Finite Group Databasebeta

← #11808825

Subgroups — #11808825

Order 1152.

1349 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 1349 conjugacy classes of subgroups — too many to draw. Only its 200 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×#64102C211yesmaximal, characteristic
2C2×#63838C211yesmaximal, characteristic, complemented
3C3×#4985C212yesmaximal, complemented
4#10591321C212yesmaximal
5#10591260C214yesmaximal, complemented
6#10591252C211yesmaximal, characteristic, complemented
7#10591216C212yesmaximal, complemented
8#10591205C212yesmaximal, complemented
9#78131—32nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C4×C3⋊D3C2212yes—
12C22×#627C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×#3752C2212yes—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16#64102—24no—
17C2×C3×Dic3⋊C4C2212yes—
18C2×#3724C2211yescharacteristic
19C2×#3722C2214yes—
20C2×#3722C2214yes—
21C2×Dic32C2212yes—
22C2×Dic32C2212yes—
23#63838—24no—
24C3×C3⋊#95C2212yes—
25C3×C3⋊#95C2214yes—
26C3×C3⋊#95C2214yes—
27#63579C2212yes—
28C2×#893—32no—
29C2×#893—61no—
30C2×#887—32no—
31C3×#400—32no—
32#4991—32no—
33#4985D312yescomplemented
34#4675—34no—
35#4673—34no—
36#4672—32no—
37#4666—34no—
38#4666—34no—
39#4648—32no—
40C23×C3⋊D3C2312yes—
41C22×C32×C4C2312yes—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3C2311yescharacteristic
44C22×C3⋊Dic3C2311yescharacteristic
45C2×C4⋊(C3⋊D3)—24no—
46C2×C4⋊(C3⋊D3)—22no—
47C2×C4×C3⋊D3—24no—
48C2×C4×C3⋊D3—28no—
49C22×C3×Dic3C2312yes—
50C22×C3×Dic3C2314yes—
51C22×C3×Dic3C2312yes—
52C2×#627—22no—
53C2×#627—24no—
54C32×C4⋊C4—22no—
55#3752—24no—
56C4×C3⋊Dic3D414yes—
57C3×Dic3⋊C4—24no—
58#3724—22no—
59#3722—28no—
60#3722—28no—
61Dic32—24no—
62Dic32—24no—
63#2398—91noSylow
64C22×D12—32no—
65C22×D12—61no—
66C22×C4×D3—34no—
67C22×C4×D3—62no—
68C22×Dic6—32no—
69C2×C3×C4⋊C4—21no—
70C2×C3×C4⋊C4—32no—
71C2×C3×C4⋊C4C2×D312yes—
72C2×(C2×D3)⋊C4—34no—
73C2×(C2×D3)⋊C4—34no—
74C2×(C2×D3)⋊C4—34no—
75C2×(C2×D3)⋊C4—34no—
76C2×(C2×D3)⋊C4—34no—
77C2×(C2×D3)⋊C4—62no—
78C2×Dic3⋊C4—32no—
79C2×Dic3⋊C4C2×D312yes—
80C2×C4×Dic3—32no—
81C2×C4×Dic3—34no—
82C2×C4×Dic3—32no—
83C2×C4×Dic3—32no—
84C2×C4×Dic3—61no—
85#893—68no—
86#893—68no—
87#887—68no—
88C3×#95—32no—
89C3×#95—34no—
90C3×#95—34no—
91C3⋊#95—34no—
92C3⋊#95C2×D312yes—
93C3⋊#95C2×D314yes—
94C3⋊#95C2×D314yes—
95C23×C32C2411yescharacteristic
96C22×C3⋊D3—22no—
97C22×C3⋊D3—22no—
98C22×C3⋊D3—24no—
99C22×C3⋊D3—24no—
100C22×C3⋊D3#4114yes—
101C2×C32×C4—22no—
102C2×C32×C4—22no—
103C2×C32×C4—24no—
104C2×C32×C4C2×D412yes—
