Finite Group Databasebeta

← #11787814

Subgroups — #11787814

Order 1152.

813 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 813 conjugacy classes of subgroups — too many to draw. Only its 164 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
1C3×#5798C211yesmaximal, characteristic
2C2×C3×#936C211yesmaximal, characteristic
3C2×#63660C211yesmaximal, characteristic
4#10591099C212yesmaximal, complemented
5#10589161C212yesmaximal, complemented
6#71723—31nomaximal
7#71649—31nomaximal
8C22×C32×D4C2211yescharacteristic
9C22×C3×Dic6C2211yescharacteristic
10C2×#3748C2212yes—
11C2×C3×#217—22no—
12C2×C3×#217—22no—
13C3×#936—22no—
14C3×#936C414yescomplemented
15C3×D4×Dic3—24no—
16C3×#926C2212yes—
17C2×C3×C4×Dic3C2211yescharacteristic
18#63660—22no—
19#63565—24no—
20C2×C3×#124—31no—
21C3×#518—31no—
22#5798D311yescharacteristic
23C2×#936D311yescharacteristic
24#5225—32no—
25C2×#833—31no—
26C2×#833—31no—
27C2×#833—61no—
28#5004—32no—
29#4532—32no—
30#4523—32no—
31C24×C32D412yes—
32C2×C32×D4—22no—
33C2×C32×D4—22no—
34C2×C32×D4C2×C412yes—
35C2×C32×D4D412yes—
36C22×C32×C4C2311yescharacteristic
37C22×C3×Dic3—21no—
38C22×C3×Dic3—21no—
39C22×C3×Dic3—24no—
40C2×C3×Dic6—22no—
41C2×C3×Dic6—22no—
42C2×C3×Dic6—21no—
43C2×C3×Dic6C2×C412yescomplemented
44#3748—22no—
45#3748—22no—
46C2×C3⋊(C3⋊C8)—22no—
47C3×#217—24no—
48C3×#217—28no—
49C3×#217—22no—
50C3×C4⋊Dic3D414yes—
51C3×C4×Dic3—21no—
52C3×C4×Dic3—22no—
53C3×C4×Dic3C2×C412yescomplemented
54#1885—91noSylow
55C22×C3×Q8—31no—
56C22×C3×D4—21no—
57C22×C3×D4C2×D311yescharacteristic
58C22×C3×D4C2×D311yescharacteristic
59C22×Dic6C2×D311yescharacteristic
60C3×#124—34no—
61C3×#124—62no—
62C3×C4×D4—64no—
63C3×#117—32no—
64C2×C3×C22⋊C4—62no—
65C2×C3×C22⋊C4—62no—
66C2×C3×C42—31no—
67C2×#217—22no—
68C2×#217—22no—
69#936—22no—
70#936Dic314yescomplemented
71D4×Dic3—24no—
72#926C2×D312yes—
73C2×C4×Dic3C2×D311yescharacteristic
74C2×#208—32no—
75C2×#208—32no—
76C2×#208—62no—
77#835—64no—
78#833—64no—
79#833—62no—
80#833—62no—
81#810—64no—
82C23×C32—22no—
83C23×C32—22no—
84C23×C32—44no—
85C23×C32C22⋊C414yes—
86C23×C32C2×D411yescharacteristic
87C32×D4—24no—
88C32×D4—24no—
89C2×C32×C4C22×C411yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91C2×C32×C4C2×D412yes—
92C2×C32×C4#4112yes—
93C2×C3×Dic3—22no—
94C2×C3×Dic3—22no—
95C2×C3×Dic3—24no—
96C2×C3×Dic3—42no—
97C2×C3×Dic3—41no—
98C2×C3×Dic3—41no—
99C2×C3×Dic3—84no—
100C3×Dic6—24no—
101C3×Dic6—42no—
102C3⋊(C3⋊C8)—42no—
103C2×#124—31no—
104#518—31no—
105#419—92no—
106C2×#100—91no—
107#339—92no—
108C24×C3—22no—
109C24×C3#6712yes—
110C24×C3#6712yes—
111C2×C3×Q8—32no—
112C2×C3×Q8—61no—
113C2×C3×Q8—62no—
114C2×C3×Q8—62no—
115C2×C3×D4—22no—
116C2×C3×D4—22no—
117C2×C3×D4—22no—
