Finite Group Databasebeta

← #11922260

Subgroups — #11922260

Order 1152.

532 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 63 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#10596586C211yesmaximal, characteristic
2C2×C3⋊(#131⋊C3)C211yesmaximal, characteristic, complemented
3C3×#5423C211yesmaximal, characteristic, complemented
4#10593222C212yesmaximal, complemented
5#10593220C212yesmaximal, complemented
6#85448—31nomaximal
7#78989—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9#64267C411yescharacteristic, complemented
10#64266C2212yes—
11#64265C411yescharacteristic, complemented
12#64264C412yescomplemented
13#63817—41nomaximal
14C3⋊(#131⋊C3)C2211yescharacteristic, complemented
15C3⋊(#131⋊C3)C2211yescharacteristic, complemented
16C3×GU(2,𝔽3)C2212yescomplemented
17#5923—31no—
18#5923—61no—
19#5822—31no—
20C2×#948D311yescharacteristic, complemented
21C2×#907—31no—
22C2×#131⋊C3—31no—
23#5423D311yescharacteristic, complemented
24#5405—32no—
25#5404—32no—
26C3×#421—31no—
27#5124—31no—
28#5005—31no—
29#4997—31no—
30#4824—32no—
31#4824—32no—
32#4823—32no—
33#4823—32no—
34#3828—41no—
35C3×#41⋊C3C2×C411yescharacteristic
36C3×#41⋊C3C2311yescharacteristic
37C2×C3×SL(2,𝔽3)C2×C411yescharacteristic
38C3⋊GL(2,𝔽3)C2×C412yes—
39C3⋊#226C2×C412yes—
40C3×#208—41no—
41C2×C3×C3⋊C8—41no—
42#3712—42no—
43#3710—42no—
44#2955—91noSylow
45C2×C3×#41C2×D311yescharacteristic
46C2×#235—31no—
47C2×#41⋊C3—21no—
48C2×#41⋊C3C2×D311yescharacteristic
49#986—31no—
50#986—61no—
51#985—32no—
52#985—62no—
53#984—31no—
54#984—61no—
55#983—32no—
56#983—62no—
57C2×C3×M16—31no—
58C3×#117—31no—
59#951—31no—
60#951—31no—
61#950—32no—
62#950—32no—
63#949—31no—
64#949—31no—
65#948—31no—
66#948—31no—
67#948C2×D311yescharacteristic
68#948C2×D311yescharacteristic
69#942—32no—
70#932—32no—
71C2×#208—31no—
72C2×#208—31no—
73C22×C3⋊C8—31no—
74#907—32no—
75#907—32no—
76#907—61no—
77#907—61no—
78#901—121no—
79C2×ΓL(1,𝔽25)—61no—
80C2×D3×C8—61no—
81#131⋊C3—31no—
82#131⋊C3—31no—
83GU(2,𝔽3)C2×D312yescomplemented
84C3×#104—32no—
85C3×#104—32no—
86#822—32no—
87#822—32no—
88#805—32no—
89#805—32no—
90#803—32no—
91C4×C3⋊C8—32no—
92C2×C32×C4—41no—
93#638—42no—
94C4⋊(C3⋊D3)—41no—
95C4×C3⋊D3—42no—
96#634—41no—
97C3×SL(2,𝔽3)C22×C411yescharacteristic
98C3×C3⋊C8—42no—
99C3×C3⋊C8—41no—
100C3×C3⋊C8—41no—
101#575—91no—
102C2×#131—31no—
103C2×#131—91no—
104#444—92no—
105#444—92no—
106#443—92no—
107#443—92no—
108#430—91no—
109#421—31no—
110#421—91no—
111#405—91no—
112C3×#41—31no—
113C3×#41—31no—
114C3×#41C4×D311yescharacteristic
115C3×#41C22×D311yescharacteristic
116C2×C3×Q8C4×D311yescharacteristic
117C2×C3×D4—31no—
118C22×C3×C4—31no—
119C2×#67—61no—
