Finite Group Databasebeta

← #25006194

Subgroups — #25006194

Order 11008.

446 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 73 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#19138902C211yesmaximal, characteristic
2#19132934C211yesmaximal, characteristic
3#19132910C211yesmaximal, characteristic
4#19132525C211yesmaximal, characteristic, complemented
5#19132524C211yesmaximal, characteristic, complemented
6#19132524C211yesmaximal, characteristic, complemented
7C43×#1317C211yesmaximal, characteristic, complemented
8C2×#13063309C411yescharacteristic
9C2×#13063308C411yescharacteristic
10C2×(C22⋊D43)⋊C4C2211yescharacteristic
11C22×Dic43⋊C4C411yescharacteristic
12#14582953—21no—
13C22⋊C8×D43—21no—
14#14582833—21no—
15#14582828—21no—
16#14582796—21no—
17#14582760C2211yescharacteristic
18#14582758—21no—
19#14582757C411yescharacteristic
20#14582624—21no—
21#14582623C2211yescharacteristic
22#14582623C2211yescharacteristic
23#14582622—21no—
24C43×#381C2211yescharacteristic
25C43×#323C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C22×C22⋊D43C2×C411yescharacteristic
28C23×Dic43C2×C411yescharacteristic
29C23×Dic43C2×C411yescharacteristic
30C22×C4×D43D411yescharacteristic
31C2×C8×D43—41no—
32#13063309—42no—
33#13063308—42no—
34(C22⋊D43)⋊C4—41no—
35(C22⋊D43)⋊C4—41no—
36C2×C4⋊Dic43—21no—
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—41no—
42C2×Dic43⋊C4—41no—
43C2×Dic43⋊C4D411yescharacteristic
44C2×C22⋊Dic43C2×C411yescharacteristic
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4D411yescharacteristic
48C2×C4×Dic43D411yescharacteristic
49Dic43⋊C8—41no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52(C2×D43)⋊C8—41no—
53#13063235—41no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95—21no—
57C23×C4×C43C2×C411yescharacteristic
58C2×C22⋊C4×C43C2×C411yescharacteristic
59C2×C22⋊C4×C43C2311yescharacteristic
60C22⋊C8×C43—21no—
61C22⋊C8×C43—21no—
62#95×C43—21no—
63#95×C43—21no—
64C24×C43C22×C411yescharacteristic
65C23×D43C22⋊C411yescharacteristic
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—41no—
71C22×C4×C43—41no—
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C2×C22⋊D43—21no—
75C2×C22⋊D43—21no—
76C2×C22⋊D43—22no—
77C2×C22⋊D43—41no—
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43—21no—
81C22×Dic43—21no—
82C22×Dic43—21no—
83C22×Dic43—21no—
84C22×Dic43—41no—
85C22×Dic43—41no—
86C22×Dic43—42no—
87C22×Dic43C22⋊C411yescharacteristic
88C22×Dic43C22⋊C411yescharacteristic
89C22×Dic43C22⋊C411yescharacteristic
90C2×C4×D43—21no—
91C2×C4×D43—21no—
92C2×C4×D43—42no—
93C2×C8×C43—41no—
94C2×C8×C43—41no—
95C22⋊C4×C43—41no—
96C22⋊C4×C43—41no—
97C22⋊Dic43—41no—
98(C2×D43)⋊C4—41no—
99(C2×D43)⋊C4—42no—
100(C2×D43)⋊C4—42no—
101C4⋊Dic43—42no—
102Dic43⋊C4—41no—
103Dic43⋊C4—42no—
104Dic43⋊C4—42no—
105Dic43⋊C4—42no—
106Dic43⋊C4—41no—
107Dic43⋊C4—41no—
108C4×Dic43—21no—
109C4×Dic43—21no—
110C2×C43⋊C8—41no—
111C2×C43⋊C8—41no—
112C8×D43—82no—
113C23×C43—21no—
114C23×C43—21no—
115C23×C43—41no—
116C23×C43—41no—
117C23×C43C2×C22⋊C411yescharacteristic
118C23×C43#13111yescharacteristic
119C23×C43#13111yescharacteristic
120C22×D43—21no—
121C22×D43—21no—
122C22×D43—41no—
123C22×D43—41no—
124C22×D43#10012yes—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
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—41no—
134C2×C4×C43—41no—
135C2×C4×C43—81no—
136C2×C4×C43—81no—
137C22⋊D43—42no—
138C22⋊D43—42no—
139C2×Dic43—22no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—42no—
145C2×Dic43—42no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—81no—
154C2×Dic43—81no—
155C2×Dic43#9911yescharacteristic
156C2×Dic43#9911yescharacteristic
157C4×D43—42no—
158C4×D43—81no—
159C8×C43—81no—
160C8×C43—81no—
161C43⋊C8—81no—
162C43⋊C8—81no—
163#11558—431nomaximal, Sylow
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—41no—
169C22×C43—41no—
170C22×C43—42no—
171C22×C43—41no—
172C22×C43—41no—
173C22×C43#40811yescharacteristic
174C22×C43C2×#9911yescharacteristic
175C22×C43C2×#10011yescharacteristic
176C2×D43—22no—
177C2×D43—41no—
178C2×D43—41no—
179C2×D43—42no—
180C2×D43—81no—
181C4×C43—41no—
182C4×C43—41no—
183C4×C43—81no—
184C4×C43—81no—
185Dic43—21no—
186Dic43—41no—
187Dic43—41no—
188Dic43—81no—
189Dic43—81no—
190Dic43#35212yes—
