Finite Group Databasebeta

← #11808796

Subgroups — #11808796

Order 1152.

1237 conjugacy classes of subgroups.

The subgroup lattice has 609 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#67⋊C4C211yesmaximal, characteristic
2C2×#63844C211yesmaximal, characteristic, complemented
3#10592646C211yesmaximal, characteristic, complemented
4C3×#4953C211yesmaximal, characteristic, complemented
5#10591708C212yesmaximal
6Dic3×#217C212yesmaximal, complemented
7#10591322C211yesmaximal, characteristic, complemented
8#10591314C211yesmaximal, characteristic, complemented
9#10591239C211yesmaximal, characteristic, complemented
10#10591237C212yesmaximal, complemented
11#10591199C212yesmaximal, complemented
12#82348—31nomaximal
13#77460—31nomaximal
14C22×#634C2211yescharacteristic
15C22×C3×#67C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C2×C32×C22⋊C4C2211yescharacteristic
19C2×#3757C2212yes—
20C2×C3×#217C2212yes—
21C2×C3×(C2×D3)⋊C4C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×Dic3⋊C4C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C3×#67⋊C4—24no—
26C2×#3724C2212yes—
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×(C2×D3)⋊Dic3C2212yes—
29C2×Dic32C2212yes—
30C2×Dic32C2212yes—
31#63844—24no—
32#63658C2212yes—
33#63658C2211yescharacteristic
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2211yescharacteristic
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×C3×C4×D4—31no—
40C2×#887—31no—
41C2×#67⋊C4D311yescharacteristic
42C2×C4×Dic6—31no—
43C3×#397—31no—
44#5222—32no—
45C4×#217—32no—
46C4×#217—32no—
47#4992—31no—
48#4985—32no—
49#4959—32no—
50#4953—31no—
51#4953D311yescharacteristic, complemented
52#4947—31no—
53#4947—31no—
54#4947—31no—
55#4947—61no—
56Dic3×C22⋊C4—32no—
57#4932—31no—
58#4673—31no—
59#4666—32no—
60#4658—32no—
61#4648—31no—
62C24×C32C2311yescharacteristic
63C23×C3×D3C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2312yes—
68C2×#634—22no—
69C2×#634—24no—
70C2×C3×#67—22no—
71C2×C3×#67—22no—
72C2×C3×#67—22no—
73C22×C3×Dic3—22no—
74C22×C3×Dic3—24no—
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2311yescharacteristic
79C22×C3×Dic3C2311yescharacteristic
80C2×C3×C4×D3—22no—
81C2×C3×C4×D3—24no—
82C32×C22⋊C4—22no—
83#3757—24no—
84C3×#217—24no—
85C3×(C2×D3)⋊C4—22no—
86C3×C4⋊Dic3—22no—
87C3×Dic3⋊C4—22no—
88C3×C4×Dic3D414yes—
89#3724—24no—
90(C2×D3)⋊Dic3—24no—
91(C2×D3)⋊Dic3—24no—
92Dic32—24no—
93Dic32—24no—
94#2398—91noSylow
95C22×C3×D4—31no—
96C23×C3×C4—31no—
97C23×C3×C4—31no—
98C22×#67C2×D311yescharacteristic
99C23×Dic3C2×D311yescharacteristic
100C22×C4×D3C2×D311yescharacteristic
101C22×Dic6—31no—
102C22×Dic6—31no—
103C22×Dic6—61no—
104C3×C4×D4—64no—
105C2×C3×C4⋊C4—31no—
106C2×C3×C4⋊C4—31no—
107C2×C3×C22⋊C4—21no—
108C2×C3×C22⋊C4—32no—
109C2×C3×C22⋊C4—31no—
110C2×C3×C22⋊C4C2×D311yescharacteristic
111C2×C3×C22⋊C4C2×D311yescharacteristic
112C2×C3×C42—31no—
113C2×#217—32no—
114C2×#217—32no—
115C2×#217—32no—
116C2×#217—32no—
117C2×#217—62no—
118C2×#217C2×D312yes—
119C2×(C2×D3)⋊C4—32no—
120C2×(C2×D3)⋊C4—32no—
121C2×(C2×D3)⋊C4C2×D311yescharacteristic
122C2×C4⋊Dic3C2×D311yescharacteristic
