Finite Group Databasebeta

← C2×#10593661 #11923069

Subgroups — C2×#10593661 #11923069

Order 1152.

916 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 916 conjugacy classes of subgroups — too many to draw. Only its 97 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×#41⋊C3C211yesmaximal, characteristic, complemented
2C22×C3⋊GL(2,𝔽3)C211yesmaximal, characteristic, complemented
3#10593661C214yesmaximal, direct product factor
4C2×C3⋊#859C211yesmaximal, characteristic, complemented
5C2×#5427—33nomaximal
6C2×#5238—31nomaximal
7C2×C3×#41⋊C3—22no—
8C2×C3×#41⋊C3C2212yescomplemented
9C22×C3×SL(2,𝔽3)C2211yescharacteristic
10C2×C3⋊GL(2,𝔽3)—22no—
11C2×C3⋊GL(2,𝔽3)C2212yescomplemented
12C2×#3752—41nomaximal
13C3⋊#859C2212yescomplemented
14C22×C3×#41D311yescharacteristic, complemented
15C22×#41⋊C3D313yescomplemented
16C22×GL(2,𝔽3)—33no—
17C22×#215—31no—
18C22×#213—31no—
19C2×#930—31no—
20#5427—312no—
21C2×#859—33no—
22#5238—34no—
23#5238—34no—
24C2×#835—31no—
25C2×#832—31no—
26C2×#830—31no—
27C23×C3⋊D3—41no—
28C22×C32×C4—41no—
29C22×C3⋊Dic3—41no—
30C3×#41⋊C3—22no—
31C2×C3×SL(2,𝔽3)D412yescomplemented
32C2×C3×SL(2,𝔽3)C2311yescharacteristic
33C3⋊GL(2,𝔽3)—22no—
34#3752—44no—
35C2×#449—91noSylow
36C2×C3×#41—22no—
37C2×C3×#41—32no—
38C2×C3×#41—62no—
39C2×C3×#41C2×D312yescomplemented
40C22×C3×Q8C2×D311yescharacteristic
41C22×C3×D4—31no—
42C23×C3×C4—31no—
43C22×#67—61no—
44C22×D12—31no—
45C2×#41⋊C3—26no—
46C2×#41⋊C3C2×D316yescomplemented
47C22×SL(2,𝔽3)C2×D313yes—
48C2×GL(2,𝔽3)—36no—
49C2×GL(2,𝔽3)—66no—
50C2×#215—32no—
51C2×#215—32no—
52C2×#215—62no—
53C2×#215—62no—
54C2×#213—34no—
55C2×#213—64no—
56#930—34no—
57#930—62no—
58C2×(C2×D3)⋊C4—61no—
59C2×(C2×D3)⋊C4—123no—
60C2×C4⋊Dic3—31no—
61C22×C3⋊C8—31no—
62C22×C3⋊C8—31no—
63#859—36no—
64#835—32no—
65#835—32no—
66#832—34no—
67#830—34no—
68C23×C32—41no—
69C22×C3⋊D3—42no—
70C22×C3⋊D3—44no—
71C22×C3⋊D3—82no—
72C22×C3⋊D3—82no—
73C2×C32×C4—42no—
74C2×C32×C4—82no—
75C2×C3⋊Dic3—42no—
76C2×C3⋊Dic3—82no—
77C3×SL(2,𝔽3)C2×D411yescharacteristic, complemented
78C22×#41C3⋊D311yescharacteristic, complemented
79C22×SD16—91no—
80C22×D8—91no—
81C2×#121—91no—
82#449—94no—
83#449—94no—
84C2×#103—91no—
85C2×#102—91no—
86C2×C22⋊C8—91no—
87C24×C3—31no—
88C23×D3—61no—
89C23×D3—123no—
90C3×#41—22no—
91C3×#41—64no—
92C3×#41—62no—
93C3×#41—64no—
94C2×C3×Q8—31no—
95C2×C3×Q8—32no—
96C2×C3×Q8#6712yes—
97C2×C3×Q8C22×D311yescharacteristic
98C2×C3×D4—32no—
99C2×C3×D4—34no—
100C2×C3×D4—61no—
101C2×C3×D4—62no—
102C22×C3×C4—31no—
103C22×C3×C4—32no—
104C22×C3×C4—32no—
105C22×C3×C4—43no—
106C22×C3×C4—62no—
107C22×C3×C4—62no—
108C22×C3×C4S411yescharacteristic