120#235—32no—
121#235—32no—
122#235—61no—
123#235—61no—
124#235—121no—
125#235—241no—
126C2×D12—31no—
127C2×C4×D3—61no—
128C2×Dic6—31no—
129#41⋊C3—21no—
130#41⋊C3—21no—
131#41⋊C3C4×D311yescharacteristic
132#41⋊C3C22×D311yescharacteristic
133C2×SL(2,𝔽3)—21no—
134C2×SL(2,𝔽3)C4×D311yescharacteristic
135GL(2,𝔽3)—32no—
136GL(2,𝔽3)—62no—
137#226—32no—
138#226—62no—
139C3×M16—32no—
140C3×M16—61no—
141C2×C3×C8—61no—
142C2×C3×C8—121no—
143C3×C4⋊C4—61no—
144C3×C22⋊C4—61no—
145C3×C42—32no—
146#216—32no—
147#216—32no—
148#215—32no—
149#215—32no—
150#214—32no—
151#214—32no—
152#213—32no—
153#213—32no—
154#208—32no—
155#208—31no—
156#208—31no—
157#208—31no—
158#208—31no—
159#208—41no—
160#208—61no—
161C2×C3⋊C8—32no—
162C2×C3⋊C8—31no—
163C2×C3⋊C8—31no—
164C2×C3⋊C8—31no—
165C2×C3⋊C8—31no—
166C2×C3⋊C8—31no—
167C2×C3⋊C8S411yescharacteristic
168ΓL(1,𝔽25)—62no—
169ΓL(1,𝔽25)—62no—
170ΓL(1,𝔽25)—122no—
171D3×C8—62no—
172D3×C8—62no—
173D3×C8—122no—
174C22×C32—41no—
175C2×C3⋊D3—42no—
176C32×C4—41no—
177C32×C4—41no—
178C3⋊Dic3—42no—
179C2×#41—91no—
180C2×#41D3211yescharacteristic
181#137—91no—
182#137—91no—
183#137—92no—
184AGL(1,ℤ/8)—92no—
185AGL(1,ℤ/8)—91no—
186AGL(1,ℤ/8)—91no—
187#135—92no—
188#135—92no—
189#131—31no—
190#131—31no—
191#131—91no—
192#131—91no—
193#131—92no—
194#131—92no—
195#131—181no—
196#131—181no—
197C2×M16—31no—
198C2×M16—91no—
199C2×M16—91no—
200C2×M16—181no—
201C22×C8—91no—
202C22×C8—181no—
203#117—31no—
204#108—92no—
205#108—92no—
206#104—32no—
207#104—32no—
208#104—92no—
209#104—92no—
210#97—92no—
211C4×C8—92no—
212C23×C3—31no—
213C22×D3—61no—
214C3×Q8—31no—
215C3×Q8C2×C4×D311yescharacteristic
216C3×D4—31no—
217C3×D4—31no—
218C3×D4—61no—
219C2×C3×C4—31no—
220C2×C3×C4—31no—
221C2×C3×C4—31no—
222C2×C3×C4—31no—
223C2×C3×C4—31no—
224C2×C3×C4—41no—
225C2×C3×C4—62no—
226C2×C3×C4—81no—
227C2×C3×C4C2×S411yescharacteristic
228#67—62no—
229#67—62no—
230#67—122no—
231#67—242no—
232C2×Dic3—61no—
233D12—32no—
234D12—61no—
235D12—121no—
236D12—241no—
237C4×D3—62no—
238C4×D3—62no—
239C4×D3—122no—
240C4×D3—242no—
241Dic6—32no—
242Dic6—61no—
243Dic6—121no—
244Dic6—241no—
245SL(2,𝔽3)—21no—
246SL(2,𝔽3)C2×C4×D311yescharacteristic
247C3×C8—62no—
248C3×C8—121no—
249C3×C8—121no—
250C3⋊C8—32no—
251C3⋊C8—32no—
252C3⋊C8—31no—
253C3⋊C8—31no—
254C3⋊C8—42no—
255C3⋊C8C2×S411yescharacteristic
256C3⋊C8C2×S411yescharacteristic
257C2×C32—41no—
258C2×C32—81no—
259C3⋊D3—82no—
260#41—31no—
261#41—31no—
262#41—92no—
263#41—92no—
264#41—181no—
265#41—181no—
266#41#62411yescharacteristic
267#41C2×D3211yescharacteristic
268C2×Q8—91no—
269C2×Q8#62411yescharacteristic
270C2×D4—31no—
271C2×D4—91no—
272C2×D4—181no—
273C22×C4—31no—
