Finite Group Databasebeta

← #11875001

Subgroups — #11875001

Order 1152.

769 conjugacy classes of subgroups.

The subgroup lattice has 473 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594448C212yesmaximal
2#10592579C211yesmaximal, characteristic
3C3×#4878C211yesmaximal, characteristic, complemented
4C3×#4874C211yesmaximal, characteristic, complemented
5#10590891C211yesmaximal, characteristic, complemented
6#10590873C211yesmaximal, characteristic, complemented
7#10590714C211yesmaximal, characteristic
8C8×#624C211yesmaximal, characteristic
9#10590574C212yesmaximal
10#10590413C212yesmaximal, complemented
11#10590412C212yesmaximal, complemented
12#81938—31nomaximal
13#81916—31nomaximal
14C2×C8×C3⋊D3C2211yescharacteristic
15#64101C2212yes—
16C3×#890C2212yes—
17C3×#888C2212yes—
18#63918C2212yes—
19#63895—22no—
20#63888—22no—
21C4×#624C2211yescharacteristic
22#63869C2212yes—
23#63849C2212yes—
24#63843—22no—
25#63838—22no—
26C2×#3710C2211yescharacteristic
27C32×#107C2211yescharacteristic
28#63645C2211yescharacteristic
29#63635C2212yes—
30C3×#818C2211yescharacteristic
31C3×#818C2211yescharacteristic
32C3×C8×Dic3C2211yescharacteristic
33C3×C8×Dic3C2211yescharacteristic
34C3×#808C2212yes—
35C3×#807C2212yes—
36#63575C2212yes—
37#63574C2212yes—
38#63573C2212yes—
39Dic3×C3⋊C8C2211yescharacteristic
40Dic3×C3⋊C8C2211yescharacteristic
41#5728—32no—
42#5688—32no—
43C3×#500—31no—
44C3×#499—31no—
45#5080—32no—
46#5065—32no—
47#4880—31no—
48#4880—31no—
49#4880—31no—
50#4880—31no—
51#4880—32no—
52#4880—61no—
53#4878—32no—
54#4878—31no—
55#4878D311yescharacteristic, complemented
56#4874—31no—
57#4874D311yescharacteristic, complemented
58#4860—32no—
59#4855—32no—
60C4×D3×C8—31no—
61C4×D3×C8—31no—
62#4683—31no—
63#4682—31no—
64C2×C4×C3⋊D3C2311yescharacteristic
65C2×C3×Dic6—22no—
66C2×#627—22no—
67C2×#624D411yescharacteristic
68C2×#624D411yescharacteristic
69C2×C32×C8C2311yescharacteristic
70C32×C4⋊C4C2312yes—
71#3752—22no—
72C4⋊(C3⋊Dic3)C2312yes—
73C4×C3⋊Dic3—22no—
74C2×C3⋊(C3⋊C8)C2311yescharacteristic
75C8×C3⋊D3Q814yescomplemented
76C3×C4⋊Dic3—22no—
77C3×C4⋊Dic3C2312yes—
78C3×C4⋊Dic3C2312yes—
79C3×Dic3⋊C4—22no—
80C3×Dic3⋊C4—22no—
81C3×C4×Dic3C2311yescharacteristic
82C3×C4×Dic3C2311yescharacteristic
83C2×C3×C3⋊C8C2311yescharacteristic
84C2×C3×C3⋊C8C2311yescharacteristic
85#3724—22no—
86Dic3⋊Dic3—22no—
87Dic3⋊Dic3—22no—
88#3722—22no—
89Dic32—22no—
90Dic32D411yescharacteristic
91Dic32D411yescharacteristic
92#3710Q814yescomplemented
93#3160—91noSylow
94C3×C4⋊Q8—32no—
95C3×#125—32no—
96#946—62no—
97Q8×Dic3—62no—
98C2×D3×C8—31no—
99C2×D3×C8—31no—
