Finite Group Databasebeta

← #11801836

Subgroups — #11801836

Order 1152.

1561 conjugacy classes of subgroups.

The subgroup lattice has 409 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C3⋊Dic3C211yesmaximal, characteristic
2C2×#63957C211yesmaximal, characteristic
3C2×#63957C211yesmaximal, characteristic
4C3×#5210C212yesmaximal
5#10591719C212yesmaximal
6#10591337C212yesmaximal, complemented
7#10591328C212yesmaximal, complemented
8#10591241C214yesmaximal, complemented
9#74378—32nomaximal
10C23×C32×C4C2211yescharacteristic
11C23×C3⋊Dic3C2211yescharacteristic
12C23×C3⋊Dic3C2211yescharacteristic
13C2×C4×C3⋊Dic3—24no—
14C2×C4×C3⋊Dic3C2212yes—
15C2×C4×C3⋊Dic3C2212yes—
16C2×C3×#217C2212yes—
17C2×C3×#217C2212yes—
18C2×C3×Dic3⋊C4C2214yes—
19C2×#3724C2211yescharacteristic
20C2×#3724C2211yescharacteristic
21C2×#3724C2212yes—
22C2×Dic3⋊Dic3C2214yes—
23#63957—24no—
24#63957C418yescomplemented
25C2×Dic32C2212yes—
26C2×Dic32C2212yes—
27C3×C3⋊#95C2214yes—
28#63579C2214yes—
29C22×C4×Dic3—32no—
30C22×C4×Dic3—61no—
31C2×#877—32no—
32C2×#877—32no—
33C3×#385—32no—
34#5210D312yes—
35#4976—34no—
36Dic3×C4⋊C4—34no—
37#4950—32no—
38#4946—32no—
39#4649—34no—
40#4647—34no—
41C24×C32C2311yescharacteristic
42C22×C32×C4—22no—
43C22×C32×C4—24no—
44C22×C32×C4C2312yes—
45C22×C3⋊Dic3—22no—
46C22×C3⋊Dic3—24no—
47C22×C3⋊Dic3C2×C414yes—
48C22×C3⋊Dic3D414yes—
49C22×C3⋊Dic3Q814yes—
50C22×C3⋊Dic3C2312yes—
51C22×C3⋊Dic3C2311yescharacteristic
52C22×C3⋊Dic3C2311yescharacteristic
53C22×C3×Dic3C2312yes—
54C22×C3×Dic3C2312yes—
55C22×C3×Dic3C2314yes—
56C4×C3⋊Dic3—24no—
57C4×C3⋊Dic3—24no—
58C3×#217—24no—
59C3×#217C2×C418yes—
60C3×Dic3⋊C4—28no—
61#3724—22no—
62#3724—22no—
63#3724C2×C418yescomplemented
64Dic3⋊Dic3—28no—
65Dic32—24no—
66Dic32C2×C418yescomplemented
67#2296—91noSylow
68C23×C3×C4—21no—
69C23×C3×C4C2×D312yes—
70C23×Dic3—32no—
71C23×Dic3—32no—
72C23×Dic3—61no—
73C23×Dic3—61no—
74C2×C3×C4⋊C4—34no—
75C2×C3×C22⋊C4—32no—
76C2×C3×C22⋊C4—32no—
77C2×#217C2×D312yes—
78C2×#217C2×D312yes—
79C2×C4⋊Dic3—34no—
80C2×Dic3⋊C4—34no—
81C2×Dic3⋊C4—32no—
82C2×Dic3⋊C4—34no—
83C2×Dic3⋊C4—32no—
84C2×Dic3⋊C4C2×D314yes—
85C2×C4×Dic3—34no—
86C2×C4×Dic3—34no—
87C2×C4×Dic3—34no—
88C2×C4×Dic3—32no—
89C2×C4×Dic3—32no—
90C2×C4×Dic3—62no—
91C2×C4×Dic3—62no—
92C2×C4×Dic3—68no—
93C2×C4×Dic3—68no—
94#877—316no—
95#877—68no—
96C3×#95—34no—
97C3⋊#95—34no—
98C3⋊#95—34no—
99C3⋊#95C2×D314yes—
100C23×C32—22no—
101C23×C32—22no—
102C23×C32C22×C412yes—
103C23×C32C2×D412yes—
104C23×C32C2×Q812yes—
105C23×C32C2411yescharacteristic
106C2×C32×C4—28no—
107C2×C32×C4—22no—
108C2×C32×C4—22no—
109C2×C32×C4#4114yes—
110C2×C3⋊Dic3—28no—
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3C4⋊C4116yescomplemented
114C2×C3⋊Dic3C22×C412yes—
115C2×C3⋊Dic3C22×C412yes—
116C2×C3⋊Dic3C2×D412yes—
117C2×C3⋊Dic3C2×D412yes—
118C2×C3⋊Dic3C2×Q812yes—
119C2×C3⋊Dic3C2×Q812yes—
120C2×C3⋊Dic3#4114yes—
