Finite Group Databasebeta

← #11796491

Subgroups — #11796491

Order 1152.

750 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 750 conjugacy classes of subgroups — too many to draw. Only its 157 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
1#10596303C211yesmaximal, characteristic
2C32×#413C211yesmaximal, characteristic, complemented
3#10592936C211yesmaximal, characteristic, complemented
4#10589344C212yesmaximal, complemented
5#10589343C212yesmaximal, complemented
6#70148—34nomaximal
7C2×C32×#41C2211yescharacteristic
8C2×#3828C411yescharacteristic
9C2×C32×M16—21no—
10#64156C2211yescharacteristic
11#64153C2211yescharacteristic
12#64149C411yescharacteristic
13#64148—21no—
14#64148—21no—
15#64145C411yescharacteristic
16C4×#638—21no—
17C4×#638—21no—
18C2×C4×C3⋊Dic3C411yescharacteristic
19C2×#3748—21no—
20C32×#101C2212yes—
21C32×#100—21no—
22#63663C2212yes—
23#63660—21no—
24#5832—34no—
25C3×#413D314yescomplemented
26#5237—34no—
27#4478—38no—
28#4477—38no—
29C32×#41—41no—
30C32×#41—41no—
31C2×C32×Q8C2311yescharacteristic
32C2×C32×D4C2×C411yescharacteristic
33C2×C32×D4D411yescharacteristic
34C2×C32×D4D411yescharacteristic
35C22×C32×C4C2×C411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C2×#638—21no—
39C2×#638—21no—
40C2×#638—21no—
41C22×C3⋊Dic3—21no—
42#3828—41no—
43#3828—41no—
44C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
45C2×C4×C3⋊D3—21no—
46C2×#634C2×C411yescharacteristic
47C32×M16—22no—
48C32×M16—41no—
49C2×C32×C8—41no—
50#3757—21no—
51#3757—21no—
52#3752—21no—
53#3752—21no—
54#3750—21no—
55#3750—21no—
56C4×C3⋊Dic3—21no—
57C4×C3⋊Dic3C2×C411yescharacteristic
58C4×C3⋊Dic3C2×C411yescharacteristic
59#3748—22no—
60#3748—41no—
61C2×C3⋊(C3⋊C8)—41no—
62#2132—91noSylow
63C2×C3×#41C2×D314yes—
64C2×#235—34no—
65C2×C3×M16—24no—
66#947—34no—
67#944—34no—
68#940—34no—
69#939—64no—
70#939—64no—
71#936—34no—
72C4×#67—64no—
73C4×#67—64no—
74C2×C4×Dic3—34no—
75C2×#208—64no—
76C3×#101C2×D318yes—
77C3×#100—24no—
78#836—38no—
79#833—64no—
80C23×C32C22⋊C411yescharacteristic
81C23×C32C22⋊C411yescharacteristic
82C23×C32C22⋊C411yescharacteristic
83C22×C3⋊D3—21no—
84C32×Q8—41no—
85C32×D4—41no—
86C32×D4—41no—
87C32×D4—41no—
88C2×C32×C4—21no—
89C2×C32×C4—21no—
90C2×C32×C4—21no—
91C2×C32×C4—21no—
92C2×C32×C4—21no—
93C2×C32×C4—21no—
94C2×C32×C4C22⋊C411yescharacteristic
95C2×C32×C4C22×C411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98#638—42no—
99#638—42no—
100#638—42no—
101C2×C3⋊Dic3—21no—
102C2×C3⋊Dic3—21no—
103C2×C3⋊Dic3—21no—
104C2×C3⋊Dic3—42no—
105C4⋊(C3⋊D3)—41no—
106C4×C3⋊D3—41no—
107C4×C3⋊D3—41no—
108#634—41no—
109C32×C8—42no—
110C3⋊(C3⋊C8)—42no—
111#532—91no—
112#413—91no—
113#413C3⋊D311yescharacteristic, complemented
114#356—92no—
115#355—92no—
116C3×#41—44no—
117C3×#41—44no—
118C2×C3×Q8C22×D314yes—
119C2×C3×D4C4×D314yes—
120C2×C3×D4D1214yes—
121C2×C3×D4#6714yes—
122C22×C3×C4C4×D314yes—
123C22×C3×C4D1214yes—
124C22×C3×C4#6714yes—
125C2×#67—64no—
126C2×#67—64no—
127C2×#67—64no—
128C22×Dic3—64no—
129#235—124no—
130#235—124no—
131C2×D12—34no—
132C2×C4×D3—64no—
133C2×Dic6—34no—
134C3×M16—28no—
135C3×M16—44no—
136C2×C3×C8—44no—
137#217—64no—
138#217—64no—
139(C2×D3)⋊C4—64no—
140(C2×D3)⋊C4—64no—
141Dic3⋊C4—64no—
142Dic3⋊C4—64no—
143C4×Dic3—34no—
144C4×Dic3—34no—
145C4×Dic3—64no—
146#208—68no—
147#208—124no—
148C2×C3⋊C8—124no—
149C22×C32—21no—
150C22×C32—21no—
151C22×C32—21no—
152C22×C32—41no—
153C22×C32—41no—
154C22×C32—41no—
155C22×C32C2×C22⋊C411yescharacteristic
156C2×C3⋊D3—41no—
157C2×C3⋊D3—41no—
158C2×C3⋊D3—41no—
159C32×C4—21no—
160C32×C4—21no—
161C32×C4—21no—
162C32×C4#9911yescharacteristic
163C32×C4#9911yescharacteristic
164C3⋊Dic3—22no—
