Finite Group Databasebeta

← #11784575

Subgroups — #11784575

Order 1152.

2385 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 2385 conjugacy classes of subgroups — too many to draw. Only its 248 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
1C23×C4×C3⋊D3C211yesmaximal, characteristic
2C2×C3×#830C212yesmaximal, complemented
3C2×#63557C214yesmaximal, complemented
4#69955—32nomaximal
5C24×C3⋊D3C411yescharacteristic
6C23×C32×C4C2211yescharacteristic
7C23×C3⋊Dic3C411yescharacteristic
8C22×C4×C3⋊D3—24no—
9C22×C4×C3⋊D3—28no—
10C22×C4×C3⋊D3C412yes—
11C22×C4×C3⋊D3C2212yes—
12C22×C3×C3⋊C8C2214yescomplemented
13C3×#830—24no—
14#63557—28no—
15C23×C4×D3—32no—
16C23×C4×D3—61no—
17C2×C3×C22⋊C8—32no—
18C2×#830D312yescomplemented
19C2×(C2×D3)⋊C8—38no—
20C24×C32C2×C411yescharacteristic
21C23×C3⋊D3—22no—
22C23×C3⋊D3—22no—
23C23×C3⋊D3—24no—
24C23×C3⋊D3—24no—
25C23×C3⋊D3C814yescomplemented
26C23×C3⋊D3C2×C412yes—
27C22×C32×C4—24no—
28C22×C32×C4C2×C411yescharacteristic
29C22×C32×C4D414yes—
30C22×C32×C4C2311yescharacteristic
31C22×C3⋊Dic3—22no—
32C22×C3⋊Dic3—24no—
33C22×C3⋊Dic3C2×C412yes—
34C2×C4×C3⋊D3—232no—
35C2×C4×C3⋊D3—24no—
36C2×C4×C3⋊D3—24no—
37C2×C4×C3⋊D3—24no—
38C2×C4×C3⋊D3—24no—
39C2×C4×C3⋊D3—24no—
40C2×C4×C3⋊D3D418yes—
41C2×C3×C3⋊C8—28no—
42C2×C3×C3⋊C8—24no—
43#1779—91noSylow
44C24×D3—32no—
45C24×D3—61no—
46C23×C3×C4—21no—
47C23×C3×C4C2×D312yes—
48C23×Dic3—32no—
49C23×Dic3—61no—
50C22×C4×D3—34no—
51C22×C4×D3—34no—
52C22×C4×D3—62no—
53C22×C4×D3—62no—
54C22×C4×D3—616no—
55C22×C4×D3—616no—
56C22×C4×D3—68no—
57C22×C4×D3—64no—
58C22×C4×D3—64no—
59C22×C3×C8—34no—
60C22×C3⋊C8C2×D314yescomplemented
61C3×C22⋊C8—64no—
62#830—24no—
63(C2×D3)⋊C8—616no—
64C23×C32—22no—
65C23×C32—22no—
66C23×C32C22⋊C412yes—
67C23×C32C2×C812yes—
68C23×C32M1612yes—
69C23×C32C22×C411yescharacteristic
70C22×C3⋊D3—216no—
71C22×C3⋊D3—28no—
72C22×C3⋊D3—28no—
73C22×C3⋊D3—28no—
74C22×C3⋊D3—22no—
75C22×C3⋊D3—22no—
76C22×C3⋊D3—22no—
77C22×C3⋊D3—22no—
78C22×C3⋊D3—216no—
79C22×C3⋊D3C22⋊C414yes—
80C22×C3⋊D3C2×C814yes—
81C22×C3⋊D3M1614yes—
82C2×C32×C4—22no—
83C2×C32×C4—28no—
84C2×C32×C4C22⋊C412yes—
85C2×C32×C4C2×D412yes—
86C2×C32×C4C2×D414yes—
87C2×C3⋊Dic3—28no—
88C2×C3⋊Dic3—22no—
89C2×C3⋊Dic3—22no—
90C2×C3⋊Dic3C22⋊C414yes—
91C4×C3⋊D3—216no—
92C4×C3⋊D3—216no—
93C3×C3⋊C8—44no—
94C24×C4—91no—
95C2×C22⋊C8—32no—
96C2×C22⋊C8—94no—
97C24×C3—21no—
98C24×C3C4×D312yes—
99C23×D3—34no—
100C23×D3—38no—
101C23×D3—64no—
102C23×D3—62no—
103C23×D3—68no—
104C23×D3—68no—
105C23×D3—68no—
106C23×D3—64no—
107C23×D3—68no—
108C23×D3—64no—
109C23×D3—64no—
110C23×D3—64no—
111C22×C3×C4—28no—
112C22×C3×C4—28no—
113C22×C3×C4—21no—
114C22×C3×C4—24no—
115C22×C3×C4—21no—
116C22×C3×C4C4×D312yes—
117C22×C3×C4D1214yes—
118C22×C3×C4#6714yes—
119C22×C3×C4C22×D312yes—
120C22×Dic3—34no—
121C22×Dic3—62no—
122C22×Dic3—68no—
