Finite Group Databasebeta

← #11805956

Subgroups — #11805956

Order 1152.

1392 conjugacy classes of subgroups.

The subgroup lattice has 369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64096C211yesmaximal, characteristic
2C32×C4×C4⋊C4C211yesmaximal, characteristic
3#10592676C211yesmaximal, characteristic
4C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic
5#10592672C211yesmaximal, characteristic
6#10592632C212yesmaximal
7#10592631C212yesmaximal
8C4×#3750C211yesmaximal, characteristic
9#10592628C211yesmaximal, characteristic
10#10592351C212yesmaximal
11#10592350C212yesmaximal
12#73644—34nomaximal
13C22×#634C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C32×C42C2211yescharacteristic
17C2×C32×C42C2212yes—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×#3750C2211yescharacteristic
20C2×#3750C2211yescharacteristic
21C2×#3750C2212yes—
22C2×C4×C3⋊Dic3C2212yes—
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C4×C3⋊Dic3C2212yes—
25C2×C4×C3⋊Dic3C2211yescharacteristic
26#64096C418yescomplemented
27C32×#95C2212yes—
28#63658C2211yescharacteristic
29#63658C2212yes—
30#63658C2212yes—
31#63658C2212yes—
32#63658C2212yes—
33#63658C2212yes—
34#63658C2212yes—
35#63658C2212yes—
36#63658C2211yescharacteristic
37C2×#887—34no—
38C3×C4×C4⋊C4D314yes—
39#4977—34no—
40Dic3×C4⋊C4—34no—
41#4973—34no—
42#4933—38no—
43#4932—38no—
44C4×Dic3⋊C4—34no—
45#4929—34no—
46#4652—38no—
47#4651—38no—
48C22×C32×C4C2311yescharacteristic
49C22×C32×C4C2312yes—
50C22×C32×C4C2312yes—
51C22×C32×C4C2311yescharacteristic
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3C2311yescharacteristic
54C22×C3⋊Dic3C2312yes—
55C22×C3⋊Dic3C2312yes—
56C22×C3⋊Dic3C2311yescharacteristic
57C22×C3⋊Dic3C2311yescharacteristic
58C22×C3⋊Dic3C2311yescharacteristic
59C2×#634—22no—
60C2×#634—22no—
61C2×#634C2×C414yes—
62C32×C4⋊C4—22no—
63C32×C4⋊C4C2×C414yes—
64C32×C42—22no—
65C32×C42—24no—
66C4⋊(C3⋊Dic3)—22no—
67#3750—22no—
68#3750—22no—
69#3750C2×C418yes—
70C4×C3⋊Dic3—22no—
71C4×C3⋊Dic3—24no—
72C4×C3⋊Dic3C2×C414yes—
73C4×C3⋊Dic3C2×C418yes—
74#2356—91noSylow
75C22×Dic6—34no—
76C2×C3×C4⋊C4C2×D314yes—
77C2×C3×C4⋊C4C2×D314yes—
78C2×C3×C42C2×D314yes—
79C2×C3×C42C2×D318yes—
80C2×C4⋊Dic3—34no—
81C2×Dic3⋊C4—38no—
82C2×Dic3⋊C4—34no—
83C2×Dic3⋊C4—34no—
84C2×C4×Dic3—38no—
85C2×C4×Dic3—34no—
86C2×C4×Dic3—38no—
87C2×C4×Dic3—34no—
88#887—332no—
89C3×#95C2×D318yes—
90C3⋊#95—34no—
91C3⋊#95—38no—
92C3⋊#95—38no—
93C3⋊#95—38no—
94C3⋊#95—38no—
95C3⋊#95—38no—
96C3⋊#95—38no—
97C3⋊#95—38no—
98C3⋊#95—34no—
99C23×C32C2411yescharacteristic
100C2×C32×C4—22no—
101C2×C32×C4—21no—
102C2×C32×C4—22no—
103C2×C32×C4—21no—
104C2×C32×C4—21no—
105C2×C32×C4—21no—
106C2×C32×C4—22no—
107C2×C32×C4—22no—
108C2×C32×C4—21no—
109C2×C32×C4—22no—
