Finite Group Databasebeta

← #25015450

Subgroups — #25015450

Order 11008.

578 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063271C211yesmaximal, characteristic, complemented
2C22×#13063268C211yesmaximal, characteristic
3C2×#14583283C211yesmaximal, characteristic
4C2×#14582702C211yesmaximal, characteristic, complemented
5C2×#14582699C211yesmaximal, characteristic
6#19132673C211yesmaximal, characteristic, complemented
7C43×#1969C211yesmaximal, characteristic, complemented
8C22×Dic172C2211yescharacteristic
9C22×#10621873—21no—
10C22×D344C2211yescharacteristic
11C2×#13063313—21no—
12C2×#13063271—22no—
13C2×#13063271—22no—
14C2×#13063271—22no—
15C2×#13063268—22no—
16C2×#13063268—22no—
17C2×#13063268—22no—
18C22×C43⋊C16C2211yescharacteristic
19C22×C43⋊C16C2211yescharacteristic
20#14583283—22no—
21#14583283—22no—
22#14582702—22no—
23#14582699—22no—
24C22×Q16×C43C2211yescharacteristic
25C2×#107×C43C2211yescharacteristic
26C2×#103×C43—21no—
27C2×C4×C8×C43C2211yescharacteristic
28C43×#391—21no—
29C22×Dic86—21no—
30C22×D172—21no—
31C2×Dic172—21no—
32C2×Dic172—21no—
33C2×Dic172—21no—
34C2×Dic172—21no—
35C2×Dic172—21no—
36C2×Dic172D412yes—
37C2×#10621873—24no—
38C2×#10621873—42no—
39C2×#10621873—42no—
40C2×D344—21no—
41C2×D344—21no—
42C2×D344—21no—
43C2×D344—21no—
44C2×D344—21no—
45C2×D344D412yes—
46#13063313—24no—
47#13063313—42no—
48C2×(C2×D43)⋊C4—42no—
49#13063271—28no—
50#13063268—28no—
51C2×C43⋊C16—21no—
52C2×C43⋊C16—21no—
53C2×C43⋊C16—21no—
54C2×C43⋊C16—21no—
55C2×C43⋊C16D412yes—
56C2×C43⋊C16D412yes—
57C22×Q8×C43—21no—
58C2×Q16×C43—21no—
59C2×Q16×C43—21no—
60C2×Q16×C43—21no—
61C2×Q16×C43—21no—
62C2×Q16×C43—21no—
63C2×Q16×C43D412yes—
64C22×C8×C43D411yescharacteristic
65C22×C8×C43C2311yescharacteristic
66C2×C4⋊C4×C43—21no—
67C2×C42×C43D411yescharacteristic
68#107×C43—21no—
69#107×C43—21no—
70#103×C43—42no—
71C4×C8×C43—21no—
72C4×C8×C43—21no—
73#95×C43—42no—
74C23×D43—41no—
75C2×Q8×C43—22no—
76C2×Q8×C43—41no—
77C2×Q8×C43—41no—
78C2×Q8×C43—41no—
79C2×Q8×C43—41no—
80C2×Q8×C43—41no—
81C22×C4×C43—41no—
82C22×C4×C43—41no—
83C22×C4×C43D812yes—
84C22×C4×C43C2×D411yescharacteristic
85C22×Dic43—41no—
86C2×D172—22no—
87C2×D172—41no—
88C2×D172—41no—
89C2×D172—41no—
90C2×D172—41no—
91C2×D172—41no—
92C2×Dic86—22no—
93C2×Dic86—41no—
94C2×Dic86—41no—
95C2×Dic86—41no—
96C2×Dic86—41no—
97C2×Dic86—41no—
98Q16×C43—22no—
99Q16×C43—22no—
100Q16×C43—41no—
101Q16×C43—41no—
102C2×C8×C43—21no—
103C2×C8×C43—21no—
104C2×C8×C43D812yes—
105C2×C8×C43C2×D411yescharacteristic
106C2×C8×C43C2×D411yescharacteristic
107C2×C8×C43C2×D411yescharacteristic
108C2×C8×C43C2×D411yescharacteristic
109C2×C8×C43C2×D411yescharacteristic
110C2×C8×C43#4111yescharacteristic
111C4⋊C4×C43—41no—
112C4⋊C4×C43—41no—
113C42×C43—21no—
114C42×C43—21no—
115(C2×D43)⋊C4—48no—
116Dic172—22no—
117Dic172—22no—
118Dic172—41no—
119Dic172—41no—
120D344—22no—
121D344—22no—
122D344—41no—
123D344—41no—
124#10621873—48no—
125C43⋊C16—22no—
126C43⋊C16—22no—