109C2×#67—64no—
110C2×#67—124no—
111C22×Dic3—61no—
112C22×Dic3—123no—
113C2×D12—32no—
114C2×D12—62no—
115C2×D12—62no—
116C2×D12—61no—
117#41⋊C3—26no—
118C2×SL(2,𝔽3)#6716yescomplemented
119C2×SL(2,𝔽3)C22×D313yes—
120GL(2,𝔽3)—66no—
121#215—64no—
122#215—62no—
123#215—62no—
124#213—68no—
125(C2×D3)⋊C4—64no—
126(C2×D3)⋊C4—1212no—
127C4⋊Dic3—32no—
128C4⋊Dic3—61no—
129C2×C3⋊C8—32no—
130C2×C3⋊C8—32no—
131C2×C3⋊C8—62no—
132C2×C3⋊C8—62no—
133C22×C32—42no—
134C22×C32—42no—
135C22×C32—42no—
136C22×C32—41no—
137C2×C3⋊D3—44no—
138C2×C3⋊D3—82no—
139C2×C3⋊D3—82no—
140C2×C3⋊D3—88no—
141C32×C4—82no—
142C3⋊Dic3—82no—
143C2×#41—22no—
144C2×#41—32no—
145C2×#41—62no—
146C2×#41C2×C3⋊D312yescomplemented
147C22×Q8C2×C3⋊D311yescharacteristic
148C22×D4—31no—
149C22×D4—91no—
150C22×D4—181no—
151C23×C4—31no—
152C2×SD16—92no—
153C2×SD16—92no—
154C2×SD16—182no—
155C2×SD16—182no—
156C2×D8—94no—
157C2×D8—184no—
158C22×C8—91no—
159C22×C8—91no—
160#121—94no—
161#121—182no—
162C2×C4⋊C4—91no—
163C2×C22⋊C4—181no—
164#103—92no—
165#103—92no—
166#102—94no—
167C22⋊C8—94no—
168C23×C3—32no—
169C23×C3—43no—
170C23×C3—62no—
171C23×C3—62no—
172C23×C3—62no—
173C23×C3C2×S411yescharacteristic
174C22×D3—62no—
175C22×D3—126no—
176C22×D3—1212no—
177C22×D3—122no—
178C22×D3—122no—
179C22×D3—122no—
180C22×D3—246no—
181C22×D3—246no—
182C3×Q8—32no—
183C3×Q8—31no—
184C3×Q8—61no—
185C3×Q8C2×#6711yescharacteristic
186C3×D4—34no—
187C3×D4—62no—
188C3×D4—64no—
189C2×C3×C4—22no—
190C2×C3×C4—32no—
191C2×C3×C4—32no—
192C2×C3×C4—31no—
193C2×C3×C4—31no—
194C2×C3×C4—46no—
195C2×C3×C4—62no—
196C2×C3×C4—62no—
197C2×C3×C4—64no—
198C2×C3×C4—86no—
199C2×C3×C4C2×S412yes—
200#67—128no—
201C2×Dic3—62no—
202C2×Dic3—126no—
203C2×Dic3—122no—
204C2×Dic3—246no—
205D12—62no—
206D12—62no—
207D12—122no—
208SL(2,𝔽3)C2×#6713yescomplemented
209C3⋊C8—62no—
210C3⋊C8—62no—
211C2×C32—41no—
212C2×C32—41no—
213C2×C32—41no—
214C2×C32—44no—
215C3⋊D3—84no—
216C24—31no—
217C24—181no—
218#41—22no—
219#41—64no—
220#41—62no—
221#41—64no—
222C2×Q8—31no—
223C2×Q8—32no—
224C2×Q8#63812yes—
225C2×Q8C22×C3⋊D311yescharacteristic
226C2×D4—32no—
227C2×D4—34no—
228C2×D4—61no—
229C2×D4—62no—
230C2×D4—92no—
231C2×D4—182no—
232C2×D4—182no—
233C2×D4—181no—
234C2×D4—184no—
235C2×D4—364no—
236C22×C4—31no—
237C22×C4—32no—
238C22×C4—32no—
239C22×C4—62no—
240C22×C4—62no—
241C22×C4—181no—
242C22×C4C3⋊S411yescharacteristic
243SD16—184no—
244SD16—182no—
245SD16—182no—
246D8—188no—
247C2×C8—92no—
248C2×C8—92no—
249C2×C8—182no—
250C2×C8—182no—
251C4⋊C4—92no—
252C4⋊C4—181no—
253C22⋊C4—184no—
254C22×C3—46no—
255C22×C3—46no—
256C22×C3—46no—
257C22×C3—43no—
