Finite Group Databasebeta

← #11774664

Subgroups — #11774664

Order 1152.

567 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#239C211yesmaximal, characteristic
2#10590336C211yesmaximal, characteristic, complemented
3C4×#3711C211yesmaximal, characteristic, complemented
4#10589401C211yesmaximal, characteristic, complemented
5C3×#4535C211yesmaximal, characteristic, complemented
6#10589081C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#71641—31nomaximal
9#68238—31nomaximal
10C2×C3×#239C411yescharacteristic
11C32×C4×Q8C2211yescharacteristic
12C3×Q8×Dic3C411yescharacteristic
13C3×#893—21no—
14C3×#893C411yescharacteristic
15C3×#892—21no—
16C3×#892C411yescharacteristic
17C3×C4×D12—21no—
18C3×C4×D12C2211yescharacteristic
19C3×C42×D3—21no—
20C3×C42×D3C2211yescharacteristic
21C2×#3711—21no—
22C2×#3711—21no—
23C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
24C4×C3⋊(C3⋊C8)C2211yescharacteristic
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27Dic3⋊(C3⋊C8)—21no—
28#63554—21no—
29C3×C4×#41—31no—
30C4×#239D311yescharacteristic
31#4924—31no—
32C4×#208—31no—
33#4837—31no—
34C4×ΓL(1,𝔽25)—31no—
35C3×Q8⋊C8—31no—
36#4535—31no—
37#4535—31no—
38#4535—61no—
39#4535D311yescharacteristic, complemented
40D4⋊(C3⋊C8)—31no—
41D4⋊(C3⋊C8)—31no—
42#4483—31no—
43#4459—31no—
44C2×C32×Q8C2×C411yescharacteristic
45C3×#239—22no—
46C3×#239—22no—
47C2×C3×D12—21no—
48C2×C3×D12C2×C411yescharacteristic
49C2×C3×C4×D3—21no—
50C2×C3×C4×D3—21no—
51C2×C3×C4×D3—21no—
52C2×C3×C4×D3C2×C411yescharacteristic
53C2×C3×C4×D3D411yescharacteristic
54C2×C3×C4×D3D411yescharacteristic
55C32×C4⋊C4—21no—
56C32×C4⋊C4C2×C411yescharacteristic
57C32×C42—21no—
58C32×C42C2311yescharacteristic
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3C2×C411yescharacteristic
66C3×C4×Dic3—21no—
67C3×C4×Dic3—21no—
68C3×C4×Dic3C2×C411yescharacteristic
69C3×C4×Dic3D411yescharacteristic
70C3×C4×Dic3D411yescharacteristic
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73#3711—24no—
74#3711—42no—
75#1489—91noSylow
76C2×C3×#41—31no—
77C2×#239Dic311yescharacteristic
78C3×C4×Q8—21no—
79C3×C4×Q8—31no—
80C3×C4×Q8C2×D311yescharacteristic
81C3×C4×Q8C2×D311yescharacteristic
82C3×C4×D4—31no—
83C3×C4×D4—31no—
84C3×C4×D4—61no—
85C3×C4×D4—61no—
86C3×#117—31no—
87C3×#117—61no—
88C2×C3×C42—31no—
89C2×C3×C42—61no—
90Q8×Dic3Dic311yescharacteristic
91C2×#208—61no—
92C2×#208—61no—
93C2×ΓL(1,𝔽25)—61no—
94C2×ΓL(1,𝔽25)—61no—
95#893—21no—
96#893Dic311yescharacteristic
97#892—21no—
98#892Dic311yescharacteristic
99C4×D12—21no—
100C4×D12C2×D311yescharacteristic
101C42×D3—21no—
102C42×D3C2×D311yescharacteristic
103C3×C4⋊C8—31no—
104C3×C4×C8—31no—
105#815—61no—
106Dic3⋊C8—61no—
