Finite Group Databasebeta

← #11774057

Subgroups — #11774057

Order 1152.

447 conjugacy classes of subgroups.

The subgroup lattice has 437 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63867C211yesmaximal, characteristic
2C3×#4718C211yesmaximal, characteristic
3#10591063C211yesmaximal, characteristic
4#10589335C211yesmaximal, characteristic
5C3×#4469C211yesmaximal, characteristic
6#10589148C211yesmaximal, characteristic
7#10589147C211yesmaximal, characteristic
8#70787—31nomaximal
9#68128—31nomaximal
10C2×#3750C2211yescharacteristic
11C2×C3×Dic3⋊C4C2211yescharacteristic
12C2×C3×C4×Dic3C2211yescharacteristic
13C2×#3724C411yescharacteristic
14C2×Dic3⋊Dic3C411yescharacteristic
15C2×Dic3⋊Dic3C411yescharacteristic
16C2×Dic3⋊Dic3C411yescharacteristic
17#63867—21no—
18#63867—21no—
19#63867—21no—
20#63867—21no—
21C32×C22⋊C8C2211yescharacteristic
22#63657C2211yescharacteristic
23C3×#830C2211yescharacteristic
24C3×#830C2211yescharacteristic
25C3×Dic3⋊C8—21no—
26C3×C8×Dic3—21no—
27Dic3⋊(C3⋊C8)—21no—
28#63554—21no—
29C2×#889—31no—
30C2×#870—31no—
31C3×#431—31no—
32#4926—31no—
33#4719—31no—
34#4718D311yescharacteristic
35C3×#324—31no—
36#4528—31no—
37#4469—31no—
38#4469—31no—
39#4469—31no—
40#4469—31no—
41#4469—31no—
42#4469—61no—
43#4469D311yescharacteristic
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3C2×C411yescharacteristic
46C22×C3⋊Dic3C2×C411yescharacteristic
47C22×C3×Dic3C2×C411yescharacteristic
48C22×C3×Dic3C2×C411yescharacteristic
49C22×C3×Dic3C2×C411yescharacteristic
50C22×C3×Dic3C2×C411yescharacteristic
51C2×C32×C8—21no—
52#3750—21no—
53#3750—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C3×Dic3⋊C4—21no—
56C3×Dic3⋊C4—21no—
57C3×C4×Dic3D411yescharacteristic
58C3×C4×Dic3D411yescharacteristic
59C3×C4×Dic3D411yescharacteristic
60C3×C4×Dic3D411yescharacteristic
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63#3724—21no—
64#3724—21no—
65Dic3⋊Dic3—21no—
66Dic3⋊Dic3—21no—
67Dic3⋊Dic3—21no—
68Dic3⋊Dic3—21no—
69Dic3⋊Dic3—21no—
70Dic3⋊Dic3—21no—
71#1470—91noSylow
72C2×C3×C4⋊C4—31no—
73C2×C3×C42—31no—
74C2×C4⋊Dic3—31no—
75C2×C4⋊Dic3—31no—
76C2×C4⋊Dic3—31no—
77C2×Dic3⋊C4—31no—
78C2×Dic3⋊C4—31no—
79C2×Dic3⋊C4—31no—
80C2×Dic3⋊C4—31no—
81C2×Dic3⋊C4—31no—
82C2×Dic3⋊C4—31no—
83C2×Dic3⋊C4—31no—
84C2×Dic3⋊C4—61no—
85C2×Dic3⋊C4C2×D311yescharacteristic
86C2×C4×Dic3C2×D311yescharacteristic
87#889—61no—
88#889—61no—
89#889—61no—
90#889—61no—
91#870—61no—
92#870—61no—
93#870—61no—
94#870—61no—
95C3×C4⋊C8—61no—
96C3×C22⋊C8—21no—
97C3×C22⋊C8—31no—
98C3×C22⋊C8—31no—
99C3×C22⋊C8C2×D311yescharacteristic
100C3×C22⋊C8C2×D311yescharacteristic
101C3×C4×C8—61no—
102#830—31no—
103#830—31no—
104#830—61no—
105#830C2×D311yescharacteristic
106#830C2×D311yescharacteristic
107#815—61no—
108Dic3⋊C8—21no—
109Dic3⋊C8—61no—
110C8×Dic3—21no—
111C4⋊(C3⋊C8)—61no—
112#803—61no—
113C23×C32C22×C411yescharacteristic
114C2×C32×C4—41no—
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C3⋊Dic3—21no—
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—41no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—41no—
130C2×C3×Dic3C22⋊C411yescharacteristic
131C2×C3×Dic3C22⋊C411yescharacteristic
