Finite Group Databasebeta

← #25007404

Subgroups — #25007404

Order 11008.

416 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 83 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#19137878C211yesmaximal, characteristic
2#19134591C211yesmaximal, characteristic, complemented
3#19132623C212yesmaximal, complemented
4#19132599C212yesmaximal
5C43×#1467C211yesmaximal, characteristic, complemented
6C2×C4×D172C411yescharacteristic
7#14582923—21no—
8C2×#13063244—21no—
9#14582838C411yescharacteristic
10#14582838C2211yescharacteristic
11#14582825—21no—
12#14582816C411yescharacteristic
13#14582816C2211yescharacteristic
14#14582810—21no—
15C4×(C2×D43)⋊C4—21no—
16C4×(C2×D43)⋊C4—21no—
17#14582745C411yescharacteristic
18#14582668C2212yes—
19C2×C4×Q8×C43C2211yescharacteristic
20C43×#432—21no—
21C43×#324—21no—
22C43×#324C2212yes—
23C22×D172C2×C411yescharacteristic
24C22×C4×D43—21no—
25C2×#10621877—22no—
26C4×D172—41no—
27C4×D172—41no—
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×(C2×D43)⋊C4—21no—
30C2×(C2×D43)⋊C4—21no—
31C2×(C2×D43)⋊C4—21no—
32C2×(C2×D43)⋊C4—21no—
33C2×(C2×D43)⋊C4—21no—
34C2×C4×Dic43—21no—
35C4⋊(C43⋊C8)—41no—
36C4⋊(C43⋊C8)—41no—
37#13063244—42no—
38C43⋊#95—21no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95C2×C411yescharacteristic
44C43⋊#95C2×C411yescharacteristic
45C22×Q8×C43D411yescharacteristic
46C4×Q8×C43—41no—
47C4×Q8×C43—41no—
48C2×C4⋊C4×C43C2×C411yescharacteristic
49C2×C4⋊C4×C43D411yescharacteristic
50C2×C4⋊C4×C43C2311yescharacteristic
51C2×C42×C43C2×C411yescharacteristic
52C2×C42×C43D411yescharacteristic
53C2×C42×C43D411yescharacteristic
54C4⋊C8×C43—41no—
55C22⋊C8×C43—22no—
56#97×C43—41no—
57C23×D43—21no—
58C2×Q8×C43—21no—
59C2×Q8×C43—21no—
60C2×Q8×C43—41no—
61C2×Q8×C43—41no—
62C22×C4×C43C22⋊C411yescharacteristic
63C22×C4×C43C22⋊C411yescharacteristic
64C22×C4×C43C22⋊C411yescharacteristic
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22×C411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—21no—
72C2×D172—42no—
73C2×D172—41no—
74C2×C4×D43—42no—
75C2×C4×D43—42no—
76C2×C4×D43—41no—
77C2×C4×D43—41no—
78C2×C8×C43—42no—
79C4⋊C4×C43—41no—
80C4⋊C4×C43—41no—
81C4⋊C4×C43—41no—
82C42×C43—21no—
83C42×C43—21no—
84C42×C43—21no—
85C42×C43—21no—
86C42×C43—21no—
87C42×C43—21no—
88(C2×D43)⋊C4—42no—
89(C2×D43)⋊C4—42no—
90(C2×D43)⋊C4—42no—
91(C2×D43)⋊C4—42no—
92(C2×D43)⋊C4—41no—
93(C2×D43)⋊C4—41no—
94C4⋊Dic43—41no—
95C4×Dic43—42no—
96#10621877—42no—
97#10621877—42no—
98C2×C43⋊C8—42no—
99C23×C43C2×C22⋊C411yescharacteristic
100C22×D43—22no—
101C22×D43—41no—
102C22×D43—41no—
103C22×D43—41no—
104C22×D43—41no—
105C22×D43—41no—
106C22×D43—41no—
107Q8×C43—42no—
108Q8×C43—42no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—22no—
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—21no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43#9911yescharacteristic
125C2×C4×C43#9911yescharacteristic
126C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C43#13711yescharacteristic
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137D172—42no—
138D172—42no—
139C4×D43—82no—
140C4×D43—82no—
141C8×C43—82no—
142C43⋊C8—82no—
143#11829—431nomaximal, Sylow
144C22×C43—21no—
145C22×C43—21no—
146C22×C43C2×#9911yescharacteristic
147C22×C43#41711yescharacteristic
148C22×C43#42111yescharacteristic
149C2×D43—42no—
150C2×D43—42no—
151C2×D43—42no—
152C2×D43—81no—
153C2×D43—81no—
154C2×D43—81no—
155C2×D43—81no—
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—41no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43—41no—
163C4×C43—41no—
164C4×C43#35512yes—
165Dic43—81no—
166Dic43—81no—
167Dic43—81no—
168#2398—431no—
169#1801—431no—
170#1467D4311yescharacteristic, complemented