274C22×C4—181no—
275Q16—92no—
276Q16—92no—
277SD16—92no—
278SD16—92no—
279SD16—92no—
280SD16—92no—
281D8—92no—
282D8—92no—
283M16—32no—
284M16—61no—
285M16—92no—
286M16—91no—
287M16—91no—
288M16—91no—
289M16—91no—
290M16—182no—
291M16—182no—
292M16—181no—
293C2×C8—31no—
294C2×C8—61no—
295C2×C8—91no—
296C2×C8—91no—
297C2×C8—91no—
298C2×C8—91no—
299C2×C8—92no—
300C2×C8—91no—
301C2×C8—182no—
302C2×C8—182no—
303C4⋊C4—61no—
304C22⋊C4—61no—
305C42—32no—
306C22×C3—31no—
307C22×C3—31no—
308C22×C3—41no—
309C22×C3—81no—
310C22×C3—121no—
311C22×C3C4×S411yescharacteristic
312C2×D3—62no—
313C2×D3—122no—
314C2×D3—122no—
315C2×D3—242no—
316C3×C4—31no—
317C3×C4—31no—
318C3×C4—41no—
319C3×C4—41no—
320C3×C4—81no—
321C3×C4—81no—
322C3×C4—122no—
323C3×C4C4×S411yescharacteristic
324C3×C4C22×S411yescharacteristic
325Dic3—62no—
326Dic3—122no—
327Dic3—242no—
328C32—41noSylow
329C23—31no—
330C23—181no—
331Q8—31no—
332Q8—92no—
333Q8—181no—
334Q8C2×#62411yescharacteristic
335D4—31no—
336D4—31no—
337D4—61no—
338D4—92no—
339D4—182no—
340D4—182no—
341D4—181no—
342C2×C4—31no—
343C2×C4—31no—
344C2×C4—31no—
345C2×C4—31no—
346C2×C4—31no—
347C2×C4—62no—
348C2×C4—182no—
349C2×C4—181no—
350C2×C4—182no—
351C2×C4D3×S411yescharacteristic
352C8—31no—
353C8—31no—
354C8—62no—
355C8—92no—
356C8—92no—
357C8—91no—
358C8—91no—
359C2×C3—21no—
360C2×C3—41no—
361C2×C3—61no—
362C2×C3—61no—
363C2×C3—81no—
364C2×C3—81no—
365C2×C3—161no—
366C2×C3C2×C4×S411yescharacteristic
367D3—122no—
368D3—242no—
369D3—482no—
370C22—31no—
371C22—31no—
372C22—121no—
373C22—182no—
374C22—362no—
375C22(C3⋊S4)⋊C411yescharacteristic
376C4—31no—
377C4—31no—
378C4—122no—
379C4—182no—
380C4(C3⋊S4)⋊C411yescharacteristic
381C4C2×D3×S411yescharacteristic
382C3—41no—
383C3—81no—
384C3#8544811yescharacteristic, complemented
385C2—21no—
386C2—61no—
387C2—61no—
388C2—362no—
389C2C2×(C3⋊S4)⋊C411yescharacteristic
subgroupG/H
center, FrattiniC4C2×D3×S4
commutator, hypocenterC3×SL(2,𝔽3)C22×C4
FittingC2×C3×#41C2×D3
socleC2×C3C2×C4×S4
prime radical#10596586C2
cosocleC3×#41⋊C3C23
hypercenterC2×C4D3×S4
LCSG ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3⋊(#131⋊C3)C2semidirect
3. C3×#5423C2semidirect
4. #10593222C2semidirect
5. #10593220C2semidirect
9. #64267C4semidirect
11. #64265C4semidirect
12. #64264C4semidirect
14. C3⋊(#131⋊C3)C22semidirect
15. C3⋊(#131⋊C3)C22semidirect
16. C3×GU(2,𝔽3)C22semidirect
20. C2×#948D3semidirect
23. #5423D3semidirect
83. GU(2,𝔽3)C2×D3semidirect
384. C3#85448semidirect

Maximal subgroups

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

subgroupindex
#105965862
C2×C3⋊(#131⋊C3)2
C3×#54232
#105932222
#105932202
#854483
#789893
#638174