Finite Group Databasebeta

← #11773907

Subgroups — #11773907

Order 1152.

543 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 543 conjugacy classes of subgroups — too many to draw. Only its 120 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×C3×#892C211yesmaximal, characteristic
2#10591063C212yesmaximal, complemented
3#10589394C211yesmaximal, characteristic, complemented
4C3×#4528C211yesmaximal, characteristic, complemented
5#10589145C212yesmaximal
6#71572—31nomaximal
7#68126—31nomaximal
8C22×C3×C4×D3C411yescharacteristic
9C2×C32×C4⋊C4C2211yescharacteristic
10C2×C3×(C2×D3)⋊C4C411yescharacteristic
11C2×C3×(C2×D3)⋊C4C2211yescharacteristic
12C2×C3×C4⋊Dic3C411yescharacteristic
13C2×C3×C4×Dic3C411yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C3×#892—22no—
16C3×#892—22no—
17#63657C2212yes—
18C3×#830C2212yes—
19Dic3⋊(C3⋊C8)—22no—
20#63554—22no—
21C2×C3×#117—31no—
22C2×#892D311yescharacteristic
23#4926—32no—
24#4719—32no—
25C3×#324—31no—
26#4528—31no—
27#4528—31no—
28#4528—61no—
29#4528D311yescharacteristic, complemented
30#4525—32no—
31#4468—32no—
32C23×C3×D3C2×C411yescharacteristic
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4C2311yescharacteristic
36C22×C3×Dic3C2×C411yescharacteristic
37C22×C3×Dic3C2×C411yescharacteristic
38C22×C3×Dic3C2×C411yescharacteristic
39C2×C3×C4×D3—22no—
40C2×C3×C4×D3—22no—
41C2×C3×C4×D3—21no—
42C2×C3×C4×D3—21no—
43C32×C4⋊C4—22no—
44C2×C3⋊(C3⋊C8)—22no—
45C3×(C2×D3)⋊C4—22no—
46C3×(C2×D3)⋊C4—22no—
47C3×C4⋊Dic3—22no—
48C3×C4×Dic3—21no—
49C3×C4×Dic3—21no—
50C3×C4×Dic3D412yes—
51C3×C4×Dic3D412yes—
52C2×C3×C3⋊C8—22no—
53#1464—91noSylow
54C23×C3×C4—31no—
55C22×C4×D3Dic311yescharacteristic
56C3×#117—62no—
57C3×#117—62no—
58C2×C3×C4⋊C4—21no—
59C2×C3×C4⋊C4—31no—
60C2×C3×C4⋊C4C2×D311yescharacteristic
61C2×C3×C4⋊C4C2×D311yescharacteristic
62C2×C3×C22⋊C4—31no—
63C2×C3×C22⋊C4—31no—
64C2×C3×C42—31no—
65C2×C3×C42—31no—
66C2×(C2×D3)⋊C4Dic311yescharacteristic
67C2×(C2×D3)⋊C4C2×D311yescharacteristic
68C2×C4⋊Dic3Dic311yescharacteristic
69C2×C4×Dic3Dic311yescharacteristic
70C2×C4×Dic3C2×D311yescharacteristic
71#892—22no—
72#892—22no—
73C3×C22⋊C8—32no—
74#830—32no—
75#830—32no—
76#830—62no—
77#830C2×D312yes—
78#815—62no—
79Dic3⋊C8—62no—
80C4⋊(C3⋊C8)—62no—
81#803—62no—
82C23×C32C22×C411yescharacteristic
83C22×C3×D3—21no—
84C22×C3×D3—21no—
85C22×C3×D3—41no—
86C22×C3×D3—41no—
87C22×C3×D3M1612yes—
88C2×C32×C4—21no—
89C2×C32×C4—21no—
90C2×C32×C4—21no—
91C2×C32×C4—41no—
92C2×C32×C4—41no—
93C2×C32×C4M1612yes—
94C2×C32×C4C2×D412yes—
95C2×C3×Dic3—21no—
96C2×C3×Dic3—21no—
97C2×C3×Dic3—21no—
98C2×C3×Dic3—41no—
99C2×C3×Dic3—41no—
100C2×C3×Dic3C22⋊C411yescharacteristic
101C2×C3×Dic3C22⋊C411yescharacteristic
102C2×C3×Dic3C22⋊C412yes—
103C3×C4×D3—24no—
104C3×C4×D3—24no—
105C3⋊(C3⋊C8)—42no—
106C3×C3⋊C8—42no—
107C2×#117—31no—
108#432—92no—
109#324—31no—
110#324—91no—
111#323—92no—
