Finite Group Databasebeta

← #11779878

Subgroups — #11779878

Order 1152.

548 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 100 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×#5577C211yesmaximal, characteristic
2#10592719C211yesmaximal, characteristic, complemented
3#10590365C211yesmaximal, characteristic, complemented
4#10590273C211yesmaximal, characteristic, complemented
5C3×#4535C211yesmaximal, characteristic, complemented
6#10589090C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#71921—31nomaximal
9#68248—31nomaximal
10C2×C3×#239—21no—
11C32×C4×Q8C2211yescharacteristic
12#64078C2211yescharacteristic
13C3×#895—22no—
14C3×#895—21no—
15C3×#874—21no—
16C3×#874C2211yescharacteristic
17C3×C4×D12—21no—
18C3×C4×D12C2211yescharacteristic
19C2×#3716—21no—
20#63662—21no—
21#63635—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63567—21no—
26#63563—22no—
27C3×#550—31no—
28#5577D311yescharacteristic
29#5070—31no—
30#5020—31no—
31#5020—31no—
32#5020—61no—
33#5019—31no—
34#4841—31no—
35#4694—31no—
36C3×Q8⋊C8—31no—
37#4544—31no—
38#4535D311yescharacteristic, complemented
39D4⋊(C3⋊C8)—31no—
40#4485—31no—
41#4459—31no—
42C2×C32×Q8D411yescharacteristic
43C2×#634—21no—
44C3×#239—42no—
45C3×#239—42no—
46C2×C3×D12—22no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12—22no—
50C2×C3×D12D411yescharacteristic
51C2×C3×D12D412yes—
52C2×C3×C4×D3—22no—
53C2×C3×C4×D3—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4D411yescharacteristic
56C32×C42—21no—
57C32×C42C2311yescharacteristic
58C4⋊(C3⋊Dic3)—21no—
59C4⋊(C3⋊Dic3)—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C3×(C2×D3)⋊C4—22no—
62C3×(C2×D3)⋊C4—21no—
63C3×C4⋊Dic3D411yescharacteristic
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66#3716—42no—
67#1642—91noSylow
68C2×C3×#41—61no—
69C2×#239—21no—
70C3×#127—31no—
71C3×#127—61no—
72C3×#121—62no—
73C3×#121—61no—
74C3×C4×Q8—21no—
75C3×C4×Q8C2×D311yescharacteristic
76C3×C4×Q8C2×D311yescharacteristic
77C3×C4×D4—31no—
78C3×C4×D4—61no—
79C2×#214—61no—
80C2×#204—61no—
81#895—22no—
82#895—21no—
83#874—21no—
84#874C2×D311yescharacteristic
85C4×D12—21no—
86C4×D12C2×D311yescharacteristic
87#869—31no—
88#869—31no—
89#869—61no—
90C3×C4⋊C8—31no—
91C3×C4×C8—31no—
92#835—62no—
93#835—61no—
94#835—61no—
95#832—62no—
96#821—62no—
97#816—61no—
98#810—61no—
99#808—62no—
100#808—61no—
101#808—61no—
102C4⋊(C3⋊C8)—31no—
103C4⋊(C3⋊C8)—31no—
104C4⋊(C3⋊C8)—61no—
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C4×C3⋊C8C2×D311yescharacteristic
107C22×C3×D3—21no—
108C22×C3×D3—22no—
109C32×Q8—21no—
110C32×Q8SD1612yescomplemented
111C2×C32×C4—21no—
112C2×C32×C4—21no—
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C3⋊Dic3—41no—
117#634—41no—
118#634—41no—
119C2×C3×Dic3—21no—
120C3×D12—21no—
121C3×D12—21no—
122C3×D12—42no—
123C3×D12—44no—
124C3×D12—41no—
125C3×D12—41no—
126C3×D12—41no—
127C3×D12—41no—
128C3×D12—82no—
129C3×C4×D3—44no—
130C3×C4×D3—41no—
131C3×C4×D3—41no—
132C3⋊(C3⋊C8)—41no—
133C3×C3⋊C8—41no—
134C3×C3⋊C8—41no—
135#550—31no—
136#486—91no—
137#475—91no—
138#461—91no—
139#331—91no—
140Q8⋊C8—31no—
141D4⋊C8—91no—
142C3×#41—122no—
143C3×#41—122no—
