Finite Group Databasebeta

← #11779789

Subgroups — #11779789

Order 1152.

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

normal subgroups only

This group has 472 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#10593951C211yesmaximal, characteristic
2#10592550C211yesmaximal, characteristic, complemented
3#10590385C211yesmaximal, characteristic, complemented
4#10590273C211yesmaximal, characteristic
5C3×#4485C211yesmaximal, characteristic
6C3×#4484C211yesmaximal, characteristic, complemented
7#10589085C211yesmaximal, characteristic, complemented
8#68406—31nomaximal
9#68262—31nomaximal
10#64078C2211yescharacteristic
11C4×#634C2211yescharacteristic
12C3×#874C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14#63898—21no—
15Dic3×D12—21no—
16#63884—22no—
17#63863—21no—
18#63860—21no—
19C2×#3719—21no—
20C32×C4⋊C8C2211yescharacteristic
21#63644—21no—
22#63643—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63567—21no—
26#63563—22no—
27#5713—31no—
28#5585—31no—
29#5070—31no—
30#5031—31no—
31#4851—31no—
32#4851—31no—
33#4851—61no—
34#4849—31no—
35#4694—31no—
36C3×#331—31no—
37C3×Q8⋊C8—31no—
38#4485D311yescharacteristic
39#4484—31no—
40#4484D311yescharacteristic, complemented
41#4456—31no—
42C2×#634—21no—
43C2×#634D411yescharacteristic
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12D412yes—
47C2×C3×Dic6D411yescharacteristic
48C2×D3×Dic3—22no—
49C2×C32×C8—21no—
50C32×C42C2311yescharacteristic
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)D411yescharacteristic
54#3750—21no—
55C4×C3⋊Dic3—21no—
56C3×C4⋊Dic3D411yescharacteristic
57C3×Dic3⋊C4—21no—
58C3×C4×Dic3—21no—
59C2×C3×C3⋊C8—21no—
60C2×C3×C3⋊C8—21no—
61(C2×D3)⋊Dic3—22no—
62(C2×D3)⋊Dic3—22no—
63(C2×D3)⋊Dic3—22no—
64#3719—42no—
65#1640—91noSylow
66C3×#127—31no—
67C3×C4×Q8—31no—
68#947—61no—
69C2×#216—61no—
70#936—61no—
71#936—61no—
72#935—62no—
73D4×Dic3—61no—
74D4×Dic3—61no—
75C2×Dic12—61no—
76#894—62no—
77#893—61no—
78#875—61no—
79#874C2×D311yescharacteristic
80C4×D12—61no—
81#869—31no—
82#869—31no—
83#869—61no—
84C4×Dic6—31no—
85C4×Dic6—31no—
86C4×Dic6—61no—
87C4×Dic6C2×D311yescharacteristic
88C3×C4⋊C8—21no—
89C3×C4⋊C8—31no—
90C3×C4⋊C8C2×D311yescharacteristic
91C3×C4⋊C8C2×D311yescharacteristic
92C3×C4×C8—31no—
93#832—62no—
94#821—62no—
95#817—61no—
96#817—61no—
97#817—62no—
98#816—61no—
99#816—61no—
100#816—62no—
101#816—61no—
102#810—61no—
103C4⋊(C3⋊C8)C2×D311yescharacteristic
104C4×C3⋊C8C2×D311yescharacteristic
105C22×C3×D3—22no—
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C3⋊Dic3—21no—
110C2×C3⋊Dic3—21no—
111C2×C3⋊Dic3—41no—
112#634—21no—
113#634—21no—
114#634—41no—
115#634—41no—
116C2×C3×Dic3—21no—
117C2×C3×Dic3—21no—
118C3×D12—42no—
119C3×D12—41no—
120C3×D12—41no—
121C3×D12—41no—
122C3×D12—41no—
123C3×Dic6—21no—
124C3×Dic6—21no—
125D3×Dic3—82no—
126C32×C8—41no—
127C3×C3⋊C8—41no—
