Finite Group Databasebeta

← C2×#5834⋊C3 #11923377

Subgroups — C2×#5834⋊C3 #11923377

Order 1152.

865 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 865 conjugacy classes of subgroups — too many to draw. Only its 111 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⋊(#41⋊C3)C211yesmaximal, characteristic, complemented
3#5834⋊C3C214yesmaximal, direct product factor
4C2×Dic3×SL(2,𝔽3)C211yesmaximal, characteristic, complemented
5C2×#5834C311yesmaximal, characteristic, complemented
6C2×C4⋊(#41⋊C3)—31nomaximal
7C2×C3×#41⋊C3—22no—
8C2×C3×#41⋊C3C2212yescomplemented
9C22×C3×SL(2,𝔽3)C2211yescharacteristic
10C2×C3⋊(#41⋊C3)—22no—
11C2×C3⋊(#41⋊C3)C2212yescomplemented
12C2×C3×Dic3⋊C4—41nomaximal
13Dic3×SL(2,𝔽3)C2212yescomplemented
14C22×C3×#41C2×C311yescharacteristic
15C22×#239C2×C311yescharacteristic
16C22×#41⋊C3—21no—
17C22×#41⋊C3—31no—
18C22×#41⋊C3D311yescharacteristic, complemented
19#5834—34no—
20#5834C2×C314yescomplemented
21C2×Q8×Dic3C2×C311yescharacteristic
22C2×#940—31no—
23C2×#938—31no—
24C2×#930—31no—
25C2×C4×#67—31no—
26C4⋊(#41⋊C3)—34no—
27C2×C4×SL(2,𝔽3)—31no—
28C22×C32×C4—41no—
29C22×C3×Dic3—41no—
30C22×C3×Dic3—41no—
31C3×#41⋊C3—22no—
32C2×C3×SL(2,𝔽3)D412yescomplemented
33C2×C3×SL(2,𝔽3)C2311yescharacteristic
34C3⋊(#41⋊C3)—22no—
35C3×Dic3⋊C4—44no—
36C2×#550—31noSylow
37C2×C3×#41—22no—
38C2×C3×#41—32no—
39C2×C3×#41—62no—
40C2×C3×#41C22×C312yes—
41C22×C3×Q8C22×C311yescharacteristic
42C22×C3×D4—31no—
43C23×C3×C4—31no—
44C22×#67—32no—
45C22×#67—31no—
46C2×#239—22no—
47C2×#239—32no—
48C2×#239—62no—
49C2×#239C22×C312yes—
50C22×D12—31no—
51C22×C4×D3—31no—
52C2×#41⋊C3—24no—
53C2×#41⋊C3—22no—
54C2×#41⋊C3—22no—
55C2×#41⋊C3—32no—
56C2×#41⋊C3—62no—
57C2×#41⋊C3C2×D312yescomplemented
58C22×SL(2,𝔽3)—21no—
59C22×SL(2,𝔽3)C2×D311yescharacteristic
60C2×C3×C4⋊C4—121no—
61C2×#217—31no—
62Q8×Dic3—32no—
63Q8×Dic3C22×C312yes—
64#940—34no—
65#940—34no—
66#938—34no—
67#938—34no—
68#930—34no—
69#930—34no—
70C4×#67—34no—
71C4×#67—34no—
72C2×(C2×D3)⋊C4—31no—
73C2×C4⋊Dic3—31no—
74C2×Dic3⋊C4A411yescharacteristic
75C2×C4×Dic3—31no—
76C4×SL(2,𝔽3)—32no—
77C23×C32—41no—
78C2×C32×C4—42no—
79C2×C32×C4—82no—
80C2×C3×Dic3—44no—
81C2×C3×Dic3—42no—
82C2×C3×Dic3—42no—
83C2×C3×Dic3—82no—
84C3×SL(2,𝔽3)C2×D411yescharacteristic, complemented
85C22×#41—31no—
86C22×#41C3×D311yescharacteristic
87#550—34no—
88#550—94no—
89C2×#127—91no—
90C2×#121—91no—
91C2×#121—91no—
92C2×C4×Q8—31no—
93C2×C4×D4—91no—
94C24×C3—31no—
95C23×D3—31no—
96C3×#41—22no—
97C3×#41—64no—
98C3×#41—64no—
99C3×#41—62no—
100C2×C3×Q8—31no—
101C2×C3×Q8—32no—
102C2×C3×Q8C3×D412yes—
103C2×C3×Q8C23×C311yescharacteristic
104C2×C3×D4—32no—
105C2×C3×D4—32no—
106C2×C3×D4—62no—
107C2×C3×D4—62no—
108C22×C3×C4—31no—
109C22×C3×C4—32no—
110C22×C3×C4—32no—
111C22×C3×C4—41no—
112C22×C3×C4—62no—
113C22×C3×C4—62no—
114C22×C3×C4—81no—
115C22×C3×C4—121no—
116C22×C3×C4—121no—
117C22×C3×C4C2×A411yescharacteristic
118C2×#67—38no—
119C2×#67—34no—
120C2×#67—64no—
121C2×#67—124no—
