Finite Group Databasebeta

← #11783648

Subgroups — #11783648

Order 1152.

849 conjugacy classes of subgroups.

The subgroup lattice has 463 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×C3⋊C8C211yesmaximal, characteristic
2C2×C4×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
3C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
4C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic
5C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
6C3×#4524C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8C22⋊C4×C3⋊C8—31nomaximal
9#68647—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4C412yes—
15C2×C3×C4×Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×D3×C3⋊C8—22no—
19C2×D3×C3⋊C8—22no—
20C2×D3×C3⋊C8C414yescomplemented
21C4×C3⋊(C3⋊C8)—22no—
22C3×C3⋊#95C412yes—
23(C2×D3)⋊(C3⋊C8)C414yescomplemented
24Dic3×C3⋊C8—22no—
25C23×C3⋊C8—31no—
26C22×D3×C8—31no—
27C3×C4×C22⋊C4—31no—
28C2×#830—31no—
29C2×(C2×D3)⋊C8—31no—
30C2×C8×Dic3—31no—
31C4×(C2×D3)⋊C4D311yescharacteristic
32C2×C4×C3⋊C8—31no—
33C2×C4×C3⋊C8—31no—
34C2×C4×C3⋊C8—31no—
35C2×C4×C3⋊C8—61no—
36C3×#336—31no—
37#4550—31no—
38#4524—31no—
39#4524D311yescharacteristic, complemented
40C23×C3×D3C2×C411yescharacteristic
41C22×C32×C4C2×C412yes—
42C22×C32×C4C2311yescharacteristic
43C22×C3×Dic3C2×C411yescharacteristic
44C22×C3×Dic3C2×C412yes—
45C2×C3×C4×D3—21no—
46C2×C3×C4×D3—21no—
47C2×C3×C4×D3—21no—
48C2×C3×C4×D3—21no—
49C2×C3×C4×D3C2×C412yes—
50C2×C3×C4×D3C2×C412yes—
51C32×C42—21no—
52C32×C42—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)C2×C412yes—
56C2×C3⋊(C3⋊C8)C2×C412yes—
57C2×C3⋊(C3⋊C8)D412yes—
58C2×C3⋊(C3⋊C8)D412yes—
59C3×(C2×D3)⋊C4C818yescomplemented
60C3×C4×Dic3—21no—
61C3×C4×Dic3—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8C2×C412yes—
67C2×C3×C3⋊C8C2×C412yes—
68D3×C3⋊C8—28no—
69C8×C22⋊C4—91noSylow
70C23×C3×C4—31no—
71C22×C4×D3C2×D311yescharacteristic
72C22×C3×C8—31no—
73C22×C3×C8—31no—
74C2×C3×C22⋊C4—32no—
75C2×C3×C42—21no—
76C2×C3×C42—31no—
77C2×C3×C42C2×D311yescharacteristic
78C2×C3×C42C2×D311yescharacteristic
79C2×(C2×D3)⋊C4Dic312yes—
80C2×C4×Dic3C2×D311yescharacteristic
81C22×C3⋊C8—31no—
82C22×C3⋊C8—31no—
83C22×C3⋊C8—31no—
84C22×C3⋊C8—31no—
85C22×C3⋊C8—34no—
86C22×C3⋊C8—61no—
87C22×C3⋊C8—61no—
88C22×C3⋊C8—62no—
89C22×C3⋊C8—62no—
90C22×C3⋊C8C2×D311yescharacteristic
91C22×C3⋊C8C2×D311yescharacteristic
92C2×D3×C8—34no—
93C2×D3×C8—62no—
94C2×D3×C8—62no—
95C3×#95—32no—
96C3⋊#95Dic312yes—
97#830—34no—
98(C2×D3)⋊C8—34no—
99C8×Dic3—62no—
100C4×C3⋊C8—62no—
101C4×C3⋊C8—62no—
102C4×C3⋊C8—62no—
103C4×C3⋊C8—64no—
104C23×C32C22×C411yescharacteristic
105C22×C3×D3—21no—
106C22×C3×D3—21no—
107C22×C3×D3—22no—
108C22×C3×D3C4212yes—
109C22×C3×D3C2×C814yes—
110C2×C32×C4—22no—
111C2×C32×C4—22no—
112C2×C32×C4C2×C814yescomplemented
113C2×C32×C4C22×C411yescharacteristic