118C2×C3×D4—22no—
119C2×C3×D4—22no—
120C2×C3×D4—22no—
121C2×C3×D4—42no—
122C2×C3×D4—42no—
123C2×C3×D4C4×D312yes—
124C2×C3×D4D1212yes—
125C2×C3×D4C2×Dic312yes—
126C2×C3×D4#6712yes—
127C22×C3×C4—21no—
128C22×C3×C4—61no—
129C22×C3×C4—61no—
130C22×C3×C4—64no—
131C22×C3×C4C22×D311yescharacteristic
132C22×C3×C4C22×D311yescharacteristic
133C22×Dic3—21no—
134C22×Dic3—21no—
135C22×Dic3—24no—
136C2×Dic6—22no—
137C2×Dic6—22no—
138C2×Dic6—21no—
139C2×Dic6C2×Dic312yescomplemented
140C3×C4⋊C4—34no—
141C3×C22⋊C4—64no—
142C3×C22⋊C4—68no—
143C3×C22⋊C4—62no—
144C3×C42—32no—
145C3×C42—61no—
146C3×C42—62no—
147#217—24no—
148#217—28no—
149#217—22no—
150C4⋊Dic3#6714yes—
151C4×Dic3—21no—
152C4×Dic3—22no—
153C4×Dic3C2×Dic312yescomplemented
154#208—64no—
155#208—62no—
156#208—62no—
157#208—62no—
158#208—62no—
159#208—122no—
160C2×C3⋊C8—62no—
161C2×C3⋊C8—62no—
162C2×C3⋊C8—122no—
163C22×C32—22no—
164C22×C32—24no—
165C22×C32—44no—
166C22×C32—44no—
167C22×C32—82no—
168C22×C32C2×C22⋊C411yescharacteristic
169C22×C32#12011yescharacteristic
170C22×C32#12311yescharacteristic
171C32×C4C4×D412yes—
172C32×C4#12112yes—
173C3×Dic3—42no—
174C3×Dic3—42no—
175C3×Dic3—44no—
176C22×Q8—31no—
177C22×D4D3211yescharacteristic
178C2×M16—92no—
179#124—34no—
180#124—62no—
181C4×D4—64no—
182#117—32no—
183C2×C22⋊C4—62no—
184C2×C22⋊C4—62no—
185C2×C42—31no—
186#103—184no—
187#100—182no—
188C23×C3—22no—
189C23×C3—22no—
190C23×C3—22no—
191C23×C3—22no—
192C23×C3—24no—
193C23×C3—21no—
194C23×C3—42no—
195C23×C3—42no—
196C23×C3—44no—
197C23×C3—44no—
198C23×C3—84no—
199C23×C3(C2×D3)⋊C414yes—
200C23×C3#21714yes—
201C23×C3C2×#6711yescharacteristic
202C23×C3C2×#6711yescharacteristic
203C3×Q8—64no—
204C3×Q8—122no—
205C3×D4—24no—
206C3×D4—24no—
207C3×D4—24no—
208C3×D4—24no—
209C3×D4—44no—
210C3×D4—44no—
211C2×C3×C4—21no—
212C2×C3×C4—22no—
213C2×C3×C4—21no—
214C2×C3×C4—22no—
215C2×C3×C4—62no—
216C2×C3×C4—62no—
217C2×C3×C4—64no—
218C2×C3×C4—122no—
219C2×C3×C4—121no—
220C2×C3×C4—121no—
221C2×C3×C4—244no—
222C2×C3×C4C2×C4×D311yescharacteristic
223C2×C3×C4C2×D1211yescharacteristic
224C2×C3×C4#23512yes—
225C2×C3×C4D3×D412yes—
226C2×C3×C4#23712yes—
227C2×C3×C4C22×Dic311yescharacteristic
228C2×C3×C4C2×#6711yescharacteristic
229C2×C3×C4C2×#6712yes—
230C2×Dic3—22no—
231C2×Dic3—22no—
232C2×Dic3—24no—
233C2×Dic3—42no—
234C2×Dic3—41no—
235C2×Dic3—41no—
236C2×Dic3—84no—
237Dic6—24no—
238Dic6—42no—
239C3⋊C8—124no—
240C3⋊C8—122no—
241C3⋊C8—122no—
242C2×C32—21no—
243C2×C32—21no—
244C2×C32—44no—
245C2×C32#38611yescharacteristic
246C2×C32#45512yes—
247C24#62512yes—
248C2×Q8—32no—
249C2×Q8—61no—
250C2×Q8—62no—
251C2×Q8—62no—
252C2×D4—22no—
253C2×D4—22no—
254C2×D4D3×Dic312yes—
255C2×D4#62612yes—
256C22×C4—61no—
257C22×C4—61no—
