Finite Group Databasebeta

← #11784805

Subgroups — #11784805

Order 1152.

1365 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 1365 conjugacy classes of subgroups — too many to draw. Only its 156 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×#64306C211yesmaximal, characteristic
2C4×#3752C211yesmaximal, characteristic, complemented
3C2×C3×#805C212yesmaximal, complemented
4C2×#63568C212yesmaximal, complemented
5#10591074C211yesmaximal, characteristic, complemented
6#70380—32nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C3×#235C2212yes—
9C2×#3811—21no—
10C2×#3805—21no—
11#64306—24no—
12#64306—24no—
13C2×#3802C411yescharacteristic, complemented
14C2×C4×D32—21no—
15C2×#3798—21no—
16C2×#3797C411yescharacteristic, complemented
17C2×#3796C412yescomplemented
18C2×C32×C42C2211yescharacteristic, complemented
19C2×#3752—21no—
20C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
21C2×C3×#208C2212yescomplemented
22#63658—21no—
23C3×#805—24no—
24#63568—24no—
25#63557—21no—
26#63557—21no—
27C2×D3×#41—32no—
28C2×C3×#104—32no—
29C2×#837—32no—
30C2×#825—32no—
31#5126—32no—
32C4×(C2×D3)⋊C4—32no—
33C4×(C2×D3)⋊C4—61no—
34C2×#805D312yescomplemented
35C23×C3⋊D3D411yescharacteristic
36C22×D32—21no—
37C22×C32×C4—21no—
38C22×C32×C4C2311yescharacteristic
39C22×C3⋊Dic3—21no—
40C22×C3⋊Dic3D411yescharacteristic
41C2×C4×C3⋊D3—22no—
42C2×C4×C3⋊D3—22no—
43C2×C4×C3⋊D3C2×C411yescharacteristic
44C2×C4×C3⋊D3C2×C411yescharacteristic
45C2×C4×C3⋊D3D411yescharacteristic
46C2×C4×C3⋊D3D411yescharacteristic
47C2×C3×#67—22no—
48C3×#235—22no—
49C3×#235—22no—
50C3×#235D414yes—
51C3×#235D414yes—
52C2×C3×D12C2×C412yes—
53C2×C3×C4×D3—22no—
54C2×C3×Dic6C2×C412yes—
55#3811—24no—
56#3811—24no—
57C2×#627—21no—
58C2×#626—22no—
59C2×#625—21no—
60C2×#624—21no—
61#3805—24no—
62#3805—24no—
63C2×D3×Dic3—22no—
64#3802—24no—
65C4×D32—28no—
66#3798—28no—
67#3797—24no—
68#3796—24no—
69#3796—24no—
70C32×C42—22no—
71#3752—24no—
72C4×C3⋊Dic3—22no—
73C3×#208—22no—
74C3×#208—22no—
75C2×C3×C3⋊C8—22no—
76#1789—91noSylow
77C2×C3×#41—32no—
78D3×#41—64no—
79D3×#41—64no—
80D3×#41—64no—
81D3×#41—64no—
82C2×#239—32no—
83C2×D3×Q8—32no—
84C2×#237—32no—
85C2×#237—62no—
86C2×D3×D4—32no—
87C2×D3×D4—62no—
88C2×#235—62no—
89C2×#235C2×D312yes—
90C22×C4×D3—32no—
91C22×C4×D3—61no—
92C22×C4×D3—62no—
93C2×C3×M16—32no—
94C2×C3×C42—21no—
95C2×C3×C42C2×D312yescomplemented
96C2×(C2×D3)⋊C4—62no—
97C2×(C2×D3)⋊C4—62no—
98C2×C4×Dic3—32no—
99C2×C4×Dic3—61no—
100C2×#208C2×D312yescomplemented
101C3×#104—64no—
102#837—64no—
103C3⋊#95—62no—
104C3⋊#95—62no—
105#825—64no—
106(C2×D3)⋊C8—62no—
107(C2×D3)⋊C8—62no—
108#805—24no—
109C23×C32C2×D411yescharacteristic
110C22×C3⋊D3—22no—
111C22×C3⋊D3—21no—
112C22×C3⋊D3—21no—
113C22×C3⋊D3—41no—
114C22×C3⋊D3C22⋊C411yescharacteristic
115C22×C3⋊D3C22⋊C411yescharacteristic
116C22×C3×D3—22no—
117C2×D32—24no—
118C2×D32—42no—
119C2×D32—42no—
