Finite Group Databasebeta

← #11802680

Subgroups — #11802680

Order 1152.

1733 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3797C211yesmaximal, characteristic
2C2×#64101C211yesmaximal, characteristic
3C2×#63874C211yesmaximal, characteristic
4C3×#4973C212yesmaximal, complemented
5#10591396C214yesmaximal, complemented
6#10591371C214yesmaximal
7#10591220C212yesmaximal, complemented
8#76610—32nomaximal
9C22×C4×C3⋊D3C2211yescharacteristic
10C22×C3×Dic6C2212yes—
11C22×#627C2212yes—
12C22×#624C2212yes—
13C2×#3797—24no—
14C2×#3797—24no—
15C2×#3797C418yescomplemented
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×#3752C2212yes—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C4×C3⋊Dic3C2212yes—
20#64101—24no—
21C2×C3×C4×Dic3C2212yes—
22C2×#3724C2212yes—
23C2×#3722C2212yes—
24#63874—24no—
25C3×C3⋊#95C2218yes—
26#63579C2218yes—
27C22×D3×Q8—32no—
28C2×#892—32no—
29C2×#892—61no—
30C2×#872—32no—
31C3×#391—32no—
32#5229—32no—
33#4973D312yescomplemented
34#4929—32no—
35#4664—38no—
36#4646—38no—
37C23×C3⋊D3C2311yescharacteristic
38C22×C32×C4C2312yes—
39C22×C32×C4C2311yescharacteristic
40C22×C3⋊Dic3C2312yes—
41C22×C3⋊Dic3C2311yescharacteristic
42C2×C4×C3⋊D3C2×C414yes—
43C2×C4×C3⋊D3D414yes—
44C2×C4×C3⋊D3D414yes—
45C22×C3×Dic3C2314yes—
46C22×C3×Dic3C2314yes—
47C2×C3×Dic6—24no—
48C2×C3×Dic6—24no—
49C2×C3×Dic6C2×C418yes—
50C2×#627—24no—
51C2×#627—24no—
52C2×#627C2×C418yes—
53C2×#624—24no—
54C2×#624—24no—
55C2×#624C2×C418yes—
56#3797—232no—
57C32×C4⋊C4—22no—
58#3752—24no—
59C4⋊(C3⋊Dic3)—22no—
60C4×C3⋊Dic3—24no—
61C3×C4×Dic3—24no—
62#3724—24no—
63#3722—24no—
64#2310—91noSylow
65C22×C3×Q8—32no—
66C2×D3×Q8—316no—
67C2×D3×Q8—68no—
68C2×D3×Q8—68no—
69C22×C4×D3—32no—
70C22×C4×D3—34no—
71C22×C4×D3—61no—
72C22×Dic6—34no—
73C22×Dic6C2×D312yes—
74C2×C3×C4⋊C4—21no—
75C2×C3×C4⋊C4C2×D312yes—
76C2×C3×C42—32no—
77C2×(C2×D3)⋊C4—34no—
78C2×(C2×D3)⋊C4—34no—
79C2×(C2×D3)⋊C4—62no—
80C2×C4⋊Dic3—32no—
81C2×C4⋊Dic3—61no—
82C2×Dic3⋊C4—34no—
83C2×C4×Dic3—34no—
84C2×C4×Dic3—62no—
85C2×C4×Dic3C2×D312yes—
86#892—68no—
87#892—68no—
88#872—68no—
89C3×#95—38no—
90C3⋊#95—38no—
91C3⋊#95—38no—
92C3⋊#95C2×D318yes—
93C23×C32C2411yescharacteristic
94C22×C3⋊D3—22no—
95C22×C3⋊D3—22no—
96C22×C3⋊D3C22×C412yes—
97C22×C3⋊D3C2×D412yes—
98C22×C3⋊D3C2×D412yes—
99C2×C32×C4—22no—
100C2×C32×C4—24no—
101C2×C32×C4C22×C412yes—
102C2×C32×C4C2×D412yes—
103C2×C32×C4C2×D412yes—
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3—24no—
106C2×C3⋊Dic3C22×C412yes—
107C2×C3⋊Dic3C2×D412yes—
108C2×C3⋊Dic3C2×D412yes—
109C4×C3⋊D3C22⋊C4116yes—
110C2×C3×Dic3—24no—
111C2×C3×Dic3—24no—
112C2×C3×Dic3—24no—
113C2×C3×Dic3—24no—
114C2×C3×Dic3—24no—
115C2×C3×Dic3C22×C418yes—
