Finite Group Databasebeta

← #11779969

Subgroups — #11779969

Order 1152.

451 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 451 conjugacy classes of subgroups — too many to draw. Only its 90 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#10593956C211yesmaximal, characteristic
2C3×#4681C211yesmaximal, characteristic, complemented
3#10590388C211yesmaximal, characteristic, complemented
4#10590269C211yesmaximal, characteristic
5#10589322C211yesmaximal, characteristic, complemented
6C3×#4459C211yesmaximal, characteristic
7#10589095C211yesmaximal, characteristic, complemented
8#71238—31nomaximal
9#68191—31nomaximal
10C4×#634C2211yescharacteristic
11C3×C4×D12C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×#869C2211yescharacteristic
14#63898—21no—
15D3×C4⋊Dic3—21no—
16#63887—22no—
17#63872—21no—
18#63857—21no—
19C2×#3719—21no—
20C32×C4×C8C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×#816—22no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24#63576—21no—
25#63566—21no—
26#63562—21no—
27#5730—31no—
28#5543—31no—
29C3×#487—31no—
30#5090—31no—
31#5087—31no—
32#5007—31no—
33#4849—31no—
34#4681D311yescharacteristic, complemented
35C3×D4⋊C8—31no—
36#4546—31no—
37#4481—31no—
38#4459D311yescharacteristic
39#4456—31no—
40#4456—31no—
41#4456—61no—
42C2×#634D411yescharacteristic
43C2×C3×D12D411yescharacteristic
44C2×C3×C4×D3—21no—
45C2×C3×Dic6—21no—
46C2×C3×Dic6D412yes—
47C2×D3×Dic3—22no—
48C2×C32×C8—21no—
49C32×C42C2311yescharacteristic
50C4⋊(C3⋊Dic3)D411yescharacteristic
51#3750—21no—
52C4×C3⋊Dic3—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C3×(C2×D3)⋊C4—21no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C2×C3×C3⋊C8—21no—
61Dic3⋊Dic3—22no—
62Dic3⋊Dic3—22no—
63(C2×D3)⋊Dic3—22no—
64#3719—42no—
65#1644—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4⋊Q8—31no—
68C3×C4×D4—31no—
69#946—62no—
70C2×#216—61no—
71D4×Dic3—61no—
72C2×C4⋊Dic3—61no—
73#924—61no—
74C2×Dic12—61no—
75#897—61no—
76#893—61no—
77D3×C4⋊C4—61no—
78#890—61no—
79#890—61no—
80#878—62no—
81C4×D12C2×D311yescharacteristic
82#869C2×D311yescharacteristic
83#869C2×D311yescharacteristic
84C4×Dic6—31no—
85C4×Dic6—31no—
86C4×Dic6—61no—
87C3×C4⋊C8—31no—
88C3×#103—62no—
89C3×C4×C8—21no—
90C3×C4×C8C2×D311yescharacteristic
91C3×C4×C8C2×D311yescharacteristic
92#835—61no—
93#832—61no—
94#816—22no—
95#816—61no—
96#809—61no—
97#807—61no—
98#807—61no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—61no—
102C4⋊(C3⋊C8)C2×D311yescharacteristic
103C22×C3×D3—21no—
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C3⋊Dic3—21no—
108C2×C3⋊Dic3—21no—
109#634—21no—
110#634—21no—
111C2×C3×Dic3—22no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—41no—
114C3×D12—21no—
115C3×D12Q1612yescomplemented
116C3×C4×D3—41no—
117C3×C4×D3—41no—
118C3×Dic6—42no—
119C3×Dic6—41no—
120C3×Dic6—41no—
