Finite Group Databasebeta

← #11922962

Subgroups — #11922962

Order 1152.

514 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 65 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
1C3×C4⋊(#41⋊C3)C211yesmaximal, characteristic, complemented
2#10593661C211yesmaximal, characteristic, complemented
3#10593661C211yesmaximal, characteristic, complemented
4#10593660C211yesmaximal, characteristic, complemented
5#10593658C211yesmaximal, characteristic, complemented
6#10593628C211yesmaximal, characteristic, complemented
7#10593623C211yesmaximal, characteristic, complemented
8#85413—33nomaximal
9#83572—31nomaximal
10C2×C3×#41⋊C3C2211yescharacteristic
11C2×C3×#41⋊C3C2211yescharacteristic
12C2×C3⋊GL(2,𝔽3)C2211yescharacteristic
13#64107—41nomaximal
14C3×C4×SL(2,𝔽3)C2211yescharacteristic
15C3⋊#859C2211yescharacteristic
16C3⋊#859C2211yescharacteristic
17C3⋊#859C2211yescharacteristic
18C3×#550D311yescharacteristic, complemented
19#5565—31no—
20C4⋊(#41⋊C3)D313yescomplemented
21#5427—33no—
22#5427—33no—
23#5426—33no—
24#5424—33no—
25#5394—33no—
26#5389—33no—
27#5238—31no—
28#5238—31no—
29#5233—31no—
30#5232—31no—
31#5072—31no—
32#5071—31no—
33#5039—31no—
34#5038—31no—
35#5035—31no—
36#5033—31no—
37#5026—31no—
38#5022—31no—
39#5011—31no—
40C3×#41⋊C3—21no—
41C3×#41⋊C3—21no—
42C2×C3×SL(2,𝔽3)C2311yescharacteristic
43C3⋊GL(2,𝔽3)—21no—
44C32×C4⋊C4—41no—
45#3752—41no—
46#3752—41no—
47#3752—41no—
48C4⋊(C3⋊Dic3)—41no—
49#3750—41no—
50C4×C3⋊Dic3—41no—
51#3309—91noSylow
52C2×C3×#41C2×D311yescharacteristic
53C2×C3×#41C2×D311yescharacteristic
54C2×#41⋊C3C2×D313yes—
55C2×#41⋊C3C2×D313yes—
56C2×GL(2,𝔽3)—33no—
57C3×#127—31no—
58C3×#121—31no—
59C3×#121—31no—
60C3×C4×Q8C2×D311yescharacteristic
61C3×C4×D4—31no—
62C2×#215—31no—
63#939—61no—
64C2×#213—31no—
65C2×#213—31no—
66#930—31no—
67#930—31no—
68#926—31no—
69C2×C4⋊Dic3—31no—
70C2×#208—31no—
71C22×C3⋊C8—31no—
72#898—61no—
73#898—123no—
74#883—61no—
75#67⋊C4—61no—
76C4×D12—31no—
77#870—31no—
78C4×SL(2,𝔽3)C2×D313yes—
79#859—33no—
80#859—33no—
81#859—33no—
82#835—31no—
83#835—31no—
84#835—31no—
85#832—31no—
86#832—31no—
87#832—31no—
88#832—31no—
89#832—31no—
90#832—31no—
91#830—31no—
92#830—31no—
93#809—31no—
94#808—31no—
95#807—31no—
96#807—31no—
97C4⋊(C3⋊C8)—31no—
98#803—31no—
99C22×C3⋊D3—41no—
100C2×C32×C4—41no—
101C2×C32×C4—41no—
102C2×C32×C4—41no—
103C2×C3⋊Dic3—41no—
104C2×C3⋊Dic3—41no—
105C2×C3⋊Dic3—41no—
106C3×SL(2,𝔽3)#4111yescharacteristic
107#553—91no—
108#550C3⋊D311yescharacteristic, complemented
109#490—91no—
110#482—91no—
111#480—91no—
112#479—91no—
113#469—91no—
114#466—91no—
115#459—91no—
116#449—91no—
117#449—91no—
118#440—91no—
119#435—91no—
120#417—91no—
121#416—91no—
122C3×#41—21no—
123C3×#41—21no—
124C3×#41—61no—
125C3×#41—61no—
126C2×C3×Q8C22×D311yescharacteristic
127C2×C3×D4—31no—
