Finite Group Databasebeta

← #11895817

Subgroups — #11895817

Order 1152.

1116 conjugacy classes of subgroups.

The subgroup lattice has 369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596013C211yesmaximal, characteristic, complemented
2D4×#634C211yesmaximal, characteristic, complemented
3C32×C4×D8C211yesmaximal, characteristic
4#10592852C212yesmaximal
5#10592718C211yesmaximal, characteristic, complemented
6#10592706C211yesmaximal, characteristic, complemented
7#10592574C212yesmaximal, complemented
8#10592464C212yesmaximal, complemented
9#10592456C212yesmaximal, complemented
10#10592380C211yesmaximal, characteristic, complemented
11#10592378C211yesmaximal, characteristic, complemented
12#79571—34nomaximal
13C22×#634—21no—
14C2×C32×D8C2211yescharacteristic
15C32×C4×D4C2211yescharacteristic
16C32×C4×D4C2211yescharacteristic
17#64145C2212yes—
18D4×C3⋊Dic3C2212yes—
19C2×#3754C2212yes—
20#64135—21no—
21#64133—21no—
22#64133—21no—
23#64097C2212yes—
24#64096C2212yes—
25#64088—22no—
26#64087—22no—
27#64078C2211yescharacteristic
28#64078C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C32×#107C2211yescharacteristic
31C32×#102C2211yescharacteristic
32C32×#102C2211yescharacteristic
33C32×C4×C8C2211yescharacteristic
34#63659C2212yes—
35#63643C2212yes—
36#63643C2212yes—
37#63642C2212yes—
38#63641C2212yes—
39#63637C2212yes—
40#63634C2212yes—
41C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
42#5542—34no—
43D4×Dic6—34no—
44C3×C4×D8D314yes—
45#5153—38no—
46#5019—34no—
47#5007—34no—
48#4875—38no—
49#4765—38no—
50#4757—38no—
51#4681—34no—
52#4679—34no—
53C2×C32×D4C2311yescharacteristic
54C2×C32×D4C2311yescharacteristic
55C22×C32×C4—21no—
56C22×C32×C4—21no—
57C22×C3⋊Dic3—22no—
58C2×#634—21no—
59C2×#634—22no—
60C2×#634—44no—
61C2×#634D411yescharacteristic
62C2×#634C2312yes—
63C32×D8—22no—
64C2×C32×C8C2311yescharacteristic
65C2×C32×C8C2311yescharacteristic
66C32×C4⋊C4C2311yescharacteristic
67C32×C4⋊C4C2311yescharacteristic
68C32×C22⋊C4—21no—
69C32×C22⋊C4—21no—
70C32×C42C2311yescharacteristic
71#3757—22no—
72#3757—22no—
73#3757—22no—
74#3754—24no—
75C4⋊(C3⋊Dic3)—21no—
76C4⋊(C3⋊Dic3)—21no—
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)D411yescharacteristic
79C4⋊(C3⋊Dic3)C2312yes—
80#3750—22no—
81#3750—22no—
82#3750D412yes—
83C4×C3⋊Dic3—22no—
84C4×C3⋊Dic3C2312yes—
85C2×C3⋊(C3⋊C8)C2312yes—
86#3367—91noSylow
87C22×Dic6—64no—
88C2×C3×D8C2×D314yes—
89C3×C4×D4C2×D314yes—
90C3×C4×D4C2×D314yes—
91#936—38no—
92D4×Dic3—38no—
93C2×#214—38no—
94#926—64no—
95#924—64no—
96#924—64no—
97#888—38no—
98#887—38no—
99#879—68no—
100#878—68no—
101#869—34no—
102#869—34no—
103C4×Dic6—34no—
104C3×#107C2×D314yes—
105C3×#102C2×D314yes—
106C3×#102C2×D314yes—
107C3×C4×C8C2×D314yes—
108#832—38no—
109#816—38no—
110#816—38no—
