Finite Group Databasebeta

← #11805073

Subgroups — #11805073

Order 1152.

862 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#117C211yesmaximal, characteristic
2#10593811C211yesmaximal, characteristic
3C2×#63781C211yesmaximal, characteristic
4#10593758C212yesmaximal, complemented
5#10593758C212yesmaximal, complemented
6#10593746C212yesmaximal
7C22⋊C4×#157C212yesmaximal
8#10593737C211yesmaximal, characteristic, complemented
9#10593736C211yesmaximal, characteristic, complemented
10C4×C4⋊#157C211yesmaximal, characteristic, complemented
11#10593733C211yesmaximal, characteristic, complemented
12C23×#157C2212yes—
13C22×C4×C3⋊D3C2211yescharacteristic
14C2×C22⋊#157C2212yes—
15C2×C4⋊#157C2212yes—
16C2×C4⋊#157C2212yes—
17C2×C4×#157C2212yes—
18C2×C4×#157C2212yes—
19C32×#117C411yescharacteristic, complemented
20#64135C411yescharacteristic, complemented
21#64101C411yescharacteristic, complemented
22#64101C411yescharacteristic, complemented
23C4⋊C4×C3⋊D3C2211yescharacteristic
24C4⋊C4×C3⋊D3C2211yescharacteristic
25C22⋊C4×C3⋊D3C2211yescharacteristic
26C22⋊C4×C3⋊D3C2211yescharacteristic
27#64086C411yescharacteristic, complemented
28#64086C411yescharacteristic, complemented
29#64081C411yescharacteristic, complemented
30#64081C411yescharacteristic, complemented
31C42×C3⋊D3C2211yescharacteristic
32C42×C3⋊D3C2211yescharacteristic
33#63781C2211yescharacteristic
34#63781C2211yescharacteristic
35#63781C2212yes—
36#63781C2211yescharacteristic
37#63781C2211yescharacteristic
38#63781C2212yes—
39#63781C2212yes—
40#63781C2212yes—
41#63781C2212yes—
42#63781C2212yes—
43D3×#117—62no—
44C23×C3⋊D3C2311yescharacteristic
45C22×#157—24no—
46C22×#157—24no—
47C22×#157—42no—
48C22×#157C2312yes—
49C22×#157C2312yes—
50C22×#157C2312yes—
51C22×#157C2312yes—
52C22×C32×C4C2×C411yescharacteristic
53C22×C3⋊Dic3C2×C411yescharacteristic
54C2×C4×C3⋊D3—24no—
55C2×C4×C3⋊D3C2×C411yescharacteristic
56C2×C4×C3⋊D3C2×C411yescharacteristic
57C2×C4×C3⋊D3C2311yescharacteristic
58C2×C4×C3⋊D3C2311yescharacteristic
59C2×C4×C3⋊D3C2311yescharacteristic
60C2×C4×C3⋊D3C2311yescharacteristic
61C2×C4×C3⋊D3C2311yescharacteristic
62C2×C4×C3⋊D3C2311yescharacteristic
63C22⋊#157—24no—
64C4⋊#157—24no—
65C4⋊#157—42no—
66C4×#157—24no—
67C4×#157—42no—
68C32×C4⋊C4C2×C411yescharacteristic, complemented
69C32×C4⋊C4C2×C411yescharacteristic, complemented
70C32×C22⋊C4C2×C411yescharacteristic
71C32×C22⋊C4C2×C411yescharacteristic
72C32×C42C2×C411yescharacteristic, complemented
73C32×C42C2×C411yescharacteristic, complemented
74#3757C2×C411yescharacteristic
75#3757C2×C411yescharacteristic
76#3752C2×C411yescharacteristic
77#3752C2×C411yescharacteristic
78#3752C2×C411yescharacteristic
79#3752C2×C411yescharacteristic
80C4⋊(C3⋊Dic3)C2×C411yescharacteristic, complemented
81C4⋊(C3⋊Dic3)C2×C411yescharacteristic, complemented
82#3750C2×C411yescharacteristic, complemented
