Finite Group Databasebeta

← #11784624

Subgroups — #11784624

Order 1152.

1329 conjugacy classes of subgroups.

The subgroup lattice has 595 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic
2C2×#63661C211yesmaximal, characteristic, complemented
3C2×C3×#834C211yesmaximal, characteristic, complemented
4C2×#63580C212yesmaximal, complemented
5#10591696C212yesmaximal, complemented
6#72139—31nomaximal
7#70027—31nomaximal
8C22×C32×D4C2211yescharacteristic
9C22×C3×#67C411yescharacteristic, complemented
10C22×C3×#67C2211yescharacteristic
11C23×C3×Dic3C411yescharacteristic, complemented
12C23×C3×Dic3C2211yescharacteristic
13C2×C3×#237—22no—
14C2×C3×#237—22no—
15C2×C3×#237—24no—
16C2×C3×#237—24no—
17C22×C3×C4×D3C411yescharacteristic, complemented
18C22×C3×Dic6C411yescharacteristic, complemented
19C2×#3757C2212yes—
20C2×C3×#217C2212yes—
21#63661—22no—
22C3×#834—22no—
23#63580—24no—
24#63579—24no—
25C22×C3×#41—31no—
26C22×#237D311yescharacteristic
27C2×C3×#99—31no—
28C2×#834—31no—
29C2×#834—31no—
30C2×#834—32no—
31C2×#834—61no—
32C2×#834D311yescharacteristic, complemented
33#5211—32no—
34C2×#806—32no—
35#4943—32no—
36C24×C32C2×C411yescharacteristic
37C24×C32C2311yescharacteristic
38C23×C3×D3C2×C411yescharacteristic
39C2×C32×D4—22no—
40C2×C32×D4—22no—
41C2×C32×D4D412yes—
42C2×C32×D4D412yes—
43C22×C32×C4C2×C411yescharacteristic
44C22×C3⋊Dic3—22no—
45C2×C3×#67—22no—
46C2×C3×#67—21no—
47C2×C3×#67—22no—
48C2×C3×#67—21no—
49C2×C3×#67—22no—
50C2×C3×#67—22no—
51C2×C3×#67D414yes—
52C22×C3×Dic3—22no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3—22no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3—22no—
57C22×C3×Dic3—22no—
58C22×C3×Dic3—22no—
59C22×C3×Dic3C2×C411yescharacteristic
60C22×C3×Dic3C2×C411yescharacteristic
61C22×C3×Dic3C2×C411yescharacteristic
62C22×C3×Dic3D414yes—
63C3×#237—216no—
64C3×#237—216no—
65C2×C3×C4×D3—22no—
66C2×C3×C4×D3—22no—
67C2×C3×C4×D3—22no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6—22no—
71#3757—22no—
72#3757—22no—
73C3×#217—22no—
74C3×#217—22no—
75#1782—91noSylow
76C2×C3×#41—64no—
77C2×C3×#41—64no—
78C2×C3×#41—62no—
79C2×C3×#41—62no—
80C22×C3×Q8—31no—
81C22×C3×D4—21no—
82C22×C3×D4—31no—
83C22×C3×D4—31no—
84C22×C3×D4C2×D311yescharacteristic
85C22×C3×D4C2×D311yescharacteristic
86C23×C3×C4—31no—
87C23×C3×C4—31no—
88C23×C3×C4—31no—
89C22×#67Dic311yescharacteristic, complemented
90C22×#67C2×D311yescharacteristic
91C23×Dic3Dic311yescharacteristic, complemented
92C23×Dic3C2×D311yescharacteristic
93C2×#237—22no—
94C2×#237—22no—
95C2×#237—24no—
96C2×#237—24no—
97C22×C4×D3Dic311yescharacteristic, complemented
98C22×Dic6Dic311yescharacteristic, complemented
99C2×C3×C22⋊C4—32no—
100C2×#217—32no—
101C2×#217—32no—
102C2×#217—62no—
103C2×#217C2×D312yes—
104C3×#99—62no—
105#834—22no—
106#834—64no—
107#834—64no—
108#834—62no—
109#834—62no—
110C3⋊#95—64no—
111C3⋊#95—64no—
112#806—64no—
113C23×C32—21no—
114C23×C32—21no—
115C23×C32—42no—
116C23×C32—42no—
117C23×C32C22⋊C412yes—
118C23×C32C22×C411yescharacteristic
119C23×C32C2×D411yescharacteristic
120C23×C32C2×D412yes—
121C23×C32C2×D412yes—
122C23×C32C2×D411yescharacteristic
123C22×C3×D3—21no—
