Finite Group Databasebeta

← C2×#10593223 #11922265

Subgroups — C2×#10593223 #11922265

Order 1152.

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

normal subgroups only

This group has 549 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×#64265C211yesmaximal, characteristic, complemented
2C2×C3×#986C211yesmaximal, characteristic
3C2×C3⋊(#131⋊C3)C211yesmaximal, characteristic, complemented
4#10593223C214yesmaximal, direct product factor
5C2×#5406—31nomaximal
6C2×#5200—31nomaximal
7C2×C3×#41⋊C3C2211yescharacteristic
8#64265—21no—
9#64265C2212yescomplemented
10C2×C3⋊#226—21no—
11C3×#986—21no—
12C3×#986C2212yes—
13C2×C3×GL(2,𝔽3)—21no—
14C2×#3716—41nomaximal
15C3⋊(#131⋊C3)C2212yescomplemented
16C2×#986D311yescharacteristic
17C2×#984—31no—
18C2×#984—61no—
19C2×C3×AGL(1,ℤ/8)—31no—
20C2×#951—31no—
21C2×#948D311yescharacteristic, complemented
22C22×#214—31no—
23C2×#131⋊C3—31no—
24#5406—34no—
25C2×#833—31no—
26#5200—34no—
27#5200—34no—
28C2×#824—31no—
29C2×#822—31no—
30C2×#634—41no—
31C2×C3×D12—41no—
32C3×#41⋊C3D411yescharacteristic
33C3×#41⋊C3C2311yescharacteristic
34C2×C3×SL(2,𝔽3)D411yescharacteristic
35C3⋊#226—22no—
36C3×GL(2,𝔽3)—22no—
37C2×C3×C3⋊C8—41no—
38#3716—44no—
39C2×#471—91noSylow
40C2×C3×#41C2×D311yescharacteristic
41C22×C3×D4—31no—
42C22×Dic6—31no—
43C2×#41⋊C3—21no—
44C2×#41⋊C3C2×D311yescharacteristic
45#986—21no—
46#986C2×D312yes—
47#984—32no—
48#984—62no—
49#984—62no—
50#984—61no—
51C2×GL(2,𝔽3)—21no—
52C2×#226—62no—
53C2×#226—61no—
54C3×AGL(1,ℤ/8)—32no—
55C3×AGL(1,ℤ/8)—32no—
56C3×AGL(1,ℤ/8)—61no—
57C3×AGL(1,ℤ/8)—61no—
58C2×C3×SD16—61no—
59C2×C3×D8—61no—
60C2×C3×M16—31no—
61#951—32no—
62#951—32no—
63#951—61no—
64#951—61no—
65#948—32no—
66#948C2×D312yescomplemented
67C2×#216—61no—
68C2×#214—34no—
69C2×#214—61no—
70C2×#214—62no—
71C2×#214—61no—
72C2×#214—61no—
73C2×#208—31no—
74C2×#208—31no—
75C22×C3⋊C8—31no—
76C2×#204—121no—
77#131⋊C3—32no—
78#833—34no—
79#824—34no—
80#822—34no—
81C22×C3×D3—81no—
82C2×C32×C4—41no—
83C2×C3⋊Dic3—81no—
84#634—42no—
85#634—81no—
86C3×D12—42no—
87C3×D12—81no—
88C3×SL(2,𝔽3)C2×D411yescharacteristic
89C3×C3⋊C8—42no—
90C2×#137—91no—
91C2×AGL(1,ℤ/8)—31no—
92C22×SD16—91no—
93C2×#131—31no—
94#471—94no—
95#471—94no—
96C2×#108—91no—
97C2×#101—91no—
98C2×#100—91no—
99C24×C3—61no—
100C3×#41—31no—
101C3×#41—31no—
102C3×#41D1211yescharacteristic
103C3×#41C22×D311yescharacteristic
104C2×C3×Q8D1211yescharacteristic
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—
112C22×C3×C4—31no—
