Finite Group Databasebeta

← #11779348

Subgroups — #11779348

Order 1152.

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

normal subgroups only

This group has 484 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#10592549C211yesmaximal, characteristic, complemented
3#10590369C211yesmaximal, characteristic
4#10590283C211yesmaximal, characteristic, complemented
5C3×#4485C211yesmaximal, characteristic
6C3×#4484C211yesmaximal, characteristic, complemented
7#10589085C211yesmaximal, characteristic, complemented
8#68404—31nomaximal
9#68260—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×#3716—22no—
20C32×C4⋊C8C2211yescharacteristic
21#63645—21no—
22#63643—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63575—21no—
26#63566—21no—
27#5713—31no—
28#5585—31no—
29#5076—31no—
30#5021—31no—
31#4850—31no—
32#4850—31no—
33#4850—31no—
34#4850—61no—
35#4693—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#3716—44no—
65#1630—91noSylow
66C3×#127—31no—
67C3×C4×Q8—31no—
68#947—61no—
69#936—61no—
70#936—61no—
71#935—62no—
72D4×Dic3—61no—
73D4×Dic3—61no—
74C2×#214—62no—
75C2×#204—62no—
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#835—61no—
94#818—61no—
95#818—61no—
96#818—62no—
97#818—61no—
98#816—61no—
99#816—61no—
100#816—62no—
101#816—61no—
102#807—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—42no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—21no—
117C3×D12—42no—
118C3×D12—41no—
119C3×D12—41no—
120C3×D12—41no—
121C3×D12—41no—
122C3×Dic6—21no—
123C3×Dic6—21no—
124D3×Dic3—82no—
125C32×C8—41no—
126C3×C3⋊C8—22no—
127C3×C3⋊C8—41no—
128#559—91no—
129#492—91no—
130#477—91no—
131#477—91no—
132#331—31no—
133Q8⋊C8—31no—
134Q8⋊C8—91no—
135C2×C3×Q8—31no—
136C2×C3×D4—32no—
137C2×C3×D4—61no—
138C2×C3×D4—61no—
139C22×Dic3—62no—
140C2×D12—21no—
141C2×D12—21no—
142C2×D12D1212yes—
143C2×C4×D3—62no—
144C2×Dic6—31no—
145C2×Dic6—31no—
146C2×Dic6—61no—
147C2×Dic6—61no—
148C2×Dic6—61no—
149C2×Dic6—121no—
150C2×Dic6D1211yescharacteristic
151C2×C3×C8—22no—
152C2×C3×C8—21no—
153C2×C3×C8—21no—
154C2×C3×C8—61no—
155C2×C3×C8—61no—
156C3×C4⋊C4—31no—
157C3×C4⋊C4—61no—
158C3×C42—21no—
159C3×C42—61no—
160C3×C42C22×D311yescharacteristic
161C3×C42C22×D311yescharacteristic
162#217—62no—
163#217—62no—
164#217—62no—
165#214—124no—
166(C2×D3)⋊C4—62no—
167(C2×D3)⋊C4—62no—
168(C2×D3)⋊C4—62no—
169C4⋊Dic3—31no—
170C4⋊Dic3—31no—
171C4⋊Dic3—61no—
172C4⋊Dic3—62no—
173C4⋊Dic3—61no—
174C4⋊Dic3—61no—
175C4⋊Dic3—61no—
176C4⋊Dic3—61no—
177C4⋊Dic3—121no—
178C4⋊Dic3D1211yescharacteristic
179Dic3⋊C4—21no—
180Dic3⋊C4—61no—
181Dic3⋊C4—61no—
182Dic3⋊C4—121no—
183C4×Dic3—21no—
184C4×Dic3—61no—
185C4×Dic3—61no—
186C4×Dic3—121no—
187C2×C3⋊C8—21no—
188C2×C3⋊C8—21no—
189#204—124no—
190C22×C32#12011yescharacteristic
191C2×C3×D3—42no—
192C2×C3×D3—42no—
193C2×C3×D3—42no—
194C32×C4—21no—
195C32×C4#13511yescharacteristic
196C32×C4#13511yescharacteristic
197C32×C4#13711yescharacteristic
198C32×C4#13711yescharacteristic
199C3⋊Dic3—41no—
200C3⋊Dic3—41no—
201C3⋊Dic3—81no—
202C3×Dic3—41no—
203C3×Dic3—41no—
204C2×SD16—182no—
205C4⋊Q8—91no—
206#127—31no—
207#124—181no—
208#124—181no—
209#123—182no—
210C4×Q8—31no—
211C4×Q8—91no—
212C4×D4—181no—
213C4×D4—181no—
214#107—181no—
215#107—181no—
216C4⋊C8—31no—
217C4⋊C8D3211yescharacteristic
218#103—181no—
219#103—181no—
220C4×C8—31no—
221C23×C3—62no—
222C22×D3—22no—
223C3×Q8—61no—
224C3×Q8—61no—
225C3×D4—122no—
226C3×D4—121no—
227C3×D4—121no—
228C3×D4—121no—
229C3×D4—121no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—61no—
234C2×C3×C4—61no—
235C2×C3×C4C2×D1211yescharacteristic
