Finite Group Databasebeta

← #11796856

Subgroups — #11796856

Order 1152.

477 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
1D3×#904C211yesmaximal, characteristic
2C3×#4860C211yesmaximal, characteristic, complemented
3D3×#812C211yesmaximal, characteristic, complemented
4#10589354C211yesmaximal, characteristic, complemented
5C3×#4488C211yesmaximal, characteristic, complemented
6#10589125C211yesmaximal, characteristic, complemented
7#10589123C211yesmaximal, characteristic, complemented
8#70656—31nomaximal
9#69251—31nomaximal
10D3×#235—21no—
11#64113C2211yescharacteristic
12C3×#904C2211yescharacteristic
13C2×C3×D3×C8C2211yescharacteristic
14C3×#892—21no—
15#63829—21no—
16#63808C411yescharacteristic, complemented
17#63807C411yescharacteristic, complemented
18#63806—21no—
19D3×Dic12C411yescharacteristic, complemented
20D3×D24C411yescharacteristic, complemented
21D3×#204—21no—
22C32×#106C2211yescharacteristic, complemented
23#63639C2211yescharacteristic, complemented
24C3×#817C2211yescharacteristic, complemented
25C3×#812C2211yescharacteristic, complemented
26C3×#807—21no—
27#63543—21no—
28D3×C3⋊C16—21no—
29D3×#135—31no—
30C2×#904—31no—
31C3×#427—31no—
32C2×#812—31no—
33D3×M32—31no—
34#4860D311yescharacteristic, complemented
35C3×#360—31no—
36#4566—31no—
37#4518—31no—
38#4488—31no—
39#4488—31no—
40#4488—31no—
41#4488—31no—
42#4488—61no—
43#4488D311yescharacteristic, complemented
44#3828—21no—
45C3×#235—21no—
46C2×C3×C4×D3D411yescharacteristic
47D3×#67—41no—
48#3804—41no—
49D3×D12—21no—
50C4×D32—41no—
51#3799—21no—
52#3798—41no—
53#3795—21no—
54D3×Dic6—21no—
55C2×C32×C8C2311yescharacteristic
56C32×C4⋊C4—21no—
57#3746C2×C411yescharacteristic
58#3745C2×C411yescharacteristic
59#3744—21no—
60C3×(C2×D3)⋊C4—41no—
61C3×C4⋊Dic3—21no—
62C3×C4×Dic3—41no—
63C2×C3×C3⋊C8D411yescharacteristic
64C3×Dic12C2×C411yescharacteristic
65C3×D24C2×C411yescharacteristic
66C3×#204—21no—
67C3×D3×C8C2×C411yescharacteristic
68C3×D3×C8C2×C411yescharacteristic
69C3×D3×C8D411yescharacteristic
70C3×D3×C8D411yescharacteristic
71#3719—21no—
72#3717—21no—
73#3716—21no—
74#3714—21no—
75C3⋊(C3⋊C16)—21no—
76C3×C3⋊C16—21no—
77#2145—91noSylow
78D3×#41—61no—
79C2×#235—61no—
80C3×#135—31no—
81C22×C3×C8—31no—
82C3×#117—61no—
83#950—61no—
84#919—31no—
85D3×Q16—31no—
86#916—61no—
87D3×SD16—61no—
88#912—31no—
89D3×D8—31no—
90C2×Dic12—31no—
91#904—31no—
92#904—31no—
93#904—31no—
94#904—31no—
95#904—61no—
96#904—61no—
97#904—61no—
98#904C2×D311yescharacteristic
99C2×D24—31no—
100C2×#204—61no—
101C2×D3×C8C2×D311yescharacteristic
102#892—21no—
103C3×M32—31no—
104C3×#107—61no—
105C3×#106—21no—
106C3×#106—31no—
107C3×#106C2×D311yescharacteristic, complemented
108C3×#106C2×D311yescharacteristic, complemented
