Finite Group Databasebeta

← #11802813

Subgroups — #11802813

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63900C211yesmaximal, characteristic
2#10592363C211yesmaximal, characteristic
3C3×#4654C212yesmaximal, complemented
4#10591367C212yesmaximal
5#10591269C212yesmaximal, complemented
6#10591249C212yesmaximal, complemented
7#10591233C212yesmaximal
8#10591219C211yesmaximal, characteristic
9#10591193C212yesmaximal, complemented
10#75296—32nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×#624C2211yescharacteristic
13C22×#624C2211yescharacteristic
14C2×#3752C2212yes—
15C2×C3×C4⋊Dic3C2212yes—
16C2×C3×Dic3⋊C4C2212yes—
17C2×C3×C4×Dic3C2212yes—
18C2×#3724C2212yes—
19C2×Dic3⋊Dic3C2212yes—
20C2×#3722C2212yes—
21C2×Dic32C2212yes—
22#63900C418yescomplemented
23C32×#95C2211yescharacteristic
24#63658C2212yes—
25#63658C2211yescharacteristic
26C3×C3⋊#95C2212yes—
27C3×C3⋊#95C2212yes—
28C3×C3⋊#95C2212yes—
29#63579C2212yes—
30#63579C2211yescharacteristic
31#63579C2212yes—
32#63579C2211yescharacteristic
33C2×D3×C4⋊C4—32no—
34C3×#387—32no—
35#4987—32no—
36#4980—32no—
37#4978—32no—
38C4×(C2×D3)⋊C4—32no—
39#4933—32no—
40#4667—32no—
41#4666—32no—
42#4664—32no—
43#4664—32no—
44#4664—61no—
45#4655—32no—
46#4654D312yescomplemented
47#4653—32no—
48#4652—32no—
49C23×C3⋊D3C2311yescharacteristic
50C22×C32×C4C2312yes—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3C2312yes—
53C22×C3⋊Dic3C2311yescharacteristic
54C2×C4×C3⋊D3—24no—
55C2×C4×C3⋊D3C2×C414yes—
56C22×C3×Dic3C2312yes—
57C22×C3×Dic3C2312yes—
58C22×C3×Dic3C2312yes—
59C22×C3×Dic3C2312yes—
60C2×#624—41no—
61C2×#624—41no—
62C2×#624—41no—
63C2×#624—41no—
64C2×#624C2×C414yes—
65C2×#624C2×C414yes—
66#3752—24no—
67C3×C4⋊Dic3C2×C418yes—
68C3×Dic3⋊C4—42no—
69C3×C4×Dic3—42no—
70#3724C2×C418yes—
71Dic3⋊Dic3—42no—
72#3722—24no—
73Dic32—42no—
74#2313—91noSylow
75C22×C4×D3—32no—
76C22×C4×D3—32no—
77C22×C4×D3—32no—
78C22×C4×D3—61no—
79C2×C3×C4⋊C4—32no—
80C2×C3×C4⋊C4—32no—
81C2×C3×C42—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⋊Dic3C2×D312yes—
89C2×Dic3⋊C4—32no—
90C2×Dic3⋊C4—32no—
91C2×Dic3⋊C4—32no—
92C2×Dic3⋊C4C2×D312yes—
93C2×C4×Dic3—32no—
94C2×C4×Dic3—32no—
95C2×C4×Dic3C2×D312yes—
96D3×C4⋊C4—316no—
97C3×#95—21no—
98C3×#95—32no—
99C3×#95—32no—
100C3×#95—32no—
101C3×#95C2×D312yes—
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—62no—
112C3⋊#95—61no—
113C3⋊#95C2×D312yes—
114C3⋊#95C2×D312yes—
115C3⋊#95C2×D312yes—
116C23×C32C2411yescharacteristic
117C22×C3⋊D3—21no—
118C22×C3⋊D3—21no—
119C22×C3⋊D3—22no—
120C22×C3⋊D3C22×C412yes—
121C22×C3⋊D3#4114yes—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C32×C4—22no—
125C2×C32×C4—22no—
126C2×C32×C4C22×C412yes—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3—22no—
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3C22×C412yes—
132C4×C3⋊D3—28no—
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×Dic3—22no—