111#815—38no—
112Dic3⋊C8—38no—
113#810—38no—
114#807—38no—
115C4⋊(C3⋊C8)—34no—
116C23×C32—21no—
117C23×C32—21no—
118C32×D4—21no—
119C32×D4—21no—
120C32×D4—21no—
121C32×D4#4112yes—
122C2×C32×C4—21no—
123C2×C32×C4—21no—
124C2×C32×C4—42no—
125C2×C32×C4—42no—
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2411yescharacteristic
129C2×C3⋊Dic3—22no—
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3—44no—
132C2×C3⋊Dic3C2×D412yes—
133C2×C3⋊Dic3C2×D412yes—
134#634—22no—
135#634—22no—
136#634—22no—
137#634—44no—
138#634—42no—
139C32×C8—21no—
140C32×C8—21no—
141C3⋊(C3⋊C8)—22no—
142#556—91no—
143D4×Q8—91no—
144#489—92no—
145#487—91no—
146#477—92no—
147#474—91no—
148#463—92no—
149#461—91no—
150#446—91no—
151#440—92no—
152C4×D8C3⋊D311yescharacteristic
153C2×C3×D4C22×D314yes—
154C2×C3×D4C22×D314yes—
155C22×C3×C4—24no—
156C22×C3×C4—24no—
157C22×Dic3—68no—
158C2×Dic6—34no—
159C2×Dic6—38no—
160C2×Dic6—68no—
161C2×Dic6—64no—
162C2×Dic6—1216no—
163C3×D8—28no—
164C2×C3×C8C22×D314yes—
165C2×C3×C8C22×D314yes—
166C3×C4⋊C4C22×D314yes—
167C3×C4⋊C4C22×D314yes—
168C3×C22⋊C4—24no—
169C3×C22⋊C4—24no—
170C3×C42C22×D314yes—
171#217—68no—
172#217—68no—
173#217—68no—
174#214—616no—
175C4⋊Dic3—34no—
176C4⋊Dic3—38no—
177C4⋊Dic3—64no—
178C4⋊Dic3—64no—
179C4⋊Dic3—64no—
180Dic3⋊C4—38no—
181Dic3⋊C4—68no—
182Dic3⋊C4—68no—
183C4×Dic3—38no—
184C4×Dic3—68no—
185C2×C3⋊C8—38no—
186C22×C32—22no—
187C22×C32—41no—
188C22×C32—41no—
189C22×C32—41no—
190C22×C32—41no—
191C22×C32—41no—
192C22×C32C22×D411yescharacteristic
193C32×C4—21no—
194C32×C4—41no—
195C32×C4—41no—
196C32×C4AGL(1,ℤ/8)12yes—
197C32×C4C2×#4111yescharacteristic
198C32×C42−1+411yescharacteristic
199C3⋊Dic3—22no—
200C3⋊Dic3—22no—
201C3⋊Dic3—42no—
202C3⋊Dic3—42no—
203C22×Q8—181no—
204C2×SD16—92no—
205C2×D8C2×C3⋊D311yescharacteristic
206C4⋊Q8—92no—
207C4⋊Q8—91no—
208C4⋊Q8—91no—
209#126—182no—
210#124—92no—
211C22⋊Q8—182no—
212C22⋊Q8—181no—
213C22⋊Q8—181no—
214C4×Q8—91no—
215C4×Q8—92no—
216C4×D4—92no—
217C4×D4C2×C3⋊D311yescharacteristic
218C4×D4C2×C3⋊D311yescharacteristic
219#117—181no—
220#107—92no—
221#107C2×C3⋊D311yescharacteristic
222C4⋊C8—92no—
223C4⋊C8—91no—
224#103—92no—
225#103—92no—
226#103—92no—
227#102—92no—
228#102C2×C3⋊D311yescharacteristic
229#102C2×C3⋊D311yescharacteristic
230#97—92no—
231C4×C8C2×C3⋊D311yescharacteristic
232C23×C3—24no—
233C23×C3—24no—
234C3×D4—24no—
235C3×D4—24no—
236C3×D4—24no—
237C3×D4#23518yes—
238C2×C3×C4—24no—
239C2×C3×C4—24no—
240C2×C3×C4—48no—
241C2×C3×C4—48no—
242C2×C3×C4D3×D414yes—
243C2×C3×C4D3×D414yes—
244C2×C3×C4C23×D314yes—
245C2×Dic3—38no—
246C2×Dic3—38no—
247C2×Dic3—68no—
248C2×Dic3—68no—
249C2×Dic3—1216no—
250Dic6—68no—
251Dic6—68no—
252Dic6—68no—
253Dic6—1216no—
254Dic6—128no—
255C3×C8—24no—
256C3×C8—24no—
257C3⋊C8—68no—
