Finite Group Databasebeta

← #11803820

Subgroups — #11803820

Order 1152.

1177 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×#64097C211yesmaximal, characteristic
2C2×#63844C212yesmaximal
3C3×#4980C212yesmaximal
4#10591360C211yesmaximal, characteristic
5#10591273C212yesmaximal
6#10591271C212yesmaximal
7#10591263C212yesmaximal
8#10591252C211yesmaximal, characteristic
9#10591197C212yesmaximal
10#74948—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×#3724C2212yes—
21C2×Dic32C2212yes—
22C2×Dic32C2211yescharacteristic
23C2×Dic32C2211yescharacteristic
24#63844—28no—
25C3×C3⋊#95C2212yes—
26C3×C3⋊#95C2212yes—
27C3×C3⋊#95C2212yes—
28C3×C3⋊#95C2212yes—
29#63579C2212yes—
30#63579C2211yescharacteristic
31#63579C2212yes—
32#63579C2212yes—
33#63579C2211yescharacteristic
34C2×#888—32no—
35C2×#888—61no—
36C2×#887—32no—
37C2×C4×Dic6—32no—
38C3×#387—32no—
39#4980D312yes—
40#4978—32no—
41#4933—32no—
42#4655—32no—
43#4654—32no—
44#4653—32no—
45#4652—32no—
46#4650—32no—
47#4648—32no—
48#4646—32no—
49#4646—32no—
50C22×C32×C4C2312yes—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3C2311yescharacteristic
53C22×C3⋊Dic3C2312yes—
54C22×C3⋊Dic3C2311yescharacteristic
55C2×#634—24no—
56C2×#634—24no—
57C2×#634C2×C418yes—
58C22×C3×Dic3C2312yes—
59C22×C3×Dic3C2312yes—
60C22×C3×Dic3C2312yes—
61C22×C3×Dic3C2312yes—
62C32×C4⋊C4C2×C414yes—
63C4⋊(C3⋊Dic3)C2×C414yes—
64#3750C2×C418yes—
65C4×C3⋊Dic3C2×C414yes—
66C3×C4⋊Dic3—24no—
67C3×C4×Dic3—24no—
68#3724—24no—
69#3724—24no—
70Dic32—22no—
71Dic32—24no—
72Dic32D414yes—
73#2327—91noSylow
74C22×Dic6—32no—
75C22×Dic6—32no—
76C22×Dic6—62no—
77C2×C3×C4⋊C4—21no—
78C2×C3×C4⋊C4—32no—
79C2×C3×C4⋊C4C2×D312yes—
80C2×C3×C42—32no—
81C2×C4⋊Dic3—32no—
82C2×C4⋊Dic3—61no—
83C2×C4⋊Dic3C2×D312yes—
84C2×Dic3⋊C4—32no—
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×C4×Dic3—32no—
92C2×C4×Dic3—32no—
93C2×C4×Dic3—32no—
94C2×C4×Dic3—32no—
95C2×C4×Dic3—32no—
96C2×C4×Dic3—61no—
97C2×C4×Dic3C2×D312yes—
98#888—316no—
99#888—68no—
100#887—68no—
101C4×Dic6—68no—
102C3×#95—32no—
103C3×#95—32no—
104C3×#95—32no—
105C3×#95—32no—
106C3⋊#95—32no—
107C3⋊#95—32no—
108C3⋊#95—32no—
109C3⋊#95—32no—
110C3⋊#95—32no—
111C3⋊#95—32no—
112C3⋊#95—32no—
113C3⋊#95—32no—
114C3⋊#95C2×D312yes—
115C3⋊#95C2×D312yes—
116C3⋊#95C2×D312yes—
117C3⋊#95C2×D312yes—
118C23×C32C2411yescharacteristic
119C2×C32×C4—22no—
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4C22×C412yes—
123C2×C32×C4C22×C414yes—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3C22×C412yes—
128C2×C3⋊Dic3C22×C414yes—
129C2×C3⋊Dic3C22×C412yes—
130C2×C3⋊Dic3C2×D412yes—
131C2×C3⋊Dic3#4112yes—
132#634—216no—
