Finite Group Databasebeta

← #11859355

Subgroups — #11859355

Order 1152.

1173 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64157C211yesmaximal, characteristic, complemented
2C3×#5828C211yesmaximal, characteristic
3C22×D3×C3⋊C8C211yesmaximal, characteristic, complemented
4C3×#5234C211yesmaximal, characteristic, complemented
5#10591151C214yesmaximal, complemented
6#67⋊(C3⋊C8)C214yesmaximal, complemented
7#10591116C211yesmaximal, characteristic, complemented
8#10591069C211yesmaximal, characteristic, complemented
9#10591057C211yesmaximal, characteristic, complemented
10#82916—31nomaximal
11#78655—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14#64157—24no—
15C2×#3748C2211yescharacteristic
16C2×#3748C2212yescomplemented
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C22×C3⋊(C3⋊C8)C2212yescomplemented
19C3×#946C412yes—
20C3×#938C412yes—
21C3×#937C412yes—
22C3×#935C412yes—
23C3×C4×#67C2214yes—
24C3×#926C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C2×D3×C3⋊C8—24no—
28C2×D3×C3⋊C8C2212yes—
29C2×D3×C3⋊C8C2212yes—
30C3×#830C2214yescomplemented
31Dic3⋊(C3⋊C8)C2214yescomplemented
32(C2×D3)⋊(C3⋊C8)C2214yes—
33#63554C2212yescomplemented
34Dic3×C3⋊C8C2212yescomplemented
35C3×#525—31no—
36#5828D311yescharacteristic
37C2×#948—31no—
38C2×#948—31no—
39C2×#948—61no—
40C23×C3⋊C8—31no—
41C22×D3×C8—31no—
42C3×#408—31no—
43#5234D311yescharacteristic, complemented
44#5207—31no—
45#5126—31no—
46#5122—31no—
47#5102—31no—
48#5011—34no—
49D4×C3⋊C8—34no—
50#4999—31no—
51#4997—31no—
52#4728—34no—
53#67⋊C8—34no—
54C23×C3×D3C2×C411yescharacteristic
55C32×#41—22no—
56C32×#41—22no—
57C2×C32×Q8C2×C411yescharacteristic
58C2×C32×D4C2×C412yes—
59C2×C32×D4C2×C411yescharacteristic
60C22×C32×C4C2312yes—
61C22×C32×C4C2311yescharacteristic
62C2×C3×#67C2×C414yes—
63C22×C3×Dic3C2×C411yescharacteristic
64C2×C3×C4×D3—22no—
65C2×C3×C4×D3—22no—
66C2×C3×C4×D3C2×C412yes—
67C2×C3×C4×D3C2312yes—
68#3748—22no—
69#3748—24no—
70C2×C3⋊(C3⋊C8)—24no—
71C2×C3⋊(C3⋊C8)D414yescomplemented
72C2×C3⋊(C3⋊C8)C2312yes—
73C2×C3⋊(C3⋊C8)C2311yescharacteristic
74C2×C3⋊(C3⋊C8)C2311yescharacteristic
75C3×#217C2×C412yes—
76C3×#217C2×C414yes—
77C3×(C2×D3)⋊C4C2×C414yes—
78C3×C4⋊Dic3C2×C412yes—
79C3×Dic3⋊C4C2×C414yes—
80C3×C4×Dic3C2312yes—
81C3×#208—22no—
82C2×C3×C3⋊C8—22no—
83C2×C3×C3⋊C8C2312yes—
84C2×C3×C3⋊C8C2312yes—
85D3×C3⋊C8—24no—
86D3×C3⋊C8—24no—
87#2929—91noSylow
88C2×C3×#41—21no—
89C2×C3×#41C2×D311yescharacteristic
90C2×C3×#41C2×D311yescharacteristic
91C23×C3×C4—31no—
92C22×C4×D3C2×D311yescharacteristic
93C2×C3×M16—31no—
94C22×C3×C8—31no—
95C3×#123—32no—
96C3×C22⋊Q8—32no—
97C3×#121—32no—
98C3×#120—32no—
99C3×C4×D4—34no—
100C3×#117—31no—
101#948—64no—
102#948—64no—
103#948—68no—
104#946Dic312yes—
105#938Dic312yes—
106#937Dic312yes—
107#935Dic312yes—
108C4×#67C2×D314yes—
109#926C2×D311yescharacteristic
110C2×#208—31no—
111C2×#208—31no—
112C2×#208—32no—