109#817C2×D311yescharacteristic, complemented
110#812—31no—
111#812—31no—
112#812—61no—
113#812—61no—
114#812C2×D311yescharacteristic, complemented
115C2×C3⋊C16—61no—
116#807—21no—
117#798—61no—
118D3×C16—61no—
119C22×C3×D3D811yescharacteristic
120C2×D32—41no—
121C2×C32×C4—41no—
122C2×C32×C4C2×D411yescharacteristic
123#638—41no—
124C4⋊(C3⋊D3)—21no—
125C4×C3⋊D3—41no—
126#634—21no—
127C3×#67—41no—
128C2×C3×Dic3—41no—
129C2×C3×Dic3D811yescharacteristic
130C3×D12—21no—
131C3×C4×D3—41no—
132C3×C4×D3C22⋊C411yescharacteristic
133C3×C4×D3C22⋊C411yescharacteristic
134C3×C4×D3SD1611yescharacteristic
135C3×C4×D3SD1611yescharacteristic
136C3×Dic6—21no—
137#627—41no—
138#626—41no—
139#626—41no—
140#625—41no—
141#624—41no—
142D3×Dic3—41no—
143D3×Dic3—41no—
144C32×C8C22×C411yescharacteristic
145C32×C8C2×D411yescharacteristic
146C3×C3⋊C8C22⋊C411yescharacteristic
147C3×C3⋊C8C22⋊C411yescharacteristic
148C2×#135—91no—
149C2×M32—91no—
150#427—31no—
151#360—31no—
152#360—91no—
153#360—91no—
154#360—91no—
155C3×#41—61no—
156C22×C3×C4—31no—
157C2×#67—121no—
158#239—61no—
159D3×Q8—61no—
160#237—61no—
161#237—121no—
162D3×D4—61no—
163D3×D4—121no—
164#235—21no—
165#235—61no—
166#235—61no—
167#235—61no—
168#235—61no—
169#235—121no—
170#235—121no—
171#235—121no—
172#235—121no—
173C2×D12—61no—
174C2×C4×D3—121no—
175C2×C4×D3—121no—
176C2×C4×D3#6711yescharacteristic
177C2×Dic6—61no—
178C3×Q16—31no—
179C3×SD16—61no—
180C3×D8—31no—
181C2×C3×C8—21no—
182C2×C3×C8—31no—
183C2×C3×C8—31no—
184C2×C3×C8—31no—
185C2×C3×C8—31no—
186C2×C3×C8—31no—
187C2×C3×C8C22×D311yescharacteristic
188C2×C3×C8C22×D311yescharacteristic
189C3×C4⋊C4—21no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—41no—
192C3×C4⋊C4—61no—
193C3×C22⋊C4—121no—
194C3×C42—121no—
195#216—61no—
196#215—61no—
197#214—61no—
198#213—61no—
199(C2×D3)⋊C4—41no—
200C4⋊Dic3—21no—
201C4×Dic3—41no—
202C2×C3⋊C8#6711yescharacteristic
203Dic12—31no—
204Dic12—31no—
205Dic12—61no—
206Dic12—61no—
207Dic12C4×D311yescharacteristic
208D24—31no—
209D24—31no—
210D24—61no—
211D24—61no—
212D24C4×D311yescharacteristic
213#204—21no—
214#204—61no—
215#204—61no—
216#204—61no—
217#204—61no—
218#204—121no—
219D3×C8C4×D311yescharacteristic
220D3×C8C4×D311yescharacteristic
221D3×C8D1211yescharacteristic
222D3×C8D1211yescharacteristic
223C3×C16—61no—
224C3⋊C16—21no—
225C3⋊C16—61no—
226C3⋊C16—61no—
227C3⋊C16—121no—
228C22×C32C2×D811yescharacteristic
229C2×C3⋊D3—41no—
230C2×C3×D3—41no—
231C2×C3×D3—41no—
232C2×C3×D3#10211yescharacteristic
233C2×C3×D3#10211yescharacteristic
234D32—82no—
235C32×C4—81no—
236C32×C4C2×C22⋊C411yescharacteristic
237C32×C4C2×SD1611yescharacteristic
238C3⋊Dic3—41no—
239C3×Dic3—41no—
240C3×Dic3—81no—
