Finite Group Databasebeta

← C2×#10592898 #11867911

Subgroups — C2×#10592898 #11867911

Order 1152.

1464 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C2×#64158C211yesmaximal, characteristic, complemented
3C2×#64157C211yesmaximal, characteristic, complemented
4C22×#3753C211yesmaximal, characteristic, complemented
5C2×#63660C211yesmaximal, characteristic, complemented
6#10592898C218yesmaximal, direct product factor
7C2×#63650C211yesmaximal, characteristic, complemented
8C2×#63649C211yesmaximal, characteristic, complemented
9C2×#5199—34nomaximal
10C2×C32×#41C2211yescharacteristic
11C22×C32×D4C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C32×AGL(1,ℤ/8)—22no—
14C32×AGL(1,ℤ/8)C2214yescomplemented
15C2×C32×SD16—21no—
16C2×C32×D8—21no—
17C2×C32×M16C2211yescharacteristic
18#64158—22no—
19#64158C2214yescomplemented
20#64157—22no—
21#64157C2214yescomplemented
22C2×#3755—21no—
23C2×#3753—21no—
24C2×#3753—21no—
25C2×#3753—21no—
26C2×#3753—22no—
27C2×#3753C2214yescomplemented
28C2×#3748—21no—
29C2×#3748C2211yescharacteristic
30C2×#3748C2211yescharacteristic
31C22×C3⋊(C3⋊C8)—21no—
32C22×C3⋊(C3⋊C8)C2211yescharacteristic
33#63660C2214yescomplemented
34#63650C2214yescomplemented
35#63649C2214yescomplemented
36C2×C3×AGL(1,ℤ/8)D314yescomplemented
37C2×#949—34no—
38C2×#948—34no—
39C22×#213—34no—
40C2×#833—34no—
41#5199—332no—
42C2×#823—34no—
43C2×#822—34no—
44C24×C32—21no—
45C23×C3⋊D3—21no—
46C32×#41—21no—
47C32×#41—21no—
48C32×#41D412yes—
49C32×#41C2312yes—
50C2×C32×Q8D411yescharacteristic
51C2×C32×D4—21no—
52C2×C32×D4—21no—
53C2×C32×D4—21no—
54C2×C32×D4—21no—
55C2×C32×D4—21no—
56C2×C32×D4—21no—
57C2×C32×D4D411yescharacteristic
58C2×C32×D4C2312yes—
59C22×C32×C4—21no—
60C22×C32×C4C2311yescharacteristic
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)—21no—
63C2×C4⋊(C3⋊D3)—21no—
64C2×C4⋊(C3⋊D3)—21no—
65C2×C4⋊(C3⋊D3)—21no—
66C2×C4⋊(C3⋊D3)C2312yes—
67C32×SD16—24no—
68C32×D8—24no—
69C32×M16—21no—
70C32×M16C2312yes—
71C2×C32×C8—21no—
72#3755—24no—
73#3753—24no—
74#3753—24no—
75#3753—24no—
76#3748—21no—
77#3748—21no—
78#3748—24no—
79#3748C2312yes—
80#3748C2312yes—
81C2×C3⋊(C3⋊C8)—21no—
82C2×C3⋊(C3⋊C8)—21no—
83C2×C3⋊(C3⋊C8)—24no—
84C2×C3⋊(C3⋊C8)D411yescharacteristic
85C2×C3⋊(C3⋊C8)D411yescharacteristic
86C2×C3⋊(C3⋊C8)D412yes—
87C2×C3⋊(C3⋊C8)C2312yes—
88C2×#472—91noSylow
89C2×C3×#41C2×D314yes—
90C22×C3×D4C2×D314yes—
91C22×D12—34no—
92C3×AGL(1,ℤ/8)—28no—
93C3×AGL(1,ℤ/8)C2×D3116yescomplemented
94C2×C3×SD16—24no—
95C2×C3×D8—24no—
96C2×C3×M16C2×D314yes—
97#949—316no—
98#949—68no—
99#948—316no—
100#948—68no—
101C2×#215—64no—
102C2×#213—316no—
103C2×#213—64no—
104C2×#213—64no—
105C2×#213—68no—
106C2×#213—64no—
107C2×#208—34no—
108C2×#208—34no—
109C2×#208—64no—
110C22×C3⋊C8—34no—
111C22×C3⋊C8—64no—
112#833—316no—
113#823—316no—
114#822—316no—
115C23×C32—21no—
116C23×C32—22no—
117C23×C32—41no—
118C23×C32—41no—
119C23×C32—82no—
120C23×C32#4111yescharacteristic
121C22×C3⋊D3—22no—
122C22×C3⋊D3—41no—
123C22×C3⋊D3—41no—
124C22×C3⋊D3—82no—
125C32×Q8—21no—
126C32×Q8C2×D412yes—
127C32×D4—22no—
128C32×D4—22no—
129C32×D4—21no—
130C32×D4—22no—
131C32×D4—22no—
132C32×D4—41no—
133C32×D4—41no—
134C32×D4C2×D412yes—
135C2×C32×C4—21no—
136C2×C32×C4—22no—
137C2×C32×C4—22no—
