Finite Group Databasebeta

← #11808654

Subgroups — #11808654

Order 1152.

1584 conjugacy classes of subgroups.

The subgroup lattice has 387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64101C211yesmaximal, characteristic
2C2×#64096C211yesmaximal, characteristic, complemented
3C32×#400C211yesmaximal, characteristic, complemented
4#10592692C211yesmaximal, characteristic
5#10592678C211yesmaximal, characteristic, complemented
6#10592375C212yesmaximal
7#10592372C211yesmaximal, characteristic
8#10592365C212yesmaximal
9#10592356C212yesmaximal, complemented
10#10592348C211yesmaximal, characteristic, complemented
11#10592348C212yesmaximal, complemented
12#78130—34nomaximal
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×#634C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×#3752C2212yes—
18C2×#3752C2212yes—
19C2×#3752C2211yescharacteristic
20C2×#3752C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×#3750C2212yes—
23C2×#3750C2212yes—
24C2×#3750C2212yes—
25C2×#3750C2212yes—
26C2×C4×C3⋊Dic3C2212yes—
27C2×C4×C3⋊Dic3C2211yescharacteristic
28C2×C4×C3⋊Dic3C2212yes—
29C2×C4×C3⋊Dic3C2211yescharacteristic
30#64101—24no—
31#64096—24no—
32C32×#95C2211yescharacteristic
33C32×#95C2212yes—
34C32×#95C2212yes—
35#63658C2212yes—
36#63658C2211yescharacteristic
37#63658C2212yes—
38C2×#892—34no—
39C2×#887—34no—
40C3×#400D314yescomplemented
41#4993—34no—
42#4979—34no—
43#4676—38no—
44#4673—34no—
45#4666—38no—
46#4657—38no—
47#4649—38no—
48#4649—34no—
49C23×C3⋊D3C2311yescharacteristic
50C22×C32×C4C2312yes—
51C22×C32×C4C2311yescharacteristic
52C22×C32×C4C2312yes—
53C22×C32×C4C2311yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3C2311yescharacteristic
56C22×C3⋊Dic3C2311yescharacteristic
57C22×C3⋊Dic3C2312yes—
58C22×C3⋊Dic3C2312yes—
59C22×C3⋊Dic3C2311yescharacteristic
60C2×C4×C3⋊D3—22no—
61C2×C4×C3⋊D3—22no—
62C2×C4×C3⋊D3Q814yescomplemented
63C2×#634—22no—
64C2×#634—24no—
65C32×C4⋊C4—22no—
66C32×C4⋊C4—22no—
67#3752—22no—
68#3752—22no—
69#3752—24no—
70#3752—24no—
71C4⋊(C3⋊Dic3)—22no—
72#3750—24no—
73#3750—24no—
74#3750—24no—
75#3750—24no—
76C4×C3⋊Dic3—24no—
77C4×C3⋊Dic3—22no—
78C4×C3⋊Dic3—24no—
79C4×C3⋊Dic3D414yes—
80#2396—91noSylow
81C22×C4×D3—34no—
82C22×Dic6—34no—
83C2×C3×C4⋊C4C2×D314yes—
84C2×C3×C4⋊C4C2×D314yes—
85C2×(C2×D3)⋊C4—38no—
86C2×(C2×D3)⋊C4—38no—
87C2×(C2×D3)⋊C4—34no—
88C2×(C2×D3)⋊C4—34no—
89C2×C4⋊Dic3—34no—
90C2×Dic3⋊C4—38no—
91C2×Dic3⋊C4—38no—
92C2×Dic3⋊C4—38no—
93C2×Dic3⋊C4—38no—
94C2×C4×Dic3—34no—
95C2×C4×Dic3—38no—
96C2×C4×Dic3—34no—
97C2×C4×Dic3—38no—
98#892—616no—
99#887—616no—
100C3×#95C2×D314yes—
101C3×#95C2×D318yes—
102C3×#95C2×D318yes—
103C3⋊#95—38no—
104C3⋊#95—34no—
105C3⋊#95—38no—
106C23×C32C2411yescharacteristic
107C22×C3⋊D3—21no—
108C22×C3⋊D3—22no—
109C22×C3⋊D3—22no—
110C22×C3⋊D3—21no—
111C22×C3⋊D3C2×Q812yes—
112C2×C32×C4—21no—
113C2×C32×C4—22no—
114C2×C32×C4—21no—
115C2×C32×C4—22no—
