Finite Group Databasebeta

← #11807965

Subgroups — #11807965

Order 1152.

993 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64097C211yesmaximal, characteristic
2C3×#4980C212yesmaximal
3#10591273C212yesmaximal
4#10591271C212yesmaximal
5#10591263C212yesmaximal
6#10591229C211yesmaximal, characteristic
7#10591229C211yesmaximal, characteristic
8#10591213C212yesmaximal
9#10591197C212yesmaximal
10#74977—32nomaximal
11C22×#634C2212yes—
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3750C2212yes—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16#64097C418yescomplemented
17C2×C3×C4⋊Dic3C2212yes—
18C2×C3×C4×Dic3C2212yes—
19C2×#3724C2212yes—
20C2×Dic32C2212yes—
21C3×C3⋊#95C2212yes—
22C3×C3⋊#95C2212yes—
23C3×C3⋊#95C2212yes—
24C3×C3⋊#95C2212yes—
25#63579C2211yescharacteristic
26#63579C2212yes—
27#63579C2212yes—
28#63579C2212yes—
29#63579C2211yescharacteristic
30#63579C2212yes—
31#63579C2211yescharacteristic
32#63579C2211yescharacteristic
33C2×#888—32no—
34C2×#888—61no—
35C3×#387—32no—
36#4980D312yes—
37#4978—32no—
38#4973—32no—
39#4933—32no—
40#4929—32no—
41#4655—32no—
42#4654—32no—
43#4653—32no—
44#4652—32no—
45#4651—32no—
46#4651—32no—
47#4646—32no—
48#4646—32no—
49C22×C32×C4C2312yes—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3C2311yescharacteristic
52C22×C3⋊Dic3C2311yescharacteristic
53C22×C3⋊Dic3C2312yes—
54C2×#634—42no—
55C2×#634—42no—
56C2×#634C2×C418yes—
57C22×C3×Dic3C2312yes—
58C22×C3×Dic3C2312yes—
59C22×C3×Dic3C2312yes—
60C22×C3×Dic3C2312yes—
61C32×C4⋊C4C2×C414yes—
62C4⋊(C3⋊Dic3)C2×C414yes—
63#3750C2×C418yes—
64C4×C3⋊Dic3C2×C414yes—
65C3×C4⋊Dic3—42no—
66C3×C4×Dic3—42no—
67#3724—42no—
68Dic32—42no—
69#2381—91noSylow
70C22×Dic6—32no—
71C22×Dic6—32no—
72C22×Dic6—62no—
73C2×C3×C4⋊C4—21no—
74C2×C3×C4⋊C4—32no—
75C2×C3×C4⋊C4C2×D312yes—
76C2×C3×C42—32no—
77C2×C4⋊Dic3—32no—
78C2×C4⋊Dic3—61no—
79C2×C4⋊Dic3C2×D312yes—
80C2×Dic3⋊C4—32no—
81C2×Dic3⋊C4—32no—
82C2×Dic3⋊C4—32no—
83C2×Dic3⋊C4—32no—
84C2×Dic3⋊C4—62no—
85C2×C4×Dic3—32no—
86C2×C4×Dic3—32no—
87C2×C4×Dic3—32no—
88C2×C4×Dic3—61no—
89C2×C4×Dic3C2×D312yes—
90#888—316no—
91#888—68no—
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—32no—
106C3⋊#95—32no—
107C3⋊#95—32no—
108C3⋊#95C2×D312yes—
109C3⋊#95C2×D312yes—
110C3⋊#95C2×D312yes—
111C3⋊#95C2×D312yes—
112C23×C32C2411yescharacteristic
113C2×C32×C4—21no—
114C2×C32×C4—21no—
115C2×C32×C4—22no—
116C2×C32×C4—22no—
117C2×C32×C4C22×C412yes—
118C2×C32×C4C22×C414yes—
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3—22no—
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3C22×C412yes—
124C2×C3⋊Dic3C22×C412yes—
125C2×C3⋊Dic3C22×C414yes—
