Finite Group Databasebeta

← #11801728

Subgroups — #11801728

Order 1152.

2281 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×C3⋊D3C211yesmaximal, characteristic
2C2×#63900C211yesmaximal, characteristic
3C2×C4×#624C211yesmaximal, characteristic
4C3×#5229C212yesmaximal, complemented
5#10591370C214yesmaximal
6#10591273C214yesmaximal, complemented
7#10591213C212yesmaximal, complemented
8D3×#391—32nomaximal
9C22×C32×Q8C2211yescharacteristic
10C2×Q8×C3⋊D3—24no—
11C2×Q8×C3⋊D3—24no—
12C2×Q8×C3⋊D3C418yescomplemented
13C22×C4×C3⋊D3C2212yes—
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×#634C2212yes—
16C22×#634C2211yescharacteristic
17C22×#624C2212yes—
18C22×#624C2212yes—
19C2×C3×C4⋊Dic3C2212yes—
20C2×C3×C4×Dic3C2212yes—
21C2×#3724C2212yes—
22C2×Dic32C2212yes—
23#63900—24no—
24C4×#624—24no—
25C3×C3⋊#95C2218yes—
26#63579C2218yes—
27C22×D3×Q8—32no—
28C22×D3×Q8—61no—
29C2×D3×C4⋊C4—32no—
30C2×C42×D3—32no—
31C3×#391—32no—
32#5229D312yescomplemented
33#4973—32no—
34#4929—32no—
35D3×#95—38no—
36#4646—38no—
37C23×C3⋊D3C2311yescharacteristic
38C2×C32×Q8—22no—
39C2×C32×Q8—22no—
40C2×C32×Q8C2×C414yescomplemented
41C22×C32×C4C2312yes—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3C2312yes—
44C22×C3⋊Dic3C2311yescharacteristic
45Q8×C3⋊D3—232no—
46C2×C4×C3⋊D3—24no—
47C2×C4×C3⋊D3—24no—
48C2×C4×C3⋊D3C2×C418yes—
49C2×C4×C3⋊D3C2×C414yes—
50C2×C4×C3⋊D3D414yes—
51C2×C4×C3⋊D3D414yes—
52C2×#634—22no—
53C2×#634—22no—
54C2×#634—24no—
55C2×#634—24no—
56C2×#634C2×C414yescomplemented
57C2×#634C2×C418yescomplemented
58C22×C3×Dic3C2314yes—
59C22×C3×Dic3C2314yes—
60C2×#624—24no—
61C2×#624—24no—
62C2×#624—24no—
63C2×#624—28no—
64C2×#624Q818yescomplemented
65C3×C4⋊Dic3—24no—
66C3×C4×Dic3—24no—
67#3724—24no—
68Dic32—24no—
69C2×#391—91noSylow
70C22×C3×Q8—21no—
71C22×C3×Q8C2×D312yes—
72C2×D3×Q8—316no—
73C2×D3×Q8—68no—
74C2×D3×Q8—68no—
75C2×D3×Q8—68no—
76C2×D3×Q8—68no—
77C2×D3×Q8—68no—
78C22×C4×D3—32no—
79C22×C4×D3—34no—
80C22×C4×D3—34no—
81C22×C4×D3—34no—
82C22×C4×D3—61no—
83C22×C4×D3—62no—
84C22×Dic6—34no—
85C22×Dic6—32no—
86C22×Dic6—62no—
87C22×Dic6—61no—
88C2×C3×C4⋊C4—32no—
89C2×C3×C42—32no—
90C2×C4⋊Dic3C2×D312yes—
91C2×Dic3⋊C4—34no—
92C2×C4×Dic3—34no—
93C2×C4×Dic3C2×D312yes—
94D3×C4⋊C4—68no—
95C42×D3—68no—
96C3×#95—38no—
97C3⋊#95—38no—
98C3⋊#95—38no—
99C3⋊#95C2×D318yes—
100C23×C32C2411yescharacteristic
101C22×C3⋊D3C22×C412yes—
102C22×C3⋊D3C2×D412yes—
103C22×C3⋊D3C2×D412yes—
104C22×C3⋊D3C2×Q814yes—
105C22×C3⋊D3#4114yes—
106C32×Q8—28no—
107C2×C32×C4—22no—
108C2×C32×C4—22no—
109C2×C32×C4C22×C414yes—
110C2×C32×C4C22×C412yes—
111C2×C32×C4C2×D412yes—
112C2×C32×C4C2×D412yes—
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3—22no—
115C2×C3⋊Dic3C22×C414yes—
116C2×C3⋊Dic3C22×C412yes—
117C2×C3⋊Dic3C2×D412yes—
118C2×C3⋊Dic3C2×D412yes—
119C4×C3⋊D3—216no—
120C4×C3⋊D3C22⋊C4116yes—
121#634—28no—
122#634—216no—
123C2×C3×Dic3—24no—
124C2×C3×Dic3—24no—
125C2×C3×Dic3—24no—
126C2×C3×Dic3—28no—
127C2×C3×Dic3C2×Q818yescomplemented
128#624—216no—
129#624—48no—
130C23×Q8—91no—
131C22×C4⋊C4—91no—
132C22×C42—91no—
133#391—32no—
