Finite Group Databasebeta

← #11786476

Subgroups — #11786476

Order 1152.

686 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 686 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C22×#3724C211yesmaximal, characteristic
2C2×C22⋊#622C211yesmaximal, characteristic
3C2×#63742C212yesmaximal, complemented
4#10591720C211yesmaximal, characteristic
5#10590075C212yesmaximal, complemented
6C23×C3⋊Dic3C2211yescharacteristic
7C23×C3×Dic3—21no—
8C22×#622C2212yes—
9C2×C3×#217—21no—
10C2×#3724—21no—
11C2×#3724—24no—
12C2×#3724C2211yescharacteristic
13C2×#3724C2211yescharacteristic
14C2×#3724C2212yes—
15C22⋊#622C414yescomplemented
16#63742—24no—
17#63579—21no—
18C22×Dic3⋊C4—61no—
19#4942—61no—
20C24×C32D411yescharacteristic
21C22×C3⋊Dic3—22no—
22C22×C3⋊Dic3—22no—
23C22×C3⋊Dic3C2×C412yes—
24C22×C3⋊Dic3D411yescharacteristic
25C22×C3⋊Dic3Q812yes—
26C22×C3⋊Dic3C2311yescharacteristic
27C22×C3×Dic3—24no—
28C22×C3×Dic3—22no—
29C22×C3×Dic3—21no—
30C22×C3×Dic3—21no—
31C22×C3×Dic3—42no—
32C22×C3×Dic3—42no—
33C2×#622—22no—
34C2×#622—22no—
35C2×#622C2×C414yescomplemented
36C3×#217—42no—
37#3724—24no—
38#3724—22no—
39#3724—22no—
40#3724—22no—
41#3724D414yes—
42#1853—91nomaximal, Sylow
43C23×C3×C4—61no—
44C23×Dic3—21no—
45C23×Dic3—61no—
46C23×Dic3—61no—
47C2×C3×C22⋊C4—61no—
48C2×#217—21no—
49C2×Dic3⋊C4—62no—
50C2×Dic3⋊C4—61no—
51C2×Dic3⋊C4—61no—
52C2×Dic3⋊C4—68no—
53C2×Dic3⋊C4—62no—
54C3⋊#95—61no—
55C3⋊#95—61no—
56C23×C32—21no—
57C23×C32—21no—
58C23×C32—21no—
59C23×C32—21no—
60C23×C32C4⋊C412yes—
61C23×C32SD1612yes—
62C23×C32SD1612yes—
63C23×C32C2×D411yescharacteristic
64C2×C3⋊Dic3—21no—
65C2×C3⋊Dic3—21no—
66C2×C3⋊Dic3—24no—
67C2×C3⋊Dic3—24no—
68C2×C3⋊Dic3C4⋊C412yes—
69C2×C3⋊Dic3C22×C411yescharacteristic
70C2×C3⋊Dic3C2×D412yes—
71C2×C3⋊Dic3C2×Q811yescharacteristic
72C2×C3⋊Dic3#4112yes—
73C2×C3×Dic3—24no—
74C2×C3×Dic3—48no—
75C2×C3×Dic3—42no—
76C2×C3×Dic3—42no—
77C2×C3×Dic3—41no—
78C2×C3×Dic3—41no—
79C2×C3×Dic3—41no—
80C2×C3×Dic3—41no—
81C2×C3×Dic3—41no—
82C2×C3×Dic3—41no—
83#622—24no—
84C22×C4⋊C4—91no—
85C2×#106—92no—
86C2×C22⋊C8—91no—
87#380—91no—
88#340—92no—
89C24×C3—21no—
90C24×C3—21no—
91C22×C3×C4—64no—
92C22×C3×C4—62no—
93C22×C3×C4—61no—
94C22×C3×C4—61no—
95C22×C3×C4—122no—
96C22×C3×C4—122no—
97C22×Dic3—24no—
98C22×Dic3—22no—
99C22×Dic3—21no—
100C22×Dic3—21no—
101C22×Dic3—42no—
102C22×Dic3—42no—
103C22×Dic3—61no—
104C22×Dic3—61no—
105C22×Dic3—61no—
106C22×Dic3—62no—
107C22×Dic3—62no—
108C22×Dic3—61no—
109C22×Dic3—62no—