116C3×Dic6—216no—
117#627—216no—
118#624—216no—
119C23×Q8—91no—
120C2×#117—91no—
121C2×#117—91no—
122#391—32no—
123#391—94no—
124#391—92no—
125#381—94no—
126C23×D3—32no—
127C23×D3—61no—
128C2×C3×Q8—38no—
129C2×C3×Q8—64no—
130C2×C3×Q8—64no—
131C22×C3×C4—21no—
132C22×C3×C4—22no—
133C22×C3×C4—34no—
134C22×C3×C4—34no—
135C22×C3×C4C22×D314yes—
136C22×C3×C4C22×D312yes—
137C22×Dic3—32no—
138C22×Dic3—34no—
139C22×Dic3—61no—
140C22×Dic3—62no—
141C22×Dic3C22×D314yes—
142C22×Dic3C22×D314yes—
143D3×Q8—664no—
144C2×C4×D3—38no—
145C2×C4×D3—38no—
146C2×C4×D3—38no—
147C2×C4×D3—316no—
148C2×C4×D3—64no—
149C2×C4×D3—64no—
150C2×C4×D3—64no—
151C2×C4×D3—68no—
152C2×C4×D3—68no—
153C2×Dic6—24no—
154C2×Dic6—24no—
155C2×Dic6—316no—
156C2×Dic6—68no—
157C2×Dic6—68no—
158C2×Dic6C4×D318yes—
159C3×C4⋊C4—24no—
160C3×C4⋊C4—24no—
161C3×C42—64no—
162(C2×D3)⋊C4—68no—
163(C2×D3)⋊C4—68no—
164(C2×D3)⋊C4—68no—
165C4⋊Dic3—64no—
166C4⋊Dic3—64no—
167Dic3⋊C4—68no—
168C4×Dic3—24no—
169C4×Dic3—68no—
170C4×Dic3—68no—
171C22×C32C23×C411yescharacteristic
172C22×C32C22×D411yescharacteristic
173C22×C32C22×D411yescharacteristic
174C22×C322−1+412yes—
175C22×C322−1+412yes—
176C2×C3⋊D3—24no—
177C2×C3⋊D3—22no—
178C2×C3⋊D3—22no—
179C2×C3⋊D3—24no—
180C2×C3⋊D3C2×C22⋊C414yes—
181C32×C4—42no—
182C32×C4C2×C22⋊C414yes—
183C3⋊Dic3—42no—
184C3⋊Dic3C2×C22⋊C414yes—
185C3×Dic3—28no—
186C3×Dic3—44no—
187C22×Q8—32no—
188C22×Q8—92no—
189C22×Q8—98no—
190C22×Q8—184no—
191C22×Q8—184no—
192C23×C4—92no—
193C23×C4—91no—
194#117—184no—
195#117—184no—
196C2×C4⋊C4—92no—
197C2×C4⋊C4—91no—
198C2×C4⋊C4D3211yescharacteristic
199C2×C22⋊C4—92no—
200C2×C22⋊C4—92no—
201C2×C42—32no—
202C2×C42—92no—
203#95—38no—
204#95—98no—
205C23×C3—21no—
206C23×C3C23×D312yes—
207C22×D3—34no—
208C22×D3—34no—
209C22×D3—34no—
210C22×D3—62no—
211C22×D3—62no—
212C22×D3—62no—
213C22×D3—64no—
214C22×D3—64no—
215C22×D3—122no—
216C22×D3—122no—
217C3×Q8—616no—
218C2×C3×C4—24no—
219C2×C3×C4—24no—
220C2×C3×C4—28no—
221C2×C3×C4—22no—
222C2×C3×C4—22no—
223C2×C3×C4—22no—
224C2×C3×C4—38no—
225C2×C3×C4—44no—
226C2×C3×C4—64no—
227C2×C3×C4—64no—
228C2×C3×C4—64no—
229C2×C3×C4—64no—
230C2×C3×C4—64no—
231C2×C3×C4C2×C4×D314yes—
232C2×C3×C4D3×D414yes—
233C2×C3×C4D3×D414yes—
234C2×Dic3—24no—
235C2×Dic3—24no—
236C2×Dic3—24no—
237C2×Dic3—24no—
238C2×Dic3—24no—
239C2×Dic3—34no—
240C2×Dic3—34no—
241C2×Dic3—34no—
242C2×Dic3—62no—
243C2×Dic3—62no—
244C2×Dic3—62no—
245C2×Dic3—64no—
246C2×Dic3—64no—
247C2×Dic3—68no—
248C2×Dic3—124no—
249C2×Dic3C2×C4×D318yes—
250C4×D3—332no—
251C4×D3—616no—
252C4×D3—632no—
253Dic6—216no—
254Dic6—632no—
255C2×C32C22×C22⋊C411yescharacteristic
256C2×C32#51912yes—
257C2×C32#53611yescharacteristic