121C2×C3×Dic3—24no—
122C2×C3×Dic3—24no—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—24no—
126C2×C3×Dic3—24no—
127C2×C3×Dic3C22×C418yes—
128C2×#117—91no—
129C2×#117—91no—
130C22×C42—91no—
131#389—92no—
132#389—92no—
133#385—32no—
134#385—92no—
135C4×C4⋊C4—94no—
136C24×C3—21no—
137C24×C3C22×D312yes—
138C22×C3×C4—24no—
139C22×C3×C4—28no—
140C22×C3×C4—24no—
141C22×C3×C4—28no—
142C22×C3×C4—22no—
143C22×C3×C4—34no—
144C22×C3×C4—32no—
145C22×C3×C4—32no—
146C22×C3×C4C22×D314yes—
147C22×Dic3—38no—
148C22×Dic3—38no—
149C22×Dic3—38no—
150C22×Dic3—32no—
151C22×Dic3—32no—
152C22×Dic3—34no—
153C22×Dic3—64no—
154C22×Dic3—61no—
155C22×Dic3—61no—
156C22×Dic3—62no—
157C22×Dic3—64no—
158C22×Dic3—64no—
159C22×Dic3—68no—
160C22×Dic3—64no—
161C22×Dic3—68no—
162C22×Dic3—64no—
163C22×Dic3C22×D312yes—
164C22×Dic3C22×D312yes—
165C22×Dic3C22×D314yes—
166C3×C4⋊C4—68no—
167C3×C22⋊C4—38no—
168C3×C22⋊C4—64no—
169#217—24no—
170#217C4×D318yes—
171C4⋊Dic3—68no—
172Dic3⋊C4—28no—
173Dic3⋊C4—316no—
174Dic3⋊C4—64no—
175Dic3⋊C4—64no—
176Dic3⋊C4—68no—
177C4×Dic3—316no—
178C4×Dic3—64no—
179C4×Dic3—64no—
180C4×Dic3—68no—
181C4×Dic3—68no—
182C4×Dic3—68no—
183C4×Dic3—68no—
184C22×C32—24no—
185C22×C32—22no—
186C22×C32—22no—
187C22×C32—24no—
188C22×C32C2×C4⋊C414yes—
189C22×C32C23×C411yescharacteristic
190C22×C32C22×D411yescharacteristic
191C22×C32C22×Q811yescharacteristic
192C22×C32C2×#4112yes—
193C22×C32C2×#4112yes—
194C32×C4—24no—
195C3⋊Dic3—24no—
196C3⋊Dic3C2×C4⋊C414yes—
197C3⋊Dic3C2×C4⋊C414yes—
198C3×Dic3—28no—
199C3×Dic3—42no—
200C3×Dic3—42no—
201C23×C4—91no—
202C23×C4—91no—
203C23×C4D3211yescharacteristic
204#117—98no—
205#117—184no—
206C2×C4⋊C4—34no—
207C2×C4⋊C4—92no—
208C2×C4⋊C4—91no—
209C2×C4⋊C4—91no—
210C2×C4⋊C4—94no—
211C2×C22⋊C4—32no—
212C2×C22⋊C4—32no—
213C2×C42—92no—
214C2×C42—92no—
215C2×C42—92no—
216C2×C42—92no—
217C2×C42—184no—
218#95—34no—
219#95—94no—
220C23×C3—24no—
221C23×C3—24no—
222C23×C3—24no—
223C23×C3—24no—
224C23×C3—21no—
225C23×C3—22no—
226C23×C3—22no—
227C23×C3—22no—
228C23×C3C2×C4×D314yes—
229C23×C3D3×D414yes—
230C23×C3D3×Q814yes—
231C23×C3C23×D312yes—
232C2×C3×C4—24no—
233C2×C3×C4—216no—
234C2×C3×C4—216no—
235C2×C3×C4—24no—
236C2×C3×C4—24no—
237C2×C3×C4—24no—
238C2×C3×C4—24no—
239C2×C3×C4—38no—
240C2×C3×C4—64no—
241C2×C3×C4—64no—
242C2×C3×C4—62no—
243C2×C3×C4—62no—
244C2×C3×C4—64no—
245C2×C3×C4—64no—
246C2×C3×C4#23718yes—
247C2×Dic3—24no—
248C2×Dic3—24no—
249C2×Dic3—22no—
250C2×Dic3—22no—
251C2×Dic3—24no—
252C2×Dic3—24no—
253C2×Dic3—332no—
254C2×Dic3—34no—
255C2×Dic3—34no—
256C2×Dic3—34no—
257C2×Dic3—34no—
258C2×Dic3—34no—
259C2×Dic3—34no—
260C2×Dic3—38no—
261C2×Dic3—616no—
262C2×Dic3—62no—
263C2×Dic3—62no—
264C2×Dic3—62no—
265C2×Dic3—62no—
266C2×Dic3—62no—
267C2×Dic3—62no—
268C2×Dic3—64no—
269C2×Dic3—64no—
270C2×Dic3—616no—
271C2×Dic3—616no—
272C2×Dic3—64no—
273C2×Dic3—64no—
274C2×Dic3—64no—
275C2×Dic3C2×C4×D318yes—
