Finite Group Databasebeta

← #25007351

Subgroups — #25007351

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#19140418C211yesmaximal, characteristic
2#19134677C211yesmaximal, characteristic
3#19132928C211yesmaximal, characteristic
4#19132626C211yesmaximal, characteristic, complemented
5#19132625C211yesmaximal, characteristic, complemented
6#19132624C211yesmaximal, characteristic, complemented
7C43×#1354C211yesmaximal, characteristic, complemented
8C2×#13063323C411yescharacteristic
9C2×#13063283C2211yescharacteristic
10#14582953—21no—
11#14582862—21no—
12#14582841—21no—
13#14582834—21no—
14#14582819C2211yescharacteristic
15#14582812C411yescharacteristic
16#14582810C411yescharacteristic
17#14582794—21no—
18#14582763C411yescharacteristic
19#14582758—21no—
20#14582668C2211yescharacteristic
21#14582667—21no—
22#14582625C2211yescharacteristic
23#14582622—21no—
24C43×#395C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×Dic86C2×C411yescharacteristic
28C22×C4×D43D411yescharacteristic
29C2×#10621877—21no—
30#13063323—41no—
31#13063323—41no—
32#13063283—41no—
33#13063283—41no—
34C2×C4⋊Dic43D411yescharacteristic
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4C2×C411yescharacteristic
42C2×(C2×D43)⋊C4D411yescharacteristic
43C2×C4×Dic43C2×C411yescharacteristic
44C2×C4×Dic43D411yescharacteristic
45Dic43⋊C8—41no—
46C22⋊(C43⋊C8)—21no—
47(C2×D43)⋊C8—41no—
48(C2×D43)⋊C8—41no—
49#13063235—41no—
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—41no—
64C2×Q8×C43—81no—
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—
80C2×Dic86—41no—
81C2×Dic86—81no—
82M16×C43—41no—
83M16×C43—41no—
84C2×C8×C43—41no—
85C2×C8×C43—41no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43—81no—
88(C2×D43)⋊C4—41no—
89(C2×D43)⋊C4—41no—
90(C2×D43)⋊C4—81no—
91(C2×D43)⋊C4—81no—
92C4⋊Dic43—41no—
93Dic43⋊C4—42no—
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—
112Q8×C43—82no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
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—41no—
125C2×C4×C43#13711yescharacteristic
126C2×C4×C43#13711yescharacteristic
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—
145Dic86—82no—
146C8×C43—81no—
147C8×C43—81no—
148C43⋊C8—81no—
149C43⋊C8—81no—
150#11819—431nomaximal, Sylow
151C22×C43—21no—
152C22×C43—21no—
153C22×C43C2×#9911yescharacteristic
154C22×C43#41911yescharacteristic
155C22×C43#42111yescharacteristic
156C2×D43—42no—
157C2×D43—41no—
158C2×D43—41no—
159C2×D43—41no—
160C2×D43—81no—
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—41no—
164C4×C43—41no—
165C4×C43—81no—
166C4×C43—81no—
167Dic43—21no—
168Dic43—21no—
169Dic43—41no—
170Dic43—41no—
171Dic43—81no—
172Dic43—81no—
173#2628—431no—
174#1822—431no—
175#1464—431no—
176#1354—431no—
177#1354—431no—
178#1354—431no—
179#1354D4311yescharacteristic, complemented
180C2×C43—21no—
181C2×C43—21no—
182C2×C43#151111yescharacteristic
183C2×C43#212211yescharacteristic
184C2×C43#213511yescharacteristic
185D43—81no—
186C2×C4⋊Q8—431no—
187C2×#117—431no—
188#432—861no—
189#407—861no—
190#400—861no—
191#399—861no—
192#395—431no—
193#395C2×D4311yescharacteristic
194#393—431no—
195#393—431no—
