Finite Group Databasebeta

← #11808814

Subgroups — #11808814

Order 1152.

1225 conjugacy classes of subgroups.

The subgroup lattice has 599 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63902C211yesmaximal, characteristic
2C2×#63843C211yesmaximal, characteristic, complemented
3#10592347C211yesmaximal, characteristic, complemented
4C3×#4674C211yesmaximal, characteristic, complemented
5C3×#4673C211yesmaximal, characteristic, complemented
6#10591390C212yesmaximal
7#10591368C212yesmaximal, complemented
8#10591368C212yesmaximal, complemented
9#10591314C211yesmaximal, characteristic, complemented
10#10591304C211yesmaximal, characteristic, complemented
11#10591211C212yesmaximal, complemented
12#77460—31nomaximal
13#76779—31nomaximal
14C22×C3×Dic6C2211yescharacteristic
15C22×#625C2211yescharacteristic
16C22×D3×Dic3C2211yescharacteristic
17C22×D3×Dic3C2211yescharacteristic
18C2×C4×C3⋊Dic3C2212yes—
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×(C2×D3)⋊C4C2211yescharacteristic
21C2×C3×(C2×D3)⋊C4C2212yes—
22C2×C3×(C2×D3)⋊C4C2211yescharacteristic
23C2×C3×(C2×D3)⋊C4C2212yes—
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×#3724C2211yescharacteristic
26C2×Dic3⋊Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×(C2×D3)⋊Dic3C2212yes—
29C2×Dic32C2212yes—
30#63902—24no—
31#63843—24no—
32C32×#95C2211yescharacteristic
33#63658C2211yescharacteristic
34#63658C2212yes—
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×Q8×Dic3—31no—
40C2×#887—31no—
41C2×#67⋊C4—31no—
42C2×#67⋊C4—31no—
43C3×#397—31no—
44C3×#393—31no—
45#5231—31no—
46#4992—31no—
47#4961—32no—
48#4959—32no—
49#4953—31no—
50#4947—31no—
51Dic3×C22⋊C4—32no—
52Dic3×C22⋊C4—32no—
53#4674D311yescharacteristic, complemented
54#4673D311yescharacteristic, complemented
55#4666—32no—
56#4666—32no—
57#4660—32no—
58#4658—32no—
59#4648—31no—
60#4648—31no—
61#4648—61no—
62C23×C3×D3C2311yescharacteristic
63C23×C3×D3C2311yescharacteristic
64C22×C32×C4C2312yes—
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2312yes—
73C2×C3×Dic6—22no—
74C2×C3×Dic6—24no—
75C2×#625—22no—
76C2×#625—22no—
77C2×#625—22no—
78C2×D3×Dic3—22no—
79C2×D3×Dic3—22no—
80C2×D3×Dic3—24no—
81C2×D3×Dic3—24no—
82C4×C3⋊Dic3—24no—
83C4×C3⋊Dic3D414yes—
84C3×(C2×D3)⋊C4—24no—
85C3×(C2×D3)⋊C4—22no—
86C3×(C2×D3)⋊C4—22no—
87C3×(C2×D3)⋊C4—24no—
88C3×C4⋊Dic3—22no—
89#3724—22no—
90Dic3⋊Dic3—24no—
91(C2×D3)⋊Dic3—24no—
92(C2×D3)⋊Dic3—24no—
93Dic32—24no—
94#2398—91noSylow
95C22×C3×Q8—31no—
96C22×#67—31no—
97C22×#67—31no—
98C23×Dic3—31no—
99C23×Dic3—31no—
100C22×C4×D3—31no—
101C22×C4×D3—31no—
102C22×Dic6C2×D311yescharacteristic
103C2×C3×C4⋊C4—31no—
104C2×C3×C22⋊C4—32no—
105C2×C3×C22⋊C4—32no—
106C2×C3×C22⋊C4—31no—
107C2×C3×C22⋊C4—31no—
108C2×#217—32no—
109C2×#217—32no—
110Q8×Dic3—64no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4C2×D312yes—
114C2×(C2×D3)⋊C4C2×D312yes—
115C2×(C2×D3)⋊C4C2×D311yescharacteristic
116C2×(C2×D3)⋊C4C2×D311yescharacteristic
117C2×C4⋊Dic3—32no—
118C2×C4⋊Dic3C2×D311yescharacteristic
119C2×Dic3⋊C4—31no—
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4—31no—
