Finite Group Databasebeta

← #11824505

Subgroups — #11824505

Order 1152.

1497 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64153C211yesmaximal, characteristic, complemented
2C2×C3×#946C212yesmaximal, complemented
3C2×C4×#625C211yesmaximal, characteristic
4C2×#63857C212yesmaximal, complemented
5#10591386C212yesmaximal
6#10591303C214yesmaximal, complemented
7#10591274C211yesmaximal, characteristic, complemented
8#10591244C212yesmaximal, complemented
9#82780—32nomaximal
10C22×C32×Q8C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C22×C3×C4×D3C2212yes—
13C22×#625C2211yescharacteristic
14#64153—24no—
15C2×#3750C2212yes—
16C2×#3750C2212yes—
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C3×#946—28no—
19C2×C3×(C2×D3)⋊C4C2214yes—
20C2×C3×C4⋊Dic3C2212yes—
21C2×C3×Dic3⋊C4C2214yes—
22C2×#3724C2211yescharacteristic
23C2×Dic3⋊Dic3C2214yes—
24C2×(C2×D3)⋊Dic3C2214yes—
25C2×(C2×D3)⋊Dic3C2212yes—
26C2×Dic32C2212yes—
27C4×#625—24no—
28#63857—28no—
29#63579C2212yes—
30C2×C3×C22⋊Q8—32no—
31C2×#946D312yescomplemented
32C2×#944—32no—
33C2×#944—61no—
34C2×C4×#67—32no—
35C2×#924—32no—
36C2×#897—32no—
37#4993—34no—
38#4975—34no—
39Dic3×C4⋊C4—32no—
40#4957—34no—
41#4949—34no—
42C23×C3×D3C2312yes—
43C2×C32×Q8—22no—
44C2×C32×Q8—24no—
45C22×C32×C4C2312yes—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3C2312yes—
48C22×C3⋊Dic3C2311yescharacteristic
49C22×C3⋊Dic3C2311yescharacteristic
50C2×#634—22no—
51C2×#634—24no—
52C22×C3×Dic3C2312yes—
53C22×C3×Dic3C2314yes—
54C2×C3×C4×D3—24no—
55C2×C3×C4×D3—24no—
56C2×C3×C4×D3—24no—
57C2×#625—22no—
58C2×#625—22no—
59C2×#625Q814yescomplemented
60#3750—24no—
61#3750—24no—
62C4×C3⋊Dic3D414yes—
63C3×(C2×D3)⋊C4—28no—
64C3×C4⋊Dic3D418yescomplemented
65C3×Dic3⋊C4—28no—
66#3724—22no—
67Dic3⋊Dic3—28no—
68(C2×D3)⋊Dic3—24no—
69(C2×D3)⋊Dic3—28no—
70Dic32—24no—
71#2542—91noSylow
72C22×C3×Q8—21no—
73C22×C3×Q8C2×D312yes—
74C23×C3×C4—32no—
75C22×#67—32no—
76C22×C4×D3C2×D312yes—
77C22×Dic6—32no—
78C22×Dic6—61no—
79C3×C22⋊Q8—68no—
80C2×C3×C4⋊C4—32no—
81C2×C3×C4⋊C4—34no—
82C2×C3×C22⋊C4—34no—
83C2×#217—32no—
84C2×#217—34no—
85#946—28no—
86#944—68no—
87#944—68no—
88C4×#67—68no—
89C2×(C2×D3)⋊C4—34no—
90C2×(C2×D3)⋊C4—32no—
91C2×(C2×D3)⋊C4C2×D314yes—
92C2×C4⋊Dic3—34no—
93C2×C4⋊Dic3C2×D312yes—
94#924—68no—
95C2×Dic3⋊C4—34no—
96C2×Dic3⋊C4—34no—
97C2×Dic3⋊C4—32no—
98C2×Dic3⋊C4—34no—
99C2×Dic3⋊C4—62no—
