Finite Group Databasebeta

← #11868092

Subgroups — #11868092

Order 1152.

1398 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#575C211yesmaximal, characteristic, complemented
2C2×#64158C211yesmaximal, characteristic, complemented
3C2×#64158C211yesmaximal, characteristic, complemented
4#10596290C211yesmaximal, characteristic, complemented
5#10592936C211yesmaximal, characteristic, complemented
6#10592902C214yesmaximal, complemented
7#10592898C214yesmaximal, complemented
8C2×#63650C211yesmaximal, characteristic, complemented
9#10592823C211yesmaximal, characteristic, complemented
10#84002—34nomaximal
11C2×C32×#41C2211yescharacteristic
12C2×C32×#41C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C32×#137—21no—
15C32×#137C2212yescomplemented
16C32×AGL(1,ℤ/8)—21no—
17C32×AGL(1,ℤ/8)C2212yescomplemented
18C32×#135—22no—
19C2×C32×M16C2211yescharacteristic
20#64158—22no—
21#64158—22no—
22#64158—22no—
23#64158C2214yes—
24#64157—22no—
25#64157C2214yescomplemented
26C2×#3755—21no—
27C2×#3755C2212yescomplemented
28C2×#3753—21no—
29C2×#3753C2212yescomplemented
30C2×#3748—22no—
31C2×#3748C2211yescharacteristic
32C2×#3748C2211yescharacteristic
33C2×#3748C2211yescharacteristic
34#63663C2212yescomplemented
35#63660C2212yescomplemented
36#63650C2214yescomplemented
37#63649C2214yescomplemented
38C3×#575D314yescomplemented
39C2×#949—34no—
40C2×#949—34no—
41#5819—34no—
42#5237—34no—
43#5203—316no—
44#5199—316no—
45C2×#823—34no—
46#5124—34no—
47C23×C3⋊D3—21no—
48C32×#41—21no—
49C32×#41—21no—
50C32×#41—21no—
51C32×#41—21no—
52C32×#41—21no—
53C32×#41—21no—
54C32×#41D412yes—
55C32×#41C2312yes—
56C2×C32×Q8D411yescharacteristic
57C2×C32×Q8C2311yescharacteristic
58C2×C32×D4—21no—
59C2×C32×D4—21no—
60C2×C32×D4D411yescharacteristic
61C2×C32×D4C2311yescharacteristic
62C22×C32×C4—21no—
63C22×C32×C4—21no—
64C22×C32×C4C2311yescharacteristic
65C2×C4⋊(C3⋊D3)—21no—
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)—21no—
70C2×C4⋊(C3⋊D3)C2312yes—
71C32×Q16—22no—
72C32×SD16—22no—
73C32×SD16—22no—
74C32×D8—22no—
75C32×M16—21no—
76C32×M16C2312yes—
77C2×C32×C8—21no—
78#3755—24no—
79#3755—24no—
80#3753—24no—
81#3753—24no—
82#3748—21no—
83#3748—21no—
84#3748—24no—
85#3748D412yes—
86#3748D412yes—
87#3748C2312yes—
88#3748C2312yes—
89C2×C3⋊(C3⋊C8)—21no—
90C2×C3⋊(C3⋊C8)—21no—
91C2×C3⋊(C3⋊C8)—24no—
92C2×C3⋊(C3⋊C8)C2312yes—
93#3068—91noSylow
94C2×C3×#41C2×D314yes—
95C2×C3×#41C2×D314yes—
96C22×D12—34no—
97C3×#137—24no—
98C3×#137C2×D318yescomplemented
99C3×AGL(1,ℤ/8)—24no—
100C3×AGL(1,ℤ/8)C2×D318yescomplemented
101C3×#135—28no—
102C2×C3×M16C2×D314yes—
103#949—316no—
104#949—68no—
105#949—68no—
106#949—68no—
107#948—316no—
108#948—68no—
109C2×#215—38no—
110C2×#215—64no—
111C2×#213—38no—
112C2×#213—64no—
113C2×#208—34no—
114C2×#208—34no—
115C2×#208—34no—
116C2×#208—68no—
117#836—38no—
118#833—38no—
119#823—316no—
120#822—316no—
121C23×C32—21no—
122C23×C32—21no—
123C23×C32#4111yescharacteristic
124C22×C3⋊D3—22no—
125C22×C3⋊D3—41no—
126C22×C3⋊D3—41no—
127C22×C3⋊D3—82no—
128C32×Q8—21no—
129C32×Q8—21no—
130C32×Q8—21no—
131C32×Q8C2×D412yes—
132C32×D4—22no—
133C32×D4—22no—
134C32×D4—21no—
135C32×D4—21no—
136C32×D4—21no—
137C32×D4—41no—
138C32×D4—41no—
139C32×D4C2×D412yes—
140C2×C32×C4—21no—
141C2×C32×C4—22no—
142C2×C32×C4—22no—
143C2×C32×C4—21no—
