Finite Group Databasebeta

← #11779437

Subgroups — #11779437

Order 1152.

476 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 96 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×#5579C211yesmaximal, characteristic
2#10592720C211yesmaximal, characteristic, complemented
3#10590386C211yesmaximal, characteristic, complemented
4#10590268C211yesmaximal, characteristic
5C3×#4535C211yesmaximal, characteristic, complemented
6#10589095C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic
8#71924—31nomaximal
9#68246—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×#946—21no—
13C3×#896—22no—
14C3×D3×C4⋊C4—21no—
15C3×C4×D12—21no—
16C3×C4×D12C2211yescharacteristic
17C3×#870—21no—
18C3×#869C2211yescharacteristic
19C2×#3719—22no—
20#63662—21no—
21#63634—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63573—21no—
26#63563—21no—
27C3×#554—31no—
28#5579D311yescharacteristic
29#5092—31no—
30#5021—31no—
31#5021—31no—
32#5021—61no—
33#5008—31no—
34#4842—31no—
35#4699—31no—
36C3×Q8⋊C8—31no—
37#4546—31no—
38#4535D311yescharacteristic, complemented
39D4⋊(C3⋊C8)—31no—
40#4481—31no—
41#4459—31no—
42C2×C32×Q8D411yescharacteristic
43C2×#634—21no—
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C2×C3×C4×D3—22no—
47C2×C3×Dic6D412yes—
48C32×C4⋊C4—21no—
49C32×C4⋊C4D411yescharacteristic
50C32×C42—21no—
51C32×C42C2311yescharacteristic
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C3×(C2×D3)⋊C4—22no—
56C3×(C2×D3)⋊C4—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×Dic3⋊C4—22no—
61C3×Dic3⋊C4—22no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64#3719—44no—
65#1632—91noSylow
66C3×C4⋊Q8—31no—
67C3×#125—61no—
68C3×C22⋊Q8—62no—
69C3×C22⋊Q8—61no—
70C3×C4×Q8—21no—
71C3×C4×Q8C2×D311yescharacteristic
72C3×C4×Q8C2×D311yescharacteristic
73C3×C4×D4—31no—
74C3×C4×D4—61no—
75C2×C3×C4⋊C4—61no—
76#946—21no—
77C2×#216—62no—
78C2×Dic12—62no—
79#896—22no—
80D3×C4⋊C4—21no—
81C4×D12—21no—
82C4×D12C2×D311yescharacteristic
83#870—21no—
84#869—31no—
85#869—31no—
86#869—61no—
87#869C2×D311yescharacteristic
88C3×C4⋊C8—31no—
89C3×C4×C8—31no—
90#835—62no—
91#835—61no—
92#835—61no—
93#832—61no—
94#821—61no—
95#817—61no—
96#808—61no—
97#807—62no—
98#807—61no—
99#807—61no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—61no—
103C4⋊(C3⋊C8)C2×D311yescharacteristic
104C4×C3⋊C8C2×D311yescharacteristic
105C22×C3×D3—21no—
106C32×Q8—21no—
107C32×Q8—21no—
108C2×C32×C4—21no—
109C2×C32×C4—21no—
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C3⋊Dic3—41no—
114#634—42no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—22no—
117C3×D12—21no—
118C3×D12Q1612yescomplemented
119C3×C4×D3—41no—
120C3×C4×D3—41no—
121C3×C4×D3—82no—
122C3×Dic6—42no—
123C3⋊(C3⋊C8)—41no—
124C3×C3⋊C8—22no—
125C3×C3⋊C8—41no—
126#554—31no—
127#494—91no—
128#477—91no—
129#476—91no—
