Finite Group Databasebeta

← #25006991

Subgroups — #25006991

Order 11008.

420 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C4×#13063242C211yesmaximal, characteristic
2#19132913C211yesmaximal, characteristic
3#19132625C212yesmaximal, complemented
4#19132601C212yesmaximal, complemented
5C43×#2638C211yesmaximal, characteristic
6C2×#13063242—21no—
7C2×C22⋊(C43⋊C8)—21no—
8C4×#10621877—21no—
9#14582668C2212yes—
10#14582625C2212yes—
11#14582623—21no—
12C2×C22⋊Q8×C43C411yescharacteristic
13C2×C4×D4×C43C2211yescharacteristic
14C43×#398C2211yescharacteristic
15C43×#397—21no—
16C43×#397C411yescharacteristic
17C43×#395C2211yescharacteristic
18C43×#394—21no—
19C43×#393C411yescharacteristic
20C43×#387—21no—
21C43×#385—21no—
22C43×#381C411yescharacteristic
23C2×#10621877—22no—
24C22×C43⋊C8—41no—
25#13063242—24no—
26C22⋊(C43⋊C8)—22no—
27C22⋊(C43⋊C8)—41no—
28#13063236—41no—
29C4×C43⋊C8—41no—
30C22×Q8×C43C2×C411yescharacteristic
31C22×D4×C43D411yescharacteristic
32C23×C4×C43C2×C411yescharacteristic
33C23×C4×C43D411yescharacteristic
34C22⋊Q8×C43—41no—
35C22⋊Q8×C43—41no—
36C4×D4×C43—41no—
37C4×D4×C43—41no—
38C2×C4⋊C4×C43—21no—
39C2×C4⋊C4×C43—21no—
40C2×C4⋊C4×C43—21no—
41C2×C4⋊C4×C43C2×C411yescharacteristic
42C2×C4⋊C4×C43C2311yescharacteristic
43C2×C22⋊C4×C43—21no—
44C2×C22⋊C4×C43—21no—
45C2×C22⋊C4×C43—21no—
46C2×C22⋊C4×C43—21no—
47C2×C22⋊C4×C43C2×C411yescharacteristic
48C2×C22⋊C4×C43D411yescharacteristic
49C2×C42×C43D411yescharacteristic
50#95×C43—21no—
51#95×C43—21no—
52#95×C43—21no—
53#95×C43—21no—
54#95×C43—21no—
55#95×C43C2×C411yescharacteristic
56#95×C43C2×C411yescharacteristic
57C24×C43C22⋊C411yescharacteristic
58C24×C43C22⋊C411yescharacteristic
59C2×Q8×C43—41no—
60C2×Q8×C43—81no—
61C2×D4×C43—22no—
62C2×D4×C43—22no—
63C2×D4×C43—41no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—81no—
73C22×C4×C43—81no—
74C22×C4×C43C22⋊C411yescharacteristic
75C22×C4×C43C22⋊C411yescharacteristic
76C22×C4×C43C22×C411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C4⋊C4×C43—41no—
80C4⋊C4×C43—41no—
81C4⋊C4×C43—41no—
82C4⋊C4×C43—41no—
83C4⋊C4×C43—42no—
84C4⋊C4×C43—81no—
85C22⋊C4×C43—41no—
86C22⋊C4×C43—41no—
87C22⋊C4×C43—42no—
88C22⋊C4×C43—42no—
89C22⋊C4×C43—81no—
90C22⋊C4×C43—81no—
91C42×C43—21no—
92C42×C43—21no—
93#10621877—24no—
94#10621877—42no—
95C2×C43⋊C8—42no—
96C2×C43⋊C8—42no—
97C2×C43⋊C8—82no—
98C23×C43—21no—
99C23×C43—21no—
100C23×C43—21no—
101C23×C43—21no—
102C23×C43—21no—
103C23×C43—41no—
104C23×C43—41no—
105C23×C43—41no—
106C23×C43—41no—
107C23×C43#10412yes—
108C23×C43C2×C22⋊C411yescharacteristic
109Q8×C43—82no—
110D4×C43—44no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—41no—
117C2×C4×C43—42no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—81no—
134C2×C4×C43—81no—
135C2×C4×C43—81no—
136C2×C4×C43#9911yescharacteristic
137C2×C4×C43#9911yescharacteristic
138C2×C4×C43#13512yes—
139C43⋊C8—44no—
140C43⋊C8—82no—
141#11739—431nomaximal, Sylow
142C22×C43—21no—
143C22×C43—21no—
144C22×C43—22no—
145C22×C43—42no—
146C22×C43—41no—
147C22×C43—41no—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—81no—
152C22×C43—81no—
153C22×C43—81no—
154C22×C43C2×#9911yescharacteristic
155C22×C43#41611yescharacteristic
156C22×C43C2×#10411yescharacteristic
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—22no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43—41no—
163C4×C43—81no—
164C4×C43—81no—
165C4×C43—81no—
166C4×C43—81no—
167#2638D4311yescharacteristic