120C2×C32×C4—22no—
121C2×C32×C4—41no—
122C2×C32×C4—41no—
123C2×C32×C4C22×C411yescharacteristic
124C2×C32×C4C2×D412yes—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D412yes—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—41no—
131C2×C3⋊Dic3—41no—
132C2×C3⋊Dic3C22⋊C411yescharacteristic
133C2×C3⋊Dic3C22⋊C411yescharacteristic
134C4×C3⋊D3—22no—
135C4×C3⋊D3—22no—
136C4×C3⋊D3—22no—
137C4×C3⋊D3—22no—
138C3×#67—24no—
139C3×#67—24no—
140C2×C3×Dic3—22no—
141C3×D12—22no—
142C3×D12C22⋊C414yescomplemented
143C3×C4×D3—24no—
144C3×C4×D3—24no—
145C3×Dic6—22no—
146C3×Dic6C22⋊C414yescomplemented
147#627—24no—
148#626—28no—
149#625—24no—
150#624—24no—
151D3×Dic3—28no—
152C3×C3⋊C8—42no—
153C22×#41—91no—
154C2×#104—32no—
155C2×#104—92no—
156#407—91no—
157C4×C22⋊C4—91no—
158C23×D3—32no—
159C23×D3—61no—
160C23×D3—62no—
161C3×#41—34no—
162C3×#41—34no—
163C3×#41—62no—
164C3×#41—62no—
165C2×C3×Q8—32no—
166C2×C3×D4—32no—
167C2×C3×D4—62no—
168C22×C3×C4—22no—
169C22×C3×C4—22no—
170C22×C3×C4—21no—
171C22×C3×C4—62no—
172C22×C3×C4C22×D312yes—
173C2×#67—22no—
174C2×#67—62no—
175C2×#67—62no—
176C22×Dic3—32no—
177C22×Dic3—61no—
178C22×Dic3—62no—
179C22×Dic3—62no—
180C22×Dic3—62no—
181#239—64no—
182#239—64no—
183D3×Q8—64no—
184D3×Q8—64no—
185#237—64no—
186#237—68no—
187#237—68no—
188#237—64no—
189D3×D4—64no—
190D3×D4—68no—
191D3×D4—68no—
192D3×D4—64no—
193#235—22no—
194#235—22no—
195#235—68no—
196#235—68no—
197#235D1214yes—
198#235#6714yes—
199C2×D12—62no—
200C2×D12C4×D312yes—
201C2×C4×D3—22no—
202C2×C4×D3—32no—
203C2×C4×D3—32no—
204C2×C4×D3—32no—
205C2×C4×D3—32no—
206C2×C4×D3—61no—
207C2×C4×D3—61no—
208C2×C4×D3—61no—
209C2×C4×D3—61no—
210C2×C4×D3—68no—
211C2×C4×D3—68no—
212C2×C4×D3—62no—
213C2×C4×D3—62no—
214C2×C4×D3—62no—
215C2×C4×D3—62no—
216C2×C4×D3—62no—
217C2×C4×D3—62no—
218C2×C4×D3—122no—
219C2×C4×D3—122no—
220C2×Dic6—62no—
221C2×Dic6C4×D312yes—
222C3×M16—62no—
223C3×M16—62no—
224C2×C3×C8—62no—
225C3×C42—22no—
226C3×C42—22no—
227C3×C42—42no—
228(C2×D3)⋊C4—68no—
229(C2×D3)⋊C4—68no—
230C4×Dic3—62no—
231C4×Dic3—62no—
232C4×Dic3—122no—
233#208—22no—
234#208—22no—
235C2×C3⋊C8—22no—
236C22×C32—21no—
237C22×C32—21no—
238C22×C32C2×C22⋊C411yescharacteristic
239C22×C32#12011yescharacteristic
240C22×C32#12011yescharacteristic
241C2×C3⋊D3—21no—
242C2×C3⋊D3—21no—
243C2×C3⋊D3—21no—
244C2×C3⋊D3—21no—
245C2×C3⋊D3—21no—
246C2×C3⋊D3—42no—
247C2×C3⋊D3—42no—
248C2×C3⋊D3#10412yescomplemented
249C2×C3×D3—24no—
250C2×C3×D3—42no—
251C2×C3×D3—42no—
252D32—48no—
253C32×C4—42no—
254C32×C4C2×C22⋊C412yes—
255C32×C4#12012yes—
256C3⋊Dic3—21no—
257C3⋊Dic3—21no—
258C3⋊Dic3—42no—
259C3×Dic3—24no—
260C2×#41—32no—
261C2×#41—92no—
262C2×#41—181no—
263C2×#41—181no—
264C2×#41—184no—
265C2×#41—184no—
266C22×Q8—91no—
267C22×D4—91no—
268C22×D4—181no—
269C23×C4—91no—
270C23×C4—181no—
271C2×M16—32no—
272C2×C22⋊C4—181no—
273C2×C42—91no—
274C2×C42D3211yescharacteristic, complemented
