Finite Group Databasebeta

← #11779021

Subgroups — #11779021

Order 1152.

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

normal subgroups only

This group has 507 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, complemented
2C3×#4693C211yesmaximal, characteristic, complemented
3#10590377C211yesmaximal, characteristic, complemented
4#10590347C211yesmaximal, characteristic
5#10589322C211yesmaximal, characteristic, complemented
6C3×#4459C211yesmaximal, characteristic, complemented
7#10589095C211yesmaximal, characteristic, complemented
8#71264—31nomaximal
9#68198—31nomaximal
10C4×#634C2211yescharacteristic
11C2×C3×#204—22no—
12C3×#874C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C3×#869C2211yescharacteristic
15#63898—21no—
16D3×C4⋊Dic3—21no—
17#63887—22no—
18#63872—21no—
19#63857—21no—
20C2×#3716—21no—
21C2×#3713—21no—
22C32×C4×C8C2211yescharacteristic
23C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63563—21no—
26#63562—21no—
27#5730—31no—
28#5543—31no—
29C3×#492—31no—
30#5075—31no—
31#5072—31no—
32#5015—31no—
33#4848—31no—
34#4693D311yescharacteristic, complemented
35C3×D4⋊C8—31no—
36#4546—31no—
37#4481—31no—
38#4459D311yescharacteristic, complemented
39#4456—31no—
40#4456—31no—
41#4456—61no—
42C2×#634D411yescharacteristic
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12D411yescharacteristic
47C2×C3×C4×D3—21no—
48C2×C3×Dic6D412yes—
49C2×D3×Dic3—22no—
50C2×C32×C8—21no—
51C32×C42C2311yescharacteristic
52C4⋊(C3⋊Dic3)D411yescharacteristic
53#3750—21no—
54C4×C3⋊Dic3—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×(C2×D3)⋊C4—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C2×C3×C3⋊C8—21no—
61C3×#204—44no—
62Dic3⋊Dic3—22no—
63Dic3⋊Dic3—22no—
64(C2×D3)⋊Dic3—22no—
65#3716—42no—
66#3713—42no—
67#1622—91noSylow
68C2×C3×SD16—62no—
69C3×C4⋊Q8—31no—
70C3×#127—31no—
71C3×C4×D4—31no—
72#946—62no—
73D4×Dic3—61no—
74C2×#214—61no—
75C2×#213—61no—
76C2×#213—61no—
77C2×C4⋊Dic3—61no—
78#924—61no—
79C2×#204—22no—
80C2×#204—61no—
81#897—61no—
82#893—61no—
83D3×C4⋊C4—61no—
84#890—61no—
85#890—61no—
86#878—62no—
87#874C2×D311yescharacteristic
88C4×D12C2×D311yescharacteristic
89#869C2×D311yescharacteristic
90C4×Dic6—31no—
91C4×Dic6—31no—
92C4×Dic6—61no—
93C3×C4⋊C8—31no—
94C3×C4×C8—21no—
95C3×C4×C8C2×D311yescharacteristic
96C3×C4×C8C2×D311yescharacteristic
97#832—61no—
98#832—61no—
99#821—61no—
100#809—61no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—31no—
103C4⋊(C3⋊C8)—61no—
104C4⋊(C3⋊C8)C2×D311yescharacteristic
105C22×C3×D3—21no—
106C22×C3×D3—41no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C3⋊Dic3—21no—
111C2×C3⋊Dic3—21no—
112#634—21no—
113#634—21no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—21no—
116C3×D12—21no—
117C3×D12—42no—
118C3×D12—41no—
119C3×D12—41no—
120C3×D12—41no—
121C3×D12—41no—
122C3×D12SD1612yescomplemented
123C3×C4×D3—41no—
124C3×C4×D3—41no—
125C3×Dic6—42no—
126D3×Dic3—82no—
127C32×C8—22no—
128C3⋊(C3⋊C8)—41no—
129C3×C3⋊C8—41no—
130#554—91no—
131#492—31no—
132#460—91no—
133#459—91no—
