Finite Group Databasebeta

← #25007496

Subgroups — #25007496

Order 11008.

432 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 79 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#19140161C211yesmaximal, characteristic
2#19134678C211yesmaximal, characteristic, complemented
3#19132623C212yesmaximal, complemented
4#19132599C212yesmaximal, complemented
5C43×#1458C211yesmaximal, characteristic, complemented
6C2×C4×D172C411yescharacteristic
7#14582863—21no—
8#14582838C2211yescharacteristic
9#14582835C411yescharacteristic
10#14582816C2211yescharacteristic
11#14582808C411yescharacteristic
12#14582790—21no—
13#14582778—21no—
14#14582775—21no—
15#14582770—21no—
16#14582767C411yescharacteristic
17#14582668—21no—
18#14582668C2212yes—
19C2×#117×C43C2211yescharacteristic
20C43×#431—21no—
21C43×#324C2212yes—
22C43×#323—21no—
23C22×D172C2×C411yescharacteristic
24C22×C22⋊D43—21no—
25C22×C4×D43—21no—
26C2×#10621877—22no—
27C4×D172—41no—
28C4×D172—41no—
29C2×C4⋊Dic43C2×C411yescharacteristic
30C2×Dic43⋊C4—21no—
31C2×C22⋊Dic43—21no—
32C2×(C2×D43)⋊C4—21no—
33C2×(C2×D43)⋊C4—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C22⋊(C43⋊C8)—41no—
37C22⋊(C43⋊C8)—41no—
38C43⋊#95—21no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95C2×C411yescharacteristic
43C43⋊#95C2×C411yescharacteristic
44C23×C4×C43D411yescharacteristic
45#117×C43—41no—
46#117×C43—41no—
47C2×C4⋊C4×C43D411yescharacteristic
48C2×C4⋊C4×C43C2311yescharacteristic
49C2×C22⋊C4×C43C2×C411yescharacteristic
50C2×C22⋊C4×C43D411yescharacteristic
51C2×C42×C43C2×C411yescharacteristic
52C2×C42×C43D411yescharacteristic
53C4⋊C8×C43—41no—
54C22⋊C8×C43—22no—
55C4×C8×C43—41no—
56C24×C43C22⋊C411yescharacteristic
57C23×D43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43—22no—
61C22×C4×C43—41no—
62C22×C4×C43C22⋊C411yescharacteristic
63C22×C4×C43C22⋊C411yescharacteristic
64C22×C4×C43C22⋊C411yescharacteristic
65C22×C4×C43C22×C411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C2×C22⋊D43—42no—
69C2×C22⋊D43—42no—
70C2×C22⋊D43—81no—
71C22×Dic43—21no—
72C22×Dic43—21no—
73C22×Dic43—21no—
74C2×D172—42no—
75C2×D172—41no—
76C2×C4×D43—42no—
77C2×C4×D43—81no—
78C2×C4×D43—81no—
79C2×C8×C43—42no—
80C4⋊C4×C43—41no—
81C4⋊C4×C43—41no—
82C22⋊C4×C43—41no—
83C22⋊C4×C43—41no—
84C42×C43—21no—
85C42×C43—21no—
86C42×C43—21no—
87C42×C43—21no—
88C22⋊Dic43—81no—
89(C2×D43)⋊C4—42no—
90(C2×D43)⋊C4—41no—
91(C2×D43)⋊C4—41no—
92(C2×D43)⋊C4—42no—
93(C2×D43)⋊C4—81no—
94C4⋊Dic43—41no—
95Dic43⋊C4—81no—
96#10621877—42no—
97#10621877—42no—
98C2×C43⋊C8—42no—
99C23×C43—21no—
100C23×C43—21no—
101C23×C43—21no—
102C23×C43—41no—
103C23×C43—41no—
104C23×C43C2×C22⋊C411yescharacteristic
105C22×D43—22no—
106C22×D43—41no—
107C22×D43—41no—
108C22×D43—41no—
109C22×D43—41no—
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—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—42no—
121C2×C4×C43—42no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43#9911yescharacteristic
127C2×C4×C43#9911yescharacteristic
128C2×C4×C43#13512yes—
129C22⋊D43—84no—
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—41no—
139D172—42no—
140D172—42no—
141C4×D43—84no—
142C8×C43—82no—
143C43⋊C8—82no—
144#11847—431nomaximal, Sylow
145C22×C43—21no—
146C22×C43—21no—
147C22×C43—42no—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—81no—
152C22×C43C2×#9911yescharacteristic
153C22×C43#41611yescharacteristic
154C22×C43#42111yescharacteristic
155C2×D43—42no—
156C2×D43—42no—
157C2×D43—42no—
158C2×D43—81no—
159C2×D43—81no—
160C2×D43—81no—
161C2×D43—81no—
162C4×C43—22no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—41no—
166C4×C43—41no—
167C4×C43—41no—
168C4×C43—41no—
169Dic43—81no—
170Dic43—81no—
171Dic43—81no—
172#2598—431no—
173#1822—431no—
