Finite Group Databasebeta

← #11805933

Subgroups — #11805933

Order 1152.

1053 conjugacy classes of subgroups.

The subgroup lattice has 433 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×Dic6C211yesmaximal, characteristic
2#10592634C211yesmaximal, characteristic
3C3×C4×C4⋊Dic3C211yesmaximal, characteristic
4#10591272C214yesmaximal
5Dic3×C4⋊Dic3C212yesmaximal
6Dic3×C4⋊Dic3C212yesmaximal
7#10591224C212yesmaximal
8#10591220C212yesmaximal
9#82462—31nomaximal
10#73640—31nomaximal
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2212yes—
14C2×C4⋊(C3⋊Dic3)C2212yes—
15C2×C4⋊(C3⋊Dic3)C2212yes—
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×Dic3⋊C4C2212yes—
20C2×C3×C4×Dic3C2212yes—
21C2×C3×C4×Dic3C2212yes—
22C3×C4×Dic6C418yescomplemented
23C2×Dic32C2214yes—
24C3×C3⋊#95C2212yes—
25#63579C2214yes—
26#63579C2214yes—
27#63579C2214yes—
28C2×C3×C4×Q8—31no—
29C2×C4×Dic6D311yescharacteristic
30C3×C4×C4⋊C4—31no—
31#5229—32no—
32#4980—34no—
33#4977—32no—
34Dic3×C4⋊C4—32no—
35Dic3×C4⋊C4—32no—
36#4936—32no—
37#4935—31no—
38#4935—31no—
39#4935—61no—
40C4×C4⋊Dic3—32no—
41C4×C4⋊Dic3—32no—
42C4×C4⋊Dic3D311yescharacteristic
43#4929—32no—
44#4655—34no—
45C22×C32×C4C2311yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3C2314yes—
49C22×C3×Dic3C2312yes—
50C22×C3×Dic3C2312yes—
51C22×C3×Dic3C2312yes—
52C22×C3×Dic3C2312yes—
53C2×C3×Dic6—22no—
54C2×C3×Dic6—22no—
55C2×C3×Dic6C2×C414yes—
56C32×C42C2×C414yes—
57C4⋊(C3⋊Dic3)—24no—
58C4⋊(C3⋊Dic3)—24no—
59C4⋊(C3⋊Dic3)—42no—
60C3×C4⋊Dic3—22no—
61C3×C4⋊Dic3C2×C414yes—
62C3×C4⋊Dic3Q814yescomplemented
63C3×Dic3⋊C4C2×C418yes—
64C3×C4×Dic3—24no—
65C3×C4×Dic3C2×C418yes—
66Dic32—44no—
67#2355—91noSylow
68C22×C3×Q8—31no—
69C22×Dic6C2×D311yescharacteristic
70C3×C4×Q8—38no—
71C2×C3×C4⋊C4—32no—
72C2×C3×C4⋊C4—31no—
73C2×C3×C4⋊C4—31no—
74C2×C3×C4⋊C4—31no—
75C2×C3×C42—21no—
76C2×C3×C42—32no—
77C2×C3×C42—32no—
78C2×C3×C42C2×D311yescharacteristic
79C2×C3×C42C2×D311yescharacteristic
80C2×C4⋊Dic3—32no—
81C2×C4⋊Dic3—32no—
82C2×C4⋊Dic3—32no—
83C2×C4⋊Dic3—32no—
84C2×C4⋊Dic3—32no—
85C2×C4⋊Dic3—32no—
86C2×C4⋊Dic3—62no—
87C2×C4⋊Dic3—62no—
88C2×C4⋊Dic3—62no—
89C2×C4⋊Dic3C2×D311yescharacteristic
90C2×C4⋊Dic3C2×D311yescharacteristic
91C2×C4⋊Dic3C2×D311yescharacteristic
92C2×Dic3⋊C4C2×D312yes—
93C2×C4×Dic3—34no—
94C2×C4×Dic3—34no—
95C2×C4×Dic3C2×D312yes—
96C2×C4×Dic3C2×D312yes—
97C4×Dic6Dic318yescomplemented
98C3×#95—32no—
99C3⋊#95—34no—
100C3⋊#95—34no—
101C3⋊#95—34no—
102C3⋊#95—34no—
103C3⋊#95—34no—
