Finite Group Databasebeta

← #11807911

Subgroups — #11807911

Order 1152.

1205 conjugacy classes of subgroups; only the 244 normal subgroups are shown.

normal subgroups only

This group has 1205 conjugacy classes of subgroups — too many to draw. Only its 244 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×#64145C211yesmaximal, characteristic
2C3×#5220C212yesmaximal
3#10591703C214yesmaximal, complemented
4#10591693C214yesmaximal, complemented
5#10591360C212yesmaximal, complemented
6#10591273C212yesmaximal, complemented
7#74684—32nomaximal
8C22×C32×D4C2211yescharacteristic
9C22×#634C2211yescharacteristic
10C23×C3×Dic3C2212yes—
11C2×#3757C2214yes—
12#64145C418yescomplemented
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×#217C2214yes—
15C2×C3×#217C2212yes—
16C2×#3724C2212yes—
17C2×#3724C2212yes—
18C2×#3724C2212yes—
19C2×Dic32C2212yes—
20C3×C3⋊#95C2214yes—
21#63579C2214yes—
22#63579C2214yes—
23C2×#936—32no—
24C2×#936—61no—
25C3×#386—32no—
26#5220D312yes—
27#5210—34no—
28#4946—34no—
29#4945—34no—
30#4944—34no—
31#4650—34no—
32#4646—34no—
33C24×C32C2312yes—
34C2×C32×D4—41no—
35C2×C32×D4—41no—
36C2×C32×D4C2×C414yes—
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3C2312yes—
39C22×C3⋊Dic3C2312yes—
40C2×#634—41no—
41C2×#634—41no—
42C2×#634C2×C414yescomplemented
43C22×C3×Dic3—42no—
44C22×C3×Dic3—44no—
45C22×C3×Dic3C2314yes—
46C22×C3×Dic3C2314yes—
47#3757C2×C4116yescomplemented
48C4×C3⋊Dic3C2×C414yescomplemented
49C3×#217—42no—
50C3×#217—44no—
51#3724—42no—
52#3724—42no—
53#3724—42no—
54Dic32—42no—
55#2379—91noSylow
56C22×C3×D4—21no—
57C22×C3×D4C2×D312yes—
58C23×C3×C4—32no—
59C23×Dic3C2×D312yes—
60C22×Dic6—32no—
61C22×Dic6—61no—
62C2×C3×C22⋊C4—32no—
63C2×C3×C22⋊C4—34no—
64C2×#217—34no—
65C2×#217—34no—
66C2×#217—64no—
67C2×#217C2×D314yes—
68C2×#217C2×D312yes—
69#936—316no—
70#936—68no—
71C2×Dic3⋊C4—34no—
72C2×Dic3⋊C4—34no—
73C2×Dic3⋊C4—34no—
74C2×C4×Dic3—32no—
75C2×C4×Dic3—34no—
76C2×C4×Dic3—61no—
77C3×#95—34no—
78C3⋊#95—34no—
79C3⋊#95—34no—
80C3⋊#95—34no—
81C3⋊#95—34no—
82C3⋊#95C2×D314yes—
83C23×C32—24no—
84C23×C32—22no—
85C23×C32—22no—
86C23×C32—24no—
87C23×C32C22×C414yes—
88C23×C32C2411yescharacteristic
89C32×D4—44no—
90C2×C32×C4—21no—
91C2×C32×C4—21no—
92C2×C32×C4C22×C412yes—
93C2×C3⋊Dic3—22no—
94C2×C3⋊Dic3—22no—
95C2×C3⋊Dic3—22no—
96C2×C3⋊Dic3—22no—
97C2×C3⋊Dic3C22×C414yes—
98C2×C3⋊Dic3C22×C414yes—
99#634—44no—
100C2×C3×Dic3—24no—
101C2×C3×Dic3—24no—
102C2×C3×Dic3—24no—
103C2×C3×Dic3—24no—
104C2×C3×Dic3—24no—
105C2×C3×Dic3—24no—
106C2×C3×Dic3—48no—
107C2×#124—91no—
108#391—92no—
109#388—94no—
110#386—32no—
111#385—94no—