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C32×C4C2411yescharacteristic
144C4⋊(C3⋊D3)—22no—
145C4⋊(C3⋊D3)—22no—
146C4⋊(C3⋊D3)—41no—
147C4⋊(C3⋊D3)—41no—
148C32×C8—22no—
149C3⋊(C3⋊C8)—22no—
150C3⋊(C3⋊C8)—22no—
151C3⋊(C3⋊C8)C2×D412yes—
152C3⋊(C3⋊C8)C2×D412yes—
153C2×AGL(1,ℤ/8)—91no—
154C2×AGL(1,ℤ/8)C3⋊D311yescharacteristic, complemented
155C22×D8—91no—
156C2×#131—91no—
157#472—98no—
158C2×#108—91no—
159C2×#100—91no—
160C2×#100—91no—
161C24×C3—24no—
162C23×D3—64no—
163C3×#41—24no—
164C3×#41—24no—
165C3×#41#6718yes—
166C3×#41C22×D318yes—
167C2×C3×Q8#6714yes—
168C2×C3×D4—24no—
169C2×C3×D4—24no—
170C2×C3×D4—24no—
171C2×C3×D4—24no—
172C2×C3×D4—24no—
173C2×C3×D4—24no—
174C2×C3×D4#6714yes—
175C2×C3×D4C22×D318yes—
176C22×C3×C4—24no—
177C22×C3×C4C22×D314yes—
178C2×D12—38no—
179C2×D12—64no—
180C2×D12—64no—
181C2×D12—64no—
182C2×D12—64no—
183C2×D12—64no—
184C3×SD16—216no—
185C3×D8—216no—
186C3×M16—24no—
187C3×M16C22×D318yes—
188C2×C3×C8—24no—
189#215—616no—
190#213—616no—
191#213—616no—
192#213—616no—
193#208—38no—
194#208—38no—
195#208—616no—
196#208—64no—
197#208—64no—
198C2×C3⋊C8—34no—
199C2×C3⋊C8—34no—
200C2×C3⋊C8—38no—
201C2×C3⋊C8—38no—
202C2×C3⋊C8—616no—
203C2×C3⋊C8—64no—
204C2×C3⋊C8—64no—
205C22×C32—22no—
206C22×C32—22no—
207C22×C32—42no—
208C22×C32—42no—
209C22×C32—82no—
210C22×C32—82no—
211C22×C32—82no—
212C22×C32#12111yescharacteristic
213C22×C32#12111yescharacteristic
214C22×C32C2×#4111yescharacteristic
215C2×C3⋊D3—42no—
216C2×C3⋊D3—82no—
217C2×C3⋊D3—82no—
218C2×C3⋊D3—82no—
219C32×C4—22no—
220C32×C4#12111yescharacteristic
221C32×C4#12111yescharacteristic
222C32×C4C22×D411yescharacteristic
223C32×C4C22×D411yescharacteristic
224C2×#41C2×C3⋊D311yescharacteristic
225C22×D4—91no—
226C22×D4C2×C3⋊D311yescharacteristic
227AGL(1,ℤ/8)—22no—
228AGL(1,ℤ/8)—94no—
229AGL(1,ℤ/8)—182no—
230AGL(1,ℤ/8)C2×C3⋊D314yescomplemented
231C2×SD16—21no—
232C2×SD16—181no—
233C2×D8—21no—
234C2×D8—94no—
235C2×D8—181no—
236C2×D8—181no—
237C2×D8—182no—
238C2×D8—181no—
239#131—94no—
240#131—182no—
241C2×M16—91no—
242C2×M16—91no—
243C2×M16—181no—
244C2×M16C2×C3⋊D311yescharacteristic
245C22×C8—91no—
246C22×C8—181no—
247#108—94no—
248#100—94no—
249#100—94no—
250C23×C3—24no—
251C23×C3—28no—
252C23×C3—44no—
253C23×C3—44no—
254C23×C3—88no—
255C23×C3#23714yes—
256C22×D3—68no—
257C22×D3—124no—
258C22×D3—124no—
259C22×D3—248no—
260C3×Q8—24no—
261C3×Q8C2×#6718yes—
262C3×D4—28no—
263C3×D4—28no—
264C3×D4—24no—
265C3×D4—28no—
266C3×D4—28no—
267C3×D4—44no—
268C3×D4—44no—
269C3×D4C2×#6718yes—
270C2×C3×C4—24no—
271C2×C3×C4—28no—
272C2×C3×C4—28no—
273C2×C3×C4D3×D414yes—
274C2×C3×C4D3×D414yes—
275C2×C3×C4#23714yes—
276C2×C3×C4C2×#6714yes—
277C2×C3×C4C2×#6714yes—
278C2×C3×C4C23×D314yes—
279D12—68no—
280D12—68no—
281D12—124no—
282D12—124no—
283C3×C8—28no—
284C3⋊C8—38no—
285C3⋊C8—38no—
286C3⋊C8—68no—
287C3⋊C8—68no—
288C2×C32—21no—
289C2×C32—21no—
290C2×C32—42no—
291C2×C32—82no—
292C2×C32#47212yescomplemented
293C2×C32C2×#12111yescharacteristic
294C3⋊D3—82no—
295C24—21no—
296C24—181no—
297#41—21no—
298#41—21no—
299#41#63812yes—
300#41C22×C3⋊D312yes—
301C2×Q8#63811yescharacteristic
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—92no—
309C2×D4—181no—
310C2×D4—181no—
311C2×D4—181no—