134#391—94no—
135#391—92no—
136C2×#95—94no—
137C23×D3—32no—
138C23×D3—61no—
139C2×C3×Q8—24no—
140C2×C3×Q8—24no—
141C2×C3×Q8—24no—
142C2×C3×Q8—24no—
143C2×C3×Q8—24no—
144C2×C3×Q8C4×D318yescomplemented
145C22×C3×C4—22no—
146C22×C3×C4—21no—
147C22×C3×C4—34no—
148C22×C3×C4—34no—
149C22×C3×C4C22×D314yes—
150C22×C3×C4C22×D312yes—
151C22×Dic3—32no—
152C22×Dic3—34no—
153C22×Dic3—61no—
154C22×Dic3—62no—
155C22×Dic3C22×D314yes—
156C22×Dic3C22×D314yes—
157D3×Q8—664no—
158D3×Q8—664no—
159C2×C4×D3—38no—
160C2×C4×D3—38no—
161C2×C4×D3—38no—
162C2×C4×D3—316no—
163C2×C4×D3—316no—
164C2×C4×D3—64no—
165C2×C4×D3—68no—
166C2×C4×D3—64no—
167C2×C4×D3—64no—
168C2×C4×D3—68no—
169C2×C4×D3—68no—
170C2×C4×D3—68no—
171C2×C4×D3—68no—
172C2×C4×D3—68no—
173C2×C4×D3—68no—
174C2×C4×D3—68no—
175C2×C4×D3—616no—
176C2×Dic6—316no—
177C2×Dic6—38no—
178C2×Dic6—68no—
179C2×Dic6—64no—
180C2×Dic6—68no—
181C2×Dic6—68no—
182C2×Dic6—68no—
183C2×Dic6—68no—
184C2×Dic6—64no—
185C2×Dic6—64no—
186C2×Dic6—64no—
187C2×Dic6—64no—
188C3×C4⋊C4—64no—
189C3×C42—64no—
190C4⋊Dic3—24no—
191Dic3⋊C4—68no—
192C4×Dic3—24no—
193C4×Dic3—68no—
194C22×C32C23×C411yescharacteristic
195C22×C32C22×D411yescharacteristic
196C22×C32C22×D411yescharacteristic
197C22×C32C22×Q812yes—
198C22×C32C2×#4112yes—
199C2×C3⋊D3C2×C22⋊C414yes—
200C2×C3⋊D3C4×Q818yes—
201C2×C3⋊D3C22⋊Q818yes—
202C2×C3⋊D3#12414yes—
203C2×C3⋊D3C4⋊Q814yes—
204C32×C4—24no—
205C32×C4C2×C22⋊C414yes—
206C3⋊Dic3—24no—
207C3⋊Dic3C2×C22⋊C414yes—
208C3×Dic3—28no—
209C3×Dic3—44no—
210C22×Q8—98no—
211C22×Q8—92no—
212C22×Q8—91no—
213C22×Q8—184no—
214C22×Q8—184no—
215C22×Q8D3211yescharacteristic
216C23×C4—92no—
217C23×C4—92no—
218C23×C4—91no—
219C23×C4—92no—
220C2×C4⋊C4—32no—
221C2×C4⋊C4—92no—
222C2×C4⋊C4—184no—
223C2×C42—32no—
224C2×C42—92no—
225C2×C42—184no—
226#95—38no—
227#95—98no—
228C23×C3—21no—
229C23×C3C23×D312yes—
230C22×D3—34no—
231C22×D3—34no—
232C22×D3—34no—
233C22×D3—38no—
234C22×D3—38no—
235C22×D3—62no—
236C22×D3—62no—
237C22×D3—62no—
238C22×D3—64no—
239C22×D3—64no—
240C3×Q8—216no—
241C3×Q8—216no—
242C2×C3×C4—24no—
243C2×C3×C4—24no—
244C2×C3×C4—24no—
245C2×C3×C4—24no—
246C2×C3×C4—24no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4—22no—
250C2×C3×C4—38no—
251C2×C3×C4—64no—
252C2×C3×C4—64no—
253C2×C3×C4—64no—
254C2×C3×C4—68no—
255C2×C3×C4C2×C4×D318yes—
256C2×C3×C4C2×C4×D314yes—
257C2×C3×C4D3×D414yes—
258C2×C3×C4D3×D414yes—
259C2×Dic3—24no—
260C2×Dic3—24no—
261C2×Dic3—24no—
262C2×Dic3—28no—
263C2×Dic3—34no—
264C2×Dic3—34no—
265C2×Dic3—34no—
266C2×Dic3—38no—
267C2×Dic3—62no—
268C2×Dic3—64no—
269C2×Dic3—62no—
270C2×Dic3—62no—
271C2×Dic3—64no—
272C2×Dic3—64no—
273C2×Dic3—64no—
274C2×Dic3—64no—
275C2×Dic3D3×Q818yescomplemented
276C4×D3—332no—
277C4×D3—616no—
278C4×D3—632no—
279C4×D3—632no—
280C4×D3—632no—
281C4×D3—1216no—
282Dic6—632no—
283Dic6—632no—
284Dic6—616no—
285Dic6—616no—
286C2×C32C22×C22⋊C411yescharacteristic
287C2×C32C2×C4×Q812yes—
288C2×C32C2×C22⋊Q812yes—
289C2×C32C2×#12411yescharacteristic
290C2×C32C2×C4⋊Q811yescharacteristic
291C3⋊D3#39118yescomplemented
292C24—91no—
293C2×Q8—22no—
