Finite Group Databasebeta

← #11781781

Subgroups — #11781781

Order 1152.

359 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 359 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C3×#4846C211yesmaximal, characteristic
2#10590387C211yesmaximal, characteristic, complemented
3#10590339C211yesmaximal, characteristic
4#10590269C211yesmaximal, characteristic
5#10589346C211yesmaximal, characteristic, complemented
6C3×#4486C211yesmaximal, characteristic, complemented
7#10589093C211yesmaximal, characteristic, complemented
8#71105—31nomaximal
9#68449—31nomaximal
10C3×C4×D12C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C2×#3718—21no—
14C2×#3718—21no—
15C2×#3711—21no—
16C32×C4⋊C8C2211yescharacteristic
17C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
18C4×C3⋊(C3⋊C8)C2211yescharacteristic
19C3×#821—21no—
20C3×#818—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22#63576—21no—
23#63562—21no—
24(C2×D3)⋊(C3⋊C8)—21no—
25C3×#474—31no—
26#5092—31no—
27#5092—31no—
28#5087—31no—
29#5012—31no—
30#5007—31no—
31#4846D311yescharacteristic
32#4838—31no—
33C3×#332—31no—
34#4547—31no—
35#4486D311yescharacteristic, complemented
36#4482—31no—
37#4480—31no—
38#4480—31no—
39#4480—61no—
40C2×C3×D12D411yescharacteristic
41C2×C3×C4×D3—21no—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—21no—
44C2×C32×C8—21no—
45C32×C42C2311yescharacteristic
46C2×C3⋊(C3⋊C8)—21no—
47C2×C3⋊(C3⋊C8)D411yescharacteristic
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49C3×(C2×D3)⋊C4—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3D411yescharacteristic
55C2×C3×C3⋊C8—21no—
56#3718—42no—
57#3718—42no—
58#3711—42no—
59#1689—91noSylow
60C3×C4⋊Q8—31no—
61C3×C4⋊Q8—31no—
62C3×C4×D4—31no—
63C2×#216—61no—
64C2×#216—61no—
65C2×#216—61no—
66C2×#216—61no—
67C2×#208—61no—
68C2×ΓL(1,𝔽25)—61no—
69C4×D12C2×D311yescharacteristic
70#869C2×D311yescharacteristic
71#869C2×D311yescharacteristic
72C3×#107—61no—
73C3×C4⋊C8—21no—
74C3×C4⋊C8—31no—
75C3×C4⋊C8C2×D311yescharacteristic
76C3×C4⋊C8C2×D311yescharacteristic
77C3×#102—61no—
78#832—61no—
79#830—61no—
80#821—21no—
81(C2×D3)⋊C8—61no—
82#818—21no—
83#809—61no—
84#807—61no—
85#807—61no—
86C4⋊(C3⋊C8)—31no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—61no—
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4×C3⋊C8—31no—
91C4×C3⋊C8—31no—
92C4×C3⋊C8—61no—
93C22×C3×D3—21no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C3×Dic3—21no—
98C2×C3×Dic3—41no—
99C2×C3×Dic3—41no—
100C3×D12—21no—
101C3×D12—21no—
102C3×C4×D3—41no—
103C3×C4×D3—41no—
104C3×Dic6—41no—
105C3×Dic6—41no—
106C3×Dic6—41no—
107C3×Dic6—41no—
108C32×C8—41no—
109C3⋊(C3⋊C8)—21no—
110C3⋊(C3⋊C8)—41no—
111C3⋊(C3⋊C8)D812yes—
112C3×C3⋊C8—41no—
113#494—91no—
114#474—31no—
115#474—91no—
116#436—91no—
117#334—91no—
118#332—31no—
119#332—91no—
120C2×C3×Q8—61no—
121C2×C3×Q8—61no—
122C2×C3×D4—31no—
123C22×C3×C4—61no—
124C2×D12#6711yescharacteristic
125C2×C4×D3—21no—
126C2×Dic6—21no—
127C2×Dic6—21no—
128C2×C3×C8—21no—
129C2×C3×C8—21no—
130C2×C3×C8—41no—
131C2×C3×C8—61no—
132C3×C4⋊C4—31no—
133C3×C4⋊C4—61no—
134C3×C4⋊C4—61no—
135C3×C4⋊C4—61no—
136C3×C4⋊C4—61no—
137C3×C22⋊C4—61no—
138C3×C42—21no—
139C3×C42C22×D311yescharacteristic
140C3×C42C22×D311yescharacteristic
141#216—122no—
142#216—122no—
143#216—122no—
144#216—122no—
145(C2×D3)⋊C4—21no—
146C4⋊Dic3—21no—
147C4⋊Dic3—21no—
148C4⋊Dic3—21no—
149C4⋊Dic3—21no—
150C4⋊Dic3#6711yescharacteristic
151#208—122no—
152C2×C3⋊C8—21no—
153C2×C3⋊C8—31no—
154C2×C3⋊C8—31no—
155C2×C3⋊C8—31no—
156C2×C3⋊C8—31no—
157C2×C3⋊C8—61no—
158C2×C3⋊C8—61no—
159C2×C3⋊C8—61no—
160C2×C3⋊C8—61no—
161C2×C3⋊C8—121no—
162ΓL(1,𝔽25)—122no—
163C22×C32#12111yescharacteristic
164C2×C3×D3—41no—
165C2×C3×D3—41no—
166C2×C3×D3—41no—
167C32×C4—21no—
168C32×C4C2×D811yescharacteristic
169C32×C4AGL(1,ℤ/8)11yescharacteristic
170C32×C4#13711yescharacteristic
171C32×C4#13711yescharacteristic
