Finite Group Databasebeta

← #11779380

Subgroups — #11779380

Order 1152.

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

normal subgroups only

This group has 560 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#10592720C211yesmaximal, characteristic, complemented
3#10590369C211yesmaximal, characteristic, complemented
4#10590268C211yesmaximal, characteristic, complemented
5C3×#4535C211yesmaximal, characteristic, complemented
6#10589090C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#71919—31nomaximal
9#68261—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—22no—
20#63662—21no—
21#63634—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63573—21no—
26#63563—21no—
27C3×#550—31no—
28#5577D311yescharacteristic
29#5076—31no—
30#5021—31no—
31#5021—31no—
32#5021—61no—
33#5008—31no—
34#4842—31no—
35#4693—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—44no—
67#1631—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—62no—
80C2×#204—62no—
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—61no—
96#821—61no—
97#817—61no—
98#808—61no—
99#807—62no—
100#807—61no—
101#807—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—42no—
118C2×C3×Dic3—21no—
119C3×D12—21no—
120C3×D12—21no—
121C3×D12—42no—
122C3×D12—44no—
123C3×D12—41no—
124C3×D12—41no—
125C3×D12—41no—
126C3×D12—41no—
127C3×D12—82no—
128C3×C4×D3—44no—
129C3×C4×D3—41no—
130C3×C4×D3—41no—
131C3⋊(C3⋊C8)—41no—
132C3×C3⋊C8—22no—
133C3×C3⋊C8—41no—
134#550—31no—
135#492—91no—
136#477—91no—
137#476—91no—
138#331—91no—
139Q8⋊C8—31no—
140D4⋊C8—91no—
141C3×#41—122no—
142C3×#41—122no—
143C2×C3×Q8—21no—
144C2×C3×Q8D1211yescharacteristic
145C2×C3×Q8#6711yescharacteristic
146C2×C3×D4—31no—
147C2×C3×D4—32no—
148C2×C3×D4—62no—
149C2×C3×D4—62no—
150C2×C3×D4—61no—
151C2×C3×D4—61no—
152C22×C3×C4—62no—
153C22×C3×C4—61no—
154#239—42no—
155#239—42no—
156C2×D12—22no—
157C2×D12—21no—
158C2×D12—21no—
159C2×D12—22no—
160C2×D12#6711yescharacteristic
161C2×D12#6712yes—
162C2×C4×D3—22no—
163C2×C4×D3—21no—
164C2×Dic6—61no—
165C2×Dic6—61no—
166C2×Dic6—121no—
167C2×C3×C8—61no—
168C2×C3×C8—61no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—31no—
173C3×C4⋊C4—41no—
174C3×C4⋊C4D1211yescharacteristic
175C3×C4⋊C4#6711yescharacteristic
176C3×C22⋊C4—62no—
177C3×C22⋊C4—61no—
178C3×C42—21no—
179C3×C42—21no—
180C3×C42—21no—
181C3×C42—41no—
182C3×C42C22×D311yescharacteristic
183C3×C42C22×D311yescharacteristic
184#214—124no—
185(C2×D3)⋊C4—22no—
186(C2×D3)⋊C4—21no—
187C4⋊Dic3—62no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191C4⋊Dic3—61no—
192C4⋊Dic3—121no—
193C4⋊Dic3#6711yescharacteristic
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—62no—
197C2×C3⋊C8—61no—
198C2×C3⋊C8—61no—
199#204—124no—
200C22×C32#12011yescharacteristic
201C2×C3×D3—42no—
202C2×C3×D3—41no—
203C2×C3×D3—41no—
204C2×C3×D3—42no—
205C2×C3×D3—42no—
206C2×C3×D3—41no—
207C32×C4—22no—
208C32×C4—21no—
209C32×C4—41no—
210C32×C4C2×SD1611yescharacteristic
211C32×C4#13511yescharacteristic
212C32×C4AGL(1,ℤ/8)11yescharacteristic
213C32×C4#13711yescharacteristic
214C3⋊Dic3—81no—
215C3×Dic3—41no—
216C2×#41—61no—
217C2×SD16—182no—
218C4⋊Q8—91no—
219#127—31no—
220#127—61no—
221#121—62no—
222#121—61no—
223C4×Q8D3211yescharacteristic
224C4×D4—31no—
225C4×D4—61no—
226#107—181no—
227#106—181no—
228C4⋊C8—31no—
229C4⋊C8—91no—
230#103—181no—
231#102—181no—
232C4×C8—31no—
233C23×C3—61no—
234C23×C3—62no—
235C22×D3—21no—
236C22×D3—22no—
237C3×Q8—21no—
238C3×Q8—21no—
239C3×Q8—22no—
240C3×Q8—41no—
241C3×Q8#20412yescomplemented
242C3×Q8#21412yescomplemented
243C3×D4—61no—
244C3×D4—61no—
245C3×D4—122no—
246C3×D4—124no—
247C3×D4—121no—
248C3×D4—121no—
249C3×D4—121no—
250C3×D4—121no—
251C3×D4—242no—
252C2×C3×C4—21no—
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—41no—
260C2×C3×C4—41no—
261C2×C3×C4—61no—
262C2×C3×C4—124no—
263C2×C3×C4—121no—
264C2×C3×C4—121no—
