Finite Group Databasebeta

← #11779876

Subgroups — #11779876

Order 1152.

560 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 90 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#10593900C211yesmaximal, characteristic
2#10592540C211yesmaximal, characteristic, complemented
3#10590301C211yesmaximal, characteristic, complemented
4#10590273C211yesmaximal, characteristic, complemented
5C3×#4485C211yesmaximal, characteristic, complemented
6C3×#4484C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic, complemented
8#68393—31nomaximal
9#68248—31nomaximal
10C2×#3796—21no—
11C2×#3744—21no—
12C4×C4⋊(C3⋊D3)C2211yescharacteristic
13#64078C2211yescharacteristic
14C3×#874C2211yescharacteristic
15C3×C4×Dic6C2211yescharacteristic
16#63916—21no—
17#63911—21no—
18Dic3×D12—21no—
19#63886—22no—
20C32×C4⋊C8C2211yescharacteristic
21#63643—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24#63573—21no—
25#63566—21no—
26#63563—22no—
27#5718—31no—
28#5577—31no—
29#5070—31no—
30#5020—31no—
31#4851—31no—
32#4841—31no—
33#4841—31no—
34#4841—61no—
35#4694—31no—
36C3×#331—31no—
37C3×Q8⋊C8—31no—
38#4485D311yescharacteristic, complemented
39#4484D311yescharacteristic, complemented
40#4483—31no—
41#4459—31no—
42C2×C4⋊(C3⋊D3)D411yescharacteristic
43C2×C4×C3⋊D3—21no—
44C2×#634—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12D412yes—
48C2×C3×Dic6D411yescharacteristic
49C2×#626—22no—
50C2×#626—22no—
51C2×D3×Dic3—22no—
52#3796—42no—
53#3796—42no—
54C2×C32×C8—21no—
55C32×C42C2311yescharacteristic
56#3752—21no—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)—21no—
59C4⋊(C3⋊Dic3)D411yescharacteristic
60#3744—42no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×Dic3⋊C4—21no—
63C3×C4×Dic3—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66(C2×D3)⋊Dic3—22no—
67#1642—91noSylow
68C2×#239—61no—
69C2×#237—61no—
70C3×#127—31no—
71C3×C4×Q8—31no—
72#940—61no—
73#939—62no—
74#938—61no—
75D4×Dic3—61no—
76C2×#204—61no—
77C2×#204—61no—
78C2×#204—62no—
79#895—61no—
80#895—62no—
81#874—61no—
82#874C2×D311yescharacteristic
83C4×D12—31no—
84C4×D12—31no—
85C4×D12—61no—
86C4×D12—61no—
87#869—31no—
88#869—31no—
89#869—61no—
90C4×Dic6C2×D311yescharacteristic
91C3×C4⋊C8—21no—
92C3×C4⋊C8—31no—
93C3×C4⋊C8C2×D311yescharacteristic
94C3×C4⋊C8C2×D311yescharacteristic
95C3×C4×C8—31no—
96#835—61no—
97#832—62no—
98#821—62no—
99#817—61no—
100#816—61no—
101#816—61no—
102#816—62no—
103#816—61no—
104#808—61no—
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C4×C3⋊C8C2×D311yescharacteristic
107C22×C3⋊D3—21no—
108C22×C3×D3—22no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C3⋊Dic3—21no—
113C2×C3⋊Dic3—41no—
114C4⋊(C3⋊D3)—21no—
115C4⋊(C3⋊D3)—21no—
116C4×C3⋊D3—41no—
117C4×C3⋊D3—41no—
118#634—41no—
119#634—41no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—21no—
122C3×D12—42no—
123C3×D12—41no—
124C3×D12—41no—
125C3×D12—41no—
126C3×D12—41no—
127C3×Dic6—21no—
128C3×Dic6SD1612yescomplemented
129#626—44no—
130#626—82no—
131D3×Dic3—44no—
132C32×C8—41no—
133C3×C3⋊C8—41no—
134C3×C3⋊C8—41no—
135#550—91no—
136#486—91no—
137#475—91no—
138#461—91no—
139#331—31no—
140Q8⋊C8—31no—
