Finite Group Databasebeta

← #11866386

Subgroups — #11866386

Order 1152.

1374 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×Q16C211yesmaximal, characteristic, complemented
2#10596287C211yesmaximal, characteristic
3#10596283C211yesmaximal, characteristic, complemented
4C2×#64151C211yesmaximal, characteristic
5#10592924C211yesmaximal, characteristic, complemented
6#10592884C214yesmaximal, complemented
7#10592881C214yesmaximal, complemented
8#10592812C211yesmaximal, characteristic
9#10592801C211yesmaximal, characteristic, complemented
10#83877—34nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×C32×Q8C2211yescharacteristic
13C2×#3828C2211yescharacteristic
14C2×C32×Q16—24no—
15C2×C32×Q16C2214yes—
16C22×C32×C8C2211yescharacteristic
17#64156C2212yes—
18#64155—22no—
19Q8×C3⋊Dic3—22no—
20Q8×C3⋊Dic3C2214yes—
21#64153C2212yes—
22C2×#3756C2212yes—
23#64151—24no—
24C2×#3755C2212yes—
25#64138—22no—
26#64135—22no—
27#64135C2211yescharacteristic
28#64135C2211yescharacteristic
29C2×#3748C2211yescharacteristic
30#63662C2214yes—
31#63648C2212yes—
32#63643C2212yes—
33#63641C2214yes—
34C22×C3×Q16D314yescomplemented
35#5816—34no—
36#5812—34no—
37C2×#942—34no—
38#5225—34no—
39#5185—316no—
40#5182—316no—
41#5113—34no—
42#5102—34no—
43C2×C32×Q8—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8—22no—
46C2×C32×Q8—22no—
47C2×C32×Q8—22no—
48C2×C32×Q8D414yes—
49C2×C32×Q8C2312yes—
50C2×C32×Q8C2312yes—
51C22×C32×C4—21no—
52C22×C32×C4—21no—
53C22×C32×C4C2311yescharacteristic
54C2×#638—21no—
55#3828—22no—
56#3828—22no—
57C2×C4⋊(C3⋊D3)C2311yescharacteristic
58C2×C4×C3⋊D3—21no—
59C2×#634C2311yescharacteristic
60C32×Q16—28no—
61C2×C32×C8—22no—
62C2×C32×C8C2312yes—
63#3757—21no—
64#3757D412yes—
65#3756—24no—
66#3755—24no—
67#3752—24no—
68C4⋊(C3⋊Dic3)—24no—
69C4⋊(C3⋊Dic3)D412yes—
70C4⋊(C3⋊Dic3)C2312yes—
71#3750—24no—
72C4×C3⋊Dic3—21no—
73C4×C3⋊Dic3—24no—
74C4×C3⋊Dic3C2312yes—
75#3748—22no—
76C2×C3⋊(C3⋊C8)C2312yes—
77#3044—91noSylow
78C22×C3×Q8C2×D314yes—
79C22×C3×Q8C2×D314yes—
80C2×#235—34no—
81C2×C3×Q16—216no—
82C2×C3×Q16C2×D3116yes—
83C22×C3×C8C2×D314yes—
84#947—38no—
85#946—68no—
86Q8×Dic3—316no—
87Q8×Dic3—68no—
88#944—38no—
89C2×#216—38no—
90#942—616no—
91C2×#215—38no—
92#929—68no—
93#926—34no—
94#926—34no—
95#926—68no—
96C2×#208—34no—
97#835—316no—
98#821—38no—
99#816—38no—
100Dic3⋊C8—316no—
101C23×C32C2×D411yescharacteristic
102C22×C3⋊D3—21no—
103C32×Q8—24no—
104C32×Q8—22no—
105C32×Q8—22no—
106C32×Q8—22no—
107C32×Q8—42no—
108C32×Q8C2×D414yes—
109C2×C32×C4—24no—
110C2×C32×C4—22no—
111C2×C32×C4—22no—
112C2×C32×C4—42no—
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D412yes—
115C2×C32×C4#4112yes—
116C2×C32×C4C2411yescharacteristic
117#638—42no—
118C2×C3⋊Dic3—22no—
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3C2×D414yes—
121C4⋊(C3⋊D3)—21no—
122C4⋊(C3⋊D3)—21no—
123C4×C3⋊D3—42no—
124#634—21no—
125#634—21no—
126C32×C8—22no—
127C3⋊(C3⋊C8)—22no—
128C2×#137—91no—
129C22×Q16C3⋊D311yescharacteristic, complemented
130#536—91no—
131#519—91no—
132#464—94no—
133#462—94no—
134#424—91no—
135#419—91no—
136#416—91no—
137C2×C3×Q8—24no—
138C2×C3×Q8—24no—
139C2×C3×Q8—28no—
140C2×C3×Q8—28no—
141C2×C3×Q8—28no—
142C2×C3×Q8#67116yes—
143C2×C3×Q8C22×D318yes—
144C2×C3×Q8C22×D318yes—
145C22×C3×C4—24no—
146C22×C3×C4—24no—
147C22×C3×C4C22×D314yes—
148C2×#67—64no—
149#235—68no—
150#235—68no—
151C2×D12—34no—
152C2×C4×D3—64no—
153C2×Dic6—34no—
154C3×Q16—232no—
155C2×C3×C8—28no—
156C2×C3×C8C22×D318yes—
157#217—38no—
158#217—64no—
159#216—616no—
160#215—616no—
161(C2×D3)⋊C4—616no—
162C4⋊Dic3—38no—
163C4⋊Dic3—38no—
164C4⋊Dic3—616no—
165Dic3⋊C4—616no—
166C4×Dic3—38no—
167C4×Dic3—616no—
168C4×Dic3—64no—
169#208—68no—
170C2×C3⋊C8—38no—