83#3750C2×C411yescharacteristic, complemented
84#3750C2×C411yescharacteristic, complemented
85#3750C2×C411yescharacteristic, complemented
86C4×C3⋊Dic3C2×C411yescharacteristic, complemented
87C4×C3⋊Dic3C2×C411yescharacteristic, complemented
88C4×C3⋊Dic3C2×C411yescharacteristic, complemented
89C4×C3⋊Dic3C2×C411yescharacteristic, complemented
90C4×C3⋊Dic3C2×C411yescharacteristic, complemented
91C4×C3⋊Dic3C2×C411yescharacteristic, complemented
92#2343—91nomaximal, Sylow
93C22×C4×D3—62no—
94C3×#117—22no—
95#926—62no—
96#892—62no—
97#892—62no—
98D3×C4⋊C4—62no—
99D3×C4⋊C4—62no—
100D3×C22⋊C4—62no—
101D3×C22⋊C4—62no—
102#877—62no—
103#877—62no—
104#872—62no—
105#872—62no—
106C42×D3—62no—
107C42×D3—62no—
108C23×C32C22×C411yescharacteristic
109C22×C3⋊D3—22no—
110C22×C3⋊D3—21no—
111C22×C3⋊D3—21no—
112C22×C3⋊D3C22×C411yescharacteristic
113C22×C3⋊D3#4114yes—
114C22×C3⋊D3C2411yescharacteristic
115C2×#157—22no—
116C2×#157—22no—
117C2×#157—22no—
118C2×#157—22no—
119C2×#157—22no—
120C2×#157—22no—
121C2×#157—22no—
122C2×#157—22no—
123C2×#157—22no—
124C2×#157—22no—
125C2×#157—22no—
126C2×#157—48no—
127C2×#157#4114yes—
128C2×C32×C4—22no—
129C2×C32×C4C22×C411yescharacteristic
130C2×C32×C4C22×C411yescharacteristic
131C2×C32×C4C22×C411yescharacteristic
132C2×C32×C4C22×C411yescharacteristic
133C2×C32×C4C22×C411yescharacteristic
134C2×C32×C4C22×C411yescharacteristic
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3C22×C411yescharacteristic
137C2×C3⋊Dic3C22×C411yescharacteristic
138C2×C3⋊Dic3C22×C411yescharacteristic
139C2×C3⋊Dic3C22×C411yescharacteristic
140C2×C3⋊Dic3C22×C411yescharacteristic
141C2×C3⋊Dic3C22×C411yescharacteristic
142C4×C3⋊D3—22no—
143C4×C3⋊D3—22no—
144C4×C3⋊D3—22no—
145C4×C3⋊D3—22no—
146C4×C3⋊D3—22no—
147C4×C3⋊D3—22no—
148C4×C3⋊D3—21no—
149C4×C3⋊D3—21no—
150C4×C3⋊D3—21no—
151C4×C3⋊D3—21no—
152C2×#117—91no—
153#387—92no—
154#387—92no—
155#385—92no—
156#383—91no—
157#382—91no—
158#381—91no—
159C4×C4⋊C4—91no—
160C4×C22⋊C4—92no—
161#376—91no—
162C2×#95—91no—
163C23×D3—62no—
164C22×C3×C4—22no—
165C22×Dic3—62no—
166C2×C4×D3—62no—
167C2×C4×D3—62no—
168C2×C4×D3—62no—
169C2×C4×D3—62no—
170C2×C4×D3—62no—
171C2×C4×D3—62no—
172C2×C4×D3—62no—
173C2×C4×D3—62no—
174C2×C4×D3—616no—
175C3×C4⋊C4—22no—
176C3×C4⋊C4—22no—
177C3×C22⋊C4—22no—
178C3×C22⋊C4—22no—
179C3×C42—22no—
180C3×C42—22no—
181#217—62no—
182#217—62no—
183(C2×D3)⋊C4—62no—
184(C2×D3)⋊C4—62no—
185(C2×D3)⋊C4—62no—
186(C2×D3)⋊C4—62no—
187C4⋊Dic3—62no—
188C4⋊Dic3—62no—
189Dic3⋊C4—62no—
190Dic3⋊C4—62no—
191Dic3⋊C4—62no—
192Dic3⋊C4—62no—
193C4×Dic3—62no—
194C4×Dic3—62no—
195C4×Dic3—62no—
196C4×Dic3—62no—
197C4×Dic3—62no—
198C4×Dic3—62no—
199C22×C32—21no—
200C22×C32—21no—
201C22×C32#11712yes—
202C22×C32C23×C411yescharacteristic
203C2×C3⋊D3—21no—
204C2×C3⋊D3—21no—
205C2×C3⋊D3—24no—
206C2×C3⋊D3—24no—
207C2×C3⋊D3#11712yes—
