Finite Group Databasebeta

← #11808786

Subgroups — #11808786

Order 1152.

1285 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 1285 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×Q8×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×#63902C211yesmaximal, characteristic
3C3×#5231C212yesmaximal, complemented
4#10591394C212yesmaximal
5#10591368C214yesmaximal, complemented
6#10591315C212yesmaximal, complemented
7#10591252C211yesmaximal, characteristic, complemented
8#10591218C212yesmaximal, complemented
9#76779—32nomaximal
10C22×C32×Q8C2211yescharacteristic
11C22×#625C2211yescharacteristic
12C22×D3×Dic3C2212yes—
13Q8×C3⋊Dic3—24no—
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2212yes—
16C2×C4×C3⋊Dic3C2212yes—
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C3×(C2×D3)⋊C4C2212yes—
19C2×C3×(C2×D3)⋊C4C2214yes—
20C2×#3724C2211yescharacteristic
21C2×(C2×D3)⋊Dic3C2214yes—
22C2×Dic32C2212yes—
23#63902—24no—
24C3×C3⋊#95C2212yes—
25C3×C3⋊#95C2214yes—
26#63579C2212yes—
27#63579C2214yes—
28C2×Q8×Dic3—32no—
29C2×Q8×Dic3—61no—
30C2×#67⋊C4—32no—
31C3×#393—32no—
32#5231D312yescomplemented
33#4961—34no—
34#4953—32no—
35Dic3×C22⋊C4—34no—
36#4674—32no—
37#4666—34no—
38#4660—34no—
39#4648—32no—
40C23×C3×D3C2312yes—
41C2×C32×Q8—22no—
42C2×C32×Q8—24no—
43C22×C32×C4C2311yescharacteristic
44C22×C32×C4C2312yes—
45C22×C3⋊Dic3C2312yes—
46C22×C3⋊Dic3C2311yescharacteristic
47C22×C3⋊Dic3C2311yescharacteristic
48C22×C3×Dic3C2312yes—
49C22×C3×Dic3C2314yes—
50C2×#625—24no—
51C2×#625—22no—
52C2×D3×Dic3—24no—
53C2×D3×Dic3—28no—
54C4⋊(C3⋊Dic3)—22no—
55C4⋊(C3⋊Dic3)—24no—
56C4×C3⋊Dic3—24no—
57C4×C3⋊Dic3D414yes—
58C3×(C2×D3)⋊C4—24no—
59C3×(C2×D3)⋊C4—28no—
60#3724—22no—
61(C2×D3)⋊Dic3—28no—
62Dic32—24no—
63#2398—91noSylow
64C22×C3×Q8—21no—
65C22×C3×Q8C2×D312yes—
66C22×#67—32no—
67C23×Dic3—32no—
68C22×C4×D3—32no—
69C2×C3×C22⋊C4—34no—
70C2×C3×C22⋊C4—32no—
71C2×#217—34no—
72Q8×Dic3—68no—
73Q8×Dic3—68no—
74C2×(C2×D3)⋊C4—34no—
75C2×(C2×D3)⋊C4C2×D314yes—
76C2×(C2×D3)⋊C4C2×D312yes—
77C2×C4⋊Dic3—34no—
78C2×C4⋊Dic3—32no—
79C2×C4⋊Dic3—62no—
80C2×C4⋊Dic3—61no—
81C2×Dic3⋊C4—32no—
82C2×C4×Dic3—32no—
83C2×C4×Dic3—34no—
84C2×C4×Dic3—34no—
85C2×C4×Dic3—61no—
86C2×C4×Dic3—62no—
87#67⋊C4—68no—
88C3×#95—32no—
89C3×#95—34no—
90C3⋊#95—34no—
91C3⋊#95—34no—
92C3⋊#95—34no—
93C3⋊#95C2×D312yes—
94C3⋊#95C2×D314yes—
95C23×C32C2411yescharacteristic
96C22×C3×D3—22no—
97C22×C3×D3—24no—
98C22×C3×D3—24no—
99C22×C3×D3—22no—
100C22×C3×D3#4114yes—
101C32×Q8—28no—
102C2×C32×C4—22no—
103C2×C32×C4—22no—
104C2×C32×C4—22no—
105C2×C32×C4C2×D412yes—
106C2×C32×C4#4114yes—
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3—24no—