100C2×Dic3⋊C4—62no—
101C2×Dic3⋊C4C2×D314yes—
102C2×C4×Dic3—32no—
103C2×C4×Dic3—34no—
104C2×C4×Dic3—61no—
105#897—68no—
106C3⋊#95—34no—
107C23×C32C2411yescharacteristic
108C22×C3×D3—22no—
109C22×C3×D3—22no—
110C22×C3×D3—22no—
111C22×C3×D3—22no—
112C22×C3×D3—22no—
113C22×C3×D3—22no—
114C22×C3×D3C2×Q814yes—
115C32×Q8—44no—
116C2×C32×C4—22no—
117C2×C32×C4—24no—
118C2×C32×C4C2×D412yes—
119C2×C32×C4C2×D414yes—
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3—22no—
122C2×C3⋊Dic3—24no—
123C2×C3⋊Dic3C2×D412yes—
124C2×C3⋊Dic3C2×D412yes—
125C2×C3⋊Dic3C2×Q812yes—
126C2×C3⋊Dic3#4112yes—
127#634—44no—
128C2×C3×Dic3—24no—
129C2×C3×Dic3—24no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—22no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3C2×D418yes—
134C3×C4×D3—48no—
135#625—28no—
136C2×C4⋊Q8—91no—
137C2×C22⋊Q8—32no—
138C2×C22⋊Q8—92no—
139C2×C4×D4—91no—
140#399—94no—
141#390—92no—
142#384—92no—
143C4×C4⋊C4—91no—
144C24×C3—32no—
145C23×D3C22×D312yes—
146C2×C3×Q8—24no—
147C2×C3×Q8—24no—
148C2×C3×Q8—24no—
149C2×C3×Q8—24no—
150C2×C3×Q8—44no—
151C22×C3×C4—21no—
152C22×C3×C4—22no—
153C22×C3×C4—34no—
154C22×C3×C4—32no—
155C22×C3×C4—64no—
156C22×C3×C4—64no—
157C22×C3×C4—64no—
158C22×C3×C4C22×D314yes—
159C22×C3×C4C22×D312yes—
160C2×#67—38no—
161C2×#67—64no—
162C2×#67—64no—
163C22×Dic3—32no—
164C22×Dic3—32no—
165C22×Dic3—34no—
166C22×Dic3—61no—
167C22×Dic3—61no—
168C22×Dic3—62no—
169C22×Dic3C22×D312yes—
170C22×Dic3C22×D314yes—
171C2×C4×D3—24no—
172C2×C4×D3—24no—
173C2×C4×D3—24no—
174C2×Dic6—64no—
175C2×Dic6—64no—
176C2×Dic6—64no—
177C2×Dic6—64no—
178C2×Dic6—124no—
179C3×C4⋊C4—38no—
180C3×C4⋊C4—68no—
181C3×C22⋊C4—68no—
182#217—64no—
183#217—68no—
184(C2×D3)⋊C4—28no—
185(C2×D3)⋊C4—64no—
186(C2×D3)⋊C4—68no—
187C4⋊Dic3—68no—
188C4⋊Dic3#6718yescomplemented
189Dic3⋊C4—28no—
190Dic3⋊C4—64no—
191Dic3⋊C4—68no—
192Dic3⋊C4—68no—
193Dic3⋊C4—68no—
194Dic3⋊C4—68no—
195Dic3⋊C4—68no—
196C4×Dic3—38no—
197C4×Dic3—64no—
198C4×Dic3—68no—
199C22×C32C22×D411yescharacteristic
200C22×C32C22×D412yes—
201C22×C32C22×Q811yescharacteristic
202C22×C32C2×#4111yescharacteristic
203C22×C322−1+412yes—
204C2×C3×D3—24no—
205C2×C3×D3—24no—
206C2×C3×D3—24no—
207C2×C3×D3—42no—
208C2×C3×D3—42no—
209C2×C3×D3—42no—
210C2×C3×D3—42no—
211C32×C4—42no—
212C32×C4#12714yes—
213C3⋊Dic3—22no—
214C3⋊Dic3—42no—
215C3⋊Dic3C22⋊Q814yescomplemented
216C3×Dic3—28no—
