Finite Group Databasebeta

← #11788859

Subgroups — #11788859

Order 1152.

933 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 933 conjugacy classes of subgroups — too many to draw. Only its 124 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#10596275C211yesmaximal, characteristic
2#10595510C211yesmaximal, characteristic, complemented
3C2×C3×#834C212yesmaximal, complemented
4C2×#63581C211yesmaximal, characteristic, complemented
5#10589186C212yesmaximal, complemented
6#70034—32nomaximal
7C22×C32×D4C2211yescharacteristic
8C22×#638C2211yescharacteristic
9#64162C412yescomplemented
10C2×#3757C2211yescharacteristic
11#64148—22no—
12#64146—21no—
13#64144—21no—
14#64138C412yescomplemented
15C2×C3×#217C2212yes—
16C2×C3×#217C2212yes—
17#63974—21no—
18#63957—21no—
19#63952—24no—
20C3×#834—24no—
21#63581—22no—
22#5804—32no—
23#5804—61no—
24#5486—32no—
25C2×C3×#99—32no—
26C2×#834D312yescomplemented
27C2×#806—32no—
28#4527—32no—
29#4526—32no—
30C24×C32C2×C411yescharacteristic, complemented
31C24×C32C2311yescharacteristic
32C23×C3⋊D3D411yescharacteristic
33C2×C32×D4—21no—
34C2×C32×D4—21no—
35C2×C32×D4—22no—
36C2×C32×D4—22no—
37C22×C32×C4C2×C411yescharacteristic, complemented
38C2×#638—22no—
39C2×#638—22no—
40C2×#638—22no—
41C2×#638C2×C412yes—
42C2×#638D412yes—
43C22×C3⋊Dic3—21no—
44C22×C3⋊Dic3D411yescharacteristic
45C22×C3×Dic3—22no—
46C22×C3×Dic3—22no—
47C2×#624—22no—
48#3757—21no—
49#3757—22no—
50#3757C2×C412yescomplemented
51#3752—22no—
52#3750—22no—
53C3×#217—22no—
54C3×#217—22no—
55C3×#217—22no—
56C3×#217D414yescomplemented
57#3724—22no—
58#3722—22no—
59Dic32—22no—
60#1913—91noSylow
61C22×C3×D4—21no—
62C22×C3×D4C2×D312yes—
63C22×#67—32no—
64C22×#67—61no—
65C2×C3×C22⋊C4—32no—
66C2×C3×C22⋊C4—32no—
67#953—34no—
68#953—62no—
69C2×#217—32no—
70C2×#217—61no—
71C2×#217C2×D312yes—
72C2×#217C2×D312yes—
73#939—64no—
74#939—64no—
75#937—62no—
76#937—62no—
77#935—62no—
78#935—62no—
79#929—34no—
80#929—62no—
81C4×#67—64no—
82#67⋊C4—64no—
83D3×C22⋊C4—62no—
84#877—62no—
85C3×#99—64no—
86#834—24no—
87#806—64no—
88C23×C32—21no—
89C23×C32—22no—
90C23×C32—81no—
91C23×C32—81no—
92C23×C32C22×C411yescharacteristic
93C23×C32C2×D411yescharacteristic
94C23×C32C2×D411yescharacteristic
95C23×C32C2×D412yes—
96C23×C32#4112yes—
97C22×C3⋊D3—21no—
98C22×C3⋊D3—21no—
99C22×C3⋊D3—81no—
100C22×C3⋊D3C22⋊C412yes—
101C32×D4—41no—
102C32×D4—42no—
103C32×D4—41no—
104C2×C32×C4—21no—
105C2×C32×C4—22no—
106#638—24no—
107#638—24no—
108#638—82no—
109C2×C3⋊Dic3—22no—
110C2×C3⋊Dic3—21no—
111C2×C3⋊Dic3—21no—
112C2×C3⋊Dic3—81no—
113C2×C3⋊Dic3C22⋊C412yes—
114C2×C3×Dic3—24no—
115C2×C3×Dic3—42no—
116C2×C3×Dic3—82no—
117C2×C3×Dic3—82no—
118#624—82no—
119#534—91no—
120#518—91no—
121C2×#99—32no—
122C2×#99—91no—
123#342—92no—
124C24×C3—21no—
125C24×C3—21no—
126C24×C3C4×D312yescomplemented
127C24×C3C22×D312yes—
128C23×D3—32no—
129C23×D3—61no—
130C2×C3×D4—22no—
131C2×C3×D4—22no—
132C2×C3×D4—22no—
133C2×C3×D4—22no—
134C2×C3×D4—22no—
135C2×C3×D4—22no—
136C2×C3×D4—22no—
137C2×C3×D4—22no—
138C2×C3×D4—42no—
139C2×C3×D4—42no—
140C22×C3×C4—21no—
141C22×C3×C4—62no—
142C22×C3×C4—62no—
143C22×C3×C4C4×D312yescomplemented