113C2×#208—32no—
114C2×#208—61no—
115C2×#208—62no—
116C2×#208C2×D311yescharacteristic
117C22×C3⋊C8—31no—
118C22×C3⋊C8—31no—
119C22×C3⋊C8—32no—
120C22×C3⋊C8—32no—
121C22×C3⋊C8—32no—
122C22×C3⋊C8—32no—
123C22×C3⋊C8—61no—
124C22×C3⋊C8—62no—
125C22×C3⋊C8—64no—
126C22×C3⋊C8C2×D311yescharacteristic
127C2×D3×C8—32no—
128C2×D3×C8—32no—
129C2×D3×C8—64no—
130C3×C22⋊C8—34no—
131#830—34no—
132#830C2×D314yescomplemented
133(C2×D3)⋊C8—34no—
134#815—32no—
135Dic3⋊C8—34no—
136C8×Dic3—32no—
137C4⋊(C3⋊C8)—34no—
138#803—32no—
139C4×C3⋊C8—32no—
140C23×C32C22×C412yes—
141C23×C32C22×C411yescharacteristic
142C22×C3×D3—22no—
143C22×C3×D3—24no—
144C22×C3×D3C22×C412yes—
145C32×Q8—22no—
146C32×D4—24no—
147C32×D4—22no—
148C2×C32×C4—22no—
149C2×C32×C4—22no—
150C2×C32×C4C22×C412yes—
151C2×C32×C4C22×C411yescharacteristic
152C2×C32×C4C2×D412yes—
153C2×C32×C4#4112yes—
154C2×C32×C4C2411yescharacteristic
155C3×#67—28no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3C22×C414yes—
158C2×C3×Dic3C22×C412yes—
159C3×C4×D3—24no—
160C3×C4×D3—22no—
161C3×C4×D3—22no—
162C3⋊(C3⋊C8)—22no—
163C3⋊(C3⋊C8)C2×D412yes—
164C3⋊(C3⋊C8)C2×D412yes—
165C3×C3⋊C8—22no—
166C3×C3⋊C8—22no—
167C2×#131—91no—
168C23×C8—91no—
169#525—31no—
170#435—94no—
171C8×D4—94no—
172#424—91no—
173#408—31no—
174#407—91no—
175#405—91no—
176C24×C3—31no—
177C23×D3C2×Dic311yescharacteristic
178C3×#41—24no—
179C3×#41—24no—
180C3×#41—22no—
181C3×#41—22no—
182C3×#41—22no—
183C3×#41—22no—
184C2×C3×Q8—21no—
185C2×C3×Q8C4×D311yescharacteristic
186C2×C3×Q8C2×Dic311yescharacteristic
187C2×C3×D4—22no—
188C2×C3×D4—21no—
189C2×C3×D4—34no—
190C2×C3×D4C4×D312yes—
191C2×C3×D4C4×D311yescharacteristic
192C2×C3×D4C2×Dic312yes—
193C2×C3×D4C2×Dic311yescharacteristic
194C22×C3×C4—22no—
195C22×C3×C4—21no—
196C22×C3×C4—31no—
197C22×C3×C4—32no—
198C22×C3×C4—32no—
199C22×C3×C4—62no—
200C22×C3×C4—62no—
201C22×C3×C4C22×D312yes—
202C22×C3×C4C22×D312yes—
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D311yescharacteristic
205C2×#67C2×Dic314yes—
206C22×Dic3C2×Dic311yescharacteristic
207C2×C4×D3—22no—
208C2×C4×D3—22no—
209C2×C4×D3C2×Dic312yes—
210C2×C4×D3C22×D312yes—
211C3×M16—62no—
212C2×C3×C8—32no—
213C2×C3×C8—32no—
214C2×C3×C8—62no—
215C3×C4⋊C4—34no—
216C3×C4⋊C4—32no—
217C3×C22⋊C4—32no—
218C3×C22⋊C4—34no—
219C3×C22⋊C4—34no—
220C3×C42—32no—
221#217C2×Dic312yes—
222#217C2×Dic314yes—
223(C2×D3)⋊C4C2×Dic314yes—
224C4⋊Dic3C2×Dic312yes—
225Dic3⋊C4C2×Dic314yes—
226C4×Dic3C22×D312yes—
227#208—22no—
228#208—64no—
229#208—64no—
230#208—68no—
231#208—64no—
232#208—62no—
233#208—62no—
234C2×C3⋊C8—22no—
235C2×C3⋊C8—34no—
236C2×C3⋊C8—34no—
237C2×C3⋊C8—31no—
238C2×C3⋊C8—31no—
239C2×C3⋊C8—31no—
240C2×C3⋊C8—31no—
241C2×C3⋊C8—32no—
242C2×C3⋊C8—32no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8—61no—
245C2×C3⋊C8—62no—
246C2×C3⋊C8—64no—
247C2×C3⋊C8—64no—
248C2×C3⋊C8—64no—
249C2×C3⋊C8—64no—
250C2×C3⋊C8—64no—
251C2×C3⋊C8—68no—
