Finite Group Databasebeta

← #11807967

Subgroups — #11807967

Order 1152.

917 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63919C211yesmaximal, characteristic
2#10592350C211yesmaximal, characteristic
3C3×#4653C212yesmaximal
4#10591333C212yesmaximal
5#10591270C212yesmaximal
6#10591255C212yesmaximal
7#10591235C212yesmaximal
8#10591229C211yesmaximal, characteristic
9#10591191C212yesmaximal
10#74977—32nomaximal
11C22×#627C2212yes—
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×C3×C4⋊Dic3C2212yes—
14C2×C3×Dic3⋊C4C2212yes—
15C2×C3×C4×Dic3C2212yes—
16C2×#3724C2211yescharacteristic
17C2×#3724C2211yescharacteristic
18C2×Dic3⋊Dic3C2212yes—
19C2×Dic32C2212yes—
20#63919C418yescomplemented
21C32×#95C2211yescharacteristic
22#63658C2212yes—
23#63658C2212yes—
24#63658C2211yescharacteristic
25C3×C3⋊#95C2212yes—
26C3×C3⋊#95C2212yes—
27C3×C3⋊#95C2212yes—
28#63579C2211yescharacteristic
29#63579C2212yes—
30#63579C2212yes—
31#63579C2212yes—
32#63579C2211yescharacteristic
33C2×#888—32no—
34C3×#387—32no—
35#4980—32no—
36#4978—32no—
37#4973—32no—
38#4933—32no—
39#4929—32no—
40#4655—32no—
41#4654—32no—
42#4653D312yes—
43#4652—32no—
44#4651—32no—
45#4651—32no—
46#4651—61no—
47#4646—32no—
48#4646—32no—
49C22×C32×C4C2312yes—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3C2312yes—
52C22×C3⋊Dic3C2311yescharacteristic
53C22×C3⋊Dic3C2311yescharacteristic
54C22×C3×Dic3C2312yes—
55C22×C3×Dic3C2312yes—
56C22×C3×Dic3C2312yes—
57C22×C3×Dic3C2312yes—
58C2×#627—42no—
59C2×#627—42no—
60C2×#627C2×C418yes—
61C4×C3⋊Dic3C2×C414yes—
62C3×C4⋊Dic3C2×C418yes—
63C3×Dic3⋊C4—42no—
64C3×C4×Dic3—42no—
65#3724C2×C414yes—
66#3724C2×C414yes—
67Dic3⋊Dic3—42no—
68Dic32—42no—
69#2381—91noSylow
70C22×Dic6—32no—
71C22×Dic6—32no—
72C2×C3×C4⋊C4—32no—
73C2×C3×C4⋊C4—32no—
74C2×C3×C42—32no—
75C2×C4⋊Dic3—32no—
76C2×C4⋊Dic3C2×D312yes—
77C2×Dic3⋊C4—32no—
78C2×Dic3⋊C4—32no—
79C2×Dic3⋊C4—32no—
80C2×Dic3⋊C4C2×D312yes—
81C2×C4×Dic3—32no—
82C2×C4×Dic3—32no—
83C2×C4×Dic3—32no—
84C2×C4×Dic3—61no—
85C2×C4×Dic3C2×D312yes—
86#888—316no—
87C3×#95—21no—
88C3×#95—32no—
89C3×#95—32no—
90C3×#95—32no—
91C3×#95C2×D312yes—
92C3⋊#95—32no—
93C3⋊#95—32no—
94C3⋊#95—32no—
95C3⋊#95—32no—
96C3⋊#95—32no—
97C3⋊#95—32no—
98C3⋊#95—32no—
99C3⋊#95—32no—
100C3⋊#95—32no—
101C3⋊#95—32no—
102C3⋊#95—32no—
103C3⋊#95—32no—
104C3⋊#95—32no—
105C3⋊#95—62no—
106C3⋊#95—61no—
107C3⋊#95—62no—
108C3⋊#95C2×D312yes—
109C3⋊#95C2×D312yes—
110C3⋊#95C2×D312yes—
111C23×C32C2411yescharacteristic
112C2×C32×C4—22no—
113C2×C32×C4—22no—
114C2×C32×C4—22no—
115C2×C32×C4—22no—
116C2×C32×C4C22×C412yes—
117C2×C3⋊Dic3—22no—
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3—22no—
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3C22×C412yes—
