Finite Group Databasebeta

← #11779022

Subgroups — #11779022

Order 1152.

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

normal subgroups only

This group has 504 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#10593960C211yesmaximal, characteristic, complemented
2C3×#4843C211yesmaximal, characteristic
3#10590369C211yesmaximal, characteristic, complemented
4#10590364C211yesmaximal, characteristic, complemented
5#10589347C211yesmaximal, characteristic, complemented
6C3×#4484C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#71016—31nomaximal
9#68244—31nomaximal
10#64078C2211yescharacteristic
11C2×C3×D24—21no—
12C3×#874C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63896—22no—
16Dic3×D12—21no—
17D3×C4⋊Dic3—21no—
18#63869—21no—
19#63856—21no—
20C2×#3716—22no—
21C2×#3715—21no—
22C32×C4⋊C8C2211yescharacteristic
23C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
24C3×#821—21no—
25C3×C4×C3⋊C8C2211yescharacteristic
26#63562—21no—
27#5579—31no—
28#5543—31no—
29C3×#459—31no—
30#5076—31no—
31#5075—31no—
32#5027—31no—
33#4843D311yescharacteristic
34#4693—31no—
35C3×Q8⋊C8—31no—
36D4⋊(C3⋊C8)—31no—
37#4484D311yescharacteristic, complemented
38#4481—31no—
39#4481—31no—
40#4481—61no—
41#4459—31no—
42C2×#634D412yes—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12D411yescharacteristic
47C2×C3×C4×D3—21no—
48C2×C3×Dic6D411yescharacteristic
49C2×D3×Dic3—22no—
50C2×C32×C8—21no—
51C32×C42C2311yescharacteristic
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C3×(C2×D3)⋊C4—21no—
56C3×C4⋊Dic3D411yescharacteristic
57C3×C4⋊Dic3D411yescharacteristic
58C3×Dic3⋊C4—21no—
59C3×C4×Dic3—21no—
60C2×C3×C3⋊C8—21no—
61C3×D24—42no—
62#3724—22no—
63Dic3⋊Dic3—22no—
64(C2×D3)⋊Dic3—22no—
65#3716—44no—
66#3715—42no—
67#1622—91noSylow
68C2×C3×D8—61no—
69C3×#127—31no—
70C3×C4×Q8—31no—
71C3×C4×D4—31no—
72#946—61no—
73C2×#215—61no—
74D4×Dic3—61no—
75C2×#214—62no—
76C2×#214—61no—
77C2×C4⋊Dic3—61no—
78#924—61no—
79C2×D24—21no—
80C2×#204—62no—
81#896—62no—
82D3×C4⋊C4—61no—
83#890—61no—
84#878—62no—
85#874C2×D311yescharacteristic
86C4×D12—61no—
87C4×D12C2×D311yescharacteristic
88#870—61no—
89#869—31no—
90#869—31no—
91#869—61no—
92C4×Dic6C2×D311yescharacteristic
93C3×C4⋊C8—21no—
94C3×C4⋊C8C2×D311yescharacteristic
95C3×C4⋊C8C2×D311yescharacteristic
96C3×#102—61no—
97C3×C4×C8—31no—
98#832—61no—
99#821—21no—
100#809—61no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—31no—
103C4⋊(C3⋊C8)—61no—
104C4×C3⋊C8C2×D311yescharacteristic
105C22×C3×D3—21no—
106C22×C3×D3—41no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C3⋊Dic3—22no—
111#634—42no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—21no—
115C3×D12—21no—
116C3×D12—42no—
117C3×D12—41no—
118C3×D12—41no—
119C3×D12—41no—
120C3×D12—41no—
121C3×D12SD1612yescomplemented
122C3×C4×D3—41no—
123C3×C4×D3—41no—
124C3×Dic6—21no—
125C3×Dic6—21no—
126D3×Dic3—82no—
127C32×C8—41no—
128C3⋊(C3⋊C8)—41no—
129C3×C3⋊C8—22no—
130#554—91no—
131#492—91no—
132#460—91no—
