Finite Group Databasebeta

← #11807870

Subgroups — #11807870

Order 1152.

1037 conjugacy classes of subgroups.

The subgroup lattice has 455 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63865C211yesmaximal, characteristic
2#10592363C211yesmaximal, characteristic
3C3×#4655C212yesmaximal, complemented
4#10591325C211yesmaximal, characteristic
5#10591265C212yesmaximal, complemented
6#10591259C212yesmaximal
7#10591249C212yesmaximal, complemented
8#10591194C212yesmaximal
9#10591191C212yesmaximal, complemented
10#74976—32nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×#627C2211yescharacteristic
13C2×#3752C2212yes—
14C2×C3×C4⋊Dic3C2212yes—
15C2×C3×Dic3⋊C4C2212yes—
16C2×C3×C4×Dic3C2212yes—
17C2×#3724C2211yescharacteristic
18C2×Dic3⋊Dic3C2212yes—
19C2×Dic3⋊Dic3C2212yes—
20C2×#3722C2211yescharacteristic
21C2×#3722C2211yescharacteristic
22C2×#3722C2212yes—
23C2×Dic32C2212yes—
24#63865C418yescomplemented
25C32×#95C2211yescharacteristic
26#63658C2212yes—
27#63658C2211yescharacteristic
28C3×C3⋊#95C2212yes—
29C3×C3⋊#95C2212yes—
30C3×C3⋊#95C2212yes—
31#63579C2212yes—
32#63579C2212yes—
33C2×#896—32no—
34C3×#387—32no—
35#4987—32no—
36#4984—32no—
37#4976—32no—
38#4940—32no—
39#4929—32no—
40#4670—32no—
41#4670—32no—
42#4669—32no—
43#4664—32no—
44#4664—61no—
45#4655—32no—
46#4655D312yescomplemented
47#4652—32no—
48#4646—32no—
49C23×C3⋊D3C2311yescharacteristic
50C22×C32×C4C2312yes—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3C2312yes—
53C22×C3⋊Dic3C2311yescharacteristic
54C2×C4×C3⋊D3—42no—
55C2×C4×C3⋊D3C2×C414yes—
56C22×C3×Dic3C2312yes—
57C22×C3×Dic3C2312yes—
58C22×C3×Dic3C2312yes—
59C22×C3×Dic3C2312yes—
60C2×#627—42no—
61C2×#627C2×C414yes—
62#3752—42no—
63C3×C4⋊Dic3—42no—
64C3×Dic3⋊C4C2×C418yes—
65C3×C4×Dic3—42no—
66#3724C2×C414yes—
67Dic3⋊Dic3—42no—
68Dic3⋊Dic3—42no—
69#3722—41no—
70#3722—41no—
71#3722C2×C418yes—
72Dic32—42no—
73#2378—91noSylow
74C22×C4×D3—32no—
75C22×C4×D3—61no—
76C22×Dic6—32no—
77C2×C3×C4⋊C4—32no—
78C2×C3×C4⋊C4—32no—
79C2×C3×C42—32no—
80C2×(C2×D3)⋊C4—32no—
81C2×(C2×D3)⋊C4—32no—
82C2×(C2×D3)⋊C4—32no—
83C2×(C2×D3)⋊C4—32no—
84C2×(C2×D3)⋊C4—32no—
85C2×(C2×D3)⋊C4—32no—
86C2×(C2×D3)⋊C4—62no—
87C2×C4⋊Dic3—32no—
88C2×C4⋊Dic3—32no—
89C2×C4⋊Dic3C2×D312yes—
90C2×Dic3⋊C4—32no—
91C2×Dic3⋊C4—32no—
92C2×Dic3⋊C4—32no—
93C2×Dic3⋊C4C2×D312yes—
94C2×C4×Dic3—32no—
95C2×C4×Dic3—32no—
96C2×C4×Dic3C2×D312yes—
97#896—316no—
98C3×#95—21no—
99C3×#95—32no—
100C3×#95—32no—
101C3×#95—32no—
102C3×#95C2×D312yes—
103C3⋊#95—32no—
104C3⋊#95—32no—
105C3⋊#95—32no—
106C3⋊#95—32no—
107C3⋊#95—32no—
108C3⋊#95—32no—
109C3⋊#95—32no—
110C3⋊#95—62no—
111C3⋊#95—61no—
112C3⋊#95C2×D312yes—
113C3⋊#95C2×D312yes—
114C3⋊#95C2×D312yes—
115C23×C32C2411yescharacteristic
116C22×C3⋊D3—22no—
117C22×C3⋊D3—21no—
118C22×C3⋊D3—22no—
119C22×C3⋊D3—21no—
120C22×C3⋊D3C22×C412yes—
121C2×C32×C4—22no—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C32×C4—22no—
125C2×C32×C4C22×C412yes—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3—22no—
130C2×C3⋊Dic3C22×C412yes—
