Finite Group Databasebeta

← #11779875

Subgroups — #11779875

Order 1152.

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

normal subgroups only

This group has 542 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#10593902C211yesmaximal, characteristic
2C3×#4841C211yesmaximal, characteristic, complemented
3#10590285C211yesmaximal, characteristic, complemented
4#10590281C211yesmaximal, characteristic, complemented
5#10589351C211yesmaximal, characteristic, complemented
6C3×#4484C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#71045—31nomaximal
9#68248—31nomaximal
10C2×#3799—21no—
11#64083C2211yescharacteristic
12C2×C3×#204—21no—
13C3×C4×D12C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C3×C4×Dic6C2211yescharacteristic
16#63911—21no—
17#63910—22no—
18#63909—21no—
19#63894—21no—
20C32×C4⋊C8C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×#816—21no—
23C3×C4×C3⋊C8C2211yescharacteristic
24#63574—21no—
25#63565—21no—
26#63564—22no—
27#5577—31no—
28#5553—31no—
29C3×#461—31no—
30#5094—31no—
31#5088—31no—
32#5020—31no—
33#4841D311yescharacteristic, complemented
34#4694—31no—
35C3×Q8⋊C8—31no—
36D4⋊(C3⋊C8)—31no—
37#4485—31no—
38#4485—31no—
39#4485—61no—
40#4484D311yescharacteristic, complemented
41#4459—31no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)D412yes—
45C2×C3×D12D411yescharacteristic
46C2×C3×C4×D3—21no—
47C2×C3×Dic6—21no—
48C2×C3×Dic6D411yescharacteristic
49C2×#626—22no—
50C2×#626—22no—
51C2×#624—22no—
52#3799—42no—
53#3799—42no—
54C2×C32×C8—21no—
55C32×C42C2311yescharacteristic
56C2×C3⋊(C3⋊C8)—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3D411yescharacteristic
61C3×C4⋊Dic3D411yescharacteristic
62C3×Dic3⋊C4—21no—
63C3×C4×Dic3—21no—
64C2×C3×C3⋊C8—21no—
65C3×#204—42no—
66#3722—22no—
67#1642—91noSylow
68C2×#239—61no—
69C2×#235—61no—
70C2×C3×SD16—61no—
71C3×C4⋊Q8—31no—
72C3×C4×Q8—31no—
73C3×C4×D4—31no—
74#940—61no—
75#930—61no—
76C2×#204—21no—
77#895—62no—
78#895—61no—
79#893—61no—
80#884—62no—
81#874—31no—
82#874—31no—
83#874—61no—
84#874—61no—
85C4×D12—61no—
86C4×D12C2×D311yescharacteristic
87#869C2×D311yescharacteristic
88C4×Dic6C2×D311yescharacteristic
89C3×C4⋊C8—21no—
90C3×C4⋊C8C2×D311yescharacteristic
91C3×C4⋊C8C2×D311yescharacteristic
92C3×#103—61no—
93C3×C4×C8—31no—
94#835—61no—
95#821—62no—
96#816—21no—
97#810—61no—
98#809—62no—
99#808—61no—
100#808—61no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—31no—
103C4⋊(C3⋊C8)—61no—
104C4×C3⋊C8C2×D311yescharacteristic
105C22×C3⋊D3—22no—
106C22×C3×D3—21no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C4⋊(C3⋊D3)—42no—
111C4⋊(C3⋊D3)—41no—
112C4⋊(C3⋊D3)—41no—
113C4⋊(C3⋊D3)—41no—
114C4⋊(C3⋊D3)—41no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—21no—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—41no—
119C3×D12—21no—
120C3×D12—21no—
121C3×C4×D3—41no—
122C3×C4×D3—41no—
123C3×Dic6—21no—
124C3×Dic6—41no—
125C3×Dic6—41no—
126C3×Dic6SD1612yescomplemented
127#626—44no—
128#626—82no—
129#624—44no—
130C32×C8—41no—
131C3⋊(C3⋊C8)—41no—
132C3×C3⋊C8—41no—
133#550—91no—
