Finite Group Databasebeta

← C2×#5819⋊C3 #11923375

Subgroups — C2×#5819⋊C3 #11923375

Order 1152.

733 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 733 conjugacy classes of subgroups — too many to draw. Only its 135 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
2#5819⋊C3C214yesmaximal, direct product factor
3C2×C3⋊(#131⋊C3)C212yesmaximal, complemented
4C2×#5819C311yesmaximal, characteristic, complemented
5C2×#568⋊C3—31nomaximal
6C2×C3×#41⋊C3C411yescharacteristic
7C2×C3×#41⋊C3C412yes—
8C2×C3×#41⋊C3C2211yescharacteristic
9C2×C3×#41⋊C3C2212yes—
10C22×C3×SL(2,𝔽3)C411yescharacteristic
11C2×C3×#208—41nomaximal
12C3⋊(#131⋊C3)C2214yescomplemented
13C22×C3×#41C2×C311yescharacteristic
14C22×#41⋊C3—21no—
15C22×#41⋊C3D311yescharacteristic
16#5819—34no—
17#5819C2×C314yescomplemented
18C2×#948—32no—
19C2×#948C2×C312yescomplemented
20C22×#208—31no—
21C22×#208—31no—
22#568⋊C3—34no—
23C2×#131⋊C3—32no—
24C22×C32×C4—41no—
25C3×#41⋊C3C2×C411yescharacteristic
26C3×#41⋊C3C2×C412yes—
27C3×#41⋊C3C2311yescharacteristic
28C2×C3×SL(2,𝔽3)C2×C411yescharacteristic
29C2×C3×SL(2,𝔽3)C2×C412yes—
30C3×#208—44no—
31C2×C3×C3⋊C8—42no—
32C2×#568—31noSylow
33C2×C3×#41—31no—
34C2×C3×#41—32no—
35C2×C3×#41—31no—
36C2×C3×#41—32no—
37C2×C3×#41C3×C411yescharacteristic
38C2×C3×#41C3×C412yes—
39C2×C3×#41C22×C311yescharacteristic
40C2×C3×#41C22×C312yes—
41C22×C3×Q8C3×C411yescharacteristic
42C22×C3×D4—31no—
43C23×C3×C4—31no—
44C2×#41⋊C3—21no—
45C2×#41⋊C3—22no—
46C2×#41⋊C3—22no—
47C2×#41⋊C3—21no—
48C2×#41⋊C3Dic311yescharacteristic
49C2×#41⋊C3Dic312yes—
50C2×#41⋊C3C2×D311yescharacteristic
51C2×#41⋊C3C2×D312yes—
52C22×SL(2,𝔽3)—21no—
53C22×SL(2,𝔽3)Dic311yescharacteristic
54C2×C3×M16—121no—
55#948—38no—
56#948—38no—
57#948—34no—
58#948C22×C314yescomplemented
59C2×#208—34no—
60C2×#208—31no—
61C2×#208—34no—
62C2×#208—34no—
63C2×#208—34no—
64C2×#208—32no—
65C2×#208—32no—
66C2×#208A411yescharacteristic
67C22×C3⋊C8—32no—
68C22×C3⋊C8—32no—
69#131⋊C3—34no—
70C23×C32—41no—
71C2×C32×C4—41no—
72C2×C32×C4—42no—
73C2×C32×C4—41no—
74C2×C32×C4—42no—
75C3×SL(2,𝔽3)C22×C411yescharacteristic
76C3×C3⋊C8—44no—
77C22×#41C3×D311yescharacteristic
78#568—34no—
79#568—94no—
80C2×#131—32no—
81C2×#131—92no—
82C22×M16—91no—
83C22×M16—91no—
84C24×C3—31no—
85C3×#41—32no—
86C3×#41—32no—
87C3×#41—34no—
88C3×#41—32no—
89C3×#41—31no—
90C3×#41—32no—
91C3×#41—32no—
92C3×#41—32no—
93C3×#41—31no—
94C3×#41—32no—
95C3×#41C2×C3×C411yescharacteristic
96C3×#41C2×C3×C412yes—
97C3×#41C23×C311yescharacteristic
98C2×C3×Q8—31no—
99C2×C3×Q8—32no—
100C2×C3×Q8C2×C3×C411yescharacteristic
101C2×C3×Q8C2×C3×C412yes—
102C2×C3×D4—31no—
103C2×C3×D4—32no—
104C2×C3×D4—31no—
105C2×C3×D4—32no—
106C2×C3×D4—32no—
107C2×C3×D4—34no—
108C22×C3×C4—31no—
109C22×C3×C4—31no—
110C22×C3×C4—32no—
