Finite Group Databasebeta

← #11808854

Subgroups — #11808854

Order 1152.

1157 conjugacy classes of subgroups.

The subgroup lattice has 397 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic
2C2×C3×C4×Dic6C211yesmaximal, characteristic
3C3×#4932C211yesmaximal, characteristic
4#10591358C212yesmaximal
5#10591354C212yesmaximal
6#10591353C212yesmaximal
7#10591346C212yesmaximal
8C4×Dic3⋊Dic3C214yesmaximal
9#82467—31nomaximal
10#73397—31nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×#3750C2212yes—
16C2×C4×C3⋊Dic3C2212yes—
17C4×#634—24no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×Dic3⋊C4C2212yes—
20C2×C3×C4×Dic3C2212yes—
21C2×C3×C4×Dic3C2212yes—
22C3×C4×Dic6—24no—
23C2×Dic3⋊Dic3C2214yes—
24C2×Dic3⋊Dic3C2214yes—
25C3×C3⋊#95C2212yes—
26C3×C3⋊#95C2212yes—
27#63579C2214yes—
28#63579C2214yes—
29C2×C3×C4×Q8—31no—
30C2×C4×Dic6—31no—
31C2×C4×Dic6—31no—
32C2×C4×Dic6—61no—
33C2×C4×Dic6D311yescharacteristic
34C3×#376—31no—
35#5230—32no—
36#4983—32no—
37#4981—32no—
38#4979—32no—
39C4×C4⋊Dic3—34no—
40#4932D311yescharacteristic
41C4×Dic3⋊C4—34no—
42#4661—32no—
43#4661—32no—
44#4656—32no—
45#4656—32no—
46C22×C32×C4C2311yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3C2312yes—
50C22×C3⋊Dic3C2312yes—
51C2×#634—22no—
52C2×#634—24no—
53C22×C3×Dic3C2312yes—
54C22×C3×Dic3C2314yes—
55C22×C3×Dic3C2312yes—
56C2×C3×Dic6—22no—
57C2×C3×Dic6—24no—
58C32×C42D414yes—
59C4⋊(C3⋊Dic3)—22no—
60#3750—24no—
61C4×C3⋊Dic3—24no—
62C3×C4⋊Dic3—22no—
63C3×Dic3⋊C4—24no—
64C3×C4×Dic3—24no—
65C3×C4×Dic3Q818yescomplemented
66Dic3⋊Dic3—28no—
67Dic3⋊Dic3—28no—
68#2399—91noSylow
69C22×C3×Q8—31no—
70C22×Dic6—31no—
71C22×Dic6—31no—
72C22×Dic6—61no—
73C22×Dic6C2×D311yescharacteristic
74C3×C4×Q8—64no—
75C2×C3×C4⋊C4—32no—
76C2×C3×C4⋊C4—31no—
77C2×C3×C42—21no—
78C2×C3×C42—32no—
79C2×C3×C42—32no—
80C2×C3×C42C2×D311yescharacteristic
81C2×C3×C42C2×D311yescharacteristic
82C2×C4⋊Dic3—31no—
83C2×C4⋊Dic3—31no—
84C2×C4⋊Dic3—34no—
85C2×C4⋊Dic3—34no—
86C2×C4⋊Dic3—61no—
87C2×C4⋊Dic3C2×D311yescharacteristic
88C2×Dic3⋊C4—32no—
89C2×Dic3⋊C4—32no—
90C2×Dic3⋊C4—34no—
91C2×Dic3⋊C4—34no—
92C2×Dic3⋊C4—62no—
93C2×Dic3⋊C4C2×D312yes—
94C2×C4×Dic3—32no—
95C2×C4×Dic3—32no—
96C2×C4×Dic3—62no—
97C2×C4×Dic3C2×D312yes—
98C2×C4×Dic3C2×D312yes—
99C4×Dic6—24no—
100C4×Dic6—68no—
101C4×Dic6—64no—
102C4×Dic6—64no—
103C3×#95—32no—
104C3×#95—32no—
105C3⋊#95—34no—
106C3⋊#95—34no—
107C3⋊#95—34no—
108C3⋊#95—34no—
109C3⋊#95C2×D312yes—
110C3⋊#95C2×D312yes—
111C23×C32C2411yescharacteristic
112C2×C32×C4—22no—
113C2×C32×C4—22no—
114C2×C32×C4C2×D412yes—
115C2×C32×C4C2×D412yes—
116C2×C32×C4C2×D412yes—
117C2×C32×C4C2×Q814yes—
118C2×C3⋊Dic3—22no—
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3—24no—
122C2×C3⋊Dic3#4114yes—
123#634—28no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—24no—
126C2×C3×Dic3—24no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—24no—