130#333—91no—
131Q8⋊C8—31no—
132D4⋊C8—91no—
133C2×C3×Q8—21no—
134C2×C3×Q8—32no—
135C2×C3×Q8D1211yescharacteristic
136C2×C3×Q8#6711yescharacteristic
137C2×C3×D4—31no—
138C22×C3×C4—62no—
139C22×C3×C4—61no—
140C2×D12#6711yescharacteristic
141C2×C4×D3—21no—
142C2×C4×D3—22no—
143C2×Dic6—61no—
144C2×Dic6—61no—
145C2×Dic6—121no—
146C2×Dic6#6712yes—
147C2×C3×C8—61no—
148C2×C3×C8—61no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4—31no—
153C3×C4⋊C4—41no—
154C3×C4⋊C4—62no—
155C3×C4⋊C4—62no—
156C3×C4⋊C4—61no—
157C3×C4⋊C4—61no—
158C3×C4⋊C4D1211yescharacteristic
159C3×C4⋊C4#6711yescharacteristic
160C3×C22⋊C4—62no—
161C3×C22⋊C4—61no—
162C3×C42—21no—
163C3×C42—21no—
164C3×C42—21no—
165C3×C42—41no—
166C3×C42C22×D311yescharacteristic
167C3×C42C22×D311yescharacteristic
168#216—124no—
169(C2×D3)⋊C4—22no—
170(C2×D3)⋊C4—21no—
171C4⋊Dic3—21no—
172C4⋊Dic3—21no—
173C4⋊Dic3—62no—
174C4⋊Dic3—61no—
175C4⋊Dic3—61no—
176C4⋊Dic3—61no—
177C4⋊Dic3—61no—
178C4⋊Dic3—121no—
179C4⋊Dic3#6711yescharacteristic
180Dic3⋊C4—22no—
181Dic3⋊C4—22no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—21no—
184C2×C3⋊C8—62no—
185C2×C3⋊C8—61no—
186C2×C3⋊C8—61no—
187Dic12—124no—
188C22×C32#12011yescharacteristic
189C2×C3×D3—22no—
190C2×C3×D3—41no—
191C2×C3×D3—41no—
192C32×C4—21no—
193C32×C4—41no—
194C32×C4—41no—
195C32×C4C2×Q1611yescharacteristic
196C32×C4#13511yescharacteristic
197C32×C4#13711yescharacteristic
198C32×C4#13711yescharacteristic
199C3⋊Dic3—81no—
200C3×Dic3—41no—
201C3×Dic3—42no—
202C2×Q16—182no—
203C4⋊Q8—31no—
204C4⋊Q8—91no—
205#125—61no—
206C22⋊Q8—62no—
207C22⋊Q8—61no—
208C4×Q8D3211yescharacteristic
209C4×D4—31no—
210C4×D4—61no—
211C2×C4⋊C4—61no—
212#107—181no—
213#106—181no—
214C4⋊C8—31no—
215C4⋊C8—91no—
216#103—181no—
217#102—181no—
218C4×C8—31no—
219C23×C3—61no—
220C22×D3—21no—
221C3×Q8—22no—
222C3×Q8—21no—
223C3×Q8—21no—
224C3×Q8—21no—
225C3×Q8—21no—
226C3×Q8—41no—
227C3×Q8—122no—
228C3×D4—32no—
229C3×D4—61no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—41no—
238C2×C3×C4—41no—
239C2×C3×C4—61no—
240C2×C3×C4—62no—
241C2×C3×C4—121no—
242C2×C3×C4—121no—
243C2×C3×C4—242no—
244C2×C3×C4C2×D1211yescharacteristic
245C2×C3×C4D3×D411yescharacteristic
246C2×C3×C4D3×D411yescharacteristic
247C2×C3×C4C2×#6711yescharacteristic
248C2×C3×C4C2×#6711yescharacteristic
249C2×C3×C4C2×#6711yescharacteristic
250C2×Dic3—21no—
251C2×Dic3—22no—
252C2×Dic3—122no—
253C2×Dic3—121no—
254C2×Dic3—121no—
255D12—21no—
256D12#21612yescomplemented
257C4×D3—41no—
258C4×D3—41no—
259C4×D3—82no—
260Dic6—42no—
261Dic6—122no—
262Dic6—122no—
263Dic6—242no—
264C3×C8—62no—
265C3×C8—121no—
266C3⋊C8—22no—
267C3⋊C8—41no—
268C3⋊C8—122no—
269C3⋊C8—121no—
270C3⋊C8—121no—
271C2×C32#45111yescharacteristic
272C2×C32#45211yescharacteristic
273C2×C32#45311yescharacteristic
274C3×D3—42no—
275C2×Q8—32no—