165C3⋊Dic3—41no—
166C3⋊Dic3—41no—
167C2×#41—91no—
168C2×#41C2×C3⋊D311yescharacteristic
169C2×M16—21no—
170C2×M16—181no—
171C4⋊Q8—91no—
172#127—91no—
173#124—91no—
174#124—91no—
175#121—181no—
176#121—181no—
177C4×D4—181no—
178C4×D4—181no—
179C2×C42—91no—
180#101—92no—
181#101C2×C3⋊D312yes—
182#100—21no—
183#100—181no—
184C23×C3(C2×D3)⋊C414yes—
185C23×C3(C2×D3)⋊C414yes—
186C23×C3(C2×D3)⋊C414yes—
187C22×D3—64no—
188C3×Q8—44no—
189C3×D4—44no—
190C3×D4—44no—
191C3×D4—44no—
192C2×C3×C4—24no—
193C2×C3×C4—24no—
194C2×C3×C4—24no—
195C2×C3×C4—24no—
196C2×C3×C4—24no—
197C2×C3×C4—24no—
198C2×C3×C4(C2×D3)⋊C414yes—
199C2×C3×C4C2×C4×D314yes—
200C2×C3×C4C2×D1214yes—
201C2×C3×C4C2×#6714yes—
202#67—128no—
203#67—128no—
204#67—128no—
205C2×Dic3—64no—
206C2×Dic3—64no—
207C2×Dic3—64no—
208C2×Dic3—128no—
209D12—124no—
210C4×D3—124no—
211C4×D3—124no—
212Dic6—124no—
213C3×C8—48no—
214C3⋊C8—128no—
215C2×C32—21no—
216C2×C32—41no—
217C2×C32—41no—
218C2×C32—41no—
219C2×C32C2×#9911yescharacteristic
220C3⋊D3—81no—
221#41—41no—
222#41—41no—
223#41—361no—
224#41—361no—
225C2×Q8—91no—
226C2×Q8C22×C3⋊D311yescharacteristic
227C2×D4—91no—
228C2×D4—181no—
229C2×D4—181no—
230C2×D4—181no—
231C2×D4C4×C3⋊D311yescharacteristic
232C2×D4C4⋊(C3⋊D3)11yescharacteristic
233C2×D4#63811yescharacteristic
234C22×C4—181no—
235C22×C4—181no—
236C22×C4C4×C3⋊D311yescharacteristic
237C22×C4C4⋊(C3⋊D3)11yescharacteristic
238C22×C4#63811yescharacteristic
239M16—22no—
240M16—41no—
241M16—182no—
242M16—361no—
243C2×C8—41no—
244C2×C8—361no—
245C4⋊C4—181no—
246C4⋊C4—181no—
247C22⋊C4—181no—
248C22⋊C4—181no—
249C22⋊C4—181no—
250C22⋊C4—181no—
251C42—91no—
252C42—91no—
253C42—181no—
254C22×C3—24no—
255C22×C3—24no—
256C22×C3—24no—
257C22×C3—44no—
258C22×C3—44no—
259C22×C3—44no—
260C22×C3C2×(C2×D3)⋊C414yes—
261C2×D3—124no—
262C2×D3—124no—
263C2×D3—124no—
264C3×C4—24no—
265C3×C4—24no—
266C3×C4—24no—
267C3×C4#80614yes—
268C3×C4#80614yes—
269Dic3—68no—
270Dic3—124no—
271Dic3—124no—
272C32#213211yescharacteristic, complemented, Sylow
273C23—181no—
274C23#375211yescharacteristic
275C23#375211yescharacteristic
276C23#375211yescharacteristic
277Q8—41no—
278Q8—361no—
279D4—41no—
280D4—41no—
281D4—41no—
282D4—361no—
283D4—362no—
284D4—362no—
285D4—362no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—181no—
293C2×C4—181no—
294C2×C4—181no—
295C2×C4—362no—
296C2×C4—361no—
297C2×C4—361no—
298C2×C4#375211yescharacteristic
299C2×C4C2×C4×C3⋊D311yescharacteristic
300C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
301C2×C4C2×#63811yescharacteristic
302C8—42no—
303C8—362no—
304C2×C3—24no—
305C2×C3—44no—
306C2×C3—44no—
307C2×C3—44no—
308C2×C3C2×#80614yes—
309D3—244no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—361no—
317C22—361no—
318C22—361no—
319C22C2×#375211yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—182no—
324C4—361no—
325C4—361no—
326C4#6363311yescharacteristic
327C4#6363311yescharacteristic
328C3#7014814yescomplemented
329C2—21no—
330C2—41no—
331C2—41no—
332C2—41no—
333C2—721no—
334C2C2×#6363311yescharacteristic
subgroupG/H
centerC4#63633
commutatorC2×C32×C4C22×C4
FrattiniC2×Q8C22×C3⋊D3
FittingC32×#413C2
socleC2×C32C2×#99
prime radical#10596303C2
cosocleC2×C32×Q8C23
hypercenter#413C3⋊D3
hypocenterC32#2132
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. C32×#413C2semidirect
3. #10592936C2semidirect
4. #10589344C2semidirect
5. #10589343C2semidirect
25. C3×#413D3semidirect
113. #413C3⋊D3semidirect
272. C32#2132semidirect
328. C3#70148semidirect

Maximal subgroups

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

subgroupindex
#105963032
C32×#4132
#105929362
#105893442
#105893432
#701483