Finite Group Databasebeta

← #11779282

Subgroups — #11779282

Order 1152.

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

normal subgroups only

This group has 464 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#10593879C211yesmaximal, characteristic, complemented
2C3×#4848C211yesmaximal, characteristic, complemented
3#10590347C211yesmaximal, characteristic
4#10590273C211yesmaximal, characteristic, complemented
5#10589352C211yesmaximal, characteristic, complemented
6C3×#4483C211yesmaximal, characteristic, complemented
7#10589084C211yesmaximal, characteristic, complemented
8#71029—31nomaximal
9#68201—31nomaximal
10#64078C2211yescharacteristic
11C2×C3×#204—21no—
12C3×#874C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63861—22no—
16#63860—21no—
17#63856—21no—
18#63844—21no—
19#63841—21no—
20C2×#3713—21no—
21C32×C4⋊C8C2211yescharacteristic
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×#821—21no—
24C3×C4×C3⋊C8C2211yescharacteristic
25#63563—22no—
26#63562—21no—
27#5584—31no—
28#5542—31no—
29C3×#460—31no—
30#5072—31no—
31#5070—31no—
32#5015—31no—
33#4848D311yescharacteristic, complemented
34#4694—31no—
35C3×D4⋊C8—31no—
36#4535—31no—
37#4486—31no—
38#4486—31no—
39#4486—61no—
40#4483D311yescharacteristic, complemented
41#4456—31no—
42C2×#634—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12D411yescharacteristic
47C2×C3×C4×D3—21no—
48C2×C3×Dic6D411yescharacteristic
49C2×C32×C8—21no—
50C32×C42C2311yescharacteristic
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)D412yes—
53C2×C3⋊(C3⋊C8)—21no—
54C3×(C2×D3)⋊C4—21no—
55C3×C4⋊Dic3D411yescharacteristic
56C3×C4⋊Dic3D411yescharacteristic
57C3×Dic3⋊C4—21no—
58C3×C4×Dic3—21no—
59C2×C3×C3⋊C8—21no—
60C3×#204—42no—
61#3724—22no—
62(C2×D3)⋊Dic3—22no—
63(C2×D3)⋊Dic3—22no—
64Dic32—22no—
65#3713—42no—
66#1628—91noSylow
67C2×C3×SD16—61no—
68C3×#127—31no—
69C3×C4×Q8—31no—
70C3×C4×D4—31no—
71#946—61no—
72#936—61no—
73C2×#213—61no—
74C2×#213—61no—
75#926—61no—
76#924—61no—
77C2×#204—21no—
78#898—62no—
79#892—61no—
80#887—61no—
81#879—62no—
82#875—61no—
83#874C2×D311yescharacteristic
84C4×D12C2×D311yescharacteristic
85#869—31no—
86#869—31no—
87#869—61no—
88C4×Dic6—61no—
89C4×Dic6C2×D311yescharacteristic
90C3×C4⋊C8—21no—
91C3×C4⋊C8C2×D311yescharacteristic
92C3×C4⋊C8C2×D311yescharacteristic
93C3×#102—61no—
94C3×C4×C8—31no—
95#832—62no—
96#832—61no—
97#821—21no—
98#821—62no—
99#809—61no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—61no—
103C4×C3⋊C8C2×D311yescharacteristic
104C22×C3×D3—21no—
105C22×C3×D3—41no—
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C3⋊Dic3—22no—
110#634—41no—
111#634—41no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—21no—
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—21no—
125C3×Dic6—21no—
