Finite Group Databasebeta

← #25007524

Subgroups — #25007524

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#19140296C211yesmaximal, characteristic
2#19134677C211yesmaximal, characteristic
3#19132908C211yesmaximal, characteristic
4#19132622C211yesmaximal, characteristic, complemented
5#19132602C211yesmaximal, characteristic, complemented
6#19132600C211yesmaximal, characteristic, complemented
7C43×#1353C211yesmaximal, characteristic, complemented
8C2×#13063316C411yescharacteristic
9C2×#13063283C2211yescharacteristic
10#14582949—21no—
11#14582862—21no—
12#14582834C411yescharacteristic
13#14582829C2211yescharacteristic
14#14582826C411yescharacteristic
15#14582796—21no—
16#14582788—21no—
17#14582786—21no—
18#14582773—21no—
19#14582744C411yescharacteristic
20#14582668C2211yescharacteristic
21#14582667—21no—
22#14582625C2211yescharacteristic
23#14582622—21no—
24C43×#400C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×C4×D43D411yescharacteristic
28C2×#10621877—21no—
29#13063316—41no—
30#13063316—41no—
31#13063283—41no—
32#13063283—41no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43C2×C411yescharacteristic
35C2×C4⋊Dic43D411yescharacteristic
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×Dic43—21no—
44C2×C4×Dic43C2×C411yescharacteristic
45C2×C4×Dic43D411yescharacteristic
46Dic43⋊C8—41no—
47C22⋊(C43⋊C8)—21no—
48(C2×D43)⋊C8—41no—
49(C2×D43)⋊C8—41no—
50C8×Dic43—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—
78M16×C43—41no—
79M16×C43—41no—
80C2×C8×C43—41no—
81C2×C8×C43—41no—
82C4⋊C4×C43—41no—
83C4⋊C4×C43—41no—
84(C2×D43)⋊C4—41no—
85(C2×D43)⋊C4—41no—
86(C2×D43)⋊C4—42no—
87(C2×D43)⋊C4—42no—
88C4⋊Dic43—41no—
89C4⋊Dic43—41no—
90C4⋊Dic43—41no—
91C4⋊Dic43—41no—
92Dic43⋊C4—42no—
93Dic43⋊C4—42no—
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—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—41no—
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#13511yescharacteristic
124C2×C4×C43#13511yescharacteristic
125C2×Dic43—21no—
126C2×Dic43—21no—
127C2×Dic43—22no—
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#9911yescharacteristic
138C2×Dic43#9911yescharacteristic
139C4×D43—41no—
140C4×D43—41no—
141C4×D43—41no—
142C4×D43—41no—
143C8×C43—81no—
144C8×C43—81no—
145C43⋊C8—81no—
146C43⋊C8—81no—
147#11853—431nomaximal, Sylow
148C22×C43—21no—
149C22×C43—21no—
150C22×C43C2×#9911yescharacteristic
151C22×C43#41611yescharacteristic
152C22×C43#42111yescharacteristic
153C2×D43—42no—
154C2×D43—41no—
155C2×D43—41no—
156C2×D43—41no—
157C2×D43—81no—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43—81no—
163C4×C43—81no—
164Dic43—21no—
165Dic43—21no—
166Dic43—42no—
167Dic43—41no—
168Dic43—41no—
169Dic43—81no—
170#2611—431no—
171#1822—431no—
172#1458—431no—
173#1353—431no—
174#1353D4311yescharacteristic, complemented
175#1346—431no—
176#1346—431no—
177C2×C43—21no—
178C2×C43—21no—
179C2×C43#151611yescharacteristic
180C2×C43#212311yescharacteristic
181C2×C43#213211yescharacteristic
182D43—81no—
183C2×#125—431no—
184C2×#117—431no—
185#431—861no—
186#407—861no—
187#400C2×D4311yescharacteristic
188#399—431no—
189#398—431no—
190#397—431no—
