Finite Group Databasebeta

← C2×#10592840 #11867852

Subgroups — C2×#10592840 #11867852

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×C32×#131C211yesmaximal, characteristic, complemented
2C2×#64160C211yesmaximal, characteristic, complemented
3C2×#64158C211yesmaximal, characteristic
4C22×#3744C211yesmaximal, characteristic, complemented
5#10592840C218yesmaximal, direct product factor
6C2×#63651C211yesmaximal, characteristic, complemented
7C2×#63650C211yesmaximal, characteristic, complemented
8C2×#63646C211yesmaximal, characteristic, complemented
9C2×#5141—34nomaximal
10C2×C32×#41C2211yescharacteristic
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C32×#131—22no—
14C32×#131C2214yescomplemented
15C2×C32×M16—21no—
16C2×C32×M16C2211yescharacteristic
17C22×C32×C8—21no—
18C22×C32×C8C2211yescharacteristic
19#64160—22no—
20#64160C2214yescomplemented
21#64158—22no—
22#64158C2214yes—
23C2×#3756—21no—
24C2×#3755—21no—
25C2×#3754—21no—
26C2×#3753—21no—
27C2×#3748C2211yescharacteristic
28C2×#3748C2211yescharacteristic
29C2×#3744—21no—
30C2×#3744—21no—
31C2×#3744—22no—
32C2×#3744C2214yescomplemented
33#63651C2214yescomplemented
34#63650C2214yescomplemented
35#63646C2214yescomplemented
36C2×C3×#131D314yescomplemented
37C2×#951—34no—
38C2×#949—34no—
39C22×#204—34no—
40#5141—332no—
41C2×#824—34no—
42C2×#823—34no—
43C2×#819—34no—
44C23×C3⋊D3—21no—
45C32×#41—21no—
46C32×#41—21no—
47C32×#41D412yes—
48C32×#41C2312yes—
49C2×C32×Q8D411yescharacteristic
50C2×C32×D4—21no—
51C2×C32×D4D411yescharacteristic
52C22×C32×C4—21no—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3—21no—
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)C2312yes—
61C2×#634—21no—
62C2×#634—21no—
63C2×#634—21no—
64C2×#634—21no—
65C2×#634—21no—
66C2×#634C2312yes—
67C32×M16—21no—
68C32×M16—24no—
69C32×M16C2312yes—
70C2×C32×C8—21no—
71C2×C32×C8—24no—
72C2×C32×C8D411yescharacteristic
73C2×C32×C8D411yescharacteristic
74C2×C32×C8D412yes—
75C2×C32×C8C2312yes—
76#3756—24no—
77#3755—24no—
78#3754—24no—
79#3753—24no—
80#3748—21no—
81#3748—21no—
82#3748C2312yes—
83#3748C2312yes—
84C2×C3⋊(C3⋊C8)—21no—
85C2×C3⋊(C3⋊C8)—21no—
86#3744—24no—
87#3744—24no—
88C2×#471—91noSylow
89C2×C3×#41C2×D314yes—
90C22×D12—34no—
91C22×Dic6—34no—
92C3×#131—28no—
93C3×#131C2×D3116yescomplemented
94C2×C3×M16—24no—
95C2×C3×M16C2×D314yes—
96C22×C3×C8—24no—
97C22×C3×C8C2×D314yes—
98#951—316no—
99#951—68no—
100#949—316no—
101#949—68no—
102C2×#216—64no—
103C2×#215—64no—
104C2×#214—64no—
105C2×#213—64no—
106C2×#208—34no—
107C2×#208—34no—
108C2×#204—316no—
109C2×#204—64no—
110C2×#204—64no—
111C2×#204—68no—
112#824—316no—
113#823—316no—
114#819—316no—
115C23×C32—21no—
116C23×C32#4111yescharacteristic
117C22×C3⋊D3—22no—
118C22×C3⋊D3—41no—
119C22×C3⋊D3—41no—
120C22×C3⋊D3—82no—
121C32×Q8—21no—
122C32×Q8C2×D412yes—
123C32×D4—22no—
124C32×D4—22no—
125C32×D4—21no—
126C32×D4C2×D412yes—
127C2×C32×C4—21no—
128C2×C32×C4—22no—
129C2×C32×C4—22no—
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4#4111yescharacteristic
135C2×C32×C4C2411yescharacteristic