127C23×C43C2×D811yescharacteristic
128C22×D43—42no—
129C22×D43—81no—
130C22×D43—81no—
131C22×D43—82no—
132C22×D43—82no—
133Q8×C43—42no—
134Q8×C43—42no—
135Q8×C43—81no—
136Q8×C43—81no—
137C2×C4×C43—22no—
138C2×C4×C43—22no—
139C2×C4×C43—22no—
140C2×C4×C43—42no—
141C2×C4×C43—81no—
142C2×C4×C43—81no—
143C2×C4×C43—81no—
144C2×C4×C43—82no—
145C2×C4×C43#12011yescharacteristic
146C2×C4×C43#12111yescharacteristic
147C2×C4×C43#12711yescharacteristic
148C2×C4×C43C2×D811yescharacteristic
149C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
151C2×Dic43—42no—
152C2×Dic43—81no—
153C2×Dic43—81no—
154D172—42no—
155D172—42no—
156D172—81no—
157D172—81no—
158Dic86—42no—
159Dic86—42no—
160Dic86—81no—
161Dic86—81no—
162C8×C43—22no—
163C8×C43#12011yescharacteristic
164C8×C43#12011yescharacteristic
165C8×C43#12111yescharacteristic
166C8×C43#12111yescharacteristic
167#13329—431nomaximal, Sylow
168C22×C43#44711yescharacteristic
169C22×C43#45911yescharacteristic
170C22×C43#49311yescharacteristic
171C22×C43#50812yes—
172C22×C43#51012yes—
173C2×D43—84no—
174C2×D43—82no—
175C2×D43—162no—
176C2×D43—161no—
177C2×D43—161no—
178C4×C43—42no—
179C4×C43—82no—
180C4×C43—161no—
181C4×C43#39211yescharacteristic
182C4×C43#44711yescharacteristic
183C4×C43#45911yescharacteristic
184C4×C43#49611yescharacteristic
185Dic43—82no—
186C22×Q32—431no—
187C22×SD32—431no—
188C2×#495—431no—
189C2×#358—431no—
190C2×#357—431no—
191#1969D4311yescharacteristic, complemented
192#1374—431no—
193C2×C43#201111yescharacteristic
194C2×C43#218912yes—
195C2×C43#221112yes—
196C2×C43#224911yescharacteristic
197C2×C43#225111yescharacteristic
198D43—162no—
199C22×Q16—431no—
200C22×Q16C2×D4311yescharacteristic
201C22×SD16—861no—
202C22×D8—431no—
203C2×#124—861no—
204C2×Q32—862no—
205C2×Q32—862no—
206C2×Q32—862no—
207C2×SD32—862no—
208C2×SD32—862no—
209C2×SD32—862no—
210C22×C16—431no—
211C22×C16—431no—
212#495—862no—
213#495—862no—
214C2×#107C2×D4311yescharacteristic
215C2×#103—21no—
216C2×C4×C8C2×D4311yescharacteristic
217#391—21no—
218#358—862no—
219#357—862no—
220C43#1332911yescharacteristic, complemented, Sylow
221C22×Q8—21no—
222C22×Q8—861no—
223C22×D4—861no—
224C2×Q16—21no—
225C2×Q16—21no—
226C2×Q16—21no—
227C2×Q16—21no—
228C2×Q16—21no—
229C2×Q16—432no—
230C2×Q16—861no—
231C2×Q16—861no—
232C2×Q16—861no—
233C2×Q16—861no—
234C2×Q16—861no—
235C2×Q16D17212yes—
236C2×SD16—864no—
237C2×SD16—1722no—
238C2×SD16—1722no—
239C2×D8—432no—
240C2×D8—861no—
241C2×D8—861no—
242C2×D8—861no—
243C2×D8—861no—
244C2×D8—861no—
245C22×C8C22⋊D4311yescharacteristic
246C22×C8C22×D4311yescharacteristic
247#124—864no—
248#124—1722no—
249C2×C4⋊C4—21no—
250C2×C22⋊C4—1722no—
251C2×C42C22⋊D4311yescharacteristic
252Q32—868no—
253SD32—868no—
254C2×C16—432no—
255C2×C16—432no—
256C2×C16—861no—
257C2×C16—861no—
258C2×C16—861no—
259C2×C16—861no—
260#107—21no—
261#107—21no—
262#103—42no—
263C4×C8—21no—
264C4×C8—21no—
265#95—42no—
266C24—1721no—
267C2×Q8—22no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—862no—
