Finite Group Databasebeta

← #11791458

Subgroups — #11791458

Order 1152.

925 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 925 conjugacy classes of subgroups — too many to draw. Only its 170 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×#63914C211yesmaximal, characteristic
2C2×#63641C211yesmaximal, characteristic, complemented
3C2×C3×#821C212yesmaximal, complemented
4#10591274C211yesmaximal, characteristic, complemented
5C2×#63562C212yesmaximal, complemented
6#70161—32nomaximal
7C22×C3×D12C2212yes—
8C22×#625—21no—
9C22×#625—21no—
10C22×C32×C8C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C2×C3×C4⋊Dic3C2212yes—
14C2×Dic32—21no—
15#63914—22no—
16#63914C414yescomplemented
17#63641—22no—
18C3×#821—24no—
19#63579—21no—
20#63562—24no—
21C2×#940—32no—
22C2×C3×#102—32no—
23C2×#832—32no—
24C2×#821D312yescomplemented
25C2×Dic3⋊C8—32no—
26C2×Dic3⋊C8—61no—
27Dic3×C4⋊C4—32no—
28C2×#809—32no—
29C23×C3×D3—22no—
30C22×C32×C4C2311yescharacteristic
31C22×C3⋊Dic3D411yescharacteristic
32C22×C3⋊Dic3D411yescharacteristic
33C22×C3×Dic3—22no—
34C2×C3×D12—22no—
35C2×C3×D12—22no—
36C2×C3×D12—22no—
37C2×C3×D12—22no—
38C2×C3×D12—22no—
39C2×C3×D12C2×C414yes—
40C2×#625—24no—
41C2×#625—24no—
42C2×#625—44no—
43C2×#625—42no—
44C2×#625—42no—
45C2×C32×C8—21no—
46C2×C32×C8—22no—
47C4×C3⋊Dic3C2×C412yes—
48C4×C3⋊Dic3D412yes—
49C2×C3⋊(C3⋊C8)—21no—
50C2×C3⋊(C3⋊C8)—22no—
51C3×C4⋊Dic3—22no—
52C3×C4⋊Dic3D414yescomplemented
53Dic32—42no—
54#1982—91noSylow
55C22×C3×D4—32no—
56C22×#67—62no—
57C22×#67—62no—
58C22×D12C2×D312yes—
59C22×C3×C8—21no—
60C22×C3×C8C2×D312yes—
61C2×C3×C4⋊C4—32no—
62#940—38no—
63#940—64no—
64C2×C4⋊Dic3C2×D312yes—
65C2×C4×Dic3—32no—
66C2×C4×Dic3—61no—
67C2×C4×Dic3—62no—
68C22×C3⋊C8—32no—
69C22×C3⋊C8—61no—
70C3×#102—64no—
71#832—64no—
72C3⋊#95—62no—
73#821—24no—
74Dic3⋊C8—64no—
75Dic3⋊C8—64no—
76#809—64no—
77C23×C32C2×D411yescharacteristic
78C22×C3×D3—24no—
79C22×C3×D3—42no—
80C22×C3×D3—42no—
81C22×C3×D3—42no—
82C22×C3×D3—42no—
83C22×C3×D3—42no—
84C22×C3×D3—42no—
85C2×C32×C4C22×C411yescharacteristic
86C2×C32×C4C2×D411yescharacteristic
87C2×C32×C4C2×D412yes—
88C2×C32×C4#4112yes—
89C2×C3⋊Dic3—22no—
90C2×C3⋊Dic3C22⋊C412yes—
91C2×C3⋊Dic3C22⋊C412yes—
92C2×C3⋊Dic3D812yes—
93C2×C3⋊Dic3SD1612yes—
94C2×C3×Dic3—24no—
95C2×C3×Dic3—42no—
96C2×C3×Dic3—42no—
97C3×D12—24no—
98C3×D12—24no—
99C3×D12—42no—
100C3×D12—42no—
101#625—48no—
102#625—48no—
103C32×C8—41no—
104C3⋊(C3⋊C8)—41no—
105C2×#127—91no—
106C2×C4⋊C8—91no—
107C2×#102—32no—
108C2×#102—92no—
109C4×C4⋊C4—91no—
110C24×C3—62no—
111C23×D3—22no—
112C2×C3×D4—34no—
113C2×C3×D4—62no—
114C2×C3×D4—62no—
115C2×C3×D4—62no—
116C2×C3×D4—62no—
117C2×C3×D4—62no—
118C22×C3×C4—21no—
119C22×C3×C4—62no—
120C22×C3×C4C22×D312yes—
121C2×#67—68no—
