Finite Group Databasebeta

← #11791854

Subgroups — #11791854

Order 1152.

809 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 809 conjugacy classes of subgroups — too many to draw. Only its 134 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×#64087C211yesmaximal, characteristic
2#10591720C211yesmaximal, characteristic
3#10591705C211yesmaximal, characteristic
4C3×#4526C212yesmaximal
5#10589187C212yesmaximal
6#68955—32nomaximal
7C23×C3⋊Dic3C2211yescharacteristic
8C22×#634C411yescharacteristic, complemented
9C2×C32×C22⋊C4C2211yescharacteristic
10C2×#3757C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
12C2×#3750C411yescharacteristic, complemented
13C2×#3750C411yescharacteristic, complemented
14#64087—21no—
15#64087—21no—
16#64087—21no—
17#64087—21no—
18C2×C3×#217C2212yes—
19C2×C3×#217C2212yes—
20C2×#3724—21no—
21C2×Dic32—21no—
22#63579—21no—
23#63579—21no—
24C2×#878—32no—
25C2×#878—61no—
26#4942—32no—
27Dic3×C22⋊C4—32no—
28C3×#342—32no—
29#4527—32no—
30#4527—32no—
31#4526D312yes—
32C24×C32C2311yescharacteristic
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4C2×C411yescharacteristic
35C22×C3⋊Dic3—42no—
36C22×C3⋊Dic3C2×C411yescharacteristic
37C22×C3⋊Dic3C2×C411yescharacteristic
38C22×C3⋊Dic3C2×C411yescharacteristic
39C22×C3⋊Dic3C2×C411yescharacteristic
40C22×C3⋊Dic3D411yescharacteristic
41C22×C3⋊Dic3D411yescharacteristic
42C22×C3⋊Dic3D411yescharacteristic
43C22×C3⋊Dic3D411yescharacteristic
44C2×#634—21no—
45C2×#634—21no—
46C2×#634—42no—
47C22×C3×Dic3—22no—
48C22×C3×Dic3—22no—
49C32×C22⋊C4—21no—
50C32×C22⋊C4—21no—
51#3757—21no—
52#3757—21no—
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)—21no—
55#3750—21no—
56#3750—21no—
57#3750—21no—
58#3750—21no—
59C3×#217—22no—
60C3×#217—22no—
61C3×#217—22no—
62C3×#217Q814yescomplemented
63#3724—42no—
64Dic32—42no—
65#1996—91noSylow
66C23×Dic3—32no—
67C23×Dic3—61no—
68C22×Dic6—32no—
69C22×Dic6—61no—
70C2×C3×C22⋊C4—21no—
71C2×C3×C22⋊C4—32no—
72C2×C3×C22⋊C4—32no—
73C2×C3×C22⋊C4C2×D312yes—
74C2×#217—32no—
75C2×#217—61no—
76C2×#217C2×D312yes—
77C2×#217C2×D312yes—
78C2×C4⋊Dic3—32no—
79C2×C4⋊Dic3—61no—
80C2×Dic3⋊C4—32no—
81C2×Dic3⋊C4—32no—
82C2×Dic3⋊C4—61no—
83C2×Dic3⋊C4—61no—
84C2×Dic3⋊C4—62no—
85C2×C4×Dic3—62no—
86#878—62no—
87#878—62no—
88#878—62no—
89#878—62no—
90#878—62no—
91#878—62no—
92#878—62no—
93#878—62no—
94C3⋊#95—62no—
95C3⋊#95—62no—
96C23×C32—41no—
97C23×C32—41no—
98C23×C32C22×C411yescharacteristic
99C23×C32C2×D411yescharacteristic
100C23×C32C2×D411yescharacteristic
