Finite Group Databasebeta

← #11805343

Subgroups — #11805343

Order 1152.

1512 conjugacy classes of subgroups.

The subgroup lattice has 411 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64101C211yesmaximal, characteristic
2C32×C4×C4⋊C4C211yesmaximal, characteristic, complemented
3#10592686C211yesmaximal, characteristic
4C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
5#10592671C211yesmaximal, characteristic, complemented
6#10592639C212yesmaximal
7C4×#3752C211yesmaximal, characteristic
8C4×#3750C212yesmaximal, complemented
9#10592627C211yesmaximal, characteristic, complemented
10#10592368C212yesmaximal
11#10592350C212yesmaximal, complemented
12#73634—34nomaximal
13C22×C4×C3⋊D3C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C32×C42C2211yescharacteristic
17C2×C32×C42C2212yes—
18C2×#3752C2211yescharacteristic
19C2×#3752C2211yescharacteristic
20C2×#3752C2212yes—
21C2×#3752C2212yes—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×#3750C2212yes—
25C2×#3750C2212yes—
26C2×C4×C3⋊Dic3C2211yescharacteristic
27C2×C4×C3⋊Dic3C2212yes—
28C2×C4×C3⋊Dic3C2212yes—
29#64101C418yescomplemented
30C32×#95C2212yes—
31#63658C2211yescharacteristic
32#63658C2212yes—
33#63658C2212yes—
34#63658C2212yes—
35#63658C2212yes—
36#63658C2211yescharacteristic
37C2×#892—34no—
38C3×C4×C4⋊C4D314yescomplemented
39#4987—34no—
40Dic3×C4⋊C4—34no—
41#4972—34no—
42#4940—38no—
43C4×(C2×D3)⋊C4—34no—
44C4×Dic3⋊C4—38no—
45#4928—34no—
46#4669—38no—
47#4651—38no—
48C23×C3⋊D3C2311yescharacteristic
49C22×C32×C4C2312yes—
50C22×C32×C4C2311yescharacteristic
51C22×C32×C4C2312yes—
52C22×C32×C4C2311yescharacteristic
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3C2312yes—
55C22×C3⋊Dic3C2311yescharacteristic
56C22×C3⋊Dic3C2311yescharacteristic
57C22×C3⋊Dic3C2312yes—
58C22×C3⋊Dic3C2311yescharacteristic
59C2×C4×C3⋊D3—22no—
60C2×C4×C3⋊D3—22no—
61C2×C4×C3⋊D3C2×C414yes—
62C32×C4⋊C4—22no—
63C32×C4⋊C4C2×C414yes—
64C32×C42—22no—
65C32×C42—42no—
66#3752—22no—
67#3752—22no—
68#3752—42no—
69#3752C2×C418yes—
70C4⋊(C3⋊Dic3)—22no—
71C4⋊(C3⋊Dic3)C2×C414yes—
72#3750—24no—
73#3750—24no—
74C4×C3⋊Dic3—22no—
75C4×C3⋊Dic3—42no—
76C4×C3⋊Dic3C2×C418yes—
77#2347—91noSylow
78C22×C4×D3—34no—
79C2×C3×C4⋊C4C2×D314yes—
80C2×C3×C4⋊C4C2×D314yes—
81C2×C3×C42C2×D314yes—
82C2×C3×C42C2×D318yes—
83C2×(C2×D3)⋊C4—38no—
84C2×(C2×D3)⋊C4—34no—
85C2×(C2×D3)⋊C4—34no—
86C2×(C2×D3)⋊C4—38no—
87C2×C4⋊Dic3—34no—
88C2×C4⋊Dic3—34no—
89C2×Dic3⋊C4—38no—
90C2×Dic3⋊C4—38no—
91C2×C4×Dic3—38no—
92C2×C4×Dic3—34no—
93C2×C4×Dic3—38no—
94#892—332no—
95C3×#95C2×D318yes—
96C3⋊#95—34no—
97C3⋊#95—38no—
98C3⋊#95—38no—
99C3⋊#95—38no—
100C3⋊#95—38no—
101C3⋊#95—34no—
102C23×C32C2411yescharacteristic
103C22×C3⋊D3—21no—
104C22×C3⋊D3—21no—
105C22×C3⋊D3—21no—
106C22×C3⋊D3—21no—
107C22×C3⋊D3—21no—
108C22×C3⋊D3—21no—
109C22×C3⋊D3C22×C412yes—
110C2×C32×C4—21no—
111C2×C32×C4—22no—
112C2×C32×C4—21no—
113C2×C32×C4—22no—
114C2×C32×C4—22no—
115C2×C32×C4—21no—
116C2×C32×C4—21no—
117C2×C32×C4—22no—
118C2×C32×C4—22no—
119C2×C32×C4—21no—
120C2×C32×C4C22×C414yes—
121C2×C32×C4C22×C412yes—
122C2×C32×C4#4112yes—
123C2×C32×C4#4112yes—