143C2×C3×Dic3C22×C414yes—
144C2×C3×Dic3C22×C414yes—
145#624—44no—
146#624—44no—
147C22×C4⋊C4—91no—
148#387—32no—
149#387—92no—
150#387—92no—
151#387—92no—
152#381—91no—
153#381—91no—
154#380—92no—
155C4×C22⋊C4—92no—
156C23×D3—32no—
157C23×D3—61no—
158C22×C3×C4—21no—
159C22×C3×C4—22no—
160C22×C3×C4—32no—
161C22×C3×C4—32no—
162C22×C3×C4—32no—
163C22×C3×C4—32no—
164C22×C3×C4C22×D312yes—
165C22×C3×C4C22×D312yes—
166C22×C3×C4C22×D312yes—
167C22×Dic3—32no—
168C22×Dic3—32no—
169C22×Dic3—32no—
170C22×Dic3—61no—
171C22×Dic3—62no—
172C22×Dic3C22×D312yes—
173C22×Dic3C22×D312yes—
174C22×Dic3C22×D312yes—
175C22×Dic3C22×D312yes—
176C2×C4×D3—38no—
177C2×C4×D3—38no—
178C2×C4×D3—38no—
179C2×C4×D3—64no—
180C2×C4×D3—64no—
181C2×C4×D3—64no—
182C2×C4×D3—124no—
183C2×C4×D3—122no—
184C2×C4×D3—122no—
185C2×C4×D3—122no—
186C2×C4×D3—122no—
187C3×C4⋊C4—38no—
188C3×C4⋊C4—122no—
189C3×C42—122no—
190(C2×D3)⋊C4—64no—
191(C2×D3)⋊C4—64no—
192(C2×D3)⋊C4—64no—
193(C2×D3)⋊C4—64no—
194(C2×D3)⋊C4—124no—
195C4⋊Dic3—122no—
196C4⋊Dic3C4×D318yes—
197Dic3⋊C4—38no—
198Dic3⋊C4—38no—
199Dic3⋊C4—42no—
200Dic3⋊C4—122no—
201C4×Dic3—42no—
202C4×Dic3—122no—
203C4×Dic3—122no—
204C22×C32C23×C411yescharacteristic
205C22×C32C2×#4112yes—
206C22×C32H(5,𝔽2)11yescharacteristic
207C22×C32H(5,𝔽2)11yescharacteristic
208C22×C322−1+412yes—
209C2×C3⋊D3—22no—
210C2×C3⋊D3—22no—
211C2×C3⋊D3—24no—
212C2×C3⋊D3—24no—
213C2×C3⋊D3#11714yes—
214C32×C4—22no—
215C32×C4—42no—
216C3⋊Dic3—22no—
217C3⋊Dic3—42no—
218C3×Dic3—24no—
219C3×Dic3—24no—
220C3×Dic3—42no—
221C3×Dic3—42no—
222C23×C4—91no—
223C23×C4—91no—
224C23×C4—91no—
225C2×C4⋊C4—32no—
226C2×C4⋊C4—32no—
227C2×C4⋊C4—98no—
228C2×C4⋊C4—92no—
229C2×C4⋊C4—92no—
230C2×C22⋊C4—92no—
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—91no—
240#95—91no—
241#95—92no—
242#95—91no—
243#95D3211yescharacteristic
244C23×C3—21no—
245C23×C3C23×D312yes—
246C22×D3—34no—
247C22×D3—34no—
248C22×D3—34no—
249C22×D3—62no—
250C22×D3—64no—
251C22×D3—62no—
252C22×D3—62no—
253C22×D3—62no—
254C22×D3—62no—
255C22×D3—122no—
256C22×D3—121no—
257C22×D3—121no—
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—22no—
266C2×C3×C4—22no—
267C2×C3×C4—34no—
268C2×C3×C4—34no—
269C2×C3×C4—42no—
270C2×C3×C4—42no—
271C2×C3×C4—42no—
272C2×C3×C4—42no—
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×C4—62no—
282C2×C3×C4—62no—
283C2×C3×C4C2×C4×D314yes—
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—22no—
293C2×Dic3—22no—
294C2×Dic3—34no—
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—62no—
304C2×Dic3—122no—
305C2×Dic3—122no—
306C2×Dic3—122no—
307C2×Dic3—122no—
308C2×Dic3C2×C4×D314yes—
309C2×Dic3C2×C4×D314yes—
310C4×D3—616no—
311C4×D3—128no—
312C4×D3—128no—
313C4×D3—128no—
314C2×C32C2×#11711yescharacteristic
315C2×C32#51811yescharacteristic
316C2×C32#51911yescharacteristic
317C2×C32#53912yes—
318C2×C32#53912yes—
319C3⋊D3—24no—
320C24—91no—