124C22×C3×D3—21no—
125C22×C3×D3—42no—
126C22×C3×D3C22⋊C412yes—
127C32×D4—24no—
128C32×D4—24no—
129C2×C32×C4—21no—
130C2×C32×C4—21no—
131C2×C32×C4C22⋊C412yes—
132C2×C3⋊Dic3—42no—
133C2×C3⋊Dic3—44no—
134C3×#67—28no—
135C3×#67—24no—
136C3×#67—24no—
137C2×C3×Dic3—28no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—24no—
145C2×C3×Dic3—24no—
146C2×C3×Dic3—44no—
147C2×C3×Dic3—42no—
148C2×C3×Dic3C22⋊C412yes—
149C2×C3×Dic3C22⋊C412yes—
150C2×C3×Dic3C22⋊C412yes—
151C3×C4×D3—28no—
152C3×Dic6—28no—
153C22×#41—31no—
154C2×#99—31no—
155C2×#99—92no—
156C2×#99—91no—
157#381—92no—
158C24×C3—21no—
159C24×C3—21no—
160C24×C3—31no—
161C24×C3C4×D311yescharacteristic
162C24×C3C2×Dic311yescharacteristic
163C24×C3C22×D311yescharacteristic
164C24×C3C22×D311yescharacteristic
165C23×D3C2×Dic311yescharacteristic
166C3×#41—616no—
167C3×#41—616no—
168C2×C3×Q8—62no—
169C2×C3×Q8—62no—
170C2×C3×Q8—62no—
171C2×C3×D4—22no—
172C2×C3×D4—22no—
173C2×C3×D4—22no—
174C2×C3×D4—22no—
175C2×C3×D4—22no—
176C2×C3×D4—22no—
177C2×C3×D4—34no—
178C2×C3×D4—42no—
179C2×C3×D4—42no—
180C2×C3×D4—62no—
181C2×C3×D4—62no—
182C2×C3×D4—62no—
183C2×C3×D4—61no—
184C2×C3×D4—62no—
185C2×C3×D4—61no—
186C2×C3×D4D1212yes—
187C2×C3×D4#6712yes—
188C2×C3×D4#6712yes—
189C2×C3×D4#6712yes—
190C22×C3×C4—21no—
191C22×C3×C4—31no—
192C22×C3×C4—31no—
193C22×C3×C4—31no—
194C22×C3×C4—34no—
195C22×C3×C4—62no—
196C22×C3×C4—62no—
197C22×C3×C4—62no—
198C22×C3×C4—62no—
199C22×C3×C4—62no—
200C22×C3×C4—61no—
201C22×C3×C4—62no—
202C22×C3×C4—61no—
203C22×C3×C4—62no—
204C22×C3×C4—62no—
205C22×C3×C4C4×D311yescharacteristic
206C22×C3×C4C2×Dic311yescharacteristic
207C2×#67—22no—
208C2×#67—21no—
209C2×#67—21no—
210C2×#67—22no—
211C2×#67—22no—
212C2×#67—22no—
213C2×#67#6714yes—
214C22×Dic3—22no—
215C22×Dic3—21no—
216C22×Dic3—21no—
217C22×Dic3—22no—
218C22×Dic3—22no—
219C22×Dic3—22no—
220C22×Dic3—22no—
221C22×Dic3—62no—
222C22×Dic3—62no—
223C22×Dic3—122no—
224C22×Dic3C2×Dic311yescharacteristic
225C22×Dic3C2×Dic311yescharacteristic
226C22×Dic3C2×Dic311yescharacteristic
227C22×Dic3#6714yes—
228#237—216no—
229#237—216no—
230C2×C4×D3—22no—
231C2×C4×D3—22no—
232C2×C4×D3—22no—
233C2×Dic6—22no—
234C2×Dic6—22no—
235C2×Dic6—22no—
236C3×C22⋊C4—62no—
237C3×C22⋊C4—62no—
238#217—22no—
239#217—22no—
240#217—64no—
241#217—62no—
242#217—62no—
243#217—62no—
244#217—62no—
245#217—122no—
246C22×C32—24no—
247C22×C32—22no—
248C22×C32—22no—
249C22×C32—41no—
250C22×C32—42no—
251C22×C32—41no—
252C22×C32—42no—
253C22×C32—42no—
254C22×C32—42no—
255C22×C32C2×C22⋊C411yescharacteristic
256C22×C32C2×C22⋊C411yescharacteristic
257C22×C32C2×C22⋊C411yescharacteristic
258C22×C32#12012yes—
259C22×C32#12012yes—
260C2×C3×D3—22no—
261C2×C3×D3—42no—
262C2×C3×D3—42no—
263C2×C3×D3—42no—
264C32×C4—22no—
265C3⋊Dic3—82no—
266C3×Dic3—22no—
267C3×Dic3—22no—
268C3×Dic3—22no—
269C3×Dic3—82no—
270C2×#41—64no—
271C2×#41—64no—
272C2×#41—62no—
273C2×#41—62no—
274C22×Q8—31no—
275C22×D4—31no—
276C22×D4—31no—
277C22×D4D3211yescharacteristic
278C23×C4—31no—
279C23×C4—31no—
280C23×C4—31no—
281C2×C22⋊C4—32no—
282C2×C22⋊C4—92no—
283#99—62no—
284#99—184no—
285#99—182no—
286#95—184no—
287C23×C3—21no—