123C22×Dic3—68no—
124C22×Dic3—64no—
125C22×Dic3—64no—
126C2×C4×D3—316no—
127C2×C4×D3—68no—
128C2×C4×D3—68no—
129C2×C4×D3—68no—
130C2×C4×D3—68no—
131C2×C4×D3—68no—
132C2×C4×D3—664no—
133C2×C4×D3—632no—
134C2×C4×D3—632no—
135C2×C4×D3—68no—
136C2×C4×D3—68no—
137C2×C4×D3—68no—
138C2×C4×D3—68no—
139C2×C4×D3—64no—
140C2×C4×D3—68no—
141C2×C4×D3—64no—
142C2×C3×C8—64no—
143C2×C3×C8—68no—
144C2×C3⋊C8—28no—
145C2×C3⋊C8—24no—
146C22×C32—22no—
147C22×C32—24no—
148C22×C32—22no—
149C22×C32—24no—
150C22×C32C22⋊C814yescomplemented
151C22×C32C2×C22⋊C412yes—
152C22×C32C2×C22⋊C411yescharacteristic
153C22×C32C22×C811yescharacteristic
154C22×C32C2×M1611yescharacteristic
155C22×C32C2×M1612yes—
156C2×C3⋊D3—232no—
157C2×C3⋊D3—24no—
158C2×C3⋊D3—24no—
159C2×C3⋊D3—24no—
160C2×C3⋊D3—24no—
161C2×C3⋊D3—24no—
162C2×C3⋊D3—24no—
163C2×C3⋊D3C22⋊C818yescomplemented
164C32×C4—22no—
165C32×C4#12014yes—
166C3⋊Dic3—24no—
167C25—91no—
168C23×C4—92no—
169C23×C4—91no—
170C23×C4—92no—
171C23×C4—188no—
172C23×C4—184no—
173C23×C4D3211yescharacteristic
174C22×C8—34no—
175C22⋊C8—64no—
176C22⋊C8—188no—
177C23×C3—24no—
178C23×C3—24no—
179C23×C3—24no—
180C23×C3—24no—
181C23×C3—22no—
182C23×C3—22no—
183C23×C3—22no—
184C23×C3—21no—
185C23×C3D3×C814yes—
186C23×C3ΓL(1,𝔽25)14yes—
187C23×C3(C2×D3)⋊C414yes—
188C23×C3C2×C4×D312yes—
189C22×D3—38no—
190C22×D3—38no—
191C22×D3—38no—
192C22×D3—64no—
193C22×D3—64no—
194C22×D3—64no—
195C22×D3—632no—
196C22×D3—616no—
197C22×D3—616no—
198C22×D3—64no—
199C22×D3—64no—
200C22×D3—632no—
201C22×D3—616no—
202C22×D3—632no—
203C22×D3—616no—
204C22×D3—632no—
205C22×D3—616no—
206C22×D3—64no—
207C22×D3—64no—
208C22×D3—616no—
209C22×D3—64no—
210C22×D3—64no—
211C22×D3—64no—
212C22×D3—64no—
213C2×C3×C4—24no—
214C2×C3×C4—216no—
215C2×C3×C4—24no—
216C2×C3×C4—28no—
217C2×C3×C4—28no—
218C2×C3×C4—22no—
219C2×C3×C4—22no—
220C2×C3×C4—24no—
221C2×C3×C4(C2×D3)⋊C414yes—
222C2×C3×C4C2×D1212yes—
223C2×C3×C4D3×D418yes—
224C2×C3×C4C2×#6712yes—
225C2×Dic3—38no—
226C2×Dic3—64no—
227C2×Dic3—616no—
228C2×Dic3—616no—
229C2×Dic3—64no—
230C2×Dic3—64no—
231C2×Dic3—64no—
232C2×Dic3—64no—
233C4×D3—632no—
234C4×D3—632no—
235C4×D3—632no—
236C4×D3—616no—
237C4×D3—616no—
238C3×C8—124no—
239C3⋊C8—44no—
240C2×C32—24no—
241C2×C32#37911yescharacteristic
242C2×C32C2×C22⋊C812yes—
243C2×C32C2×C22⋊C811yescharacteristic
244C2×C32#40711yescharacteristic
245C2×C32#40712yes—
246C3⋊D3—28no—
247C24—92no—
248C24—94no—
249C24—184no—
250C24—184no—
251C24—182no—
252C24—182no—
253C24#62411yescharacteristic
254C22×C4—24no—
255C22×C4—92no—
256C22×C4—98no—
257C22×C4—184no—
258C22×C4—184no—
259C22×C4—1832no—
260C22×C4—184no—
261C22×C4—182no—
262C22×C4—184no—
263C22×C4—184no—
264C22×C4—184no—
265C22×C4#62411yescharacteristic
266C22×C4#62614yes—
267C22×C4C2×D3211yescharacteristic
268C2×C8—64no—
269C2×C8—68no—
270C22×C3—24no—
