Finite Group Databasebeta

← #11868095

Subgroups — #11868095

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
1#10596293C211yesmaximal, characteristic, complemented
2C2×#64158C211yesmaximal, characteristic, complemented
3C2×#64117C211yesmaximal, characteristic, complemented
4#10596216C211yesmaximal, characteristic, complemented
5C32×#413C211yesmaximal, characteristic, complemented
6C2×#63650C211yesmaximal, characteristic, complemented
7#10592823C211yesmaximal, characteristic, complemented
8#10592453C214yesmaximal, complemented
9#10592448C214yesmaximal, complemented
10#78720—34nomaximal
11C2×C32×#41C2211yescharacteristic
12C2×#3828C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16#64160—21no—
17#64159—22no—
18#64158—21no—
19#64158—22no—
20#64158—22no—
21#64151C2212yescomplemented
22C2×#3755C2212yescomplemented
23#64141C2212yescomplemented
24C2×#3753C2212yescomplemented
25C2×#3748C2211yescharacteristic
26C2×#3748C2211yescharacteristic
27#64117—22no—
28#64117C2214yes—
29#64116C2214yescomplemented
30M16×C3⋊D3—22no—
31C2×#3745—21no—
32C2×#3744—21no—
33#64110—22no—
34C32×#101C2212yescomplemented
35C32×#100C2212yescomplemented
36#63650C2214yescomplemented
37#63649C2214yescomplemented
38#5822—34no—
39C2×#949—34no—
40C2×#908—34no—
41#5745—34no—
42C3×#413D314yescomplemented
43C2×#823—34no—
44#5124—34no—
45#4754—316no—
46#4749—316no—
47C23×C3⋊D3—21no—
48C32×#41—21no—
49C32×#41—21no—
50C32×#41—21no—
51C32×#41—21no—
52C2×C32×Q8C2311yescharacteristic
53C2×C32×D4—21no—
54C2×C32×D4C2311yescharacteristic
55C22×C32×C4—21no—
56C22×C32×C4C2311yescharacteristic
57C2×#638—21no—
58#3828—21no—
59#3828—21no—
60#3828D412yes—
61#3828C2312yes—
62C2×C4⋊(C3⋊D3)—21no—
63C2×C4⋊(C3⋊D3)—21no—
64C2×C4⋊(C3⋊D3)—21no—
65C2×C4⋊(C3⋊D3)—21no—
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)D411yescharacteristic
68C2×C4⋊(C3⋊D3)C2312yes—
69C2×C4×C3⋊D3—21no—
70C2×#634D411yescharacteristic
71C32×M16—21no—
72C32×M16—21no—
73C32×M16C2312yes—
74C32×M16C2312yes—
75C2×C32×C8—21no—
76C2×C32×C8—21no—
77#3756—22no—
78#3755—22no—
79#3755—24no—
80#3754—22no—
81#3753—22no—
82#3753—24no—
83#3748—21no—
84#3748D412yes—
85#3748D412yes—
86#3748C2312yes—
87C2×C3⋊(C3⋊C8)—21no—
88C2×C3⋊(C3⋊C8)C2312yes—
89#3745—24no—
90#3744—24no—
91#3743—24no—
92C8×C3⋊D3—24no—
93#3068—91noSylow
94C2×C3×#41C2×D314yes—
95C2×#235—34no—
96C22×D12—34no—
97C2×C3×M16C2×D314yes—
98C2×C3×M16C2×D314yes—
99#951—64no—
100#950—68no—
101#949—68no—
102#949—68no—
103#949—64no—
104#942—38no—
105C2×#215—38no—
106#932—38no—
107C2×#213—38no—
108C2×#208—34no—
109C2×#208—34no—
110#908—316no—
111#908—68no—
112#907—316no—
113D3×M16—68no—
114C2×D24—64no—
115C2×#204—64no—
116#901—68no—
117C3×#101C2×D318yescomplemented
118C3×#100C2×D318yescomplemented
119#823—316no—
120#822—316no—
121C23×C32—21no—
122C23×C32#4111yescharacteristic
123C22×C3⋊D3—21no—
124C22×C3⋊D3—22no—
125C22×C3⋊D3—41no—
126C22×C3⋊D3—41no—
127C22×C3⋊D3—82no—
128C32×Q8—21no—
129C32×Q8—21no—
130C32×D4—21no—
131C32×D4—21no—
132C32×D4—41no—
133C32×D4—41no—
134C2×C32×C4—21no—
135C2×C32×C4—41no—
136C2×C32×C4—41no—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C32×C4C2411yescharacteristic
143#638—22no—
144#638—22no—
145C2×C3⋊Dic3—21no—
