Finite Group Databasebeta

← C2×#5837⋊C3 #11923402

Subgroups — C2×#5837⋊C3 #11923402

Order 1152.

733 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 733 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C2×C3×2−1+4⋊C3C211yesmaximal, characteristic, complemented
2C2×C3⋊#994C211yesmaximal, characteristic, complemented
3#5837⋊C3C214yesmaximal, direct product factor
4C2×C3⋊(#131⋊C3)C211yesmaximal, characteristic, complemented
5C2×#5837C311yesmaximal, characteristic, complemented
6C2×#577⋊C3—31nomaximal
7C3×2−1+4⋊C3—21no—
8C3×2−1+4⋊C3C2212yescomplemented
9C2×C3×#41⋊C3C2211yescharacteristic
10C22×C3×SL(2,𝔽3)—21no—
11C3⋊#994—21no—
12C3⋊#994C2212yescomplemented
13C2×C3⋊(#41⋊C3)—21no—
14C2×C3×#214—41nomaximal
15C3⋊(#131⋊C3)C2212yescomplemented
16C2×C3×2−1+4C2×C311yescharacteristic
17C2×#1009C2×C311yescharacteristic, complemented
18C2×2−1+4⋊C3—21no—
19C2×2−1+4⋊C3D311yescharacteristic, complemented
20C2×#994—31no—
21#5837—34no—
22#5837C2×C314yescomplemented
23C2×#950—31no—
24C2×#949—31no—
25C2×#948C2×C311yescharacteristic, complemented
26C2×#942—31no—
27C22×#215—31no—
28#577⋊C3—34no—
29C2×#131⋊C3—31no—
30C2×C32×D4—41no—
31C2×C3×Dic6—41no—
32C3×#41⋊C3D411yescharacteristic
33C3×#41⋊C3C2311yescharacteristic
34C2×C3×SL(2,𝔽3)—22no—
35C2×C3×SL(2,𝔽3)D411yescharacteristic
36C3⋊(#41⋊C3)—22no—
37C3×#214—44no—
38C2×C3×C3⋊C8—41no—
39C2×#577—31noSylow
40C3×2−1+4—21no—
41C3×2−1+4—32no—
42C3×2−1+4—61no—
43C3×2−1+4C22×C312yes—
44C2×C3×#41—31no—
45C2×C3×#41—61no—
46C2×C3×#41C22×C311yescharacteristic
47C22×C3×Q8—21no—
48C22×C3×Q8—31no—
49#1009—21no—
50#1009—32no—
51#1009—61no—
52#1009C22×C312yescomplemented
53C2×#239—21no—
54C2×D3×D4—61no—
55C2×#235—31no—
56C22×D12—31no—
572−1+4⋊C3—22no—
582−1+4⋊C3—21no—
592−1+4⋊C3—22no—
602−1+4⋊C3C2×D312yescomplemented
61#994—32no—
62#994—61no—
63C2×#41⋊C3—21no—
64C2×#41⋊C3—61no—
65C2×#41⋊C3C2×D311yescharacteristic
66C22×SL(2,𝔽3)—22no—
67C22×SL(2,𝔽3)—21no—
68C2×C3×SD16—121no—
69#950—34no—
70#950—34no—
71#949—34no—
72#949—34no—
73#948—32no—
74#948C22×C312yescomplemented
75C2×#216—31no—
76#942—34no—
77#942—34no—
78C2×#215—32no—
79C2×#215—34no—
80C2×#215—34no—
81C2×#215—31no—
82C2×#214A411yescharacteristic
83C2×#213—31no—
84C2×#208—31no—
85C22×C3⋊C8—31no—
86#131⋊C3—32no—
87C23×C32—81no—
88C32×D4—42no—
89C32×D4—81no—
90C2×C32×C4—41no—