144C2×C3×Q8—21no—
145C2×C3×Q8D1211yescharacteristic
146C2×C3×Q8#6711yescharacteristic
147C2×C3×D4—31no—
148C2×C3×D4—32no—
149C2×C3×D4—62no—
150C2×C3×D4—62no—
151C2×C3×D4—61no—
152C2×C3×D4—61no—
153C22×C3×C4—62no—
154C22×C3×C4—61no—
155#239—42no—
156#239—42no—
157C2×D12—22no—
158C2×D12—21no—
159C2×D12—21no—
160C2×D12—22no—
161C2×D12#6711yescharacteristic
162C2×D12#6712yes—
163C2×C4×D3—22no—
164C2×C4×D3—21no—
165C2×Dic6—61no—
166C2×Dic6—61no—
167C2×Dic6—121no—
168C2×C3×C8—61no—
169C2×C3×C8—61no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—31no—
174C3×C4⋊C4—41no—
175C3×C4⋊C4D1211yescharacteristic
176C3×C4⋊C4#6711yescharacteristic
177C3×C22⋊C4—62no—
178C3×C22⋊C4—61no—
179C3×C42—21no—
180C3×C42—21no—
181C3×C42—21no—
182C3×C42—41no—
183C3×C42C22×D311yescharacteristic
184C3×C42C22×D311yescharacteristic
185#214—122no—
186(C2×D3)⋊C4—22no—
187(C2×D3)⋊C4—21no—
188C4⋊Dic3—62no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191C4⋊Dic3—61no—
192C4⋊Dic3—61no—
193C4⋊Dic3—121no—
194C4⋊Dic3#6711yescharacteristic
195C2×C3⋊C8—21no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—62no—
198C2×C3⋊C8—61no—
199C2×C3⋊C8—61no—
200#204—122no—
201C22×C32#12011yescharacteristic
202C2×C3×D3—41no—
203C2×C3×D3—42no—
204C2×C3×D3—42no—
205C2×C3×D3—41no—
206C2×C3×D3—42no—
207C2×C3×D3—41no—
208C32×C4—22no—
209C32×C4—21no—
210C32×C4—41no—
211C32×C4C2×SD1611yescharacteristic
212C32×C4#13511yescharacteristic
213C32×C4AGL(1,ℤ/8)11yescharacteristic
214C32×C4AGL(1,ℤ/8)11yescharacteristic
215C3⋊Dic3—81no—
216C3×Dic3—41no—
217C2×#41—61no—
218C2×SD16—181no—
219C4⋊Q8—91no—
220#127—31no—
221#127—61no—
222#121—62no—
223#121—61no—
224C4×Q8D3211yescharacteristic
225C4×D4—31no—
226C4×D4—61no—
227#106—181no—
228C4⋊C8—31no—
229C4⋊C8—91no—
230#103—181no—
231#103—181no—
232#102—182no—
233C4×C8—31no—
234C23×C3—61no—
235C23×C3—62no—
236C22×D3—21no—
237C22×D3—22no—
238C3×Q8—21no—
239C3×Q8—21no—
240C3×Q8—22no—
241C3×Q8—41no—
242C3×Q8#20412yescomplemented
243C3×Q8#21412yescomplemented
244C3×D4—61no—
245C3×D4—61no—
246C3×D4—122no—
247C3×D4—124no—
248C3×D4—121no—
249C3×D4—121no—
250C3×D4—121no—
251C3×D4—121no—
252C3×D4—242no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—41no—
261C2×C3×C4—41no—
262C2×C3×C4—61no—
263C2×C3×C4—124no—
264C2×C3×C4—121no—
265C2×C3×C4—121no—
266C2×C3×C4C2×D1211yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4C2×#6711yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271C2×C3×C4C2×#6711yescharacteristic
272C2×Dic3—21no—
273C2×Dic3—122no—
274C2×Dic3—121no—
275C2×Dic3—121no—
276D12—21no—
277D12—21no—
278D12—42no—
279D12—44no—
280D12—41no—
281D12—41no—
282D12—41no—
283D12—41no—
284D12—82no—
285C4×D3—44no—
286C4×D3—41no—
287C4×D3—41no—
288Dic6—121no—
289Dic6—121no—
290Dic6—121no—
291Dic6—121no—
292Dic6—241no—
293Dic6—241no—
294C3×C8—121no—
295C3×C8—121no—
296C3⋊C8—41no—
297C3⋊C8—41no—
298C3⋊C8—122no—
299C3⋊C8—121no—
300C3⋊C8—121no—
301C2×C32#44911yescharacteristic
302C2×C32#45011yescharacteristic
303C2×C32#45511yescharacteristic
304C3×D3—81no—
305C3×D3—82no—
306#41—122no—
307#41—122no—
308C2×Q8—181no—
309C2×Q8#62611yescharacteristic
310C2×D4—31no—
311C2×D4—32no—
312C2×D4—62no—
