Finite Group Databasebeta

← #11796858

Subgroups — #11796858

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
1C3×D3×#135C211yesmaximal, characteristic
2#10590706C211yesmaximal, characteristic, complemented
3D3×#812C211yesmaximal, characteristic, complemented
4#10589432C211yesmaximal, characteristic, complemented
5C3×#4566C211yesmaximal, characteristic, complemented
6#10589124C211yesmaximal, characteristic, complemented
7#10589123C211yesmaximal, characteristic, complemented
8#72076—31nomaximal
9#69251—31nomaximal
10C3×D3×#41—21no—
11C32×#135C2211yescharacteristic
12C3×#950—21no—
13C3×#919C411yescharacteristic, complemented
14C3×D3×Q16C411yescharacteristic, complemented
15C3×#916—21no—
16C3×D3×SD16—21no—
17C3×#912C411yescharacteristic, complemented
18C3×D3×D8C411yescharacteristic, complemented
19C3×#904C2211yescharacteristic
20C2×C3×D3×C8C2211yescharacteristic
21#63841—21no—
22#63644C2211yescharacteristic, complemented
23#63639C2211yescharacteristic, complemented
24C3×#817C2211yescharacteristic, complemented
25C3×#812C2211yescharacteristic, complemented
26#63575—21no—
27#63543—21no—
28D3×C3⋊C16—21no—
29C2×C3×#135—31no—
30D3×#135D311yescharacteristic
31#5106—31no—
32C2×#812—31no—
33D3×M32—31no—
34#4860—31no—
35C3×#360—31no—
36#4566—31no—
37#4566—31no—
38#4566—31no—
39#4566—31no—
40#4566—61no—
41#4566D311yescharacteristic, complemented
42#4518—31no—
43#4488—31no—
44C32×#41—21no—
45C3×#239—21no—
46C3×D3×Q8—21no—
47C3×#237—21no—
48C3×#237—41no—
49C3×D3×D4—21no—
50C3×D3×D4—41no—
51C3×#235—21no—
52C3×#235—41no—
53C2×C3×C4×D3—41no—
54C2×C3×C4×D3D411yescharacteristic
55C32×Q16C2×C411yescharacteristic
56C32×SD16—21no—
57C32×D8C2×C411yescharacteristic
58C2×C32×C8C2311yescharacteristic
59C4⋊(C3⋊Dic3)—21no—
60C3×#216—21no—
61C3×#215—21no—
62C3×#214—21no—
63C3×#213—21no—
64C3×C4⋊Dic3—21no—
65C2×C3×C3⋊C8D411yescharacteristic
66C3×Dic12C2×C411yescharacteristic
67C3×D24C2×C411yescharacteristic
68C3×#204—21no—
69C3×D3×C8C2×C411yescharacteristic
70C3×D3×C8C2×C411yescharacteristic
71C3×D3×C8D411yescharacteristic
72C3×D3×C8D411yescharacteristic
73(C2×D3)⋊Dic3—41no—
74Dic32—41no—
75C3⋊(C3⋊C16)—21no—
76C3×C3⋊C16—21no—
77#2145—91noSylow
78C2×C3×#41—61no—
79D3×#41—21no—
80C3×#135—21no—
81C3×#135—31no—
82C3×#135—31no—
83C3×#135—31no—
84C3×#135—61no—
85C3×#135—61no—
86C3×#135C2×D311yescharacteristic
87C3×#135C2×D311yescharacteristic
88C2×C3×Q16—31no—
89C2×C3×SD16—61no—
90C2×C3×D8—31no—
91C22×C3×C8—31no—
92#950—21no—
93#926—61no—
94#919Dic311yescharacteristic, complemented
95D3×Q16Dic311yescharacteristic, complemented
96#916—21no—
97D3×SD16—21no—
98#912Dic311yescharacteristic, complemented
99D3×D8Dic311yescharacteristic, complemented
