Finite Group Databasebeta

← C2×#10593210 #11922116

Subgroups — C2×#10593210 #11922116

Order 1152.

733 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 733 conjugacy classes of subgroups — too many to draw. Only its 83 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×D3×SL(2,𝔽3)C211yesmaximal, characteristic
2C22×C3×#226C211yesmaximal, characteristic, complemented
3C2×C3⋊#859C211yesmaximal, characteristic, complemented
4#10593210C214yesmaximal, direct product factor
5C2×#5419—31nomaximal
6C2×#5186—31nomaximal
7C22×C3×SL(2,𝔽3)C2211yescharacteristic
8C2×D3×SL(2,𝔽3)—22no—
9C2×D3×SL(2,𝔽3)C2212yes—
10C2×C3×#226—22no—
11C2×C3×#226C2212yescomplemented
12C2×(C2×D3)⋊Dic3—41nomaximal
13C3⋊#859C2212yescomplemented
14C22×D3×Q8D311yescharacteristic
15C23×SL(2,𝔽3)—31no—
16C22×#226D311yescharacteristic, complemented
17C22×C3×Q16—31no—
18C2×#946—31no—
19C22×#216—31no—
20#5419—34no—
21C2×#859—31no—
22C2×#859—61no—
23C2×#835—31no—
24#5186—34no—
25#5186—34no—
26C2×(C2×D3)⋊C8—31no—
27C2×#816—31no—
28C23×C3×D3—41no—
29C22×C3⋊Dic3—41no—
30C22×C3×Dic3—41no—
31C2×C3×SL(2,𝔽3)D412yes—
32C2×C3×SL(2,𝔽3)C2311yescharacteristic
33D3×SL(2,𝔽3)—22no—
34C3×#226—22no—
35(C2×D3)⋊Dic3—44no—
36C2×#451—91noSylow
37C22×C3×Q8—31no—
38C22×C3×Q8C2×D311yescharacteristic
39C2×D3×Q8—22no—
40C2×D3×Q8—32no—
41C2×D3×Q8—62no—
42C2×D3×Q8C2×D312yes—
43C22×C4×D3—31no—
44C22×Dic6—31no—
45C22×SL(2,𝔽3)—21no—
46C22×SL(2,𝔽3)—32no—
47C22×SL(2,𝔽3)—62no—
48C22×SL(2,𝔽3)C2×D311yescharacteristic
49C2×#226—22no—
50C2×#226C2×D312yescomplemented
51C2×C3×Q16—32no—
52C2×C3×Q16—32no—
53C2×C3×Q16—62no—
54C2×C3×Q16—62no—
55C22×C3×C8—31no—
56C2×#217—121no—
57#946—34no—
58#946—62no—
59C2×#216—34no—
60C2×#216—64no—
61C2×(C2×D3)⋊C4—61no—
62C2×C4⋊Dic3—31no—
63C2×Dic3⋊C4—61no—
64C22×C3⋊C8—31no—
65#859—32no—
66#859—62no—
67#835—32no—
68#835—32no—
69(C2×D3)⋊C8—34no—
70#816—34no—
71C23×C32—41no—
72C22×C3×D3—44no—
73C22×C3×D3—42no—
74C22×C3×D3—82no—
75C22×C3×D3—82no—
76C2×C3⋊Dic3—42no—
77C2×C3⋊Dic3—82no—
78C2×C3×Dic3—42no—
79C2×C3×Dic3—82no—
80C3×SL(2,𝔽3)C2×D411yescharacteristic
81C23×Q8—31no—
82C22×Q16—31no—
83C22×Q16—91no—
84C2×C22⋊Q8—91no—
85#451—94no—
86#451—94no—
87C2×#103—91no—
88C2×#103—91no—
89C2×C22⋊C8—91no—
90C24×C3—121no—
91C23×D3S411yescharacteristic
92C2×C3×Q8—31no—
93C2×C3×Q8—32no—
94C2×C3×Q8—32no—
95C2×C3×Q8—61no—
96C2×C3×Q8—62no—
97C2×C3×Q8—62no—
98C2×C3×Q8#6712yes—
99C2×C3×Q8C22×D311yescharacteristic
100C22×C3×C4—31no—
101C22×C3×C4—61no—
102C22×Dic3—31no—
103C22×Dic3—41no—
104C22×Dic3—61no—
105C22×Dic3—121no—
106C22×Dic3—241no—
