Finite Group Databasebeta

← #11874985

Subgroups — #11874985

Order 1152.

761 conjugacy classes of subgroups.

The subgroup lattice has 429 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594477C212yesmaximal
2#10592554C211yesmaximal, characteristic, complemented
3C3×#4860C211yesmaximal, characteristic
4C3×#4858C211yesmaximal, characteristic, complemented
5#10590900C211yesmaximal, characteristic, complemented
6#10590871C211yesmaximal, characteristic, complemented
7#10590706C211yesmaximal, characteristic
8D3×C8×Dic3C211yesmaximal, characteristic
9#10590571C212yesmaximal
10#10590415C212yesmaximal, complemented
11#10590413C212yesmaximal, complemented
12#81916—31nomaximal
13#79170—31nomaximal
14#64097C2212yes—
15C2×C3×D3×C8C2211yescharacteristic
16C3×#892C2212yes—
17C3×#890C2212yes—
18#63919C2212yes—
19#63899—22no—
20#63896—22no—
21C4×D3×Dic3C2211yescharacteristic
22#63869C2212yes—
23#63844—22no—
24#63841C2212yes—
25#63837—22no—
26C2×D3×C3⋊C8C2211yescharacteristic
27C32×#106C2211yescharacteristic
28#63644C2211yescharacteristic
29C8×C3⋊Dic3C2211yescharacteristic
30#63635C2212yes—
31C3×#817C2211yescharacteristic
32C3×#817C2211yescharacteristic
33C3×C8×Dic3C2211yescharacteristic
34C3×#807C2212yes—
35C3×#807C2212yes—
36#63575C2212yes—
37#63575C2212yes—
38#63574C2212yes—
39#63553C2211yescharacteristic
40Dic3×C3⋊C8C2211yescharacteristic
41#5688—32no—
42#5517—32no—
43C3×#499—31no—
44C3×#427—31no—
45#5106—31no—
46C2×C8×Dic3—31no—
47#5065—32no—
48#4998—32no—
49#4880—32no—
50#4878—32no—
51#4874—32no—
52#4874—32no—
53#4860—31no—
54#4860D311yescharacteristic
55#4858—31no—
56#4858D311yescharacteristic, complemented
57#4855—31no—
58#4855—31no—
59#4855—31no—
60#4855—31no—
61#4855—61no—
62C4×D3×C8—31no—
63#4683—31no—
64C2×#634—22no—
65C2×C3×C4×D3C2311yescharacteristic
66C2×#627—22no—
67C2×D3×Dic3D412yes—
68C2×C32×C8C2311yescharacteristic
69C32×C4⋊C4C2312yes—
70C4⋊(C3⋊Dic3)C2312yes—
71#3750—22no—
72C4×C3⋊Dic3C2311yescharacteristic
73C2×C3⋊(C3⋊C8)C2311yescharacteristic
74C3×(C2×D3)⋊C4—22no—
75C3×C4⋊Dic3—22no—
76C3×C4⋊Dic3C2312yes—
77C3×C4⋊Dic3C2312yes—
78C3×Dic3⋊C4—22no—
79C3×C4×Dic3—22no—
80C3×C4×Dic3C2311yescharacteristic
81C2×C3×C3⋊C8C2311yescharacteristic
82C2×C3×C3⋊C8C2311yescharacteristic
83C3×D3×C8Q814yescomplemented
84#3724—22no—
85#3724—22no—
86Dic3⋊Dic3—22no—
87(C2×D3)⋊Dic3—22no—
88Dic32—22no—
89Dic32D412yes—
90D3×C3⋊C8Q814yescomplemented
91#3160—91noSylow
92C22×C3×C8—31no—
93C3×#125—32no—
94C3×#117—32no—
95#926—32no—
96C2×C4×Dic3—31no—
97C22×C3⋊C8—31no—
98C2×D3×C8—31no—
99C2×D3×C8C2×D311yescharacteristic
100#896—62no—
101#896—62no—
102#892—32no—
103#892C2×D312yes—
104#890—32no—
105#890C2×D312yes—
106#888—32no—
107#888—32no—
108#888—32no—
109#888—32no—
110#888—62no—
111#887—62no—
112#887—62no—
113#878—62no—
114#878—62no—
115C42×D3—31no—
116#870—32no—
117C4×Dic6—62no—
118C4×Dic6—62no—
119C3×#107—32no—
120C3×#107—32no—
121C3×#106—21no—
122C3×#106—31no—
123C3×#106—31no—
124C3×#106C2×D311yescharacteristic
125C3×#106C2×D311yescharacteristic
126C3×C4×C8—31no—
127#818—32no—
128#818—32no—
129#817—31no—
130#817—31no—
131#817—61no—
132#817C2×D311yescharacteristic
133#817C2×D311yescharacteristic
