Finite Group Databasebeta

← #11807963

Subgroups — #11807963

Order 1152.

917 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63919C211yesmaximal, characteristic
2#10592350C211yesmaximal, characteristic
3C3×#4654C212yesmaximal
4#10591269C212yesmaximal
5#10591249C212yesmaximal
6#10591235C212yesmaximal
7#10591229C211yesmaximal, characteristic
8#10591193C212yesmaximal
9#10591191C212yesmaximal
10#74977—32nomaximal
11C22×#627C2211yescharacteristic
12C22×#627C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic3C2212yes—
15C2×C3×Dic3⋊C4C2212yes—
16C2×C3×C4×Dic3C2212yes—
17C2×#3724C2212yes—
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#63579C2212yes—
29#63579C2212yes—
30#63579C2211yescharacteristic
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#4654D312yes—
42#4653—32no—
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—41no—
59C2×#627—41no—
60C2×#627—41no—
61C2×#627—41no—
62C2×#627C2×C414yes—
63C2×#627C2×C414yes—
64C4×C3⋊Dic3C2×C414yes—
65C3×C4⋊Dic3C2×C418yes—
66C3×Dic3⋊C4—42no—
67C3×C4×Dic3—42no—
68#3724C2×C418yes—
69Dic3⋊Dic3—42no—
70Dic32—42no—
71#2381—91noSylow
72C22×Dic6—32no—
73C22×Dic6—32no—
74C2×C3×C4⋊C4—32no—
75C2×C3×C4⋊C4—32no—
76C2×C3×C42—32no—
77C2×C4⋊Dic3—32no—
78C2×C4⋊Dic3C2×D312yes—
79C2×Dic3⋊C4—32no—
80C2×Dic3⋊C4—32no—
81C2×Dic3⋊C4—32no—
82C2×Dic3⋊C4C2×D312yes—
83C2×C4×Dic3—32no—
84C2×C4×Dic3—32no—
85C2×C4×Dic3—32no—
86C2×C4×Dic3—61no—
87C2×C4×Dic3C2×D312yes—
88#888—316no—
89C3×#95—21no—
90C3×#95—32no—
91C3×#95—32no—
92C3×#95—32no—
93C3×#95C2×D312yes—
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—32no—
106C3⋊#95—32no—
107C3⋊#95—62no—
108C3⋊#95—61no—
109C3⋊#95—62no—
110C3⋊#95C2×D312yes—
111C3⋊#95C2×D312yes—
112C3⋊#95C2×D312yes—
113C23×C32C2411yescharacteristic
114C2×C32×C4—22no—
115C2×C32×C4—22no—
116C2×C32×C4—22no—
117C2×C32×C4—22no—
118C2×C32×C4C22×C412yes—
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—22no—
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3C22×C412yes—
126C2×C3⋊Dic3C22×C412yes—
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×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3C22×C414yes—
138C2×C3×Dic3C22×C414yes—
139#627—44no—
140#627—44no—
141C2×C4⋊Q8—91no—
142#391—92no—
143#391—92no—
144#387—32no—
145#387—92no—
146#387—92no—
147#387—92no—
148#383—91no—
149#383—91no—
150C22×C3×C4—21no—
151C22×C3×C4—22no—
152C22×C3×C4—32no—
153C22×C3×C4—32no—
154C22×C3×C4—32no—
155C22×C3×C4—32no—
156C22×C3×C4C22×D312yes—
157C22×C3×C4C22×D312yes—
158C22×C3×C4C22×D312yes—
159C22×Dic3—32no—
160C22×Dic3—32no—
161C22×Dic3—32no—
162C22×Dic3—32no—
163C22×Dic3—61no—
164C22×Dic3—61no—
165C22×Dic3—62no—
166C22×Dic3C22×D312yes—
167C22×Dic3C22×D312yes—
168C22×Dic3C22×D312yes—
169C22×Dic3C22×D312yes—
170C2×Dic6—38no—
171C2×Dic6—38no—
172C2×Dic6—122no—
173C2×Dic6—122no—
174C2×Dic6—122no—
175C2×Dic6—122no—
176C3×C4⋊C4—38no—
177C3×C4⋊C4—122no—
178C3×C42—122no—
179C4⋊Dic3—122no—
180C4⋊Dic3C4×D318yes—
181Dic3⋊C4—38no—
182Dic3⋊C4—38no—
183Dic3⋊C4—42no—
184Dic3⋊C4—122no—
185C4×Dic3—38no—
186C4×Dic3—42no—
187C4×Dic3—64no—
188C4×Dic3—122no—
189C4×Dic3—122no—
190C22×C32C23×C411yescharacteristic
191C22×C32H(5,𝔽2)11yescharacteristic
192C22×C32H(5,𝔽2)11yescharacteristic
193C22×C322−1+412yes—
194C22×C322−1+412yes—
195C32×C4—22no—
196C32×C4—42no—
197C3⋊Dic3—22no—
198C3⋊Dic3—22no—
199C3⋊Dic3—42no—
200C3×Dic3—24no—
201C3×Dic3—24no—
202C3×Dic3—42no—
203C3×Dic3—42no—
204C22×Q8—91no—
205C22×Q8—91no—
206C4⋊Q8—98no—
207C2×C4⋊C4—32no—
208C2×C4⋊C4—32no—
209C2×C4⋊C4—92no—