101C23×C32C2×Q812yes—
102C23×C32#4112yes—
103C2×C32×C4—21no—
104C2×C32×C4—21no—
105C2×C32×C4—41no—
106C2×C32×C4—41no—
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3—21no—
109C2×C3⋊Dic3—21no—
110C2×C3⋊Dic3—22no—
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3—41no—
113C2×C3⋊Dic3—41no—
114C2×C3⋊Dic3—41no—
115C2×C3⋊Dic3—41no—
116C2×C3⋊Dic3—41no—
117C2×C3⋊Dic3C22⋊C411yescharacteristic
118C2×C3⋊Dic3C22⋊C411yescharacteristic
119C2×C3⋊Dic3C22⋊C411yescharacteristic
120C2×C3⋊Dic3C22⋊C411yescharacteristic
121#634—42no—
122#634—42no—
123C2×C3×Dic3—24no—
124C2×C3×Dic3—42no—
125C2×C3×Dic3—42no—
126C2×C3×Dic3—42no—
127C2×C3×Dic3—42no—
128C2×C3×Dic3—42no—
129C2×C22⋊Q8—91no—
130#380—91no—
131C4×C22⋊C4—91no—
132#342—32no—
133#342—92no—
134C24×C3—21no—
135C24×C3C22×D312yes—
136C22×C3×C4—21no—
137C22×C3×C4—21no—
138C22×C3×C4—62no—
139C22×C3×C4—62no—
140C22×C3×C4C4×D312yes—
141C22×C3×C4C4×D312yes—
142C22×Dic3—22no—
143C22×Dic3—22no—
144C22×Dic3—32no—
145C22×Dic3—32no—
146C22×Dic3—32no—
147C22×Dic3—32no—
148C22×Dic3—32no—
149C22×Dic3—32no—
150C22×Dic3—32no—
151C22×Dic3—32no—
152C22×Dic3—61no—
153C22×Dic3—61no—
154C22×Dic3—61no—
155C22×Dic3—61no—
156C22×Dic3—61no—
157C22×Dic3—61no—
158C22×Dic3—61no—
159C22×Dic3—61no—
160C22×Dic3—124no—
161C22×Dic3—124no—
162C2×Dic6—62no—
163C2×Dic6—62no—
164C2×Dic6—62no—
165C2×Dic6—62no—
166C2×Dic6—124no—
167C2×Dic6—124no—
168C3×C22⋊C4—22no—
169C3×C22⋊C4—22no—
170C3×C22⋊C4—22no—
171C3×C22⋊C4—22no—
172C3×C22⋊C4—34no—
173C3×C22⋊C4—62no—
174C3×C22⋊C4—62no—
175C3×C22⋊C4—62no—
176#217—22no—
177#217—22no—
178#217—22no—
179#217—62no—
180#217—62no—
181#217—62no—
182#217—62no—
183#217Dic614yescomplemented
184C4⋊Dic3—62no—
185C4⋊Dic3—62no—
186C4⋊Dic3—62no—
187C4⋊Dic3—62no—
188Dic3⋊C4—62no—
189Dic3⋊C4—62no—
190Dic3⋊C4—62no—
191Dic3⋊C4—62no—
192Dic3⋊C4—62no—
193Dic3⋊C4—62no—
194Dic3⋊C4—62no—
195Dic3⋊C4—62no—
196Dic3⋊C4—124no—
197C4×Dic3—124no—
198C22×C32—21no—
199C22×C32—21no—
200C22×C32—21no—
201C22×C32—21no—
202C22×C32—21no—
203C22×C32—21no—
204C22×C32—42no—
205C22×C32—42no—
206C22×C32C2×C22⋊C411yescharacteristic
207C22×C32C4×Q812yes—
208C22×C32C22⋊Q812yes—
209C22×C32#12411yescharacteristic
210C22×C32C4⋊Q811yescharacteristic
211C32×C4—41no—
212C32×C4—41no—
213C3⋊Dic3—21no—
214C3⋊Dic3—21no—
215C3⋊Dic3—21no—
216C3⋊Dic3—41no—
217C3⋊Dic3—41no—
218C3⋊Dic3#9912yes—
219C3×Dic3—44no—
220C3×Dic3—82no—
221C22×Q8—91no—
222C23×C4—91no—
223C22⋊Q8—181no—
224C22⋊Q8—181no—
225C22⋊Q8—181no—
226C22⋊Q8—181no—
