Finite Group Databasebeta

← #24984696

Subgroups — #24984696

Order 11008.

514 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137076C211yesmaximal, characteristic
2#19134574C211yesmaximal, characteristic
3#19134574C211yesmaximal, characteristic
4#19132419C211yesmaximal, characteristic, complemented
5#19132418C211yesmaximal, characteristic, complemented
6#19132417C211yesmaximal, characteristic, complemented
7C43×#1271C211yesmaximal, characteristic, complemented
8C2×#13063283C411yescharacteristic
9C2×#13063283C411yescharacteristic
10C2×C42×D43C2211yescharacteristic
11C2×Dic43⋊C8—21no—
12C2×Dic43⋊C8—21no—
13C2×(C2×D43)⋊C8—21no—
14C2×(C2×D43)⋊C8—21no—
15#14582798C411yescharacteristic
16#14582797C2211yescharacteristic
17#14582795C411yescharacteristic
18#14582773—21no—
19#14582770—21no—
20C4⋊C4×Dic43—21no—
21#14582750—21no—
22#14582654C2211yescharacteristic
23#14582654C2211yescharacteristic
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#13063283—22no—
33#13063283—42no—
34#13063283C814yescomplemented
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43C2×C411yescharacteristic
37C2×C4⋊Dic43C2×C411yescharacteristic
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×C4×Dic43—21no—
43C2×C4×Dic43—21no—
44C2×C4×Dic43C2×C411yescharacteristic
45C2×C4×Dic43D411yescharacteristic
46C2×C4×Dic43D411yescharacteristic
47C42×D43—42no—
48Dic43⋊C8—42no—
49Dic43⋊C8—42no—
50(C2×D43)⋊C8—42no—
51(C2×D43)⋊C8—42no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C22×C8×C43—21no—
56C22×C8×C43—21no—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43C2×C411yescharacteristic
59C2×C4⋊C4×C43C2×C411yescharacteristic
60C2×C42×C43C2311yescharacteristic
61#95×C43—21no—
62C23×D43C22⋊C411yescharacteristic
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43C22×C411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43C22⋊C411yescharacteristic
71C22×Dic43C22⋊C411yescharacteristic
72C22×Dic43C22⋊C411yescharacteristic
73C2×C4×D43—22no—
74C2×C4×D43—22no—
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43—41no—
80C2×C4×D43—41no—
81C2×C4×D43—41no—
82C2×C4×D43—41no—
83C2×C4×D43C2×C812yes—
84C2×C4×D43M1612yes—
85C2×C8×C43—41no—
86C2×C8×C43—41no—
87C2×C8×C43—41no—
88C2×C8×C43—41no—
89C2×C8×C43—41no—
90C2×C8×C43—41no—
91C4⋊C4×C43—21no—
92C4⋊C4×C43—41no—
93C4⋊C4×C43—41no—
94C4⋊C4×C43—41no—
95C4⋊C4×C43C2×C812yes—
96C42×C43—41no—
97(C2×D43)⋊C4—24no—
98(C2×D43)⋊C4—42no—
99C4⋊Dic43—21no—
100C4⋊Dic43—42no—
101C4⋊Dic43—41no—
102C4⋊Dic43C2×C812yes—
103Dic43⋊C4—42no—
104Dic43⋊C4—41no—
105Dic43⋊C4—41no—
106C4×Dic43—24no—
107C4×Dic43—22no—
108C4×Dic43—22no—
109C4×Dic43—41no—
110C4×Dic43—42no—
111C2×C43⋊C8—41no—
112C2×C43⋊C8—41no—
113C2×C43⋊C8—41no—
114C2×C43⋊C8—41no—
115C2×C43⋊C8—41no—
116C2×C43⋊C8—41no—
117C23×C43C2×C22⋊C411yescharacteristic
118C22×D43—21no—
119C22×D43—21no—
120C22×D43—21no—
121C22×D43—21no—
122C22×D43—21no—
123C22×D43—21no—
124C22×D43C22⋊C812yes—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—22no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43C22×C811yescharacteristic
138C2×C4×C43C2×M1611yescharacteristic
139C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C43#13711yescharacteristic
142C2×C4×C43#13711yescharacteristic
143C2×Dic43—22no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43C22⋊C812yes—
156C2×Dic43#9912yes—
157C2×Dic43#10112yes—
158C4×D43—24no—
159C4×D43—24no—
160C4×D43—42no—
161C4×D43—42no—
162C4×D43—42no—
163C4×D43—42no—
164C8×C43—81no—
165C8×C43—81no—
166C43⋊C8—81no—
167C43⋊C8—81no—
168#7598—431nomaximal, Sylow
169C22×C43C2×C22⋊C811yescharacteristic
170C22×C43C2×#9911yescharacteristic
171C22×C43C2×#10111yescharacteristic
172C22×C43#41711yescharacteristic
173C22×C43#41711yescharacteristic
174C22×C43#42111yescharacteristic
175C22×C43#42111yescharacteristic
176C2×D43—22no—
177C2×D43—22no—
178C2×D43—22no—
179C2×D43—41no—
180C2×D43—41no—
181C2×D43—41no—
182C2×D43—41no—
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—42no—
190C4×C43—81no—
191Dic43—42no—
192Dic43—41no—
193Dic43—41no—
194Dic43—81no—
195Dic43#32414yes—
196#2296—431no—
197#1797—431no—
198#1797—431no—
199#1271—431no—
200#1271—431no—
201#1271—431no—
202#1271D4311yescharacteristic, complemented
203C2×C43C2×#32411yescharacteristic
204C2×C43#147711yescharacteristic
