Finite Group Databasebeta

← #11805613

Subgroups — #11805613

Order 1152.

1181 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63838C211yesmaximal, characteristic
2C2×#63837C212yesmaximal
3#10592349C211yesmaximal, characteristic
4C3×#4647C212yesmaximal
5#10591274C211yesmaximal, characteristic
6#10591265C212yesmaximal
7#10591256C212yesmaximal
8#10591245C212yesmaximal
9Dic3×Dic3⋊C4C212yesmaximal
10#75982—32nomaximal
11C22×#627C2211yescharacteristic
12C2×#3750C2212yes—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic3C2212yes—
15C2×C3×Dic3⋊C4C2212yes—
16C2×C3×Dic3⋊C4C2212yes—
17C2×C3×Dic3⋊C4C2212yes—
18C2×C3×C4×Dic3C2212yes—
19C2×#3724C2211yescharacteristic
20C2×Dic3⋊Dic3C2212yes—
21C2×Dic3⋊Dic3C2212yes—
22C2×Dic32C2212yes—
23C2×Dic32C2212yes—
24C2×Dic32C2212yes—
25#63838C418yescomplemented
26#63837—28no—
27C32×#95C2211yescharacteristic
28#63658C2212yes—
29#63658C2211yescharacteristic
30C3×C3⋊#95C2212yes—
31#63579C2211yescharacteristic
32#63579C2211yescharacteristic
33#63579C2212yes—
34C2×#887—32no—
35C2×#887—32no—
36C2×C4×Dic6—32no—
37C3×#389—32no—
38#4984—32no—
39#4977—32no—
40#4976—32no—
41#4976—32no—
42Dic3×C4⋊C4—32no—
43Dic3×C4⋊C4—32no—
44C4×Dic3⋊C4—32no—
45#4650—32no—
46#4650—32no—
47#4650—61no—
48#4647—32no—
49#4647D312yes—
50C22×C32×C4C2312yes—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3C2312yes—
53C22×C3⋊Dic3C2311yescharacteristic
54C22×C3⋊Dic3C2311yescharacteristic
55C22×C3×Dic3C2312yes—
56C22×C3×Dic3C2312yes—
57C22×C3×Dic3C2312yes—
58C22×C3×Dic3C2312yes—
59C2×#627C2×C414yes—
60C2×#627D414yes—
61C2×#627Q814yes—
62#3750—24no—
63C4×C3⋊Dic3C2×C414yes—
64C3×C4⋊Dic3—24no—
65C3×Dic3⋊C4—24no—
66C3×Dic3⋊C4—24no—
67C3×Dic3⋊C4C2×C418yes—
68C3×C4×Dic3—24no—
69#3724C2×C414yes—
70Dic3⋊Dic3—24no—
71Dic3⋊Dic3—24no—
72Dic32—24no—
73Dic32—24no—
74Dic32C2×C418yes—
75#2351—91noSylow
76C22×Dic6—32no—
77C2×C3×C4⋊C4—32no—
78C2×C3×C4⋊C4—32no—
79C2×C3×C4⋊C4—32no—
80C2×C3×C4⋊C4—32no—
81C2×C3×C42—32no—
82C2×C4⋊Dic3—32no—
83C2×C4⋊Dic3—32no—
84C2×C4⋊Dic3C2×D312yes—
85C2×Dic3⋊C4—32no—
86C2×Dic3⋊C4—32no—
87C2×Dic3⋊C4—32no—
88C2×Dic3⋊C4—32no—
89C2×Dic3⋊C4—32no—
90C2×Dic3⋊C4—62no—
91C2×Dic3⋊C4C2×D312yes—
92C2×Dic3⋊C4C2×D312yes—
93C2×Dic3⋊C4C2×D312yes—
94C2×C4×Dic3—32no—
95C2×C4×Dic3—32no—
96C2×C4×Dic3—32no—
97C2×C4×Dic3—32no—
98C2×C4×Dic3—32no—
99C2×C4×Dic3—32no—
100C2×C4×Dic3—32no—
101C2×C4×Dic3—61no—
102C2×C4×Dic3C2×D312yes—
103#887—316no—
104#887—68no—
105C4×Dic6—68no—
106C3×#95—21no—
107C3×#95—32no—
108C3×#95C2×D312yes—
109C3⋊#95—32no—
110C3⋊#95—32no—
111C3⋊#95—32no—
112C3⋊#95—32no—
113C3⋊#95—32no—
114C3⋊#95—32no—
115C3⋊#95—32no—
116C3⋊#95—62no—
117C3⋊#95—61no—
118C3⋊#95C2×D312yes—
119C23×C32C2411yescharacteristic
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C32×C4C22×C412yes—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3C22×C412yes—
130C2×C3⋊Dic3C22×C412yes—
131C2×C3⋊Dic3C2×D412yes—
