Finite Group Databasebeta

← #11808813

Subgroups — #11808813

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×#63880C211yesmaximal, characteristic
2C2×#63844C211yesmaximal, characteristic, complemented
3#10592372C211yesmaximal, characteristic, complemented
4C3×#4674C211yesmaximal, characteristic, complemented
5C3×#4648C211yesmaximal, characteristic, complemented
6Dic3×(C2×D3)⋊C4C212yesmaximal, complemented
7#10591326C211yesmaximal, characteristic, complemented
8#10591322C211yesmaximal, characteristic, complemented
9#10591292C212yesmaximal
10#10591233C212yesmaximal, complemented
11#10591209C212yesmaximal, complemented
12#77460—31nomaximal
13#73419—31nomaximal
14C22×#634C2211yescharacteristic
15C22×#626C2211yescharacteristic
16C22×#624C2211yescharacteristic
17C22×D3×Dic3C2211yescharacteristic
18C2×#3752C2212yes—
19C2×#3752C2211yescharacteristic
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×C3×(C2×D3)⋊C4C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2212yes—
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×#3724C2212yes—
26C2×Dic3⋊Dic3C2211yescharacteristic
27C2×#3722C2212yes—
28C2×(C2×D3)⋊Dic3C2212yes—
29C2×Dic32C2212yes—
30#63880—24no—
31#63844—24no—
32C32×#95C2211yescharacteristic
33#63658C2212yes—
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2211yescharacteristic
37#63579C2212yes—
38#63579C2212yes—
39C2×#887—31no—
40C2×#67⋊C4—31no—
41C2×C4×D12—31no—
42C2×C4×Dic6—31no—
43C3×#397—31no—
44C3×#376—31no—
45#4992—31no—
46#4959—32no—
47#4947—31no—
48Dic3×C22⋊C4—32no—
49C4×(C2×D3)⋊C4—32no—
50C4×(C2×D3)⋊C4—32no—
51#4674—31no—
52#4674D311yescharacteristic, complemented
53#4673—31no—
54#4673—31no—
55#4673—31no—
56#4673—61no—
57#4672—32no—
58#4666—32no—
59#4659—32no—
60#4658—32no—
61#4648D311yescharacteristic, complemented
62C23×C3⋊D3C2311yescharacteristic
63C23×C3×D3C2311yescharacteristic
64C22×C32×C4C2312yes—
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2312yes—
68C2×#634—22no—
69C2×#634—24no—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C2×#626—22no—
76C2×#626—22no—
77C2×#626—22no—
78C2×#624—22no—
79C2×#624—24no—
80C2×D3×Dic3—22no—
81C2×D3×Dic3—24no—
82#3752—22no—
83#3752—24no—
84C3×(C2×D3)⋊C4—24no—
85C3×(C2×D3)⋊C4—22no—
86C3×C4⋊Dic3—22no—
87C3×C4×Dic3—24no—
88C3×C4×Dic3D414yes—
89#3724—24no—
90Dic3⋊Dic3—22no—
91#3722—24no—
92(C2×D3)⋊Dic3—24no—
93Dic32—24no—
94#2398—91noSylow
95C22×#67—31no—
96C23×Dic3—31no—
97C22×D12—31no—
98C22×C4×D3—31no—
99C22×C4×D3—31no—
100C22×C4×D3—31no—
101C22×Dic6—31no—
102C22×Dic6—31no—
103C22×Dic6—61no—
104C2×C3×C4⋊C4—31no—
105C2×C3×C22⋊C4—32no—
106C2×C3×C22⋊C4—31no—
107C2×C3×C42—31no—
108C2×C3×C42—32no—
109C2×#217—32no—
110C2×(C2×D3)⋊C4—32no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—31no—
