Finite Group Databasebeta

← #11874987

Subgroups — #11874987

Order 1152.

755 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594445C212yesmaximal
2#10592557C211yesmaximal, characteristic, complemented
3C3×#4860C211yesmaximal, characteristic
4C3×#4855C211yesmaximal, characteristic, complemented
5#10590889C211yesmaximal, characteristic, complemented
6#10590874C211yesmaximal, characteristic, complemented
7#10590706C211yesmaximal, characteristic
8D3×C8×Dic3C211yesmaximal, characteristic
9#10590572C212yesmaximal
10#10590417C212yesmaximal, complemented
11#10590411C212yesmaximal, complemented
12#81891—31nomaximal
13#79170—31nomaximal
14#64099C2212yes—
15C2×C3×D3×C8C2211yescharacteristic
16C3×#892C2212yes—
17C3×#888C2212yes—
18#63918C2212yes—
19#63893—22no—
20#63887—22no—
21C4×D3×Dic3C2211yescharacteristic
22#63872C2212yes—
23Dic3×Dic6—22no—
24#63841C2212yes—
25#63837—22no—
26C2×D3×C3⋊C8C2211yescharacteristic
27C32×#106C2211yescharacteristic
28#63644C2211yescharacteristic
29C8×C3⋊Dic3C2211yescharacteristic
30#63634C2212yes—
31C3×#817C2211yescharacteristic
32C3×#817C2211yescharacteristic
33C3×C8×Dic3C2211yescharacteristic
34C3×#808C2212yes—
35C3×#807C2212yes—
36#63576C2212yes—
37#63575C2212yes—
38#63573C2212yes—
39#63553C2211yescharacteristic
40Dic3×C3⋊C8C2211yescharacteristic
41#5728—32no—
42#5517—32no—
43C3×#498—31no—
44C3×#427—31no—
45#5106—31no—
46C2×C8×Dic3—31no—
47#5078—32no—
48#4998—32no—
49#4878—32no—
50#4874—32no—
51#4860—31no—
52#4860—32no—
53#4860D311yescharacteristic
54#4858—31no—
55#4858—31no—
56#4858—31no—
57#4858—31no—
58#4858—32no—
59#4858—61no—
60#4855—31no—
61#4855D311yescharacteristic, complemented
62C4×D3×C8—31no—
63#4680—31no—
64C2×C3×C4×D3C2311yescharacteristic
65C2×C3×Dic6—22no—
66C2×#627—22no—
67C2×D3×Dic3D412yes—
68C2×C32×C8C2311yescharacteristic
69C32×C4⋊C4C2312yes—
70C4⋊(C3⋊Dic3)—22no—
71C4⋊(C3⋊Dic3)C2312yes—
72#3750—22no—
73C4×C3⋊Dic3C2311yescharacteristic
74C2×C3⋊(C3⋊C8)C2311yescharacteristic
75C3×(C2×D3)⋊C4—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
84Dic3⋊Dic3—22no—
85Dic3⋊Dic3—22no—
86Dic3⋊Dic3—22no—
87(C2×D3)⋊Dic3—22no—
88Dic32—22no—
89Dic32D412yes—
90D3×C3⋊C8Q814yescomplemented
91#3160—91noSylow
92C22×C3×C8—31no—
93C3×C4⋊Q8—32no—
94C3×#117—32no—
95#946—62no—
96Q8×Dic3—62no—
97#926—32no—
98C2×C4×Dic3—31no—
99C22×C3⋊C8—31no—
100C2×D3×C8—31no—
101C2×D3×C8C2×D311yescharacteristic
102#897—62no—
103#892—32no—
104#892C2×D312yes—
105#890—32no—
106#890—32no—
107#890—32no—
108#890—32no—
109#890—62no—
110#888—32no—
111#888C2×D312yes—
112#887—62no—
113#878—62no—
114#878—62no—
115C42×D3—31no—
116#869—32no—
117C4×Dic6—62no—
118C4×Dic6—62no—
119C3×#107—32no—
120C3×#106—21no—
121C3×#106—31no—
