Finite Group Databasebeta

← #11805271

Subgroups — #11805271

Order 1152.

1213 conjugacy classes of subgroups.

The subgroup lattice has 465 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63900C211yesmaximal, characteristic
2#10592366C211yesmaximal, characteristic
3C3×#4653C212yesmaximal, complemented
4#10591367C212yesmaximal
5#10591270C212yesmaximal, complemented
6#10591260C211yesmaximal, characteristic
7#10591256C212yesmaximal, complemented
8#10591243C212yesmaximal, complemented
9#10591233C212yesmaximal
10#74962—32nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×#624C2212yes—
13C2×#3752C2212yes—
14C2×#3750C2212yes—
15C2×C3×C4⋊Dic3C2212yes—
16C2×C3×Dic3⋊C4C2212yes—
17C2×C3×C4×Dic3C2212yes—
18C2×#3724C2211yescharacteristic
19C2×#3724C2211yescharacteristic
20C2×Dic3⋊Dic3C2212yes—
21C2×#3722C2211yescharacteristic
22C2×#3722C2211yescharacteristic
23C2×Dic32C2212yes—
24C2×Dic32C2212yes—
25#63900C418yescomplemented
26C32×#95C2211yescharacteristic
27#63658C2211yescharacteristic
28C3×C3⋊#95C2212yes—
29C3×C3⋊#95C2212yes—
30C3×C3⋊#95C2212yes—
31#63579C2212yes—
32#63579C2212yes—
33C2×D3×C4⋊C4—32no—
34C3×#387—32no—
35#4987—32no—
36#4980—32no—
37#4976—32no—
38C4×(C2×D3)⋊C4—32no—
39C4×Dic3⋊C4—32no—
40#4667—32no—
41#4667—32no—
42#4667—61no—
43#4666—32no—
44#4666—32no—
45#4654—32no—
46#4653D312yescomplemented
47#4649—32no—
48#4647—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—42no—
61C2×#624—42no—
62C2×#624C2×C418yes—
63#3752—24no—
64#3750—24no—
65C3×C4⋊Dic3C2×C418yes—
66C3×Dic3⋊C4—42no—
67C3×C4×Dic3—42no—
68#3724C2×C414yes—
69#3724C2×C414yes—
70Dic3⋊Dic3—42no—
71#3722—22no—
72#3722Q814yes—
73Dic32—24no—
74Dic32—42no—
75#2345—91noSylow
76C22×C4×D3—32no—
77C22×C4×D3—32no—
78C22×C4×D3—32no—
79C22×C4×D3—61no—
80C2×C3×C4⋊C4—32no—
81C2×C3×C4⋊C4—32no—
82C2×C3×C42—32no—
83C2×(C2×D3)⋊C4—32no—
84C2×(C2×D3)⋊C4—32no—
85C2×(C2×D3)⋊C4—32no—
86C2×(C2×D3)⋊C4—32no—
87C2×(C2×D3)⋊C4—62no—
88C2×C4⋊Dic3—32no—
89C2×C4⋊Dic3C2×D312yes—
90C2×Dic3⋊C4—32no—
91C2×Dic3⋊C4—32no—
92C2×Dic3⋊C4—32no—
93C2×Dic3⋊C4—32no—
94C2×Dic3⋊C4—32no—
95C2×Dic3⋊C4—62no—
96C2×Dic3⋊C4C2×D312yes—
97C2×C4×Dic3—32no—
98C2×C4×Dic3—32no—
99C2×C4×Dic3—32no—
100C2×C4×Dic3—32no—
101C2×C4×Dic3C2×D312yes—
102D3×C4⋊C4—316no—
103C3×#95—21no—
104C3×#95—32no—
105C3×#95—32no—
106C3×#95—32no—
107C3×#95C2×D312yes—
108C3⋊#95—32no—
109C3⋊#95—32no—
110C3⋊#95—32no—
111C3⋊#95—32no—
112C3⋊#95—32no—
113C3⋊#95—61no—
114C3⋊#95C2×D312yes—
115C3⋊#95C2×D312yes—
116C3⋊#95C2×D312yes—
117C23×C32C2411yescharacteristic
118C22×C3⋊D3—22no—
119C22×C3⋊D3—22no—
120C22×C3⋊D3C22×C412yes—
121C22×C3⋊D3C2×Q812yes—
122C22×C3⋊D3#4112yes—
123C2×C32×C4—22no—
124C2×C32×C4—22no—
125C2×C32×C4—22no—
126C2×C32×C4—22no—
127C2×C32×C4C22×C412yes—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3—22no—
