Finite Group Databasebeta

← #25006255

Subgroups — #25006255

Order 11008.

416 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 71 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#19139794C211yesmaximal, characteristic
2#19132932C211yesmaximal, characteristic
3#19132912C211yesmaximal, characteristic
4#19132540C211yesmaximal, characteristic, complemented
5#19132540C211yesmaximal, characteristic, complemented
6#19132539C211yesmaximal, characteristic, complemented
7C43×#1324C211yesmaximal, characteristic, complemented
8C2×#13063316C411yescharacteristic
9C2×#13063287C2211yescharacteristic
10#14582861—21no—
11C22⋊C8×D43—21no—
12#14582823—21no—
13#14582823—21no—
14#14582801C411yescharacteristic
15#14582800C411yescharacteristic
16#14582773—21no—
17#14582773—21no—
18#14582768C2211yescharacteristic
19C4×Dic43⋊C4C411yescharacteristic
20#14582625C2211yescharacteristic
21#14582625C2211yescharacteristic
22#14582622—21no—
23#14582622—21no—
24C43×#382C2211yescharacteristic
25C43×#324C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×D172C2×C411yescharacteristic
28C22×C4×D43D411yescharacteristic
29C22×C4×D43D411yescharacteristic
30C2×#10621872—41no—
31C2×C8×D43—41no—
32#13063316—41no—
33#13063316—41no—
34#13063287—41no—
35#13063287—41no—
36C2×C4⋊Dic43—21no—
37C2×C4⋊Dic43C2×C411yescharacteristic
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4D411yescharacteristic
47C2×(C2×D43)⋊C4D411yescharacteristic
48C2×C4×Dic43C2×C411yescharacteristic
49C2×C4×Dic43C2×C411yescharacteristic
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52(C2×D43)⋊C8—41no—
53(C2×D43)⋊C8—41no—
54C43⋊#95—21no—
55C2×C4⋊C4×C43C2×C411yescharacteristic
56C2×C4⋊C4×C43C2311yescharacteristic
57C2×C42×C43C2×C411yescharacteristic
58C22⋊C8×C43—21no—
59C22⋊C8×C43—21no—
60#95×C43—21no—
61#95×C43—21no—
62C23×D43C22⋊C411yescharacteristic
63C23×D43C22⋊C411yescharacteristic
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43C22×C411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43C22⋊C411yescharacteristic
72C22×Dic43C22⋊C411yescharacteristic
73C2×D172—21no—
74C2×D172—21no—
75C2×D172—22no—
76C2×D172—41no—
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43—81no—
82C2×C4×D43—81no—
83C2×C8×C43—41no—
84C2×C8×C43—41no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—41no—
87C42×C43—21no—
88C42×C43—21no—
89(C2×D43)⋊C4—41no—
90(C2×D43)⋊C4—41no—
91(C2×D43)⋊C4—42no—
92(C2×D43)⋊C4—42no—
93(C2×D43)⋊C4—81no—
94(C2×D43)⋊C4—81no—
95C4⋊Dic43—41no—
96C4⋊Dic43—41no—
97C4⋊Dic43—41no—
98Dic43⋊C4—42no—
99Dic43⋊C4—42no—
100Dic43⋊C4—81no—
101Dic43⋊C4—81no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43—21no—
105C4×Dic43—21no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8—41no—
108#10621872—82no—
109C8×D43—82no—
110C23×C43C2×C22⋊C411yescharacteristic
111C22×D43—21no—
112C22×D43—21no—
113C22×D43—21no—
114C22×D43—21no—
115C22×D43—21no—
116C22×D43—41no—
117C22×D43—41no—
118C22×D43—41no—
119C22×D43—41no—
120C22×D43#10112yes—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43#13111yescharacteristic
134C2×C4×C43#13111yescharacteristic
135C2×Dic43—22no—
136C2×Dic43—21no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43#9911yescharacteristic
145C2×Dic43#9911yescharacteristic
146D172—42no—
147D172—42no—
148C4×D43—42no—
149C4×D43—42no—
150C4×D43—81no—
151C4×D43—81no—
152C8×C43—81no—
153C8×C43—81no—
154C43⋊C8—81no—
155C43⋊C8—81no—
156#11572—431nomaximal, Sylow
157C22×C43—21no—
158C22×C43—21no—
159C22×C43#40811yescharacteristic
160C22×C43C2×#9911yescharacteristic
161C22×C43C2×#10111yescharacteristic
162C2×D43—22no—
163C2×D43—41no—
164C2×D43—41no—
165C2×D43—42no—
166C2×D43—42no—
167C2×D43—41no—
168C2×D43—41no—
169C2×D43—41no—
170C2×D43—81no—
171C2×D43—81no—
172C4×C43—21no—
173C4×C43—21no—
174C4×C43—41no—
175C4×C43—41no—
176C4×C43—81no—
177C4×C43—81no—
178Dic43—21no—
179Dic43—21no—
180Dic43—42no—
181Dic43—41no—
182Dic43—81no—
183#2566—431no—
184#1465—431no—
185#1459—431no—
186#1325—431no—
