Finite Group Databasebeta

← C2×#10592876 #11867843

Subgroups — C2×#10592876 #11867843

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
1C22×C32×SD16C211yesmaximal, characteristic, complemented
2C2×#64151C211yesmaximal, characteristic, complemented
3C2×#64141C211yesmaximal, characteristic
4C2×#64110C211yesmaximal, characteristic, complemented
5C2×#63663C211yesmaximal, characteristic, complemented
6C2×#63660C211yesmaximal, characteristic, complemented
7#10592876C218yesmaximal, direct product factor
8C2×#63646C211yesmaximal, characteristic, complemented
9C2×#5177—34nomaximal
10C22×C32×Q8C2211yescharacteristic
11C22×C32×D4C2211yescharacteristic
12C2×#3828C2211yescharacteristic
13C2×C32×SD16—21no—
14C2×C32×SD16—21no—
15C2×C32×SD16—22no—
16C2×C32×SD16C2214yescomplemented
17C22×C32×C8C2211yescharacteristic
18C2×#3756—21no—
19#64151—22no—
20#64151C2214yescomplemented
21C2×#3755—21no—
22C2×#3754—21no—
23#64141—22no—
24#64141C2214yes—
25C2×#3753—21no—
26C2×#3748C2211yescharacteristic
27C2×#3748C2211yescharacteristic
28C2×#3748C2211yescharacteristic
29#64110—22no—
30#64110C2214yescomplemented
31C2×#3743—21no—
32C2×C8×C3⋊D3—21no—
33#63663C2214yescomplemented
34#63660C2214yescomplemented
35#63646C2214yescomplemented
36C22×C3×SD16D314yescomplemented
37C2×#942—34no—
38C2×#932—34no—
39C2×#901—34no—
40C2×#836—34no—
41C2×#833—34no—
42#5177—332no—
43C2×#819—34no—
44C24×C32—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8—21no—
48C2×C32×Q8—21no—
49C2×C32×Q8—21no—
50C2×C32×Q8C2312yes—
51C2×C32×D4—21no—
52C2×C32×D4—21no—
53C2×C32×D4—21no—
54C2×C32×D4—21no—
55C2×C32×D4—21no—
56C2×C32×D4C2312yes—
57C22×C32×C4—21no—
58C22×C32×C4C2311yescharacteristic
59C2×#638—21no—
60#3828—21no—
61#3828—21no—
62#3828D412yes—
63#3828C2312yes—
64C2×C4⋊(C3⋊D3)D411yescharacteristic
65C2×C4×C3⋊D3—21no—
66C2×#634D411yescharacteristic
67C32×SD16—24no—
68C32×SD16—24no—
69C2×C32×C8D411yescharacteristic
70C2×C32×C8D411yescharacteristic
71C2×C32×C8D412yes—
72C2×C32×C8C2312yes—
73#3756—24no—
74#3755—24no—
75#3754—24no—
76#3753—24no—
77#3748—21no—
78#3748—21no—
79#3748—21no—
80#3748C2312yes—
81#3748C2312yes—
82#3748C2312yes—
83C2×C3⋊(C3⋊C8)—21no—
84C2×C3⋊(C3⋊C8)—21no—
85C2×C3⋊(C3⋊C8)—21no—
86#3743—24no—
87C8×C3⋊D3—24no—
88C2×#471—91noSylow
89C22×C3×Q8C2×D314yes—
90C22×C3×D4C2×D314yes—
91C2×#235—34no—
92C2×C3×SD16—24no—
93C2×C3×SD16—24no—
94C2×C3×SD16—28no—
95C2×C3×SD16C2×D3116yescomplemented
96C22×C3×C8C2×D314yes—
97C2×#216—64no—
98#942—316no—
99#942—68no—
100C2×#215—64no—
101C2×#214—64no—
102#932—316no—
103#932—68no—
104C2×#213—64no—
105C2×#208—34no—
106C2×#208—34no—
107C2×#208—34no—
108#901—316no—
109#901—68no—
110C2×ΓL(1,𝔽25)—64no—
111C2×D3×C8—64no—
112#836—316no—
113#833—316no—
114#819—316no—
115C23×C32—22no—
116C23×C32—41no—
117C23×C32—41no—
118C23×C32—82no—
119C23×C32#4111yescharacteristic
120C22×C3⋊D3—21no—
121C32×Q8—22no—
122C32×Q8—22no—
123C32×Q8—41no—
124C32×Q8—41no—
125C32×D4—22no—
126C32×D4—22no—
127C32×D4—41no—
128C32×D4—41no—
129C2×C32×C4—22no—