144C2×#67—34no—
145C2×#67—34no—
146C2×#67—62no—
147C2×#67—62no—
148C2×#67—62no—
149C2×#67—62no—
150C2×#67—62no—
151C2×#67—62no—
152C2×#67—64no—
153C2×#67—64no—
154C2×#67—122no—
155C2×#67—122no—
156C22×Dic3—22no—
157C22×Dic3—22no—
158C22×Dic3—32no—
159C22×Dic3—61no—
160C22×Dic3—62no—
161C22×Dic3—62no—
162C2×C4×D3—64no—
163C3×C22⋊C4—34no—
164C3×C22⋊C4—62no—
165C3×C22⋊C4—62no—
166C3×C22⋊C4—62no—
167#217—22no—
168#217—22no—
169#217—22no—
170#217—34no—
171#217—62no—
172#217—64no—
173#217—62no—
174#217—64no—
175#217—62no—
176#217#6714yescomplemented
177(C2×D3)⋊C4—64no—
178(C2×D3)⋊C4—64no—
179(C2×D3)⋊C4—64no—
180Dic3⋊C4—64no—
181Dic3⋊C4—64no—
182Dic3⋊C4—64no—
183C4×Dic3—64no—
184C22×C32—41no—
185C22×C32—41no—
186C22×C32—41no—
187C22×C32—42no—
188C22×C32—41no—
189C22×C32—42no—
190C22×C32—42no—
191C22×C32—82no—
192C22×C32C2×C22⋊C411yescharacteristic
193C22×C32C4×D412yes—
194C22×C32#12011yescharacteristic
195C22×C32#12112yes—
196C22×C32#12311yescharacteristic
197C2×C3⋊D3—22no—
198C2×C3⋊D3—42no—
199C2×C3⋊D3—42no—
200C2×C3⋊D3—81no—
201C32×C4—41no—
202C3⋊Dic3—22no—
203C3⋊Dic3—42no—
204C3×Dic3—44no—
205C3×Dic3—82no—
206C22×D4—91no—
207C22×D4D3211yescharacteristic
208#123—92no—
209#123—181no—
210#121—182no—
211#120—92no—
212#120—181no—
213C4×D4—184no—
214#117—181no—
215C2×C22⋊C4—32no—
216C2×C22⋊C4—32no—
217C2×C22⋊C4—91no—
218C2×C22⋊C4—181no—
219#99—64no—
220#99—182no—
221C23×C3—22no—
222C23×C3—22no—
223C23×C3—22no—
224C23×C3—22no—
225C23×C3—22no—
226C23×C3—21no—
227C23×C3—22no—
228C23×C3—21no—
229C23×C3—21no—
230C23×C3—42no—
231C23×C3—82no—
232C23×C3—82no—
233C23×C3—82no—
234C23×C3—82no—
235C23×C3C2×C4×D312yes—
236C23×C3#23512yes—
237C23×C3D3×D412yes—
238C23×C3D3×D412yes—
239C23×C3D3×D412yes—
240C23×C3#23712yes—
241C23×C3C2×#6712yes—
242C22×D3—34no—
243C22×D3—62no—
244C22×D3—62no—
245C22×D3—62no—
246C22×D3—121no—
247C22×D3—121no—
248C22×D3—242no—
249C22×D3—242no—
250C3×D4—44no—
251C3×D4—42no—
252C3×D4—42no—
253C3×D4—42no—
254C3×D4—42no—
255C3×D4—42no—
256C3×D4—42no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4—42no—
262C2×C3×C4—64no—
263C2×C3×C4—122no—
264C2×C3×C4—242no—
265C2×C3×C4—242no—
266#67—64no—
267#67—64no—
268#67—64no—
269#67—64no—
270#67—124no—
271#67—124no—
272#67—244no—
273#67—244no—
274C2×Dic3—24no—
275C2×Dic3—34no—
276C2×Dic3—42no—
277C2×Dic3—62no—
278C2×Dic3—62no—
279C2×Dic3—62no—
280C2×Dic3—64no—
281C2×Dic3—64no—
282C2×Dic3—82no—
283C2×Dic3—82no—
284C2×Dic3—121no—
285C2×Dic3—121no—
286C2×Dic3—242no—
287C2×Dic3—242no—
288C4×D3—244no—
289C2×C32—21no—
290C2×C32—21no—
291C2×C32—22no—
292C2×C32—21no—
293C2×C32—22no—
294C2×C32—81no—
295C2×C32#38611yescharacteristic
296C3⋊D3—42no—
297C24—91no—
298C24#62411yescharacteristic, complemented
299C24C2×D3211yescharacteristic
300C2×D4—22no—
301C2×D4—22no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—92no—
305C2×D4—92no—
306C2×D4—182no—
307C2×D4—182no—
308C2×D4—182no—
309C22×C4—62no—
310C22×C4—62no—
311C22×C4—91no—
312C22×C4—182no—
313C22×C4—181no—
314C22×C4#62411yescharacteristic, complemented
315C4⋊C4—182no—
316C4⋊C4—182no—
317C22⋊C4—34no—
318C22⋊C4—62no—
319C22⋊C4—62no—
320C22⋊C4—62no—
