Finite Group Databasebeta

← C2×#10593662 #11923073

Subgroups — C2×#10593662 #11923073

Order 1152.

712 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 712 conjugacy classes of subgroups — too many to draw. Only its 81 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×#994C211yesmaximal, characteristic
2C2×#64265C211yesmaximal, characteristic, complemented
3#10593662C214yesmaximal, direct product factor
4C2×C3⋊GU(2,𝔽3)C211yesmaximal, characteristic, complemented
5C2×#5428—33nomaximal
6C2×#5242—31nomaximal
7C3×#994—21no—
8C3×#994C2212yes—
9C2×C3×#41⋊C3—21no—
10C2×C3×#41⋊C3C2211yescharacteristic
11#64265—21no—
12#64265C2212yescomplemented
13C2×C3⋊#226—21no—
14C2×#3756—41nomaximal
15C3⋊GU(2,𝔽3)C2212yescomplemented
16C2×C3×H(5,𝔽2)D311yescharacteristic
17C2×#994D313yes—
18C2×#984—33no—
19C2×#951—31no—
20C2×#951—31no—
21C2×#936—31no—
22#5428—312no—
23C2×GU(2,𝔽3)—33no—
24#5242—34no—
25#5242—34no—
26C2×#837—31no—
27C2×#837—31no—
28C2×#833—31no—
29C2×C32×Q8—41no—
30C2×#634—41no—
31C3×#41⋊C3—22no—
32C3×#41⋊C3D411yescharacteristic
33C3×#41⋊C3C2311yescharacteristic
34C2×C3×SL(2,𝔽3)D411yescharacteristic
35C3⋊#226—22no—
36#3756—44no—
37C2×C3⋊(C3⋊C8)—41no—
38C2×#455—91noSylow
39C3×H(5,𝔽2)—21no—
40C3×H(5,𝔽2)—32no—
41C3×H(5,𝔽2)—61no—
42C3×H(5,𝔽2)C2×D312yes—
43C2×C3×#41—21no—
44C2×C3×#41—31no—
45C2×C3×#41C2×D311yescharacteristic
46C22×C3×D4—31no—
47C22×C3×D4—61no—
48C22×Dic6—31no—
49#994—23no—
50#994C2×D316yes—
51C2×#41⋊C3—23no—
52C2×#41⋊C3C2×D313yes—
53#984—36no—
54#984—63no—
55C2×#226—63no—
56C2×#217—62no—
57#951—32no—
58#951—34no—
59#951—32no—
60#951—61no—
61#951—62no—
62#951—61no—
63C2×#216—61no—
64C2×#216—61no—
65C2×#216—123no—
66#936—34no—
67#936—62no—
68C2×#214—61no—
69C2×#214—61no—
70C2×C4×Dic3—31no—
71C2×#208—31no—
72C2×#208—31no—
73GU(2,𝔽3)—36no—
74#837—32no—
75#837—34no—
76#837—32no—
77#833—34no—
78C32×Q8—42no—
79C32×Q8—81no—
80C2×C32×C4—41no—
81C2×C32×C4—81no—
82C2×C3⋊Dic3—81no—
83#634—42no—
84#634—81no—
85C3×SL(2,𝔽3)C2×D411yescharacteristic
86C3⋊(C3⋊C8)—42no—
87C2×H(5,𝔽2)C3⋊D311yescharacteristic
88C2×#137—91no—
89C2×#137—91no—
90C2×#124—91no—
91#455—94no—
92#455—94no—
93C2×#104—91no—
94C2×#104—91no—
95C2×#100—91no—
96C24×C3—32no—
97C3×#41—22no—
98C3×#41—31no—
99C3×#41—31no—
100C3×#41—32no—
101C3×#41—32no—
102C3×#41—61no—
103C3×#41—61no—
104C3×#41—62no—
105C3×#41#6711yescharacteristic
106C3×#41C22×D311yescharacteristic
107C2×C3×Q8—43no—
108C2×C3×Q8#6711yescharacteristic
109C2×C3×Q8S411yescharacteristic
110C2×C3×D4—31no—
111C2×C3×D4—32no—
112C2×C3×D4—32no—