107D3×Q8—22no—
108D3×Q8—62no—
109D3×Q8—64no—
110D3×Q8—64no—
111C2×C4×D3—32no—
112C2×C4×D3—32no—
113C2×C4×D3—62no—
114C2×C4×D3—62no—
115C2×Dic6—32no—
116C2×Dic6—34no—
117C2×Dic6—61no—
118C2×Dic6—62no—
119C2×SL(2,𝔽3)—22no—
120C2×SL(2,𝔽3)—21no—
121C2×SL(2,𝔽3)—62no—
122C2×SL(2,𝔽3)#6712yes—
123C2×SL(2,𝔽3)C22×D311yescharacteristic
124#226—22no—
125C3×Q16—64no—
126C3×Q16—62no—
127C3×Q16—62no—
128C2×C3×C8—32no—
129C2×C3×C8—62no—
130#217—124no—
131#216—68no—
132(C2×D3)⋊C4—64no—
133C4⋊Dic3—32no—
134C4⋊Dic3—61no—
135Dic3⋊C4—64no—
136C2×C3⋊C8—32no—
137C2×C3⋊C8—62no—
138C22×C32—42no—
139C22×C32—42no—
140C22×C32—42no—
141C22×C32—41no—
142C2×C3×D3—44no—
143C2×C3×D3—82no—
144C2×C3×D3—88no—
145C2×C3×D3—82no—
146C3⋊Dic3—82no—
147C3×Dic3—82no—
148C22×Q8—31no—
149C22×Q8—32no—
150C22×Q8—62no—
151C22×Q8—91no—
152C22×Q8—92no—
153C22×Q8—182no—
154C22×Q8D3211yescharacteristic
155C23×C4—91no—
156C2×Q16—32no—
157C2×Q16—32no—
158C2×Q16—62no—
159C2×Q16—62no—
160C2×Q16—94no—
161C2×Q16—184no—
162C22×C8—31no—
163C22×C8—91no—
164C22⋊Q8—94no—
165C22⋊Q8—182no—
166C2×C4⋊C4—91no—
167C2×C4⋊C4—181no—
168C2×C22⋊C4—181no—
169#103—94no—
170#103—92no—
171#103—92no—
172C22⋊C8—94no—
173C23×C3—41no—
174C23×C3—81no—
175C23×C3—122no—
176C23×C3—124no—
177C23×C3—242no—
178C23×C3—242no—
179C23×C3C2×S411yescharacteristic
180C22×D3—22no—
181C22×D3—22no—
182C22×D3#22614yescomplemented
183C22×D3C2×S412yes—
184C3×Q8—32no—
185C3×Q8—31no—
186C3×Q8—61no—
187C3×Q8—62no—
188C3×Q8—62no—
189C3×Q8—122no—
190C3×Q8C2×#6711yescharacteristic
191C2×C3×C4—32no—
192C2×C3×C4—32no—
193C2×C3×C4—31no—
194C2×C3×C4—31no—
195C2×C3×C4—62no—
196C2×C3×C4—122no—
197C2×Dic3—32no—
198C2×Dic3—42no—
199C2×Dic3—62no—
200C2×Dic3—62no—
201C2×Dic3—82no—
202C2×Dic3—122no—
203C2×Dic3—122no—
204C2×Dic3—242no—
205C2×Dic3—242no—
206C2×Dic3—244no—
207C4×D3—62no—
208C4×D3—62no—
209C4×D3—64no—
210Dic6—34no—
211Dic6—64no—
212Dic6—62no—
213SL(2,𝔽3)—21no—
214SL(2,𝔽3)C2×#6711yescharacteristic
215C3×C8—62no—
216C3⋊C8—62no—
217C2×C32—41no—
218C2×C32—41no—
219C2×C32—41no—
220C2×C32—44no—
221C3×D3—84no—
222C24—31no—
223C2×Q8—31no—
224C2×Q8—32no—
225C2×Q8—32no—
226C2×Q8—61no—
227C2×Q8—62no—
228C2×Q8—62no—
229C2×Q8—62no—
230C2×Q8—92no—
231C2×Q8—94no—
232C2×Q8—181no—
233C2×Q8—182no—
234C2×Q8—184no—
235C2×Q8—182no—
236C2×Q8—184no—
237C2×Q8#62512yes—
238C2×Q8C2×D3211yescharacteristic
239C22×C4—31no—
240C22×C4—61no—
241C22×C4—92no—
242C22×C4—92no—
243C22×C4—91no—
244C22×C4—182no—
245C22×C4—182no—
246C22×C4—181no—
247Q16—64no—
248Q16—62no—
249Q16—62no—
250Q16—188no—
251C2×C8—32no—
252C2×C8—62no—
