Finite Group Databasebeta

← #11779283

Subgroups — #11779283

Order 1152.

473 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 473 conjugacy classes of subgroups — too many to draw. Only its 86 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#10593865C211yesmaximal, characteristic, complemented
2C3×#4848C211yesmaximal, characteristic, complemented
3#10590355C211yesmaximal, characteristic
4#10590277C211yesmaximal, characteristic, complemented
5#10589349C211yesmaximal, characteristic, complemented
6C3×#4486C211yesmaximal, characteristic, complemented
7#10589083C211yesmaximal, characteristic, complemented
8#71029—31nomaximal
9#68433—31nomaximal
10C4×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C3×#204—21no—
12C3×#874C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63871—21no—
16#63864—21no—
17#63849—21no—
18#63848—22no—
19Dic3×Dic6—21no—
20C2×#3714—21no—
21C32×C4⋊C8C2211yescharacteristic
22C4×C3⋊(C3⋊C8)C2211yescharacteristic
23C3×#821—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63563—21no—
26#63562—22no—
27#5732—31no—
28#5584—31no—
29C3×#460—31no—
30#5088—31no—
31#5072—31no—
32#5070—31no—
33#4848D311yescharacteristic, complemented
34#4843—31no—
35C3×#332—31no—
36#4535—31no—
37#4486D311yescharacteristic, complemented
38#4484—31no—
39#4483—31no—
40#4483—31no—
41#4483—61no—
42C2×C4⋊(C3⋊D3)D411yescharacteristic
43C2×C4×C3⋊D3—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×Dic6—21no—
48C2×C3×Dic6D411yescharacteristic
49C2×C32×C8—21no—
50C32×C42C2311yescharacteristic
51#3752—21no—
52C4⋊(C3⋊Dic3)D411yescharacteristic
53C2×C3⋊(C3⋊C8)—21no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3D412yes—
56C3×C4⋊Dic3D411yescharacteristic
57C3×Dic3⋊C4—21no—
58C3×C4×Dic3—21no—
59C2×C3×C3⋊C8—21no—
60C3×#204—42no—
61Dic3⋊Dic3—22no—
62#3722—22no—
63#3722—22no—
64Dic32—22no—
65#3714—42no—
66#1628—91noSylow
67C2×C3×SD16—61no—
68C3×C4⋊Q8—31no—
69C3×#127—31no—
70C3×C4×Q8—31no—
71#947—61no—
72#946—61no—
73Q8×Dic3—61no—
74C2×#213—61no—
75C2×D24—61no—
76C2×#204—21no—
77#898—62no—
78#898—62no—
79#897—61no—
80#892—61no—
81#892—61no—
82#875—61no—
83#874C2×D311yescharacteristic
84C4×D12—31no—
85C4×D12—31no—
86C4×D12—61no—
87#869C2×D311yescharacteristic
88C4×Dic6—61no—
89C4×Dic6C2×D311yescharacteristic
90C3×C4⋊C8—21no—
91C3×C4⋊C8—31no—
92C3×C4⋊C8C2×D311yescharacteristic
93C3×C4⋊C8C2×D311yescharacteristic
94C3×#102—61no—
95#832—61no—
96#832—62no—
97#821—21no—
98#821—61no—
99#809—62no—
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—
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C3⋊Dic3—21no—
110C4⋊(C3⋊D3)—21no—
111C4⋊(C3⋊D3)—21no—
112C4×C3⋊D3—41no—
113C4×C3⋊D3—41no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—22no—
116C2×C3×Dic3—21no—
117C3×D12—42no—
118C3×D12—41no—
119C3×D12—41no—
120C3×D12—41no—
121C3×D12—41no—
122C3×Dic6—21no—
123C3×Dic6—21no—
124C3×Dic6—41no—
125C3×Dic6—41no—
126C32×C8—41no—
127C3⋊(C3⋊C8)—41no—
128C3×C3⋊C8—41no—
129#556—91no—
130#486—91no—