111C22×C3×C4—31no—
112C22×C3×C4—32no—
113C22×C3×C4—31no—
114C22×C3×C4—31no—
115C22×C3×C4—32no—
116C22×C3×C4—32no—
117C22×C3×C4—41no—
118C22×C3×C4—81no—
119C22×C3×C4C2×A411yescharacteristic
120#41⋊C3—22no—
121#41⋊C3—21no—
122#41⋊C3—21no—
123#41⋊C3C2×Dic311yescharacteristic
124#41⋊C3C2×Dic312yes—
125#41⋊C3C22×D311yescharacteristic
126C2×SL(2,𝔽3)—22no—
127C2×SL(2,𝔽3)—21no—
128C2×SL(2,𝔽3)C2×Dic311yescharacteristic
129C2×SL(2,𝔽3)C2×Dic312yes—
130C3×M16—124no—
131C2×C3×C8—122no—
132#208—34no—
133#208—34no—
134#208—38no—
135#208—34no—
136#208C2×A414yes—
137C2×C3⋊C8—38no—
138C2×C3⋊C8—32no—
139C2×C3⋊C8—34no—
140C2×C3⋊C8—34no—
141C2×C3⋊C8C2×A412yes—
142C22×C32—41no—
143C22×C32—42no—
144C22×C32—82no—
145C32×C4—41no—
146C32×C4—42no—
147C32×C4—41no—
148C2×#41—31no—
149C2×#41—32no—
150C2×#41—31no—
151C2×#41—32no—
152C2×#41C3×Dic311yescharacteristic
153C2×#41C3×Dic312yes—
154C2×#41C2×C3×D311yescharacteristic
155C2×#41C2×C3×D312yes—
156C22×Q8C3×Dic311yescharacteristic
157C22×D4—31no—
158C23×C4—31no—
159#131—34no—
160#131—98no—
161#131—98no—
162#131—94no—
163C2×M16—31no—
164C2×M16—92no—
165C2×M16—94no—
166C2×M16—94no—
167C2×M16—94no—
168C2×M16—91no—
169C2×M16—94no—
170C2×M16—92no—
171C22×C8—92no—
172C22×C8—92no—
173C23×C3—31no—
174C23×C3—31no—
175C23×C3—32no—
176C23×C3—32no—
177C23×C3—41no—
178C23×C3—81no—
179C23×C3—122no—
180C23×C3C4×A411yescharacteristic
181C3×Q8—32no—
182C3×Q8—31no—
183C3×Q8—32no—
184C3×Q8C22×C3×C411yescharacteristic
185C3×D4—32no—
186C3×D4—31no—
187C3×D4—31no—
188C3×D4—32no—
189C3×D4—34no—
190C3×D4—32no—
191C3×D4—34no—
192C2×C3×C4—32no—
193C2×C3×C4—31no—
194C2×C3×C4—32no—
195C2×C3×C4—31no—
196C2×C3×C4—31no—
197C2×C3×C4—32no—
198C2×C3×C4—32no—
199C2×C3×C4—32no—
200C2×C3×C4—32no—
201C2×C3×C4—31no—
202C2×C3×C4—32no—
203C2×C3×C4—32no—
204C2×C3×C4—31no—
205C2×C3×C4—31no—
206C2×C3×C4—42no—
207C2×C3×C4—41no—
208C2×C3×C4—41no—
209C2×C3×C4—42no—
210C2×C3×C4—82no—
211C2×C3×C4—81no—
212C2×C3×C4—81no—
213C2×C3×C4—82no—
214C2×C3×C4C4×A412yes—
215C2×C3×C4C4×A411yescharacteristic
216C2×C3×C4C22×A412yes—
217C2×C3×C4C22×A411yescharacteristic
218SL(2,𝔽3)—21no—
219SL(2,𝔽3)C22×Dic311yescharacteristic
220C3×C8—124no—
221C3⋊C8—34no—
222C3⋊C8C22×A414yes—
223C2×C32—41no—
224C2×C32—42no—
225C2×C32—82no—
226C24—31no—
227#41—32no—
228#41—32no—
229#41—34no—
230#41—32no—
231#41—31no—
232#41—32no—
233#41—32no—
234#41—32no—
235#41—31no—
236#41—32no—
237#41C2×C3×Dic311yescharacteristic
238#41C2×C3×Dic312yes—
239#41C22×C3×D311yescharacteristic
240C2×Q8—31no—
241C2×Q8—32no—
242C2×Q8C2×C3×Dic311yescharacteristic
243C2×Q8C2×C3×Dic312yes—
244C2×D4—31no—
245C2×D4—32no—
246C2×D4—31no—
247C2×D4—32no—
248C2×D4—32no—
249C2×D4—34no—
250C22×C4—31no—
251C22×C4—32no—
252C22×C4—32no—
253C22×C4—31no—
254C22×C4—31no—