100C2×D3×C8—31no—
101C2×D3×C8—31no—
102C2×D3×C8—61no—
103#897—62no—
104#896—62no—
105#896—62no—
106#892—32no—
107#892—32no—
108#892—32no—
109#892—32no—
110#892—62no—
111#890—32no—
112#890C2×D312yes—
113#888—32no—
114#888C2×D312yes—
115#887—62no—
116#887—62no—
117#887—62no—
118C42×D3—31no—
119C42×D3—31no—
120#870—32no—
121#869—32no—
122C3×#107—21no—
123C3×#107—31no—
124C3×#107—31no—
125C3×#107—32no—
126C3×#107C2×D311yescharacteristic
127C3×#107C2×D311yescharacteristic
128C3×#106—32no—
129C3×C4×C8—31no—
130C3×C4×C8—31no—
131#818—31no—
132#818—31no—
133#818—32no—
134#818—61no—
135#818C2×D311yescharacteristic
136#818C2×D311yescharacteristic
137#817—32no—
138C8×Dic3—31no—
139C8×Dic3—31no—
140C8×Dic3C2×D311yescharacteristic
141C8×Dic3C2×D311yescharacteristic
142#808—32no—
143#808—32no—
144#808—32no—
145#808—32no—
146#808—32no—
147#808—62no—
148#808C2×D312yes—
149#807—32no—
150#807C2×D312yes—
151C4×C3⋊C8—31no—
152C4×C3⋊C8—31no—
153C22×C3⋊D3C2×D411yescharacteristic
154C2×C32×C4—22no—
155C2×C32×C4C2411yescharacteristic
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3C2×D411yescharacteristic
158C4×C3⋊D3C2×Q812yes—
159C4×C3⋊D3C2×Q812yes—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3C2×D411yescharacteristic
163C2×C3×Dic3C2×D411yescharacteristic
164C2×C3×Dic3C2×D411yescharacteristic
165C2×C3×Dic3C2×D411yescharacteristic
166C3×Dic6—44no—
167#627—44no—
168#624—22no—
169#624—22no—
170C32×C8C2×Q812yes—
171C3⋊(C3⋊C8)C2×Q812yes—
172C3×C3⋊C8C2×Q812yes—
173C3×C3⋊C8C2×Q812yes—
174#533—92no—
175#500—31no—
176#500—91no—
177#499—31no—
178#499—91no—
179#499—92no—
180#498—92no—
181#427—92no—
182#427—91no—
183#427—91no—
184C2×C4×C8—91no—
185C2×C3×Q8—62no—
186C2×C4×D3—31no—
187C2×C4×D3—31no—
188C2×C4×D3—31no—
189C2×C4×D3—31no—
190C2×C4×D3—31no—
191C2×C4×D3—31no—
192C2×C4×D3—61no—
193C2×Dic6—22no—
194C2×Dic6—62no—
195C2×Dic6—62no—
196C2×C3×C8—21no—
197C2×C3×C8—31no—
198C2×C3×C8—31no—
199C2×C3×C8C22×D311yescharacteristic
200C2×C3×C8C22×D311yescharacteristic
201C3×C4⋊C4—22no—
202C3×C4⋊C4—32no—
203C3×C4⋊C4—32no—
204C3×C4⋊C4—62no—
205C3×C4⋊C4—62no—
206C3×C4⋊C4—62no—
207C3×C4⋊C4C22×D312yes—
208C3×C4⋊C4C22×D312yes—
209C3×C42—31no—
210C3×C42—31no—
211(C2×D3)⋊C4—62no—
212(C2×D3)⋊C4—62no—
213(C2×D3)⋊C4—62no—
214(C2×D3)⋊C4—62no—
215(C2×D3)⋊C4—122no—
216C4⋊Dic3—22no—
217C4⋊Dic3—32no—
218C4⋊Dic3—32no—
219C4⋊Dic3—62no—
220C4⋊Dic3—62no—
221C4⋊Dic3—62no—
222C4⋊Dic3C22×D312yes—
223C4⋊Dic3C22×D312yes—
224Dic3⋊C4—22no—
225Dic3⋊C4—22no—
226Dic3⋊C4—62no—
227Dic3⋊C4—62no—
228Dic3⋊C4—62no—
229Dic3⋊C4—62no—
230C4×Dic3—31no—
231C4×Dic3—31no—
232C4×Dic3—31no—
233C4×Dic3—31no—
