Finite Group Databasebeta

← #11868154

Subgroups — #11868154

Order 1152.

1338 conjugacy classes of subgroups.

The subgroup lattice has 429 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#137C211yesmaximal, characteristic, complemented
2#10596293C211yesmaximal, characteristic
3#10596290C211yesmaximal, characteristic, complemented
4C2×#64151C211yesmaximal, characteristic, complemented
5C2×#63663C211yesmaximal, characteristic, complemented
6#10592903C214yesmaximal, complemented
7#10592902C214yesmaximal, complemented
8#10592831C211yesmaximal, characteristic, complemented
9#10592823C211yesmaximal, characteristic, complemented
10#83978—34nomaximal
11C2×C32×#41C2211yescharacteristic
12C22×C32×Q8C2211yescharacteristic
13C2×#3828C2211yescharacteristic
14C32×#137—22no—
15C32×#137C2214yes—
16C2×C32×Q16—21no—
17C2×C32×SD16—21no—
18C2×C32×M16C2211yescharacteristic
19#64160C2212yes—
20#64159—22no—
21#64158C2212yes—
22#64157—22no—
23#64157C2214yes—
24C2×#3756C2212yescomplemented
25#64151—21no—
26#64151—22no—
27#64151—22no—
28C2×#3755C2212yescomplemented
29#64141—21no—
30C2×#3748—22no—
31C2×#3748C2211yescharacteristic
32C2×#3748C2211yescharacteristic
33C2×#3748C2211yescharacteristic
34#63663C2214yescomplemented
35#63651C2212yescomplemented
36#63650C2212yescomplemented
37#63649C2214yescomplemented
38C2×C3×#137D314yescomplemented
39#5822—34no—
40#5819—34no—
41C2×#942—34no—
42C2×#836—34no—
43#5204—316no—
44#5203—316no—
45#5132—34no—
46#5124—34no—
47C32×#41—21no—
48C32×#41—21no—
49C32×#41D412yes—
50C32×#41C2312yes—
51C2×C32×Q8—21no—
52C2×C32×Q8—21no—
53C2×C32×Q8—21no—
54C2×C32×Q8—21no—
55C2×C32×Q8—21no—
56C2×C32×Q8D411yescharacteristic
57C2×C32×Q8C2312yes—
58C2×C32×D4—21no—
59C2×C32×D4D411yescharacteristic
60C22×C32×C4—21no—
61C22×C32×C4—21no—
62C22×C32×C4C2311yescharacteristic
63C2×#638—21no—
64#3828—21no—
65#3828—21no—
66#3828—21no—
67#3828—21no—
68C2×C4⋊(C3⋊D3)C2311yescharacteristic
69C2×C4×C3⋊D3—21no—
70C2×#634C2311yescharacteristic
71C32×Q16—24no—
72C32×SD16—24no—
73C32×M16—21no—
74C32×M16C2312yes—
75C2×C32×C8—21no—
76#3756—22no—
77#3756—24no—
78#3755—22no—
79#3755—24no—
80#3754—22no—
81#3753—22no—
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#3069—91noSylow
94C2×C3×#41C2×D314yes—
95C22×C3×Q8C2×D314yes—
96C2×#235—34no—
97C3×#137—28no—
98C3×#137C2×D3116yes—
99C2×C3×Q16—24no—
100C2×C3×SD16—24no—
101C2×C3×M16C2×D314yes—
102#951—38no—
103#950—68no—
104#949—38no—
105#948—316no—
106#948—68no—
107C2×#216—38no—
108#942—68no—
109#942—68no—
110#942—64no—
111C2×#215—38no—
112#932—64no—
113C2×#208—34no—
114C2×#208—34no—
115C2×#208—34no—
116C2×#208—68no—
117#836—316no—
118#824—38no—
119#823—38no—
120#822—316no—
121C23×C32—21no—
122C23×C32#4111yescharacteristic
123C22×C3⋊D3—21no—
124C32×Q8—21no—
125C32×Q8—22no—
126C32×Q8—22no—
127C32×Q8—41no—
128C32×Q8—41no—
129C32×Q8C2×D412yes—
130C32×D4—22no—
131C32×D4—22no—
132C32×D4—21no—
133C32×D4C2×D412yes—
134C2×C32×C4—21no—
135C2×C32×C4—22no—
136C2×C32×C4—22no—
137C2×C32×C4—22no—
138C2×C32×C4—41no—
139C2×C32×C4—41no—
