Finite Group Databasebeta

← C2×#10593201 #11922098

Subgroups — C2×#10593201 #11922098

Order 1152.

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

normal subgroups only

This group has 593 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×C3⋊#226C211yesmaximal, characteristic
2C22×C3×#226C211yesmaximal, characteristic
3C2×Dic3×SL(2,𝔽3)C211yesmaximal, characteristic
4#10593201C214yesmaximal, direct product factor
5C2×C4⋊#226—31nomaximal
6C2×#5182—31nomaximal
7C22×C3×SL(2,𝔽3)C2211yescharacteristic
8C2×C3⋊#226—22no—
9C2×C3⋊#226C2212yes—
10C2×C3×#226—22no—
11C2×C3×#226C2212yes—
12C2×Dic3⋊Dic3—41nomaximal
13Dic3×SL(2,𝔽3)C2212yes—
14C22×#226—31no—
15C22×#226—61no—
16C22×#226D311yescharacteristic
17C22×C3×Q16—31no—
18C2×Q8×Dic3D311yescharacteristic
19C2×#944—31no—
20C22×#216—31no—
21C2×C4×SL(2,𝔽3)—31no—
22C4⋊#226—34no—
23C2×#835—31no—
24#5182—34no—
25#5182—34no—
26C2×#816—31no—
27C2×Dic3⋊C8—31no—
28C22×C3⋊Dic3—41no—
29C22×C3×Dic3—41no—
30C22×C3×Dic3—41no—
31C2×C3×SL(2,𝔽3)D412yes—
32C2×C3×SL(2,𝔽3)C2311yescharacteristic
33C3⋊#226—22no—
34C3×#226—22no—
35Dic3⋊Dic3—44no—
36C2×#462—91noSylow
37C22×C3×Q8—31no—
38C22×C3×Q8C2×D311yescharacteristic
39C22×Dic6—31no—
40C22×SL(2,𝔽3)—21no—
41C22×SL(2,𝔽3)C2×D311yescharacteristic
42C2×#226—22no—
43C2×#226—32no—
44C2×#226—62no—
45C2×#226—64no—
46C2×#226—62no—
47C2×#226C2×D312yes—
48C2×C3×Q16—32no—
49C2×C3×Q16—32no—
50C2×C3×Q16—62no—
51C2×C3×Q16—62no—
52C22×C3×C8—31no—
53Q8×Dic3—32no—
54Q8×Dic3C2×D312yes—
55#944—34no—
56#944—62no—
57C2×#216—32no—
58C2×#216—32no—
59C2×#216—62no—
60C2×#216—62no—
61C2×C4⋊Dic3—31no—
62C2×C4⋊Dic3—121no—
63C2×Dic3⋊C4—61no—
64C2×Dic3⋊C4—61no—
65C2×C4×Dic3—31no—
66C22×C3⋊C8—31no—
67C4×SL(2,𝔽3)—32no—
68#835—34no—
69#816—34no—
70Dic3⋊C8—34no—
71C23×C32—41no—
72C2×C3⋊Dic3—42no—
73C2×C3⋊Dic3—82no—
74C2×C3×Dic3—42no—
75C2×C3×Dic3—44no—
76C2×C3×Dic3—42no—
77C2×C3×Dic3—82no—
78C3×SL(2,𝔽3)C2×D411yescharacteristic
79C22×Q16—31no—
80C22×Q16—91no—
81C2×C4⋊Q8—91no—
82C2×C4×Q8—31no—
83#462—94no—
84#462—94no—
85C2×C4⋊C8—91no—
86C2×#103—91no—
87C2×#103—91no—
88C2×C3×Q8—31no—
89C2×C3×Q8—32no—
90C2×C3×Q8—32no—
91C2×C3×Q8—61no—
92C2×C3×Q8—62no—
93C2×C3×Q8—62no—
94C2×C3×Q8D1212yes—
95C2×C3×Q8C22×D311yescharacteristic
96C22×C3×C4—31no—
