Finite Group Databasebeta

← #25007347

Subgroups — #25007347

Order 11008.

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

normal subgroups only

This group has 368 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#19140423C211yesmaximal, characteristic
2#19134677C211yesmaximal, characteristic
3#19132928C211yesmaximal, characteristic
4#19132623C211yesmaximal, characteristic, complemented
5#19132622C211yesmaximal, characteristic, complemented
6#19132621C211yesmaximal, characteristic, complemented
7C43×#1353C211yesmaximal, characteristic, complemented
8C2×#13063324C411yescharacteristic
9C2×#13063283C2211yescharacteristic
10#14582953—21no—
11#14582862—21no—
12#14582838C2211yescharacteristic
13#14582836C411yescharacteristic
14#14582834C411yescharacteristic
15#14582820—21no—
16#14582812—21no—
17#14582796—21no—
18#14582763C411yescharacteristic
19#14582758—21no—
20#14582668C2211yescharacteristic
21#14582667—21no—
22#14582625C2211yescharacteristic
23#14582622—21no—
24C43×#400C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×Dic86—21no—
28C22×C4×D43D411yescharacteristic
29C2×#10621877—21no—
30#13063324—41no—
31#13063324—41no—
32#13063283—41no—
33#13063283—41no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43C2×C411yescharacteristic
36C2×C4⋊Dic43D411yescharacteristic
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4C2×C411yescharacteristic
43C2×(C2×D43)⋊C4D411yescharacteristic
44C2×C4×Dic43C2×C411yescharacteristic
45C2×C4×Dic43D411yescharacteristic
46Dic43⋊C8—41no—
47C22⋊(C43⋊C8)—21no—
48(C2×D43)⋊C8—41no—
49(C2×D43)⋊C8—41no—
50#13063235—41no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95C2×C411yescharacteristic
55C2×M16×C43—21no—
56C2×C4⋊C4×C43C2×C411yescharacteristic
57C2×C4⋊C4×C43C2311yescharacteristic
58C22⋊C8×C43—21no—
59#95×C43—21no—
60#95×C43—21no—
61#95×C43C2×C411yescharacteristic
62C23×D43C22⋊C411yescharacteristic
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43C22×C411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43C22⋊C411yescharacteristic
71C22×Dic43C22⋊C411yescharacteristic
72C22×Dic43C22⋊C411yescharacteristic
73C2×C4×D43—21no—
74C2×C4×D43—21no—
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43—41no—
78C2×Dic86—42no—
79C2×Dic86—81no—
80C2×Dic86—81no—
81M16×C43—41no—
82M16×C43—41no—
83C2×C8×C43—41no—
84C2×C8×C43—41no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—41no—
87(C2×D43)⋊C4—41no—
88(C2×D43)⋊C4—41no—
89(C2×D43)⋊C4—81no—
90(C2×D43)⋊C4—81no—
91C4⋊Dic43—41no—
92C4⋊Dic43—41no—
93C4⋊Dic43—81no—
94Dic43⋊C4—42no—
95Dic43⋊C4—41no—
96Dic43⋊C4—41no—
97Dic43⋊C4—81no—
98C4×Dic43—21no—
99C4×Dic43—21no—
100C4×Dic43—21no—
101C4×Dic43—21no—
102#10621877—41no—
103#10621877—41no—
104C2×C43⋊C8—41no—
105C2×C43⋊C8—41no—
106C23×C43C2×C22⋊C411yescharacteristic
107C22×D43—21no—
108C22×D43—21no—
109C22×D43—21no—
110C22×D43—41no—
111C22×D43—41no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
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#13711yescharacteristic
125C2×C4×C43#13711yescharacteristic
126C2×Dic43—21no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43#9911yescharacteristic
139C2×Dic43#9911yescharacteristic
140C4×D43—41no—
141C4×D43—41no—
142C4×D43—41no—
143C4×D43—41no—
144Dic86—84no—
145C8×C43—81no—
146C8×C43—81no—
147C43⋊C8—81no—
148C43⋊C8—81no—
149#11818—431nomaximal, Sylow
150C22×C43—21no—
151C22×C43—21no—
152C22×C43C2×#9911yescharacteristic
153C22×C43#41911yescharacteristic
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—41no—
164C4×C43—81no—
165C4×C43—81no—
166Dic43—21no—
167Dic43—21no—
168Dic43—41no—
169Dic43—41no—