116C2×C32×C4—21no—
117C2×C32×C4—22no—
118C2×C32×C4—22no—
119C2×C32×C4—22no—
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4—22no—
123C2×C32×C4C2×D412yes—
124C2×C32×C4C2×Q812yes—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3—22no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3C2×D412yes—
133C2×C3⋊Dic3C2×D412yes—
134C2×C3⋊Dic3C2×Q812yes—
135C2×C3⋊Dic3#4114yes—
136C2×C3⋊Dic3#4114yes—
137C2×C3⋊Dic3#4112yes—
138C4×C3⋊D3—28no—
139#634—28no—
140C2×C4×Q8—91no—
141C2×#117—91no—
142#400C3⋊D311yescharacteristic, complemented
143#399—91no—
144#398—92no—
145#396—92no—
146#395—91no—
147#393—91no—
148C4×C4⋊C4—92no—
149C4×C4⋊C4—91no—
150C4×C22⋊C4—92no—
151C23×D3—34no—
152C22×C3×C4C22×D318yes—
153C22×C3×C4C22×D318yes—
154C22×C3×C4C22×D314yes—
155C22×C3×C4C22×D314yes—
156C22×C3×C4C22×D314yes—
157C22×Dic3—34no—
158C22×Dic3—38no—
159C22×Dic3—38no—
160C22×Dic3—34no—
161C22×Dic3—34no—
162C2×C4×D3—316no—
163C2×C4×D3—68no—
164C2×C4×D3—68no—
165C2×Dic6—616no—
166C2×Dic6—68no—
167C3×C4⋊C4—28no—
168C3×C4⋊C4—28no—
169(C2×D3)⋊C4—68no—
170(C2×D3)⋊C4—616no—
171(C2×D3)⋊C4—616no—
172(C2×D3)⋊C4—68no—
173C4⋊Dic3—68no—
174Dic3⋊C4—616no—
175Dic3⋊C4—616no—
176Dic3⋊C4—616no—
177Dic3⋊C4—616no—
178C4×Dic3—316no—
179C4×Dic3—616no—
180C4×Dic3—68no—
181C4×Dic3—616no—
182C22×C32C22×D411yescharacteristic
183C22×C32C22×Q811yescharacteristic
184C22×C32C2×#4111yescharacteristic
185C22×C32C2×#4112yes—
186C22×C32C2×#4112yes—
187C2×C3⋊D3—22no—
188C2×C3⋊D3—24no—
189C2×C3⋊D3—41no—
190C2×C3⋊D3—42no—
191C2×C3⋊D3—41no—
192C32×C4—22no—
193C32×C4—22no—
194C32×C4—41no—
195C32×C4—42no—
196C32×C4—42no—
197C3⋊Dic3—24no—
198C3⋊Dic3—24no—
199C3⋊Dic3—22no—
200C3⋊Dic3—41no—
201C3⋊Dic3C22⋊Q814yes—
202C22×Q8—91no—
203C23×C4—91no—
204C4×Q8—184no—
205#117—184no—
206C2×C4⋊C4—91no—
207C2×C4⋊C4—92no—
208C2×C4⋊C4—92no—
209C2×C4⋊C4—92no—
210C2×C4⋊C4—92no—
211C2×C4⋊C4C2×C3⋊D311yescharacteristic
212C2×C4⋊C4C2×C3⋊D311yescharacteristic
213C2×C22⋊C4—91no—
214C2×C22⋊C4—91no—
215C2×C22⋊C4—92no—
216C2×C22⋊C4—92no—
217C2×C42—91no—
218C2×C42—91no—
219C2×C42—92no—
220C2×C42—92no—
221#95—92no—
222#95—92no—
223#95—91no—
224#95C2×C3⋊D312yes—
225#95C2×C3⋊D311yescharacteristic
226#95C2×C3⋊D312yes—
227C23×C3C23×D314yes—
228C22×D3—38no—
229C22×D3—64no—
230C22×D3—68no—
231C22×D3—68no—
232C22×D3—64no—
233C2×C3×C4—24no—
234C2×C3×C4—28no—
235C2×C3×C4—24no—
236C2×C3×C4—28no—
237C2×C3×C4—24no—
238C2×C3×C4—28no—
239C2×C3×C4—28no—
240C2×C3×C4—28no—
241C2×C3×C4—28no—
242C2×C3×C4—28no—
243C2×C3×C4—28no—
244C2×C3×C4D3×D418yes—
245C2×C3×C4D3×Q818yes—
246C2×Dic3—38no—
247C2×Dic3—38no—
248C2×Dic3—38no—
249C2×Dic3—38no—
250C2×Dic3—316no—
251C2×Dic3—316no—
252C2×Dic3—68no—
253C2×Dic3—68no—
254C2×Dic3—68no—
255C2×Dic3—68no—
256C2×Dic3—68no—
257C2×Dic3—64no—
258C2×Dic3—68no—
259C4×D3—632no—
260Dic6—632no—
261C2×C32C2×C22⋊Q811yescharacteristic
262C2×C32#52511yescharacteristic
263C2×C32#52912yes—