241C3×Dic3#10211yescharacteristic
242C3×Dic3#10211yescharacteristic
243C2×#41—181no—
244#135—31no—
245#135—91no—
246#135—91no—
247#135—91no—
248#135—181no—
249#135—181no—
250C2×Q16—91no—
251C2×SD16—181no—
252C2×D8—91no—
253C22×C8—31no—
254#117—61no—
255M32—31no—
256M32—91no—
257M32—181no—
258C2×C16—181no—
259#107—61no—
260#106—31no—
261#106D3211yescharacteristic, complemented
262C23×C3—31no—
263C22×D3—121no—
264C22×D3—121no—
265C22×D3#21311yescharacteristic
266C3×Q8—61no—
267C3×D4—61no—
268C3×D4—121no—
269C2×C3×C4—21no—
270C2×C3×C4—31no—
271C2×C3×C4—31no—
272C2×C3×C4—31no—
273C2×C3×C4—31no—
274C2×C3×C4—31no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—81no—
278C2×C3×C4—121no—
279C2×C3×C4—121no—
280C2×C3×C4D3×D411yescharacteristic
281C2×C3×C4C2×#6711yescharacteristic
282#67—41no—
283#67—121no—
284#67—121no—
285#67—121no—
286#67—121no—
287#67—121no—
288#67—121no—
289#67—241no—
290C2×Dic3—41no—
291C2×Dic3—121no—
292C2×Dic3—121no—
293C2×Dic3#21311yescharacteristic
294D12—21no—
295D12—61no—
296D12—61no—
297D12—121no—
298D12—121no—
299D12—121no—
300C4×D3—41no—
301C4×D3—121no—
302C4×D3—121no—
303C4×D3—121no—
304C4×D3—121no—
305C4×D3—121no—
306C4×D3—121no—
307C4×D3—241no—
308C4×D3(C2×D3)⋊C411yescharacteristic
309C4×D3(C2×D3)⋊C411yescharacteristic
310C4×D3#21511yescharacteristic
311C4×D3#21511yescharacteristic
312Dic6—21no—
313Dic6—61no—
314Dic6—61no—
315Dic6—121no—
316Dic6—121no—
317Dic6—121no—
318C3×C8—21no—
319C3×C8—21no—
320C3×C8—31no—
321C3×C8—31no—
322C3×C8C2×C4×D311yescharacteristic
323C3×C8C2×C4×D311yescharacteristic
324C3×C8C2×D1211yescharacteristic
325C3×C8D3×D411yescharacteristic
326C3⋊C8(C2×D3)⋊C411yescharacteristic
327C3⋊C8(C2×D3)⋊C411yescharacteristic
328C2×C32—21no—
329C2×C32C2×#10211yescharacteristic
330C3⋊D3—81no—
331C3×D3—21no—
332C3×D3—21no—
333C3×D3—81no—
334#41—61no—
335#41—181no—
336#41—181no—
337#41—181no—
338#41—361no—
339#41—361no—
340C2×Q8—181no—
341C2×D4—181no—
342C2×D4—361no—
343C22×C4—31no—
344C22×C4—361no—
345Q16—31no—
346Q16—91no—
347Q16—181no—
348SD16—61no—
349SD16—181no—
350SD16—181no—
351SD16—181no—
352D8—31no—
353D8—91no—
354D8—181no—
355C2×C8—31no—
356C2×C8—31no—
357C2×C8—31no—
358C2×C8—31no—
359C2×C8—31no—
360C2×C8C2×D3211yescharacteristic
361C4⋊C4—21no—
362C4⋊C4—61no—
363C22⋊C4—121no—
364C42—121no—
365C16—61no—
366C16—181no—
367C22×C3—21no—
368C22×C3—31no—
369C22×C3—31no—
370C22×C3—121no—
371C22×C3—121no—
372C22×C3D3×D811yescharacteristic
373C22×C3C2×#21311yescharacteristic
374C2×D3—41no—
375C2×D3—41no—
376C2×D3—121no—
377C2×D3—121no—
378C2×D3—241no—
379C2×D3—242no—
380C2×D3—242no—
381C2×D3#80911yescharacteristic
382C2×D3#80911yescharacteristic
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—31no—
