Finite Group Databasebeta

← C2×#10593203 #11922107

Subgroups — C2×#10593203 #11922107

Order 1152.

765 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 765 conjugacy classes of subgroups — too many to draw. Only its 75 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⋊C3)C211yesmaximal, characteristic, complemented
2C22×C3×GL(2,𝔽3)C211yesmaximal, characteristic, complemented
3C2×C3⋊#859C211yesmaximal, characteristic, complemented
4#10593203C214yesmaximal, direct product factor
5C2×#5427—31nomaximal
6C2×#5172—31nomaximal
7C22×C3×SL(2,𝔽3)C2211yescharacteristic
8C2×C3⋊(#41⋊C3)—22no—
9C2×C3⋊(#41⋊C3)C2212yescomplemented
10C2×C3×GL(2,𝔽3)—22no—
11C2×C3×GL(2,𝔽3)C2212yescomplemented
12C2×(C2×D3)⋊Dic3—41nomaximal
13C3⋊#859C2212yescomplemented
14C22×#239D311yescharacteristic, complemented
15C22×#41⋊C3—31no—
16C22×GL(2,𝔽3)D311yescharacteristic, complemented
17C22×C3×SD16—31no—
18C2×#938—31no—
19C22×#213—31no—
20#5427—34no—
21C2×#859—31no—
22C2×#859—61no—
23C2×#835—31no—
24#5172—34no—
25#5172—34no—
26C2×#821—31no—
27C2×(C2×D3)⋊C8—31no—
28C23×C3×D3—41no—
29C22×C3⋊Dic3—41no—
30C22×C3×Dic3—41no—
31C2×C3×SL(2,𝔽3)D412yescomplemented
32C2×C3×SL(2,𝔽3)C2311yescharacteristic
33C3⋊(#41⋊C3)—22no—
34C3×GL(2,𝔽3)—22no—
35(C2×D3)⋊Dic3—44no—
36C2×#449—91noSylow
37C22×C3×Q8C2×D311yescharacteristic
38C22×C3×D4—31no—
39C22×#67—61no—
40C2×#239—22no—
41C2×#239—32no—
42C2×#239—62no—
43C2×#239C2×D312yescomplemented
44C22×D12—31no—
45C22×C4×D3—31no—
46C2×#41⋊C3—32no—
47C2×#41⋊C3—62no—
48C22×SL(2,𝔽3)—21no—
49C22×SL(2,𝔽3)C2×D311yescharacteristic
50C2×GL(2,𝔽3)—22no—
51C2×GL(2,𝔽3)C2×D312yescomplemented
52C2×C3×SD16—32no—
53C2×C3×SD16—32no—
54C2×C3×SD16—62no—
55C2×C3×SD16—62no—
56C22×C3×C8—31no—
57C2×#217—61no—
58#938—34no—
59#938—62no—
60C2×#213—34no—
61C2×#213—64no—
62C2×(C2×D3)⋊C4—121no—
63C2×C4⋊Dic3—31no—
64C22×C3⋊C8—31no—
65#859—32no—
66#859—62no—
67#835—32no—
68#835—32no—
69#821—34no—
70(C2×D3)⋊C8—34no—
71C23×C32—41no—
72C22×C3×D3—42no—
73C22×C3×D3—44no—
74C22×C3×D3—82no—
75C22×C3×D3—82no—
76C2×C3⋊Dic3—42no—
77C2×C3⋊Dic3—82no—
78C2×C3×Dic3—42no—
79C2×C3×Dic3—82no—
80C3×SL(2,𝔽3)C2×D411yescharacteristic, complemented
81C22×#41—31no—
82C22×SD16—31no—
83C22×D8—91no—
84C2×#121—91no—
85#449—94no—
86#449—94no—
87C2×#103—91no—
88C2×#102—91no—
89C2×C22⋊C8—91no—
90C24×C3—61no—
91C23×D3—31no—
92C23×D3—41no—
93C2×C3×Q8—31no—
94C2×C3×Q8—32no—
95C2×C3×Q8#6712yes—
96C2×C3×Q8C22×D311yescharacteristic
97C2×C3×D4—32no—
98C2×C3×D4—62no—
99C2×C3×D4—62no—
100C2×C3×D4—61no—
101C22×C3×C4—31no—
102C22×C3×C4—121no—
103C2×#67—64no—
104C2×#67—124no—
105C22×Dic3—61no—
106C22×Dic3—121no—
107C22×Dic3—241no—
108C22×Dic3S411yescharacteristic
109#239—22no—
110#239—64no—
111#239—62no—
