Finite Group Databasebeta

← #25006256

Subgroups — #25006256

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#19139791C211yesmaximal, characteristic
2#19132933C211yesmaximal, characteristic
3#19132540C212yesmaximal, complemented
4#19132538C212yesmaximal, complemented
5C43×#1459C211yesmaximal, characteristic
6C2×#13063317C411yescharacteristic
7#14582863—21no—
8#14582822—21no—
9#14582822—21no—
10#14582802C411yescharacteristic
11#14582802C411yescharacteristic
12#14582772—21no—
13#14582772—21no—
14#14582768C2211yescharacteristic
15#14582764C2211yescharacteristic
16C4×C4⋊Dic43C411yescharacteristic
17#14582625C2212yes—
18#14582623—21no—
19C2×C4×D4×C43C2211yescharacteristic
20C2×C22⋊C8×C43—21no—
21C43×#324C2212yes—
22C43×#323—21no—
23C2×#10621877—41no—
24#13063317—41no—
25#13063317—41no—
26C2×C4⋊Dic43—21no—
27C2×C4⋊Dic43C2×C411yescharacteristic
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—21no—
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43—21no—
37C2×C4×Dic43C2×C411yescharacteristic
38C2×C4×Dic43C2×C411yescharacteristic
39C22⋊(C43⋊C8)—22no—
40C22⋊(C43⋊C8)—41no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C22×D4×C43C2×C411yescharacteristic
45C23×C4×C43D411yescharacteristic
46C23×C4×C43D411yescharacteristic
47C22×C8×C43—41no—
48C4×D4×C43—41no—
49C4×D4×C43—41no—
50C2×C4⋊C4×C43C2311yescharacteristic
51C2×C22⋊C4×C43D411yescharacteristic
52C2×C22⋊C4×C43D411yescharacteristic
53C2×C42×C43C2×C411yescharacteristic
54C22⋊C8×C43—22no—
55C22⋊C8×C43—41no—
56C24×C43C22⋊C411yescharacteristic
57C24×C43C22⋊C411yescharacteristic
58C2×D4×C43—22no—
59C2×D4×C43—22no—
60C2×D4×C43—41no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—81no—
66C22×C4×C43—81no—
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22×C411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C2×C8×C43—42no—
77C2×C8×C43—82no—
78C4⋊C4×C43—41no—
79C22⋊C4×C43—41no—
80C22⋊C4×C43—41no—
81C42×C43—21no—
82C42×C43—21no—
83C22⋊Dic43—42no—
84C22⋊Dic43—42no—
85C22⋊Dic43—81no—
86C22⋊Dic43—81no—
87C4⋊Dic43—42no—
88C4⋊Dic43—41no—
89C4⋊Dic43—41no—
90Dic43⋊C4—42no—
91Dic43⋊C4—41no—
92Dic43⋊C4—41no—
93Dic43⋊C4—81no—
94Dic43⋊C4—81no—
95C4×Dic43—22no—
96C4×Dic43—22no—
97#10621877—82no—
98C2×C43⋊C8—42no—
99C23×C43—21no—
100C23×C43—21no—
101C23×C43—21no—
102C23×C43—21no—
103C23×C43—21no—
104C23×C43—41no—
105C23×C43—41no—
106C23×C43—41no—
107C23×C43—41no—
108C23×C43#10112yes—
109C23×C43C2×C22⋊C411yescharacteristic
110D4×C43—44no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—41no—
117C2×C4×C43—42no—
118C2×C4×C43—42no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—81no—
123C2×C4×C43—81no—
124C2×C4×C43#9911yescharacteristic
125C2×C4×C43#9911yescharacteristic
126C2×C4×C43#13112yes—
127C2×Dic43—22no—
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—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C8×C43—82no—
140C43⋊C8—82no—
141#11572—431nomaximal, Sylow
142C22×C43—21no—
143C22×C43—21no—
144C22×C43—22no—
145C22×C43—42no—
146C22×C43—42no—
147C22×C43—41no—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43—81no—
153C22×C43—81no—
154C22×C43#40811yescharacteristic
155C22×C43C2×#9911yescharacteristic
156C22×C43C2×#10111yescharacteristic
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—22no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43—41no—
163Dic43—42no—
164Dic43—81no—
165Dic43—81no—
166Dic43—81no—
167#2566—431no—
168#1465—431no—
169#1459D4311yescharacteristic
