Finite Group Databasebeta

← #11779270

Subgroups — #11779270

Order 1152.

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

normal subgroups only

This group has 502 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×#5542C211yesmaximal, characteristic, complemented
2#10592714C211yesmaximal, characteristic
3#10590367C211yesmaximal, characteristic, complemented
4#10590281C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#10589092C211yesmaximal, characteristic, complemented
7#10589084C211yesmaximal, characteristic, complemented
8#71931—31nomaximal
9#68201—31nomaximal
10C32×C4×D4C2211yescharacteristic
11C2×#3753—21no—
12#64083C2211yescharacteristic
13C3×#936—21no—
14C3×#926—21no—
15C3×#924—21no—
16C3×#887—21no—
17C3×#879—22no—
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20C2×#3717—21no—
21#63636—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63564—22no—
26#63564—21no—
27C3×#556—31no—
28#5542D311yescharacteristic, complemented
29#5088—31no—
30#5027—31no—
31#5015—31no—
32#5015—31no—
33#5015—61no—
34#4848—31no—
35#4694—31no—
36C3×D4⋊C8—31no—
37#4547—31no—
38#4535—31no—
39D4⋊(C3⋊C8)D311yescharacteristic, complemented
40#4486—31no—
41#4456—31no—
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C3×Dic6—21no—
48C2×C3×Dic6D411yescharacteristic
49C32×C4⋊C4D411yescharacteristic
50C32×C22⋊C4—21no—
51C32×C42C2311yescharacteristic
52#3753—42no—
53C2×C3⋊(C3⋊C8)—21no—
54C3×#217—22no—
55C3×#217—22no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3D412yes—
58C3×C4⋊Dic3D411yescharacteristic
59C3×Dic3⋊C4—22no—
60C3×Dic3⋊C4—21no—
61C3×C4×Dic3—22no—
62C3×C4×Dic3—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65#3717—42no—
66#1628—91noSylow
67C3×C4⋊Q8—31no—
68C3×#126—62no—
69C3×#124—61no—
70C3×C22⋊Q8—61no—
71C3×C4×Q8—31no—
72C3×C4×Q8—61no—
73C3×C4×D4—21no—
74C3×C4×D4C2×D311yescharacteristic
75C3×C4×D4C2×D311yescharacteristic
76C3×#117—61no—
77C2×#215—61no—
78#936—21no—
79C2×#213—62no—
80C2×#213—61no—
81C2×#213—61no—
82#926—21no—
83#924—21no—
84C2×#204—61no—
85#887—21no—
86#879—22no—
87#874—31no—
88#874—31no—
89#874—61no—
90#869C2×D311yescharacteristic
91C4×Dic6C2×D311yescharacteristic
92C3×C4⋊C8—31no—
93C3×C4×C8—31no—
94#821—62no—
95#821—61no—
96#809—61no—
97#809—62no—
98#809—62no—
99#809—61no—
100#809—61no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—31no—
103C4⋊(C3⋊C8)—61no—
104C4⋊(C3⋊C8)C2×D311yescharacteristic
105C4×C3⋊C8C2×D311yescharacteristic
106C23×C32—21no—
107C22×C3⋊D3—41no—
108C32×D4—21no—
109C32×D4—21no—
110C2×C32×C4—21no—
111C2×C32×C4—41no—
112C2×C32×C4—41no—
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C4⋊(C3⋊D3)—41no—
117C4⋊(C3⋊D3)—41no—
118C4⋊(C3⋊D3)—42no—
119C4⋊(C3⋊D3)—41no—
120C4⋊(C3⋊D3)—41no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—22no—
124C3×Dic6—21no—
125C3×Dic6—21no—
126C3×Dic6—41no—
127C3×Dic6—41no—
128C3⋊(C3⋊C8)—41no—
129C3×C3⋊C8—41no—
130C3×C3⋊C8—41no—
131#556—31no—
132#486—91no—
133#460—91no—
134#459—91no—
135#332—91no—
136Q8⋊C8—91no—
137D4⋊C8—31no—
138C2×C3×Q8—31no—
139C2×C3×Q8—61no—
140C2×C3×D4—21no—
141C2×C3×D4D1211yescharacteristic