191#389—861no—
192#388—861no—
193#387—861no—
194#385—861no—
195#376—431no—
196#343—431no—
197#343—861no—
198#343C2×D4311yescharacteristic
199#324—431no—
200#324C2×D4311yescharacteristic
201#323—861no—
202C43#1185311yescharacteristic, complemented, Sylow
203C23×C4—431no—
204C2×M16—21no—
205C2×M16—861no—
206#125—1721no—
207#125—1721no—
208#117—1721no—
209#117—1721no—
210C2×C4⋊C4—431no—
211C2×C4⋊C4—431no—
212C2×C4⋊C4—861no—
213C2×C4⋊C4—861no—
214C2×C4⋊C4—861no—
215C2×C4⋊C4—861no—
216C2×C4⋊C4C4×D4311yescharacteristic
217C2×C4⋊C4C22×D4311yescharacteristic
218C2×C22⋊C4—431no—
219C2×C22⋊C4—431no—
220C2×C22⋊C4—861no—
221C2×C22⋊C4—861no—
222C2×C42—431no—
223C2×C42—431no—
224C2×C42—861no—
225C4⋊C8—1721no—
226C22⋊C8—21no—
227C22⋊C8—861no—
228C22⋊C8—1721no—
229C22⋊C8—1721no—
230C4×C8—1721no—
231#95—21no—
232#95—21no—
233#95—431no—
234#95—861no—
235#95—861no—
236#95—861no—
237#95C4×D4311yescharacteristic
238C24—431no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—431no—
242C22×C4—431no—
243C22×C4—431no—
244C22×C4—861no—
245C22×C4—861no—
246C22×C4—861no—
247C22×C4—861no—
248C22×C4—861no—
249C22×C4—861no—
250C22×C4—1721no—
251C22×C4C2×C4×D4311yescharacteristic
252C22×C4D4×D4311yescharacteristic
253C22×C4D4×D4311yescharacteristic
254M16—41no—
255M16—41no—
256M16—1721no—
257M16—1721no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—1721no—
261C2×C8—1721no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—1721no—
265C4⋊C4—1721no—
266C4⋊C4—1721no—
267C4⋊C4—1721no—
268C4⋊C4—1722no—
269C4⋊C4—1722no—
270C4⋊C4—1721no—
271C4⋊C4—1721no—
272C22⋊C4—1721no—
273C22⋊C4—1721no—
274C22⋊C4—1722no—
275C22⋊C4—1722no—
276C42—861no—
277C42—861no—
278C42—861no—
279C42—861no—
280C42—1722no—
281C23—861no—
282C23—861no—
283C23—861no—
284C23—1721no—
285C23—1721no—
286C23C22⋊C4×D4311yescharacteristic
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—431no—
300C2×C4—431no—
301C2×C4—861no—
302C2×C4—861no—
303C2×C4—862no—
304C2×C4—861no—
305C2×C4—861no—
306C2×C4—1721no—
307C2×C4—1721no—
308C2×C4—1721no—
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#1306334611yescharacteristic
318C2×C4#1306334811yescharacteristic
319C8—81no—
320C8—81no—
321C8—3441no—
322C8—3441no—
323C22—21no—
324C22—21no—
325C22—3441no—
326C22—1722no—
327C22—1721no—
328C22—1721no—
329C22—1721no—
330C22#99×D4311yescharacteristic
331C22#1458289411yescharacteristic
332C22#1458291411yescharacteristic
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—81no—
338C4—81no—
339C4—861no—
340C4—861no—
341C4—3441no—
342C4—1722no—
343C4—1721no—
344C4—1721no—
345C2—21no—
346C2—21no—
347C2—3441no—
348C2#1913315011yescharacteristic
349C2#1913624711yescharacteristic
350C2#1913627711yescharacteristic
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#11853
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. #19132622C2semidirect
5. #19132602C2semidirect
6. #19132600C2semidirect
7. C43×#1353C2semidirect
174. #1353D43semidirect
202. C43#11853semidirect

Maximal subgroups

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

subgroupindex
#191402962
#191346772
#191329082
#191326222
#191326022
#191326002
C43×#13532
#1185343