Finite Group Databasebeta

← #11860348

Subgroups — #11860348

Order 1152.

916 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 916 conjugacy classes of subgroups — too many to draw. Only its 153 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64236C211yesmaximal, characteristic
2C2×#63902C211yesmaximal, characteristic, complemented
3C4×#3805C211yesmaximal, characteristic, complemented
4C4×#3792C211yesmaximal, characteristic, complemented
5#10593507C211yesmaximal, characteristic, complemented
6#10593496C211yesmaximal, characteristic, complemented
7#10593493C211yesmaximal, characteristic, complemented
8#10593433C212yesmaximal, complemented
9#10593432C212yesmaximal, complemented
10#10593420C212yesmaximal, complemented
11#10593419C212yesmaximal, complemented
12C22×#625C2211yescharacteristic
13C2×#3805C2211yescharacteristic
14C22×D3×Dic3—21no—
15C2×#3792C2211yescharacteristic
16C2×#3792C2211yescharacteristic
17C2×#3775C2212yes—
18#64236C418yescomplemented
19C2×#3774C2212yes—
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C3×C4×#67—21no—
22C2×C3×(C2×D3)⋊C4—21no—
23#67⋊Dic3—21no—
24C2×#3724C2211yescharacteristic
25#63957C2211yescharacteristic
26C4×#627C2211yescharacteristic, complemented
27#63902—21no—
28#63902—21no—
29#63902C2212yes—
30#63902C2212yes—
31#63902C2211yescharacteristic, complemented
32C4×#625C2211yescharacteristic, complemented
33#63878—21no—
34C4×D3×Dic3—21no—
35#63838C2211yescharacteristic, complemented
36#63777C2212yescomplemented
37C4×#622C2212yescomplemented
38#63743C2212yescomplemented
39#63742C2212yescomplemented
40#63740C2212yescomplemented
41#63739C2212yes—
42#63739C2212yes—
43#63739C2212yescomplemented
44C4×#237—61no—
45C2×#67⋊C4—61no—
46C23×C3×D3—21no—
47C22×C32×C4D411yescharacteristic
48C22×C3⋊Dic3D411yescharacteristic
49C22×C3⋊Dic3C2311yescharacteristic
50C2×C3×#67—21no—
51C22×C3×Dic3—21no—
52C2×C3×C4×D3—21no—
53C2×#627C2311yescharacteristic
54C2×#625—21no—
55C2×#625—22no—
56C2×#625C2×C414yescomplemented
57C2×#625C2312yes—
58C2×#625C2311yescharacteristic
59#3805—22no—
60#3805C2×C414yescomplemented
61C2×D3×Dic3—21no—
62C2×D3×Dic3—22no—
63C2×D3×Dic3—22no—
64C2×D3×Dic3—21no—
65C2×D3×Dic3—44no—
66#3792—22no—
67#3792C2×C414yescomplemented
68C2×#622C2312yes—
69C2×#622C2312yes—
70#3775C2×C418yescomplemented
71#3774C2×C418yescomplemented
72C4×C3⋊Dic3D411yescharacteristic
73C4×C3⋊Dic3D411yescharacteristic
74C4×C3⋊Dic3C2311yescharacteristic
75C4×C3⋊Dic3C2311yescharacteristic
76C3×#217—21no—
77C3×(C2×D3)⋊C4—22no—
78C3×(C2×D3)⋊C4—22no—
79C3×(C2×D3)⋊C4—21no—
80C3×Dic3⋊C4—21no—
81C3×C4×Dic3—21no—
82#3724—21no—
83#3724C2311yescharacteristic
84#3724C2312yes—
85#3724C2311yescharacteristic
86Dic3⋊Dic3—21no—
87(C2×D3)⋊Dic3—21no—
88Dic32—21no—
89Dic32—21no—
90C4×AGL(1,ℤ/8)—91nomaximal, Sylow
91C22×#67—61no—
92C23×Dic3—61no—