187#1325—431no—
188#1324—431no—
189#1324D4311yescharacteristic, complemented
190C2×C43—21no—
191C2×C43—21no—
192C2×C43#147211yescharacteristic
193C2×C43#212711yescharacteristic
194C2×C43#213211yescharacteristic
195D43—42no—
196D43—81no—
197C2×#125—431no—
198C2×C4×D4—431no—
199#407—861no—
200C2×C22⋊C8—861no—
201#396—861no—
202#396—861no—
203#390—431no—
204#390—431no—
205#385—861no—
206#385—861no—
207#384—431no—
208#382C2×D4311yescharacteristic
209C4×C4⋊C4—431no—
210#324—431no—
211#324—431no—
212#324C2×D4311yescharacteristic
213#324C2×D4311yescharacteristic
214#323—861no—
215#323—861no—
216C43#1157211yescharacteristic, complemented, Sylow
217C22×D4—431no—
218C23×C4—431no—
219C23×C4—431no—
220C2×M16—1721no—
221C22×C8—1721no—
222#125—1721no—
223#125—1721no—
224C4×D4—1721no—
225C4×D4—1721no—
226C2×C4⋊C4—431no—
227C2×C4⋊C4—861no—
228C2×C4⋊C4—861no—
229C2×C4⋊C4—861no—
230C2×C4⋊C4—861no—
231C2×C4⋊C4—861no—
232C2×C4⋊C4C4×D4311yescharacteristic
233C2×C4⋊C4C22×D4311yescharacteristic
234C2×C22⋊C4—431no—
235C2×C22⋊C4—431no—
236C2×C22⋊C4—861no—
237C2×C22⋊C4—861no—
238C2×C22⋊C4—861no—
239C2×C22⋊C4—861no—
240C2×C42—431no—
241C2×C42—431no—
242C2×C42C4×D4311yescharacteristic
243C22⋊C8—21no—
244C22⋊C8—21no—
245C22⋊C8—861no—
246C22⋊C8—861no—
247C22⋊C8—1721no—
248C22⋊C8—1721no—
249#95—21no—
250#95—21no—
251#95—861no—
252C24—431no—
253C24—431no—
254C2×D4—862no—
255C2×D4—861no—
256C2×D4—861no—
257C2×D4—1721no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—431no—
261C22×C4—431no—
262C22×C4—861no—
263C22×C4—861no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4—861no—
268C22×C4—3441no—
269C22×C4—3441no—
270C22×C4C2×C4×D4311yescharacteristic
271C22×C4D4×D4311yescharacteristic
272C22×C4D4×D4311yescharacteristic
273M16—3442no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—3442no—
277C2×C8—1721no—
278C2×C8—1721no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—3441no—
282C4⋊C4—3441no—
283C4⋊C4—1721no—
284C4⋊C4—1721no—
285C4⋊C4—1721no—
286C4⋊C4—1722no—
287C4⋊C4—1722no—
288C22⋊C4—3441no—
289C22⋊C4—3441no—
290C22⋊C4—1721no—
291C22⋊C4—1721no—
292C22⋊C4—1722no—
293C22⋊C4—1722no—
294C42—21no—
295C42—21no—
296C42—861no—
297C42—861no—
298C42—861no—
299C42—861no—
300C23—432no—
301C23—861no—
302C23—861no—
303C23—861no—
304C23—861no—
305C23—861no—
306C23—1721no—
307C23—1721no—
308C23—1721no—
309C23—1721no—
310C23C22⋊C4×D4311yescharacteristic
311D4—1722no—
312D4—1722no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—431no—
326C2×C4—431no—
327C2×C4—862no—
328C2×C4—861no—
329C2×C4—3441no—
330C2×C4—3441no—
331C2×C4—1722no—
332C2×C4—1722no—
333C2×C4—1721no—
334C2×C4—1721no—
335C2×C4—1721no—
336C2×C4—1721no—
337C2×C4—1721no—
338C2×C4—1721no—
339C2×C4—1721no—
340C2×C4#1306333111yescharacteristic
341C2×C4#1306333311yescharacteristic
342C8—81no—
343C8—81no—
344C8—3441no—
345C8—3441no—
346C22—21no—
347C22—21no—
348C22—862no—
349C22—3441no—
350C22—3441no—
351C22—1722no—
352C22—1722no—
353C22—1721no—
354C22—1721no—
355C22—1721no—
356C22—1721no—
357C22—1721no—
358C22#1458286411yescharacteristic
359C22#99×D4311yescharacteristic
360C22#101×D4311yescharacteristic
361C4—21no—
362C4—21no—
363C4—41no—
364C4—41no—
365C4—81no—
366C4—81no—
367C4—861no—
368C4—861no—
369C4—3441no—
370C4—1722no—
371C4—1721no—
372C2—21no—
373C2—21no—
374C2—3441no—
375C2—1722no—
376C2#1913295711yescharacteristic
377C2#1913626311yescharacteristic
378C2#1913627711yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1324C2
socleC22×C43C2×#99
prime radicalC22×D172C2×C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1324D43
hypocenterC43#11572
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
4. #19132540C2semidirect
5. #19132540C2semidirect
6. #19132539C2semidirect
7. C43×#1324C2semidirect
189. #1324D43semidirect
216. C43#11572semidirect

Maximal subgroups

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

subgroupindex
#191397942
#191329322
#191329122
#191325402
#191325392
C43×#13242
#1157243