Finite Group Databasebeta

← #11780554

Subgroups — #11780554

Order 1152.

394 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 70 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#10593868C211yesmaximal, characteristic, complemented
2C3×#4713C211yesmaximal, characteristic
3#10590279C211yesmaximal, characteristic
4#10590275C211yesmaximal, characteristic
5#10589331C211yesmaximal, characteristic, complemented
6C3×#4465C211yesmaximal, characteristic, complemented
7#10589088C211yesmaximal, characteristic, complemented
8#71250—31nomaximal
9#68375—31nomaximal
10#64079C2211yescharacteristic
11C3×#874C2211yescharacteristic
12C3×#870C2211yescharacteristic
13C3×#870C2211yescharacteristic
14#63847—21no—
15#63847—21no—
16#63846—21no—
17#63846—21no—
18#63845—21no—
19#63845—21no—
20C32×#97C2211yescharacteristic
21#63630C2211yescharacteristic
22C3×#821—21no—
23C3×#821—21no—
24C3×#803C2211yescharacteristic
25#63563—21no—
26#63563—21no—
27#63562—21no—
28#63562—21no—
29C3⋊#564—31no—
30C3⋊#564—31no—
31C3×#490—31no—
32#5071—31no—
33#5071—31no—
34#5067—31no—
35#4713—31no—
36#4713D311yescharacteristic
37C3×#330—31no—
38#4543—31no—
39#4465—31no—
40#4465—31no—
41#4465—31no—
42#4465—61no—
43#4465D311yescharacteristic, complemented
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C32×C8—21no—
48C32×C42C2311yescharacteristic
49C4⋊(C3⋊Dic3)D411yescharacteristic
50C4⋊(C3⋊Dic3)D411yescharacteristic
51#3750—21no—
52#3750—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C3×C4⋊Dic3D411yescharacteristic
55C3×C4⋊Dic3D411yescharacteristic
56C3×C4⋊Dic3D411yescharacteristic
57C3×C4⋊Dic3D411yescharacteristic
58C3×Dic3⋊C4—21no—
59C3×Dic3⋊C4—21no—
60C3×Dic3⋊C4—21no—
61C3×Dic3⋊C4—21no—
62C2×C3×C3⋊C8—21no—
63#3724—21no—
64#3724—21no—
65Dic3⋊Dic3—21no—
66Dic3⋊Dic3—21no—
67Dic3⋊Dic3—21no—
68Dic3⋊Dic3—21no—
69Dic32—21no—
70Dic32—21no—
71#1658—91noSylow
72C3×#127—31no—
73C3×#125—31no—
74C3×#125—31no—
75#890—61no—
76#890—61no—
77#890—61no—
78#890—61no—
79#889—61no—
80#889—61no—
81#889—61no—
82#889—61no—
83#889—61no—
84#889—61no—
85#889—61no—
86#889—61no—
87#874C2×D311yescharacteristic
88#870—31no—
89#870—31no—
90#870—61no—
91#870C2×D311yescharacteristic
92#870C2×D311yescharacteristic
93C3×#102—61no—
94C3×#102—61no—
95C3×#97—21no—
96C3×#97—31no—
97C3×#97C2×D311yescharacteristic
98C3×#97C2×D311yescharacteristic
99#832—61no—
100#832—61no—
101#832—61no—
102#832—61no—
103#821—21no—
104#821—21no—
105#821—61no—
106#821—61no—
107#809—61no—
108#809—61no—
109#803—31no—
110#803—31no—
111#803—61no—
112#803C2×D311yescharacteristic
113C22×C3×D3—41no—
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C3⋊Dic3—21no—