132C2×C3×Dic3C22⋊C411yescharacteristic
133C2×C3×Dic3C22⋊C411yescharacteristic
134C32×C8—41no—
135C3⋊(C3⋊C8)—41no—
136C3×C3⋊C8—41no—
137C3×C3⋊C8—41no—
138C2×#125—91no—
139#432—91no—
140#431—31no—
141#324—31no—
142#324—91no—
143#324—91no—
144#324—91no—
145C22×C3×C4—21no—
146C22×C3×C4—31no—
147C22×C3×C4—31no—
148C22×C3×C4—31no—
149C22×C3×C4—31no—
150C22×C3×C4C22×D311yescharacteristic
151C22×C3×C4C22×D311yescharacteristic
152C22×Dic3—31no—
153C22×Dic3—31no—
154C22×Dic3—31no—
155C22×Dic3—31no—
156C22×Dic3—61no—
157C22×Dic3—61no—
158C22×Dic3C4×D311yescharacteristic
159C22×Dic3C4×D311yescharacteristic
160C22×Dic3C4×D311yescharacteristic
161C22×Dic3C4×D311yescharacteristic
162C2×C3×C8—21no—
163C2×C3×C8—21no—
164C2×C3×C8—41no—
165C2×C3×C8—61no—
166C2×C3×C8—61no—
167C3×C4⋊C4—61no—
168C3×C4⋊C4—61no—
169C3×C42—31no—
170C3×C42—31no—
171C3×C42—31no—
172C3×C42—31no—
173C4⋊Dic3—61no—
174C4⋊Dic3—61no—
175C4⋊Dic3—61no—
176C4⋊Dic3—61no—
177C4⋊Dic3—61no—
178C4⋊Dic3—61no—
179Dic3⋊C4—21no—
180Dic3⋊C4—21no—
181Dic3⋊C4—61no—
182Dic3⋊C4—61no—
183Dic3⋊C4—61no—
184Dic3⋊C4—61no—
185Dic3⋊C4—61no—
186Dic3⋊C4—61no—
187Dic3⋊C4—61no—
188Dic3⋊C4—61no—
189Dic3⋊C4—61no—
190Dic3⋊C4—61no—
191Dic3⋊C4—61no—
192Dic3⋊C4—61no—
193Dic3⋊C4—61no—
194Dic3⋊C4—61no—
195Dic3⋊C4—121no—
196Dic3⋊C4—121no—
197C4×Dic3D1211yescharacteristic
198C4×Dic3D1211yescharacteristic
199C4×Dic3#6711yescharacteristic
200C4×Dic3#6711yescharacteristic
201C2×C3⋊C8—21no—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—61no—
205C2×C3⋊C8—121no—
206C22×C32—21no—
207C22×C32—21no—
208C22×C32C2×C22⋊C411yescharacteristic
209C22×C32#13111yescharacteristic
210C22×C32#13111yescharacteristic
211C32×C4—21no—
212C32×C4—21no—
213C3⋊Dic3—41no—
214C3⋊Dic3—41no—
215C3×Dic3—21no—
216C3×Dic3—21no—
217C3×Dic3—21no—
218C3×Dic3—41no—
219C3×Dic3—41no—
220C3×Dic3#10112yes—
221#125—181no—
222#125—181no—
223#125—181no—
224#125—181no—
225C2×C4⋊C4—31no—
226C2×C4⋊C4—91no—
227C2×C4⋊C4—91no—
228C2×C4⋊C4—91no—
229C2×C4⋊C4—91no—
230C2×C4⋊C4—91no—
231C2×C42—31no—
232C4⋊C8—61no—
233C4⋊C8—181no—
234C22⋊C8—31no—
235C22⋊C8—31no—
236C22⋊C8—91no—
237C22⋊C8D3211yescharacteristic
238#97—181no—
239C4×C8—61no—
240C23×C3—21no—
241C23×C3C2×C4×D311yescharacteristic
242C23×C3C2×C4×D311yescharacteristic
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—31no—
246C2×C3×C4—31no—
247C2×C3×C4—31no—
248C2×C3×C4—31no—
249C2×C3×C4—41no—
250C2×C3×C4—41no—
251C2×C3×C4—62no—
252C2×C3×C4—61no—
253C2×C3×C4—61no—
254C2×C3×C4—61no—
255C2×C3×C4—61no—
256C2×C3×C4—61no—
257C2×C3×C4—61no—
258C2×C3×C4—81no—
259C2×C3×C4—121no—
260C2×C3×C4C2×D1211yescharacteristic
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4D3×D411yescharacteristic
263C2×C3×C4C2×#6711yescharacteristic
264C2×Dic3—21no—
265C2×Dic3—21no—
266C2×Dic3—22no—
267C2×Dic3—21no—
268C2×Dic3—21no—
269C2×Dic3—21no—
270C2×Dic3—21no—
271C2×Dic3—41no—
272C2×Dic3—62no—
273C2×Dic3—61no—
274C2×Dic3—61no—
275C2×Dic3—61no—
276C2×Dic3—61no—
277C2×Dic3—61no—
278C2×Dic3—61no—
279C2×Dic3—61no—
280C2×Dic3—61no—
281C2×Dic3—121no—
282C2×Dic3—121no—
283C2×Dic3—121no—
284C2×Dic3—121no—
285C2×Dic3—121no—
286C2×Dic3—241no—
287C2×Dic3(C2×D3)⋊C411yescharacteristic