114C2×(C2×D3)⋊C4—31no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4—32no—
117C2×(C2×D3)⋊C4—61no—
118C2×(C2×D3)⋊C4—62no—
119C2×(C2×D3)⋊C4C2×D312yes—
120C2×(C2×D3)⋊C4C2×D311yescharacteristic
121C2×C4⋊Dic3—31no—
122C2×C4⋊Dic3C2×D311yescharacteristic
123C2×Dic3⋊C4—31no—
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4—32no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3C2×D312yes—
129C2×C4×Dic3C2×D311yescharacteristic
130#887—64no—
131#67⋊C4—64no—
132C4×D12—64no—
133C4×Dic6—64no—
134C3×#95—21no—
135C3×#95—32no—
136C3×#95—32no—
137C3×#95—31no—
138C3×#95C2×D311yescharacteristic
139C3×#95C2×D311yescharacteristic
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—62no—
147C3⋊#95C2×D312yes—
148C3⋊#95C2×D311yescharacteristic
149C3⋊#95C2×D312yes—
150C23×C32C2411yescharacteristic
151C22×C3⋊D3—21no—
152C22×C3⋊D3—22no—
153C22×C3⋊D3—22no—
154C22×C3⋊D3—21no—
155C22×C3⋊D3#4112yes—
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—22no—
163C2×C32×C4—22no—
164C2×C32×C4—22no—
165C2×C32×C4C2×D412yes—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3#4114yes—
171#634—28no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3C2×D412yes—
183C2×C3×Dic3C2×D412yes—
184C2×C3×Dic3#4114yes—
185#626—28no—
186#624—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—91no—
195#393—91no—
196C4×C22⋊C4—92no—
197C4×C22⋊C4—92no—
198#376—31no—
199C24×C3—31no—
200C23×D3—31no—
201C23×D3—31no—
202C23×D3—61no—
203C23×D3C22×D311yescharacteristic
204C22×C3×C4—21no—
205C22×C3×C4—22no—
206C22×C3×C4—31no—
207C22×C3×C4—31no—
208C22×C3×C4—31no—
209C22×C3×C4—32no—
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—
218C22×Dic3—32no—
219C22×Dic3—32no—
220C22×Dic3—31no—
221C22×Dic3—31no—
222C22×Dic3—62no—
223C22×Dic3—61no—
224C22×Dic3—62no—
225C22×Dic3—64no—
226C22×Dic3C22×D312yes—
227C22×Dic3C22×D311yescharacteristic
228C22×Dic3C22×D312yes—
229C22×Dic3C22×D311yescharacteristic
230C22×Dic3C22×D311yescharacteristic
231C2×D12—62no—
232C2×D12—62no—
233C2×D12—62no—
234C2×C4×D3—62no—
235C2×C4×D3—64no—
236C2×C4×D3—62no—
237C2×C4×D3—64no—
238C2×C4×D3—62no—
239C2×C4×D3—64no—
240C2×Dic6—64no—
241C2×Dic6—64no—
242C2×Dic6—62no—
243C2×Dic6—62no—
244C2×Dic6—124no—
245C2×Dic6—122no—
246C3×C4⋊C4—62no—
247C3×C22⋊C4—64no—
248C3×C22⋊C4—62no—
249C3×C42—34no—
250C3×C42—64no—
251#217—64no—
252(C2×D3)⋊C4—24no—
253(C2×D3)⋊C4—22no—
254(C2×D3)⋊C4—64no—
255(C2×D3)⋊C4—64no—
256(C2×D3)⋊C4—64no—
257(C2×D3)⋊C4—64no—
258(C2×D3)⋊C4—64no—
259(C2×D3)⋊C4—62no—
260(C2×D3)⋊C4—62no—
261(C2×D3)⋊C4—124no—
262(C2×D3)⋊C4—122no—
263C4⋊Dic3—22no—
264C4⋊Dic3—62no—
265Dic3⋊C4—64no—
266Dic3⋊C4—62no—
267Dic3⋊C4—64no—
268C4×Dic3—24no—
269C4×Dic3—64no—
270C4×Dic3—64no—
271C4×Dic3D1214yes—
272C22×C32C22×D411yescharacteristic
273C22×C32C2×#4112yes—
274C22×C32C2×#4111yescharacteristic
275C22×C32C2×#4111yescharacteristic