91C2×C3×Dic3—81no—
92C3×Dic6—42no—
93C3×Dic6—81no—
94C3×SL(2,𝔽3)C2×D411yescharacteristic
95C3×C3⋊C8—42no—
96C2×2−1+4C3×D311yescharacteristic
97C2×H(5,𝔽2)—31no—
98#577—34no—
99#577—94no—
100C2×#137—91no—
101C2×AGL(1,ℤ/8)—91no—
102C2×#135—91no—
103C22×SD16—91no—
104C2×#131—31no—
105C23×D3—61no—
106C3×#41—31no—
107C3×#41—31no—
108C3×#41—32no—
109C3×#41—32no—
110C3×#41—61no—
111C3×#41—61no—
112C3×#41—64no—
113C3×#41—62no—
114C3×#41—62no—
115C3×#41C3×D411yescharacteristic
116C3×#41C23×C311yescharacteristic
117C2×C3×Q8—22no—
118C2×C3×Q8—32no—
119C2×C3×Q8—32no—
120C2×C3×Q8—31no—
121C2×C3×Q8—61no—
122C2×C3×Q8—61no—
123C2×C3×Q8—61no—
124C2×C3×Q8—62no—
125C2×C3×Q8—121no—
126C2×C3×Q8C3×D411yescharacteristic
127C2×C3×D4—31no—
128C2×C3×D4—41no—
129C2×C3×D4—61no—
130C2×C3×D4—81no—
131C2×C3×D4C2×A411yescharacteristic
132C22×C3×C4—31no—
133C22×C3×C4—61no—
134C22×C3×C4—61no—
135C2×#67—61no—
136#239—22no—
137#239—62no—
138D3×D4—64no—
139D3×D4—62no—
140D3×D4—62no—
141#235—32no—
142#235—32no—
143#235—61no—
144#235—61no—
145C2×D12—32no—
146C2×D12—31no—
147C2×D12—32no—
148C2×D12—61no—
149C2×D12—61no—
150C2×D12—61no—
151C2×C4×D3—61no—
152C2×Dic6C2×A411yescharacteristic
153#41⋊C3—21no—
154#41⋊C3—21no—
155#41⋊C3—62no—
156#41⋊C3#6711yescharacteristic
157#41⋊C3C22×D311yescharacteristic
158C2×SL(2,𝔽3)—24no—
159C2×SL(2,𝔽3)—22no—
160C2×SL(2,𝔽3)—21no—
161C2×SL(2,𝔽3)#6711yescharacteristic
162C3×SD16—124no—
163C2×C3×C8—121no—
164#216—34no—
165#215—38no—
166#215—34no—
167#214C2×A414yes—
168#213—34no—
169#208—32no—
170#208—32no—
171C2×C3⋊C8—31no—
172C2×C3⋊C8—32no—
173C2×C3⋊C8—32no—
174C2×C3⋊C8C2×A411yescharacteristic
175C22×C32—41no—
176C22×C32—82no—
177C22×C32—162no—
178C32×C4—41no—
179C32×C4—41no—
180C3×Dic3—82no—
1812−1+4—21no—
1822−1+4—32no—
1832−1+4—61no—
1842−1+4C2×C3×D312yes—
185H(5,𝔽2)—32no—
186H(5,𝔽2)—61no—
187H(5,𝔽2)—92no—
188H(5,𝔽2)—181no—
189C2×#41—31no—
190C2×#41—61no—
191C2×#41—61no—
192C2×#41—91no—
193C2×#41C2×C3×D311yescharacteristic
194C22×Q8—21no—
195C22×Q8—31no—
196C22×D4—91no—
197C22×D4—181no—
198#137—94no—
199#137—94no—
200AGL(1,ℤ/8)—94no—
201AGL(1,ℤ/8)—94no—
202#135—94no—
203#135—94no—
204C2×Q16—91no—
205C2×SD16—31no—
206C2×SD16—91no—
207C2×SD16—92no—
208C2×SD16—94no—
209C2×SD16—94no—
210C2×D8—91no—
211#131—32no—
212#131—92no—
213C2×M16—91no—
214C22×C8—91no—