252C2×C3⋊C8C22×D312yes—
253C2×C3⋊C8C22×D312yes—
254D3×C8—64no—
255D3×C8—64no—
256C22×C32—22no—
257C22×C32—22no—
258C22×C32—24no—
259C22×C32C4×D412yes—
260C22×C32C23×C411yescharacteristic
261C2×C3×D3—28no—
262C2×C3×D3—22no—
263C2×C3×D3—22no—
264C2×C3×D3#13114yescomplemented
265C32×C4—22no—
266C32×C4C4×D412yes—
267C32×C4C22×D411yescharacteristic
268C32×C4C2×#4111yescharacteristic
269C3×Dic3—22no—
270C3×Dic3—24no—
271C2×#41D3211yescharacteristic
272C23×C4—31no—
273#131—184no—
274C2×M16—31no—
275C2×M16—91no—
276C2×M16—92no—
277C22×C8—31no—
278C22×C8—92no—
279C22×C8—92no—
280C22×C8—91no—
281C22×C8—92no—
282C22×C8—184no—
283#123—32no—
284C22⋊Q8—32no—
285#121—32no—
286#120—32no—
287C4×D4—34no—
288#117—31no—
289C4⋊C8—94no—
290C22⋊C8—34no—
291C22⋊C8—94no—
292#97—92no—
293C4×C8—92no—
294C23×C3—22no—
295C23×C3—21no—
296C23×C3—32no—
297C23×C3—64no—
298C23×C3—62no—
299C23×C3C2×C4×D312yes—
300C23×C3C2×C4×D311yescharacteristic
301C23×C3C22×Dic312yes—
302C23×C3C22×Dic311yescharacteristic
303C22×D3—22no—
304C22×D3—24no—
305C22×D3C22×Dic312yes—
306C3×Q8—24no—
307C3×Q8—22no—
308C3×Q8—22no—
309C3×D4—28no—
310C3×D4—24no—
311C3×D4—24no—
312C3×D4—24no—
313C3×D4—22no—
314C3×D4—22no—
315C3×D4—68no—
316C2×C3×C4—24no—
317C2×C3×C4—24no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—21no—
323C2×C3×C4—22no—
324C2×C3×C4—21no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—34no—
328C2×C3×C4—32no—
329C2×C3×C4—62no—
330C2×C3×C4—64no—
331C2×C3×C4—62no—
332C2×C3×C4—62no—
333C2×C3×C4C2×C4×D312yes—
334C2×C3×C4C2×C4×D311yescharacteristic
335C2×C3×C4D3×D412yes—
336C2×C3×C4D3×D412yes—
337C2×C3×C4#23712yes—
338C2×C3×C4#23712yes—
339C2×C3×C4C22×Dic312yes—
340C2×C3×C4C22×Dic311yescharacteristic
341C2×C3×C4C23×D311yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343#67—28no—
344C2×Dic3—22no—
345C2×Dic3C22×Dic314yes—
346C2×Dic3C22×Dic312yes—
347C4×D3—24no—
348C4×D3—22no—
349C4×D3—22no—
350C3×C8—62no—
351C3×C8—62no—
352C3⋊C8—22no—
353C3⋊C8—22no—
354C3⋊C8—32no—
355C3⋊C8—32no—
356C3⋊C8—32no—
357C3⋊C8—32no—
358C3⋊C8—62no—
359C3⋊C8—62no—
360C3⋊C8—64no—
361C3⋊C8—62no—
362C3⋊C8—62no—
363C2×C32—22no—
364C2×C32—42no—
365C2×C32C2×C4×D411yescharacteristic
366C2×C32C2×#13112yes—
367C3×D3—24no—
368C24—31no—
369#41—22no—
370#41—22no—
371C2×Q8D3×Dic311yescharacteristic
372C2×D4—34no—
373C2×D4D3×Dic312yes—
374C2×D4D3×Dic311yescharacteristic
375C22×C4—31no—
376C22×C4—32no—
377C22×C4—32no—
378C22×C4—62no—
379C22×C4—62no—
380C22×C4C2×D3212yes—
381C22×C4C2×D3211yescharacteristic
382M16—62no—
383M16—184no—
384M16—182no—
385C2×C8—32no—
386C2×C8—32no—
387C2×C8—62no—
388C2×C8—91no—
389C2×C8—91no—
390C2×C8—94no—
391C2×C8—92no—
392C2×C8—184no—
393C2×C8—184no—
394C2×C8—184no—
395C4⋊C4—32no—
396C4⋊C4—34no—
397C22⋊C4—32no—
398C22⋊C4—34no—
399C22⋊C4—34no—
400C42—32no—
401C22×C3—22no—
402C22×C3—22no—
403C22×C3—24no—
404C22×C3—22no—
405C22×C3—24no—
406C22×C3—22no—
407C22×C3—24no—
