Finite Group Databasebeta

← #11779787

Subgroups — #11779787

Order 1152.

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

normal subgroups only

This group has 466 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×#4851C211yesmaximal, characteristic, complemented
3#10590384C211yesmaximal, characteristic, complemented
4#10590281C211yesmaximal, characteristic
5#10589351C211yesmaximal, characteristic
6C3×#4484C211yesmaximal, characteristic, complemented
7#10589084C211yesmaximal, characteristic, complemented
8#71128—31nomaximal
9#68262—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×#3718—21no—
20C32×C4⋊C8C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×#817—21no—
23C3×#816—21no—
24C3×C4×C3⋊C8C2211yescharacteristic
25#63565—21no—
26#63564—22no—
27#5585—31no—
28#5585—31no—
29C3×#475—31no—
30#5090—31no—
31#5088—31no—
32#5031—31no—
33#4851D311yescharacteristic, complemented
34#4694—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#3718—42no—
65#1640—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4×Q8—31no—
68C3×C4×Q8—31no—
69#947—61no—
70#947—61no—
71C2×#216—61no—
72C2×#216—61no—
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×#106—61no—
88C3×C4⋊C8—21no—
89C3×C4⋊C8C2×D311yescharacteristic
90C3×C4⋊C8C2×D311yescharacteristic
91C3×#103—61no—
92C3×C4×C8—31no—
93#835—61no—
94#821—62no—
95#817—21no—
96#816—21no—
97#810—61no—
98#809—62no—
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—41no—
122C3×Dic6—41no—
123#624—82no—
124C32×C8—41no—
125C3⋊(C3⋊C8)—41no—
126C3×C3⋊C8—41no—
127#559—91no—
128#486—91no—
129#475—31no—
130#462—91no—
131#331—91no—
132Q8⋊C8—31no—
133Q8⋊C8—91no—
134C2×C3×Q8—31no—
135C2×C3×Q8—31no—
136C2×C3×Q8—61no—
137C2×D12—32no—
138C2×D12—32no—
139C2×D12—62no—
140C2×D12—61no—
141C2×D12—61no—
142C2×D12—61no—
143C2×D12—61no—
144C2×D12—121no—
145C2×D12—121no—
146C2×C4×D3—62no—
147C2×C4×D3—62no—
148C2×Dic6—21no—
149C2×Dic6D1211yescharacteristic
150C2×Dic6#6711yescharacteristic
151C2×C3×C8—21no—
152C2×C3×C8—21no—
153C2×C3×C8—41no—
154C2×C3×C8—61no—
155C3×C4⋊C4—31no—
156C3×C4⋊C4—31no—
157C3×C4⋊C4—61no—
158C3×C4⋊C4—61no—
159C3×C4⋊C4—61no—
160C3×C4⋊C4—61no—
161C3×C42—21no—
162C3×C42—61no—
163C3×C42—61no—
164C3×C42C22×D311yescharacteristic
165C3×C42C22×D311yescharacteristic
166#216—122no—
167#216—122no—
168(C2×D3)⋊C4—62no—
169(C2×D3)⋊C4—62no—
170(C2×D3)⋊C4—62no—
171(C2×D3)⋊C4—62no—
172(C2×D3)⋊C4—62no—
173(C2×D3)⋊C4—62no—
174C4⋊Dic3—21no—
175C4⋊Dic3—21no—
176C4⋊Dic3D1211yescharacteristic
177C4⋊Dic3#6711yescharacteristic
178Dic3⋊C4—21no—
179Dic3⋊C4—21no—
180C4×Dic3—21no—
181C4×Dic3—21no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—61no—
184C2×C3⋊C8—61no—
185C2×C3⋊C8—121no—
186C22×C32#12011yescharacteristic
187C2×C3⋊D3—42no—
188C2×C3⋊D3—42no—
189C2×C3⋊D3—42no—
190C32×C4—21no—
191C32×C4#13511yescharacteristic
192C32×C4#13511yescharacteristic
193C32×C4AGL(1,ℤ/8)11yescharacteristic
194C32×C4#13711yescharacteristic
195C3×Dic3—41no—
196C3×Dic3—41no—
197C3×Dic3—41no—
198C3×Dic3—41no—
199C3×Dic3—81no—
200C2×Q16—181no—
201C4⋊Q8—31no—
202#127—91no—
203#124—181no—
204#124—181no—
205#123—182no—
206C4×Q8—31no—
207C4×Q8—31no—
208C4×D4—181no—
209C4×D4—181no—
210#106—61no—
211C4⋊C8—91no—
212C4⋊C8D3211yescharacteristic
213#103—61no—
214#103—181no—
215#102—182no—
216C4×C8—31no—
217C22×D3—62no—
218C22×D3—62no—
219C22×D3—122no—
220C3×Q8—61no—
221C3×Q8—61no—
222C3×Q8—61no—
223C3×Q8—61no—
224C3×Q8—121no—
225C3×Q8—121no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—61no—
230C2×C3×C4—61no—
231C2×C3×C4—61no—
232C2×C3×C4—61no—
233C2×C3×C4—121no—
234C2×C3×C4C2×D1211yescharacteristic
235C2×C3×C4D3×D411yescharacteristic
