Finite Group Databasebeta

← #11790840

Subgroups — #11790840

Order 1152.

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

normal subgroups only

This group has 933 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×#63980C211yesmaximal, characteristic
2#10592641C211yesmaximal, characteristic, complemented
3C2×C3×#806C212yesmaximal, complemented
4#10591705C211yesmaximal, characteristic, complemented
5C2×#63580C212yesmaximal, complemented
6#70030—32nomaximal
7C23×C3⋊Dic3C2211yescharacteristic
8C22×C3×#67C2212yes—
9C22×#625C411yescharacteristic, complemented
10C2×C32×C22⋊C4C2211yescharacteristic
11C2×#3757C2211yescharacteristic
12C2×#3750—21no—
13C2×C3×#217C2212yes—
14#63980—21no—
15#63980—21no—
16#63980—21no—
17#63980—21no—
18C2×#3724C411yescharacteristic, complemented
19C2×(C2×D3)⋊Dic3C412yescomplemented
20C2×Dic32—21no—
21#63658—21no—
22C3×#806—24no—
23#63580—24no—
24#63579—21no—
25C2×#939—32no—
26C2×C3×#99—32no—
27C2×#834—32no—
28C2×#806—32no—
29C2×#806D312yescomplemented
30#4942—32no—
31#4942—61no—
32Dic3×C22⋊C4—32no—
33C24×C32C2311yescharacteristic
34C23×C3×D3C2×C412yes—
35C22×C32×C4—21no—
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3—42no—
38C22×C3⋊Dic3C2×C411yescharacteristic
39C22×C3⋊Dic3C2×C411yescharacteristic
40C22×C3⋊Dic3D411yescharacteristic
41C22×C3⋊Dic3D411yescharacteristic
42C22×C3⋊Dic3D411yescharacteristic
43C22×C3⋊Dic3D411yescharacteristic
44C2×C3×#67—22no—
45C2×C3×#67—22no—
46C2×C3×#67—22no—
47C2×C3×#67—22no—
48C2×C3×#67—22no—
49C2×C3×#67—22no—
50C22×C3×Dic3—22no—
51C22×C3×Dic3C2×C412yes—
52C2×#625—21no—
53C2×#625—21no—
54C2×#625—42no—
55C32×C22⋊C4—22no—
56#3757—22no—
57#3750—42no—
58C3×#217—22no—
59C3×#217D414yescomplemented
60#3724—21no—
61#3724—21no—
62(C2×D3)⋊Dic3—22no—
63(C2×D3)⋊Dic3—22no—
64Dic32—42no—
65#1964—91noSylow
66C22×C3×D4—32no—
67C22×#67—32no—
68C22×#67C2×D312yes—
69C23×Dic3—32no—
70C23×Dic3—61no—
71C2×C3×C22⋊C4—21no—
72C2×C3×C22⋊C4—32no—
73C2×C3×C22⋊C4C2×D312yes—
74C2×#217—32no—
75C2×#217—32no—
76C2×#217—61no—
77C2×#217C2×D312yes—
78#939—62no—
79#939—62no—
80#939—62no—
81#939—62no—
82C2×(C2×D3)⋊C4—32no—
83C2×Dic3⋊C4—32no—
84C2×Dic3⋊C4—62no—
85C2×Dic3⋊C4—62no—
86C2×C4×Dic3—62no—
87C3×#99—64no—
88#834—64no—
89C3⋊#95—62no—
90C3⋊#95—62no—
91C3⋊#95—62no—
92#806—24no—
93#806—64no—
94C23×C32—41no—
95C23×C32—41no—
96C23×C32C22×C411yescharacteristic
97C23×C32C2×D411yescharacteristic
98C23×C32C2×D411yescharacteristic
99C23×C32C2×D412yes—
100C23×C32#4112yes—
101C22×C3×D3—22no—
102C22×C3×D3—22no—
103C22×C3×D3—22no—
104C22×C3×D3—42no—
105C22×C3×D3—42no—
106C2×C32×C4—41no—