112#382—92no—
113C24×C3—22no—
114C24×C3C22×D312yes—
115C24×C3C22×D312yes—
116C2×C3×D4—24no—
117C2×C3×D4—42no—
118C2×C3×D4—42no—
119C2×C3×D4—42no—
120C2×C3×D4—42no—
121C2×C3×D4C4×D318yes—
122C22×C3×C4—21no—
123C22×C3×C4—34no—
124C22×C3×C4—34no—
125C22×C3×C4—122no—
126C22×C3×C4—124no—
127C22×C3×C4C22×D312yes—
128C22×Dic3—34no—
129C22×Dic3—34no—
130C22×Dic3—42no—
131C22×Dic3—44no—
132C22×Dic3—62no—
133C22×Dic3—62no—
134C22×Dic3C22×D314yes—
135C22×Dic3C22×D314yes—
136C2×Dic6—38no—
137C2×Dic6—64no—
138C2×Dic6—122no—
139C2×Dic6—122no—
140C2×Dic6—122no—
141C2×Dic6—122no—
142C3×C22⋊C4—122no—
143C3×C22⋊C4—124no—
144#217—316no—
145#217—316no—
146#217—42no—
147#217—44no—
148#217—616no—
149Dic3⋊C4—124no—
150Dic3⋊C4—124no—
151Dic3⋊C4—124no—
152C4×Dic3—38no—
153C4×Dic3—64no—
154C4×Dic3—124no—
155C22×C32—24no—
156C22×C32—28no—
157C22×C32—42no—
158C22×C32—44no—
159C22×C32—42no—
160C22×C32C23×C411yescharacteristic
161C22×C32H(5,𝔽2)11yescharacteristic
162C22×C32H(5,𝔽2)11yescharacteristic
163C22×C32H(5,𝔽2)12yes—
164C22×C322−1+412yes—
165C32×C4—22no—
166C3⋊Dic3—24no—
167C3⋊Dic3—24no—
168C3×Dic3—44no—
169C3×Dic3—44no—
170C22×Q8—91no—
171C22×D4D3211yescharacteristic
172C23×C4—32no—
173#124—98no—
174C2×C4⋊C4—92no—
175C2×C4⋊C4—92no—
176C2×C4⋊C4—92no—
177C2×C22⋊C4—34no—
178C2×C22⋊C4—32no—
179C2×C22⋊C4—94no—
180C2×C42—91no—
181C2×C42—92no—
182#95—34no—
183#95—94no—
184#95—94no—
185C23×C3—24no—
186C23×C3—22no—
187C23×C3—24no—
188C23×C3—22no—
189C23×C3—22no—
190C23×C3—22no—
191C23×C3—24no—
192C23×C3—24no—
193C23×C3—21no—
194C23×C3—24no—
195C23×C3—42no—
196C23×C3—42no—
197C23×C3—44no—
198C23×C3—44no—
199C23×C3C2×C4×D314yes—
200C23×C3C2×C4×D314yes—
201C23×C3C23×D312yes—
202C3×D4—48no—
203C3×D4—48no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—22no—
207C2×C3×C4—22no—
208C2×C3×C4—22no—
209C2×C3×C4—64no—
210C2×C3×C4—64no—
211C2×C3×C4—64no—
212C2×C3×C4—64no—
213C2×C3×C4—64no—
214C2×C3×C4—64no—
215C2×C3×C4—128no—
216C2×C3×C4C2×C4×D314yes—
217C2×Dic3—24no—
218C2×Dic3—24no—
219C2×Dic3—24no—
220C2×Dic3—24no—
221C2×Dic3—24no—
222C2×Dic3—24no—
223C2×Dic3—38no—
224C2×Dic3—38no—
225C2×Dic3—48no—
226C2×Dic3—64no—
227C2×Dic3—64no—
228C2×Dic3—64no—
229C2×Dic3—64no—
230C2×Dic3—64no—
231C2×Dic3—64no—
232C2×Dic3—122no—
233C2×Dic3—122no—
234C2×Dic3—122no—
235C2×Dic3—122no—
236Dic6—128no—
237Dic6—128no—
238C2×C32—44no—
239C2×C32#51811yescharacteristic
240C2×C32#52012yes—
241C2×C32H(3,𝔽4)11yescharacteristic
242C2×C32#56212yes—
243C2×C32#56311yescharacteristic
244C24C2×D3212yes—
245C2×Q8—94no—
246C2×Q8—361no—
247C2×Q8—361no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4#62414yes—
