Finite Group Databasebeta

← #11779347

Subgroups — #11779347

Order 1152.

478 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 86 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#10593963C211yesmaximal, characteristic
2C3×#4850C211yesmaximal, characteristic, complemented
3#10590373C211yesmaximal, characteristic
4#10590310C211yesmaximal, characteristic, complemented
5#10589351C211yesmaximal, characteristic
6C3×#4484C211yesmaximal, characteristic, complemented
7#10589084C211yesmaximal, characteristic, complemented
8#71159—31nomaximal
9#68260—31nomaximal
10#64083C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14#63897—22no—
15#63894—21no—
16#63894—21no—
17#63864—21no—
18#63864—21no—
19C2×#3717—22no—
20C32×C4⋊C8C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×#818—21no—
23C3×#816—21no—
24C3×C4×C3⋊C8C2211yescharacteristic
25#63576—21no—
26#63565—21no—
27#5585—31no—
28#5585—31no—
29C3×#477—31no—
30#5091—31no—
31#5085—31no—
32#5021—31no—
33#4850D311yescharacteristic, complemented
34#4693—31no—
35C3×Q8⋊C8—31no—
36#4535—31no—
37#4485—31no—
38#4485—31no—
39#4485—61no—
40#4484D311yescharacteristic, complemented
41#4456—31no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)D412yes—
45C2×C3×Dic6—21no—
46C2×C3×Dic6D411yescharacteristic
47C2×C3×Dic6D411yescharacteristic
48C2×#624—22no—
49C2×C32×C8—21no—
50C32×C42C2311yescharacteristic
51C2×C3⋊(C3⋊C8)—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3D411yescharacteristic
55C3×C4⋊Dic3D411yescharacteristic
56C3×Dic3⋊C4—21no—
57C3×Dic3⋊C4—21no—
58C3×C4×Dic3—21no—
59C3×C4×Dic3—21no—
60C2×C3×C3⋊C8—21no—
61#3722—22no—
62#3722—22no—
63#3722—22no—
64#3717—44no—
65#1630—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4×Q8—31no—
68C3×C4×Q8—31no—
69#947—61no—
70#947—61no—
71C2×#215—62no—
72C2×#204—62no—
73#894—62no—
74#894—62no—
75#893—61no—
76#893—61no—
77#875—61no—
78#875—61no—
79#874—31no—
80#874—31no—
81#874—61no—
82C4×D12—61no—
83C4×D12—61no—
84#869C2×D311yescharacteristic
85C4×Dic6C2×D311yescharacteristic
86C4×Dic6C2×D311yescharacteristic
87C3×#107—61no—
88C3×C4⋊C8—21no—
89C3×C4⋊C8C2×D311yescharacteristic
90C3×C4⋊C8C2×D311yescharacteristic
91C3×#103—61no—
92C3×C4×C8—31no—
93#835—61no—
94#818—21no—
95#816—21no—
96#810—61no—
97#807—61no—
98#807—61no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—61no—
102C4×C3⋊C8C2×D311yescharacteristic
103C22×C3⋊D3—22no—
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C4⋊(C3⋊D3)—42no—
108C4⋊(C3⋊D3)—41no—
109C4⋊(C3⋊D3)—41no—
110C4⋊(C3⋊D3)—41no—
111C4⋊(C3⋊D3)—41no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—41no—
117C3×Dic6—21no—
118C3×Dic6—21no—
119C3×Dic6—21no—
120C3×Dic6—21no—
121C3×Dic6—42no—
122#624—82no—
123C32×C8—41no—
124C3⋊(C3⋊C8)—41no—
125C3×C3⋊C8—22no—
126#559—91no—
127#492—91no—
128#477—31no—