172C3×Dic3—41no—
173C3×Dic3—81no—
174C3×Dic3—81no—
175C2×Q16—181no—
176C2×Q16—181no—
177C2×M16—181no—
178C4⋊Q8—31no—
179C4⋊Q8—31no—
180C4×D4—31no—
181#107—61no—
182#107—181no—
183C4⋊C8—31no—
184C4⋊C8—91no—
185C4⋊C8D3211yescharacteristic
186#102—61no—
187#102—181no—
188C22⋊C8—181no—
189C4×C8—91no—
190C23×C3—61no—
191C22×D3—21no—
192C3×Q8—121no—
193C3×Q8—121no—
194C3×Q8—121no—
195C3×Q8—121no—
196C3×D4—61no—
197C3×D4—61no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—61no—
202C2×C3×C4—121no—
203C2×C3×C4—121no—
204C2×C3×C4—121no—
205C2×C3×C4—121no—
206C2×C3×C4#23511yescharacteristic
207C2×C3×C4D3×D411yescharacteristic
208C2×C3×C4D3×D411yescharacteristic
209C2×C3×C4D3×D411yescharacteristic
210C2×C3×C4#23711yescharacteristic
211C2×C3×C4C2×#6711yescharacteristic
212C2×Dic3—21no—
213C2×Dic3—41no—
214C2×Dic3—41no—
215D12—21no—
216D12—21no—
217C4×D3—41no—
218C4×D3—41no—
219Dic6—41no—
220Dic6—41no—
221Dic6—41no—
222Dic6—41no—
223C3×C8—41no—
224C3×C8—41no—
225C3×C8—81no—
226C3×C8—121no—
227C3⋊C8—32no—
228C3⋊C8—32no—
229C3⋊C8—41no—
230C3⋊C8—62no—
231C3⋊C8—61no—
232C3⋊C8—61no—
233C3⋊C8—121no—
234C3⋊C8—121no—
235C3⋊C8—121no—
236C3⋊C8—241no—
237C2×C32#45911yescharacteristic
238C2×C32#47011yescharacteristic
239C2×C32#47311yescharacteristic
240C3×D3—81no—
241C2×Q8—61no—
242C2×Q8—61no—
243C2×D4—31no—
244C22×C4—61no—
245Q16—362no—
246Q16—362no—
247M16—362no—
248C2×C8—21no—
249C2×C8—61no—
250C2×C8—91no—
251C2×C8—91no—
252C2×C8—181no—
253C4⋊C4—31no—
254C4⋊C4—61no—
255C4⋊C4—61no—
256C4⋊C4—61no—
257C4⋊C4—61no—
258C22⋊C4—61no—
259C42C2×D3211yescharacteristic
260C22×C3—21no—
261C22×C3—121no—
262C22×C3—121no—
263C22×C3—121no—
264C22×C3#88411yescharacteristic
265C22×C3#93911yescharacteristic
266C2×D3—41no—
267C2×D3—41no—
268C2×D3—41no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—41no—
276C3×C4—121no—
277C3×C4—241no—
278C3×C4—241no—
279C3×C4D3×D811yescharacteristic
280C3×C4D3×D811yescharacteristic
281C3×C4#91111yescharacteristic
282C3×C4#91411yescharacteristic
283C3×C4#91511yescharacteristic
284C3×C4#91811yescharacteristic
285C3×C4#94211yescharacteristic
286C3×C4#95111yescharacteristic
287Dic3—41no—
288Dic3—81no—
289Dic3—81no—
290C32#168911yescharacteristic, complemented, Sylow
291C23—61no—
292Q8—121no—
293Q8—121no—
294Q8—121no—
295Q8—121no—
296D4—61no—
297D4—61no—
298C2×C4—61no—
299C2×C4—121no—
300C2×C4—121no—
301C2×C4—121no—
302C2×C4—121no—
303C2×C4#379511yescharacteristic
304C2×C4#380211yescharacteristic
305C2×C4D3×#6711yescharacteristic
306C8—41no—
307C8—92no—
308C8—121no—
309C8—181no—
310C8—361no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—241no—
315C2×C3#475511yescharacteristic
316C2×C3#478611yescharacteristic
317C2×C3#481611yescharacteristic
318C2×C3#505211yescharacteristic
319C2×C3#515011yescharacteristic
320C2×C3#520411yescharacteristic
321D3—81no—
322C22—121no—
323C22—121no—
324C22—121no—
325C22#6388511yescharacteristic
326C4—21no—
327C4—121no—
328C4—241no—
329C4—241no—
330C4#6379711yescharacteristic
331C4#6379811yescharacteristic
332C4#6392911yescharacteristic
333C4#6394811yescharacteristic
334C3—21no—
335C3#6844911yescharacteristic, complemented
336C3#7110511yescharacteristic, complemented
337C2—241no—
338C2#1059052011yescharacteristic
339C2#1059074911yescharacteristic
340C2#1059098111yescharacteristic
subgroupG/H
centerC22#63885
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radicalC2×C3×D12D4
hypercenterC4⋊C8D32
hypocenterC32#1689
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. #10590387C2semidirect
5. #10589346C2semidirect
6. C3×#4486C2semidirect
7. #10589093C2semidirect
35. #4486D3semidirect
290. C32#1689semidirect
335. C3#68449semidirect
336. C3#71105semidirect

Maximal subgroups

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

subgroupindex
C3×#48462
#105903872
#105903392
#105902692
#105893462
C3×#44862
#105890932
#711053
#684493