Finite Group Databasebeta

← #11868160

Subgroups — #11868160

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×#64151C211yesmaximal, characteristic, complemented
2C2×#64151C211yesmaximal, characteristic, complemented
3#10596219C211yesmaximal, characteristic
4#10596216C211yesmaximal, characteristic, complemented
5C2×C32×#101C211yesmaximal, characteristic, complemented
6#10592831C211yesmaximal, characteristic, complemented
7#10592823C211yesmaximal, characteristic, complemented
8#10592454C214yesmaximal, complemented
9#10592453C214yesmaximal, complemented
10#78712—34nomaximal
11C22×C32×Q8C2211yescharacteristic
12C2×#3828C2211yescharacteristic
13C2×#3828C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16C2×#3756—21no—
17C2×#3756C2212yescomplemented
18#64151—22no—
19#64151—22no—
20#64151—22no—
21#64151C2214yes—
22C2×#3755—21no—
23C2×#3755C2212yescomplemented
24C2×#3748C2211yescharacteristic
25C2×#3748C2211yescharacteristic
26#64118—21no—
27#64118C2212yes—
28#64117—21no—
29#64117C2212yes—
30#64116C2214yes—
31M16×C3⋊D3—22no—
32#64113—22no—
33#64110—22no—
34C32×#101C2214yescomplemented
35#63651C2212yescomplemented
36#63650C2212yescomplemented
37#63649C2214yescomplemented
38C2×#942—34no—
39C2×#942—34no—
40#5748—34no—
41#5745—34no—
42C2×C3×#101D314yescomplemented
43#5132—34no—
44#5124—34no—
45#4755—316no—
46#4754—316no—
47C2×C32×Q8—21no—
48C2×C32×Q8—21no—
49C2×C32×Q8—21no—
50C2×C32×Q8—21no—
51C2×C32×Q8—21no—
52C2×C32×Q8C2312yes—
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C2×#638—21no—
56C2×#638—21no—
57#3828—21no—
58#3828—21no—
59#3828—21no—
60#3828—21no—
61#3828—21no—
62#3828—21no—
63#3828D412yes—
64#3828C2312yes—
65C2×C4⋊(C3⋊D3)D411yescharacteristic
66C2×C4⋊(C3⋊D3)C2311yescharacteristic
67C2×C4×C3⋊D3—21no—
68C2×C4×C3⋊D3—21no—
69C2×#634D411yescharacteristic
70C2×#634C2311yescharacteristic
71C32×M16—21no—
72C32×M16—21no—
73C32×M16C2312yes—
74C32×M16C2312yes—
75C2×C32×C8—21no—
76C2×C32×C8—21no—
77#3756—24no—
78#3756—24no—
79#3755—24no—
80#3755—24no—
81#3748—21no—
82#3748D412yes—
83#3748D412yes—
84#3748C2312yes—
85C2×C3⋊(C3⋊C8)—21no—
86C2×C3⋊(C3⋊C8)C2312yes—
87#3746—22no—
88#3745—22no—
89#3744—22no—
90#3744—22no—
91#3743—24no—
92C8×C3⋊D3—24no—
93#3069—91noSylow
94C22×C3×Q8C2×D314yes—
95C2×#235—34no—
96C2×#235—34no—
97C2×C3×M16C2×D314yes—
98C2×C3×M16C2×D314yes—
99C2×#216—38no—
100C2×#216—64no—
101#942—316no—
102#942—68no—
103#942—68no—
104#942—68no—
105C2×#215—38no—
106C2×#215—64no—
107C2×#208—34no—
108C2×#208—34no—
109#909—38no—
110#909—64no—
111#908—38no—
112#908—64no—
113#907—316no—
114D3×M16—68no—
115#904—68no—
116#901—68no—
117C3×#101C2×D3116yescomplemented
118#824—38no—
119#823—38no—
120#822—316no—
121C23×C32#4111yescharacteristic
122C22×C3⋊D3—21no—
123C22×C3⋊D3—21no—
124C32×Q8—22no—
125C32×Q8—22no—
126C32×Q8—41no—
127C32×Q8—41no—
128C2×C32×C4—22no—
129C2×C32×C4—41no—
130C2×C32×C4—41no—
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C32×C4C2411yescharacteristic
137#638—22no—
138#638—22no—
139#638—41no—
140#638—41no—
141C2×C3⋊Dic3—21no—
142C2×C3⋊Dic3—21no—