265C2×C3×C4C2×D1211yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4C2×#6711yescharacteristic
269C2×C3×C4C2×#6711yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271C2×Dic3—21no—
272C2×Dic3—122no—
273C2×Dic3—121no—
274C2×Dic3—121no—
275D12—21no—
276D12—21no—
277D12—42no—
278D12—44no—
279D12—41no—
280D12—41no—
281D12—41no—
282D12—41no—
283D12—82no—
284C4×D3—44no—
285C4×D3—41no—
286C4×D3—41no—
287Dic6—122no—
288Dic6—122no—
289Dic6—242no—
290C3×C8—62no—
291C3×C8—121no—
292C3⋊C8—22no—
293C3⋊C8—41no—
294C3⋊C8—122no—
295C3⋊C8—121no—
296C3⋊C8—121no—
297C2×C32#45011yescharacteristic
298C2×C32#45211yescharacteristic
299C2×C32#45311yescharacteristic
300C3×D3—81no—
301C3×D3—82no—
302#41—122no—
303#41—122no—
304C2×Q8—181no—
305C2×Q8#62611yescharacteristic
306C2×D4—31no—
307C2×D4—32no—
308C2×D4—62no—
309C2×D4—62no—
310C2×D4—61no—
311C2×D4—61no—
312C22×C4—62no—
313C22×C4—61no—
314SD16—364no—
315C2×C8—61no—
316C2×C8—61no—
317C2×C8—181no—
318C4⋊C4—21no—
319C4⋊C4—31no—
320C4⋊C4—181no—
321C4⋊C4—181no—
322C4⋊C4#62611yescharacteristic
323C22⋊C4—62no—
324C22⋊C4—61no—
325C42—21no—
326C42C2×D3211yescharacteristic
327C22×C3—21no—
328C22×C3—122no—
329C22×C3—121no—
330C22×C3—121no—
331C22×C3—122no—
332C22×C3—122no—
333C22×C3—121no—
334C22×C3#88211yescharacteristic
335C22×C3#95311yescharacteristic
336C2×D3—42no—
337C2×D3—41no—
338C2×D3—41no—
339C2×D3—42no—
340C2×D3—42no—
341C2×D3—41no—
342C3×C4—22no—
343C3×C4—21no—
344C3×C4—22no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—41no—
351C3×C4—42no—
352C3×C4—41no—
353C3×C4—41no—
354C3×C4—81no—
355C3×C4—121no—
356C3×C4C2×#20411yescharacteristic
357C3×C4#90811yescharacteristic
358C3×C4#91611yescharacteristic
359C3×C4#91811yescharacteristic
360C3×C4#93211yescharacteristic
361C3×C4C2×#21411yescharacteristic
362C3×C4#95011yescharacteristic
363C3×C4#95111yescharacteristic
364Dic3—41no—
365Dic3—242no—
366Dic3—241no—
367Dic3—241no—
368C32#163111yescharacteristic, complemented, Sylow
369C23—61no—
370C23—62no—
371Q8—21no—
372Q8—362no—
373Q8#371612yescomplemented
374D4—61no—
375D4—61no—
376D4—122no—
377D4—124no—
378D4—121no—
379D4—121no—
380D4—121no—
381D4—121no—
382D4—242no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—61no—
386C2×C4—124no—
387C2×C4—121no—
388C2×C4—121no—
389C2×C4—361no—
390C2×C4C2×#62611yescharacteristic
391C2×C4D3×#6711yescharacteristic
392C2×C4D3×#6711yescharacteristic
393C8—62no—
394C8—121no—
395C8—361no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—241no—
400C2×C3—242no—
401C2×C3#473111yescharacteristic
402C2×C3#480811yescharacteristic
403C2×C3#482211yescharacteristic
404C2×C3#521811yescharacteristic
405C2×C3#523911yescharacteristic
406C2×C3#524111yescharacteristic
407D3—81no—
408D3—82no—
409C22—121no—
410C22—122no—
411C22—122no—
412C22—121no—
413C22—122no—
414C22—121no—
415C22#6397711yescharacteristic
416C4—21no—
417C4—22no—
418C4—41no—
419C4—121no—
420C4—721no—
421C4C2×#371611yescharacteristic
422C4#6383011yescharacteristic
423C4#6394311yescharacteristic
424C4#6394711yescharacteristic
425C3—21no—
426C3#6826111yescharacteristic, complemented
427C3#7191911yescharacteristic, complemented
428C2—241no—
429C2—242no—
430C2#1059117211yescharacteristic
431C2#1059159911yescharacteristic
432C2#1059166611yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32#120
prime radicalC3×#5577C2
hypercenterC4×Q8D32
hypocenterC32#1631
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. #10592720C2semidirect
3. #10590369C2semidirect
4. #10590268C2semidirect
5. C3×#4535C2semidirect
6. #10589090C2semidirect
7. #10589081C2semidirect
38. #4535D3semidirect
110. C32×Q8SD16semidirect
241. C3×Q8#204semidirect
242. C3×Q8#214semidirect
368. C32#1631semidirect
373. Q8#3716semidirect
426. C3#68261semidirect
427. C3#71919semidirect

Maximal subgroups

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

subgroupindex
C3×#55772
#105927202
#105903692
#105902682
C3×#45352
#105890902
#105890812
#719193
#682613