Finite Group Databasebeta

← #11779228

Subgroups — #11779228

Order 1152.

532 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 94 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
1Dic6×D12C211yesmaximal, characteristic, complemented
2C3×#4848C211yesmaximal, characteristic, complemented
3#10590347C211yesmaximal, characteristic
4#10590273C211yesmaximal, characteristic, complemented
5#10589348C211yesmaximal, characteristic, complemented
6C3×#4483C211yesmaximal, characteristic, complemented
7#10589084C211yesmaximal, characteristic, complemented
8#71035—31nomaximal
9#68187—31nomaximal
10C2×D3×Dic6—21no—
11#64078C2211yescharacteristic
12C2×C3×#204—21no—
13C3×#874C2211yescharacteristic
14C3×C4×D12C2211yescharacteristic
15C3×C4×Dic6C2211yescharacteristic
16#63918—21no—
17#63893—22no—
18Dic3×D12—21no—
19#63857—21no—
20C2×#3713—21no—
21C32×C4⋊C8C2211yescharacteristic
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×#821—21no—
24C3×C4×C3⋊C8C2211yescharacteristic
25#63563—22no—
26#63562—21no—
27Q8×D12—31no—
28D4×Dic6—31no—
29C3×#460—31no—
30#5072—31no—
31#5070—31no—
32#5015—31no—
33#4848D311yescharacteristic, complemented
34#4694—31no—
35C3×D4⋊C8—31no—
36#4535—31no—
37#4483D311yescharacteristic, complemented
38#4482—31no—
39#4482—31no—
40#4482—61no—
41#4456—31no—
42C2×#634—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12D411yescharacteristic
47C2×C3×C4×D3—21no—
48C2×C3×Dic6D411yescharacteristic
49C2×#627—22no—
50C2×D3×Dic3—22no—
51D3×Dic6—42no—
52D3×Dic6—42no—
53C2×C32×C8—21no—
54C32×C42C2311yescharacteristic
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)D412yes—
57C2×C3⋊(C3⋊C8)—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×C4⋊Dic3D411yescharacteristic
61C3×Dic3⋊C4—21no—
62C3×C4×Dic3—21no—
63C2×C3×C3⋊C8—21no—
64C3×#204—42no—
65Dic3⋊Dic3—22no—
66(C2×D3)⋊Dic3—22no—
67#3713—42no—
68#1627—91noSylow
69C2×D3×Q8—61no—
70C22×Dic6—61no—
71C2×C3×SD16—61no—
72C3×#127—31no—
73C3×C4×Q8—31no—
74C3×C4×D4—31no—
75D4×Dic3—61no—
76C2×#213—61no—
77C2×#213—61no—
78#924—61no—
79C2×#204—21no—
80#897—62no—
81#897—61no—
82#888—61no—
83#878—62no—
84#874C2×D311yescharacteristic
85C4×D12—61no—
86C4×D12C2×D311yescharacteristic
87#869—31no—
88#869—31no—
89#869—61no—
90#869—61no—
91C4×Dic6C2×D311yescharacteristic
92C3×C4⋊C8—21no—
93C3×C4⋊C8C2×D311yescharacteristic
94C3×C4⋊C8C2×D311yescharacteristic
95C3×#102—61no—
96C3×C4×C8—31no—
97#832—62no—
98#832—61no—
99#821—21no—
100#821—62no—
101#809—61no—
102C4⋊(C3⋊C8)—31no—
103C4⋊(C3⋊C8)—31no—
104C4⋊(C3⋊C8)—61no—
105C4×C3⋊C8C2×D311yescharacteristic
106C22×C3×D3—21no—
107C22×C3×D3—41no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C3⋊Dic3—22no—
112#634—41no—
113#634—41no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—21no—
117C3×D12—21no—
118C3×D12—42no—
119C3×D12—41no—
120C3×D12—41no—
121C3×D12—41no—
122C3×D12—41no—
123C3×D12SD1612yescomplemented
124C3×C4×D3—41no—
125C3×C4×D3—41no—
126C3×Dic6—21no—
127C3×Dic6D812yescomplemented
128#627—44no—
129D3×Dic3—44no—
130C32×C8—41no—
131C3⋊(C3⋊C8)—41no—
132C3×C3⋊C8—41no—
133D4×Q8—91no—
134#486—91no—
135#460—31no—