205C2×C43#147711yescharacteristic
206C2×C43#151311yescharacteristic
207C2×C43#151311yescharacteristic
208C2×C43#153711yescharacteristic
209C2×C43#156111yescharacteristic
210D43—42no—
211C2×#117—431no—
212C2×#117—431no—
213C22×C42—431no—
214C2×C4⋊C8—861no—
215C2×C4⋊C8—861no—
216C2×C22⋊C8—861no—
217C2×C22⋊C8—861no—
218#389—431no—
219#389—431no—
220#389—431no—
221#389C2×D4311yescharacteristic
222#385—861no—
223#385—861no—
224C4×C4⋊C4—861no—
225C4×C4⋊C4—861no—
226#336—431no—
227#336—431no—
228#336C2×D4311yescharacteristic
229#336C2×D4311yescharacteristic
230C43#759811yescharacteristic, complemented, Sylow
231C23×C4—431no—
232C23×C4—431no—
233C23×C4—431no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—861no—
237C22×C8—861no—
238#117—434no—
239#117—862no—
240#117—1722no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—431no—
243C2×C4⋊C4—431no—
244C2×C4⋊C4—861no—
245C2×C4⋊C4—861no—
246C2×C4⋊C4—861no—
247C2×C4⋊C4C4×D4311yescharacteristic
248C2×C4⋊C4C4×D4311yescharacteristic
249C2×C22⋊C4—861no—
250C2×C22⋊C4—861no—
251C2×C42—431no—
252C2×C42—431no—
253C2×C42—431no—
254C2×C42—861no—
255C2×C42—861no—
256C2×C42—1722no—
257C2×C42C22×D4311yescharacteristic
258C4⋊C8—1722no—
259C4⋊C8—1722no—
260C22⋊C8—1722no—
261C22⋊C8—1722no—
262#95—21no—
263#95—861no—
264#95—861no—
265#95—861no—
266C24—431no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—431no—
270C22×C4—432no—
271C22×C4—432no—
272C22×C4—431no—
273C22×C4—431no—
274C22×C4—862no—
275C22×C4—862no—
276C22×C4—861no—
277C22×C4—861no—
278C22×C4—861no—
279C22×C4—861no—
280C22×C4—861no—
281C22×C4—861no—
282C22×C4—1721no—
283C22×C4—1721no—
284C22×C4—1721no—
285C22×C4—1721no—
286C22×C4C2×C4×D4311yescharacteristic
287C22×C4D4×D4311yescharacteristic
288C22×C4D4×D4311yescharacteristic
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—1721no—
296C2×C8—1721no—
297C2×C8—1721no—
298C2×C8—1721no—
299C2×C8—1721no—
300C2×C8—1721no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—432no—
306C4⋊C4—861no—
307C4⋊C4—1721no—
308C4⋊C4—1722no—
309C4⋊C4—1722no—
310C4⋊C4—1721no—
311C4⋊C4—1721no—
312C4⋊C4C8×D4312yes—
313C22⋊C4—864no—
314C22⋊C4—1722no—
315C42—41no—
316C42—862no—
317C42—862no—
318C42—864no—
319C42—1721no—
320C42—1722no—
321C23—432no—
322C23—861no—
323C23—861no—
324C23—861no—
325C23—861no—
326C23—861no—
327C23—861no—
328C23C22⋊C4×D4311yescharacteristic
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—22no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—432no—
342C2×C4—432no—
343C2×C4—432no—
344C2×C4—864no—
345C2×C4—864no—
346C2×C4—862no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—861no—
350C2×C4—861no—
351C2×C4—861no—
352C2×C4—861no—
353C2×C4—1722no—
354C2×C4—1722no—
355C2×C4—1722no—
356C2×C4—1722no—
357C2×C4—1721no—
358C2×C4—1721no—
359C2×C4—1721no—
360C2×C4—1721no—
361C2×C4—1721no—
362C2×C4C2×C8×D4311yescharacteristic
363C2×C4M16×D4311yescharacteristic
364C2×C4#1306334911yescharacteristic
365C2×C4#1306335211yescharacteristic
366C2×C4#1306335411yescharacteristic
367C2×C4#1306335711yescharacteristic
368C8—81no—
369C8—81no—
370C8—3441no—
371C8—3441no—
372C22—862no—
373C22—862no—
374C22—862no—
375C22—1721no—
376C22—1721no—
377C22—1721no—
378C22—1721no—
379C22C22⋊C8×D4311yescharacteristic
380C22#99×D4311yescharacteristic
381C22#101×D4311yescharacteristic
382C22#1458289711yescharacteristic
383C22#1458289911yescharacteristic
384C22#1458291411yescharacteristic
385C22#1458291411yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—42no—
393C4—81no—
394C4—434no—
395C4—3441no—
396C4—1722no—
397C4—1721no—
398C4—1721no—
399C2—1722no—
400C2#324×D4311yescharacteristic
401C2#1913297911yescharacteristic
402C2#1913298111yescharacteristic
403C2#1913313511yescharacteristic
404C2#1913313711yescharacteristic
405C2#1913323111yescharacteristic
406C2#1913333111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#1271C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1271D43
hypocenterC43#7598
LCSG ▷ C2×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
34. #13063283C8semidirect
202. #1271D43semidirect
230. C43#7598semidirect

Maximal subgroups

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

subgroupindex
#191370762
#191345742
#191324192
#191324182
#191324172
C43×#12712
#759843