258C2×C32#53611yescharacteristic
259C2×C32#53612yes—
260C3⋊D3—24no—
261C24—91no—
262C2×Q8—38no—
263C2×Q8—64no—
264C2×Q8—64no—
265C2×Q8—98no—
266C2×Q8—184no—
267C2×Q8—184no—
268C2×Q8—1832no—
269C22×C4—34no—
270C22×C4—34no—
271C22×C4—98no—
272C22×C4—91no—
273C22×C4—94no—
274C22×C4—94no—
275C22×C4—94no—
276C22×C4—92no—
277C22×C4—184no—
278C22×C4—184no—
279C22×C4C2×D3212yes—
280C22×C4C2×D3211yescharacteristic
281C4⋊C4—22no—
282C4⋊C4—184no—
283C4⋊C4—182no—
284C22⋊C4—184no—
285C22⋊C4—184no—
286C42—64no—
287C42—184no—
288C22×C3—21no—
289C22×C3—21no—
290C22×C3—22no—
291C22×C3—22no—
292C22×C3—21no—
293C22×C3C22×C4×D312yes—
294C22×C3C2×D3×D412yes—
295C22×C3C2×D3×D412yes—
296C22×C3#100714yes—
297C22×C3#101014yes—
298C2×D3—38no—
299C2×D3—64no—
300C2×D3—64no—
301C2×D3—64no—
302C2×D3—68no—
303C2×D3—68no—
304C2×D3—122no—
305C2×D3—124no—
306C2×D3—122no—
307C2×D3—124no—
308C3×C4—24no—
309C3×C4—44no—
310C3×C4—44no—
311C3×C4—68no—
312C3×C4—124no—
313C3×C4D3×C22⋊C418yes—
314Dic3—28no—
315Dic3—38no—
316Dic3—44no—
317Dic3—64no—
318Dic3—124no—
319Dic3—124no—
320C32#231011yescharacteristic, complemented, Sylow
321C23—92no—
322C23—92no—
323C23—92no—
324C23—182no—
325C23—182no—
326C23C22×D3211yescharacteristic
327Q8—616no—
328Q8—1816no—
329C2×C4—24no—
330C2×C4—22no—
331C2×C4—38no—
332C2×C4—64no—
333C2×C4—64no—
334C2×C4—64no—
335C2×C4—64no—
336C2×C4—64no—
337C2×C4—92no—
338C2×C4—92no—
339C2×C4—92no—
340C2×C4—916no—
341C2×C4—1816no—
342C2×C4—184no—
343C2×C4—182no—
344C2×C4C4×D3212yes—
345C2×C4#380212yes—
346C2×C4#381112yes—
347C2×C3—21no—
348C2×C3—22no—
349C2×C3—21no—
350C2×C3—22no—
351C2×C3—21no—
352C2×C3C2×D3×C22⋊C412yes—
353C2×C3#557214yes—
354C2×C3#562814yes—
355C2×C3#567512yes—
356C2×C3#572412yes—
357D3—68no—
358D3—124no—
359C22—94no—
360C22—182no—
361C22—184no—
362C22—182no—
363C22—184no—
364C22C2×C4×D3211yescharacteristic
365C22C2×#380211yescharacteristic
366C22#6430912yes—
367C22#6431612yes—
368C22C2×#381111yescharacteristic
369C4—42no—
370C4—68no—
371C4—94no—
372C4—124no—
373C4—362no—
374C4#6392114yes—
375C3—21no—
376C3#7661012yescomplemented
377C2—184no—
378C2#1059434712yes—
379C2#1059452912yes—
380C2C2×#6392111yescharacteristic
381C2#1059517111yescharacteristic
382C2#1059535011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2310
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C3×#4973C2semidirect
5. #10591396C2semidirect
7. #10591220C2semidirect
15. C2×#3797C4semidirect
33. #4973D3semidirect
320. C32#2310semidirect
376. C3#76610semidirect

Maximal subgroups

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

subgroupindex
C22×#37972
C2×#641012
C2×#638742
C3×#49732
#105913962
#105913712
#105912202
#766103