191#2486—431no—
192#1466—431no—
193#1459—431no—
194#1317—431no—
195#1317—431no—
196#1317—431no—
197#1317D4311yescharacteristic, complemented
198C2×C43—21no—
199C2×C43—21no—
200C2×C43—41no—
201C2×C43—41no—
202C2×C43#147111yescharacteristic
203C2×C43C2×#35211yescharacteristic
204C2×C43#212311yescharacteristic
205D43—42no—
206C2×#123—431no—
207C2×#123—431no—
208C2×C4×D4—431no—
209C22×C4⋊C4—431no—
210#432—861no—
211C2×C22⋊C8—861no—
212#398—861no—
213#397—861no—
214#389—861no—
215#381—431no—
216#381C2×D4311yescharacteristic
217#380—431no—
218#380—861no—
219#324—861no—
220#323—431no—
221#323—431no—
222#323—861no—
223#323C2×D4311yescharacteristic
224#323C2×D4311yescharacteristic
225C43#1155811yescharacteristic, complemented, Sylow
226C22×D4—431no—
227C23×C4—431no—
228C23×C4—431no—
229C23×C4—431no—
230C23×C4C4×D4311yescharacteristic
231C22×C8—1721no—
232#123—1722no—
233#123—1722no—
234C4×D4—1721no—
235C4×D4—1721no—
236C2×C4⋊C4—431no—
237C2×C4⋊C4—861no—
238C2×C4⋊C4—861no—
239C2×C4⋊C4—861no—
240C2×C4⋊C4—861no—
241C2×C4⋊C4—861no—
242C2×C4⋊C4—1721no—
243C2×C4⋊C4—1721no—
244C2×C22⋊C4—431no—
245C2×C22⋊C4—431no—
246C2×C22⋊C4—861no—
247C2×C22⋊C4—861no—
248C2×C22⋊C4C4×D4311yescharacteristic
249C2×C22⋊C4C22×D4311yescharacteristic
250C2×C42—431no—
251C4⋊C8—1721no—
252C22⋊C8—21no—
253C22⋊C8—21no—
254C22⋊C8—861no—
255C22⋊C8—861no—
256C22⋊C8—1721no—
257#97—1721no—
258#95—21no—
259#95—21no—
260#95—861no—
261#95—861no—
262#95—861no—
263C24—431no—
264C24C2×C4×D4311yescharacteristic
265C2×D4—862no—
266C2×D4—861no—
267C2×D4—861no—
268C2×D4—1721no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—431no—
276C22×C4—431no—
277C22×C4—431no—
278C22×C4—861no—
279C22×C4—861no—
280C22×C4—861no—
281C22×C4—861no—
282C22×C4—861no—
283C22×C4—861no—
284C22×C4—861no—
285C22×C4—861no—
286C22×C4—1722no—
287C22×C4—1722no—
288C22×C4—1721no—
289C22×C4—1721no—
290C22×C4D4×D4311yescharacteristic
291C22×C4D4×D4311yescharacteristic
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—3442no—
295C2×C8—1721no—
296C2×C8—1721no—
297C4⋊C4—1721no—
298C4⋊C4—1721no—
299C4⋊C4—1721no—
300C4⋊C4—1722no—
301C4⋊C4—1722no—
302C4⋊C4—1722no—
303C4⋊C4—1722no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—1721no—
307C22⋊C4—1722no—
308C22⋊C4—1722no—
309C22⋊C4—1721no—
310C42—861no—
311C42—861no—
312C23—21no—
313C23—21no—
314C23—41no—
315C23—41no—
316C23—432no—
317C23—861no—
318C23—861no—
319C23—1721no—
320C23—1721no—
321C23C22⋊C4×D4311yescharacteristic
322C23#1306333111yescharacteristic
323C23#1306333311yescharacteristic
324D4—1722no—
325D4—1722no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—431no—
339C2×C4—431no—
340C2×C4—862no—
341C2×C4—861no—
342C2×C4—861no—
343C2×C4—861no—
344C2×C4—861no—
345C2×C4—3441no—
346C2×C4—3441no—
347C2×C4—3441no—
348C2×C4—1722no—
349C2×C4—1722no—
350C2×C4—1722no—
351C2×C4—1721no—
352C2×C4—1721no—
353C2×C4—1721no—
354C2×C4—1721no—
355C2×C4—1721no—
356C2×C4—1721no—
357C2×C4—1721no—
358C8—81no—
359C8—81no—
360C8—3441no—
361C8—3441no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—41no—
367C22—41no—
368C22—42no—
369C22—41no—
370C22—41no—
371C22—862no—
372C22—3441no—
373C22—1722no—
374C22—1721no—
375C22—1721no—
376C22#1458286411yescharacteristic
377C22#99×D4311yescharacteristic
378C22#100×D4311yescharacteristic
379C4—41no—
380C4—41no—
381C4—81no—
382C4—81no—
383C4—432no—
384C4—861no—
385C4—3441no—
386C4—3441no—
387C4—1721no—
388C4—1721no—
389C2—21no—
390C2—21no—
391C2—41no—
392C2—41no—
393C2—1722no—
394C2#1913295311yescharacteristic
395C2#352×D4311yescharacteristic
396C2#1913624711yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC24×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1317C2
socleC22×C43C2×#99
prime radicalC22×C22⋊D43C2×C4
cosocleC2×C22⋊C4×C43C23
hypercenter#1317D43
hypocenterC43#11558
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1317

Complements

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

NH ≅ G/Ntype
4. #19132525C2semidirect
5. #19132524C2semidirect
6. #19132524C2semidirect
7. C43×#1317C2semidirect
197. #1317D43semidirect
225. C43#11558semidirect

Maximal subgroups

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

subgroupindex
#191389022
#191329342
#191329102
#191325252
#191325242
C43×#13172
#1155843