131#460—31no—
132#459—91no—
133#332—31no—
134Q8⋊C8—91no—
135D4⋊C8—91no—
136C2×C3×Q8—31no—
137C2×C3×Q8—61no—
138C2×C3×D4—61no—
139C2×C3×D4—61no—
140C2×C3×D4—61no—
141C2×D12—21no—
142C2×D12—21no—
143C2×D12—21no—
144C2×D12—31no—
145C2×D12—31no—
146C2×D12—61no—
147C2×C4×D3—61no—
148C2×C4×D3—61no—
149C2×C4×D3—121no—
150C2×Dic6—21no—
151C2×Dic6#6711yescharacteristic
152C3×SD16—122no—
153C2×C3×C8—21no—
154C2×C3×C8—21no—
155C2×C3×C8—41no—
156C2×C3×C8—61no—
157C3×C4⋊C4—32no—
158C3×C4⋊C4—31no—
159C3×C4⋊C4—61no—
160C3×C4⋊C4—61no—
161C3×C42—21no—
162C3×C42—61no—
163C3×C42C22×D311yescharacteristic
164C3×C42C22×D311yescharacteristic
165#213—122no—
166(C2×D3)⋊C4—62no—
167(C2×D3)⋊C4—62no—
168(C2×D3)⋊C4—62no—
169(C2×D3)⋊C4—62no—
170(C2×D3)⋊C4—61no—
171(C2×D3)⋊C4—61no—
172(C2×D3)⋊C4—121no—
173C4⋊Dic3—21no—
174C4⋊Dic3—31no—
175C4⋊Dic3—31no—
176C4⋊Dic3—61no—
177C4⋊Dic3—62no—
178C4⋊Dic3D1212yes—
179C4⋊Dic3#6711yescharacteristic
180Dic3⋊C4—21no—
181Dic3⋊C4—62no—
182C4×Dic3—21no—
183C4×Dic3—62no—
184C4×Dic3—62no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—61no—
187C2×C3⋊C8—61no—
188C2×C3⋊C8—121no—
189D24—122no—
190#204—42no—
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#13511yescharacteristic
200C32×C4#13511yescharacteristic
201C32×C4AGL(1,ℤ/8)11yescharacteristic
202C32×C4AGL(1,ℤ/8)11yescharacteristic
203C3⋊Dic3—41no—
204C3×Dic3—41no—
205C3×Dic3—42no—
206C3×Dic3—41no—
207C2×SD16—61no—
208C2×D8—181no—
209C4⋊Q8—31no—
210#127—31no—
211#126—182no—
212#124—181no—
213C22⋊Q8—181no—
214C4×Q8—31no—
215C4×Q8—181no—
216C4×D4—91no—
217#117—181no—
218C4⋊C8—31no—
219C4⋊C8D3211yescharacteristic
220#102—61no—
221#102—182no—
222#102—181no—
223C4×C8—91no—
224C23×C3—121no—
225C22×D3—41no—
226C22×D3—61no—
227C22×D3—61no—
228C22×D3—121no—
229C3×Q8—61no—
230C3×Q8—61no—
231C3×Q8—121no—
232C3×Q8—121no—
233C3×D4—122no—
234C3×D4—121no—
235C3×D4—121no—
236C3×D4—121no—
237C3×D4—121no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—61no—
242C2×C3×C4—61no—
243C2×C3×C4—62no—
244C2×C3×C4C2×D1211yescharacteristic
245C2×C3×C4D3×D411yescharacteristic
246C2×C3×C4D3×D411yescharacteristic
247C2×C3×C4D3×D411yescharacteristic
248C2×C3×C4D3×D411yescharacteristic
249C2×C3×C4C2×#6711yescharacteristic
250C2×Dic3—22no—
251C2×Dic3—21no—
252C2×Dic3—21no—
253C2×Dic3—61no—
254C2×Dic3—61no—
255C2×Dic3—121no—
256D12—42no—
257D12—41no—
258D12—41no—
259D12—41no—
260D12—41no—
261D12—62no—
262D12—61no—
263D12—61no—
264D12—61no—
265D12—61no—
266D12—121no—
267C4×D3—121no—
268C4×D3—121no—
269C4×D3—121no—
270C4×D3—121no—
271C4×D3—241no—
272C4×D3—241no—
273Dic6—21no—
274Dic6—21no—
275Dic6—41no—
276Dic6—41no—
277C3×C8—41no—
278C3×C8—41no—
279C3×C8—81no—
280C3×C8—121no—
281C3⋊C8—41no—
282C3⋊C8—121no—
283C3⋊C8—121no—
284C3⋊C8—122no—
285C2×C32#44911yescharacteristic
286C2×C32#44911yescharacteristic
287C2×C32#45411yescharacteristic
288C3⋊D3—81no—
289C3×D3—161no—
290C2×Q8—31no—
291C2×Q8—61no—
292C2×D4—61no—
293C2×D4—61no—
294C2×D4—61no—
295C2×D4—91no—
