Finite Group Databasebeta

← C2×#10593194 #11922089

Subgroups — C2×#10593194 #11922089

Order 1152.

673 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 673 conjugacy classes of subgroups — too many to draw. Only its 75 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⋊C3)C211yesmaximal, characteristic
2C22×C3×#226C211yesmaximal, characteristic, complemented
3C2×C3⋊#859C211yesmaximal, characteristic, complemented
4#10593194C214yesmaximal, direct product factor
5C2×#5425—31nomaximal
6C2×#5187—31nomaximal
7C22×C3×SL(2,𝔽3)C2211yescharacteristic
8C2×C3⋊(#41⋊C3)—22no—
9C2×C3⋊(#41⋊C3)C2212yes—
10C2×C3×#226—22no—
11C2×C3×#226C2212yescomplemented
12C2×#3724—41nomaximal
13C3⋊#859C2212yescomplemented
14C22×#239D311yescharacteristic
15C22×#41⋊C3—31no—
16C22×#226D311yescharacteristic, complemented
17C22×C3×Q16—31no—
18C2×#946—31no—
19C22×#215—31no—
20#5425—34no—
21C2×#859—31no—
22C2×#859—61no—
23C2×#835—31no—
24#5187—34no—
25#5187—34no—
26C2×#821—31no—
27C2×(C2×D3)⋊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⋊(#41⋊C3)—22no—
34C3×#226—22no—
35#3724—44no—
36C2×#452—91noSylow
37C22×C3×Q8—31no—
38C22×C3×Q8C2×D311yescharacteristic
39C2×#239—22no—
40C2×#239—32no—
41C2×#239—62no—
42C2×#239C2×D312yes—
43C22×D12—31no—
44C22×C4×D3—31no—
45C2×#41⋊C3—32no—
46C2×#41⋊C3—62no—
47C22×SL(2,𝔽3)—21no—
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—
56#946—34no—
57#946—62no—
58C2×#215—34no—
59C2×#215—64no—
60C2×(C2×D3)⋊C4—61no—
61C2×C4⋊Dic3—31no—
62C2×Dic3⋊C4—61no—
63C2×Dic3⋊C4—121no—
64C22×C3⋊C8—31no—
65#859—32no—
66#859—62no—
67#835—32no—
68#835—32no—
69#821—34no—
70(C2×D3)⋊C8—34no—
71C23×C32—41no—
72C2×C3⋊Dic3—42no—
73C2×C3⋊Dic3—44no—
74C2×C3×Dic3—42no—
75C2×C3×Dic3—42no—
76C2×C3×Dic3—82no—
77C2×C3×Dic3—82no—
78C3×SL(2,𝔽3)C2×D411yescharacteristic
79C22×#41—31no—
80C22×Q16—31no—
81C22×SD16—91no—
82C2×C22⋊Q8—91no—
83#452—94no—
84#452—94no—
85C2×#103—91no—
86C2×#102—91no—
87C2×C22⋊C8—91no—
88C23×D3—31no—
89C2×C3×Q8—31no—
90C2×C3×Q8—32no—
91C2×C3×Q8—32no—
92C2×C3×Q8—61no—
93C2×C3×Q8—62no—
94C2×C3×Q8—62no—
95C2×C3×Q8#6712yes—
96C2×C3×Q8C22×D311yescharacteristic
97C22×C3×C4—31no—
98C22×C3×C4—61no—
99C22×C3×C4—121no—
100C22×Dic3—41no—
101C22×Dic3—61no—
102C22×Dic3—121no—
103C22×Dic3—241no—
104C22×Dic3S411yescharacteristic
105#239—22no—
106#239—64no—
107#239—62no—
108#239—64no—
109C2×D12—32no—
110C2×D12—34no—
111C2×D12—61no—
112C2×D12—62no—
113C2×C4×D3—32no—
114C2×C4×D3—32no—
115C2×C4×D3—62no—
116C2×C4×D3—62no—
117#41⋊C3—62no—
118C2×SL(2,𝔽3)—22no—
119C2×SL(2,𝔽3)—21no—
120C2×SL(2,𝔽3)#6712yes—
121C2×SL(2,𝔽3)C22×D311yescharacteristic
122#226—22no—
123C3×Q16—64no—
124C3×Q16—62no—
125C3×Q16—62no—
126C2×C3×C8—32no—
127C2×C3×C8—62no—
128#215—68no—
129(C2×D3)⋊C4—64no—
130C4⋊Dic3—32no—
131C4⋊Dic3—61no—
132Dic3⋊C4—64no—
133Dic3⋊C4—124no—
134C2×C3⋊C8—32no—
135C2×C3⋊C8—62no—
136C22×C32—42no—
137C22×C32—42no—
138C22×C32—42no—
139C22×C32—41no—
140C3⋊Dic3—44no—
141C3×Dic3—82no—
142C3×Dic3—82no—
143C2×#41—32no—
144C2×#41—62no—
145C2×#41—92no—
146C2×#41—182no—
147C22×Q8—31no—
148C22×Q8D3211yescharacteristic
149C22×D4—91no—
150C23×C4—91no—
151C2×Q16—32no—
152C2×Q16—32no—
153C2×Q16—62no—
154C2×Q16—62no—
155C2×SD16—94no—
156C2×SD16—184no—
157C22×C8—31no—
158C22×C8—91no—
159C22⋊Q8—94no—
160C22⋊Q8—182no—
161C2×C4⋊C4—91no—
162C2×C4⋊C4—181no—
163C2×C22⋊C4—181no—
164#103—92no—
165#103—92no—
166#102—94no—
167C22⋊C8—94no—
168C23×C3—41no—
169C23×C3—81no—
170C23×C3C2×S411yescharacteristic