122C2×C4×Dic3—31no—
123C2×C4×Dic3—31no—
124C2×C4×Dic3—32no—
125C2×C4×Dic3—32no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—61no—
129C2×C4×Dic3—62no—
130#887—64no—
131#67⋊C4—64no—
132#67⋊C4—64no—
133C3×#95—21no—
134C3×#95—32no—
135C3×#95—32no—
136C3×#95C2×D311yescharacteristic
137C3×#95C2×D311yescharacteristic
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—31no—
141C3⋊#95—31no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—61no—
147C3⋊#95—62no—
148C3⋊#95C2×D312yes—
149C3⋊#95C2×D312yes—
150C23×C32C2411yescharacteristic
151C22×C3×D3—21no—
152C22×C3×D3—21no—
153C22×C3×D3—22no—
154C22×C3×D3—22no—
155C22×C3×D3—22no—
156C22×C3×D3—22no—
157C22×C3×D3—21no—
158C22×C3×D3—21no—
159C22×C3×D3#4112yes—
160C22×C3×D3#4112yes—
161C2×C32×C4—22no—
162C2×C32×C4—22no—
163C2×C32×C4—22no—
164C2×C32×C4—22no—
165C2×C32×C4C2×D412yes—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3C2×D412yes—
172C2×C3⋊Dic3C2×D412yes—
173C2×C3⋊Dic3#4114yes—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3#4114yes—
184C3×Dic6—28no—
185#625—28no—
186D3×Dic3—44no—
187D3×Dic3—44no—
188C2×C4×Q8—91no—
189C2×C4×D4—91no—
190#400—92no—
191#397—31no—
192#397—91no—
193#394—92no—
194#393—31no—
195#393—91no—
196C4×C22⋊C4—92no—
197C4×C22⋊C4—92no—
198#376—91no—
199C24×C3—31no—
200C24×C3—31no—
201C23×D3C22×D311yescharacteristic
202C23×D3C22×D311yescharacteristic
203C2×C3×Q8—64no—
204C2×C3×Q8—62no—
205C22×C3×C4—22no—
206C22×C3×C4—21no—
207C22×C3×C4—32no—
208C22×C3×C4—31no—
209C22×C3×C4—31no—
210C22×C3×C4—32no—
211C22×C3×C4C22×D312yes—
212C22×C3×C4C22×D312yes—
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C2×#67—62no—
216C2×#67—62no—
217C2×#67—62no—
218C2×#67—62no—
219C2×#67—62no—
220C2×#67—62no—
221C22×Dic3—31no—
222C22×Dic3—31no—
223C22×Dic3—31no—
224C22×Dic3—31no—
225C22×Dic3—32no—
226C22×Dic3—32no—
227C22×Dic3—61no—
228C22×Dic3—61no—
229C22×Dic3—62no—
230C22×Dic3—62no—
231C22×Dic3—62no—
232C22×Dic3—64no—
233C22×Dic3—64no—
234C22×Dic3C22×D311yescharacteristic
235C22×Dic3C22×D311yescharacteristic
236C22×Dic3C22×D312yes—
237C22×Dic3C22×D312yes—
238C2×C4×D3—62no—
239C2×C4×D3—62no—
240C2×C4×D3—64no—
241C2×C4×D3—64no—
242C2×Dic6—22no—
243C2×Dic6—24no—
244C3×C4⋊C4—62no—
245C3×C22⋊C4—64no—
246C3×C22⋊C4—64no—
247C3×C22⋊C4—62no—
248C3×C22⋊C4—62no—
249#217—64no—
250#217—64no—
251(C2×D3)⋊C4—24no—
252(C2×D3)⋊C4—22no—
253(C2×D3)⋊C4—22no—
254(C2×D3)⋊C4—24no—
255(C2×D3)⋊C4—64no—
256(C2×D3)⋊C4—64no—
257C4⋊Dic3—22no—
258C4⋊Dic3—64no—
259Dic3⋊C4—62no—
260Dic3⋊C4—62no—
261Dic3⋊C4—64no—
262C4×Dic3—34no—
263C4×Dic3—34no—
264C4×Dic3—64no—
265C4×Dic3—64no—
266C4×Dic3—64no—
267C4×Dic3—64no—
268C4×Dic3—64no—
269C4×Dic3—68no—
270C22×C32C22×D411yescharacteristic
271C22×C32C2×#4111yescharacteristic
272C22×C32C2×#4112yes—
273C22×C32C2×#4111yescharacteristic
274C22×C32C2×#4112yes—
275C2×C3×D3—22no—
276C2×C3×D3—22no—
277C2×C3×D3—24no—
278C2×C3×D3—24no—
279C2×C3×D3—41no—
280C2×C3×D3—41no—
281C2×C3×D3—41no—
282C2×C3×D3—41no—
283C2×C3×D3—42no—
284C2×C3×D3—42no—
285C32×C4—22no—
286C32×C4—42no—
287C3⋊Dic3—22no—
288C3⋊Dic3—42no—
