Finite Group Databasebeta

← #11868017

Subgroups — #11868017

Order 1152.

1356 conjugacy classes of subgroups.

The subgroup lattice has 399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596219C212yesmaximal, complemented
2C2×#64113C211yesmaximal, characteristic, complemented
3C2×#64110C211yesmaximal, characteristic, complemented
4C2×C32×#108C211yesmaximal, characteristic, complemented
5#10592831C212yesmaximal, complemented
6#10592597C214yesmaximal, complemented
7#10592596C212yesmaximal, complemented
8#10592595C212yesmaximal, complemented
9#79256—34nomaximal
10C2×#3828C2211yescharacteristic
11C2×#3828C2212yes—
12C2×C32×M16C2212yes—
13C22×C32×C8C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15#64118—22no—
16#64118C2214yes—
17#64117—22no—
18#64117C2214yes—
19C2×#3746C2211yescharacteristic, complemented
20#64113—24no—
21#64113—21no—
22#64113—21no—
23#64113—21no—
24#64113—21no—
25C2×#3745C2211yescharacteristic, complemented
26C2×#3744C2212yescomplemented
27#64110—21no—
28#64110—21no—
29#64110C2212yes—
30#64110C2212yes—
31C2×#3743—21no—
32C2×C8×C3⋊D3—21no—
33C32×#108C2212yescomplemented
34C32×#108C2212yescomplemented
35#63651C2214yescomplemented
36#63650C2214yescomplemented
37#5748—38no—
38C2×#904—34no—
39C2×#901—34no—
40C2×C3×#108D314yescomplemented
41#5132—38no—
42#4898—316no—
43#4897—38no—
44#4896—38no—
45C22×C32×C4C2311yescharacteristic
46C2×#638—21no—
47C2×#638—22no—
48#3828—21no—
49#3828—21no—
50#3828—22no—
51#3828—22no—
52#3828—22no—
53#3828—22no—
54#3828D412yes—
55#3828C2312yes—
56C2×C4⋊(C3⋊D3)D411yescharacteristic
57C2×C4⋊(C3⋊D3)C2312yes—
58C2×C4×C3⋊D3—21no—
59C2×C4×C3⋊D3—22no—
60C2×#634D411yescharacteristic
61C2×#634C2312yes—
62C32×M16—22no—
63C32×M16C2314yes—
64C2×C32×C8—22no—
65C2×C32×C8D411yescharacteristic
66C2×C32×C8D411yescharacteristic
67C2×C32×C8D411yescharacteristic
68C2×C32×C8D411yescharacteristic
69C2×C32×C8C2311yescharacteristic
70C2×C32×C8C2311yescharacteristic
71#3748—21no—
72#3748C2312yes—
73C2×C3⋊(C3⋊C8)—21no—
74#3746—24no—
75#3746—21no—
76#3746—21no—
77#3745—24no—
78#3745—21no—
79#3745—21no—
80#3744—24no—
81#3744—24no—
82#3744—22no—
83#3744—22no—
84#3743—22no—
85#3743—22no—
86C8×C3⋊D3—22no—
87C8×C3⋊D3—22no—
88#3067—91noSylow
89C2×#235—34no—
90C2×#235—38no—
91C2×C3×M16C2×D318yes—
92C22×C3×C8C2×D314yes—
93C2×#208—34no—
94#909—316no—
95#909—68no—
96#908—316no—
97#908—68no—
98C2×Dic12—34no—
99#904—616no—
100#904—64no—
101#904—64no—
102#904—64no—
103#904—64no—
104C2×D24—34no—
105C2×#204—38no—
106#901—38no—
107#901—38no—
108#901—64no—
109#901—64no—
110C2×ΓL(1,𝔽25)—64no—
111C2×D3×C8—64no—
112C3×#108C2×D318yescomplemented
113C3×#108C2×D318yescomplemented
114#824—316no—
115#823—316no—
116C23×C32#4111yescharacteristic
117C22×C3⋊D3—21no—
118C22×C3⋊D3—22no—
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C32×C4C2411yescharacteristic
125#638—22no—
126#638—22no—
127#638—42no—
128#638—42no—
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—22no—
131C4⋊(C3⋊D3)—21no—
132C4⋊(C3⋊D3)—22no—
133C4⋊(C3⋊D3)—22no—
134C4⋊(C3⋊D3)C2×D412yes—
135C4×C3⋊D3—22no—
136C4×C3⋊D3—22no—
137C4×C3⋊D3—42no—