143C4⋊(C3⋊D3)—21no—
144C4⋊(C3⋊D3)—21no—
145C4⋊(C3⋊D3)—21no—
146C4⋊(C3⋊D3)C2×D412yes—
147C4×C3⋊D3—22no—
148C4×C3⋊D3—22no—
149C4×C3⋊D3—41no—
150C4×C3⋊D3—41no—
151#634—21no—
152#634—21no—
153#634—21no—
154#634C2×D412yes—
155C32×C8—22no—
156C32×C8—22no—
157C3⋊(C3⋊C8)—22no—
158C3⋊(C3⋊C8)C2×D414yes—
159#575—91no—
160C2×#137—91no—
161C2×#137—91no—
162#568—91no—
163#473—94no—
164#471—94no—
165#430—91no—
166#413—91no—
167C2×#101C3⋊D311yescharacteristic, complemented
168C2×C3×Q8—24no—
169C2×C3×Q8—24no—
170C2×C3×Q8—24no—
171C2×C3×Q8—24no—
172C2×C3×Q8—24no—
173C2×C3×Q8C22×D318yes—
174C22×C3×C4—24no—
175C22×C3×C4C22×D314yes—
176C2×#67—64no—
177C2×#67—64no—
178#235—38no—
179#235—38no—
180#235—64no—
181#235—64no—
182#235—64no—
183#235—64no—
184#235—64no—
185#235—64no—
186C2×D12—34no—
187C2×D12—34no—
188C2×C4×D3—64no—
189C2×C4×D3—64no—
190C2×Dic6—34no—
191C2×Dic6—34no—
192C3×M16—24no—
193C3×M16—24no—
194C3×M16C22×D318yes—
195C3×M16C22×D318yes—
196C2×C3×C8—24no—
197C2×C3×C8—24no—
198#216—616no—
199#216—616no—
200#215—616no—
201#215—616no—
202#208—38no—
203#208—38no—
204#208—38no—
205#208—64no—
206C2×C3⋊C8—38no—
207C2×C3⋊C8—64no—
208Dic12—68no—
209D24—68no—
210#204—68no—
211#204—68no—
212ΓL(1,𝔽25)—616no—
213D3×C8—616no—
214C22×C32—41no—
215C22×C32#12111yescharacteristic
216C22×C32#12111yescharacteristic
217C22×C32C2×#4111yescharacteristic
218C2×C3⋊D3—22no—
219C2×C3⋊D3—41no—
220C2×C3⋊D3—81no—
221C2×C3⋊D3—81no—
222C32×C4—42no—
223C32×C4#12111yescharacteristic
224C32×C4#12111yescharacteristic
225C32×C4C22×D411yescharacteristic
226C32×C4C22×D411yescharacteristic
227C3⋊Dic3—22no—
228C3⋊Dic3—41no—
229C2×#41—91no—
230C2×#41—91no—
231C22×Q8C2×C3⋊D311yescharacteristic
232#137—94no—
233#137—92no—
234#137—181no—
235#137—182no—
236#137—182no—
237#137—182no—
238AGL(1,ℤ/8)—92no—
239AGL(1,ℤ/8)—181no—
240#135—182no—
241C2×Q16—92no—
242C2×Q16—181no—
243C2×SD16—92no—
244C2×SD16—181no—
245#131—94no—
246#131—182no—
247C2×M16—91no—
248C2×M16—91no—
249C2×M16—182no—
250C2×M16C2×C3⋊D311yescharacteristic
251C2×M16C2×C3⋊D311yescharacteristic
252#108—94no—
253#101—92no—
254#101C2×C3⋊D314yescomplemented
255#100—92no—
256C23×C3#23514yes—
257C22×D3—64no—
258C22×D3—64no—
259C3×Q8—28no—
260C3×Q8—28no—
261C3×Q8—44no—
262C3×Q8—44no—
263C2×C3×C4—28no—
264C2×C3×C4—44no—
265C2×C3×C4—44no—
266C2×C3×C4#23514yes—
267C2×C3×C4D3×D414yes—
268C2×C3×C4D3×D414yes—
269C2×C3×C4D3×D414yes—
270C2×C3×C4D3×D414yes—
271C2×C3×C4C23×D314yes—
272#67—68no—
273#67—68no—
274#67—124no—
275#67—124no—
276C2×Dic3—64no—
277C2×Dic3—64no—
278D12—38no—
279D12—64no—
280D12—64no—
281D12—64no—
282C4×D3—68no—
283C4×D3—68no—
284C4×D3—124no—
285C4×D3—124no—
286Dic6—38no—
287Dic6—64no—
288Dic6—64no—
289Dic6—64no—
290C3×C8—28no—
291C3×C8—28no—
292C3⋊C8—316no—
293C3⋊C8—68no—
294C2×C32—21no—
295C2×C32—21no—
296C2×C32—21no—
297C2×C32C2×#12111yescharacteristic
298C3⋊D3—42no—
299C3⋊D3—81no—
300#41—92no—
301#41—92no—
302#41—181no—
303#41—181no—
304#41—181no—
305#41—181no—
306#41—181no—
307#41—181no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—91no—