253C2×C8—92no—
254C2×C8—182no—
255C4⋊C4—92no—
256C4⋊C4—181no—
257C4⋊C4—184no—
258C22⋊C4—184no—
259C22×C3—41no—
260C22×C3—42no—
261C22×C3—42no—
262C22×C3—42no—
263C22×C3—81no—
264C22×C3—82no—
265C22×C3—82no—
266C22×C3—82no—
267C22×C3—124no—
268C22×C3—242no—
269C22×C3—248no—
270C22×C3—242no—
271C22×C3C2×#22612yes—
272C22×C3#98312yes—
273C22×C3GL(2,ℤ/4)12yes—
274C22×C3C22×S411yescharacteristic
275C2×D3—22no—
276C2×D3—22no—
277C2×D3—28no—
278C2×D3C2×#22614yescomplemented
279C3×C4—31no—
280C3×C4—31no—
281C3×C4—32no—
282C3×C4—122no—
283Dic3—62no—
284Dic3—82no—
285Dic3—122no—
286Dic3—242no—
287Dic3—244no—
288C32—41noSylow
289C23—32no—
290C23—34no—
291C23—62no—
292C23—62no—
293C23D3×S411yescharacteristic
294Q8—32no—
295Q8—31no—
296Q8—61no—
297Q8—62no—
298Q8—62no—
299Q8—94no—
300Q8—122no—
301Q8—182no—
302Q8—184no—
303Q8C2×#62511yescharacteristic
304C2×C4—31no—
305C2×C4—31no—
306C2×C4—32no—
307C2×C4—32no—
308C2×C4—62no—
309C2×C4—92no—
310C2×C4—122no—
311C2×C4—182no—
312C2×C4—182no—
313C2×C4—184no—
314C2×C4—182no—
315C2×C4—182no—
316C2×C4—362no—
317C8—62no—
318C8—182no—
319C2×C3—41no—
320C2×C3—41no—
321C2×C3—41no—
322C2×C3—44no—
323C2×C3—81no—
324C2×C3—81no—
325C2×C3—81no—
326C2×C3—84no—
327C2×C3—244no—
328C2×C3#541914yescomplemented
329C2×C3C22×#22611yescharacteristic
330C2×C3C2×#98311yescharacteristic
331C2×C3C2×GL(2,ℤ/4)11yescharacteristic
332D3—24no—
333C22—34no—
334C22—62no—
335C22—62no—
336C22—68no—
337C22D3×#22612yes—
338C22#6420212yes—
339C22#6420912yes—
340C22C2×D3×S411yescharacteristic
341C4—31no—
342C4—31no—
343C4—32no—
344C4—122no—
345C4—182no—
346C4—362no—
347C3—41no—
348C3—81no—
349C3C2×#541911yescharacteristic, complemented
350C2—64no—
351C2#1059321014yesdirect product factor
352C2C2×D3×#22611yescharacteristic
353C2C2×#6420211yescharacteristic
354C2C2×#6420911yescharacteristic
subgroupG/H
center, hypercenterC23D3×S4
commutator, cosocleC2×C3×SL(2,𝔽3)C23
FrattiniC22C2×D3×S4
FittingC22×C3×Q8C2×D3
socleC23×C3C2×S4
prime radicalC22×D3×SL(2,𝔽3)C2
hypocenterC3×SL(2,𝔽3)C2×D4
LCSG ▷ C2×C3×SL(2,𝔽3) ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C22×C3×#226C2semidirect
3. C2×C3⋊#859C2semidirect
4. #10593210C2direct (N × H)
11. C2×C3×#226C22semidirect
13. C3⋊#859C22semidirect
16. C22×#226D3semidirect
50. C2×#226C2×D3semidirect
182. C22×D3#226semidirect
278. C2×D3C2×#226semidirect
328. C2×C3#5419semidirect
349. C3C2×#5419semidirect
351. C2#10593210direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×SL(2,𝔽3)2
C22×C3×#2262
C2×C3⋊#8592
#105932102
C2×#54193
C2×#51863
C2×(C2×D3)⋊Dic34