Finite Group Databasebeta

← #11875000

Subgroups — #11875000

Order 1152.

761 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594477C212yesmaximal
2#10592573C211yesmaximal, characteristic, complemented
3C3×#4880C211yesmaximal, characteristic
4C3×#4878C211yesmaximal, characteristic, complemented
5#10590902C211yesmaximal, characteristic, complemented
6#10590873C211yesmaximal, characteristic, complemented
7#10590707C211yesmaximal, characteristic
8D3×C8×Dic3C211yesmaximal, characteristic
9#10590572C212yesmaximal
10#10590416C212yesmaximal, complemented
11#10590414C212yesmaximal, 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×#107C2211yescharacteristic
28#63645C2211yescharacteristic
29C8×C3⋊Dic3C2211yescharacteristic
30#63634C2212yes—
31C3×#818C2211yescharacteristic
32C3×#818C2211yescharacteristic
33C3×C8×Dic3C2211yescharacteristic
34C3×#808C2212yes—
35C3×#808C2212yes—
36#63576C2212yes—
37#63573C2212yes—
38#63573C2212yes—
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—31no—
50#4880D311yescharacteristic
51#4878—31no—
52#4878D311yescharacteristic, complemented
53#4874—31no—
54#4874—31no—
55#4874—31no—
56#4874—31no—
57#4874—61no—
58#4860—32no—
59#4858—32no—
60#4855—32no—
61#4855—32no—
62C4×D3×C8—31no—
63#4683—31no—
64C2×#634—22no—
65C2×C3×C4×D3C2311yescharacteristic
66C2×#627—22no—
67C2×D3×Dic3D411yescharacteristic
68C2×D3×Dic3D411yescharacteristic
69C2×C32×C8C2311yescharacteristic
70C32×C4⋊C4C2312yes—
71C4⋊(C3⋊Dic3)C2312yes—
72#3750—22no—
73C4×C3⋊Dic3C2311yescharacteristic
74C2×C3⋊(C3⋊C8)C2311yescharacteristic
75C3×(C2×D3)⋊C4—22no—
76C3×C4⋊Dic3—22no—
77C3×C4⋊Dic3C2312yes—
78C3×C4⋊Dic3C2312yes—
79C3×Dic3⋊C4—22no—
80C3×C4×Dic3—22no—
81C3×C4×Dic3C2311yescharacteristic
82C2×C3×C3⋊C8C2311yescharacteristic
83C2×C3×C3⋊C8C2311yescharacteristic
84C3×D3×C8Q814yescomplemented
85#3724—22no—
86#3724—22no—
87Dic3⋊Dic3—22no—
88(C2×D3)⋊Dic3—22no—
89Dic32—22no—
90Dic32D411yescharacteristic
91Dic32D411yescharacteristic
92D3×C3⋊C8Q814yescomplemented
93#3160—91noSylow
94C22×C3×C8—31no—
95C3×#125—32no—
96C3×#117—32no—
97#926—32no—
98C2×C4×Dic3—31no—
99C22×C3⋊C8—31no—
100C2×D3×C8—31no—
101C2×D3×C8C2×D311yescharacteristic
102#896—62no—
103#896—62no—
104#892—32no—
105#892C2×D312yes—
106#890—32no—
107#890C2×D312yes—
108#888—32no—
109#888—32no—
110#888—32no—
111#888—32no—
112#888—62no—
113#887—62no—
114#887—62no—
115#878—62no—
116#878—62no—
117C42×D3—31no—
118#870—32no—
119C4×Dic6—62no—
120C4×Dic6—62no—
121C3×#107—21no—
122C3×#107—31no—
123C3×#107—31no—
124C3×#107C2×D311yescharacteristic
125C3×#107C2×D311yescharacteristic
126C3×#106—32no—
127C3×#106—32no—
128C3×C4×C8—31no—
129#818—31no—
130#818—31no—
131#818—61no—
132#818C2×D311yescharacteristic
133#818C2×D311yescharacteristic
134#817—32no—
135#817—32no—
136C8×Dic3—31no—
137C8×Dic3—31no—
138C8×Dic3—31no—
139C8×Dic3—31no—
140C8×Dic3—31no—
141C8×Dic3—61no—
142C8×Dic3C2×D311yescharacteristic
143#808—32no—
144#808—32no—
145#808C2×D312yes—
146#808C2×D312yes—
147#807—32no—
148#807—32no—
149#807—32no—
150#807—32no—
151#807—62no—
152C4×C3⋊C8—31no—
153C22×C3×D3C2×D411yescharacteristic
154C2×C32×C4—22no—
155C2×C32×C4C2411yescharacteristic
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3C2×D411yescharacteristic
158C2×C3⋊Dic3C2×D411yescharacteristic