118C2×C3⋊Dic3—21no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—21no—
123C3×D12—42no—
124C3×D12—42no—
125C3×D12—42no—
126C32×C8—41no—
127C3⋊(C3⋊C8)—41no—
128C3×C3⋊C8—41no—
129#564—91no—
130#490—31no—
131#490—91no—
132#490—91no—
133#330—31no—
134#330—91no—
135#330—91no—
136C2×C3×D4—61no—
137C2×C3×D4—61no—
138C2×C3×D4—61no—
139C2×D12—21no—
140C2×D12—21no—
141C2×D12—21no—
142C2×C3×C8—21no—
143C2×C3×C8—21no—
144C2×C3×C8—41no—
145C2×C3×C8—61no—
146C3×C4⋊C4—31no—
147C3×C4⋊C4—31no—
148C3×C4⋊C4—31no—
149C3×C4⋊C4—31no—
150C3×C4⋊C4—61no—
151C3×C4⋊C4—61no—
152C3×C4⋊C4—61no—
153C3×C4⋊C4—61no—
154C3×C42—21no—
155C3×C42C22×D311yescharacteristic
156C3×C42C22×D311yescharacteristic
157C4⋊Dic3—31no—
158C4⋊Dic3—31no—
159C4⋊Dic3—31no—
160C4⋊Dic3—31no—
161C4⋊Dic3—61no—
162C4⋊Dic3—61no—
163C4⋊Dic3—61no—
164C4⋊Dic3—61no—
165C4⋊Dic3—61no—
166C4⋊Dic3—61no—
167C4⋊Dic3D1211yescharacteristic
168C4⋊Dic3D1211yescharacteristic
169C4⋊Dic3#6711yescharacteristic
170C4⋊Dic3#6711yescharacteristic
171Dic3⋊C4—21no—
172Dic3⋊C4—21no—
173Dic3⋊C4—21no—
174Dic3⋊C4—21no—
175Dic3⋊C4—61no—
176Dic3⋊C4—61no—
177Dic3⋊C4—61no—
178Dic3⋊C4—61no—
179Dic3⋊C4—61no—
180Dic3⋊C4—61no—
181Dic3⋊C4—61no—
182Dic3⋊C4—61no—
183Dic3⋊C4—61no—
184Dic3⋊C4—61no—
185Dic3⋊C4—61no—
186Dic3⋊C4—61no—
187Dic3⋊C4—121no—
188Dic3⋊C4—121no—
189C4×Dic3—61no—
190C4×Dic3—61no—
191C4×Dic3—61no—
192C4×Dic3—61no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—61no—
195C2×C3⋊C8—61no—
196C2×C3⋊C8—121no—
197C22×C32#12011yescharacteristic
198C2×C3×D3—81no—
199C2×C3×D3—81no—
200C2×C3×D3—81no—
201C32×C4—21no—
202C32×C4—21no—
203C32×C4—21no—
204C3⋊Dic3—41no—
205C3⋊Dic3—41no—
206C3×Dic3—41no—
207C3×Dic3—41no—
208C3×Dic3—41no—
209C3×Dic3—41no—
210#127—31no—
211#125—31no—
212#125—31no—
213#125—91no—
214#125—181no—
215#125—181no—
216#125—181no—
217#125—181no—
218#125—181no—
219#125—181no—
220#102—61no—
221#102—61no—
222#102—181no—
223#102—181no—
224#102—181no—
225#102—181no—
226#97—31no—
227#97—91no—
228#97D3211yescharacteristic
229C23×C3—121no—
230C22×D3—41no—
231C3×D4—122no—
232C3×D4—122no—
233C3×D4—122no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—61no—
238C2×C3×C4—61no—
239C2×C3×C4—61no—
240C2×C3×C4—61no—
241C2×C3×C4C2×D1211yescharacteristic
242C2×C3×C4D3×D411yescharacteristic
243C2×C3×C4D3×D411yescharacteristic
244C2×C3×C4D3×D411yescharacteristic
245C2×C3×C4D3×D411yescharacteristic
246C2×C3×C4C2×#6711yescharacteristic
247C2×Dic3—21no—
248C2×Dic3—21no—
249C2×Dic3—21no—
250C2×Dic3—21no—
251C2×Dic3—61no—
252C2×Dic3—61no—
253C2×Dic3—61no—
254C2×Dic3—61no—
255C2×Dic3—121no—
256C2×Dic3—121no—
257D12—42no—
258D12—42no—
259D12—42no—
260C3×C8—41no—
261C3×C8—41no—
262C3×C8—42no—
263C3×C8—121no—