130C2×C3×Dic3C2×Q818yes—
131C2×C3×Dic3#4114yes—
132C3×Dic6—28no—
133C2×C4×Q8—31no—
134C2×C4×Q8—91no—
135#398—92no—
136#398—92no—
137#395—92no—
138#395—92no—
139C4×C4⋊C4—94no—
140#376—31no—
141C2×C3×Q8—64no—
142C2×C3×Q8—62no—
143C22×C3×C4—21no—
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4—34no—
147C22×C3×C4—32no—
148C22×C3×C4—32no—
149C22×C3×C4C22×D311yescharacteristic
150C22×C3×C4C22×D311yescharacteristic
151C22×C3×C4C22×D311yescharacteristic
152C22×C3×C4C22×D311yescharacteristic
153C22×C3×C4C22×D311yescharacteristic
154C22×C3×C4C22×D311yescharacteristic
155C22×Dic3—32no—
156C22×Dic3—32no—
157C22×Dic3—32no—
158C22×Dic3—32no—
159C22×Dic3—62no—
160C22×Dic3—62no—
161C22×Dic3C22×D312yes—
162C22×Dic3C22×D314yes—
163C22×Dic3C22×D312yes—
164C2×Dic6—22no—
165C2×Dic6—24no—
166C2×Dic6—64no—
167C2×Dic6—64no—
168C2×Dic6—64no—
169C2×Dic6—68no—
170C2×Dic6—62no—
171C2×Dic6—62no—
172C3×C4⋊C4—64no—
173C3×C4⋊C4—62no—
174C3×C42—24no—
175C3×C42—38no—
176C3×C42—64no—
177C3×C42D1214yes—
178C3×C42#6714yes—
179C4⋊Dic3—22no—
180C4⋊Dic3—68no—
181C4⋊Dic3—64no—
182C4⋊Dic3—62no—
183C4⋊Dic3—62no—
184C4⋊Dic3—68no—
185Dic3⋊C4—24no—
186Dic3⋊C4—68no—
187Dic3⋊C4—68no—
188Dic3⋊C4—68no—
189Dic3⋊C4—64no—
190Dic3⋊C4—64no—
191C4×Dic3—24no—
192C4×Dic3—68no—
193C4×Dic3—64no—
194C4×Dic3—64no—
195C4×Dic3Dic618yescomplemented
196C22×C32C22×D411yescharacteristic
197C22×C32C22×Q812yes—
198C22×C32C2×#4112yes—
199C22×C32C2×#4112yes—
200C32×C4—22no—
201C32×C4—22no—
202C32×C4C4⋊Q814yes—
203C3⋊Dic3—24no—
204C3⋊Dic3—42no—
205C3×Dic3—24no—
206C3×Dic3—28no—
207C3×Dic3—42no—
208C22×Q8—31no—
209C22×Q8—91no—
210C4×Q8—64no—
211C4×Q8—184no—
212C2×C4⋊C4—32no—
213C2×C4⋊C4—31no—
214C2×C4⋊C4—94no—
215C2×C4⋊C4—94no—
216C2×C4⋊C4—92no—
217C2×C4⋊C4—91no—
218C2×C42—32no—
219C2×C42—32no—
220C2×C42—92no—
221C2×C42D3211yescharacteristic
222#95—32no—
223#95—32no—
224#95—94no—
225#95—94no—
226C23×C3—21no—
227C23×C3C23×D311yescharacteristic
228C23×C3C23×D311yescharacteristic
229C3×Q8—68no—
230C2×C3×C4—24no—
231C2×C3×C4—22no—
232C2×C3×C4—22no—
233C2×C3×C4—22no—
234C2×C3×C4—22no—
235C2×C3×C4—24no—
236C2×C3×C4—22no—
237C2×C3×C4—22no—
238C2×C3×C4—22no—
239C2×C3×C4—38no—
240C2×C3×C4—34no—
241C2×C3×C4—42no—
242C2×C3×C4—62no—
243C2×C3×C4—64no—
244C2×C3×C4—64no—
245C2×C3×C4—62no—
246C2×C3×C4—62no—
247C2×C3×C4—64no—
248C2×C3×C4C2×Dic614yes—
249C2×C3×C4C2×D1212yes—
250C2×C3×C4C2×D1212yes—
251C2×C3×C4C2×D1212yes—
252C2×C3×C4D3×Q814yes—
253C2×C3×C4C2×#6712yes—
254C2×C3×C4C2×#6712yes—
255C2×C3×C4C2×#6712yes—
256C2×Dic3—22no—
257C2×Dic3—24no—
258C2×Dic3—24no—
259C2×Dic3—22no—
260C2×Dic3—24no—
261C2×Dic3—22no—
262C2×Dic3—34no—
263C2×Dic3—34no—
264C2×Dic3—64no—
265C2×Dic3—64no—
266C2×Dic3—64no—
267C2×Dic3—62no—
268C2×Dic3—62no—
269C2×Dic3—62no—
270C2×Dic3—62no—
271C2×Dic3—64no—
272C2×Dic3—62no—
273C2×Dic3—64no—
274C2×Dic3—64no—
275C2×Dic3—62no—
276C2×Dic3—124no—