258C22×C4—64no—
259C22×C4C2×D3211yescharacteristic
260M16—182no—
261M16—182no—
262C2×C8—182no—
263C4⋊C4—34no—
264C22⋊C4—64no—
265C22⋊C4—68no—
266C22⋊C4—62no—
267C42—32no—
268C42—61no—
269C42—62no—
270C22×C3—22no—
271C22×C3—22no—
272C22×C3—24no—
273C22×C3—24no—
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—42no—
278C22×C3—44no—
279C22×C3—44no—
280C22×C3—44no—
281C22×C3—44no—
282C22×C3—44no—
283C22×C3—84no—
284C22×C3—84no—
285C22×C3—82no—
286C22×C3—82no—
287C22×C3—84no—
288C22×C3C2×(C2×D3)⋊C411yescharacteristic
289C22×C3#92911yescharacteristic
290C22×C3#93511yescharacteristic
291C22×C3#93711yescharacteristic
292C22×C3C2×#21711yescharacteristic
293C22×C3#95311yescharacteristic
294C3×C4—22no—
295C3×C4—22no—
296C3×C4—122no—
297C3×C4—122no—
298C3×C4—124no—
299C3×C4C4×#6712yes—
300C3×C4#93012yes—
301C3×C4D4×Dic312yes—
302C3×C4#93912yes—
303Dic3—42no—
304Dic3—42no—
305Dic3—44no—
306C32#188511yescharacteristic, complemented, Sylow
307C23—22no—
308C23—22no—
309C23—44no—
310C23(C2×D3)⋊Dic314yes—
311C23C2×#62511yescharacteristic
312Q8—64no—
313Q8—122no—
314D4—24no—
315D4—24no—
316C2×C4—62no—
317C2×C4—62no—
318C2×C4—64no—
319C2×C4—122no—
320C2×C4—121no—
321C2×C4—121no—
322C2×C4—244no—
323C2×C4C2×D3×Dic311yescharacteristic
324C2×C4#380412yes—
325C2×C4C2×#62611yescharacteristic
326C2×C4D3×#6712yes—
327C8—362no—
328C2×C3—21no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—22no—
333C2×C3—21no—
334C2×C3—41no—
335C2×C3—41no—
336C2×C3—44no—
337C2×C3—44no—
338C2×C3—84no—
339C2×C3#506112yes—
340C2×C3#521311yescharacteristic
341C2×C3#522011yescharacteristic
342C2×C3#524212yes—
343C22—22no—
344C22—24no—
345C22—44no—
346C22—44no—
347C22—82no—
348C22C2×(C2×D3)⋊Dic311yescharacteristic
349C22#6396111yescharacteristic
350C22#6397611yescharacteristic
351C4—122no—
352C4—124no—
353C4—122no—
354C4Dic3×#6712yes—
355C4#6397812yes—
356C3—21no—
357C3#7164911yescharacteristic, complemented
358C3#7172311yescharacteristic, complemented
359C2—21no—
360C2—21no—
361C2—44no—
362C2#1059151212yes—
363C2#1059171011yescharacteristic
subgroupG/H
centerC22#63976
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32#120
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1885
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #10591099C2semidirect
5. #10589161C2semidirect
14. C3×#936C4semidirect
43. C2×C3×Dic6C2×C4semidirect
53. C3×C4×Dic3C2×C4semidirect
70. #936Dic3semidirect
139. C2×Dic6C2×Dic3semidirect
153. C4×Dic3C2×Dic3semidirect
306. C32#1885semidirect
357. C3#71649semidirect
358. C3#71723semidirect

Maximal subgroups

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

subgroupindex
C3×#57982
C2×C3×#9362
C2×#636602
#105910992
#105891612
#717233
#716493