159#634—44no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3C2×D411yescharacteristic
163C2×C3×Dic3C2×D411yescharacteristic
164C2×C3×Dic3C2×D411yescharacteristic
165C3×C4×D3C2×Q812yes—
166C3×C4×D3C2×Q812yes—
167#627—44no—
168D3×Dic3—22no—
169D3×Dic3—22no—
170C32×C8C2×Q812yes—
171C3⋊(C3⋊C8)C2×Q812yes—
172C3×C3⋊C8C2×Q812yes—
173C3×C3⋊C8C2×Q812yes—
174#533—92no—
175#500—91no—
176#500—91no—
177#499—31no—
178#499—91no—
179#499—92no—
180#498—92no—
181#427—31no—
182#427—92no—
183#427—91no—
184C2×C4×C8—91no—
185C22×C3×C4—31no—
186C22×Dic3—31no—
187C22×Dic3—31no—
188C2×C4×D3—31no—
189C2×C4×D3—31no—
190C2×C4×D3C22×D311yescharacteristic
191C2×Dic6—62no—
192C2×Dic6—62no—
193C2×Dic6—62no—
194C2×Dic6—62no—
195C2×Dic6—122no—
196C2×C3×C8—21no—
197C2×C3×C8—31no—
198C2×C3×C8—31no—
199C2×C3×C8—34no—
200C2×C3×C8C22×D311yescharacteristic
201C2×C3×C8C22×D311yescharacteristic
202C3×C4⋊C4—22no—
203C3×C4⋊C4—32no—
204C3×C4⋊C4—32no—
205C3×C4⋊C4—62no—
206C3×C4⋊C4—62no—
207C3×C4⋊C4C22×D312yes—
208C3×C4⋊C4C22×D312yes—
209C3×C22⋊C4—62no—
210C3×C42—31no—
211C3×C42—62no—
212#217—62no—
213(C2×D3)⋊C4—22no—
214(C2×D3)⋊C4—62no—
215C4⋊Dic3—22no—
216C4⋊Dic3—32no—
217C4⋊Dic3—32no—
218C4⋊Dic3—62no—
219C4⋊Dic3—62no—
220C4⋊Dic3C22×D312yes—
221C4⋊Dic3C22×D312yes—
222Dic3⋊C4—22no—
223Dic3⋊C4—62no—
224Dic3⋊C4—62no—
225Dic3⋊C4—62no—
226Dic3⋊C4—62no—
227Dic3⋊C4—62no—
228Dic3⋊C4—62no—
229Dic3⋊C4—62no—
230Dic3⋊C4—122no—
231C4×Dic3—22no—
232C4×Dic3—31no—
233C4×Dic3—31no—
234C4×Dic3—31no—
235C4×Dic3—31no—
236C4×Dic3—31no—
237C4×Dic3—31no—
238C4×Dic3—61no—
239C4×Dic3—62no—
240C4×Dic3—62no—
241C4×Dic3C22×D311yescharacteristic
242C2×C3⋊C8—31no—
243C2×C3⋊C8—31no—
244C2×C3⋊C8—34no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8C22×D311yescharacteristic
247C2×C3⋊C8C22×D311yescharacteristic
248D3×C8—34no—
249D3×C8Dic614yescomplemented
250C22×C32C22×D411yescharacteristic
251C2×C3×D3—21no—
252C2×C3×D3—21no—
253C2×C3×D3C4⋊Q812yes—
254C32×C4—42no—
255C32×C4C22×Q811yescharacteristic
256C32×C4C22×Q811yescharacteristic
257C3⋊Dic3—42no—
258C3⋊Dic3#13512yes—
259C3⋊Dic3#13512yes—
260C3×Dic3—21no—
261C3×Dic3—21no—
262C3×Dic3—42no—
263C3×Dic3—42no—
264C3×Dic3C4⋊Q812yes—
265C22×C8—31no—
266C22×C8—91no—
267C4⋊Q8—92no—
268C4⋊Q8—92no—
269#125—32no—
270#125—92no—
271C22⋊Q8—182no—
272C22⋊Q8—182no—
273C4×Q8—182no—
274C4×Q8—182no—
275#117—32no—
276#117—92no—
277C2×C42—91no—
278#107—31no—
279#107—31no—
280#107—92no—
281#107—91no—
282#107—92no—
283#107D3211yescharacteristic
284#106—32no—
285#106—32no—
286#106—92no—
287#106—92no—
288C4×C8—31no—
289C4×C8—91no—
290C4×C8—91no—
291C4×C8—91no—
292C23×C3—31no—
293C22×D3D3×D411yescharacteristic
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—21no—
297C2×C3×C4—31no—
298C2×C3×C4—32no—
299C2×C3×C4—32no—
300C2×C3×C4—31no—
301C2×C3×C4—31no—
302C2×C3×C4—42no—
303C2×C3×C4—62no—
304C2×C3×C4—62no—
305C2×C3×C4C23×D311yescharacteristic
306C2×C3×C4C23×D311yescharacteristic
307C2×Dic3—22no—
308C2×Dic3—22no—
309C2×Dic3—31no—
310C2×Dic3—31no—
311C2×Dic3—31no—
312C2×Dic3—31no—
313C2×Dic3—61no—
314C2×Dic3—61no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—122no—
320C2×Dic3D3×D411yescharacteristic
321C2×Dic3D3×D411yescharacteristic
322C2×Dic3D3×D411yescharacteristic
323C4×D3—62no—
324C4×D3—62no—
325C4×D3C2×Dic612yes—
326C4×D3D3×Q812yes—
327Dic6—124no—
328Dic6—124no—
329Dic6—124no—