134#486—91no—
135#475—91no—
136#461—31no—
137#331—91no—
138Q8⋊C8—31no—
139D4⋊C8—91no—
140C2×C3×Q8—31no—
141C2×C3×Q8—61no—
142C2×C3×D4—31no—
143C22×C3×C4—61no—
144C2×#67—62no—
145C2×#67—62no—
146#239—122no—
147#239—122no—
148#235—122no—
149#235—122no—
150C2×D12—32no—
151C2×D12—32no—
152C2×D12—62no—
153C2×D12—62no—
154C2×D12—61no—
155C2×D12—61no—
156C2×D12—61no—
157C2×D12—61no—
158C2×D12—62no—
159C2×D12—121no—
160C2×D12—121no—
161C2×D12#6711yescharacteristic
162C2×C4×D3—21no—
163C2×C4×D3—62no—
164C2×C4×D3—62no—
165C2×Dic6—21no—
166C2×Dic6D1211yescharacteristic
167C3×SD16—122no—
168C2×C3×C8—21no—
169C2×C3×C8—21no—
170C2×C3×C8—41no—
171C2×C3×C8—61no—
172C3×C4⋊C4—31no—
173C3×C4⋊C4—31no—
174C3×C4⋊C4—61no—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C22⋊C4—61no—
178C3×C42—21no—
179C3×C42—61no—
180C3×C42C22×D311yescharacteristic
181C3×C42C22×D311yescharacteristic
182(C2×D3)⋊C4—21no—
183(C2×D3)⋊C4—62no—
184(C2×D3)⋊C4—62no—
185C4⋊Dic3—21no—
186C4⋊Dic3—21no—
187C4⋊Dic3D1211yescharacteristic
188C4⋊Dic3#6711yescharacteristic
189Dic3⋊C4—21no—
190C4×Dic3—21no—
191C2×C3⋊C8—21no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—121no—
195#204—42no—
196C22×C32#12011yescharacteristic
197C2×C3⋊D3—42no—
198C2×C3⋊D3—42no—
199C2×C3⋊D3—42no—
200C2×C3×D3—41no—
201C2×C3×D3—41no—
202C2×C3×D3—41no—
203C32×C4—21no—
204C32×C4C2×SD1611yescharacteristic
205C32×C4#13511yescharacteristic
206C32×C4AGL(1,ℤ/8)11yescharacteristic
207C32×C4AGL(1,ℤ/8)11yescharacteristic
208C3×Dic3—22no—
209C3×Dic3—41no—
210C3×Dic3—41no—
211C3×Dic3—81no—
212C2×#41—181no—
213C2×SD16—61no—
214C4⋊Q8—31no—
215#127—91no—
216#127—181no—
217#121—182no—
218#121—181no—
219C4×Q8—31no—
220C4×D4—31no—
221C4×D4—181no—
222#106—181no—
223C4⋊C8—91no—
224C4⋊C8D3211yescharacteristic
225#103—61no—
226#103—181no—
227#102—182no—
228C4×C8—31no—
229C23×C3—61no—
230C22×D3—21no—
231C22×D3—62no—
232C22×D3—62no—
233C22×D3—122no—
234C3×Q8—32no—
235C3×Q8—61no—
236C3×Q8—121no—
237C3×Q8—121no—
238C3×D4—61no—
239C3×D4—61no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—61no—
244C2×C3×C4—61no—
245C2×C3×C4—61no—
246C2×C3×C4—121no—
247C2×C3×C4—121no—
248C2×C3×C4—121no—
249C2×C3×C4C2×D1211yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4C2×#6711yescharacteristic
255#67—124no—
256#67—242no—
257C2×Dic3—21no—
258C2×Dic3—21no—
259C2×Dic3—21no—
260C2×Dic3—41no—
261D12—21no—
262D12—21no—
263D12—122no—
264D12—122no—
265D12—124no—
266D12—121no—
267D12—121no—
268D12—121no—
269D12—121no—
270D12—121no—
271D12—121no—
272D12—121no—
273D12—121no—
274D12—241no—
275D12—241no—
276D12—241no—
277D12—241no—
278D12—242no—
279D12—242no—
280C4×D3—41no—
281C4×D3—41no—
282C4×D3—124no—
283C4×D3—124no—
284Dic6—21no—
285Dic6—41no—
286Dic6—41no—
287Dic6#20412yescomplemented
288C3×C8—41no—
289C3×C8—41no—
290C3×C8—81no—
291C3×C8—121no—
292C3⋊C8—41no—
293C3⋊C8—121no—
294C3⋊C8—121no—
295C3⋊C8—241no—
296C2×C32#44911yescharacteristic
297C2×C32#45011yescharacteristic
298C2×C32#45511yescharacteristic
299C3⋊D3—82no—
300C3×D3—81no—
301#41—362no—
302#41—362no—
303C2×Q8—31no—
304C2×Q8—61no—