130C2×C32×C4—41no—
131C2×C32×C4—41no—
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C2×C32×C4C2411yescharacteristic
138#638—22no—
139#638—22no—
140C2×C3⋊Dic3—21no—
141C4⋊(C3⋊D3)—21no—
142C4⋊(C3⋊D3)C2×D412yes—
143C4×C3⋊D3—22no—
144C4×C3⋊D3—22no—
145#634—21no—
146#634C2×D412yes—
147C32×C8C2×D412yes—
148C32×C8C2×D412yes—
149C3⋊(C3⋊C8)—22no—
150C3⋊(C3⋊C8)—22no—
151C3⋊(C3⋊C8)—22no—
152C2×#137—91no—
153C2×AGL(1,ℤ/8)—91no—
154C22×SD16C3⋊D311yescharacteristic, complemented
155C2×#131—91no—
156#471—98no—
157C2×#108—91no—
158C2×#101—91no—
159C2×#100—91no—
160C24×C3—24no—
161C2×C3×Q8—24no—
162C2×C3×Q8—24no—
163C2×C3×Q8—24no—
164C2×C3×Q8—24no—
165C2×C3×Q8—24no—
166C2×C3×Q8C22×D318yes—
167C2×C3×D4—24no—
168C2×C3×D4—24no—
169C2×C3×D4—24no—
170C2×C3×D4—24no—
171C2×C3×D4—24no—
172C2×C3×D4C22×D318yes—
173C22×C3×C4—24no—
174C22×C3×C4C22×D314yes—
175C2×#67—64no—
176#235—38no—
177#235—38no—
178#235—64no—
179#235—64no—
180C2×D12—34no—
181C2×C4×D3—64no—
182C2×Dic6—34no—
183C3×SD16—216no—
184C3×SD16—216no—
185C2×C3×C8#6714yes—
186C2×C3×C8#6714yes—
187C2×C3×C8#6718yes—
188C2×C3×C8C22×D318yes—
189#216—616no—
190#215—616no—
191#214—616no—
192#213—616no—
193#208—38no—
194#208—38no—
195#208—38no—
196#208—64no—
197#208—64no—
198#208—64no—
199C2×C3⋊C8—64no—
200C2×C3⋊C8—64no—
201C2×C3⋊C8—64no—
202ΓL(1,𝔽25)—616no—
203D3×C8—616no—
204C22×C32—22no—
205C22×C32—42no—
206C22×C32—82no—
207C22×C32—82no—
208C22×C32—82no—
209C22×C32#12111yescharacteristic
210C22×C32#12111yescharacteristic
211C22×C32C2×#4111yescharacteristic
212C2×C3⋊D3—22no—
213C2×C3⋊D3—42no—
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×D4C2×C3⋊D311yescharacteristic
223#137—94no—
224#137—182no—
225AGL(1,ℤ/8)—94no—
226AGL(1,ℤ/8)—182no—
227C2×Q16—181no—
228C2×SD16—21no—
229C2×SD16—21no—
230C2×SD16—22no—
231C2×SD16—181no—
232C2×SD16—181no—
233C2×SD16C2×C3⋊D314yescomplemented
234C2×D8—181no—
235#131—94no—
236#131—182no—
237C2×M16—91no—
238C2×M16—91no—
239C2×M16—91no—
240C2×M16—181no—
241C22×C8—181no—
242C22×C8C2×C3⋊D311yescharacteristic
243#108—94no—
244#101—94no—
245#100—94no—
246C23×C3—28no—
247C23×C3—44no—
248C23×C3—44no—
249C23×C3—88no—
250C23×C3#23714yes—
251C22×D3—64no—
252C3×Q8—28no—
253C3×Q8—28no—
254C3×Q8—44no—
255C3×Q8—44no—
256C3×D4—28no—
257C3×D4—28no—
258C3×D4—44no—
259C3×D4—44no—
260C2×C3×C4—28no—
261C2×C3×C4—44no—
262C2×C3×C4—44no—
263C2×C3×C4D3×D414yes—
264C2×C3×C4D3×D414yes—
265C2×C3×C4#23714yes—
266C2×C3×C4C2×#6714yes—
267C2×C3×C4C2×#6714yes—
268C2×C3×C4C23×D314yes—
269#67—68no—
270#67—68no—
271C2×Dic3—64no—
272D12—38no—
273D12—64no—
274C4×D3—68no—
275C4×D3—68no—
276Dic6—38no—
277Dic6—64no—
278C3×C8C2×#6718yes—
279C3×C8C2×#6718yes—
280C3⋊C8—68no—
281C3⋊C8—68no—
282C3⋊C8—68no—
283C2×C32—21no—
284C2×C32—21no—
285C2×C32—82no—
286C2×C32#47112yescomplemented
287C2×C32C2×#12111yescharacteristic
288C3⋊D3—42no—
289C24—21no—
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—21no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—91no—
307C2×D4—181no—
308C2×D4C22×C3⋊D312yes—