129#477—91no—
130#331—91no—
131Q8⋊C8—31no—
132Q8⋊C8—91no—
133C2×C3×Q8—31no—
134C2×C3×Q8—31no—
135C2×C3×Q8—61no—
136C2×D12—32no—
137C2×D12—32no—
138C2×D12—62no—
139C2×D12—61no—
140C2×D12—61no—
141C2×D12—61no—
142C2×D12—61no—
143C2×D12—121no—
144C2×D12—121no—
145C2×C4×D3—62no—
146C2×C4×D3—62no—
147C2×Dic6—21no—
148C2×Dic6D1211yescharacteristic
149C2×Dic6#6711yescharacteristic
150C2×C3×C8—21no—
151C2×C3×C8—21no—
152C2×C3×C8—41no—
153C2×C3×C8—61no—
154C3×C4⋊C4—31no—
155C3×C4⋊C4—31no—
156C3×C4⋊C4—61no—
157C3×C4⋊C4—61no—
158C3×C4⋊C4—61no—
159C3×C4⋊C4—61no—
160C3×C42—21no—
161C3×C42—61no—
162C3×C42—61no—
163C3×C42C22×D311yescharacteristic
164C3×C42C22×D311yescharacteristic
165#215—124no—
166(C2×D3)⋊C4—62no—
167(C2×D3)⋊C4—62no—
168(C2×D3)⋊C4—62no—
169(C2×D3)⋊C4—62no—
170(C2×D3)⋊C4—62no—
171(C2×D3)⋊C4—62no—
172C4⋊Dic3—21no—
173C4⋊Dic3—21no—
174C4⋊Dic3D1211yescharacteristic
175C4⋊Dic3#6711yescharacteristic
176Dic3⋊C4—21no—
177Dic3⋊C4—21no—
178C4×Dic3—21no—
179C4×Dic3—21no—
180C2×C3⋊C8—21no—
181C2×C3⋊C8—61no—
182C2×C3⋊C8—61no—
183C2×C3⋊C8—121no—
184#204—124no—
185C22×C32#12011yescharacteristic
186C2×C3⋊D3—42no—
187C2×C3⋊D3—42no—
188C2×C3⋊D3—42no—
189C32×C4—21no—
190C32×C4#13511yescharacteristic
191C32×C4#13511yescharacteristic
192C32×C4#13711yescharacteristic
193C32×C4#13711yescharacteristic
194C3×Dic3—41no—
195C3×Dic3—41no—
196C3×Dic3—41no—
197C3×Dic3—41no—
198C3×Dic3—81no—
199C2×SD16—182no—
200C4⋊Q8—31no—
201#127—91no—
202#124—181no—
203#124—181no—
204#123—182no—
205C4×Q8—31no—
206C4×Q8—31no—
207C4×D4—181no—
208C4×D4—181no—
209#107—61no—
210#107—181no—
211C4⋊C8—91no—
212C4⋊C8D3211yescharacteristic
213#103—61no—
214#103—181no—
215C4×C8—31no—
216C22×D3—62no—
217C22×D3—62no—
218C22×D3—122no—
219C3×Q8—61no—
220C3×Q8—61no—
221C3×Q8—61no—
222C3×Q8—61no—
223C3×Q8—122no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—61no—
228C2×C3×C4—61no—
229C2×C3×C4—61no—
230C2×C3×C4—61no—
231C2×C3×C4—121no—
232C2×C3×C4C2×D1211yescharacteristic
233C2×C3×C4D3×D411yescharacteristic
234C2×C3×C4D3×D411yescharacteristic
235C2×C3×C4D3×D411yescharacteristic
236C2×C3×C4D3×D411yescharacteristic
237C2×C3×C4C2×#6711yescharacteristic
238C2×Dic3—21no—
239C2×Dic3—21no—
240C2×Dic3—21no—
241C2×Dic3—21no—
242C2×Dic3—41no—
243D12—122no—
244D12—122no—
245D12—121no—
246D12—121no—
247D12—121no—
248D12—121no—
249D12—121no—
250D12—121no—
251D12—121no—
252D12—121no—
253D12—241no—
254D12—241no—
255D12—241no—
256D12—241no—
257D12—242no—
258C4×D3—242no—
259C4×D3—242no—
260Dic6—21no—
261Dic6—21no—
262Dic6—21no—
263Dic6—21no—
264Dic6—42no—
265C3×C8—41no—
266C3×C8—41no—
267C3×C8—62no—
268C3×C8—81no—
269C3⋊C8—22no—
270C3⋊C8—121no—
271C3⋊C8—121no—
272C3⋊C8—241no—
273C2×C32#45211yescharacteristic
274C2×C32#45211yescharacteristic
275C2×C32#45311yescharacteristic
276C3⋊D3—82no—
277C2×Q8—31no—