146C4⋊(C3⋊D3)—21no—
147C4⋊(C3⋊D3)—22no—
148C4⋊(C3⋊D3)—22no—
149C4⋊(C3⋊D3)—41no—
150C4⋊(C3⋊D3)—41no—
151C4⋊(C3⋊D3)C2×D412yes—
152C4×C3⋊D3—22no—
153C4×C3⋊D3—22no—
154#634—21no—
155#634C2×D412yes—
156C32×C8—22no—
157C32×C8—22no—
158C3⋊(C3⋊C8)—22no—
159C3⋊(C3⋊C8)C2×D414yes—
160#575—91no—
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#413C3⋊D311yescharacteristic, complemented
168C2×#100—91no—
169C23×D3—64no—
170C3×#41—24no—
171C3×#41—24no—
172C3×#41—24no—
173C3×#41—24no—
174C2×C3×Q8C22×D314yes—
175C2×C3×D4—24no—
176C2×C3×D4C22×D314yes—
177C22×C3×C4—24no—
178C22×C3×C4C22×D314yes—
179C2×#67—64no—
180#235—38no—
181#235—38no—
182#235—64no—
183#235—64no—
184C2×D12—34no—
185C2×D12—38no—
186C2×D12—64no—
187C2×D12—64no—
188C2×D12—64no—
189C2×D12—64no—
190C2×D12—64no—
191C2×C4×D3—64no—
192C2×Dic6—34no—
193C3×M16—24no—
194C3×M16—24no—
195C3×M16C22×D318yes—
196C3×M16C22×D318yes—
197C2×C3×C8—24no—
198C2×C3×C8—24no—
199#216—68no—
200#215—616no—
201#215—68no—
202#214—68no—
203#213—616no—
204#213—68no—
205#208—38no—
206#208—38no—
207#208—38no—
208#208—64no—
209C2×C3⋊C8—38no—
210C2×C3⋊C8—64no—
211D24—616no—
212#204—616no—
213ΓL(1,𝔽25)—616no—
214D3×C8—616no—
215C22×C32—41no—
216C22×C32—41no—
217C22×C32—81no—
218C22×C32#12111yescharacteristic
219C22×C32#12111yescharacteristic
220C22×C32C2×#4111yescharacteristic
221C2×C3⋊D3—22no—
222C2×C3⋊D3—42no—
223C2×C3⋊D3—81no—
224C2×C3⋊D3—82no—
225C2×C3⋊D3—82no—
226C2×C3⋊D3—82no—
227C32×C4—41no—
228C32×C4#12111yescharacteristic
229C32×C4#12111yescharacteristic
230C32×C4C22×D411yescharacteristic
231C32×C4C22×D411yescharacteristic
232C3⋊Dic3—22no—
233C2×#41—91no—
234C2×#41C2×C3⋊D311yescharacteristic
235C22×D4—91no—
236#137—92no—
237#137—181no—
238AGL(1,ℤ/8)—92no—
239AGL(1,ℤ/8)—94no—
240AGL(1,ℤ/8)—182no—
241AGL(1,ℤ/8)—182no—
242AGL(1,ℤ/8)—182no—
243AGL(1,ℤ/8)—181no—
244#135—182no—
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—182no—
254C2×M16C2×C3⋊D311yescharacteristic
255C2×M16C2×C3⋊D311yescharacteristic
256#108—94no—
257#101C2×C3⋊D312yescomplemented
258#100—94no—
259#100C2×C3⋊D312yescomplemented
260C23×C3—24no—
261C23×C3#23514yes—
262C22×D3—64no—
263C22×D3—68no—
264C22×D3—124no—
265C22×D3—124no—
266C22×D3—248no—
267C3×Q8—24no—
268C3×Q8—24no—
269C3×D4—24no—
270C3×D4—24no—
271C3×D4—44no—
272C3×D4—44no—
273C2×C3×C4—24no—
274C2×C3×C4—44no—
275C2×C3×C4—44no—
276C2×C3×C4#23514yes—
277C2×C3×C4D3×D414yes—
278C2×C3×C4D3×D414yes—
279C2×C3×C4D3×D414yes—
280C2×C3×C4D3×D414yes—
281C2×C3×C4C23×D314yes—
282#67—68no—
283#67—68no—
284C2×Dic3—64no—
285D12—38no—
286D12—64no—
287D12—68no—
288D12—68no—
289D12—124no—
290D12—124no—
291C4×D3—68no—
292C4×D3—68no—
293Dic6—38no—
294Dic6—64no—
295C3×C8—28no—
296C3×C8—28no—
297C3⋊C8—316no—
298C3⋊C8—68no—
299C2×C32—21no—
300C2×C32—21no—
301C2×C32—21no—
302C2×C32—81no—
303C2×C32C2×#12111yescharacteristic
304C3⋊D3—42no—
305C3⋊D3—82no—
306C24—181no—
307#41—21no—
308#41—21no—
309#41—21no—
310#41—21no—
311#41—92no—
312#41—92no—
313#41—181no—
314#41—181no—
315C2×Q8—91no—
316C2×Q8C22×C3⋊D311yescharacteristic
317C2×D4—21no—
318C2×D4—92no—
319C2×D4—91no—
320C2×D4—181no—
321C2×D4—181no—
322C2×D4—181no—
323C2×D4—181no—
324C2×D4—181no—
325C2×D4—181no—
