Finite Group Databasebeta

← #11805338

Subgroups — #11805338

Order 1152.

1125 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63957C211yesmaximal, characteristic
2#10592641C211yesmaximal, characteristic
3C3×#4945C212yesmaximal
4#10591705C211yesmaximal, characteristic
5#10591701C212yesmaximal
6#10591256C212yesmaximal, complemented
7#10591245C212yesmaximal, complemented
8#10591243C212yesmaximal, complemented
9#10591239C212yesmaximal, complemented
10#75473—32nomaximal
11C23×C3⋊Dic3C2211yescharacteristic
12C2×C32×C22⋊C4C2211yescharacteristic
13C2×#3757C2211yescharacteristic
14C2×#3750C2212yes—
15C2×C3×#217C2212yes—
16C2×C3×#217C2212yes—
17C2×C3×Dic3⋊C4C2212yes—
18C2×C3×C4×Dic3C2212yes—
19C2×#3724C2211yescharacteristic
20C2×#3724C2211yescharacteristic
21C2×Dic3⋊Dic3C2212yes—
22#63957C418yescomplemented
23C2×Dic32C2212yes—
24C2×Dic32C2212yes—
25C2×Dic32C2212yes—
26#63658C2212yes—
27C3×C3⋊#95C2212yes—
28C3×C3⋊#95C2212yes—
29#63579C2211yescharacteristic
30#63579C2212yes—
31#63579C2212yes—
32#63579C2211yescharacteristic
33C2×#877—32no—
34C3×#388—32no—
35#4977—32no—
36#4976—32no—
37#4951—32no—
38#4945D312yes—
39#4944—32no—
40#4942—32no—
41#4942—61no—
42Dic3×C22⋊C4—32no—
43#4932—32no—
44C4×Dic3⋊C4—32no—
45#4650—32no—
46#4649—32no—
47#4648—32no—
48#4647—32no—
49C24×C32C2311yescharacteristic
50C22×C32×C4C2312yes—
51C22×C3⋊Dic3—24no—
52C22×C3⋊Dic3C2×C414yes—
53C22×C3⋊Dic3C2312yes—
54C22×C3⋊Dic3C2311yescharacteristic
55C22×C3⋊Dic3C2311yescharacteristic
56C22×C3×Dic3C2312yes—
57C22×C3×Dic3C2312yes—
58C22×C3×Dic3C2312yes—
59C22×C3×Dic3C2312yes—
60C32×C22⋊C4—41no—
61#3757—41no—
62#3750—24no—
63C3×#217—24no—
64C3×#217C2×C418yes—
65C3×Dic3⋊C4—42no—
66C3×C4×Dic3—24no—
67#3724C2×C414yes—
68#3724C2×C414yes—
69Dic3⋊Dic3—42no—
70Dic32—24no—
71Dic32—24no—
72Dic32C2×C418yes—
73#2346—91noSylow
74C23×Dic3—32no—
75C23×Dic3—61no—
76C2×C3×C4⋊C4—32no—
77C2×C3×C22⋊C4—21no—
78C2×C3×C22⋊C4—32no—
79C2×C3×C22⋊C4—32no—
80C2×C3×C22⋊C4C2×D312yes—
81C2×C3×C42—32no—
82C2×#217—32no—
83C2×#217—61no—
84C2×#217C2×D312yes—
85C2×#217C2×D312yes—
86C2×C4⋊Dic3—32no—
87C2×Dic3⋊C4—32no—
88C2×Dic3⋊C4—32no—
89C2×Dic3⋊C4—32no—
90C2×Dic3⋊C4—32no—
91C2×Dic3⋊C4—32no—
92C2×Dic3⋊C4—62no—
93C2×Dic3⋊C4C2×D312yes—
94C2×C4×Dic3—32no—
95C2×C4×Dic3—32no—
96C2×C4×Dic3—32no—
97C2×C4×Dic3—32no—
98C2×C4×Dic3—32no—
99C2×C4×Dic3—32no—
100C2×C4×Dic3C2×D312yes—
101#877—316no—
102C3×#95—32no—
103C3×#95—32no—
104C3⋊#95—32no—
105C3⋊#95—32no—
106C3⋊#95—32no—
107C3⋊#95—32no—
108C3⋊#95—32no—
109C3⋊#95—32no—
110C3⋊#95—32no—
111C3⋊#95—32no—
112C3⋊#95—62no—
113C3⋊#95C2×D312yes—
114C3⋊#95C2×D312yes—
115C23×C32—21no—
116C23×C32—21no—
117C23×C32—22no—
118C23×C32—22no—
119C23×C32C22×C412yes—
120C23×C32C2411yescharacteristic
121C2×C32×C4—22no—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—28no—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3C22×C412yes—
130C2×C3⋊Dic3C22×C412yes—
131C2×C3⋊Dic3#4114yes—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3C22×C414yes—
142C2×C3×Dic3C22×C414yes—
143C2×C3×Dic3#4114yes—
