Finite Group Databasebeta

← C2×#10592453 #11867861

Subgroups — C2×#10592453 #11867861

Order 1152.

1404 conjugacy classes of subgroups.

The subgroup lattice has 417 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64151C211yesmaximal, characteristic, complemented
2C22×#3755C211yesmaximal, characteristic, complemented
3C2×#64117C211yesmaximal, characteristic
4C2×#64116C211yesmaximal, characteristic, complemented
5C2×C32×#101C211yesmaximal, characteristic, complemented
6C2×#63650C211yesmaximal, characteristic, complemented
7C2×#63649C211yesmaximal, characteristic, complemented
8#10592453C218yesmaximal, direct product factor
9C2×#4754—34nomaximal
10C22×C32×Q8C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C2×#3756—21no—
16#64151—22no—
17#64151C2214yescomplemented
18C2×#3755—21no—
19C2×#3755—21no—
20C2×#3755—21no—
21C2×#3755—22no—
22C2×#3755C2214yescomplemented
23C2×#3748C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25#64117—22no—
26#64117C2214yes—
27#64116—22no—
28#64116C2214yescomplemented
29C2×#3745—21no—
30C2×#3744—21no—
31C2×#3743—21no—
32C2×C8×C3⋊D3—21no—
33C32×#101C2214yescomplemented
34#63650C2214yescomplemented
35#63649C2214yescomplemented
36C2×#942—34no—
37C22×#215—34no—
38C2×#908—34no—
39C2×#907—34no—
40C2×C3×#101D314yescomplemented
41C2×#823—34no—
42C2×#822—34no—
43#4754—332no—
44C23×C3⋊D3—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8—21no—
48C2×C32×Q8—21no—
49C2×C32×Q8—21no—
50C2×C32×Q8C2312yes—
51C22×C32×C4—21no—
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#3756—24no—
74#3755—24no—
75#3755—24no—
76#3755—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×#471—91noSylow
89C22×C3×Q8C2×D314yes—
90C2×#235—34no—
91C22×D12—34no—
92C2×C3×M16C2×D314yes—
93C2×C3×M16C2×D314yes—
94C2×#216—64no—
95#942—316no—
96#942—68no—
97C2×#215—316no—
98C2×#215—64no—
99C2×#215—64no—
100C2×#215—68no—
101C2×#215—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×#101C2×D3116yescomplemented
113#823—316no—
114#822—316no—
115C23×C32#4111yescharacteristic
116C22×C3⋊D3—21no—
117C22×C3⋊D3—22no—
118C22×C3⋊D3—41no—
119C22×C3⋊D3—41no—
120C22×C3⋊D3—82no—
121C32×Q8—22no—
122C32×Q8—22no—
123C32×Q8—41no—
124C32×Q8—41no—
125C2×C32×C4—22no—
126C2×C32×C4—41no—
127C2×C32×C4—41no—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C32×C4C2411yescharacteristic
134#638—22no—
135#638—22no—
136C2×C3⋊Dic3—21no—
137C4⋊(C3⋊D3)—21no—
138C4⋊(C3⋊D3)—22no—
139C4⋊(C3⋊D3)—22no—
140C4⋊(C3⋊D3)—41no—
141C4⋊(C3⋊D3)—41no—
142C4⋊(C3⋊D3)C2×D412yes—
143C4×C3⋊D3—22no—
144C4×C3⋊D3—22no—
145#634—21no—
146#634C2×D412yes—
147C32×C8—22no—
148C32×C8—22no—
149C3⋊(C3⋊C8)—22no—
150C3⋊(C3⋊C8)C2×D412yes—
151C3⋊(C3⋊C8)C2×D412yes—
152C2×#137—91no—
153C2×AGL(1,ℤ/8)—91no—
154C22×SD16—91no—
155C2×#131—91no—
156#471—98no—
157C2×#108—91no—
158C2×#101C3⋊D311yescharacteristic, complemented
