Finite Group Databasebeta

← #25007504

Subgroups — #25007504

Order 11008.

376 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 69 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#19140167C211yesmaximal, characteristic
2#19134677C211yesmaximal, characteristic
3#19132908C211yesmaximal, characteristic
4#19132625C211yesmaximal, characteristic, complemented
5#19132602C211yesmaximal, characteristic, complemented
6#19132600C211yesmaximal, characteristic, complemented
7C43×#1354C211yesmaximal, characteristic, complemented
8C2×Q8×Dic43C411yescharacteristic
9C2×#13063283C2211yescharacteristic
10#14582949—21no—
11#14582862—21no—
12#14582829C2211yescharacteristic
13#14582826C411yescharacteristic
14#14582810C411yescharacteristic
15#14582789—21no—
16#14582786—21no—
17#14582785—21no—
18#14582773—21no—
19#14582766C411yescharacteristic
20#14582668C2211yescharacteristic
21#14582667—21no—
22#14582625C2211yescharacteristic
23#14582622—21no—
24C43×#395C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×C4×D43D411yescharacteristic
28C2×#10621877—21no—
29Q8×Dic43—41no—
30Q8×Dic43—41no—
31#13063283—41no—
32#13063283—41no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43C2×C411yescharacteristic
35C2×C4⋊Dic43D411yescharacteristic
36C2×Dic43⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4C2×C411yescharacteristic
40C2×(C2×D43)⋊C4D411yescharacteristic
41C2×C4×Dic43—21no—
42C2×C4×Dic43C2×C411yescharacteristic
43C2×C4×Dic43D411yescharacteristic
44Dic43⋊C8—41no—
45C22⋊(C43⋊C8)—21no—
46(C2×D43)⋊C8—41no—
47(C2×D43)⋊C8—41no—
48C8×Dic43—41no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95C2×C411yescharacteristic
55C22×Q8×C43C2×C411yescharacteristic
56C2×M16×C43—21no—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43C2311yescharacteristic
59C22⋊C8×C43—21no—
60#95×C43—21no—
61#95×C43C2×C411yescharacteristic
62C23×D43C22⋊C411yescharacteristic
63C2×Q8×C43—42no—
64C2×Q8×C43—41no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43C22⋊C411yescharacteristic
73C22×Dic43C22⋊C411yescharacteristic
74C22×Dic43C22⋊C411yescharacteristic
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43—41no—
80M16×C43—41no—
81M16×C43—41no—
82C2×C8×C43—41no—
83C2×C8×C43—41no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—42no—
86(C2×D43)⋊C4—41no—
87(C2×D43)⋊C4—41no—
88(C2×D43)⋊C4—42no—
89(C2×D43)⋊C4—42no—
90C4⋊Dic43—41no—
91C4⋊Dic43—41no—
92C4⋊Dic43—41no—
93C4⋊Dic43—41no—
94Dic43⋊C4—41no—
95Dic43⋊C4—41no—
96C4×Dic43—21no—
97C4×Dic43—21no—
98C4×Dic43—21no—
99C4×Dic43—21no—
100C4×Dic43—42no—
101#10621877—41no—
102#10621877—41no—
103C2×C43⋊C8—41no—
104C2×C43⋊C8—41no—
105C23×C43C2×C22⋊C411yescharacteristic
106C22×D43—21no—
107C22×D43—21no—
108C22×D43—21no—
109C22×D43—41no—
110C22×D43—41no—
111Q8×C43—42no—
112Q8×C43—42no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—22no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
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#13511yescharacteristic
126C2×C4×C43#13511yescharacteristic
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43#9911yescharacteristic
140C2×Dic43#9911yescharacteristic
141C4×D43—41no—
142C4×D43—41no—
143C4×D43—41no—
144C4×D43—41no—
145C8×C43—81no—
146C8×C43—81no—
147C43⋊C8—81no—
148C43⋊C8—81no—
149#11849—431nomaximal, Sylow
150C22×C43—21no—
151C22×C43—21no—
152C22×C43C2×#9911yescharacteristic
153C22×C43#41611yescharacteristic
154C22×C43#42111yescharacteristic
155C2×D43—42no—
156C2×D43—41no—
157C2×D43—41no—
158C2×D43—41no—
159C2×D43—81no—
160C4×C43—21no—
161C4×C43—21no—
162C4×C43—41no—
163C4×C43—42no—
164C4×C43—41no—
165C4×C43—81no—
166Dic43—21no—
167Dic43—21no—
168Dic43—41no—
169Dic43—41no—
170Dic43—81no—
171Dic43—81no—
172#2599—431no—
173#1822—431no—
174#1458—431no—
175#1354—431no—