131C4×C3⋊D3—44no—
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×Dic3—22no—
142C2×C3×Dic3C22×C414yes—
143C2×C3×Dic3C22×C414yes—
144#627—44no—
145C2×C22⋊Q8—91no—
146#391—92no—
147#389—92no—
148#388—92no—
149#388—92no—
150#387—32no—
151#387—92no—
152#381—91no—
153#380—91no—
154C23×D3—32no—
155C23×D3—61no—
156C22×C3×C4—21no—
157C22×C3×C4—22no—
158C22×C3×C4—32no—
159C22×C3×C4—32no—
160C22×C3×C4—32no—
161C22×C3×C4—32no—
162C22×C3×C4C22×D312yes—
163C22×C3×C4C22×D312yes—
164C22×C3×C4C22×D312yes—
165C22×Dic3—32no—
166C22×Dic3—32no—
167C22×Dic3—32no—
168C22×Dic3—61no—
169C22×Dic3—62no—
170C22×Dic3C22×D312yes—
171C22×Dic3C22×D312yes—
172C22×Dic3C22×D312yes—
173C22×Dic3C22×D312yes—
174C2×C4×D3—38no—
175C2×C4×D3—64no—
176C2×C4×D3—122no—
177C2×C4×D3—122no—
178C2×C4×D3—124no—
179C2×Dic6—38no—
180C2×Dic6—122no—
181C2×Dic6—122no—
182C3×C4⋊C4—38no—
183C3×C4⋊C4—122no—
184C3×C42—122no—
185(C2×D3)⋊C4—38no—
186(C2×D3)⋊C4—38no—
187(C2×D3)⋊C4—122no—
188(C2×D3)⋊C4—122no—
189(C2×D3)⋊C4—122no—
190(C2×D3)⋊C4—122no—
191(C2×D3)⋊C4—124no—
192C4⋊Dic3—42no—
193C4⋊Dic3—122no—
194C4⋊Dic3—122no—
195Dic3⋊C4—38no—
196Dic3⋊C4—122no—
197Dic3⋊C4—122no—
198Dic3⋊C4C4×D318yes—
199C4×Dic3—42no—
200C4×Dic3—122no—
201C4×Dic3—122no—
202C22×C32C23×C411yescharacteristic
203C22×C32H(5,𝔽2)12yes—
204C22×C32H(5,𝔽2)11yescharacteristic
205C22×C322−1+412yes—
206C22×C322−1+411yescharacteristic
207C2×C3⋊D3—22no—
208C2×C3⋊D3—22no—
209C2×C3⋊D3—22no—
210C2×C3⋊D3—42no—
211C2×C3⋊D3—42no—
212C32×C4—22no—
213C32×C4—42no—
214C3⋊Dic3—22no—
215C3⋊Dic3—42no—
216C3×Dic3—24no—
217C3×Dic3—24no—
218C3×Dic3—42no—
219C3×Dic3—42no—
220C22×Q8—91no—
221C23×C4—91no—
222C22⋊Q8—98no—
223C2×C4⋊C4—32no—
224C2×C4⋊C4—32no—
225C2×C4⋊C4—91no—
226C2×C4⋊C4—92no—
227C2×C4⋊C4—92no—
228C2×C22⋊C4—92no—
229C2×C22⋊C4—91no—
230C2×C22⋊C4—91no—
231C2×C22⋊C4—92no—
232C2×C42—32no—
233C2×C42—92no—
234#95—32no—
235#95—32no—
236#95—32no—
237#95—92no—
238#95—92no—
239#95—92no—
240#95—91no—
241#95D3211yescharacteristic
242C23×C3—21no—
243C23×C3C23×D312yes—
244C22×D3—34no—
245C22×D3—62no—
246C22×D3—64no—
247C22×D3—62no—
248C22×D3—62no—
249C22×D3—62no—
250C22×D3—62no—
251C22×D3—62no—
252C22×D3—62no—
253C22×D3—122no—
254C22×D3—121no—
255C22×D3—121no—
256C2×C3×C4—22no—
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—22no—
264C2×C3×C4—22no—
265C2×C3×C4—34no—
266C2×C3×C4—34no—
267C2×C3×C4—42no—
268C2×C3×C4—42no—
269C2×C3×C4—42no—
270C2×C3×C4—42no—
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×C3×C4—62no—
279C2×C3×C4—62no—
280C2×C3×C4—62no—
281C2×C3×C4C2×C4×D314yes—
282C2×Dic3—22no—
283C2×Dic3—22no—
284C2×Dic3—22no—
285C2×Dic3—22no—
286C2×Dic3—22no—
287C2×Dic3—22no—
288C2×Dic3—22no—
289C2×Dic3—22no—
290C2×Dic3—22no—
291C2×Dic3—22no—
292C2×Dic3—34no—
293C2×Dic3—62no—
294C2×Dic3—62no—
295C2×Dic3—62no—
296C2×Dic3—62no—
297C2×Dic3—62no—
298C2×Dic3—62no—
299C2×Dic3—62no—
300C2×Dic3—62no—
301C2×Dic3—62no—
302C2×Dic3—122no—
303C2×Dic3—122no—
304C2×Dic3—122no—
305C2×Dic3—122no—
306C2×Dic3C2×C4×D314yes—
307C2×Dic3C2×C4×D314yes—
