Finite Group Databasebeta

← #11802971

Subgroups — #11802971

Order 1152.

1409 conjugacy classes of subgroups.

The subgroup lattice has 403 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3750C211yesmaximal, characteristic
2C2×#63957C211yesmaximal, characteristic
3C2×#63957C211yesmaximal, characteristic
4C3×#5210C212yesmaximal
5#10591719C212yesmaximal
6#10591256C214yesmaximal, complemented
7#10591247C212yesmaximal, complemented
8#10591244C212yesmaximal, complemented
9#74382—32nomaximal
10C23×C32×C4C2211yescharacteristic
11C23×C3⋊Dic3C2211yescharacteristic
12C23×C3⋊Dic3C2211yescharacteristic
13C2×#3750—24no—
14C2×#3750C2212yes—
15C2×#3750C2212yes—
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×Dic3⋊C4—32no—
30C22×Dic3⋊C4—61no—
31C2×#877—32no—
32C2×#877—32no—
33C3×#385—32no—
34#5210D312yes—
35#4976—34no—
36#4975—34no—
37#4950—32no—
38#4946—32no—
39#4650—34no—
40#4647—34no—
41C24×C32C2311yescharacteristic
42C22×C32×C4—22no—
43C22×C32×C4—42no—
44C22×C32×C4C2312yes—
45C22×C3⋊Dic3—22no—
46C22×C3⋊Dic3—42no—
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—
56#3750—24no—
57#3750—24no—
58C3×#217—24no—
59C3×#217C2×C418yes—
60C3×Dic3⋊C4—44no—
61#3724—22no—
62#3724—22no—
63#3724C2×C418yescomplemented
64Dic3⋊Dic3—44no—
65Dic32—24no—
66Dic32C2×C418yescomplemented
67#2317—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—34no—
82C2×Dic3⋊C4—34no—
83C2×Dic3⋊C4—32no—
84C2×Dic3⋊C4—32no—
85C2×Dic3⋊C4—34no—
86C2×Dic3⋊C4—62no—
87C2×Dic3⋊C4—62no—
88C2×Dic3⋊C4—68no—
89C2×Dic3⋊C4—68no—
90C2×Dic3⋊C4C2×D314yes—
91C2×C4×Dic3—34no—
92C2×C4×Dic3—32no—
93C2×C4×Dic3—32no—
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—22no—
107C2×C32×C4—24no—
108C2×C32×C4—44no—
109C2×C3⋊Dic3—22no—
110C2×C3⋊Dic3—24no—
111C2×C3⋊Dic3—44no—
112C2×C3⋊Dic3C4⋊C4116yescomplemented
113C2×C3⋊Dic3C22×C412yes—
114C2×C3⋊Dic3C22×C412yes—
115C2×C3⋊Dic3C2×D412yes—
116C2×C3⋊Dic3C2×D412yes—
117C2×C3⋊Dic3C2×Q812yes—
118C2×C3⋊Dic3C2×Q812yes—
119C2×C3×Dic3—24no—
120C2×C3×Dic3—24no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—22no—
123C2×C3×Dic3—24no—
124C2×C3×Dic3—24no—
125C2×C3×Dic3C22×C418yes—
126C2×#117—91no—
127C2×#117—91no—
128C22×C4⋊C4—91no—
129#389—94no—
130#385—32no—
131#385—92no—
132#384—92no—
133#382—92no—
134C24×C3—21no—
135C24×C3C22×D312yes—
136C22×C3×C4—24no—
137C22×C3×C4—24no—
138C22×C3×C4—22no—
139C22×C3×C4—34no—
140C22×C3×C4—32no—
141C22×C3×C4—32no—
142C22×C3×C4—44no—
143C22×C3×C4—44no—
144C22×C3×C4C22×D314yes—
145C22×Dic3—38no—
146C22×Dic3—38no—
147C22×Dic3—38no—
148C22×Dic3—32no—
149C22×Dic3—32no—
150C22×Dic3—34no—
