Finite Group Databasebeta

← #11787981

Subgroups — #11787981

Order 1152.

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

normal subgroups only

This group has 943 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×#64095C211yesmaximal, characteristic
2#10595510C211yesmaximal, characteristic
3C2×#63581C211yesmaximal, characteristic
4#10591697C212yesmaximal, complemented
5C3×#4527C212yesmaximal, complemented
6#68963—32nomaximal
7C22×#638C2211yescharacteristic
8C23×C3⋊Dic3C2211yescharacteristic
9C2×C32×C22⋊C4C2211yescharacteristic
10C2×#3752—21no—
11C2×C4⋊(C3⋊Dic3)—21no—
12#64095—22no—
13#64095C414yescomplemented
14C2×C3×#217C2212yes—
15C2×C3×#217C2212yes—
16#63974—21no—
17#63957—21no—
18#63952—24no—
19#63581—22no—
20#63579—24no—
21C2×#886—32no—
22C2×#886—61no—
23#5486—32no—
24C2×#806—32no—
25#4943—32no—
26#4943—32no—
27C3×#342—32no—
28#4527D312yescomplemented
29C24×C32C2311yescharacteristic
30C23×C3⋊D3D411yescharacteristic
31C22×C32×C4—21no—
32C2×#638—22no—
33C2×#638—22no—
34C2×#638C2×C412yes—
35C2×#638D412yes—
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3—21no—
38C22×C3⋊Dic3—22no—
39C22×C3⋊Dic3—22no—
40C22×C3⋊Dic3C2×C412yescomplemented
41C22×C3⋊Dic3D411yescharacteristic
42C22×C3×Dic3—22no—
43C22×C3×Dic3D414yes—
44C2×#624—22no—
45C32×C22⋊C4—21no—
46C32×C22⋊C4C2×C412yescomplemented
47#3752—24no—
48C4⋊(C3⋊Dic3)—24no—
49C3×#217—22no—
50C3×#217—22no—
51C3×#217—22no—
52C3×#217—22no—
53#3724—22no—
54#3722—22no—
55Dic32—22no—
56#1890—91noSylow
57C22×#67—32no—
58C22×#67—61no—
59C23×Dic3—32no—
60C23×Dic3—61no—
61C2×C3×C22⋊C4—21no—
62C2×C3×C22⋊C4—32no—
63C2×C3×C22⋊C4—32no—
64C2×C3×C22⋊C4C2×D312yes—
65C2×#217C2×D312yes—
66C2×#217C2×D312yes—
67C4×#67—64no—
68C2×(C2×D3)⋊C4—62no—
69C2×(C2×D3)⋊C4—62no—
70C2×C4⋊Dic3—62no—
71C2×C4⋊Dic3—62no—
72#886—38no—
73#886—64no—
74#886—64no—
75#886—64no—
76#67⋊C4—64no—
77D3×C22⋊C4—62no—
78#877—62no—
79C3⋊#95—64no—
80C3⋊#95—64no—
81#806—64no—
82C23×C32—42no—
83C23×C32C22×C411yescharacteristic
84C23×C32C2×D412yes—
85C23×C32C2×D411yescharacteristic
86C23×C32C2×D411yescharacteristic
87C23×C32#4112yes—
88C22×C3⋊D3—21no—
89C22×C3⋊D3—21no—
90C22×C3⋊D3—42no—
91C22×C3⋊D3C22⋊C412yes—
92C2×C32×C4—22no—
93C2×C32×C4—42no—
94#638—24no—
95#638—24no—
96C2×C3⋊Dic3—22no—
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—24no—
100C2×C3⋊Dic3—41no—
101C2×C3⋊Dic3—42no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3C22⋊C412yes—
104C2×C3×Dic3—24no—
105C2×C3×Dic3—44no—
106C2×C3×Dic3—44no—
107C2×C3×Dic3—42no—
108#624—82no—
109C2×#123—91no—
110#518—91no—
111C2×#99—91no—
112#381—92no—
113#342—32no—
114C24×C3—21no—
115C24×C3C22×D312yes—
116C23×D3—32no—
117C23×D3—61no—
118C22×C3×C4—22no—
119C22×C3×C4—22no—
120C22×C3×C4—34no—
121C22×C3×C4—62no—
122C2×#67—34no—
123C2×#67—34no—
124C2×#67—62no—
125C2×#67—62no—
126C2×#67—62no—