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—91no—
134Q8⋊C8—91no—
135D4⋊C8—31no—
136C2×C3×Q8—31no—
137C2×C3×D4—31no—
138C2×C3×D4—61no—
139C2×C3×D4—61no—
140C2×C3×D4—61no—
141C22×C3×C4—61no—
142C2×D12—21no—
143C2×D12—21no—
144C2×D12—21no—
145C2×D12D1211yescharacteristic
146C2×C4×D3—21no—
147C2×Dic6—61no—
148C2×Dic6—61no—
149C2×Dic6—121no—
150C2×Dic6#6711yescharacteristic
151C3×SD16—122no—
152C2×C3×C8—21no—
153C2×C3×C8—21no—
154C2×C3×C8—41no—
155C2×C3×C8—61no—
156C3×C4⋊C4—31no—
157C3×C4⋊C4—31no—
158C3×C4⋊C4—61no—
159C3×C22⋊C4—61no—
160C3×C42—21no—
161C3×C42—61no—
162C3×C42C22×D311yescharacteristic
163C3×C42C22×D311yescharacteristic
164#217—62no—
165#217—62no—
166#213—122no—
167#213—122no—
168(C2×D3)⋊C4—21no—
169(C2×D3)⋊C4—62no—
170(C2×D3)⋊C4—62no—
171C4⋊Dic3—32no—
172C4⋊Dic3—32no—
173C4⋊Dic3—62no—
174C4⋊Dic3—61no—
175C4⋊Dic3—61no—
176C4⋊Dic3—121no—
177C4⋊Dic3D1211yescharacteristic
178C4⋊Dic3#6711yescharacteristic
179Dic3⋊C4—21no—
180Dic3⋊C4—62no—
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—
189#204—42no—
190C22×C32#12011yescharacteristic
191C2×C3×D3—41no—
192C2×C3×D3—41no—
193C2×C3×D3—41no—
194C2×C3×D3—81no—
195C2×C3×D3—81no—
196C2×C3×D3—81no—
197C32×C4—21no—
198C32×C4#13511yescharacteristic
199C32×C4#13511yescharacteristic
200C32×C4AGL(1,ℤ/8)11yescharacteristic
201C32×C4AGL(1,ℤ/8)11yescharacteristic
202C3⋊Dic3—42no—
203C3×Dic3—41no—
204C3×Dic3—41no—
205C3×Dic3—41no—
206C2×SD16—61no—
207C2×D8—181no—
208C4⋊Q8—91no—
209#127—31no—
210#126—182no—
211#124—181no—
212C22⋊Q8—181no—
213C4×Q8—31no—
214C4×Q8—181no—
215C4×D4—31no—
216#117—181no—
217C4⋊C8—91no—
218C4⋊C8D3211yescharacteristic
219#102—61no—
220#102—181no—
221#102—182no—
222C4×C8—31no—
223C23×C3—61no—
224C23×C3—121no—
225C22×D3—21no—
226C22×D3—41no—
227C3×Q8—61no—
228C3×Q8—61no—
229C3×D4—61no—
230C3×D4—61no—
231C3×D4—122no—
232C3×D4—121no—
233C3×D4—121no—
234C3×D4—121no—
235C3×D4—121no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—61no—
240C2×C3×C4—61no—
241C2×C3×C4—61no—
242C2×C3×C4—121no—
243C2×C3×C4—121no—
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—21no—
251C2×Dic3—21no—
252C2×Dic3—21no—
253C2×Dic3—62no—
254C2×Dic3—62no—
255C2×Dic3—122no—
256D12—21no—
257D12—21no—
258D12—42no—
259D12—41no—
260D12—41no—
261D12—41no—
262D12—41no—
263C4×D3—41no—
264C4×D3—41no—
265Dic6—21no—
266Dic6—21no—
267Dic6—121no—
268Dic6—121no—
269Dic6—121no—
270Dic6—121no—
271Dic6—241no—
272Dic6—241no—
273C3×C8—41no—
274C3×C8—41no—
275C3×C8—81no—
276C3×C8—121no—
277C3⋊C8—41no—
278C3⋊C8—121no—
279C3⋊C8—121no—
280C3⋊C8—241no—
281C2×C32#44911yescharacteristic
282C2×C32#44911yescharacteristic
283C2×C32#45411yescharacteristic
284C3×D3—81no—
285C3×D3—161no—
286C2×Q8—31no—
287C2×Q8—181no—
288C2×D4—31no—
289C2×D4—61no—
290C2×D4—61no—
291C2×D4—61no—
292C22×C4—61no—
293SD16—122no—
294D8—362no—
295C2×C8—21no—