170#1325—432no—
171#1324—432no—
172C2×C43—21no—
173C2×C43—21no—
174C2×C43—42no—
175C2×C43—81no—
176C2×C43#147211yescharacteristic
177C2×C43#212711yescharacteristic
178C2×C43#213211yescharacteristic
179C2×#125—431no—
180C2×C4×D4C2×D4311yescharacteristic
181#407—861no—
182C2×C22⋊C8—21no—
183#396—861no—
184#396—861no—
185#390—431no—
186#390—431no—
187#385—861no—
188#385—861no—
189#384—431no—
190#382—431no—
191C4×C4⋊C4—431no—
192#324—432no—
193#324C2×D4312yes—
194#323—21no—
195#323—861no—
196C43#1157211yescharacteristic, complemented, Sylow
197C22×D4C4×D4311yescharacteristic
198C23×C4D17211yescharacteristic
199C23×C4C22⋊D4311yescharacteristic
200C2×M16—1721no—
201C22×C8—41no—
202#125—1721no—
203#125—1721no—
204C4×D4—41no—
205C4×D4—41no—
206C2×C4⋊C4—431no—
207C2×C4⋊C4—431no—
208C2×C4⋊C4—861no—
209C2×C4⋊C4—861no—
210C2×C4⋊C4—861no—
211C2×C4⋊C4—861no—
212C2×C4⋊C4—861no—
213C2×C4⋊C4C22×D4311yescharacteristic
214C2×C22⋊C4—861no—
215C2×C22⋊C4—861no—
216C2×C22⋊C4—861no—
217C2×C22⋊C4—861no—
218C2×C22⋊C4D17211yescharacteristic
219C2×C22⋊C4C22⋊D4311yescharacteristic
220C2×C42—431no—
221C2×C42—431no—
222C2×C42C4×D4311yescharacteristic
223C22⋊C8—22no—
224C22⋊C8—41no—
225C22⋊C8—862no—
226C22⋊C8—1721no—
227#95—861no—
228#95—861no—
229#95—861no—
230C24(C2×D43)⋊C411yescharacteristic
231C24(C2×D43)⋊C411yescharacteristic
232C2×D4—22no—
233C2×D4—22no—
234C2×D4—41no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—81no—
240C22×C4—81no—
241C22×C4—861no—
242C22×C4—861no—
243C22×C4—861no—
244C22×C4—861no—
245C22×C4(C2×D43)⋊C411yescharacteristic
246C22×C4(C2×D43)⋊C411yescharacteristic
247C22×C4C2×C4×D4311yescharacteristic
248C22×C4C2×D17211yescharacteristic
249C22×C4C2×C22⋊D4311yescharacteristic
250M16—3442no—
251C2×C8—42no—
252C2×C8—82no—
253C2×C8—1722no—
254C4⋊C4—41no—
255C4⋊C4—3441no—
256C4⋊C4—3441no—
257C4⋊C4—1721no—
258C4⋊C4—1721no—
259C4⋊C4—1722no—
260C4⋊C4—1722no—
261C4⋊C4—1721no—
262C4⋊C4—1721no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—3441no—
266C22⋊C4—3441no—
267C22⋊C4—1722no—
268C22⋊C4—1722no—
269C42—21no—
270C42—21no—
271C42—862no—
272C42—862no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23#1306324312yes—
283C23C2×(C2×D43)⋊C411yescharacteristic
284D4—44no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—862no—
299C2×C4—1721no—
300C2×C4—1721no—
301C2×C4—1721no—
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#1306323911yescharacteristic
311C2×C4#1306323911yescharacteristic
312C2×C4#1306333112yes—
313C8—82no—
314C8—3442no—
315C22—21no—
316C22—21no—
317C22—22no—
318C22—42no—
319C22—42no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—81no—
326C22—81no—
327C22#1458286511yescharacteristic
328C22C2×#1306323911yescharacteristic
329C22C2×#1306324311yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—3441no—
337C4—3441no—
338C4—3441no—
339C4—1722no—
340C2—21no—
341C2—21no—
342C2—42no—
343C2—81no—
344C2#1913295811yescharacteristic
345C2#1913626211yescharacteristic
346C2#1913627811yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1459C2
socleC22×C43C2×#99
prime radicalC22×D4×C43C2×C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1459D43
hypocenterC43#11572
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #19132540C2semidirect
4. #19132538C2semidirect
196. C43#11572semidirect

Maximal subgroups

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

subgroupindex
#191397912
#191329332
#191325402
#191325382
C43×#14592
#1157243