171#1353—432no—
172#1345—432no—
173C2×C43—21no—
174C2×C43—21no—
175C2×C43#151311yescharacteristic
176C2×C43#212011yescharacteristic
177C2×C43C2×#35511yescharacteristic
178D43—82no—
179C2×C4×Q8C2×D4311yescharacteristic
180C2×C4×D4—431no—
181#432—21no—
182#423—861no—
183C2×#101—861no—
184#400—431no—
185#400—431no—
186#397—861no—
187#394—431no—
188#394—431no—
189#393—861no—
190C4×C22⋊C4—861no—
191C4×C22⋊C4—861no—
192#376—431no—
193#343—432no—
194#324—21no—
195#324C2×D4312yes—
196C43#1182911yescharacteristic, complemented, Sylow
197C22×Q8D17211yescharacteristic
198C22×D4—431no—
199C23×C4—861no—
200C2×M16—862no—
201C4×Q8—41no—
202C4×Q8—41no—
203C4×D4—1721no—
204C4×D4—1721no—
205C2×C4⋊C4—431no—
206C2×C4⋊C4C4×D4311yescharacteristic
207C2×C4⋊C4C22⋊D4311yescharacteristic
208C2×C4⋊C4C22×D4311yescharacteristic
209C2×C22⋊C4—861no—
210C2×C22⋊C4—861no—
211C2×C22⋊C4—861no—
212C2×C22⋊C4—861no—
213C2×C22⋊C4—861no—
214C2×C42—861no—
215C2×C42C4×D4311yescharacteristic
216C2×C42D17211yescharacteristic
217C2×C42C22⋊D4311yescharacteristic
218C4⋊C8—41no—
219C4⋊C8—1721no—
220C4⋊C8—1721no—
221#101—1722no—
222C22⋊C8—22no—
223#97—41no—
224#95—431no—
225#95—431no—
226#95—861no—
227#95—861no—
228#95—861no—
229#95—861no—
230#95—861no—
231C24—861no—
232C2×Q8—21no—
233C2×Q8—21no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×D4—1721no—
237C2×D4—1722no—
238C22×C4—861no—
239C22×C4—861no—
240C22×C4—861no—
241C22×C4—1722no—
242C22×C4—1722no—
243C22×C4—1721no—
244C22×C4—1721no—
245C22×C4(C2×D43)⋊C411yescharacteristic
246C22×C4(C2×D43)⋊C411yescharacteristic
247C22×C4(C2×D43)⋊C411yescharacteristic
248C22×C4(C2×D43)⋊C411yescharacteristic
249C22×C4C2×C4×D4311yescharacteristic
250C22×C4C2×D17211yescharacteristic
251C22×C4C2×C22⋊D4311yescharacteristic
252M16—1722no—
253M16—1722no—
254C2×C8—42no—
255C2×C8—1722no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—1721no—
260C22⋊C4—1722no—
261C22⋊C4—1722no—
262C22⋊C4—1722no—
263C22⋊C4—1722no—
264C22⋊C4—1721no—
265C22⋊C4—1721no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42—21no—
272C42—1722no—
273C23—862no—
274C23—1721no—
275C23—1721no—
276C23—1721no—
277C23—1721no—
278C23—1721no—
279C23—1721no—
280C23C2×(C2×D43)⋊C411yescharacteristic
281Q8—42no—
282Q8—42no—
283D4—1722no—
284D4—1722no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—3442no—
301C2×C4—3442no—
302C2×C4—1721no—
303C2×C4—1721no—
304C2×C4—1721no—
305C2×C4—1721no—
306C2×C4—1721no—
307C2×C4—1721no—
308C2×C4—1721no—
309C2×C4—1721no—
310C2×C4—1721no—
311C2×C4#1306323911yescharacteristic
312C2×C4#1306323911yescharacteristic
313C2×C4#1306335311yescharacteristic
314C2×C4#1306335811yescharacteristic
315C8—82no—
316C8—3442no—
317C22—21no—
318C22—21no—
319C22—3441no—
320C22—3441no—
321C22—3441no—
322C22—3441no—
323C22—1722no—
324C22—1722no—
325C22—1722no—
326C22C2×#1306323911yescharacteristic
327C22#1458290111yescharacteristic
328C22#1458291511yescharacteristic
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—3441no—
338C4—3441no—
339C4—3441no—
340C4#1458269512yes—
341C2—21no—
342C2—21no—
343C2—3442no—
344C2#1913313911yescharacteristic
345C2#1913623411yescharacteristic
346C2C2×#1458269511yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1467C2
socleC22×C43C2×#99
prime radicalC22×D172C2×C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1467D43
hypocenterC43#11829
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
2. #19134591C2semidirect
3. #19132623C2semidirect
5. C43×#1467C2semidirect
170. #1467D43semidirect
196. C43#11829semidirect

Maximal subgroups

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

subgroupindex
#191378782
#191345912
#191326232
#191325992
C43×#14672
#1182943