Finite Group Databasebeta

← #11922410

Subgroups — #11922410

Order 1152.

659 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 659 conjugacy classes of subgroups — too many to draw. Only its 83 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
2#10593660C211yesmaximal, characteristic, complemented
3C3×#5424C211yesmaximal, characteristic, complemented
4D3×#859C212yesmaximal, complemented
5#10593209C212yesmaximal, complemented
6#85534—31nomaximal
7#78832—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9#1010⋊C3C414yescomplemented
10C2×D3×SL(2,𝔽3)C2212yes—
11Dic3×D12—41nomaximal
12C3⋊#859C2212yes—
13C3×#859C2211yescharacteristic
14C3×#859C2211yescharacteristic
15C2×#1010D311yescharacteristic
16C2×2−1+4⋊C3—31no—
17C2×#901—31no—
18#5523—31no—
19#5426—31no—
20#5426—61no—
21#5424D311yescharacteristic, complemented
22#5420—32no—
23C2×#859—32no—
24C3×#416—31no—
25#5232—31no—
26C2×#816—31no—
27#5004—31no—
28#4802—32no—
29D3×#103—32no—
30#4772—32no—
31#4771—32no—
32C2×C3×D12—41no—
33C3×#41⋊C3C2×C412yescomplemented
34C2×C3×SL(2,𝔽3)C2311yescharacteristic
35C2×D3×Dic3—42no—
36D3×SL(2,𝔽3)C2×C414yescomplemented
37C4⋊(C3⋊Dic3)—41no—
38C3×C4×Dic3—41no—
39(C2×D3)⋊Dic3—42no—
40#2898—91noSylow
41C2×C3×#41C2×D311yescharacteristic
42#1010—34no—
43#1010Dic314yescomplemented
44C2×D3×Q8C2×D312yes—
45C2×#237—32no—
46C2×#235—31no—
47C22×Dic6—31no—
482−1+4⋊C3—34no—
49C2×#41⋊C3—21no—
50C2×#41⋊C3C2×D311yescharacteristic
51C22×SL(2,𝔽3)—32no—
52C22×C3×C8—31no—
53C3×#117—31no—
54D4×Dic3—121no—
55C2×C4⋊Dic3—31no—
56C2×#208—31no—
57#901—64no—
58C2×ΓL(1,𝔽25)—32no—
59C2×D3×C8—32no—
60#892—32no—
61D3×C4⋊C4—32no—
62#67⋊C4—62no—
63C4×D12—61no—
64C4×Dic6—61no—
65#859—32no—
66#859—62no—
67#859C2×D311yescharacteristic
68#859C2×D311yescharacteristic
69C3×#103—31no—
70C3×#103—31no—
71C3×#102—31no—
72C3×#102—31no—
73#835—32no—
74#832—32no—
75#816—32no—
76#816—32no—
77#810—32no—
78#810—32no—
79C22×C3×D3—42no—
80C2×C32×C4—41no—
81C2×C3⋊Dic3—42no—
82C2×C3×Dic3—41no—
83C2×C3×Dic3—41no—
84C3×D12—44no—
85C3×SL(2,𝔽3)C22×C411yescharacteristic
86D3×Dic3—84no—
87C2×2−1+4—31no—
88C2×#131—91no—
89#520—91no—
90#419—92no—
91#419—91no—
92#417—92no—
93#417—91no—
94#416—31no—
95#416—92no—
96C2×#103—92no—
97C2×#103—91no—
98C3×#41—32no—
99C3×#41C2×Dic312yescomplemented
100C2×C3×Q8C22×D311yescharacteristic
101C2×C3×D4—31no—
102C2×C3×D4—121no—
103C22×C3×C4—31no—
104C2×#67—32no—
105C22×Dic3—61no—
106C22×Dic3—61no—
107C22×Dic3—122no—
108D3×Q8—34no—
109D3×Q8C2×Dic314yescomplemented