208C2×C3⋊D3C2×#4112yes—
209C2×C3⋊D3C2×#4112yes—
210C2×C3⋊D3H(5,𝔽2)11yescharacteristic
211C2×C3⋊D32−1+411yescharacteristic
212#157—24no—
213#157—42no—
214#157—42no—
215#157—42no—
216C32×C4—21no—
217C32×C4—21no—
218C32×C4—21no—
219C32×C4—21no—
220C32×C4—21no—
221C32×C4—21no—
222C3⋊Dic3—21no—
223C3⋊Dic3—21no—
224C3⋊Dic3—21no—
225C3⋊Dic3—21no—
226C3⋊Dic3—21no—
227C3⋊Dic3—21no—
228C23×C4—91no—
229C23×C4—92no—
230#117—91no—
231#117—91no—
232#117—91no—
233#117—91no—
234#117—91no—
235#117—91no—
236#117—91no—
237#117#15711yescharacteristic, complemented
238C2×C4⋊C4—91no—
239C2×C4⋊C4—91no—
240C2×C4⋊C4—92no—
241C2×C4⋊C4—92no—
242C2×C22⋊C4—91no—
243C2×C22⋊C4—91no—
244C2×C22⋊C4—92no—
245C2×C42—91no—
246C2×C42—91no—
247C2×C42—92no—
248C2×C42—92no—
249#95—91no—
250#95—91no—
251#95—92no—
252#95—91no—
253#95—92no—
254#95—92no—
255#95—92no—
256#95—91no—
257#95—92no—
258#95—92no—
259C23×C3—22no—
260C22×D3—62no—
261C22×D3—62no—
262C22×D3—68no—
263C22×D3—124no—
264C22×D3—122no—
265C22×D3—122no—
266C2×C3×C4—28no—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—22no—
272C2×C3×C4—22no—
273C2×Dic3—62no—
274C2×Dic3—62no—
275C2×Dic3—62no—
276C2×Dic3—62no—
277C2×Dic3—62no—
278C2×Dic3—62no—
279C2×Dic3—68no—
280C4×D3—68no—
281C4×D3—68no—
282C4×D3—68no—
283C4×D3—68no—
284C4×D3—124no—
285C4×D3—122no—
286C4×D3—124no—
287C4×D3—122no—
288C4×D3—122no—
289C4×D3—122no—
290C2×C32—22no—
291C2×C32C2×#11711yescharacteristic
292C2×C32C4×#4111yescharacteristic
293C2×C32#52011yescharacteristic
294C3⋊D3—22no—
295C3⋊D3#55112yes—
296C3⋊D3#55212yes—
297C24—91no—
298C22×C4—92no—
299C22×C4—91no—
300C22×C4—91no—
301C22×C4—91no—
302C22×C4—91no—
303C22×C4—91no—
304C22×C4—91no—
305C22×C4—91no—
306C22×C4—91no—
307C22×C4—91no—
308C22×C4—92no—
309C22×C4—92no—
310C22×C4—92no—
311C22×C4—184no—
312C22×C4—184no—
313C22×C4—184no—
314C22×C4—362no—
315C22×C4C2×#15711yescharacteristic
316C4⋊C4—91no—
317C4⋊C4—91no—
318C4⋊C4—91no—
319C4⋊C4—91no—
320C4⋊C4—91no—
321C4⋊C4—91no—
322C4⋊C4—184no—
323C4⋊C4—362no—
324C4⋊C4C2×#15711yescharacteristic, complemented
325C4⋊C4C2×#15711yescharacteristic, complemented
326C22⋊C4—91no—
327C22⋊C4—91no—
328C22⋊C4—91no—
329C22⋊C4—91no—
330C22⋊C4—91no—
331C22⋊C4—91no—
332C22⋊C4—184no—
333C22⋊C4C2×#15711yescharacteristic
334C22⋊C4C2×#15711yescharacteristic
335C42—91no—
336C42—91no—
337C42—91no—
338C42—91no—
339C42—91no—
340C42—91no—
341C42—184no—
342C42—362no—
343C42C2×#15711yescharacteristic, complemented
344C42C2×#15711yescharacteristic, complemented
345C22×C3—24no—
346C22×C3—22no—
347C22×C3—42no—
348C22×C3—42no—
349C2×D3—64no—
350C2×D3—64no—
351C2×D3—62no—
352C2×D3—62no—
353C2×D3—64no—
354C2×D3—128no—
355C2×D3—128no—
356C2×D3—122no—
357C2×D3—122no—
358C3×C4—24no—
359C3×C4—24no—
360C3×C4—42no—
361C3×C4—42no—
362C3×C4—42no—
363C3×C4—42no—
364Dic3—64no—
365Dic3—64no—
366Dic3—122no—
367Dic3—122no—
368Dic3—122no—
