Finite Group Databasebeta

← #24985281

Subgroups — #24985281

Order 11008.

450 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 95 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#19142904C211yesmaximal, characteristic
2#19134662C211yesmaximal, characteristic
3#19134574C211yesmaximal, characteristic
4#19132419C211yesmaximal, characteristic, complemented
5#19132418C211yesmaximal, characteristic, complemented
6#19132417C211yesmaximal, characteristic, complemented
7C43×#1271C211yesmaximal, characteristic, complemented
8C2×#13063316C411yescharacteristic
9C2×C42×D43C2211yescharacteristic
10C2×Dic43⋊C8—21no—
11C2×(C2×D43)⋊C8—21no—
12C2×(C2×D43)⋊C8—21no—
13#14582797C2211yescharacteristic
14#14582785—21no—
15#14582781—21no—
16#14582773—21no—
17#14582770—21no—
18#14582764C411yescharacteristic
19#14582756C411yescharacteristic
20#14582756C411yescharacteristic
21#14582654C2211yescharacteristic
22#14582654C2211yescharacteristic
23#14582653—21no—
24C43×#389C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×C4×D43C2×C411yescharacteristic
28C22×C4×D43D411yescharacteristic
29C22×C4×D43D411yescharacteristic
30C22×C43⋊C8—21no—
31C22×C43⋊C8—21no—
32#13063316—42no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43C2×C411yescharacteristic
35C2×C4⋊Dic43C2×C411yescharacteristic
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×C4×Dic43C2×C411yescharacteristic
41C2×C4×Dic43D411yescharacteristic
42C2×C4×Dic43D411yescharacteristic
43C42×D43—42no—
44Dic43⋊C8—42no—
45(C2×D43)⋊C8—42no—
46(C2×D43)⋊C8—42no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C22×C8×C43—21no—
53C22×C8×C43—21no—
54C2×C4⋊C4×C43—21no—
55C2×C4⋊C4×C43C2×C411yescharacteristic
56C2×C4⋊C4×C43C2×C411yescharacteristic
57C2×C42×C43C2311yescharacteristic
58#95×C43—21no—
59C23×D43C22⋊C411yescharacteristic
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43C22×C411yescharacteristic
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C22×Dic43—21no—
66C22×Dic43—21no—
67C22×Dic43C22⋊C411yescharacteristic
68C22×Dic43C22⋊C411yescharacteristic
69C22×Dic43C22⋊C411yescharacteristic
70C2×C4×D43—21no—
71C2×C4×D43—21no—
72C2×C4×D43—21no—
73C2×C4×D43—21no—
74C2×C4×D43—21no—
75C2×C4×D43—21no—
76C2×C4×D43—22no—
77C2×C4×D43—22no—
78C2×C4×D43—41no—
79C2×C4×D43—41no—
80C2×C4×D43—41no—
81C2×C4×D43—41no—
82C2×C8×C43—41no—
83C2×C8×C43—41no—
84C2×C8×C43—41no—
85C2×C8×C43—41no—
86C2×C8×C43—41no—
87C2×C8×C43—41no—
88C4⋊C4×C43—21no—
89C4⋊C4×C43—21no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92C4⋊C4×C43—41no—
93C42×C43—41no—
94(C2×D43)⋊C4—42no—
95(C2×D43)⋊C4—42no—
96C4⋊Dic43—21no—
97C4⋊Dic43—21no—
98C4⋊Dic43—42no—
99C4⋊Dic43—41no—
100Dic43⋊C4—41no—
101Dic43⋊C4—41no—
102Dic43⋊C4—42no—
103C4×Dic43—22no—
104C4×Dic43—22no—
105C4×Dic43—41no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8—41no—
108C2×C43⋊C8—41no—
109C2×C43⋊C8—41no—
110C2×C43⋊C8—41no—
111C2×C43⋊C8—41no—
112C23×C43C2×C22⋊C411yescharacteristic
113C22×D43—21no—
114C22×D43—21no—
115C22×D43—21no—
116C22×D43—21no—
117C22×D43—21no—
118C22×D43—21no—
119C22×D43#10112yes—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
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#13111yescharacteristic
133C2×C4×C43#13111yescharacteristic
134C2×C4×C43#13511yescharacteristic
135C2×C4×C43#13511yescharacteristic
136C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C43#13711yescharacteristic
138C2×Dic43—21no—
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43#9912yes—
153C4×D43—42no—
154C4×D43—42no—
155C4×D43—42no—
156C4×D43—42no—
157C4×D43—42no—
158C4×D43—42no—
159C8×C43—81no—
160C8×C43—81no—
161C43⋊C8—81no—
162C43⋊C8—81no—
163#7731—431nomaximal, Sylow
164C22×C43#40811yescharacteristic
165C22×C43C2×#9911yescharacteristic
166C22×C43C2×#10111yescharacteristic
167C22×C43#41611yescharacteristic
168C22×C43#41711yescharacteristic
169C22×C43#42111yescharacteristic
170C22×C43#42111yescharacteristic
171C2×D43—22no—
172C2×D43—22no—
173C2×D43—22no—
174C2×D43—41no—
175C2×D43—41no—
176C2×D43—41no—
177C2×D43—41no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—81no—
185C4×C43—81no—
186Dic43—22no—
187Dic43—41no—
188Dic43—41no—
189Dic43—81no—
190Dic43—81no—
191#2851—431no—
192#1817—431no—
193#1797—431no—
194#1271—431no—
195#1271—431no—