110#237—38no—
111#237—64no—
112#235—34no—
113#235—34no—
114C2×D12S411yescharacteristic
115C2×C4×D3—32no—
116C2×C4×D3—62no—
117C2×Dic6—31no—
118C2×Dic6—34no—
119C2×Dic6—32no—
120C2×Dic6—62no—
121#41⋊C3—22no—
122#41⋊C3C4×D312yescomplemented
123C2×SL(2,𝔽3)—21no—
124C2×SL(2,𝔽3)—34no—
125C2×SL(2,𝔽3)C22×D311yescharacteristic
126C2×C3×C8—31no—
127C2×C3×C8—31no—
128C2×C3×C8—62no—
129C3×C4⋊C4—31no—
130C3×C4⋊C4—31no—
131C3×C22⋊C4—61no—
132C3×C42—61no—
133#217—122no—
134(C2×D3)⋊C4—62no—
135C4⋊Dic3—32no—
136C4⋊Dic3—61no—
137C4⋊Dic3—121no—
138C4⋊Dic3—241no—
139Dic3⋊C4—62no—
140C4×Dic3—41no—
141C4×Dic3—62no—
142#208—62no—
143C2×C3⋊C8—32no—
144ΓL(1,𝔽25)—64no—
145D3×C8—64no—
146C22×C32—41no—
147C2×C3×D3—44no—
148C2×C3×D3—82no—
149C2×C3×D3—82no—
150C32×C4—42no—
151C3⋊Dic3—82no—
152C3×Dic3—42no—
153C3×Dic3—81no—
1542−1+4—34no—
1552−1+4—94no—
156C2×#41—91no—
157C2×#41—92no—
158C2×#41D3211yescharacteristic
159C22×Q8—32no—
160C22×Q8—91no—
161#131—184no—
162C2×M16—92no—
163C2×M16—91no—
164C22×C8—31no—
165C22×C8—92no—
166C4×Q8—181no—
167C4×D4—181no—
168C4×D4—182no—
169#117—31no—
170#117—92no—
171C2×C4⋊C4—92no—
172C2×C4⋊C4—91no—
173#103—31no—
174#103—31no—
175#103—92no—
176#103—92no—
177#103—92no—
178#103—92no—
179#103—92no—
180#102—31no—
181#102—31no—
182#102—92no—
183C23×C3—31no—
184C23×C3—122no—
185C22×D3C2×S412yes—
186C3×Q8—31no—
187C3×Q8C22×Dic311yescharacteristic
188C3×D4—32no—
189C3×D4—61no—
190C3×D4—124no—
191C2×C3×C4—31no—
192C2×C3×C4—32no—
193C2×C3×C4—32no—
194C2×C3×C4—41no—
195C2×C3×C4—61no—
196C2×C3×C4—61no—
197C2×C3×C4—81no—
198C2×C3×C4C2×S411yescharacteristic
199#67—38no—
200C2×Dic3—32no—
201C2×Dic3—41no—
202C2×Dic3—41no—
203C2×Dic3—64no—
204C2×Dic3—62no—
205C2×Dic3—122no—
206C2×Dic3—242no—
207C2×Dic3—244no—
208C2×Dic3—241no—
209D12SL(2,ℤ/4)14yes—
210C4×D3—34no—
211C4×D3—34no—
212C4×D3—242no—
213Dic6—34no—
214Dic6—34no—
215Dic6—62no—
216SL(2,𝔽3)—21no—
217SL(2,𝔽3)C2×C4×D311yescharacteristic
218C3×C8—61no—
219C3×C8—61no—
220C3⋊C8—62no—
221C2×C32—41no—
222C2×C32—41no—
223C2×C32—41no—
224C3×D3—84no—
225#41—32no—
226#41—94no—
227#41—94no—
228#41—98no—
229#41—184no—
230#41D3×Dic312yescomplemented
231C2×Q8—34no—
232C2×Q8—92no—
233C2×Q8—94no—
234C2×Q8—91no—
235C2×Q8—94no—
236C2×Q8—182no—
237C2×Q8C2×D3211yescharacteristic
238C2×D4—31no—
239C2×D4—31no—
240C2×D4—92no—
241C22×C4—31no—
242C22×C4—92no—
243C22×C4—182no—
244C22×C4—181no—
245C22×C4—181no—
246M16—184no—
247M16—182no—
248C2×C8—31no—
249C2×C8—31no—
250C2×C8—62no—