277C2×Dic3C2×Dic618yes—
278C2×Dic3#23514yes—
279Dic6—28no—
280Dic6—616no—
281Dic6—68no—
282Dic6—68no—
283C2×C32#52511yescharacteristic
284C2×C32#52511yescharacteristic
285C2×C32C2×C4⋊Q811yescharacteristic
286C2×C32#53314yes—
287C2×Q8—64no—
288C2×Q8—62no—
289C2×Q8—184no—
290C2×Q8—182no—
291C22×C4—34no—
292C22×C4—32no—
293C22×C4—32no—
294C22×C4—92no—
295C22×C4—92no—
296C22×C4C2×D3211yescharacteristic
297C22×C4C2×D3211yescharacteristic
298C22×C4C2×D3211yescharacteristic
299C4⋊C4—64no—
300C4⋊C4—62no—
301C4⋊C4—188no—
302C4⋊C4—188no—
303C4⋊C4—184no—
304C4⋊C4—182no—
305C42—38no—
306C42—64no—
307C42—184no—
308C42#62614yes—
309C22×C3—22no—
310C22×C3—22no—
311C22×C3—22no—
312C22×C3—21no—
313C22×C3C22×Dic612yes—
314C22×C3C22×D1211yescharacteristic
315C22×C3C2×#23512yes—
316C22×C3C2×D3×Q812yes—
317C22×C3D3×#4112yes—
318C22×C3D3×#4112yes—
319C22×C3D3×#4112yes—
320C22×C3C22×#6711yescharacteristic
321C3×C4—24no—
322C3×C4—22no—
323C3×C4—22no—
324C3×C4—22no—
325C3×C4—22no—
326C3×C4—24no—
327C3×C4—42no—
328C3×C4—64no—
329C3×C4—68no—
330C3×C4—122no—
331C3×C4#86914yes—
332C3×C4#94414yes—
333Dic3—28no—
334Dic3—24no—
335Dic3—42no—
336Dic3—68no—
337Dic3—64no—
338Dic3—64no—
339Dic3—124no—
340Dic3—122no—
341Dic3—122no—
342C32#239911yescharacteristic, complemented, Sylow
343C23C22×D3211yescharacteristic
344Q8—68no—
345Q8—188no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—38no—
349C2×C4—34no—
350C2×C4—64no—
351C2×C4—62no—
352C2×C4—64no—
353C2×C4—62no—
354C2×C4—64no—
355C2×C4—62no—
356C2×C4—94no—
357C2×C4—182no—
358C2×C4—182no—
359C2×C4—184no—
360C2×C4—182no—
361C2×C4D3×Dic614yes—
362C2×C4C2×#62612yes—
363C2×C4C2×#62612yes—
364C2×C4C2×#62612yes—
365C2×C3—21no—
366C2×C3—24no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3C2×#86911yescharacteristic
370C2×C3#551714yes—
371C2×C3#552411yescharacteristic
372C2×C3#552411yescharacteristic
373C2×C3#557814yes—
374C2×C3#579111yescharacteristic
375C2×C3C2×#94411yescharacteristic
376C2×C3#582811yescharacteristic
377C22C2×D3×Dic612yes—
378C22D3×#23512yes—
379C22#6430612yes—
380C22C22×#62611yescharacteristic
381C4—22no—
382C4—22no—
383C4—68no—
384C4—64no—
385C4—122no—
386C4—184no—
387C4—362no—
388C4#6386614yes—
389C3—21no—
390C3#7339711yescharacteristic, complemented
391C3#8246711yescharacteristic, complemented
392C2#1059392614yes—
393C2C2×#6386611yescharacteristic
394C2#1059502311yescharacteristic
395C2#1059503411yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, socle, prime radical, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#2399
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
65. C3×C4×Dic3Q8semidirect
195. C4×Dic3Dic6semidirect
342. C32#2399semidirect
390. C3#73397semidirect
391. C3#82467semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C2×C3×C4×Dic62
C3×#49322
#105913582
#105913542
#105913532
#105913462
C4×Dic3⋊Dic32
#824673
#733973