104C3⋊#95—34no—
105C3⋊#95C2×D312yes—
106C23×C32C2411yescharacteristic
107C2×C32×C4—21no—
108C2×C32×C4—21no—
109C2×C32×C4C22×C412yes—
110C2×C32×C4C22×C412yes—
111C2×C32×C4C22×C412yes—
112C2×C32×C4C2×Q812yes—
113C2×C32×C4#4112yes—
114C2×C32×C4#4112yes—
115C2×C32×C4#4112yes—
116C2×C3⋊Dic3—24no—
117C2×C3⋊Dic3—24no—
118C2×C3⋊Dic3—24no—
119C2×C3×Dic3—22no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—22no—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3C22×C414yes—
129C2×C3×Dic3C22×C414yes—
130C2×C3×Dic3C2×Q814yes—
131C3×Dic6—28no—
132C2×C4×Q8—31no—
133#391—92no—
134#387—94no—
135#384—91no—
136#382—92no—
137C4×C4⋊C4—31no—
138C4×C4⋊C4—92no—
139C4×C4⋊C4—92no—
140C2×C3×Q8—34no—
141C2×C3×Q8—62no—
142C2×C3×Q8—62no—
143C22×C3×C4—21no—
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4—32no—
147C22×C3×C4—32no—
148C22×C3×C4—32no—
149C22×C3×C4—32no—
150C22×C3×C4C22×D311yescharacteristic
151C22×C3×C4C22×D311yescharacteristic
152C22×C3×C4C22×D311yescharacteristic
153C22×C3×C4C22×D311yescharacteristic
154C22×C3×C4C22×D311yescharacteristic
155C22×C3×C4C22×D311yescharacteristic
156C22×Dic3—34no—
157C22×Dic3—34no—
158C22×Dic3—64no—
159C22×Dic3C22×D312yes—
160C22×Dic3C22×D312yes—
161C22×Dic3C22×D312yes—
162C22×Dic3C22×D312yes—
163C2×Dic6—22no—
164C2×Dic6—22no—
165C2×Dic6C2×Dic314yes—
166C3×C4⋊C4—38no—
167C3×C4⋊C4—34no—
168C3×C4⋊C4—34no—
169C3×C4⋊C4—62no—
170C3×C42—24no—
171C3×C42—38no—
172C3×C42—64no—
173C3×C42C4×D314yes—
174C3×C42C2×Dic314yes—
175C4⋊Dic3—22no—
176C4⋊Dic3—64no—
177C4⋊Dic3—64no—
178C4⋊Dic3—64no—
179C4⋊Dic3—64no—
180C4⋊Dic3—124no—
181C4⋊Dic3—124no—
182C4⋊Dic3—122no—
183C4⋊Dic3—122no—
184C4⋊Dic3—124no—
185C4⋊Dic3Dic614yescomplemented
186C4⋊Dic3C2×Dic314yes—
187Dic3⋊C4C2×Dic318yes—
188C4×Dic3—24no—
189C4×Dic3—124no—
190C4×Dic3—124no—
191C4×Dic3C2×Dic318yes—
192C22×C32C23×C411yescharacteristic
193C22×C32C22×Q811yescharacteristic
194C22×C32C2×#4111yescharacteristic
195C22×C32C2×#4111yescharacteristic
196C22×C32C2×#4111yescharacteristic
197C22×C32H(5,𝔽2)11yescharacteristic
198C22×C322−1+411yescharacteristic
199C32×C4—22no—
200C32×C4#11714yes—
201C32×C4C4×Q814yes—
202C3⋊Dic3—44no—
203C3×Dic3—24no—
204C3×Dic3—24no—
205C3×Dic3—24no—
206C3×Dic3—42no—
207C22×Q8—31no—
208C4×Q8—38no—
209C2×C4⋊C4—31no—
210C2×C4⋊C4—32no—
211C2×C4⋊C4—31no—
212C2×C4⋊C4—31no—
213C2×C4⋊C4—92no—
214C2×C4⋊C4—92no—
215C2×C4⋊C4—92no—
216C2×C42—32no—
217C2×C42—32no—
218C2×C42—94no—
219C2×C42D3211yescharacteristic
220#95—32no—
221#95—94no—
222#95—94no—