251C2×C8—92no—
252C2×C8—184no—
253C4⋊C4—31no—
254C4⋊C4—31no—
255C4⋊C4—92no—
256C4⋊C4—182no—
257C4⋊C4—181no—
258C22⋊C4—61no—
259C22⋊C4—182no—
260C42—61no—
261C42—182no—
262C22×C3—32no—
263C22×C3—41no—
264C22×C3—61no—
265C22×C3—61no—
266C22×C3—81no—
267C22×C3—124no—
268C22×C3—242no—
269C22×C3—242no—
270C22×C3C22×S411yescharacteristic
271C2×D3—22no—
272C2×D3—22no—
273C2×D3C2×SL(2,ℤ/4)14yes—
274C3×C4—31no—
275C3×C4—31no—
276C3×C4—42no—
277C3×C4—82no—
278C3×C4—121no—
279C3×C4—121no—
280C3×C4C2×SL(2,ℤ/4)12yes—
281Dic3—34no—
282Dic3—42no—
283Dic3—81no—
284Dic3—122no—
285Dic3—242no—
286Dic3—482no—
287C32—41noSylow
288C23—31no—
289C23—32no—
290Q8—31no—
291Q8—94no—
292Q8—94no—
293Q8—182no—
294Q8C2×D3×Dic311yescharacteristic
295D4—32no—
296D4—34no—
297D4—61no—
298D4—98no—
299C2×C4—31no—
300C2×C4—32no—
301C2×C4—32no—
302C2×C4—61no—
303C2×C4—61no—
304C2×C4—94no—
305C2×C4—94no—
306C2×C4—92no—
307C2×C4—184no—
308C2×C4—182no—
309C2×C4—722no—
310C2×C4—721no—
311C2×C4D3×S411yescharacteristic
312C8—61no—
313C8—61no—
314C8—182no—
315C2×C3—41no—
316C2×C3—41no—
317C2×C3—41no—
318C2×C3—62no—
319C2×C3—81no—
320C2×C3—81no—
321C2×C3—81no—
322C2×C3—244no—
323C2×C3#592611yescharacteristic
324C2×C3#592711yescharacteristic
325C2×C3C22×SL(2,ℤ/4)11yescharacteristic
326D3—24no—
327C22—32no—
328C22—34no—
329C22—62no—
330C22—61no—
331C22—62no—
332C22—61no—
333C22C2×D3×S411yescharacteristic
334C4—31no—
335C4—31no—
336C4—94no—
337C4—121no—
338C4—121no—
339C4—362no—
340C4D3×SL(2,ℤ/4)12yes—
341C3—41no—
342C3—81no—
343C3#8553411yescharacteristic, complemented
344C2—64no—
345C2—62no—
346C2#1059645211yescharacteristic
347C2#1059645911yescharacteristic
348C2C2×D3×SL(2,ℤ/4)11yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×S4
commutator, hypocenterC3×SL(2,𝔽3)C22×C4
FittingC2×C3×#41C2×D3
socleC22×C3C22×S4
prime radicalC2×#1010⋊C3C2
cosocleC2×C3×SL(2,𝔽3)C23
hypercenterC2×C4D3×S4
LCSG ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #10593660C2semidirect
3. C3×#5424C2semidirect
4. D3×#859C2semidirect
5. #10593209C2semidirect
9. #1010⋊C3C4semidirect
21. #5424D3semidirect
33. C3×#41⋊C3C2×C4semidirect
36. D3×SL(2,𝔽3)C2×C4semidirect
43. #1010Dic3semidirect
99. C3×#41C2×Dic3semidirect
109. D3×Q8C2×Dic3semidirect
122. #41⋊C3C4×D3semidirect
230. #41D3×Dic3semidirect
343. C3#85534semidirect

Maximal subgroups

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

subgroupindex
C2×#1010⋊C32
#105936602
C3×#54242
D3×#8592
#105932092
#855343
#788323
Dic3×D124