Finite Group Databasebeta

← #11791187

Subgroups — #11791187

Order 1152.

681 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 681 conjugacy classes of subgroups — too many to draw. Only its 132 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×#63822C211yesmaximal, characteristic
2C2×C4×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
3C2×C3×#805C212yesmaximal, complemented
4C2×#63578C211yesmaximal, characteristic, complemented
5#10591071C212yesmaximal, complemented
6#70373—32nomaximal
7C2×C3×#235C2212yes—
8C2×C32×C42C2211yescharacteristic
9C22×C3⋊(C3⋊C8)C2211yescharacteristic
10C22×C3⋊(C3⋊C8)C2211yescharacteristic
11C2×C3×#208C2212yes—
12C2×#3718C411yescharacteristic, complemented
13C2×#3715C412yescomplemented
14#63822—22no—
15#63822—22no—
16C2×#3713C411yescharacteristic, complemented
17C4×C3⋊(C3⋊C8)—22no—
18C3×#805—24no—
19#63578—22no—
20(C2×D3)⋊(C3⋊C8)—24no—
21C2×#950—32no—
22C2×C3×#104—32no—
23#5234—32no—
24#5129—32no—
25C2×#822—32no—
26C2×#805D312yescomplemented
27C2×C4×C3⋊C8—32no—
28C2×C4×C3⋊C8—61no—
29C22×C32×C4—21no—
30C22×C32×C4C2311yescharacteristic
31C2×C3×#67—22no—
32C3×#235—22no—
33C3×#235—22no—
34C3×#235—22no—
35C3×#235—22no—
36C2×C3×D12C2×C412yes—
37C2×C3×C4×D3—22no—
38C2×C3×Dic6C2×C412yes—
39C32×C42—21no—
40C32×C42D412yes—
41C2×C3⋊(C3⋊C8)—21no—
42C2×C3⋊(C3⋊C8)—21no—
43C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
44C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
45C2×C3⋊(C3⋊C8)D412yes—
46C2×C3⋊(C3⋊C8)D412yes—
47C2×C3⋊(C3⋊C8)D412yes—
48C3×#208—22no—
49C3×#208—22no—
50C2×C3×C3⋊C8—22no—
51#3718—22no—
52#3715—24no—
53#3713—22no—
54#1974—91noSylow
55C2×C3×#41—32no—
56C2×#235C2×D312yes—
57C2×C3×M16—32no—
58C2×C3×C42—21no—
59C2×C3×C42C2×D312yes—
60#950—64no—
61#950—64no—
62C2×#216—32no—
63C2×#215—32no—
64C2×#214—32no—
65C2×#213—32no—
66C2×#208C2×D312yes—
67C22×C3⋊C8—32no—
68C22×C3⋊C8—32no—
69C22×C3⋊C8—61no—
70C22×C3⋊C8—61no—
71C3×#104—64no—
72#830—64no—
73#822—64no—
74(C2×D3)⋊C8—64no—
75#805—24no—
76C4×C3⋊C8—64no—
77C4×C3⋊C8—64no—
78C23×C32#4111yescharacteristic
79C22×C3×D3—22no—
80C2×C32×C4—24no—
81C2×C32×C4—22no—
82C2×C32×C4C22×C411yescharacteristic
83C2×C32×C4C2×D411yescharacteristic
84C2×C32×C4C2×D411yescharacteristic
85C2×C32×C4C2×D411yescharacteristic
86C2×C32×C4C2×D411yescharacteristic
87C2×C32×C4#4111yescharacteristic
88C3×#67—42no—
89C3×#67—42no—
90C2×C3×Dic3—22no—
91C3×D12—22no—
92C3×D12—22no—
93C3×C4×D3—42no—
94C3×C4×D3—42no—
95C3×Dic6—22no—
96C3×Dic6—22no—
97C3⋊(C3⋊C8)—22no—
98C3⋊(C3⋊C8)C22⋊C412yes—
99C3⋊(C3⋊C8)C22⋊C412yes—
100C3×C3⋊C8—42no—
101C2×#135—91no—
102C2×#108—91no—
103C2×#104—32no—
104#408—92no—
105C2×C4×C8—91no—
106C3×#41—62no—
107C3×#41—62no—
108C3×#41—62no—
109C3×#41—62no—
110C2×C3×Q8—32no—
111C2×C3×D4—32no—
112C2×C3×D4—62no—
113C22×C3×C4—22no—
114C22×C3×C4—22no—
115C22×C3×C4—21no—
116C22×C3×C4—62no—
117C22×C3×C4C22×D312yes—
118C2×#67—22no—
119#235—22no—
120#235—22no—
121#235—22no—
122#235—22no—
123C2×D12C4×D312yes—
124C2×C4×D3—22no—
125C2×Dic6C4×D312yes—
126C3×M16—62no—
127C3×M16—62no—
128C2×C3×C8—62no—
129C3×C42—22no—
130C3×C42—22no—
131C3×C42—22no—
132C3×C42#6714yes—
133#216—64no—
134#215—64no—
135#214—64no—
136#213—64no—
137#208—22no—
138#208—22no—
139C2×C3⋊C8—22no—
140C2×C3⋊C8—32no—
141C2×C3⋊C8—32no—
142C2×C3⋊C8—34no—
143C2×C3⋊C8—34no—
144C2×C3⋊C8—34no—
145C2×C3⋊C8—62no—
146C2×C3⋊C8—61no—
147C2×C3⋊C8—61no—
148C2×C3⋊C8—62no—
149C2×C3⋊C8—62no—
150C2×C3⋊C8—62no—
151C2×C3⋊C8—62no—
152C2×C3⋊C8—62no—
153C2×C3⋊C8—62no—
154C22×C32—22no—
155C22×C32C4×D411yescharacteristic
156C22×C32#12111yescharacteristic
157C22×C32#12411yescharacteristic
158C2×C3×D3—42no—
159C2×C3×D3—44no—
160C32×C4—24no—