113C22×Dic3—61no—
114C2×D12—41no—
115C2×Dic6—32no—
116C2×Dic6—61no—
117C2×Dic6—61no—
118C2×Dic6—61no—
119C2×Dic6—61no—
120C2×Dic6—61no—
121C2×Dic6—121no—
122C2×Dic6—241no—
123#41⋊C3—21no—
124#41⋊C3—21no—
125#41⋊C3#6711yescharacteristic
126#41⋊C3C22×D311yescharacteristic
127C2×SL(2,𝔽3)—21no—
128C2×SL(2,𝔽3)#6711yescharacteristic
129GL(2,𝔽3)—22no—
130#226—64no—
131#226—62no—
132C3×SD16—62no—
133C3×SD16—62no—
134C3×D8—62no—
135C3×D8—62no—
136C3×M16—32no—
137C3×M16—61no—
138C2×C3×C8—61no—
139C2×C3×C8—121no—
140#216—62no—
141#216—62no—
142#214—64no—
143#214—62no—
144#214—62no—
145#214—64no—
146#208—32no—
147#208—32no—
148#208—61no—
149#208—61no—
150C2×C3⋊C8—31no—
151C2×C3⋊C8—32no—
152C2×C3⋊C8—32no—
153C2×C3⋊C8—61no—
154C2×C3⋊C8S411yescharacteristic
155#204—124no—
156C22×C32—41no—
157C2×C3×D3—82no—
158C2×C3×D3—162no—
159C32×C4—41no—
160C32×C4—41no—
161C3⋊Dic3—82no—
162C2×#41D3211yescharacteristic
163C22×Q8—91no—
164C22×D4—31no—
165#137—92no—
166#137—92no—
167#137—181no—
168#137—181no—
169AGL(1,ℤ/8)—32no—
170AGL(1,ℤ/8)—32no—
171AGL(1,ℤ/8)—61no—
172AGL(1,ℤ/8)—61no—
173C2×Q16—181no—
174C2×SD16—61no—
175C2×SD16—94no—
176C2×SD16—181no—
177C2×SD16—182no—
178C2×SD16—181no—
179C2×SD16—181no—
180C2×D8—61no—
181#131—32no—
182#131—92no—
183C2×M16—31no—
184C2×M16—91no—
185C2×M16—91no—
186C22×C8—91no—
187#108—94no—
188#101—94no—
189#100—94no—
190C23×C3—31no—
191C23×C3—62no—
192C23×C3—121no—
193C23×C3—121no—
194C23×C3—242no—
195C22×D3—81no—
196C3×Q8—31no—
197C3×Q8C2×D1211yescharacteristic
198C3×D4—31no—
199C3×D4—31no—
200C3×D4—61no—
201C3×D4—62no—
202C3×D4—62no—
203C3×D4—121no—
204C3×D4—121no—
205C2×C3×C4—31no—
206C2×C3×C4—31no—
207C2×C3×C4—31no—
208C2×C3×C4—31no—
209C2×C3×C4—31no—
210C2×C3×C4—41no—
211C2×C3×C4—81no—
212C2×C3×C4C2×S411yescharacteristic
213C2×Dic3—62no—
214C2×Dic3—121no—
215C2×Dic3—121no—
216C2×Dic3—241no—
217C2×Dic3—242no—
218D12—42no—
219D12—81no—
220Dic6—62no—
221Dic6—62no—
222Dic6—122no—
223Dic6—121no—
224Dic6—121no—
225Dic6—242no—
226Dic6—241no—
227Dic6—242no—
228SL(2,𝔽3)—21no—
229SL(2,𝔽3)C2×#6711yescharacteristic
230C3×C8—62no—
231C3×C8—122no—
232C3⋊C8—32no—
233C3⋊C8—62no—
234C3⋊C8C2×S412yes—
235C2×C32—41no—
236C2×C32—42no—
237C3×D3—162no—
238C24—61no—
239#41—31no—
240#41—31no—
241#41#62611yescharacteristic
242#41C2×D3211yescharacteristic
243C2×Q8—92no—
244C2×Q8—181no—
245C2×Q8—181no—
246C2×Q8—181no—
247C2×Q8—181no—
248C2×Q8—181no—
249C2×Q8#62611yescharacteristic
250C2×D4—31no—
251C2×D4—32no—
252C2×D4—61no—