113C2×C3×D4—31no—
114C2×C3×D4—61no—
115C2×C3×D4—61no—
116C2×C3×D4—61no—
117C2×C3×D4—61no—
118C2×C3×D4—62no—
119C2×C3×D4—62no—
120C2×C3×D4—64no—
121C22×C3×C4—31no—
122C22×C3×C4—61no—
123C22×Dic3—61no—
124C22×Dic3—61no—
125C2×Dic6—32no—
126C2×Dic6—61no—
127C2×Dic6—61no—
128C2×Dic6—61no—
129C2×Dic6—61no—
130C2×Dic6—61no—
131C2×Dic6—123no—
132#41⋊C3—26no—
133#41⋊C3#6713yes—
134#41⋊C3C22×D313yes—
135C2×SL(2,𝔽3)#6713yes—
136#226—66no—
137#217—68no—
138#216—62no—
139#216—62no—
140#216—64no—
141#216—1212no—
142#214—62no—
143#214—62no—
144#214—64no—
145C4×Dic3—32no—
146C4×Dic3—61no—
147#208—32no—
148#208—32no—
149#208—61no—
150#208—61no—
151C2×C3⋊C8—61no—
152C2×C3⋊C8—61no—
153C2×C3⋊C8—123no—
154C22×C32—41no—
155C32×C4—41no—
156C32×C4—41no—
157C32×C4—82no—
158C3⋊Dic3—82no—
159H(5,𝔽2)—21no—
160H(5,𝔽2)—32no—
161H(5,𝔽2)—61no—
162H(5,𝔽2)C2×C3⋊D312yes—
163C2×#41—21no—
164C2×#41—31no—
165C2×#41C2×C3⋊D311yescharacteristic
166C22×Q8—91no—
167C22×D4—31no—
168C22×D4—61no—
169#137—92no—
170#137—94no—
171#137—92no—
172#137—181no—
173#137—182no—
174#137—181no—
175C2×Q16—181no—
176C2×Q16—181no—
177C2×SD16—181no—
178C2×SD16—181no—
179C2×M16—91no—
180C2×M16—91no—
181#124—94no—
182#124—182no—
183C2×C22⋊C4—182no—
184C2×C42—91no—
185#104—92no—
186#104—94no—
187#104—92no—
188#100—94no—
189C23×C3—31no—
190C23×C3—34no—
191C23×C3—62no—
192C23×C3—61no—
193C23×C3—124no—
194C3×Q8—21no—
195C3×Q8—31no—
196C3×Q8—46no—
197C3×Q8—83no—
198C3×Q8C2×#6711yescharacteristic
199C3×Q8C2×S412yes—
200C3×D4—31no—
201C3×D4—31no—
202C3×D4—32no—
203C3×D4—62no—
204C3×D4—62no—
205C3×D4—61no—
206C3×D4—62no—
207C3×D4—62no—
208C3×D4—61no—
209C2×C3×C4—21no—
210C2×C3×C4—31no—
211C2×C3×C4—31no—
212C2×C3×C4—31no—
213C2×C3×C4—31no—
214C2×C3×C4—31no—
215C2×C3×C4—43no—
216C2×C3×C4—62no—
217C2×C3×C4—62no—
218C2×C3×C4—83no—
219C2×C3×C4C2×S411yescharacteristic
220C2×Dic3—62no—
221C2×Dic3—62no—
222C2×Dic3—121no—
223C2×Dic3—122no—
224C2×Dic3—121no—
225C2×Dic3—243no—
226Dic6—62no—
227Dic6—62no—
228Dic6—126no—
229Dic6—121no—
230Dic6—121no—
231Dic6—243no—
232SL(2,𝔽3)C2×#6713yes—
233C3⋊C8—62no—
234C3⋊C8—62no—
235C3⋊C8—126no—
236C2×C32—41no—
237C2×C32—42no—
238C24—32no—
239#41—22no—
240#41—31no—
241#41—31no—
242#41—32no—
243#41—32no—
244#41—61no—
245#41—61no—
246#41—62no—
247#41#63811yescharacteristic
248#41C22×C3⋊D311yescharacteristic
249C2×Q8—92no—
250C2×Q8—181no—
251C2×Q8—181no—
252C2×Q8—181no—
253C2×Q8—181no—
254C2×Q8—181no—
255C2×Q8#63811yescharacteristic
256C2×Q8C3⋊S411yescharacteristic
257C2×D4—31no—
258C2×D4—32no—
259C2×D4—32no—
260C2×D4—31no—