122C22×Dic3—31no—
123C22×Dic3C2×A411yescharacteristic
124C22×Dic3C2×A411yescharacteristic
125#239—22no—
126#239—64no—
127#239—64no—
128#239—62no—
129C2×D12—32no—
130C2×D12—32no—
131C2×D12—62no—
132C2×D12—62no—
133C2×C4×D3—32no—
134C2×C4×D3—32no—
135C2×C4×D3—62no—
136C2×C4×D3—62no—
137#41⋊C3—24no—
138#41⋊C3—22no—
139#41⋊C3—62no—
140C2×SL(2,𝔽3)—22no—
141C2×SL(2,𝔽3)—21no—
142C2×SL(2,𝔽3)#6712yescomplemented
143C2×SL(2,𝔽3)C22×D311yescharacteristic
144C3×C4⋊C4—124no—
145#217—34no—
146(C2×D3)⋊C4—34no—
147C4⋊Dic3—32no—
148C4⋊Dic3—32no—
149Dic3⋊C4C2×A414yes—
150C4×Dic3—32no—
151C4×Dic3—32no—
152C22×C32—42no—
153C22×C32—42no—
154C22×C32—42no—
155C22×C32—41no—
156C32×C4—82no—
157C3×Dic3—44no—
158C3×Dic3—82no—
159C2×#41—22no—
160C2×#41—32no—
161C2×#41—32no—
162C2×#41—62no—
163C2×#41—62no—
164C2×#41—92no—
165C2×#41—182no—
166C2×#41C2×C3×D312yes—
167C22×Q8C2×C3×D311yescharacteristic
168C22×D4—31no—
169C22×D4—91no—
170C22×D4—91no—
171C22×D4—92no—
172C23×C4—31no—
173C23×C4—91no—
174#127—94no—
175#127—94no—
176#121—94no—
177#121—94no—
178#121—94no—
179#121—94no—
180C4×Q8—32no—
181C4×Q8—92no—
182C4×D4—94no—
183C4×D4—94no—
184C2×C4⋊C4—31no—
185C2×C4⋊C4—91no—
186C2×C22⋊C4—91no—
187C2×C22⋊C4—91no—
188C2×C42—91no—
189C23×C3—32no—
190C23×C3—41no—
191C23×C3—62no—
192C23×C3—62no—
193C23×C3—62no—
194C23×C3—81no—
195C23×C3C22×A411yescharacteristic
196C22×D3—32no—
197C22×D3—62no—
198C22×D3—62no—
199C22×D3—62no—
200C3×Q8—32no—
201C3×Q8—31no—
202C3×Q8—32no—
203C3×Q8C2×C3×D411yescharacteristic
204C3×D4—62no—
205C3×D4—62no—
206C3×D4—64no—
207C2×C3×C4—22no—
208C2×C3×C4—32no—
209C2×C3×C4—32no—
210C2×C3×C4—31no—
211C2×C3×C4—31no—
212C2×C3×C4—42no—
213C2×C3×C4—62no—
214C2×C3×C4—64no—
215C2×C3×C4—62no—
216C2×C3×C4—82no—
217C2×C3×C4—84no—
218C2×C3×C4—82no—
219C2×C3×C4—122no—
220C2×C3×C4—124no—
221C2×C3×C4—122no—
222C2×C3×C4—242no—
223C2×C3×C4C22×A412yes—
224#67—68no—
225#67—128no—
226C2×Dic3—22no—
227C2×Dic3—32no—
228C2×Dic3—62no—
229C2×Dic3#41⋊C314yescomplemented
230C2×Dic3C22×A412yes—
231C2×Dic3C22×A412yes—
232D12—62no—
233D12—62no—
234D12—64no—
235C4×D3—62no—
236C4×D3—64no—
237C4×D3—62no—
238SL(2,𝔽3)—21no—
239SL(2,𝔽3)C2×#6711yescharacteristic, complemented
240C2×C32—41no—
241C2×C32—41no—
242C2×C32—41no—
243C2×C32—44no—
244C24—31no—
245C24—91no—
246#41—22no—
247#41—64no—
248#41—64no—
249#41—62no—
250#41—62no—
251#41—184no—
252#41—184no—
253#41—182no—
254C2×Q8—31no—
255C2×Q8—32no—
256C2×Q8C3×#6712yes—
257C2×Q8C22×C3×D311yescharacteristic
258C2×D4—32no—
259C2×D4—32no—
260C2×D4—62no—
261C2×D4—62no—
262C2×D4—94no—
263C2×D4—92no—
264C2×D4—92no—
265C2×D4—98no—
266C2×D4—184no—
267C2×D4—182no—
268C2×D4—182no—
269C2×D4—364no—
270C22×C4—31no—
271C22×C4—31no—
272C22×C4—31no—
273C22×C4—32no—
274C22×C4—32no—
275C22×C4—62no—
276C22×C4—62no—
277C22×C4—92no—
278C22×C4—92no—
279C22×C4—91no—
280C22×C4—182no—
281C22×C4—182no—
282C22×C4D3×A411yescharacteristic
283C4⋊C4—34no—
284C4⋊C4—92no—
285C4⋊C4—92no—
286C22⋊C4—94no—
287C22⋊C4—94no—
