Finite Group Databasebeta

← #11808800

Subgroups — #11808800

Order 1152.

1349 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 1349 conjugacy classes of subgroups — too many to draw. Only its 212 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
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic
2C2×#63838C211yesmaximal, characteristic, complemented
3C3×#5222C212yesmaximal
4#10591705C214yesmaximal, complemented
5#10591694C212yesmaximal, complemented
6#10591692C212yesmaximal, complemented
7#10591252C211yesmaximal, characteristic, complemented
8#10591226C212yesmaximal, complemented
9#76893—32nomaximal
10C22×C32×D4C2211yescharacteristic
11C23×C3⋊Dic3C2212yes—
12C22×#627C2211yescharacteristic
13C2×#3757C2212yes—
14D4×C3⋊Dic3—24no—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C3×#217C2214yes—
18C2×C3×#217C2214yes—
19C2×C3×Dic3⋊C4C2212yes—
20C2×#3724C2211yescharacteristic
21C2×Dic32C2212yes—
22C2×Dic32C2212yes—
23#63838—24no—
24C3×C3⋊#95C2212yes—
25#63579C2212yes—
26#63579C2214yes—
27#63579C2214yes—
28C2×D4×Dic3—32no—
29C2×D4×Dic3—61no—
30C2×#887—32no—
31C3×#394—32no—
32#5222D312yes—
33#4986—32no—
34#4952—34no—
35#4947—34no—
36Dic3×C22⋊C4—34no—
37Dic3×C22⋊C4—34no—
38#4659—32no—
39#4648—32no—
40C24×C32C2312yes—
41C2×C32×D4—24no—
42C2×C32×D4—22no—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3—24no—
45C22×C3⋊Dic3—28no—
46C22×C3⋊Dic3C2312yes—
47C22×C3⋊Dic3C2311yescharacteristic
48C22×C3⋊Dic3C2311yescharacteristic
49C22×C3×Dic3C2312yes—
50C22×C3×Dic3C2314yes—
51C22×C3×Dic3C2312yes—
52C2×#627—22no—
53C2×#627—24no—
54#3757—24no—
55C4⋊(C3⋊Dic3)—22no—
56C4×C3⋊Dic3D414yes—
57C3×#217—28no—
58C3×#217—28no—
59C3×Dic3⋊C4—24no—
60#3724—22no—
61Dic32—24no—
62Dic32—24no—
63#2398—91noSylow
64C22×C3×D4—21no—
65C22×C3×D4C2×D312yes—
66C23×Dic3—34no—
67C23×Dic3—62no—
68C22×Dic6—32no—
69C2×C3×C4⋊C4—32no—
70C2×C3×C22⋊C4—34no—
71C2×C3×C22⋊C4—34no—
72C2×#217—34no—
73C2×#217—62no—
74C2×#217C2×D314yes—
75C2×#217C2×D314yes—
76D4×Dic3—68no—
77D4×Dic3—68no—
78C2×C4⋊Dic3—32no—
79C2×C4⋊Dic3—61no—
80C2×Dic3⋊C4—32no—
81C2×Dic3⋊C4C2×D312yes—
82C2×C4×Dic3—32no—
83C2×C4×Dic3—34no—
84C2×C4×Dic3—32no—
85C2×C4×Dic3—32no—
86C2×C4×Dic3—61no—
87#887—68no—
88C3×#95—32no—
89C3⋊#95—34no—
90C3⋊#95—34no—
91C3⋊#95—34no—
92C3⋊#95—34no—
93C3⋊#95—34no—
94C3⋊#95C2×D312yes—
95C23×C32—22no—
96C23×C32—22no—
97C23×C32—24no—
98C23×C32—24no—
99C23×C32#4114yes—
100C23×C32C2411yescharacteristic
101C32×D4—28no—
102C2×C32×C4—22no—
103C2×C32×C4C2×D412yes—
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3—22no—
106C2×C3⋊Dic3—24no—
107C2×C3⋊Dic3—48no—
108C2×C3⋊Dic3C2×D412yes—
109C2×C3⋊Dic3C2×D412yes—
110C2×C3⋊Dic3#4114yes—