134#333—91no—
135Q8⋊C8—91no—
136D4⋊C8—31no—
137C2×C3×Q8—32no—
138C2×C3×D4—31no—
139C2×C3×D4—61no—
140C2×C3×D4—61no—
141C2×C3×D4—61no—
142C22×C3×C4—61no—
143C22×Dic3—62no—
144C2×D12—21no—
145C2×D12—21no—
146C2×D12—21no—
147C2×D12D1211yescharacteristic
148C2×C4×D3—21no—
149C2×C4×D3—62no—
150C2×Dic6—31no—
151C2×Dic6—31no—
152C2×Dic6—61no—
153C2×Dic6#6712yes—
154C3×SD16—124no—
155C2×C3×C8—21no—
156C2×C3×C8—21no—
157C2×C3×C8—41no—
158C2×C3×C8—61no—
159C3×C4⋊C4—31no—
160C3×C4⋊C4—61no—
161C3×C4⋊C4—61no—
162C3×C22⋊C4—61no—
163C3×C42—21no—
164C3×C42C22×D311yescharacteristic
165C3×C42C22×D311yescharacteristic
166#217—62no—
167#214—122no—
168#213—122no—
169#213—122no—
170(C2×D3)⋊C4—21no—
171(C2×D3)⋊C4—62no—
172C4⋊Dic3—21no—
173C4⋊Dic3—21no—
174C4⋊Dic3—31no—
175C4⋊Dic3—31no—
176C4⋊Dic3—61no—
177C4⋊Dic3—62no—
178C4⋊Dic3—62no—
179C4⋊Dic3D1211yescharacteristic
180Dic3⋊C4—62no—
181Dic3⋊C4—62no—
182Dic3⋊C4—61no—
183Dic3⋊C4—61no—
184Dic3⋊C4—121no—
185C4×Dic3—61no—
186C4×Dic3—61no—
187C4×Dic3—121no—
188C2×C3⋊C8—21no—
189C2×C3⋊C8—61no—
190C2×C3⋊C8—61no—
191C2×C3⋊C8—121no—
192#204—44no—
193#204—122no—
194C22×C32#12011yescharacteristic
195C2×C3×D3—22no—
196C2×C3×D3—41no—
197C2×C3×D3—41no—
198C2×C3×D3—81no—
199C2×C3×D3—81no—
200C2×C3×D3—81no—
201C32×C4—21no—
202C32×C4C2×SD1611yescharacteristic
203C32×C4#13511yescharacteristic
204C32×C4AGL(1,ℤ/8)11yescharacteristic
205C32×C4#13711yescharacteristic
206C3⋊Dic3—41no—
207C3⋊Dic3—41no—
208C3×Dic3—41no—
209C3×Dic3—42no—
210C2×SD16—62no—
211C2×SD16—181no—
212C2×D8—181no—
213C4⋊Q8—31no—
214#127—31no—
215#125—181no—
216C22⋊Q8—182no—
217C22⋊Q8—181no—
218C4×Q8—91no—
219C4×D4—31no—
220C4×D4—181no—
221C2×C4⋊C4—181no—
222C4⋊C8—31no—
223C4⋊C8—91no—
224#102—181no—
225#102—181no—
226C4×C8D3211yescharacteristic
227C23×C3—61no—
228C23×C3—121no—
229C22×D3—21no—
230C22×D3—41no—
231C3×Q8—122no—
232C3×D4—32no—
233C3×D4—61no—
234C3×D4—122no—
235C3×D4—121no—
236C3×D4—121no—
237C3×D4—121no—
238C3×D4—121no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—62no—
243C2×C3×C4—61no—
244C2×C3×C4—121no—
245C2×C3×C4—121no—
246C2×C3×C4C2×D1211yescharacteristic
247C2×C3×C4D3×D411yescharacteristic
248C2×C3×C4D3×D411yescharacteristic
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4C2×#6711yescharacteristic
252C2×Dic3—21no—
253C2×Dic3—22no—
254C2×Dic3—61no—
255C2×Dic3—61no—
256C2×Dic3—61no—
257C2×Dic3—61no—
258C2×Dic3—121no—
259C2×Dic3—121no—
260C2×Dic3—242no—
261D12—21no—
262D12—42no—
263D12—41no—
264D12—41no—
265D12—41no—
266D12—41no—
267D12#20412yescomplemented
268C4×D3—41no—
269C4×D3—41no—
270C4×D3—242no—
271Dic6—42no—
272Dic6—62no—
273Dic6—61no—
274Dic6—61no—
275Dic6—61no—
276Dic6—61no—
277Dic6—121no—
278C3×C8—22no—
279C3×C8—22no—
280C3×C8—42no—
281C3×C8—121no—
282C3⋊C8—41no—
283C3⋊C8—121no—
284C3⋊C8—121no—
285C3⋊C8—241no—
286C2×C32#44811yescharacteristic
287C2×C32#44911yescharacteristic
288C2×C32#45311yescharacteristic
289C3×D3—42no—
290C3×D3—161no—
291C2×Q8—32no—
292C2×Q8—91no—
293C2×D4—31no—
294C2×D4—61no—
295C2×D4—61no—
296C2×D4—61no—