133#459—31no—
134#333—91no—
135Q8⋊C8—31no—
136D4⋊C8—91no—
137C2×C3×Q8—31no—
138C2×C3×D4—31no—
139C2×C3×D4—61no—
140C2×C3×D4—61no—
141C2×C3×D4—61no—
142C22×C3×C4—61no—
143C22×Dic3—62no—
144C2×D12—21no—
145C2×D12—21no—
146C2×D12—21no—
147C2×D12#6711yescharacteristic
148C2×C4×D3—21no—
149C2×C4×D3—62no—
150C2×Dic6—32no—
151C2×Dic6—32no—
152C2×Dic6—62no—
153C2×Dic6D1211yescharacteristic
154C3×D8—122no—
155C2×C3×C8—21no—
156C2×C3×C8—21no—
157C2×C3×C8—41no—
158C2×C3×C8—61no—
159C3×C4⋊C4—31no—
160C3×C4⋊C4—31no—
161C3×C4⋊C4—61no—
162C3×C22⋊C4—61no—
163C3×C42—21no—
164C3×C42—61no—
165C3×C42C22×D311yescharacteristic
166C3×C42C22×D311yescharacteristic
167#217—62no—
168#215—122no—
169#214—124no—
170#214—122no—
171(C2×D3)⋊C4—21no—
172(C2×D3)⋊C4—62no—
173C4⋊Dic3—62no—
174C4⋊Dic3—61no—
175C4⋊Dic3—61no—
176C4⋊Dic3—61no—
177C4⋊Dic3—61no—
178C4⋊Dic3—121no—
179C4⋊Dic3—121no—
180C4⋊Dic3D1211yescharacteristic
181C4⋊Dic3#6711yescharacteristic
182Dic3⋊C4—21no—
183Dic3⋊C4—62no—
184Dic3⋊C4—62no—
185Dic3⋊C4—62no—
186C4×Dic3—21no—
187C2×C3⋊C8—21no—
188C2×C3⋊C8—61no—
189C2×C3⋊C8—61no—
190C2×C3⋊C8—121no—
191D24—42no—
192#204—124no—
193C22×C32#12011yescharacteristic
194C2×C3×D3—22no—
195C2×C3×D3—41no—
196C2×C3×D3—41no—
197C2×C3×D3—81no—
198C2×C3×D3—81no—
199C2×C3×D3—81no—
200C32×C4—21no—
201C32×C4C2×SD1611yescharacteristic
202C32×C4#13511yescharacteristic
203C32×C4AGL(1,ℤ/8)11yescharacteristic
204C32×C4#13711yescharacteristic
205C3⋊Dic3—42no—
206C3×Dic3—41no—
207C3×Dic3—41no—
208C3×Dic3—41no—
209C2×SD16—182no—
210C2×SD16—181no—
211C2×D8—61no—
212C4⋊Q8—91no—
213#127—31no—
214#125—181no—
215C22⋊Q8—182no—
216C22⋊Q8—181no—
217C4×Q8—31no—
218C4×D4—31no—
219C4×D4—181no—
220C2×C4⋊C4—181no—
221C4⋊C8—91no—
222C4⋊C8D3211yescharacteristic
223#102—61no—
224#102—181no—
225C4×C8—31no—
226C23×C3—61no—
227C23×C3—121no—
228C22×D3—21no—
229C22×D3—41no—
230C3×Q8—61no—
231C3×Q8—61no—
232C3×D4—32no—
233C3×D4—61no—
234C3×D4—122no—
235C3×D4—121no—
236C3×D4—121no—
237C3×D4—121no—
238C3×D4—121no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—61no—
243C2×C3×C4—61no—
244C2×C3×C4—61no—
245C2×C3×C4—121no—
246C2×C3×C4—121no—
247C2×C3×C4C2×D1211yescharacteristic
248C2×C3×C4D3×D411yescharacteristic
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4C2×#6711yescharacteristic
253C2×Dic3—21no—
254C2×Dic3—21no—
255C2×Dic3—21no—
256C2×Dic3—62no—
257C2×Dic3—62no—
258C2×Dic3—122no—
259C2×Dic3—242no—
260D12—21no—
261D12—42no—
262D12—41no—
263D12—41no—
264D12—41no—
265D12—41no—
266D12#21412yescomplemented
267C4×D3—41no—
268C4×D3—41no—
269C4×D3—242no—
270Dic6—21no—
271Dic6—21no—
272Dic6—122no—
273Dic6—122no—
274Dic6—242no—
275C3×C8—41no—
276C3×C8—41no—
277C3×C8—62no—
278C3×C8—81no—
279C3⋊C8—22no—
280C3⋊C8—121no—
281C3⋊C8—121no—
282C3⋊C8—241no—
283C2×C32#44811yescharacteristic
284C2×C32#44911yescharacteristic
285C2×C32#45311yescharacteristic
286C3×D3—42no—
287C3×D3—161no—
288C2×Q8—31no—
289C2×Q8—92no—
290C2×D4—31no—
291C2×D4—61no—
292C2×D4—61no—