312C2×D4—181no—
313C2×D4—181no—
314C2×D4#63811yescharacteristic
315C2×D4C22×C3⋊D312yes—
316C22×C4—21no—
317C22×C4C22×C3⋊D311yescharacteristic
318SD16—24no—
319SD16—184no—
320D8—24no—
321D8—184no—
322D8—184no—
323D8—184no—
324M16—21no—
325M16—92no—
326M16—92no—
327M16—184no—
328M16—181no—
329M16—181no—
330M16C22×C3⋊D312yes—
331C2×C8—21no—
332C2×C8—92no—
333C2×C8—91no—
334C2×C8—91no—
335C2×C8—92no—
336C2×C8—184no—
337C2×C8—181no—
338C2×C8—181no—
339C22×C3—28no—
340C22×C3—28no—
341C22×C3—48no—
342C22×C3—48no—
343C22×C3—88no—
344C22×C3—88no—
345C22×C3—88no—
346C22×C3#93914yes—
347C22×C3#93914yes—
348C22×C3C2×#23714yes—
349C2×D3—128no—
350C2×D3—248no—
351C2×D3—248no—
352C2×D3—248no—
353C3×C4—28no—
354C3×C4#93914yes—
355C3×C4#93914yes—
356C3×C4C2×D3×D414yes—
357C3×C4C22×#6714yes—
358C32C2×#47211yescharacteristic, complemented, Sylow
359C23—21no—
360C23—22no—
361C23—41no—
362C23—41no—
363C23—82no—
364C23—182no—
365C23—361no—
366C23—361no—
367C23—722no—
368C23#383011yescharacteristic
369Q8—21no—
370Q8C2×#63812yes—
371D4—22no—
372D4—22no—
373D4—22no—
374D4—22no—
375D4—21no—
376D4—41no—
377D4—41no—
378D4—182no—
379D4—182no—
380D4—361no—
381D4—361no—
382D4C2×#63812yes—
383C2×C4—21no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4D4×C3⋊D311yescharacteristic
387C2×C4D4×C3⋊D311yescharacteristic
388C2×C4#383011yescharacteristic
389C2×C4C2×#63811yescharacteristic
390C2×C4C2×#63811yescharacteristic
391C2×C4C23×C3⋊D311yescharacteristic
392C8—22no—
393C8—92no—
394C8—92no—
395C8—182no—
396C8—182no—
397C2×C3—24no—
398C2×C3—24no—
399C2×C3—48no—
400C2×C3—88no—
401C2×C3#519918yescomplemented
402C2×C3C2×#93914yes—
403D3—248no—
404C22—22no—
405C22—22no—
406C22—42no—
407C22—42no—
408C22—82no—
409C22—82no—
410C22—82no—
411C22—362no—
412C22—722no—
413C22—722no—
414C22—722no—
415C22#6414811yescharacteristic
416C22#6414811yescharacteristic
417C22C2×#383011yescharacteristic
418C4—22no—
419C4#6414811yescharacteristic
420C4#6414811yescharacteristic
421C4C2×D4×C3⋊D311yescharacteristic
422C4C22×#63811yescharacteristic
423C3C2×#519914yescomplemented
424C2—21no—
425C2—21no—
426C2—42no—
427C2—82no—
428C2—722no—
429C2#1059289812yesdirect product factor
430C2C2×#6414811yescharacteristic
subgroupG/H
centerC22#64148
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×AGL(1,ℤ/8)C2
socleC22×C32#121
hypercenterC2×AGL(1,ℤ/8)C3⋊D3
hypocenterC32C2×#472
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×C32×AGL(1,ℤ/8)C2semidirect
2. C2×#64158C2semidirect
3. C2×#64157C2semidirect
4. C22×#3753C2semidirect
5. C2×#63660C2semidirect
6. #10592898C2direct (N × H)
7. C2×#63650C2semidirect
8. C2×#63649C2semidirect
14. C32×AGL(1,ℤ/8)C22semidirect
19. #64158C22semidirect
21. #64157C22semidirect
27. C2×#3753C22semidirect
33. #63660C22semidirect
34. #63650C22semidirect
35. #63649C22semidirect
36. C2×C3×AGL(1,ℤ/8)D3semidirect
93. C3×AGL(1,ℤ/8)C2×D3semidirect
154. C2×AGL(1,ℤ/8)C3⋊D3semidirect
230. AGL(1,ℤ/8)C2×C3⋊D3semidirect
292. C2×C32#472semidirect
358. C32C2×#472semidirect
401. C2×C3#5199semidirect
423. C3C2×#5199semidirect
429. C2#10592898direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×AGL(1,ℤ/8)2
C2×#641582
C2×#641572
C22×#37532
C2×#636602
#105928982
C2×#636502
C2×#636492
C2×#51993