Finite Group Databasebeta

← #11773903

Subgroups — #11773903

Order 1152.

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

normal subgroups only

This group has 553 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×#877C211yesmaximal, characteristic
2#10591063C212yesmaximal, complemented
3#10589391C211yesmaximal, characteristic
4C3×#4525C211yesmaximal, characteristic
5#10589147C212yesmaximal, complemented
6#71572—31nomaximal
7#68102—31nomaximal
8C23×C3×Dic3C411yescharacteristic
9C2×C32×C22⋊C4C2211yescharacteristic
10C2×C3×#217C411yescharacteristic
11C2×C3×Dic3⋊C4C411yescharacteristic
12C2×C3×Dic3⋊C4C2211yescharacteristic
13C2×C3×C4×Dic3C411yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C3×#877—22no—
16C3×#877—22no—
17#63657C2212yes—
18C3×#830C2212yes—
19Dic3⋊(C3⋊C8)—22no—
20#63554—22no—
21C2×C3×#117—31no—
22C2×#877D311yescharacteristic
23#4926—32no—
24#4719—32no—
25C3×#323—31no—
26#4528—32no—
27#4525—31no—
28#4525—31no—
29#4525—61no—
30#4525D311yescharacteristic
31#4469—32no—
32C24×C32C2×C411yescharacteristic
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C22×C3×Dic3—22no—
36C22×C3×Dic3—21no—
37C22×C3×Dic3—21no—
38C22×C3×Dic3—22no—
39C22×C3×Dic3C2×C411yescharacteristic
40C22×C3×Dic3C2×C411yescharacteristic
41C22×C3×Dic3C2×C411yescharacteristic
42C22×C3×Dic3C2×C411yescharacteristic
43C32×C22⋊C4—22no—
44C2×C3⋊(C3⋊C8)—22no—
45C3×#217—22no—
46C3×Dic3⋊C4—22no—
47C3×Dic3⋊C4—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—
55C23×Dic3Dic311yescharacteristic
56C3×#117—62no—
57C3×#117—62no—
58C2×C3×C4⋊C4—31no—
59C2×C3×C4⋊C4—31no—
60C2×C3×C22⋊C4—21no—
61C2×C3×C22⋊C4—31no—
62C2×C3×C22⋊C4C2×D311yescharacteristic
63C2×C3×C22⋊C4C2×D311yescharacteristic
64C2×C3×C42—31no—
65C2×C3×C42—31no—
66C2×#217Dic311yescharacteristic
67C2×Dic3⋊C4Dic311yescharacteristic
68C2×Dic3⋊C4C2×D311yescharacteristic
69C2×C4×Dic3Dic311yescharacteristic
70C2×C4×Dic3C2×D311yescharacteristic
71#877—22no—
72#877—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×C32—21no—
83C23×C32—21no—
84C23×C32—41no—
85C23×C32—41no—
86C23×C32M1612yes—
87C23×C32C22×C411yescharacteristic
88C2×C32×C4—21no—
89C2×C32×C4—41no—
90C2×C32×C4—41no—
91C2×C32×C4C2×D412yes—
92C2×C3×Dic3—24no—
93C2×C3×Dic3—24no—
94C2×C3×Dic3—21no—
95C2×C3×Dic3—21no—
96C2×C3×Dic3—21no—
97C2×C3×Dic3—21no—
98C2×C3×Dic3—21no—
99C2×C3×Dic3—41no—
100C2×C3×Dic3—41no—
101C2×C3×Dic3C22⋊C411yescharacteristic
102C2×C3×Dic3C22⋊C411yescharacteristic
103C2×C3×Dic3C22⋊C412yes—
104C2×C3×Dic3M1612yes—
105C3⋊(C3⋊C8)—42no—
106C3×C3⋊C8—42no—
107C2×#117—31no—
108#432—92no—
109#324—92no—
110#323—31no—
111#323—91no—
112C24×C3—21no—
113C24×C3C4×D311yescharacteristic
114C24×C3C2×Dic311yescharacteristic
115C22×C3×C4—21no—
116C22×C3×C4—21no—
117C22×C3×C4—31no—
118C22×C3×C4—31no—
