Finite Group Databasebeta

← C2×#10592448 #11867914

Subgroups — C2×#10592448 #11867914

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×#64141C211yesmaximal, characteristic, complemented
2C22×#3753C211yesmaximal, characteristic, complemented
3C2×#64117C211yesmaximal, characteristic, complemented
4C2×#64116C211yesmaximal, characteristic, complemented
5C2×C32×#100C211yesmaximal, characteristic, complemented
6C2×#63650C211yesmaximal, characteristic, complemented
7C2×#63649C211yesmaximal, characteristic, complemented
8#10592448C218yesmaximal, direct product factor
9C2×#4749—34nomaximal
10C22×C32×D4C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C2×#3754—21no—
16#64141—22no—
17#64141C2214yescomplemented
18C2×#3753—21no—
19C2×#3753—21no—
20C2×#3753—21no—
21C2×#3753—22no—
22C2×#3753C2214yescomplemented
23C2×#3748C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25#64117—22no—
26#64117C2214yescomplemented
27#64116—22no—
28#64116C2214yescomplemented
29C2×#3745—21no—
30C2×#3744—21no—
31C2×#3743—21no—
32C2×C8×C3⋊D3—21no—
33C32×#100C2214yescomplemented
34#63650C2214yescomplemented
35#63649C2214yescomplemented
36C2×#932—34no—
37C22×#213—34no—
38C2×#908—34no—
39C2×#907—34no—
40C2×C3×#100D314yescomplemented
41C2×#823—34no—
42C2×#822—34no—
43#4749—332no—
44C24×C32—21no—
45C23×C3⋊D3—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4—21no—
50C2×C32×D4—21no—
51C2×C32×D4C2312yes—
52C22×C32×C4C2311yescharacteristic
53C2×#638—21no—
54#3828—21no—
55#3828—21no—
56#3828D412yes—
57#3828C2312yes—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)—21no—
63C2×C4⋊(C3⋊D3)D411yescharacteristic
64C2×C4⋊(C3⋊D3)C2312yes—
65C2×C4×C3⋊D3—21no—
66C2×#634D411yescharacteristic
67C32×M16—21no—
68C32×M16—21no—
69C32×M16C2312yes—
70C32×M16C2312yes—
71C2×C32×C8—21no—
72C2×C32×C8—21no—
73#3754—24no—
74#3753—24no—
75#3753—24no—
76#3753—24no—
77#3748—21no—
78#3748C2312yes—
79C2×C3⋊(C3⋊C8)—21no—
80C2×C3⋊(C3⋊C8)D411yescharacteristic
81C2×C3⋊(C3⋊C8)D411yescharacteristic
82C2×C3⋊(C3⋊C8)D412yes—
83C2×C3⋊(C3⋊C8)C2312yes—
84#3745—24no—
85#3744—24no—
86#3743—24no—
87C8×C3⋊D3—24no—
88C2×#472—91noSylow
89C22×C3×D4C2×D314yes—
90C2×#235—34no—
91C22×D12—34no—
92C2×C3×M16C2×D314yes—
93C2×C3×M16C2×D314yes—
94C2×#214—64no—
95#932—316no—
96#932—68no—
97C2×#213—316no—
98C2×#213—64no—
99C2×#213—64no—
100C2×#213—68no—
101C2×#213—64no—
102C2×#208—34no—
103C22×C3⋊C8—34no—
104#908—316no—
105#908—68no—
106#907—316no—
107#907—68no—
108C2×D24—64no—
109C2×#204—64no—
110C2×ΓL(1,𝔽25)—64no—
111C2×D3×C8—64no—
112C3×#100C2×D3116yescomplemented
113#823—316no—
114#822—316no—
115C23×C32—22no—
116C23×C32—41no—
117C23×C32—41no—
118C23×C32—82no—
119C23×C32#4111yescharacteristic
120C22×C3⋊D3—21no—
121C22×C3⋊D3—22no—
122C22×C3⋊D3—41no—
123C22×C3⋊D3—41no—
124C22×C3⋊D3—82no—
125C32×D4—22no—
126C32×D4—22no—
127C32×D4—41no—
128C32×D4—41no—
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C2×C32×C4C2411yescharacteristic
135#638—22no—
136#638—22no—
137C2×C3⋊Dic3—21no—
138C4⋊(C3⋊D3)—21no—
139C4⋊(C3⋊D3)—22no—
140C4⋊(C3⋊D3)—22no—
141C4⋊(C3⋊D3)—41no—
142C4⋊(C3⋊D3)—41no—