217C3×Dic3—42no—
218C22×Q8—91no—
219C22×Q8D3211yescharacteristic
220C22×D4—91no—
221C23×C4—32no—
222C4⋊Q8—184no—
223C22⋊Q8—68no—
224C22⋊Q8—188no—
225C4×D4—184no—
226C2×C4⋊C4—32no—
227C2×C4⋊C4—34no—
228C2×C4⋊C4—91no—
229C2×C4⋊C4—94no—
230C2×C4⋊C4—92no—
231C2×C4⋊C4—92no—
232C2×C22⋊C4—34no—
233C2×C22⋊C4—92no—
234C2×C22⋊C4—94no—
235C2×C42—91no—
236C2×C42—92no—
237#95—92no—
238C23×C3—21no—
239C23×C3—34no—
240C23×C3—62no—
241C23×C3—62no—
242C23×C3—62no—
243C23×C3—62no—
244C23×C3—62no—
245C23×C3—62no—
246C23×C3C23×D312yes—
247C22×D3—22no—
248C22×D3—22no—
249C22×D3—22no—
250C22×D3—22no—
251C22×D3—22no—
252C22×D3—22no—
253C22×D3D3×Q814yes—
254C3×Q8—48no—
255C3×Q8—48no—
256C2×C3×C4—24no—
257C2×C3×C4—24no—
258C2×C3×C4—24no—
259C2×C3×C4—24no—
260C2×C3×C4—24no—
261C2×C3×C4—22no—
262C2×C3×C4—38no—
263C2×C3×C4—44no—
264C2×C3×C4—64no—
265C2×C3×C4—64no—
266C2×C3×C4—62no—
267C2×C3×C4—62no—
268C2×C3×C4—62no—
269C2×C3×C4—128no—
270C2×C3×C4D3×D414yes—
271C2×C3×C4D3×D414yes—
272C2×C3×C4C2×#6714yes—
273#67—616no—
274C2×Dic3—24no—
275C2×Dic3—24no—
276C2×Dic3—22no—
277C2×Dic3—22no—
278C2×Dic3—22no—
279C2×Dic3—34no—
280C2×Dic3—34no—
281C2×Dic3—34no—
282C2×Dic3—34no—
283C2×Dic3—62no—
284C2×Dic3—62no—
285C2×Dic3—62no—
286C2×Dic3—62no—
287C2×Dic3—64no—
288C2×Dic3—62no—
289C2×Dic3—62no—
290C2×Dic3—64no—
291C2×Dic3—64no—
292C2×Dic3—64no—
293C2×Dic3—64no—
294C2×Dic3—124no—
295C2×Dic3C2×#6718yes—
296C4×D3—48no—
297Dic6—128no—
298Dic6—128no—
299C2×C32C2×C22⋊Q811yescharacteristic
300C2×C32C2×#12711yescharacteristic
301C2×C32#53611yescharacteristic
302C2×C32#54712yes—
303C2×C32D4×Q812yes—
304C3×D3—44no—
305C24—32no—
306C2×Q8—24no—
307C2×Q8—22no—
308C2×Q8—184no—
309C2×Q8—182no—
310C2×D4—94no—
311C2×D4—182no—
312C2×D4—182no—
313C22×C4—34no—
314C22×C4—32no—
315C22×C4—64no—
316C22×C4—64no—
317C22×C4—64no—
318C22×C4—91no—
319C22×C4—91no—
320C22×C4—92no—
321C22×C4C2×D3212yes—
322C22×C4C2×D3211yescharacteristic
323C4⋊C4—38no—
324C4⋊C4—68no—
325C4⋊C4—184no—
326C4⋊C4—184no—
327C4⋊C4—188no—
328C4⋊C4—182no—
329C22⋊C4—68no—
330C22⋊C4—188no—
331C22⋊C4—184no—
332C42—94no—
333C42—184no—
334C22×C3—22no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—22no—
338C22×C3—21no—
339C22×C3—64no—
340C22×C3—64no—
341C22×C3—64no—
342C22×C3—122no—
343C22×C3—122no—
344C22×C3—122no—
345C22×C3—122no—
346C22×C3C2×D3×D412yes—
347C22×C3C2×D3×D412yes—
348C22×C3C2×D3×Q812yes—