288C23×C3—21no—
289C23×C3—21no—
290C23×C3—21no—
291C23×C3—22no—
292C23×C3—21no—
293C23×C3—21no—
294C23×C3—21no—
295C23×C3—22no—
296C23×C3—22no—
297C23×C3—32no—
298C23×C3—41no—
299C23×C3—41no—
300C23×C3—42no—
301C23×C3—42no—
302C23×C3—42no—
303C23×C3—42no—
304C23×C3—61no—
305C23×C3—61no—
306C23×C3—82no—
307C23×C3—82no—
308C23×C3—122no—
309C23×C3(C2×D3)⋊C412yes—
310C23×C3#21712yes—
311C23×C3C2×C4×D311yescharacteristic
312C23×C3C2×D1211yescharacteristic
313C23×C3D3×D412yes—
314C23×C3D3×D412yes—
315C23×C3C22×Dic311yescharacteristic
316C23×C3C2×#6711yescharacteristic
317C23×C3C2×#6711yescharacteristic
318C23×C3C2×#6711yescharacteristic
319C23×C3C2×#6712yes—
320C23×C3C2×#6712yes—
321C22×D3—21no—
322C22×D3—21no—
323C22×D3—42no—
324C22×D3#21712yes—
325C3×Q8—68no—
326C3×D4—24no—
327C3×D4—24no—
328C3×D4—24no—
329C3×D4—24no—
330C3×D4—44no—
331C3×D4—44no—
332C3×D4—68no—
333C3×D4—64no—
334C3×D4—64no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—22no—
340C2×C3×C4—32no—
341C2×C3×C4—32no—
342C2×C3×C4—32no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—68no—
346C2×C3×C4—68no—
347C2×C3×C4—61no—
348C2×C3×C4—61no—
349C2×C3×C4—61no—
350C2×C3×C4—64no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—61no—
354C2×C3×C4—64no—
355C2×C3×C4—124no—
356C2×C3×C4—122no—
357C2×C3×C4(C2×D3)⋊C412yes—
358C2×C3×C4#21712yes—
359#67—28no—
360#67—24no—
361#67—24no—
362C2×Dic3—28no—
363C2×Dic3—21no—
364C2×Dic3—21no—
365C2×Dic3—21no—
366C2×Dic3—21no—
367C2×Dic3—21no—
368C2×Dic3—21no—
369C2×Dic3—24no—
370C2×Dic3—24no—
371C2×Dic3—44no—
372C2×Dic3—42no—
373C2×Dic3—124no—
374C2×Dic3—124no—
375C2×Dic3—124no—
376C2×Dic3—122no—
377C2×Dic3—122no—
378C2×Dic3—244no—
379C2×Dic3#21712yes—
380C2×Dic3#21712yes—
381C2×Dic3#21712yes—
382C4×D3—28no—
383Dic6—28no—
384C2×C32—22no—
385C2×C32—22no—
386C2×C32—21no—
387C2×C32—21no—
388C2×C32—42no—
389C2×C32#37911yescharacteristic
390C2×C32#41012yes—
391C3×D3—42no—
392C24—31no—
393C24D3×Dic311yescharacteristic
394C24C2×D3211yescharacteristic
395#41—616no—
396#41—616no—
397C2×Q8—62no—
398C2×Q8—62no—
399C2×Q8—62no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—34no—
403C2×D4—62no—
404C2×D4—62no—
405C2×D4—62no—
406C2×D4—61no—
407C2×D4—61no—
408C2×D4—62no—
409C2×D4#62512yes—
410C2×D4#62612yes—
411C22×C4—31no—
412C22×C4—31no—
413C22×C4—31no—
414C22×C4—34no—
415C22×C4—62no—
416C22×C4—62no—
417C22×C4—62no—
418C22×C4—62no—
419C22×C4—62no—
420C22×C4—61no—
421C22×C4—61no—
422C22×C4—62no—
423C22×C4—62no—
424C22×C4—62no—
425C22×C4—182no—
426C22×C4D3×Dic311yescharacteristic
427C22⋊C4—62no—
428C22⋊C4—62no—
429C22⋊C4—182no—
430C22⋊C4—182no—
431C22×C3—24no—
432C22×C3—22no—
433C22×C3—24no—
434C22×C3—22no—
435C22×C3—22no—
436C22×C3—22no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—22no—
441C22×C3—22no—
442C22×C3—44no—
443C22×C3—42no—
444C22×C3—42no—
445C22×C3—41no—
446C22×C3—42no—
447C22×C3—41no—
448C22×C3—41no—
449C22×C3—41no—
450C22×C3—42no—
451C22×C3—42no—
452C22×C3—42no—
453C22×C3—42no—
454C22×C3—42no—
455C22×C3—42no—
456C22×C3—42no—
457C22×C3—62no—
458C22×C3—82no—
459C22×C3—81no—
460C22×C3—81no—
461C22×C3—82no—
462C22×C3—82no—
463C22×C3—82no—
464C22×C3—122no—