136#459—91no—
137#332—91no—
138Q8⋊C8—91no—
139D4⋊C8—31no—
140C2×C3×Q8—31no—
141C2×C3×D4—31no—
142C2×C3×D4—61no—
143C2×C3×D4—61no—
144C2×C3×D4—61no—
145C22×C3×C4—61no—
146C22×Dic3—62no—
147D3×Q8—122no—
148D3×Q8—122no—
149C2×D12—21no—
150C2×D12—21no—
151C2×D12—21no—
152C2×D12D1211yescharacteristic
153C2×C4×D3—21no—
154C2×C4×D3—62no—
155C2×Dic6—62no—
156C2×Dic6—62no—
157C2×Dic6—61no—
158C2×Dic6—61no—
159C2×Dic6—121no—
160C2×Dic6—122no—
161C2×Dic6—122no—
162C2×Dic6#6711yescharacteristic
163C3×SD16—122no—
164C2×C3×C8—21no—
165C2×C3×C8—21no—
166C2×C3×C8—41no—
167C2×C3×C8—61no—
168C3×C4⋊C4—31no—
169C3×C4⋊C4—31no—
170C3×C4⋊C4—61no—
171C3×C22⋊C4—61no—
172C3×C42—21no—
173C3×C42—61no—
174C3×C42C22×D311yescharacteristic
175C3×C42C22×D311yescharacteristic
176#217—62no—
177#213—122no—
178#213—122no—
179(C2×D3)⋊C4—21no—
180(C2×D3)⋊C4—62no—
181C4⋊Dic3—32no—
182C4⋊Dic3—32no—
183C4⋊Dic3—62no—
184C4⋊Dic3—62no—
185C4⋊Dic3—61no—
186C4⋊Dic3—61no—
187C4⋊Dic3—121no—
188C4⋊Dic3D1211yescharacteristic
189C4⋊Dic3#6711yescharacteristic
190Dic3⋊C4—21no—
191Dic3⋊C4—62no—
192C4×Dic3—21no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—61no—
195C2×C3⋊C8—61no—
196C2×C3⋊C8—121no—
197#204—42no—
198C22×C32#12011yescharacteristic
199C2×C3×D3—22no—
200C2×C3×D3—41no—
201C2×C3×D3—41no—
202C2×C3×D3—81no—
203C2×C3×D3—81no—
204C2×C3×D3—81no—
205C32×C4—21no—
206C32×C4C2×D811yescharacteristic
207C32×C4C2×SD1611yescharacteristic
208C32×C4AGL(1,ℤ/8)11yescharacteristic
209C32×C4#13711yescharacteristic
210C3⋊Dic3—42no—
211C3×Dic3—22no—
212C3×Dic3—41no—
213C3×Dic3—41no—
214C22×Q8—181no—
215C2×SD16—61no—
216C2×D8—181no—
217C4⋊Q8—91no—
218C4⋊Q8—181no—
219#127—31no—
220C22⋊Q8—182no—
221C22⋊Q8—181no—
222C4×Q8—31no—
223C4×D4—31no—
224C4×D4—181no—
225C4⋊C8—91no—
226C4⋊C8D3211yescharacteristic
227#102—61no—
228#102—181no—
229#102—182no—
230C4×C8—31no—
231C23×C3—61no—
232C23×C3—121no—
233C22×D3—21no—
234C22×D3—41no—
235C3×Q8—32no—
236C3×Q8—61no—
237C3×D4—32no—
238C3×D4—61no—
239C3×D4—122no—
240C3×D4—121no—
241C3×D4—121no—
242C3×D4—121no—
243C3×D4—121no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—61no—
248C2×C3×C4—61no—
249C2×C3×C4—61no—
250C2×C3×C4—121no—
251C2×C3×C4—121no—
252C2×C3×C4C2×D1211yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4D3×D411yescharacteristic
257C2×C3×C4C2×#6711yescharacteristic
258C2×Dic3—21no—
259C2×Dic3—21no—
260C2×Dic3—21no—
261C2×Dic3—62no—
262C2×Dic3—62no—
263C2×Dic3—122no—
264C2×Dic3—124no—
265D12—21no—
266D12—42no—
267D12—41no—
268D12—41no—
269D12—41no—
270D12—41no—
271D12#20412yescomplemented
272C4×D3—41no—
273C4×D3—41no—
274C4×D3—124no—
275Dic6—21no—
276Dic6—124no—
277Dic6—124no—
278Dic6—121no—
279Dic6—121no—
280Dic6—121no—
281Dic6—121no—
282Dic6—241no—
283Dic6—241no—
284Dic6#21312yescomplemented
285C3×C8—41no—
286C3×C8—41no—
287C3×C8—81no—
288C3×C8—121no—
289C3⋊C8—41no—
290C3⋊C8—121no—
291C3⋊C8—121no—
292C3⋊C8—241no—
293C2×C32#44711yescharacteristic
294C2×C32#44811yescharacteristic
295C2×C32#45411yescharacteristic
296C3×D3—42no—
297C3×D3—161no—
298C2×Q8—31no—
299C2×Q8—182no—
300C2×Q8—181no—
301C2×Q8—362no—
302C2×Q8—362no—