107C2×C32×C4—41no—
108C2×C32×C4—41no—
109C2×C3⋊Dic3—22no—
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⋊Dic3—41no—
118C2×C3⋊Dic3C22⋊C411yescharacteristic
119C2×C3⋊Dic3C22⋊C411yescharacteristic
120C2×C3⋊Dic3C22⋊C411yescharacteristic
121C2×C3⋊Dic3C22⋊C411yescharacteristic
122C3×#67—42no—
123C3×#67—42no—
124C3×#67—42no—
125C3×#67—42no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—24no—
130C2×C3×Dic3—42no—
131C2×C3×Dic3—42no—
132#625—42no—
133#625—42no—
134C2×#121—91no—
135C2×#99—32no—
136C2×#99—92no—
137#380—91no—
138C4×C22⋊C4—91no—
139C24×C3—21no—
140C24×C3—32no—
141C24×C3C22×D312yes—
142C23×D3C4×D312yes—
143C2×C3×D4—62no—
144C2×C3×D4—62no—
145C2×C3×D4—62no—
146C2×C3×D4—62no—
147C2×C3×D4—62no—
148C2×C3×D4—62no—
149C22×C3×C4—22no—
150C22×C3×C4—22no—
151C22×C3×C4—32no—
152C22×C3×C4—62no—
153C2×#67—22no—
154C2×#67—22no—
155C2×#67—22no—
156C2×#67—22no—
157C2×#67—22no—
158C2×#67—22no—
159C2×#67—62no—
160C2×#67—62no—
161C2×#67—124no—
162C22×Dic3—22no—
163C22×Dic3—32no—
164C22×Dic3—32no—
165C22×Dic3—32no—
166C22×Dic3—32no—
167C22×Dic3—32no—
168C22×Dic3—32no—
169C22×Dic3—61no—
170C22×Dic3—61no—
171C22×Dic3—61no—
172C22×Dic3—61no—
173C22×Dic3—61no—
174C22×Dic3—61no—
175C22×Dic3—62no—
176C22×Dic3—62no—
177C22×Dic3—124no—
178C22×Dic3—124no—
179C22×Dic3C4×D312yes—
180C3×C22⋊C4—22no—
181C3×C22⋊C4—22no—
182C3×C22⋊C4—34no—
183C3×C22⋊C4—42no—
184C3×C22⋊C4—62no—
185#217—22no—
186#217—62no—
187#217—62no—
188#217—62no—
189#217—62no—
190#217—122no—
191#217#6714yescomplemented
192(C2×D3)⋊C4—62no—
193(C2×D3)⋊C4—62no—
194Dic3⋊C4—62no—
195Dic3⋊C4—62no—
196Dic3⋊C4—124no—
197Dic3⋊C4—124no—
198C4×Dic3—124no—
199C22×C32—21no—
200C22×C32—21no—
201C22×C32—21no—
202C22×C32—21no—
203C22×C32—21no—
204C22×C32—21no—
205C22×C32—42no—
206C22×C32—42no—
207C22×C32C2×C22⋊C411yescharacteristic
208C22×C32C4×D412yes—
209C22×C32#12112yes—
210C22×C32#12411yescharacteristic
211C22×C32#12711yescharacteristic
212C2×C3×D3—42no—
213C2×C3×D3—42no—
214C2×C3×D3—42no—
215C2×C3×D3—82no—
216C2×C3×D3—82no—
217C32×C4—81no—
218C3⋊Dic3—21no—
219C3⋊Dic3—21no—
220C3⋊Dic3—21no—
221C3⋊Dic3—81no—
222C3⋊Dic3#9912yescomplemented
223C3×Dic3—44no—
224C3×Dic3—42no—
225C22×D4—32no—
226C22×D4—91no—
227C23×C4—91no—
228#121—181no—
229#121—181no—
230#121—181no—
231#121—181no—
232C2×C4⋊C4—91no—
233C2×C4⋊C4—181no—
234C2×C22⋊C4—32no—
235C2×C22⋊C4—92no—
236C2×C22⋊C4—91no—
237C2×C22⋊C4D3211yescharacteristic
238C2×C42—181no—
239#99—64no—
240#99—184no—
241#95—181no—
242#95—181no—
243C23×C3—22no—
244C23×C3—21no—
245C23×C3—21no—
246C23×C3—22no—
247C23×C3—21no—
248C23×C3—42no—
249C23×C3—42no—
