Finite Group Databasebeta

← C2×#10593229 #11922320

Subgroups — C2×#10593229 #11922320

Order 1152.

641 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 641 conjugacy classes of subgroups — too many to draw. Only its 59 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×#1010⋊C3C211yesmaximal, characteristic, complemented
2C2×C3×#986C211yesmaximal, characteristic, complemented
3C2×C3⋊GU(2,𝔽3)C211yesmaximal, characteristic, complemented
4#10593229C214yesmaximal, direct product factor
5C2×#5431—31nomaximal
6C2×#5201—31nomaximal
7C2×C3×#41⋊C3C2211yescharacteristic
8#1010⋊C3—21no—
9#1010⋊C3C2212yescomplemented
10C2×D3×SL(2,𝔽3)—21no—
11C3×#986—21no—
12C3×#986C2212yescomplemented
13C2×C3×GL(2,𝔽3)—21no—
14C2×#3713—41nomaximal
15C3⋊GU(2,𝔽3)C2212yescomplemented
16C2×#1010D311yescharacteristic, complemented
17C2×2−1+4⋊C3—31no—
18C2×#986D311yescharacteristic, complemented
19C2×C3×AGL(1,ℤ/8)—31no—
20C2×#936—31no—
21C2×#932—31no—
22#5431—34no—
23C2×GU(2,𝔽3)—31no—
24C2×GU(2,𝔽3)—61no—
25C2×#837—31no—
26#5201—34no—
27#5201—34no—
28C2×#825—31no—
29C2×#824—31no—
30C2×C3×D12—41no—
31C2×C3×D12—41no—
32C3×#41⋊C3D411yescharacteristic
33C3×#41⋊C3C2311yescharacteristic
34C2×C3×SL(2,𝔽3)D411yescharacteristic
35D3×SL(2,𝔽3)—22no—
36C3×GL(2,𝔽3)—22no—
37C2×C3⋊(C3⋊C8)—41no—
38#3713—44no—
39C2×#454—91noSylow
40C2×C3×#41C2×D311yescharacteristic
41C22×C3×D4—31no—
42#1010—21no—
43#1010—32no—
44#1010—61no—
45#1010C2×D312yescomplemented
46C2×D3×Q8—21no—
47C2×#237—61no—
48C2×#235—31no—
49C22×Dic6—31no—
502−1+4⋊C3—32no—
512−1+4⋊C3—61no—
52C2×#41⋊C3—21no—
53C2×#41⋊C3C2×D311yescharacteristic
54C22×SL(2,𝔽3)—61no—
55#986—21no—
56#986C2×D312yescomplemented
57C2×GL(2,𝔽3)—21no—
58C3×AGL(1,ℤ/8)—32no—
59C3×AGL(1,ℤ/8)—32no—
60C3×AGL(1,ℤ/8)—61no—
61C3×AGL(1,ℤ/8)—61no—
62C2×C3×SD16—61no—
63C2×C3×D8—61no—
64C2×C3×M16—31no—
65C2×#217—62no—
66#936—34no—
67#936—62no—
68C2×#214—61no—
69#932—34no—
70#932—62no—
71C2×#213—61no—
72C2×#213—121no—
73C2×C4×Dic3—31no—
74C2×#208—31no—
75GU(2,𝔽3)—32no—
76GU(2,𝔽3)—62no—
77#837—32no—
78#837—32no—
79#825—34no—
80#824—34no—
81C22×C3×D3—81no—
82C22×C3×D3—81no—
83C2×C32×C4—41no—
84C3×D12—42no—
85C3×D12—42no—
86C3×D12—81no—
87C3×D12—81no—
88C3×SL(2,𝔽3)C2×D411yescharacteristic
89C3⋊(C3⋊C8)—42no—
90C2×2−1+4—31no—
91C2×AGL(1,ℤ/8)—31no—
92C2×AGL(1,ℤ/8)—91no—
93C2×#124—91no—
94#454—94no—
95#454—94no—
96C2×#104—91no—
97C2×#104—91no—
98C2×#101—91no—
99C24×C3—61no—
100C3×#41—31no—
101C3×#41—31no—
102C3×#41#6711yescharacteristic
103C3×#41C22×D311yescharacteristic
104C2×C3×Q8#6711yescharacteristic
105C2×C3×D4—31no—
106C2×C3×D4—32no—
107C2×C3×D4—61no—
108C2×C3×D4—61no—
109C2×C3×D4—61no—
110C2×C3×D4—61no—
111C2×C3×D4—61no—
112C2×C3×D4—121no—
113C22×C3×C4—31no—
114C2×#67—61no—
115C22×Dic3—32no—
116C22×Dic3—61no—
117D3×Q8—22no—
118D3×Q8—62no—