303C2×D4—31no—
304C2×D4—61no—
305C2×D4—61no—
306C2×D4—61no—
307C22×C4—61no—
308C22×C4—182no—
309SD16—122no—
310D8—362no—
311C2×C8—21no—
312C2×C8—61no—
313C2×C8—181no—
314C4⋊C4—31no—
315C4⋊C4—31no—
316C4⋊C4—61no—
317C4⋊C4—92no—
318C4⋊C4—182no—
319C4⋊C4—181no—
320C22⋊C4—61no—
321C22⋊C4—182no—
322C42—61no—
323C42C2×D3211yescharacteristic
324C22×C3—21no—
325C22×C3—62no—
326C22×C3—121no—
327C22×C3—121no—
328C22×C3—241no—
329C22×C3—241no—
330C22×C3—241no—
331C22×C3#88211yescharacteristic
332C22×C3#93711yescharacteristic
333C2×D3—22no—
334C2×D3—41no—
335C2×D3—41no—
336C2×D3—81no—
337C2×D3—81no—
338C2×D3—81no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—41no—
346C3×C4—62no—
347C3×C4—121no—
348C3×C4—121no—
349C3×C4C2×#20411yescharacteristic
350C3×C4#90911yescharacteristic
351C3×C4D3×D811yescharacteristic
352C3×C4D3×SD1611yescharacteristic
353C3×C4#91411yescharacteristic
354C3×C4#91511yescharacteristic
355C3×C4C2×#21311yescharacteristic
356C3×C4#94911yescharacteristic
357Dic3—22no—
358Dic3—41no—
359Dic3—41no—
360Dic3—122no—
361Dic3—122no—
362Dic3—242no—
363C32#162711yescharacteristic, complemented, Sylow
364C23—61no—
365C23—121no—
366Q8—32no—
367Q8—61no—
368Q8—364no—
369Q8—361no—
370Q8—361no—
371D4—32no—
372D4—61no—
373D4—122no—
374D4—121no—
375D4—121no—
376D4—121no—
377D4—121no—
378C2×C4—61no—
379C2×C4—61no—
380C2×C4—61no—
381C2×C4—121no—
382C2×C4—121no—
383C2×C4—182no—
384C2×C4—364no—
385C2×C4D3×D1211yescharacteristic
386C2×C4#380211yescharacteristic
387C2×C4D3×#6711yescharacteristic
388C8—41no—
389C8—121no—
390C8—361no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—122no—
395C2×C3—481no—
396C2×C3#473811yescharacteristic
397C2×C3#477311yescharacteristic
398C2×C3#482711yescharacteristic
399C2×C3#503611yescharacteristic
400C2×C3#517011yescharacteristic
401C2×C3#520111yescharacteristic
402D3—42no—
403D3—161no—
404C22—62no—
405C22—121no—
406C22—121no—
407C22—241no—
408C22—241no—
409C22—241no—
410C22#6392211yescharacteristic
411C4—21no—
412C4—62no—
413C4—121no—
414C4—121no—
415C4—362no—
416C4D3×#20411yescharacteristic
417C4#6380011yescharacteristic
418C4D3×#21311yescharacteristic
419C4#6393911yescharacteristic
420C3—21no—
421C3#6818711yescharacteristic, complemented
422C3#7103511yescharacteristic, complemented
423C2—122no—
424C2—481no—
425C2#1059059511yescharacteristic
426C2#1059082211yescharacteristic
427C2#1059101911yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#10590347C2
hypercenterC4⋊C8D32
hypocenterC32#1627
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
1. Dic6×D12C2semidirect
2. C3×#4848C2semidirect
4. #10590273C2semidirect
5. #10589348C2semidirect
6. C3×#4483C2semidirect
7. #10589084C2semidirect
33. #4848D3semidirect
37. #4483D3semidirect
123. C3×D12SD16semidirect
127. C3×Dic6D8semidirect
271. D12#204semidirect
284. Dic6#213semidirect
363. C32#1627semidirect
421. C3#68187semidirect
422. C3#71035semidirect

Maximal subgroups

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

subgroupindex
Dic6×D122
C3×#48482
#105903472
#105902732
#105893482
C3×#44832
#105890842
#710353
#681873