138C4×C3⋊D3—42no—
139#634—21no—
140#634—22no—
141#634—22no—
142#634C2×D412yes—
143C32×C8—24no—
144C32×C8C2×D411yescharacteristic
145C32×C8C2×D411yescharacteristic
146C32×C8C2×D411yescharacteristic
147C32×C8C2×D411yescharacteristic
148C3⋊(C3⋊C8)—22no—
149#575—92no—
150C2×#135—91no—
151C2×#131—91no—
152#473—92no—
153#472—92no—
154#471—94no—
155C2×#108C3⋊D311yescharacteristic, complemented
156#413—92no—
157C22×C3×C4C22×D314yes—
158C2×#67—64no—
159C2×#67—68no—
160#235—38no—
161#235—38no—
162#235—64no—
163#235—64no—
164#235—68no—
165#235—68no—
166#235—68no—
167#235—68no—
168C2×D12—34no—
169C2×D12—38no—
170C2×C4×D3—64no—
171C2×C4×D3—68no—
172C2×Dic6—34no—
173C2×Dic6—38no—
174C3×M16—28no—
175C3×M16C22×D3116yes—
176C2×C3×C8—28no—
177C2×C3×C8D1214yes—
178C2×C3×C8D1214yes—
179C2×C3×C8D1214yes—
180C2×C3×C8D1214yes—
181C2×C3×C8C22×D314yes—
182C2×C3×C8C22×D314yes—
183#208—38no—
184#208—64no—
185C2×C3⋊C8—64no—
186Dic12—616no—
187Dic12—64no—
188Dic12—64no—
189D24—616no—
190D24—64no—
191D24—64no—
192#204—616no—
193#204—616no—
194#204—68no—
195#204—68no—
196ΓL(1,𝔽25)—68no—
197ΓL(1,𝔽25)—68no—
198D3×C8—68no—
199D3×C8—68no—
200C22×C32—41no—
201C22×C32#12111yescharacteristic
202C22×C32#12111yescharacteristic
203C22×C32C2×#4111yescharacteristic
204C2×C3⋊D3—22no—
205C2×C3⋊D3—42no—
206C2×C3⋊D3—42no—
207C2×C3⋊D3—82no—
208C32×C4#12111yescharacteristic
209C32×C4#12111yescharacteristic
210C32×C4C22×D411yescharacteristic
211C32×C4C22×D411yescharacteristic
212C3⋊Dic3—22no—
213C3⋊Dic3—42no—
214C2×#41—91no—
215C2×#41—92no—
216#137—94no—
217#137—182no—
218AGL(1,ℤ/8)—94no—
219AGL(1,ℤ/8)—182no—
220#135—184no—
221#135—181no—
222#135—181no—
223#135—181no—
224#135—181no—
225C2×Q16—91no—
226C2×SD16—92no—
227C2×D8—91no—
228#131—92no—
229#131—92no—
230#131—181no—
231#131—181no—
232C2×M16—91no—
233C2×M16—181no—
234C2×M16C2×C3⋊D312yes—
235C22×C8—181no—
236C22×C8C2×C3⋊D311yescharacteristic
237#108C2×C3⋊D312yescomplemented
238#108C2×C3⋊D312yescomplemented
239#101—94no—
240#100—94no—
241C23×C3#23914yes—
242C22×D3—64no—
243C22×D3—68no—
244C2×C3×C4C2×D1214yes—
245C2×C3×C4C2×D1214yes—
246C2×C3×C4D3×D414yes—
247C2×C3×C4D3×D414yes—
248C2×C3×C4#23914yes—
249C2×C3×C4C23×D314yes—
250#67—68no—
251#67—68no—
252#67—128no—
253#67—128no—
254C2×Dic3—64no—
255C2×Dic3—68no—
256D12—38no—
257D12—64no—
258D12—68no—
259D12—68no—
260C4×D3—68no—
261C4×D3—68no—
262C4×D3—128no—
263C4×D3—128no—
264Dic6—38no—
265Dic6—64no—
266Dic6—68no—
267Dic6—68no—
268C3×C8—216no—
269C3×C8C2×D1214yes—
270C3×C8C2×D1214yes—
271C3×C8C2×D1214yes—
272C3×C8C2×D1214yes—
273C3⋊C8—68no—
274C2×C32—21no—
275C2×C32—21no—
276C2×C32—21no—
277C2×C32C2×#12111yescharacteristic
278C3⋊D3—42no—
279C3⋊D3—82no—
280#41—92no—
281#41—92no—
282#41—181no—
283#41—181no—
284#41—182no—
285#41—182no—
286#41—182no—
287#41—182no—
288C2×Q8—92no—
289C2×Q8—91no—
290C2×D4—92no—
291C2×D4—91no—
292C2×D4—181no—
293C2×D4—182no—
294C22×C4—181no—
295C22×C4—182no—
296C22×C4C22×C3⋊D311yescharacteristic
297Q16—184no—
298Q16—181no—
299Q16—181no—
300SD16—184no—
301SD16—184no—
302SD16—182no—
303SD16—182no—
304D8—184no—
305D8—181no—