144C2×#117—91no—
145#389—92no—
146#388—32no—
147#388—92no—
148#382—92no—
149#380—91no—
150C4×C4⋊C4—92no—
151C4×C22⋊C4—91no—
152#376—92no—
153C24×C3—21no—
154C24×C3C22×D312yes—
155C22×C3×C4—22no—
156C22×C3×C4—32no—
157C22×C3×C4—32no—
158C22×C3×C4—32no—
159C22×C3×C4—32no—
160C22×C3×C4C22×D312yes—
161C22×C3×C4C22×D312yes—
162C22×Dic3—32no—
163C22×Dic3—38no—
164C22×Dic3—32no—
165C22×Dic3—32no—
166C22×Dic3—32no—
167C22×Dic3—61no—
168C22×Dic3—61no—
169C22×Dic3—64no—
170C22×Dic3—62no—
171C22×Dic3—64no—
172C22×Dic3—64no—
173C22×Dic3—124no—
174C22×Dic3C22×D312yes—
175C22×Dic3C22×D312yes—
176C22×Dic3C22×D312yes—
177C22×Dic3C22×D312yes—
178C3×C4⋊C4—122no—
179C3×C22⋊C4—38no—
180C3×C22⋊C4—42no—
181C3×C22⋊C4—42no—
182C3×C22⋊C4—64no—
183C3×C42—64no—
184#217—24no—
185#217—122no—
186#217—122no—
187#217C4×D318yes—
188C4⋊Dic3—122no—
189Dic3⋊C4—38no—
190Dic3⋊C4—38no—
191Dic3⋊C4—42no—
192Dic3⋊C4—64no—
193Dic3⋊C4—64no—
194Dic3⋊C4—124no—
195Dic3⋊C4—122no—
196C4×Dic3—24no—
197C4×Dic3—38no—
198C4×Dic3—38no—
199C4×Dic3—64no—
200C4×Dic3—64no—
201C4×Dic3—64no—
202C4×Dic3—64no—
203C22×C32—22no—
204C22×C32—22no—
205C22×C32—22no—
206C22×C32—42no—
207C22×C32—42no—
208C22×C32C23×C411yescharacteristic
209C22×C32C2×#4112yes—
210C22×C32C2×#4112yes—
211C22×C32H(5,𝔽2)11yescharacteristic
212C22×C322−1+411yescharacteristic
213C32×C4—42no—
214C3⋊Dic3—22no—
215C3⋊Dic3—42no—
216C3⋊Dic3#11714yes—
217C3×Dic3—24no—
218C3×Dic3—24no—
219C3×Dic3—24no—
220C3×Dic3—42no—
221C23×C4—91no—
222#117—98no—
223C2×C4⋊C4—32no—
224C2×C4⋊C4—91no—
225C2×C4⋊C4—91no—
226C2×C4⋊C4—92no—
227C2×C4⋊C4—92no—
228C2×C22⋊C4—32no—
229C2×C22⋊C4—32no—
230C2×C22⋊C4—91no—
231C2×C22⋊C4D3211yescharacteristic
232C2×C42—32no—
233C2×C42—92no—
234C2×C42—92no—
235C2×C42—92no—
236#95—32no—
237#95—32no—
238#95—91no—
239#95—92no—
240#95—91no—
241#95—92no—
242#95—92no—
243C23×C3—22no—
244C23×C3—22no—
245C23×C3—22no—
246C23×C3—22no—
247C23×C3—22no—
248C23×C3—22no—
249C23×C3—22no—
250C23×C3—22no—
251C23×C3—21no—
252C23×C3—22no—
253C23×C3—42no—
254C23×C3—42no—
255C23×C3C2×C4×D314yes—
256C23×C3C23×D312yes—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4—22no—
262C2×C3×C4—22no—
263C2×C3×C4—34no—
264C2×C3×C4—34no—
265C2×C3×C4—34no—
266C2×C3×C4—42no—
267C2×C3×C4—42no—
268C2×C3×C4—42no—
269C2×C3×C4—62no—
270C2×C3×C4—62no—
271C2×C3×C4—62no—
272C2×C3×C4—62no—
273C2×C3×C4—62no—
274C2×C3×C4—62no—
275C2×C3×C4—62no—
276C2×C3×C4—62no—
277C2×C3×C4—62no—
278C2×Dic3—22no—
279C2×Dic3—22no—
280C2×Dic3—22no—
281C2×Dic3—22no—
282C2×Dic3—22no—
283C2×Dic3—22no—
284C2×Dic3—22no—
285C2×Dic3—22no—
286C2×Dic3—22no—
287C2×Dic3—34no—
288C2×Dic3—34no—
289C2×Dic3—34no—
290C2×Dic3—34no—
291C2×Dic3—62no—
292C2×Dic3—64no—
293C2×Dic3—62no—
294C2×Dic3—616no—
295C2×Dic3—62no—
296C2×Dic3—62no—
297C2×Dic3—62no—
298C2×Dic3—62no—
299C2×Dic3—62no—
300C2×Dic3—62no—
301C2×Dic3—62no—
302C2×Dic3—62no—
303C2×Dic3—128no—
304C2×Dic3—122no—
305C2×Dic3—122no—
306C2×Dic3—122no—
307C2×Dic3—122no—
308C2×Dic3C2×C4×D314yes—
309C2×Dic3C2×C4×D314yes—
310C2×Dic3#23714yes—