250C23×C3—42no—
251C23×C3—42no—
252C23×C3—62no—
253C23×C3—62no—
254C23×C3—62no—
255C23×C3—122no—
256C23×C3—122no—
257C23×C3C2×C4×D312yes—
258C23×C3#23512yes—
259C23×C3D3×D412yes—
260C23×C3D3×D412yes—
261C23×C3D3×D412yes—
262C23×C3#23712yes—
263C23×C3C2×#6712yes—
264C22×D3—22no—
265C22×D3—22no—
266C22×D3—22no—
267C22×D3—42no—
268C22×D3—42no—
269C3×D4—122no—
270C3×D4—122no—
271C3×D4—122no—
272C3×D4—122no—
273C2×C3×C4—42no—
274C2×C3×C4—42no—
275C2×C3×C4—42no—
276C2×C3×C4—42no—
277C2×C3×C4—42no—
278C2×C3×C4—42no—
279C2×C3×C4—62no—
280C2×C3×C4—62no—
281C2×C3×C4—64no—
282C2×C3×C4—62no—
283C2×C3×C4—122no—
284C2×C3×C4—122no—
285#67—42no—
286#67—42no—
287#67—42no—
288#67—42no—
289#67—124no—
290#67—124no—
291C2×Dic3—22no—
292C2×Dic3—22no—
293C2×Dic3—22no—
294C2×Dic3—24no—
295C2×Dic3—32no—
296C2×Dic3—32no—
297C2×Dic3—32no—
298C2×Dic3—32no—
299C2×Dic3—42no—
300C2×Dic3—42no—
301C2×Dic3—61no—
302C2×Dic3—61no—
303C2×Dic3—61no—
304C2×Dic3—61no—
305C2×Dic3—64no—
306C2×Dic3—64no—
307C2×Dic3—64no—
308C2×Dic3—64no—
309C2×Dic3—122no—
310C2×Dic3—122no—
311C2×Dic3—122no—
312C2×Dic3—122no—
313C2×Dic3—122no—
314C2×Dic3—122no—
315C2×Dic3—122no—
316C2×Dic3—122no—
317C2×Dic3—122no—
318C2×Dic3—122no—
319C2×Dic3—122no—
320C2×Dic3—122no—
321C2×Dic3—122no—
322C2×Dic3—122no—
323C2×C32—21no—
324C2×C32—21no—
325C2×C32—22no—
326C2×C32—22no—
327C2×C32#39011yescharacteristic
328C2×C32C2×#9911yescharacteristic
329C2×C32#41011yescharacteristic
330C3×D3—82no—
331C24—32no—
332C24C2×D3211yescharacteristic
333C2×D4—62no—
334C2×D4—62no—
335C2×D4—62no—
336C2×D4—62no—
337C2×D4—62no—
338C2×D4—62no—
339C2×D4—181no—
340C2×D4—181no—
341C2×D4—362no—
342C22×C4—21no—
343C22×C4—32no—
344C22×C4—62no—
345C22×C4—91no—
346C22×C4—91no—
347C22×C4—91no—
348C22×C4—91no—
349C22×C4—91no—
350C22×C4—91no—
351C22×C4—181no—
352C22×C4—362no—
353C4⋊C4—181no—
354C4⋊C4—181no—
355C4⋊C4—362no—
356C22⋊C4—22no—
357C22⋊C4—34no—
358C22⋊C4—62no—
359C22⋊C4—182no—
360C22⋊C4—182no—
361C22⋊C4—182no—
362C42—362no—
363C22×C3—22no—
364C22×C3—22no—
365C22×C3—22no—
366C22×C3—22no—
367C22×C3—22no—
368C22×C3—22no—
369C22×C3—22no—
370C22×C3—22no—
371C22×C3—22no—
372C22×C3—22no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—41no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3—41no—
380C22×C3—42no—
381C22×C3—42no—
382C22×C3—42no—
383C22×C3—42no—
384C22×C3—44no—
385C22×C3—44no—
386C22×C3—122no—
387C22×C3—122no—
388C22×C3—122no—
389C22×C3—242no—
390C22×C3—242no—
391C22×C3D3×C22⋊C412yes—
392C22×C3#67⋊C412yes—
393C22×C3#88412yes—
394C22×C3#88512yes—
395C22×C3C4×#6712yes—
396C22×C3#93912yes—
397C22×C3#94012yes—
