Finite Group Databasebeta

← #11779782

Subgroups — #11779782

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#10593951C211yesmaximal, characteristic
2#10592548C211yesmaximal, characteristic, complemented
3#10590301C211yesmaximal, characteristic, complemented
4#10590273C211yesmaximal, characteristic
5C3×#4485C211yesmaximal, characteristic
6C3×#4484C211yesmaximal, characteristic, complemented
7#10589085C211yesmaximal, characteristic, complemented
8#68406—31nomaximal
9#68254—31nomaximal
10C2×#3746—21no—
11#64078C2211yescharacteristic
12C4×#634C2211yescharacteristic
13C3×#874C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63898—21no—
16Dic3×D12—21no—
17#63884—22no—
18#63863—21no—
19#63860—21no—
20C32×C4⋊C8C2211yescharacteristic
21#63643—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24#63573—21no—
25#63566—21no—
26#63563—22no—
27#5713—31no—
28#5585—31no—
29#5070—31no—
30#5020—31no—
31#4851—31no—
32#4849—31no—
33#4849—31no—
34#4849—61no—
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—
56#3746—42no—
57C3×C4⋊Dic3D411yescharacteristic
58C3×Dic3⋊C4—21no—
59C3×C4×Dic3—21no—
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62(C2×D3)⋊Dic3—22no—
63(C2×D3)⋊Dic3—22no—
64(C2×D3)⋊Dic3—22no—
65#1640—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×Dic12—61no—
75C2×Dic12—61no—
76C2×Dic12—62no—
77#894—62no—
78#893—61no—
79#875—61no—
80#874C2×D311yescharacteristic
81C4×D12—61no—
82#869—31no—
83#869—31no—
84#869—61no—
85C4×Dic6—31no—
86C4×Dic6—31no—
87C4×Dic6—61no—
88C4×Dic6C2×D311yescharacteristic
89C3×C4⋊C8—21no—
90C3×C4⋊C8—31no—
91C3×C4⋊C8C2×D311yescharacteristic
92C3×C4⋊C8C2×D311yescharacteristic
93C3×C4×C8—31no—
94#835—61no—
95#832—62no—
96#821—62no—
97#817—61no—
98#816—61no—
99#816—61no—
100#816—62no—
101#816—61no—
102#808—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—62no—
149C2×Dic6—61no—
150C2×Dic6—61no—
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(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—61no—
173C4⋊Dic3—61no—
174C4⋊Dic3—61no—
175C4⋊Dic3—61no—
176C4⋊Dic3—121no—
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—
189Dic12—124no—
190Dic12—122no—
191Dic12—122no—
192C22×C32#12011yescharacteristic
193C2×C3×D3—42no—
194C2×C3×D3—42no—
195C2×C3×D3—42no—
196C32×C4—21no—
197C32×C4#13511yescharacteristic
198C32×C4#13511yescharacteristic
199C32×C4AGL(1,ℤ/8)11yescharacteristic
200C32×C4#13711yescharacteristic
201C3⋊Dic3—41no—
202C3⋊Dic3—41no—
203C3⋊Dic3—81no—
204C3×Dic3—41no—
205C3×Dic3—41no—
206C2×Q16—181no—
207C4⋊Q8—91no—
208#127—31no—
209#124—181no—
210#124—181no—
211#123—182no—
212C4×Q8—31no—
213C4×Q8—91no—
214C4×D4—181no—
215C4×D4—181no—
216#106—181no—
217C4⋊C8—31no—
218C4⋊C8D3211yescharacteristic
219#103—181no—
220#103—181no—
221#102—182no—
222C4×C8—31no—
223C23×C3—62no—
224C22×D3—22no—
225C3×Q8—61no—
226C3×Q8—61no—
227C3×D4—122no—
228C3×D4—121no—
229C3×D4—121no—
230C3×D4—121no—
231C3×D4—121no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—61no—
236C2×C3×C4—61no—
237C2×C3×C4C2×D1211yescharacteristic
238C2×C3×C4C2×D1211yescharacteristic
239C2×C3×C4D3×D411yescharacteristic
240C2×C3×C4D3×D411yescharacteristic
241C2×C3×C4D3×D411yescharacteristic
242C2×C3×C4D3×D411yescharacteristic
243C2×Dic3—21no—
244C2×Dic3—21no—
245C2×Dic3—61no—
246C2×Dic3—61no—
247C2×Dic3—61no—