465C22×C3—122no—
466C22×C3—122no—
467C22×C3D3×C22⋊C411yescharacteristic
468C22×C3D3×C22⋊C411yescharacteristic
469C22×C3#88212yes—
470C22×C3C2×(C2×D3)⋊C411yescharacteristic
471C22×C3#93712yes—
472C22×C3C2×#21711yescharacteristic
473C22×C3C2×#21711yescharacteristic
474C22×C3C2×#21711yescharacteristic
475C22×C3#95312yes—
476C22×C3#95312yes—
477C2×D3—22no—
478C2×D3—42no—
479C2×D3—42no—
480C2×D3—42no—
481C3×C4—22no—
482C3×C4—22no—
483C3×C4—42no—
484C3×C4—62no—
485C3×C4—62no—
486C3×C4—62no—
487C3×C4—242no—
488Dic3—22no—
489Dic3—22no—
490Dic3—22no—
491Dic3—82no—
492Dic3—242no—
493Dic3—242no—
494Dic3—244no—
495C32#178211yescharacteristic, complemented, Sylow
496C23—21no—
497C23—21no—
498C23—32no—
499C23—42no—
500C23—42no—
501C23—61no—
502C23—61no—
503C23—122no—
504C23(C2×D3)⋊Dic312yes—
505C23C2×D3×Dic311yescharacteristic
506C23C2×#62511yescharacteristic
507C23C2×#62611yescharacteristic
508C23D3×#6712yes—
509C23D3×#6712yes—
510Q8—68no—
511D4—24no—
512D4—24no—
513D4—68no—
514D4—64no—
515D4—64no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—32no—
519C2×C4—32no—
520C2×C4—32no—
521C2×C4—68no—
522C2×C4—68no—
523C2×C4—61no—
524C2×C4—61no—
525C2×C4—61no—
526C2×C4—61no—
527C2×C4—61no—
528C2×C4—61no—
529C2×C4—64no—
530C2×C4—64no—
531C2×C4—124no—
532C2×C4—122no—
533C2×C4—364no—
534C2×C4—362no—
535C2×C4(C2×D3)⋊Dic312yes—
536C2×C3—22no—
537C2×C3—22no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—22no—
541C2×C3—22no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—22no—
545C2×C3—21no—
546C2×C3—42no—
547C2×C3—41no—
548C2×C3—41no—
549C2×C3—42no—
550C2×C3—42no—
551C2×C3—42no—
552C2×C3—82no—
553C2×C3—122no—
554C2×C3#474012yes—
555C2×C3#495511yescharacteristic
556C2×C3#524012yes—
557C2×C3#524711yescharacteristic
558D3—42no—
559C22—24no—
560C22—22no—
561C22—22no—
562C22—41no—
563C22—41no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—42no—
568C22—62no—
569C22—122no—
570C22—122no—
571C22—122no—
572C22C2×(C2×D3)⋊Dic311yescharacteristic
573C22D3×#21711yescharacteristic
574C22D3×#21711yescharacteristic
575C22#6397612yes—
576C22#6397712yes—
577C4—22no—
578C4—62no—
579C4—62no—
580C4—62no—
581C4—242no—
582C4—722no—
583C3—21no—
584C3#7002711yescharacteristic, complemented
585C3#7213911yescharacteristic, complemented
586C2—22no—
587C2—22no—
588C2—21no—
589C2—21no—
590C2—42no—
591C2—122no—
592C2#1059152812yes—
593C2#1059170611yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC22×C32×D4C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×#237C2
cosocleC24×C32C23
hypercenterC22×D4D32
hypocenterC32#1782
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63661C2semidirect
3. C2×C3×#834C2semidirect
4. C2×#63580C2semidirect
5. #10591696C2semidirect
9. C22×C3×#67C4semidirect
11. C23×C3×Dic3C4semidirect
17. C22×C3×C4×D3C4semidirect
18. C22×C3×Dic6C4semidirect
32. C2×#834D3semidirect
89. C22×#67Dic3semidirect
91. C23×Dic3Dic3semidirect
97. C22×C4×D3Dic3semidirect
98. C22×Dic6Dic3semidirect
495. C32#1782semidirect
584. C3#70027semidirect
585. C3#72139semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C2×#636612
C2×C3×#8342
C2×#635802
#105916962
#721393
#700273