100#904C2×D311yescharacteristic
101C2×D3×C8C2×D311yescharacteristic
102#892—61no—
103C3×M32—31no—
104C3×#106—31no—
105#818—61no—
106#817—31no—
107#817—31no—
108#817—61no—
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—61no—
117#798—61no—
118D3×C16—61no—
119C22×C3×D3—41no—
120C22×C3×D3D811yescharacteristic
121C32×Q8—21no—
122C32×D4—21no—
123C32×D4—41no—
124C2×C32×C4—41no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C3⋊Dic3—41no—
127C3×#67—41no—
128C3×#67—41no—
129C3×#67—41no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3D811yescharacteristic
133C3×D12—21no—
134C3×D12—41no—
135C3×C4×D3—41no—
136C3×C4×D3—41no—
137C3×C4×D3—41no—
138C3×C4×D3C22⋊C411yescharacteristic
139C3×C4×D3C22⋊C411yescharacteristic
140C3×C4×D3SD1611yescharacteristic
141C3×C4×D3SD1611yescharacteristic
142C3×Dic6—21no—
143C3×Dic6—41no—
144C32×C8C22×C411yescharacteristic
145C32×C8C2×D411yescharacteristic
146C3×C3⋊C8C22⋊C411yescharacteristic
147C3×C3⋊C8C22⋊C411yescharacteristic
148C2×#135—31no—
149C2×M32—91no—
150#427—91no—
151#360—31no—
152#360—91no—
153#360—91no—
154#360—91no—
155C3×#41—21no—
156C3×#41—21no—
157C3×#41—41no—
158C3×#41—61no—
159C3×#41—61no—
160C3×#41—61no—
161C3×#41—121no—
162C3×#41—121no—
163C2×C3×Q8—61no—
164C2×C3×D4—61no—
165C2×C3×D4—121no—
166C22×C3×C4—31no—
167C22×C3×C4—121no—
168#239—21no—
169D3×Q8—21no—
170#237—21no—
171#237—41no—
172D3×D4—21no—
173D3×D4—41no—
174#235—21no—
175#235—41no—
176C2×C4×D3—41no—
177C2×C4×D3#6711yescharacteristic
178C3×Q16—21no—
179C3×Q16—31no—
180C3×Q16—61no—
181C3×Q16C4×D311yescharacteristic
182C3×Q16C2×Dic311yescharacteristic
183C3×SD16—21no—
184C3×SD16—21no—
185C3×SD16—41no—
186C3×SD16—61no—
187C3×SD16—61no—
188C3×SD16—61no—
189C3×D8—21no—
190C3×D8—31no—
191C3×D8—61no—
192C3×D8C4×D311yescharacteristic
193C3×D8C2×Dic311yescharacteristic
194C2×C3×C8—21no—
195C2×C3×C8—31no—
196C2×C3×C8—31no—
197C2×C3×C8—31no—
198C2×C3×C8—31no—
199C2×C3×C8—31no—
200C2×C3×C8C22×D311yescharacteristic
201C2×C3×C8C22×D311yescharacteristic
202C3×C4⋊C4—61no—
203#217—121no—
204#216—21no—
205#215—21no—
206#214—21no—
207#213—21no—
208(C2×D3)⋊C4—121no—
209C4⋊Dic3—21no—
210C4⋊Dic3—61no—
211C4⋊Dic3—61no—
212C4⋊Dic3—121no—
213C4×Dic3—121no—
214C4×Dic3—121no—
215C2×C3⋊C8#6711yescharacteristic
216Dic12C2×Dic311yescharacteristic
217D24C2×Dic311yescharacteristic
218#204—21no—
219D3×C8C2×Dic311yescharacteristic
220D3×C8C2×Dic311yescharacteristic
221D3×C8#6711yescharacteristic
222D3×C8#6711yescharacteristic
223C3×C16—61no—
224C3⋊C16—21no—
225C3⋊C16—61no—
226C3⋊C16—61no—
227C3⋊C16—121no—
228C22×C32—41no—
229C22×C32C2×D811yescharacteristic
230C2×C3×D3—41no—
231C2×C3×D3—41no—
232C2×C3×D3—82no—
233C2×C3×D3#10211yescharacteristic