264C2×C32#53211yescharacteristic
265C2×C32#53312yes—
266C3⋊D3—42no—
267C24—91no—
268C2×Q8—184no—
269C2×Q8—182no—
270C22×C4—91no—
271C22×C4—92no—
272C22×C4—92no—
273C22×C4—91no—
274C22×C4—94no—
275C22×C4—91no—
276C22×C4—182no—
277C22×C4—182no—
278C22×C4C22×C3⋊D312yes—
279C22×C4C22×C3⋊D311yescharacteristic
280C22×C4C22×C3⋊D312yes—
281C22×C4C22×C3⋊D311yescharacteristic
282C22×C4C22×C3⋊D311yescharacteristic
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—182no—
286C4⋊C4—184no—
287C4⋊C4—184no—
288C4⋊C4—184no—
289C4⋊C4—184no—
290C22⋊C4—182no—
291C22⋊C4—184no—
292C22⋊C4—184no—
293C22⋊C4—182no—
294C42—94no—
295C42—182no—
296C42—184no—
297C42—184no—
298C22×C3C2×D3×D414yes—
299C22×C3C2×D3×Q814yes—
300C22×C3D3×#4118yes—
301C22×C3D3×#4118yes—
302C22×C3D3×#4114yes—
303C2×D3—616no—
304C2×D3—68no—
305C2×D3—124no—
306C2×D3—124no—
307C2×D3—128no—
308C3×C4—28no—
309C3×C4—28no—
310C3×C4—44no—
311C3×C4—48no—
312C3×C4—48no—
313Dic3—316no—
314Dic3—616no—
315Dic3—68no—
316Dic3—616no—
317Dic3—124no—
318C32#239611yescharacteristic, complemented, Sylow
319C23—92no—
320C23—181no—
321C23—182no—
322C23—182no—
323C23—181no—
324C23C23×C3⋊D311yescharacteristic
325Q8—188no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—21no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—92no—
338C2×C4—92no—
339C2×C4—92no—
340C2×C4—92no—
341C2×C4—94no—
342C2×C4—94no—
343C2×C4—188no—
344C2×C4—182no—
345C2×C4—182no—
346C2×C4—182no—
347C2×C4—182no—
348C2×C4—182no—
349C2×C4—181no—
350C2×C4—182no—
351C2×C4D4×C3⋊D312yes—
352C2×C4Q8×C3⋊D312yes—
353C2×C3D3×C22⋊Q814yes—
354C2×C3#565614yes—
355C2×C3#566814yes—
356C2×C3#568818yes—
357C2×C3#570618yes—
358D3—128no—
359C22—182no—
360C22—184no—
361C22—361no—
362C22—361no—
363C22—362no—
364C22C2×D4×C3⋊D311yescharacteristic
365C22C2×Q8×C3⋊D311yescharacteristic
366C22#41×C3⋊D311yescharacteristic
367C22#41×C3⋊D312yes—
368C22#41×C3⋊D312yes—
369C4—22no—
370C4—22no—
371C4—41no—
372C4—42no—
373C4—42no—
374C4—94no—
375C4—184no—
376C4—182no—
377C4—184no—
378C4—361no—
379C3#7813014yescomplemented
380C2—362no—
381C2C3⋊D3×C22⋊Q811yescharacteristic
382C2#1059612711yescharacteristic
383C2#1059613911yescharacteristic
384C2#1059615912yes—
385C2#1059617712yes—
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×#400C2
prime radicalC23×C3⋊D3C23
hypercenter#400C3⋊D3
hypocenterC32#2396
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
2. C2×#64096C2semidirect
3. C32×#400C2semidirect
5. #10592678C2semidirect
9. #10592356C2semidirect
10. #10592348C2semidirect
11. #10592348C2semidirect
40. C3×#400D3semidirect
62. C2×C4×C3⋊D3Q8semidirect
142. #400C3⋊D3semidirect
318. C32#2396semidirect
379. C3#78130semidirect

Maximal subgroups

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

subgroupindex
C2×#641012
C2×#640962
C32×#4002
#105926922
#105926782
#105923752
#105923722
#105923652
#105923562
#105923482
#781303