128C3×C3⋊C8—41no—
129#559—91no—
130#486—91no—
131#475—91no—
132#462—91no—
133#331—31no—
134Q8⋊C8—31no—
135Q8⋊C8—91no—
136C2×C3×Q8—31no—
137C2×C3×D4—32no—
138C2×C3×D4—61no—
139C2×C3×D4—61no—
140C22×Dic3—62no—
141C2×D12—21no—
142C2×D12—21no—
143C2×D12D1212yes—
144C2×C4×D3—62no—
145C2×Dic6—31no—
146C2×Dic6—31no—
147C2×Dic6—61no—
148C2×Dic6—61no—
149C2×Dic6—61no—
150C2×Dic6—121no—
151C2×Dic6D1211yescharacteristic
152C2×C3×C8—22no—
153C2×C3×C8—21no—
154C2×C3×C8—21no—
155C2×C3×C8—61no—
156C2×C3×C8—61no—
157C3×C4⋊C4—31no—
158C3×C4⋊C4—61no—
159C3×C42—21no—
160C3×C42—61no—
161C3×C42C22×D311yescharacteristic
162C3×C42C22×D311yescharacteristic
163#217—62no—
164#217—62no—
165#217—62no—
166#216—122no—
167(C2×D3)⋊C4—62no—
168(C2×D3)⋊C4—62no—
169(C2×D3)⋊C4—62no—
170C4⋊Dic3—31no—
171C4⋊Dic3—31no—
172C4⋊Dic3—61no—
173C4⋊Dic3—62no—
174C4⋊Dic3—61no—
175C4⋊Dic3—61no—
176C4⋊Dic3—61no—
177C4⋊Dic3—61no—
178C4⋊Dic3—121no—
179C4⋊Dic3D1211yescharacteristic
180Dic3⋊C4—21no—
181Dic3⋊C4—61no—
182Dic3⋊C4—61no—
183Dic3⋊C4—121no—
184C4×Dic3—21no—
185C4×Dic3—61no—
186C4×Dic3—61no—
187C4×Dic3—121no—
188C2×C3⋊C8—21no—
189C2×C3⋊C8—21no—
190Dic12—122no—
191C22×C32#12011yescharacteristic
192C2×C3×D3—42no—
193C2×C3×D3—42no—
194C2×C3×D3—42no—
195C32×C4—21no—
196C32×C4#13511yescharacteristic
197C32×C4#13511yescharacteristic
198C32×C4AGL(1,ℤ/8)11yescharacteristic
199C32×C4#13711yescharacteristic
200C3⋊Dic3—41no—
201C3⋊Dic3—41no—
202C3⋊Dic3—81no—
203C3×Dic3—41no—
204C3×Dic3—41no—
205C2×Q16—181no—
206C4⋊Q8—91no—
207#127—31no—
208#124—181no—
209#124—181no—
210#123—182no—
211C4×Q8—31no—
212C4×Q8—91no—
213C4×D4—181no—
214C4×D4—181no—
215#106—181no—
216C4⋊C8—31no—
217C4⋊C8D3211yescharacteristic
218#103—181no—
219#103—181no—
220#102—182no—
221C4×C8—31no—
222C23×C3—62no—
223C22×D3—22no—
224C3×Q8—61no—
225C3×Q8—61no—
226C3×D4—122no—
227C3×D4—121no—
228C3×D4—121no—
229C3×D4—121no—
230C3×D4—121no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—61no—
235C2×C3×C4—61no—
236C2×C3×C4C2×D1211yescharacteristic
237C2×C3×C4C2×D1211yescharacteristic
238C2×C3×C4D3×D411yescharacteristic
239C2×C3×C4D3×D411yescharacteristic
240C2×C3×C4D3×D411yescharacteristic
241C2×C3×C4D3×D411yescharacteristic
242C2×Dic3—21no—
243C2×Dic3—21no—
244C2×Dic3—61no—
245C2×Dic3—61no—
246C2×Dic3—61no—
247C2×Dic3—61no—
248C2×Dic3—121no—
249C2×Dic3—121no—
250C2×Dic3—122no—
251C2×Dic3—121no—
252C2×Dic3—121no—
253C2×Dic3—242no—
254D12—42no—
255D12—41no—
256D12—41no—
257D12—41no—
258D12—41no—
259C4×D3—242no—
260Dic6—21no—
261Dic6—21no—
262Dic6—62no—
263Dic6—61no—
264Dic6—61no—
265Dic6—61no—
266Dic6—61no—
267Dic6—121no—
268Dic6—121no—
269Dic6—121no—
270Dic6—121no—
271Dic6—121no—
272Dic6—241no—
273Dic6—241no—
274C3×C8—42no—
275C3×C8—41no—
276C3×C8—41no—
277C3×C8—121no—
278C3×C8—121no—
279C3⋊C8—41no—
280C3⋊C8—41no—
281C2×C32#44911yescharacteristic