134C8×Dic3—31no—
135C8×Dic3—31no—
136C8×Dic3—31no—
137C8×Dic3—31no—
138C8×Dic3—31no—
139C8×Dic3—61no—
140C8×Dic3C2×D311yescharacteristic
141#808—32no—
142#808—32no—
143#808—32no—
144#808—32no—
145#808—62no—
146#807—32no—
147#807—32no—
148#807C2×D312yes—
149#807C2×D312yes—
150C4×C3⋊C8—31no—
151C22×C3×D3C2×D411yescharacteristic
152C2×C32×C4—22no—
153C2×C32×C4C2411yescharacteristic
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3C2×D412yes—
156#634—44no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3C2×D412yes—
160C2×C3×Dic3C2×D411yescharacteristic
161C3×C4×D3C2×Q812yes—
162C3×C4×D3C2×Q812yes—
163#627—44no—
164D3×Dic3—24no—
165C32×C8C2×Q812yes—
166C3⋊(C3⋊C8)C2×Q812yes—
167C3×C3⋊C8C2×Q812yes—
168C3×C3⋊C8C2×Q812yes—
169#533—92no—
170#500—92no—
171#499—31no—
172#499—91no—
173#499—92no—
174#498—91no—
175#498—91no—
176#427—31no—
177#427—91no—
178#427—92no—
179C2×C4×C8—91no—
180C22×C3×C4—31no—
181C22×Dic3—32no—
182C2×C4×D3—32no—
183C2×C4×D3C22×D311yescharacteristic
184C2×Dic6—62no—
185C2×Dic6—62no—
186C2×Dic6—62no—
187C2×Dic6—62no—
188C2×Dic6—122no—
189C2×C3×C8—21no—
190C2×C3×C8—31no—
191C2×C3×C8—31no—
192C2×C3×C8—34no—
193C2×C3×C8C22×D311yescharacteristic
194C2×C3×C8C22×D311yescharacteristic
195C3×C4⋊C4—22no—
196C3×C4⋊C4—32no—
197C3×C4⋊C4—32no—
198C3×C4⋊C4—62no—
199C3×C4⋊C4—62no—
200C3×C4⋊C4C22×D312yes—
201C3×C4⋊C4C22×D312yes—
202C3×C22⋊C4—62no—
203C3×C42—31no—
204C3×C42—62no—
205#217—62no—
206(C2×D3)⋊C4—22no—
207(C2×D3)⋊C4—62no—
208C4⋊Dic3—22no—
209C4⋊Dic3—32no—
210C4⋊Dic3—32no—
211C4⋊Dic3—62no—
212C4⋊Dic3—62no—
213C4⋊Dic3C22×D312yes—
214C4⋊Dic3C22×D312yes—
215Dic3⋊C4—22no—
216Dic3⋊C4—62no—
217Dic3⋊C4—62no—
218Dic3⋊C4—62no—
219Dic3⋊C4—62no—
220Dic3⋊C4—62no—
221Dic3⋊C4—62no—
222Dic3⋊C4—62no—
223Dic3⋊C4—122no—
224C4×Dic3—22no—
225C4×Dic3—31no—
226C4×Dic3—31no—
227C4×Dic3—32no—
228C4×Dic3—32no—
229C4×Dic3—61no—
230C4×Dic3—62no—
231C4×Dic3—62no—
232C4×Dic3C22×D311yescharacteristic
233C2×C3⋊C8—31no—
234C2×C3⋊C8—31no—
235C2×C3⋊C8—34no—
236C2×C3⋊C8—61no—
237C2×C3⋊C8C22×D311yescharacteristic
238C2×C3⋊C8C22×D311yescharacteristic
239D3×C8—34no—
240D3×C8Dic614yescomplemented
241C22×C32C22×D411yescharacteristic
242C2×C3×D3—22no—
243C2×C3×D3C4⋊Q812yes—
244C32×C4—42no—
245C32×C4C22×Q811yescharacteristic
246C32×C4C22×Q811yescharacteristic
247C3⋊Dic3—42no—
248C3⋊Dic3#13514yes—
249C3×Dic3—22no—
250C3×Dic3—42no—
251C3×Dic3—42no—
252C3×Dic3C4⋊Q812yes—
253C22×C8—31no—
254C22×C8—91no—
255C4⋊Q8—92no—
256C4⋊Q8—92no—
257#125—32no—
258#125—92no—
259C22⋊Q8—182no—
260C22⋊Q8—182no—
261C4×Q8—182no—
262C4×Q8—182no—
263#117—32no—
264#117—92no—
265C2×C42—91no—
266#107—32no—
267#107—32no—
268#107—92no—
269#107—92no—
270#106—31no—
271#106—31no—
272#106—92no—
273#106—91no—
274#106—92no—
275#106D3211yescharacteristic
276C4×C8—31no—
277C4×C8—91no—
278C4×C8—91no—
279C4×C8—91no—
280C23×C3—31no—
281C22×D3D3×D411yescharacteristic
282C2×C3×C4—22no—
283C2×C3×C4—22no—
284C2×C3×C4—21no—
285C2×C3×C4—31no—
286C2×C3×C4—32no—
287C2×C3×C4—32no—
288C2×C3×C4—32no—
289C2×C3×C4—42no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4C23×D311yescharacteristic
293C2×C3×C4C23×D311yescharacteristic
294C2×Dic3—22no—
295C2×Dic3—22no—
