Finite Group Databasebeta

← #11778787

Subgroups — #11778787

Order 1152.

559 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 559 conjugacy classes of subgroups — too many to draw. Only its 92 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×#5510C211yesmaximal, characteristic
2#10592685C211yesmaximal, characteristic, complemented
3#10591092C212yesmaximal, complemented
4C3×#4528C211yesmaximal, characteristic, complemented
5#10589150C212yesmaximal, complemented
6#71875—31nomaximal
7#68137—31nomaximal
8C2×C3×#235—21no—
9C2×C32×C4⋊C4C2211yescharacteristic
10C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
11C3×#930—21no—
12C3×#930C2212yes—
13C3×#897—22no—
14C3×#895—22no—
15#63658—21no—
16#63658—21no—
17#63658C2211yescharacteristic
18C3×#830C2212yes—
19#63573—22no—
20#63563—22no—
21C3×#537—31no—
22#5510D311yescharacteristic
23#5034—32no—
24#4986—31no—
25#4986—31no—
26#4986—61no—
27#4735—32no—
28C3×#324—31no—
29#4537—32no—
30#4528D311yescharacteristic, complemented
31#4470—32no—
32C22×C32×C4D411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3—21no—
37C2×C3×#67—22no—
38C3×#235—42no—
39C3×#235—42no—
40C2×C3×D12—21no—
41C2×C3×D12—21no—
42C2×C3×D12D412yes—
43C2×C3×C4×D3—22no—
44C2×C3×Dic6—21no—
45C32×C4⋊C4—22no—
46C4⋊(C3⋊Dic3)—22no—
47C3×(C2×D3)⋊C4—22no—
48C3×(C2×D3)⋊C4—22no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3D412yes—
51C2×C3×C3⋊C8—22no—
52#1616—91noSylow
53C2×C3×#41—61no—
54C2×#235—21no—
55C3×C22⋊Q8—62no—
56C3×#121—32no—
57C3×#121—62no—
58C3×#121—61no—
59C2×C3×C4⋊C4—21no—
60C2×C3×C4⋊C4C2×D311yescharacteristic
61C2×C3×C4⋊C4C2×D311yescharacteristic
62#930—21no—
63#930C2×D312yes—
64C2×C4⋊Dic3—31no—
65C2×C4⋊Dic3—31no—
66C2×C4⋊Dic3—61no—
67#897—22no—
68#895—22no—
69C3×C22⋊C8—32no—
70#832—62no—
71C3⋊#95—31no—
72C3⋊#95—31no—
73C3⋊#95—61no—
74C3⋊#95—62no—
75C3⋊#95—62no—
76C3⋊#95—61no—
77C3⋊#95—61no—
78C3⋊#95—61no—
79C3⋊#95—61no—
80#830C2×D312yes—
81#821—62no—
82#817—62no—
83#808—62no—
84C23×C32C2×D411yescharacteristic
85C22×C3×D3—22no—
86C2×C32×C4—21no—
87C2×C32×C4—21no—
88C2×C32×C4—21no—
89C2×C32×C4—41no—
90C2×C32×C4—41no—
91C2×C32×C4SD1612yes—
92C2×C32×C4C2×D412yes—
93C2×C3⋊Dic3—41no—
94C2×C3⋊Dic3—41no—
95C2×C3⋊Dic3—42no—
96C2×C3⋊Dic3—41no—
97C2×C3⋊Dic3—41no—
98C3×#67—42no—
99C3×#67—42no—
100C2×C3×Dic3—22no—
101C3×D12—42no—
102C3×D12—42no—
103C3×D12—81no—
104C3×C4×D3—44no—
105C3×Dic6—42no—
106C3×C3⋊C8—42no—
107#537—31no—
108#481—92no—
109#400—91no—
110#327—92no—
111#324—31no—
112C3×#41—122no—
113C3×#41—122no—
114C2×C3×Q8—61no—
115C2×C3×D4—32no—
116C2×C3×D4—61no—
117C2×C3×D4—61no—
118C2×C3×D4—62no—
119C22×C3×C4—21no—
