Finite Group Databasebeta

← #11779281

Subgroups — #11779281

Order 1152.

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

normal subgroups only

This group has 467 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×#5584C211yesmaximal, characteristic, complemented
2C3×#5027C211yesmaximal, characteristic, complemented
3#10590347C211yesmaximal, characteristic
4#10590277C211yesmaximal, characteristic, complemented
5#10589401C211yesmaximal, characteristic, complemented
6#10589092C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#71931—31nomaximal
9#71029—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11C3×#946—21no—
12C2×C3×#215—21no—
13C3×#898—22no—
14C3×#892—21no—
15C3×#875—21no—
16C3×#874C2211yescharacteristic
17C3×C4×D12C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×C4×Dic6—21no—
20C2×#3713—21no—
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C4×C3⋊(C3⋊C8)C2211yescharacteristic
23C3×#809—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63562—22no—
26#63562—21no—
27C3×#556—31no—
28#5584D311yescharacteristic, complemented
29C3×#460—31no—
30#5088—31no—
31#5072—31no—
32#5070—31no—
33#5027D311yescharacteristic, complemented
34#5015—31no—
35#4547—31no—
36#4535—31no—
37#4535—31no—
38#4535—61no—
39D4⋊(C3⋊C8)—31no—
40#4486—31no—
41#4483—31no—
42C2×C32×Q8D411yescharacteristic
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12D411yescharacteristic
47C2×C3×C4×D3—21no—
48C2×C3×Dic6—21no—
49C32×C4⋊C4—21no—
50C32×C4⋊C4D411yescharacteristic
51C32×C42—21no—
52C32×C42C2311yescharacteristic
53C2×C3⋊(C3⋊C8)—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C3×#215—42no—
56C3×(C2×D3)⋊C4—22no—
57C3×(C2×D3)⋊C4—22no—
58C3×(C2×D3)⋊C4—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3D412yes—
61C3×C4⋊Dic3D411yescharacteristic
62C3×Dic3⋊C4—22no—
63C3×C4×Dic3—22no—
64C2×C3×C3⋊C8—21no—
65#3713—42no—
66#1628—91noSylow
67C2×C3×SD16—61no—
68C3×C4⋊Q8—31no—
69C3×#127—31no—
70C3×#126—62no—
71C3×#124—61no—
72C3×C22⋊Q8—61no—
73C3×C4×Q8—21no—
74C3×C4×Q8—61no—
75C3×C4×Q8C2×D311yescharacteristic
76C3×C4×Q8C2×D311yescharacteristic
77C3×C4×D4—31no—
78C3×#117—61no—
79#946—21no—
80C2×#215—21no—
81C2×#213—61no—
82C2×#213—61no—
83#898—22no—
84#892—21no—
85#875—21no—
86#874C2×D311yescharacteristic
87C4×D12C2×D311yescharacteristic
88#869C2×D311yescharacteristic
89C4×Dic6—21no—
90C3×C4⋊C8—31no—
91C3×#102—61no—
92#832—62no—
93#832—61no—
94#809—21no—
95#809—61no—
96#809—62no—
97C4⋊(C3⋊C8)—31no—
98C4⋊(C3⋊C8)—31no—
99C4⋊(C3⋊C8)—61no—
100C4⋊(C3⋊C8)C2×D311yescharacteristic
101C4×C3⋊C8—31no—
102C4×C3⋊C8—31no—
103C4×C3⋊C8—61no—
104C22×C3×D3—21no—
105C22×C3×D3—41no—
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—21no—
114C2×C3×Dic3—22no—
115C3×D12—21no—
116C3×D12—21no—
117C3×D12—42no—
118C3×D12—41no—
119C3×D12—41no—
120C3×D12—41no—
121C3×D12—41no—
122C3×C4×D3—41no—
123C3×C4×D3—41no—
124C3×Dic6—41no—
125C3×Dic6—41no—
126C3⋊(C3⋊C8)—41no—
127C3⋊(C3⋊C8)—41no—
128C3×C3⋊C8—41no—
129#556—31no—
130#486—91no—
131#460—31no—
132#459—91no—