174#1458D4311yescharacteristic, complemented
175#1353—432no—
176#1345—432no—
177C2×C43—21no—
178C2×C43—21no—
179C2×C43—81no—
180C2×C43#151611yescharacteristic
181C2×C43#212011yescharacteristic
182C2×C43#213411yescharacteristic
183D43—82no—
184C2×C4×D4—431no—
185C2×#117C2×D4311yescharacteristic
186#431—21no—
187#407—861no—
188#400—431no—
189#399—431no—
190#394—431no—
191#392—431no—
192#388—861no—
193#386—861no—
194#386—861no—
195#385—861no—
196#383—431no—
197#343—432no—
198#343—861no—
199#324C2×D4312yes—
200#323—21no—
201C43#1184711yescharacteristic, complemented, Sylow
202C22×D4—431no—
203C22×D4—861no—
204C23×C4—861no—
205C23×C4D17211yescharacteristic
206C2×M16—862no—
207C4×D4—1721no—
208C4×D4—1721no—
209#117—41no—
210#117—41no—
211C2×C4⋊C4—431no—
212C2×C4⋊C4—861no—
213C2×C4⋊C4D17211yescharacteristic
214C2×C4⋊C4C22×D4311yescharacteristic
215C2×C22⋊C4—861no—
216C2×C22⋊C4—861no—
217C2×C22⋊C4—861no—
218C2×C22⋊C4—861no—
219C2×C22⋊C4—861no—
220C2×C22⋊C4C4×D4311yescharacteristic
221C2×C22⋊C4C22⋊D4311yescharacteristic
222C2×C42C4×D4311yescharacteristic
223C2×C42C22⋊D4311yescharacteristic
224C4⋊C8—41no—
225C22⋊C8—22no—
226C22⋊C8—1721no—
227C22⋊C8—1721no—
228C4×C8—41no—
229#95—431no—
230#95—431no—
231#95—861no—
232#95—861no—
233#95—861no—
234#95—861no—
235C24—861no—
236C24(C2×D43)⋊C411yescharacteristic
237C2×D4—3441no—
238C2×D4—1721no—
239C2×D4—1722no—
240C2×D4—1722no—
241C2×D4—1722no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—22no—
245C22×C4—41no—
246C22×C4—861no—
247C22×C4—861no—
248C22×C4—861no—
249C22×C4—3441no—
250C22×C4—3441no—
251C22×C4—1722no—
252C22×C4(C2×D43)⋊C411yescharacteristic
253C22×C4(C2×D43)⋊C411yescharacteristic
254C22×C4(C2×D43)⋊C411yescharacteristic
255C22×C4C2×C4×D4311yescharacteristic
256C22×C4C2×D17211yescharacteristic
257C22×C4C2×C22⋊D4311yescharacteristic
258M16—1722no—
259M16—1722no—
260C2×C8—42no—
261C2×C8—1722no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—3441no—
265C4⋊C4—1721no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—3441no—
269C22⋊C4—3441no—
270C22⋊C4—1722no—
271C22⋊C4—1721no—
272C22⋊C4—1721no—
273C22⋊C4—1722no—
274C42—21no—
275C42—21no—
276C42—21no—
277C42—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—41no—
282C23—41no—
283C23—862no—
284C23—1721no—
285C23—1721no—
286C23—1721no—
287C23—1721no—
288C23—1721no—
289C23—1721no—
290C23C2×(C2×D43)⋊C411yescharacteristic
291D4—3444no—
292D4—1722no—
293D4—1722no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—3444no—
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#1306323911yescharacteristic
319C2×C4#1306323911yescharacteristic
320C2×C4#1306334712yes—
321C8—82no—
322C8—3442no—
323C22—21no—
324C22—21no—
325C22—42no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—81no—
330C22—3441no—
331C22—3441no—
332C22—3441no—
333C22—3441no—
334C22—1722no—
335C22—1722no—
336C22—1722no—
337C22C2×#1306323911yescharacteristic
338C22#1458289611yescharacteristic
339C22#1458291511yescharacteristic
340C4—22no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—3441no—
348C4—3441no—
349C4—3441no—
350C2—21no—
351C2—21no—
352C2—81no—
353C2—3442no—
354C2#1913315211yescharacteristic
355C2#1913623411yescharacteristic
356C2#1913628611yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1458C2
socleC22×C43C2×#99
prime radical#14582808C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1458D43
hypocenterC43#11847
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
2. #19134678C2semidirect
3. #19132623C2semidirect
4. #19132599C2semidirect
5. C43×#1458C2semidirect
174. #1458D43semidirect
201. C43#11847semidirect

Maximal subgroups

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

subgroupindex
#191401612
#191346782
#191326232
#191325992
C43×#14582
#1184743