408C22×C3—21no—
409C22×C3—22no—
410C22×C3—34no—
411C22×C3—42no—
412C22×C3—44no—
413C22×C3—68no—
414C22×C3—62no—
415C22×C3—62no—
416C22×C3#67⋊C412yes—
417C22×C3D4×Dic312yes—
418C22×C3C22×C4×D311yescharacteristic
419C22×C3C23×Dic311yescharacteristic
420C2×D3—28no—
421C2×D3—22no—
422C2×D3—22no—
423C2×D3#94814yescomplemented
424C3×C4—24no—
425C3×C4—22no—
426C3×C4—22no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—22no—
430C3×C4—62no—
431C3×C4—64no—
432C3×C4#67⋊C412yes—
433C3×C4D4×Dic312yes—
434C3×C4C2×D3×D411yescharacteristic
435C3×C4C2×D3×D411yescharacteristic
436C3×C4C2×#23711yescharacteristic
437C3×C4C2×#23711yescharacteristic
438Dic3—22no—
439Dic3—24no—
440C32#292911yescharacteristic, complemented, Sylow
441C23—32no—
442C23—64no—
443C23—62no—
444C23C2×D3×Dic312yes—
445C23C2×D3×Dic311yescharacteristic
446Q8—22no—
447D4—24no—
448D4—22no—
449D4—68no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—34no—
453C2×C4—32no—
454C2×C4—62no—
455C2×C4—62no—
456C2×C4—62no—
457C2×C4—64no—
458C2×C4C2×D3×Dic312yes—
459C2×C4C2×D3×Dic311yescharacteristic
460C2×C4#380512yes—
461C2×C4#381112yes—
462C2×C4C22×D3211yescharacteristic
463C8—62no—
464C8—62no—
465C8—92no—
466C8—92no—
467C8—182no—
468C2×C3—22no—
469C2×C3—22no—
470C2×C3—22no—
471C2×C3—21no—
472C2×C3—42no—
473C2×C3—44no—
474C2×C3—42no—
475C2×C3—42no—
476C2×C3—64no—
477C2×C3C2×#67⋊C411yescharacteristic
478C2×C3D3×#13112yes—
479C2×C3C2×D4×Dic311yescharacteristic
480C2×C3C2×#94812yes—
481D3—24no—
482C22—22no—
483C22—24no—
484C22—22no—
485C22—34no—
486C22—68no—
487C22—62no—
488C22—62no—
489C22#67⋊Dic312yes—
490C22C22×D3×Dic311yescharacteristic
491C4—22no—
492C4—64no—
493C4—62no—
494C4#67⋊Dic312yes—
495C4C2×#380511yescharacteristic
496C4C2×#381111yescharacteristic
497C3—21no—
498C3#7865511yescharacteristic, complemented
499C3#8291611yescharacteristic, complemented
500C2—22no—
501C2—42no—
502C2—64no—
503C2D3×#94812yes—
504C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC2×C32×#41C22
prime radicalC3×#5828C2
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32#2929
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64157C2semidirect
3. C22×D3×C3⋊C8C2semidirect
4. C3×#5234C2semidirect
5. #10591151C2semidirect
6. #67⋊(C3⋊C8)C2semidirect
7. #10591116C2semidirect
8. #10591069C2semidirect
9. #10591057C2semidirect
16. C2×#3748C22semidirect
18. C22×C3⋊(C3⋊C8)C22semidirect
30. C3×#830C22semidirect
31. Dic3⋊(C3⋊C8)C22semidirect
33. #63554C22semidirect
34. Dic3×C3⋊C8C22semidirect
43. #5234D3semidirect
71. C2×C3⋊(C3⋊C8)D4semidirect
132. #830C2×D3semidirect
264. C2×C3×D3#131semidirect
423. C2×D3#948semidirect
440. C32#2929semidirect
498. C3#78655semidirect
499. C3#82916semidirect

Maximal subgroups

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

subgroupindex
C2×#641572
C3×#58282
C22×D3×C3⋊C82
C3×#52342
#105911512
#67⋊(C3⋊C8)2
#105911162
#105910692
#105910572
#829163
#786553