Finite Group Databasebeta

← #25015434

Subgroups — #25015434

Order 11008.

614 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063268C211yesmaximal, characteristic, complemented
2C22×#13063266C211yesmaximal, characteristic
3C2×#14582703C211yesmaximal, characteristic, complemented
4C2×#14582700C211yesmaximal, characteristic, complemented
5#19135461C211yesmaximal, characteristic, complemented
6#19132673C211yesmaximal, characteristic, complemented
7C2×C43×#495C211yesmaximal, characteristic, complemented
8C22×D344C2211yescharacteristic
9C2×#13063268—22no—
10C2×#13063268—22no—
11C2×#13063268—22no—
12C2×#13063266—22no—
13C2×#13063266—22no—
14C2×#13063266—22no—
15C22×C43⋊C16C2211yescharacteristic
16C22×C43⋊C16C2211yescharacteristic
17C2×#13063259C2211yescharacteristic
18C2×#13063247—21no—
19#14582801—21no—
20#14582703—22no—
21#14582700—22no—
22C22×Q16×C43C2211yescharacteristic
23C22×SD16×C43—21no—
24C22×D8×C43C2211yescharacteristic
25C2×#124×C43—21no—
26C43×#495—22no—
27C43×#495—22no—
28C2×C4×C8×C43C2211yescharacteristic
29C22×D172—21no—
30C2×D344—21no—
31C2×D344—21no—
32C2×D344—21no—
33C2×D344—21no—
34C2×D344—21no—
35C2×D344D412yes—
36C2×C4⋊Dic43—21no—
37C2×(C2×D43)⋊C4—42no—
38#13063268—28no—
39#13063266—28no—
40C2×C43⋊C16—21no—
41C2×C43⋊C16—21no—
42C2×C43⋊C16—21no—
43C2×C43⋊C16—21no—
44C2×C43⋊C16D412yes—
45C2×C43⋊C16D412yes—
46#13063259—21no—
47#13063259—21no—
48#13063247—42no—
49C22×Q8×C43—21no—
50C22×D4×C43—21no—
51C2×Q16×C43—21no—
52C2×Q16×C43—21no—
53C2×Q16×C43—21no—
54C2×Q16×C43—21no—
55C2×Q16×C43—21no—
56C2×Q16×C43D412yes—
57C2×SD16×C43—24no—
58C2×SD16×C43—42no—
59C2×SD16×C43—42no—
60C2×D8×C43—21no—
61C2×D8×C43—21no—
62C2×D8×C43—21no—
63C2×D8×C43—21no—
64C2×D8×C43—21no—
65C2×D8×C43D412yes—
66C22×C8×C43D411yescharacteristic
67C22×C8×C43C2311yescharacteristic
68#124×C43—24no—
69#124×C43—42no—
70C2×C22⋊C4×C43—42no—
71C2×C42×C43D411yescharacteristic
72C4×C8×C43—21no—
73C4×C8×C43—21no—
74C24×C43—41no—
75C23×D43—41no—
76C2×Q8×C43—22no—
77C2×Q8×C43—41no—
78C2×Q8×C43—41no—
79C2×Q8×C43—41no—
80C2×Q8×C43—41no—
81C2×Q8×C43—41no—
82C2×D4×C43—22no—
83C2×D4×C43—41no—
84C2×D4×C43—41no—
85C2×D4×C43—41no—
86C2×D4×C43—41no—
87C2×D4×C43—41no—
88C22×C4×C43—41no—
89C22×C4×C43D812yes—
90C22×C4×C43C2×D411yescharacteristic
91C22×Dic43—41no—
92C2×D172—22no—
93C2×D172—41no—
94C2×D172—41no—
95C2×D172—41no—
96C2×D172—41no—
97C2×D172—41no—
98Q16×C43—22no—
99Q16×C43—22no—
100Q16×C43—41no—
101Q16×C43—41no—
102SD16×C43—48no—
103D8×C43—22no—
104D8×C43—22no—
105D8×C43—41no—
106D8×C43—41no—
107C2×C8×C43—21no—
108C2×C8×C43—21no—
109C2×C8×C43D812yes—
110C2×C8×C43C2×D411yescharacteristic
111C2×C8×C43C2×D411yescharacteristic
112C2×C8×C43C2×D411yescharacteristic
113C2×C8×C43C2×D411yescharacteristic
114C2×C8×C43C2×D411yescharacteristic
115C2×C8×C43#4111yescharacteristic
116C22⋊C4×C43—48no—
117C42×C43—21no—
118C42×C43—21no—
119(C2×D43)⋊C4—84no—
120C4⋊Dic43—41no—
121C4⋊Dic43—41no—
122D344—22no—
123D344—22no—
124D344—41no—
125D344—41no—
126C43⋊C16—22no—
127C43⋊C16—22no—
128C23×C43—42no—
129C23×C43—81no—
130C23×C43—81no—