159C2×#100—91no—
160C23×D3—64no—
161C2×C3×Q8—24no—
162C2×C3×Q8—24no—
163C2×C3×Q8—24no—
164C2×C3×Q8—24no—
165C2×C3×Q8—24no—
166C2×C3×Q8C22×D318yes—
167C22×C3×C4—24no—
168C22×C3×C4C22×D314yes—
169C2×#67—64no—
170#235—38no—
171#235—38no—
172#235—64no—
173#235—64no—
174C2×D12—34no—
175C2×D12—38no—
176C2×D12—64no—
177C2×D12—64no—
178C2×D12—64no—
179C2×D12—64no—
180C2×D12—64no—
181C2×C4×D3—64no—
182C2×Dic6—34no—
183C3×M16—24no—
184C3×M16—24no—
185C3×M16C22×D318yes—
186C3×M16C22×D318yes—
187C2×C3×C8—24no—
188C2×C3×C8—24no—
189#216—616no—
190#215—616no—
191#215—616no—
192#215—616no—
193#208—38no—
194#208—64no—
195C2×C3⋊C8—34no—
196C2×C3⋊C8—34no—
197C2×C3⋊C8—38no—
198C2×C3⋊C8—38no—
199C2×C3⋊C8—64no—
200D24—616no—
201#204—616no—
202ΓL(1,𝔽25)—616no—
203D3×C8—616no—
204C22×C32—22no—
205C22×C32#12111yescharacteristic
206C22×C32#12111yescharacteristic
207C22×C32C2×#4111yescharacteristic
208C2×C3⋊D3—22no—
209C2×C3⋊D3—42no—
210C2×C3⋊D3—42no—
211C2×C3⋊D3—82no—
212C2×C3⋊D3—82no—
213C2×C3⋊D3—82no—
214C32×C4—42no—
215C32×C4#12111yescharacteristic
216C32×C4#12111yescharacteristic
217C32×C4C22×D411yescharacteristic
218C32×C4C22×D411yescharacteristic
219C3⋊Dic3—22no—
220C2×#41—91no—
221C22×Q8C2×C3⋊D311yescharacteristic
222C22×D4—91no—
223#137—94no—
224#137—182no—
225AGL(1,ℤ/8)—94no—
226AGL(1,ℤ/8)—182no—
227C2×Q16—181no—
228C2×SD16—94no—
229C2×SD16—181no—
230C2×SD16—181no—
231C2×SD16—181no—
232C2×SD16—182no—
233C2×SD16—181no—
234C2×D8—181no—
235#131—94no—
236#131—182no—
237C2×M16—91no—
238C2×M16—181no—
239C2×M16C2×C3⋊D311yescharacteristic
240C2×M16C2×C3⋊D311yescharacteristic
241C22×C8—91no—
242C22×C8—181no—
243#108—94no—
244#101C2×C3⋊D314yescomplemented
245#100—94no—
246C23×C3#23514yes—
247C22×D3—64no—
248C22×D3—68no—
249C22×D3—124no—
250C22×D3—124no—
251C22×D3—248no—
252C3×Q8—28no—
253C3×Q8—28no—
254C3×Q8—44no—
255C3×Q8—44no—
256C2×C3×C4—28no—
257C2×C3×C4—44no—
258C2×C3×C4—44no—
259C2×C3×C4#23514yes—
260C2×C3×C4D3×D414yes—
261C2×C3×C4D3×D414yes—
262C2×C3×C4D3×D414yes—
263C2×C3×C4D3×D414yes—
264C2×C3×C4C23×D314yes—
265#67—68no—
266#67—68no—
267C2×Dic3—64no—
268D12—38no—
269D12—64no—
270D12—68no—
271D12—68no—
272D12—124no—
273D12—124no—
274C4×D3—68no—
275C4×D3—68no—
276Dic6—38no—
277Dic6—64no—
278C3×C8—28no—
279C3×C8—28no—
280C3⋊C8—38no—
281C3⋊C8—38no—
282C3⋊C8—68no—
283C2×C32—21no—
284C2×C32—21no—
285C2×C32#47112yescomplemented
286C2×C32C2×#12111yescharacteristic
287C3⋊D3—42no—
288C3⋊D3—82no—
289C24—181no—
290#41—92no—
291#41—92no—
292#41—181no—
293#41—181no—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—91no—
300C2×Q8C22×C3⋊D312yes—
301C2×D4—92no—
302C2×D4—91no—
303C2×D4—181no—
304C2×D4—181no—
305C2×D4—181no—
306C2×D4—181no—
307C2×D4—181no—
308C2×D4—181no—
309C22×C4—21no—
310C22×C4—181no—
311C22×C4C22×C3⋊D311yescharacteristic
312Q16—184no—
313SD16—184no—
314SD16—184no—
315SD16—184no—