132C2×C3⋊Dic3C2×Q812yes—
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×C3×Dic3—22no—
140C2×C3×Dic3C22×C414yes—
141C2×C3×Dic3C22×C414yes—
142C2×C3×Dic3C2×D414yes—
143C2×C3×Dic3C2×Q814yes—
144C2×C3×Dic3#4114yes—
145#627C4⋊C4116yescomplemented
146C2×C4×Q8—92no—
147C2×C4×Q8—91no—
148#389—32no—
149#389—92no—
150#389—92no—
151#382—92no—
152#382—91no—
153C4×C4⋊C4—92no—
154C4×C4⋊C4—91no—
155C22×C3×C4—21no—
156C22×C3×C4—22no—
157C22×C3×C4—32no—
158C22×C3×C4—32no—
159C22×C3×C4—32no—
160C22×C3×C4—32no—
161C22×C3×C4C22×D312yes—
162C22×C3×C4C22×D312yes—
163C22×C3×C4C22×D312yes—
164C22×Dic3—32no—
165C22×Dic3—32no—
166C22×Dic3—32no—
167C22×Dic3—32no—
168C22×Dic3—61no—
169C22×Dic3—61no—
170C22×Dic3—62no—
171C22×Dic3C22×D312yes—
172C22×Dic3C22×D312yes—
173C22×Dic3C22×D312yes—
174C22×Dic3C22×D312yes—
175C2×Dic6—38no—
176C2×Dic6—38no—
177C2×Dic6—38no—
178C3×C4⋊C4—38no—
179C3×C4⋊C4—64no—
180C3×C4⋊C4—64no—
181C3×C4⋊C4—64no—
182C3×C42—64no—
183C4⋊Dic3—24no—
184C4⋊Dic3—64no—
185C4⋊Dic3—64no—
186Dic3⋊C4—24no—
187Dic3⋊C4—24no—
188Dic3⋊C4—38no—
189Dic3⋊C4—64no—
190Dic3⋊C4—64no—
191Dic3⋊C4—64no—
192Dic3⋊C4—64no—
193Dic3⋊C4—124no—
194Dic3⋊C4C4×D318yes—
195C4×Dic3—24no—
196C4×Dic3—38no—
197C4×Dic3—38no—
198C4×Dic3—38no—
199C4×Dic3—64no—
200C4×Dic3—64no—
201C4×Dic3—64no—
202C4×Dic3—64no—
203C4×Dic3—64no—
204C22×C32C23×C411yescharacteristic
205C22×C32C22×D411yescharacteristic
206C22×C32C22×Q811yescharacteristic
207C22×C32C2×#4112yes—
208C22×C322−1+412yes—
209C32×C4—22no—
210C32×C4—42no—
211C3⋊Dic3—22no—
212C3⋊Dic3—42no—
213C3⋊Dic3C2×C4⋊C414yes—
214C3×Dic3—24no—
215C3×Dic3—24no—
216C3×Dic3—42no—
217C3×Dic3C2×C4⋊C418yes—
218C22×Q8—91no—
219C4×Q8—98no—
220C4×Q8—188no—
221C2×C4⋊C4—32no—
222C2×C4⋊C4—32no—
223C2×C4⋊C4—32no—
224C2×C4⋊C4—32no—
225C2×C4⋊C4—91no—
226C2×C4⋊C4—92no—
227C2×C4⋊C4—92no—
228C2×C4⋊C4—92no—
229C2×C42—32no—
230C2×C42—92no—
231C2×C42—91no—
232C2×C42—92no—
233C2×C42—92no—
234#95—32no—
235#95—91no—
236#95—91no—
237#95—92no—
238#95—92no—
239#95—91no—
240#95D3211yescharacteristic
241C23×C3—21no—
242C23×C3C23×D312yes—
243C2×C3×C4—22no—
244C2×C3×C4—22no—
245C2×C3×C4—22no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4—22no—
250C2×C3×C4—22no—
251C2×C3×C4—22no—
252C2×C3×C4—34no—
253C2×C3×C4—34no—
254C2×C3×C4—34no—
255C2×C3×C4—34no—
256C2×C3×C4—34no—
257C2×C3×C4—42no—
258C2×C3×C4—42no—
259C2×C3×C4—42no—
260C2×C3×C4—42no—
261C2×C3×C4—62no—
262C2×C3×C4—62no—
263C2×C3×C4—62no—
264C2×C3×C4—62no—
265C2×C3×C4—62no—
266C2×C3×C4—62no—
267C2×C3×C4—62no—
268C2×C3×C4C2×C4×D314yes—
269C2×Dic3—22no—
270C2×Dic3—22no—
271C2×Dic3—22no—
272C2×Dic3—22no—
273C2×Dic3—22no—
274C2×Dic3—22no—
275C2×Dic3—22no—
276C2×Dic3—34no—
277C2×Dic3—34no—
278C2×Dic3—34no—
279C2×Dic3—34no—
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—62no—
289C2×Dic3—62no—
290C2×Dic3—62no—
291C2×Dic3—62no—
292C2×Dic3—122no—
293C2×Dic3—122no—
294C2×Dic3—122no—