170Dic43—81no—
171Dic43—81no—
172#2628—431no—
173#1822—431no—
174#1464—431no—
175#1353—431no—
176#1353—431no—
177#1353—431no—
178#1353D4311yescharacteristic, complemented
179C2×C43—21no—
180C2×C43—21no—
181C2×C43#151111yescharacteristic
182C2×C43#212311yescharacteristic
183C2×C43#213411yescharacteristic
184D43—81no—
185C2×C4⋊Q8—431no—
186C2×#117—431no—
187#432—861no—
188#407—861no—
189#400—431no—
190#400C2×D4311yescharacteristic
191#399—431no—
192#399—431no—
193#395—861no—
194#393—861no—
195#389—861no—
196#382—431no—
197#380—861no—
198#343—431no—
199#343—861no—
200#343C2×D4311yescharacteristic
201#324—431no—
202#324C2×D4311yescharacteristic
203#323—861no—
204C43#1181811yescharacteristic, complemented, Sylow
205C22×Q8—861no—
206C23×C4—431no—
207C2×M16—21no—
208C2×M16—861no—
209C4⋊Q8—1721no—
210C4⋊Q8—1721no—
211#117—1721no—
212#117—1721no—
213C2×C4⋊C4—431no—
214C2×C4⋊C4—431no—
215C2×C4⋊C4—861no—
216C2×C4⋊C4—861no—
217C2×C4⋊C4—861no—
218C2×C4⋊C4—861no—
219C2×C4⋊C4C4×D4311yescharacteristic
220C2×C4⋊C4C22×D4311yescharacteristic
221C2×C22⋊C4—431no—
222C2×C22⋊C4—431no—
223C2×C22⋊C4—861no—
224C2×C22⋊C4—861no—
225C2×C42—431no—
226C2×C42—431no—
227C4⋊C8—1721no—
228C22⋊C8—21no—
229C22⋊C8—861no—
230C22⋊C8—1721no—
231C22⋊C8—1721no—
232#97—1721no—
233#95—21no—
234#95—21no—
235#95—431no—
236#95—861no—
237#95—861no—
238#95—861no—
239#95C4×D4311yescharacteristic
240C24—431no—
241C2×Q8—3441no—
242C2×Q8—3441no—
243C2×Q8—1722no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—431no—
247C22×C4—431no—
248C22×C4—431no—
249C22×C4—861no—
250C22×C4—861no—
251C22×C4—861no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4—861no—
255C22×C4—1721no—
256C22×C4C2×C4×D4311yescharacteristic
257C22×C4D4×D4311yescharacteristic
258C22×C4D4×D4311yescharacteristic
259M16—41no—
260M16—41no—
261M16—1721no—
262M16—1721no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—1721no—
266C2×C8—1721no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—3441no—
270C4⋊C4—3441no—
271C4⋊C4—1721no—
272C4⋊C4—1721no—
273C4⋊C4—1721no—
274C4⋊C4—1721no—
275C4⋊C4—1722no—
276C22⋊C4—3441no—
277C22⋊C4—3441no—
278C22⋊C4—1721no—
279C22⋊C4—1721no—
280C42—861no—
281C42—861no—
282C42—861no—
283C42—861no—
284C23—861no—
285C23—861no—
286C23—861no—
287C23—1721no—
288C23—1721no—
289C23C22⋊C4×D4311yescharacteristic
290Q8—3444no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
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—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#1306335411yescharacteristic
322C2×C4#1306335711yescharacteristic
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#1458290611yescharacteristic
336C22#1458291411yescharacteristic
337C4—21no—
338C4—21no—
339C4—41no—
340C4—41no—
341C4—81no—
342C4—81no—
343C4—861no—
344C4—861no—
345C4—3441no—
346C4—3441no—
347C4—1721no—
348C4—1721no—
349C2—21no—
350C2—21no—
351C2—3441no—
352C2#1913312611yescharacteristic
353C2#1913624711yescharacteristic
354C2#1913628511yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1353C2
socleC22×C43C2×#99
prime radicalC23×D43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1353D43
hypocenterC43#11818
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1353

Complements

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

NH ≅ G/Ntype
4. #19132623C2semidirect
5. #19132622C2semidirect
6. #19132621C2semidirect
7. C43×#1353C2semidirect
178. #1353D43semidirect
204. C43#11818semidirect

Maximal subgroups

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

subgroupindex
#191404232
#191346772
#191329282
#191326232
#191326222
#191326212
C43×#13532
#1181843