276C22×C32C2×#4112yes—
277C2×C3⋊D3—22no—
278C2×C3⋊D3—24no—
279C2×C3⋊D3—41no—
280C2×C3⋊D3—41no—
281C2×C3⋊D3—42no—
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—42no—
289C3⋊Dic3—24no—
290C3⋊Dic3—41no—
291C3×Dic3—22no—
292C3×Dic3—42no—
293C3×Dic3—41no—
294C3×Dic3—42no—
295C3×Dic3#12414yes—
296C22×Q8—91no—
297C22×D4—91no—
298C23×C4—91no—
299C23×C4—91no—
300C4×Q8—184no—
301C4×D4—184no—
302C2×C4⋊C4—31no—
303C2×C4⋊C4—91no—
304C2×C4⋊C4—92no—
305C2×C22⋊C4—31no—
306C2×C22⋊C4—32no—
307C2×C22⋊C4—92no—
308C2×C22⋊C4—92no—
309C2×C22⋊C4—91no—
310C2×C22⋊C4—92no—
311C2×C42—31no—
312C2×C42—32no—
313C2×C42—92no—
314#95—31no—
315#95—32no—
316#95—32no—
317#95—92no—
318#95—92no—
319#95—92no—
320#95D3211yescharacteristic
321C23×C3—21no—
322C23×C3—32no—
323C23×C3—61no—
324C23×C3—62no—
325C23×C3—62no—
326C23×C3—61no—
327C23×C3C23×D311yescharacteristic
328C23×C3C23×D311yescharacteristic
329C22×D3—21no—
330C22×D3—22no—
331C22×D3—22no—
332C22×D3—21no—
333C22×D3—32no—
334C22×D3—32no—
335C22×D3—62no—
336C22×D3—61no—
337C22×D3—62no—
338C22×D3—61no—
339C22×D3—61no—
340C22×D3—62no—
341C22×D3—62no—
342C22×D3—62no—
343C22×D3—61no—
344C22×D3—121no—
345C22×D3—122no—
346C22×D3—122no—
347C22×D3—121no—
348C22×D3#23712yes—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—32no—
359C2×C3×C4—34no—
360C2×C3×C4—32no—
361C2×C3×C4—42no—
362C2×C3×C4—42no—
363C2×C3×C4—42no—
364C2×C3×C4—42no—
365C2×C3×C4—61no—
366C2×C3×C4—61no—
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—62no—
374C2×C3×C4—62no—
375C2×C3×C4C2×D1212yes—
376C2×C3×C4D3×D412yes—
377#67—68no—
378C2×Dic3—21no—
379C2×Dic3—21no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—21no—
383C2×Dic3—22no—
384C2×Dic3—22no—
385C2×Dic3—22no—
386C2×Dic3—22no—
387C2×Dic3—22no—
388C2×Dic3—34no—
389C2×Dic3—34no—
390C2×Dic3—64no—
391C2×Dic3—62no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—61no—
396C2×Dic3—62no—
397C2×Dic3—61no—
398C2×Dic3—62no—
399C2×Dic3—122no—
400C2×Dic3—122no—
401C2×Dic3—121no—
402C2×Dic3—122no—
403C2×Dic3—124no—
404C2×Dic3C2×D1212yes—
405C2×Dic3C2×D1212yes—
406C2×Dic3#23514yes—
407D12—68no—
408C4×D3—124no—
409C4×D3—124no—
410C4×D3—124no—
411Dic6—68no—
412Dic6—68no—
413Dic6—128no—
414C2×C32#52511yescharacteristic
415C2×C32#52511yescharacteristic
416C2×C32C2×#12411yescharacteristic
417C2×C32#52912yes—
418C2×C32#52912yes—
419C3⋊D3—42no—
420C3×D3—42no—
421C24—31no—
422C24—91no—
423C2×Q8—184no—
424C2×Q8—182no—
425C2×D4—182no—
426C2×D4—182no—
427C2×D4—182no—
428C22×C4—31no—
429C22×C4—31no—
430C22×C4—32no—
431C22×C4—31no—
432C22×C4—32no—
433C22×C4—92no—
434C22×C4—91no—
435C22×C4—182no—
436C22×C4—184no—
437C22×C4—182no—
438C22×C4—184no—
439C22×C4C2×D3212yes—
440C22×C4C2×D3211yescharacteristic
441C4⋊C4—62no—
442C4⋊C4—182no—
443C4⋊C4—184no—
444C22⋊C4—64no—
445C22⋊C4—62no—