326C2×D4C22×C3⋊D311yescharacteristic
327C22×C4—21no—
328C22×C4—181no—
329C22×C4C22×C3⋊D311yescharacteristic
330Q16—182no—
331SD16—184no—
332SD16—184no—
333SD16—182no—
334SD16—182no—
335D8—184no—
336D8—184no—
337D8—182no—
338M16—21no—
339M16—21no—
340M16—92no—
341M16—92no—
342M16—92no—
343M16—184no—
344M16—181no—
345M16C22×C3⋊D312yes—
346M16C22×C3⋊D312yes—
347C2×C8—21no—
348C2×C8—21no—
349C2×C8—92no—
350C2×C8—184no—
351C2×C8—181no—
352C22×C3—44no—
353C22×C3—44no—
354C22×C3—84no—
355C22×C3#88414yes—
356C22×C3#88414yes—
357C22×C3C2×#23514yes—
358C2×D3—68no—
359C2×D3—128no—
360C2×D3—244no—
361C2×D3—248no—
362C2×D3—248no—
363C2×D3—248no—
364C3×C4—44no—
365C3×C4#88414yes—
366C3×C4#88414yes—
367C3×C4C2×D3×D414yes—
368C3×C4C2×D3×D414yes—
369Dic3—68no—
370C32#306811yescharacteristic, complemented, Sylow
371C23—21no—
372C23—181no—
373C23—182no—
374C23—361no—
375C23—361no—
376C23—722no—
377C23#382811yescharacteristic
378Q8—21no—
379Q8—21no—
380Q8—92no—
381Q8—181no—
382D4—21no—
383D4—21no—
384D4—41no—
385D4—41no—
386D4—92no—
387D4—182no—
388D4—182no—
389D4—181no—
390D4—182no—
391D4—182no—
392D4—361no—
393D4—361no—
394C2×C4—21no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—181no—
398C2×C4—182no—
399C2×C4—182no—
400C2×C4#382811yescharacteristic
401C2×C4D4×C3⋊D311yescharacteristic
402C2×C4D4×C3⋊D311yescharacteristic
403C2×C4D4×C3⋊D311yescharacteristic
404C2×C4D4×C3⋊D311yescharacteristic
405C2×C4C23×C3⋊D311yescharacteristic
406C8—22no—
407C8—22no—
408C8—94no—
409C8—182no—
410C2×C3—24no—
411C2×C3—24no—
412C2×C3—24no—
413C2×C3—84no—
414C2×C3C2×#88414yes—
415D3—128no—
416D3—248no—
417C22—41no—
418C22—41no—
419C22—81no—
420C22—182no—
421C22—362no—
422C22—721no—
423C22—722no—
424C22—722no—
425C22—722no—
426C22#6409311yescharacteristic
427C22#6409311yescharacteristic
428C22C2×#382811yescharacteristic
429C4—41no—
430C4—182no—
431C4#6409311yescharacteristic
432C4#6409311yescharacteristic
433C4C2×D4×C3⋊D311yescharacteristic
434C4C2×D4×C3⋊D311yescharacteristic
435C3#7872014yescomplemented
436C2—21no—
437C2—21no—
438C2—21no—
439C2—81no—
440C2—362no—
441C2—722no—
442C2C2×#6409311yescharacteristic
subgroupG/H
centerC2C2×#64093
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#413C2
socleC2×C32C2×#121
hypercenter#413C3⋊D3
hypocenterC32#3068
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
1. #10596293C2semidirect
2. C2×#64158C2semidirect
3. C2×#64117C2semidirect
4. #10596216C2semidirect
5. C32×#413C2semidirect
6. C2×#63650C2semidirect
7. #10592823C2semidirect
8. #10592453C2semidirect
9. #10592448C2semidirect
21. #64151C22semidirect
22. C2×#3755C22semidirect
23. #64141C22semidirect
24. C2×#3753C22semidirect
29. #64116C22semidirect
34. C32×#101C22semidirect
35. C32×#100C22semidirect
36. #63650C22semidirect
37. #63649C22semidirect
42. C3×#413D3semidirect
117. C3×#101C2×D3semidirect
118. C3×#100C2×D3semidirect
167. #413C3⋊D3semidirect
257. #101C2×C3⋊D3semidirect
259. #100C2×C3⋊D3semidirect
370. C32#3068semidirect
435. C3#78720semidirect

Maximal subgroups

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

subgroupindex
#105962932
C2×#641582
C2×#641172
#105962162
C32×#4132
C2×#636502
#105928232
#105924532
#105924482
#787203