112#239—64no—
113C2×D12—32no—
114C2×D12—34no—
115C2×D12—61no—
116C2×D12—62no—
117C2×C4×D3—32no—
118C2×C4×D3—32no—
119C2×C4×D3—62no—
120C2×C4×D3—62no—
121#41⋊C3—62no—
122C2×SL(2,𝔽3)—22no—
123C2×SL(2,𝔽3)—21no—
124C2×SL(2,𝔽3)#6712yescomplemented
125C2×SL(2,𝔽3)C22×D311yescharacteristic
126GL(2,𝔽3)—22no—
127C3×SD16—64no—
128C3×SD16—62no—
129C3×SD16—62no—
130C2×C3×C8—32no—
131C2×C3×C8—62no—
132#217—64no—
133#213—68no—
134(C2×D3)⋊C4—124no—
135C4⋊Dic3—32no—
136C4⋊Dic3—61no—
137C2×C3⋊C8—32no—
138C2×C3⋊C8—62no—
139C22×C32—42no—
140C22×C32—42no—
141C22×C32—42no—
142C22×C32—41no—
143C2×C3×D3—44no—
144C2×C3×D3—82no—
145C2×C3×D3—82no—
146C2×C3×D3—88no—
147C3⋊Dic3—82no—
148C3×Dic3—82no—
149C2×#41—32no—
150C2×#41—62no—
151C2×#41—92no—
152C2×#41—182no—
153C22×Q8D3211yescharacteristic
154C22×D4—31no—
155C22×D4—91no—
156C22×D4—181no—
157C23×C4—91no—
158C2×SD16—32no—
159C2×SD16—32no—
160C2×SD16—62no—
161C2×SD16—62no—
162C2×D8—94no—
163C2×D8—184no—
164C22×C8—31no—
165C22×C8—91no—
166#121—94no—
167#121—182no—
168C2×C4⋊C4—91no—
169C2×C22⋊C4—181no—
170#103—92no—
171#103—92no—
172#102—94no—
173C22⋊C8—94no—
174C23×C3—41no—
175C23×C3—62no—
176C23×C3—81no—
177C23×C3—122no—
178C23×C3—122no—
179C23×C3—122no—
180C23×C3C2×S411yescharacteristic
181C22×D3—32no—
182C22×D3—42no—
183C22×D3—44no—
184C22×D3—62no—
185C22×D3—62no—
186C22×D3—62no—
187C22×D3—82no—
188C22×D3—82no—
189C3×Q8—32no—
190C3×Q8—31no—
191C3×Q8—61no—
192C3×Q8C2×#6711yescharacteristic
193C3×D4—62no—
194C3×D4—62no—
195C3×D4—122no—
196C2×C3×C4—32no—
197C2×C3×C4—32no—
198C2×C3×C4—31no—
199C2×C3×C4—31no—
200C2×C3×C4—122no—
201C2×C3×C4—242no—
202#67—128no—
203C2×Dic3—22no—
204C2×Dic3—62no—
205C2×Dic3—122no—
206C2×Dic3—122no—
207C2×Dic3—242no—
208C2×Dic3—242no—
209C2×Dic3—244no—
210C2×Dic3C2×S412yes—
211D12—34no—
212D12—62no—
213D12—64no—
214C4×D3—62no—
215C4×D3—62no—
216C4×D3—64no—
217SL(2,𝔽3)—21no—
218SL(2,𝔽3)C2×#6711yescharacteristic, complemented
219C3×C8—62no—
220C3⋊C8—62no—
221C2×C32—41no—
222C2×C32—41no—
223C2×C32—41no—
224C2×C32—44no—
225C3×D3—84no—
226C24—61no—
227C24—91no—
228#41—62no—
229#41—184no—
230#41—182no—
231#41—184no—
232C2×Q8—31no—
233C2×Q8—32no—
234C2×Q8#62512yes—
235C2×Q8C2×D3211yescharacteristic
236C2×D4—32no—
237C2×D4—62no—
238C2×D4—62no—
239C2×D4—61no—
240C2×D4—92no—
241C2×D4—94no—
242C2×D4—181no—
243C2×D4—182no—
244C2×D4—184no—
245C2×D4—364no—
246C22×C4—31no—
247C22×C4—31no—
248C22×C4—92no—
249C22×C4—92no—
250C22×C4—182no—
251C22×C4—182no—
252C22×C4—181no—
253SD16—64no—
254SD16—62no—
255SD16—62no—
256D8—188no—
257C2×C8—32no—
258C2×C8—62no—
259C2×C8—92no—
260C2×C8—182no—
261C4⋊C4—92no—
262C4⋊C4—181no—
263C22⋊C4—184no—
264C22×C3—41no—
265C22×C3—42no—
266C22×C3—42no—
267C22×C3—42no—