111C2×C3×Dic3—22no—
112C2×C3×Dic3—22no—
113C2×C3×Dic3—22no—
114C2×C3×Dic3—24no—
115C2×C3×Dic3—24no—
116C2×C3×Dic3—24no—
117C2×C3×Dic3—24no—
118C2×C3×Dic3#4114yes—
119#627—28no—
120C2×C4×Q8—91no—
121C2×C4×D4—91no—
122#400—92no—
123#397—92no—
124#394—32no—
125#393—92no—
126C4×C22⋊C4—94no—
127#376—91no—
128C24×C3—22no—
129C24×C3C22×D314yes—
130C2×C3×D4—24no—
131C2×C3×D4—28no—
132C2×C3×D4—28no—
133C2×C3×D4—24no—
134C22×C3×C4—21no—
135C22×C3×C4—32no—
136C22×C3×C4—34no—
137C22×C3×C4—32no—
138C22×C3×C4C22×D312yes—
139C22×Dic3—32no—
140C22×Dic3—32no—
141C22×Dic3—34no—
142C22×Dic3—61no—
143C22×Dic3—61no—
144C22×Dic3—62no—
145C22×Dic3—68no—
146C22×Dic3—68no—
147C22×Dic3—68no—
148C22×Dic3—68no—
149C22×Dic3—128no—
150C22×Dic3C22×D314yes—
151C22×Dic3C22×D312yes—
152C22×Dic3C22×D312yes—
153C2×Dic6—64no—
154C2×Dic6—64no—
155C2×Dic6—64no—
156C3×C4⋊C4—64no—
157C3×C22⋊C4—68no—
158C3×C22⋊C4—68no—
159#217—28no—
160#217—28no—
161#217—68no—
162#217—68no—
163C4⋊Dic3—64no—
164C4⋊Dic3—64no—
165Dic3⋊C4—24no—
166Dic3⋊C4—64no—
167C4×Dic3—38no—
168C4×Dic3—64no—
169C4×Dic3—64no—
170C4×Dic3—64no—
171C4×Dic3—68no—
172C22×C32—24no—
173C22×C32—28no—
174C22×C32—42no—
175C22×C32—42no—
176C22×C32—44no—
177C22×C32C22×D411yescharacteristic
178C22×C32C2×#4112yes—
179C22×C32C2×#4112yes—
180C22×C32C2×#4112yes—
181C32×C4—22no—
182C3⋊Dic3—22no—
183C3⋊Dic3—42no—
184C3⋊Dic3#12414yes—
185C3×Dic3—24no—
186C3×Dic3—42no—
187C3×Dic3—44no—
188C22×Q8—91no—
189C22×D4D3211yescharacteristic
190C23×C4—92no—
191C4×Q8—184no—
192C4×D4—184no—
193C2×C4⋊C4—32no—
194C2×C4⋊C4—91no—
195C2×C4⋊C4—91no—
196C2×C22⋊C4—34no—
197C2×C22⋊C4—34no—
198C2×C22⋊C4—92no—
199C2×C42—91no—
200C2×C42—92no—
201C2×C42—92no—
202#95—32no—
203#95—92no—
204#95—94no—
205#95—94no—
206C23×C3—24no—
207C23×C3—24no—
208C23×C3—24no—
209C23×C3—24no—
210C23×C3—24no—
211C23×C3—24no—
212C23×C3—24no—
213C23×C3—24no—
214C23×C3—21no—
215C23×C3—24no—
216C23×C3—44no—
217C23×C3—44no—
218C23×C3#23718yes—
219C23×C3C23×D312yes—
220C3×D4—216no—
221C3×D4—216no—
222C2×C3×C4—24no—
223C2×C3×C4—24no—
224C2×C3×C4—22no—
225C2×C3×C4—34no—
226C2×C3×C4—62no—
227C2×C3×C4—62no—
228C2×C3×C4—62no—
229C2×C3×C4—64no—
230C2×C3×C4—64no—
231C2×C3×C4—64no—
232C2×C3×C4—64no—
233C2×C3×C4D3×D414yes—
234C2×Dic3—22no—
235C2×Dic3—22no—
236C2×Dic3—22no—
237C2×Dic3—24no—
238C2×Dic3—24no—
239C2×Dic3—24no—
240C2×Dic3—24no—
241C2×Dic3—34no—
242C2×Dic3—38no—
243C2×Dic3—34no—
244C2×Dic3—62no—
245C2×Dic3—64no—
246C2×Dic3—62no—
247C2×Dic3—62no—
248C2×Dic3—62no—
249C2×Dic3—64no—
250C2×Dic3—64no—
251C2×Dic3—64no—
252C2×Dic3—64no—
253C2×Dic3—122no—
254C2×Dic3—124no—
255C2×Dic3—1216no—
256C2×Dic3—1216no—
257C2×Dic3#23714yes—
258Dic6—616no—
259C2×C32—44no—