297C22×C4—61no—
298C22×C4—182no—
299SD16—124no—
300SD16—362no—
301D8—362no—
302C2×C8—21no—
303C2×C8—61no—
304C2×C8—181no—
305C4⋊C4—31no—
306C4⋊C4—61no—
307C4⋊C4—61no—
308C4⋊C4—91no—
309C4⋊C4—182no—
310C4⋊C4—182no—
311C4⋊C4—181no—
312C22⋊C4—61no—
313C22⋊C4—182no—
314C42—181no—
315C42C2×D3211yescharacteristic
316C22×C3—21no—
317C22×C3—62no—
318C22×C3—121no—
319C22×C3—121no—
320C22×C3—241no—
321C22×C3—241no—
322C22×C3—241no—
323C22×C3#88211yescharacteristic
324C22×C3#93711yescharacteristic
325C2×D3—22no—
326C2×D3—41no—
327C2×D3—41no—
328C2×D3—81no—
329C2×D3—81no—
330C2×D3—81no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—41no—
338C3×C4—121no—
339C3×C4—122no—
340C3×C4C2×#20411yescharacteristic
341C3×C4#90911yescharacteristic
342C3×C4#91111yescharacteristic
343C3×C4D3×SD1611yescharacteristic
344C3×C4#91411yescharacteristic
345C3×C4#91511yescharacteristic
346C3×C4#91611yescharacteristic
347C3×C4#91611yescharacteristic
348Dic3—41no—
349Dic3—42no—
350Dic3—122no—
351Dic3—121no—
352Dic3—121no—
353Dic3—121no—
354Dic3—121no—
355Dic3—241no—
356C32#162211yescharacteristic, complemented, Sylow
357C23—61no—
358C23—121no—
359Q8—122no—
360Q8—181no—
361Q8—181no—
362D4—32no—
363D4—61no—
364D4—122no—
365D4—121no—
366D4—121no—
367D4—121no—
368D4—121no—
369C2×C4—61no—
370C2×C4—62no—
371C2×C4—121no—
372C2×C4—121no—
373C2×C4—181no—
374C2×C4—181no—
375C2×C4—722no—
376C2×C4D3×D1211yescharacteristic
377C2×C4#380211yescharacteristic
378C2×C4D3×#6711yescharacteristic
379C8—22no—
380C8—121no—
381C8—361no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—122no—
386C2×C3—481no—
387C2×C3#473811yescharacteristic
388C2×C3#478111yescharacteristic
389C2×C3#482211yescharacteristic
390C2×C3#507711yescharacteristic
391C2×C3#517011yescharacteristic
392C2×C3#517211yescharacteristic
393D3—42no—
394D3—161no—
395C22—62no—
396C22—121no—
397C22—121no—
398C22—241no—
399C22—241no—
400C22—241no—
401C22#6392211yescharacteristic
402C4—21no—
403C4—122no—
404C4—121no—
405C4—361no—
406C4—361no—
407C4D3×#20411yescharacteristic
408C4#6379811yescharacteristic
409C4#6380011yescharacteristic
410C4#6380911yescharacteristic
411C3—21no—
412C3#6819811yescharacteristic, complemented
413C3#7126411yescharacteristic, complemented
414C2—122no—
415C2—481no—
416C2#1059039511yescharacteristic
417C2#1059082211yescharacteristic
418C2#1059096411yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#120
prime radical#10590347C2
hypercenterC4×C8D32
hypocenterC32#1622
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. #10593956C2semidirect
2. C3×#4693C2semidirect
3. #10590377C2semidirect
5. #10589322C2semidirect
6. C3×#4459C2semidirect
7. #10589095C2semidirect
34. #4693D3semidirect
38. #4459D3semidirect
122. C3×D12SD16semidirect
267. D12#204semidirect
356. C32#1622semidirect
412. C3#68198semidirect
413. C3#71264semidirect

Maximal subgroups

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

subgroupindex
#105939562
C3×#46932
#105903772
#105903472
#105893222
C3×#44592
#105890952
#712643
#681983