114C2×C32×C4C22×C411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C3×Dic3—22no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—22no—
123C2×C3×Dic3C4212yes—
124C2×C3×Dic3C2×C814yescomplemented
125C3×C4×D3—22no—
126C3×C4×D3—22no—
127C3×C4×D3—22no—
128C3×C4×D3—22no—
129C3⋊(C3⋊C8)—22no—
130C3⋊(C3⋊C8)C22⋊C414yescomplemented
131C3×C3⋊C8—22no—
132C3×C3⋊C8—22no—
133C23×C8—91no—
134C2×C22⋊C8—91no—
135C2×C4×C8—91no—
136C2×C4×C8—91no—
137C4×C22⋊C4—31no—
138#336—31no—
139#336—91no—
140C24×C3—31no—
141C23×D3C2×Dic311yescharacteristic
142C22×C3×C4—22no—
143C22×C3×C4—21no—
144C22×C3×C4—31no—
145C22×C3×C4—32no—
146C22×C3×C4—32no—
147C22×C3×C4—32no—
148C22×C3×C4—61no—
149C22×C3×C4—61no—
150C22×C3×C4—61no—
151C22×C3×C4—61no—
152C22×C3×C4C4×D312yes—
153C22×C3×C4C2×Dic312yes—
154C22×C3×C4C22×D311yescharacteristic
155C22×C3×C4C22×D311yescharacteristic
156C22×Dic3C2×Dic312yes—
157C22×Dic3C2×Dic311yescharacteristic
158C2×C4×D3—21no—
159C2×C4×D3—21no—
160C2×C4×D3—21no—
161C2×C4×D3—21no—
162C2×C4×D3C4×D312yes—
163C2×C4×D3C4×D312yes—
164C2×C3×C8—32no—
165C2×C3×C8—32no—
166C2×C3×C8—61no—
167C2×C3×C8—61no—
168C2×C3×C8—61no—
169C2×C3×C8—61no—
170C3×C22⋊C4—38no—
171C3×C42—22no—
172C3×C42—22no—
173C3×C42—21no—
174C3×C42—21no—
175C3×C42—21no—
176C3×C42—21no—
177C3×C42—61no—
178C3×C42—61no—
179(C2×D3)⋊C4C3⋊C818yescomplemented
180C4×Dic3—21no—
181C4×Dic3—21no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—21no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—32no—
187C2×C3⋊C8—32no—
188C2×C3⋊C8—32no—
189C2×C3⋊C8—32no—
190C2×C3⋊C8—32no—
191C2×C3⋊C8—32no—
192C2×C3⋊C8—32no—
193C2×C3⋊C8—32no—
194C2×C3⋊C8—62no—
195C2×C3⋊C8—62no—
196C2×C3⋊C8—62no—
197C2×C3⋊C8—62no—
198C2×C3⋊C8—68no—
199C2×C3⋊C8—62no—
200C2×C3⋊C8—62no—
201C2×C3⋊C8—61no—
202C2×C3⋊C8—61no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—61no—
205C2×C3⋊C8C4×D312yes—
206C2×C3⋊C8C4×D312yes—
207D3×C8—68no—
208C22×C32C2×C4211yescharacteristic
209C22×C32C4×D411yescharacteristic
210C22×C32C4×D411yescharacteristic
211C22×C32C22×C812yes—
212C22×C32#13112yes—
213C2×C3×D3—22no—
214C2×C3×D3—22no—
215C2×C3×D3—24no—
216C2×C3×D3—24no—
217C2×C3×D3C4×C814yescomplemented
218C32×C4—24no—
219C32×C4C2×C22⋊C411yescharacteristic
220C32×C4#11711yescharacteristic
221C32×C4C4×D411yescharacteristic
222C32×C4C4×D411yescharacteristic
223C3×Dic3—22no—
224C3×Dic3—24no—
225C23×C4—31no—
226C22×C8—31no—
227C22×C8—31no—
228C22×C8—94no—
229C22×C8—91no—
230C22×C8—91no—
231C22×C8—182no—
232C22×C8—182no—
233C2×C22⋊C4—32no—
234C2×C42—31no—
235C2×C42D3211yescharacteristic
236C22⋊C8—94no—
237C4×C8—182no—
238C4×C8—182no—
239#95—32no—
240C23×C3—21no—
241C23×C3—32no—
242C23×C3—34no—
243C23×C3—61no—
244C23×C3—61no—
245C23×C3—62no—
246C23×C3C2×C4×D311yescharacteristic
247C23×C3C22×Dic311yescharacteristic
248C22×D3—21no—
249C22×D3—21no—
250C22×D3—22no—