110C22×Dic3—62no—
111C22×Dic3—64no—
112C22×Dic3—64no—
113C22×Dic3—122no—
114C22×Dic3—122no—
115C3×C22⋊C4—122no—
116#217—42no—
117Dic3⋊C4—64no—
118Dic3⋊C4—64no—
119Dic3⋊C4—68no—
120Dic3⋊C4—122no—
121Dic3⋊C4—122no—
122C22×C32—22no—
123C22×C32—22no—
124C22×C32—22no—
125C22×C32—22no—
126C22×C32—22no—
127C22×C32—22no—
128C22×C32#10614yescomplemented
129C22×C32C2×C4⋊C411yescharacteristic
130C22×C32#12011yescharacteristic
131C22×C32#12311yescharacteristic
132C22×C32C2×SD1611yescharacteristic
133C22×C32C2×SD1611yescharacteristic
134C22×C32AGL(1,ℤ/8)11yescharacteristic
135C22×C32#13711yescharacteristic
136C3⋊Dic3—22no—
137C3⋊Dic3C4×D412yes—
138C3⋊Dic3C22⋊Q812yes—
139C3×Dic3—44no—
140C3×Dic3—81no—
141C3×Dic3—81no—
142C23×C4—61no—
143C23×C4—91no—
144C22×C8—92no—
145C2×C4⋊C4—92no—
146C2×C4⋊C4—91no—
147C2×C4⋊C4—91no—
148C2×C4⋊C4—184no—
149C2×C4⋊C4—181no—
150C2×C22⋊C4—61no—
151#106—184no—
152C22⋊C8—94no—
153#95—181no—
154C23×C3—22no—
155C23×C3—22no—
156C23×C3—22no—
157C23×C3—22no—
158C23×C3—21no—
159C23×C3—21no—
160C23×C3—22no—
161C23×C3—22no—
162C23×C3—22no—
163C23×C3—22no—
164C23×C3—22no—
165C23×C3—22no—
166C23×C3—41no—
167C23×C3—41no—
168C23×C3—41no—
169C23×C3—41no—
170C2×C3×C4—64no—
171C2×C3×C4—128no—
172C2×C3×C4—122no—
173C2×C3×C4—122no—
174C2×C3×C4—121no—
175C2×C3×C4—121no—
176C2×C3×C4—121no—
177C2×C3×C4—121no—
178C2×C3×C4—121no—
179C2×C3×C4—121no—
180C2×Dic3—24no—
181C2×Dic3—48no—
182C2×Dic3—42no—
183C2×Dic3—42no—
184C2×Dic3—41no—
185C2×Dic3—41no—
186C2×Dic3—41no—
187C2×Dic3—41no—
188C2×Dic3—41no—
189C2×Dic3—41no—
190C2×Dic3—62no—
191C2×Dic3—61no—
192C2×Dic3—61no—
193C2×Dic3—62no—
194C2×Dic3—62no—
195C2×Dic3—61no—
196C2×Dic3—61no—
197C2×Dic3—62no—
198C2×Dic3—62no—
199C2×Dic3—62no—
200C2×Dic3—62no—
201C2×Dic3—68no—
202C2×Dic3—68no—
203C2×Dic3—62no—
204C2×Dic3—124no—
205C2×Dic3—124no—
206C2×Dic3—121no—
207C2×Dic3—121no—
208C2×C32—24no—
209C2×C32#38511yescharacteristic
210C2×C32C2×#10611yescharacteristic
211C2×C32#42811yescharacteristic
212C2×C32#44811yescharacteristic
213C2×C32#45011yescharacteristic
214C2×C32#48111yescharacteristic
215C2×C32#48311yescharacteristic
216C24GO+(4,𝔽2)11yescharacteristic
217C22×C4—64no—
218C22×C4—62no—
219C22×C4—61no—
220C22×C4—61no—
221C22×C4—91no—
222C22×C4—91no—
223C22×C4—92no—
224C22×C4—92no—
225C22×C4—122no—
226C22×C4—122no—
227C22×C4—182no—
228C22×C4—182no—
229C2×C8—94no—
230C2×C8—182no—
231C2×C8—182no—
232C4⋊C4—94no—
233C4⋊C4—182no—
234C4⋊C4—184no—
235C4⋊C4—182no—