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4#4111yescharacteristic
145C2×C32×C4C2411yescharacteristic
146#638—41no—
147#638—41no—
148C2×C3⋊Dic3—21no—
149C4⋊(C3⋊D3)—21no—
150C4⋊(C3⋊D3)—21no—
151C4×C3⋊D3—41no—
152C4×C3⋊D3—41no—
153#634—21no—
154#634—21no—
155C32×C8—22no—
156C3⋊(C3⋊C8)—22no—
157C3⋊(C3⋊C8)—22no—
158C3⋊(C3⋊C8)C2×D414yes—
159#575—91no—
160C2×#137—91no—
161C2×#137C3⋊D311yescharacteristic, complemented
162#568—91no—
163#473—94no—
164#471—94no—
165#430—91no—
166#413—91no—
167C2×#101—91no—
168C3×#41—24no—
169C3×#41—24no—
170C3×#41#6718yes—
171C3×#41C22×D318yes—
172C2×C3×Q8—24no—
173C2×C3×Q8—24no—
174C2×C3×Q8—24no—
175C2×C3×Q8—24no—
176C2×C3×Q8—24no—
177C2×C3×Q8#6714yes—
178C2×C3×Q8C22×D318yes—
179C2×C3×D4—24no—
180C2×C3×D4#6714yes—
181C22×C3×C4—24no—
182C22×C3×C4—24no—
183C22×C3×C4C22×D314yes—
184C2×#67—64no—
185#235—64no—
186#235—64no—
187#235—64no—
188#235—64no—
189C2×D12—34no—
190C2×C4×D3—64no—
191C2×Dic6—34no—
192C3×Q16—216no—
193C3×SD16—216no—
194C3×M16—24no—
195C3×M16C22×D318yes—
196C2×C3×C8—24no—
197#216—616no—
198#216—68no—
199#215—616no—
200#215—68no—
201#214—68no—
202#213—68no—
203#208—38no—
204#208—38no—
205#208—38no—
206#208—38no—
207#208—616no—
208#208—64no—
209#208—64no—
210C2×C3⋊C8—38no—
211C2×C3⋊C8—616no—
212C2×C3⋊C8—64no—
213C2×C3⋊C8—64no—
214C22×C32—22no—
215C22×C32—41no—
216C22×C32—81no—
217C22×C32#12111yescharacteristic
218C22×C32#12111yescharacteristic
219C22×C32C2×#4111yescharacteristic
220C2×C3⋊D3—41no—
221C2×C3⋊D3—81no—
222C32×C4—22no—
223C32×C4—42no—
224C32×C4#12111yescharacteristic
225C32×C4#12111yescharacteristic
226C32×C4C22×D411yescharacteristic
227C32×C4C22×D411yescharacteristic
228C3⋊Dic3—41no—
229C2×#41—91no—
230C2×#41C2×C3⋊D311yescharacteristic
231C22×Q8C2×C3⋊D311yescharacteristic
232#137—22no—
233#137—92no—
234#137—182no—
235#137—182no—
236#137—181no—
237#137C2×C3⋊D314yes—
238AGL(1,ℤ/8)—92no—
239AGL(1,ℤ/8)—181no—
240#135—182no—
241C2×Q16—21no—
242C2×Q16—92no—
243C2×SD16—21no—
244C2×SD16—92no—
245#131—94no—
246#131—182no—
247C2×M16—91no—
248C2×M16—91no—
249C2×M16—91no—
250C2×M16—182no—
251C2×M16C2×C3⋊D311yescharacteristic
252#108—94no—
253#101—94no—
254#101—92no—
255#100—92no—
256C23×C3—24no—
257C23×C3#23714yes—
258C22×D3—64no—
259C3×Q8—24no—
260C3×Q8—28no—
261C3×Q8—28no—
262C3×Q8—44no—
263C3×Q8—44no—
264C3×Q8C2×#6718yes—
265C3×D4—28no—
266C3×D4—28no—
267C3×D4—24no—
268C3×D4C2×#6718yes—
269C2×C3×C4—24no—
270C2×C3×C4—28no—
271C2×C3×C4—28no—
272C2×C3×C4—28no—
273C2×C3×C4—44no—
274C2×C3×C4—44no—
275C2×C3×C4D3×D414yes—
276C2×C3×C4D3×D414yes—
277C2×C3×C4#23714yes—
278C2×C3×C4C2×#6714yes—
279C2×C3×C4C2×#6714yes—
280C2×C3×C4C23×D314yes—
281#67—124no—
282#67—124no—
283C2×Dic3—64no—
284D12—64no—
285D12—64no—
286C4×D3—124no—
287C4×D3—124no—
288Dic6—64no—
289Dic6—64no—
290C3×C8—28no—
291C3⋊C8—316no—
292C3⋊C8—68no—
293C3⋊C8—68no—
294C2×C32—21no—
295C2×C32—21no—
296C2×C32—21no—
297C2×C32—42no—
298C2×C32C2×#12111yescharacteristic
299C3⋊D3—81no—
300#41—21no—
301#41—21no—
302#41—181no—
303#41—181no—
304#41—181no—