215C23×C3—21no—
216C23×C3—31no—
217C23×C3—81no—
218C23×C3—82no—
219C22×D3—61no—
220C22×D3—62no—
221C22×D3—62no—
222C22×D3—242no—
223C3×Q8—31no—
224C3×Q8—32no—
225C3×Q8—62no—
226C3×Q8—62no—
227C3×Q8—61no—
228C3×Q8—122no—
229C3×Q8—241no—
230C3×Q8C2×C3×D411yescharacteristic
231C3×D4—21no—
232C3×D4—31no—
233C3×D4—31no—
234C3×D4—32no—
235C3×D4—42no—
236C3×D4—62no—
237C3×D4—62no—
238C3×D4—81no—
239C3×D4—82no—
240C3×D4—82no—
241C3×D4C22×A412yes—
242C2×C3×C4—31no—
243C2×C3×C4—31no—
244C2×C3×C4—31no—
245C2×C3×C4—31no—
246C2×C3×C4—31no—
247C2×C3×C4—41no—
248C2×C3×C4—62no—
249C2×C3×C4—62no—
250C2×C3×C4—62no—
251C2×C3×C4—61no—
252C2×C3×C4—62no—
253C2×C3×C4—81no—
254C2×C3×C4—241no—
255C2×C3×C4C22×A411yescharacteristic
256#67—62no—
257#67—62no—
258C2×Dic3—21no—
259D12—32no—
260D12—62no—
261D12—62no—
262D12—61no—
263C4×D3—62no—
264C4×D3—62no—
265Dic6—21no—
266Dic6C22×A412yes—
267SL(2,𝔽3)—21no—
268SL(2,𝔽3)C2×#6711yescharacteristic
269C3×C8—122no—
270C3⋊C8—32no—
271C3⋊C8C22×A412yes—
272C2×C32—41no—
273C2×C32—42no—
274C2×C32—162no—
275C24—181no—
276#41—31no—
277#41—31no—
278#41—32no—
279#41—32no—
280#41—61no—
281#41—61no—
282#41—64no—
283#41—62no—
284#41—62no—
285#41—62no—
286#41—92no—
287#41—92no—
288#41—181no—
289#41—181no—
290#41—182no—
291#41C3×#6711yescharacteristic
292#41C22×C3×D311yescharacteristic
293C2×Q8—22no—
294C2×Q8—32no—
295C2×Q8—32no—
296C2×Q8—31no—
297C2×Q8—31no—
298C2×Q8—61no—
299C2×Q8—61no—
300C2×Q8—61no—
301C2×Q8—62no—
302C2×Q8C3×#6711yescharacteristic
303C2×D4—31no—
304C2×D4—61no—
305C2×D4—92no—
306C2×D4—92no—
307C2×D4—91no—
308C2×D4—181no—
309C2×D4—181no—
310C2×D4—181no—
311C2×D4—181no—
312C2×D4—184no—
313C2×D4—182no—
314C2×D4—182no—
315C2×D4D3×A411yescharacteristic
316C22×C4—31no—
317C22×C4—61no—
318C22×C4—61no—
319C22×C4—181no—
320Q16—94no—
321SD16—34no—
322SD16—94no—
323SD16—98no—
324D8—94no—
325M16—92no—
326M16—92no—
327C2×C8—31no—
328C2×C8—92no—
329C2×C8—92no—
330C2×C8—91no—
331C22×C3—22no—
332C22×C3—31no—
333C22×C3—31no—
334C22×C3—42no—
335C22×C3—41no—
336C22×C3—62no—
337C22×C3—82no—
338C22×C3—84no—
339C22×C3—81no—
340C22×C3—162no—
341C22×C3—164no—
342C22×C3D4×A411yescharacteristic
343C2×D3—62no—
344C2×D3—122no—
345C2×D3—242no—
346C2×D3—242no—
347C3×C4—31no—
348C3×C4—31no—
349C3×C4—41no—
350C3×C4—41no—
351C3×C4—62no—
352C3×C4—81no—