120C22×C3×C4—21no—
121C22×C3×C4—21no—
122C22×C3×C4—62no—
123C22×C3×C4D1211yescharacteristic
124C22×C3×C4D1211yescharacteristic
125C22×C3×C4#6711yescharacteristic
126C22×C3×C4#6711yescharacteristic
127C22×C3×C4C22×D311yescharacteristic
128C22×C3×C4C22×D311yescharacteristic
129C2×#67—22no—
130C22×Dic3—62no—
131C22×Dic3—62no—
132C22×Dic3—61no—
133C22×Dic3—61no—
134C22×Dic3—61no—
135C22×Dic3—61no—
136#235—42no—
137#235—42no—
138C2×D12—21no—
139C2×D12—21no—
140C2×D12#6712yes—
141C2×C4×D3—22no—
142C2×Dic6—21no—
143C2×C3×C8—62no—
144C3×C4⋊C4—22no—
145C3×C4⋊C4—22no—
146C3×C4⋊C4—32no—
147C3×C4⋊C4—42no—
148C3×C4⋊C4—61no—
149C3×C22⋊C4—62no—
150C3×C22⋊C4—62no—
151(C2×D3)⋊C4—22no—
152(C2×D3)⋊C4—22no—
153C4⋊Dic3—21no—
154C4⋊Dic3—62no—
155C4⋊Dic3—62no—
156C4⋊Dic3—122no—
157C4⋊Dic3#6712yes—
158C2×C3⋊C8—22no—
159C22×C32—21no—
160C22×C32—21no—
161C22×C32#12011yescharacteristic
162C22×C32C2×SD1611yescharacteristic
163C22×C32AGL(1,ℤ/8)11yescharacteristic
164C2×C3×D3—42no—
165C2×C3×D3—42no—
166C2×C3×D3—42no—
167C32×C4—22no—
168C32×C4—22no—
169C32×C4—41no—
170C3⋊Dic3—81no—
171C3⋊Dic3—81no—
172C3×Dic3—42no—
173C2×#41—61no—
174C22⋊Q8—62no—
175#121—32no—
176#121—62no—
177#121—61no—
178C2×C4⋊C4—91no—
179C2×C4⋊C4D3211yescharacteristic
180#106—182no—
181#102—182no—
182C22⋊C8—32no—
183#95—91no—
184#95—181no—
185#95—181no—
186C23×C3—21no—
187C23×C3—62no—
188C23×C3C2×D1211yescharacteristic
189C23×C3C2×#6711yescharacteristic
190C22×D3—22no—
191C3×Q8—122no—
192C3×D4—122no—
193C3×D4—122no—
194C3×D4—122no—
195C3×D4—122no—
196C3×D4—241no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—22no—
204C2×C3×C4—22no—
205C2×C3×C4—41no—
206C2×C3×C4—41no—
207C2×C3×C4—41no—
208C2×C3×C4—41no—
209C2×C3×C4—41no—
210C2×C3×C4—42no—
211C2×C3×C4—41no—
212C2×C3×C4—41no—
213C2×C3×C4—42no—
214C2×C3×C4—62no—
215C2×C3×C4—124no—
216C2×C3×C4#20412yes—
217C2×C3×C4#21412yes—
218C2×C3×C4D3×D412yes—
219C2×C3×C4C2×#6712yes—
220#67—42no—
221#67—42no—
222C2×Dic3—22no—
223C2×Dic3—122no—
224C2×Dic3—122no—
225C2×Dic3—124no—
226C2×Dic3—122no—
227C2×Dic3—121no—
228C2×Dic3—121no—
229C2×Dic3—121no—
230C2×Dic3—121no—
231C2×Dic3—122no—
232C2×Dic3—122no—
233C2×Dic3—122no—
234C2×Dic3—121no—
235C2×Dic3—121no—
236C2×Dic3—121no—
237C2×Dic3—121no—
238D12—42no—
239D12—42no—
240D12—81no—
241C4×D3—44no—
242Dic6—42no—
243C3×C8—122no—
244C3⋊C8—42no—
245C2×C32—21no—
246C2×C32—21no—
247C2×C32#45011yescharacteristic
248C2×C32#45411yescharacteristic
249C2×C32#45811yescharacteristic
250C3×D3—82no—
251#41—122no—
252#41—122no—
253C2×Q8—61no—
254C2×D4—32no—
255C2×D4—61no—
256C2×D4—61no—
257C2×D4—62no—
258C22×C4—62no—