128C2×C3×D4—31no—
129C2×C3×D4—31no—
130C2×C3×D4—61no—
131C22×C3×C4—31no—
132C22×C3×C4—31no—
133C2×#67—61no—
134C2×#67—61no—
135C22×Dic3—61no—
136C2×D12—31no—
137C2×C4×D3—61no—
138#41⋊C3—23no—
139#41⋊C3—23no—
140C2×SL(2,𝔽3)C22×D313yes—
141GL(2,𝔽3)—63no—
142C3×C4⋊C4—31no—
143C3×C4⋊C4—43no—
144C3×C4⋊C4S411yescharacteristic
145C3×C22⋊C4—31no—
146C3×C22⋊C4—31no—
147C3×C42—31no—
148#217—61no—
149#215—61no—
150#215—61no—
151#213—121no—
152#213—121no—
153(C2×D3)⋊C4—61no—
154(C2×D3)⋊C4—61no—
155(C2×D3)⋊C4—61no—
156(C2×D3)⋊C4—123no—
157(C2×D3)⋊C4—123no—
158(C2×D3)⋊C4—123no—
159C4⋊Dic3—31no—
160C4⋊Dic3—31no—
161C4⋊Dic3—31no—
162C4⋊Dic3—61no—
163C4⋊Dic3—123no—
164Dic3⋊C4—61no—
165Dic3⋊C4—61no—
166Dic3⋊C4—123no—
167C4×Dic3—61no—
168C4×Dic3—123no—
169#208—121no—
170C2×C3⋊C8—31no—
171C2×C3⋊C8—31no—
172C2×C3⋊C8—31no—
173C2×C3⋊C8—31no—
174C2×C3⋊C8—121no—
175C22×C32—41no—
176C2×C3⋊D3—81no—
177C2×C3⋊D3—81no—
178C2×C3⋊D3—81no—
179C32×C4—81no—
180C32×C4—81no—
181C32×C4—81no—
182C3⋊Dic3—81no—
183C3⋊Dic3—81no—
184C3⋊Dic3—81no—
185C2×#41C2×C3⋊D311yescharacteristic
186C2×#41C2×C3⋊D311yescharacteristic
187C2×SD16—91no—
188C2×D8—91no—
189C2×D8—91no—
190C2×M16—91no—
191C22×C8—91no—
192#127—31no—
193#126—181no—
194#125—91no—
195#123—181no—
196#121—31no—
197#121—31no—
198#121—91no—
199#121—91no—
200#121—181no—
201C4×Q8C2×C3⋊D311yescharacteristic
202C4×D4—31no—
203C4×D4—91no—
204C4×D4—181no—
205#117—91no—
206C2×C4⋊C4—91no—
207#107—91no—
208#107—91no—
209#106—91no—
210C4⋊C8—91no—
211#103—91no—
212#103—91no—
213#103—91no—
214#102—91no—
215#102—91no—
216#102—91no—
217#102—91no—
218#102—91no—
219#102—91no—
220#102—91no—
221C22⋊C8—91no—
222C22⋊C8—91no—
223#97—91no—
224C23×C3—31no—
225C23×C3—31no—
226C22×D3—61no—
227C22×D3—123no—
228C3×Q8—31no—
229C3×Q8#23711yescharacteristic
230C3×D4—61no—
231C3×D4—61no—
232C3×D4—61no—
233C3×D4—61no—
234C3×D4—121no—
235C3×D4—241no—
236C2×C3×C4—31no—
237C2×C3×C4—31no—
238C2×C3×C4—43no—
239C2×C3×C4—43no—
240C2×C3×C4—43no—
241C2×C3×C4—61no—
242C2×C3×C4—61no—
243C2×C3×C4—61no—
244C2×C3×C4—61no—
245C2×C3×C4C2×S411yescharacteristic
246C2×C3×C4C2×S411yescharacteristic
247C2×C3×C4C2×S411yescharacteristic
248#67—122no—
249#67—241no—
250C2×Dic3—61no—
251C2×Dic3—61no—
252C2×Dic3—61no—
253C2×Dic3—123no—
254C2×Dic3—123no—
255C2×Dic3—123no—
256C2×Dic3—241no—
257D12—61no—
258D12—61no—
259C4×D3—241no—
260SL(2,𝔽3)#23713yes—
261C3⋊C8—61no—
262C3⋊C8—61no—
263C3⋊C8—61no—
264C3⋊C8—61no—
265C2×C32—41no—
266C2×C32—41no—
267C2×C32—41no—
268C3⋊D3—161no—
269#41—21no—
270#41—21no—
271#41—61no—
272#41—61no—
273C2×Q8C22×C3⋊D311yescharacteristic
274C2×D4—31no—
275C2×D4—31no—
276C2×D4—31no—
277C2×D4—61no—
278C2×D4—91no—
279C2×D4—181no—
280C2×D4—181no—
281C22×C4—31no—
282C22×C4—31no—
283C22×C4—181no—
284C22×C4—181no—
285SD16—181no—
286SD16—181no—