234C2×C3×D3#10211yescharacteristic
235C32×C4—41no—
236C32×C4C2×C22⋊C411yescharacteristic
237C32×C4C2×SD1611yescharacteristic
238C3⋊Dic3—81no—
239C3×Dic3—41no—
240C3×Dic3—81no—
241C3×Dic3#10211yescharacteristic
242C3×Dic3#10211yescharacteristic
243C2×#41—61no—
244#135—31no—
245#135—31no—
246#135—31no—
247#135—61no—
248#135—61no—
249#135D3211yescharacteristic
250C2×Q16—31no—
251C2×SD16—61no—
252C2×D8—31no—
253C22×C8—31no—
254#117—181no—
255M32—31no—
256M32—91no—
257M32—181no—
258C2×C16—181no—
259#107—181no—
260#106—31no—
261#106—91no—
262C23×C3—31no—
263C23×C3—121no—
264C22×D3—41no—
265C22×D3#21311yescharacteristic
266C3×Q8—21no—
267C3×Q8—21no—
268C3×Q8—41no—
269C3×Q8—61no—
270C3×Q8—121no—
271C3×D4—21no—
272C3×D4—21no—
273C3×D4—41no—
274C3×D4—41no—
275C3×D4—41no—
276C3×D4—61no—
277C3×D4—81no—
278C3×D4—121no—
279C3×D4—121no—
280C3×D4—121no—
281C3×D4—121no—
282C2×C3×C4—21no—
283C2×C3×C4—31no—
284C2×C3×C4—31no—
285C2×C3×C4—31no—
286C2×C3×C4—31no—
287C2×C3×C4—31no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—81no—
291C2×C3×C4—121no—
292C2×C3×C4—121no—
293C2×C3×C4—121no—
294C2×C3×C4—121no—
295C2×C3×C4—121no—
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4C2×#6711yescharacteristic
298#67—41no—
299#67—41no—
300#67—41no—
301C2×Dic3—41no—
302C2×Dic3—41no—
303C2×Dic3—121no—
304C2×Dic3—121no—
305C2×Dic3—241no—
306C2×Dic3#21311yescharacteristic
307D12—21no—
308D12—41no—
309C4×D3—41no—
310C4×D3—41no—
311C4×D3—41no—
312C4×D3#21411yescharacteristic
313C4×D3#21411yescharacteristic
314C4×D3#21711yescharacteristic
315C4×D3#21711yescharacteristic
316Dic6—21no—
317Dic6—41no—
318C3×C8—21no—
319C3×C8—21no—
320C3×C8—31no—
321C3×C8—31no—
322C3×C8C2×C4×D311yescharacteristic
323C3×C8D3×D411yescharacteristic
324C3×C8C22×Dic311yescharacteristic
325C3×C8C2×#6711yescharacteristic
326C3⋊C8#21711yescharacteristic
327C3⋊C8#21711yescharacteristic
328C2×C32—21no—
329C2×C32—81no—
330C2×C32C2×#10211yescharacteristic
331C3×D3—21no—
332C3×D3—21no—
333C3×D3—81no—
334#41—21no—
335#41—61no—
336#41—61no—
337#41—61no—
338#41—121no—
339#41—121no—
340C2×Q8—61no—
341C2×D4—61no—
342C2×D4—121no—
343C22×C4—31no—
344C22×C4—121no—
345Q16—31no—
346Q16—61no—
347Q16D3×Dic311yescharacteristic
348SD16—21no—
349SD16—61no—
350SD16—61no—
351SD16—61no—
352D8—31no—
353D8—61no—
354D8D3×Dic311yescharacteristic
355C2×C8—31no—
356C2×C8—31no—
357C2×C8—31no—
358C2×C8—31no—
359C2×C8—31no—
360C2×C8C2×D3211yescharacteristic
361C4⋊C4—61no—
362C4⋊C4—181no—
363C22⋊C4—361no—
364C42—361no—
365C16—61no—
366C16—181no—
367C22×C3—21no—
368C22×C3—31no—
369C22×C3—31no—
370C22×C3—41no—
371C22×C3—41no—
372C22×C3—81no—
373C22×C3—121no—
374C22×C3—121no—
375C22×C3—242no—
376C22×C3D3×D811yescharacteristic