289C3⋊Dic3#12414yes—
290C3×Dic3—24no—
291C3×Dic3—42no—
292C3×Dic3—41no—
293C3×Dic3—41no—
294C22×Q8—31no—
295C22×D4—91no—
296C23×C4—91no—
297C23×C4—91no—
298C4×Q8—184no—
299C4×D4—184no—
300C2×C4⋊C4—31no—
301C2×C4⋊C4—91no—
302C2×C4⋊C4—92no—
303C2×C22⋊C4—31no—
304C2×C22⋊C4—31no—
305C2×C22⋊C4—32no—
306C2×C22⋊C4—32no—
307C2×C22⋊C4—92no—
308C2×C22⋊C4—92no—
309C2×C42—91no—
310C2×C42—92no—
311C2×C42—92no—
312#95—32no—
313#95—32no—
314#95—92no—
315#95—92no—
316#95—91no—
317#95—92no—
318#95D3211yescharacteristic
319C23×C3—21no—
320C23×C3—32no—
321C23×C3—32no—
322C23×C3—61no—
323C23×C3—61no—
324C23×C3—62no—
325C23×C3—61no—
326C23×C3—61no—
327C23×C3—62no—
328C23×C3—62no—
329C23×C3—62no—
330C23×C3C23×D311yescharacteristic
331C23×C3C23×D311yescharacteristic
332C22×D3—21no—
333C22×D3—21no—
334C22×D3—22no—
335C22×D3—22no—
336C22×D3—22no—
337C22×D3—22no—
338C22×D3—21no—
339C22×D3—21no—
340C22×D3#23712yes—
341C22×D3#23912yes—
342C3×Q8—68no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—24no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—34no—
354C2×C3×C4—42no—
355C2×C3×C4—42no—
356C2×C3×C4—42no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—61no—
361C2×C3×C4—61no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4D3×D412yes—
367C2×C3×C4D3×D412yes—
368#67—68no—
369#67—68no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—21no—
374C2×Dic3—21no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—32no—
380C2×Dic3—32no—
381C2×Dic3—34no—
382C2×Dic3—34no—
383C2×Dic3—32no—
384C2×Dic3—32no—
385C2×Dic3—62no—
386C2×Dic3—64no—
387C2×Dic3—62no—
388C2×Dic3—61no—
389C2×Dic3—61no—
390C2×Dic3—61no—
391C2×Dic3—61no—
392C2×Dic3—64no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—62no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—62no—
399C2×Dic3—121no—
400C2×Dic3—121no—
401C2×Dic3—122no—
402C2×Dic3—122no—
403C2×Dic3—124no—
404C2×Dic3—124no—
405C2×Dic3#23714yes—
406C4×D3—124no—
407C4×D3—124no—
408Dic6—28no—
409C2×C32#52511yescharacteristic
410C2×C32#52511yescharacteristic
411C2×C32C2×#12411yescharacteristic
412C2×C32#52912yes—
413C2×C32#52912yes—
414C3×D3—42no—
415C3×D3—42no—
416C24—31no—
417C24—31no—
418C2×Q8—64no—
419C2×Q8—62no—
420C2×D4—182no—
421C2×D4—182no—
422C2×D4—182no—
423C22×C4—32no—
424C22×C4—31no—
425C22×C4—31no—
426C22×C4—32no—
427C22×C4—91no—
428C22×C4—91no—
429C22×C4—92no—
430C22×C4—182no—
431C22×C4—182no—
432C22×C4—184no—
433C22×C4—184no—
434C22×C4C2×D3212yes—
435C22×C4C2×D3211yescharacteristic
436C4⋊C4—62no—
437C4⋊C4—182no—
438C4⋊C4—184no—
439C22⋊C4—64no—
440C22⋊C4—64no—
441C22⋊C4—62no—
442C22⋊C4—62no—
443C22⋊C4—184no—
444C22⋊C4—184no—
445C42—94no—
446C42—184no—
447C42—184no—
448C22×C3—21no—
449C22×C3—22no—
450C22×C3—22no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—64no—
454C22×C3—64no—
455C22×C3—62no—
456C22×C3—62no—
457C22×C3—122no—
458C22×C3—121no—
459C22×C3—121no—
460C22×C3—121no—
461C22×C3—121no—
462C22×C3—122no—
463C22×C3C2×D3×D411yescharacteristic
464C22×C3C2×D3×D411yescharacteristic
465C22×C3C2×#23711yescharacteristic
466C22×C3C2×#23712yes—