234C4×Dic3—62no—
235C4×Dic3—62no—
236C4×Dic3—62no—
237C4×Dic3—62no—
238C4×Dic3—122no—
239C4×Dic3C22×D311yescharacteristic
240C4×Dic3C22×D311yescharacteristic
241C2×C3⋊C8—31no—
242C2×C3⋊C8—31no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8C22×D311yescharacteristic
245C2×C3⋊C8C22×D311yescharacteristic
246D3×C8—34no—
247D3×C8—34no—
248D3×C8—34no—
249D3×C8—34no—
250D3×C8—64no—
251C22×C32C22×D411yescharacteristic
252C2×C3⋊D3—21no—
253C2×C3⋊D3—21no—
254C2×C3⋊D3C4⋊Q812yes—
255C32×C4—42no—
256C32×C4C22×Q811yescharacteristic
257C32×C4C22×Q811yescharacteristic
258C3⋊Dic3—42no—
259C3⋊Dic3C4⋊Q812yes—
260C3×Dic3—21no—
261C3×Dic3—21no—
262C3×Dic3—42no—
263C3×Dic3—42no—
264C3×Dic3#13512yes—
265C3×Dic3#13512yes—
266C22×C8—91no—
267C22×C8—91no—
268C4⋊Q8—32no—
269C4⋊Q8—92no—
270#125—32no—
271#125—92no—
272C22⋊Q8—182no—
273C22⋊Q8—182no—
274C4×Q8—182no—
275C4×Q8—182no—
276#117—92no—
277#117—92no—
278C2×C42—91no—
279#107—31no—
280#107—31no—
281#107—32no—
282#107—92no—
283#107—91no—
284#107D3211yescharacteristic
285#106—32no—
286#106—92no—
287#106—92no—
288#106—92no—
289C4×C8—31no—
290C4×C8—31no—
291C4×C8—91no—
292C4×C8—91no—
293C22×D3—31no—
294C22×D3—31no—
295C22×D3—61no—
296C3×Q8—124no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—21no—
300C2×C3×C4—31no—
301C2×C3×C4—31no—
302C2×C3×C4—31no—
303C2×C3×C4—31no—
304C2×C3×C4—42no—
305C2×C3×C4—62no—
306C2×C3×C4—62no—
307C2×C3×C4C23×D311yescharacteristic
308C2×C3×C4C23×D311yescharacteristic
309C2×Dic3—22no—
310C2×Dic3—22no—
311C2×Dic3—31no—
312C2×Dic3—31no—
313C2×Dic3—61no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316C2×Dic3—122no—
317C2×Dic3D3×D411yescharacteristic
318C2×Dic3D3×D411yescharacteristic
319C2×Dic3D3×D411yescharacteristic
320C2×Dic3D3×D411yescharacteristic
321C4×D3—32no—
322C4×D3—32no—
323C4×D3—32no—
324C4×D3—32no—
325C4×D3—62no—
326C4×D3—62no—
327C4×D3—62no—
328C4×D3—62no—
329C4×D3—62no—
330C4×D3—62no—
331Dic6—44no—
332Dic6—124no—
333Dic6—124no—
334C3×C8—22no—
335C3×C8—32no—
336C3×C8—32no—
337C3×C8D3×Q812yes—
338C3×C8D3×Q812yes—
339C3⋊C8—32no—
340C3⋊C8—32no—
341C3⋊C8—62no—
342C3⋊C8D3×Q812yes—
343C3⋊C8D3×Q812yes—
344C2×C32C2×C4⋊Q811yescharacteristic
345C2×C32C2×#13511yescharacteristic
346C2×C32C2×#13511yescharacteristic
347C3⋊D3—22no—
348C2×Q8—62no—
349C2×Q8—182no—
350C22×C4—91no—
351C22×C4—91no—
352C22×C4—91no—
353C2×C8—31no—
354C2×C8—31no—
355C2×C8—94no—
356C2×C8—91no—
357C2×C8—94no—
358C2×C8C2×D3211yescharacteristic
359C4⋊C4—32no—
360C4⋊C4—32no—
361C4⋊C4—62no—
362C4⋊C4—62no—
363C4⋊C4—62no—
364C4⋊C4—92no—
365C4⋊C4—182no—
366C4⋊C4—182no—
367C4⋊C4—182no—
368C4⋊C4C2×D3212yes—