127C2×#67—62no—
128C2×#67—62no—
129C2×#67—62no—
130C2×#67—122no—
131C2×#67—122no—
132C22×Dic3—22no—
133C22×Dic3—32no—
134C22×Dic3—34no—
135C22×Dic3—62no—
136C22×Dic3—61no—
137C22×Dic3—62no—
138C22×Dic3—62no—
139C22×Dic3—62no—
140C22×Dic3—62no—
141C22×Dic3—62no—
142C22×Dic3—62no—
143C22×Dic3—62no—
144C22×Dic3—62no—
145C22×Dic3—122no—
146C22×Dic3—122no—
147C22×Dic3D1214yes—
148C2×C4×D3—64no—
149C3×C22⋊C4—22no—
150C3×C22⋊C4—22no—
151C3×C22⋊C4—22no—
152C3×C22⋊C4—62no—
153C3×C22⋊C4—62no—
154C3×C22⋊C4—62no—
155C3×C22⋊C4—62no—
156C3×C22⋊C4C4×D314yescomplemented
157#217—22no—
158#217—22no—
159#217—22no—
160#217—22no—
161(C2×D3)⋊C4—64no—
162(C2×D3)⋊C4—68no—
163(C2×D3)⋊C4—68no—
164C4⋊Dic3—68no—
165C4⋊Dic3—68no—
166Dic3⋊C4—64no—
167C4×Dic3—64no—
168C22×C32—22no—
169C22×C32—24no—
170C22×C32—41no—
171C22×C32—41no—
172C22×C32—42no—
173C22×C32C2×C22⋊C411yescharacteristic
174C22×C32C4×D412yes—
175C22×C32#12011yescharacteristic
176C22×C32#12112yes—
177C22×C32#12311yescharacteristic
178C2×C3⋊D3—22no—
179C2×C3⋊D3—42no—
180C2×C3⋊D3—42no—
181C2×C3⋊D3—81no—
182C32×C4—42no—
183C3⋊Dic3—22no—
184C3⋊Dic3—42no—
185C3×Dic3—44no—
186C3×Dic3—82no—
187C22×D4—91no—
188C23×C4—91no—
189#123—94no—
190#123—182no—
191C4×D4—184no—
192#117—181no—
193C2×C4⋊C4—181no—
194C2×C22⋊C4—32no—
195C2×C22⋊C4—32no—
196C2×C22⋊C4—181no—
197C2×C22⋊C4—181no—
198C2×C22⋊C4D3211yescharacteristic
199#99—182no—
200#95—184no—
201C23×C3—22no—
202C23×C3—22no—
203C23×C3—21no—
204C23×C3—21no—
205C23×C3—21no—
206C23×C3—44no—
207C23×C3—44no—
208C23×C3C2×C4×D312yes—
209C23×C3C2×D1212yes—
210C23×C3#23512yes—
211C23×C3D3×D412yes—
212C23×C3D3×D412yes—
213C23×C3D3×D412yes—
214C23×C3#23912yes—
215C22×D3—34no—
216C22×D3—62no—
217C22×D3—62no—
218C22×D3—62no—
219C22×D3—121no—
220C22×D3—121no—
221C22×D3—124no—
222C22×D3—124no—
223C2×C3×C4—24no—
224C2×C3×C4—24no—
225C2×C3×C4—44no—
226C2×C3×C4—44no—
227C2×C3×C4—64no—
228C2×C3×C4—124no—
229C2×C3×C4—124no—
230C2×C3×C4—122no—
231#67—64no—
232#67—64no—
233#67—64no—
234#67—64no—
235#67—124no—
236#67—124no—
237C2×Dic3—24no—
238C2×Dic3—34no—
239C2×Dic3—44no—
240C2×Dic3—44no—
241C2×Dic3—42no—
242C2×Dic3—62no—
243C2×Dic3—62no—
244C2×Dic3—62no—
245C2×Dic3—64no—
246C2×Dic3—64no—
247C2×Dic3—64no—
248C2×Dic3—64no—
249C2×Dic3—124no—
250C2×Dic3—121no—
251C2×Dic3—121no—
252C2×Dic3—122no—
253C2×Dic3—124no—
254C2×Dic3—122no—
255C2×Dic3—122no—
256C2×Dic3—122no—
257C2×Dic3—122no—
258C2×Dic3—122no—
259C4×D3—244no—
260C2×C32—21no—
261C2×C32—21no—
262C2×C32—22no—
263C2×C32—22no—
264C2×C32#38611yescharacteristic
265C2×C32#45812yes—
266C3⋊D3—42no—
267C24—91no—
268C24C2×D3211yescharacteristic
269C2×D4—92no—
270C2×D4—92no—
271C2×D4—182no—
272C2×D4—182no—
273C22×C4—21no—
274C22×C4—34no—
275C22×C4—62no—
276C22×C4—91no—
277C22×C4—92no—
278C22×C4—182no—
279C22×C4—182no—
280C22×C4—182no—
281C22×C4—181no—