314C2×Q8—91no—
315C2×Q8C22×C3⋊D312yes—
316C2×D4—91no—
317C2×D4—91no—
318C2×D4—181no—
319C2×D4—181no—
320C22×C4—21no—
321C22×C4—181no—
322C22×C4—181no—
323C22×C4C22×C3⋊D311yescharacteristic
324Q16—182no—
325Q16—184no—
326Q16—184no—
327SD16—182no—
328SD16—182no—
329SD16—184no—
330SD16—184no—
331D8—182no—
332M16—21no—
333M16—21no—
334M16—92no—
335M16—92no—
336M16—92no—
337M16—184no—
338M16—181no—
339M16C22×C3⋊D312yes—
340M16C22×C3⋊D312yes—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—92no—
344C2×C8—184no—
345C2×C8—181no—
346C22×C3—44no—
347C22×C3#88414yes—
348C22×C3#88414yes—
349C22×C3C2×#23514yes—
350C2×D3—68no—
351C2×D3—124no—
352C2×D3—244no—
353C2×D3—244no—
354C3×C4—48no—
355C3×C4#88414yes—
356C3×C4#88414yes—
357C3×C4C2×D3×D414yes—
358C3×C4C2×D3×D414yes—
359Dic3—68no—
360Dic3—124no—
361C32#306911yescharacteristic, complemented, Sylow
362C23—181no—
363C23—181no—
364C23#382811yescharacteristic
365Q8—22no—
366Q8—22no—
367Q8—41no—
368Q8—41no—
369Q8—92no—
370Q8—181no—
371Q8—181no—
372Q8—181no—
373D4—92no—
374D4—182no—
375D4—182no—
376D4—181no—
377D4—181no—
378D4—181no—
379D4—361no—
380D4—361no—
381C2×C4—22no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—181no—
385C2×C4—182no—
386C2×C4—182no—
387C2×C4—181no—
388C2×C4—361no—
389C2×C4—361no—
390C2×C4#382811yescharacteristic
391C2×C4D4×C3⋊D311yescharacteristic
392C2×C4D4×C3⋊D311yescharacteristic
393C2×C4D4×C3⋊D311yescharacteristic
394C2×C4D4×C3⋊D311yescharacteristic
395C2×C4C23×C3⋊D311yescharacteristic
396C8—22no—
397C8—22no—
398C8—94no—
399C8—182no—
400C2×C3—24no—
401C2×C3—24no—
402C2×C3—24no—
403C2×C3C2×#88414yes—
404D3—128no—
405D3—244no—
406C22—41no—
407C22—182no—
408C22—361no—
409C22—721no—
410C22—721no—
411C22#6409311yescharacteristic
412C22#6409311yescharacteristic
413C22C2×#382811yescharacteristic
414C4—42no—
415C4—182no—
416C4—361no—
417C4#6409311yescharacteristic
418C4#6409311yescharacteristic
419C4C2×D4×C3⋊D311yescharacteristic
420C4C2×D4×C3⋊D311yescharacteristic
421C3#7871214yescomplemented
422C2—21no—
423C2—21no—
424C2—21no—
425C2—362no—
426C2—721no—
427C2C2×#6409311yescharacteristic
subgroupG/H
centerC2C2×#64093
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#101C2
socleC2×C32C2×#121
prime radical#10596219C2
hypercenterC2×#101C3⋊D3
hypocenterC32#3069
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
1. C2×#64151C2semidirect
2. C2×#64151C2semidirect
4. #10596216C2semidirect
5. C2×C32×#101C2semidirect
6. #10592831C2semidirect
7. #10592823C2semidirect
8. #10592454C2semidirect
9. #10592453C2semidirect
17. C2×#3756C22semidirect
23. C2×#3755C22semidirect
34. C32×#101C22semidirect
35. #63651C22semidirect
36. #63650C22semidirect
37. #63649C22semidirect
42. C2×C3×#101D3semidirect
117. C3×#101C2×D3semidirect
167. C2×#101C3⋊D3semidirect
254. #101C2×C3⋊D3semidirect
361. C32#3069semidirect
421. C3#78712semidirect

Maximal subgroups

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

subgroupindex
C2×#641512
#105962192
#105962162
C2×C32×#1012
#105928312
#105928232
#105924542
#105924532
#787123