275#104—64no—
276#104—184no—
277C22⋊C8—181no—
278C22⋊C8—181no—
279#95—181no—
280C23×C3—21no—
281C23×C3—62no—
282C23×C3D3×D412yes—
283C22×D3—22no—
284C22×D3—32no—
285C22×D3—32no—
286C22×D3—61no—
287C22×D3—61no—
288C22×D3—68no—
289C22×D3—64no—
290C22×D3—64no—
291C22×D3—62no—
292C22×D3—62no—
293C22×D3—121no—
294C22×D3—121no—
295C22×D3—124no—
296C22×D3—124no—
297C22×D3—122no—
298C22×D3—122no—
299C3×Q8—34no—
300C3×Q8—62no—
301C3×D4—34no—
302C3×D4—64no—
303C3×D4—64no—
304C3×D4—62no—
305C2×C3×C4—24no—
306C2×C3×C4—24no—
307C2×C3×C4—21no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—22no—
311C2×C3×C4—42no—
312C2×C3×C4—42no—
313C2×C3×C4—42no—
314C2×C3×C4—42no—
315C2×C3×C4—62no—
316C2×C3×C4—64no—
317C2×C3×C4—64no—
318C2×C3×C4C2×C4×D312yes—
319C2×C3×C4C2×D1212yes—
320C2×C3×C4D3×D412yes—
321C2×C3×C4D3×D412yes—
322C2×C3×C4D3×D412yes—
323C2×C3×C4C2×#6712yes—
324#67—24no—
325#67—24no—
326#67—68no—
327#67—68no—
328C2×Dic3—22no—
329C2×Dic3—32no—
330C2×Dic3—32no—
331C2×Dic3—61no—
332C2×Dic3—61no—
333C2×Dic3—68no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—64no—
337C2×Dic3—64no—
338C2×Dic3—121no—
339C2×Dic3—121no—
340C2×Dic3—122no—
341C2×Dic3—122no—
342C2×Dic3—122no—
343C2×Dic3—122no—
344D12—22no—
345D12—68no—
346D12(C2×D3)⋊C414yescomplemented
347C4×D3—24no—
348C4×D3—24no—
349C4×D3—68no—
350C4×D3—68no—
351C4×D3—62no—
352C4×D3—62no—
353C4×D3—62no—
354C4×D3—62no—
355C4×D3—62no—
356C4×D3—62no—
357C4×D3—62no—
358C4×D3—62no—
359C4×D3—122no—
360C4×D3—122no—
361C4×D3—122no—
362C4×D3—122no—
363Dic6—22no—
364Dic6—68no—
365Dic6(C2×D3)⋊C414yescomplemented
366C3×C8—122no—
367C3⋊C8—42no—
368C2×C32—21no—
369C2×C32—21no—
370C2×C32#37911yescharacteristic
371C2×C32C2×#10411yescharacteristic
372C2×C32#42111yescharacteristic
373C3⋊D3—22no—
374C3⋊D3—41no—
375C3×D3—44no—
376C24—91no—
377C24—181no—
378#41—34no—
379#41—34no—
380#41—62no—
381#41—62no—
382#41—188no—
383#41—184no—
384#41—184no—
385#41—184no—
386#41—184no—
387C2×Q8—32no—
388C2×Q8—181no—
389C2×Q8—184no—
390C2×D4—32no—
391C2×D4—62no—
392C2×D4—182no—
393C2×D4—181no—
394C2×D4—184no—
395C2×D4—184no—
396C2×D4—184no—
397C22×C4—21no—
398C22×C4—62no—
399C22×C4—91no—
400C22×C4—91no—
401C22×C4—91no—
402C22×C4—91no—
403C22×C4—91no—
404C22×C4—181no—
405C22×C4—188no—
406C22×C4—182no—
407C22×C4—182no—
408C22×C4—182no—
409C22×C4—181no—
410C22×C4C2×D3211yescharacteristic
411M16—62no—
412M16—62no—
413C2×C8—62no—
414C22⋊C4—184no—
415C42—22no—
416C42—182no—
417C22×C3—22no—
418C22×C3—22no—
419C22×C3—22no—
420C22×C3—22no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—64no—
425C22×C3—122no—
426C22×C3—122no—
427C22×C3D3×C22⋊C412yes—
428C22×C3#88212yes—
429C22×C3#93712yes—
430C2×D3—24no—
431C2×D3—34no—
432C2×D3—42no—
433C2×D3—42no—
434C2×D3—62no—
435C2×D3—62no—
436C2×D3—62no—
437C2×D3—62no—
438C2×D3—62no—
439C2×D3—62no—
440C2×D3—62no—
441C2×D3—121no—
442C2×D3—121no—