110C2×C3⋊Dic3C2×D412yes—
111C2×C3⋊Dic3C2×D412yes—
112C2×C3⋊Dic3#4114yes—
113C2×C3×Dic3—22no—
114C2×C3×Dic3—24no—
115C2×C3×Dic3—24no—
116C2×C3×Dic3—24no—
117C2×C3×Dic3—24no—
118#625—28no—
119D3×Dic3—48no—
120C2×C4×Q8—91no—
121C2×C4×D4—91no—
122#400—92no—
123#397—92no—
124#394—92no—
125#393—32no—
126C4×C22⋊C4—94no—
127#376—91no—
128C24×C3—32no—
129C23×D3C22×D312yes—
130C2×C3×Q8—24no—
131C2×C3×Q8—28no—
132C2×C3×Q8—24no—
133C2×C3×Q8—28no—
134C22×C3×C4—22no—
135C22×C3×C4—21no—
136C22×C3×C4—34no—
137C22×C3×C4—32no—
138C22×C3×C4C22×D312yes—
139C22×C3×C4C22×D314yes—
140C2×#67—64no—
141C2×#67—64no—
142C2×#67—64no—
143C22×Dic3—32no—
144C22×Dic3—32no—
145C22×Dic3—34no—
146C22×Dic3—61no—
147C22×Dic3—61no—
148C22×Dic3—62no—
149C22×Dic3—64no—
150C22×Dic3—68no—
151C22×Dic3C22×D314yes—
152C22×Dic3C22×D312yes—
153C2×C4×D3—64no—
154C2×C4×D3—68no—
155C3×C22⋊C4—64no—
156C3×C22⋊C4—68no—
157#217—68no—
158(C2×D3)⋊C4—24no—
159(C2×D3)⋊C4—28no—
160(C2×D3)⋊C4—68no—
161C4⋊Dic3—68no—
162C4⋊Dic3—68no—
163C4⋊Dic3—64no—
164C4⋊Dic3—64no—
165Dic3⋊C4—64no—
166C4×Dic3—38no—
167C4×Dic3—64no—
168C4×Dic3—68no—
169C4×Dic3—68no—
170C4×Dic3—68no—
171C22×C32C22×D411yescharacteristic
172C22×C32C2×#4112yes—
173C22×C32C2×#4112yes—
174C22×C32C2×#4112yes—
175C2×C3×D3—24no—
176C2×C3×D3—28no—
177C2×C3×D3—42no—
178C2×C3×D3—42no—
179C2×C3×D3—44no—
180C32×C4—22no—
181C32×C4—24no—
182C3⋊Dic3—22no—
183C3⋊Dic3—42no—
184C3⋊Dic3#12414yes—
185C3×Dic3—42no—
186C3×Dic3—44no—
187C22×Q8D3211yescharacteristic
188C22×D4—91no—
189C23×C4—92no—
190C4×Q8—184no—
191C4×D4—184no—
192C2×C4⋊C4—91no—
193C2×C4⋊C4—92no—
194C2×C4⋊C4—91no—
195C2×C22⋊C4—32no—
196C2×C22⋊C4—34no—
197C2×C22⋊C4—94no—
198C2×C42—91no—
199C2×C42—92no—
200C2×C42—92no—
201#95—32no—
202#95—34no—
203#95—92no—
204#95—94no—
205C23×C3—21no—
206C23×C3—34no—
207C23×C3—62no—
208C23×C3—64no—
209C23×C3—62no—
210C23×C3—64no—
211C23×C3C23×D312yes—
212C22×D3—22no—
213C22×D3—24no—
214C22×D3—24no—
215C22×D3—22no—
216C22×D3#23914yes—
217C3×Q8—216no—
218C3×Q8—216no—
219C2×C3×C4—24no—
220C2×C3×C4—24no—
221C2×C3×C4—24no—
222C2×C3×C4—24no—
223C2×C3×C4—24no—
224C2×C3×C4—24no—
225C2×C3×C4—24no—
226C2×C3×C4—22no—
227C2×C3×C4—62no—
228C2×C3×C4—64no—
229C2×C3×C4—64no—
230C2×C3×C4—64no—
231C2×C3×C4—64no—
232C2×C3×C4D3×D414yes—
233C2×C3×C4#23718yes—
234#67—616no—
235C2×Dic3—22no—
236C2×Dic3—24no—
237C2×Dic3—24no—
238C2×Dic3—24no—
239C2×Dic3—24no—
240C2×Dic3—34no—
241C2×Dic3—38no—
242C2×Dic3—34no—
243C2×Dic3—62no—
244C2×Dic3—64no—
245C2×Dic3—62no—
246C2×Dic3—62no—
247C2×Dic3—62no—
248C2×Dic3—64no—
249C2×Dic3—64no—
250C2×Dic3—64no—
251C2×Dic3—64no—
252C2×Dic3—122no—
253C2×Dic3—124no—
254C2×Dic3—128no—
255C4×D3—128no—