93C2×#237—61no—
94C22×C4×D3—61no—
95C3×C4×D4—61no—
96C2×C3×C22⋊C4—61no—
97D4×Dic3—61no—
98C4×#67—21no—
99C4×#67—61no—
100C2×(C2×D3)⋊C4—21no—
101C2×Dic3⋊C4—61no—
102C2×C4×Dic3—61no—
103C2×C4×Dic3—61no—
104C2×C4×Dic3—61no—
105#892—61no—
106#887—61no—
107#67⋊C4—62no—
108#67⋊C4—62no—
109#67⋊C4—61no—
110#67⋊C4—62no—
111#67⋊C4—62no—
112#67⋊C4—61no—
113#877—61no—
114#877—61no—
115C42×D3—61no—
116C4×Dic6—61no—
117C23×C32C2×D411yescharacteristic
118C22×C3×D3—24no—
119C22×C3×D3—22no—
120C22×C3×D3—21no—
121C22×C3×D3—42no—
122C22×C3×D3—42no—
123C2×C32×C4—41no—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3C22×C412yes—
128C2×C3⋊Dic3C2×D411yescharacteristic
129C2×C3⋊Dic3C2×D411yescharacteristic
130C2×C3⋊Dic3C2×D411yescharacteristic
131C2×C3⋊Dic3#4112yes—
132C2×C3⋊Dic3C2411yescharacteristic
133C3×#67—24no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—42no—
139C3×C4×D3—42no—
140#627—21no—
141#627C22×C412yescomplemented
142#625—24no—
143#625—21no—
144#625—22no—
145#625C22×C414yes—
146#625C22×C412yescomplemented
147D3×Dic3—24no—
148D3×Dic3—44no—
149D3×Dic3—42no—
150D3×Dic3—44no—
151#622—22no—
152#622C22×C414yescomplemented
153C2×AGL(1,ℤ/8)—91no—
154C4×#41—91no—
155C2×C4×D4—91no—
156#442—92no—
157#440—92no—
158C4×SD16—92no—
159C4×D8—92no—
160#428—91no—
161#418—91no—
162#417—91no—
163C4×M16—91no—
164C24×C3—61no—
165C23×D3—21no—
166C2×C3×D4—61no—
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4—61no—
170C22×C3×C4—61no—
171C2×#67—21no—
172C2×#67—62no—
173C2×#67—61no—
174C2×#67—64no—
175C2×#67—62no—
176C2×#67—64no—
177C22×Dic3—21no—
178C22×Dic3—61no—
179C22×Dic3—61no—
180C22×Dic3—61no—
181C22×Dic3—61no—
182C22×Dic3—61no—
183C22×Dic3—62no—
184C22×Dic3—62no—
185C22×Dic3—61no—
186C22×Dic3—124no—
187#237—64no—
188#237—64no—
189C2×C4×D3—21no—
190C2×C4×D3—61no—
191C2×C4×D3—61no—
192C2×C4×D3—62no—
193C2×C4×D3—62no—
194C2×C4×D3—124no—
195C2×Dic6—61no—
196C3×C4⋊C4—61no—
197C3×C22⋊C4—61no—
198C3×C22⋊C4—62no—
199C3×C22⋊C4—62no—
200C3×C22⋊C4—61no—
201C3×C42—61no—
202#217—21no—
203#217—61no—
204(C2×D3)⋊C4—22no—
205(C2×D3)⋊C4—22no—
206(C2×D3)⋊C4—21no—
207(C2×D3)⋊C4—61no—
208C4⋊Dic3—61no—
209Dic3⋊C4—21no—
210Dic3⋊C4—61no—
211Dic3⋊C4—61no—
212Dic3⋊C4—62no—
213Dic3⋊C4—61no—
214Dic3⋊C4—62no—
215C4×Dic3—21no—
216C4×Dic3—61no—
217C4×Dic3—61no—
218C4×Dic3—61no—
219C4×Dic3—61no—
220C4×Dic3—61no—
221C4×Dic3—61no—
222C4×Dic3—61no—
223C4×Dic3—61no—
224C4×Dic3—61no—
225C4×Dic3—61no—
226C4×Dic3—61no—
227C4×Dic3—61no—
228C22×C32—21no—
229C22×C32—21no—
230C22×C32C4×D412yes—
231C22×C32C22×D411yescharacteristic
232C2×C3×D3—22no—
233C2×C3×D3—24no—
234C2×C3×D3—48no—
235C2×C3×D3—42no—
236C2×C3×D3—41no—
237C2×C3×D3—41no—
238C2×C3×D3—42no—
239C32×C4—21no—
240C32×C4—21no—
241C3⋊Dic3—21no—
242C3⋊Dic3C4×D412yes—
243C3⋊Dic3AGL(1,ℤ/8)12yescomplemented
244C3⋊Dic3C23×C411yescharacteristic