398C2×D3—42no—
399C2×D3—42no—
400C2×D3—42no—
401C2×D3—82no—
402C2×D3—82no—
403C3×C4—82no—
404C3×C4—82no—
405C3×C4—124no—
406C3×C4—122no—
407Dic3—34no—
408Dic3—44no—
409Dic3—42no—
410Dic3—62no—
411Dic3—62no—
412Dic3—62no—
413Dic3—62no—
414Dic3—62no—
415Dic3—121no—
416Dic3—121no—
417Dic3—242no—
418Dic3—242no—
419C32#196411yescharacteristic, complemented, Sylow
420C23—41no—
421C23—41no—
422C23—62no—
423C23—62no—
424C23—62no—
425C23—122no—
426C23—122no—
427C23#379512yes—
428C23C4×D3211yescharacteristic
429C23#380211yescharacteristic
430C23D3×#6712yes—
431C23#381111yescharacteristic
432D4—122no—
433D4—122no—
434D4—122no—
435D4—122no—
436D4—362no—
437D4—362no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—62no—
442C2×C4—62no—
443C2×C4—64no—
444C2×C4—62no—
445C2×C4—91no—
446C2×C4—91no—
447C2×C4—91no—
448C2×C4—91no—
449C2×C4—122no—
450C2×C4—122no—
451C2×C4—182no—
452C2×C4—182no—
453C2×C4—182no—
454C2×C4—361no—
455C2×C4—361no—
456C2×C4—361no—
457C2×C4—361no—
458C2×C4—361no—
459C2×C4—361no—
460C2×C3—22no—
461C2×C3—22no—
462C2×C3—22no—
463C2×C3—22no—
464C2×C3—22no—
465C2×C3—22no—
466C2×C3—22no—
467C2×C3—22no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—42no—
472C2×C3—42no—
473C2×C3—242no—
474C2×C3#474012yes—
475C2×C3D3×#9912yes—
476C2×C3#495712yes—
477D3—82no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—42no—
485C22—42no—
486C22—122no—
487C22—122no—
488C22—122no—
489C22—242no—
490C22—242no—
491C22#6387912yes—
492C22#6388512yes—
493C22#6391311yescharacteristic
494C22#6392111yescharacteristic
495C22#6397911yescharacteristic
496C4—81no—
497C4—92no—
498C4—124no—
499C4—122no—
500C4—181no—
501C4—181no—
502C4—181no—
503C4—721no—
504C3—21no—
505C3#7003012yescomplemented
506C2—21no—
507C2—22no—
508C2—22no—
509C2—21no—
510C2—242no—
511C2#1059040411yescharacteristic
512C2#1059040611yescharacteristic
513C2#1059138611yescharacteristic
subgroupG/H
centerC22#63921
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#63980C2
cosocleC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#1964
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
2. #10592641C2semidirect
3. C2×C3×#806C2semidirect
4. #10591705C2semidirect
5. C2×#63580C2semidirect
9. C22×#625C4semidirect
18. C2×#3724C4semidirect
19. C2×(C2×D3)⋊Dic3C4semidirect
29. C2×#806D3semidirect
59. C3×#217D4semidirect
191. #217#67semidirect
222. C3⋊Dic3#99semidirect
419. C32#1964semidirect
505. C3#70030semidirect

Maximal subgroups

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

subgroupindex
C2×#639802
#105926412
C2×C3×#8062
#105917052
C2×#635802
#700303