236C4⋊C4—182no—
237C22⋊C4—122no—
238C22×C3—24no—
239C22×C3—24no—
240C22×C3—24no—
241C22×C3—24no—
242C22×C3—24no—
243C22×C3—24no—
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—21no—
249C22×C3—21no—
250C22×C3—21no—
251C22×C3—21no—
252C22×C3—21no—
253C22×C3—21no—
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—21no—
258C22×C3—24no—
259C22×C3—24no—
260C22×C3—42no—
261C22×C3—42no—
262C22×C3—42no—
263C22×C3—42no—
264C22×C3—42no—
265C22×C3—42no—
266C3×C4—124no—
267C3×C4—241no—
268C3×C4—241no—
269Dic3—44no—
270Dic3—62no—
271Dic3—62no—
272Dic3—62no—
273Dic3—62no—
274Dic3—64no—
275Dic3—81no—
276Dic3—81no—
277Dic3—122no—
278C32#185311yescharacteristic, complemented, Sylow
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23#377312yes—
284C23#377512yes—
285C23#377512yes—
286C23C2×GO+(4,𝔽2)11yescharacteristic
287C2×C4—64no—
288C2×C4—92no—
289C2×C4—91no—
290C2×C4—91no—
291C2×C4—92no—
292C2×C4—92no—
293C2×C4—128no—
294C2×C4—122no—
295C2×C4—122no—
296C2×C4—121no—
297C2×C4—121no—
298C2×C4—121no—
299C2×C4—121no—
300C2×C4—121no—
301C2×C4—121no—
302C2×C4—184no—
303C2×C4—184no—
304C2×C4—181no—
305C2×C4—181no—
306C8—184no—
307C2×C3—28no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3—44no—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—22no—
327C22—22no—
328C22—22no—
329C22#6374214yescomplemented
330C22#6423311yescharacteristic
331C22C2×#377311yescharacteristic
332C22#6423611yescharacteristic
333C22C2×#377511yescharacteristic
334C22C2×#377511yescharacteristic
335C22#6423911yescharacteristic
336C22#6424111yescharacteristic
337C4—92no—
338C4—92no—
339C4—124no—
340C4—182no—
341C4—241no—
342C4—241no—
343C3—21no—
344C3—21no—
345C2—24no—
346C2#1059348511yescharacteristic
347C2#1059349711yescharacteristic
348C2#1059350411yescharacteristic
349C2#1059350711yescharacteristic
350C2C2×#6374211yescharacteristic
351C2#1059352311yescharacteristic
352C2#1059352511yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
Fitting, prime radicalC24×C32D4
socleC23×C32C2×D4
cosocleC22×C3⋊Dic3C23
hypercenterC24GO+(4,𝔽2)
hypocenterC32#1853
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
3. C2×#63742C2semidirect
5. #10590075C2semidirect
15. C22⋊#622C4semidirect
35. C2×#622C2×C4semidirect
128. C22×C32#106semidirect
278. C32#1853semidirect
329. C22#63742semidirect

Maximal subgroups

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

subgroupindex
C22×#37242
C2×C22⋊#6222
C2×#637422
#105917202
#105900752
#18539