295C2×Dic3—122no—
296C2×Dic3C2×C4×D314yes—
297C2×Dic3C2×C4×D314yes—
298C2×Dic3D3×D414yes—
299C2×Dic3#23714yes—
300C2×Dic3D3×Q814yes—
301Dic6—332no—
302C2×C32C22×C4⋊C411yescharacteristic
303C2×C32C4×#4111yescharacteristic
304C2×C32#51911yescharacteristic
305C2×C32#54812yes—
306C2×C32#55712yes—
307C2×Q8—94no—
308C2×Q8—94no—
309C2×Q8—94no—
310C22×C4—32no—
311C22×C4—32no—
312C22×C4—32no—
313C22×C4—32no—
314C22×C4—91no—
315C22×C4—91no—
316C22×C4—92no—
317C22×C4C2×D3212yes—
318C22×C4C2×D3211yescharacteristic
319C4⋊C4—38no—
320C4⋊C4—64no—
321C4⋊C4—64no—
322C4⋊C4—64no—
323C4⋊C4—94no—
324C4⋊C4—184no—
325C4⋊C4—184no—
326C4⋊C4—184no—
327C42—64no—
328C42—98no—
329C42—94no—
330C42—184no—
331C42—184no—
332C22×C3—22no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—22no—
336C22×C3—21no—
337C22×C3C22×C4×D312yes—
338C22×C3C2×D3×D412yes—
339C22×C3C2×#23712yes—
340C22×C3C2×D3×Q812yes—
341C22×C3#100712yes—
342C22×C3D3×#4112yes—
343C22×C3#101012yes—
344C3×C4—24no—
345C3×C4—38no—
346C3×C4—42no—
347C3×C4—42no—
348C3×C4—42no—
349C3×C4—64no—
350C3×C4—64no—
351C3×C4—82no—
352C3×C4—122no—
353Dic3—24no—
354Dic3—24no—
355Dic3—38no—
356Dic3—42no—
357Dic3—64no—
358Dic3—64no—
359Dic3—122no—
360Dic3—122no—
361Dic3—122no—
362Dic3—242no—
363Dic3D3×C4⋊C418yes—
364C32#235111yescharacteristic, complemented, Sylow
365C23C22×D3211yescharacteristic
366Q8—916no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—34no—
372C2×C4—34no—
373C2×C4—34no—
374C2×C4—34no—
375C2×C4—34no—
376C2×C4—62no—
377C2×C4—62no—
378C2×C4—62no—
379C2×C4—62no—
380C2×C4—62no—
381C2×C4—62no—
382C2×C4—62no—
383C2×C4—92no—
384C2×C4—92no—
385C2×C4—92no—
386C2×C4—92no—
387C2×C4—182no—
388C2×C4—182no—
389C2×C4—182no—
390C2×C4—182no—
391C2×C4C4×D3212yes—
392C2×C3—21no—
393C2×C3—22no—
394C2×C3—22no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3C2×D3×C4⋊C412yes—
398C2×C3C4×#23712yes—
399C2×C3#557212yes—
400C2×C3#559812yes—
401C2×C3#563312yes—
402C2×C3#568512yes—
403C2×C3#572112yes—
404C22#6429712yes—
405C22C2×C4×D3211yescharacteristic
406C22D32×D411yescharacteristic
407C22D3×#23712yes—
408C22D32×Q811yescharacteristic
409C4—22no—
410C4—38no—
411C4—42no—
412C4—64no—
413C4—64no—
414C4—94no—
415C4—122no—
416C4—182no—
417C4—362no—
418C3—21no—
419C3#7598212yescomplemented
420C2#1059384811yescharacteristic
421C2#1059405011yescharacteristic
422C2#1059407412yes—
423C2#1059431412yes—
424C2D32×C4⋊C411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, prime radical, cosocleC23×C32C24
hypercenter#95D32
hypocenterC32#2351
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
25. #63838C4semidirect
145. #627C4⋊C4semidirect
364. C32#2351semidirect
419. C3#75982semidirect

Maximal subgroups

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

subgroupindex
C2×#638382
C2×#638372
#105923492
C3×#46472
#105912742
#105912652
#105912562
#105912452
Dic3×Dic3⋊C42
#759823