Finite Group Databasebeta

← C2×#10593231 #11922326

Subgroups — C2×#10593231 #11922326

Order 1152.

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

normal subgroups only

This group has 613 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
2C2×C3×#984C211yesmaximal, characteristic, complemented
3C2×C3⋊GU(2,𝔽3)C211yesmaximal, characteristic, complemented
4#10593231C214yesmaximal, direct product factor
5C2×#5430—31nomaximal
6C2×#5205—31nomaximal
7C2×C3×#41⋊C3C2211yescharacteristic
8#1010⋊C3—21no—
9#1010⋊C3C2212yes—
10C2×D3×SL(2,𝔽3)—21no—
11C3×#984—21no—
12C3×#984C2212yescomplemented
13C2×C3×#226—21no—
14C2×#3715—41nomaximal
15C3⋊GU(2,𝔽3)C2212yescomplemented
16C2×#1010D311yescharacteristic
17C2×2−1+4⋊C3—31no—
18C2×#984D311yescharacteristic, complemented
19C2×C3×#137—31no—
20C2×#944—31no—
21C2×#942—31no—
22#5430—34no—
23C2×GU(2,𝔽3)—31no—
24C2×GU(2,𝔽3)—61no—
25C2×#837—31no—
26#5205—34no—
27#5205—34no—
28C2×#825—31no—
29C2×#824—31no—
30C2×C3×D12—41no—
31C2×C3×Dic6—41no—
32C3×#41⋊C3D411yescharacteristic
33C3×#41⋊C3C2311yescharacteristic
34C2×C3×SL(2,𝔽3)D411yescharacteristic
35D3×SL(2,𝔽3)—22no—
36C3×#226—22no—
37C2×C3⋊(C3⋊C8)—41no—
38#3715—44no—
39C2×#456—91noSylow
40C2×C3×#41C2×D311yescharacteristic
41C22×C3×Q8—31no—
42#1010—21no—
43#1010—32no—
44#1010—61no—
45#1010C2×D312yes—
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#984—21no—
56#984C2×D312yescomplemented
57C2×#226—21no—
58C3×#137—32no—
59C3×#137—32no—
60C3×#137—61no—
61C3×#137—61no—
62C2×C3×Q16—61no—
63C2×C3×SD16—61no—
64C2×C3×M16—31no—
65#944—34no—
66#944—62no—
67C2×#216—61no—
68#942—34no—
69#942—62no—
70C2×#215—61no—
71C2×#214—121no—
72C2×Dic3⋊C4—62no—
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—
82C2×C32×C4—41no—
83C2×C3×Dic3—81no—
84C3×D12—42no—
85C3×D12—81no—
86C3×Dic6—42no—
87C3×Dic6—81no—
88C3×SL(2,𝔽3)C2×D411yescharacteristic
89C3⋊(C3⋊C8)—42no—
90C2×2−1+4—31no—
91C2×#137—31no—
92C2×#137—91no—
93C2×C4⋊Q8—91no—
94#456—94no—
95#456—94no—
96C2×#104—91no—
97C2×#104—91no—
98C2×#101—91no—
99C3×#41—31no—
100C3×#41—31no—
101C3×#41#6711yescharacteristic
102C3×#41C22×D311yescharacteristic
103C2×C3×Q8—32no—
104C2×C3×Q8—61no—
105C2×C3×Q8—61no—
106C2×C3×Q8—61no—
107C2×C3×Q8—61no—
108C2×C3×Q8—61no—
109C2×C3×Q8#6711yescharacteristic
110C2×C3×D4—31no—
111C2×C3×D4—121no—
112C22×C3×C4—31no—
113C22×C3×C4—61no—
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×D12S411yescharacteristic
127C2×C4×D3—61no—
128C2×Dic6—31no—
129C2×Dic6—32no—
130C2×Dic6—32no—
131C2×Dic6—41no—
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
142#226—22no—
143C3×Q16—62no—
144C3×Q16—62no—
145C3×SD16—62no—
146C3×SD16—62no—
147C3×M16—32no—
148C3×M16—61no—
149C2×C3×C8—61no—
150#216—64no—
151#215—64no—
152#214—124no—
153Dic3⋊C4—68no—
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—162no—
164C32×C4—41no—
165C32×C4—41no—
166C3×Dic3—82no—
1672−1+4—32no—
1682−1+4—61no—
1692−1+4—92no—
1702−1+4—181no—
171C2×#41—91no—
172C2×#41—181no—
173C2×#41D3211yescharacteristic
174C22×Q8—31no—
175C22×Q8—61no—
176C22×Q8—91no—
177#137—32no—
178#137—32no—
179#137—61no—
180#137—61no—
181#137—94no—
182#137—182no—
183C2×Q16—61no—
184C2×Q16—181no—
185C2×SD16—61no—
186C2×SD16—181no—
187C2×M16—31no—
188C2×M16—91no—
189C4⋊Q8—94no—
190C4⋊Q8—182no—
191C2×C4⋊C4—182no—
192C2×C42—91no—
193#104—94no—
194#104—92no—
195#104—92no—
196#101—94no—
197C23×C3—31no—
198C23×C3—241no—
199C22×D3—21no—
200C3×Q8—31no—
201C3×Q8—62no—
202C3×Q8—62no—
203C3×Q8—121no—
204C3×Q8—121no—
205C3×Q8C2×#6711yescharacteristic
206C3×D4—31no—
207C3×D4—31no—
208C3×D4—61no—
209C3×D4—122no—
210C3×D4—241no—