278C2×Q8—31no—
279C2×Q8—61no—
280C2×D4—92no—
281C2×D4—181no—
282C2×D4—181no—
283C22×C4—182no—
284SD16—364no—
285C2×C8—21no—
286C2×C8—61no—
287C2×C8—181no—
288C4⋊C4—31no—
289C4⋊C4—31no—
290C4⋊C4—61no—
291C4⋊C4—61no—
292C4⋊C4—61no—
293C4⋊C4—61no—
294C22⋊C4—182no—
295C22⋊C4—182no—
296C22⋊C4—182no—
297C42—61no—
298C42—61no—
299C42C2×D3211yescharacteristic
300C22×C3—21no—
301C22×C3#88211yescharacteristic
302C22×C3#93711yescharacteristic
303C2×D3—122no—
304C2×D3—122no—
305C2×D3—122no—
306C2×D3—122no—
307C2×D3—122no—
308C2×D3—122no—
309C2×D3—242no—
310C2×D3—242no—
311C2×D3—242no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—41no—
319C3×C4—121no—
320C3×C4—121no—
321C3×C4—121no—
322C3×C4—121no—
323C3×C4—241no—
324C3×C4#90411yescharacteristic
325C3×C4#90911yescharacteristic
326C3×C4#91611yescharacteristic
327C3×C4#91811yescharacteristic
328C3×C4#91811yescharacteristic
329C3×C4#91911yescharacteristic
330C3×C4#94211yescharacteristic
331C3×C4#95011yescharacteristic
332Dic3—41no—
333Dic3—41no—
334Dic3—41no—
335Dic3—41no—
336Dic3—81no—
337C32#163011yescharacteristic, complemented, Sylow
338C23—182no—
339Q8—61no—
340Q8—61no—
341Q8—61no—
342Q8—61no—
343Q8—122no—
344D4—362no—
345D4—361no—
346D4—361no—
347D4—361no—
348D4—361no—
349C2×C4—61no—
350C2×C4—61no—
351C2×C4—61no—
352C2×C4—61no—
353C2×C4—121no—
354C2×C4—722no—
355C2×C4D3×D1211yescharacteristic
356C2×C4#380211yescharacteristic
357C2×C4D3×#6711yescharacteristic
358C8—41no—
359C8—62no—
360C8—361no—
361C2×C3—21no—
362C2×C3—21no—
363C2×C3—21no—
364C2×C3#473311yescharacteristic
365C2×C3#480811yescharacteristic
366C2×C3#482211yescharacteristic
367C2×C3#504711yescharacteristic
368C2×C3#518711yescharacteristic
369C2×C3#519811yescharacteristic
370D3—242no—
371D3—242no—
372D3—482no—
373C22—362no—
374C22—362no—
375C22—362no—
376C22#6392211yescharacteristic
377C4—21no—
378C4—121no—
379C4—121no—
380C4—121no—
381C4—121no—
382C4—241no—
383C4#6380111yescharacteristic
384C4#6380811yescharacteristic
385C4#6393511yescharacteristic
386C4#6394811yescharacteristic
387C3—21no—
388C3#6826011yescharacteristic, complemented
389C3#7115911yescharacteristic, complemented
390C2—722no—
391C2#1059061611yescharacteristic
392C2#1059096611yescharacteristic
393C2#1059101311yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#64083C22
hypercenterC4⋊C8D32
hypocenterC32#1630
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×#4850C2semidirect
4. #10590310C2semidirect
6. C3×#4484C2semidirect
7. #10589084C2semidirect
33. #4850D3semidirect
40. #4484D3semidirect
337. C32#1630semidirect
388. C3#68260semidirect
389. C3#71159semidirect

Maximal subgroups

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

subgroupindex
#105939632
C3×#48502
#105903732
#105903102
#105893512
C3×#44842
#105890842
#711593
#682603