Finite Group Databasebeta

← #11803116

Subgroups — #11803116

Order 1152.

1620 conjugacy classes of subgroups.

The subgroup lattice has 405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic
2C32×#380C211yesmaximal, characteristic, complemented
3#10592910C211yesmaximal, characteristic, complemented
4#10592689C212yesmaximal, complemented
5#10592675C212yesmaximal, complemented
6#10592656C212yesmaximal
7#10592643C212yesmaximal, complemented
8#10592366C211yesmaximal, characteristic, complemented
9#10592363C211yesmaximal, characteristic, complemented
10#10592348C211yesmaximal, characteristic, complemented
11#10592347C211yesmaximal, characteristic, complemented
12#73870—34nomaximal
13C23×C32×C4C2211yescharacteristic
14C22×#638C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C2×C32×C4⋊C4C2212yes—
17C2×C32×C22⋊C4C2212yes—
18C2×#3757C2212yes—
19C2×#3757C2211yescharacteristic
20C4×#638C418yescomplemented
21C2×#3752C2212yes—
22C2×#3752C2212yes—
23C2×#3752C2211yescharacteristic
24C2×#3750C2212yes—
25C2×#3750C2212yes—
26C2×#3750C2211yescharacteristic
27C2×C4×C3⋊Dic3C2212yes—
28C2×C4×C3⋊Dic3C2212yes—
29C2×C4×C3⋊Dic3C2211yescharacteristic
30C32×#95C2211yescharacteristic
31C32×#95C2211yescharacteristic
32#63658C2211yescharacteristic
33#63658C2212yes—
34#63658C2211yescharacteristic
35#63658C2212yes—
36#63658C2212yes—
37C2×C4×#67—34no—
38C3×#380D314yescomplemented
39#5211—34no—
40#4990—38no—
41#4976—38no—
42#4957—38no—
43#4944—38no—
44#4667—34no—
45#4664—34no—
46#4649—34no—
47#4648—34no—
48C24×C32C2311yescharacteristic
49C23×C3⋊D3C2311yescharacteristic
50C22×C32×C4—42no—
51C22×C32×C4C2×C414yes—
52C22×C32×C4C2312yes—
53C22×C32×C4C2312yes—
54C22×C32×C4C2311yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C2×#638—24no—
57C2×#638C2×C414yes—
58C22×C3⋊Dic3C2312yes—
59C22×C3⋊Dic3C2312yes—
60C22×C3⋊Dic3C2311yescharacteristic
61C22×C3⋊Dic3C2311yescharacteristic
62C22×C3⋊Dic3C2311yescharacteristic
63C2×C4×C3⋊D3—42no—
64C2×C4×C3⋊D3C2×C414yes—
65C32×C4⋊C4—42no—
66C32×C22⋊C4—42no—
67#3757—42no—
68#3757C2×C414yes—
69#3752—42no—
70#3752—42no—
71#3752C2×C414yes—
72#3750—24no—
73#3750—42no—
74#3750C2×C414yes—
75C4×C3⋊Dic3—24no—
76C4×C3⋊Dic3—42no—
77C4×C3⋊Dic3C2×C414yes—
78#2319—91noSylow
79C23×C3×C4C2×D314yes—
80C22×#67—34no—
81C22×C4×D3—34no—
82C2×C3×C4⋊C4C2×D318yes—
83C2×C3×C22⋊C4C2×D318yes—
84C2×#217—34no—
85C2×#217—38no—
86C4×#67—332no—
87C2×(C2×D3)⋊C4—34no—
88C2×(C2×D3)⋊C4—38no—
89C2×(C2×D3)⋊C4—38no—
90C2×Dic3⋊C4—34no—
91C2×Dic3⋊C4—38no—
92C2×Dic3⋊C4—38no—
93C2×C4×Dic3—34no—
94C2×C4×Dic3—38no—
95C2×C4×Dic3—38no—
96C3×#95C2×D314yes—
97C3×#95C2×D314yes—
98C3⋊#95—34no—
99C3⋊#95—38no—
100C3⋊#95—34no—
101C3⋊#95—38no—
102C3⋊#95—38no—
103C23×C32—22no—
104C23×C32—22no—
105C23×C32—21no—
106C23×C32—21no—
107C23×C32C22×C412yes—
108C23×C32C2411yescharacteristic
109C22×C3⋊D3—22no—
110C22×C3⋊D3—21no—
111C22×C3⋊D3—22no—
112C22×C3⋊D3—21no—
113C22×C3⋊D3C22×C412yes—
114C2×C32×C4—22no—
115C2×C32×C4—22no—
116C2×C32×C4—22no—
117C2×C32×C4—22no—