296C2×C8—61no—
297C2×C8—181no—
298C4⋊C4—31no—
299C4⋊C4—31no—
300C4⋊C4—61no—
301C4⋊C4—92no—
302C4⋊C4—182no—
303C4⋊C4—181no—
304C22⋊C4—61no—
305C22⋊C4—182no—
306C22⋊C4—182no—
307C42—61no—
308C42—182no—
309C42C2×D3211yescharacteristic
310C22×C3—21no—
311C22×C3—121no—
312C22×C3—121no—
313C22×C3—121no—
314C22×C3—241no—
315C22×C3—241no—
316C22×C3—241no—
317C22×C3#88211yescharacteristic
318C22×C3#93711yescharacteristic
319C2×D3—41no—
320C2×D3—41no—
321C2×D3—41no—
322C2×D3—81no—
323C2×D3—81no—
324C2×D3—81no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—41no—
332C3×C4—121no—
333C3×C4—121no—
334C3×C4—121no—
335C3×C4#90411yescharacteristic
336C3×C4#90811yescharacteristic
337C3×C4#91111yescharacteristic
338C3×C4#91411yescharacteristic
339C3×C4#91611yescharacteristic
340C3×C4#91611yescharacteristic
341C3×C4#93211yescharacteristic
342C3×C4#95011yescharacteristic
343Dic3—41no—
344Dic3—41no—
345Dic3—41no—
346Dic3—122no—
347Dic3—122no—
348Dic3—242no—
349C32#162811yescharacteristic, complemented, Sylow
350C23—61no—
351C23—121no—
352Q8—61no—
353Q8—61no—
354Q8—361no—
355Q8—361no—
356D4—61no—
357D4—61no—
358D4—122no—
359D4—121no—
360D4—121no—
361D4—121no—
362D4—121no—
363C2×C4—61no—
364C2×C4—61no—
365C2×C4—61no—
366C2×C4—121no—
367C2×C4—121no—
368C2×C4—182no—
369C2×C4D3×D1211yescharacteristic
370C2×C4#380211yescharacteristic
371C2×C4D3×#6711yescharacteristic
372C8—41no—
373C8—121no—
374C8—361no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—241no—
379C2×C3—481no—
380C2×C3#473411yescharacteristic
381C2×C3#478111yescharacteristic
382C2×C3#482711yescharacteristic
383C2×C3#503711yescharacteristic
384C2×C3#517211yescharacteristic
385C2×C3#520111yescharacteristic
386D3—81no—
387D3—161no—
388C22—121no—
389C22—121no—
390C22—121no—
391C22—241no—
392C22—241no—
393C22—241no—
394C22#6392211yescharacteristic
395C4—21no—
396C4—121no—
397C4—121no—
398C4—121no—
399C4—362no—
400C4#6379411yescharacteristic
401C4#6380611yescharacteristic
402C4#6393211yescharacteristic
403C4#6394711yescharacteristic
404C3—21no—
405C3#6820111yescharacteristic, complemented
406C3#7102911yescharacteristic, complemented
407C2—241no—
408C2—481no—
409C2#1059061311yescharacteristic
410C2#1059082311yescharacteristic
411C2#1059101911yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#10590347C2
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. #10593879C2semidirect
2. C3×#4848C2semidirect
4. #10590273C2semidirect
5. #10589352C2semidirect
6. C3×#4483C2semidirect
7. #10589084C2semidirect
33. #4848D3semidirect
40. #4483D3semidirect
349. C32#1628semidirect
405. C3#68201semidirect
406. C3#71029semidirect

Maximal subgroups

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

subgroupindex
#105938792
C3×#48482
#105903472
#105902732
#105893522
C3×#44832
#105890842
#710293
#682013