308C4×D3—128no—
309C4×D3—128no—
310Dic6—128no—
311C2×C32#51811yescharacteristic
312C2×C32#51911yescharacteristic
313C2×C32#52011yescharacteristic
314C2×C32#56212yes—
315C2×C32#56312yes—
316C3⋊D3—42no—
317C24—91no—
318C2×Q8—94no—
319C2×Q8—362no—
320C22×C4—32no—
321C22×C4—32no—
322C22×C4—32no—
323C22×C4—32no—
324C22×C4—91no—
325C22×C4—94no—
326C22×C4—92no—
327C22×C4—362no—
328C22×C4C2×D3212yes—
329C22×C4C2×D3211yescharacteristic
330C4⋊C4—38no—
331C4⋊C4—94no—
332C4⋊C4—122no—
333C4⋊C4—362no—
334C4⋊C4—362no—
335C22⋊C4—98no—
336C22⋊C4—362no—
337C22⋊C4—361no—
338C22⋊C4—361no—
339C42—122no—
340C42—362no—
341C22×C3—22no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—22no—
345C22×C3—21no—
346C22×C3C22×C4×D312yes—
347C22×C3#100412yes—
348C22×C3#100712yes—
349C22×C3#100912yes—
350C22×C3#100912yes—
351C22×C3#101012yes—
352C22×C3#101012yes—
353C2×D3—64no—
354C2×D3—64no—
355C2×D3—64no—
356C2×D3—64no—
357C2×D3—122no—
358C2×D3—122no—
359C2×D3—124no—
360C2×D3—124no—
361C2×D3—122no—
362C2×D3—122no—
363C2×D3—122no—
364C2×D3—122no—
365C3×C4—24no—
366C3×C4—42no—
367C3×C4—42no—
368C3×C4—42no—
369C3×C4—64no—
370C3×C4—64no—
371C3×C4—82no—
372C3×C4—122no—
373C3×C4—122no—
374Dic3—24no—
375Dic3—24no—
376Dic3—42no—
377Dic3—42no—
378Dic3—64no—
379Dic3—122no—
380Dic3—122no—
381Dic3—122no—
382Dic3—242no—
383C32#237811yescharacteristic, complemented, Sylow
384C23—92no—
385C23—182no—
386C23—181no—
387C23—182no—
388C23—181no—
389C23C22×D3211yescharacteristic
390Q8—364no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—34no—
396C2×C4—34no—
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—62no—
406C2×C4—62no—
407C2×C4—92no—
408C2×C4—182no—
409C2×C4—182no—
410C2×C4—182no—
411C2×C4—182no—
412C2×C4—364no—
413C2×C4C4×D3212yes—
414C2×C3—21no—
415C2×C3—22no—
416C2×C3—22no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3#552312yes—
420C2×C3#554512yes—
421C2×C3#557212yes—
422C2×C3#564612yes—
423C2×C3#566712yes—
424C2×C3#570012yes—
425C2×C3#571212yes—
426D3—124no—
427D3—124no—
428C22—182no—
429C22—182no—
430C22—182no—
431C22—362no—
432C22—362no—
433C22#6429712yes—
434C22C2×C4×D3211yescharacteristic
435C22#6430911yescharacteristic
436C22#6431412yes—
437C22#6432011yescharacteristic
438C4—22no—
439C4—42no—
440C4—64no—
441C4—64no—
442C4—122no—
443C4—122no—
444C4—182no—
445C4—362no—
446C3—21no—
447C3#7497612yescomplemented
448C2—362no—
449C2#1059384811yescharacteristic
450C2#1059425112yes—
451C2#1059425611yescharacteristic
452C2#1059450012yes—
453C2#1059451111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32#2378
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. C3×#4655C2semidirect
5. #10591265C2semidirect
7. #10591249C2semidirect
9. #10591191C2semidirect
24. #63865C4semidirect
46. #4655D3semidirect
383. C32#2378semidirect
447. C3#74976semidirect

Maximal subgroups

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

subgroupindex
C2×#638652
#105923632
C3×#46552
#105913252
#105912652
#105912592
#105912492
#105911942
#105911912
#749763