97C22×C3×C4—61no—
98C22×C3×C4—121no—
99C22×Dic3—31no—
100C22×Dic3—41no—
101C22×Dic3—61no—
102C22×Dic3—121no—
103C22×Dic3—241no—
104C22×Dic3S411yescharacteristic
105C2×Dic6—32no—
106C2×Dic6—62no—
107C2×Dic6—62no—
108C2×Dic6—61no—
109C2×SL(2,𝔽3)—22no—
110C2×SL(2,𝔽3)—21no—
111C2×SL(2,𝔽3)#6712yes—
112C2×SL(2,𝔽3)C22×D311yescharacteristic
113#226—22no—
114#226—64no—
115#226—62no—
116C3×Q16—64no—
117C3×Q16—62no—
118C3×Q16—62no—
119C2×C3×C8—32no—
120C2×C3×C8—62no—
121#216—64no—
122#216—62no—
123#216—62no—
124C4⋊Dic3—32no—
125C4⋊Dic3—61no—
126C4⋊Dic3—124no—
127Dic3⋊C4—64no—
128Dic3⋊C4—64no—
129C4×Dic3—32no—
130C4×Dic3—32no—
131C2×C3⋊C8—32no—
132C2×C3⋊C8—62no—
133C22×C32—42no—
134C22×C32—42no—
135C22×C32—42no—
136C22×C32—41no—
137C3⋊Dic3—82no—
138C3×Dic3—44no—
139C3×Dic3—82no—
140C22×Q8—31no—
141C22×Q8—91no—
142C22×Q8D3211yescharacteristic
143C2×Q16—32no—
144C2×Q16—32no—
145C2×Q16—62no—
146C2×Q16—62no—
147C2×Q16—92no—
148C2×Q16—92no—
149C2×Q16—182no—
150C2×Q16—182no—
151C22×C8—31no—
152C22×C8—91no—
153C4⋊Q8—94no—
154C4⋊Q8—182no—
155C4×Q8—32no—
156C4×Q8—92no—
157C2×C4⋊C4—91no—
158C2×C4⋊C4—181no—
159C2×C4⋊C4—181no—
160C2×C42—91no—
161C4⋊C8—94no—
162#103—94no—
163#103—94no—
164C23×C3—41no—
165C23×C3—81no—
166C23×C3C2×S411yescharacteristic
167C3×Q8—32no—
168C3×Q8—31no—
169C3×Q8—61no—
170C3×Q8—62no—
171C3×Q8—62no—
172C3×Q8—122no—
173C3×Q8C2×D1211yescharacteristic
174C2×C3×C4—32no—
175C2×C3×C4—32no—
176C2×C3×C4—31no—
177C2×C3×C4—31no—
178C2×C3×C4—62no—
179C2×C3×C4—122no—
180C2×C3×C4—124no—
181C2×C3×C4—122no—
182C2×Dic3—32no—
183C2×Dic3—42no—
184C2×Dic3—62no—
185C2×Dic3—62no—
186C2×Dic3—82no—
187C2×Dic3—122no—
188C2×Dic3—122no—
189C2×Dic3—242no—
190C2×Dic3—242no—
191C2×Dic3—244no—
192C2×Dic3#22614yescomplemented
193C2×Dic3C2×S412yes—
194Dic6—62no—
195Dic6—62no—
196Dic6—122no—
197SL(2,𝔽3)—21no—
198SL(2,𝔽3)C2×#6711yescharacteristic
199C3×C8—62no—
200C3⋊C8—62no—
201C2×C32—44no—
202C2×C32—41no—
203C2×C32—41no—
204C2×C32—41no—
205C2×Q8—31no—
206C2×Q8—32no—
207C2×Q8—32no—
208C2×Q8—61no—
209C2×Q8—62no—
210C2×Q8—62no—
211C2×Q8—92no—
212C2×Q8—181no—
213C2×Q8—182no—
214C2×Q8—182no—
215C2×Q8#62612yes—
216C2×Q8C2×D3211yescharacteristic
217C22×C4—31no—
218C22×C4—31no—
219C22×C4—61no—
220C22×C4—91no—
221C22×C4—181no—