251C22×C4—34no—
252C22×C4—34no—
253C22×C4—92no—
254C22×C4—92no—
255C22×C4—124no—
256C22×C4—122no—
257C22×C4C2×D3211yescharacteristic
258C4⋊C4—362no—
259C4⋊C4—362no—
260C4⋊C4—362no—
261C22⋊C4—916no—
262C22⋊C4—124no—
263C22⋊C4—122no—
264C42—94no—
265C42—362no—
266C22×C3—24no—
267C22×C3—24no—
268C22×C3—28no—
269C22×C3—28no—
270C22×C3—22no—
271C22×C3—22no—
272C22×C3—21no—
273C22×C3—21no—
274C22×C3—21no—
275C22×C3—44no—
276C22×C3—48no—
277C22×C3—42no—
278C22×C3—42no—
279C22×C3—42no—
280C22×C3—42no—
281C22×C3—44no—
282C22×C3—44no—
283C22×C3—84no—
284C22×C3—82no—
285C22×C3—82no—
286C22×C3C22×C4×D312yes—
287C22×C3#100414yes—
288C22×C3#100412yes—
289C22×C3#100412yes—
290C22×C3#101014yes—
291C3×C4—24no—
292C3×C4—24no—
293C3×C4—124no—
294C3×C4—124no—
295Dic3—44no—
296Dic3—44no—
297Dic3—68no—
298Dic3—68no—
299Dic3—124no—
300Dic3—124no—
301C32#237911yescharacteristic, complemented, Sylow
302C23—24no—
303C23—24no—
304C23—22no—
305C23—22no—
306C23C2×#62414yes—
307C23C22×D3211yescharacteristic
308Q8—364no—
309D4—44no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—64no—
313C2×C4—64no—
314C2×C4—64no—
315C2×C4—64no—
316C2×C4—64no—
317C2×C4—64no—
318C2×C4—94no—
319C2×C4—94no—
320C2×C4—128no—
321C2×C4—182no—
322C2×C4—182no—
323C2×C4—182no—
324C2×C4—182no—
325C2×C4C2×#62412yes—
326C2×C3—22no—
327C2×C3—22no—
328C2×C3—21no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—44no—
332C2×C3—44no—
333C2×C3—84no—
334C2×C3#548612yes—
335C2×C3#554614yes—
336C2×C3#559412yes—
337C2×C3#562114yes—
338C2×C3#565112yes—
339C22—28no—
340C22—24no—
341C22—44no—
342C22—42no—
343C22—42no—
344C22#6430912yes—
345C22#6431312yes—
346C22C22×#62411yescharacteristic
347C22#6433011yescharacteristic
348C22#6433011yescharacteristic
349C4—22no—
350C4—124no—
351C4—124no—
352C4—184no—
353C4—184no—
354C3—21no—
355C3#7468412yescomplemented
356C2—44no—
357C2#1059521312yes—
358C2#1059521912yes—
359C2#1059525611yescharacteristic
360C2#1059527511yescharacteristic
361C2#1059551011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
Fitting, prime radicalC22×C32×D4C22
socle, cosocleC23×C32C24
hypercenterC22×D4D32
hypocenterC32#2379
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
3. #10591703C2semidirect
4. #10591693C2semidirect
5. #10591360C2semidirect
6. #10591273C2semidirect
12. #64145C4semidirect
42. C2×#634C2×C4semidirect
47. #3757C2×C4semidirect
48. C4×C3⋊Dic3C2×C4semidirect
301. C32#2379semidirect
355. C3#74684semidirect

Maximal subgroups

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

subgroupindex
C2×#641452
C3×#52202
#105917032
#105916932
#105913602
#105912732
#746843