Finite Group Databasebeta

← C2×#10590605 #11863677

Subgroups — C2×#10590605 #11863677

Order 1152.

1641 conjugacy classes of subgroups; only the 252 normal subgroups are shown.

normal subgroups only

This group has 1641 conjugacy classes of subgroups — too many to draw. Only its 252 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3797C211yesmaximal, characteristic
2C2×#64106C211yesmaximal, characteristic
3C22×#3719C212yesmaximal, complemented
4C2×C3×#810C212yesmaximal, complemented
5C2×#63557C211yesmaximal, characteristic
6#10590605C218yesmaximal, direct product factor
7C2×#4809—32nomaximal
8C22×C4×C3⋊D3C2211yescharacteristic
9C22×#634C2211yescharacteristic
10C22×C3×Dic6C2212yes—
11C22×#627—21no—
12C22×#624—21no—
13C2×#3797—22no—
14C2×#3797—28no—
15C2×#3797C2214yes—
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×#3752—21no—
18C2×C4⋊(C3⋊Dic3)—21no—
19#64106—22no—
20#64106C2214yes—
21C22×C3×C3⋊C8C2212yes—
22C2×#3719—28no—
23C2×#3719C2218yescomplemented
24C3×#810C2218yescomplemented
25#63557C2214yes—
26C22×D3×Q8—32no—
27C22×#216—32no—
28C22×Dic12—32no—
29C2×#897—32no—
30C2×#897—61no—
31C2×C3×#103—32no—
32C2×(C2×D3)⋊C8—32no—
33C2×#810D312yescomplemented
34#4809—316no—
35C23×C3⋊D3D411yescharacteristic
36C22×C32×C4—21no—
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3—21no—
39C22×C3⋊Dic3D411yescharacteristic
40C2×C4×C3⋊D3—24no—
41C2×C4×C3⋊D3D412yes—
42C2×C4×C3⋊D3C2312yes—
43C2×#634—24no—
44C2×#634—21no—
45C2×#634C2312yes—
46C22×C3×Dic3—22no—
47C2×C3×Dic6—22no—
48C2×C3×Dic6—24no—
49C2×C3×Dic6D418yes—
50C2×C3×Dic6C2314yes—
51C2×#627—28no—
52C2×#627—24no—
53C2×#624—28no—
54C2×#624—24no—
55#3797—216no—
56#3797—216no—
57C32×C4⋊C4—21no—
58C32×C4⋊C4C2312yes—
59#3752—24no—
60C4⋊(C3⋊Dic3)—24no—
61C2×C3×C3⋊C8—24no—
62C2×C3×C3⋊C8C2314yes—
63#3719—216no—
64C2×#451—91noSylow
65C22×C3×Q8—32no—
66C2×D3×Q8—38no—
67C2×D3×Q8—64no—
68C2×D3×Q8—68no—
69C2×D3×Q8—68no—
70C22×C4×D3—32no—
71C22×C4×D3—61no—
72C22×C4×D3—62no—
73C22×Dic6—32no—
74C22×Dic6—61no—
75C22×Dic6—62no—
76C22×Dic6C2×D312yes—
77C22×C3×C8—32no—
78C2×C3×C4⋊C4—21no—
79C2×C3×C4⋊C4C2×D312yes—
80C2×#216—38no—
81C2×#216—68no—
82C2×(C2×D3)⋊C4—62no—
83C2×(C2×D3)⋊C4—62no—
84C2×C4⋊Dic3—62no—
85C2×C4⋊Dic3—62no—
86C22×C3⋊C8C2×D312yes—
87C2×Dic12—38no—
88C2×Dic12—68no—
89#897—38no—
90#897—64no—
91#897—64no—
92#897—64no—
93C3×#103—38no—
94(C2×D3)⋊C8—38no—
95#810C2×D318yescomplemented
96C23×C32C2×D411yescharacteristic
97C22×C3⋊D3—22no—
98C22×C3⋊D3—22no—
99C22×C3⋊D3Q1614yescomplemented
100C22×C3⋊D3C2×D412yes—
101C2×C32×C4—22no—
102C2×C32×C4—42no—
103C2×C32×C4C2×D414yes—
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2411yescharacteristic
106C2×C3⋊Dic3—22no—
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3—42no—
109C2×C3⋊Dic3C2×D412yes—
110C4×C3⋊D3—24no—
111C4×C3⋊D3—24no—
112#634—24no—