227C2×C4⋊C4—91no—
228C2×C4⋊C4—91no—
229C2×C4⋊C4—91no—
230C2×C4⋊C4—181no—
231C2×C22⋊C4—32no—
232C2×C22⋊C4—32no—
233C2×C22⋊C4—91no—
234C2×C22⋊C4D3211yescharacteristic
235C2×C42—181no—
236#95—181no—
237#95—181no—
238C23×C3—22no—
239C23×C3—22no—
240C23×C3—21no—
241C23×C3—21no—
242C23×C3—21no—
243C23×C3—42no—
244C23×C3—42no—
245C23×C3—42no—
246C23×C3—42no—
247C23×C3C2×Dic612yes—
248C23×C3C2×C4×D312yes—
249C23×C3#23512yes—
250C23×C3D3×D412yes—
251C23×C3D3×D412yes—
252C23×C3#23712yes—
253C23×C3D3×Q812yes—
254C2×C3×C4—22no—
255C2×C3×C4—22no—
256C2×C3×C4—22no—
257C2×C3×C4—22no—
258C2×C3×C4—42no—
259C2×C3×C4—42no—
260C2×C3×C4—42no—
261C2×C3×C4—42no—
262C2×C3×C4—64no—
263C2×C3×C4—122no—
264C2×C3×C4—122no—
265C2×C3×C4—122no—
266C2×C3×C4—122no—
267C2×C3×C4—122no—
268C2×Dic3—24no—
269C2×Dic3—32no—
270C2×Dic3—32no—
271C2×Dic3—32no—
272C2×Dic3—32no—
273C2×Dic3—42no—
274C2×Dic3—42no—
275C2×Dic3—42no—
276C2×Dic3—42no—
277C2×Dic3—42no—
278C2×Dic3—61no—
279C2×Dic3—61no—
280C2×Dic3—61no—
281C2×Dic3—61no—
282C2×Dic3—64no—
283C2×Dic3—64no—
284C2×Dic3—64no—
285C2×Dic3—64no—
286C2×Dic3—62no—
287C2×Dic3—62no—
288C2×Dic3—62no—
289C2×Dic3—62no—
290C2×Dic3—122no—
291C2×Dic3—122no—
292C2×Dic3—122no—
293C2×Dic3—122no—
294C2×Dic3—122no—
295C2×Dic3—122no—
296C2×Dic3—122no—
297C2×Dic3—122no—
298C2×Dic3—122no—
299C2×Dic3—122no—
300C2×Dic3—122no—
301C2×Dic3—122no—
302Dic6—124no—
303Dic6—124no—
304Dic6—124no—
305Dic6—124no—
306C2×C32—22no—
307C2×C32—22no—
308C2×C32—21no—
309C2×C32—21no—
310C2×C32#39111yescharacteristic
311C2×C32C2×#9911yescharacteristic
312C2×C32#41011yescharacteristic
313C24C2×D3211yescharacteristic
314C2×Q8—181no—
315C2×Q8—181no—
316C2×Q8—362no—
317C22×C4—62no—
318C22×C4—62no—
319C22×C4—91no—
320C22×C4—91no—
321C22×C4—91no—
322C22×C4—91no—
323C22×C4—91no—
324C22×C4—91no—
325C22×C4—91no—
326C22×C4—91no—
327C22×C4—362no—
328C22×C4#62411yescharacteristic
329C22×C4#62411yescharacteristic
330C4⋊C4—181no—
331C4⋊C4—181no—
332C4⋊C4—181no—
333C4⋊C4—181no—
334C4⋊C4—181no—
335C4⋊C4—181no—
336C4⋊C4—362no—
337C22⋊C4—21no—
338C22⋊C4—21no—
339C22⋊C4—34no—
340C22⋊C4—62no—
341C22⋊C4—62no—
342C22⋊C4—62no—
343C22⋊C4—181no—
344C22⋊C4—181no—
345C42—362no—
346C22×C3—22no—
347C22×C3—22no—
348C22×C3—22no—
349C22×C3—22no—
350C22×C3—22no—
351C22×C3—22no—
352C22×C3—22no—
353C22×C3—22no—
354C22×C3—21no—
355C22×C3—22no—
356C22×C3—22no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—41no—
360C22×C3—41no—
361C22×C3—41no—
362C22×C3—41no—
363C22×C3—42no—
364C22×C3—42no—