143C4⋊(C3⋊D3)C2×D412yes—
144C4×C3⋊D3—22no—
145C4×C3⋊D3—22no—
146#634—21no—
147#634C2×D412yes—
148C32×C8—22no—
149C32×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)—91no—
155C22×D8—91no—
156C2×#131—91no—
157#472—98no—
158C2×#108—91no—
159C2×#100—91no—
160C2×#100C3⋊D311yescharacteristic, complemented
161C24×C3—24no—
162C23×D3—64no—
163C2×C3×D4—24no—
164C2×C3×D4—24no—
165C2×C3×D4—24no—
166C2×C3×D4—24no—
167C2×C3×D4—24no—
168C2×C3×D4C22×D318yes—
169C22×C3×C4C22×D314yes—
170C2×#67—64no—
171#235—38no—
172#235—38no—
173#235—64no—
174#235—64no—
175C2×D12—34no—
176C2×D12—38no—
177C2×D12—64no—
178C2×D12—64no—
179C2×D12—64no—
180C2×D12—64no—
181C2×D12—64no—
182C2×C4×D3—64no—
183C2×Dic6—34no—
184C3×M16—24no—
185C3×M16—24no—
186C3×M16C22×D318yes—
187C3×M16C22×D318yes—
188C2×C3×C8—24no—
189C2×C3×C8—24no—
190#214—616no—
191#213—616no—
192#213—616no—
193#213—616no—
194#208—38no—
195#208—64no—
196C2×C3⋊C8—34no—
197C2×C3⋊C8—34no—
198C2×C3⋊C8—38no—
199C2×C3⋊C8—38no—
200C2×C3⋊C8—64no—
201D24—616no—
202#204—616no—
203ΓL(1,𝔽25)—616no—
204D3×C8—616no—
205C22×C32—22no—
206C22×C32—42no—
207C22×C32—82no—
208C22×C32—82no—
209C22×C32—82no—
210C22×C32#12111yescharacteristic
211C22×C32#12111yescharacteristic
212C22×C32C2×#4111yescharacteristic
213C2×C3⋊D3—22no—
214C2×C3⋊D3—42no—
215C2×C3⋊D3—42no—
216C2×C3⋊D3—82no—
217C2×C3⋊D3—82no—
218C2×C3⋊D3—82no—
219C32×C4#12111yescharacteristic
220C32×C4#12111yescharacteristic
221C32×C4C22×D411yescharacteristic
222C32×C4C22×D411yescharacteristic
223C3⋊Dic3—22no—
224C2×#41—91no—
225C22×D4—91no—
226C22×D4C2×C3⋊D311yescharacteristic
227AGL(1,ℤ/8)—94no—
228AGL(1,ℤ/8)—94no—
229AGL(1,ℤ/8)—182no—
230AGL(1,ℤ/8)—182no—
231C2×SD16—181no—
232C2×SD16—181no—
233C2×D8—94no—
234C2×D8—181no—
235C2×D8—181no—
236C2×D8—181no—
237C2×D8—182no—
238C2×D8—181no—
239#131—94no—
240#131—182no—
241C2×M16—91no—
242C2×M16—181no—
243C2×M16C2×C3⋊D311yescharacteristic
244C2×M16C2×C3⋊D311yescharacteristic
245C22×C8—91no—
246C22×C8—181no—
247#108—94no—
248#100—94no—
249#100C2×C3⋊D314yescomplemented
250C23×C3—28no—
251C23×C3—44no—
252C23×C3—44no—
253C23×C3—88no—
254C23×C3#23514yes—
255C22×D3—64no—
256C22×D3—68no—
257C22×D3—124no—
258C22×D3—124no—
259C22×D3—248no—
260C3×D4—28no—
261C3×D4—28no—
262C3×D4—44no—
263C3×D4—44no—
264C2×C3×C4#23514yes—
265C2×C3×C4D3×D414yes—
266C2×C3×C4D3×D414yes—
267C2×C3×C4D3×D414yes—
268C2×C3×C4D3×D414yes—
269C2×C3×C4C23×D314yes—
270#67—68no—
271#67—68no—
272C2×Dic3—64no—
273D12—38no—
274D12—64no—
275D12—68no—
276D12—68no—
277D12—124no—
278D12—124no—
279C4×D3—68no—
280C4×D3—68no—
281Dic6—38no—
282Dic6—64no—
283C3×C8—28no—
284C3×C8—28no—
285C3⋊C8—38no—
286C3⋊C8—38no—
287C3⋊C8—68no—
288C2×C32—21no—
289C2×C32—21no—
290C2×C32—82no—
291C2×C32#47212yescomplemented
292C2×C32C2×#12111yescharacteristic
293C3⋊D3—42no—
294C3⋊D3—82no—
295C24—21no—
296C24—181no—
297#41—92no—
298#41—92no—
299#41—181no—
300#41—181no—
301C2×Q8—91no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—92no—
308C2×D4—91no—
309C2×D4—181no—
310C2×D4—181no—
311C2×D4—181no—
312C2×D4—181no—
313C2×D4—181no—
314C2×D4—181no—
315C2×D4C22×C3⋊D312yes—