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3C22×C412yes—
132C2×C3⋊Dic3#4114yes—
133C4×C3⋊D3—28no—
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—
145C2×C3×Dic3C2×Q814yes—
146#624—48no—
147C22×C4⋊C4—91no—
148#389—92no—
149#387—32no—
150#387—92no—
151#380—92no—
152#380—91no—
153C4×C4⋊C4—92no—
154C4×C22⋊C4—91no—
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—38no—
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—64no—
201Dic3⋊C4—64no—
202Dic3⋊C4—124no—
203Dic3⋊C4—122no—
204C4×Dic3—42no—
205C4×Dic3—64no—
206C4×Dic3—64no—
207C4×Dic3—122no—
208C4×Dic3—122no—
209C22×C32C23×C411yescharacteristic
210C22×C32C22×Q811yescharacteristic
211C22×C32C2×#4112yes—
212C22×C32C2×#4111yescharacteristic
213C22×C32H(5,𝔽2)12yes—
214C2×C3⋊D3—22no—
215C2×C3⋊D3—22no—
216C2×C3⋊D3—24no—
217C2×C3⋊D3—24no—
218C2×C3⋊D3C4×Q814yes—
219C32×C4—22no—
220C32×C4—42no—
221C3⋊Dic3—42no—
222C3⋊Dic3#11714yes—
223C3×Dic3—24no—
224C3×Dic3—24no—
225C3×Dic3—24no—
226C3×Dic3—42no—
227C23×C4—92no—
228C23×C4—91no—
229C2×C4⋊C4—32no—
230C2×C4⋊C4—32no—
231C2×C4⋊C4—98no—
232C2×C4⋊C4—91no—
233C2×C4⋊C4—91no—
234C2×C4⋊C4—92no—
235C2×C4⋊C4—92no—
236C2×C22⋊C4—91no—
237C2×C22⋊C4—91no—
238C2×C22⋊C4—92no—
239C2×C42—32no—
240C2×C42—92no—
241C2×C42—92no—
242#95—32no—
243#95—32no—
244#95—32no—
245#95—92no—
246#95—92no—
247#95—91no—
248#95D3211yescharacteristic
249C23×C3—21no—
250C23×C3C23×D312yes—
251C22×D3—34no—
252C22×D3—34no—
253C22×D3—34no—
254C22×D3—62no—
255C22×D3—62no—
256C22×D3—62no—
257C22×D3—62no—
258C22×D3—62no—
259C22×D3—62no—
260C22×D3—62no—
261C22×D3—122no—
262C22×D3—122no—
263C2×C3×C4—22no—
264C2×C3×C4—22no—
265C2×C3×C4—22no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—22no—
272C2×C3×C4—34no—
273C2×C3×C4—34no—
274C2×C3×C4—34no—
275C2×C3×C4—42no—
276C2×C3×C4—42no—
277C2×C3×C4—42no—
278C2×C3×C4—42no—
279C2×C3×C4—62no—
280C2×C3×C4—62no—
281C2×C3×C4—62no—
282C2×C3×C4—62no—
283C2×C3×C4—62no—
284C2×C3×C4—62no—
285C2×C3×C4—62no—
286C2×C3×C4—62no—
287C2×C3×C4—62no—
288C2×C3×C4C2×C4×D314yes—
289C2×Dic3—22no—
290C2×Dic3—22no—
291C2×Dic3—22no—
292C2×Dic3—22no—
293C2×Dic3—22no—
294C2×Dic3—22no—
295C2×Dic3—22no—
296C2×Dic3—22no—
297C2×Dic3—22no—
298C2×Dic3—34no—
299C2×Dic3—34no—
300C2×Dic3—34no—
301C2×Dic3—62no—
302C2×Dic3—64no—
303C2×Dic3—62no—
304C2×Dic3—62no—
305C2×Dic3—62no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—62no—
309C2×Dic3—122no—
310C2×Dic3—122no—
311C2×Dic3—122no—
312C2×Dic3C2×C4×D314yes—
313C2×Dic3C2×C4×D314yes—
314C2×Dic3D3×Q814yes—
315C4×D3—616no—
316C4×D3—128no—
317C4×D3—128no—
318C4×D3—128no—
319C2×C32C2×#11711yescharacteristic
320C2×C32C2×C4×Q811yescharacteristic
321C2×C32#51811yescharacteristic
322C2×C32#55312yes—
323C2×C32#55412yes—
324C3⋊D3—24no—
325C24—91no—
326C22×C4—32no—
327C22×C4—32no—
328C22×C4—32no—
329C22×C4—32no—
330C22×C4—98no—
331C22×C4—91no—