110C2×C32×C4C22×C414yes—
111C2×C32×C4C22×C412yes—
112C2×C32×C4#4112yes—
113C2×C32×C4#4112yes—
114C2×C32×C4#4112yes—
115C2×C3⋊Dic3—21no—
116C2×C3⋊Dic3—21no—
117C2×C3⋊Dic3—21no—
118C2×C3⋊Dic3—22no—
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3C22×C412yes—
130C2×C3⋊Dic3C22×C412yes—
131C2×C3⋊Dic3C22×C414yes—
132C2×C3⋊Dic3#4112yes—
133#634—28no—
134C2×C4×Q8—91no—
135#391—91no—
136#391—91no—
137#387—92no—
138#387—92no—
139#383—92no—
140#382—91no—
141C4×C4⋊C4—91no—
142C4×C4⋊C4—91no—
143C4×C4⋊C4C3⋊D311yescharacteristic
144#376—92no—
145C22×C3×C4C22×D318yes—
146C22×C3×C4C22×D314yes—
147C22×C3×C4C22×D318yes—
148C22×C3×C4C22×D314yes—
149C22×C3×C4C22×D314yes—
150C22×Dic3—34no—
151C22×Dic3—38no—
152C22×Dic3—34no—
153C22×Dic3—34no—
154C22×Dic3—34no—
155C22×Dic3—38no—
156C2×Dic6—316no—
157C2×Dic6—68no—
158C2×Dic6—68no—
159C3×C4⋊C4—28no—
160C3×C4⋊C4C4×D3116yes—
161C3×C42—28no—
162C3×C42—216no—
163C4⋊Dic3—68no—
164Dic3⋊C4—332no—
165Dic3⋊C4—68no—
166Dic3⋊C4—68no—
167C4×Dic3—316no—
168C4×Dic3—332no—
169C4×Dic3—616no—
170C4×Dic3—68no—
171C22×C32C23×C411yescharacteristic
172C22×C32C2×#4111yescharacteristic
173C22×C32C2×#4111yescharacteristic
174C22×C32C2×#4111yescharacteristic
175C22×C32C2×#4111yescharacteristic
176C22×C322−1+411yescharacteristic
177C22×C322−1+411yescharacteristic
178C32×C4—24no—
179C32×C4—22no—
180C32×C4—41no—
181C32×C4—42no—
182C32×C4#11714yes—
183C3⋊Dic3—24no—
184C3⋊Dic3—22no—
185C3⋊Dic3—22no—
186C3⋊Dic3—22no—
187C3⋊Dic3—41no—
188C3⋊Dic3—42no—
189C22×Q8—91no—
190C4×Q8—98no—
191C2×C4⋊C4—92no—
192C2×C4⋊C4—91no—
193C2×C4⋊C4—91no—
194C2×C4⋊C4—91no—
195C2×C4⋊C4C2×C3⋊D311yescharacteristic
196C2×C4⋊C4C2×C3⋊D311yescharacteristic
197C2×C42—92no—
198C2×C42—91no—
199C2×C42—92no—
200C2×C42—91no—
201C2×C42C2×C3⋊D312yes—
202C2×C42C2×C3⋊D311yescharacteristic
203#95—91no—
204#95—92no—
205#95—92no—
206#95—92no—
207#95—91no—
208#95—92no—
209#95—92no—
210#95—92no—
211#95—92no—
212#95C2×C3⋊D312yes—
213C23×C3C23×D314yes—
214C2×C3×C4—24no—
215C2×C3×C4—28no—
216C2×C3×C4—24no—
217C2×C3×C4—28no—
218C2×C3×C4—24no—
219C2×C3×C4—28no—
220C2×C3×C4—28no—
221C2×C3×C4—24no—
222C2×C3×C4—24no—
223C2×C3×C4—28no—
224C2×C3×C4C2×C4×D3116yes—
225C2×C3×C4C2×C4×D318yes—
226C2×C3×C4#23518yes—
227C2×C3×C4#23518yes—
228C2×C3×C4#23718yes—
229C2×Dic3—38no—
230C2×Dic3—38no—
231C2×Dic3—316no—
232C2×Dic3—38no—
233C2×Dic3—64no—
234C2×Dic3—68no—
235C2×Dic3—68no—
236C2×Dic3—64no—
237C2×Dic3—64no—
238C2×Dic3—64no—
239C2×Dic3—64no—
240C2×Dic3—64no—
241C2×Dic3—64no—
242C2×Dic3—68no—
243C2×Dic3—64no—
244C2×Dic3—64no—
245C2×Dic3—68no—
246C2×Dic3—68no—
247Dic6—632no—
248C2×C32C2×#11711yescharacteristic
249C2×C32C4×#4111yescharacteristic
250C2×C32#51911yescharacteristic
251C2×C32#55211yescharacteristic