161C32×C4C2×C22⋊C411yescharacteristic
162C32×C4C4×D411yescharacteristic
163C32×C4#12111yescharacteristic
164C32×C4#12711yescharacteristic
165C3×Dic3—42no—
166C2×#41—32no—
167#135—182no—
168#135—182no—
169C2×Q16—91no—
170C2×SD16—92no—
171C2×D8—91no—
172C2×M16—32no—
173C22×C8—91no—
174C22×C8—91no—
175C2×C42D3211yescharacteristic
176#108—182no—
177#104—64no—
178C22⋊C8—184no—
179C4×C8—182no—
180C23×C3—21no—
181C23×C3—62no—
182C23×C3#23712yes—
183C22×D3—22no—
184C3×Q8—62no—
185C3×Q8—62no—
186C3×D4—62no—
187C3×D4—62no—
188C3×D4—122no—
189C3×D4—122no—
190C2×C3×C4—24no—
191C2×C3×C4—28no—
192C2×C3×C4—28no—
193C2×C3×C4—24no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—62no—
201C2×C3×C4—122no—
202C2×C3×C4—122no—
203C2×C3×C4C2×C4×D312yes—
204C2×C3×C4#23512yes—
205C2×C3×C4D3×D412yes—
206C2×C3×C4D3×D412yes—
207C2×C3×C4D3×D412yes—
208C2×C3×C4C2×#6712yes—
209#67—42no—
210#67—42no—
211C2×Dic3—22no—
212D12—22no—
213D12—22no—
214C4×D3—42no—
215C4×D3—42no—
216Dic6—22no—
217Dic6—22no—
218C3×C8—122no—
219C3⋊C8—34no—
220C3⋊C8—34no—
221C3⋊C8—42no—
222C3⋊C8—62no—
223C3⋊C8—62no—
224C3⋊C8—64no—
225C3⋊C8—64no—
226C2×C32—21no—
227C2×C32—21no—
228C2×C32#39011yescharacteristic
229C2×C32#44312yes—
230C3×D3—82no—
231#41—62no—
232#41—62no—
233#41—62no—
234#41—62no—
235C2×Q8—32no—
236C2×D4—32no—
237C2×D4—62no—
238C22×C4—21no—
239C22×C4—62no—
240C22×C4C2×D3211yescharacteristic
241Q16—182no—
242SD16—184no—
243D8—182no—
244M16—62no—
245M16—62no—
246C2×C8—62no—
247C2×C8—91no—
248C2×C8—91no—
249C2×C8—92no—
250C2×C8—92no—
251C2×C8—92no—
252C2×C8—181no—
253C2×C8—181no—
254C42—21no—
255C42#62512yes—
256C22×C3—24no—
257C22×C3—24no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—21no—
261C22×C3—122no—
262C22×C3—124no—
263C22×C3#67⋊C412yes—
264C22×C3#88512yes—
265C22×C3#93912yes—
266C2×D3—42no—
267C2×D3—44no—
268C3×C4—28no—
269C3×C4—28no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—122no—
275C3×C4D3×C22⋊C412yes—
276C3×C4#88412yes—
277C3×C4C4×#6712yes—
278C3×C4#94012yes—
279Dic3—42no—
280C32#197411yescharacteristic, complemented, Sylow
281C23—62no—
282C23#380511yescharacteristic
283Q8—62no—
284Q8—62no—
285D4—62no—
286D4—62no—
287D4—122no—
288D4—122no—
289C2×C4—24no—
290C2×C4—22no—
291C2×C4—62no—
292C2×C4—122no—
293C2×C4—122no—
294C2×C4#379811yescharacteristic
295C2×C4C4×D3211yescharacteristic
296C2×C4#380211yescharacteristic
297C2×C4#380211yescharacteristic
298C2×C4C2×#62511yescharacteristic
299C2×C4#381111yescharacteristic
300C8—92no—
301C8—92no—
302C8—122no—
303C8—182no—
304C2×C3—22no—
305C2×C3—22no—
306C2×C3—22no—
307C2×C3—22no—
308C2×C3—21no—
309C2×C3—22no—
310C2×C3—242no—
311C2×C3#482414yes—
312C2×C3#495712yes—
313D3—82no—
314C22—22no—
315C22—122no—
316C22—124no—
317C22#6390211yescharacteristic
318C22#6391511yescharacteristic
319C22#6398011yescharacteristic
320C4—24no—
321C4—122no—
322C4C4×#62511yescharacteristic
323C4#6391211yescharacteristic
324C4#6391411yescharacteristic
325C4#6392111yescharacteristic
326C3—21no—
327C3#7037312yescomplemented
328C2—21no—
329C2—21no—
330C2—242no—
331C2#1059038912yes—
332C2#1059138511yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C4×D4
prime radicalC2×#63822C2
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1974
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C4×C3⋊(C3⋊C8)C2semidirect
3. C2×C3×#805C2semidirect
4. C2×#63578C2semidirect
5. #10591071C2semidirect
12. C2×#3718C4semidirect
13. C2×#3715C4semidirect
16. C2×#3713C4semidirect
26. C2×#805D3semidirect
280. C32#1974semidirect
327. C3#70373semidirect

Maximal subgroups

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

subgroupindex
C2×#638222
C2×C4×C3⋊(C3⋊C8)2
C2×C3×#8052
C2×#635782
#105910712
#703733