Finite Group Databasebeta

← #11808853

Subgroups — #11808853

Order 1152.

1105 conjugacy classes of subgroups.

The subgroup lattice has 423 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63838C212yesmaximal
2#10592348C211yesmaximal, characteristic
3C3×#4657C212yesmaximal
4#10591338C212yesmaximal
5#10591274C211yesmaximal, characteristic
6#10591252C211yesmaximal, characteristic
7#10591241C212yesmaximal
8#10591198C212yesmaximal
9#10591195C212yesmaximal
10#77740—32nomaximal
11C22×#627C2212yes—
12C2×#3750C2212yes—
13C2×C4×C3⋊Dic3C2212yes—
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2212yes—
16C2×C3×Dic3⋊C4C2212yes—
17C2×C3×Dic3⋊C4C2212yes—
18C2×C3×Dic3⋊C4C2212yes—
19C2×#3724C2212yes—
20C2×Dic3⋊Dic3C2212yes—
21C2×Dic32C2212yes—
22C2×Dic32C2211yescharacteristic
23C2×Dic32C2211yescharacteristic
24#63838—28no—
25C32×#95C2211yescharacteristic
26#63658C2211yescharacteristic
27C3×C3⋊#95C2212yes—
28C3×C3⋊#95C2212yes—
29#63579C2212yes—
30#63579C2212yes—
31#63579C2211yescharacteristic
32#63579C2211yescharacteristic
33C2×#887—32no—
34C2×#887—32no—
35C3×#398—32no—
36#4983—32no—
37#4979—32no—
38#4979—32no—
39#4979—32no—
40Dic3×C4⋊C4—32no—
41Dic3×C4⋊C4—32no—
42#4657—32no—
43#4657D312yes—
44#4656—32no—
45#4649—32no—
46#4649—32no—
47#4649—61no—
48#4648—32no—
49C22×C32×C4C2312yes—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3C2311yescharacteristic
52C22×C3⋊Dic3C2312yes—
53C22×C3⋊Dic3C2311yescharacteristic
54C22×C3×Dic3C2312yes—
55C22×C3×Dic3C2312yes—
56C22×C3×Dic3C2312yes—
57C22×C3×Dic3C2312yes—
58C2×#627—24no—
59C2×#627—24no—
60C2×#627—24no—
61#3750—24no—
62C4×C3⋊Dic3—24no—
63C4×C3⋊Dic3Q814yescomplemented
64C3×C4⋊Dic3—24no—
65C3×Dic3⋊C4—24no—
66C3×Dic3⋊C4—24no—
67C3×Dic3⋊C4—24no—
68#3724—24no—
69Dic3⋊Dic3—24no—
70Dic32—24no—
71Dic32D414yes—
72Dic32Q814yescomplemented
73#2399—91noSylow
74C22×Dic6—32no—
75C22×Dic6—32no—
76C2×C3×C4⋊C4—32no—
77C2×C3×C4⋊C4—32no—
78C2×C3×C4⋊C4—32no—
79C2×C3×C4⋊C4—32no—
80C2×C4⋊Dic3—32no—
81C2×C4⋊Dic3C2×D312yes—
82C2×Dic3⋊C4—32no—
83C2×Dic3⋊C4—32no—
84C2×Dic3⋊C4—32no—
85C2×Dic3⋊C4—32no—
86C2×Dic3⋊C4—32no—
87C2×Dic3⋊C4—62no—
88C2×Dic3⋊C4C2×D312yes—
89C2×Dic3⋊C4C2×D312yes—
90C2×Dic3⋊C4C2×D312yes—
91C2×C4×Dic3—32no—
92C2×C4×Dic3—32no—
93C2×C4×Dic3—32no—
94C2×C4×Dic3—32no—
95C2×C4×Dic3—32no—
96C2×C4×Dic3—32no—
97C2×C4×Dic3—32no—
98C2×C4×Dic3—61no—
99C2×C4×Dic3—62no—
100#887—68no—
101#887—68no—
102C3×#95—21no—
103C3×#95—32no—
104C3×#95—32no—
105C3×#95C2×D312yes—
106C3⋊#95—32no—
107C3⋊#95—32no—
108C3⋊#95—32no—
109C3⋊#95—32no—
110C3⋊#95—32no—
111C3⋊#95—32no—
112C3⋊#95—32no—
113C3⋊#95—61no—
114C3⋊#95C2×D312yes—
115C3⋊#95C2×D312yes—
116C23×C32C2411yescharacteristic
117C2×C32×C4—22no—
118C2×C32×C4—22no—
119C2×C32×C4—22no—
120C2×C32×C4—22no—
121C2×C32×C4C2×Q812yes—