296C22×C4—181no—
297SD16—122no—
298D8—362no—
299C2×C8—21no—
300C2×C8—61no—
301C2×C8—181no—
302C4⋊C4—32no—
303C4⋊C4—31no—
304C4⋊C4—61no—
305C4⋊C4—61no—
306C4⋊C4—91no—
307C4⋊C4—182no—
308C22⋊C4—182no—
309C22⋊C4—182no—
310C22⋊C4—181no—
311C42—61no—
312C42—182no—
313C42C2×D3211yescharacteristic
314C22×C3—21no—
315C22×C3—241no—
316C22×C3—241no—
317C22×C3—241no—
318C22×C3#88211yescharacteristic
319C22×C3#93711yescharacteristic
320C2×D3—81no—
321C2×D3—81no—
322C2×D3—81no—
323C2×D3—122no—
324C2×D3—121no—
325C2×D3—121no—
326C2×D3—121no—
327C2×D3—121no—
328C2×D3—121no—
329C2×D3—121no—
330C2×D3—241no—
331C2×D3—241no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—41no—
339C3×C4—122no—
340C3×C4—121no—
341C3×C4—121no—
342C3×C4#91111yescharacteristic
343C3×C4#91411yescharacteristic
344C3×C4#91411yescharacteristic
345C3×C4#91611yescharacteristic
346C3×C4#91611yescharacteristic
347C3×C4#91911yescharacteristic
348C3×C4#93211yescharacteristic
349C3×C4#95011yescharacteristic
350Dic3—41no—
351Dic3—42no—
352Dic3—41no—
353Dic3—121no—
354Dic3—121no—
355Dic3—241no—
356C32#162811yescharacteristic, complemented, Sylow
357C23—121no—
358C23—181no—
359Q8—61no—
360Q8—61no—
361Q8—121no—
362Q8—121no—
363D4—122no—
364D4—121no—
365D4—121no—
366D4—121no—
367D4—121no—
368D4—181no—
369D4—181no—
370C2×C4—61no—
371C2×C4—61no—
372C2×C4—62no—
373C2×C4—181no—
374C2×C4—361no—
375C2×C4—361no—
376C2×C4D3×D1211yescharacteristic
377C2×C4#380211yescharacteristic
378C2×C4D3×#6711yescharacteristic
379C8—41no—
380C8—121no—
381C8—361no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—481no—
386C2×C3#475311yescharacteristic
387C2×C3#478111yescharacteristic
388C2×C3#481011yescharacteristic
389C2×C3#503711yescharacteristic
390C2×C3#517211yescharacteristic
391C2×C3#520111yescharacteristic
392D3—161no—
393D3—242no—
394D3—241no—
395D3—241no—
396C22—241no—
397C22—241no—
398C22—241no—
399C22—361no—
400C22—361no—
401C22—361no—
402C22#6392211yescharacteristic
403C4—21no—
404C4—121no—
405C4—121no—
406C4—122no—
407C4—361no—
408C4#6379811yescharacteristic
409C4#6380911yescharacteristic
410C4#6393411yescharacteristic
411C4#6394911yescharacteristic
412C3—21no—
413C3#6843311yescharacteristic, complemented
414C3#7102911yescharacteristic, complemented
415C2—481no—
416C2—721no—
417C2#1059061511yescharacteristic
418C2#1059096411yescharacteristic
419C2#1059102011yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#10590355C2
hypercenterC4⋊C8D32
hypocenterC32#1628
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
1. #10593865C2semidirect
2. C3×#4848C2semidirect
4. #10590277C2semidirect
5. #10589349C2semidirect
6. C3×#4486C2semidirect
7. #10589083C2semidirect
33. #4848D3semidirect
37. #4486D3semidirect
356. C32#1628semidirect
413. C3#68433semidirect
414. C3#71029semidirect

Maximal subgroups

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

subgroupindex
#105938652
C3×#48482
#105903552
#105902772
#105893492
C3×#44862
#105890832
#710293
#684333