122C2×#67—68no—
123C2×#67—124no—
124C2×#67—124no—
125C2×#67—124no—
126C2×#67—124no—
127C22×Dic3—22no—
128C22×Dic3—32no—
129C22×Dic3—32no—
130C22×Dic3—61no—
131C22×Dic3—61no—
132C2×D12—22no—
133C2×D12—22no—
134C2×D12—22no—
135C2×D12—22no—
136C2×D12—22no—
137C2×D12C4×D314yes—
138C2×C3×C8—22no—
139C2×C3×C8—22no—
140C2×C3×C8—22no—
141C2×C3×C8—22no—
142C2×C3×C8—42no—
143C3×C4⋊C4—34no—
144C3×C4⋊C4—62no—
145C4⋊Dic3—22no—
146C4⋊Dic3#6714yescomplemented
147C4×Dic3—34no—
148C4×Dic3—34no—
149C4×Dic3—62no—
150C4×Dic3—62no—
151C4×Dic3—124no—
152C2×C3⋊C8—62no—
153C2×C3⋊C8—62no—
154C2×C3⋊C8—62no—
155C2×C3⋊C8—62no—
156C2×C3⋊C8—122no—
157C22×C32C2×C22⋊C411yescharacteristic
158C22×C32#12112yes—
159C22×C32C2×D811yescharacteristic
160C22×C32C2×SD1611yescharacteristic
161C22×C32AGL(1,ℤ/8)12yes—
162C2×C3×D3—44no—
163C2×C3×D3—44no—
164C2×C3×D3—44no—
165C2×C3×D3—82no—
166C2×C3×D3—82no—
167C2×C3×D3—82no—
168C2×C3×D3—82no—
169C32×C4C4×D412yes—
170C32×C4#12411yescharacteristic
171C32×C4#12711yescharacteristic
172C3⋊Dic3—22no—
173C3⋊Dic3#10214yescomplemented
174C3×Dic3—44no—
175C22×D4—32no—
176C22×D4—181no—
177C22×D4—181no—
178C22×C8—91no—
179C22×C8D3211yescharacteristic
180#127—94no—
181#127—182no—
182C2×C4⋊C4—32no—
183C2×C42—91no—
184C2×C42—181no—
185C4⋊C8—182no—
186#102—64no—
187#102—184no—
188#95—181no—
189C23×C3—21no—
190C23×C3—64no—
191C23×C3—122no—
192C23×C3—122no—
193C23×C3—122no—
194C23×C3—122no—
195C23×C3—122no—
196C23×C3—122no—
197C23×C3D3×D412yes—
198C22×D3—24no—
199C22×D3—42no—
200C22×D3—42no—
201C22×D3—42no—
202C22×D3—42no—
203C22×D3—42no—
204C22×D3—42no—
205C3×D4—64no—
206C3×D4—64no—
207C3×D4—122no—
208C3×D4—122no—
209C2×C3×C4—22no—
210C2×C3×C4—21no—
211C2×C3×C4—22no—
212C2×C3×C4—21no—
213C2×C3×C4—64no—
214C2×C3×C4—122no—
215C2×C3×C4—122no—
216C2×C3×C4C2×C4×D312yes—
217C2×C3×C4#23512yes—
218C2×C3×C4D3×D412yes—
219C2×C3×C4D3×D412yes—
220C2×C3×C4#23712yes—
221C2×C3×C4C2×#6712yes—
222#67—1216no—
223#67—1216no—
224C2×Dic3—24no—
225C2×Dic3—34no—
226C2×Dic3—34no—
227C2×Dic3—34no—
228C2×Dic3—34no—
229C2×Dic3—42no—
230C2×Dic3—42no—
231C2×Dic3—62no—
232C2×Dic3—62no—
233C2×Dic3—62no—
234C2×Dic3—62no—
235C2×Dic3—62no—
236C2×Dic3—62no—
237C2×Dic3—122no—
238D12—24no—
239D12—24no—
240D12—42no—
241D12—42no—
242C3×C8—42no—
243C3×C8—42no—
244C3⋊C8—122no—
245C3⋊C8—122no—
246C2×C32#39011yescharacteristic
247C2×C32C2×#10211yescharacteristic
248C2×C32#41811yescharacteristic
249C2×C32#45912yes—
250C2×C32#46012yes—
251C3×D3—84no—
252C24—62no—
253C2×D4—34no—
254C2×D4—62no—
255C2×D4—62no—
256C2×D4—62no—
257C2×D4—62no—
258C2×D4—62no—
259C2×D4—184no—
260C2×D4—184no—
261C2×D4—362no—
262C2×D4—362no—
263C2×D4—364no—
264C22×C4—62no—
265C22×C4—91no—
266C22×C4—91no—
267C22×C4C2×D3211yescharacteristic
268C2×C8—22no—
269C2×C8—21no—