124C2×C32×C4#4112yes—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3C22×C412yes—
138C2×C3⋊Dic3C22×C414yes—
139C2×C3⋊Dic3#4112yes—
140C4×C3⋊D3—28no—
141C2×#117—91no—
142#389—91no—
143#389—91no—
144#388—92no—
145#388—92no—
146#383—92no—
147#380—91no—
148C4×C4⋊C4—91no—
149C4×C4⋊C4—92no—
150C4×C4⋊C4C3⋊D311yescharacteristic, complemented
151C4×C22⋊C4—91no—
152C23×D3—34no—
153C22×C3×C4C22×D314yes—
154C22×C3×C4C22×D318yes—
155C22×C3×C4C22×D318yes—
156C22×C3×C4C22×D314yes—
157C22×C3×C4C22×D314yes—
158C22×Dic3—34no—
159C22×Dic3—38no—
160C22×Dic3—34no—
161C22×Dic3—34no—
162C22×Dic3—38no—
163C2×C4×D3—316no—
164C2×C4×D3—68no—
165C2×C4×D3—68no—
166C3×C4⋊C4—28no—
167C3×C4⋊C4C4×D3116yes—
168C3×C42—28no—
169C3×C42—48no—
170(C2×D3)⋊C4—332no—
171(C2×D3)⋊C4—68no—
172(C2×D3)⋊C4—68no—
173(C2×D3)⋊C4—128no—
174C4⋊Dic3—316no—
175C4⋊Dic3—68no—
176Dic3⋊C4—616no—
177Dic3⋊C4—616no—
178C4×Dic3—332no—
179C4×Dic3—68no—
180C4×Dic3—128no—
181C22×C32C23×C411yescharacteristic
182C22×C32C2×#4111yescharacteristic
183C22×C32C2×#4111yescharacteristic
184C22×C32C2×#4111yescharacteristic
185C22×C32C2×#4111yescharacteristic
186C22×C32H(5,𝔽2)11yescharacteristic
187C22×C322−1+411yescharacteristic
188C2×C3⋊D3—22no—
189C2×C3⋊D3—22no—
190C2×C3⋊D3—22no—
191C2×C3⋊D3—41no—
192C2×C3⋊D3—41no—
193C2×C3⋊D3—41no—
194C2×C3⋊D3—41no—
195C32×C4—24no—
196C32×C4—22no—
197C32×C4—42no—
198C32×C4—41no—
199C32×C4#11714yes—
200C3⋊Dic3—22no—
201C3⋊Dic3—24no—
202C3⋊Dic3—22no—
203C3⋊Dic3—42no—
204C3⋊Dic3—41no—
205C23×C4—91no—
206#117—98no—
207C2×C4⋊C4—91no—
208C2×C4⋊C4—91no—
209C2×C4⋊C4—92no—
210C2×C4⋊C4—92no—
211C2×C4⋊C4C2×C3⋊D311yescharacteristic
212C2×C4⋊C4C2×C3⋊D311yescharacteristic
213C2×C22⋊C4—92no—
214C2×C22⋊C4—91no—
215C2×C22⋊C4—91no—
216C2×C22⋊C4—92no—
217C2×C42—92no—
218C2×C42—91no—
219C2×C42—92no—
220C2×C42C2×C3⋊D311yescharacteristic
221C2×C42C2×C3⋊D312yes—
222#95—91no—
223#95—91no—
224#95—92no—
225#95—92no—
226#95—92no—
227#95—92no—
228#95C2×C3⋊D312yes—
229C23×C3C23×D314yes—
230C22×D3—38no—
231C22×D3—64no—
232C22×D3—64no—
233C22×D3—64no—
234C22×D3—64no—
235C22×D3—64no—
236C22×D3—64no—
237C2×C3×C4—24no—
238C2×C3×C4—28no—
239C2×C3×C4—24no—
240C2×C3×C4—28no—
241C2×C3×C4—24no—
242C2×C3×C4—28no—
243C2×C3×C4—28no—
244C2×C3×C4—28no—
245C2×C3×C4—24no—
246C2×C3×C4—24no—
247C2×C3×C4C2×C4×D3116yes—
248C2×C3×C4C2×C4×D318yes—
249C2×C3×C4#23518yes—
250C2×C3×C4#23518yes—
251C2×C3×C4#23918yes—
252C2×Dic3—38no—
253C2×Dic3—316no—
254C2×Dic3—38no—
255C2×Dic3—64no—
256C2×Dic3—64no—
257C2×Dic3—64no—
258C2×Dic3—64no—
259C2×Dic3—68no—
260C2×Dic3—68no—
261C2×Dic3—64no—
262C2×Dic3—68no—
263C2×Dic3—68no—
264C2×Dic3—68no—
265C2×Dic3—64no—
266C2×Dic3—64no—
267C4×D3—632no—
268C2×C32C2×#11711yescharacteristic
269C2×C32C4×#4111yescharacteristic
270C2×C32#52011yescharacteristic
271C2×C32#55311yescharacteristic
272C2×C32#55311yescharacteristic
273C2×C32#55611yescharacteristic
274C2×C32#55611yescharacteristic
275C3⋊D3—42no—
276C24—91no—
277C22×C4—91no—
278C22×C4—92no—
279C22×C4—91no—
280C22×C4—94no—
281C22×C4—91no—
282C22×C4—92no—
283C22×C4—182no—
284C22×C4—182no—
285C22×C4C22×C3⋊D311yescharacteristic
