Finite Group Databasebeta

← C2×#10591654 #11863666

Subgroups — C2×#10591654 #11863666

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×#64155C211yesmaximal, characteristic
3C22×C3×#216C212yesmaximal, complemented
4#10591654C218yesmaximal, direct product factor
5C2×#63566C212yesmaximal, complemented
6C2×#63557C211yesmaximal, characteristic
7C2×#5186—32nomaximal
8C22×C32×Q8C2211yescharacteristic
9C22×C4×C3⋊D3C2211yescharacteristic
10C22×C3×Dic6C2212yes—
11C22×#627—21no—
12C22×#624—21no—
13C2×#3797—22no—
14C2×#3797—28no—
15C2×#3797C2214yes—
16#64155—22no—
17#64155C2214yes—
18C2×#3752—21no—
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×#3750—21no—
21C2×C3×#216—28no—
22C2×C3×#216C2218yescomplemented
23C22×C3×C3⋊C8C2212yes—
24#63566C2218yescomplemented
25#63557C2214yes—
26C22×D3×Q8—32no—
27C22×C3×Q16—32no—
28C2×#946—32no—
29C2×#946—61no—
30C22×#216D312yescomplemented
31C2×#835—32no—
32#5186—316no—
33C2×(C2×D3)⋊C8—32no—
34C2×#816—32no—
35C23×C3⋊D3D411yescharacteristic
36C2×C32×Q8—21no—
37C2×C32×Q8—24no—
38C2×C32×Q8C2312yes—
39C22×C32×C4—21no—
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3—21no—
42C22×C3⋊Dic3D411yescharacteristic
43C2×C4×C3⋊D3—24no—
44C2×C4×C3⋊D3D412yes—
45C2×C4×C3⋊D3C2312yes—
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—
57#3752—24no—
58C4⋊(C3⋊Dic3)—21no—
59C4⋊(C3⋊Dic3)C2312yes—
60#3750—24no—
61C3×#216—216no—
62C2×C3×C3⋊C8—24no—
63C2×C3×C3⋊C8C2314yes—
64C2×#451—91noSylow
65C22×C3×Q8—21no—
66C22×C3×Q8—32no—
67C22×C3×Q8C2×D312yes—
68C2×D3×Q8—38no—
69C2×D3×Q8—64no—
70C2×D3×Q8—68no—
71C2×D3×Q8—68no—
72C22×C4×D3—32no—
73C22×C4×D3—61no—
74C22×C4×D3—62no—
75C22×Dic6—62no—
76C22×Dic6C2×D312yes—
77C2×C3×Q16—38no—
78C2×C3×Q16—68no—
79C22×C3×C8—32no—
80#946—38no—
81#946—64no—
82#946—64no—
83#946—64no—
84C2×#216—28no—
85C2×#216C2×D318yescomplemented
86C2×(C2×D3)⋊C4—62no—
87C2×(C2×D3)⋊C4—62no—
88C2×C4⋊Dic3—32no—
89C2×C4⋊Dic3—61no—
90C2×Dic3⋊C4—62no—
91C2×Dic3⋊C4—62no—
92C22×C3⋊C8C2×D312yes—
93#835—38no—
94(C2×D3)⋊C8—38no—
95#816—38no—
96C23×C32C2×D411yescharacteristic
97C22×C3⋊D3—22no—
98C22×C3⋊D3—22no—
99C22×C3⋊D3Q1614yescomplemented
100C22×C3⋊D3C2×D412yes—
101C32×Q8—24no—
102C32×Q8—42no—
103C2×C32×C4—22no—
104C2×C32×C4—42no—
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D414yes—
107C2×C32×C4C2411yescharacteristic
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3—22no—
110C2×C3⋊Dic3—42no—
111C2×C3⋊Dic3C2×D412yes—
112C4×C3⋊D3—24no—
113C4×C3⋊D3—24no—
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—32no—
124C2×C22⋊Q8—91no—
125#451—98no—
126C2×#103—92no—
127C2×C22⋊C8—91no—
128C23×D3—32no—
129C23×D3—61no—
130C2×C3×Q8—22no—
131C2×C3×Q8—22no—
132C2×C3×Q8—24no—
133C2×C3×Q8—24no—
134C2×C3×Q8—22no—
135C2×C3×Q8—38no—
136C2×C3×Q8—34no—
137C2×C3×Q8—44no—
138C2×C3×Q8—62no—
139C2×C3×Q8—64no—
140C2×C3×Q8C22×D314yes—
141C22×C3×C4—22no—
142C22×C3×C4—22no—
143C22×C3×C4—21no—
144C22×C3×C4—62no—
145C22×C3×C4C22×D312yes—
146C22×Dic3—22no—
147C22×Dic3—32no—
148C22×Dic3—61no—
149C22×Dic3—62no—
150C22×Dic3—62no—
151D3×Q8—616no—
152D3×Q8—632no—
153D3×Q8—616no—
154C2×C4×D3—34no—
155C2×C4×D3—34no—
156C2×C4×D3—62no—
157C2×C4×D3—62no—
158C2×C4×D3—68no—
159C2×C4×D3—616no—
160C2×C4×D3—64no—
161C2×C4×D3—64no—
162C2×C4×D3—124no—
163C2×Dic6—24no—
164C2×Dic6—22no—
165C2×Dic6—68no—
166C2×Dic6—616no—
167C2×Dic6#6718yes—
168C2×Dic6C22×D314yes—
169C3×Q16—616no—
170C2×C3×C8—34no—
171C2×C3×C8—64no—
172#216—216no—
173(C2×D3)⋊C4—68no—
174(C2×D3)⋊C4—68no—