211C2×C3×C4—31no—
212C2×C3×C4—31no—
213C2×C3×C4—31no—
214C2×C3×C4—31no—
215C2×C3×C4—31no—
216C2×C3×C4—41no—
217C2×C3×C4—62no—
218C2×C3×C4—81no—
219C2×C3×C4—121no—
220C2×C3×C4—121no—
221C2×C3×C4C2×S411yescharacteristic
222#67—62no—
223#67—62no—
224C2×Dic3—34no—
225C2×Dic3—62no—
226C2×Dic3—62no—
227C2×Dic3—64no—
228C2×Dic3—61no—
229C2×Dic3—81no—
230D12—21no—
231D12C2×S412yes—
232C4×D3—62no—
233C4×D3—62no—
234Dic6—32no—
235Dic6—42no—
236Dic6—62no—
237Dic6—61no—
238Dic6—62no—
239Dic6—81no—
240SL(2,𝔽3)—21no—
241SL(2,𝔽3)C2×#6711yescharacteristic
242C3×C8—62no—
243C3⋊C8—62no—
244C3⋊C8—122no—
245C3⋊C8—242no—
246C2×C32—41no—
247C2×C32—42no—
248C3×D3—162no—
249#41—31no—
250#41—31no—
251#41—92no—
252#41—92no—
253#41—181no—
254#41—181no—
255#41—182no—
256#41—184no—
257#41—182no—
258#41#62511yescharacteristic
259#41C2×D3211yescharacteristic
260C2×Q8—32no—
261C2×Q8—61no—
262C2×Q8—61no—
263C2×Q8—61no—
264C2×Q8—61no—
265C2×Q8—61no—
266C2×Q8—62no—
267C2×Q8—92no—
268C2×Q8—92no—
269C2×Q8—91no—
270C2×Q8—181no—
271C2×Q8—181no—
272C2×Q8—181no—
273C2×Q8—182no—
274C2×Q8#62511yescharacteristic
275C2×D4—31no—
276C2×D4—31no—
277C2×D4—181no—
278C22×C4—31no—
279C22×C4—61no—
280C22×C4—92no—
281C22×C4—181no—
282C22×C4—181no—
283Q16—62no—
284Q16—62no—
285Q16—184no—
286SD16—62no—
287SD16—62no—
288SD16—184no—
289M16—32no—
290M16—61no—
291M16—92no—
292M16—181no—
293C2×C8—61no—
294C2×C8—181no—
295C4⋊C4—188no—
296C42—92no—
297C42—181no—
298C22×C3—31no—
299C22×C3—31no—
300C22×C3—41no—
301C22×C3—62no—
302C22×C3—81no—
303C22×C3—242no—
304C22×C3—482no—
305C22×C3GL(2,ℤ/4)11yescharacteristic
306C2×D3—22no—
307C2×D3—42no—
308C3×C4—31no—
309C3×C4—31no—
310C3×C4—41no—
311C3×C4—41no—
312C3×C4—81no—
313C3×C4—81no—
314C3×C4—122no—
315C3×C4GL(2,ℤ/4)11yescharacteristic
316C3×C4C22×S411yescharacteristic
317Dic3—64no—
318Dic3—62no—
319Dic3—82no—
320C32—41noSylow
321C23—31no—
322C23—61no—
323Q8—31no—
324Q8—62no—
325Q8—62no—
326Q8—92no—
327Q8—121no—
328Q8—121no—
329Q8—182no—
330Q8—182no—
331Q8—181no—
332Q8C2×#62511yescharacteristic
333D4—31no—
334D4—31no—
335D4—32no—
336D4—61no—
337D4—61no—
338D4—182no—
339D4—182no—
340C2×C4—31no—
341C2×C4—31no—
342C2×C4—31no—
343C2×C4—31no—
344C2×C4—31no—
345C2×C4—62no—
346C2×C4—94no—
347C2×C4—121no—
348C2×C4—121no—
349C2×C4—182no—
350C2×C4—182no—
351C2×C4—182no—
352C2×C4—182no—
353C2×C4—184no—
354C2×C4—181no—
355C2×C4D3×S411yescharacteristic
356C8—62no—
357C8—182no—
358C2×C3—41no—
359C2×C3—42no—
360C2×C3—61no—
361C2×C3—61no—
362C2×C3—81no—
363C2×C3—82no—
364C2×C3—482no—
365C2×C3#543012yescomplemented
366C2×C3C2×GL(2,ℤ/4)11yescharacteristic
367D3—42no—
368C22—31no—
369C22—31no—
370C22—62no—
371C22—62no—
372C22—122no—
373C22#6420911yescharacteristic
374C4—31no—
375C4—31no—
376C4—122no—
377C4—184no—
378C4—182no—
379C4#6420911yescharacteristic
380C4C2×D3×S411yescharacteristic
381C3—41no—
382C3—81no—
383C3C2×#543011yescharacteristic, complemented
384C2—61no—
385C2—61no—
386C2—122no—
387C2#1059323112yesdirect product factor
388C2C2×#6420911yescharacteristic
subgroupG/H
centerC22#64209
commutator, cosocleC3×#41⋊C3C23
FrattiniC4C2×D3×S4
FittingC2×C3×#41C2×D3
socleC22×C3GL(2,ℤ/4)
prime radicalC2×#1010⋊C3C2
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
2. C2×C3×#984C2semidirect
3. C2×C3⋊GU(2,𝔽3)C2semidirect
4. #10593231C2direct (N × H)
12. C3×#984C22semidirect
15. C3⋊GU(2,𝔽3)C22semidirect
18. C2×#984D3semidirect
56. #984C2×D3semidirect
365. C2×C3#5430semidirect
383. C3C2×#5430semidirect
387. C2#10593231direct (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×#9842
C2×C3⋊GU(2,𝔽3)2
#105932312
C2×#54303
C2×#52053
C2×#37154