276C2×C32—24no—
277C2×C32C22×C4⋊C411yescharacteristic
278C2×C32C4×#4112yes—
279C2×C32#52511yescharacteristic
280C2×C32#52511yescharacteristic
281C2×C32#53312yes—
282C24C2×D3211yescharacteristic
283C22×C4—22no—
284C22×C4—24no—
285C22×C4—34no—
286C22×C4—32no—
287C22×C4—32no—
288C22×C4—91no—
289C22×C4—91no—
290C22×C4—94no—
291C22×C4—94no—
292C22×C4—94no—
293C22×C4—92no—
294C22×C4—184no—
295C22×C4—182no—
296C22×C4C2×D3212yes—
297C4⋊C4—68no—
298C4⋊C4—98no—
299C4⋊C4—182no—
300C4⋊C4—182no—
301C4⋊C4—188no—
302C22⋊C4—38no—
303C22⋊C4—64no—
304C42—98no—
305C42—184no—
306C42—184no—
307C42—184no—
308C22×C3—24no—
309C22×C3—24no—
310C22×C3—28no—
311C22×C3—28no—
312C22×C3—24no—
313C22×C3—28no—
314C22×C3—24no—
315C22×C3—28no—
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—22no—
319C22×C3—22no—
320C22×C3—21no—
321C22×C3—24no—
322C22×C3D3×C4⋊C418yes—
323C22×C3C22×C4×D312yes—
324C22×C3C2×D3×D412yes—
325C22×C3C2×#23714yes—
326C22×C3C2×D3×Q812yes—
327C22×C3D3×#4114yes—
328C3×C4—28no—
329C3×C4—28no—
330C3×C4—68no—
331C3×C4—122no—
332C3×C4—122no—
333Dic3—28no—
334Dic3—38no—
335Dic3—38no—
336Dic3—42no—
337Dic3—42no—
338Dic3—64no—
339Dic3—64no—
340Dic3—68no—
341Dic3—68no—
342C32#229611yescharacteristic, complemented, Sylow
343C23—22no—
344C23—22no—
345C23#379712yes—
346C23C4×D3212yes—
347C23#381112yes—
348C23C22×D3211yescharacteristic
349C2×C4—28no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—38no—
353C2×C4—64no—
354C2×C4—64no—
355C2×C4—64no—
356C2×C4—64no—
357C2×C4—62no—
358C2×C4—62no—
359C2×C4—92no—
360C2×C4—92no—
361C2×C4—92no—
362C2×C4—92no—
363C2×C4—92no—
364C2×C4—92no—
365C2×C4—916no—
366C2×C4—94no—
367C2×C4—188no—
368C2×C4—182no—
369C2×C4—182no—
370C2×C4#380514yes—
371C2×C3—28no—
372C2×C3—28no—
373C2×C3—22no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—22no—
378C2×C3C2×D3×C4⋊C412yes—
379C2×C3C4×#23714yes—
380C2×C3#558612yes—
381C2×C3#562214yes—
382C2×C3#565612yes—
383C22—24no—
384C22—22no—
385C22—22no—
386C22—24no—
387C22#6388314yes—
388C22C2×#379711yescharacteristic
389C22C2×C4×D3211yescharacteristic
390C22#6430612yes—
391C22C2×#380512yes—
392C22C2×#381111yescharacteristic
393C4—24no—
394C4—68no—
395C4—94no—
396C4—94no—
397C4—122no—
398C4—122no—
399C4—184no—
400C3—21no—
401C3#7437812yescomplemented
402C2—24no—
403C2#1059481012yes—
404C2C4×#380512yes—
405C2C2×#6388311yescharacteristic
406C2#1059492011yescharacteristic
407C2#1059550111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32#2296
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
6. #10591337C2semidirect
7. #10591328C2semidirect
8. #10591241C2semidirect
24. #63957C4semidirect
63. #3724C2×C4semidirect
66. Dic32C2×C4semidirect
113. C2×C3⋊Dic3C4⋊C4semidirect
342. C32#2296semidirect
401. C3#74378semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C3⋊Dic32
C2×#639572
C3×#52102
#105917192
#105913372
#105913282
#105912412
#743783