321C22⋊C4—92no—
322C22⋊C4—182no—
323C22⋊C4—182no—
324C22⋊C4—182no—
325C22⋊C4—181no—
326C42—182no—
327C22×C3—22no—
328C22×C3—22no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—42no—
333C22×C3—42no—
334C22×C3—42no—
335C22×C3—42no—
336C22×C3—42no—
337C22×C3—42no—
338C22×C3—42no—
339C22×C3—42no—
340C22×C3—42no—
341C22×C3—42no—
342C22×C3—44no—
343C22×C3—44no—
344C22×C3—42no—
345C22×C3—42no—
346C22×C3—82no—
347C22×C3—82no—
348C22×C3—82no—
349C22×C3—82no—
350C22×C3—84no—
351C22×C3D3×C22⋊C412yes—
352C22×C3#67⋊C412yes—
353C22×C3#88312yes—
354C22×C3#88412yes—
355C22×C3C4×#6712yes—
356C22×C3#93712yes—
357C22×C3#93812yes—
358C2×D3—64no—
359C2×D3—122no—
360C2×D3—124no—
361C2×D3—124no—
362C2×D3—124no—
363C2×D3—242no—
364C2×D3—242no—
365C2×D3—242no—
366C3×C4—42no—
367C3×C4—42no—
368C3×C4—124no—
369C3×C4—242no—
370Dic3—44no—
371Dic3—64no—
372Dic3—82no—
373Dic3—122no—
374Dic3—124no—
375Dic3—124no—
376C32#191311yescharacteristic, complemented, Sylow
377C23—21no—
378C23—22no—
379C23—81no—
380C23—81no—
381C23—92no—
382C23—181no—
383C23—181no—
384C23—721no—
385C23#380412yes—
386C23C2×#62411yescharacteristic
387C23D3×#6712yes—
388C23#381111yescharacteristic
389C23#381111yescharacteristic
390D4—42no—
391D4—41no—
392D4—41no—
393D4—184no—
394D4—184no—
395D4—722no—
396C2×C4—22no—
397C2×C4—21no—
398C2×C4—64no—
399C2×C4—92no—
400C2×C4—122no—
401C2×C4—181no—
402C2×C4—181no—
403C2×C4—182no—
404C2×C4—242no—
405C2×C4—242no—
406C2×C4—722no—
407C2×C4—721no—
408C2×C3—22no—
409C2×C3—22no—
410C2×C3—22no—
411C2×C3—22no—
412C2×C3—22no—
413C2×C3—22no—
414C2×C3—22no—
415C2×C3—22no—
416C2×C3—21no—
417C2×C3—41no—
418C2×C3—41no—
419C2×C3—42no—
420C2×C3—42no—
421C2×C3—82no—
422C2×C3—82no—
423C2×C3#495612yes—
424D3—124no—
425D3—242no—
426C22—42no—
427C22—42no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—42no—
432C22—41no—
433C22—82no—
434C22—182no—
435C22—362no—
436C22—362no—
437C22—721no—
438C22#6395212yes—
439C22#6395812yes—
440C22#6397411yescharacteristic
441C22#6397511yescharacteristic
442C22#6398311yescharacteristic
443C4—41no—
444C4—124no—
445C4—182no—
446C4—242no—
447C4—362no—
448C3—21no—
449C3#7003412yescomplemented
450C2—21no—
451C2—22no—
452C2—21no—
453C2—22no—
454C2—21no—
455C2—81no—
456C2—362no—
457C2#1059172211yescharacteristic
subgroupG/H
centerC2#10591722
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC22×C32×D4C22
socleC2×C32#386
prime radical#10596275C2
cosocleC24×C32C23
hypercenterC22×D4D32
hypocenterC32#1913
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #10595510C2semidirect
3. C2×C3×#834C2semidirect
4. C2×#63581C2semidirect
5. #10589186C2semidirect
9. #64162C4semidirect
14. #64138C4semidirect
26. C2×#834D3semidirect
30. C24×C32C2×C4semidirect
37. C22×C32×C4C2×C4semidirect
50. #3757C2×C4semidirect
56. C3×#217D4semidirect
126. C24×C3C4×D3semidirect
143. C22×C3×C4C4×D3semidirect
176. #217#67semidirect
298. C24#624semidirect
314. C22×C4#624semidirect
376. C32#1913semidirect
449. C3#70034semidirect

Maximal subgroups

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

subgroupindex
#105962752
#105955102
C2×C3×#8342
C2×#635812
#105891862
#700343