151C22×Dic3—64no—
152C22×Dic3—61no—
153C22×Dic3—61no—
154C22×Dic3—64no—
155C22×Dic3—64no—
156C22×Dic3—62no—
157C22×Dic3—64no—
158C22×Dic3—64no—
159C22×Dic3—124no—
160C22×Dic3—124no—
161C22×Dic3C22×D312yes—
162C22×Dic3C22×D312yes—
163C22×Dic3C22×D314yes—
164C3×C4⋊C4—124no—
165C3×C22⋊C4—38no—
166C3×C22⋊C4—64no—
167#217—24no—
168#217C4×D318yes—
169C4⋊Dic3—124no—
170Dic3⋊C4—316no—
171Dic3⋊C4—44no—
172Dic3⋊C4—64no—
173Dic3⋊C4—64no—
174Dic3⋊C4—68no—
175Dic3⋊C4—68no—
176Dic3⋊C4—68no—
177Dic3⋊C4—68no—
178Dic3⋊C4—124no—
179C4×Dic3—316no—
180C4×Dic3—64no—
181C4×Dic3—64no—
182C22×C32—24no—
183C22×C32—22no—
184C22×C32—22no—
185C22×C32—24no—
186C22×C32C2×C4⋊C414yes—
187C22×C32C23×C411yescharacteristic
188C22×C32C22×D411yescharacteristic
189C22×C32C22×Q811yescharacteristic
190C22×C32H(5,𝔽2)12yes—
191C22×C322−1+412yes—
192C32×C4—42no—
193C3⋊Dic3—42no—
194C3⋊Dic3C2×C4⋊C414yes—
195C3⋊Dic3C2×C4⋊C414yes—
196C3×Dic3—28no—
197C3×Dic3—42no—
198C3×Dic3—42no—
199C23×C4—91no—
200C23×C4—91no—
201C23×C4D3211yescharacteristic
202#117—98no—
203#117—184no—
204C2×C4⋊C4—34no—
205C2×C4⋊C4—92no—
206C2×C4⋊C4—91no—
207C2×C4⋊C4—91no—
208C2×C4⋊C4—92no—
209C2×C4⋊C4—92no—
210C2×C4⋊C4—94no—
211C2×C4⋊C4—184no—
212C2×C22⋊C4—32no—
213C2×C22⋊C4—32no—
214C2×C42—92no—
215C2×C42—92no—
216#95—34no—
217#95—94no—
218C23×C3—24no—
219C23×C3—24no—
220C23×C3—24no—
221C23×C3—24no—
222C23×C3—21no—
223C23×C3—22no—
224C23×C3—22no—
225C23×C3—22no—
226C23×C3C2×C4×D314yes—
227C23×C3D3×D414yes—
228C23×C3D3×Q814yes—
229C23×C3C23×D312yes—
230C2×C3×C4—24no—
231C2×C3×C4—24no—
232C2×C3×C4—24no—
233C2×C3×C4—24no—
234C2×C3×C4—38no—
235C2×C3×C4—44no—
236C2×C3×C4—48no—
237C2×C3×C4—48no—
238C2×C3×C4—64no—
239C2×C3×C4—64no—
240C2×C3×C4—62no—
241C2×C3×C4—62no—
242C2×C3×C4—64no—
243C2×C3×C4—64no—
244C2×Dic3—24no—
245C2×Dic3—24no—
246C2×Dic3—22no—
247C2×Dic3—22no—
248C2×Dic3—24no—
249C2×Dic3—24no—
250C2×Dic3—332no—
251C2×Dic3—34no—
252C2×Dic3—34no—
253C2×Dic3—34no—
254C2×Dic3—34no—
255C2×Dic3—34no—
256C2×Dic3—34no—
257C2×Dic3—616no—
258C2×Dic3—62no—
259C2×Dic3—62no—
260C2×Dic3—62no—
261C2×Dic3—62no—
262C2×Dic3—62no—
263C2×Dic3—62no—
264C2×Dic3—64no—
265C2×Dic3—64no—
266C2×Dic3—64no—
267C2×Dic3—64no—
268C2×Dic3—124no—
269C2×Dic3—128no—
270C2×Dic3—128no—
271C2×Dic3C2×C4×D318yes—
272C2×C32—24no—
273C2×C32C22×C4⋊C411yescharacteristic
274C2×C32#52012yes—
275C2×C32#53511yescharacteristic
276C2×C32#53611yescharacteristic
277C2×C32#54412yes—
278C24C2×D3211yescharacteristic
279C22×C4—22no—
280C22×C4—34no—
281C22×C4—32no—
282C22×C4—32no—
283C22×C4—42no—
284C22×C4—91no—
285C22×C4—91no—