258C22×C3—62no—
259C22×C3—62no—
260C22×C3—62no—
261C22×C3—124no—
262C22×C3#98512yes—
263C22×C3#98612yes—
264C22×C3GL(2,ℤ/4)12yes—
265C22×C3C22×S411yescharacteristic
266C2×D3—1212no—
267C2×D3—122no—
268C2×D3—122no—
269C2×D3—122no—
270C2×D3—246no—
271C2×D3—246no—
272C2×D3—2424no—
273C2×D3—244no—
274C3×C4—22no—
275C3×C4—31no—
276C3×C4—31no—
277C3×C4—32no—
278C3×C4—86no—
279Dic3—122no—
280Dic3—246no—
281C32—41noSylow
282C23—32no—
283C23—62no—
284C23—62no—
285C23—62no—
286C23—182no—
287C23—362no—
288C23—362no—
289C23—362no—
290C23C2×C3⋊S411yescharacteristic
291Q8—32no—
292Q8—31no—
293Q8—61no—
294Q8C2×#63811yescharacteristic
295D4—34no—
296D4—62no—
297D4—64no—
298D4—182no—
299D4—182no—
300D4—362no—
301D4—368no—
302C2×C4—22no—
303C2×C4—32no—
304C2×C4—32no—
305C2×C4—31no—
306C2×C4—31no—
307C2×C4—62no—
308C2×C4—62no—
309C2×C4—64no—
310C2×C4—182no—
311C2×C4—362no—
312C2×C4C2×C3⋊S412yes—
313C8—182no—
314C8—182no—
315C2×C3—412no—
316C2×C3—43no—
317C2×C3—43no—
318C2×C3—43no—
319C2×C3—122no—
320C2×C3#542714yescomplemented
321C2×C3C2×#98511yescharacteristic
322C2×C3C2×#98611yescharacteristic
323C2×C3C2×GL(2,ℤ/4)11yescharacteristic
324D3—2412no—
325D3—242no—
326C22—62no—
327C22—62no—
328C22—62no—
329C22—124no—
330C22—362no—
331C22—362no—
332C22—362no—
333C22—724no—
334C22#6426612yes—
335C22#6426712yes—
336C22#6426912yes—
337C22C22×C3⋊S411yescharacteristic
338C4—22no—
339C4—31no—
340C4—31no—
341C4—32no—
342C4—362no—
343C3—43no—
344C3C2×#542711yescharacteristic, complemented
345C2—122no—
346C2—722no—
347C2#1059366114yesdirect product factor
348C2C2×#6426611yescharacteristic
349C2C2×#6426711yescharacteristic
350C2C2×#6426911yescharacteristic
subgroupG/H
centerC23C2×C3⋊S4
commutator, cosocleC2×C3×SL(2,𝔽3)C23
FrattiniC22C22×C3⋊S4
FittingC22×C3×#41D3
socleC23×C3C2×S4
hypercenterC22×C4C3⋊S4
hypocenterC3×SL(2,𝔽3)C2×D4
LCSG ▷ C2×C3×SL(2,𝔽3) ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#41⋊C3C2semidirect
2. C22×C3⋊GL(2,𝔽3)C2semidirect
3. #10593661C2direct (N × H)
4. C2×C3⋊#859C2semidirect
8. C2×C3×#41⋊C3C22semidirect
11. C2×C3⋊GL(2,𝔽3)C22semidirect
13. C3⋊#859C22semidirect
14. C22×C3×#41D3semidirect
15. C22×#41⋊C3D3semidirect
31. C2×C3×SL(2,𝔽3)D4semidirect
39. C2×C3×#41C2×D3semidirect
46. C2×#41⋊C3C2×D3semidirect
77. C3×SL(2,𝔽3)C2×D4semidirect
78. C22×#41C3⋊D3semidirect
118. C2×SL(2,𝔽3)#67semidirect
146. C2×#41C2×C3⋊D3semidirect
208. SL(2,𝔽3)C2×#67semidirect
320. C2×C3#5427semidirect
344. C3C2×#5427semidirect
347. C2#10593661direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#41⋊C32
C22×C3⋊GL(2,𝔽3)2
#105936612
C2×C3⋊#8592
C2×#54273
C2×#52383
C2×#37524