126#634—48no—
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×Dic3—22no—
138C2×C3×Dic3—22no—
139C2×C4⋊Q8—91no—
140#391—92no—
141#391—92no—
142#387—32no—
143#387—92no—
144#387—92no—
145#387—92no—
146#383—91no—
147#383—91no—
148C22×C3×C4—21no—
149C22×C3×C4—22no—
150C22×C3×C4—32no—
151C22×C3×C4—32no—
152C22×C3×C4—32no—
153C22×C3×C4—32no—
154C22×C3×C4C22×D312yes—
155C22×C3×C4C22×D312yes—
156C22×C3×C4C22×D312yes—
157C22×Dic3—32no—
158C22×Dic3—32no—
159C22×Dic3—32no—
160C22×Dic3—32no—
161C22×Dic3—61no—
162C22×Dic3—61no—
163C22×Dic3—62no—
164C22×Dic3C22×D312yes—
165C22×Dic3C22×D312yes—
166C22×Dic3C22×D312yes—
167C22×Dic3C22×D312yes—
168C2×Dic6—38no—
169C2×Dic6—38no—
170C2×Dic6—68no—
171C2×Dic6—122no—
172C2×Dic6—122no—
173C2×Dic6—122no—
174C2×Dic6—122no—
175C2×Dic6—124no—
176C2×Dic6—124no—
177C3×C4⋊C4—24no—
178C3×C4⋊C4—122no—
179C3×C4⋊C4C4×D318yes—
180C3×C42—122no—
181C4⋊Dic3—38no—
182C4⋊Dic3—42no—
183C4⋊Dic3—64no—
184Dic3⋊C4—38no—
185Dic3⋊C4—38no—
186Dic3⋊C4—68no—
187Dic3⋊C4—122no—
188Dic3⋊C4—122no—
189C4×Dic3—38no—
190C4×Dic3—42no—
191C4×Dic3—64no—
192C4×Dic3—122no—
193C4×Dic3—122no—
194C22×C32C23×C411yescharacteristic
195C22×C32H(5,𝔽2)12yes—
196C22×C322−1+412yes—
197C22×C322−1+411yescharacteristic
198C22×C322−1+411yescharacteristic
199C32×C4—22no—
200C32×C4—24no—
201C3⋊Dic3—22no—
202C3⋊Dic3—22no—
203C3⋊Dic3—24no—
204C3×Dic3—42no—
205C3×Dic3—42no—
206C3×Dic3—42no—
207C3×Dic3—42no—
208C22×Q8—92no—
209C4⋊Q8—98no—
210C2×C4⋊C4—32no—
211C2×C4⋊C4—92no—
212C2×C4⋊C4—91no—
213C2×C4⋊C4—92no—
214C2×C4⋊C4D3211yescharacteristic
215C2×C42—32no—
216C2×C42—91no—
217C2×C42—92no—
218#95—32no—
219#95—32no—
220#95—32no—
221#95—32no—
222#95—92no—
223#95—91no—
224#95—91no—
225#95—91no—
226#95—92no—
227#95—91no—
228#95—92no—
229#95—92no—
230C23×C3—21no—
231C23×C3C23×D312yes—
232C2×C3×C4—22no—
233C2×C3×C4—22no—
234C2×C3×C4—22no—
235C2×C3×C4—22no—
236C2×C3×C4—22no—
237C2×C3×C4—22no—
238C2×C3×C4—22no—
239C2×C3×C4—22no—
240C2×C3×C4—22no—
241C2×C3×C4—24no—
242C2×C3×C4—42no—
243C2×C3×C4—42no—
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×C4—62no—
254C2×C3×C4—62no—
255C2×C3×C4—62no—
256C2×C3×C4C2×C4×D314yes—
257C2×C3×C4C2×C4×D314yes—
258C2×C3×C4C2×C4×D314yes—
259C2×Dic3—22no—
260C2×Dic3—22no—
261C2×Dic3—22no—
262C2×Dic3—22no—
263C2×Dic3—22no—
264C2×Dic3—22no—
265C2×Dic3—22no—
266C2×Dic3—22no—
267C2×Dic3—22no—
268C2×Dic3—22no—
269C2×Dic3—22no—
270C2×Dic3—22no—
271C2×Dic3—34no—
272C2×Dic3—34no—
273C2×Dic3—34no—
274C2×Dic3—34no—
275C2×Dic3—62no—
276C2×Dic3—62no—
277C2×Dic3—64no—
278C2×Dic3—64no—
279C2×Dic3—64no—
280C2×Dic3—62no—
281C2×Dic3—62no—
282C2×Dic3—62no—