255C22×C4—31no—
256C22×C4—32no—
257C22×C4—31no—
258C22×C4—32no—
259C22×C4D3×A411yescharacteristic
260M16—34no—
261M16—98no—
262M16—94no—
263M16—94no—
264M16—94no—
265C2×C8—32no—
266C2×C8—94no—
267C2×C8—94no—
268C2×C8—98no—
269C2×C8—92no—
270C22×C3—22no—
271C22×C3—31no—
272C22×C3—32no—
273C22×C3—31no—
274C22×C3—41no—
275C22×C3—42no—
276C22×C3—62no—
277C22×C3—62no—
278C22×C3—82no—
279C22×C3—84no—
280C22×C3—82no—
281C22×C3—81no—
282C22×C3—122no—
283C22×C3—122no—
284C22×C3C2×C4×A412yes—
285C22×C3C2×C4×A411yescharacteristic
286C3×C4—31no—
287C3×C4—32no—
288C3×C4—31no—
289C3×C4—42no—
290C3×C4—41no—
291C3×C4—41no—
292C3×C4—82no—
293C3×C4—81no—
294C3×C4—81no—
295C3×C4C2×C4×A412yes—
296C3×C4C2×C4×A411yescharacteristic
297C3×C4C23×A411yescharacteristic
298C32—41noSylow
299C23—31no—
300C23—31no—
301C23—32no—
302C23—32no—
303C23—122no—
304C23Dic3×A411yescharacteristic
305Q8—32no—
306Q8—31no—
307Q8—32no—
308Q8C22×C3×Dic311yescharacteristic
309D4—32no—
310D4—31no—
311D4—31no—
312D4—32no—
313D4—34no—
314D4—32no—
315D4—34no—
316C2×C4—32no—
317C2×C4—31no—
318C2×C4—32no—
319C2×C4—31no—
320C2×C4—32no—
321C2×C4—31no—
322C2×C4—32no—
323C2×C4—32no—
324C2×C4—32no—
325C2×C4—31no—
326C2×C4—32no—
327C2×C4—31no—
328C2×C4—31no—
329C2×C4—32no—
330C2×C4Dic3×A411yescharacteristic
331C2×C4Dic3×A412yes—
332C2×C4C2×D3×A412yes—
333C2×C4C2×D3×A411yescharacteristic
334C8—34no—
335C8—94no—
336C2×C3—22no—
337C2×C3—41no—
338C2×C3—42no—
339C2×C3—61no—
340C2×C3—62no—
341C2×C3—61no—
342C2×C3—82no—
343C2×C3—84no—
344C2×C3—81no—
345C2×C3—82no—
346C2×C3#568⋊C312yescomplemented
347C2×C3C22×C4×A411yescharacteristic
348C22—22no—
349C22—32no—
350C22—31no—
351C22—31no—
352C22—62no—
353C22—62no—
354C22—122no—
355C22—122no—
356C22C2×Dic3×A412yes—
357C22C2×Dic3×A411yescharacteristic
358C4—31no—
359C4—32no—
360C4—31no—
361C4C2×Dic3×A412yes—
362C4C2×Dic3×A411yescharacteristic
363C4C22×D3×A411yescharacteristic
364C3—41no—
365C3—81no—
366C3C2×#568⋊C311yescharacteristic, complemented
367C2—22no—
368C2—62no—
369C2—61no—
370C2—61no—
371C2#5819⋊C312yesdirect product factor
372C2C22×Dic3×A411yescharacteristic
subgroupG/H
centerC2×C4C2×D3×A4
commutator, hypocenterC3×Q8C22×C3×C4
FrattiniC4C22×D3×A4
FittingC22×C3×#41C2×C3
socleC22×C3C2×C4×A4
prime radicalC22×C3×#41⋊C3C2
cosocleC3×#41C23×C3
hypercenterC22×C4D3×A4
LCSG ▷ C3×Q8
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #5819⋊C3C2direct (N × H)
3. C2×C3⋊(#131⋊C3)C2semidirect
4. C2×#5819C3semidirect
12. C3⋊(#131⋊C3)C22semidirect
17. #5819C2×C3semidirect
19. C2×#948C2×C3semidirect
58. #948C22×C3semidirect
346. C2×C3#568⋊C3semidirect
366. C3C2×#568⋊C3semidirect
371. C2#5819⋊C3direct (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
#5819⋊C32
C2×C3⋊(#131⋊C3)2
C2×#58193
C2×#568⋊C33
C2×C3×#2084