316SD16—184no—
317D8—184no—
318M16—21no—
319M16—21no—
320M16—92no—
321M16—184no—
322M16—181no—
323M16C22×C3⋊D312yes—
324M16C22×C3⋊D312yes—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—92no—
328C2×C8—91no—
329C2×C8—91no—
330C2×C8—92no—
331C2×C8—184no—
332C2×C8—181no—
333C22×C3—28no—
334C22×C3#88414yes—
335C22×C3#88414yes—
336C22×C3C2×#23514yes—
337C2×D3—68no—
338C2×D3—128no—
339C2×D3—128no—
340C2×D3—248no—
341C2×D3—248no—
342C2×D3—248no—
343C3×C4—48no—
344C3×C4#88414yes—
345C3×C4#88414yes—
346C3×C4C2×D3×D414yes—
347C3×C4C2×D3×D414yes—
348Dic3—68no—
349C32C2×#47111yescharacteristic, complemented, Sylow
350C23—181no—
351C23—182no—
352C23—361no—
353C23—361no—
354C23—722no—
355C23#382811yescharacteristic
356Q8—22no—
357Q8—22no—
358Q8—41no—
359Q8—41no—
360Q8—92no—
361Q8—181no—
362D4—92no—
363D4—182no—
364D4—182no—
365D4—181no—
366D4—182no—
367D4—182no—
368D4—361no—
369D4—361no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—181no—
374C2×C4—182no—
375C2×C4—182no—
376C2×C4#382811yescharacteristic
377C2×C4D4×C3⋊D311yescharacteristic
378C2×C4D4×C3⋊D311yescharacteristic
379C2×C4D4×C3⋊D311yescharacteristic
380C2×C4D4×C3⋊D311yescharacteristic
381C2×C4C23×C3⋊D311yescharacteristic
382C8—22no—
383C8—22no—
384C8—92no—
385C8—92no—
386C8—182no—
387C2×C3—24no—
388C2×C3—24no—
389C2×C3#475418yescomplemented
390C2×C3C2×#88414yes—
391D3—128no—
392D3—248no—
393C22—22no—
394C22—182no—
395C22—362no—
396C22—362no—
397C22—722no—
398C22—722no—
399C22—722no—
400C22#6409311yescharacteristic
401C22#6409311yescharacteristic
402C22C2×#382811yescharacteristic
403C4—42no—
404C4—182no—
405C4#6409311yescharacteristic
406C4#6409311yescharacteristic
407C4C2×D4×C3⋊D311yescharacteristic
408C4C2×D4×C3⋊D311yescharacteristic
409C3C2×#475414yescomplemented
410C2—21no—
411C2—21no—
412C2—362no—
413C2—722no—
414C2#1059245312yesdirect product factor
415C2C2×#6409311yescharacteristic
subgroupG/H
centerC22#64093
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#101C2
socleC22×C32#121
prime radicalC2×#64117C2
hypercenterC2×#101C3⋊D3
hypocenterC32C2×#471
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
1. C2×#64151C2semidirect
2. C22×#3755C2semidirect
4. C2×#64116C2semidirect
5. C2×C32×#101C2semidirect
6. C2×#63650C2semidirect
7. C2×#63649C2semidirect
8. #10592453C2direct (N × H)
17. #64151C22semidirect
22. C2×#3755C22semidirect
28. #64116C22semidirect
33. C32×#101C22semidirect
34. #63650C22semidirect
35. #63649C22semidirect
40. C2×C3×#101D3semidirect
112. C3×#101C2×D3semidirect
158. C2×#101C3⋊D3semidirect
244. #101C2×C3⋊D3semidirect
285. C2×C32#471semidirect
349. C32C2×#471semidirect
389. C2×C3#4754semidirect
409. C3C2×#4754semidirect
414. C2#10592453direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641512
C22×#37552
C2×#641172
C2×#641162
C2×C32×#1012
C2×#636502
C2×#636492
#105924532
C2×#47543