133#332—91no—
134Q8⋊C8—91no—
135D4⋊C8—91no—
136C2×C3×Q8—21no—
137C2×C3×Q8—61no—
138C2×C3×Q8#6711yescharacteristic
139C2×C3×Q8#6711yescharacteristic
140C2×C3×D4—31no—
141C2×C3×D4—61no—
142C2×C3×D4—61no—
143C2×C3×D4—61no—
144C22×C3×C4—61no—
145C2×D12—21no—
146C2×D12—21no—
147C2×D12—21no—
148C2×D12#6711yescharacteristic
149C2×C4×D3—21no—
150C2×Dic6—21no—
151C3×SD16—122no—
152C2×C3×C8—61no—
153C3×C4⋊C4—21no—
154C3×C4⋊C4—21no—
155C3×C4⋊C4—21no—
156C3×C4⋊C4—31no—
157C3×C4⋊C4—32no—
158C3×C4⋊C4—41no—
159C3×C4⋊C4—62no—
160C3×C4⋊C4—61no—
161C3×C4⋊C4#6711yescharacteristic
162C3×C4⋊C4#6711yescharacteristic
163C3×C22⋊C4—62no—
164C3×C22⋊C4—62no—
165C3×C22⋊C4—61no—
166C3×C42—21no—
167C3×C42—21no—
168C3×C42—21no—
169C3×C42—41no—
170C3×C42—62no—
171C3×C42C22×D311yescharacteristic
172C3×C42C22×D311yescharacteristic
173#215—42no—
174#213—122no—
175#213—122no—
176(C2×D3)⋊C4—22no—
177(C2×D3)⋊C4—22no—
178(C2×D3)⋊C4—21no—
179C4⋊Dic3—21no—
180C4⋊Dic3#6711yescharacteristic
181C4⋊Dic3#6712yes—
182Dic3⋊C4—22no—
183C4×Dic3—22no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—61no—
186C2×C3⋊C8—61no—
187C2×C3⋊C8—61no—
188C2×C3⋊C8—61no—
189C2×C3⋊C8—121no—
190C2×C3⋊C8—121no—
191C22×C32#12011yescharacteristic
192C2×C3×D3—41no—
193C2×C3×D3—41no—
194C2×C3×D3—41no—
195C2×C3×D3—81no—
196C2×C3×D3—81no—
197C2×C3×D3—81no—
198C32×C4—21no—
199C32×C4—41no—
200C32×C4—41no—
201C32×C4#13511yescharacteristic
202C32×C4#13511yescharacteristic
203C32×C4AGL(1,ℤ/8)11yescharacteristic
204C32×C4AGL(1,ℤ/8)11yescharacteristic
205C3×Dic3—42no—
206C3×Dic3—41no—
207C2×SD16—61no—
208C2×D8—181no—
209C4⋊Q8—31no—
210#127—31no—
211#126—62no—
212#124—61no—
213C22⋊Q8—61no—
214C4×Q8—61no—
215C4×Q8D3211yescharacteristic
216C4×D4—31no—
217#117—61no—
218C4⋊C8—31no—
219C4⋊C8—91no—
220#102—61no—
221#102—181no—
222#102—182no—
223C4×C8—91no—
224C23×C3—61no—
225C23×C3—121no—
226C22×D3—21no—
227C22×D3—41no—
228C3×Q8—22no—
229C3×Q8—21no—
230C3×Q8—21no—
231C3×Q8—21no—
232C3×Q8—21no—
233C3×Q8—41no—
234C3×Q8—121no—
235C3×Q8—121no—
236C3×D4—61no—
237C3×D4—61no—
238C3×D4—122no—
239C3×D4—121no—
240C3×D4—121no—
241C3×D4—121no—
242C3×D4—121no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—41no—
251C2×C3×C4—41no—
252C2×C3×C4—61no—
253C2×C3×C4—62no—
254C2×C3×C4—121no—
255C2×C3×C4—121no—
256C2×C3×C4D3×D411yescharacteristic
257C2×C3×C4D3×D411yescharacteristic
258C2×C3×C4C2×#6711yescharacteristic
259C2×C3×C4C2×#6711yescharacteristic
260C2×C3×C4C2×#6711yescharacteristic
261C2×C3×C4C2×#6711yescharacteristic
262C2×Dic3—21no—
263C2×Dic3—22no—
264D12—21no—
265D12—21no—
266D12—42no—
267D12—41no—
268D12—41no—
269D12—41no—
270D12—41no—
271C4×D3—41no—
272C4×D3—41no—
273Dic6—41no—
274Dic6—41no—
275C3×C8—121no—
276C3⋊C8—41no—
277C3⋊C8—121no—
278C3⋊C8—121no—
279C3⋊C8—122no—
280C3⋊C8—121no—
281C3⋊C8—121no—
282C3⋊C8—241no—
283C2×C32#44911yescharacteristic
284C2×C32#44911yescharacteristic
285C2×C32#45411yescharacteristic
286C3×D3—81no—
287C3×D3—161no—
288C2×Q8—61no—
289C2×Q8#62511yescharacteristic
290C2×D4—31no—