124C2×C3⋊Dic3C22×C412yes—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—22no—
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×C414yes—
136C2×C3×Dic3C22×C414yes—
137#627—48no—
138C2×C4⋊Q8—91no—
139#391—92no—
140#391—92no—
141#387—32no—
142#387—92no—
143#387—92no—
144#387—92no—
145#383—91no—
146#383—91no—
147C22×C3×C4—21no—
148C22×C3×C4—22no—
149C22×C3×C4—32no—
150C22×C3×C4—32no—
151C22×C3×C4—32no—
152C22×C3×C4—32no—
153C22×C3×C4C22×D312yes—
154C22×C3×C4C22×D312yes—
155C22×C3×C4C22×D312yes—
156C22×Dic3—32no—
157C22×Dic3—32no—
158C22×Dic3—32no—
159C22×Dic3—32no—
160C22×Dic3—61no—
161C22×Dic3—61no—
162C22×Dic3—62no—
163C22×Dic3C22×D312yes—
164C22×Dic3C22×D312yes—
165C22×Dic3C22×D312yes—
166C22×Dic3C22×D312yes—
167C2×Dic6—38no—
168C2×Dic6—38no—
169C2×Dic6—122no—
170C2×Dic6—122no—
171C2×Dic6—122no—
172C2×Dic6—122no—
173C3×C4⋊C4—38no—
174C3×C4⋊C4—122no—
175C3×C42—122no—
176C4⋊Dic3—122no—
177C4⋊Dic3C4×D318yes—
178Dic3⋊C4—38no—
179Dic3⋊C4—38no—
180Dic3⋊C4—42no—
181Dic3⋊C4—122no—
182C4×Dic3—38no—
183C4×Dic3—42no—
184C4×Dic3—64no—
185C4×Dic3—122no—
186C4×Dic3—122no—
187C22×C32C23×C411yescharacteristic
188C22×C32H(5,𝔽2)12yes—
189C22×C322−1+411yescharacteristic
190C22×C322−1+412yes—
191C22×C322−1+411yescharacteristic
192C32×C4—22no—
193C32×C4—42no—
194C3⋊Dic3—22no—
195C3⋊Dic3—22no—
196C3⋊Dic3—42no—
197C3×Dic3—24no—
198C3×Dic3—24no—
199C3×Dic3—42no—
200C3×Dic3—42no—
201C22×Q8—92no—
202C4⋊Q8—98no—
203C2×C4⋊C4—32no—
204C2×C4⋊C4—32no—
205C2×C4⋊C4—91no—
206C2×C4⋊C4—91no—
207C2×C4⋊C4—92no—
208C2×C42—32no—
209C2×C42—91no—
210C2×C42—92no—
211#95—32no—
212#95—32no—
213#95—32no—
214#95—92no—
215#95—91no—
216#95—91no—
217#95—92no—
218#95—92no—
219#95—92no—
220#95—91no—
221#95—92no—
222#95D3211yescharacteristic
223C23×C3—21no—
224C23×C3C23×D312yes—
225C2×C3×C4—22no—
226C2×C3×C4—22no—
227C2×C3×C4—22no—
228C2×C3×C4—22no—
229C2×C3×C4—22no—
230C2×C3×C4—22no—
231C2×C3×C4—22no—
232C2×C3×C4—22no—
233C2×C3×C4—22no—
234C2×C3×C4—34no—
235C2×C3×C4—34no—
236C2×C3×C4—42no—
237C2×C3×C4—42no—
238C2×C3×C4—42no—
239C2×C3×C4—42no—
240C2×C3×C4—62no—
241C2×C3×C4—62no—
242C2×C3×C4—62no—
243C2×C3×C4—62no—
244C2×C3×C4—62no—
245C2×C3×C4—62no—
246C2×C3×C4—62no—
247C2×C3×C4—62no—
248C2×C3×C4—62no—
249C2×C3×C4—62no—
250C2×C3×C4C2×C4×D314yes—
251C2×Dic3—22no—
252C2×Dic3—22no—
253C2×Dic3—22no—
254C2×Dic3—22no—
255C2×Dic3—22no—
256C2×Dic3—22no—
257C2×Dic3—22no—
258C2×Dic3—22no—
259C2×Dic3—22no—
260C2×Dic3—22no—
261C2×Dic3—34no—
262C2×Dic3—34no—
263C2×Dic3—62no—
264C2×Dic3—62no—
265C2×Dic3—62no—
266C2×Dic3—62no—
267C2×Dic3—62no—
268C2×Dic3—62no—
269C2×Dic3—62no—
270C2×Dic3—62no—
271C2×Dic3—62no—
272C2×Dic3—62no—
273C2×Dic3—62no—
274C2×Dic3—62no—
275C2×Dic3—122no—
276C2×Dic3—121no—
277C2×Dic3—121no—