321C22×C4—32no—
322C22×C4—32no—
323C22×C4—32no—
324C22×C4—32no—
325C22×C4—94no—
326C22×C4—94no—
327C22×C4—91no—
328C22×C4—94no—
329C22×C4—92no—
330C22×C4—184no—
331C22×C4—361no—
332C22×C4—361no—
333C22×C4—361no—
334C22×C4—361no—
335C22×C4C2×D3212yes—
336C22×C4C2×D3211yescharacteristic
337C4⋊C4—38no—
338C4⋊C4—98no—
339C4⋊C4—122no—
340C4⋊C4—362no—
341C22⋊C4—184no—
342C22⋊C4—184no—
343C42—122no—
344C42—362no—
345C22×C3—22no—
346C22×C3—21no—
347C22×C3—22no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3C22×C4×D312yes—
351C22×C3#100412yes—
352C22×C3#100712yes—
353C22×C3D3×#4112yes—
354C22×C3D3×#4112yes—
355C22×C3#100912yes—
356C22×C3#101012yes—
357C2×D3—38no—
358C2×D3—64no—
359C2×D3—64no—
360C2×D3—64no—
361C2×D3—64no—
362C2×D3—64no—
363C2×D3—64no—
364C2×D3—64no—
365C2×D3—122no—
366C2×D3—122no—
367C2×D3—124no—
368C2×D3—124no—
369C3×C4—24no—
370C3×C4—42no—
371C3×C4—42no—
372C3×C4—42no—
373C3×C4—64no—
374C3×C4—64no—
375C3×C4—82no—
376C3×C4—122no—
377C3×C4—122no—
378Dic3—24no—
379Dic3—24no—
380Dic3—42no—
381Dic3—42no—
382Dic3—64no—
383Dic3—122no—
384Dic3—122no—
385Dic3—122no—
386Dic3—242no—
387C32#231311yescharacteristic, complemented, Sylow
388C23—92no—
389C23—94no—
390C23—182no—
391C23—181no—
392C23—181no—
393C23C22×D3211yescharacteristic
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—34no—
399C2×C4—34no—
400C2×C4—62no—
401C2×C4—62no—
402C2×C4—62no—
403C2×C4—62no—
404C2×C4—62no—
405C2×C4—62no—
406C2×C4—62no—
407C2×C4—62no—
408C2×C4—62no—
409C2×C4—62no—
410C2×C4—92no—
411C2×C4—188no—
412C2×C4—182no—
413C2×C4—182no—
414C2×C4—182no—
415C2×C4—182no—
416C2×C4—364no—
417C2×C4—364no—
418C2×C4C4×D3212yes—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—22no—
423C2×C3—22no—
424C2×C3D3×#11712yes—
425C2×C3#554512yes—
426C2×C3#557212yes—
427C2×C3#563812yes—
428C2×C3#566012yes—
429C2×C3#569212yes—
430C2×C3#570712yes—
431D3—68no—
432D3—124no—
433C22—94no—
434C22—182no—
435C22—182no—
436C22—184no—
437C22—184no—
438C22#6429712yes—
439C22C2×C4×D3211yescharacteristic
440C22#6431212yes—
441C22#6431311yescharacteristic
442C22#6432011yescharacteristic
443C4—22no—
444C4—42no—
445C4—64no—
446C4—64no—
447C4—122no—
448C4—122no—
449C4—182no—
450C4—362no—
451C3—21no—
452C3#7529612yescomplemented
453C2—184no—
454C2#1059384811yescharacteristic
455C2#1059404112yes—
456C2#1059405211yescharacteristic
457C2#1059448112yes—
458C2#1059460611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32#2313
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. C3×#4654C2semidirect
5. #10591269C2semidirect
6. #10591249C2semidirect
9. #10591193C2semidirect
22. #63900C4semidirect
46. #4654D3semidirect
387. C32#2313semidirect
452. C3#75296semidirect

Maximal subgroups

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

subgroupindex
C2×#639002
#105923632
C3×#46542
#105913672
#105912692
#105912492
#105912332
#105912192
#105911932
#752963