119C22×C3×C4—31no—
120C22×C3×C4—31no—
121C22×C3×C4—61no—
122C22×C3×C4—61no—
123C22×C3×C4—62no—
124C22×C3×C4—62no—
125C22×C3×C4C4×D311yescharacteristic
126C22×C3×C4C2×Dic311yescharacteristic
127C22×C3×C4C22×D311yescharacteristic
128C22×C3×C4C22×D311yescharacteristic
129C22×Dic3—22no—
130C22×Dic3—22no—
131C22×Dic3—21no—
132C22×Dic3—21no—
133C22×Dic3C2×Dic311yescharacteristic
134C22×Dic3C2×Dic311yescharacteristic
135C22×Dic3C2×Dic311yescharacteristic
136C22×Dic3C2×Dic311yescharacteristic
137C2×C3×C8—62no—
138C3×C4⋊C4—62no—
139C3×C4⋊C4—62no—
140C3×C22⋊C4—22no—
141C3×C22⋊C4—22no—
142C3×C22⋊C4—42no—
143C3×C22⋊C4—62no—
144C3×C42—32no—
145C3×C42—32no—
146C3×C42—61no—
147C3×C42—61no—
148#217—22no—
149Dic3⋊C4—22no—
150Dic3⋊C4—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×C32—22no—
162C22×C32—42no—
163C22×C32—42no—
164C22×C32—41no—
165C22×C32—41no—
166C22×C32C2×C22⋊C411yescharacteristic
167C22×C32C2×M1611yescharacteristic
168C22×C32C2×M1611yescharacteristic
169C32×C4—22no—
170C32×C4—41no—
171C3×Dic3—21no—
172C3×Dic3—21no—
173C3×Dic3—22no—
174C3×Dic3—22no—
175C3×Dic3—41no—
176C23×C4—31no—
177#117—62no—
178#117—62no—
179C2×C4⋊C4—31no—
180C2×C4⋊C4—31no—
181C2×C22⋊C4—31no—
182C2×C22⋊C4D3211yescharacteristic
183C2×C42—31no—
184C2×C42—31no—
185C4⋊C8—182no—
186C22⋊C8—32no—
187C22⋊C8—92no—
188#97—182no—
189C23×C3—21no—
190C23×C3—21no—
191C23×C3—21no—
192C23×C3—21no—
193C23×C3—22no—
194C23×C3—21no—
195C23×C3—41no—
196C23×C3—41no—
197C23×C3—41no—
198C23×C3—41no—
199C23×C3—41no—
200C23×C3—41no—
201C23×C3—81no—
202C23×C3—81no—
203C23×C3ΓL(1,𝔽25)12yes—
204C23×C3#20812yes—
205C23×C3C2×C4×D311yescharacteristic
206C23×C3C22×Dic311yescharacteristic
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—22no—
210C2×C3×C4—31no—
211C2×C3×C4—31no—
212C2×C3×C4—32no—
213C2×C3×C4—32no—
214C2×C3×C4—41no—
215C2×C3×C4—41no—
216C2×C3×C4—41no—
217C2×C3×C4—41no—
218C2×C3×C4—41no—
219C2×C3×C4—64no—
220C2×C3×C4—64no—
221C2×C3×C4—61no—
222C2×C3×C4—61no—
223C2×C3×C4—61no—
224C2×C3×C4—61no—
225C2×C3×C4—61no—
226C2×C3×C4—81no—
227C2×C3×C4—81no—
228C2×C3×C4—121no—
229C2×C3×C4—121no—
230C2×C3×C4D3×D412yes—
231C2×C3×C4C2×#6712yes—
232C2×Dic3—24no—
233C2×Dic3—24no—
234C2×Dic3—21no—
235C2×Dic3—21no—
236C2×Dic3—21no—
237C2×Dic3—21no—
238C2×Dic3—21no—
239C2×Dic3—41no—
240C2×Dic3—41no—
241C2×Dic3#20812yes—
242C2×Dic3#21711yescharacteristic
243C2×Dic3#21711yescharacteristic
244C2×Dic3#21712yes—
245C3×C8—122no—
246C3⋊C8—42no—
247C3⋊C8—122no—
248C3⋊C8—122no—
249C3⋊C8—242no—
250C2×C32—21no—
251C2×C32—21no—
252C2×C32—42no—
253C2×C32#40711yescharacteristic
254C2×C32#41011yescharacteristic
255C2×C32#41311yescharacteristic
256C24D3×Dic311yescharacteristic
257C22×C4—31no—
258C22×C4—31no—
259C22×C4—31no—
260C22×C4—31no—
261C22×C4—61no—
262C22×C4—61no—
263C22×C4—62no—