283C2×Dic3—62no—
284C2×Dic3—62no—
285C2×Dic3—62no—
286C2×Dic3—62no—
287C2×Dic3—62no—
288C2×Dic3—122no—
289C2×Dic3—122no—
290Dic6—128no—
291Dic6—128no—
292Dic6—1216no—
293C2×C32#51811yescharacteristic
294C2×C32#51911yescharacteristic
295C2×C32#51911yescharacteristic
296C2×C32#56312yes—
297C2×C32#56312yes—
298C2×Q8—98no—
299C2×Q8—362no—
300C2×Q8—362no—
301C22×C4—32no—
302C22×C4—32no—
303C22×C4—32no—
304C22×C4—32no—
305C22×C4—91no—
306C22×C4—91no—
307C22×C4—92no—
308C22×C4C2×D3211yescharacteristic
309C22×C4C2×D3212yes—
310C4⋊C4—98no—
311C4⋊C4—94no—
312C4⋊C4—122no—
313C4⋊C4—362no—
314C4⋊C4#62414yes—
315C42—94no—
316C42—122no—
317C42—362no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—22no—
321C22×C3—22no—
322C22×C3—21no—
323C22×C3C22×C4×D312yes—
324C22×C3#100412yes—
325C22×C3#100712yes—
326C22×C3#100912yes—
327C22×C3#101012yes—
328C22×C3#101012yes—
329C22×C3#101012yes—
330C3×C4—24no—
331C3×C4—24no—
332C3×C4—24no—
333C3×C4—24no—
334C3×C4—44no—
335C3×C4—122no—
336C3×C4—122no—
337C3×C4—122no—
338C3×C4—122no—
339Dic3—42no—
340Dic3—42no—
341Dic3—42no—
342Dic3—42no—
343Dic3—64no—
344Dic3—64no—
345Dic3—64no—
346Dic3—64no—
347Dic3—64no—
348Dic3—64no—
349Dic3—124no—
350C32#238111yescharacteristic, complemented, Sylow
351C23C22×D3211yescharacteristic
352Q8—368no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—22no—
356C2×C4—22no—
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—62no—
368C2×C4—62no—
369C2×C4—92no—
370C2×C4—92no—
371C2×C4—94no—
372C2×C4—182no—
373C2×C4—182no—
374C2×C4—182no—
375C2×C4—182no—
376C2×C4C2×#62412yes—
377C2×C4C2×#62414yes—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—22no—
381C2×C3—21no—
382C2×C3—22no—
383C2×C3#551612yes—
384C2×C3#554512yes—
385C2×C3#557212yes—
386C2×C3#564612yes—
387C2×C3#565112yes—
388C2×C3#569912yes—
389C2×C3#571212yes—
390C22#6429811yescharacteristic
391C22#6429811yescharacteristic
392C22#6431412yes—
393C22#6431512yes—
394C22C22×#62411yescharacteristic
395C4—22no—
396C4—24no—
397C4—122no—
398C4—122no—
399C4—122no—
400C4—122no—
401C4—182no—
402C4—182no—
403C4—184no—
404C3—21no—
405C3#7497712yescomplemented
406C2#1059449912yes—
407C2#1059459112yes—
408C2#1059482811yescharacteristic
409C2#1059522311yescharacteristic
410C2#1059533911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32#2381
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
16. #64097C4semidirect
350. C32#2381semidirect
405. C3#74977semidirect

Maximal subgroups

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

subgroupindex
C2×#640972
C3×#49802
#105912732
#105912712
#105912632
#105912292
#105912132
#105911972
#749773