236C2×C3×C4D3×D411yescharacteristic
237C2×C3×C4D3×D411yescharacteristic
238C2×C3×C4D3×D411yescharacteristic
239C2×C3×C4C2×#6711yescharacteristic
240C2×Dic3—21no—
241C2×Dic3—21no—
242C2×Dic3—21no—
243C2×Dic3—21no—
244C2×Dic3—41no—
245D12—122no—
246D12—122no—
247D12—121no—
248D12—121no—
249D12—121no—
250D12—121no—
251D12—121no—
252D12—121no—
253D12—121no—
254D12—121no—
255D12—241no—
256D12—241no—
257D12—241no—
258D12—241no—
259D12—242no—
260C4×D3—242no—
261C4×D3—242no—
262Dic6—21no—
263Dic6—21no—
264Dic6—21no—
265Dic6—21no—
266Dic6—41no—
267Dic6—41no—
268C3×C8—41no—
269C3×C8—41no—
270C3×C8—81no—
271C3×C8—121no—
272C3⋊C8—41no—
273C3⋊C8—121no—
274C3⋊C8—121no—
275C3⋊C8—241no—
276C2×C32#44911yescharacteristic
277C2×C32#45211yescharacteristic
278C2×C32#45511yescharacteristic
279C3⋊D3—82no—
280C2×Q8—31no—
281C2×Q8—31no—
282C2×Q8—61no—
283C2×D4—92no—
284C2×D4—181no—
285C2×D4—181no—
286C22×C4—182no—
287Q16—362no—
288C2×C8—21no—
289C2×C8—61no—
290C2×C8—181no—
291C4⋊C4—31no—
292C4⋊C4—31no—
293C4⋊C4—61no—
294C4⋊C4—61no—
295C4⋊C4—61no—
296C4⋊C4—61no—
297C22⋊C4—182no—
298C22⋊C4—182no—
299C22⋊C4—182no—
300C42—61no—
301C42—61no—
302C42C2×D3211yescharacteristic
303C22×C3—21no—
304C22×C3#88211yescharacteristic
305C22×C3#93711yescharacteristic
306C2×D3—122no—
307C2×D3—122no—
308C2×D3—122no—
309C2×D3—122no—
310C2×D3—122no—
311C2×D3—122no—
312C2×D3—242no—
313C2×D3—242no—
314C2×D3—242no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—41no—
322C3×C4—121no—
323C3×C4—121no—
324C3×C4—121no—
325C3×C4—121no—
326C3×C4—241no—
327C3×C4#90411yescharacteristic
328C3×C4#90811yescharacteristic
329C3×C4#91411yescharacteristic
330C3×C4#91611yescharacteristic
331C3×C4#91611yescharacteristic
332C3×C4#91811yescharacteristic
333C3×C4#94211yescharacteristic
334C3×C4#95011yescharacteristic
335Dic3—41no—
336Dic3—41no—
337Dic3—41no—
338Dic3—41no—
339Dic3—81no—
340C32#164011yescharacteristic, complemented, Sylow
341C23—182no—
342Q8—61no—
343Q8—61no—
344Q8—61no—
345Q8—61no—
346Q8—121no—
347Q8—121no—
348D4—362no—
349D4—361no—
350D4—361no—
351D4—361no—
352D4—361no—
353C2×C4—61no—
354C2×C4—61no—
355C2×C4—61no—
356C2×C4—61no—
357C2×C4—121no—
358C2×C4—722no—
359C2×C4D3×D1211yescharacteristic
360C2×C4#380211yescharacteristic
361C2×C4D3×#6711yescharacteristic
362C8—41no—
363C8—121no—
364C8—361no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3#473411yescharacteristic
369C2×C3#480811yescharacteristic
370C2×C3#482511yescharacteristic
371C2×C3#504711yescharacteristic
372C2×C3#517211yescharacteristic
373C2×C3#520211yescharacteristic
374D3—242no—
375D3—242no—
376D3—482no—
377C22—362no—
378C22—362no—
379C22—362no—
380C22#6392211yescharacteristic
381C4—21no—
382C4—121no—
383C4—121no—
384C4—121no—
385C4—121no—
386C4—241no—
387C4#6379411yescharacteristic
388C4#6380611yescharacteristic
389C4#6393511yescharacteristic
390C4#6394811yescharacteristic
391C3—21no—
392C3#6826211yescharacteristic, complemented
393C3#7112811yescharacteristic, complemented
394C2—722no—
395C2#1059061611yescharacteristic
396C2#1059082311yescharacteristic
397C2#1059101111yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#64083C22
hypercenterC4⋊C8D32
hypocenterC32#1640
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×#4851C2semidirect
3. #10590384C2semidirect
6. C3×#4484C2semidirect
7. #10589084C2semidirect
33. #4851D3semidirect
40. #4484D3semidirect
340. C32#1640semidirect
392. C3#68262semidirect
393. C3#71128semidirect

Maximal subgroups

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

subgroupindex
#105939632
C3×#48512
#105903842
#105902812
#105893512
C3×#44842
#105890842
#711283
#682623