121D3×Dic3—82no—
122C32×C8—41no—
123C3⋊(C3⋊C8)—41no—
124C3×C3⋊C8—41no—
125#554—91no—
126#487—31no—
127#474—91no—
128#462—91no—
129#333—91no—
130Q8⋊C8—91no—
131D4⋊C8—31no—
132C2×C3×Q8—32no—
133C2×C3×Q8—61no—
134C2×C3×D4—31no—
135C22×C3×C4—61no—
136C22×Dic3—62no—
137C2×D12D1211yescharacteristic
138C2×C4×D3—21no—
139C2×C4×D3—62no—
140C2×Dic6—21no—
141C2×Dic6—31no—
142C2×Dic6—31no—
143C2×Dic6—61no—
144C2×Dic6#6712yes—
145C2×C3×C8—21no—
146C2×C3×C8—21no—
147C2×C3×C8—41no—
148C2×C3×C8—61no—
149C3×C4⋊C4—31no—
150C3×C4⋊C4—61no—
151C3×C4⋊C4—61no—
152C3×C4⋊C4—61no—
153C3×C4⋊C4—61no—
154C3×C22⋊C4—61no—
155C3×C42—21no—
156C3×C42C22×D311yescharacteristic
157C3×C42C22×D311yescharacteristic
158#217—62no—
159#216—122no—
160(C2×D3)⋊C4—21no—
161(C2×D3)⋊C4—62no—
162C4⋊Dic3—21no—
163C4⋊Dic3—21no—
164C4⋊Dic3—21no—
165C4⋊Dic3—21no—
166C4⋊Dic3—31no—
167C4⋊Dic3—31no—
168C4⋊Dic3—61no—
169C4⋊Dic3—62no—
170C4⋊Dic3—62no—
171C4⋊Dic3D1211yescharacteristic
172Dic3⋊C4—62no—
173Dic3⋊C4—62no—
174Dic3⋊C4—61no—
175Dic3⋊C4—61no—
176Dic3⋊C4—121no—
177C4×Dic3—61no—
178C4×Dic3—61no—
179C4×Dic3—121no—
180C2×C3⋊C8—21no—
181C2×C3⋊C8—61no—
182C2×C3⋊C8—61no—
183C2×C3⋊C8—121no—
184Dic12—122no—
185C22×C32#12011yescharacteristic
186C2×C3×D3—22no—
187C2×C3×D3—41no—
188C2×C3×D3—41no—
189C32×C4—21no—
190C32×C4C2×Q1611yescharacteristic
191C32×C4#13511yescharacteristic
192C32×C4AGL(1,ℤ/8)11yescharacteristic
193C32×C4#13711yescharacteristic
194C3⋊Dic3—41no—
195C3⋊Dic3—41no—
196C3×Dic3—41no—
197C3×Dic3—42no—
198C3×Dic3—81no—
199C2×Q16—181no—
200C4⋊Q8—31no—
201C4⋊Q8—31no—
202#125—181no—
203C22⋊Q8—182no—
204C22⋊Q8—181no—
205C4×Q8—91no—
206C4×D4—31no—
207C4×D4—181no—
208C2×C4⋊C4—181no—
209#107—181no—
210C4⋊C8—31no—
211C4⋊C8—91no—
212#103—62no—
213#103—181no—
214#102—181no—
215C4×C8D3211yescharacteristic
216C23×C3—61no—
217C22×D3—21no—
218C3×Q8—122no—
219C3×Q8—121no—
220C3×Q8—121no—
221C3×D4—32no—
222C3×D4—61no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—62no—
227C2×C3×C4—61no—
228C2×C3×C4—121no—
229C2×C3×C4—121no—
230C2×C3×C4—121no—
231C2×C3×C4C2×D1211yescharacteristic
232C2×C3×C4D3×D411yescharacteristic
233C2×C3×C4D3×D411yescharacteristic
234C2×C3×C4D3×D411yescharacteristic
235C2×C3×C4D3×D411yescharacteristic
236C2×C3×C4C2×#6711yescharacteristic
237C2×Dic3—21no—
238C2×Dic3—22no—
239C2×Dic3—41no—
240C2×Dic3—61no—
241C2×Dic3—61no—
242C2×Dic3—61no—
243C2×Dic3—61no—
244C2×Dic3—121no—
245C2×Dic3—121no—
246C2×Dic3—242no—
247D12—21no—
248D12Dic1212yescomplemented
249C4×D3—41no—
250C4×D3—41no—
251C4×D3—242no—
252Dic6—42no—
253Dic6—41no—
254Dic6—41no—
255Dic6—62no—
256Dic6—61no—
257Dic6—61no—
258Dic6—61no—
259Dic6—61no—
260Dic6—121no—
261C3×C8—41no—
262C3×C8—41no—
263C3×C8—42no—
264C3×C8—121no—
265C3⋊C8—41no—
266C3⋊C8—121no—
267C3⋊C8—121no—
268C3⋊C8—241no—
269C2×C32#44911yescharacteristic
270C2×C32#45111yescharacteristic