119#237—62no—
120#237—64no—
121#237—62no—
122#235—32no—
123#235—32no—
124#235—61no—
125#235—61no—
126C2×D12—41no—
127C2×D12S411yescharacteristic
128C2×C4×D3—61no—
129C2×Dic6—31no—
130C2×Dic6—32no—
131C2×Dic6—32no—
132C2×Dic6—61no—
133C2×Dic6—61no—
134C2×Dic6—61no—
135#41⋊C3—21no—
136#41⋊C3—21no—
137#41⋊C3#6711yescharacteristic
138#41⋊C3C22×D311yescharacteristic
139C2×SL(2,𝔽3)—21no—
140C2×SL(2,𝔽3)—62no—
141C2×SL(2,𝔽3)#6711yescharacteristic
142GL(2,𝔽3)—22no—
143C3×SD16—62no—
144C3×SD16—62no—
145C3×D8—62no—
146C3×D8—62no—
147C3×M16—32no—
148C3×M16—61no—
149C2×C3×C8—61no—
150#217—68no—
151#214—64no—
152#213—64no—
153#213—124no—
154C4×Dic3—32no—
155C4×Dic3—61no—
156#208—32no—
157#208—61no—
158C2×C3⋊C8—61no—
159C2×C3⋊C8—121no—
160C2×C3⋊C8—241no—
161C22×C32—41no—
162C2×C3×D3—82no—
163C2×C3×D3—82no—
164C2×C3×D3—162no—
165C2×C3×D3—162no—
166C32×C4—41no—
167C32×C4—41no—
1682−1+4—32no—
1692−1+4—61no—
1702−1+4—92no—
1712−1+4—181no—
172C2×#41—91no—
173C2×#41—181no—
174C2×#41D3211yescharacteristic
175C22×Q8—61no—
176C22×Q8—91no—
177C22×D4—31no—
178AGL(1,ℤ/8)—32no—
179AGL(1,ℤ/8)—32no—
180AGL(1,ℤ/8)—61no—
181AGL(1,ℤ/8)—61no—
182AGL(1,ℤ/8)—94no—
183AGL(1,ℤ/8)—182no—
184C2×SD16—61no—
185C2×SD16—181no—
186C2×D8—61no—
187C2×D8—181no—
188C2×M16—31no—
189C2×M16—91no—
190#124—94no—
191#124—182no—
192C2×C22⋊C4—182no—
193C2×C42—91no—
194#104—94no—
195#104—92no—
196#104—92no—
197#101—94no—
198C23×C3—31no—
199C23×C3—62no—
200C23×C3—121no—
201C23×C3—124no—
202C23×C3—121no—
203C23×C3—241no—
204C22×D3—21no—
205C22×D3—81no—
206C3×Q8—31no—
207C3×Q8C2×#6711yescharacteristic
208C3×D4—31no—
209C3×D4—31no—
210C3×D4—61no—
211C3×D4—62no—
212C3×D4—62no—
213C3×D4—122no—
214C3×D4—121no—
215C3×D4—121no—
216C3×D4—241no—
217C2×C3×C4—31no—
218C2×C3×C4—31no—
219C2×C3×C4—31no—
220C2×C3×C4—31no—
221C2×C3×C4—31no—
222C2×C3×C4—41no—
223C2×C3×C4—81no—
224C2×C3×C4C2×S411yescharacteristic
225#67—62no—
226#67—62no—
227C2×Dic3—34no—
228C2×Dic3—62no—
229C2×Dic3—61no—
230C2×Dic3—62no—
231C2×Dic3—122no—
232D12—21no—
233D12—42no—
234D12—81no—
235D12C2×S412yes—
236C4×D3—62no—
237C4×D3—62no—
238Dic6—32no—
239Dic6—62no—
240Dic6—61no—
241Dic6—62no—
242SL(2,𝔽3)—21no—
243SL(2,𝔽3)C2×#6711yescharacteristic
244C3×C8—62no—
245C3⋊C8—62no—
246C3⋊C8—122no—
247C3⋊C8—242no—
248C2×C32—41no—
249C2×C32—42no—
250C3×D3—162no—
251C3×D3—162no—
252C24—61no—
253#41—31no—
254#41—31no—
255#41—92no—
256#41—92no—
257#41—181no—
258#41—181no—
259#41—182no—
260#41—184no—
261#41—182no—
262#41#62511yescharacteristic
263#41C2×D3211yescharacteristic
264C2×Q8—62no—
265C2×Q8—92no—
266C2×Q8—92no—
267C2×Q8—91no—
268C2×Q8—181no—
269C2×Q8—181no—
270C2×Q8—181no—
271C2×Q8—182no—
272C2×Q8#62511yescharacteristic
273C2×D4—31no—
274C2×D4—32no—
275C2×D4—31no—
276C2×D4—61no—
277C2×D4—61no—
278C2×D4—61no—
279C2×D4—61no—