131C23×C43—82no—
132C23×C43—82no—
133C23×C43C2×D811yescharacteristic
134C22×D43—42no—
135C22×D43—81no—
136C22×D43—81no—
137C22×D43—82no—
138C22×D43—82no—
139Q8×C43—42no—
140Q8×C43—42no—
141Q8×C43—81no—
142Q8×C43—81no—
143D4×C43—42no—
144D4×C43—42no—
145D4×C43—81no—
146D4×C43—81no—
147C2×C4×C43—22no—
148C2×C4×C43—22no—
149C2×C4×C43—22no—
150C2×C4×C43—42no—
151C2×C4×C43—81no—
152C2×C4×C43—81no—
153C2×C4×C43#12011yescharacteristic
154C2×C4×C43#12111yescharacteristic
155C2×C4×C43#12711yescharacteristic
156C2×C4×C43C2×D811yescharacteristic
157C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
159C2×Dic43—81no—
160C2×Dic43—82no—
161D172—42no—
162D172—42no—
163D172—81no—
164D172—81no—
165C8×C43—22no—
166C8×C43#12011yescharacteristic
167C8×C43#12011yescharacteristic
168C8×C43#12111yescharacteristic
169C8×C43#12111yescharacteristic
170#13326—431nomaximal, Sylow
171C22×C43—84no—
172C22×C43—82no—
173C22×C43—162no—
174C22×C43—161no—
175C22×C43—161no—
176C22×C43#44711yescharacteristic
177C22×C43#45911yescharacteristic
178C22×C43#49311yescharacteristic
179C22×C43#50812yes—
180C22×C43#50912yes—
181C2×D43—84no—
182C2×D43—82no—
183C2×D43—162no—
184C2×D43—161no—
185C2×D43—161no—
186C4×C43—42no—
187C4×C43—82no—
188C4×C43#39211yescharacteristic
189C4×C43#44711yescharacteristic
190C4×C43#45911yescharacteristic
191C4×C43#49611yescharacteristic
192Dic43—161no—
193C22×SD32—431no—
194C22×D16—431no—
195C2×#495D4311yescharacteristic, complemented
196C2×#358—431no—
197C2×#357—431no—
198#1970—431no—
199#1374—431no—
200C2×C43—162no—
201C2×C43#201111yescharacteristic
202C2×C43#218612yes—
203C2×C43#221012yes—
204C2×C43#224911yescharacteristic
205C2×C43#225011yescharacteristic
206D43—162no—
207C22×Q16C2×D4311yescharacteristic
208C22×SD16—21no—
209C22×D8—431no—
210C22×D8C2×D4311yescharacteristic
211C2×#124—21no—
212C2×SD32—862no—
213C2×SD32—862no—
214C2×SD32—862no—
215C2×D16—862no—
216C2×D16—862no—
217C2×D16—862no—
218C22×C16—431no—
219C22×C16—431no—
220#495—22no—
221#495—22no—
222C2×#107—431no—
223C2×#102—861no—
224C2×C4×C8C2×D4311yescharacteristic
225#390—861no—
226#358—862no—
227#357—862no—
228C43#1332611yescharacteristic, complemented, Sylow
229C22×Q8—21no—
230C22×D4—21no—
231C22×D4—861no—
232C2×Q16—21no—
233C2×Q16—21no—
234C2×Q16—21no—
235C2×Q16—21no—
236C2×Q16—21no—
237C2×Q16C22⋊D4312yes—
238C2×SD16—24no—
239C2×SD16—42no—
240C2×SD16—42no—
241C2×D8—21no—
242C2×D8—21no—
243C2×D8—21no—
244C2×D8—21no—
245C2×D8—21no—
246C2×D8—432no—
247C2×D8—861no—
248C2×D8—861no—
249C2×D8—861no—
250C2×D8—861no—
251C2×D8—861no—
252C2×D8C22⋊D4312yes—
253C22×C8C22⋊D4311yescharacteristic
254C22×C8C22×D4311yescharacteristic
255#124—24no—
256#124—42no—
257C2×C4⋊C4—861no—
258C2×C22⋊C4—42no—
259C2×C22⋊C4—1722no—
260C2×C42C22⋊D4311yescharacteristic
261SD32—868no—
262D16—868no—
263C2×C16—432no—
264C2×C16—432no—
265C2×C16—861no—
266C2×C16—861no—
267C2×C16—861no—
268C2×C16—861no—
269#107—861no—
270#107—861no—
271#102—1722no—
272C4×C8—21no—
273C4×C8—21no—
274C24—41no—
275C24—1721no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×D4—22no—
