Finite Group Databasebeta

← #11779644

Subgroups — #11779644

Order 1152.

488 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 94 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
1Dic6×D12C211yesmaximal, characteristic
2C3×#4842C211yesmaximal, characteristic
3#10590310C211yesmaximal, characteristic, complemented
4#10590287C211yesmaximal, characteristic, complemented
5#10589352C211yesmaximal, characteristic, complemented
6C3×#4484C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic
8#71142—31nomaximal
9#68269—31nomaximal
10C2×D3×Dic6—21no—
11#64078C2211yescharacteristic
12C3×C4×D12C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63918—21no—
16#63893—22no—
17Dic3×D12—21no—
18#63857—21no—
19C32×C4⋊C8C2211yescharacteristic
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C3×#821—21no—
22C3×#817—21no—
23C3×C4×C3⋊C8C2211yescharacteristic
24#63576—21no—
25#63566—22no—
26#63565—21no—
27Q8×D12—31no—
28D4×Dic6—31no—
29C3×#476—31no—
30#5091—31no—
31#5079—31no—
32#5021—31no—
33#4842D311yescharacteristic
34#4681—31no—
35C3×Q8⋊C8—31no—
36D4⋊(C3⋊C8)—31no—
37#4486—31no—
38#4486—31no—
39#4486—61no—
40#4484D311yescharacteristic, complemented
41#4459—31no—
42C2×#634—21no—
43C2×C3×D12D411yescharacteristic
44C2×C3×C4×D3—21no—
45C2×C3×Dic6—21no—
46C2×C3×Dic6D411yescharacteristic
47C2×#627—22no—
48C2×D3×Dic3—22no—
49D3×Dic6—42no—
50D3×Dic6—42no—
51C2×C32×C8—21no—
52C32×C42C2311yescharacteristic
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)D412yes—
55C2×C3⋊(C3⋊C8)—21no—
56C3×(C2×D3)⋊C4—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×C4⋊Dic3D411yescharacteristic
61C3×Dic3⋊C4—21no—
62C3×C4×Dic3—21no—
63C2×C3×C3⋊C8—21no—
64Dic3⋊Dic3—22no—
65(C2×D3)⋊Dic3—22no—
66#1637—91noSylow
67C2×D3×Q8—61no—
68C22×Dic6—61no—
69C3×C4⋊Q8—31no—
70C3×C4×Q8—31no—
71C3×C4×D4—31no—
72D4×Dic3—61no—
73#924—61no—
74#897—62no—
75#897—61no—
76#888—61no—
77#878—62no—
78C4×D12—61no—
79C4×D12C2×D311yescharacteristic
80#869—31no—
81#869—31no—
82#869—61no—
83#869—61no—
84#869C2×D311yescharacteristic
85C4×Dic6C2×D311yescharacteristic
86C3×#106—61no—
87C3×C4⋊C8—21no—
88C3×C4⋊C8C2×D311yescharacteristic
89C3×C4⋊C8C2×D311yescharacteristic
90C3×#102—61no—
91C3×C4×C8—31no—
92#835—62no—
93#835—61no—
94#821—21no—
95#817—21no—
96#816—62no—
97#810—61no—
98#807—61no—
99#807—61no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—61no—
103C4×C3⋊C8C2×D311yescharacteristic
104C22×C3×D3—21no—
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C3⋊Dic3—22no—
109#634—41no—
110#634—41no—
111C2×C3×Dic3—21no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—41no—
115C3×D12—21no—
116C3×D12Q1612yes—
117C3×C4×D3—41no—
118C3×C4×D3—41no—
119C3×Dic6—21no—
120C3×Dic6—42no—
121C3×Dic6SD1612yes—
122#627—44no—
123D3×Dic3—44no—
124C32×C8—41no—
125C3⋊(C3⋊C8)—41no—
126C3×C3⋊C8—41no—
127D4×Q8—91no—