305C2×D4—31no—
306C2×D4—92no—
307C2×D4—182no—
308C2×D4—182no—
309C2×D4—181no—
310C2×D4—181no—
311C22×C4—61no—
312C22×C4—182no—
313SD16—122no—
314C2×C8—21no—
315C2×C8—61no—
316C2×C8—181no—
317C4⋊C4—31no—
318C4⋊C4—31no—
319C4⋊C4—61no—
320C4⋊C4—61no—
321C4⋊C4—61no—
322C22⋊C4—61no—
323C22⋊C4—182no—
324C42—61no—
325C42C2×D3211yescharacteristic
326C22×C3—21no—
327C22×C3—121no—
328C22×C3—121no—
329C22×C3—121no—
330C22×C3#88211yescharacteristic
331C22×C3#93711yescharacteristic
332C2×D3—41no—
333C2×D3—41no—
334C2×D3—41no—
335C2×D3—122no—
336C2×D3—122no—
337C2×D3—122no—
338C2×D3—122no—
339C2×D3—122no—
340C2×D3—122no—
341C2×D3—242no—
342C2×D3—242no—
343C2×D3—242no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—41no—
351C3×C4—62no—
352C3×C4—121no—
353C3×C4—121no—
354C3×C4—241no—
355C3×C4C2×#20411yescharacteristic
356C3×C4#90811yescharacteristic
357C3×C4D3×SD1611yescharacteristic
358C3×C4#91411yescharacteristic
359C3×C4#91411yescharacteristic
360C3×C4#91911yescharacteristic
361C3×C4#93211yescharacteristic
362C3×C4#95011yescharacteristic
363Dic3—22no—
364Dic3—41no—
365Dic3—41no—
366Dic3—81no—
367C32#164211yescharacteristic, complemented, Sylow
368C23—61no—
369C23—182no—
370Q8—32no—
371Q8—61no—
372Q8—121no—
373Q8—121no—
374D4—61no—
375D4—61no—
376D4—362no—
377D4—364no—
378D4—361no—
379D4—361no—
380D4—361no—
381D4—361no—
382D4—722no—
383C2×C4—61no—
384C2×C4—61no—
385C2×C4—61no—
386C2×C4—121no—
387C2×C4—121no—
388C2×C4—121no—
389C2×C4—364no—
390C2×C4D3×D1211yescharacteristic
391C2×C4#380211yescharacteristic
392C2×C4D3×#6711yescharacteristic
393C8—41no—
394C8—121no—
395C8—361no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—241no—
400C2×C3#473111yescharacteristic
401C2×C3#481011yescharacteristic
402C2×C3#482511yescharacteristic
403C2×C3#503711yescharacteristic
404C2×C3#516911yescharacteristic
405C2×C3#520211yescharacteristic
406D3—81no—
407D3—242no—
408D3—242no—
409D3—482no—
410C22—121no—
411C22—121no—
412C22—121no—
413C22—362no—
414C22—362no—
415C22—362no—
416C22#6392211yescharacteristic
417C4—21no—
418C4—62no—
419C4—121no—
420C4—121no—
421C4—241no—
422C4D3×#20411yescharacteristic
423C4#6379411yescharacteristic
424C4#6393411yescharacteristic
425C4#6394911yescharacteristic
426C3—21no—
427C3#6824811yescharacteristic, complemented
428C3#7104511yescharacteristic, complemented
429C2—241no—
430C2—722no—
431C2#1059061511yescharacteristic
432C2#1059094211yescharacteristic
433C2#1059101111yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#10593902C2
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. C3×#4841C2semidirect
3. #10590285C2semidirect
4. #10590281C2semidirect
5. #10589351C2semidirect
6. C3×#4484C2semidirect
7. #10589081C2semidirect
33. #4841D3semidirect
40. #4484D3semidirect
126. C3×Dic6SD16semidirect
287. Dic6#204semidirect
367. C32#1642semidirect
427. C3#68248semidirect
428. C3#71045semidirect

Maximal subgroups

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

subgroupindex
#105939022
C3×#48412
#105902852
#105902812
#105893512
C3×#44842
#105890812
#710453
#682483