112C24×C3—31no—
113C23×D3C2×Dic311yescharacteristic
114C22×C3×C4—21no—
115C22×C3×C4—21no—
116C22×C3×C4—21no—
117C22×C3×C4—31no—
118C22×C3×C4—31no—
119C22×C3×C4—31no—
120C22×C3×C4—61no—
121C22×C3×C4—61no—
122C22×C3×C4—62no—
123C22×C3×C4—62no—
124C22×C3×C4C4×D311yescharacteristic
125C22×C3×C4C4×D311yescharacteristic
126C22×C3×C4C2×Dic311yescharacteristic
127C22×C3×C4C2×Dic311yescharacteristic
128C22×C3×C4C22×D311yescharacteristic
129C22×C3×C4C22×D311yescharacteristic
130C22×Dic3C2×Dic311yescharacteristic
131C22×Dic3C2×Dic311yescharacteristic
132C22×Dic3C2×Dic311yescharacteristic
133C2×C4×D3—22no—
134C2×C4×D3—22no—
135C2×C4×D3—21no—
136C2×C4×D3—21no—
137C2×C3×C8—62no—
138C3×C4⋊C4—22no—
139C3×C4⋊C4—22no—
140C3×C4⋊C4—42no—
141C3×C4⋊C4—62no—
142C3×C22⋊C4—62no—
143C3×C22⋊C4—62no—
144C3×C42—32no—
145C3×C42—32no—
146C3×C42—61no—
147C3×C42—61no—
148(C2×D3)⋊C4—22no—
149(C2×D3)⋊C4—22no—
150C4⋊Dic3—22no—
151C4×Dic3—21no—
152C4×Dic3—21no—
153C4×Dic3#6712yes—
154C4×Dic3#6712yes—
155C2×C3⋊C8—22no—
156C2×C3⋊C8—62no—
157C2×C3⋊C8—62no—
158C2×C3⋊C8—122no—
159C22×C32—21no—
160C22×C32—21no—
161C22×C32C2×C22⋊C411yescharacteristic
162C22×C32C2×M1611yescharacteristic
163C22×C32C2×M1611yescharacteristic
164C2×C3×D3—22no—
165C2×C3×D3—42no—
166C2×C3×D3—41no—
167C2×C3×D3—41no—
168C2×C3×D3—42no—
169C32×C4—22no—
170C32×C4—22no—
171C32×C4—41no—
172C3×Dic3—21no—
173C3×Dic3—21no—
174C3×Dic3—22no—
175C3×Dic3—41no—
176C23×C4—31no—
177#117—62no—
178#117—62no—
179C2×C4⋊C4—31no—
180C2×C4⋊C4D3211yescharacteristic
181C2×C22⋊C4—31no—
182C2×C22⋊C4—31no—
183C2×C42—31no—
184C2×C42—31no—
185C4⋊C8—182no—
186C22⋊C8—32no—
187C22⋊C8—92no—
188#97—182no—
189C23×C3—21no—
190C23×C3—32no—
191C23×C3—61no—
192C23×C3—61no—
193C23×C3—121no—
194C23×C3—121no—
195C23×C3C2×C4×D311yescharacteristic
196C23×C3C22×Dic311yescharacteristic
197C22×D3—21no—
198C22×D3—21no—
199C22×D3—41no—
200C22×D3—41no—
201C22×D3#20812yes—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4—31no—
211C2×C3×C4—31no—
212C2×C3×C4—32no—
213C2×C3×C4—41no—
214C2×C3×C4—41no—
215C2×C3×C4—41no—
216C2×C3×C4—41no—
217C2×C3×C4—41no—
218C2×C3×C4—41no—
219C2×C3×C4—41no—
220C2×C3×C4—64no—
221C2×C3×C4—64no—
222C2×C3×C4—61no—
223C2×C3×C4—61no—
224C2×C3×C4—61no—
225C2×C3×C4—81no—
226C2×C3×C4—81no—
227C2×C3×C4—121no—
228C2×C3×C4—121no—
229C2×C3×C4ΓL(1,𝔽25)12yes—
230C2×C3×C4#20812yes—
231C2×C3×C4D3×D412yes—
232C2×C3×C4C2×#6712yes—
233C2×Dic3—21no—
234C2×Dic3—21no—
235C2×Dic3—21no—
236C2×Dic3—41no—
237C2×Dic3—41no—
238C2×Dic3#21711yescharacteristic
239C2×Dic3#21711yescharacteristic
240C2×Dic3#21712yes—
241C4×D3—24no—
242C4×D3—24no—
243C3×C8—122no—
244C3⋊C8—42no—
245C3⋊C8—122no—
246C3⋊C8—122no—
247C3⋊C8—242no—
248C2×C32—21no—
249C2×C32—21no—
250C2×C32#40711yescharacteristic
251C2×C32#41011yescharacteristic
252C2×C32#41311yescharacteristic
253C3×D3—42no—
254C24—31no—
255C22×C4—31no—