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4C2×D311yescharacteristic
126C2×C4×Dic3—32no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3—32no—
130C2×C4×Dic3C2×D311yescharacteristic
131#887—64no—
132#67⋊C4—24no—
133C4×Dic6—64no—
134C3×#95—31no—
135C3×#95—32no—
136C3⋊#95—31no—
137C3⋊#95—32no—
138C3⋊#95—31no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—61no—
147C3⋊#95—62no—
148C3⋊#95C2×D311yescharacteristic
149C3⋊#95C2×D312yes—
150C23×C32—21no—
151C23×C32—22no—
152C23×C32—22no—
153C23×C32—21no—
154C23×C32#4112yes—
155C23×C32C2411yescharacteristic
156C22×C3×D3—21no—
157C22×C3×D3—22no—
158C22×C3×D3—22no—
159C22×C3×D3—21no—
160C22×C3×D3#4112yes—
161C2×C32×C4—22no—
162C2×C32×C4—21no—
163C2×C32×C4—22no—
164C2×C32×C4C2×D412yes—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3#4114yes—
171#634—28no—
172C3×#67—28no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—44no—
184C2×C3×Dic3C2×D412yes—
185C2×C3×Dic3C2×D412yes—
186C2×C3×Dic3#4114yes—
187C3×C4×D3—44no—
188C2×C4×Q8—91no—
189C2×C4×D4—31no—
190#400—92no—
191#397—31no—
192#397—91no—
193#394—92no—
194#393—91no—
195#393—91no—
196C4×C22⋊C4—92no—
197C4×C22⋊C4—92no—
198#376—91no—
199C24×C3—21no—
200C24×C3—31no—
201C24×C3C22×D311yescharacteristic
202C24×C3C22×D311yescharacteristic
203C23×D3C22×D311yescharacteristic
204C2×C3×D4—62no—
205C2×C3×D4—62no—
206C2×C3×D4—62no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—31no—
210C22×C3×C4—31no—
211C22×C3×C4—31no—
212C22×C3×C4—32no—
213C22×C3×C4—32no—
214C22×C3×C4—62no—
215C22×C3×C4—64no—
216C22×C3×C4—62no—
217C22×C3×C4—64no—
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C22×D311yescharacteristic
222C2×#67—22no—
223C2×#67—22no—
224C2×#67—22no—
225C22×Dic3—24no—
226C22×Dic3—22no—
227C22×Dic3—32no—
228C22×Dic3—32no—
229C22×Dic3—32no—
230C22×Dic3—32no—
231C22×Dic3—62no—
232C22×Dic3—62no—
233C22×Dic3C22×D311yescharacteristic
234C22×Dic3C22×D312yes—
235C22×Dic3C22×D312yes—
236C22×Dic3C22×D311yescharacteristic
237C22×Dic3C22×D311yescharacteristic
238C2×C4×D3—24no—
239C2×C4×D3—22no—
240C2×Dic6—64no—
241C2×Dic6—64no—
242C2×Dic6—62no—
243C2×Dic6—62no—
244C2×Dic6—124no—
245C2×Dic6—122no—
246C3×C4⋊C4—62no—
247C3×C4⋊C4—62no—
248C3×C22⋊C4—22no—
249C3×C22⋊C4—22no—
250C3×C22⋊C4—42no—
251C3×C22⋊C4—64no—
252C3×C22⋊C4—62no—
253C3×C42—34no—
254#217—24no—
255#217—64no—
256#217—64no—
257#217—64no—
258#217—64no—
259#217—124no—
260(C2×D3)⋊C4—22no—
261(C2×D3)⋊C4—64no—
262(C2×D3)⋊C4—64no—
263C4⋊Dic3—22no—
264Dic3⋊C4—22no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267C4×Dic3—64no—
268C4×Dic3—64no—
269C4×Dic3—64no—
270C4×Dic3—64no—
271C4×Dic3#6714yes—
272C22×C32—22no—
273C22×C32—24no—
274C22×C32—41no—
275C22×C32—41no—
276C22×C32—42no—
277C22×C32C22×D411yescharacteristic
278C22×C32C2×#4111yescharacteristic
279C22×C32C2×#4111yescharacteristic
280C22×C32C2×#4112yes—
281C22×C32C2×#4112yes—
282C2×C3×D3—22no—
283C2×C3×D3—24no—
284C2×C3×D3—41no—
285C2×C3×D3—41no—
286C2×C3×D3—42no—
287C32×C4—22no—
288C32×C4—41no—
289C3⋊Dic3—24no—
290C3⋊Dic3—42no—
291C3×Dic3—22no—
292C3×Dic3—42no—
293C3×Dic3—41no—
294C3×Dic3—42no—
295C3×Dic3#12414yes—
296C22×Q8—91no—
297C22×D4—31no—
298C23×C4—31no—