309C22×C4—21no—
310C22×C4—181no—
311C22×C4C22×C3⋊D311yescharacteristic
312Q16—184no—
313SD16—24no—
314SD16—24no—
315SD16—184no—
316SD16—184no—
317D8—184no—
318M16—92no—
319M16—92no—
320M16—92no—
321M16—181no—
322M16—181no—
323M16—181no—
324M16—184no—
325C2×C8—181no—
326C2×C8—181no—
327C2×C8—181no—
328C2×C8—184no—
329C2×C8#63811yescharacteristic
330C2×C8#63811yescharacteristic
331C2×C8#63812yes—
332C2×C8C22×C3⋊D312yes—
333C22×C3—28no—
334C22×C3—48no—
335C22×C3—88no—
336C22×C3—88no—
337C22×C3—88no—
338C22×C3#93814yes—
339C22×C3#93814yes—
340C22×C3C2×#23714yes—
341C2×D3—68no—
342C2×D3—128no—
343C3×C4—48no—
344C3×C4#93814yes—
345C3×C4#93814yes—
346C3×C4C2×D3×D414yes—
347C3×C4C22×#6714yes—
348Dic3—68no—
349C32C2×#47111yescharacteristic, complemented, Sylow
350C23—22no—
351C23—41no—
352C23—41no—
353C23—82no—
354C23—181no—
355C23#383011yescharacteristic
356Q8—22no—
357Q8—22no—
358Q8—41no—
359Q8—41no—
360Q8—92no—
361Q8—181no—
362D4—22no—
363D4—22no—
364D4—41no—
365D4—41no—
366D4—92no—
367D4—182no—
368D4—182no—
369D4—181no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—181no—
374C2×C4—182no—
375C2×C4—182no—
376C2×C4D4×C3⋊D311yescharacteristic
377C2×C4D4×C3⋊D311yescharacteristic
378C2×C4#383011yescharacteristic
379C2×C4C2×#63811yescharacteristic
380C2×C4C2×#63811yescharacteristic
381C2×C4C23×C3⋊D311yescharacteristic
382C8—182no—
383C8—182no—
384C8—182no—
385C8C2×#63812yes—
386C8C2×#63812yes—
387C2×C3—24no—
388C2×C3—24no—
389C2×C3—88no—
390C2×C3#517718yescomplemented
391C2×C3C2×#93814yes—
392D3—128no—
393C22—22no—
394C22—42no—
395C22—82no—
396C22—82no—
397C22—82no—
398C22—182no—
399C22—362no—
400C22#6414711yescharacteristic
401C22#6414711yescharacteristic
402C22C2×#383011yescharacteristic
403C4—42no—
404C4—182no—
405C4#6414711yescharacteristic
406C4#6414711yescharacteristic
407C4C2×D4×C3⋊D311yescharacteristic
408C4C22×#63811yescharacteristic
409C3C2×#517714yescomplemented
410C2—21no—
411C2—21no—
412C2—82no—
413C2—362no—
414C2#1059287612yesdirect product factor
415C2C2×#6414711yescharacteristic
subgroupG/H
centerC22#64147
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC22×C32×SD16C2
socleC22×C32#121
prime radicalC2×#64141C2
hypercenterC22×SD16C3⋊D3
hypocenterC32C2×#471
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×C32×SD16C2semidirect
2. C2×#64151C2semidirect
4. C2×#64110C2semidirect
5. C2×#63663C2semidirect
6. C2×#63660C2semidirect
7. #10592876C2direct (N × H)
8. C2×#63646C2semidirect
16. C2×C32×SD16C22semidirect
20. #64151C22semidirect
30. #64110C22semidirect
33. #63663C22semidirect
34. #63660C22semidirect
35. #63646C22semidirect
36. C22×C3×SD16D3semidirect
95. C2×C3×SD16C2×D3semidirect
154. C22×SD16C3⋊D3semidirect
233. C2×SD16C2×C3⋊D3semidirect
286. C2×C32#471semidirect
349. C32C2×#471semidirect
390. C2×C3#5177semidirect
409. C3C2×#5177semidirect
414. C2#10592876direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×SD162
C2×#641512
C2×#641412
C2×#641102
C2×#636632
C2×#636602
#105928762
C2×#636462
C2×#51773