286C22×C4—94no—
287C22×C4—94no—
288C22×C4—94no—
289C22×C4—92no—
290C22×C4—182no—
291C22×C4—362no—
292C22×C4C2×D3212yes—
293C4⋊C4—98no—
294C4⋊C4—124no—
295C4⋊C4—184no—
296C4⋊C4—184no—
297C4⋊C4—182no—
298C4⋊C4—182no—
299C4⋊C4—364no—
300C22⋊C4—38no—
301C22⋊C4—64no—
302C42—98no—
303C42—184no—
304C22×C3—24no—
305C22×C3—28no—
306C22×C3—24no—
307C22×C3—28no—
308C22×C3—24no—
309C22×C3—28no—
310C22×C3—24no—
311C22×C3—28no—
312C22×C3—22no—
313C22×C3—21no—
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—22no—
317C22×C3—24no—
318C22×C3D3×C4⋊C418yes—
319C22×C3C22×C4×D312yes—
320C22×C3C2×D3×D412yes—
321C22×C3#100414yes—
322C22×C3C2×D3×Q812yes—
323C22×C3#101014yes—
324C3×C4—44no—
325C3×C4—44no—
326C3×C4—68no—
327C3×C4—122no—
328C3×C4—122no—
329Dic3—28no—
330Dic3—38no—
331Dic3—38no—
332Dic3—42no—
333Dic3—42no—
334Dic3—64no—
335Dic3—64no—
336Dic3—124no—
337Dic3—124no—
338C32#231711yescharacteristic, complemented, Sylow
339C23—22no—
340C23—22no—
341C23#379712yes—
342C23C4×D3212yes—
343C23#381112yes—
344C23C22×D3211yescharacteristic
345C2×C4—22no—
346C2×C4—24no—
347C2×C4—38no—
348C2×C4—44no—
349C2×C4—64no—
350C2×C4—64no—
351C2×C4—64no—
352C2×C4—62no—
353C2×C4—62no—
354C2×C4—64no—
355C2×C4—92no—
356C2×C4—92no—
357C2×C4—92no—
358C2×C4—92no—
359C2×C4—92no—
360C2×C4—92no—
361C2×C4—916no—
362C2×C4—182no—
363C2×C4—184no—
364C2×C4—364no—
365C2×C3—28no—
366C2×C3—28no—
367C2×C3—22no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—22no—
372C2×C3C2×D3×C4⋊C412yes—
373C2×C3#554614yes—
374C2×C3#559212yes—
375C2×C3#562314yes—
376C2×C3#564812yes—
377C22—24no—
378C22—22no—
379C22—22no—
380C22—24no—
381C22#6388314yes—
382C22#6429812yes—
383C22C2×#379711yescharacteristic
384C22C2×C4×D3211yescharacteristic
385C22C2×#381111yescharacteristic
386C22#6433012yes—
387C4—42no—
388C4—68no—
389C4—94no—
390C4—94no—
391C4—122no—
392C4—122no—
393C4—362no—
394C3—21no—
395C3#7438212yescomplemented
396C2—24no—
397C2#1059481312yes—
398C2#1059487612yes—
399C2C2×#6388311yescharacteristic
400C2#1059492111yescharacteristic
401C2#1059550211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32#2317
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
6. #10591256C2semidirect
7. #10591247C2semidirect
8. #10591244C2semidirect
24. #63957C4semidirect
63. #3724C2×C4semidirect
66. Dic32C2×C4semidirect
112. C2×C3⋊Dic3C4⋊C4semidirect
338. C32#2317semidirect
395. C3#74382semidirect

Maximal subgroups

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

subgroupindex
C22×#37502
C2×#639572
C3×#52102
#105917192
#105912562
#105912472
#105912442
#743823