Finite Group Databasebeta

← #25069376

Subgroups — #25069376

Order 11008.

1250 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 1250 conjugacy classes of subgroups — too many to draw. Only its 183 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#19144713C212yesmaximal, complemented
2#19137879C211yesmaximal, characteristic, complemented
3#19133581C214yesmaximal, complemented
4#19133547C214yesmaximal, complemented
5#19133103C212yesmaximal, complemented
6#19132936C211yesmaximal, characteristic, complemented
7C43×#3496C211yesmaximal, characteristic
8C2×C4×Dic86C2211yescharacteristic, complemented
9#14583210C2214yescomplemented
10#14583191—22no—
11#14583096—22no—
12#14583037C2214yescomplemented
13#14582999—24no—
14#14582956C2212yescomplemented
15#14582837—21no—
16#14582824C2212yescomplemented
17#14582813—21no—
18#14582811C2212yescomplemented
19C4×C22⋊Dic43—22no—
20#14582745C2211yescharacteristic, complemented
21#14582633C2218yescomplemented
22#14582623C2214yescomplemented
23C2×H(5,𝔽2)×C43—21no—
24C43×#547—22no—
25C43×#546—24no—
26D42×C43—22no—
27C43×#537—21no—
28C43×#534C2214yes—
29C43×#532C2212yes—
30C2×#121×C43—22no—
31C2×C4×D4×C43C2211yescharacteristic
32C22×Dic86C2311yescharacteristic
33C2×#10621883—24no—
34C4×Dic86—22no—
35C4×Dic86—22no—
36C2×C4⋊Dic43C2311yescharacteristic
37C2×Dic43⋊C4—21no—
38C2×C22⋊Dic43—22no—
39C2×C22⋊Dic43—22no—
40C2×C4×Dic43—21no—
41C2×C4×Dic43—21no—
42#13063258—24no—
43C4⋊(C43⋊C8)—22no—
44#13063248—24no—
45#13063246—24no—
46C22⋊(C43⋊C8)C2314yes—
47#13063236—22no—
48C43⋊#95—22no—
49C43⋊#95—21no—
50C43⋊#95—22no—
51C43⋊#95C2312yes—
52H(5,𝔽2)×C43—48no—
53C2×#41×C43—24no—
54C2×#41×C43—22no—
55C22×D4×C43—24no—
56C22×D4×C43—24no—
57C22×D4×C43—22no—
58C22×D4×C43D411yescharacteristic
59C23×C4×C43D412yes—
60C4⋊Q8×C43D412yes—
61#127×C43D412yes—
62#124×C43—22no—
63#123×C43—28no—
64C22⋊Q8×C43—24no—
65#121×C43—24no—
66#121×C43—24no—
67#121×C43—24no—
68#121×C43—22no—
69#121×C43—24no—
70#121×C43C2314yes—
71#120×C43—28no—
72C4×D4×C43—22no—
73C4×D4×C43—22no—
74C4×D4×C43—22no—
75C4×D4×C43D414yes—
76C2×C4⋊C4×C43—22no—
77C2×C4⋊C4×C43D411yescharacteristic
78C2×C22⋊C4×C43—24no—
79C2×C22⋊C4×C43C2312yes—
80C2×C42×C43C2311yescharacteristic
81C24×C43—24no—
82C24×C43C2×D412yes—
83#41×C43—48no—
84#41×C43—416no—
85C2×Q8×C43—22no—
86C2×D4×C43—28no—
87C2×D4×C43—24no—
88C2×D4×C43—22no—
89C2×D4×C43—22no—
90C2×D4×C43—22no—
91C2×D4×C43—24no—
92C2×D4×C43—24no—
93C2×D4×C43—48no—
94C2×D4×C43—416no—
95C2×D4×C43—48no—
96C2×D4×C43—84no—
97C2×D4×C43C2×D414yes—
98C22×C4×C43—24no—
99C22×C4×C43—22no—
100C22×C4×C43—24no—
101C22×C4×C43—22no—
102C22×C4×C43—44no—
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2×D412yes—
106C22×C4×C43C2411yescharacteristic
107C22×Dic43—21no—
108C22×Dic43—22no—
109C22×Dic43—21no—
110C2×Dic86—22no—
111C2×Dic86—42no—
112C4⋊C4×C43—24no—
113C4⋊C4×C43—22no—
114C4⋊C4×C43—22no—
115C4⋊C4×C43C2×D414yes—
116C22⋊C4×C43—28no—
117C22⋊C4×C43—24no—
118C22⋊C4×C43—24no—
119C22⋊C4×C43—24no—
120C42×C43C2×D412yes—
121C42×C43C2×D412yes—