311C2×C32—42no—
312C2×C32C2×#11711yescharacteristic
313C2×C32C4×#4111yescharacteristic
314C2×C32#52011yescharacteristic
315C2×C32#55212yes—
316C2×C32#55512yes—
317C24C2×D3211yescharacteristic
318C22×C4—32no—
319C22×C4—32no—
320C22×C4—32no—
321C22×C4—32no—
322C22×C4—91no—
323C22×C4—91no—
324C22×C4—94no—
325C22×C4—92no—
326C22×C4—184no—
327C22×C4C2×D3212yes—
328C4⋊C4—94no—
329C4⋊C4—94no—
330C4⋊C4—122no—
331C4⋊C4—184no—
332C4⋊C4—362no—
333C22⋊C4—38no—
334C22⋊C4—41no—
335C22⋊C4—64no—
336C22⋊C4—361no—
337C42—64no—
338C42—98no—
339C42—184no—
340C42—184no—
341C22×C3—24no—
342C22×C3—24no—
343C22×C3—24no—
344C22×C3—24no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—22no—
348C22×C3—22no—
349C22×C3—21no—
350C22×C3—42no—
351C22×C3—42no—
352C22×C3—44no—
353C22×C3—44no—
354C22×C3—42no—
355C22×C3—42no—
356C22×C3—42no—
357C22×C3—42no—
358C22×C3C22×C4×D312yes—
359C22×C3C2×#23712yes—
360C22×C3#100412yes—
361C22×C3D3×#4112yes—
362C22×C3D3×#4112yes—
363C22×C3D3×#4112yes—
364C22×C3#101012yes—
365C3×C4—42no—
366C3×C4—42no—
367C3×C4—64no—
368C3×C4—64no—
369C3×C4—64no—
370C3×C4—82no—
371C3×C4—122no—
372Dic3—24no—
373Dic3—24no—
374Dic3—24no—
375Dic3—38no—
376Dic3—42no—
377Dic3—64no—
378Dic3—64no—
379Dic3—122no—
380Dic3—122no—
381Dic3—122no—
382Dic3—242no—
383C32#234611yescharacteristic, complemented, Sylow
384C23—21no—
385C23—22no—
386C23—22no—
387C23—21no—
388C23C4×D3212yes—
389C23C22×D3211yescharacteristic
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—34no—
394C2×C4—34no—
395C2×C4—34no—
396C2×C4—62no—
397C2×C4—62no—
398C2×C4—62no—
399C2×C4—62no—
400C2×C4—62no—
401C2×C4—62no—
402C2×C4—62no—
403C2×C4—62no—
404C2×C4—62no—
405C2×C4—92no—
406C2×C4—94no—
407C2×C4—92no—
408C2×C4—188no—
409C2×C4—182no—
410C2×C4—182no—
411C2×C4—182no—
412C2×C4—182no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—22no—
417C2×C3—22no—
418C2×C3—44no—
419C2×C3—44no—
420C2×C3D3×#11712yes—
421C2×C3C4×#23712yes—
422C2×C3#554612yes—
423C2×C3#561612yes—
424C2×C3#565012yes—
425C2×C3#567012yes—
426C2×C3#570812yes—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—42no—
431C22—42no—
432C22#6429811yescharacteristic
433C22C2×C4×D3211yescharacteristic
434C22D3×#23712yes—
435C22#6431212yes—
436C22#6433011yescharacteristic
437C4—42no—
438C4—64no—
439C4—64no—
440C4—64no—
441C4—94no—
442C4—122no—
443C4—182no—
444C4—362no—
445C3—21no—
446C3#7547312yescomplemented
447C2—42no—
448C2#1059405011yescharacteristic
449C2#1059405211yescharacteristic
450C2#1059411612yes—
451C2#1059487611yescharacteristic
452C2#1059519412yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#2346
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
6. #10591256C2semidirect
7. #10591245C2semidirect
8. #10591243C2semidirect
9. #10591239C2semidirect
22. #63957C4semidirect
383. C32#2346semidirect
446. C3#75473semidirect

Maximal subgroups

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

subgroupindex
C2×#639572
#105926412
C3×#49452
#105917052
#105917012
#105912562
#105912452
#105912432
#105912392
#754733