282C2×C32#45211yescharacteristic
283C2×C32#45511yescharacteristic
284C3×D3—82no—
285C2×Q8—31no—
286C2×Q8—91no—
287C2×Q8—181no—
288C2×D4—32no—
289C2×D4—61no—
290C2×D4—61no—
291C22×C4—182no—
292Q16—362no—
293C2×C8—21no—
294C2×C8—61no—
295C2×C8—61no—
296C4⋊C4—31no—
297C4⋊C4—61no—
298C4⋊C4—91no—
299C4⋊C4—181no—
300C4⋊C4—181no—
301C4⋊C4—181no—
302C22⋊C4—182no—
303C22⋊C4—182no—
304C22⋊C4—182no—
305C42—61no—
306C42—181no—
307C42C2×D3211yescharacteristic
308C22×C3—21no—
309C22×C3—122no—
310C22×C3—122no—
311C22×C3—122no—
312C22×C3#88211yescharacteristic
313C22×C3#88211yescharacteristic
314C2×D3—42no—
315C2×D3—42no—
316C2×D3—42no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—41no—
324C3×C4—121no—
325C3×C4—121no—
326C3×C4#90411yescharacteristic
327C3×C4#90811yescharacteristic
328C3×C4#91111yescharacteristic
329C3×C4#91211yescharacteristic
330C3×C4#91511yescharacteristic
331C3×C4#91611yescharacteristic
332C3×C4#91611yescharacteristic
333C3×C4#91811yescharacteristic
334Dic3—41no—
335Dic3—41no—
336Dic3—122no—
337Dic3—121no—
338Dic3—121no—
339Dic3—121no—
340Dic3—121no—
341Dic3—241no—
342Dic3—242no—
343Dic3—241no—
344Dic3—241no—
345C32#164011yescharacteristic, complemented, Sylow
346C23—62no—
347Q8—61no—
348Q8—61no—
349Q8—181no—
350Q8—181no—
351Q8—361no—
352Q8—361no—
353D4—122no—
354D4—121no—
355D4—121no—
356D4—121no—
357D4—121no—
358C2×C4—61no—
359C2×C4—61no—
360C2×C4—181no—
361C2×C4—181no—
362C2×C4—361no—
363C2×C4—722no—
364C2×C4D3×D1211yescharacteristic
365C2×C4D3×D1211yescharacteristic
366C2×C4#381111yescharacteristic
367C8—41no—
368C8—121no—
369C8—121no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—242no—
374C2×C3#473411yescharacteristic
375C2×C3#474611yescharacteristic
376C2×C3#478111yescharacteristic
377C2×C3#478311yescharacteristic
378C2×C3#480811yescharacteristic
379C2×C3#482511yescharacteristic
380D3—82no—
381C22—122no—
382C22—122no—
383C22—122no—
384C22#6392311yescharacteristic
385C4—21no—
386C4—121no—
387C4—121no—
388C4—361no—
389C4—361no—
390C4—721no—
391C4#6379511yescharacteristic
392C4#6380611yescharacteristic
393C4#6393611yescharacteristic
394C4#6395111yescharacteristic
395C3—21no—
396C3#6826211yescharacteristic, complemented
397C3#6840611yescharacteristic, complemented
398C2—242no—
399C2#1059061811yescharacteristic
400C2#1059096811yescharacteristic
401C2#1059101611yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radicalC3×#874C22
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. #10592550C2semidirect
3. #10590385C2semidirect
6. C3×#4484C2semidirect
7. #10589085C2semidirect
40. #4484D3semidirect
345. C32#1640semidirect
396. C3#68262semidirect
397. C3#68406semidirect

Maximal subgroups

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

subgroupindex
#105939512
#105925502
#105903852
#105902732
C3×#44852
C3×#44842
#105890852
#684063
#682623