251C22×D3C2×C3⋊C814yes—
252C22×D3C4×Dic312yes—
253C2×C3×C4—24no—
254C2×C3×C4—24no—
255C2×C3×C4—22no—
256C2×C3×C4—22no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—24no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—32no—
267C2×C3×C4—34no—
268C2×C3×C4—61no—
269C2×C3×C4—62no—
270C2×C3×C4—61no—
271C2×C3×C4—62no—
272C2×C3×C4—62no—
273C2×C3×C4—62no—
274C2×C3×C4—62no—
275C2×C3×C4—62no—
276C2×C3×C4D3×C814yescomplemented
277C2×C3×C4C2×C3⋊C814yescomplemented
278C2×C3×C4C2×C4×D311yescharacteristic
279C2×C3×C4C2×C4×D311yescharacteristic
280C2×C3×C4C2×C4×D311yescharacteristic
281C2×C3×C4C2×C4×D311yescharacteristic
282C2×C3×C4D3×D411yescharacteristic
283C2×C3×C4D3×D411yescharacteristic
284C2×C3×C4D3×D411yescharacteristic
285C2×C3×C4D3×D411yescharacteristic
286C2×C3×C4#23711yescharacteristic
287C2×C3×C4#23711yescharacteristic
288C2×C3×C4#23711yescharacteristic
289C2×C3×C4#23911yescharacteristic
290C2×Dic3—22no—
291C2×Dic3—21no—
292C2×Dic3—21no—
293C2×Dic3—22no—
294C2×Dic3C2×C3⋊C814yescomplemented
295C2×Dic3C4×Dic312yes—
296C4×D3—22no—
297C4×D3—22no—
298C4×D3—22no—
299C4×D3—22no—
300C3×C8—62no—
301C3×C8—62no—
302C3⋊C8—22no—
303C3⋊C8—22no—
304C3⋊C8—34no—
305C3⋊C8—34no—
306C3⋊C8—64no—
307C3⋊C8—64no—
308C3⋊C8—62no—
309C3⋊C8—62no—
310C2×C32C4×C22⋊C411yescharacteristic
311C2×C32C2×C4×C811yescharacteristic
312C2×C32#40511yescharacteristic
313C2×C32C8×D412yes—
314C2×C32C8×D412yes—
315C3×D3—24no—
316C24—31no—
317C22×C4—31no—
318C22×C4—32no—
319C22×C4—32no—
320C22×C4—32no—
321C22×C4—61no—
322C22×C4—61no—
323C22×C4—61no—
324C22×C4—61no—
325C22×C4D3×Dic312yes—
326C22×C4C2×D3211yescharacteristic
327C2×C8—32no—
328C2×C8—32no—
329C2×C8—61no—
330C2×C8—61no—
331C2×C8—61no—
332C2×C8—61no—
333C2×C8—92no—
334C2×C8—92no—
335C2×C8—92no—
336C2×C8—92no—
337C2×C8—188no—
338C2×C8—181no—
339C2×C8—181no—
340C22⋊C4—38no—
341C42—21no—
342C42—21no—
343C42—61no—
344C42—61no—
345C22×C3—22no—
346C22×C3—22no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—34no—
351C22×C3—62no—
352C22×C3—62no—
353C22×C3—64no—
354C22×C3—64no—
355C22×C3C42×D311yescharacteristic
356C22×C3#67⋊C411yescharacteristic
357C22×C3#89311yescharacteristic
358C22×C3C2×D3×C812yes—
359C22×C3#90712yes—
360C22×C3C22×C3⋊C812yes—
361C22×C3C2×C4×Dic311yescharacteristic
362C22×C3D4×Dic311yescharacteristic
363C22×C3D4×Dic311yescharacteristic
364C22×C3#94812yes—
365C2×D3—22no—
366C2×D3—22no—
367C2×D3—24no—
368C2×D3—24no—
369C2×D3C4×C3⋊C814yescomplemented
370C3×C4—28no—
371C3×C4—24no—
372C3×C4—24no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—62no—
378C3×C4—64no—
379C3×C4#87711yescharacteristic
380C3×C4D3×C22⋊C411yescharacteristic
381C3×C4D3×C22⋊C411yescharacteristic
382C3×C4#67⋊C411yescharacteristic
383C3×C4#67⋊C411yescharacteristic
384C3×C4#67⋊C411yescharacteristic
385C3×C4#89211yescharacteristic
386C3×C4#89311yescharacteristic