142C2×C3×D4#6711yescharacteristic
143C22×C3×C4—21no—
144C22×C3×C4—21no—
145C22×C3×C4—41no—
146C2×D12—62no—
147C2×D12—61no—
148C2×D12—61no—
149C2×D12—61no—
150C2×D12—61no—
151C2×D12—61no—
152C2×D12—61no—
153C2×D12—121no—
154C2×D12—121no—
155C2×Dic6—21no—
156C2×Dic6#6711yescharacteristic
157C2×C3×C8—61no—
158C2×C3×C8—61no—
159C3×C4⋊C4—21no—
160C3×C4⋊C4—31no—
161C3×C4⋊C4—32no—
162C3×C4⋊C4—62no—
163C3×C4⋊C4—61no—
164C3×C4⋊C4—61no—
165C3×C4⋊C4D1211yescharacteristic
166C3×C4⋊C4#6711yescharacteristic
167C3×C22⋊C4—21no—
168C3×C22⋊C4—21no—
169C3×C22⋊C4—41no—
170C3×C22⋊C4—62no—
171C3×C22⋊C4—62no—
172C3×C42—21no—
173C3×C42—62no—
174C3×C42—61no—
175C3×C42C22×D311yescharacteristic
176C3×C42C22×D311yescharacteristic
177#217—22no—
178#217—22no—
179#215—122no—
180#213—124no—
181#213—122no—
182#213—122no—
183C4⋊Dic3—21no—
184C4⋊Dic3#6711yescharacteristic
185C4⋊Dic3#6712yes—
186Dic3⋊C4—22no—
187Dic3⋊C4—21no—
188C4×Dic3—22no—
189C4×Dic3—21no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—21no—
192C2×C3⋊C8—62no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—61no—
195#204—122no—
196C22×C32—41no—
197C22×C32—41no—
198C22×C32—41no—
199C22×C32#12011yescharacteristic
200C2×C3⋊D3—81no—
201C2×C3⋊D3—81no—
202C2×C3⋊D3—81no—
203C32×C4—21no—
204C32×C4—41no—
205C32×C4#13511yescharacteristic
206C32×C4#13511yescharacteristic
207C32×C4AGL(1,ℤ/8)11yescharacteristic
208C32×C4AGL(1,ℤ/8)11yescharacteristic
209C3×Dic3—41no—
210C3×Dic3—42no—
211C3×Dic3—41no—
212C2×SD16—181no—
213C2×D8—181no—
214C4⋊Q8—31no—
215#127—91no—
216#126—62no—
217#124—61no—
218C22⋊Q8—61no—
219C4×Q8—31no—
220C4×Q8—61no—
221C4×D4D3211yescharacteristic
222#117—61no—
223C4⋊C8—31no—
224C4⋊C8—91no—
225#102—181no—
226#102—182no—
227#102—181no—
228C4×C8—31no—
229C23×C3—21no—
230C23×C3—21no—
231C23×C3—41no—
232C22×D3—122no—
233C22×D3—121no—
234C22×D3—121no—
235C3×Q8—61no—
236C3×Q8—61no—
237C3×Q8—121no—
238C3×Q8—121no—
239C3×D4—22no—
240C3×D4—21no—
241C3×D4—21no—
242C3×D4—21no—
243C3×D4—21no—
244C3×D4—41no—
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—41no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4—61no—
256C2×C3×C4—62no—
257C2×C3×C4—61no—
258C2×C3×C4—81no—
259C2×C3×C4—81no—
260C2×C3×C4C2×D1211yescharacteristic
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4D3×D411yescharacteristic
263C2×C3×C4C2×#6711yescharacteristic
264C2×C3×C4C2×#6711yescharacteristic
265C2×C3×C4C2×#6711yescharacteristic
266C2×Dic3—21no—
267C2×Dic3—21no—
268C2×Dic3—22no—
269D12—122no—
270D12—122no—
271D12—122no—
272D12—122no—
273D12—121no—
274D12—121no—
275D12—121no—
276D12—121no—
277D12—121no—
278D12—121no—
279D12—121no—
280D12—121no—
281D12—241no—
282D12—241no—
283D12—242no—
284Dic6—21no—
285Dic6—21no—
286Dic6—41no—
287Dic6—41no—
288C3×C8—121no—
289C3×C8—121no—
290C3⋊C8—41no—
291C3⋊C8—41no—
292C3⋊C8—122no—
293C3⋊C8—121no—
294C3⋊C8—121no—
295C2×C32—81no—
296C2×C32#44911yescharacteristic
297C2×C32#44911yescharacteristic
298C2×C32#45411yescharacteristic
299C3⋊D3—161no—
300C2×Q8—31no—
301C2×Q8—61no—
302C2×D4—181no—
303C2×D4—181no—
304C2×D4—181no—
305C2×D4#62611yescharacteristic