264C3⋊C8—41no—
265C3⋊C8—121no—
266C3⋊C8—121no—
267C3⋊C8—122no—
268C2×C32#45411yescharacteristic
269C2×C32#45411yescharacteristic
270C2×C32#45411yescharacteristic
271C3×D3—161no—
272C2×D4—61no—
273C2×D4—61no—
274C2×D4—61no—
275C2×C8—21no—
276C2×C8—61no—
277C2×C8—181no—
278C4⋊C4—31no—
279C4⋊C4—31no—
280C4⋊C4—31no—
281C4⋊C4—31no—
282C4⋊C4—61no—
283C4⋊C4—61no—
284C4⋊C4—61no—
285C4⋊C4—61no—
286C4⋊C4—91no—
287C4⋊C4—91no—
288C4⋊C4—181no—
289C4⋊C4—181no—
290C4⋊C4—181no—
291C4⋊C4—181no—
292C4⋊C4—181no—
293C4⋊C4—181no—
294C4⋊C4—181no—
295C4⋊C4—181no—
296C42—181no—
297C42—181no—
298C42C2×D3211yescharacteristic
299C22×C3—21no—
300C22×C3—241no—
301C22×C3—241no—
302C22×C3—241no—
303C22×C3#88211yescharacteristic
304C22×C3#93711yescharacteristic
305C2×D3—81no—
306C2×D3—81no—
307C2×D3—81no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—41no—
315C3×C4—41no—
316C3×C4—41no—
317C3×C4—121no—
318C3×C4—121no—
319C3×C4—121no—
320C3×C4—121no—
321Dic3—41no—
322Dic3—41no—
323Dic3—41no—
324Dic3—41no—
325Dic3—121no—
326Dic3—121no—
327Dic3—121no—
328Dic3—121no—
329Dic3—241no—
330Dic3—241no—
331C32#165811yescharacteristic, complemented, Sylow
332C23—121no—
333D4—122no—
334D4—122no—
335D4—122no—
336C2×C4—61no—
337C2×C4—61no—
338C2×C4—61no—
339C2×C4—61no—
340C2×C4—181no—
341C2×C4—181no—
342C2×C4D3×D1211yescharacteristic
343C2×C4#380211yescharacteristic
344C2×C4D3×#6711yescharacteristic
345C8—41no—
346C8—121no—
347C8—361no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—481no—
352C2×C3#475311yescharacteristic
353C2×C3#482711yescharacteristic
354C2×C3#482711yescharacteristic
355C2×C3#506211yescharacteristic
356C2×C3#520111yescharacteristic
357C2×C3#520111yescharacteristic
358D3—161no—
359C22—241no—
360C22—241no—
361C22—241no—
362C22#6392211yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—121no—
367C4—121no—
368C4—121no—
369C4—121no—
370C4—361no—
371C4—361no—
372C3—21no—
373C3#6837511yescharacteristic, complemented
374C3#7125011yescharacteristic, complemented
375C2—481no—
376C2#1059040011yescharacteristic
377C2#1059101911yescharacteristic
378C2#1059102011yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#97C22
socleC22×C32#120
prime radicalC3×#874C22
hypercenter#97D32
hypocenterC32#1658
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #10593868C2semidirect
5. #10589331C2semidirect
6. C3×#4465C2semidirect
7. #10589088C2semidirect
43. #4465D3semidirect
331. C32#1658semidirect
373. C3#68375semidirect
374. C3#71250semidirect

Maximal subgroups

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

subgroupindex
#105938682
C3×#47132
#105902792
#105902752
#105893312
C3×#44652
#105890882
#712503
#683753