377C22×C3C2×#21311yescharacteristic
378C2×D3—41no—
379C2×D3—41no—
380C2×D3—82no—
381C2×D3#83211yescharacteristic
382C2×D3#83211yescharacteristic
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—31no—
386C3×C4—31no—
387C3×C4—41no—
388C3×C4—41no—
389C3×C4—81no—
390C3×C4—121no—
391C3×C4—241no—
392C3×C4D3×C22⋊C411yescharacteristic
393C3×C4D3×SD1611yescharacteristic
394C3×C4C2×#21411yescharacteristic
395C3×C4C2×#21711yescharacteristic
396Dic3—41no—
397Dic3—81no—
398Dic3—241no—
399Dic3—241no—
400Dic3—481no—
401Dic3#83211yescharacteristic
402Dic3#83211yescharacteristic
403C32#214511yescharacteristic, complemented, Sylow
404C23—31no—
405C23—121no—
406Q8—21no—
407Q8—61no—
408Q8—121no—
409D4—21no—
410D4—41no—
411D4—61no—
412D4—121no—
413D4—121no—
414D4—121no—
415D4—121no—
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—121no—
425C2×C4—121no—
426C2×C4—121no—
427C2×C4—361no—
428C2×C4D3×#6711yescharacteristic
429C8—31no—
430C8—31no—
431C8C2×D3×Dic311yescharacteristic
432C8D3×#6711yescharacteristic
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—41no—
437C2×C3—61no—
438C2×C3—61no—
439C2×C3—81no—
440C2×C3—81no—
441C2×C3—161no—
442C2×C3—241no—
443C2×C3D3×#10211yescharacteristic
444C2×C3C2×#83211yescharacteristic
445D3—21no—
446D3—21no—
447D3—81no—
448C22—31no—
449C22—31no—
450C22—41no—
451C22—121no—
452C22—121no—
453C22—242no—
454C22D3×#21311yescharacteristic
455C4—31no—
456C4—31no—
457C4—41no—
458C4—121no—
459C4—241no—
460C4—721no—
461C4D3×#21411yescharacteristic
462C4D3×#21711yescharacteristic
463C3—21no—
464C3#6925111yescharacteristic, complemented
465C3#7207611yescharacteristic, complemented
466C2—21no—
467C2—61no—
468C2—61no—
469C2—81no—
470C2—241no—
471C2D3×#83211yescharacteristic
subgroupG/H
centerC2D3×#832
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×#135C22
socleC2×C32C2×#102
prime radicalC3×D3×#135C2
cosocleC2×C32×C8C23
hypercenter#135D32
hypocenterC32#2145
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
2. #10590706C2semidirect
3. D3×#812C2semidirect
4. #10589432C2semidirect
5. C3×#4566C2semidirect
6. #10589124C2semidirect
7. #10589123C2semidirect
13. C3×#919C4semidirect
14. C3×D3×Q16C4semidirect
17. C3×#912C4semidirect
18. C3×D3×D8C4semidirect
22. #63644C22semidirect
23. #63639C22semidirect
24. C3×#817C22semidirect
25. C3×#812C22semidirect
41. #4566D3semidirect
94. #919Dic3semidirect
95. D3×Q16Dic3semidirect
98. #912Dic3semidirect
99. D3×D8Dic3semidirect
109. #817C2×D3semidirect
114. #812C2×D3semidirect
403. C32#2145semidirect
464. C3#69251semidirect
465. C3#72076semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1352
#105907062
D3×#8122
#105894322
C3×#45662
#105891242
#105891232
#720763
#692513