288C2×Dic3(C2×D3)⋊C411yescharacteristic
289C2×Dic3(C2×D3)⋊C411yescharacteristic
290C2×Dic3(C2×D3)⋊C411yescharacteristic
291C3×C8—41no—
292C3×C8—41no—
293C3×C8—81no—
294C3×C8—121no—
295C3×C8—121no—
296C3⋊C8—41no—
297C3⋊C8—41no—
298C3⋊C8—121no—
299C3⋊C8—121no—
300C3⋊C8—241no—
301C2×C32—21no—
302C2×C32—21no—
303C2×C32#40811yescharacteristic
304C2×C32#41011yescharacteristic
305C2×C32C2×#10111yescharacteristic
306C22×C4—31no—
307C22×C4—31no—
308C22×C4—31no—
309C22×C4—31no—
310C22×C4—91no—
311C22×C4—91no—
312C22×C4C2×D3211yescharacteristic
313C2×C8—21no—
314C2×C8—61no—
315C2×C8—61no—
316C2×C8—181no—
317C4⋊C4—61no—
318C4⋊C4—61no—
319C4⋊C4—181no—
320C4⋊C4—181no—
321C4⋊C4—181no—
322C4⋊C4—181no—
323C4⋊C4—181no—
324C4⋊C4—181no—
325C4⋊C4—181no—
326C4⋊C4—181no—
327C4⋊C4—181no—
328C4⋊C4—181no—
329C42—31no—
330C42—31no—
331C42—31no—
332C42—31no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—41no—
341C22×C3—41no—
342C22×C3D3×C22⋊C411yescharacteristic
343C22×C3#90111yescharacteristic
344C22×C3#90111yescharacteristic
345C22×C3#90111yescharacteristic
346C22×C3#90711yescharacteristic
347C22×C3C2×(C2×D3)⋊C411yescharacteristic
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—32no—
353C3×C4—41no—
354C3×C4—41no—
355C3×C4—61no—
356C3×C4—61no—
357C3×C4—61no—
358C3×C4—121no—
359C3×C4—121no—
360Dic3—21no—
361Dic3—21no—
362Dic3—21no—
363Dic3—41no—
364Dic3—41no—
365Dic3—122no—
366Dic3—121no—
367Dic3—121no—
368Dic3—121no—
369Dic3—121no—
370Dic3—241no—
371Dic3#82412yes—
372C32#147011yescharacteristic, complemented, Sylow
373C23C4×D3211yescharacteristic
374C2×C4—31no—
375C2×C4—31no—
376C2×C4—31no—
377C2×C4—31no—
378C2×C4—41no—
379C2×C4—62no—
380C2×C4—61no—
381C2×C4—61no—
382C2×C4—61no—
383C2×C4—61no—
384C2×C4—61no—
385C2×C4—61no—
386C2×C4—121no—
387C2×C4—181no—
388C2×C4—181no—
389C2×C4—181no—
390C2×C4—181no—
391C2×C4—361no—
392C2×C4D3×D1211yescharacteristic
393C2×C4D3×#6711yescharacteristic
394C8—41no—
395C8—121no—
396C8—121no—
397C8—361no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—41no—
406C2×C3—41no—
407C2×C3#472711yescharacteristic
408C2×C3#474011yescharacteristic
409C2×C3D3×#10111yescharacteristic
410C2×C3#500611yescharacteristic
411C2×C3#511011yescharacteristic
412C2×C3C2×#82411yescharacteristic
413C22—21no—
414C22—21no—
415C22#6380311yescharacteristic
416C22#6380411yescharacteristic
417C22D3×(C2×D3)⋊C411yescharacteristic
418C4—21no—
419C4—21no—
420C4—32no—
421C4—61no—
422C4—61no—
423C4—61no—
424C4—121no—
425C4—121no—
426C4—361no—
427C4—361no—
428C3—21no—
429C3#6812811yescharacteristic, complemented
430C3#7078711yescharacteristic, complemented
431C2—21no—
432C2—21no—
433C2#1059040511yescharacteristic
434C2#1059095311yescharacteristic
435C2D3×#82411yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutator, prime radicalC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1470
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
372. C32#1470semidirect
429. C3#68128semidirect
430. C3#70787semidirect

Maximal subgroups

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

subgroupindex
C2×#638672
C3×#47182
#105910632
#105893352
C3×#44692
#105891482
#105891472
#707873
#681283