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—41no—
138C2×C3⋊Dic3—41no—
139C4⋊(C3⋊D3)—22no—
140C4⋊(C3⋊D3)—22no—
141C4⋊(C3⋊D3)—41no—
142C4⋊(C3⋊D3)—41no—
143#634—22no—
144#634—22no—
145#634—41no—
146#634—41no—
147C32×C8—22no—
148C32×C8C2×D412yes—
149C32×C8C2×D412yes—
150C3⋊(C3⋊C8)—22no—
151C3⋊(C3⋊C8)—22no—
152C2×#137—91no—
153C2×AGL(1,ℤ/8)—91no—
154C22×SD16—91no—
155C2×#131C3⋊D311yescharacteristic, complemented
156#471—98no—
157C2×#108—91no—
158C2×#101—91no—
159C2×#100—91no—
160C23×D3—64no—
161C3×#41—24no—
162C3×#41—24no—
163C3×#41D1218yes—
164C3×#41C22×D318yes—
165C2×C3×Q8D1214yes—
166C2×C3×D4—24no—
167C2×C3×D4D1214yes—
168C22×C3×C4—24no—
169C22×C3×C4C22×D314yes—
170C22×Dic3—64no—
171C2×D12—38no—
172C2×D12—64no—
173C2×D12—64no—
174C2×D12—64no—
175C2×D12—64no—
176C2×D12—64no—
177C2×Dic6—38no—
178C2×Dic6—64no—
179C2×Dic6—64no—
180C2×Dic6—64no—
181C2×Dic6—64no—
182C2×Dic6—64no—
183C3×M16—24no—
184C3×M16—216no—
185C3×M16C22×D318yes—
186C2×C3×C8—24no—
187C2×C3×C8—216no—
188C2×C3×C8#6714yes—
189C2×C3×C8#6714yes—
190C2×C3×C8#6718yes—
191C2×C3×C8C22×D318yes—
192#216—616no—
193#215—616no—
194#214—616no—
195#213—616no—
196#208—38no—
197#208—38no—
198#208—64no—
199#208—64no—
200C2×C3⋊C8—64no—
201C2×C3⋊C8—64no—
202#204—616no—
203#204—616no—
204C22×C32—22no—
205C22×C32—22no—
206C22×C32—42no—
207C22×C32#12111yescharacteristic
208C22×C32#12111yescharacteristic
209C22×C32C2×#4111yescharacteristic
210C2×C3⋊D3—42no—
211C2×C3⋊D3—82no—
212C2×C3⋊D3—82no—
213C2×C3⋊D3—82no—
214C32×C4—22no—
215C32×C4#12111yescharacteristic
216C32×C4#12111yescharacteristic
217C32×C4C22×D411yescharacteristic
218C32×C4C22×D411yescharacteristic
219C3⋊Dic3—42no—
220C2×#41C2×C3⋊D311yescharacteristic
221C22×Q8—91no—
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—181no—
233C2×SD16—182no—
234C2×D8—181no—
235#131—22no—
236#131C2×C3⋊D314yescomplemented
237C2×M16—21no—
238C2×M16—91no—
239C2×M16—91no—
240C2×M16C2×C3⋊D311yescharacteristic
241C22×C8—21no—
242C22×C8C2×C3⋊D311yescharacteristic
243#108—94no—
244#101—94no—
245#100—94no—
246C23×C3—24no—
247C23×C3#23514yes—
248C22×D3—68no—
249C22×D3—124no—
250C22×D3—124no—
251C22×D3—248no—
252C3×Q8—24no—
253C3×Q8C2×D1218yes—
254C3×D4—28no—
255C3×D4—28no—
256C3×D4—24no—
257C3×D4C2×D1218yes—
258C2×C3×C4—24no—
259C2×C3×C4—28no—
260C2×C3×C4—28no—
261C2×C3×C4C2×D1214yes—
262C2×C3×C4C2×D1214yes—
263C2×C3×C4#23514yes—
264C2×C3×C4C2×#6714yes—
265C2×C3×C4C2×#6714yes—
266C2×C3×C4C23×D314yes—
267C2×Dic3—68no—
268C2×Dic3—124no—
269C2×Dic3—124no—
270D12—68no—
271D12—68no—
272D12—124no—
273D12—124no—
274Dic6—68no—
275Dic6—68no—
276Dic6—124no—
277Dic6—124no—
278C3×C8—28no—
279C3×C8C2×#6718yes—
280C3×C8C2×#6718yes—
281C3⋊C8—68no—
282C3⋊C8—68no—
283C2×C32—21no—
284C2×C32—21no—
285C2×C32—42no—
286C2×C32#47112yescomplemented
287C2×C32C2×#12111yescharacteristic
288C3⋊D3—82no—
289C24—181no—
290#41—21no—
291#41—21no—
292#41C4⋊(C3⋊D3)12yes—
293#41C22×C3⋊D312yes—
294C2×Q8—92no—
295C2×Q8—181no—
296C2×Q8—181no—
297C2×Q8—181no—
298C2×Q8—181no—
299C2×Q8—181no—
300C2×Q8C4⋊(C3⋊D3)11yescharacteristic
301C2×D4—21no—
302C2×D4—92no—