252C2×C32#55211yescharacteristic
253C2×C32#55611yescharacteristic
254C2×C32#55611yescharacteristic
255C2×Q8—94no—
256C2×Q8—182no—
257C2×Q8—182no—
258C22×C4—91no—
259C22×C4—92no—
260C22×C4—91no—
261C22×C4—91no—
262C22×C4—91no—
263C22×C4—92no—
264C22×C4C22×C3⋊D312yes—
265C22×C4C22×C3⋊D311yescharacteristic
266C22×C4C22×C3⋊D312yes—
267C22×C4C22×C3⋊D311yescharacteristic
268C22×C4C22×C3⋊D311yescharacteristic
269C4⋊C4—22no—
270C4⋊C4—98no—
271C4⋊C4—182no—
272C4⋊C4—182no—
273C4⋊C4—182no—
274C4⋊C4C4×C3⋊D314yes—
275C42—22no—
276C42—24no—
277C42—94no—
278C42—98no—
279C42—184no—
280C42—182no—
281C22×C3C22×C4×D314yes—
282C22×C3C2×#23514yes—
283C22×C3C2×#23514yes—
284C22×C3C2×#23714yes—
285C22×C3#100714yes—
286C22×C3D3×#4114yes—
287C22×C3#101014yes—
288C3×C4—28no—
289C3×C4—216no—
290C3×C4—44no—
291C3×C4—48no—
292C3×C4#872116yes—
293Dic3—616no—
294Dic3—68no—
295Dic3—68no—
296Dic3—68no—
297Dic3—124no—
298Dic3—128no—
299C32#235611yescharacteristic, complemented, Sylow
300C23C23×C3⋊D311yescharacteristic
301Q8—188no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—92no—
313C2×C4—92no—
314C2×C4—94no—
315C2×C4—92no—
316C2×C4—181no—
317C2×C4—182no—
318C2×C4—182no—
319C2×C4—181no—
320C2×C4—181no—
321C2×C4—181no—
322C2×C4—181no—
323C2×C4—181no—
324C2×C4—181no—
325C2×C4—182no—
326C2×C4—181no—
327C2×C4—181no—
328C2×C4—182no—
329C2×C4—182no—
330C2×C4C2×C4×C3⋊D314yes—
331C2×C4C2×C4×C3⋊D312yes—
332C2×C4#382812yes—
333C2×C4#382812yes—
334C2×C4#383012yes—
335C2×C3C2×#87214yes—
336C2×C3#551314yes—
337C2×C3#552914yes—
338C2×C3C4×#23714yes—
339C2×C3#554214yes—
340C2×C3#556814yes—
341C2×C3#557214yes—
342C22C22×C4×C3⋊D311yescharacteristic
343C22C2×#382811yescharacteristic
344C22C2×#382811yescharacteristic
345C22C2×#383011yescharacteristic
346C22#6436411yescharacteristic
347C22#41×C3⋊D311yescharacteristic
348C22#6436711yescharacteristic
349C4—22no—
350C4—24no—
351C4—41no—
352C4—42no—
353C4—184no—
354C4—182no—
355C4—182no—
356C4—182no—
357C4—361no—
358C4—362no—
359C4#6408114yes—
360C3#7364414yescomplemented
361C2C2×#6408111yescharacteristic
362C2#1059598411yescharacteristic
363C2#1059600011yescharacteristic
364C2C4×#383011yescharacteristic
365C2#1059601311yescharacteristic
366C2#1059603911yescharacteristic
367C2#1059604311yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×C4×C4⋊C4C2
socle, prime radical, cosocleC23×C32C24
hypercenterC4×C4⋊C4C3⋊D3
hypocenterC32#2356
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
26. #64096C4semidirect
299. C32#2356semidirect
360. C3#73644semidirect

Maximal subgroups

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

subgroupindex
C2×#640962
C32×C4×C4⋊C42
#105926762
C4⋊C4×C3⋊Dic32
#105926722
#105926322
#105926312
C4×#37502
#105926282
#105923512
#105923502
#736443