196#389—861no—
197#382—431no—
198#380—861no—
199#343—431no—
200#343—861no—
201#343C2×D4311yescharacteristic
202#324—431no—
203#324C2×D4311yescharacteristic
204#323—861no—
205C43#1181911yescharacteristic, complemented, Sylow
206C22×Q8—431no—
207C22×Q8C4×D4311yescharacteristic
208C23×C4—431no—
209C2×M16—21no—
210C2×M16—861no—
211C4⋊Q8—1721no—
212C4⋊Q8—1721no—
213#117—1721no—
214#117—1721no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—431no—
217C2×C4⋊C4—861no—
218C2×C4⋊C4—861no—
219C2×C4⋊C4—861no—
220C2×C4⋊C4—861no—
221C2×C4⋊C4C22×D4311yescharacteristic
222C2×C22⋊C4—431no—
223C2×C22⋊C4—431no—
224C2×C22⋊C4—861no—
225C2×C22⋊C4—861no—
226C2×C42—431no—
227C2×C42—431no—
228C4⋊C8—1721no—
229C22⋊C8—21no—
230C22⋊C8—861no—
231C22⋊C8—1721no—
232C22⋊C8—1721no—
233#97—1721no—
234#95—21no—
235#95—431no—
236#95—861no—
237#95—861no—
238#95—861no—
239#95—861no—
240#95C4×D4311yescharacteristic
241C24—431no—
242C2×Q8—41no—
243C2×Q8—81no—
244C2×Q8—3441no—
245C2×Q8—1721no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—431no—
249C22×C4—431no—
250C22×C4—431no—
251C22×C4—861no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4—861no—
255C22×C4—861no—
256C22×C4—861no—
257C22×C4—1721no—
258C22×C4C2×C4×D4311yescharacteristic
259C22×C4D4×D4311yescharacteristic
260C22×C4D4×D4311yescharacteristic
261M16—41no—
262M16—41no—
263M16—1721no—
264M16—1721no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—1721no—
268C2×C8—1721no—
269C4⋊C4—41no—
270C4⋊C4—81no—
271C4⋊C4—3441no—
272C4⋊C4—1721no—
273C4⋊C4—1721no—
274C4⋊C4—1721no—
275C4⋊C4—1722no—
276C4⋊C4—1722no—
277C22⋊C4—3441no—
278C22⋊C4—3441no—
279C22⋊C4—1721no—
280C22⋊C4—1721no—
281C42—861no—
282C42—861no—
283C42—861no—
284C42—861no—
285C23—861no—
286C23—861no—
287C23—861no—
288C23—1721no—
289C23—1721no—
290C23C22⋊C4×D4311yescharacteristic
291Q8—82no—
292Q8—3442no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
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—431no—
306C2×C4—431no—
307C2×C4—861no—
308C2×C4—861no—
309C2×C4—861no—
310C2×C4—861no—
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—1721no—
322C2×C4—1721no—
323C2×C4#1306335411yescharacteristic
324C2×C4#1306335711yescharacteristic
325C8—81no—
326C8—81no—
327C8—3441no—
328C8—3441no—
329C22—21no—
330C22—21no—
331C22—3441no—
332C22—1722no—
333C22—1721no—
334C22—1721no—
335C22—1721no—
336C22#99×D4311yescharacteristic
337C22#1458290611yescharacteristic
338C22#1458291411yescharacteristic
339C4—21no—
340C4—21no—
341C4—41no—
342C4—41no—
343C4—81no—
344C4—81no—
345C4—861no—
346C4—861no—
347C4—3441no—
348C4—3441no—
349C4—1721no—
350C4—1721no—
351C2—21no—
352C2—21no—
353C2—3441no—
354C2#1913312611yescharacteristic
355C2#1913624311yescharacteristic
356C2#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#11819
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. #19132626C2semidirect
5. #19132625C2semidirect
6. #19132624C2semidirect
7. C43×#1354C2semidirect
179. #1354D43semidirect
205. C43#11819semidirect

Maximal subgroups

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

subgroupindex
#191404182
#191346772
#191329282
#191326262
#191326252
#191326242
C43×#13542
#1181943