258C2×C32—42no—
259C2×C32—81no—
260C2×C32#54811yescharacteristic
261C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
262C2×C32#57811yescharacteristic
263C2×Q8—91no—
264C2×Q8—92no—
265C2×Q8—182no—
266C2×Q8—181no—
267C2×Q8—364no—
268C2×D4C22×C3⋊D311yescharacteristic
269C2×D4C22×C3⋊D311yescharacteristic
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—182no—
273SD16—184no—
274D8—22no—
275C2×C8—92no—
276C2×C8C22×C3⋊D311yescharacteristic
277C2×C8C22×C3⋊D311yescharacteristic
278C4⋊C4—91no—
279C4⋊C4—92no—
280C4⋊C4—92no—
281C4⋊C4—182no—
282C4⋊C4—182no—
283C4⋊C4—181no—
284C4⋊C4—181no—
285C4⋊C4—181no—
286C4⋊C4C22×C3⋊D311yescharacteristic
287C4⋊C4C22×C3⋊D311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—182no—
291C22⋊C4—182no—
292C22⋊C4—182no—
293C42—92no—
294C42—182no—
295C42C22×C3⋊D311yescharacteristic
296C22×C3—28no—
297C22×C3—44no—
298C22×C3—44no—
299C22×C3—44no—
300C22×C3—44no—
301C22×C3—44no—
302C22×C3C2×D3×D414yes—
303C3×C4—24no—
304C3×C4—44no—
305C3×C4—44no—
306C3×C4#91118yes—
307C3×C4C2×#23514yes—
308C3×C4#101014yes—
309Dic3—68no—
310Dic3—68no—
311Dic3—128no—
312Dic3—128no—
313C32#336711yescharacteristic, complemented, Sylow
314C23—21no—
315C23—21no—
316Q8—182no—
317Q8—182no—
318Q8—182no—
319Q8—364no—
320Q8—362no—
321D4—21no—
322D4—21no—
323D4—21no—
324D4#382812yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—92no—
330C2×C4—92no—
331C2×C4—182no—
332C2×C4—182no—
333C2×C4—364no—
334C2×C4D4×C3⋊D311yescharacteristic
335C2×C4D4×C3⋊D311yescharacteristic
336C2×C4C23×C3⋊D311yescharacteristic
337C8—21no—
338C8—21no—
339C8—182no—
340C2×C3—48no—
341C2×C3—84no—
342C2×C3#555214yes—
343C2×C3C2×#91114yes—
344C2×C3#577114yes—
345C22—22no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22C2×D4×C3⋊D311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—182no—
356C4—182no—
357C4—362no—
358C4—362no—
359C4#6412012yes—
360C4C2×#382811yescharacteristic
361C4#6436711yescharacteristic
362C3#7957114yescomplemented
363C2—42no—
364C2—81no—
365C2#1059602311yescharacteristic
366C2C2×#6412011yescharacteristic
367C2#1059624211yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×C4×D8C2
socleC22×C32C22×D4
prime radicalC2×C32×D8C22
hypercenterC4×D8C3⋊D3
hypocenterC32#3367
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #10596013C2semidirect
2. D4×#634C2semidirect
5. #10592718C2semidirect
6. #10592706C2semidirect
7. #10592574C2semidirect
8. #10592464C2semidirect
9. #10592456C2semidirect
10. #10592380C2semidirect
11. #10592378C2semidirect
313. C32#3367semidirect
362. C3#79571semidirect

Maximal subgroups

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

subgroupindex
#105960132
D4×#6342
C32×C4×D82
#105928522
#105927182
#105927062
#105925742
#105924642
#105924562
#105923802
#105923782
#795713