105C2×C3⋊Dic3—22no—
106C2×C3⋊Dic3C2×D412yes—
107C2×C3⋊Dic3C2×D412yes—
108C2×C3⋊Dic3#4114yes—
109C4⋊(C3⋊D3)—28no—
110C4×C3⋊D3—48no—
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—32no—
123#397—92no—
124#394—92no—
125#393—92no—
126C4×C22⋊C4—94no—
127#376—91no—
128C23×D3—34no—
129C23×D3—62no—
130C22×C3×C4—21no—
131C22×C3×C4—22no—
132C22×C3×C4—32no—
133C22×C3×C4—34no—
134C22×C3×C4—32no—
135C22×C3×C4C22×D314yes—
136C22×C3×C4C22×D312yes—
137C22×Dic3—32no—
138C22×Dic3—32no—
139C22×Dic3—61no—
140C22×Dic3—61no—
141C22×Dic3C22×D314yes—
142C22×Dic3C22×D312yes—
143C22×Dic3C22×D312yes—
144C2×D12—68no—
145C2×D12—64no—
146C2×D12—68no—
147C2×D12—64no—
148C2×C4×D3—68no—
149C2×C4×D3—68no—
150C2×C4×D3—68no—
151C2×C4×D3—68no—
152C2×C4×D3—128no—
153C2×Dic6—64no—
154C2×Dic6—64no—
155C2×Dic6—64no—
156C3×C4⋊C4—24no—
157C3×C4⋊C4—24no—
158C3×C4⋊C4—64no—
159(C2×D3)⋊C4—68no—
160(C2×D3)⋊C4—68no—
161(C2×D3)⋊C4—68no—
162(C2×D3)⋊C4—68no—
163(C2×D3)⋊C4—68no—
164(C2×D3)⋊C4—68no—
165Dic3⋊C4—24no—
166Dic3⋊C4—64no—
167C4×Dic3—38no—
168C4×Dic3—64no—
169C4×Dic3—64no—
170C4×Dic3—64no—
171C4×Dic3—68no—
172C22×C32C22×D411yescharacteristic
173C22×C32C2×#4112yes—
174C22×C32C2×#4112yes—
175C22×C32C2×#4112yes—
176C2×C3⋊D3—24no—
177C2×C3⋊D3—28no—
178C2×C3⋊D3—42no—
179C2×C3⋊D3—42no—
180C2×C3⋊D3—44no—
181C32×C4—22no—
182C32×C4—42no—
183C3⋊Dic3—22no—
184C3⋊Dic3#12414yes—
185C3×Dic3—24no—
186C3×Dic3—42no—
187C3×Dic3—44no—
188C22×Q8—91no—
189C22×D4—91no—
190C23×C4—92no—
191C4×Q8—184no—
192C4×D4—184no—
193C2×C4⋊C4—32no—
194C2×C4⋊C4—91no—
195C2×C4⋊C4D3211yescharacteristic
196C2×C22⋊C4—94no—
197C2×C22⋊C4—94no—
198C2×C22⋊C4—92no—
199C2×C42—91no—
200C2×C42—92no—
201C2×C42—92no—
202#95—32no—
203#95—34no—
204#95—34no—
205#95—92no—
206C23×C3—21no—
207C23×C3C23×D312yes—
208C22×D3—38no—
209C22×D3—64no—
210C22×D3—64no—
211C22×D3—64no—
212C22×D3—64no—
213C22×D3—64no—
214C22×D3—64no—
215C22×D3—64no—
216C22×D3—64no—
217C22×D3—64no—
218C22×D3—124no—
219C22×D3—124no—
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—34no—
228C2×C3×C4—44no—
229C2×C3×C4—62no—
230C2×C3×C4—62no—
231C2×C3×C4—62no—
232C2×C3×C4—64no—
233C2×C3×C4—64no—
234C2×C3×C4—64no—
235C2×C3×C4—64no—
236C2×C3×C4D3×D414yes—
237C2×Dic3—22no—
238C2×Dic3—22no—
239C2×Dic3—22no—
240C2×Dic3—24no—
241C2×Dic3—24no—
242C2×Dic3—24no—
243C2×Dic3—24no—
244C2×Dic3—34no—
245C2×Dic3—38no—
246C2×Dic3—34no—
247C2×Dic3—62no—
248C2×Dic3—64no—
249C2×Dic3—62no—
250C2×Dic3—62no—
251C2×Dic3—62no—
252C2×Dic3—122no—
253C2×Dic3#23914yes—
254D12—616no—
255D12—616no—
256C4×D3—1216no—
257C4×D3—1216no—
258Dic6—616no—