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3C2×D412yes—
126C2×C3⋊Dic3C2×Q812yes—
127C2×C3⋊Dic3C2×Q812yes—
128C2×C3⋊Dic3C2×Q812yes—
129C2×C3⋊Dic3#4114yes—
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×C3×Dic3C2×D414yes—
140C2×C3×Dic3C2×Q814yes—
141C2×C3×Dic3#4114yes—
142#627—216no—
143C2×C4×Q8—92no—
144#398—32no—
145#398—92no—
146#395—92no—
147#395—92no—
148C4×C4⋊C4—92no—
149C4×C4⋊C4—91no—
150C4×C4⋊C4—91no—
151#376—91no—
152C22×C3×C4—21no—
153C22×C3×C4—22no—
154C22×C3×C4—32no—
155C22×C3×C4—32no—
156C22×C3×C4—32no—
157C22×C3×C4—32no—
158C22×C3×C4C22×D312yes—
159C22×C3×C4C22×D312yes—
160C22×C3×C4C22×D312yes—
161C22×Dic3—32no—
162C22×Dic3—32no—
163C22×Dic3—32no—
164C22×Dic3—32no—
165C22×Dic3—61no—
166C22×Dic3—61no—
167C22×Dic3—62no—
168C22×Dic3C22×D312yes—
169C22×Dic3C22×D312yes—
170C22×Dic3C22×D312yes—
171C22×Dic3C22×D312yes—
172C2×Dic6—64no—
173C2×Dic6—64no—
174C2×Dic6—64no—
175C2×Dic6—64no—
176C2×Dic6—64no—
177C2×Dic6—64no—
178C3×C4⋊C4—64no—
179C3×C4⋊C4—64no—
180C3×C4⋊C4—64no—
181C3×C4⋊C4—64no—
182C4⋊Dic3—24no—
183C4⋊Dic3—64no—
184Dic3⋊C4—24no—
185Dic3⋊C4—24no—
186Dic3⋊C4—24no—
187Dic3⋊C4—64no—
188Dic3⋊C4—64no—
189Dic3⋊C4—64no—
190Dic3⋊C4—64no—
191Dic3⋊C4—68no—
192Dic3⋊C4—64no—
193C4×Dic3—38no—
194C4×Dic3—38no—
195C4×Dic3—38no—
196C4×Dic3—64no—
197C4×Dic3—64no—
198C4×Dic3—64no—
199C4×Dic3—64no—
200C4×Dic3—64no—
201C4×Dic3—124no—
202C22×C32C22×D411yescharacteristic
203C22×C32C22×Q811yescharacteristic
204C22×C32C22×Q811yescharacteristic
205C22×C32C2×#4112yes—
206C22×C32C2×#4112yes—
207C32×C4—22no—
208C32×C4—42no—
209C3⋊Dic3—22no—
210C3⋊Dic3—24no—
211C3⋊Dic3C4⋊Q814yes—
212C3×Dic3—24no—
213C3×Dic3—24no—
214C3×Dic3—24no—
215C3×Dic3—42no—
216C22×Q8—92no—
217C4×Q8—188no—
218C2×C4⋊C4—32no—
219C2×C4⋊C4—32no—
220C2×C4⋊C4—32no—
221C2×C4⋊C4—32no—
222C2×C4⋊C4—92no—
223C2×C4⋊C4—92no—
224C2×C4⋊C4—92no—
225C2×C42—91no—
226C2×C42—91no—
227C2×C42—91no—
228C2×C42—92no—
229C2×C42—92no—
230#95—32no—
231#95—32no—
232#95—92no—
233#95—92no—
234#95—91no—
235#95—91no—
236#95—91no—
237#95D3211yescharacteristic
238C23×C3—21no—
239C23×C3C23×D312yes—
240C2×C3×C4—22no—
241C2×C3×C4—22no—
242C2×C3×C4—24no—
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—34no—
251C2×C3×C4—34no—
252C2×C3×C4—34no—
253C2×C3×C4—42no—
254C2×C3×C4—42no—
255C2×C3×C4—42no—
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×C4D3×Q814yes—
266C2×Dic3—22no—
267C2×Dic3—22no—
268C2×Dic3—22no—
269C2×Dic3—22no—
270C2×Dic3—22no—
271C2×Dic3—22no—
272C2×Dic3—22no—
273C2×Dic3—22no—
274C2×Dic3—22no—
275C2×Dic3—34no—
276C2×Dic3—34no—
277C2×Dic3—34no—
278C2×Dic3—34no—
279C2×Dic3—34no—
280C2×Dic3—34no—
281C2×Dic3—62no—
282C2×Dic3—62no—
283C2×Dic3—62no—
284C2×Dic3—62no—
285C2×Dic3—64no—
286C2×Dic3—64no—
287C2×Dic3—62no—
288C2×Dic3—62no—
289C2×Dic3—62no—
290C2×Dic3—62no—