256C22×C4—31no—
257C22×C4—31no—
258C22×C4—61no—
259C22×C4—61no—
260C22×C4—62no—
261C22×C4—62no—
262C22×C4D3×Dic311yescharacteristic
263C22×C4D3×Dic311yescharacteristic
264C22×C4C2×D3211yescharacteristic
265C2×C8—62no—
266C2×C8—182no—
267C4⋊C4—22no—
268C4⋊C4—62no—
269C22⋊C4—62no—
270C22⋊C4—62no—
271C42—32no—
272C42—32no—
273C42—61no—
274C42—61no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—21no—
278C22×C3—21no—
279C22×C3—21no—
280C22×C3—21no—
281C22×C3—21no—
282C22×C3—41no—
283C22×C3—41no—
284C22×C3—62no—
285C22×C3—122no—
286C22×C3—122no—
287C22×C3—121no—
288C22×C3—121no—
289C22×C3D3×C22⋊C411yescharacteristic
290C22×C3C2×ΓL(1,𝔽25)11yescharacteristic
291C22×C3D3×M1611yescharacteristic
292C22×C3C2×#20811yescharacteristic
293C22×C3C2×#20811yescharacteristic
294C22×C3C2×#21711yescharacteristic
295C2×D3—22no—
296C2×D3—42no—
297C2×D3—41no—
298C2×D3—41no—
299C2×D3—42no—
300C3×C4—22no—
301C3×C4—22no—
302C3×C4—22no—
303C3×C4—22no—
304C3×C4—42no—
305C3×C4—42no—
306C3×C4—41no—
307C3×C4—41no—
308C3×C4—61no—
309C3×C4—61no—
310C3×C4—62no—
311C3×C4—81no—
312C3×C4—121no—
313Dic3—21no—
314Dic3—21no—
315Dic3—22no—
316Dic3—41no—
317C32#146411yescharacteristic, complemented, Sylow
318C23—32no—
319C23—61no—
320C23—61no—
321C23—121no—
322C23—121no—
323C23C2×D3×Dic311yescharacteristic
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—31no—
328C2×C4—31no—
329C2×C4—32no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—64no—
333C2×C4—64no—
334C2×C4—61no—
335C2×C4—61no—
336C2×C4—61no—
337C2×C4—121no—
338C2×C4—121no—
339C2×C4#371112yes—
340C2×C4D3×#6712yes—
341C8—122no—
342C8—362no—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—41no—
351C2×C3—41no—
352C2×C3—122no—
353C2×C3#472611yescharacteristic
354C2×C3#474011yescharacteristic
355C2×C3#475111yescharacteristic
356C2×C3#520711yescharacteristic
357C2×C3#523711yescharacteristic
358C2×C3#524011yescharacteristic
359D3—42no—
360C22—21no—
361C22—21no—
362C22—62no—
363C22—122no—
364C22—122no—
365C22—121no—
366C22—121no—
367C22D3×#20811yescharacteristic
368C22C2×#371111yescharacteristic
369C22D3×#21711yescharacteristic
370C4—22no—
371C4—22no—
372C4—41no—
373C4—62no—
374C4—61no—
375C4—61no—
376C4—121no—
377C3—21no—
378C3#6812611yescharacteristic, complemented
379C3#7157211yescharacteristic, complemented
380C2—21no—
381C2—21no—
382C2—122no—
383C2#1059115411yescharacteristic
384C2#1059152811yescharacteristic
385C2#1059163711yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3×D3C2×C4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1464
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10591063C2semidirect
3. #10589394C2semidirect
4. C3×#4528C2semidirect
29. #4528D3semidirect
317. C32#1464semidirect
378. C3#68126semidirect
379. C3#71572semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8922
#105910632
#105893942
C3×#45282
#105891452
#715723
#681263