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×Dic3—22no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3C2×D414yes—
145C2×C4⋊Q8—91no—
146C2×C4×Q8—92no—
147#391—92no—
148#387—32no—
149#387—92no—
150#387—92no—
151#387—92no—
152#382—91no—
153#376—91no—
154C22×C3×C4—21no—
155C22×C3×C4—22no—
156C22×C3×C4—32no—
157C22×C3×C4—32no—
158C22×C3×C4—32no—
159C22×C3×C4—32no—
160C22×C3×C4C22×D312yes—
161C22×C3×C4C22×D312yes—
162C22×C3×C4C22×D312yes—
163C22×Dic3—32no—
164C22×Dic3—32no—
165C22×Dic3—32no—
166C22×Dic3—32no—
167C22×Dic3—61no—
168C22×Dic3—61no—
169C22×Dic3—62no—
170C22×Dic3C22×D312yes—
171C22×Dic3C22×D312yes—
172C22×Dic3C22×D312yes—
173C22×Dic3C22×D312yes—
174C2×Dic6—38no—
175C2×Dic6—38no—
176C2×Dic6—68no—
177C2×Dic6—64no—
178C2×Dic6—64no—
179C2×Dic6—64no—
180C2×Dic6—64no—
181C2×Dic6—124no—
182C2×Dic6—124no—
183C3×C4⋊C4—24no—
184C3×C4⋊C4—64no—
185C3×C4⋊C4C4×D318yes—
186C3×C42—64no—
187C4⋊Dic3—24no—
188C4⋊Dic3—38no—
189C4⋊Dic3—64no—
190Dic3⋊C4—38no—
191Dic3⋊C4—38no—
192Dic3⋊C4—68no—
193Dic3⋊C4—64no—
194Dic3⋊C4—64no—
195Dic3⋊C4—64no—
196Dic3⋊C4—64no—
197C4×Dic3—24no—
198C4×Dic3—38no—
199C4×Dic3—38no—
200C4×Dic3—64no—
201C4×Dic3—64no—
202C4×Dic3—64no—
203C4×Dic3—64no—
204C22×C32C23×C411yescharacteristic
205C22×C32C22×D411yescharacteristic
206C22×C32C2×#4111yescharacteristic
207C22×C322−1+412yes—
208C22×C322−1+412yes—
209C32×C4—22no—
210C32×C4—24no—
211C3⋊Dic3—22no—
212C3⋊Dic3—24no—
213C3⋊Dic3C4×D414yes—
214C3×Dic3—24no—
215C3×Dic3—42no—
216C3×Dic3—42no—
217C3×Dic3—42no—
218C22×Q8—92no—
219C4⋊Q8—98no—
220C4×Q8—188no—
221C2×C4⋊C4—32no—
222C2×C4⋊C4—92no—
223C2×C4⋊C4—91no—
224C2×C4⋊C4—92no—
225C2×C4⋊C4—92no—
226C2×C4⋊C4D3211yescharacteristic
227C2×C42—32no—
228C2×C42—91no—
229C2×C42—91no—
230C2×C42—92no—
231C2×C42—91no—
232#95—32no—
233#95—32no—
234#95—32no—
235#95—32no—
236#95—92no—
237#95—91no—
238#95—91no—
239#95—92no—
240#95—92no—
241C23×C3—21no—
242C23×C3C23×D312yes—
243C2×C3×C4—24no—
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—24no—
252C2×C3×C4—34no—
253C2×C3×C4—42no—
254C2×C3×C4—42no—
255C2×C3×C4—62no—
256C2×C3×C4—62no—
257C2×C3×C4—62no—
258C2×C3×C4—62no—
259C2×C3×C4—62no—
260C2×C3×C4—62no—
261C2×C3×C4—62no—
262C2×C3×C4—62no—
263C2×C3×C4—62no—
264C2×C3×C4—62no—
265C2×C3×C4—62no—
266C2×C3×C4C2×C4×D314yes—
267C2×C3×C4C2×C4×D314yes—
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—22no—
277C2×Dic3—22no—
278C2×Dic3—22no—
279C2×Dic3—22no—
280C2×Dic3—34no—
281C2×Dic3—34no—
282C2×Dic3—34no—
283C2×Dic3—34no—
284C2×Dic3—34no—
285C2×Dic3—34no—
286C2×Dic3—62no—
287C2×Dic3—62no—
288C2×Dic3—62no—
289C2×Dic3—62no—
290C2×Dic3—64no—
291C2×Dic3—64no—
292C2×Dic3—62no—
293C2×Dic3—62no—
294C2×Dic3—62no—
295C2×Dic3—62no—
296C2×Dic3—62no—
297C2×Dic3—62no—