274C2×Q8—1721no—
275C2×Q8—1721no—
276C2×Q8—1721no—
277C2×Q8—1721no—
278C2×Q8—1721no—
279C2×D4—862no—
280C2×D4—1721no—
281C2×D4—1721no—
282C2×D4—1721no—
283C2×D4—1721no—
284C2×D4—1721no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—1721no—
288C22×C4#1062188212yes—
289C22×C4C2×C22⋊D4311yescharacteristic
290Q16—22no—
291Q16—22no—
292Q16—41no—
293Q16—41no—
294Q16—862no—
295Q16—862no—
296Q16—1721no—
297Q16—1721no—
298SD16—1728no—
299D8—862no—
300D8—862no—
301D8—1721no—
302D8—1721no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8#1062188212yes—
306C2×C8C2×D17211yescharacteristic
307C2×C8#1062189811yescharacteristic
308C2×C8D4×D4311yescharacteristic
309C2×C8D4×D4311yescharacteristic
310C2×C8D4×D4311yescharacteristic
311C2×C8D4×D4311yescharacteristic
312C4⋊C4—41no—
313C4⋊C4—41no—
314C22⋊C4—1728no—
315C42—21no—
316C42—21no—
317C16—862no—
318C16—862no—
319C23—3442no—
320C23—3442no—
321C23—3441no—
322C23—3441no—
323C23—1722no—
324C23C2×#1062188211yescharacteristic
325Q8—42no—
326Q8—42no—
327Q8—81no—
328Q8—81no—
329Q8—3441no—
330Q8—3441no—
331Q8—1722no—
332Q8—1722no—
333D4—3441no—
334D4—3441no—
335D4—1722no—
336D4—1722no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—42no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—82no—
344C2×C4—81no—
345C2×C4—3441no—
346C2×C4—3441no—
347C2×C4—1722no—
348C2×C4#1306329311yescharacteristic
349C2×C4#1306329911yescharacteristic
350C2×C4#1306332111yescharacteristic
351C2×C4C2×#1062188211yescharacteristic
352C2×C4#1306335011yescharacteristic
353C2×C4#1306335011yescharacteristic
354C8—22no—
355C8#1306329511yescharacteristic
356C8#1306329511yescharacteristic
357C8#1306329811yescharacteristic
358C8#1306329811yescharacteristic
359C22—3444no—
360C22—3442no—
361C22—6881no—
362C22—6881no—
363C22—6882no—
364C22#1458303211yescharacteristic
365C22#1458309411yescharacteristic
366C22#1458327511yescharacteristic
367C22#1458332912yes—
368C22#1458334012yes—
369C4—42no—
370C4—82no—
371C4—161no—
372C4—3442no—
373C4#1458280811yescharacteristic
374C4#1458303211yescharacteristic
375C4#1458309411yescharacteristic
376C4#1458328911yescharacteristic
377C2—6882no—
378C2#1913566511yescharacteristic
379C2#1913653312yes—
380C2#1913665712yes—
381C2#1913685411yescharacteristic
382C2#1913686411yescharacteristic
subgroupG/H
centerC23C2×#10621882
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC43×#1969C2
socleC23×C43C2×D8
prime radicalC22×D344C22
hypercenter#1969D43
hypocenterC43#13329
LCSG ▷ C22×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1969

Complements

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

NH ≅ G/Ntype
1. C22×#13063271C2semidirect
4. C2×#14582702C2semidirect
6. #19132673C2semidirect
7. C43×#1969C2semidirect
191. #1969D43semidirect
220. C43#13329semidirect

Maximal subgroups

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

subgroupindex
C22×#130632712
C22×#130632682
C2×#145832832
C2×#145827022
C2×#145826992
#191326732
C43×#19692
#1332943