278C2×Dic3—122no—
279C2×Dic3—122no—
280C2×Dic3—122no—
281C2×Dic3C2×C4×D314yes—
282C2×Dic3C2×C4×D314yes—
283Dic6—128no—
284Dic6—128no—
285C2×C32#51811yescharacteristic
286C2×C32#51911yescharacteristic
287C2×C32#51911yescharacteristic
288C2×C32#56312yes—
289C2×C32#56312yes—
290C2×Q8—98no—
291C2×Q8—362no—
292C2×Q8—362no—
293C22×C4—32no—
294C22×C4—32no—
295C22×C4—32no—
296C22×C4—32no—
297C22×C4—91no—
298C22×C4—91no—
299C22×C4—92no—
300C22×C4C2×D3212yes—
301C22×C4C2×D3211yescharacteristic
302C4⋊C4—38no—
303C4⋊C4—94no—
304C4⋊C4—94no—
305C4⋊C4—122no—
306C4⋊C4—362no—
307C42—94no—
308C42—122no—
309C42—362no—
310C22×C3—21no—
311C22×C3—22no—
312C22×C3—22no—
313C22×C3—21no—
314C22×C3—21no—
315C22×C3C22×C4×D312yes—
316C22×C3#100412yes—
317C22×C3#100712yes—
318C22×C3#100912yes—
319C22×C3#101012yes—
320C22×C3#101012yes—
321C22×C3#101012yes—
322C3×C4—24no—
323C3×C4—42no—
324C3×C4—42no—
325C3×C4—42no—
326C3×C4—64no—
327C3×C4—64no—
328C3×C4—82no—
329C3×C4—122no—
330C3×C4—122no—
331Dic3—24no—
332Dic3—24no—
333Dic3—42no—
334Dic3—42no—
335Dic3—64no—
336Dic3—64no—
337Dic3—122no—
338Dic3—122no—
339Dic3—122no—
340Dic3—122no—
341Dic3—242no—
342C32#238111yescharacteristic, complemented, Sylow
343C23C22×D3211yescharacteristic
344Q8—368no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—34no—
350C2×C4—34no—
351C2×C4—62no—
352C2×C4—62no—
353C2×C4—62no—
354C2×C4—62no—
355C2×C4—62no—
356C2×C4—62no—
357C2×C4—62no—
358C2×C4—62no—
359C2×C4—62no—
360C2×C4—62no—
361C2×C4—92no—
362C2×C4—92no—
363C2×C4—182no—
364C2×C4—181no—
365C2×C4—181no—
366C2×C4—182no—
367C2×C4—182no—
368C2×C4—182no—
369C2×C4C4×D3212yes—
370C2×C3—22no—
371C2×C3—21no—
372C2×C3—22no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3#551612yes—
376C2×C3#554512yes—
377C2×C3#557212yes—
378C2×C3#564612yes—
379C2×C3#565112yes—
380C2×C3#569912yes—
381C2×C3#571212yes—
382C22C2×C4×D3211yescharacteristic
383C22#6430712yes—
384C22#6430912yes—
385C22#6430911yescharacteristic
386C22#6431611yescharacteristic
387C4—22no—
388C4—42no—
389C4—64no—
390C4—64no—
391C4—122no—
392C4—122no—
393C4—182no—
394C4—182no—
395C4—362no—
396C3—21no—
397C3#7497712yescomplemented
398C2#1059399611yescharacteristic
399C2#1059416912yes—
400C2#1059424511yescharacteristic
401C2#1059434711yescharacteristic
402C2#1059458712yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, prime radical, cosocleC23×C32C24
hypercenter#95D32
hypocenterC32#2381
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
20. #63919C4semidirect
342. C32#2381semidirect
397. C3#74977semidirect

Maximal subgroups

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

subgroupindex
C2×#639192
#105923502
C3×#46532
#105913332
#105912702
#105912552
#105912352
#105912292
#105911912
#749773