353C3×C4—81no—
354C3×C4—242no—
355C3×C4D4×A411yescharacteristic
356C3×C4C23×A411yescharacteristic
357Dic3—22no—
358C32—41noSylow
359C23—21no—
360C23—31no—
361C23—182no—
362C23—182no—
363C23—181no—
364C23—722no—
365Q8—31no—
366Q8—32no—
367Q8—32no—
368Q8—62no—
369Q8—62no—
370Q8—61no—
371Q8—61no—
372Q8C2×C3×#6711yescharacteristic
373D4—21no—
374D4—31no—
375D4—31no—
376D4—32no—
377D4—62no—
378D4—62no—
379D4—92no—
380D4—182no—
381D4—182no—
382D4—182no—
383D4—182no—
384D4—181no—
385D4C2×D3×A412yes—
386C2×C4—31no—
387C2×C4—31no—
388C2×C4—31no—
389C2×C4—31no—
390C2×C4—31no—
391C2×C4—62no—
392C2×C4—62no—
393C2×C4—62no—
394C2×C4—61no—
395C2×C4—61no—
396C2×C4—62no—
397C2×C4—182no—
398C2×C4—182no—
399C2×C4C2×D3×A411yescharacteristic
400C8—32no—
401C8—92no—
402C2×C3—42no—
403C2×C3—41no—
404C2×C3—42no—
405C2×C3—61no—
406C2×C3—61no—
407C2×C3—81no—
408C2×C3—82no—
409C2×C3—162no—
410C2×C3—164no—
411C2×C3#577⋊C312yescomplemented
412C2×C3C2×D4×A411yescharacteristic
413D3—122no—
414C22—22no—
415C22—31no—
416C22—31no—
417C22—42no—
418C22—62no—
419C22—182no—
420C22—362no—
421C22—722no—
422C22—722no—
423C22A4×#6711yescharacteristic
424C4—31no—
425C4—31no—
426C4—62no—
427C4—62no—
428C4A4×#6711yescharacteristic
429C4C22×D3×A411yescharacteristic
430C3—41no—
431C3—81no—
432C3C2×#577⋊C311yescharacteristic, complemented
433C2—42no—
434C2—61no—
435C2—61no—
436C2—362no—
437C2#5837⋊C312yesdirect product factor
438C2C2×A4×#6711yescharacteristic
subgroupG/H
centerC22A4×#67
commutator, cosocleC3×#41C23×C3
FrattiniC4C22×D3×A4
FittingC2×C3×2−1+4C2×C3
socleC22×C3D4×A4
hypercenterC2×D4D3×A4
hypocenterC3×Q8C2×C3×D4
LCSG ▷ C3×#41 ▷ C3×Q8
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×2−1+4⋊C3C2semidirect
2. C2×C3⋊#994C2semidirect
3. #5837⋊C3C2direct (N × H)
4. C2×C3⋊(#131⋊C3)C2semidirect
5. C2×#5837C3semidirect
8. C3×2−1+4⋊C3C22semidirect
12. C3⋊#994C22semidirect
15. C3⋊(#131⋊C3)C22semidirect
17. C2×#1009C2×C3semidirect
19. C2×2−1+4⋊C3D3semidirect
22. #5837C2×C3semidirect
25. C2×#948C2×C3semidirect
52. #1009C22×C3semidirect
60. 2−1+4⋊C3C2×D3semidirect
74. #948C22×C3semidirect
411. C2×C3#577⋊C3semidirect
432. C3C2×#577⋊C3semidirect
437. C2#5837⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×2−1+4⋊C32
C2×C3⋊#9942
#5837⋊C32
C2×C3⋊(#131⋊C3)2
C2×#58373
C2×#577⋊C33
C2×C3×#2144