122C3×#106—31no—
123C3×#106—32no—
124C3×#106C2×D311yescharacteristic
125C3×#106C2×D311yescharacteristic
126C3×C4×C8—31no—
127#818—32no—
128#817—31no—
129#817—31no—
130#817—32no—
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#808C2×D312yes—
143#807—32no—
144#807—32no—
145#807—32no—
146#807—32no—
147#807—32no—
148#807—62no—
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—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3C2×D411yescharacteristic
159C2×C3×Dic3C2×D412yes—
160C3×C4×D3C2×Q812yes—
161C3×C4×D3C2×Q812yes—
162C3×Dic6—44no—
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—91no—
172#499—92no—
173#499—91no—
174#498—31no—
175#498—91no—
176#427—31no—
177#427—92no—
178#427—91no—
179C2×C4×C8—91no—
180C2×C3×Q8—62no—
181C22×C3×C4—31no—
182C22×Dic3—32no—
183C2×C4×D3—32no—
184C2×C4×D3C22×D311yescharacteristic
185C2×Dic6—22no—
186C2×Dic6—62no—
187C2×Dic6—62no—
188C2×C3×C8—21no—
189C2×C3×C8—31no—
190C2×C3×C8—31no—
191C2×C3×C8—34no—
192C2×C3×C8C22×D311yescharacteristic
193C2×C3×C8C22×D311yescharacteristic
194C3×C4⋊C4—22no—
195C3×C4⋊C4—32no—
196C3×C4⋊C4—32no—
197C3×C4⋊C4—62no—
198C3×C4⋊C4C22×D312yes—
199C3×C4⋊C4C22×D312yes—
200C3×C22⋊C4—62no—
201C3×C42—31no—
202C3×C42—62no—
203#217—62no—
204(C2×D3)⋊C4—22no—
205(C2×D3)⋊C4—62no—
206C4⋊Dic3—32no—
207C4⋊Dic3—32no—
208C4⋊Dic3—62no—
209C4⋊Dic3—62no—
210C4⋊Dic3—62no—
211C4⋊Dic3—62no—
212C4⋊Dic3—62no—
213C4⋊Dic3—62no—
214C4⋊Dic3—122no—
215C4⋊Dic3C22×D312yes—
216C4⋊Dic3C22×D312yes—
217Dic3⋊C4—22no—
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—22no—
248C3⋊Dic3—42no—
249C3×Dic3—42no—
250C3×Dic3—42no—
251C3×Dic3C4⋊Q812yes—
252C3×Dic3#13514yes—
253C22×C8—31no—
254C22×C8—91no—
255C4⋊Q8—32no—
256C4⋊Q8—92no—
257#125—92no—
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—92no—
268#107—92no—
269#107—92no—
270#106—31no—
271#106—31no—
272#106—32no—
273#106—92no—
274#106—91no—
275#106D3211yescharacteristic
276C4×C8—31no—
277C4×C8—91no—
278C4×C8—91no—
279C4×C8—91no—
280C23×C3—31no—
281C22×D3D3×D411yescharacteristic
282C3×Q8—124no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—21no—
286C2×C3×C4—31no—
287C2×C3×C4—32no—
288C2×C3×C4—32no—
289C2×C3×C4—32no—
290C2×C3×C4—42no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4C23×D311yescharacteristic
294C2×C3×C4C23×D311yescharacteristic
295C2×Dic3—22no—
296C2×Dic3—22no—
297C2×Dic3—32no—
298C2×Dic3—32no—
299C2×Dic3—62no—
300C2×Dic3—64no—
301C2×Dic3—62no—
302C2×Dic3—62no—
303C2×Dic3—122no—
304C2×Dic3D3×D411yescharacteristic
305C2×Dic3D3×D412yes—
306C4×D3—64no—
307C4×D3C2×Dic612yes—
308C4×D3D3×Q812yes—
309Dic6—44no—
310Dic6—124no—
311Dic6—124no—
312C3×C8—22no—
313C3×C8—32no—
314C3×C8—32no—
315C3×C8C2×Dic612yes—
316C3×C8D3×Q812yes—