223#95—94no—
224C23×C3—21no—
225C23×C3C23×D311yescharacteristic
226C23×C3C23×D311yescharacteristic
227C3×Q8—68no—
228C2×C3×C4—22no—
229C2×C3×C4—22no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—22no—
235C2×C3×C4—22no—
236C2×C3×C4—22no—
237C2×C3×C4—22no—
238C2×C3×C4—22no—
239C2×C3×C4—22no—
240C2×C3×C4—22no—
241C2×C3×C4—34no—
242C2×C3×C4—34no—
243C2×C3×C4—34no—
244C2×C3×C4—62no—
245C2×C3×C4—62no—
246C2×C3×C4—62no—
247C2×C3×C4—62no—
248C2×C3×C4—62no—
249C2×C3×C4—62no—
250C2×C3×C4—62no—
251C2×C3×C4—62no—
252C2×C3×C4—62no—
253C2×C3×C4C2×Dic612yes—
254C2×C3×C4C2×C4×D312yes—
255C2×C3×C4C2×C4×D312yes—
256C2×C3×C4C2×C4×D312yes—
257C2×C3×C4#23512yes—
258C2×C3×C4#23512yes—
259C2×C3×C4#23512yes—
260C2×C3×C4#23712yes—
261C2×C3×C4D3×Q812yes—
262C2×C3×C4#23912yes—
263C2×C3×C4#23912yes—
264C2×C3×C4C22×Dic312yes—
265C2×C3×C4C22×Dic312yes—
266C2×C3×C4C22×Dic312yes—
267C2×Dic3—22no—
268C2×Dic3—22no—
269C2×Dic3—22no—
270C2×Dic3—22no—
271C2×Dic3—22no—
272C2×Dic3—22no—
273C2×Dic3—22no—
274C2×Dic3—22no—
275C2×Dic3—22no—
276C2×Dic3—64no—
277C2×Dic3—64no—
278C2×Dic3—64no—
279C2×Dic3—64no—
280C2×Dic3—64no—
281C2×Dic3—64no—
282C2×Dic3—124no—
283C2×Dic3—124no—
284C2×Dic3—124no—
285C2×Dic3C2×Dic614yes—
286C2×Dic3C22×Dic314yes—
287C2×Dic3C22×Dic314yes—
288Dic6—28no—
289C2×C32C2×#11711yescharacteristic
290C2×C32C2×C4×Q811yescharacteristic
291C2×C32#52011yescharacteristic
292C2×C32#55411yescharacteristic
293C2×C32#55611yescharacteristic
294C2×C32#55711yescharacteristic
295C2×C32#55911yescharacteristic
296C2×Q8—34no—
297C2×Q8—62no—
298C2×Q8—62no—
299C22×C4—32no—
300C22×C4—32no—
301C22×C4—32no—
302C22×C4—32no—
303C22×C4—94no—
304C22×C4C2×D3211yescharacteristic
305C22×C4C2×D3211yescharacteristic
306C22×C4C2×D3211yescharacteristic
307C4⋊C4—34no—
308C4⋊C4—38no—
309C4⋊C4—34no—
310C4⋊C4—62no—
311C4⋊C4—184no—
312C4⋊C4—184no—
313C4⋊C4—362no—
314C42—38no—
315C42—64no—
316C42—364no—
317C42D3×Dic314yes—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3C22×Dic611yescharacteristic
326C22×C3C22×C4×D311yescharacteristic
327C22×C3C2×#23511yescharacteristic
328C22×C3C2×#23511yescharacteristic
329C22×C3C2×#23511yescharacteristic
330C22×C3C2×#23711yescharacteristic
331C22×C3C2×D3×Q811yescharacteristic
332C22×C3C2×#23911yescharacteristic
333C22×C3C2×#23911yescharacteristic
334C22×C3#100911yescharacteristic
335C22×C3#100911yescharacteristic
336C22×C3#101011yescharacteristic
337C22×C3#101011yescharacteristic
338C22×C3C23×Dic311yescharacteristic
339C3×C4—24no—