299C23×C4—31no—
300C4×Q8—184no—
301C4×D4—64no—
302C2×C4⋊C4—31no—
303C2×C4⋊C4—31no—
304C2×C4⋊C4—92no—
305C2×C22⋊C4—32no—
306C2×C22⋊C4—31no—
307C2×C22⋊C4—92no—
308C2×C22⋊C4—92no—
309C2×C22⋊C4—92no—
310C2×C22⋊C4D3211yescharacteristic
311C2×C42—31no—
312C2×C42—92no—
313C2×C42—92no—
314#95—31no—
315#95—32no—
316#95—92no—
317#95—92no—
318#95—92no—
319#95—91no—
320#95—92no—
321C23×C3—21no—
322C23×C3—21no—
323C23×C3—22no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—22no—
327C23×C3—21no—
328C23×C3—21no—
329C23×C3—21no—
330C23×C3—22no—
331C23×C3—32no—
332C23×C3—42no—
333C23×C3—41no—
334C23×C3—41no—
335C23×C3—42no—
336C23×C3—61no—
337C23×C3—61no—
338C23×C3—62no—
339C23×C3—62no—
340C23×C3#23512yes—
341C23×C3#23712yes—
342C23×C3C23×D311yescharacteristic
343C23×C3C23×D311yescharacteristic
344C22×D3—21no—
345C22×D3—22no—
346C22×D3—22no—
347C22×D3—21no—
348C22×D3#23512yes—
349C3×D4—68no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—21no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—21no—
356C2×C3×C4—22no—
357C2×C3×C4—32no—
358C2×C3×C4—34no—
359C2×C3×C4—32no—
360C2×C3×C4—42no—
361C2×C3×C4—41no—
362C2×C3×C4—42no—
363C2×C3×C4—61no—
364C2×C3×C4—61no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4—62no—
368C2×C3×C4—61no—
369C2×C3×C4—62no—
370C2×C3×C4—62no—
371C2×C3×C4—62no—
372C2×C3×C4—62no—
373C2×C3×C4—124no—
374C2×C3×C4—124no—
375C2×C3×C4D3×D412yes—
376C2×C3×C4C2×#6712yes—
377#67—28no—
378C2×Dic3—21no—
379C2×Dic3—21no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—22no—
383C2×Dic3—22no—
384C2×Dic3—22no—
385C2×Dic3—22no—
386C2×Dic3—22no—
387C2×Dic3—21no—
388C2×Dic3—34no—
389C2×Dic3—34no—
390C2×Dic3—44no—
391C2×Dic3—64no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—62no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—62no—
399C2×Dic3—62no—
400C2×Dic3—62no—
401C2×Dic3—62no—
402C2×Dic3—122no—
403C2×Dic3—122no—
404C2×Dic3—122no—
405C2×Dic3—122no—
406C2×Dic3—122no—
407C2×Dic3#23714yes—
408C2×Dic3C2×#6712yes—
409C2×Dic3C2×#6712yes—
410C4×D3—44no—
411Dic6—68no—
412Dic6—68no—
413Dic6—128no—
414C2×C32—42no—
415C2×C32#52511yescharacteristic
416C2×C32#52511yescharacteristic
417C2×C32C2×#12411yescharacteristic
418C2×C32#52912yes—
419C2×C32#52912yes—
420C3×D3—42no—
421C24—31no—
422C24C2×D3211yescharacteristic
423C2×Q8—184no—
424C2×Q8—182no—
425C2×D4—62no—
426C2×D4—62no—
427C2×D4—62no—
428C22×C4—31no—
429C22×C4—31no—
430C22×C4—32no—
431C22×C4—32no—
432C22×C4—31no—
433C22×C4—62no—
434C22×C4—64no—
435C22×C4—62no—
436C22×C4—64no—
437C22×C4—92no—
438C22×C4—92no—
439C22×C4C2×D3211yescharacteristic
440C22×C4C2×D3211yescharacteristic
441C4⋊C4—62no—
442C4⋊C4—62no—
443C4⋊C4—184no—
444C22⋊C4—22no—
445C22⋊C4—64no—
446C22⋊C4—62no—
447C22⋊C4—184no—
448C22⋊C4—184no—
449C22⋊C4—184no—
450C42—34no—
451C42—184no—
452C42—184no—
453C22×C3—24no—
454C22×C3—22no—
455C22×C3—24no—
456C22×C3—22no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—22no—
460C22×C3—22no—
461C22×C3—21no—
462C22×C3—42no—
463C22×C3—44no—
464C22×C3—41no—
465C22×C3—41no—
466C22×C3—42no—
467C22×C3—42no—
468C22×C3—41no—
469C22×C3—41no—
470C22×C3—64no—
471C22×C3—62no—
472C22×C3—82no—