271C22×C3—24no—
272C22×C3—28no—
273C22×C3—28no—
274C22×C3—24no—
275C22×C3—24no—
276C22×C3—28no—
277C22×C3—28no—
278C22×C3—24no—
279C22×C3—21no—
280C22×C3—22no—
281C22×C3—21no—
282C22×C3—21no—
283C22×C3—22no—
284C22×C3(C2×D3)⋊C818yescomplemented
285C22×C3D3×C22⋊C414yes—
286C22×C3C2×D3×C812yes—
287C22×C3C2×ΓL(1,𝔽25)12yes—
288C22×C3D3×M1614yes—
289C22×C3C2×(C2×D3)⋊C412yes—
290C2×D3—316no—
291C2×D3—68no—
292C2×D3—68no—
293C2×D3—664no—
294C2×D3—664no—
295C2×D3—68no—
296C2×D3—68no—
297C2×D3—68no—
298C2×D3—68no—
299C2×D3—68no—
300C2×D3—68no—
301C2×D3—68no—
302C2×D3—68no—
303C2×D3—68no—
304C2×D3—68no—
305C2×D3—68no—
306C3×C4—24no—
307C3×C4—24no—
308C3×C4—24no—
309C3×C4#88214yes—
310C3×C4#93714yes—
311Dic3—68no—
312Dic3—68no—
313C32#177911yescharacteristic, complemented, Sylow
314C23—22no—
315C23—22no—
316C23—94no—
317C23—94no—
318C23—94no—
319C23—1816no—
320C23—188no—
321C23—188no—
322C23—1816no—
323C23—188no—
324C23—182no—
325C23—182no—
326C23—182no—
327C23—182no—
328C23#371012yes—
329C23#371212yes—
330C23#372212yes—
331C23C2×#62411yescharacteristic
332C2×C4—22no—
333C2×C4—28no—
334C2×C4—94no—
335C2×C4—1816no—
336C2×C4—188no—
337C2×C4—182no—
338C2×C4—182no—
339C2×C4—1816no—
340C2×C4#372212yes—
341C2×C4C2×#62612yes—
342C2×C4#381114yes—
343C8—124no—
344C2×C3—28no—
345C2×C3—28no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—22no—
349C2×C3—22no—
350C2×C3—21no—
351C2×C3D3×C22⋊C814yes—
352C2×C3#472614yes—
353C2×C3#495512yes—
354C2×C3C2×(C2×D3)⋊C812yes—
355C2×C3#512612yes—
356D3—616no—
357D3—616no—
358C22—22no—
359C22—24no—
360C22—24no—
361C22—22no—
362C22—98no—
363C22—1832no—
364C22—184no—
365C22—184no—
366C22—184no—
367C22—184no—
368C22—184no—
369C22—184no—
370C22#6355714yescomplemented
371C22C2×#371011yescharacteristic
372C22#6381812yes—
373C22C2×#371211yescharacteristic
374C22C2×#372211yescharacteristic
375C22#6397412yes—
376C4—22no—
377C4—184no—
378C4#6398114yes—
379C3—21no—
380C3#6995512yescomplemented
381C2—24no—
382C2—188no—
383C2C2×#6355711yescharacteristic
384C2#1059107411yescharacteristic
385C2#1059115212yes—
386C2#1059115912yes—
387C2#1059171411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutatorC22×C32C22×C8
FittingC23×C32×C4C22
socleC23×C32C22×C4
prime radicalC24×C3⋊D3C4
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1779
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#830C2semidirect
3. C2×#63557C2semidirect
12. C22×C3×C3⋊C8C22semidirect
18. C2×#830D3semidirect
25. C23×C3⋊D3C8semidirect
60. C22×C3⋊C8C2×D3semidirect
150. C22×C32C22⋊C8semidirect
163. C2×C3⋊D3C22⋊C8semidirect
284. C22×C3(C2×D3)⋊C8semidirect
313. C32#1779semidirect
370. C22#63557semidirect
380. C3#69955semidirect

Maximal subgroups

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

subgroupindex
C23×C4×C3⋊D32
C2×C3×#8302
C2×#635572
#699553