141D4⋊C8—91no—
142C2×C3×Q8—31no—
143C2×C3×D4—32no—
144C2×C3×D4—61no—
145C2×C3×D4—61no—
146C2×#67—62no—
147C2×#67—62no—
148C22×Dic3—62no—
149#239—122no—
150#239—122no—
151#237—122no—
152#237—122no—
153C2×D12—21no—
154C2×D12—21no—
155C2×D12—31no—
156C2×D12—31no—
157C2×D12—61no—
158C2×D12—62no—
159C2×D12—62no—
160C2×D12D1212yes—
161C2×C4×D3—62no—
162C2×C4×D3—61no—
163C2×C4×D3—61no—
164C2×C4×D3—121no—
165C2×Dic6—62no—
166C2×Dic6—61no—
167C2×Dic6—61no—
168C2×Dic6D1211yescharacteristic
169C2×C3×C8—22no—
170C2×C3×C8—21no—
171C2×C3×C8—21no—
172C2×C3×C8—61no—
173C2×C3×C8—61no—
174C3×C4⋊C4—31no—
175C3×C4⋊C4—61no—
176C3×C42—21no—
177C3×C42—61no—
178C3×C42C22×D311yescharacteristic
179C3×C42C22×D311yescharacteristic
180#217—62no—
181(C2×D3)⋊C4—62no—
182(C2×D3)⋊C4—61no—
183(C2×D3)⋊C4—61no—
184(C2×D3)⋊C4—121no—
185C4⋊Dic3—31no—
186C4⋊Dic3—31no—
187C4⋊Dic3—61no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191C4⋊Dic3—61no—
192C4⋊Dic3—121no—
193C4⋊Dic3—121no—
194C4⋊Dic3D1211yescharacteristic
195Dic3⋊C4—21no—
196C4×Dic3—21no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—21no—
199#204—124no—
200#204—122no—
201#204—122no—
202C22×C32#12011yescharacteristic
203C2×C3⋊D3—41no—
204C2×C3⋊D3—41no—
205C2×C3⋊D3—41no—
206C2×C3×D3—42no—
207C2×C3×D3—42no—
208C2×C3×D3—42no—
209C32×C4—21no—
210C32×C4C2×SD1611yescharacteristic
211C32×C4#13511yescharacteristic
212C32×C4AGL(1,ℤ/8)11yescharacteristic
213C32×C4AGL(1,ℤ/8)11yescharacteristic
214C3⋊Dic3—41no—
215C3⋊Dic3—81no—
216C3×Dic3—22no—
217C3×Dic3—41no—
218C2×#41—181no—
219C2×SD16—181no—
220C4⋊Q8—91no—
221#127—31no—
222#127—181no—
223#121—181no—
224#121—182no—
225C4×Q8—31no—
226C4×D4—91no—
227C4×D4—181no—
228#106—181no—
229C4⋊C8—31no—
230C4⋊C8D3211yescharacteristic
231#103—181no—
232#103—181no—
233#102—182no—
234C4×C8—31no—
235C23×C3—62no—
236C22×D3—22no—
237C22×D3—61no—
238C22×D3—61no—
239C22×D3—121no—
240C3×Q8—32no—
241C3×Q8—61no—
242C3×D4—122no—
243C3×D4—121no—
244C3×D4—121no—
245C3×D4—121no—
246C3×D4—121no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—61no—
251C2×C3×C4—61no—
252C2×C3×C4C2×D1211yescharacteristic
253C2×C3×C4C2×D1211yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4D3×D411yescharacteristic
257C2×C3×C4D3×D411yescharacteristic
258#67—124no—
259#67—242no—
260C2×Dic3—21no—
261C2×Dic3—21no—
262C2×Dic3—61no—
263C2×Dic3—61no—
264C2×Dic3—121no—
265C2×Dic3—124no—
266C2×Dic3—122no—
267C2×Dic3—121no—
268C2×Dic3—121no—
269D12—42no—
270D12—41no—
271D12—41no—
272D12—41no—
273D12—41no—
274D12—62no—
275D12—61no—
276D12—61no—
277D12—61no—
278D12—61no—
279D12—121no—
280D12—124no—
281D12—242no—
282C4×D3—124no—
283C4×D3—121no—
284C4×D3—121no—
285C4×D3—121no—
286C4×D3—121no—
287C4×D3—241no—
288C4×D3—241no—
289Dic6—21no—
290Dic6—122no—
291Dic6—122no—
292Dic6—121no—
293Dic6—121no—
294Dic6—121no—
295Dic6—121no—
296Dic6#20412yescomplemented
297C3×C8—42no—
298C3×C8—41no—
299C3×C8—41no—
300C3×C8—121no—
301C3×C8—121no—
302C3⋊C8—41no—
303C3⋊C8—41no—
304C2×C32#44911yescharacteristic
305C2×C32#45011yescharacteristic
306C2×C32#45511yescharacteristic
307C3⋊D3—81no—
308C3×D3—82no—
309#41—362no—
310#41—362no—
311C2×Q8—31no—
312C2×Q8—181no—