306D8—181no—
307M16—22no—
308M16—92no—
309M16—181no—
310M16—182no—
311M16—182no—
312M16C22×C3⋊D314yes—
313C2×C8—22no—
314C2×C8—181no—
315C2×C8—182no—
316C2×C8—182no—
317C2×C8C4⋊(C3⋊D3)11yescharacteristic
318C2×C8C4⋊(C3⋊D3)11yescharacteristic
319C2×C8C4⋊(C3⋊D3)11yescharacteristic
320C2×C8C4⋊(C3⋊D3)11yescharacteristic
321C2×C8C22×C3⋊D311yescharacteristic
322C2×C8C22×C3⋊D311yescharacteristic
323C22×C3—44no—
324C22×C3#89514yes—
325C22×C3#89514yes—
326C22×C3C2×#23914yes—
327C2×D3—68no—
328C2×D3—128no—
329C2×D3—128no—
330C2×D3—248no—
331C3×C4#89514yes—
332C3×C4#89514yes—
333C3×C4C22×D1214yes—
334C3×C4C2×D3×D414yes—
335Dic3—68no—
336Dic3—128no—
337C32#306711yescharacteristic, complemented, Sylow
338C23—181no—
339C23—182no—
340C23#383211yescharacteristic
341Q8—92no—
342Q8—181no—
343Q8—182no—
344Q8—182no—
345D4—92no—
346D4—182no—
347D4—182no—
348D4—182no—
349D4—182no—
350D4—181no—
351D4—362no—
352D4—362no—
353C2×C4—181no—
354C2×C4—182no—
355C2×C4—182no—
356C2×C4—182no—
357C2×C4—362no—
358C2×C4—362no—
359C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
360C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
361C2×C4D4×C3⋊D311yescharacteristic
362C2×C4D4×C3⋊D311yescharacteristic
363C2×C4#383211yescharacteristic
364C2×C4C23×C3⋊D311yescharacteristic
365C8—24no—
366C8—182no—
367C8C2×C4⋊(C3⋊D3)11yescharacteristic
368C8C2×C4⋊(C3⋊D3)11yescharacteristic
369C8C2×C4⋊(C3⋊D3)11yescharacteristic
370C8C2×C4⋊(C3⋊D3)11yescharacteristic
371C2×C3—24no—
372C2×C3—24no—
373C2×C3—24no—
374C2×C3C2×#89514yes—
375D3—128no—
376D3—248no—
377C22—41no—
378C22—182no—
379C22—362no—
380C22—362no—
381C22—722no—
382C22#6410411yescharacteristic
383C22#6410411yescharacteristic
384C22C2×#383211yescharacteristic
385C4—182no—
386C4—362no—
387C4#6410411yescharacteristic
388C4#6410411yescharacteristic
389C4C22×C4⋊(C3⋊D3)11yescharacteristic
390C4C2×D4×C3⋊D311yescharacteristic
391C3#7925614yescomplemented
392C2—21no—
393C2—21no—
394C2—21no—
395C2—362no—
396C2—722no—
397C2C2×#6410411yescharacteristic
subgroupG/H
centerC4#64104
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#108C2
socleC2×C32C2×#121
hypercenterC2×#108C3⋊D3
hypocenterC32#3067
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#108

Complements

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

NH ≅ G/Ntype
1. #10596219C2semidirect
2. C2×#64113C2semidirect
3. C2×#64110C2semidirect
4. C2×C32×#108C2semidirect
5. #10592831C2semidirect
6. #10592597C2semidirect
7. #10592596C2semidirect
8. #10592595C2semidirect
19. C2×#3746C22semidirect
25. C2×#3745C22semidirect
26. C2×#3744C22semidirect
33. C32×#108C22semidirect
34. C32×#108C22semidirect
35. #63651C22semidirect
36. #63650C22semidirect
40. C2×C3×#108D3semidirect
112. C3×#108C2×D3semidirect
113. C3×#108C2×D3semidirect
155. C2×#108C3⋊D3semidirect
237. #108C2×C3⋊D3semidirect
238. #108C2×C3⋊D3semidirect
337. C32#3067semidirect
391. C3#79256semidirect

Maximal subgroups

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

subgroupindex
#105962192
C2×#641132
C2×#641102
C2×C32×#1082
#105928312
#105925972
#105925962
#105925952
#792563