107C4⋊(C3⋊C8)—31no—
108C4⋊(C3⋊C8)—31no—
109C4⋊(C3⋊C8)—61no—
110C4⋊(C3⋊C8)—61no—
111C4⋊(C3⋊C8)C2×D311yescharacteristic
112#803—61no—
113C4×C3⋊C8—31no—
114C4×C3⋊C8—31no—
115C4×C3⋊C8—61no—
116C4×C3⋊C8C2×D311yescharacteristic
117C22×C3×D3—21no—
118C22×C3×D3C22⋊C411yescharacteristic
119C32×Q8—21no—
120C32×Q8M1612yescomplemented
121C2×C32×C4—21no—
122C2×C32×C4—21no—
123C2×C32×C4C22×C411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C3×Dic3—21no—
127C2×C3×Dic3C22⋊C411yescharacteristic
128C2×C3×Dic3C22⋊C411yescharacteristic
129C2×C3×Dic3C22⋊C411yescharacteristic
130C3×D12—24no—
131C3×D12—21no—
132C3×D12M1612yescomplemented
133C3×C4×D3—24no—
134C3×C4×D3—21no—
135C3×C4×D3—21no—
136C3×C4×D3—21no—
137C3×C4×D3—21no—
138C3×C4×D3—22no—
139C3×C4×D3—41no—
140C3×C4×D3—41no—
141C3×C4×D3—42no—
142C3⋊(C3⋊C8)—22no—
143C3⋊(C3⋊C8)—41no—
144C3×C3⋊C8—22no—
145C3×C3⋊C8—41no—
146C4×#41—31no—
147#423—91no—
148C4×M16—91no—
149Q8⋊C8—31no—
150Q8⋊C8—91no—
151D4⋊C8—91no—
152D4⋊C8—91no—
153C3×#41—62no—
154C3×#41—62no—
155C2×C3×Q8—21no—
156C2×C3×Q8C4×D311yescharacteristic
157C2×C3×Q8C2×Dic311yescharacteristic
158C2×C3×D4—31no—
159C2×C3×D4—61no—
160C22×C3×C4—31no—
161C22×C3×C4—31no—
162C22×C3×C4—31no—
163C22×C3×C4—61no—
164C22×C3×C4—61no—
165C22×C3×C4—61no—
166#239—22no—
167#239—22no—
168C2×D12—21no—
169C2×D12C2×Dic311yescharacteristic
170C2×C4×D3—21no—
171C2×C4×D3—21no—
172C2×C4×D3—21no—
173C2×C4×D3C2×Dic311yescharacteristic
174C2×C4×D3#6711yescharacteristic
175C2×C4×D3#6711yescharacteristic
176C2×C3×C8—61no—
177C2×C3×C8—61no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—31no—
182C3×C4⋊C4—41no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4C4×D311yescharacteristic
185C3×C4⋊C4C2×Dic311yescharacteristic
186C3×C22⋊C4—61no—
187C3×C22⋊C4—61no—
188C3×C22⋊C4—61no—
189C3×C42—21no—
190C3×C42—21no—
191C3×C42—21no—
192C3×C42—31no—
193C3×C42—31no—
194C3×C42—31no—
195C3×C42—41no—
196C3×C42—61no—
197C3×C42—61no—
198C3×C42C22×D311yescharacteristic
199C3×C42C22×D311yescharacteristic
200(C2×D3)⋊C4—21no—
201(C2×D3)⋊C4—21no—
202(C2×D3)⋊C4—21no—
203C4⋊Dic3—21no—
204C4⋊Dic3C2×Dic311yescharacteristic
205C4×Dic3—21no—
206C4×Dic3—21no—
207C4×Dic3C2×Dic311yescharacteristic
208C4×Dic3#6711yescharacteristic
209C4×Dic3#6711yescharacteristic
210#208—64no—
211#208—122no—
212C2×C3⋊C8—21no—
213C2×C3⋊C8—21no—
214C2×C3⋊C8—61no—
215C2×C3⋊C8—61no—
216C2×C3⋊C8—61no—
217C2×C3⋊C8—61no—
218C2×C3⋊C8—121no—
219C2×C3⋊C8—121no—
220ΓL(1,𝔽25)—64no—
221ΓL(1,𝔽25)—122no—
222C22×C32C2×C22⋊C411yescharacteristic
223C2×C3×D3—21no—
224C2×C3×D3—22no—
225C2×C3×D3—21no—
226C2×C3×D3—21no—
227C2×C3×D3—41no—
228C2×C3×D3—41no—
229C32×C4—22no—
230C32×C4—21no—
231C32×C4—41no—
232C32×C4C2×M1611yescharacteristic