144C2×C32×C4—41no—
145C2×C32×C4—41no—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4#4111yescharacteristic
151C2×C32×C4C2411yescharacteristic
152C4⋊(C3⋊D3)—22no—
153C4⋊(C3⋊D3)—22no—
154C4⋊(C3⋊D3)—41no—
155C4⋊(C3⋊D3)—41no—
156C32×C8—22no—
157C3⋊(C3⋊C8)—22no—
158C3⋊(C3⋊C8)—22no—
159C3⋊(C3⋊C8)C2×D414yes—
160#575C3⋊D311yescharacteristic, complemented
161C2×AGL(1,ℤ/8)—91no—
162C2×AGL(1,ℤ/8)—91no—
163#568—91no—
164#472—94no—
165#471—94no—
166#430—91no—
167#413—91no—
168C2×#100—91no—
169C23×D3—64no—
170C3×#41—24no—
171C3×#41—24no—
172C3×#41—24no—
173C3×#41—24no—
174C3×#41—24no—
175C3×#41—24no—
176C3×#41#6718yes—
177C3×#41C22×D318yes—
178C2×C3×Q8#6714yes—
179C2×C3×Q8C22×D314yes—
180C2×C3×D4—24no—
181C2×C3×D4—24no—
182C2×C3×D4#6714yes—
183C2×C3×D4C22×D314yes—
184C22×C3×C4—24no—
185C22×C3×C4—24no—
186C22×C3×C4C22×D314yes—
187C2×D12—38no—
188C2×D12—64no—
189C2×D12—64no—
190C2×D12—64no—
191C2×D12—64no—
192C2×D12—64no—
193C3×Q16—28no—
194C3×SD16—28no—
195C3×SD16—28no—
196C3×D8—28no—
197C3×M16—24no—
198C3×M16C22×D318yes—
199C2×C3×C8—24no—
200#215—616no—
201#215—616no—
202#213—616no—
203#213—616no—
204#208—38no—
205#208—38no—
206#208—38no—
207#208—38no—
208#208—616no—
209#208—64no—
210#208—64no—
211C2×C3⋊C8—38no—
212C2×C3⋊C8—616no—
213C2×C3⋊C8—64no—
214C2×C3⋊C8—64no—
215C22×C32—22no—
216C22×C32—41no—
217C22×C32—41no—
218C22×C32—81no—
219C22×C32—81no—
220C22×C32#12111yescharacteristic
221C22×C32#12111yescharacteristic
222C22×C32C2×#4111yescharacteristic
223C2×C3⋊D3—42no—
224C2×C3⋊D3—82no—
225C2×C3⋊D3—82no—
226C2×C3⋊D3—82no—
227C32×C4—22no—
228C32×C4—41no—
229C32×C4#12111yescharacteristic
230C32×C4#12111yescharacteristic
231C32×C4C22×D411yescharacteristic
232C32×C4C22×D411yescharacteristic
233C2×#41C2×C3⋊D311yescharacteristic
234C2×#41C2×C3⋊D311yescharacteristic
235C22×D4—91no—
236#137—21no—
237#137C2×C3⋊D312yescomplemented
238AGL(1,ℤ/8)—21no—
239AGL(1,ℤ/8)—94no—
240AGL(1,ℤ/8)—182no—
241AGL(1,ℤ/8)—182no—
242AGL(1,ℤ/8)—182no—
243AGL(1,ℤ/8)C2×C3⋊D312yescomplemented
244#135—22no—
245C2×SD16—92no—
246C2×SD16—181no—
247C2×D8—92no—
248C2×D8—181no—
249#131—94no—
250#131—182no—
251C2×M16—91no—
252C2×M16—91no—
253C2×M16—91no—
254C2×M16—182no—
255C2×M16C2×C3⋊D311yescharacteristic
256#108—94no—
257#101—92no—
258#100—92no—
259#100—94no—
260C23×C3—24no—
261C23×C3—24no—
262C23×C3#23714yes—
263C22×D3—68no—
264C22×D3—124no—
265C22×D3—124no—
266C22×D3—248no—
267C3×Q8—24no—
268C3×Q8—24no—
269C3×Q8—24no—
270C3×Q8C2×#6718yes—
271C3×D4—28no—
272C3×D4—28no—
273C3×D4—24no—
274C3×D4—24no—
275C3×D4—24no—
276C3×D4—44no—
277C3×D4—44no—
278C3×D4C2×#6718yes—
279C2×C3×C4—24no—
280C2×C3×C4—28no—
281C2×C3×C4—28no—
282C2×C3×C4—24no—
283C2×C3×C4—44no—
284C2×C3×C4—44no—
285C2×C3×C4D3×D414yes—
286C2×C3×C4D3×D414yes—
287C2×C3×C4#23714yes—
288C2×C3×C4C2×#6714yes—
289C2×C3×C4C2×#6714yes—
290C2×C3×C4C23×D314yes—
291D12—68no—
292D12—68no—
293D12—124no—
294D12—124no—
295C3×C8—28no—
296C3⋊C8—316no—
297C3⋊C8—68no—
298C3⋊C8—68no—
299C2×C32—21no—
300C2×C32—21no—
301C2×C32—21no—
302C2×C32—42no—
303C2×C32—81no—
304C2×C32C2×#12111yescharacteristic
305C3⋊D3—82no—
306C24—181no—
307#41—21no—
308#41—21no—
309#41—21no—
310#41—21no—
311#41—21no—
312#41—21no—
313#41#63812yes—
314#41C22×C3⋊D312yes—
315C2×Q8#63811yescharacteristic
316C2×Q8C22×C3⋊D311yescharacteristic