317C3⋊C8—32no—
318C3⋊C8—32no—
319C3⋊C8—62no—
320C3⋊C8C2×Dic612yes—
321C3⋊C8D3×Q812yes—
322C2×C32C2×C4⋊Q811yescharacteristic
323C2×C32C2×#13512yes—
324C3×D3—22no—
325C2×Q8—62no—
326C2×Q8—182no—
327C22×C4—31no—
328C22×C4—92no—
329C2×C8—31no—
330C2×C8—31no—
331C2×C8—34no—
332C2×C8—94no—
333C2×C8—91no—
334C2×C8C2×D3211yescharacteristic
335C4⋊C4—32no—
336C4⋊C4—32no—
337C4⋊C4—62no—
338C4⋊C4—92no—
339C4⋊C4—182no—
340C4⋊C4—182no—
341C4⋊C4—182no—
342C4⋊C4—182no—
343C4⋊C4—182no—
344C4⋊C4C2×D3212yes—
345C22⋊C4—62no—
346C22⋊C4—182no—
347C42—31no—
348C42—62no—
349C42—92no—
350C42—91no—
351C42—182no—
352C22×C3—21no—
353C22×C3—32no—
354C22×C3—62no—
355C22×C3C2×D3×D411yescharacteristic
356C22×C3C2×D3×D411yescharacteristic
357C2×D3—22no—
358C2×D3#88812yes—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—32no—
362C3×C4—34no—
363C3×C4—42no—
364C3×C4—42no—
365C3×C4—82no—
366C3×C4—122no—
367C3×C4—122no—
368C3×C4C22×Dic611yescharacteristic
369C3×C4C2×D3×Q811yescharacteristic
370C3×C4C2×D3×Q811yescharacteristic
371C3×C4C2×D3×Q811yescharacteristic
372Dic3—42no—
373Dic3—42no—
374Dic3—62no—
375Dic3—62no—
376Dic3—122no—
377Dic3—122no—
378Dic3—122no—
379Dic3—242no—
380Dic3#88812yes—
381Dic3#91614yes—
382C32#316011yescharacteristic, complemented, Sylow
383C23—31no—
384Q8—124no—
385Q8—364no—
386C2×C4—22no—
387C2×C4—32no—
388C2×C4—31no—
389C2×C4—32no—
390C2×C4—32no—
391C2×C4—62no—
392C2×C4—62no—
393C2×C4—92no—
394C2×C4—184no—
395C2×C4—182no—
396C2×C4C22×D3211yescharacteristic
397C8—32no—
398C8—32no—
399C8—92no—
400C8D3×Dic612yes—
401C2×C3—21no—
402C2×C3—22no—
403C2×C3—62no—
404C2×C3C2×#88811yescharacteristic
405C2×C3D3×C4⋊Q811yescharacteristic
406C2×C3C2×#91612yes—
407C2×C3D3×#13512yes—
408D3—22no—
409C22—32no—
410C22—62no—
411C22D32×D411yescharacteristic
412C4—32no—
413C4—34no—
414C4—42no—
415C4—122no—
416C4—122no—
417C4—182no—
418C4—362no—
419C4C2×D3×Dic611yescharacteristic
420C4D32×Q811yescharacteristic
421C3—21no—
422C3#7917011yescharacteristic, complemented
423C3#8189111yescharacteristic, complemented
424C2—62no—
425C2D3×#88811yescharacteristic
426C2D3×#91612yes—
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. #10592557C2semidirect
4. C3×#4855C2semidirect
5. #10590889C2semidirect
6. #10590874C2semidirect
10. #10590417C2semidirect
11. #10590411C2semidirect
61. #4855D3semidirect
83. C3×D3×C8Q8semidirect
90. D3×C3⋊C8Q8semidirect
240. D3×C8Dic6semidirect
382. C32#3160semidirect
422. C3#79170semidirect
423. C3#81891semidirect

Maximal subgroups

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

subgroupindex
#105944452
#105925572
C3×#48602
C3×#48552
#105908892
#105908742
#105907062
D3×C8×Dic32
#105905722
#105904172
#105904112
#818913
#791703