270C2×C8—182no—
271C2×C8—181no—
272C4⋊C4—34no—
273C4⋊C4—62no—
274C42—92no—
275C42—92no—
276C42—362no—
277C22×C3—21no—
278C22×C3—21no—
279C22×C3—22no—
280C22×C3—22no—
281C22×C3—21no—
282C22×C3—124no—
283C22×C3—124no—
284C22×C3—124no—
285C22×C3—242no—
286C22×C3—242no—
287C22×C3—242no—
288C22×C3—242no—
289C22×C3D3×C22⋊C412yes—
290C22×C3#88412yes—
291C22×C3D3×D812yes—
292C22×C3#91112yes—
293C22×C3D3×SD1612yes—
294C22×C3#91412yes—
295C22×C3#93912yes—
296C2×D3—44no—
297C2×D3—44no—
298C2×D3—44no—
299C2×D3—82no—
300C2×D3—82no—
301C2×D3—82no—
302C2×D3—82no—
303C3×C4—22no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—124no—
307C3×C4#67⋊C412yes—
308C3×C4#88512yes—
309C3×C4C4×#6712yes—
310C3×C4#94012yes—
311Dic3—38no—
312Dic3—44no—
313Dic3—64no—
314Dic3—64no—
315Dic3—122no—
316C32#198211yescharacteristic, complemented, Sylow
317C23—64no—
318C23—122no—
319C23—122no—
320C23—122no—
321C23—122no—
322C23—122no—
323C23—122no—
324C23#380211yescharacteristic
325D4—64no—
326D4—64no—
327D4—122no—
328D4—122no—
329D4—368no—
330D4—368no—
331C2×C4—64no—
332C2×C4—92no—
333C2×C4—92no—
334C2×C4—92no—
335C2×C4—92no—
336C2×C4—122no—
337C2×C4—122no—
338C2×C4—182no—
339C2×C4#379512yes—
340C2×C4C4×D3211yescharacteristic
341C2×C4D3×#6712yes—
342C2×C4#381111yescharacteristic
343C8—41no—
344C8—361no—
345C2×C3—22no—
346C2×C3—21no—
347C2×C3—22no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—244no—
351C2×C3#476212yes—
352C2×C3D3×#10212yes—
353C2×C3#477012yes—
354C2×C3#478612yes—
355C2×C3#495712yes—
356C2×C3#515012yes—
357C2×C3#516312yes—
358D3—84no—
359C22—124no—
360C22—124no—
361C22—124no—
362C22—242no—
363C22—242no—
364C22—242no—
365C22—242no—
366C22#6379611yescharacteristic
367C22#6379711yescharacteristic
368C22#6379812yes—
369C22#6388512yes—
370C22#6392111yescharacteristic
371C4—94no—
372C4—124no—
373C4—182no—
374C4#6387912yes—
375C4#6391311yescharacteristic
376C4#6397911yescharacteristic
377C3—21no—
378C3#7016112yescomplemented
379C2—244no—
380C2#1059074912yes—
381C2#1059087612yes—
382C2#1059094011yescharacteristic
383C2#1059094111yescharacteristic
384C2#1059138611yescharacteristic
subgroupG/H
centerC23#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC2×#63914C2
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1982
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63641C2semidirect
3. C2×C3×#821C2semidirect
4. #10591274C2semidirect
5. C2×#63562C2semidirect
16. #63914C4semidirect
24. C2×#821D3semidirect
52. C3×C4⋊Dic3D4semidirect
146. C4⋊Dic3#67semidirect
173. C3⋊Dic3#102semidirect
316. C32#1982semidirect
378. C3#70161semidirect

Maximal subgroups

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

subgroupindex
C2×#639142
C2×#636412
C2×C3×#8212
#105912742
C2×#635622
#701613