282C22×C4—181no—
283C4⋊C4—184no—
284C4⋊C4—182no—
285C22⋊C4—21no—
286C22⋊C4—62no—
287C22⋊C4—62no—
288C22⋊C4—62no—
289C22⋊C4—62no—
290C22⋊C4—184no—
291C22⋊C4—182no—
292C22⋊C4#62412yescomplemented
293C42—182no—
294C22×C3—24no—
295C22×C3—24no—
296C22×C3—24no—
297C22×C3—24no—
298C22×C3—22no—
299C22×C3—21no—
300C22×C3—22no—
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—44no—
304C22×C3—42no—
305C22×C3—42no—
306C22×C3—42no—
307C22×C3—42no—
308C22×C3—44no—
309C22×C3—42no—
310C22×C3—42no—
311C22×C3C4×D1212yes—
312C22×C3D3×C22⋊C412yes—
313C22×C3#88212yes—
314C22×C3#88412yes—
315C22×C3#89312yes—
316C22×C3#89412yes—
317C22×C3#89512yes—
318C2×D3—64no—
319C2×D3—122no—
320C2×D3—124no—
321C2×D3—124no—
322C2×D3—124no—
323C2×D3—242no—
324C2×D3—242no—
325C2×D3—242no—
326C3×C4—44no—
327C3×C4—44no—
328C3×C4—124no—
329C3×C4—242no—
330Dic3—44no—
331Dic3—64no—
332Dic3—82no—
333Dic3—122no—
334Dic3—124no—
335Dic3—124no—
336C32#189011yescharacteristic, complemented, Sylow
337C23—42no—
338C23—92no—
339C23—181no—
340C23—181no—
341C23—362no—
342C23#379912yes—
343C23D3×D1212yes—
344C23C2×#62411yescharacteristic
345C23#381111yescharacteristic
346C23#381111yescharacteristic
347D4—184no—
348D4—184no—
349C2×C4—22no—
350C2×C4—42no—
351C2×C4—64no—
352C2×C4—92no—
353C2×C4—124no—
354C2×C4—124no—
355C2×C4—122no—
356C2×C4—181no—
357C2×C4—181no—
358C2×C4—184no—
359C2×C4—182no—
360C2×C4—361no—
361C2×C4—362no—
362C2×C4—361no—
363C2×C4—722no—
364C2×C3—22no—
365C2×C3—22no—
366C2×C3—22no—
367C2×C3—22no—
368C2×C3—22no—
369C2×C3—22no—
370C2×C3—22no—
371C2×C3—22no—
372C2×C3—21no—
373C2×C3—22no—
374C2×C3—42no—
375C2×C3—42no—
376C2×C3#466512yes—
377C2×C3#474214yes—
378D3—124no—
379D3—242no—
380C22—22no—
381C22—24no—
382C22—42no—
383C22—41no—
384C22—41no—
385C22—182no—
386C22—362no—
387C22—362no—
388C22—721no—
389C22#6389412yes—
390C22#6389711yescharacteristic
391C22#6391012yes—
392C22#6392311yescharacteristic
393C22#6397411yescharacteristic
394C4—42no—
395C4—124no—
396C4—182no—
397C4—242no—
398C4—362no—
399C3—21no—
400C3#6896312yescomplemented
401C2—21no—
402C2—22no—
403C2—21no—
404C2—22no—
405C2—362no—
406C2#1059040912yes—
407C2#1059138011yescharacteristic
subgroupG/H
centerC22#63923
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32#120
prime radicalC22×#638C22
cosocleC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#1890
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. #10591697C2semidirect
5. C3×#4527C2semidirect
13. #64095C4semidirect
28. #4527D3semidirect
40. C22×C3⋊Dic3C2×C4semidirect
46. C32×C22⋊C4C2×C4semidirect
156. C3×C22⋊C4C4×D3semidirect
292. C22⋊C4#624semidirect
336. C32#1890semidirect
400. C3#68963semidirect

Maximal subgroups

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

subgroupindex
C2×#640952
#105955102
C2×#635812
#105916972
C3×#45272
#689633