287D8—361no—
288D8—361no—
289M16—361no—
290C2×C8—91no—
291C2×C8—91no—
292C2×C8—91no—
293C2×C8—91no—
294C2×C8—361no—
295C4⋊C4—31no—
296C4⋊C4—91no—
297C4⋊C4—91no—
298C4⋊C4—91no—
299C4⋊C4—181no—
300C4⋊C4—181no—
301C4⋊C4—181no—
302C4⋊C4C3⋊S411yescharacteristic
303C22⋊C4—31no—
304C22⋊C4—31no—
305C22⋊C4—181no—
306C22⋊C4—181no—
307C22⋊C4—181no—
308C22⋊C4—181no—
309C42—31no—
310C42—181no—
311C22×C3—43no—
312C22×C3—61no—
313C22×C3—61no—
314C22×C3—61no—
315C22×C3—61no—
316C22×C3—61no—
317C22×C3—61no—
318C22×C3C22×S411yescharacteristic
319C2×D3—121no—
320C2×D3—121no—
321C2×D3—121no—
322C2×D3—243no—
323C2×D3—243no—
324C2×D3—243no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—31no—
329C3×C4—31no—
330C3×C4—61no—
331C3×C4—83no—
332C3×C4—83no—
333C3×C4—83no—
334Dic3—121no—
335Dic3—121no—
336Dic3—121no—
337Dic3—243no—
338Dic3—243no—
339Dic3—243no—
340C32—41noSylow
341C23—31no—
342C23—31no—
343C23—181no—
344Q8—31no—
345Q8#383011yescharacteristic
346D4—61no—
347D4—61no—
348D4—61no—
349D4—61no—
350D4—121no—
351D4—181no—
352D4—181no—
353D4—241no—
354D4—362no—
355D4—721no—
356C2×C4—31no—
357C2×C4—31no—
358C2×C4—61no—
359C2×C4—61no—
360C2×C4—61no—
361C2×C4—61no—
362C2×C4—181no—
363C2×C4—181no—
364C2×C4—181no—
365C2×C4—721no—
366C2×C4—721no—
367C2×C4C2×C3⋊S411yescharacteristic
368C2×C4C2×C3⋊S411yescharacteristic
369C2×C4C2×C3⋊S411yescharacteristic
370C8—181no—
371C8—181no—
372C8—181no—
373C8—181no—
374C2×C3—43no—
375C2×C3—43no—
376C2×C3—43no—
377C2×C3—121no—
378C2×C3—121no—
379C2×C3#591411yescharacteristic
380C2×C3#592311yescharacteristic
381C2×C3#592511yescharacteristic
382D3—241no—
383D3—483no—
384C22—61no—
385C22—61no—
386C22—61no—
387C22—61no—
388C22—61no—
389C22—61no—
390C22—361no—
391C22—361no—
392C22—361no—
393C22C22×C3⋊S411yescharacteristic
394C4—21no—
395C4—21no—
396C4—21no—
397C4—31no—
398C4—31no—
399C4—61no—
400C4—361no—
401C4—361no—
402C4—361no—
403C3—43no—
404C3#8541311yescharacteristic, complemented
405C2—121no—
406C2—121no—
407C2—721no—
408C2#1059657711yescharacteristic
409C2#1059658611yescharacteristic
410C2#1059658811yescharacteristic
subgroupG/H
center, FrattiniC22C22×C3⋊S4
commutator, cosocleC2×C3×SL(2,𝔽3)C23
FittingC3×#550D3
socleC22×C3C22×S4
hypercenterC4⋊C4C3⋊S4
hypocenterC3×SL(2,𝔽3)#41
LCSG ▷ C2×C3×SL(2,𝔽3) ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×C4⋊(#41⋊C3)C2semidirect
2. #10593661C2semidirect
3. #10593661C2semidirect
4. #10593660C2semidirect
5. #10593658C2semidirect
6. #10593628C2semidirect
7. #10593623C2semidirect
18. C3×#550D3semidirect
20. C4⋊(#41⋊C3)D3semidirect
108. #550C3⋊D3semidirect
404. C3#85413semidirect

Maximal subgroups

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

subgroupindex
C3×C4⋊(#41⋊C3)2
#105936612
#105936602
#105936582
#105936282
#105936232
#854133
#835723
#641074