176#1354D4311yescharacteristic, complemented
177#1346—431no—
178#1346—431no—
179C2×C43—21no—
180C2×C43—21no—
181C2×C43#151611yescharacteristic
182C2×C43#212011yescharacteristic
183C2×C43#213511yescharacteristic
184D43—81no—
185C2×C4×Q8—431no—
186C2×#117—431no—
187#431—861no—
188#407—861no—
189#398—431no—
190#397—431no—
191#395C2×D4311yescharacteristic
192#393—431no—
193#388—861no—
194#387—861no—
195#387—861no—
196#385—861no—
197#383—431no—
198#343—431no—
199#343—861no—
200#343C2×D4311yescharacteristic
201#324—431no—
202#324C2×D4311yescharacteristic
203#323—861no—
204C43#1184911yescharacteristic, complemented, Sylow
205C22×Q8C4×D4311yescharacteristic
206C23×C4—431no—
207C2×M16—21no—
208C2×M16—861no—
209C4×Q8—1721no—
210C4×Q8—1721no—
211#117—1721no—
212#117—1721no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—431no—
215C2×C4⋊C4—431no—
216C2×C4⋊C4—861no—
217C2×C4⋊C4—861no—
218C2×C4⋊C4C22×D4311yescharacteristic
219C2×C22⋊C4—431no—
220C2×C22⋊C4—431no—
221C2×C22⋊C4—861no—
222C2×C22⋊C4—861no—
223C2×C42—431no—
224C2×C42—431no—
225C2×C42—861no—
226C4⋊C8—1721no—
227C22⋊C8—21no—
228C22⋊C8—861no—
229C22⋊C8—1721no—
230C22⋊C8—1721no—
231C4×C8—1721no—
232#95—21no—
233#95—431no—
234#95—861no—
235#95—861no—
236#95—861no—
237#95—861no—
238#95—861no—
239#95C4×D4311yescharacteristic
240C24—431no—
241C2×Q8—42no—
242C2×Q8—41no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—431no—
246C22×C4—431no—
247C22×C4—431no—
248C22×C4—861no—
249C22×C4—861no—
250C22×C4—861no—
251C22×C4—861no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4—1721no—
255C22×C4C2×C4×D4311yescharacteristic
256C22×C4D4×D4311yescharacteristic
257C22×C4D4×D4311yescharacteristic
258M16—41no—
259M16—41no—
260M16—1721no—
261M16—1721no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—1721no—
265C2×C8—1721no—
266C4⋊C4—41no—
267C4⋊C4—42no—
268C4⋊C4—1721no—
269C4⋊C4—1721no—
270C4⋊C4—1721no—
271C4⋊C4—1721no—
272C4⋊C4—1721no—
273C4⋊C4—1721no—
274C22⋊C4—1721no—
275C22⋊C4—1721no—
276C22⋊C4—1722no—
277C22⋊C4—1722no—
278C42—861no—
279C42—861no—
280C42—861no—
281C42—861no—
282C42—1722no—
283C23—861no—
284C23—861no—
285C23—861no—
286C23—1721no—
287C23—1721no—
288C23C22⋊C4×D4311yescharacteristic
289Q8—42no—
290Q8—42no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—431no—
304C2×C4—431no—
305C2×C4—861no—
306C2×C4—861no—
307C2×C4—861no—
308C2×C4—861no—
309C2×C4—1721no—
310C2×C4—1721no—
311C2×C4—1721no—
312C2×C4—1721no—
313C2×C4—1721no—
314C2×C4—1721no—
315C2×C4—1721no—
316C2×C4—1721no—
317C2×C4—1721no—
318C2×C4—1721no—
319C2×C4—1721no—
320C2×C4—1721no—
321C2×C4#1306334611yescharacteristic
322C2×C4#1306334811yescharacteristic
323C8—81no—
324C8—81no—
325C8—3441no—
326C8—3441no—
327C22—21no—
328C22—21no—
329C22—3441no—
330C22—1722no—
331C22—1721no—
332C22—1721no—
333C22—1721no—
334C22#99×D4311yescharacteristic
335C22#1458289411yescharacteristic
336C22#1458291411yescharacteristic
337C4—21no—
338C4—21no—
339C4—41no—
340C4—42no—
341C4—41no—
342C4—81no—
343C4—861no—
344C4—861no—
345C4—3441no—
346C4—3441no—
347C4—1721no—
348C4—1721no—
349C2—21no—
350C2—21no—
351C2—3441no—
352C2#1913315011yescharacteristic
353C2#1913623311yescharacteristic
354C2#1913628811yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1354C2
socleC22×C43C2×#99
prime radicalC23×D43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1354D43
hypocenterC43#11849
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
4. #19132625C2semidirect
5. #19132602C2semidirect
6. #19132600C2semidirect
7. C43×#1354C2semidirect
176. #1354D43semidirect
204. C43#11849semidirect

Maximal subgroups

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

subgroupindex
#191401672
#191346772
#191329082
#191326252
#191326022
#191326002
C43×#13542
#1184943