386C3×C4—31no—
387C3×C4—81no—
388C3×C4—81no—
389C3×C4—121no—
390C3×C4—161no—
391C3×C4—241no—
392C3×C4D3×C22⋊C411yescharacteristic
393C3×C4D3×SD1611yescharacteristic
394C3×C4C2×(C2×D3)⋊C411yescharacteristic
395C3×C4C2×#21511yescharacteristic
396Dic3—41no—
397Dic3—81no—
398Dic3—121no—
399Dic3—121no—
400Dic3—241no—
401Dic3#80911yescharacteristic
402Dic3#80911yescharacteristic
403C32#214511yescharacteristic, complemented, Sylow
404C23—31no—
405C23—361no—
406Q8—61no—
407Q8—181no—
408Q8—361no—
409D4—61no—
410D4—121no—
411D4—181no—
412D4—361no—
413D4—361no—
414D4—361no—
415D4—361no—
416C2×C4—31no—
417C2×C4—31no—
418C2×C4—31no—
419C2×C4—31no—
420C2×C4—31no—
421C2×C4—41no—
422C2×C4—121no—
423C2×C4—121no—
424C2×C4—361no—
425C2×C4—361no—
426C2×C4—361no—
427C2×C4—361no—
428C2×C4D3×#6711yescharacteristic
429C8—31no—
430C8—31no—
431C8C4×D3211yescharacteristic
432C8D3×D1211yescharacteristic
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—41no—
437C2×C3—61no—
438C2×C3—61no—
439C2×C3—241no—
440C2×C3D3×#10211yescharacteristic
441C2×C3C2×#80911yescharacteristic
442D3—21no—
443D3—21no—
444D3—81no—
445D3—241no—
446D3—241no—
447D3—481no—
448C22—31no—
449C22—31no—
450C22—121no—
451C22—121no—
452C22—361no—
453C22—722no—
454C22D3×#21311yescharacteristic
455C4—31no—
456C4—31no—
457C4—81no—
458C4—121no—
459C4—241no—
460C4—361no—
461C4D3×(C2×D3)⋊C411yescharacteristic
462C4D3×#21511yescharacteristic
463C3—21no—
464C3#6925111yescharacteristic, complemented
465C3#7065611yescharacteristic, complemented
466C2—21no—
467C2—61no—
468C2—61no—
469C2—241no—
470C2—721no—
471C2D3×#80911yescharacteristic
subgroupG/H
centerC2D3×#809
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×#106C22
socleC2×C32C2×#102
prime radicalD3×#904C2
cosocleC2×C32×C8C23
hypercenter#106D32
hypocenterC32#2145
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #106

Complements

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

NH ≅ G/Ntype
2. C3×#4860C2semidirect
3. D3×#812C2semidirect
4. #10589354C2semidirect
5. C3×#4488C2semidirect
6. #10589125C2semidirect
7. #10589123C2semidirect
16. #63808C4semidirect
17. #63807C4semidirect
19. D3×Dic12C4semidirect
20. D3×D24C4semidirect
22. C32×#106C22semidirect
23. #63639C22semidirect
24. C3×#817C22semidirect
25. C3×#812C22semidirect
34. #4860D3semidirect
43. #4488D3semidirect
107. C3×#106C2×D3semidirect
108. C3×#106C2×D3semidirect
109. #817C2×D3semidirect
114. #812C2×D3semidirect
261. #106D32semidirect
403. C32#2145semidirect
464. C3#69251semidirect
465. C3#70656semidirect

Maximal subgroups

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

subgroupindex
D3×#9042
C3×#48602
D3×#8122
#105893542
C3×#44882
#105891252
#105891232
#706563
#692513