369C22⋊C4—182no—
370C22⋊C4—182no—
371C42—31no—
372C42—31no—
373C42—91no—
374C42—91no—
375C42—182no—
376C42—182no—
377C22×C3—21no—
378C22×C3C2×D3×D411yescharacteristic
379C22×C3C2×D3×D411yescharacteristic
380C2×D3—32no—
381C2×D3—32no—
382C2×D3—62no—
383C2×D3—61no—
384C2×D3—61no—
385C2×D3—61no—
386C2×D3—61no—
387C2×D3—121no—
388C2×D3—121no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—32no—
392C3×C4—32no—
393C3×C4—42no—
394C3×C4—42no—
395C3×C4—61no—
396C3×C4—61no—
397C3×C4—82no—
398C3×C4—122no—
399C3×C4—122no—
400C3×C4C2×D3×Q811yescharacteristic
401C3×C4C2×D3×Q811yescharacteristic
402C3×C4C2×D3×Q811yescharacteristic
403C3×C4C2×D3×Q811yescharacteristic
404Dic3—21no—
405Dic3—21no—
406Dic3—32no—
407Dic3—32no—
408Dic3—42no—
409Dic3—42no—
410Dic3—62no—
411Dic3—122no—
412Dic3—122no—
413Dic3—242no—
414Dic3#91212yes—
415Dic3#91912yes—
416C32#316011yescharacteristic, complemented, Sylow
417C23—91no—
418Q8—124no—
419Q8—364no—
420C2×C4—22no—
421C2×C4—31no—
422C2×C4—31no—
423C2×C4—31no—
424C2×C4—31no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—91no—
428C2×C4—92no—
429C2×C4—92no—
430C2×C4—182no—
431C2×C4—182no—
432C2×C4—182no—
433C2×C4C22×D3211yescharacteristic
434C8—32no—
435C8—32no—
436C8—92no—
437C8#379712yes—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3D3×C4⋊Q811yescharacteristic
442C2×C3D3×C4⋊Q811yescharacteristic
443C2×C3C2×#91211yescharacteristic
444C2×C3C2×#91911yescharacteristic
445C2×C3D3×#13511yescharacteristic
446C2×C3D3×#13511yescharacteristic
447D3—62no—
448D3—62no—
449D3—122no—
450C22—92no—
451C22—181no—
452C22—181no—
453C22D32×D411yescharacteristic
454C4—32no—
455C4—32no—
456C4—42no—
457C4—61no—
458C4—61no—
459C4—92no—
460C4—122no—
461C4—122no—
462C4—362no—
463C4C2×#379711yescharacteristic
464C4D32×Q811yescharacteristic
465C3—21no—
466C3#8191611yescharacteristic, complemented
467C3#8193811yescharacteristic, complemented
468C2—182no—
469C2#1059437411yescharacteristic
470C2D3×#91211yescharacteristic
471C2D3×#91911yescharacteristic
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
3. C3×#4878C2semidirect
4. C3×#4874C2semidirect
5. #10590891C2semidirect
6. #10590873C2semidirect
10. #10590413C2semidirect
11. #10590412C2semidirect
55. #4878D3semidirect
57. #4874D3semidirect
75. C8×C3⋊D3Q8semidirect
92. #3710Q8semidirect
416. C32#3160semidirect
466. C3#81916semidirect
467. C3#81938semidirect

Maximal subgroups

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

subgroupindex
#105944482
#105925792
C3×#48782
C3×#48742
#105908912
#105908732
#105907142
C8×#6242
#105905742
#105904132
#105904122
#819383
#819163