118C2×C32×C4—22no—
119C2×C32×C4—22no—
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4—44no—
123C2×C32×C4C22×C412yes—
124C2×C32×C4C22×C412yes—
125#638—28no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—22no—
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3C22×C412yes—
136C2×C3⋊Dic3C22×C412yes—
137C2×C3⋊Dic3C22×C412yes—
138C2×C3⋊Dic3#4114yes—
139C4×C3⋊D3—44no—
140C2×C4×D4—91no—
141#390—92no—
142#389—92no—
143#388—92no—
144#388—92no—
145#381—91no—
146#381—91no—
147#380—91no—
148#380C3⋊D311yescharacteristic, complemented
149C4×C4⋊C4—91no—
150#376—91no—
151C24×C3C22×D314yes—
152C23×D3—34no—
153C22×C3×C4—48no—
154C22×C3×C4C4×D3116yes—
155C22×C3×C4C22×D318yes—
156C22×C3×C4C22×D318yes—
157C22×C3×C4C22×D314yes—
158C22×C3×C4C22×D314yes—
159C2×#67—316no—
160C2×#67—616no—
161C22×Dic3—34no—
162C22×Dic3—34no—
163C22×Dic3—34no—
164C22×Dic3—38no—
165C22×Dic3—38no—
166C2×C4×D3—316no—
167C2×C4×D3—128no—
168C3×C4⋊C4—48no—
169C3×C22⋊C4—48no—
170#217—316no—
171#217—128no—
172(C2×D3)⋊C4—316no—
173(C2×D3)⋊C4—128no—
174(C2×D3)⋊C4—128no—
175Dic3⋊C4—316no—
176Dic3⋊C4—616no—
177Dic3⋊C4—128no—
178C4×Dic3—316no—
179C4×Dic3—616no—
180C4×Dic3—128no—
181C22×C32—22no—
182C22×C32—22no—
183C22×C32—22no—
184C22×C32—42no—
185C22×C32—42no—
186C22×C32C23×C411yescharacteristic
187C22×C32C2×#4112yes—
188C22×C32H(5,𝔽2)12yes—
189C22×C32H(5,𝔽2)11yescharacteristic
190C22×C322−1+411yescharacteristic
191C2×C3⋊D3—22no—
192C2×C3⋊D3—22no—
193C2×C3⋊D3—22no—
194C2×C3⋊D3—42no—
195C2×C3⋊D3—42no—
196C32×C4—22no—
197C32×C4—22no—
198C32×C4—42no—
199C32×C4—42no—
200C3⋊Dic3—22no—
201C3⋊Dic3—22no—
202C3⋊Dic3—42no—
203C3⋊Dic3—42no—
204C3⋊Dic3#11714yes—
205C22×D4—91no—
206C23×C4—91no—
207C23×C4C2×C3⋊D311yescharacteristic
208C4×D4—98no—
209C2×C4⋊C4—91no—
210C2×C4⋊C4—92no—
211C2×C4⋊C4—92no—
212C2×C4⋊C4C2×C3⋊D312yes—
213C2×C22⋊C4—91no—
214C2×C22⋊C4—91no—
215C2×C22⋊C4—92no—
216C2×C22⋊C4—92no—
217C2×C22⋊C4—92no—
218C2×C22⋊C4C2×C3⋊D312yes—
219C2×C42—91no—
220C2×C42—92no—
221C2×C42—92no—
222#95—91no—
223#95—92no—
224#95—91no—
225#95—92no—
226#95—92no—
227#95C2×C3⋊D311yescharacteristic
228#95C2×C3⋊D311yescharacteristic
229C23×C3—28no—
230C23×C3—24no—
231C23×C3—24no—
232C23×C3—28no—
233C23×C3C2×C4×D318yes—
234C23×C3C23×D314yes—
235C22×D3—38no—
236C22×D3—64no—
237C22×D3—68no—
238C22×D3—64no—
239C22×D3—68no—
240C2×C3×C4—28no—
241C2×C3×C4—28no—
242C2×C3×C4—28no—
243C2×C3×C4—28no—
244C2×C3×C4—28no—
245C2×C3×C4—28no—
246C2×C3×C4—28no—
247C2×C3×C4—28no—
248C2×C3×C4—416no—
249C2×C3×C4C2×C4×D318yes—
250C2×C3×C4C2×C4×D318yes—
251#67—632no—
252C2×Dic3—38no—
253C2×Dic3—316no—
254C2×Dic3—38no—
255C2×Dic3—38no—
256C2×Dic3—64no—
257C2×Dic3—68no—
258C2×Dic3—64no—
259C2×Dic3—68no—
260C2×Dic3—68no—
261C2×Dic3—68no—
262C2×Dic3—68no—
263C2×Dic3—68no—
264C2×Dic3—68no—
265C4×D3—1216no—
266C2×C32—42no—
267C2×C32C2×#11711yescharacteristic
268C2×C32#51811yescharacteristic
269C2×C32#52011yescharacteristic
270C2×C32#54012yes—
271C2×C32#54212yes—
272C3⋊D3—42no—
273C24—91no—