298C2×Dic3—122no—
299C2×Dic3—122no—
300C2×Dic3D3×D414yes—
301Dic6—616no—
302Dic6—616no—
303Dic6—1216no—
304C2×C32C2×C4×D411yescharacteristic
305C2×C32#51911yescharacteristic
306C2×C32#51911yescharacteristic
307C2×C32#53612yes—
308C2×C32#54112yes—
309C2×Q8—98no—
310C2×Q8—184no—
311C2×Q8—184no—
312C22×C4—32no—
313C22×C4—32no—
314C22×C4—32no—
315C22×C4—32no—
316C22×C4—91no—
317C22×C4—91no—
318C22×C4—92no—
319C22×C4C2×D3211yescharacteristic
320C22×C4C2×D3212yes—
321C4⋊C4—64no—
322C4⋊C4—98no—
323C4⋊C4—94no—
324C4⋊C4—184no—
325C4⋊C4—184no—
326C4⋊C4#62414yes—
327C42—64no—
328C42—94no—
329C42—94no—
330C42—184no—
331C42—182no—
332C22×C3—22no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—22no—
336C22×C3—21no—
337C22×C3C22×C4×D312yes—
338C22×C3C2×D3×D412yes—
339C22×C3#100712yes—
340C22×C3D3×#4112yes—
341C22×C3#101012yes—
342C22×C3#101012yes—
343C22×C3#101012yes—
344C3×C4—24no—
345C3×C4—24no—
346C3×C4—24no—
347C3×C4—24no—
348C3×C4—44no—
349C3×C4—64no—
350C3×C4—122no—
351C3×C4—122no—
352C3×C4—122no—
353Dic3—24no—
354Dic3—38no—
355Dic3—42no—
356Dic3—42no—
357Dic3—42no—
358Dic3—64no—
359Dic3—64no—
360Dic3—64no—
361Dic3—64no—
362Dic3—64no—
363Dic3—124no—
364C32#232711yescharacteristic, complemented, Sylow
365C23C22×D3211yescharacteristic
366Q8—1816no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—34no—
371C2×C4—62no—
372C2×C4—62no—
373C2×C4—62no—
374C2×C4—62no—
375C2×C4—62no—
376C2×C4—62no—
377C2×C4—62no—
378C2×C4—62no—
379C2×C4—62no—
380C2×C4—62no—
381C2×C4—62no—
382C2×C4—92no—
383C2×C4—92no—
384C2×C4—92no—
385C2×C4—92no—
386C2×C4—94no—
387C2×C4—182no—
388C2×C4—182no—
389C2×C4—182no—
390C2×C4C2×#62412yes—
391C2×C4C2×#62414yes—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—22no—
395C2×C3—21no—
396C2×C3—22no—
397C2×C3#551612yes—
398C2×C3C4×D3×D412yes—
399C2×C3#557212yes—
400C2×C3#562812yes—
401C2×C3#564812yes—
402C2×C3#569612yes—
403C2×C3#570112yes—
404C22#6429812yes—
405C22D32×D411yescharacteristic
406C22#6431211yescharacteristic
407C22#6431512yes—
408C22C22×#62411yescharacteristic
409C4—22no—
410C4—24no—
411C4—64no—
412C4—94no—
413C4—122no—
414C4—122no—
415C4—122no—
416C4—182no—
417C4—184no—
418C3—21no—
419C3#7494812yescomplemented
420C2#1059436512yes—
421C2#1059447912yes—
422C2#1059482811yescharacteristic
423C2D4×#62411yescharacteristic
424C2#1059533911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32#2327
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
364. C32#2327semidirect
419. C3#74948semidirect

Maximal subgroups

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

subgroupindex
C2×#640972
C2×#638442
C3×#49802
#105913602
#105912732
#105912712
#105912632
#105912522
#105911972
#749483