4—22no—
202C2×C4⋊C4—861no—
203C2×C4⋊C4—861no—
204C2×C4⋊C4C22⋊D4311yescharacteristic
205C2×C22⋊C4—862no—
206C2×C22⋊C4—861no—
207C2×C22⋊C4—861no—
208C2×C22⋊C4—861no—
209C2×C22⋊C4—861no—
210C2×C22⋊C4D17211yescharacteristic
211C2×C22⋊C4C22⋊D4311yescharacteristic
212C2×C42—861no—
213C2×C42—861no—
214C2×C42—862no—
215C2×C42—861no—
216C2×C42C4×D4311yescharacteristic
217#99—864no—
218C22⋊C8—22no—
219C22⋊C8—22no—
220#95—431no—
221#95—431no—
222#95—431no—
223#95—431no—
224#95—861no—
225#95—861no—
226#95—861no—
227#95—862no—
228C24(C2×D43)⋊C411yescharacteristic
229C24C2×D17211yescharacteristic
230C2×D4—22no—
231C2×D4—22no—
232C2×D4—41no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—81no—
236C22×C4—81no—
237C22×C4—861no—
238C22×C4—861no—
239C22×C4—861no—
240C22×C4—861no—
241C22×C4—1722no—
242C22×C4(C2×D43)⋊C411yescharacteristic
243C22×C4(C2×D43)⋊C411yescharacteristic
244C22×C4(C2×D43)⋊C411yescharacteristic
245C22×C4C2×C4×D4311yescharacteristic
246C22×C4#1062190012yes—
247C22×C4#1062190012yes—
248C22×C4C2×C22⋊D4311yescharacteristic
249M16—82no—
250C2×C8—42no—
251C4⋊C4—22no—
252C4⋊C4—1722no—
253C4⋊C4—1722no—
254C22⋊C4—22no—
255C22⋊C4—22no—
256C22⋊C4—864no—
257C22⋊C4—3441no—
258C22⋊C4—3441no—
259C22⋊C4—1722no—
260C22⋊C4—1722no—
261C22⋊C4—1722no—
262C42—21no—
263C42—21no—
264C42—3442no—
265C42—3441no—
266C42—3441no—
267C42—1722no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23C2×(C2×D43)⋊C411yescharacteristic
278C23#1306330912yes—
279D4—44no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—862no—
293C2×C4—3442no—
294C2×C4—3442no—
295C2×C4—1721no—
296C2×C4—1721no—
297C2×C4—1724no—
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#1306325112yes—
308C2×C4#1306328111yescharacteristic
309C2×C4#1306328111yescharacteristic
310C2×C4#1306330612yes—
311C8—82no—
312C22—21no—
313C22—21no—
314C22—22no—
315C22—22no—
316C22—22no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—81no—
321C22—81no—
322C22—81no—
323C22—81no—
324C22#1458276011yescharacteristic
325C22C2×#1306325111yescharacteristic
326C22#1458291511yescharacteristic
327C4—22no—
328C4—22no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—3441no—
334C4—3441no—
335C4—3441no—
336C4—3444no—
337C4—1722no—
338C2—21no—
339C2—21no—
340C2—42no—
341C2—81no—
342C2#1913469211yescharacteristic
343C2#1913470011yescharacteristic
344C2#1913470111yescharacteristic
subgroupG/H
centerC22#14582760
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1465C2
socleC22×C43#381
prime radicalC22×D4×C43D4
cosocleC23×C4×C43C23
hypercenter#1465D43
hypocenterC43#8779
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1465

Complements

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

NH ≅ G/Ntype
3. #19132480C2semidirect
4. #19132449C2semidirect
10. #14582765C4semidirect
11. #14582762C4semidirect
14. C4×C4⋊Dic43C4semidirect
15. C4×C22⋊Dic43C4semidirect
195. C43#8779semidirect

Maximal subgroups

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

subgroupindex
#191375682
C4×#130632402
#191324802
#191324492
C43×#14652
#877943