196#1271—431no—
197#1271D4311yescharacteristic, complemented
198C2×C43#147211yescharacteristic
199C2×C43#148211yescharacteristic
200C2×C43#149511yescharacteristic
201C2×C43#151311yescharacteristic
202C2×C43#151611yescharacteristic
203C2×C43#153411yescharacteristic
204C2×C43#155211yescharacteristic
205D43—42no—
206C2×#125—431no—
207C22×C42—431no—
208C2×C4⋊C8—861no—
209C2×C22⋊C8—861no—
210C2×C22⋊C8—861no—
211#389—431no—
212#389C2×D4311yescharacteristic
213#387—861no—
214#387—861no—
215#385—861no—
216#385—861no—
217#382—431no—
218#380—431no—
219#380—431no—
220#336—431no—
221#336—431no—
222#336—861no—
223#336C2×D4311yescharacteristic
224#336C2×D4311yescharacteristic
225C43#773111yescharacteristic, complemented, Sylow
226C23×C4—431no—
227C23×C4—431no—
228C23×C4—431no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—861no—
232C22×C8—861no—
233#125—1722no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—431no—
236C2×C4⋊C4—431no—
237C2×C4⋊C4—861no—
238C2×C4⋊C4—861no—
239C2×C4⋊C4—861no—
240C2×C4⋊C4C4×D4311yescharacteristic
241C2×C4⋊C4C4×D4311yescharacteristic
242C2×C22⋊C4—861no—
243C2×C22⋊C4—861no—
244C2×C42—431no—
245C2×C42—431no—
246C2×C42—431no—
247C2×C42—1722no—
248C2×C42C22×D4311yescharacteristic
249C4⋊C8—1722no—
250C22⋊C8—1722no—
251C22⋊C8—1722no—
252#95—21no—
253#95—861no—
254#95—861no—
255#95—861no—
256#95—861no—
257#95—861no—
258C24—431no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—431no—
262C22×C4—431no—
263C22×C4—431no—
264C22×C4—862no—
265C22×C4—862no—
266C22×C4—861no—
267C22×C4—861no—
268C22×C4—861no—
269C22×C4—861no—
270C22×C4—861no—
271C22×C4—861no—
272C22×C4—861no—
273C22×C4—861no—
274C22×C4—1721no—
275C22×C4—1721no—
276C22×C4—1721no—
277C22×C4—1721no—
278C22×C4C2×C4×D4311yescharacteristic
279C22×C4D4×D4311yescharacteristic
280C22×C4D4×D4311yescharacteristic
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—1721no—
288C2×C8—1721no—
289C2×C8—1721no—
290C2×C8—1721no—
291C2×C8—1721no—
292C2×C8—1721no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—861no—
299C4⋊C4—861no—
300C4⋊C4—1721no—
301C4⋊C4—1722no—
302C4⋊C4—1722no—
303C4⋊C4—1721no—
304C4⋊C4—1721no—
305C22⋊C4—1722no—
306C22⋊C4—1722no—
307C42—41no—
308C42—862no—
309C42—862no—
310C42—1721no—
311C23—432no—
312C23—861no—
313C23—861no—
314C23—861no—
315C23—861no—
316C23—861no—
317C23—861no—
318C23C22⋊C4×D4311yescharacteristic
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—432no—
332C2×C4—861no—
333C2×C4—861no—
334C2×C4—861no—
335C2×C4—861no—
336C2×C4—861no—
337C2×C4—861no—
338C2×C4—861no—
339C2×C4—861no—
340C2×C4—1722no—
341C2×C4—1722no—
342C2×C4—1722no—
343C2×C4—1722no—
344C2×C4—1722no—
345C2×C4—1722no—
346C2×C4—1721no—
347C2×C4—1721no—
348C2×C4—1721no—
349C2×C4—1721no—
350C2×C4—1721no—
351C2×C4—1721no—
352C2×C4#1306333111yescharacteristic
353C2×C4#1306333311yescharacteristic
354C2×C4#1306334411yescharacteristic
355C2×C4#1306334611yescharacteristic
356C2×C4#1306335211yescharacteristic
357C2×C4#1306335711yescharacteristic
358C8—81no—
359C8—81no—
360C8—3441no—
361C8—3441no—
362C22—862no—
363C22—862no—
364C22—862no—
365C22—1721no—
366C22—1721no—
367C22—1721no—
368C22—1721no—
369C22#1458286411yescharacteristic
370C22#99×D4311yescharacteristic
371C22#101×D4311yescharacteristic
372C22#1458289211yescharacteristic
373C22#1458289911yescharacteristic
374C22#1458291411yescharacteristic
375C22#1458291411yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—81no—
383C4—81no—
384C4—862no—
385C4—3441no—
386C4—3441no—
387C4—1721no—
388C4—1721no—
389C2—1722no—
390C2#1913295711yescharacteristic
391C2#1913300011yescharacteristic
392C2#1913305911yescharacteristic
393C2#1913313711yescharacteristic
394C2#1913314811yescharacteristic
395C2#1913322011yescharacteristic
396C2#1913329211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1271C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1271D43
hypocenterC43#7731
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
4. #19132419C2semidirect
5. #19132418C2semidirect
6. #19132417C2semidirect
7. C43×#1271C2semidirect
197. #1271D43semidirect
225. C43#7731semidirect

Maximal subgroups

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

subgroupindex
#191429042
#191346622
#191345742
#191324192
#191324182
#191324172
C43×#12712
#773143