294C2×Q8—22no—
295C2×Q8—98no—
296C2×Q8—94no—
297C2×Q8—184no—
298C2×Q8—184no—
299C2×Q8—1832no—
300C2×Q8—182no—
301C2×Q8—182no—
302C2×Q8#62414yescomplemented
303C22×C4—34no—
304C22×C4—34no—
305C22×C4—98no—
306C22×C4—91no—
307C22×C4—94no—
308C22×C4—94no—
309C22×C4—94no—
310C22×C4—92no—
311C22×C4—98no—
312C22×C4—184no—
313C22×C4—184no—
314C22×C4—184no—
315C22×C4—184no—
316C22×C4—184no—
317C22×C4—188no—
318C22×C4C2×D3212yes—
319C22×C4C2×D3211yescharacteristic
320C4⋊C4—64no—
321C4⋊C4—184no—
322C42—64no—
323C42—184no—
324C22×C3—22no—
325C22×C3—22no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3C22×C4×D312yes—
330C22×C3C2×D3×D412yes—
331C22×C3C2×D3×D412yes—
332C22×C3C2×D3×Q814yes—
333C22×C3D3×#4114yes—
334C2×D3—38no—
335C2×D3—38no—
336C2×D3—38no—
337C2×D3—316no—
338C2×D3—316no—
339C2×D3—64no—
340C2×D3—68no—
341C2×D3—68no—
342C2×D3—64no—
343C2×D3—64no—
344C3×C4—28no—
345C3×C4—28no—
346C3×C4—24no—
347C3×C4—68no—
348C3×C4—124no—
349C3×C4D3×C22⋊C418yes—
350Dic3—28no—
351Dic3—38no—
352Dic3—44no—
353Dic3—64no—
354Dic3—68no—
355Dic3—68no—
356C32C2×#39111yescharacteristic, complemented, Sylow
357C23—94no—
358C23—94no—
359C23—92no—
360C23—92no—
361C23—92no—
362C23C22×D3211yescharacteristic
363Q8—28no—
364Q8—1816no—
365Q8—188no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—38no—
369C2×C4—64no—
370C2×C4—64no—
371C2×C4—68no—
372C2×C4—64no—
373C2×C4—92no—
374C2×C4—92no—
375C2×C4—92no—
376C2×C4—916no—
377C2×C4—94no—
378C2×C4—1816no—
379C2×C4—1816no—
380C2×C4—182no—
381C2×C4—182no—
382C2×C4—368no—
383C2×C4C2×#62414yes—
384C2×C4C2×#62412yes—
385C2×C4#381112yes—
386C2×C4#381112yes—
387C2×C3—21no—
388C2×C3—22no—
389C2×C3—22no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3C2×D3×C22⋊C412yes—
393C2×C3C4×D3×Q814yes—
394C2×C3D3×C22⋊Q814yes—
395C2×C3D3×#12412yes—
396C2×C3D3×C4⋊Q812yes—
397D3—316no—
398D3—68no—
399C22—94no—
400C22—98no—
401C22—98no—
402C22—94no—
403C22—94no—
404C22D32×Q812yes—
405C22#6431912yes—
406C22C22×#62411yescharacteristic
407C22C2×#381111yescharacteristic
408C22C2×#381111yescharacteristic
409C4—24no—
410C4—68no—
411C4—94no—
412C4—124no—
413C4—184no—
414C4#6397414yes—
415C3—21no—
416C3D3×#39112yescomplemented
417C2—98no—
418C2#1059536511yescharacteristic
419C2Q8×#62412yes—
420C2#1059542912yes—
421C2#1059543211yescharacteristic
422C2C2×#6397411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×Q8C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC22×Q8D32
hypocenterC32C2×#391
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
4. C3×#5229C2semidirect
6. #10591273C2semidirect
7. #10591213C2semidirect
12. C2×Q8×C3⋊D3C4semidirect
32. #5229D3semidirect
40. C2×C32×Q8C2×C4semidirect
56. C2×#634C2×C4semidirect
57. C2×#634C2×C4semidirect
64. C2×#624Q8semidirect
127. C2×C3×Dic3C2×Q8semidirect
144. C2×C3×Q8C4×D3semidirect
275. C2×Dic3D3×Q8semidirect
291. C3⋊D3#391semidirect
302. C2×Q8#624semidirect
356. C32C2×#391semidirect
416. C3D3×#391semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×C3⋊D32
C2×#639002
C2×C4×#6242
C3×#52292
#105913702
#105912732
#105912132
D3×#3913