268C22×C3—81no—
269C22×C3—82no—
270C22×C3—82no—
271C22×C3—82no—
272C22×C3—122no—
273C22×C3—122no—
274C22×C3—122no—
275C22×C3—244no—
276C22×C3#98512yes—
277C22×C3#98612yes—
278C22×C3GL(2,ℤ/4)12yes—
279C22×C3C22×S411yescharacteristic
280C2×D3—44no—
281C2×D3—62no—
282C2×D3—62no—
283C2×D3—62no—
284C2×D3—82no—
285C2×D3—82no—
286C2×D3—88no—
287C2×D3—124no—
288C3×C4—31no—
289C3×C4—31no—
290C3×C4—32no—
291C3×C4—242no—
292Dic3—22no—
293Dic3—122no—
294Dic3—242no—
295Dic3—244no—
296C32—41noSylow
297C23—62no—
298C23—92no—
299C23—122no—
300C23—122no—
301C23—122no—
302C23—182no—
303C23—182no—
304C23—182no—
305C23D3×S411yescharacteristic
306Q8—32no—
307Q8—31no—
308Q8—61no—
309Q8C2×#62511yescharacteristic
310D4—62no—
311D4—62no—
312D4—94no—
313D4—122no—
314D4—182no—
315D4—184no—
316D4—368no—
317C2×C4—31no—
318C2×C4—31no—
319C2×C4—32no—
320C2×C4—32no—
321C2×C4—32no—
322C2×C4—62no—
323C2×C4—182no—
324C2×C4—182no—
325C2×C4—184no—
326C2×C4—182no—
327C2×C4—362no—
328C8—62no—
329C8—182no—
330C2×C3—41no—
331C2×C3—41no—
332C2×C3—41no—
333C2×C3—44no—
334C2×C3—81no—
335C2×C3—81no—
336C2×C3—81no—
337C2×C3—84no—
338C2×C3—242no—
339C2×C3#542714yescomplemented
340C2×C3C2×#98511yescharacteristic
341C2×C3C2×#98611yescharacteristic
342C2×C3C2×GL(2,ℤ/4)11yescharacteristic
343D3—84no—
344D3—122no—
345C22—122no—
346C22—122no—
347C22—122no—
348C22—182no—
349C22—182no—
350C22—182no—
351C22—244no—
352C22—364no—
353C22#6419712yes—
354C22#6419912yes—
355C22#6420912yes—
356C22C2×D3×S411yescharacteristic
357C4—31no—
358C4—31no—
359C4—32no—
360C4—62no—
361C4—362no—
362C3—41no—
363C3—81no—
364C3C2×#542711yescharacteristic, complemented
365C2—242no—
366C2—362no—
367C2#1059320314yesdirect product factor
368C2C2×#6419711yescharacteristic
369C2C2×#6419911yescharacteristic
370C2C2×#6420911yescharacteristic
subgroupG/H
center, hypercenterC23D3×S4
commutator, cosocleC2×C3×SL(2,𝔽3)C23
FrattiniC22C2×D3×S4
FittingC22×C3×Q8C2×D3
socleC23×C3C2×S4
hypocenterC3×SL(2,𝔽3)C2×D4
LCSG ▷ C2×C3×SL(2,𝔽3) ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C22×C3⋊(#41⋊C3)C2semidirect
2. C22×C3×GL(2,𝔽3)C2semidirect
3. C2×C3⋊#859C2semidirect
4. #10593203C2direct (N × H)
9. C2×C3⋊(#41⋊C3)C22semidirect
11. C2×C3×GL(2,𝔽3)C22semidirect
13. C3⋊#859C22semidirect
14. C22×#239D3semidirect
16. C22×GL(2,𝔽3)D3semidirect
31. C2×C3×SL(2,𝔽3)D4semidirect
43. C2×#239C2×D3semidirect
51. C2×GL(2,𝔽3)C2×D3semidirect
80. C3×SL(2,𝔽3)C2×D4semidirect
124. C2×SL(2,𝔽3)#67semidirect
218. SL(2,𝔽3)C2×#67semidirect
339. C2×C3#5427semidirect
364. C3C2×#5427semidirect
367. C2#10593203direct (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⋊C3)2
C22×C3×GL(2,𝔽3)2
C2×C3⋊#8592
#105932032
C2×#54273
C2×#51723
C2×(C2×D3)⋊Dic34