122C22⋊Dic43—44no—
123C22⋊Dic43—44no—
124#10621883—48no—
125C4⋊Dic43—22no—
126Dic43⋊C4—42no—
127C4×Dic43—42no—
128C4×Dic43—41no—
129C4×Dic43—41no—
130C2×C43⋊C8—24no—
131C23×C43—22no—
132C23×C43—22no—
133C23×C43—24no—
134C23×C43—42no—
135C23×C43—42no—
136C23×C43—48no—
137C23×C43—84no—
138C23×C43—84no—
139C23×C43AGL(1,ℤ/8)14yes—
140C23×C43C22×D411yescharacteristic
141Q8×C43—44no—
142D4×C43—28no—
143D4×C43—44no—
144D4×C43—44no—
145D4×C43—416no—
146D4×C43—48no—
147D4×C43—44no—
148D4×C43—84no—
149C2×C4×C43—22no—
150C2×C4×C43—22no—
151C2×C4×C43—22no—
152C2×C4×C43—24no—
153C2×C4×C43—41no—
154C2×C4×C43—48no—
155C2×C4×C43—48no—
156C2×C4×C43—44no—
157C2×C4×C43—42no—
158C2×C4×C43—82no—
159C2×C4×C43#12011yescharacteristic
160C2×C4×C43#12012yes—
161C2×C4×C43#12011yescharacteristic
162C2×C4×C43C22×D412yes—
163C2×Dic43—22no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—42no—
167C2×Dic43—42no—
168C2×Dic43—41no—
169C2×Dic43—42no—
170C2×Dic43—42no—
171Dic86—24no—
172Dic86—42no—
173C43⋊C8—44no—
174#18179—431nomaximal, Sylow
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—24no—
178C22×C43—44no—
179C22×C43—42no—
180C22×C43—42no—
181C22×C43—44no—
182C22×C43—44no—
183C22×C43—44no—
184C22×C43—82no—
185C22×C43—168no—
186C22×C43C2×#12011yescharacteristic
187C22×C43C2×AGL(1,ℤ/8)12yes—
188C4×C43—22no—
189C4×C43—21no—
190C4×C43—22no—
191C4×C43—44no—
192C4×C43—42no—
193C4×C43#45512yes—
194Dic43—42no—
195Dic43—82no—
196Dic43—81no—
197#3496D4311yescharacteristic
198#3112—432no—
199#2398—431no—
200#1607—434no—
201#1601—434no—
202#1505—432no—
203#1466—431no—
204C2×C43—22no—
205C2×C43—44no—
206C2×C43—84no—
207C2×C43#300311yescharacteristic
208C2×C43C2×#45511yescharacteristic
209C2×C43#302511yescharacteristic
210C2×H(5,𝔽2)—21no—
211#547—22no—
212#546—24no—
213D42—22no—
214#537—21no—
215#534C2×D4314yes—
216#532C2×D4312yes—
217C2×#121—22no—
218C2×C4×Q8—431no—
219C2×C4×D4C2×D4311yescharacteristic
220#480—434no—
221#477—862no—
222#460—862no—
223#448—434no—
224#440—864no—
225#432—432no—
226#400—861no—
227#397—432no—
228#394—861no—
229#393—432no—
230C4×C22⋊C4—862no—
231#376—431no—
232#327—438no—
233#323—434no—
234C43#1817911yescharacteristic, complemented, Sylow
235H(5,𝔽2)—48no—
236C2×#41—24no—
237C2×#41—22no—
238C22×Q8—431no—
239C22×D4—24no—
240C22×D4—24no—
241C22×D4—22no—
242C22×D4C22⋊D4311yescharacteristic
243C23×C4C22⋊D4312yes—
244C2×SD16—864no—
245C4⋊Q8C22⋊D4312yes—
246#127C22⋊D4312yes—
247#124—22no—
248#123—28no—
249C22⋊Q8—24no—
250#121—24no—
251#121—24no—
252#121—24no—
253#121—22no—
254#121—24no—
255#121C22×D4314yes—
256#120—28no—
257C4×Q8—862no—
258C4×Q8—862no—
259C4×D4—22no—
260C4×D4—22no—
261C4×D4—22no—
262C4×D4C22⋊D4314yes—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—431no—
265C2×C4⋊C4—861no—
266C2×C4⋊C4C22⋊D4311yescharacteristic
267C2×C22⋊C4—24no—
268C2×C22⋊C4—862no—
269C2×C22⋊C4—862no—
270C2×C22⋊C4C22×D4312yes—
271C2×C42—861no—
272C2×C42—861no—
273C2×C42C22×D4311yescharacteristic
274#107—864no—
275C4⋊C8—862no—
276#103—864no—
277#102—864no—
278C22⋊C8—434no—