259C2×C32#52511yescharacteristic
260C2×C32#52511yescharacteristic
261C2×C32C2×#12411yescharacteristic
262C2×C32#52914yes—
263C3⋊D3—44no—
264C24—92no—
265C2×Q8—184no—
266C2×Q8—182no—
267C2×D4—184no—
268C2×D4—182no—
269C22×C4—32no—
270C22×C4—34no—
271C22×C4—32no—
272C22×C4—91no—
273C22×C4—91no—
274C22×C4—184no—
275C22×C4—188no—
276C22×C4C2×D3212yes—
277C22×C4C2×D3211yescharacteristic
278C4⋊C4—22no—
279C4⋊C4—64no—
280C4⋊C4—182no—
281C22⋊C4—184no—
282C22⋊C4—188no—
283C22⋊C4—188no—
284C42—94no—
285C42—184no—
286C42—184no—
287C22×C3—22no—
288C22×C3—22no—
289C22×C3—22no—
290C22×C3—21no—
291C22×C3C2×D3×D412yes—
292C22×C3C2×#23912yes—
293C22×C3D3×#4114yes—
294C22×C3D3×#4114yes—
295C22×C3D3×#4112yes—
296C2×D3—68no—
297C2×D3—68no—
298C2×D3—68no—
299C2×D3—68no—
300C2×D3—128no—
301C2×D3—124no—
302C2×D3—124no—
303C2×D3—128no—
304C2×D3—124no—
305C2×D3—124no—
306C2×D3—124no—
307C2×D3—124no—
308C3×C4—24no—
309C3×C4—24no—
310C3×C4—44no—
311C3×C4—44no—
312C3×C4—64no—
313C3×C4—122no—
314C3×C4—124no—
315Dic3—24no—
316Dic3—38no—
317Dic3—42no—
318Dic3—44no—
319Dic3—64no—
320Dic3—64no—
321Dic3—122no—
322C32#239811yescharacteristic, complemented, Sylow
323C23—94no—
324C23—182no—
325C23—184no—
326C23—184no—
327C23—182no—
328C23C22×D3211yescharacteristic
329Q8—188no—
330D4—188no—
331C2×C4—22no—
332C2×C4—24no—
333C2×C4—22no—
334C2×C4—34no—
335C2×C4—62no—
336C2×C4—62no—
337C2×C4—64no—
338C2×C4—64no—
339C2×C4—64no—
340C2×C4—64no—
341C2×C4—62no—
342C2×C4—94no—
343C2×C4—92no—
344C2×C4—92no—
345C2×C4—182no—
346C2×C4—368no—
347C2×C4#381112yes—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—24no—
352C2×C3#562712yes—
353C2×C3#565612yes—
354C2×C3D3×#12412yes—
355C2×C3#569114yes—
356C2×C3#570614yes—
357D3—128no—
358D3—128no—
359C22—184no—
360C22—188no—
361C22—362no—
362C22—362no—
363C22—364no—
364C22#6430612yes—
365C22#6431212yes—
366C22D3×#23912yes—
367C22C2×#381111yescharacteristic
368C4—22no—
369C4—42no—
370C4—64no—
371C4—94no—
372C4—122no—
373C4—124no—
374C4—182no—
375C3—21no—
376C3#7813112yescomplemented
377C2—364no—
378C2#1059446514yes—
379C2#1059492011yescharacteristic
380C2#1059517011yescharacteristic
381C2#1059543011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63838C2semidirect
3. C3×#4985C2semidirect
5. #10591260C2semidirect
6. #10591252C2semidirect
7. #10591216C2semidirect
8. #10591205C2semidirect
33. #4985D3semidirect
322. C32#2398semidirect
376. C3#78131semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
C2×#638382
C3×#49852
#105913212
#105912602
#105912522
#105912162
#105912052
#781313