286C22×C4C22×C3⋊D312yes—
287C22×C4C22×C3⋊D312yes—
288C22×C4C22×C3⋊D311yescharacteristic
289C22×C4C22×C3⋊D311yescharacteristic
290C4⋊C4—22no—
291C4⋊C4—94no—
292C4⋊C4—184no—
293C4⋊C4—182no—
294C4⋊C4—184no—
295C4⋊C4C4×C3⋊D314yes—
296C22⋊C4—98no—
297C22⋊C4—182no—
298C22⋊C4—182no—
299C22⋊C4—362no—
300C42—22no—
301C42—42no—
302C42—98no—
303C42—182no—
304C42—362no—
305C22×C3C22×C4×D314yes—
306C22×C3C2×#23514yes—
307C22×C3C2×#23514yes—
308C22×C3#100414yes—
309C22×C3C2×#23914yes—
310C22×C3D3×#4114yes—
311C22×C3#101014yes—
312C2×D3—68no—
313C2×D3—68no—
314C2×D3—68no—
315C2×D3—124no—
316C2×D3—124no—
317C2×D3—124no—
318C2×D3—124no—
319C3×C4—28no—
320C3×C4—216no—
321C3×C4—44no—
322C3×C4—48no—
323C3×C4#872116yes—
324Dic3—68no—
325Dic3—68no—
326Dic3—616no—
327Dic3—128no—
328Dic3—124no—
329C32#234711yescharacteristic, complemented, Sylow
330C23—92no—
331C23—181no—
332C23—181no—
333C23—181no—
334C23—181no—
335C23—181no—
336C23—181no—
337C23C23×C3⋊D311yescharacteristic
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—21no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—21no—
346C2×C4—22no—
347C2×C4—21no—
348C2×C4—92no—
349C2×C4—94no—
350C2×C4—92no—
351C2×C4—181no—
352C2×C4—181no—
353C2×C4—181no—
354C2×C4—181no—
355C2×C4—182no—
356C2×C4—182no—
357C2×C4—188no—
358C2×C4—181no—
359C2×C4—182no—
360C2×C4—182no—
361C2×C4—181no—
362C2×C4—182no—
363C2×C4—181no—
364C2×C4C2×C4×C3⋊D314yes—
365C2×C4C2×C4×C3⋊D312yes—
366C2×C4#382812yes—
367C2×C4#382812yes—
368C2×C4#383212yes—
369C2×C3C2×#87214yes—
370C2×C3#551414yes—
371C2×C3#553314yes—
372C2×C3#554614yes—
373C2×C3#555814yes—
374C2×C3C4×#23914yes—
375C2×C3#558414yes—
376D3—128no—
377C22—182no—
378C22—182no—
379C22—182no—
380C22—361no—
381C22—361no—
382C22—361no—
383C22—361no—
384C22C22×C4×C3⋊D311yescharacteristic
385C22C2×#382811yescharacteristic
386C22C2×#382811yescharacteristic
387C22#6436111yescharacteristic
388C22C2×#383211yescharacteristic
389C22#41×C3⋊D311yescharacteristic
390C22#6436711yescharacteristic
391C4—22no—
392C4—24no—
393C4—41no—
394C4—42no—
395C4—182no—
396C4—182no—
397C4—184no—
398C4—362no—
399C4—361no—
400C4#6408114yes—
401C3#7363414yescomplemented
402C2—362no—
403C2C2×#6408111yescharacteristic
404C2#1059598511yescharacteristic
405C2#1059600411yescharacteristic
406C2#1059601711yescharacteristic
407C2#1059602911yescharacteristic
408C2C4×#383211yescharacteristic
409C2#1059605511yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×C4×C4⋊C4C2
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC4×C4⋊C4C3⋊D3
hypocenterC32#2347
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C32×C4×C4⋊C4C2semidirect
4. C4⋊C4×C3⋊Dic3C2semidirect
5. #10592671C2semidirect
8. C4×#3750C2semidirect
9. #10592627C2semidirect
11. #10592350C2semidirect
29. #64101C4semidirect
38. C3×C4×C4⋊C4D3semidirect
150. C4×C4⋊C4C3⋊D3semidirect
329. C32#2347semidirect
401. C3#73634semidirect

Maximal subgroups

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

subgroupindex
C2×#641012
C32×C4×C4⋊C42
#105926862
C4⋊C4×C3⋊Dic32
#105926712
#105926392
C4×#37522
C4×#37502
#105926272
#105923682
#105923502
#736343