175C4⋊Dic3—34no—
176C4⋊Dic3—62no—
177C4⋊Dic3—62no—
178C4⋊Dic3—62no—
179Dic3⋊C4—68no—
180Dic3⋊C4—68no—
181C2×C3⋊C8—24no—
182C2×C3⋊C8C22×D314yes—
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—181no—
200C22×Q8—182no—
201C22×Q8—188no—
202C22×Q8D3211yescharacteristic
203C23×C4—91no—
204C23×C4—181no—
205C2×Q16—38no—
206C2×Q16—68no—
207C22×C8—32no—
208C22⋊Q8—94no—
209C22⋊Q8—182no—
210C2×C4⋊C4—91no—
211C2×C4⋊C4—181no—
212C2×C22⋊C4—181no—
213#103—98no—
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—24no—
226C3×Q8—24no—
227C3×Q8—38no—
228C3×Q8—44no—
229C3×Q8—44no—
230C3×Q8—44no—
231C3×Q8—68no—
232C3×Q8—64no—
233C2×C3×C4—24no—
234C2×C3×C4—24no—
235C2×C3×C4—21no—
236C2×C3×C4—24no—
237C2×C3×C4—21no—
238C2×C3×C4—44no—
239C2×C3×C4—44no—
240C2×C3×C4—68no—
241C2×C3×C4—64no—
242C2×C3×C4D3×D414yes—
243C2×C3×C4D3×D412yes—
244C2×C3×C4C2×#6714yes—
245C2×C3×C4C23×D312yes—
246C2×Dic3—28no—
247C2×Dic3—24no—
248C2×Dic3—34no—
249C2×Dic3—62no—
250C2×Dic3—64no—
251C2×Dic3—64no—
252C2×Dic3—64no—
253C2×Dic3—122no—
254C2×Dic3—124no—
255C2×Dic3—124no—
256C4×D3—632no—
257C4×D3—68no—
258C4×D3—64no—
259C4×D3—64no—
260C4×D3—124no—
261C4×D3—124no—
262Dic6—28no—
263Dic6—24no—
264Dic6—632no—
265Dic6C2×#6718yes—
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—21no—
275C2×Q8—24no—
276C2×Q8—34no—
277C2×Q8—38no—
278C2×Q8—64no—
279C2×Q8—62no—
280C2×Q8—184no—
281C2×Q8—188no—
282C2×Q8—1816no—
283C2×Q8—1816no—
284C2×Q8C2×D3212yes—
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—616no—
296C2×C8—34no—
297C2×C8—64no—
298C4⋊C4—92no—
299C4⋊C4—184no—
300C4⋊C4—181no—
301C22⋊C4—184no—
302C22×C3—21no—
303C22×C3—22no—
304C22×C3—22no—
305C22×C3—22no—
306C22×C3D3×Q1614yes—
307C22×C3#91814yes—
308C22×C3#93714yes—
309C22×C3C2×D3×D412yes—
310C2×D3—38no—
311C2×D3—64no—
312C2×D3—616no—
313C2×D3—64no—
314C2×D3—64no—
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#93714yes—
324C3×C4C2×D3×D412yes—
325C3×C4C22×#6712yes—
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—24no—
338Q8—38no—
339Q8—42no—
340Q8—64no—
341Q8—68no—
342Q8—1816no—
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×#6714yes—
355C2×C4#381111yescharacteristic
356C2×C4C22×D3211yescharacteristic
357C8—64no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—24no—
361C2×C3—21no—
362C2×C3#518618yescomplemented
363C2×C3C2×D3×Q1612yes—
364C2×C3C2×#91812yes—
365C2×C3C2×#93712yes—
366D3—68no—
367D3—124no—
368C22—94no—
369C22—182no—
370C22—188no—
371C22—182no—
372C22#6394412yes—
373C22#6394512yes—
374C22#6398312yes—
375C22C2×#381111yescharacteristic
376C4—42no—
377C4—68no—
378C4—182no—
379C4—362no—
380C4#6398312yes—
381C4C2×D3×#6712yes—
382C3—21no—
383C3C2×#518612yescomplemented
384C2—184no—
385C2#1059165414yesdirect product factor
386C2C2×#6394411yescharacteristic
387C2C2×#6394511yescharacteristic
388C2C2×#6398311yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
hypercenterC22×Q8D32
hypocenterC32C2×#451
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. C22×C3×#216C2semidirect
4. #10591654C2direct (N × H)
5. C2×#63566C2semidirect
22. C2×C3×#216C22semidirect
24. #63566C22semidirect
30. C22×#216D3semidirect
85. C2×#216C2×D3semidirect
99. C22×C3⋊D3Q16semidirect
190. C2×C3⋊D3C2×Q16semidirect
268. C2×C32#451semidirect
331. C32C2×#451semidirect
362. C2×C3#5186semidirect
383. C3C2×#5186semidirect
385. C2#10591654direct (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×#641552
C22×C3×#2162
#105916542
C2×#635662
C2×#635572
C2×#51863