313C2×D4—32no—
314C2×D4—61no—
315C2×D4—61no—
316C2×D4—91no—
317C2×D4—182no—
318C2×D4—182no—
319C22×C4—182no—
320C22×C4—181no—
321SD16—362no—
322C2×C8—21no—
323C2×C8—61no—
324C2×C8—61no—
325C4⋊C4—31no—
326C4⋊C4—61no—
327C4⋊C4—91no—
328C4⋊C4—181no—
329C4⋊C4—181no—
330C22⋊C4—182no—
331C22⋊C4—181no—
332C42—61no—
333C42C2×D3211yescharacteristic
334C22×C3—21no—
335C22×C3—122no—
336C22×C3—122no—
337C22×C3—122no—
338C22×C3#88211yescharacteristic
339C22×C3#88211yescharacteristic
340C2×D3—42no—
341C2×D3—42no—
342C2×D3—42no—
343C2×D3—122no—
344C2×D3—121no—
345C2×D3—121no—
346C2×D3—121no—
347C2×D3—121no—
348C2×D3—121no—
349C2×D3—121no—
350C2×D3—241no—
351C2×D3—241no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—41no—
359C3×C4—62no—
360C3×C4—121no—
361C3×C4C2×#20411yescharacteristic
362C3×C4#90811yescharacteristic
363C3×C4#91111yescharacteristic
364C3×C4#91111yescharacteristic
365C3×C4D3×SD1611yescharacteristic
366C3×C4#91411yescharacteristic
367C3×C4#91611yescharacteristic
368C3×C4#91911yescharacteristic
369Dic3—22no—
370Dic3—41no—
371Dic3—121no—
372Dic3—121no—
373Dic3—241no—
374Dic3—242no—
375Dic3—241no—
376Dic3—241no—
377C32#164211yescharacteristic, complemented, Sylow
378C23—62no—
379C23—181no—
380Q8—32no—
381Q8—61no—
382Q8—361no—
383Q8—361no—
384D4—122no—
385D4—121no—
386D4—121no—
387D4—121no—
388D4—121no—
389D4—181no—
390D4—181no—
391D4—364no—
392D4—722no—
393C2×C4—61no—
394C2×C4—61no—
395C2×C4—181no—
396C2×C4—364no—
397C2×C4—361no—
398C2×C4—361no—
399C2×C4—361no—
400C2×C4D3×D1211yescharacteristic
401C2×C4D3×D1211yescharacteristic
402C2×C4#381111yescharacteristic
403C8—41no—
404C8—121no—
405C8—121no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—242no—
410C2×C3#473111yescharacteristic
411C2×C3#474611yescharacteristic
412C2×C3#477611yescharacteristic
413C2×C3#478111yescharacteristic
414C2×C3#481011yescharacteristic
415C2×C3#482511yescharacteristic
416D3—82no—
417D3—242no—
418D3—241no—
419D3—241no—
420C22—122no—
421C22—122no—
422C22—122no—
423C22—361no—
424C22—361no—
425C22—361no—
426C22#6392311yescharacteristic
427C4—21no—
428C4—62no—
429C4—121no—
430C4—361no—
431C4—721no—
432C4D3×#20411yescharacteristic
433C4#6379511yescharacteristic
434C4#6393711yescharacteristic
435C4#6395011yescharacteristic
436C3—21no—
437C3#6824811yescharacteristic, complemented
438C3#6839311yescharacteristic, complemented
439C2—242no—
440C2—721no—
441C2#1059061711yescharacteristic
442C2#1059094611yescharacteristic
443C2#1059101611yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#10593900C2
hypercenterC4⋊C8D32
hypocenterC32#1642
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592540C2semidirect
3. #10590301C2semidirect
4. #10590273C2semidirect
5. C3×#4485C2semidirect
6. C3×#4484C2semidirect
7. #10589082C2semidirect
38. #4485D3semidirect
39. #4484D3semidirect
128. C3×Dic6SD16semidirect
296. Dic6#204semidirect
377. C32#1642semidirect
437. C3#68248semidirect
438. C3#68393semidirect

Maximal subgroups

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

subgroupindex
#105939002
#105925402
#105903012
#105902732
C3×#44852
C3×#44842
#105890822
#683933
#682483