253C2×D4—61no—
254C2×D4—61no—
255C2×D4—61no—
256C2×D4—61no—
257C22×C4—31no—
258C22×C4—181no—
259Q16—182no—
260Q16—182no—
261SD16—62no—
262SD16—62no—
263SD16—184no—
264SD16—184no—
265SD16—182no—
266SD16—182no—
267D8—62no—
268D8—62no—
269M16—32no—
270M16—61no—
271M16—92no—
272M16—92no—
273M16—181no—
274M16—181no—
275C2×C8—31no—
276C2×C8—61no—
277C2×C8—92no—
278C2×C8—92no—
279C2×C8—91no—
280C2×C8—181no—
281C22×C3—31no—
282C22×C3—31no—
283C22×C3—41no—
284C22×C3—62no—
285C22×C3—81no—
286C22×C3—122no—
287C22×C3—242no—
288C22×C3—242no—
289C22×C3—242no—
290C22×C3C4⋊S411yescharacteristic
291C2×D3—82no—
292C2×D3—162no—
293C3×C4—31no—
294C3×C4—31no—
295C3×C4—41no—
296C3×C4—41no—
297C3×C4—81no—
298C3×C4—81no—
299C3×C4C4⋊S411yescharacteristic
300C3×C4C22×S411yescharacteristic
301Dic3—122no—
302Dic3—242no—
303Dic3—244no—
304C32—41noSylow
305C23—31no—
306C23—62no—
307C23—121no—
308C23—121no—
309C23—242no—
310Q8—31no—
311Q8—182no—
312Q8—182no—
313Q8—361no—
314Q8—361no—
315Q8C2×#62611yescharacteristic
316D4—31no—
317D4—31no—
318D4—61no—
319D4—62no—
320D4—62no—
321D4—121no—
322D4—121no—
323C2×C4—31no—
324C2×C4—31no—
325C2×C4—31no—
326C2×C4—31no—
327C2×C4—31no—
328C2×C4—182no—
329C2×C4—361no—
330C2×C4—361no—
331C2×C4D3×S411yescharacteristic
332C8—32no—
333C8—62no—
334C8—92no—
335C8—182no—
336C2×C3—41no—
337C2×C3—42no—
338C2×C3—61no—
339C2×C3—61no—
340C2×C3—81no—
341C2×C3—82no—
342C2×C3—242no—
343C2×C3#540612yescomplemented
344C2×C3C2×C4⋊S411yescharacteristic
345D3—162no—
346C22—31no—
347C22—31no—
348C22—62no—
349C22—122no—
350C22—242no—
351C22—242no—
352C22—242no—
353C22#6420711yescharacteristic
354C4—31no—
355C4—31no—
356C4—362no—
357C4#6420711yescharacteristic
358C4C2×D3×S411yescharacteristic
359C3—41no—
360C3—81no—
361C3C2×#540611yescharacteristic, complemented
362C2—61no—
363C2—61no—
364C2—242no—
365C2#1059322312yesdirect product factor
366C2C2×#6420711yescharacteristic
subgroupG/H
centerC22#64207
commutator, cosocleC3×#41⋊C3C23
FrattiniC4C2×D3×S4
FittingC2×C3×#41C2×D3
socleC22×C3C4⋊S4
prime radicalC2×C3×#986C2
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×#64265C2semidirect
3. C2×C3⋊(#131⋊C3)C2semidirect
4. #10593223C2direct (N × H)
9. #64265C22semidirect
15. C3⋊(#131⋊C3)C22semidirect
21. C2×#948D3semidirect
66. #948C2×D3semidirect
343. C2×C3#5406semidirect
361. C3C2×#5406semidirect
365. C2#10593223direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#642652
C2×C3×#9862
C2×C3⋊(#131⋊C3)2
#105932232
C2×#54063
C2×#52003
C2×#37164