256C2×C32#52511yescharacteristic
257C2×C32#52511yescharacteristic
258C2×C32C2×#12411yescharacteristic
259C2×C32#52914yes—
260C3×D3—44no—
261C24—32no—
262C2×Q8—24no—
263C2×Q8—22no—
264C2×D4—182no—
265C2×D4—184no—
266C22×C4—34no—
267C22×C4—32no—
268C22×C4—91no—
269C22×C4—91no—
270C22×C4—92no—
271C22×C4—184no—
272C22×C4—188no—
273C22×C4C2×D3212yes—
274C22×C4C2×D3211yescharacteristic
275C4⋊C4—184no—
276C4⋊C4—182no—
277C4⋊C4—182no—
278C22⋊C4—68no—
279C22⋊C4—64no—
280C22⋊C4—188no—
281C42—94no—
282C42—184no—
283C42—184no—
284C22×C3—22no—
285C22×C3—22no—
286C22×C3—22no—
287C22×C3—21no—
288C22×C3—68no—
289C22×C3—64no—
290C22×C3—122no—
291C22×C3—122no—
292C22×C3—124no—
293C22×C3C2×D3×D412yes—
294C22×C3C2×#23714yes—
295C22×C3C2×#23912yes—
296C22×C3D3×#4112yes—
297C22×C3D3×#4114yes—
298C2×D3—28no—
299C2×D3—24no—
300C2×D3—42no—
301C2×D3—44no—
302C2×D3—42no—
303C3×C4—28no—
304C3×C4—24no—
305C3×C4—24no—
306C3×C4—28no—
307C3×C4—122no—
308C3×C4—124no—
309Dic3—38no—
310Dic3—42no—
311Dic3—44no—
312Dic3—64no—
313Dic3—64no—
314Dic3—122no—
315Dic3—124no—
316Dic3—124no—
317C32#239811yescharacteristic, complemented, Sylow
318C23—34no—
319C23—62no—
320C23—64no—
321C23—64no—
322C23—62no—
323C23C22×D3211yescharacteristic
324Q8—28no—
325D4—188no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—64no—
330C2×C4—64no—
331C2×C4—64no—
332C2×C4—64no—
333C2×C4—62no—
334C2×C4—94no—
335C2×C4—92no—
336C2×C4—92no—
337C2×C4—182no—
338C2×C4—184no—
339C2×C4—182no—
340C2×C4—368no—
341C2×C4#380514yes—
342C2×C4#381112yes—
343C2×C3—24no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—124no—
348C2×C3#558612yes—
349C2×C3#562414yes—
350C2×C3#562712yes—
351C2×C3D3×#12412yes—
352C2×C3#568014yes—
353D3—44no—
354C22—68no—
355C22—64no—
356C22—124no—
357C22—122no—
358C22—122no—
359C22D3×#23912yes—
360C22#6431912yes—
361C22C2×#380512yes—
362C22C2×#381111yescharacteristic
363C4—24no—
364C4—22no—
365C4—94no—
366C4—124no—
367C4—122no—
368C4—182no—
369C4—362no—
370C3—21no—
371C3#7677912yescomplemented
372C2—124no—
373C2#1059537714yes—
374C2#1059543011yescharacteristic
375C2#1059543211yescharacteristic
376C2#1059550111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×Q8C22
prime radicalC22×#625C22
hypercenterC22×Q8D32
hypocenterC32#2398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C3⋊Dic3C2semidirect
3. C3×#5231C2semidirect
5. #10591368C2semidirect
6. #10591315C2semidirect
7. #10591252C2semidirect
8. #10591218C2semidirect
32. #5231D3semidirect
317. C32#2398semidirect
371. C3#76779semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊Dic32
C2×#639022
C3×#52312
#105913942
#105913682
#105913152
#105912522
#105912182
#767793