280C2×D4—61no—
281C2×D4—181no—
282C22×C4—31no—
283C22×C4—92no—
284C22×C4—181no—
285C22×C4—181no—
286SD16—62no—
287SD16—62no—
288SD16—184no—
289D8—62no—
290D8—62no—
291D8—184no—
292M16—32no—
293M16—61no—
294M16—92no—
295M16—181no—
296C2×C8—61no—
297C2×C8—181no—
298C22⋊C4—188no—
299C42—92no—
300C42—181no—
301C22×C3—31no—
302C22×C3—31no—
303C22×C3—41no—
304C22×C3—62no—
305C22×C3—81no—
306C22×C3—124no—
307C22×C3—122no—
308C22×C3—242no—
309C22×C3—242no—
310C22×C3—242no—
311C22×C3—482no—
312C22×C3GL(2,ℤ/4)11yescharacteristic
313C2×D3—22no—
314C2×D3—42no—
315C2×D3—82no—
316C2×D3—162no—
317C3×C4—31no—
318C3×C4—31no—
319C3×C4—41no—
320C3×C4—41no—
321C3×C4—81no—
322C3×C4—81no—
323C3×C4GL(2,ℤ/4)11yescharacteristic
324C3×C4C22×S411yescharacteristic
325Dic3—62no—
326Dic3—122no—
327C32—41noSylow
328C23—31no—
329C23—62no—
330C23—61no—
331C23—121no—
332C23—124no—
333C23—121no—
334Q8—31no—
335Q8—92no—
336Q8—182no—
337Q8—182no—
338Q8—181no—
339Q8C2×#62511yescharacteristic
340D4—31no—
341D4—31no—
342D4—32no—
343D4—61no—
344D4—62no—
345D4—62no—
346D4—61no—
347D4—121no—
348D4—121no—
349D4—182no—
350D4—182no—
351C2×C4—31no—
352C2×C4—31no—
353C2×C4—31no—
354C2×C4—31no—
355C2×C4—31no—
356C2×C4—94no—
357C2×C4—182no—
358C2×C4—182no—
359C2×C4—182no—
360C2×C4—181no—
361C2×C4—182no—
362C2×C4—362no—
363C2×C4D3×S411yescharacteristic
364C8—62no—
365C8—182no—
366C2×C3—41no—
367C2×C3—42no—
368C2×C3—61no—
369C2×C3—61no—
370C2×C3—81no—
371C2×C3—82no—
372C2×C3—242no—
373C2×C3—482no—
374C2×C3#543112yescomplemented
375C2×C3C2×GL(2,ℤ/4)11yescharacteristic
376D3—42no—
377D3—162no—
378C22—31no—
379C22—31no—
380C22—62no—
381C22—62no—
382C22—124no—
383C22—122no—
384C22—122no—
385C22—242no—
386C22—242no—
387C22#6420911yescharacteristic
388C4—31no—
389C4—31no—
390C4—182no—
391C4—362no—
392C4#6420911yescharacteristic
393C4C2×D3×S411yescharacteristic
394C3—41no—
395C3—81no—
396C3C2×#543111yescharacteristic, complemented
397C2—61no—
398C2—61no—
399C2—122no—
400C2—242no—
401C2#1059322912yesdirect product factor
402C2C2×#6420911yescharacteristic
subgroupG/H
centerC22#64209
commutator, cosocleC3×#41⋊C3C23
FrattiniC4C2×D3×S4
FittingC2×C3×#41C2×D3
socleC22×C3GL(2,ℤ/4)
hypercenterC2×C4D3×S4
hypocenterC3×SL(2,𝔽3)C2×D4
LCSG ▷ C3×#41⋊C3 ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#1010⋊C3C2semidirect
2. C2×C3×#986C2semidirect
3. C2×C3⋊GU(2,𝔽3)C2semidirect
4. #10593229C2direct (N × H)
9. #1010⋊C3C22semidirect
12. C3×#986C22semidirect
15. C3⋊GU(2,𝔽3)C22semidirect
16. C2×#1010D3semidirect
18. C2×#986D3semidirect
45. #1010C2×D3semidirect
56. #986C2×D3semidirect
374. C2×C3#5431semidirect
396. C3C2×#5431semidirect
401. C2#10593229direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#1010⋊C32
C2×C3×#9862
C2×C3⋊GU(2,𝔽3)2
#105932292
C2×#54313
C2×#52013
C2×#37134