Finite Group Databasebeta

← C2×#5838⋊C3 #11923400

Subgroups — C2×#5838⋊C3 #11923400

Order 1152.

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

normal subgroups only

This group has 729 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×#1010⋊C3C211yesmaximal, characteristic, complemented
3#5838⋊C3C214yesmaximal, direct product factor
4C2×C3⋊(#131⋊C3)C211yesmaximal, characteristic, complemented
5C2×#5838C311yesmaximal, characteristic, complemented
6C2×#578⋊C3—31nomaximal
7C3×2−1+4⋊C3—21no—
8C3×2−1+4⋊C3C2212yescomplemented
9C2×C3×#41⋊C3C2211yescharacteristic
10C22×C3×SL(2,𝔽3)—21no—
11#1010⋊C3—21no—
12#1010⋊C3C2212yescomplemented
13C2×D3×SL(2,𝔽3)—21no—
14C2×C3×#213—41nomaximal
15C3⋊(#131⋊C3)C2212yescomplemented
16C2×C3×2−1+4C2×C311yescharacteristic, complemented
17C2×#1010C2×C311yescharacteristic, complemented
18C2×2−1+4⋊C3—21no—
19C2×2−1+4⋊C3—31no—
20C2×2−1+4⋊C3D311yescharacteristic, complemented
21#5838—34no—
22#5838C2×C314yescomplemented
23C2×#951—31no—
24C2×#950—31no—
25C2×#948C2×C311yescharacteristic, complemented
26C22×#216—31no—
27C2×#942—31no—
28#578⋊C3—34no—
29C2×#131⋊C3—31no—
30C2×C32×D4—41no—
31C2×C3×D12—41no—
32C3×#41⋊C3D411yescharacteristic
33C3×#41⋊C3C2311yescharacteristic
34C2×C3×SL(2,𝔽3)—22no—
35C2×C3×SL(2,𝔽3)D411yescharacteristic
36D3×SL(2,𝔽3)—22no—
37C3×#213—44no—
38C2×C3×C3⋊C8—41no—
39C2×#578—31noSylow
40C3×2−1+4—21no—
41C3×2−1+4—32no—
42C3×2−1+4—61no—
43C3×2−1+4C22×C312yescomplemented
44C2×C3×#41—31no—
45C2×C3×#41—61no—
46C2×C3×#41C22×C311yescharacteristic
47C22×C3×Q8—21no—
48C22×C3×Q8—31no—
49#1010—21no—
50#1010—32no—
51#1010—61no—
52#1010C22×C312yescomplemented
53C2×D3×Q8—21no—
54C2×#237—61no—
55C2×#235—31no—
56C22×Dic6—31no—
572−1+4⋊C3—22no—
582−1+4⋊C3—21no—
592−1+4⋊C3—22no—
602−1+4⋊C3—32no—
612−1+4⋊C3—61no—
622−1+4⋊C3C2×D312yescomplemented
63C2×#41⋊C3—21no—
64C2×#41⋊C3C2×D311yescharacteristic
65C22×SL(2,𝔽3)—22no—
66C22×SL(2,𝔽3)—21no—
67C22×SL(2,𝔽3)—61no—
68C2×C3×D8—121no—
69#951—34no—
70#951—34no—
71#950—34no—
72#950—34no—
73#948—32no—
74#948C22×C312yescomplemented
75C2×#216—32no—
76C2×#216—34no—
77C2×#216—34no—
78C2×#216—31no—
79#942—34no—
80#942—34no—
81C2×#215—31no—
82C2×#214—31no—
83C2×#213A411yescharacteristic
84C2×#208—31no—
85C22×C3⋊C8—31no—
86#131⋊C3—32no—
87C23×C32—81no—
88C22×C3×D3—81no—
89C32×D4—42no—
90C32×D4—81no—
91C2×C32×C4—41no—
92C3×D12—42no—
93C3×D12—81no—
94C3×SL(2,𝔽3)C2×D411yescharacteristic
95C3×C3⋊C8—42no—
96C2×2−1+4—31no—
97C2×2−1+4C3×D311yescharacteristic, complemented
98#578—34no—
99#578—94no—
100C2×#137—91no—
101C2×#137—91no—
102C2×#135—91no—
103C22×Q16—91no—
104C2×#131—31no—
105C3×#41—31no—
106C3×#41—31no—
107C3×#41—32no—
108C3×#41—32no—
109C3×#41—61no—
110C3×#41—61no—
111C3×#41—64no—
112C3×#41—62no—
113C3×#41—62no—
114C3×#41C3×D411yescharacteristic
115C3×#41C23×C311yescharacteristic
116C2×C3×Q8—22no—
117C2×C3×Q8—32no—
118C2×C3×Q8—32no—
119C2×C3×Q8—31no—
120C2×C3×Q8—61no—
121C2×C3×Q8—61no—