259C22×C4—181no—
260C22×C4—181no—
261C22×C4#62611yescharacteristic
262C22×C4#62611yescharacteristic
263C22×C4C2×D3211yescharacteristic
264C2×C8—62no—
265C4⋊C4—22no—
266C4⋊C4—32no—
267C4⋊C4—61no—
268C4⋊C4—182no—
269C22⋊C4—62no—
270C22⋊C4—62no—
271C22×C3—22no—
272C22×C3—22no—
273C22×C3—21no—
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—21no—
278C22×C3—21no—
279C22×C3—21no—
280C22×C3—122no—
281C22×C3—122no—
282C22×C3—122no—
283C22×C3#88211yescharacteristic
284C22×C3C2×#20411yescharacteristic
285C22×C3#90811yescharacteristic
286C22×C3#93211yescharacteristic
287C22×C3C2×#21411yescharacteristic
288C22×C3#95311yescharacteristic
289C2×D3—42no—
290C2×D3—42no—
291C2×D3—42no—
292C3×C4—22no—
293C3×C4—22no—
294C3×C4—22no—
295C3×C4—22no—
296C3×C4—42no—
297C3×C4—42no—
298C3×C4—41no—
299C3×C4—41no—
300C3×C4—81no—
301C3×C4—122no—
302Dic3—42no—
303Dic3—242no—
304Dic3—241no—
305Dic3—241no—
306Dic3—242no—
307Dic3—241no—
308Dic3—241no—
309C32#161611yescharacteristic, complemented, Sylow
310C23—62no—
311C23C2×#62611yescharacteristic
312Q8—122no—
313D4—122no—
314D4—122no—
315D4—122no—
316D4—122no—
317D4—241no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—62no—
324C2×C4—124no—
325C2×C4—361no—
326C2×C4—361no—
327C2×C4—362no—
328C2×C4—361no—
329C2×C4—361no—
330C2×C4#371612yes—
331C2×C4D3×#6712yes—
332C8—122no—
333C2×C3—22no—
334C2×C3—22no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—242no—
343C2×C3#473111yescharacteristic
344C2×C3#474211yescharacteristic
345C2×C3#475311yescharacteristic
346C2×C3#521811yescharacteristic
347C2×C3#524311yescharacteristic
348C2×C3#524511yescharacteristic
349D3—82no—
350C22—21no—
351C22—21no—
352C22—122no—
353C22—122no—
354C22—122no—
355C22C2×#371611yescharacteristic
356C22#6383011yescharacteristic
357C22#6397711yescharacteristic
358C4—22no—
359C4—22no—
360C4—41no—
361C4—122no—
362C4—721no—
363C4—721no—
364C3—21no—
365C3#6813711yescharacteristic, complemented
366C3#7187511yescharacteristic, complemented
367C2—21no—
368C2—21no—
369C2—242no—
370C2#1059117211yescharacteristic
371C2#1059153411yescharacteristic
372C2#1059164611yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC3×#5510C2
hypercenterC2×C4⋊C4D32
hypocenterC32#1616
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10592685C2semidirect
3. #10591092C2semidirect
4. C3×#4528C2semidirect
5. #10589150C2semidirect
30. #4528D3semidirect
309. C32#1616semidirect
365. C3#68137semidirect
366. C3#71875semidirect

Maximal subgroups

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

subgroupindex
C3×#55102
#105926852
#105910922
C3×#45282
#105891502
#718753
#681373