330Dic6—124no—
331Dic6—244no—
332C3×C8—22no—
333C3×C8—32no—
334C3×C8—32no—
335C3×C8C2×Dic612yes—
336C3×C8D3×Q812yes—
337C3⋊C8—32no—
338C3⋊C8—32no—
339C3⋊C8—62no—
340C3⋊C8C2×Dic612yes—
341C3⋊C8D3×Q812yes—
342C2×C32C2×C4⋊Q811yescharacteristic
343C2×C32C2×#13511yescharacteristic
344C2×C32C2×#13511yescharacteristic
345C3×D3—22no—
346C2×Q8—182no—
347C2×Q8—182no—
348C22×C4—31no—
349C22×C4—91no—
350C22×C4—91no—
351C2×C8—31no—
352C2×C8—31no—
353C2×C8—34no—
354C2×C8—94no—
355C2×C8—91no—
356C2×C8C2×D3211yescharacteristic
357C4⋊C4—32no—
358C4⋊C4—32no—
359C4⋊C4—62no—
360C4⋊C4—62no—
361C4⋊C4—92no—
362C4⋊C4—182no—
363C4⋊C4—182no—
364C4⋊C4—182no—
365C4⋊C4—182no—
366C4⋊C4C2×D3212yes—
367C22⋊C4—62no—
368C22⋊C4—182no—
369C42—31no—
370C42—62no—
371C42—91no—
372C42—91no—
373C42—91no—
374C42—182no—
375C22×C3—21no—
376C22×C3—32no—
377C22×C3—61no—
378C22×C3—61no—
379C22×C3C2×D3×D411yescharacteristic
380C22×C3C2×D3×D411yescharacteristic
381C2×D3—21no—
382C2×D3—21no—
383C2×D3#88812yes—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—32no—
387C3×C4—42no—
388C3×C4—42no—
389C3×C4—61no—
390C3×C4—61no—
391C3×C4—82no—
392C3×C4—122no—
393C3×C4—122no—
394C3×C4C22×Dic611yescharacteristic
395C3×C4C2×D3×Q811yescharacteristic
396C3×C4C2×D3×Q811yescharacteristic
397C3×C4C2×D3×Q811yescharacteristic
398Dic3—21no—
399Dic3—21no—
400Dic3—32no—
401Dic3—32no—
402Dic3—32no—
403Dic3—32no—
404Dic3—42no—
405Dic3—42no—
406Dic3—62no—
407Dic3—62no—
408Dic3—122no—
409Dic3—122no—
410Dic3—242no—
411Dic3#88812yes—
412C32#316011yescharacteristic, complemented, Sylow
413C23—31no—
414Q8—364no—
415Q8—364no—
416C2×C4—22no—
417C2×C4—31no—
418C2×C4—32no—
419C2×C4—32no—
420C2×C4—31no—
421C2×C4—31no—
422C2×C4—62no—
423C2×C4—62no—
424C2×C4—91no—
425C2×C4—91no—
426C2×C4—182no—
427C2×C4—182no—
428C2×C4—182no—
429C2×C4C22×D3211yescharacteristic
430C8—32no—
431C8—32no—
432C8—92no—
433C8D3×Dic612yes—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—62no—
438C2×C3C2×#88811yescharacteristic
439C2×C3D3×C4⋊Q811yescharacteristic
440C2×C3D3×#13511yescharacteristic
441C2×C3D3×#13511yescharacteristic
442C2×C3D3×#13511yescharacteristic
443C2×C3D3×#13511yescharacteristic
444D3—22no—
445C22—32no—
446C22—61no—
447C22—61no—
448C22D32×D411yescharacteristic
449C4—32no—
450C4—42no—
451C4—61no—
452C4—61no—
453C4—92no—
454C4—92no—
455C4—122no—
456C4—122no—
457C4—362no—
458C4C2×D3×Dic611yescharacteristic
459C4D32×Q811yescharacteristic
460C3—21no—
461C3#7917011yescharacteristic, complemented
462C3#8191611yescharacteristic, complemented
463C2—62no—
464C2D3×#88811yescharacteristic
465C2#1059473011yescharacteristic
466C2#1059476411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenter#107D32
hypocenterC32#3160
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #10592573C2semidirect
4. C3×#4878C2semidirect
5. #10590902C2semidirect
6. #10590873C2semidirect
10. #10590416C2semidirect
11. #10590414C2semidirect
52. #4878D3semidirect
84. C3×D3×C8Q8semidirect
92. D3×C3⋊C8Q8semidirect
249. D3×C8Dic6semidirect
412. C32#3160semidirect
461. C3#79170semidirect
462. C3#81916semidirect

Maximal subgroups

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

subgroupindex
#105944772
#105925732
C3×#48802
C3×#48782
#105909022
#105908732
#105907072
D3×C8×Dic32
#105905722
#105904162
#105904142
#819163
#791703