122C2×C3×Q8—61no—
123C2×C3×Q8—62no—
124C2×C3×Q8C3×D411yescharacteristic
125C2×C3×D4—31no—
126C2×C3×D4—41no—
127C2×C3×D4—61no—
128C2×C3×D4—81no—
129C2×C3×D4—121no—
130C2×C3×D4C2×A411yescharacteristic
131C22×C3×C4—31no—
132C22×C3×C4—61no—
133C22×C3×C4—61no—
134C2×#67—61no—
135C22×Dic3—61no—
136D3×Q8—22no—
137D3×Q8—62no—
138#237—64no—
139#237—62no—
140#237—62no—
141#235—32no—
142#235—32no—
143#235—61no—
144#235—61no—
145C2×D12C2×A411yescharacteristic
146C2×C4×D3—61no—
147C2×Dic6—32no—
148C2×Dic6—31no—
149C2×Dic6—32no—
150C2×Dic6—61no—
151C2×Dic6—61no—
152C2×Dic6—61no—
153#41⋊C3—21no—
154#41⋊C3—21no—
155#41⋊C3#6711yescharacteristic
156#41⋊C3C22×D311yescharacteristic
157C2×SL(2,𝔽3)—24no—
158C2×SL(2,𝔽3)—22no—
159C2×SL(2,𝔽3)—21no—
160C2×SL(2,𝔽3)—62no—
161C2×SL(2,𝔽3)#6711yescharacteristic
162C3×D8—124no—
163C2×C3×C8—121no—
164#216—38no—
165#216—34no—
166#215—34no—
167#214—34no—
168#213C2×A414yes—
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—
178C2×C3×D3—82no—
179C2×C3×D3—162no—
180C32×C4—41no—
181C32×C4—41no—
1822−1+4—21no—
1832−1+4—32no—
1842−1+4—32no—
1852−1+4—61no—
1862−1+4—61no—
1872−1+4—92no—
1882−1+4—181no—
1892−1+4C2×C3×D312yescomplemented
190C2×#41—31no—
191C2×#41—61no—
192C2×#41—91no—
193C2×#41—181no—
194C2×#41C2×C3×D311yescharacteristic
195C22×Q8—21no—
196C22×Q8—31no—
197C22×Q8—61no—
198C22×Q8—91no—
199#137—94no—
200#137—94no—
201#137—94no—
202#137—94no—
203#135—94no—
204#135—94no—
205C2×Q16—91no—
206C2×Q16—92no—
207C2×Q16—94no—
208C2×Q16—94no—
209C2×SD16—91no—
210C2×SD16—91no—
211C2×D8—31no—
212#131—32no—
213#131—92no—
214C2×M16—91no—
215C22×C8—91no—
216C23×C3—21no—
217C23×C3—31no—
218C23×C3—81no—
219C23×C3—82no—
220C23×C3—241no—
221C22×D3—21no—
222C3×Q8—31no—
223C3×Q8—32no—
224C3×Q8—62no—
225C3×Q8—62no—
226C3×Q8—61no—
227C3×Q8C2×C3×D411yescharacteristic
228C3×D4—21no—
229C3×D4—31no—
230C3×D4—31no—
231C3×D4—32no—
232C3×D4—42no—
233C3×D4—62no—
234C3×D4—62no—
235C3×D4—81no—
236C3×D4—82no—
237C3×D4—82no—
238C3×D4—122no—
239C3×D4—241no—
240C3×D4C22×A412yes—
241C2×C3×C4—31no—
242C2×C3×C4—31no—
243C2×C3×C4—31no—
244C2×C3×C4—31no—
245C2×C3×C4—31no—
246C2×C3×C4—41no—
247C2×C3×C4—62no—
248C2×C3×C4—62no—
249C2×C3×C4—62no—
250C2×C3×C4—61no—
251C2×C3×C4—62no—
252C2×C3×C4—81no—
253C2×C3×C4C22×A411yescharacteristic
254#67—62no—
255#67—62no—
256C2×Dic3—62no—
257C2×Dic3—61no—
258C2×Dic3—62no—
259D12—21no—
260D12C22×A412yes—
261C4×D3—62no—
262C4×D3—62no—
263Dic6—32no—
264Dic6—62no—
265Dic6—61no—
266Dic6—62no—
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—
275C3×D3—162no—
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—92no—
286#41—92no—
287#41—181no—
288#41—181no—
289#41—184no—
290#41—182no—
291#41—182no—
292#41C3×#6711yescharacteristic
293#41C22×C3×D311yescharacteristic
294C2×Q8—22no—
295C2×Q8—32no—
296C2×Q8—32no—
297C2×Q8—31no—
298C2×Q8—61no—
299C2×Q8—61no—
300C2×Q8—61no—
301C2×Q8—62no—
302C2×Q8—62no—
303C2×Q8—92no—
304C2×Q8—92no—
305C2×Q8—91no—