274C24C22×C3⋊D311yescharacteristic
275C2×D4—94no—
276C2×D4—184no—
277C22×C4—42no—
278C22×C4—91no—
279C22×C4—91no—
280C22×C4—91no—
281C22×C4—94no—
282C22×C4—92no—
283C22×C4—92no—
284C22×C4—362no—
285C22×C4C4×C3⋊D314yes—
286C22×C4C22×C3⋊D312yes—
287C22×C4C22×C3⋊D312yes—
288C22×C4C22×C3⋊D311yescharacteristic
289C22×C4C22×C3⋊D311yescharacteristic
290C4⋊C4—42no—
291C4⋊C4—94no—
292C4⋊C4—184no—
293C4⋊C4—362no—
294C22⋊C4—42no—
295C22⋊C4—94no—
296C22⋊C4—94no—
297C22⋊C4—362no—
298C22⋊C4—362no—
299C22⋊C4—362no—
300C42—94no—
301C42—184no—
302C42—362no—
303C22×C3—28no—
304C22×C3—28no—
305C22×C3—28no—
306C22×C3—48no—
307C22×C3—48no—
308C22×C3C22×C4×D314yes—
309C22×C3#100418yes—
310C22×C3#100414yes—
311C22×C3#100714yes—
312C22×C3D3×#4118yes—
313C2×D3—68no—
314C2×D3—68no—
315C2×D3—68no—
316C2×D3—128no—
317C2×D3—128no—
318C3×C4—28no—
319C3×C4—28no—
320C3×C4—48no—
321C3×C4—48no—
322Dic3—316no—
323Dic3—68no—
324Dic3—68no—
325Dic3—128no—
326Dic3—128no—
327C32#231911yescharacteristic, complemented, Sylow
328C23—21no—
329C23—22no—
330C23—21no—
331C23—22no—
332C23—92no—
333C23—181no—
334C23—182no—
335C23—181no—
336C23—182no—
337C23C2×C4×C3⋊D312yes—
338C23C23×C3⋊D311yescharacteristic
339D4—188no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—44no—
349C2×C4—92no—
350C2×C4—94no—
351C2×C4—92no—
352C2×C4—92no—
353C2×C4—181no—
354C2×C4—182no—
355C2×C4—181no—
356C2×C4—182no—
357C2×C4—182no—
358C2×C4—182no—
359C2×C4—182no—
360C2×C4—182no—
361C2×C4—182no—
362C2×C4—364no—
363C2×C4C2×C4×C3⋊D312yes—
364C2×C4C2×C4×C3⋊D312yes—
365C2×C3—48no—
366C2×C3#548614yes—
367C2×C3#550414yes—
368C2×C3D3×#11714yes—
369C2×C3#561518yes—
370C2×C3#564018yes—
371D3—128no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—42no—
376C22—42no—
377C22—182no—
378C22—182no—
379C22—182no—
380C22—362no—
381C22—362no—
382C22C22×C4×C3⋊D311yescharacteristic
383C22#6436112yes—
384C22#6436111yescharacteristic
385C22#6436411yescharacteristic
386C22#41×C3⋊D312yes—
387C4—22no—
388C4—22no—
389C4—42no—
390C4—42no—
391C4—94no—
392C4—182no—
393C4—182no—
394C4—362no—
395C4—362no—
396C3#7387014yescomplemented
397C2—42no—
398C2—362no—
399C2#1059595711yescharacteristic
400C2#1059597511yescharacteristic
401C2C3⋊D3×#11711yescharacteristic
402C2#1059608612yes—
403C2#1059611112yes—
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#380C2
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenter#380C3⋊D3
hypocenterC32#2319
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C32×#380C2semidirect
3. #10592910C2semidirect
4. #10592689C2semidirect
5. #10592675C2semidirect
7. #10592643C2semidirect
8. #10592366C2semidirect
9. #10592363C2semidirect
10. #10592348C2semidirect
11. #10592347C2semidirect
20. C4×#638C4semidirect
38. C3×#380D3semidirect
148. #380C3⋊D3semidirect
327. C32#2319semidirect
396. C3#73870semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C32×#3802
#105929102
#105926892
#105926752
#105926562
#105926432
#105923662
#105923632
#105923482
#105923472
#738703