306C22×C4—21no—
307SD16—362no—
308D8—362no—
309C2×C8—61no—
310C2×C8—61no—
311C2×C8—181no—
312C4⋊C4—31no—
313C4⋊C4—32no—
314C4⋊C4—62no—
315C4⋊C4—61no—
316C4⋊C4—61no—
317C4⋊C4#62611yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—62no—
320C22⋊C4—62no—
321C42—62no—
322C42—61no—
323C42C2×D3211yescharacteristic
324C22×C3—21no—
325C22×C3—42no—
326C22×C3—41no—
327C22×C3—41no—
328C22×C3—41no—
329C22×C3—41no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—81no—
333C22×C3—81no—
334C22×C3#88211yescharacteristic
335C22×C3#95311yescharacteristic
336C2×D3—242no—
337C2×D3—242no—
338C2×D3—242no—
339C2×D3—241no—
340C2×D3—241no—
341C2×D3—241no—
342C2×D3—241no—
343C2×D3—241no—
344C2×D3—241no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—41no—
352C3×C4—41no—
353C3×C4—41no—
354C3×C4—81no—
355C3×C4—122no—
356C3×C4—121no—
357C3×C4—121no—
358C3×C4#90411yescharacteristic
359C3×C4#90811yescharacteristic
360C3×C4#91111yescharacteristic
361C3×C4#91611yescharacteristic
362C3×C4#94911yescharacteristic
363C3×C4#94911yescharacteristic
364C3×C4#95011yescharacteristic
365C3×C4#95011yescharacteristic
366Dic3—41no—
367Dic3—42no—
368Dic3—41no—
369C32#162811yescharacteristic, complemented, Sylow
370C23—21no—
371C23—361no—
372Q8—61no—
373Q8—61no—
374Q8—121no—
375Q8—121no—
376D4—21no—
377D4—21no—
378D4—362no—
379D4—361no—
380D4—361no—
381D4—361no—
382D4—361no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—61no—
387C2×C4—62no—
388C2×C4—61no—
389C2×C4C2×#62611yescharacteristic
390C2×C4D3×#6711yescharacteristic
391C2×C4D3×#6711yescharacteristic
392C8—121no—
393C8—121no—
394C8—361no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—82no—
399C2×C3—81no—
400C2×C3—81no—
401C2×C3#473411yescharacteristic
402C2×C3#478111yescharacteristic
403C2×C3#482711yescharacteristic
404C2×C3#523811yescharacteristic
405C2×C3#523811yescharacteristic
406C2×C3#524511yescharacteristic
407D3—482no—
408D3—481no—
409D3—481no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—721no—
414C22—721no—
415C22—721no—
416C22#6397711yescharacteristic
417C4—21no—
418C4—41no—
419C4—122no—
420C4—121no—
421C4—121no—
422C4#6382511yescharacteristic
423C4#6382911yescharacteristic
424C4#6392511yescharacteristic
425C4#6393511yescharacteristic
426C3—21no—
427C3#6820111yescharacteristic, complemented
428C3#7193111yescharacteristic, complemented
429C2—81no—
430C2—1441no—
431C2#1059116311yescharacteristic
432C2#1059145211yescharacteristic
433C2#1059168511yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#120
prime radical#10592714C2
hypercenterC4×D4D32
hypocenterC32#1628
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#5542C2semidirect
3. #10590367C2semidirect
4. #10590281C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
6. #10589092C2semidirect
7. #10589084C2semidirect
28. #5542D3semidirect
39. D4⋊(C3⋊C8)D3semidirect
369. C32#1628semidirect
427. C3#68201semidirect
428. C3#71931semidirect

Maximal subgroups

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

subgroupindex
C3×#55422
#105927142
#105903672
#105902812
C3×D4⋊(C3⋊C8)2
#105890922
#105890842
#719313
#682013