288C42—92no—
289C42—92no—
290C22×C3—42no—
291C22×C3—42no—
292C22×C3—42no—
293C22×C3—41no—
294C22×C3—62no—
295C22×C3—62no—
296C22×C3—62no—
297C22×C3—82no—
298C22×C3—82no—
299C22×C3—82no—
300C22×C3—81no—
301C22×C3—124no—
302C22×C3D4×A412yes—
303C22×C3C2×#41⋊C312yes—
304C22×C3#99412yes—
305C22×C3C23×A411yescharacteristic
306C2×D3—62no—
307C2×D3—62no—
308C2×D3—62no—
309C2×D3—124no—
310C3×C4—22no—
311C3×C4—31no—
312C3×C4—32no—
313C3×C4—31no—
314C3×C4—82no—
315C3×C4—84no—
316C3×C4—124no—
317C3×C4—242no—
318Dic3—22no—
319Dic3—62no—
320Dic3C2×#41⋊C314yescomplemented
321C32—41noSylow
322C23—32no—
323C23—62no—
324C23—62no—
325C23—62no—
326C23—92no—
327C23—182no—
328C23—182no—
329C23—182no—
330C23C2×D3×A411yescharacteristic
331Q8—32no—
332Q8—31no—
333Q8—32no—
334Q8C2×C3×#6711yescharacteristic
335D4—62no—
336D4—62no—
337D4—64no—
338D4—188no—
339D4—182no—
340D4—182no—
341D4—184no—
342D4—368no—
343C2×C4—22no—
344C2×C4—34no—
345C2×C4—32no—
346C2×C4—32no—
347C2×C4—32no—
348C2×C4—31no—
349C2×C4—31no—
350C2×C4—32no—
351C2×C4—62no—
352C2×C4—62no—
353C2×C4—64no—
354C2×C4—62no—
355C2×C4—92no—
356C2×C4—182no—
357C2×C4—182no—
358C2×C4—184no—
359C2×C4—182no—
360C2×C4C2×D3×A412yes—
361C2×C3—41no—
362C2×C3—41no—
363C2×C3—41no—
364C2×C3—44no—
365C2×C3—81no—
366C2×C3—81no—
367C2×C3—81no—
368C2×C3—84no—
369C2×C3—122no—
370C2×C3C4⋊(#41⋊C3)14yescomplemented
371C2×C3C2×D4×A411yescharacteristic
372C2×C3C22×#41⋊C311yescharacteristic
373C2×C3C2×#99411yescharacteristic
374D3—122no—
375C22—62no—
376C22—62no—
377C22—62no—
378C22—124no—
379C22—182no—
380C22—182no—
381C22—182no—
382C22—364no—
383C22C3⋊#99412yes—
384C22D3×#41⋊C312yes—
385C22A4×#6712yes—
386C22C22×D3×A411yescharacteristic
387C4—22no—
388C4—34no—
389C4—31no—
390C4—32no—
391C4—31no—
392C4—62no—
393C4—182no—
394C3—41no—
395C3—81no—
396C3C2×C4⋊(#41⋊C3)11yescharacteristic, complemented
397C2—122no—
398C2—362no—
399C2#5834⋊C314yesdirect product factor
400C2C2×C3⋊#99411yescharacteristic
401C2C2×D3×#41⋊C311yescharacteristic
402C2C2×A4×#6711yescharacteristic
subgroupG/H
centerC23C2×D3×A4
commutator, cosocleC2×C3×Q8C23×C3
FrattiniC22C22×D3×A4
FittingC22×C3×#41C2×C3
socleC23×C3C22×A4
hypercenterC22×C4D3×A4
hypocenterC3×Q8C2×C3×D4
LCSG ▷ C2×C3×Q8 ▷ C3×Q8
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⋊(#41⋊C3)C2semidirect
3. #5834⋊C3C2direct (N × H)
4. C2×Dic3×SL(2,𝔽3)C2semidirect
5. C2×#5834C3semidirect
8. C2×C3×#41⋊C3C22semidirect
11. C2×C3⋊(#41⋊C3)C22semidirect
13. Dic3×SL(2,𝔽3)C22semidirect
18. C22×#41⋊C3D3semidirect
20. #5834C2×C3semidirect
32. C2×C3×SL(2,𝔽3)D4semidirect
57. C2×#41⋊C3C2×D3semidirect
84. C3×SL(2,𝔽3)C2×D4semidirect
142. C2×SL(2,𝔽3)#67semidirect
229. C2×Dic3#41⋊C3semidirect
239. SL(2,𝔽3)C2×#67semidirect
320. Dic3C2×#41⋊C3semidirect
370. C2×C3C4⋊(#41⋊C3)semidirect
396. C3C2×C4⋊(#41⋊C3)semidirect
399. C2#5834⋊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
C22×C3⋊(#41⋊C3)2
#5834⋊C32
C2×Dic3×SL(2,𝔽3)2
C2×#58343
C2×C4⋊(#41⋊C3)3
C2×C3×Dic3⋊C44