306C2×Q8—181no—
307C2×Q8—181no—
308C2×Q8—181no—
309C2×Q8—182no—
310C2×Q8C3×#6711yescharacteristic
311C2×D4—31no—
312C2×D4—31no—
313C2×D4—61no—
314C2×D4—181no—
315C2×D4D3×A411yescharacteristic
316C22×C4—31no—
317C22×C4—61no—
318C22×C4—61no—
319C22×C4—181no—
320C22×C4—181no—
321Q16—94no—
322Q16—98no—
323SD16—94no—
324SD16—94no—
325D8—34no—
326M16—92no—
327M16—92no—
328C2×C8—31no—
329C2×C8—92no—
330C2×C8—92no—
331C2×C8—91no—
332C22×C3—22no—
333C22×C3—31no—
334C22×C3—31no—
335C22×C3—42no—
336C22×C3—41no—
337C22×C3—62no—
338C22×C3—82no—
339C22×C3—84no—
340C22×C3—81no—
341C22×C3—162no—
342C22×C3—164no—
343C22×C3—242no—
344C22×C3—482no—
345C22×C3D4×A411yescharacteristic
346C2×D3—22no—
347C2×D3—42no—
348C3×C4—31no—
349C3×C4—31no—
350C3×C4—41no—
351C3×C4—41no—
352C3×C4—62no—
353C3×C4—81no—
354C3×C4—81no—
355C3×C4D4×A411yescharacteristic
356C3×C4C23×A411yescharacteristic
357Dic3—62no—
358C32—41noSylow
359C23—21no—
360C23—31no—
361C23—61no—
362Q8—31no—
363Q8—32no—
364Q8—62no—
365Q8—62no—
366Q8—61no—
367Q8—92no—
368Q8—182no—
369Q8—182no—
370Q8—181no—
371Q8C2×C3×#6711yescharacteristic
372D4—21no—
373D4—31no—
374D4—31no—
375D4—32no—
376D4—32no—
377D4—62no—
378D4—62no—
379D4—61no—
380D4—182no—
381D4—182no—
382D4C2×D3×A412yes—
383C2×C4—31no—
384C2×C4—31no—
385C2×C4—31no—
386C2×C4—31no—
387C2×C4—31no—
388C2×C4—62no—
389C2×C4—62no—
390C2×C4—62no—
391C2×C4—61no—
392C2×C4—62no—
393C2×C4—182no—
394C2×C4—182no—
395C2×C4—182no—
396C2×C4—181no—
397C2×C4—182no—
398C2×C4C2×D3×A411yescharacteristic
399C8—32no—
400C8—92no—
401C2×C3—42no—
402C2×C3—41no—
403C2×C3—42no—
404C2×C3—61no—
405C2×C3—61no—
406C2×C3—81no—
407C2×C3—82no—
408C2×C3—162no—
409C2×C3—164no—
410C2×C3—482no—
411C2×C3#578⋊C312yescomplemented
412C2×C3C2×D4×A411yescharacteristic
413D3—42no—
414C22—22no—
415C22—31no—
416C22—31no—
417C22—42no—
418C22—62no—
419C22—62no—
420C22—122no—
421C22A4×#6711yescharacteristic
422C4—31no—
423C4—31no—
424C4—62no—
425C4—182no—
426C4A4×#6711yescharacteristic
427C4C22×D3×A411yescharacteristic
428C3—41no—
429C3—81no—
430C3C2×#578⋊C311yescharacteristic, complemented
431C2—42no—
432C2—61no—
433C2—61no—
434C2—122no—
435C2#5838⋊C312yesdirect product factor
436C2C2×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×#1010⋊C3C2semidirect
3. #5838⋊C3C2direct (N × H)
4. C2×C3⋊(#131⋊C3)C2semidirect
5. C2×#5838C3semidirect
8. C3×2−1+4⋊C3C22semidirect
12. #1010⋊C3C22semidirect
15. C3⋊(#131⋊C3)C22semidirect
16. C2×C3×2−1+4C2×C3semidirect
17. C2×#1010C2×C3semidirect
20. C2×2−1+4⋊C3D3semidirect
22. #5838C2×C3semidirect
25. C2×#948C2×C3semidirect
43. C3×2−1+4C22×C3semidirect
52. #1010C22×C3semidirect
62. 2−1+4⋊C3C2×D3semidirect
74. #948C22×C3semidirect
97. C2×2−1+4C3×D3semidirect
189. 2−1+4C2×C3×D3semidirect
411. C2×C3#578⋊C3semidirect
430. C3C2×#578⋊C3semidirect
435. C2#5838⋊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×#1010⋊C32
#5838⋊C32
C2×C3⋊(#131⋊C3)2
C2×#58383
C2×#578⋊C33
C2×C3×#2134