349C22×C3#100712yes—
350C22×C3D3×#4112yes—
351C22×C3#101012yes—
352C22×C3C22×#6712yes—
353C2×D3—24no—
354C2×D3—24no—
355C2×D3—24no—
356C2×D3—42no—
357C2×D3—42no—
358C2×D3—42no—
359C2×D3—42no—
360C3×C4—24no—
361C3×C4—44no—
362C3×C4—44no—
363C3×C4—68no—
364C3×C4—122no—
365C3×C4#94018yes—
366Dic3—28no—
367Dic3—38no—
368Dic3—42no—
369Dic3—64no—
370Dic3—64no—
371Dic3—64no—
372Dic3—124no—
373Dic3—124no—
374C32#254211yescharacteristic, complemented, Sylow
375C23—34no—
376C23—62no—
377C23—62no—
378C23—62no—
379C23—62no—
380C23—62no—
381C23—62no—
382C23C22×D3211yescharacteristic
383Q8—44no—
384Q8—364no—
385D4—188no—
386C2×C4—24no—
387C2×C4—22no—
388C2×C4—38no—
389C2×C4—64no—
390C2×C4—64no—
391C2×C4—62no—
392C2×C4—62no—
393C2×C4—62no—
394C2×C4—92no—
395C2×C4—92no—
396C2×C4—92no—
397C2×C4—92no—
398C2×C4—128no—
399C2×C4—182no—
400C2×C4—184no—
401C2×C4—182no—
402C2×C4D3×#6714yes—
403C2×C4#381112yes—
404C2×C3—22no—
405C2×C3—22no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—124no—
410C2×C3D3×C22⋊Q812yes—
411C2×C3#562812yes—
412C2×C3#563112yes—
413C2×C3#563212yes—
414C2×C3C2×#94012yes—
415C2×C3Q8×#6712yes—
416C2×C3#582412yes—
417D3—44no—
418C22—64no—
419C22—64no—
420C22—64no—
421C22—122no—
422C22—122no—
423C22—122no—
424C22—122no—
425C22#6431512yes—
426C22D32×Q811yescharacteristic
427C22#6431911yescharacteristic
428C22C2×D3×#6712yes—
429C22C2×#381111yescharacteristic
430C4—42no—
431C4—68no—
432C4—94no—
433C4—122no—
434C4—182no—
435C4—362no—
436C4#6397914yes—
437C3—21no—
438C3#8278012yescomplemented
439C2—124no—
440C2#1059535712yes—
441C2#1059540012yes—
442C2#1059540511yescharacteristic
443C2#1059542911yescharacteristic
444C2C2×#6397911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×Q8C22
prime radicalC22×#625C22
hypercenterC22×Q8D32
hypocenterC32#2542
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64153C2semidirect
2. C2×C3×#946C2semidirect
4. C2×#63857C2semidirect
6. #10591303C2semidirect
7. #10591274C2semidirect
8. #10591244C2semidirect
31. C2×#946D3semidirect
59. C2×#625Q8semidirect
64. C3×C4⋊Dic3D4semidirect
188. C4⋊Dic3#67semidirect
215. C3⋊Dic3C22⋊Q8semidirect
374. C32#2542semidirect
438. C3#82780semidirect

Maximal subgroups

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

subgroupindex
C2×#641532
C2×C3×#9462
C2×C4×#6252
C2×#638572
#105913862
#105913032
#105912742
#105912442
#827803