443C2×D3—121no—
444C2×D3—121no—
445C2×D3—1216no—
446C2×D3—124no—
447C2×D3—124no—
448C2×D3—124no—
449C2×D3—124no—
450C3×C4—22no—
451C3×C4—22no—
452C3×C4—44no—
453C3×C4—44no—
454C3×C4—64no—
455C3×C4D3×C22⋊C412yes—
456C3×C4#88212yes—
457C3×C4C2×(C2×D3)⋊C412yes—
458C3×C4#93712yes—
459Dic3—24no—
460Dic3—62no—
461Dic3—62no—
462Dic3—121no—
463Dic3—121no—
464Dic3—124no—
465Dic3—124no—
466C32#178911yescharacteristic, complemented, Sylow
467C23—62no—
468C23—91no—
469C23—91no—
470C23—182no—
471C23—184no—
472C23—181no—
473C23—181no—
474C23—361no—
475C23—362no—
476C23—362no—
477C23#381111yescharacteristic
478Q8—34no—
479Q8—62no—
480Q8—184no—
481D4—34no—
482D4—64no—
483D4—64no—
484D4—62no—
485D4—188no—
486D4—184no—
487C2×C4—22no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—62no—
491C2×C4—64no—
492C2×C4—64no—
493C2×C4—91no—
494C2×C4—91no—
495C2×C4—184no—
496C2×C4—188no—
497C2×C4—181no—
498C2×C4—181no—
499C2×C4—182no—
500C2×C4—182no—
501C2×C4—182no—
502C2×C4—182no—
503C2×C4—182no—
504C2×C4—361no—
505C2×C4—361no—
506C2×C4C4×D3211yescharacteristic
507C2×C4D3×D1212yes—
508C2×C4#380211yescharacteristic
509C2×C4D3×#6712yes—
510C8—122no—
511C2×C3—22no—
512C2×C3—22no—
513C2×C3—22no—
514C2×C3—22no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—124no—
519C2×C3D3×#10412yes—
520C2×C3#482112yes—
521C2×C3#495512yes—
522D3—44no—
523D3—64no—
524D3—122no—
525D3—122no—
526D3—122no—
527C22—21no—
528C22—21no—
529C22—64no—
530C22—92no—
531C22—122no—
532C22—122no—
533C22—181no—
534C22—181no—
535C22—181no—
536C22—181no—
537C22—181no—
538C22—362no—
539C22—362no—
540C22—368no—
541C22#6392111yescharacteristic
542C22#6392311yescharacteristic
543C22#6398311yescharacteristic
544C4—42no—
545C4—64no—
546C4—181no—
547C4—181no—
548C4—362no—
549C4D3×(C2×D3)⋊C412yes—
550C4#6392212yes—
551C3—21no—
552C3#7038012yescomplemented
553C2—21no—
554C2—21no—
555C2—124no—
556C2—182no—
557C2—361no—
558C2#1059039311yescharacteristic
559C2#1059039411yescharacteristic
560C2#1059139911yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#64306C2
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1789
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C4×#3752C2semidirect
3. C2×C3×#805C2semidirect
4. C2×#63568C2semidirect
5. #10591074C2semidirect
13. C2×#3802C4semidirect
16. C2×#3797C4semidirect
17. C2×#3796C4semidirect
18. C2×C32×C42C22semidirect
20. C2×C4×C3⋊Dic3C22semidirect
21. C2×C3×#208C22semidirect
34. C2×#805D3semidirect
95. C2×C3×C42C2×D3semidirect
100. C2×#208C2×D3semidirect
142. C3×D12C22⋊C4semidirect
146. C3×Dic6C22⋊C4semidirect
248. C2×C3⋊D3#104semidirect
274. C2×C42D32semidirect
346. D12(C2×D3)⋊C4semidirect
365. Dic6(C2×D3)⋊C4semidirect
466. C32#1789semidirect
552. C3#70380semidirect

Maximal subgroups

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

subgroupindex
C2×#643062
C4×#37522
C2×C3×#8052
C2×#635682
#105910742
#703803