303C2×D4—181no—
304C2×D4—181no—
305C2×D4—181no—
306C2×D4—181no—
307C2×D4—181no—
308C2×D4C4⋊(C3⋊D3)11yescharacteristic
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—24no—
320M16—92no—
321M16—92no—
322M16—181no—
323M16—181no—
324M16C22×C3⋊D312yes—
325C2×C8—21no—
326C2×C8—24no—
327C2×C8—181no—
328C2×C8—181no—
329C2×C8#63811yescharacteristic
330C2×C8#63811yescharacteristic
331C2×C8#63812yes—
332C2×C8C22×C3⋊D312yes—
333C22×C3—28no—
334C22×C3—28no—
335C22×C3—48no—
336C22×C3#93014yes—
337C22×C3#93014yes—
338C22×C3C2×#23514yes—
339C2×D3—128no—
340C2×D3—248no—
341C2×D3—248no—
342C2×D3—248no—
343C3×C4—28no—
344C3×C4#93014yes—
345C3×C4#93014yes—
346C3×C4C22×D1214yes—
347C3×C4C22×#6714yes—
348Dic3—128no—
349C32C2×#47111yescharacteristic, complemented, Sylow
350C23—21no—
351C23—182no—
352C23—361no—
353C23—361no—
354C23—722no—
355C23#382811yescharacteristic
356Q8—21no—
357Q8—182no—
358Q8—182no—
359Q8—361no—
360Q8—361no—
361Q8C2×C4⋊(C3⋊D3)12yes—
362D4—22no—
363D4—22no—
364D4—21no—
365D4—182no—
366D4—182no—
367D4—361no—
368D4—361no—
369D4C2×C4⋊(C3⋊D3)12yes—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—182no—
374C2×C4—361no—
375C2×C4—361no—
376C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
377C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
378C2×C4#382811yescharacteristic
379C2×C4C2×#63811yescharacteristic
380C2×C4C2×#63811yescharacteristic
381C2×C4C23×C3⋊D311yescharacteristic
382C8—22no—
383C8—182no—
384C8—182no—
385C8C2×#63812yes—
386C8C2×#63812yes—
387C2×C3—24no—
388C2×C3—24no—
389C2×C3—48no—
390C2×C3#514118yescomplemented
391C2×C3C2×#93014yes—
392D3—248no—
393C22—22no—
394C22—22no—
395C22—42no—
396C22—362no—
397C22—722no—
398C22—722no—
399C22—722no—
400C22#6413911yescharacteristic
401C22#6413911yescharacteristic
402C22C2×#382811yescharacteristic
403C4—22no—
404C4—362no—
405C4#6413911yescharacteristic
406C4#6413911yescharacteristic
407C4C22×C4⋊(C3⋊D3)11yescharacteristic
408C4C22×#63811yescharacteristic
409C3C2×#514114yescomplemented
410C2—21no—
411C2—21no—
412C2—42no—
413C2—722no—
414C2#1059284012yesdirect product factor
415C2C2×#6413911yescharacteristic
subgroupG/H
centerC22#64139
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#131C2
socleC22×C32#121
prime radicalC2×#64158C2
hypercenterC2×#131C3⋊D3
hypocenterC32C2×#471
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. C2×C32×#131C2semidirect
2. C2×#64160C2semidirect
4. C22×#3744C2semidirect
5. #10592840C2direct (N × H)
6. C2×#63651C2semidirect
7. C2×#63650C2semidirect
8. C2×#63646C2semidirect
14. C32×#131C22semidirect
20. #64160C22semidirect
32. C2×#3744C22semidirect
33. #63651C22semidirect
34. #63650C22semidirect
35. #63646C22semidirect
36. C2×C3×#131D3semidirect
93. C3×#131C2×D3semidirect
155. C2×#131C3⋊D3semidirect
236. #131C2×C3⋊D3semidirect
286. C2×C32#471semidirect
349. C32C2×#471semidirect
390. C2×C3#5141semidirect
409. C3C2×#5141semidirect
414. C2#10592840direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1312
C2×#641602
C2×#641582
C22×#37442
#105928402
C2×#636512
C2×#636502
C2×#636462
C2×#51413