387Dic3—22no—
388Dic3—24no—
389C32C8×C22⋊C411yescharacteristic, complemented, Sylow
390C23—34no—
391C23—32no—
392C23—62no—
393C23—61no—
394C23—61no—
395C23C2×D3×Dic311yescharacteristic
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—34no—
399C2×C4—32no—
400C2×C4—62no—
401C2×C4—62no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—62no—
405C2×C4—62no—
406C2×C4—62no—
407C2×C4—62no—
408C2×C4D3×C3⋊C814yescomplemented
409C2×C4#379611yescharacteristic
410C2×C4C4×D3211yescharacteristic
411C2×C4C4×D3211yescharacteristic
412C2×C4#380211yescharacteristic
413C2×C4#380511yescharacteristic
414C2×C4#381111yescharacteristic
415C8—62no—
416C8—62no—
417C8—94no—
418C8—182no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—22no—
422C2×C3—21no—
423C2×C3—22no—
424C2×C3—64no—
425C2×C3#466611yescharacteristic
426C2×C3C4×D3×C811yescharacteristic
427C2×C3#470811yescharacteristic
428C2×C3#67⋊C812yes—
429C2×C3#483412yes—
430C2×C3C2×C4×C3⋊C811yescharacteristic
431C2×C3Dic3×C22⋊C411yescharacteristic
432C2×C3#499711yescharacteristic
433C2×C3D4×C3⋊C812yes—
434C2×C3D4×C3⋊C812yes—
435D3—24no—
436C22—34no—
437C22—62no—
438C22—64no—
439C22—62no—
440C22—64no—
441C22C2×D3×C3⋊C812yes—
442C22#6381512yes—
443C22C4×D3×Dic311yescharacteristic
444C22#6389811yescharacteristic
445C22#67⋊Dic311yescharacteristic
446C4—24no—
447C4—64no—
448C4—62no—
449C4#6387811yescharacteristic
450C4#6388111yescharacteristic
451C4#6390211yescharacteristic
452C4#6392111yescharacteristic
453C3—21no—
454C3#6864711yescharacteristic, complemented
455C3C22⋊C4×C3⋊C811yescharacteristic, complemented
456C2—64no—
457C2C4×D3×C3⋊C811yescharacteristic
458C2#1059031911yescharacteristic
459C2#1059032912yes—
460C2#67⋊(C3⋊C8)12yes—
461C2#1059136811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutatorC2×C32C2×C4×C8
FittingC2×C32×C42C22
socleC23×C32C22×C4
prime radicalC23×C3×D3C2×C4
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32C8×C22⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C4×C3⋊(C3⋊C8)C2semidirect
5. C2×Dic3×C3⋊C8C2semidirect
6. C3×#4524C2semidirect
7. #10589155C2semidirect
20. C2×D3×C3⋊C8C4semidirect
23. (C2×D3)⋊(C3⋊C8)C4semidirect
39. #4524D3semidirect
59. C3×(C2×D3)⋊C4C8semidirect
112. C2×C32×C4C2×C8semidirect
124. C2×C3×Dic3C2×C8semidirect
130. C3⋊(C3⋊C8)C22⋊C4semidirect
179. (C2×D3)⋊C4C3⋊C8semidirect
217. C2×C3×D3C4×C8semidirect
276. C2×C3×C4D3×C8semidirect
277. C2×C3×C4C2×C3⋊C8semidirect
294. C2×Dic3C2×C3⋊C8semidirect
369. C2×D3C4×C3⋊C8semidirect
389. C32C8×C22⋊C4semidirect
408. C2×C4D3×C3⋊C8semidirect
454. C3#68647semidirect
455. C3C22⋊C4×C3⋊C8semidirect

Maximal subgroups

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

subgroupindex
C22×D3×C3⋊C82
C2×C4×C3⋊(C3⋊C8)2
C3×C4×(C2×D3)⋊C42
C2×(C2×D3)⋊(C3⋊C8)2
C2×Dic3×C3⋊C82
C3×#45242
#105891552
C22⋊C4×C3⋊C83
#686473