264C22×C4—62no—
265C22×C4D3×Dic311yescharacteristic
266C22×C4C2×D3211yescharacteristic
267C2×C8—62no—
268C2×C8—182no—
269C4⋊C4—62no—
270C4⋊C4—62no—
271C22⋊C4—22no—
272C22⋊C4—62no—
273C42—32no—
274C42—32no—
275C42—61no—
276C42—61no—
277C22×C3—21no—
278C22×C3—21no—
279C22×C3—21no—
280C22×C3—21no—
281C22×C3—22no—
282C22×C3—22no—
283C22×C3—21no—
284C22×C3—21no—
285C22×C3—21no—
286C22×C3—41no—
287C22×C3—41no—
288C22×C3—42no—
289C22×C3—42no—
290C22×C3—42no—
291C22×C3—42no—
292C22×C3—42no—
293C22×C3—41no—
294C22×C3—41no—
295C22×C3—41no—
296C22×C3—41no—
297C22×C3—81no—
298C22×C3—81no—
299C22×C3—82no—
300C22×C3—82no—
301C22×C3D3×C22⋊C411yescharacteristic
302C22×C3C2×ΓL(1,𝔽25)11yescharacteristic
303C22×C3D3×M1611yescharacteristic
304C22×C3C2×#20811yescharacteristic
305C22×C3C2×#20811yescharacteristic
306C22×C3C2×#21711yescharacteristic
307C3×C4—22no—
308C3×C4—22no—
309C3×C4—42no—
310C3×C4—41no—
311C3×C4—41no—
312C3×C4—61no—
313C3×C4—61no—
314C3×C4—62no—
315C3×C4—62no—
316C3×C4—81no—
317C3×C4—121no—
318Dic3—22no—
319Dic3—21no—
320Dic3—21no—
321Dic3—22no—
322Dic3—41no—
323C32#146411yescharacteristic, complemented, Sylow
324C23—21no—
325C23—21no—
326C23—41no—
327C23—41no—
328C23#371112yes—
329C23C2×D3×Dic311yescharacteristic
330C2×C4—21no—
331C2×C4—32no—
332C2×C4—31no—
333C2×C4—31no—
334C2×C4—32no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—64no—
338C2×C4—64no—
339C2×C4—61no—
340C2×C4—61no—
341C2×C4—61no—
342C2×C4—61no—
343C2×C4—61no—
344C2×C4—121no—
345C2×C4—121no—
346C2×C4D3×#6712yes—
347C8—122no—
348C8—362no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—21no—
356C2×C3—41no—
357C2×C3—41no—
358C2×C3—42no—
359C2×C3—42no—
360C2×C3—82no—
361C2×C3#472611yescharacteristic
362C2×C3#474011yescharacteristic
363C2×C3#474511yescharacteristic
364C2×C3#520711yescharacteristic
365C2×C3#523711yescharacteristic
366C2×C3#524011yescharacteristic
367C22—21no—
368C22—21no—
369C22—22no—
370C22—42no—
371C22—42no—
372C22—41no—
373C22—41no—
374C22D3×#20811yescharacteristic
375C22C2×#371111yescharacteristic
376C22D3×#21711yescharacteristic
377C4—22no—
378C4—41no—
379C4—62no—
380C4—62no—
381C4—61no—
382C4—61no—
383C4—121no—
384C3—21no—
385C3#6810211yescharacteristic, complemented
386C3#7157211yescharacteristic, complemented
387C2—21no—
388C2—21no—
389C2—42no—
390C2#1059115411yescharacteristic
391C2#1059150111yescharacteristic
392C2#1059152811yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C32×C4C23
hypercenterC2×C22⋊C4D32
hypocenterC32#1464
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #10591063C2semidirect
5. #10589147C2semidirect
323. C32#1464semidirect
385. C3#68102semidirect
386. C3#71572semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8772
#105910632
#105893912
C3×#45252
#105891472
#715723
#681023