261C2×D4—61no—
262C2×D4—61no—
263C2×D4—61no—
264C2×D4—61no—
265C2×D4—62no—
266C2×D4—62no—
267C2×D4—64no—
268C22×C4—31no—
269C22×C4—61no—
270C22×C4—181no—
271C22×C4—181no—
272Q16—182no—
273Q16—184no—
274Q16—182no—
275SD16—182no—
276SD16—182no—
277SD16—184no—
278M16—92no—
279M16—92no—
280M16—181no—
281M16—181no—
282C2×C8—181no—
283C2×C8—181no—
284C22⋊C4—188no—
285C42—92no—
286C42—181no—
287C22×C3—31no—
288C22×C3—31no—
289C22×C3—43no—
290C22×C3—62no—
291C22×C3—62no—
292C22×C3—124no—
293C22×C3—122no—
294C22×C3—242no—
295C22×C3GL(2,ℤ/4)11yescharacteristic
296C3×C4—22no—
297C3×C4—31no—
298C3×C4—31no—
299C3×C4—43no—
300C3×C4—43no—
301C3×C4—86no—
302C3×C4GL(2,ℤ/4)11yescharacteristic
303C3×C4C22×S411yescharacteristic
304Dic3—122no—
305Dic3—122no—
306Dic3—246no—
307C32—41noSylow
308C23—31no—
309C23—34no—
310C23—62no—
311C23—61no—
312C23—124no—
313Q8—21no—
314Q8—31no—
315Q8—182no—
316Q8—182no—
317Q8—361no—
318Q8—361no—
319Q8C2×#63811yescharacteristic
320Q8C2×C3⋊S412yes—
321D4—31no—
322D4—31no—
323D4—32no—
324D4—62no—
325D4—62no—
326D4—61no—
327D4—62no—
328D4—62no—
329D4—61no—
330C2×C4—21no—
331C2×C4—31no—
332C2×C4—31no—
333C2×C4—31no—
334C2×C4—31no—
335C2×C4—31no—
336C2×C4—62no—
337C2×C4—62no—
338C2×C4—182no—
339C2×C4—182no—
340C2×C4—361no—
341C2×C4—362no—
342C2×C4—361no—
343C2×C4C2×C3⋊S411yescharacteristic
344C8—182no—
345C8—182no—
346C2×C3—46no—
347C2×C3—43no—
348C2×C3—61no—
349C2×C3—61no—
350C2×C3—122no—
351C2×C3#542812yescomplemented
352C2×C3C2×GL(2,ℤ/4)11yescharacteristic
353C22—31no—
354C22—31no—
355C22—62no—
356C22—62no—
357C22—124no—
358C22—122no—
359C22—242no—
360C22#6426911yescharacteristic
361C4—22no—
362C4—31no—
363C4—31no—
364C4—362no—
365C4—362no—
366C4#6426911yescharacteristic
367C4C22×C3⋊S411yescharacteristic
368C3—43no—
369C3C2×#542811yescharacteristic, complemented
370C2—61no—
371C2—61no—
372C2—122no—
373C2#1059366212yesdirect product factor
374C2C2×#6426911yescharacteristic
subgroupG/H
centerC22#64269
commutator, cosocleC3×#41⋊C3C23
FrattiniC4C22×C3⋊S4
FittingC2×C3×H(5,𝔽2)D3
socleC22×C3GL(2,ℤ/4)
prime radicalC2×C3×#994C2
hypercenterC2×Q8C3⋊S4
hypocenterC3×SL(2,𝔽3)C2×D4
LCSG ▷ C3×#41⋊C3 ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#64265C2semidirect
3. #10593662C2direct (N × H)
4. C2×C3⋊GU(2,𝔽3)C2semidirect
12. #64265C22semidirect
15. C3⋊GU(2,𝔽3)C22semidirect
351. C2×C3#5428semidirect
369. C3C2×#5428semidirect
373. C2#10593662direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9942
C2×#642652
#105936622
C2×C3⋊GU(2,𝔽3)2
C2×#54283
C2×#52423
C2×#37564