291C2×D4—61no—
292C2×D4—61no—
293C2×D4—61no—
294C22×C4—61no—
295SD16—122no—
296D8—362no—
297C2×C8—61no—
298C2×C8—181no—
299C2×C8—181no—
300C4⋊C4—21no—
301C4⋊C4—31no—
302C4⋊C4—32no—
303C4⋊C4—62no—
304C4⋊C4—61no—
305C4⋊C4#62511yescharacteristic
306C22⋊C4—62no—
307C22⋊C4—62no—
308C22⋊C4—61no—
309C42—21no—
310C42—62no—
311C42C2×D3211yescharacteristic
312C22×C3—21no—
313C22×C3—121no—
314C22×C3—121no—
315C22×C3—121no—
316C22×C3—241no—
317C22×C3—241no—
318C22×C3—241no—
319C22×C3#93711yescharacteristic
320C22×C3#95311yescharacteristic
321C2×D3—41no—
322C2×D3—41no—
323C2×D3—41no—
324C2×D3—81no—
325C2×D3—81no—
326C2×D3—81no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—41no—
334C3×C4—42no—
335C3×C4—41no—
336C3×C4—41no—
337C3×C4—41no—
338C3×C4—41no—
339C3×C4—81no—
340C3×C4—122no—
341C3×C4—121no—
342C3×C4#91411yescharacteristic
343C3×C4#91611yescharacteristic
344C3×C4#93211yescharacteristic
345C3×C4#94911yescharacteristic
346C3×C4#94911yescharacteristic
347C3×C4#95011yescharacteristic
348C3×C4#95011yescharacteristic
349C3×C4#95011yescharacteristic
350Dic3—42no—
351Dic3—41no—
352C32#162811yescharacteristic, complemented, Sylow
353C23—61no—
354C23—121no—
355Q8—21no—
356Q8—21no—
357Q8—121no—
358Q8—121no—
359D4—61no—
360D4—61no—
361D4—122no—
362D4—121no—
363D4—121no—
364D4—121no—
365D4—121no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—61no—
369C2×C4—62no—
370C2×C4—121no—
371C2×C4—121no—
372C2×C4C2×#62511yescharacteristic
373C2×C4D3×#6711yescharacteristic
374C2×C4D3×#6711yescharacteristic
375C8—121no—
376C8—361no—
377C8—361no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—241no—
382C2×C3—481no—
383C2×C3#503711yescharacteristic
384C2×C3#517211yescharacteristic
385C2×C3#520111yescharacteristic
386C2×C3#523811yescharacteristic
387C2×C3#523811yescharacteristic
388C2×C3#524511yescharacteristic
389D3—81no—
390D3—161no—
391C22—121no—
392C22—121no—
393C22—121no—
394C22—241no—
395C22—241no—
396C22—241no—
397C22#6397611yescharacteristic
398C4—21no—
399C4—41no—
400C4—41no—
401C4—122no—
402C4—121no—
403C4#6382211yescharacteristic
404C4#6382311yescharacteristic
405C4#6393911yescharacteristic
406C4#6394711yescharacteristic
407C3—21no—
408C3#7102911yescharacteristic, complemented
409C3#7193111yescharacteristic, complemented
410C2—241no—
411C2—481no—
412C2#1059116111yescharacteristic
413C2#1059158611yescharacteristic
414C2#1059168411yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32#120
prime radical#10590347C2
hypercenterC4×Q8D32
hypocenterC32#1628
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
1. C3×#5584C2semidirect
2. C3×#5027C2semidirect
4. #10590277C2semidirect
5. #10589401C2semidirect
6. #10589092C2semidirect
7. #10589080C2semidirect
28. #5584D3semidirect
33. #5027D3semidirect
352. C32#1628semidirect
408. C3#71029semidirect
409. C3#71931semidirect

Maximal subgroups

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

subgroupindex
C3×#55842
C3×#50272
#105903472
#105902772
#105894012
#105890922
#105890802
#719313
#710293