245C3⋊Dic3C2×#4111yescharacteristic
246C3×Dic3—22no—
247C3×Dic3—42no—
248C3×Dic3—41no—
249C3×Dic3—41no—
250C2×#41—91no—
251C22×D4—91no—
252C23×C4—181no—
253AGL(1,ℤ/8)—98no—
254C2×SD16—92no—
255C2×D8—92no—
256C2×M16—91no—
257C2×M16—91no—
258C4×Q8—91no—
259C4×Q8—91no—
260C4×D4—61no—
261C4×D4—92no—
262C4×D4—92no—
263C4×D4—91no—
264C4×D4—91no—
265C4×D4—181no—
266C4×D4—181no—
267C4×D4—181no—
268#117—91no—
269#117—181no—
270C2×C4⋊C4—91no—
271C2×C22⋊C4—61no—
272C2×C42—91no—
273C2×C42—181no—
274#107—92no—
275#106—92no—
276#103—92no—
277#102—92no—
278#102—92no—
279#102—92no—
280#97—92no—
281C4×C8—92no—
282C23×C3—21no—
283C23×C3—21no—
284C23×C3—61no—
285C23×C3—62no—
286C23×C3—64no—
287C23×C3—122no—
288C23×C3—122no—
289C22×D3—22no—
290C22×D3—21no—
291C22×D3—24no—
292C22×D3—42no—
293C22×D3—42no—
294C3×D4—64no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—42no—
300C2×C3×C4—42no—
301C2×C3×C4—61no—
302C2×C3×C4—61no—
303C2×C3×C4—61no—
304C2×C3×C4—62no—
305C2×C3×C4—122no—
306C2×C3×C4—122no—
307#67—24no—
308#67—64no—
309#67—62no—
310#67—62no—
311#67—68no—
312#67—64no—
313C2×Dic3—21no—
314C2×Dic3—21no—
315C2×Dic3—21no—
316C2×Dic3—22no—
317C2×Dic3—42no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—61no—
321C2×Dic3—61no—
322C2×Dic3—61no—
323C2×Dic3—61no—
324C2×Dic3—61no—
325C2×Dic3—62no—
326C2×Dic3—62no—
327C2×Dic3—61no—
328C2×Dic3—61no—
329C2×Dic3—61no—
330C2×Dic3—64no—
331C2×Dic3—64no—
332C2×Dic3—122no—
333C2×Dic3—122no—
334C2×Dic3—124no—
335C2×Dic3—124no—
336C4×D3—42no—
337C4×D3—64no—
338C4×D3—122no—
339C4×D3—124no—
340C4×D3—124no—
341Dic6—62no—
342Dic6—62no—
343C2×C32—22no—
344C2×C32C2×C4×D411yescharacteristic
345C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
346C2×C32#57511yescharacteristic
347C3×D3—42no—
348C3×D3—44no—
349C24—61no—
350#41—94no—
351#41—182no—
352C2×Q8—91no—
353C2×D4—61no—
354C2×D4—91no—
355C2×D4—92no—
356C2×D4—94no—
357C2×D4—181no—
358C2×D4—182no—
359C22×C4—61no—
360C22×C4—61no—
361C22×C4—91no—
362C22×C4—91no—
363C22×C4—181no—
364C22×C4—181no—
365C22×C4—182no—
366C22×C4—182no—
367C22×C4—364no—
368C22×C4GO+(4,𝔽2)11yescharacteristic
369SD16—98no—
370D8—98no—
371M16—94no—
372M16—182no—
373C2×C8—92no—
374C2×C8—92no—
375C4⋊C4—61no—
376C4⋊C4—91no—
377C4⋊C4—91no—
378C4⋊C4—92no—
379C4⋊C4—181no—
380C4⋊C4—181no—
381C22⋊C4—61no—
382C22⋊C4—62no—
383C22⋊C4—62no—
384C22⋊C4—61no—
385C22⋊C4—181no—
386C42—61no—
387C42—91no—
388C42—91no—
389C42—91no—
390C42—91no—
391C42—181no—
392C42—181no—
393C22×C3—22no—
394C22×C3—22no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—22no—
398C22×C3—22no—
399C22×C3—41no—
400C22×C3—41no—
401C22×C3—62no—
402C22×C3—64no—
403C22×C3—122no—
404C22×C3—121no—
405C22×C3—121no—
406C22×C3—128no—
407C22×C3—122no—
408C2×D3—22no—
409C2×D3—24no—
410C2×D3—41no—
411C2×D3—42no—
412C2×D3—41no—