332C22×C4—94no—
333C22×C4—92no—
334C22×C4—184no—
335C22×C4—362no—
336C22×C4—362no—
337C22×C4C2×D3212yes—
338C22×C4C2×D3211yescharacteristic
339C4⋊C4—38no—
340C4⋊C4—94no—
341C4⋊C4—94no—
342C4⋊C4—122no—
343C4⋊C4—184no—
344C4⋊C4—362no—
345C22⋊C4—94no—
346C22⋊C4—184no—
347C22⋊C4—182no—
348C42—122no—
349C42—184no—
350C42—362no—
351C22×C3—21no—
352C22×C3—22no—
353C22×C3—22no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3C22×C4×D312yes—
357C22×C3#100412yes—
358C22×C3C2×D3×Q812yes—
359C22×C3D3×#4112yes—
360C22×C3D3×#4112yes—
361C22×C3D3×#4112yes—
362C22×C3#100912yes—
363C2×D3—38no—
364C2×D3—64no—
365C2×D3—64no—
366C2×D3—64no—
367C2×D3—64no—
368C2×D3—64no—
369C2×D3—64no—
370C2×D3—64no—
371C2×D3—122no—
372C2×D3—124no—
373C2×D3—124no—
374C2×D3—122no—
375C3×C4—24no—
376C3×C4—42no—
377C3×C4—42no—
378C3×C4—42no—
379C3×C4—64no—
380C3×C4—64no—
381C3×C4—64no—
382C3×C4—82no—
383C3×C4—122no—
384Dic3—24no—
385Dic3—24no—
386Dic3—24no—
387Dic3—38no—
388Dic3—42no—
389Dic3—64no—
390Dic3—122no—
391Dic3—122no—
392Dic3—242no—
393C32#234511yescharacteristic, complemented, Sylow
394C23—92no—
395C23—92no—
396C23—92no—
397C23—182no—
398C23—182no—
399C23C22×D3211yescharacteristic
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—34no—
405C2×C4—34no—
406C2×C4—34no—
407C2×C4—62no—
408C2×C4—62no—
409C2×C4—62no—
410C2×C4—62no—
411C2×C4—62no—
412C2×C4—62no—
413C2×C4—62no—
414C2×C4—62no—
415C2×C4—62no—
416C2×C4—92no—
417C2×C4—94no—
418C2×C4—188no—
419C2×C4—182no—
420C2×C4—182no—
421C2×C4—182no—
422C2×C4—368no—
423C2×C4C4×D3212yes—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—22no—
427C2×C3—22no—
428C2×C3—21no—
429C2×C3D3×#11712yes—
430C2×C3#554512yes—
431C2×C3C4×D3×Q812yes—
432C2×C3#563612yes—
433C2×C3#566112yes—
434C2×C3#569012yes—
435C2×C3#570912yes—
436D3—68no—
437D3—124no—
438C22—94no—
439C22—182no—
440C22—184no—
441C22—184no—
442C22—182no—
443C22C2×C4×D3211yescharacteristic
444C22#6430712yes—
445C22#6431212yes—
446C22#6431211yescharacteristic
447C22D32×Q811yescharacteristic
448C4—22no—
449C4—42no—
450C4—64no—
451C4—64no—
452C4—64no—
453C4—94no—
454C4—122no—
455C4—362no—
456C3—21no—
457C3#7496212yescomplemented
458C2—184no—
459C2#1059399611yescharacteristic
460C2#1059405211yescharacteristic
461C2#1059415712yes—
462C2#1059436311yescharacteristic
463C2#1059439512yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32#2345
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. C3×#4653C2semidirect
5. #10591270C2semidirect
7. #10591256C2semidirect
8. #10591243C2semidirect
25. #63900C4semidirect
46. #4653D3semidirect
393. C32#2345semidirect
457. C3#74962semidirect

Maximal subgroups

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

subgroupindex
C2×#639002
#105923662
C3×#46532
#105913672
#105912702
#105912602
#105912562
#105912432
#105912332
#749623