313C2×D4—62no—
314C2×D4—61no—
315C2×D4—61no—
316C22×C4—62no—
317C22×C4—61no—
318SD16—362no—
319C2×C8—61no—
320C2×C8—61no—
321C2×C8—181no—
322C4⋊C4—21no—
323C4⋊C4—31no—
324C4⋊C4—181no—
325C4⋊C4—181no—
326C4⋊C4#62611yescharacteristic
327C22⋊C4—62no—
328C22⋊C4—61no—
329C42—21no—
330C42C2×D3211yescharacteristic
331C22×C3—21no—
332C22×C3—122no—
333C22×C3—121no—
334C22×C3—121no—
335C22×C3—122no—
336C22×C3—122no—
337C22×C3—121no—
338C22×C3#88211yescharacteristic
339C22×C3#95311yescharacteristic
340C2×D3—42no—
341C2×D3—41no—
342C2×D3—41no—
343C2×D3—42no—
344C2×D3—42no—
345C2×D3—41no—
346C3×C4—22no—
347C3×C4—21no—
348C3×C4—22no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—41no—
355C3×C4—42no—
356C3×C4—41no—
357C3×C4—41no—
358C3×C4—81no—
359C3×C4—121no—
360C3×C4C2×#20411yescharacteristic
361C3×C4#90811yescharacteristic
362C3×C4#91411yescharacteristic
363C3×C4#91911yescharacteristic
364C3×C4#93211yescharacteristic
365C3×C4C2×#21411yescharacteristic
366C3×C4#94911yescharacteristic
367C3×C4#95011yescharacteristic
368Dic3—41no—
369Dic3—242no—
370Dic3—241no—
371Dic3—241no—
372C32#164211yescharacteristic, complemented, Sylow
373C23—61no—
374C23—62no—
375Q8—21no—
376Q8—361no—
377Q8—361no—
378Q8#371612yescomplemented
379D4—61no—
380D4—61no—
381D4—122no—
382D4—124no—
383D4—121no—
384D4—121no—
385D4—121no—
386D4—121no—
387D4—242no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—61no—
391C2×C4—124no—
392C2×C4—121no—
393C2×C4—121no—
394C2×C4—361no—
395C2×C4C2×#62611yescharacteristic
396C2×C4D3×#6711yescharacteristic
397C2×C4D3×#6711yescharacteristic
398C8—121no—
399C8—121no—
400C8—361no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—241no—
405C2×C3—242no—
406C2×C3#473111yescharacteristic
407C2×C3#481011yescharacteristic
408C2×C3#482511yescharacteristic
409C2×C3#521811yescharacteristic
410C2×C3#523811yescharacteristic
411C2×C3#524211yescharacteristic
412D3—81no—
413D3—82no—
414C22—121no—
415C22—122no—
416C22—122no—
417C22—121no—
418C22—122no—
419C22—121no—
420C22#6397711yescharacteristic
421C4—22no—
422C4—21no—
423C4—41no—
424C4—121no—
425C4—721no—
426C4C2×#371611yescharacteristic
427C4#6383011yescharacteristic
428C4#6393911yescharacteristic
429C4#6394911yescharacteristic
430C3—21no—
431C3#6824811yescharacteristic, complemented
432C3#7192111yescharacteristic, complemented
433C2—241no—
434C2—242no—
435C2#1059117211yescharacteristic
436C2#1059158811yescharacteristic
437C2#1059168811yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32#120
prime radicalC3×#5577C2
hypercenterC4×Q8D32
hypocenterC32#1642
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
2. #10592719C2semidirect
3. #10590365C2semidirect
4. #10590273C2semidirect
5. C3×#4535C2semidirect
6. #10589090C2semidirect
7. #10589081C2semidirect
38. #4535D3semidirect
110. C32×Q8SD16semidirect
242. C3×Q8#204semidirect
243. C3×Q8#214semidirect
372. C32#1642semidirect
378. Q8#3716semidirect
431. C3#68248semidirect
432. C3#71921semidirect

Maximal subgroups

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

subgroupindex
C3×#55772
#105927192
#105903652
#105902732
C3×#45352
#105890902
#105890812
#719213
#682483