283C2×D4—41no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—862no—
289C2×D4—1721no—
290C2×D4—1721no—
291C2×D4—1721no—
292C2×D4—1721no—
293C2×D4—1721no—
294C22×C4—41no—
295C22×C4—1721no—
296C22×C4#1062188212yes—
297C22×C4C2×C22⋊D4311yescharacteristic
298Q16—22no—
299Q16—22no—
300Q16—41no—
301Q16—41no—
302SD16—48no—
303D8—22no—
304D8—22no—
305D8—41no—
306D8—41no—
307D8—862no—
308D8—862no—
309D8—1721no—
310D8—1721no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8#1062188212yes—
314C2×C8D4×D4311yescharacteristic
315C2×C8D4×D4311yescharacteristic
316C2×C8D4×D4311yescharacteristic
317C2×C8#1062190011yescharacteristic
318C2×C8C2×C22⋊D4311yescharacteristic
319C2×C8C2×C22⋊D4311yescharacteristic
320C4⋊C4—1721no—
321C4⋊C4—1721no—
322C22⋊C4—48no—
323C22⋊C4—3444no—
324C42—21no—
325C42—21no—
326C16—862no—
327C16—862no—
328C23—42no—
329C23—82no—
330C23—82no—
331C23—81no—
332C23—81no—
333C23—3442no—
334C23—3442no—
335C23—3441no—
336C23—3441no—
337C23—1722no—
338C23C2×#1062188211yescharacteristic
339Q8—42no—
340Q8—42no—
341Q8—81no—
342Q8—81no—
343D4—42no—
344D4—42no—
345D4—81no—
346D4—81no—
347D4—3441no—
348D4—3441no—
349D4—1722no—
350D4—1722no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—42no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—3442no—
358C2×C4—3441no—
359C2×C4#1306329411yescharacteristic
360C2×C4#1306329611yescharacteristic
361C2×C4#1306332111yescharacteristic
362C2×C4C2×#1062188211yescharacteristic
363C2×C4#1306335111yescharacteristic
364C2×C4#1306335111yescharacteristic
365C8—22no—
366C8#1306329311yescharacteristic
367C8#1306329311yescharacteristic
368C8#1306329711yescharacteristic
369C8#1306329711yescharacteristic
370C22—84no—
371C22—82no—
372C22—161no—
373C22—161no—
374C22—162no—
375C22—3444no—
376C22—3442no—
377C22—6882no—
378C22—6881no—
379C22—6881no—
380C22#1458303311yescharacteristic
381C22#1458309111yescharacteristic
382C22#1458327511yescharacteristic
383C22#1458332912yes—
384C22#1458333412yes—
385C4—42no—
386C4—82no—
387C4—6881no—
388C4#1458280711yescharacteristic
389C4#1458303311yescharacteristic
390C4#1458309111yescharacteristic
391C4#1458328611yescharacteristic
392C2—162no—
393C2—6882no—
394C2#1913566611yescharacteristic
395C2#1913651812yes—
396C2#1913664712yes—
397C2#1913685411yescharacteristic
398C2#1913686211yescharacteristic
subgroupG/H
centerC23C2×#10621882
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC2×C43×#495C2
socleC23×C43C2×D8
prime radicalC22×#13063266C2
hypercenterC2×#495D43
hypocenterC43#13326
LCSG ▷ C22×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×#495

Complements

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

NH ≅ G/Ntype
1. C22×#13063268C2semidirect
3. C2×#14582703C2semidirect
4. C2×#14582700C2semidirect
5. #19135461C2semidirect
6. #19132673C2semidirect
7. C2×C43×#495C2semidirect
195. C2×#495D43semidirect
228. C43#13326semidirect

Maximal subgroups

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

subgroupindex
C22×#130632682
C22×#130632662
C2×#145827032
C2×#145827002
#191354612
#191326732
C2×C43×#4952
#1332643