222Q16—64no—
223Q16—62no—
224Q16—62no—
225Q16—184no—
226Q16—182no—
227Q16—182no—
228C2×C8—32no—
229C2×C8—62no—
230C2×C8—92no—
231C2×C8—182no—
232C4⋊C4—92no—
233C4⋊C4—184no—
234C4⋊C4—181no—
235C4⋊C4—184no—
236C42—92no—
237C42—92no—
238C22×C3—41no—
239C22×C3—42no—
240C22×C3—42no—
241C22×C3—42no—
242C22×C3—81no—
243C22×C3—82no—
244C22×C3—82no—
245C22×C3—82no—
246C22×C3C4⋊S412yes—
247C22×C3C2×#22612yes—
248C22×C3#98412yes—
249C22×C3C22×S411yescharacteristic
250C3×C4—31no—
251C3×C4—31no—
252C3×C4—32no—
253C3×C4—124no—
254C3×C4—122no—
255Dic3—62no—
256Dic3—82no—
257Dic3—122no—
258Dic3—242no—
259Dic3—244no—
260Dic3C2×#22614yescomplemented
261C32—41noSylow
262C23D3×S411yescharacteristic
263Q8—32no—
264Q8—31no—
265Q8—61no—
266Q8—62no—
267Q8—62no—
268Q8—122no—
269Q8—182no—
270Q8—182no—
271Q8—362no—
272Q8C2×#62611yescharacteristic
273C2×C4—31no—
274C2×C4—32no—
275C2×C4—31no—
276C2×C4—34no—
277C2×C4—32no—
278C2×C4—32no—
279C2×C4—62no—
280C2×C4—92no—
281C2×C4—122no—
282C2×C4—182no—
283C2×C4—182no—
284C2×C4—362no—
285C8—62no—
286C8—182no—
287C2×C3—41no—
288C2×C3—41no—
289C2×C3—41no—
290C2×C3—44no—
291C2×C3—81no—
292C2×C3—81no—
293C2×C3—81no—
294C2×C3—84no—
295C2×C3C4⋊#22614yescomplemented
296C2×C3C2×C4⋊S411yescharacteristic
297C2×C3C22×#22611yescharacteristic
298C2×C3C2×#98411yescharacteristic
299C22#6419612yes—
300C22D3×#22612yes—
301C22#6420712yes—
302C22C2×D3×S411yescharacteristic
303C4—34no—
304C4—31no—
305C4—31no—
306C4—32no—
307C4—122no—
308C4—182no—
309C4—362no—
310C3—41no—
311C3—81no—
312C3C2×C4⋊#22611yescharacteristic, complemented
313C2#1059320114yesdirect product factor
314C2C2×#6419611yescharacteristic
315C2C2×D3×#22611yescharacteristic
316C2C2×#6420711yescharacteristic
subgroupG/H
center, hypercenterC23D3×S4
commutator, cosocleC2×C3×SL(2,𝔽3)C23
FrattiniC22C2×D3×S4
FittingC22×C3×Q8C2×D3
socleC23×C3C2×S4
prime radicalC22×C3×SL(2,𝔽3)C22
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
4. #10593201C2direct (N × H)
192. C2×Dic3#226semidirect
260. Dic3C2×#226semidirect
295. C2×C3C4⋊#226semidirect
312. C3C2×C4⋊#226semidirect
313. C2#10593201direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3⋊#2262
C22×C3×#2262
C2×Dic3×SL(2,𝔽3)2
#105932012
C2×C4⋊#2263
C2×#51823
C2×Dic3⋊Dic34