365C22×C3—42no—
366C22×C3—42no—
367C22×C3—44no—
368C22×C3—44no—
369C22×C3C4×Dic612yes—
370C22×C3#87812yes—
371C22×C3D3×C22⋊C412yes—
372C22×C3#88512yes—
373C22×C3#88712yes—
374C22×C3#88812yes—
375C22×C3#89612yes—
376C3×C4—42no—
377C3×C4—42no—
378C3×C4—42no—
379C3×C4—42no—
380C3×C4—124no—
381C3×C4—242no—
382Dic3—34no—
383Dic3—44no—
384Dic3—62no—
385Dic3—62no—
386Dic3—62no—
387Dic3—62no—
388Dic3—62no—
389Dic3—82no—
390Dic3—121no—
391Dic3—121no—
392Dic3—122no—
393Dic3—122no—
394Dic3—122no—
395Dic3—122no—
396C32#199611yescharacteristic, complemented, Sylow
397C23—41no—
398C23—41no—
399C23D3×Dic612yes—
400C23#379512yes—
401C23C2×#62411yescharacteristic
402C23#381111yescharacteristic
403C23#381111yescharacteristic
404Q8—362no—
405Q8—362no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—64no—
411C2×C4—91no—
412C2×C4—91no—
413C2×C4—91no—
414C2×C4—91no—
415C2×C4—122no—
416C2×C4—122no—
417C2×C4—122no—
418C2×C4—122no—
419C2×C4—122no—
420C2×C4—182no—
421C2×C4—182no—
422C2×C4—182no—
423C2×C4—181no—
424C2×C4—181no—
425C2×C4—361no—
426C2×C4—361no—
427C2×C4—361no—
428C2×C4—361no—
429C2×C4—361no—
430C2×C3—24no—
431C2×C3—22no—
432C2×C3—22no—
433C2×C3—22no—
434C2×C3—22no—
435C2×C3—22no—
436C2×C3—22no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—42no—
441C2×C3—41no—
442C2×C3—41no—
443C2×C3#464612yes—
444C2×C3#474012yes—
445C2×C3D3×#9912yes—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—42no—
453C22—42no—
454C22#6384011yescharacteristic
455C22#6384412yes—
456C22#6389612yes—
457C22#6391311yescharacteristic
458C22#6397411yescharacteristic
459C4—41no—
460C4—41no—
461C4—92no—
462C4—124no—
463C4—181no—
464C4—181no—
465C4—181no—
466C4—242no—
467C4—361no—
468C4—361no—
469C3—21no—
470C3#6895512yescomplemented
471C2—22no—
472C2—21no—
473C2—21no—
474C2—22no—
475C2#1059127311yescharacteristic
476C2#1059152711yescharacteristic
477C2#1059152911yescharacteristic
subgroupG/H
centerC22#63974
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32C2×C22⋊C4
prime radical, cosocleC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#1996
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
8. C22×#634C4semidirect
11. C2×C4⋊(C3⋊Dic3)C4semidirect
12. C2×#3750C4semidirect
13. C2×#3750C4semidirect
62. C3×#217Q8semidirect
183. #217Dic6semidirect
396. C32#1996semidirect
470. C3#68955semidirect

Maximal subgroups

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

subgroupindex
C2×#640872
#105917202
#105917052
C3×#45262
#105891872
#689553