473C22×C3—81no—
474C22×C3—81no—
475C22×C3—122no—
476C22×C3—121no—
477C22×C3—121no—
478C22×C3C2×#23511yescharacteristic
479C22×C3C2×#23511yescharacteristic
480C22×C3C2×D3×D411yescharacteristic
481C22×C3C2×#23711yescharacteristic
482C22×C3C2×#23712yes—
483C22×C3D3×#4111yescharacteristic
484C22×C3D3×#4112yes—
485C22×C3D3×#4112yes—
486C22×C3D3×#4112yes—
487C22×C3C22×#6711yescharacteristic
488C2×D3—22no—
489C2×D3—24no—
490C2×D3—42no—
491C2×D3—41no—
492C2×D3—41no—
493C3×C4—22no—
494C3×C4—22no—
495C3×C4—34no—
496C3×C4—42no—
497C3×C4—41no—
498C3×C4—41no—
499C3×C4—62no—
500C3×C4—81no—
501C3×C4—121no—
502C3×C4—122no—
503C3×C4—122no—
504Dic3—22no—
505Dic3—42no—
506Dic3—41no—
507Dic3—42no—
508Dic3—64no—
509Dic3—64no—
510Dic3—124no—
511Dic3—122no—
512Dic3—122no—
513Dic3—242no—
514Dic3#93614yes—
515C32#239811yescharacteristic, complemented, Sylow
516C23—21no—
517C23—22no—
518C23—22no—
519C23—21no—
520C23—32no—
521C23—61no—
522C23—62no—
523C23—62no—
524C23—61no—
525C23#379512yes—
526C23C22×D3211yescharacteristic
527Q8—188no—
528D4—68no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—34no—
533C2×C4—32no—
534C2×C4—32no—
535C2×C4—61no—
536C2×C4—61no—
537C2×C4—62no—
538C2×C4—62no—
539C2×C4—62no—
540C2×C4—62no—
541C2×C4—62no—
542C2×C4—62no—
543C2×C4—62no—
544C2×C4—61no—
545C2×C4—94no—
546C2×C4—124no—
547C2×C4—124no—
548C2×C4—182no—
549C2×C4—182no—
550C2×C4—182no—
551C2×C4—182no—
552C2×C4—182no—
553C2×C4D3×#6712yes—
554C2×C3—22no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—22no—
558C2×C3—21no—
559C2×C3—42no—
560C2×C3—42no—
561C2×C3—82no—
562C2×C3—122no—
563C2×C3#553812yes—
564C2×C3#553812yes—
565C2×C3#560611yescharacteristic
566C2×C3#564912yes—
567C2×C3#565611yescharacteristic
568C2×C3D3×#12411yescharacteristic
569C2×C3#570612yes—
570C2×C3#579111yescharacteristic
571C2×C3C2×#93611yescharacteristic
572C2×C3#582811yescharacteristic
573D3—42no—
574C22—22no—
575C22—24no—
576C22—42no—
577C22—41no—
578C22—41no—
579C22—64no—
580C22—62no—
581C22—121no—
582C22—122no—
583C22—121no—
584C22C2×#379511yescharacteristic
585C22D3×#23511yescharacteristic
586C22D3×#23712yes—
587C22#6431212yes—
588C22C2×D3×#6711yescharacteristic
589C4—22no—
590C4—34no—
591C4—41no—
592C4—62no—
593C4—121no—
594C4—122no—
595C4—122no—
596C4—184no—
597C4—362no—
598C3—21no—
599C3#7746011yescharacteristic, complemented
600C3#8234811yescharacteristic, complemented
601C2—42no—
602C2—122no—
603C2#1059408912yes—
604C2#1059413112yes—
605C2#1059489211yescharacteristic
606C2D3×#93611yescharacteristic
607C2#1059515911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC22×C3×#67C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63844C2semidirect
3. #10592646C2semidirect
4. C3×#4953C2semidirect
6. Dic3×#217C2semidirect
7. #10591322C2semidirect
8. #10591314C2semidirect
9. #10591239C2semidirect
10. #10591237C2semidirect
11. #10591199C2semidirect
51. #4953D3semidirect
515. C32#2398semidirect
599. C3#77460semidirect
600. C3#82348semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#67⋊C42
C2×#638442
#105926462
C3×#49532
#105917082
Dic3×#2172
#105913222
#105913142
#105912392
#105912372
#105911992
#823483
#774603