233C32×C4C2×M1611yescharacteristic
234C32×C4AGL(1,ℤ/8)11yescharacteristic
235C32×C4#13711yescharacteristic
236C3×Dic3—21no—
237C3×Dic3—21no—
238C3×Dic3—41no—
239C3×Dic3#10412yes—
240C2×#41—31no—
241C2×M16—181no—
242C2×M16—181no—
243C4×Q8—31no—
244C4×Q8D3211yescharacteristic
245C4×D4—31no—
246C4×D4—31no—
247C4×D4—61no—
248C4×D4—61no—
249#117—31no—
250#117—61no—
251C2×C42—31no—
252C2×C42—61no—
253C4⋊C8—31no—
254C4⋊C8—91no—
255C4⋊C8—181no—
256#97—181no—
257C4×C8—31no—
258C4×C8—91no—
259C23×C3—31no—
260C23×C3—61no—
261C22×D3—21no—
262C22×D3#21711yescharacteristic
263C3×Q8—21no—
264C3×Q8—21no—
265C3×Q8—22no—
266C3×Q8—41no—
267C3×Q8ΓL(1,𝔽25)12yescomplemented
268C3×Q8#20812yescomplemented
269C3×D4—32no—
270C3×D4—64no—
271C3×D4—61no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—31no—
280C2×C3×C4—31no—
281C2×C3×C4—31no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—62no—
285C2×C3×C4—64no—
286C2×C3×C4—61no—
287C2×C3×C4—61no—
288C2×C3×C4—61no—
289C2×C3×C4—61no—
290C2×C3×C4—61no—
291C2×C3×C4—122no—
292C2×C3×C4—121no—
293C2×C3×C4—121no—
294C2×C3×C4C2×C4×D311yescharacteristic
295C2×C3×C4D3×D411yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4C22×Dic311yescharacteristic
298C2×C3×C4C2×#6711yescharacteristic
299C2×C3×C4C2×#6711yescharacteristic
300C2×Dic3—21no—
301C2×Dic3#21711yescharacteristic
302C2×Dic3#21711yescharacteristic
303C2×Dic3#21711yescharacteristic
304D12—24no—
305D12—21no—
306D12#20812yescomplemented
307C4×D3—24no—
308C4×D3—21no—
309C4×D3—21no—
310C4×D3—21no—
311C4×D3—21no—
312C4×D3—22no—
313C4×D3—41no—
314C4×D3—41no—
315C4×D3—42no—
316C3×C8—62no—
317C3×C8—121no—
318C3⋊C8—22no—
319C3⋊C8—41no—
320C3⋊C8—62no—
321C3⋊C8—62no—
322C3⋊C8—122no—
323C3⋊C8—121no—
324C3⋊C8—121no—
325C3⋊C8—241no—
326C2×C32#40711yescharacteristic
327C2×C32#41711yescharacteristic
328C2×C32C2×#10411yescharacteristic
329C3×D3—41no—
330C3×D3—42no—
331#41—62no—
332#41—62no—
333C2×Q8D3×Dic311yescharacteristic
334C2×D4—31no—
335C2×D4—61no—
336C22×C4—31no—
337C22×C4—31no—
338C22×C4—31no—
339C22×C4—61no—
340C22×C4—61no—
341C22×C4—61no—
342M16—184no—
343M16—362no—
344C2×C8—61no—
345C2×C8—61no—
346C2×C8—181no—
347C2×C8—181no—
348C4⋊C4—21no—
349C4⋊C4—31no—
350C4⋊C4—61no—
351C4⋊C4D3×Dic311yescharacteristic
352C22⋊C4—61no—
353C22⋊C4—61no—
354C22⋊C4—61no—
355C42—21no—
356C42—31no—
357C42—31no—
358C42—31no—
359C42—61no—
360C42—61no—
361C42C2×D3211yescharacteristic
362C22×C3—21no—
363C22×C3—62no—
364C22×C3—61no—
365C22×C3—61no—
366C22×C3—61no—
367C22×C3—121no—
368C22×C3—121no—
369C22×C3D3×C22⋊C411yescharacteristic
370C22×C3C2×#21711yescharacteristic
371C2×D3—21no—
372C2×D3—22no—
373C2×D3—21no—
374C2×D3—21no—
375C2×D3—41no—
376C2×D3—41no—