210C2×C4⋊C4—92no—
211C2×C42—32no—
212C2×C42—91no—
213C2×C42—92no—
214#95—32no—
215#95—32no—
216#95—32no—
217#95—91no—
218#95—91no—
219#95—92no—
220#95—92no—
221#95—92no—
222#95—92no—
223#95—91no—
224#95—92no—
225#95D3211yescharacteristic
226C23×C3—21no—
227C23×C3C23×D312yes—
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—22no—
235C2×C3×C4—22no—
236C2×C3×C4—22no—
237C2×C3×C4—34no—
238C2×C3×C4—34no—
239C2×C3×C4—42no—
240C2×C3×C4—42no—
241C2×C3×C4—42no—
242C2×C3×C4—42no—
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×C4—62no—
251C2×C3×C4—62no—
252C2×C3×C4—62no—
253C2×C3×C4C2×C4×D314yes—
254C2×Dic3—22no—
255C2×Dic3—22no—
256C2×Dic3—22no—
257C2×Dic3—22no—
258C2×Dic3—22no—
259C2×Dic3—22no—
260C2×Dic3—22no—
261C2×Dic3—22no—
262C2×Dic3—22no—
263C2×Dic3—22no—
264C2×Dic3—34no—
265C2×Dic3—34no—
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—62no—
276C2×Dic3—62no—
277C2×Dic3—62no—
278C2×Dic3—122no—
279C2×Dic3—121no—
280C2×Dic3—121no—
281C2×Dic3—122no—
282C2×Dic3—122no—
283C2×Dic3—122no—
284C2×Dic3C2×C4×D314yes—
285C2×Dic3C2×C4×D314yes—
286Dic6—128no—
287Dic6—128no—
288C2×C32#51811yescharacteristic
289C2×C32#51911yescharacteristic
290C2×C32#51911yescharacteristic
291C2×C32#56312yes—
292C2×C32#56312yes—
293C2×Q8—94no—
294C2×Q8—94no—
295C2×Q8—361no—
296C2×Q8—361no—
297C2×Q8—361no—
298C2×Q8—361no—
299C22×C4—32no—
300C22×C4—32no—
301C22×C4—32no—
302C22×C4—32no—
303C22×C4—91no—
304C22×C4—91no—
305C22×C4—92no—
306C22×C4C2×D3212yes—
307C22×C4C2×D3211yescharacteristic
308C4⋊C4—38no—
309C4⋊C4—98no—
310C4⋊C4—122no—
311C4⋊C4—362no—
312C42—94no—
313C42—122no—
314C42—362no—
315C22×C3—22no—
316C22×C3—21no—
317C22×C3—22no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3C22×C4×D312yes—
321C22×C3#100412yes—
322C22×C3#100712yes—
323C22×C3#100912yes—
324C22×C3#101012yes—
325C22×C3#101012yes—
326C22×C3#101012yes—
327C3×C4—24no—
328C3×C4—42no—
329C3×C4—42no—
330C3×C4—42no—
331C3×C4—64no—
332C3×C4—64no—
333C3×C4—82no—
334C3×C4—122no—
335C3×C4—122no—
336Dic3—24no—
337Dic3—24no—
338Dic3—42no—
339Dic3—42no—
340Dic3—64no—
341Dic3—64no—
342Dic3—122no—
343Dic3—122no—
344Dic3—122no—
345Dic3—122no—
346Dic3—242no—
347C32#238111yescharacteristic, complemented, Sylow
348C23C22×D3211yescharacteristic
349Q8—364no—
350Q8—364no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—34no—
356C2×C4—34no—
357C2×C4—62no—
358C2×C4—62no—
359C2×C4—62no—
360C2×C4—62no—
361C2×C4—62no—
362C2×C4—62no—
363C2×C4—62no—
364C2×C4—62no—
365C2×C4—62no—
366C2×C4—62no—
367C2×C4—92no—
368C2×C4—92no—
369C2×C4—182no—
370C2×C4—181no—
371C2×C4—181no—
372C2×C4—182no—
373C2×C4—182no—
374C2×C4—182no—
375C2×C4C4×D3212yes—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—22no—
380C2×C3—22no—
381C2×C3#551612yes—
382C2×C3#554512yes—
383C2×C3#557212yes—
384C2×C3#564612yes—
385C2×C3#565112yes—
386C2×C3#569912yes—
387C2×C3#571212yes—
388C22#6429712yes—
389C22C2×C4×D3211yescharacteristic
390C22#6430912yes—
391C22#6431311yescharacteristic
392C22#6432011yescharacteristic
393C4—22no—
394C4—42no—
395C4—64no—
396C4—64no—
397C4—122no—
398C4—122no—
399C4—182no—
400C4—182no—
401C4—362no—
402C3—21no—
403C3#7497712yescomplemented
404C2#1059384811yescharacteristic
405C2#1059404212yes—
406C2#1059424511yescharacteristic
407C2#1059450612yes—
408C2#1059460611yescharacteristic
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
347. C32#2381semidirect
403. 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×#46542
#105912692
#105912492
#105912352
#105912292
#105911932
#105911912
#749773