271C2×C32#45511yescharacteristic
272C3×D3—42no—
273C2×Q8—32no—
274C2×Q8—61no—
275C2×Q8—91no—
276C2×D4—31no—
277C22×C4—61no—
278C22×C4—182no—
279Q16—362no—
280C2×C8—21no—
281C2×C8—61no—
282C2×C8—181no—
283C4⋊C4—31no—
284C4⋊C4—61no—
285C4⋊C4—61no—
286C4⋊C4—61no—
287C4⋊C4—61no—
288C4⋊C4—91no—
289C4⋊C4—182no—
290C4⋊C4—182no—
291C4⋊C4—181no—
292C22⋊C4—61no—
293C22⋊C4—182no—
294C42—181no—
295C42C2×D3211yescharacteristic
296C22×C3—21no—
297C22×C3—62no—
298C22×C3—121no—
299C22×C3—121no—
300C22×C3#88211yescharacteristic
301C22×C3#93711yescharacteristic
302C2×D3—22no—
303C2×D3—41no—
304C2×D3—41no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—41no—
312C3×C4—121no—
313C3×C4—122no—
314C3×C4—241no—
315C3×C4C2×Dic1211yescharacteristic
316C3×C4#90911yescharacteristic
317C3×C4#91111yescharacteristic
318C3×C4#91411yescharacteristic
319C3×C4#91611yescharacteristic
320C3×C4#91611yescharacteristic
321C3×C4D3×Q1611yescharacteristic
322C3×C4#91811yescharacteristic
323Dic3—41no—
324Dic3—42no—
325Dic3—81no—
326Dic3—122no—
327Dic3—121no—
328Dic3—121no—
329Dic3—121no—
330Dic3—121no—
331Dic3—241no—
332C32#164411yescharacteristic, complemented, Sylow
333C23—61no—
334Q8—122no—
335Q8—121no—
336Q8—121no—
337Q8—181no—
338Q8—181no—
339D4—32no—
340D4—61no—
341C2×C4—61no—
342C2×C4—62no—
343C2×C4—121no—
344C2×C4—121no—
345C2×C4—121no—
346C2×C4—181no—
347C2×C4—181no—
348C2×C4—722no—
349C2×C4D3×D1211yescharacteristic
350C2×C4#380211yescharacteristic
351C2×C4D3×#6711yescharacteristic
352C8—41no—
353C8—121no—
354C8—361no—
355C2×C3—21no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3—122no—
359C2×C3#473911yescharacteristic
360C2×C3#478111yescharacteristic
361C2×C3#482511yescharacteristic
362C2×C3#506111yescharacteristic
363C2×C3#517211yescharacteristic
364C2×C3#518611yescharacteristic
365D3—42no—
366C22—62no—
367C22—121no—
368C22—121no—
369C22#6392211yescharacteristic
370C4—21no—
371C4—122no—
372C4—121no—
373C4—241no—
374C4—361no—
375C4—361no—
376C4#6379811yescharacteristic
377C4D3×Dic1211yescharacteristic
378C4#6380111yescharacteristic
379C4#6380911yescharacteristic
380C3—21no—
381C3#6819111yescharacteristic, complemented
382C3#7123811yescharacteristic, complemented
383C2—122no—
384C2#1059039611yescharacteristic
385C2#1059094911yescharacteristic
386C2#1059096411yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC4×C8D32
hypocenterC32#1644
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. C3×#4681C2semidirect
3. #10590388C2semidirect
5. #10589322C2semidirect
7. #10589095C2semidirect
34. #4681D3semidirect
115. C3×D12Q16semidirect
248. D12Dic12semidirect
332. C32#1644semidirect
381. C3#68191semidirect
382. C3#71238semidirect

Maximal subgroups

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

subgroupindex
#105939562
C3×#46812
#105903882
#105902692
#105893222
C3×#44592
#105890952
#712383
#681913