291C2×Dic3—62no—
292C2×Dic3—62no—
293C2×Dic3—122no—
294C2×Dic3—122no—
295C2×Dic3D3×D414yes—
296C2×Dic3#23714yes—
297C2×Dic3D3×Q814yes—
298Dic6—616no—
299Dic6—616no—
300C2×C32#52512yes—
301C2×C32C2×C4⋊Q811yescharacteristic
302C2×C32#53311yescharacteristic
303C2×C32#53312yes—
304C2×C32#53311yescharacteristic
305C2×Q8—184no—
306C2×Q8—184no—
307C2×Q8—184no—
308C22×C4—32no—
309C22×C4—32no—
310C22×C4—32no—
311C22×C4—32no—
312C22×C4—91no—
313C22×C4—91no—
314C22×C4—92no—
315C22×C4C2×D3212yes—
316C22×C4C2×D3211yescharacteristic
317C4⋊C4—64no—
318C4⋊C4—64no—
319C4⋊C4—64no—
320C4⋊C4—64no—
321C4⋊C4—184no—
322C4⋊C4—184no—
323C4⋊C4—184no—
324C42—94no—
325C42—94no—
326C42—94no—
327C42—184no—
328C42—184no—
329C22×C3—21no—
330C22×C3—22no—
331C22×C3—21no—
332C22×C3—22no—
333C22×C3—21no—
334C22×C3C2×D3×D412yes—
335C22×C3C2×#23712yes—
336C22×C3C2×D3×Q812yes—
337C22×C3C2×D3×Q812yes—
338C22×C3D3×#4112yes—
339C22×C3D3×#4112yes—
340C22×C3D3×#4112yes—
341C3×C4—24no—
342C3×C4—42no—
343C3×C4—44no—
344C3×C4—42no—
345C3×C4—42no—
346C3×C4—64no—
347C3×C4—64no—
348C3×C4—64no—
349C3×C4—122no—
350Dic3—24no—
351Dic3—24no—
352Dic3—24no—
353Dic3—38no—
354Dic3—42no—
355Dic3—64no—
356Dic3—64no—
357Dic3—64no—
358Dic3—64no—
359Dic3—64no—
360Dic3—124no—
361C32#239911yescharacteristic, complemented, Sylow
362C23C22×D3211yescharacteristic
363Q8—1816no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—34no—
369C2×C4—34no—
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—92no—
381C2×C4—92no—
382C2×C4—92no—
383C2×C4—92no—
384C2×C4—94no—
385C2×C4—182no—
386C2×C4—182no—
387C2×C4—182no—
388C2×C4#379712yes—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—22no—
392C2×C3—22no—
393C2×C3—21no—
394C2×C3#560612yes—
395C2×C3#562212yes—
396C2×C3#562212yes—
397C2×C3#565612yes—
398C2×C3#568812yes—
399C2×C3#568812yes—
400C2×C3D3×C4⋊Q812yes—
401C22C2×#379711yescharacteristic
402C22#6430612yes—
403C22D32×D411yescharacteristic
404C22D3×#23712yes—
405C22D32×Q811yescharacteristic
406C4—22no—
407C4—42no—
408C4—64no—
409C4—64no—
410C4—64no—
411C4—94no—
412C4—122no—
413C4—182no—
414C4—184no—
415C3—21no—
416C3#7774012yescomplemented
417C2#1059385411yescharacteristic
418C2#1059403011yescharacteristic
419C2#1059426712yes—
420C2#1059437411yescharacteristic
421C2#1059438812yes—
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, prime radical, cosocleC23×C32C24
FittingC32×#95C22
hypercenter#95D32
hypocenterC32#2399
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
63. C4×C3⋊Dic3Q8semidirect
72. Dic32Q8semidirect
361. C32#2399semidirect
416. C3#77740semidirect

Maximal subgroups

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

subgroupindex
C2×#638382
#105923482
C3×#46572
#105913382
#105912742
#105912522
#105912412
#105911982
#105911952
#777403