171C22×C32—22no—
172C22×C32#12112yes—
173C22×C32C22×D411yescharacteristic
174C2×C3⋊D3—41no—
175C2×C3⋊D3—42no—
176C32×C4—24no—
177C32×C4—42no—
178C32×C4#12112yes—
179C32×C4C22×D411yescharacteristic
180C32×C4C2×#4111yescharacteristic
181C3⋊Dic3—24no—
182C3⋊Dic3—41no—
183C3⋊Dic3—42no—
184C2×#41—91no—
185C22×Q8C2×C3⋊D311yescharacteristic
186C22×Q8C2×C3⋊D311yescharacteristic
187#137—184no—
188C2×Q16—24no—
189C2×Q16—92no—
190C2×Q16C2×C3⋊D314yes—
191C2×SD16—92no—
192C2×M16—91no—
193C22×C8C2×C3⋊D311yescharacteristic
194C4⋊Q8—92no—
195#124—92no—
196#123—182no—
197C22⋊Q8—182no—
198C4×Q8—94no—
199C4×Q8—182no—
200#117—91no—
201#117—91no—
202#117—182no—
203C4⋊C8—94no—
204#103—94no—
205#103—92no—
206#102—92no—
207C23×C3D3×D414yes—
208C22×D3—64no—
209C3×Q8—216no—
210C3×Q8—28no—
211C3×Q8—28no—
212C3×Q8—28no—
213C3×Q8—48no—
214C3×Q8C2×#67116yes—
215C2×C3×C4—216no—
216C2×C3×C4—28no—
217C2×C3×C4—28no—
218C2×C3×C4—48no—
219C2×C3×C4D3×D414yes—
220C2×C3×C4#23718yes—
221C2×C3×C4C2×#6718yes—
222C2×C3×C4C23×D314yes—
223#67—128no—
224C2×Dic3—316no—
225C2×Dic3—68no—
226C2×Dic3—64no—
227D12—64no—
228D12—64no—
229C4×D3—128no—
230Dic6—64no—
231Dic6—64no—
232C3×C8—28no—
233C3⋊C8—68no—
234C2×C32—22no—
235C2×C32C2×#12111yescharacteristic
236C2×C32#57812yes—
237C3⋊D3—81no—
238#41—182no—
239#41—182no—
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—22no—
243C2×Q8—22no—
244C2×Q8—22no—
245C2×Q8—91no—
246C2×Q8#63814yes—
247C2×Q8C22×C3⋊D312yes—
248C2×Q8C22×C3⋊D312yes—
249C2×D4—91no—
250C2×D4—181no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—181no—
254C22×C4C22×C3⋊D311yescharacteristic
255Q16—28no—
256Q16—184no—
257SD16—184no—
258M16—182no—
259C2×C8—22no—
260C2×C8—92no—
261C2×C8C22×C3⋊D312yes—
262C4⋊C4—92no—
263C4⋊C4—92no—
264C4⋊C4—184no—
265C4⋊C4—184no—
266C22⋊C4—92no—
267C22⋊C4—184no—
268C22⋊C4—181no—
269C42—92no—
270C42—184no—
271C42—181no—
272C22×C3—28no—
273C22×C3#93918yes—
274C22×C3C2×D3×D414yes—
275C2×D3—128no—
276C2×D3—124no—
277C3×C4—216no—
278C3×C4—48no—
279C3×C4#93918yes—
280C3×C4C2×#23714yes—
281C3×C4C22×#6714yes—
282Dic3—616no—
283Dic3—128no—
284Dic3—124no—
285C32#304411yescharacteristic, complemented, Sylow
286C23—181no—
287C23D4×C3⋊D311yescharacteristic
288Q8—22no—
289Q8—24no—
290Q8—22no—
291Q8—22no—
292Q8—42no—
293Q8—181no—
294Q8—181no—
295Q8C2×#63814yes—
296D4—181no—
297D4—181no—
298D4—362no—
299C2×C4—22no—
300C2×C4—24no—
301C2×C4—22no—
302C2×C4—42no—
303C2×C4—94no—
304C2×C4—182no—
305C2×C4—181no—
306C2×C4—362no—
307C2×C4D4×C3⋊D311yescharacteristic
308C2×C4#383012yes—
309C2×C4C2×#63812yes—
310C2×C4C23×C3⋊D311yescharacteristic
311C8—22no—
312C8—182no—
313C2×C3—28no—
314C2×C3#576618yes—
315C2×C3C2×#93914yes—
316D3—244no—
317C22—22no—
318C22—362no—
319C22—361no—
320C22#6414812yes—
321C22C2×D4×C3⋊D311yescharacteristic
322C4—24no—
323C4—42no—
324C4—184no—
325C4—362no—
326C4—361no—
327C4#6414812yes—
328C4C2×#383011yescharacteristic
329C4C22×#63811yescharacteristic
330C3#8387714yescomplemented
331C2—22no—
332C2—721no—
333C2#1059623712yes—
334C2C2×#6414811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC22×C32×Q16C2
socleC22×C32C22×D4
prime radicalC2×#3828C22
hypercenterC22×Q16C3⋊D3
hypocenterC32#3044
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
1. C22×C32×Q16C2semidirect
3. #10596283C2semidirect
5. #10592924C2semidirect
6. #10592884C2semidirect
7. #10592881C2semidirect
9. #10592801C2semidirect
34. C22×C3×Q16D3semidirect
129. C22×Q16C3⋊D3semidirect
285. C32#3044semidirect
330. C3#83877semidirect

Maximal subgroups

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

subgroupindex
C22×C32×Q162
#105962872
#105962832
C2×#641512
#105929242
#105928842
#105928812
#105928122
#105928012
#838773