305#41—181no—
306#41#63812yes—
307#41C22×C3⋊D312yes—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—91no—
314C2×Q8#63811yescharacteristic
315C2×Q8C22×C3⋊D312yes—
316C2×D4—21no—
317C2×D4—91no—
318C2×D4—181no—
319C2×D4#63811yescharacteristic
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—181no—
323C22×C4C22×C3⋊D311yescharacteristic
324Q16—24no—
325Q16—184no—
326Q16—182no—
327SD16—24no—
328SD16—184no—
329SD16—182no—
330SD16—182no—
331D8—182no—
332M16—21no—
333M16—92no—
334M16—92no—
335M16—92no—
336M16—92no—
337M16—184no—
338M16—181no—
339M16—181no—
340M16C22×C3⋊D312yes—
341C2×C8—21no—
342C2×C8—92no—
343C2×C8—184no—
344C2×C8—181no—
345C2×C8—181no—
346C22×C3—28no—
347C22×C3—44no—
348C22×C3—84no—
349C22×C3#93914yes—
350C22×C3#93914yes—
351C22×C3C2×#23714yes—
352C2×D3—124no—
353C2×D3—244no—
354C3×C4—28no—
355C3×C4—48no—
356C3×C4#93914yes—
357C3×C4#93914yes—
358C3×C4C2×D3×D414yes—
359C3×C4C22×#6714yes—
360Dic3—124no—
361C32#306911yescharacteristic, complemented, Sylow
362C23—21no—
363C23—181no—
364C23#383011yescharacteristic
365Q8—21no—
366Q8—22no—
367Q8—22no—
368Q8—41no—
369Q8—41no—
370Q8—181no—
371Q8—181no—
372Q8C2×#63812yes—
373D4—22no—
374D4—22no—
375D4—21no—
376D4—181no—
377D4—181no—
378D4—361no—
379D4—361no—
380D4C2×#63812yes—
381C2×C4—21no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—181no—
388C2×C4—361no—
389C2×C4—361no—
390C2×C4D4×C3⋊D311yescharacteristic
391C2×C4D4×C3⋊D311yescharacteristic
392C2×C4#383011yescharacteristic
393C2×C4C2×#63811yescharacteristic
394C2×C4C2×#63811yescharacteristic
395C2×C4C23×C3⋊D311yescharacteristic
396C8—22no—
397C8—94no—
398C8—182no—
399C8—182no—
400C2×C3—24no—
401C2×C3—24no—
402C2×C3—24no—
403C2×C3—48no—
404C2×C3C2×#93914yes—
405D3—244no—
406C22—22no—
407C22—41no—
408C22—81no—
409C22—361no—
410C22—721no—
411C22#6414811yescharacteristic
412C22#6414811yescharacteristic
413C22C2×#383011yescharacteristic
414C4—22no—
415C4—42no—
416C4—361no—
417C4#6414811yescharacteristic
418C4#6414811yescharacteristic
419C4C2×D4×C3⋊D311yescharacteristic
420C4C22×#63811yescharacteristic
421C3#8397814yescomplemented
422C2—21no—
423C2—21no—
424C2—21no—
425C2—42no—
426C2—721no—
427C2C2×#6414811yescharacteristic
subgroupG/H
centerC2C2×#64148
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#137C2
socleC2×C32C2×#121
prime radical#10596293C2
hypercenterC2×#137C3⋊D3
hypocenterC32#3069
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×C32×#137C2semidirect
3. #10596290C2semidirect
4. C2×#64151C2semidirect
5. C2×#63663C2semidirect
6. #10592903C2semidirect
7. #10592902C2semidirect
8. #10592831C2semidirect
9. #10592823C2semidirect
24. C2×#3756C22semidirect
28. C2×#3755C22semidirect
34. #63663C22semidirect
35. #63651C22semidirect
36. #63650C22semidirect
37. #63649C22semidirect
38. C2×C3×#137D3semidirect
161. C2×#137C3⋊D3semidirect
361. C32#3069semidirect
421. C3#83978semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1372
#105962932
#105962902
C2×#641512
C2×#636632
#105929032
#105929022
#105928312
#105928232
#839783