467C22×C3C2×#23911yescharacteristic
468C22×C3D3×#4112yes—
469C22×C3D3×#4112yes—
470C22×C3D3×#4112yes—
471C22×C3D3×#4111yescharacteristic
472C22×C3D3×#4111yescharacteristic
473C2×D3—24no—
474C2×D3—22no—
475C2×D3—24no—
476C2×D3—22no—
477C2×D3—41no—
478C2×D3—41no—
479C2×D3—41no—
480C2×D3—42no—
481C2×D3—42no—
482C2×D3—41no—
483C3×C4—22no—
484C3×C4—22no—
485C3×C4—42no—
486C3×C4—44no—
487C3×C4—42no—
488C3×C4—42no—
489C3×C4—64no—
490C3×C4—121no—
491C3×C4—121no—
492C3×C4—122no—
493Dic3—24no—
494Dic3—34no—
495Dic3—34no—
496Dic3—41no—
497Dic3—41no—
498Dic3—42no—
499Dic3—64no—
500Dic3—62no—
501Dic3—62no—
502Dic3—122no—
503Dic3—124no—
504Dic3—122no—
505Dic3—122no—
506C32#239811yescharacteristic, complemented, Sylow
507C23—32no—
508C23—32no—
509C23—61no—
510C23—61no—
511C23—62no—
512C23—62no—
513C23—62no—
514C23—62no—
515C23—61no—
516C23—61no—
517C23C22×D3211yescharacteristic
518Q8—68no—
519D4—188no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—34no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—62no—
528C2×C4—61no—
529C2×C4—61no—
530C2×C4—62no—
531C2×C4—62no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—92no—
535C2×C4—94no—
536C2×C4—92no—
537C2×C4—181no—
538C2×C4—181no—
539C2×C4—182no—
540C2×C4—182no—
541C2×C4—182no—
542C2×C4—364no—
543C2×C4—364no—
544C2×C4#380212yes—
545C2×C3—21no—
546C2×C3—22no—
547C2×C3—21no—
548C2×C3—22no—
549C2×C3—21no—
550C2×C3—122no—
551C2×C3—122no—
552C2×C3#558611yescharacteristic
553C2×C3#560611yescharacteristic
554C2×C3#562412yes—
555C2×C3#562711yescharacteristic
556C2×C3#564912yes—
557C2×C3#565611yescharacteristic
558C2×C3D3×#12411yescharacteristic
559C2×C3D3×#12411yescharacteristic
560C2×C3#568012yes—
561C2×C3#570612yes—
562D3—42no—
563D3—42no—
564C22—64no—
565C22—62no—
566C22—62no—
567C22—64no—
568C22—121no—
569C22—121no—
570C22—122no—
571C22—122no—
572C22—121no—
573C22—121no—
574C22C2×#380211yescharacteristic
575C22#6430612yes—
576C22D3×#23712yes—
577C22D3×#23711yescharacteristic
578C22D3×#23911yescharacteristic
579C4—22no—
580C4—42no—
581C4—64no—
582C4—94no—
583C4—122no—
584C4—121no—
585C4—121no—
586C4—182no—
587C4—362no—
588C3—21no—
589C3#7677911yescharacteristic, complemented
590C3#7746011yescharacteristic, complemented
591C2—122no—
592C2—122no—
593C2#1059400911yescharacteristic
594C2#1059408211yescharacteristic
595C2#1059411112yes—
596C2#1059444212yes—
597C2#1059463211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC22×#625C22
hypercenter#95D32
hypocenterC32#2398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#63843C2semidirect
3. #10592347C2semidirect
4. C3×#4674C2semidirect
5. C3×#4673C2semidirect
7. #10591368C2semidirect
8. #10591368C2semidirect
9. #10591314C2semidirect
10. #10591304C2semidirect
11. #10591211C2semidirect
53. #4674D3semidirect
54. #4673D3semidirect
506. C32#2398semidirect
589. C3#76779semidirect
590. C3#77460semidirect

Maximal subgroups

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

subgroupindex
C2×#639022
C2×#638432
#105923472
C3×#46742
C3×#46732
#105913902
#105913682
#105913142
#105913042
#105912112
#774603
#767793