340C3×C4—22no—
341C3×C4—22no—
342C3×C4—24no—
343C3×C4—24no—
344C3×C4—64no—
345C3×C4—64no—
346C3×C4—64no—
347C3×C4—122no—
348C3×C4C4×Dic614yes—
349C3×C4#89214yes—
350C3×C4#92614yes—
351C3×C4Q8×Dic314yes—
352Dic3—24no—
353Dic3—24no—
354Dic3—24no—
355Dic3—42no—
356Dic3—124no—
357Dic3—124no—
358Dic3—244no—
359C32#235511yescharacteristic, complemented, Sylow
360C23C22×D3211yescharacteristic
361Q8—68no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—34no—
365C2×C4—34no—
366C2×C4—34no—
367C2×C4—62no—
368C2×C4—62no—
369C2×C4—62no—
370C2×C4—62no—
371C2×C4—62no—
372C2×C4—62no—
373C2×C4—62no—
374C2×C4—62no—
375C2×C4—62no—
376C2×C4—184no—
377C2×C4—184no—
378C2×C4—184no—
379C2×C4D3×Dic612yes—
380C2×C4#379512yes—
381C2×C4#379912yes—
382C2×C4#379912yes—
383C2×C4C2×D3×Dic312yes—
384C2×C4C2×D3×Dic312yes—
385C2×C4C2×D3×Dic312yes—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3C2×C4×Dic611yescharacteristic
394C2×C3C2×#89211yescharacteristic
395C2×C3#552311yescharacteristic
396C2×C3#554211yescharacteristic
397C2×C3#554311yescharacteristic
398C2×C3#556711yescharacteristic
399C2×C3#557011yescharacteristic
400C2×C3#557911yescharacteristic
401C2×C3#558411yescharacteristic
402C2×C3#558511yescharacteristic
403C2×C3#558511yescharacteristic
404C2×C3C2×#92611yescharacteristic
405C2×C3C2×Q8×Dic311yescharacteristic
406C2×C3#582711yescharacteristic
407C22C2×D3×Dic611yescharacteristic
408C22C2×#379511yescharacteristic
409C22#6429811yescharacteristic
410C22C2×#379911yescharacteristic
411C22C2×#379911yescharacteristic
412C22#6430811yescharacteristic
413C22C22×D3×Dic311yescharacteristic
414C4—22no—
415C4—64no—
416C4—64no—
417C4—64no—
418C4—122no—
419C4—364no—
420C4#6384114yes—
421C4Dic3×Dic614yes—
422C3—21no—
423C3#7364011yescharacteristic, complemented
424C3#8246211yescharacteristic, complemented
425C2#1059386011yescharacteristic
426C2#1059387911yescharacteristic
427C2#1059396011yescharacteristic
428C2#1059396311yescharacteristic
429C2C2×#6384111yescharacteristic
430C2C2×Dic3×Dic611yescharacteristic
431C2#1059499211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2355
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
22. C3×C4×Dic6C4semidirect
62. C3×C4⋊Dic3Q8semidirect
97. C4×Dic6Dic3semidirect
185. C4⋊Dic3Dic6semidirect
359. C32#2355semidirect
423. C3#73640semidirect
424. C3#82462semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×Dic62
#105926342
C3×C4×C4⋊Dic32
#105912722
Dic3×C4⋊Dic32
#105912242
#105912202
#824623
#736403