113#634—42no—
114C2×C3×Dic3—28no—
115C2×C3×Dic3—24no—
116C3×Dic6—28no—
117C3×Dic6—24no—
118C3×Dic6C2×D418yes—
119#627—216no—
120#624—216no—
121C3×C3⋊C8—24no—
122C23×Q8—91no—
123C22×Q16—92no—
124C2×C22⋊Q8—91no—
125#451—98no—
126C2×#103—32no—
127C2×C22⋊C8—91no—
128C23×D3—32no—
129C23×D3—61no—
130C2×C3×Q8—38no—
131C2×C3×Q8—34no—
132C2×C3×Q8—64no—
133C2×C3×Q8—62no—
134C22×C3×C4—22no—
135C22×C3×C4—22no—
136C22×C3×C4—21no—
137C22×C3×C4—62no—
138C22×C3×C4C22×D312yes—
139C22×Dic3—22no—
140C22×Dic3—32no—
141C22×Dic3—61no—
142C22×Dic3—62no—
143C22×Dic3—62no—
144D3×Q8—616no—
145D3×Q8—632no—
146D3×Q8—616no—
147C2×C4×D3—34no—
148C2×C4×D3—34no—
149C2×C4×D3—62no—
150C2×C4×D3—62no—
151C2×C4×D3—68no—
152C2×C4×D3—616no—
153C2×C4×D3—64no—
154C2×C4×D3—64no—
155C2×C4×D3—124no—
156C2×Dic6—24no—
157C2×Dic6—22no—
158C2×Dic6—34no—
159C2×Dic6—62no—
160C2×Dic6—68no—
161C2×Dic6—616no—
162C2×Dic6—64no—
163C2×Dic6—64no—
164C2×Dic6—62no—
165C2×Dic6—62no—
166C2×Dic6—124no—
167C2×Dic6D1218yes—
168C2×Dic6C22×D314yes—
169C2×C3×C8—34no—
170C2×C3×C8—64no—
171C3×C4⋊C4—22no—
172C3×C4⋊C4—22no—
173C3×C4⋊C4—22no—
174C3×C4⋊C4C22×D314yes—
175#216—616no—
176(C2×D3)⋊C4—68no—
177(C2×D3)⋊C4—68no—
178C4⋊Dic3—68no—
179C4⋊Dic3—68no—
180C2×C3⋊C8—24no—
181C2×C3⋊C8C22×D314yes—
182Dic12—616no—
183C22×C32#12012yes—
184C22×C32C2×Q1612yes—
185C22×C32#13712yes—
186C22×C32C22×D411yescharacteristic
187C2×C3⋊D3—22no—
188C2×C3⋊D3—22no—
189C2×C3⋊D3—28no—
190C2×C3⋊D3C2×Q1614yescomplemented
191C32×C4—42no—
192C32×C4#12012yes—
193C32×C4C22×D412yes—
194C3⋊Dic3—22no—
195C3⋊Dic3—42no—
196C3×Dic3—28no—
197C22×Q8—32no—
198C22×Q8—94no—
199C22×Q8—91no—
200C22×Q8—181no—
201C22×Q8—182no—
202C22×Q8—188no—
203C23×C4—91no—
204C23×C4—181no—
205C2×Q16—98no—
206C2×Q16—188no—
207C22×C8—32no—
208C22⋊Q8—94no—
209C22⋊Q8—182no—
210C2×C4⋊C4—181no—
211C2×C4⋊C4D3211yescharacteristic
212C2×C22⋊C4—181no—
213#103—38no—
214C22⋊C8—94no—
215C23×C3—21no—
216C23×C3D3×D412yes—
217C22×D3—38no—
218C22×D3—34no—
219C22×D3—64no—
220C22×D3—62no—
221C22×D3—64no—
222C22×D3—64no—
223C22×D3—122no—
224C22×D3—122no—
225C3×Q8—38no—
226C3×Q8—68no—
227C3×Q8—64no—
228C2×C3×C4—24no—
229C2×C3×C4—24no—
230C2×C3×C4—21no—
231C2×C3×C4—24no—
232C2×C3×C4—21no—
233C2×C3×C4—44no—
234C2×C3×C4—44no—
235C2×C3×C4—68no—
236C2×C3×C4—64no—
237C2×C3×C4C2×D1214yes—
238C2×C3×C4D3×D414yes—
239C2×C3×C4D3×D412yes—
240C2×C3×C4C23×D312yes—
241C2×Dic3—28no—
242C2×Dic3—24no—
243C2×Dic3—34no—
244C2×Dic3—62no—
245C2×Dic3—64no—
246C2×Dic3—64no—
247C2×Dic3—64no—
248C2×Dic3—122no—
249C2×Dic3—124no—
250C2×Dic3—124no—
251C4×D3—632no—
252C4×D3—68no—
253C4×D3—64no—
254C4×D3—64no—
255C4×D3—124no—
256C4×D3—124no—
257Dic6—28no—
258Dic6—24no—
259Dic6—632no—
260Dic6—64no—
261Dic6—64no—
262Dic6—124no—
263Dic6—124no—
264Dic6—124no—
265Dic6C2×D1218yes—
266C3×C8—64no—
267C3⋊C8—24no—
268C2×C32#45114yescomplemented