171C22×D3—32no—
172C22×D3—62no—
173C22×D3—62no—
174C22×D3—62no—
175C3×Q8—32no—
176C3×Q8—31no—
177C3×Q8—61no—
178C3×Q8—62no—
179C3×Q8—62no—
180C3×Q8—122no—
181C3×Q8C2×#6711yescharacteristic
182C2×C3×C4—32no—
183C2×C3×C4—32no—
184C2×C3×C4—31no—
185C2×C3×C4—31no—
186C2×C3×C4—62no—
187C2×C3×C4—122no—
188C2×C3×C4—122no—
189C2×C3×C4—242no—
190C2×Dic3—22no—
191C2×Dic3—42no—
192C2×Dic3—62no—
193C2×Dic3—82no—
194C2×Dic3—122no—
195C2×Dic3—124no—
196C2×Dic3—122no—
197C2×Dic3—242no—
198C2×Dic3—244no—
199C2×Dic3C2×S412yes—
200D12—34no—
201D12—62no—
202D12—64no—
203C4×D3—62no—
204C4×D3—62no—
205C4×D3—64no—
206SL(2,𝔽3)—21no—
207SL(2,𝔽3)C2×#6711yescharacteristic
208C3×C8—62no—
209C3⋊C8—62no—
210C2×C32—41no—
211C2×C32—41no—
212C2×C32—41no—
213C2×C32—44no—
214C24—91no—
215#41—62no—
216#41—184no—
217#41—182no—
218#41—184no—
219C2×Q8—31no—
220C2×Q8—32no—
221C2×Q8—32no—
222C2×Q8—61no—
223C2×Q8—62no—
224C2×Q8—62no—
225C2×Q8#62512yes—
226C2×Q8C2×D3211yescharacteristic
227C2×D4—92no—
228C2×D4—94no—
229C2×D4—181no—
230C2×D4—182no—
231C22×C4—31no—
232C22×C4—31no—
233C22×C4—61no—
234C22×C4—92no—
235C22×C4—92no—
236C22×C4—182no—
237C22×C4—182no—
238C22×C4—181no—
239Q16—64no—
240Q16—62no—
241Q16—62no—
242SD16—188no—
243C2×C8—32no—
244C2×C8—62no—
245C2×C8—92no—
246C2×C8—182no—
247C4⋊C4—92no—
248C4⋊C4—184no—
249C4⋊C4—181no—
250C22⋊C4—184no—
251C22×C3—41no—
252C22×C3—42no—
253C22×C3—42no—
254C22×C3—42no—
255C22×C3—81no—
256C22×C3—82no—
257C22×C3—82no—
258C22×C3—82no—
259C22×C3#98412yes—
260C22×C3#98512yes—
261C22×C3GL(2,ℤ/4)12yes—
262C22×C3C22×S411yescharacteristic
263C2×D3—62no—
264C2×D3—62no—
265C2×D3—62no—
266C2×D3—124no—
267C3×C4—31no—
268C3×C4—31no—
269C3×C4—32no—
270C3×C4—122no—
271C3×C4—242no—
272Dic3—22no—
273Dic3—82no—
274Dic3—124no—
275Dic3—122no—
276Dic3—244no—
277C32—41noSylow
278C23—92no—
279C23—182no—
280C23—182no—
281C23—182no—
282C23D3×S411yescharacteristic
283Q8—32no—
284Q8—31no—
285Q8—61no—
286Q8—62no—
287Q8—62no—
288Q8—122no—
289Q8C2×#62511yescharacteristic
290D4—94no—
291D4—182no—
292D4—184no—
293C2×C4—31no—
294C2×C4—31no—
295C2×C4—32no—
296C2×C4—32no—
297C2×C4—32no—
298C2×C4—62no—
299C2×C4—62no—
300C2×C4—122no—
301C2×C4—182no—
302C2×C4—182no—
303C2×C4—184no—
304C2×C4—182no—
305C2×C4—362no—
306C8—62no—
307C8—182no—
308C2×C3—41no—
309C2×C3—41no—
310C2×C3—41no—
311C2×C3—44no—
312C2×C3—81no—
313C2×C3—81no—
314C2×C3—81no—
315C2×C3—84no—
316C2×C3#542514yescomplemented
317C2×C3C2×#98411yescharacteristic
318C2×C3C2×#98511yescharacteristic
319C2×C3C2×GL(2,ℤ/4)11yescharacteristic
320D3—122no—
321C22—182no—
322C22—182no—
323C22—182no—
324C22—364no—
325C22#6419612yes—
326C22#6419812yes—
327C22#6420912yes—
328C22C2×D3×S411yescharacteristic
329C4—31no—
330C4—31no—
331C4—32no—
332C4—62no—
333C4—122no—
334C4—362no—
335C3—41no—
336C3—81no—
337C3C2×#542511yescharacteristic, complemented
338C2—362no—
339C2#1059319414yesdirect product factor
340C2C2×#6419611yescharacteristic
341C2C2×#6419811yescharacteristic
342C2C2×#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×C3⋊(#41⋊C3)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. #10593194C2direct (N × H)
11. C2×C3×#226C22semidirect
13. C3⋊#859C22semidirect
16. C22×#226D3semidirect
50. C2×#226C2×D3semidirect
316. C2×C3#5425semidirect
337. C3C2×#5425semidirect
339. C2#10593194direct (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⋊C3)2
C22×C3×#2262
C2×C3⋊#8592
#105931942
C2×#54253
C2×#51873
C2×#37244