276C2×Q8—181no—
277C2×Q8#62611yescharacteristic
278C2×D4—31no—
279C22×C4—62no—
280C22×C4—61no—
281Q16—364no—
282C2×C8—61no—
283C2×C8—61no—
284C2×C8—181no—
285C4⋊C4—21no—
286C4⋊C4—31no—
287C4⋊C4—62no—
288C4⋊C4—62no—
289C4⋊C4—61no—
290C4⋊C4—61no—
291C4⋊C4—181no—
292C4⋊C4—181no—
293C4⋊C4#62611yescharacteristic
294C22⋊C4—62no—
295C22⋊C4—61no—
296C42—21no—
297C42C2×D3211yescharacteristic
298C22×C3—21no—
299C22×C3—62no—
300C22×C3—121no—
301C22×C3—121no—
302C22×C3#88211yescharacteristic
303C22×C3#95311yescharacteristic
304C2×D3—22no—
305C2×D3—41no—
306C2×D3—41no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—41no—
314C3×C4—42no—
315C3×C4—41no—
316C3×C4—41no—
317C3×C4—41no—
318C3×C4—41no—
319C3×C4—81no—
320C3×C4—121no—
321C3×C4—122no—
322C3×C4#90411yescharacteristic
323C3×C4#90911yescharacteristic
324C3×C4#91511yescharacteristic
325C3×C4D3×Q1611yescharacteristic
326C3×C4#94211yescharacteristic
327C3×C4C2×#21611yescharacteristic
328C3×C4#95011yescharacteristic
329C3×C4#95111yescharacteristic
330Dic3—41no—
331Dic3—42no—
332Dic3—242no—
333Dic3—241no—
334Dic3—241no—
335C32#163211yescharacteristic, complemented, Sylow
336C23—61no—
337Q8—21no—
338Q8—21no—
339Q8—122no—
340Q8—362no—
341D4—32no—
342D4—61no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—61no—
346C2×C4—62no—
347C2×C4—121no—
348C2×C4—121no—
349C2×C4—242no—
350C2×C4—361no—
351C2×C4C2×#62611yescharacteristic
352C2×C4D3×#6711yescharacteristic
353C2×C4D3×#6711yescharacteristic
354C8—62no—
355C8—121no—
356C8—361no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—122no—
361C2×C3#473311yescharacteristic
362C2×C3#480911yescharacteristic
363C2×C3#482211yescharacteristic
364C2×C3#522811yescharacteristic
365C2×C3#523911yescharacteristic
366C2×C3#524111yescharacteristic
367D3—42no—
368C22—62no—
369C22—121no—
370C22—121no—
371C22#6397711yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—122no—
376C4—121no—
377C4—721no—
378C4#6382911yescharacteristic
379C4#6383111yescharacteristic
380C4D3×#21611yescharacteristic
381C4#6394611yescharacteristic
382C3—21no—
383C3#6824611yescharacteristic, complemented
384C3#7192411yescharacteristic, complemented
385C2—122no—
386C2#1059117311yescharacteristic
387C2#1059159511yescharacteristic
388C2#1059166611yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC4×Q8D32
hypocenterC32#1632
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. #10592720C2semidirect
3. #10590386C2semidirect
5. C3×#4535C2semidirect
6. #10589095C2semidirect
38. #4535D3semidirect
118. C3×D12Q16semidirect
256. D12#216semidirect
335. C32#1632semidirect
383. C3#68246semidirect
384. C3#71924semidirect

Maximal subgroups

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

subgroupindex
C3×#55792
#105927202
#105903862
#105902682
C3×#45352
#105890952
#105890812
#719243
#682463