260C2×C32#52511yescharacteristic
261C2×C32#52511yescharacteristic
262C2×C32C2×#12411yescharacteristic
263C2×C32#52914yes—
264C24C2×D3212yes—
265C2×Q8—184no—
266C2×Q8—182no—
267C2×D4—24no—
268C2×D4—22no—
269C22×C4—32no—
270C22×C4—34no—
271C22×C4—32no—
272C22×C4—91no—
273C22×C4—91no—
274C22×C4—92no—
275C22×C4—184no—
276C22×C4—188no—
277C22×C4C2×D3211yescharacteristic
278C4⋊C4—64no—
279C4⋊C4—182no—
280C4⋊C4—182no—
281C22⋊C4—68no—
282C22⋊C4—68no—
283C22⋊C4—184no—
284C42—94no—
285C42—184no—
286C42—184no—
287C22×C3—28no—
288C22×C3—28no—
289C22×C3—28no—
290C22×C3—28no—
291C22×C3—22no—
292C22×C3—22no—
293C22×C3—22no—
294C22×C3—21no—
295C22×C3—48no—
296C22×C3—44no—
297C22×C3—48no—
298C22×C3—44no—
299C22×C3—44no—
300C22×C3—44no—
301C22×C3—44no—
302C22×C3—44no—
303C22×C3C2×D3×D412yes—
304C22×C3C2×#23712yes—
305C22×C3C2×#23714yes—
306C22×C3D3×#4112yes—
307C22×C3D3×#4114yes—
308C3×C4—24no—
309C3×C4—24no—
310C3×C4—64no—
311C3×C4—124no—
312C3×C4—122no—
313Dic3—24no—
314Dic3—38no—
315Dic3—42no—
316Dic3—44no—
317Dic3—64no—
318Dic3—64no—
319Dic3—122no—
320Dic3—124no—
321Dic3—124no—
322C32#239811yescharacteristic, complemented, Sylow
323C23—24no—
324C23—24no—
325C23—22no—
326C23—22no—
327C23#380514yes—
328C23C22×D3211yescharacteristic
329Q8—188no—
330D4—28no—
331C2×C4—22no—
332C2×C4—34no—
333C2×C4—62no—
334C2×C4—62no—
335C2×C4—64no—
336C2×C4—64no—
337C2×C4—64no—
338C2×C4—64no—
339C2×C4—62no—
340C2×C4—94no—
341C2×C4—92no—
342C2×C4—92no—
343C2×C4—182no—
344C2×C4—184no—
345C2×C4—182no—
346C2×C4—368no—
347C2×C4#381112yes—
348C2×C3—21no—
349C2×C3—24no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—48no—
353C2×C3—48no—
354C2×C3#558612yes—
355C2×C3#560014yes—
356C2×C3#560612yes—
357C2×C3#564914yes—
358C2×C3D3×#12412yes—
359C22—28no—
360C22—24no—
361C22—42no—
362C22—44no—
363C22—42no—
364C22D3×#23712yes—
365C22#6431212yes—
366C22C2×#380512yes—
367C22C2×#381111yescharacteristic
368C4—22no—
369C4—64no—
370C4—94no—
371C4—124no—
372C4—122no—
373C4—182no—
374C4—362no—
375C3—21no—
376C3#7689312yescomplemented
377C2—44no—
378C2#1059517011yescharacteristic
379C2#1059520214yes—
380C2#1059530611yescharacteristic
381C2#1059550111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
Fitting, prime radicalC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#2398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63838C2semidirect
4. #10591705C2semidirect
5. #10591694C2semidirect
6. #10591692C2semidirect
7. #10591252C2semidirect
8. #10591226C2semidirect
322. C32#2398semidirect
376. C3#76893semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C2×#638382
C3×#52222
#105917052
#105916942
#105916922
#105912522
#105912262
#768933