316C22×C4—181no—
317C22×C4C22×C3⋊D311yescharacteristic
318SD16—184no—
319SD16—184no—
320D8—184no—
321D8—184no—
322D8—184no—
323D8—184no—
324M16—21no—
325M16—21no—
326M16—92no—
327M16—184no—
328M16—181no—
329M16C22×C3⋊D312yes—
330M16C22×C3⋊D312yes—
331C2×C8—21no—
332C2×C8—21no—
333C2×C8—92no—
334C2×C8—91no—
335C2×C8—91no—
336C2×C8—92no—
337C2×C8—184no—
338C2×C8—181no—
339C22×C3—28no—
340C22×C3—48no—
341C22×C3—88no—
342C22×C3—88no—
343C22×C3—88no—
344C22×C3#88414yes—
345C22×C3#88414yes—
346C22×C3C2×#23514yes—
347C2×D3—68no—
348C2×D3—128no—
349C2×D3—128no—
350C2×D3—248no—
351C2×D3—248no—
352C2×D3—248no—
353C3×C4#88414yes—
354C3×C4#88414yes—
355C3×C4C2×D3×D414yes—
356C3×C4C2×D3×D414yes—
357Dic3—68no—
358C32C2×#47211yescharacteristic, complemented, Sylow
359C23—22no—
360C23—41no—
361C23—41no—
362C23—82no—
363C23—181no—
364C23—182no—
365C23—361no—
366C23—361no—
367C23—722no—
368C23#382811yescharacteristic
369Q8—92no—
370Q8—181no—
371D4—22no—
372D4—22no—
373D4—41no—
374D4—41no—
375D4—92no—
376D4—182no—
377D4—182no—
378D4—181no—
379D4—182no—
380D4—182no—
381D4—361no—
382D4—361no—
383C2×C4—181no—
384C2×C4—182no—
385C2×C4—182no—
386C2×C4#382811yescharacteristic
387C2×C4D4×C3⋊D311yescharacteristic
388C2×C4D4×C3⋊D311yescharacteristic
389C2×C4D4×C3⋊D311yescharacteristic
390C2×C4D4×C3⋊D311yescharacteristic
391C2×C4C23×C3⋊D311yescharacteristic
392C8—22no—
393C8—22no—
394C8—92no—
395C8—92no—
396C8—182no—
397C2×C3—24no—
398C2×C3—24no—
399C2×C3—88no—
400C2×C3#474918yescomplemented
401C2×C3C2×#88414yes—
402D3—128no—
403D3—248no—
404C22—22no—
405C22—42no—
406C22—82no—
407C22—82no—
408C22—82no—
409C22—182no—
410C22—362no—
411C22—362no—
412C22—722no—
413C22—722no—
414C22—722no—
415C22#6409311yescharacteristic
416C22#6409311yescharacteristic
417C22C2×#382811yescharacteristic
418C4—182no—
419C4#6409311yescharacteristic
420C4#6409311yescharacteristic
421C4C2×D4×C3⋊D311yescharacteristic
422C4C2×D4×C3⋊D311yescharacteristic
423C3C2×#474914yescomplemented
424C2—21no—
425C2—21no—
426C2—82no—
427C2—362no—
428C2—722no—
429C2#1059244812yesdirect product factor
430C2C2×#6409311yescharacteristic
subgroupG/H
centerC22#64093
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#100C2
socleC22×C32#121
hypercenterC2×#100C3⋊D3
hypocenterC32C2×#472
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. C2×#64141C2semidirect
2. C22×#3753C2semidirect
3. C2×#64117C2semidirect
4. C2×#64116C2semidirect
5. C2×C32×#100C2semidirect
6. C2×#63650C2semidirect
7. C2×#63649C2semidirect
8. #10592448C2direct (N × H)
17. #64141C22semidirect
22. C2×#3753C22semidirect
26. #64117C22semidirect
28. #64116C22semidirect
33. C32×#100C22semidirect
34. #63650C22semidirect
35. #63649C22semidirect
40. C2×C3×#100D3semidirect
112. C3×#100C2×D3semidirect
160. C2×#100C3⋊D3semidirect
249. #100C2×C3⋊D3semidirect
291. C2×C32#472semidirect
358. C32C2×#472semidirect
400. C2×C3#4749semidirect
423. C3C2×#4749semidirect
429. C2#10592448direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641412
C22×#37532
C2×#641172
C2×#641162
C2×C32×#1002
C2×#636502
C2×#636492
#105924482
C2×#47493