296C2×Dic3—32no—
297C2×Dic3—32no—
298C2×Dic3—62no—
299C2×Dic3—64no—
300C2×Dic3—62no—
301C2×Dic3—62no—
302C2×Dic3—122no—
303C2×Dic3D3×D412yes—
304C2×Dic3D3×D411yescharacteristic
305C4×D3—64no—
306C4×D3C2×Dic612yes—
307C4×D3D3×Q812yes—
308Dic6—124no—
309Dic6—124no—
310Dic6—124no—
311Dic6—124no—
312Dic6—244no—
313C3×C8—22no—
314C3×C8—32no—
315C3×C8—32no—
316C3×C8C2×Dic612yes—
317C3×C8D3×Q812yes—
318C3⋊C8—32no—
319C3⋊C8—32no—
320C3⋊C8—62no—
321C3⋊C8C2×Dic612yes—
322C3⋊C8D3×Q812yes—
323C2×C32C2×C4⋊Q811yescharacteristic
324C2×C32C2×#13512yes—
325C3×D3—22no—
326C2×Q8—182no—
327C2×Q8—182no—
328C22×C4—31no—
329C22×C4—92no—
330C2×C8—31no—
331C2×C8—31no—
332C2×C8—34no—
333C2×C8—94no—
334C2×C8—91no—
335C2×C8C2×D3211yescharacteristic
336C4⋊C4—32no—
337C4⋊C4—32no—
338C4⋊C4—62no—
339C4⋊C4—62no—
340C4⋊C4—92no—
341C4⋊C4—182no—
342C4⋊C4—182no—
343C4⋊C4—182no—
344C4⋊C4—182no—
345C4⋊C4C2×D3212yes—
346C22⋊C4—62no—
347C22⋊C4—182no—
348C42—31no—
349C42—62no—
350C42—92no—
351C42—91no—
352C42—182no—
353C22×C3—21no—
354C22×C3—32no—
355C22×C3—62no—
356C22×C3C2×D3×D411yescharacteristic
357C22×C3C2×D3×D411yescharacteristic
358C2×D3—22no—
359C2×D3#88812yes—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—32no—
363C3×C4—42no—
364C3×C4—42no—
365C3×C4—62no—
366C3×C4—82no—
367C3×C4—122no—
368C3×C4—122no—
369C3×C4C22×Dic611yescharacteristic
370C3×C4C2×D3×Q811yescharacteristic
371C3×C4C2×D3×Q811yescharacteristic
372C3×C4C2×D3×Q811yescharacteristic
373Dic3—22no—
374Dic3—34no—
375Dic3—34no—
376Dic3—42no—
377Dic3—42no—
378Dic3—64no—
379Dic3—122no—
380Dic3—122no—
381Dic3—242no—
382Dic3#88812yes—
383C32#316011yescharacteristic, complemented, Sylow
384C23—31no—
385Q8—364no—
386Q8—364no—
387C2×C4—22no—
388C2×C4—31no—
389C2×C4—32no—
390C2×C4—32no—
391C2×C4—32no—
392C2×C4—62no—
393C2×C4—62no—
394C2×C4—92no—
395C2×C4—184no—
396C2×C4—182no—
397C2×C4C22×D3211yescharacteristic
398C8—32no—
399C8—32no—
400C8—92no—
401C8D3×Dic612yes—
402C2×C3—21no—
403C2×C3—22no—
404C2×C3—62no—
405C2×C3C2×#88811yescharacteristic
406C2×C3D3×C4⋊Q811yescharacteristic
407C2×C3D3×#13512yes—
408C2×C3D3×#13512yes—
409D3—22no—
410C22—32no—
411C22—62no—
412C22D32×D411yescharacteristic
413C4—32no—
414C4—42no—
415C4—62no—
416C4—94no—
417C4—122no—
418C4—122no—
419C4—362no—
420C4C2×D3×Dic611yescharacteristic
421C4D32×Q811yescharacteristic
422C3—21no—
423C3#7917011yescharacteristic, complemented
424C3#8191611yescharacteristic, complemented
425C2—62no—
426C2D3×#88811yescharacteristic
427C2#1059474712yes—
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenter#106D32
hypocenterC32#3160
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #10592554C2semidirect
4. C3×#4858C2semidirect
5. #10590900C2semidirect
6. #10590871C2semidirect
10. #10590415C2semidirect
11. #10590413C2semidirect
56. #4858D3semidirect
83. C3×D3×C8Q8semidirect
90. D3×C3⋊C8Q8semidirect
240. D3×C8Dic6semidirect
383. C32#3160semidirect
423. C3#79170semidirect
424. C3#81916semidirect

Maximal subgroups

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

subgroupindex
#105944772
#105925542
C3×#48602
C3×#48582
#105909002
#105908712
#105907062
D3×C8×Dic32
#105905712
#105904152
#105904132
#819163
#791703