279#97—862no—
280#95—432no—
281#95—861no—
282#95—862no—
283#95—862no—
284C24—24no—
285C24C2×C22⋊D4312yes—
286#41—48no—
287#41—416no—
288C2×Q8—22no—
289C2×Q8—862no—
290C2×Q8—1722no—
291C2×D4—24no—
292C2×D4—28no—
293C2×D4—24no—
294C2×D4—24no—
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—416no—
299C2×D4—48no—
300C2×D4—48no—
301C2×D4—84no—
302C2×D4C2×C22⋊D4314yes—
303C22×C4—24no—
304C22×C4—22no—
305C22×C4—24no—
306C22×C4—22no—
307C22×C4—44no—
308C22×C4—861no—
309C22×C4—862no—
310C22×C4—861no—
311C22×C4C2×C22⋊D4311yescharacteristic
312C22×C4C2×C22⋊D4311yescharacteristic
313C22×C4C2×C22⋊D4312yes—
314C22×C4C23×D4311yescharacteristic
315SD16—1728no—
316C2×C8—864no—
317C4⋊C4—24no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—862no—
321C4⋊C4—1722no—
322C4⋊C4C2×C22⋊D4314yes—
323C22⋊C4—28no—
324C22⋊C4—24no—
325C22⋊C4—24no—
326C22⋊C4—24no—
327C22⋊C4—1724no—
328C22⋊C4—1724no—
329C42—1722no—
330C42—1721no—
331C42—1721no—
332C42C2×C22⋊D4312yes—
333C42C2×C22⋊D4312yes—
334C23—22no—
335C23—22no—
336C23—24no—
337C23—42no—
338C23—42no—
339C23—48no—
340C23—84no—
341C23—84no—
342C23#1306335114yes—
343C23C22×C22⋊D4311yescharacteristic
344Q8—44no—
345Q8—864no—
346Q8—1722no—
347D4—28no—
348D4—44no—
349D4—44no—
350D4—416no—
351D4—48no—
352D4—44no—
353D4—84no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—24no—
358C2×C4—41no—
359C2×C4—48no—
360C2×C4—48no—
361C2×C4—44no—
362C2×C4—42no—
363C2×C4—82no—
364C2×C4—862no—
365C2×C4—1722no—
366C2×C4—1722no—
367C2×C4—1721no—
368C2×C4—1722no—
369C2×C4—1722no—
370C2×C4—1721no—
371C2×C4—1721no—
372C2×C4#1306329411yescharacteristic
373C2×C4#1306329412yes—
374C2×C4#1306329411yescharacteristic
375C2×C4C22×C22⋊D4312yes—
376C8—1724no—
377C22—21no—
378C22—21no—
379C22—24no—
380C22—44no—
381C22—42no—
382C22—42no—
383C22—44no—
384C22—44no—
385C22—44no—
386C22—82no—
387C22—168no—
388C22C2×#1306329411yescharacteristic
389C22C2×#1306335112yes—
390C4—22no—
391C4—22no—
392C4—21no—
393C4—44no—
394C4—42no—
395C4—3442no—
396C4—3441no—
397C4—1722no—
398C4#1458307712yes—
399C2—22no—
400C2—44no—
401C2—84no—
402C2#1914382211yescharacteristic
403C2C2×#1458307711yescharacteristic
404C2#1914398711yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#3496C2
socleC22×C43C2×#120
hypercenter#3496D43
hypocenterC43#18179
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3496

Complements

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

NH ≅ G/Ntype
1. #19144713C2semidirect
2. #19137879C2semidirect
3. #19133581C2semidirect
4. #19133547C2semidirect
5. #19133103C2semidirect
6. #19132936C2semidirect
8. C2×C4×Dic86C22semidirect
9. #14583210C22semidirect
12. #14583037C22semidirect
14. #14582956C22semidirect
16. #14582824C22semidirect
18. #14582811C22semidirect
20. #14582745C22semidirect
21. #14582633C22semidirect
22. #14582623C22semidirect
234. C43#18179semidirect

Maximal subgroups

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

subgroupindex
#191447132
#191378792
#191335812
#191335472
#191331032
#191329362
C43×#34962
#1817943