269C2×C32C2×#12011yescharacteristic
270C2×C32C22×Q1611yescharacteristic
271C2×C32C2×#13711yescharacteristic
272C3⋊D3—24no—
273C24—91no—
274C2×Q8—34no—
275C2×Q8—38no—
276C2×Q8—64no—
277C2×Q8—62no—
278C2×Q8—92no—
279C2×Q8—184no—
280C2×Q8—188no—
281C2×Q8—1816no—
282C2×Q8—1816no—
283C2×Q8—181no—
284C2×Q8—184no—
285C22×C4—21no—
286C22×C4—62no—
287C22×C4—91no—
288C22×C4—92no—
289C22×C4—92no—
290C22×C4—184no—
291C22×C4—188no—
292C22×C4—184no—
293C22×C4—181no—
294C22×C4C2×D3211yescharacteristic
295Q16—1816no—
296C2×C8—34no—
297C2×C8—64no—
298C4⋊C4—21no—
299C4⋊C4—184no—
300C4⋊C4C2×D3212yes—
301C22⋊C4—184no—
302C22×C3—21no—
303C22×C3—22no—
304C22×C3—22no—
305C22×C3—22no—
306C22×C3#88214yes—
307C22×C3#91514yes—
308C22×C3D3×Q1614yes—
309C22×C3C2×D3×D412yes—
310C2×D3—38no—
311C2×D3—64no—
312C2×D3—64no—
313C2×D3—64no—
314C2×D3—616no—
315C2×D3—122no—
316C2×D3—122no—
317C2×D3—128no—
318C3×C4—22no—
319C3×C4—22no—
320C3×C4—44no—
321C3×C4—44no—
322C3×C4—68no—
323C3×C4#88214yes—
324C3×C4C22×D1212yes—
325C3×C4C2×D3×D412yes—
326Dic3—28no—
327Dic3—64no—
328Dic3—122no—
329Dic3—124no—
330Dic3—124no—
331C32C2×#45111yescharacteristic, complemented, Sylow
332C23—92no—
333C23—94no—
334C23—182no—
335C23—182no—
336C23#381111yescharacteristic
337Q8—38no—
338Q8—64no—
339Q8—68no—
340Q8—1816no—
341Q8—184no—
342Q8—362no—
343C2×C4—22no—
344C2×C4—42no—
345C2×C4—64no—
346C2×C4—68no—
347C2×C4—92no—
348C2×C4—1816no—
349C2×C4—182no—
350C2×C4—184no—
351C2×C4—184no—
352C2×C4—182no—
353C2×C4—362no—
354C2×C4D3×D1214yes—
355C2×C4#381111yescharacteristic
356C2×C4C22×D3211yescharacteristic
357C8—64no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—24no—
361C2×C3—21no—
362C2×C3#480918yescomplemented
363C2×C3C2×#88212yes—
364C2×C3C2×#91512yes—
365C2×C3C2×D3×Q1612yes—
366D3—68no—
367D3—124no—
368C22—94no—
369C22—182no—
370C22—188no—
371C22—182no—
372C22#6392312yes—
373C22#6393112yes—
374C22#6394412yes—
375C22C2×#381111yescharacteristic
376C4—42no—
377C4—68no—
378C4—182no—
379C4—362no—
380C4#6392312yes—
381C4C2×D3×D1212yes—
382C3—21no—
383C3C2×#480912yescomplemented
384C2—184no—
385C2#1059060514yesdirect product factor
386C2C2×#6392311yescharacteristic
387C2C2×#6393111yescharacteristic
388C2C2×#6394411yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#451
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×#3719C2semidirect
4. C2×C3×#810C2semidirect
6. #10590605C2direct (N × H)
23. C2×#3719C22semidirect
24. C3×#810C22semidirect
33. C2×#810D3semidirect
95. #810C2×D3semidirect
99. C22×C3⋊D3Q16semidirect
190. C2×C3⋊D3C2×Q16semidirect
268. C2×C32#451semidirect
331. C32C2×#451semidirect
362. C2×C3#4809semidirect
383. C3C2×#4809semidirect
385. C2#10590605direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37972
C2×#641062
C22×#37192
C2×C3×#8102
C2×#635572
#105906052
C2×#48093