128#487—91no—
129#477—91no—
130#476—31no—
131#332—91no—
132Q8⋊C8—31no—
133D4⋊C8—91no—
134C2×C3×Q8—31no—
135C2×C3×Q8—61no—
136C2×C3×D4—31no—
137C22×C3×C4—61no—
138C22×Dic3—62no—
139D3×Q8—122no—
140D3×Q8—122no—
141C2×D12#6711yescharacteristic
142C2×C4×D3—21no—
143C2×C4×D3—62no—
144C2×Dic6—21no—
145C2×Dic6—62no—
146C2×Dic6—62no—
147C2×Dic6—61no—
148C2×Dic6—61no—
149C2×Dic6—121no—
150C2×Dic6—122no—
151C2×Dic6—122no—
152C2×Dic6D1211yescharacteristic
153C2×C3×C8—21no—
154C2×C3×C8—21no—
155C2×C3×C8—41no—
156C2×C3×C8—61no—
157C3×C4⋊C4—31no—
158C3×C4⋊C4—31no—
159C3×C4⋊C4—61no—
160C3×C4⋊C4—61no—
161C3×C4⋊C4—61no—
162C3×C22⋊C4—61no—
163C3×C42—21no—
164C3×C42—61no—
165C3×C42C22×D311yescharacteristic
166C3×C42C22×D311yescharacteristic
167#217—62no—
168(C2×D3)⋊C4—21no—
169(C2×D3)⋊C4—62no—
170C4⋊Dic3—21no—
171C4⋊Dic3—21no—
172C4⋊Dic3—32no—
173C4⋊Dic3—32no—
174C4⋊Dic3—62no—
175C4⋊Dic3—62no—
176C4⋊Dic3—61no—
177C4⋊Dic3—61no—
178C4⋊Dic3—121no—
179C4⋊Dic3D1211yescharacteristic
180C4⋊Dic3#6711yescharacteristic
181Dic3⋊C4—21no—
182Dic3⋊C4—62no—
183C4×Dic3—21no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—61no—
186C2×C3⋊C8—61no—
187C2×C3⋊C8—121no—
188C22×C32#12011yescharacteristic
189C2×C3×D3—22no—
190C2×C3×D3—41no—
191C2×C3×D3—41no—
192C32×C4—21no—
193C32×C4C2×SD1611yescharacteristic
194C32×C4C2×Q1611yescharacteristic
195C32×C4AGL(1,ℤ/8)11yescharacteristic
196C32×C4#13711yescharacteristic
197C3⋊Dic3—42no—
198C3×Dic3—22no—
199C3×Dic3—41no—
200C3×Dic3—41no—
201C3×Dic3—81no—
202C22×Q8—181no—
203C4⋊Q8—31no—
204C4⋊Q8—91no—
205C4⋊Q8—181no—
206C22⋊Q8—182no—
207C22⋊Q8—181no—
208C4×Q8—31no—
209C4×D4—31no—
210C4×D4—181no—
211#107—181no—
212#106—61no—
213C4⋊C8—91no—
214C4⋊C8D3211yescharacteristic
215#103—181no—
216#103—182no—
217#102—61no—
218C4×C8—31no—
219C23×C3—61no—
220C22×D3—21no—
221C3×Q8—32no—
222C3×Q8—61no—
223C3×Q8—122no—
224C3×D4—32no—
225C3×D4—61no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—61no—
230C2×C3×C4—61no—
231C2×C3×C4—61no—
232C2×C3×C4—121no—
233C2×C3×C4—121no—
234C2×C3×C4—121no—
235C2×C3×C4C2×D1211yescharacteristic
236C2×C3×C4D3×D411yescharacteristic
237C2×C3×C4D3×D411yescharacteristic
238C2×C3×C4D3×D411yescharacteristic
239C2×C3×C4D3×D411yescharacteristic
240C2×C3×C4C2×#6711yescharacteristic
241C2×Dic3—21no—
242C2×Dic3—21no—
243C2×Dic3—21no—
244C2×Dic3—41no—
245C2×Dic3—62no—
246C2×Dic3—62no—
247C2×Dic3—122no—
248C2×Dic3—124no—
249D12—21no—
250D12#21612yes—
251C4×D3—41no—
252C4×D3—41no—
253C4×D3—124no—
254Dic6—21no—
255Dic6—42no—
256Dic6—124no—
257Dic6—124no—
258Dic6—121no—
259Dic6—121no—
260Dic6—121no—
261Dic6—121no—
262Dic6—241no—
263Dic6—241no—
264Dic6#20412yes—
265C3×C8—41no—
266C3×C8—41no—
267C3×C8—81no—
268C3×C8—121no—
269C3⋊C8—41no—
270C3⋊C8—121no—
271C3⋊C8—121no—
272C3⋊C8—241no—
273C2×C32#45011yescharacteristic
274C2×C32#45111yescharacteristic