236C2×C3×C4C2×D1211yescharacteristic
237C2×C3×C4D3×D411yescharacteristic
238C2×C3×C4D3×D411yescharacteristic
239C2×C3×C4D3×D411yescharacteristic
240C2×C3×C4D3×D411yescharacteristic
241C2×Dic3—21no—
242C2×Dic3—21no—
243C2×Dic3—61no—
244C2×Dic3—61no—
245C2×Dic3—61no—
246C2×Dic3—61no—
247C2×Dic3—121no—
248C2×Dic3—121no—
249C2×Dic3—122no—
250C2×Dic3—121no—
251C2×Dic3—121no—
252C2×Dic3—242no—
253D12—42no—
254D12—41no—
255D12—41no—
256D12—41no—
257D12—41no—
258C4×D3—242no—
259Dic6—21no—
260Dic6—21no—
261Dic6—62no—
262Dic6—61no—
263Dic6—61no—
264Dic6—61no—
265Dic6—61no—
266Dic6—121no—
267Dic6—122no—
268Dic6—122no—
269Dic6—242no—
270C3×C8—42no—
271C3×C8—41no—
272C3×C8—41no—
273C3×C8—62no—
274C3×C8—121no—
275C3⋊C8—22no—
276C3⋊C8—41no—
277C2×C32#45211yescharacteristic
278C2×C32#45211yescharacteristic
279C2×C32#45311yescharacteristic
280C3×D3—82no—
281C2×Q8—31no—
282C2×Q8—91no—
283C2×Q8—181no—
284C2×D4—32no—
285C2×D4—61no—
286C2×D4—61no—
287C22×C4—182no—
288SD16—364no—
289C2×C8—21no—
290C2×C8—61no—
291C2×C8—61no—
292C4⋊C4—31no—
293C4⋊C4—61no—
294C4⋊C4—91no—
295C4⋊C4—181no—
296C4⋊C4—181no—
297C4⋊C4—181no—
298C22⋊C4—182no—
299C22⋊C4—182no—
300C22⋊C4—182no—
301C42—61no—
302C42—181no—
303C42C2×D3211yescharacteristic
304C22×C3—21no—
305C22×C3—122no—
306C22×C3—122no—
307C22×C3—122no—
308C22×C3#88211yescharacteristic
309C22×C3#88211yescharacteristic
310C2×D3—42no—
311C2×D3—42no—
312C2×D3—42no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—41no—
320C3×C4—121no—
321C3×C4—121no—
322C3×C4#90411yescharacteristic
323C3×C4#90911yescharacteristic
324C3×C4#91211yescharacteristic
325C3×C4#91211yescharacteristic
326C3×C4#91511yescharacteristic
327C3×C4#91511yescharacteristic
328C3×C4#91611yescharacteristic
329C3×C4#91811yescharacteristic
330Dic3—41no—
331Dic3—41no—
332Dic3—122no—
333Dic3—121no—
334Dic3—121no—
335Dic3—121no—
336Dic3—121no—
337Dic3—241no—
338Dic3—242no—
339Dic3—241no—
340Dic3—241no—
341C32#163011yescharacteristic, complemented, Sylow
342C23—62no—
343Q8—61no—
344Q8—61no—
345Q8—181no—
346Q8—181no—
347Q8—362no—
348D4—122no—
349D4—121no—
350D4—121no—
351D4—121no—
352D4—121no—
353C2×C4—61no—
354C2×C4—61no—
355C2×C4—181no—
356C2×C4—181no—
357C2×C4—361no—
358C2×C4—722no—
359C2×C4D3×D1211yescharacteristic
360C2×C4D3×D1211yescharacteristic
361C2×C4#381111yescharacteristic
362C8—41no—
363C8—62no—
364C8—121no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—242no—
369C2×C3#473311yescharacteristic
370C2×C3#474711yescharacteristic
371C2×C3#478311yescharacteristic
372C2×C3#478311yescharacteristic
373C2×C3#480811yescharacteristic
374C2×C3#482211yescharacteristic
375D3—82no—
376C22—122no—
377C22—122no—
378C22—122no—
379C22#6392311yescharacteristic
380C4—21no—
381C4—121no—
382C4—121no—
383C4—361no—
384C4—361no—
385C4—721no—
386C4#6380011yescharacteristic
387C4#6380711yescharacteristic
388C4#6393611yescharacteristic
389C4#6395111yescharacteristic
390C3—21no—
391C3#6826011yescharacteristic, complemented
392C3#6840411yescharacteristic, complemented
393C2—242no—
394C2#1059061811yescharacteristic
395C2#1059096911yescharacteristic
396C2#1059101511yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radicalC3×#874C22
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. #10592549C2semidirect
4. #10590283C2semidirect
6. C3×#4484C2semidirect
7. #10589085C2semidirect
40. #4484D3semidirect
341. C32#1630semidirect
391. C3#68260semidirect
392. C3#68404semidirect

Maximal subgroups

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

subgroupindex
#105939512
#105925492
#105903692
#105902832
C3×#44852
C3×#44842
#105890852
#684043
#682603