413C2×D3—48no—
414C2×D3—42no—
415C3×C4—22no—
416C3×C4—41no—
417C3×C4—41no—
418C3×C4—41no—
419C3×C4—62no—
420C3×C4—122no—
421C3×C4—121no—
422C3×C4—121no—
423Dic3—22no—
424Dic3—41no—
425Dic3—42no—
426Dic3—41no—
427Dic3—61no—
428Dic3—61no—
429Dic3—62no—
430Dic3—62no—
431Dic3—62no—
432Dic3—62no—
433Dic3—61no—
434Dic3—61no—
435Dic3—62no—
436Dic3—121no—
437C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
438C23—62no—
439C23—61no—
440C23—64no—
441C23—122no—
442C23—122no—
443C23C2×GO+(4,𝔽2)11yescharacteristic
444Q8—92no—
445Q8—181no—
446D4—64no—
447D4—92no—
448D4—94no—
449D4—182no—
450D4—184no—
451D4—181no—
452C2×C4—41no—
453C2×C4—61no—
454C2×C4—61no—
455C2×C4—61no—
456C2×C4—62no—
457C2×C4—91no—
458C2×C4—91no—
459C2×C4—91no—
460C2×C4—92no—
461C2×C4—92no—
462C2×C4—91no—
463C2×C4—122no—
464C2×C4—122no—
465C2×C4—184no—
466C2×C4—182no—
467C2×C4—364no—
468C2×C4—362no—
469C2×C4—364no—
470C2×C4C2×GO+(4,𝔽2)11yescharacteristic
471C2×C4C2×GO+(4,𝔽2)11yescharacteristic
472C8—94no—
473C8—182no—
474C2×C3—24no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—42no—
482C2×C3—124no—
483C2×C3—122no—
484D3—44no—
485D3—42no—
486C22—21no—
487C22—21no—
488C22—62no—
489C22—64no—
490C22—128no—
491C22—122no—
492C22—121no—
493C22—121no—
494C22—122no—
495C22C4×GO+(4,𝔽2)12yes—
496C22C22×GO+(4,𝔽2)11yescharacteristic
497C4—21no—
498C4—21no—
499C4—62no—
500C4—92no—
501C4—91no—
502C4—91no—
503C4—92no—
504C4—122no—
505C4—121no—
506C4—121no—
507C4—181no—
508C3—21no—
509C3—21no—
510C2—22no—
511C2—124no—
512C2—122no—
513C2#1059650111yescharacteristic
514C2C2×C4×GO+(4,𝔽2)11yescharacteristic
515C2#1059653211yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC22×C32×C4D4
socleC22×C32C22×D4
prime radicalC2×#64236C2
cosocleC2×C3⋊Dic3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C4×AGL(1,ℤ/8)
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63902C2semidirect
3. C4×#3805C2semidirect
4. C4×#3792C2semidirect
5. #10593507C2semidirect
6. #10593496C2semidirect
7. #10593493C2semidirect
8. #10593433C2semidirect
9. #10593432C2semidirect
10. #10593420C2semidirect
11. #10593419C2semidirect
18. #64236C4semidirect
26. C4×#627C22semidirect
31. #63902C22semidirect
32. C4×#625C22semidirect
35. #63838C22semidirect
36. #63777C22semidirect
37. C4×#622C22semidirect
38. #63743C22semidirect
39. #63742C22semidirect
40. #63740C22semidirect
43. #63739C22semidirect
56. C2×#625C2×C4semidirect
60. #3805C2×C4semidirect
67. #3792C2×C4semidirect
70. #3775C2×C4semidirect
71. #3774C2×C4semidirect
141. #627C22×C4semidirect
146. #625C22×C4semidirect
152. #622C22×C4semidirect
243. C3⋊Dic3AGL(1,ℤ/8)semidirect
437. C32C4×AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
C2×#642362
C2×#639022
C4×#38052
C4×#37922
#105935072
#105934962
#105934932
#105934332
#105934322
#105934202
#105934192
C4×AGL(1,ℤ/8)9