293C2×D4—61no—
294C22×C4—61no—
295C22×C4—182no—
296SD16—364no—
297SD16—362no—
298D8—122no—
299C2×C8—21no—
300C2×C8—61no—
301C2×C8—181no—
302C4⋊C4—31no—
303C4⋊C4—31no—
304C4⋊C4—61no—
305C4⋊C4—182no—
306C4⋊C4—182no—
307C4⋊C4—181no—
308C4⋊C4—181no—
309C22⋊C4—61no—
310C22⋊C4—182no—
311C42—61no—
312C42C2×D3211yescharacteristic
313C22×C3—21no—
314C22×C3—62no—
315C22×C3—121no—
316C22×C3—121no—
317C22×C3—241no—
318C22×C3—241no—
319C22×C3—241no—
320C22×C3#88211yescharacteristic
321C22×C3#93711yescharacteristic
322C2×D3—22no—
323C2×D3—41no—
324C2×D3—41no—
325C2×D3—81no—
326C2×D3—81no—
327C2×D3—81no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—41no—
335C3×C4—121no—
336C3×C4—121no—
337C3×C4—121no—
338C3×C4#90411yescharacteristic
339C3×C4#90811yescharacteristic
340C3×C4#91111yescharacteristic
341C3×C4#91211yescharacteristic
342C3×C4D3×SD1611yescharacteristic
343C3×C4#91811yescharacteristic
344C3×C4C2×#21411yescharacteristic
345C3×C4#95111yescharacteristic
346Dic3—41no—
347Dic3—41no—
348Dic3—41no—
349Dic3—122no—
350Dic3—122no—
351Dic3—242no—
352C32#162211yescharacteristic, complemented, Sylow
353C23—61no—
354C23—121no—
355Q8—61no—
356Q8—61no—
357Q8—362no—
358D4—32no—
359D4—61no—
360D4—122no—
361D4—121no—
362D4—121no—
363D4—121no—
364D4—121no—
365C2×C4—61no—
366C2×C4—61no—
367C2×C4—61no—
368C2×C4—121no—
369C2×C4—121no—
370C2×C4—182no—
371C2×C4—722no—
372C2×C4D3×D1211yescharacteristic
373C2×C4#380211yescharacteristic
374C2×C4D3×#6711yescharacteristic
375C8—41no—
376C8—62no—
377C8—361no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—122no—
382C2×C3—481no—
383C2×C3#473411yescharacteristic
384C2×C3#480611yescharacteristic
385C2×C3#482211yescharacteristic
386C2×C3#504011yescharacteristic
387C2×C3#515811yescharacteristic
388C2×C3#519811yescharacteristic
389D3—42no—
390D3—161no—
391C22—62no—
392C22—121no—
393C22—121no—
394C22—241no—
395C22—241no—
396C22—241no—
397C22#6392211yescharacteristic
398C4—21no—
399C4—121no—
400C4—121no—
401C4—121no—
402C4—362no—
403C4#6379511yescharacteristic
404C4#6380711yescharacteristic
405C4D3×#21411yescharacteristic
406C4#6394311yescharacteristic
407C3—21no—
408C3#6824411yescharacteristic, complemented
409C3#7101611yescharacteristic, complemented
410C2—122no—
411C2—481no—
412C2#1059060311yescharacteristic
413C2#1059096211yescharacteristic
414C2#1059101311yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radicalC3×#4843C2
hypercenterC4⋊C8D32
hypocenterC32#1622
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. #10593960C2semidirect
3. #10590369C2semidirect
4. #10590364C2semidirect
5. #10589347C2semidirect
6. C3×#4484C2semidirect
7. #10589081C2semidirect
37. #4484D3semidirect
121. C3×D12SD16semidirect
266. D12#214semidirect
352. C32#1622semidirect
408. C3#68244semidirect
409. C3#71016semidirect

Maximal subgroups

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

subgroupindex
#105939602
C3×#48432
#105903692
#105903642
#105893472
C3×#44842
#105890812
#710163
#682443