168C4×#100—431no—
169#1459—431no—
170#1354—432no—
171#1346—432no—
172C2×C43—21no—
173C2×C43—21no—
174C2×C43—42no—
175C2×C43—81no—
176C2×C43#150111yescharacteristic
177C2×C43#212111yescharacteristic
178C2×C43#213511yescharacteristic
179C2×C22⋊Q8Dic4311yescharacteristic
180C2×C4×D4C2×D4311yescharacteristic
181C2×#100—861no—
182C2×C22⋊C8—861no—
183C4×M16—861no—
184#398C2×D4311yescharacteristic
185#397—21no—
186#397Dic4311yescharacteristic
187#395C2×D4311yescharacteristic
188#394—21no—
189#393Dic4311yescharacteristic
190#387—21no—
191#385—21no—
192#381Dic4311yescharacteristic
193#343—432no—
194#324—432no—
195#323—861no—
196C43#1173911yescharacteristic, complemented, Sylow
197C22×Q8C2×Dic4311yescharacteristic
198C22×D4C22⋊D4311yescharacteristic
199C23×C4C2×Dic4311yescharacteristic
200C23×C4C22⋊D4311yescharacteristic
201C2×M16—862no—
202C22×C8—1721no—
203C22⋊Q8—41no—
204C22⋊Q8—41no—
205C4×D4—41no—
206C4×D4—41no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4C2×Dic4311yescharacteristic
211C2×C4⋊C4C22×D4311yescharacteristic
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4C2×Dic4311yescharacteristic
217C2×C22⋊C4C22⋊D4311yescharacteristic
218C2×C42C22⋊D4311yescharacteristic
219#100—864no—
220C22⋊C8—862no—
221C22⋊C8—1721no—
222#97—1721no—
223C4×C8—1721no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95C2×Dic4311yescharacteristic
230#95C2×Dic4311yescharacteristic
231C24C22⋊Dic4311yescharacteristic
232C24C22⋊Dic4311yescharacteristic
233C2×Q8—41no—
234C2×Q8—81no—
235C2×D4—22no—
236C2×D4—22no—
237C2×D4—41no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—81no—
247C22×C4—81no—
248C22×C4C22⋊Dic4311yescharacteristic
249C22×C4C22⋊Dic4311yescharacteristic
250C22×C4C22×Dic4311yescharacteristic
251C22×C4C2×C22⋊D4311yescharacteristic
252C22×C4C2×C22⋊D4311yescharacteristic
253M16—864no—
254M16—1722no—
255C2×C8—3442no—
256C2×C8—1722no—
257C2×C8—1722no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—42no—
263C4⋊C4—81no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C22⋊C4—81no—
269C22⋊C4—81no—
270C42—21no—
271C42—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23#1306325212yes—
282C23C2×C22⋊Dic4311yescharacteristic
283Q8—82no—
284D4—44no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4#1306324011yescharacteristic
311C2×C4#1306324011yescharacteristic
312C2×C4#1306334512yes—
313C8—3442no—
314C8—1724no—
315C22—21no—
316C22—21no—
317C22—22no—
318C22—42no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22C2×#1306324011yescharacteristic
328C22#1458289511yescharacteristic
329C22C2×#1306325211yescharacteristic
330C4—22no—
331C4—21no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—81no—
337C4—81no—
338C4—81no—
339C4—81no—
340C2—21no—
341C2—21no—
342C2—42no—
343C2—81no—
344C2#1913308611yescharacteristic
345C2#1913624111yescharacteristic
346C2#1913629011yescharacteristic
subgroupG/H
centerC22C2×#13063240
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2638C2
socleC22×C43C2×#99
prime radicalC22×D4×C43D4
cosocleC2×C4⋊C4×C43C23
hypercenter#2638D43
hypocenterC43#11739
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2638

Complements

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

NH ≅ G/Ntype
3. #19132625C2semidirect
4. #19132601C2semidirect
196. C43#11739semidirect

Maximal subgroups

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

subgroupindex
C4×#130632422
#191329132
#191326252
#191326012
C43×#26382
#1173943