248C2×Dic3—61no—
249C2×Dic3—121no—
250C2×Dic3—121no—
251C2×Dic3—122no—
252C2×Dic3—121no—
253C2×Dic3—121no—
254C2×Dic3—242no—
255D12—42no—
256D12—41no—
257D12—41no—
258D12—41no—
259D12—41no—
260C4×D3—242no—
261Dic6—21no—
262Dic6—21no—
263Dic6—62no—
264Dic6—61no—
265Dic6—61no—
266Dic6—61no—
267Dic6—61no—
268Dic6—121no—
269Dic6—122no—
270Dic6—122no—
271Dic6—121no—
272Dic6—121no—
273Dic6—121no—
274Dic6—121no—
275C3×C8—42no—
276C3×C8—41no—
277C3×C8—41no—
278C3×C8—121no—
279C3×C8—121no—
280C3⋊C8—41no—
281C3⋊C8—41no—
282C2×C32#44911yescharacteristic
283C2×C32#45211yescharacteristic
284C2×C32#45511yescharacteristic
285C3×D3—82no—
286C2×Q8—31no—
287C2×Q8—91no—
288C2×Q8—181no—
289C2×D4—32no—
290C2×D4—61no—
291C2×D4—61no—
292C22×C4—182no—
293Q16—362no—
294C2×C8—21no—
295C2×C8—61no—
296C2×C8—61no—
297C4⋊C4—31no—
298C4⋊C4—61no—
299C4⋊C4—91no—
300C4⋊C4—181no—
301C4⋊C4—181no—
302C4⋊C4—181no—
303C22⋊C4—182no—
304C22⋊C4—182no—
305C22⋊C4—182no—
306C42—61no—
307C42—181no—
308C42C2×D3211yescharacteristic
309C22×C3—21no—
310C22×C3—122no—
311C22×C3—122no—
312C22×C3—122no—
313C22×C3#88211yescharacteristic
314C22×C3#88211yescharacteristic
315C2×D3—42no—
316C2×D3—42no—
317C2×D3—42no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—41no—
325C3×C4—121no—
326C3×C4—121no—
327C3×C4#90411yescharacteristic
328C3×C4#90911yescharacteristic
329C3×C4#91111yescharacteristic
330C3×C4#91211yescharacteristic
331C3×C4#91411yescharacteristic
332C3×C4#91511yescharacteristic
333C3×C4#91611yescharacteristic
334C3×C4#91911yescharacteristic
335Dic3—41no—
336Dic3—41no—
337Dic3—122no—
338Dic3—121no—
339Dic3—121no—
340Dic3—121no—
341Dic3—121no—
342Dic3—241no—
343Dic3—242no—
344Dic3—241no—
345Dic3—241no—
346C32#164011yescharacteristic, complemented, Sylow
347C23—62no—
348Q8—61no—
349Q8—61no—
350Q8—181no—
351Q8—181no—
352Q8—361no—
353Q8—361no—
354D4—122no—
355D4—121no—
356D4—121no—
357D4—121no—
358D4—121no—
359C2×C4—61no—
360C2×C4—61no—
361C2×C4—181no—
362C2×C4—181no—
363C2×C4—361no—
364C2×C4—722no—
365C2×C4D3×D1211yescharacteristic
366C2×C4D3×D1211yescharacteristic
367C2×C4#381111yescharacteristic
368C8—41no—
369C8—121no—
370C8—121no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—242no—
375C2×C3#473311yescharacteristic
376C2×C3#474611yescharacteristic
377C2×C3#478111yescharacteristic
378C2×C3#478311yescharacteristic
379C2×C3#481011yescharacteristic
380C2×C3#482511yescharacteristic
381D3—82no—
382C22—122no—
383C22—122no—
384C22—122no—
385C22#6392311yescharacteristic
386C4—21no—
387C4—121no—
388C4—121no—
389C4—361no—
390C4—361no—
391C4—721no—
392C4#6380011yescharacteristic
393C4#6380711yescharacteristic
394C4#6393711yescharacteristic
395C4#6395011yescharacteristic
396C3—21no—
397C3#6825411yescharacteristic, complemented
398C3#6840611yescharacteristic, complemented
399C2—242no—
400C2#1059061711yescharacteristic
401C2#1059096911yescharacteristic
402C2#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. #10592548C2semidirect
3. #10590301C2semidirect
6. C3×#4484C2semidirect
7. #10589085C2semidirect
40. #4484D3semidirect
346. C32#1640semidirect
397. C3#68254semidirect
398. C3#68406semidirect

Maximal subgroups

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

subgroupindex
#105939512
#105925482
#105903012
#105902732
C3×#44852
C3×#44842
#105890852
#684063
#682543