275C2×C32#45411yescharacteristic
276C3×D3—42no—
277C2×Q8—31no—
278C2×Q8—61no—
279C2×Q8—182no—
280C2×Q8—181no—
281C2×Q8—362no—
282C2×Q8—362no—
283C2×D4—31no—
284C22×C4—61no—
285C22×C4—182no—
286C2×C8—21no—
287C2×C8—61no—
288C2×C8—181no—
289C4⋊C4—31no—
290C4⋊C4—31no—
291C4⋊C4—61no—
292C4⋊C4—61no—
293C4⋊C4—61no—
294C4⋊C4—92no—
295C4⋊C4—182no—
296C4⋊C4—181no—
297C22⋊C4—61no—
298C22⋊C4—182no—
299C42—61no—
300C42C2×D3211yescharacteristic
301C22×C3—21no—
302C22×C3—62no—
303C22×C3—121no—
304C22×C3—121no—
305C22×C3#88211yescharacteristic
306C22×C3#93711yescharacteristic
307C2×D3—22no—
308C2×D3—41no—
309C2×D3—41no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—41no—
317C3×C4—62no—
318C3×C4—121no—
319C3×C4—121no—
320C3×C4—241no—
321C3×C4C2×#20411yescharacteristic
322C3×C4#90811yescharacteristic
323C3×C4D3×SD1611yescharacteristic
324C3×C4#91411yescharacteristic
325C3×C4#91511yescharacteristic
326C3×C4D3×Q1611yescharacteristic
327C3×C4C2×#21611yescharacteristic
328C3×C4#95111yescharacteristic
329Dic3—22no—
330Dic3—41no—
331Dic3—41no—
332Dic3—81no—
333Dic3—122no—
334Dic3—122no—
335Dic3—242no—
336C32#163711yescharacteristic, complemented, Sylow
337C23—61no—
338Q8—32no—
339Q8—61no—
340Q8—122no—
341Q8—364no—
342Q8—361no—
343Q8—361no—
344D4—32no—
345D4—61no—
346C2×C4—61no—
347C2×C4—61no—
348C2×C4—61no—
349C2×C4—121no—
350C2×C4—121no—
351C2×C4—121no—
352C2×C4—182no—
353C2×C4—364no—
354C2×C4D3×D1211yescharacteristic
355C2×C4#380211yescharacteristic
356C2×C4D3×#6711yescharacteristic
357C8—41no—
358C8—121no—
359C8—361no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—21no—
363C2×C3—122no—
364C2×C3#473111yescharacteristic
365C2×C3#480911yescharacteristic
366C2×C3#482711yescharacteristic
367C2×C3#505011yescharacteristic
368C2×C3#516911yescharacteristic
369C2×C3#520111yescharacteristic
370D3—42no—
371C22—62no—
372C22—121no—
373C22—121no—
374C22#6392211yescharacteristic
375C4—21no—
376C4—62no—
377C4—121no—
378C4—121no—
379C4—241no—
380C4—362no—
381C4D3×#20411yescharacteristic
382C4#6379411yescharacteristic
383C4#6392911yescharacteristic
384C4D3×#21611yescharacteristic
385C3—21no—
386C3#6826911yescharacteristic, complemented
387C3#7114211yescharacteristic, complemented
388C2—122no—
389C2#1059060411yescharacteristic
390C2#1059094211yescharacteristic
391C2#1059101911yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC4⋊C8D32
hypocenterC32#1637
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
3. #10590310C2semidirect
4. #10590287C2semidirect
5. #10589352C2semidirect
6. C3×#4484C2semidirect
40. #4484D3semidirect
336. C32#1637semidirect
386. C3#68269semidirect
387. C3#71142semidirect

Maximal subgroups

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

subgroupindex
Dic6×D122
C3×#48422
#105903102
#105902872
#105893522
C3×#44842
#105890812
#711423
#682693