377C3×C4—22no—
378C3×C4—21no—
379C3×C4—22no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—32no—
386C3×C4—41no—
387C3×C4—42no—
388C3×C4—41no—
389C3×C4—41no—
390C3×C4—61no—
391C3×C4—61no—
392C3×C4—81no—
393C3×C4—121no—
394C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
395C3×C4D3×M1611yescharacteristic
396C3×C4#91411yescharacteristic
397C3×C4#91811yescharacteristic
398C3×C4C2×#20811yescharacteristic
399C3×C4C2×#20811yescharacteristic
400C3×C4#94911yescharacteristic
401C3×C4#95111yescharacteristic
402Dic3—21no—
403Dic3—21no—
404Dic3—41no—
405Dic3#83712yes—
406C32#148911yescharacteristic, complemented, Sylow
407C23—31no—
408C23—61no—
409Q8—21no—
410Q8#371112yescomplemented
411D4—32no—
412D4—64no—
413D4—61no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—31no—
417C2×C4—31no—
418C2×C4—31no—
419C2×C4—62no—
420C2×C4—64no—
421C2×C4—61no—
422C2×C4—61no—
423C2×C4—61no—
424C2×C4—61no—
425C2×C4—61no—
426C2×C4—122no—
427C2×C4—121no—
428C2×C4—121no—
429C2×C4C2×D3×Dic311yescharacteristic
430C2×C4D3×#6711yescharacteristic
431C2×C4D3×#6711yescharacteristic
432C8—62no—
433C8—121no—
434C8—182no—
435C8—361no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—121no—
440C2×C3—122no—
441C2×C3#472611yescharacteristic
442C2×C3#480311yescharacteristic
443C2×C3D3×#10411yescharacteristic
444C2×C3#520711yescharacteristic
445C2×C3#523211yescharacteristic
446C2×C3C2×#83711yescharacteristic
447D3—41no—
448D3—42no—
449C22—61no—
450C22—62no—
451C22—61no—
452C22—61no—
453C22—121no—
454C22—121no—
455C22D3×#21711yescharacteristic
456C4—22no—
457C4—21no—
458C4—32no—
459C4—41no—
460C4—61no—
461C4—61no—
462C4—121no—
463C4D3×#20811yescharacteristic
464C4C2×#371111yescharacteristic
465C4#6393911yescharacteristic
466C4#6394311yescharacteristic
467C3—21no—
468C3#6823811yescharacteristic, complemented
469C3#7164111yescharacteristic, complemented
470C2—121no—
471C2—122no—
472C2#1059115411yescharacteristic
473C2#1059155011yescharacteristic
474C2D3×#83711yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#239C4
cosocleC32×C42C23
hypercenterC4×Q8D32
hypocenterC32#1489
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. #10590336C2semidirect
3. C4×#3711C2semidirect
4. #10589401C2semidirect
5. C3×#4535C2semidirect
6. #10589081C2semidirect
7. #10589080C2semidirect
39. #4535D3semidirect
120. C32×Q8M16semidirect
132. C3×D12M16semidirect
267. C3×Q8ΓL(1,𝔽25)semidirect
268. C3×Q8#208semidirect
306. D12#208semidirect
406. C32#1489semidirect
410. Q8#3711semidirect
468. C3#68238semidirect
469. C3#71641semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2392
#105903362
C4×#37112
#105894012
C3×#45352
#105890812
#105890802
#716413
#682383