369Dic3—122no—
370C32#234311yescharacteristic, complemented, Sylow
371C23—91no—
372C23—94no—
373C23—91no—
374C23—182no—
375C23—181no—
376C23—181no—
377C23C22×#15711yescharacteristic
378C2×C4—22no—
379C2×C4—94no—
380C2×C4—91no—
381C2×C4—91no—
382C2×C4—91no—
383C2×C4—91no—
384C2×C4—91no—
385C2×C4—91no—
386C2×C4—182no—
387C2×C4—181no—
388C2×C4—182no—
389C2×C4—181no—
390C2×C4—182no—
391C2×C4—182no—
392C2×C4—182no—
393C2×C4—182no—
394C2×C4—181no—
395C2×C4—181no—
396C2×C4—182no—
397C2×C4—182no—
398C2×C4—182no—
399C2×C4—182no—
400C2×C4—182no—
401C2×C4—182no—
402C2×C4—182no—
403C2×C4—182no—
404C2×C4—182no—
405C2×C4—182no—
406C2×C4—182no—
407C2×C4—182no—
408C2×C4—368no—
409C2×C4C22×#15711yescharacteristic
410C2×C4C22×#15711yescharacteristic
411C2×C4C22×#15711yescharacteristic
412C2×C4C22×#15711yescharacteristic
413C2×C4C22×#15711yescharacteristic
414C2×C4C22×#15711yescharacteristic
415C2×C3—22no—
416C2×C3—22no—
417C2×C3—22no—
418C2×C3—44no—
419D3—64no—
420D3—64no—
421D3—124no—
422C22—21no—
423C22—21no—
424C22—92no—
425C22—92no—
426C22—91no—
427C22—91no—
428C22—92no—
429C22—184no—
430C22—184no—
431C22—181no—
432C22—181no—
433C22#6428612yes—
434C22C23×#15711yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—184no—
442C4—181no—
443C4—181no—
444C4—181no—
445C4—181no—
446C4—181no—
447C4—181no—
448C4—362no—
449C4—362no—
450C4—362no—
451C3—22no—
452C2—22no—
453C2—92no—
454C2—92no—
455C2—182no—
456C2C2×#6428611yescharacteristic
457C2#41×#15711yescharacteristic
458C2#1059665011yescharacteristic
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×#117C4
prime radicalC23×C3⋊D3C23
cosocleC22×C3⋊D3C24
hypercenter#117#157
hypocenterC32#2343
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
4. #10593758C2semidirect
5. #10593758C2semidirect
8. #10593737C2semidirect
9. #10593736C2semidirect
10. C4×C4⋊#157C2semidirect
11. #10593733C2semidirect
19. C32×#117C4semidirect
20. #64135C4semidirect
21. #64101C4semidirect
22. #64101C4semidirect
27. #64086C4semidirect
28. #64086C4semidirect
29. #64081C4semidirect
30. #64081C4semidirect
68. C32×C4⋊C4C2×C4semidirect
69. C32×C4⋊C4C2×C4semidirect
72. C32×C42C2×C4semidirect
73. C32×C42C2×C4semidirect
80. C4⋊(C3⋊Dic3)C2×C4semidirect
81. C4⋊(C3⋊Dic3)C2×C4semidirect
82. #3750C2×C4semidirect
83. #3750C2×C4semidirect
84. #3750C2×C4semidirect
85. #3750C2×C4semidirect
86. C4×C3⋊Dic3C2×C4semidirect
87. C4×C3⋊Dic3C2×C4semidirect
88. C4×C3⋊Dic3C2×C4semidirect
89. C4×C3⋊Dic3C2×C4semidirect
90. C4×C3⋊Dic3C2×C4semidirect
91. C4×C3⋊Dic3C2×C4semidirect
237. #117#157semidirect
324. C4⋊C4C2×#157semidirect
325. C4⋊C4C2×#157semidirect
343. C42C2×#157semidirect
344. C42C2×#157semidirect
370. C32#2343semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1172
#105938112
C2×#637812
#105937582
#105937462
C22⋊C4×#1572
#105937372
#105937362
C4×C4⋊#1572
#105937332
#23439