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—92no—
320C2×D4—181no—
321C2×D4—181no—
322C2×D4—181no—
323C2×D4—181no—
324C2×D4—181no—
325C2×D4#63811yescharacteristic
326C2×D4C22×C3⋊D311yescharacteristic
327C22×C4—21no—
328C22×C4—21no—
329C22×C4C22×C3⋊D311yescharacteristic
330Q16—22no—
331SD16—22no—
332SD16—22no—
333SD16—184no—
334SD16—184no—
335D8—22no—
336D8—184no—
337D8—184no—
338M16—21no—
339M16—92no—
340M16—92no—
341M16—92no—
342M16—92no—
343M16—184no—
344M16—181no—
345M16—181no—
346M16C22×C3⋊D312yes—
347C2×C8—21no—
348C2×C8—92no—
349C2×C8—184no—
350C2×C8—181no—
351C2×C8—181no—
352C22×C3—28no—
353C22×C3—44no—
354C22×C3—44no—
355C22×C3—84no—
356C22×C3—84no—
357C22×C3#93914yes—
358C22×C3#93914yes—
359C22×C3C2×#23714yes—
360C2×D3—128no—
361C2×D3—248no—
362C2×D3—248no—
363C2×D3—248no—
364C3×C4—28no—
365C3×C4—44no—
366C3×C4#93914yes—
367C3×C4#93914yes—
368C3×C4C2×D3×D414yes—
369C3×C4C22×#6714yes—
370C32#306811yescharacteristic, complemented, Sylow
371C23—21no—
372C23—21no—
373C23—182no—
374C23—361no—
375C23—361no—
376C23—722no—
377C23#383011yescharacteristic
378Q8—21no—
379Q8—21no—
380Q8—21no—
381Q8C2×#63812yes—
382D4—22no—
383D4—22no—
384D4—21no—
385D4—21no—
386D4—21no—
387D4—41no—
388D4—41no—
389D4—182no—
390D4—182no—
391D4—361no—
392D4—361no—
393D4C2×#63812yes—
394C2×C4—21no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4D4×C3⋊D311yescharacteristic
401C2×C4D4×C3⋊D311yescharacteristic
402C2×C4#383011yescharacteristic
403C2×C4C2×#63811yescharacteristic
404C2×C4C2×#63811yescharacteristic
405C2×C4C23×C3⋊D311yescharacteristic
406C8—22no—
407C8—94no—
408C8—182no—
409C8—182no—
410C2×C3—24no—
411C2×C3—24no—
412C2×C3—24no—
413C2×C3—48no—
414C2×C3—84no—
415C2×C3C2×#93914yes—
416D3—248no—
417C22—22no—
418C22—41no—
419C22—41no—
420C22—81no—
421C22—81no—
422C22—362no—
423C22—722no—
424C22—722no—
425C22—722no—
426C22#6414811yescharacteristic
427C22#6414811yescharacteristic
428C22C2×#383011yescharacteristic
429C4—22no—
430C4—41no—
431C4#6414811yescharacteristic
432C4#6414811yescharacteristic
433C4C2×D4×C3⋊D311yescharacteristic
434C4C22×#63811yescharacteristic
435C3#8400214yescomplemented
436C2—21no—
437C2—21no—
438C2—21no—
439C2—42no—
440C2—81no—
441C2—722no—
442C2C2×#6414811yescharacteristic
subgroupG/H
centerC2C2×#64148
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#575C2
socleC2×C32C2×#121
hypercenter#575C3⋊D3
hypocenterC32#3068
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. C32×#575C2semidirect
2. C2×#64158C2semidirect
3. C2×#64158C2semidirect
4. #10596290C2semidirect
5. #10592936C2semidirect
6. #10592902C2semidirect
7. #10592898C2semidirect
8. C2×#63650C2semidirect
9. #10592823C2semidirect
15. C32×#137C22semidirect
17. C32×AGL(1,ℤ/8)C22semidirect
25. #64157C22semidirect
27. C2×#3755C22semidirect
29. C2×#3753C22semidirect
34. #63663C22semidirect
35. #63660C22semidirect
36. #63650C22semidirect
37. #63649C22semidirect
38. C3×#575D3semidirect
98. C3×#137C2×D3semidirect
100. C3×AGL(1,ℤ/8)C2×D3semidirect
160. #575C3⋊D3semidirect
237. #137C2×C3⋊D3semidirect
243. AGL(1,ℤ/8)C2×C3⋊D3semidirect
370. C32#3068semidirect
435. C3#84002semidirect

Maximal subgroups

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

subgroupindex
C32×#5752
C2×#641582
#105962902
#105929362
#105929022
#105928982
C2×#636502
#105928232
#840023