446C22⋊C4—184no—
447C22⋊C4—184no—
448C22⋊C4—184no—
449C22⋊C4—182no—
450C42—34no—
451C42—64no—
452C42—184no—
453C22×C3—21no—
454C22×C3—22no—
455C22×C3—21no—
456C22×C3—22no—
457C22×C3—21no—
458C22×C3—62no—
459C22×C3—64no—
460C22×C3—121no—
461C22×C3—121no—
462C22×C3—122no—
463C22×C3C22×D1211yescharacteristic
464C22×C3C2×#23512yes—
465C22×C3C2×D3×D411yescharacteristic
466C22×C3C2×#23711yescharacteristic
467C22×C3D3×#4112yes—
468C22×C3D3×#4111yescharacteristic
469C22×C3D3×#4112yes—
470C22×C3D3×#4112yes—
471C22×C3D3×#4111yescharacteristic
472C22×C3D3×#4111yescharacteristic
473C2×D3—24no—
474C2×D3—22no—
475C2×D3—41no—
476C2×D3—41no—
477C2×D3—42no—
478C2×D3—64no—
479C2×D3—62no—
480C2×D3—64no—
481C2×D3—62no—
482C2×D3—122no—
483C2×D3—124no—
484C2×D3—122no—
485C2×D3—121no—
486C2×D3—121no—
487C2×D3—121no—
488C2×D3—121no—
489C2×D3—122no—
490C2×D3—241no—
491C2×D3—242no—
492C2×D3—241no—
493C3×C4—22no—
494C3×C4—22no—
495C3×C4—34no—
496C3×C4—42no—
497C3×C4—42no—
498C3×C4—42no—
499C3×C4—62no—
500C3×C4—82no—
501C3×C4—122no—
502C3×C4—121no—
503C3×C4—122no—
504Dic3—22no—
505Dic3—41no—
506Dic3—42no—
507Dic3—42no—
508Dic3—64no—
509Dic3—64no—
510Dic3—124no—
511Dic3—121no—
512Dic3—121no—
513Dic3—241no—
514Dic3#87514yes—
515C32#239811yescharacteristic, complemented, Sylow
516C23—32no—
517C23—61no—
518C23—62no—
519C23—62no—
520C23—61no—
521C23—92no—
522C23—181no—
523C23—182no—
524C23—181no—
525C23—182no—
526C23C22×D3211yescharacteristic
527Q8—188no—
528D4—188no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—32no—
534C2×C4—34no—
535C2×C4—32no—
536C2×C4—61no—
537C2×C4—61no—
538C2×C4—62no—
539C2×C4—61no—
540C2×C4—62no—
541C2×C4—62no—
542C2×C4—62no—
543C2×C4—62no—
544C2×C4—62no—
545C2×C4—62no—
546C2×C4—94no—
547C2×C4—182no—
548C2×C4—182no—
549C2×C4—181no—
550C2×C4—182no—
551C2×C4—364no—
552C2×C4—364no—
553C2×C4D3×D1212yes—
554C2×C3—21no—
555C2×C3—22no—
556C2×C3—21no—
557C2×C3—22no—
558C2×C3—21no—
559C2×C3—122no—
560C2×C3C2×#87511yescharacteristic
561C2×C3#552411yescharacteristic
562C2×C3#552411yescharacteristic
563C2×C3#552812yes—
564C2×C3#552812yes—
565C2×C3#560611yescharacteristic
566C2×C3#564912yes—
567C2×C3#565611yescharacteristic
568C2×C3D3×#12411yescharacteristic
569C2×C3#570612yes—
570D3—42no—
571D3—122no—
572D3—122no—
573D3—242no—
574C22—64no—
575C22—62no—
576C22—121no—
577C22—122no—
578C22—121no—
579C22—182no—
580C22—184no—
581C22—361no—
582C22—362no—
583C22—361no—
584C22C2×D3×D1211yescharacteristic
585C22D3×#23512yes—
586C22D3×#23711yescharacteristic
587C22#6431212yes—
588C22#6431911yescharacteristic
589C4—22no—
590C4—34no—
591C4—42no—
592C4—62no—
593C4—122no—
594C4—122no—
595C4—121no—
596C4—184no—
597C4—361no—
598C3—21no—
599C3#7341911yescharacteristic, complemented
600C3#7746011yescharacteristic, complemented
601C2—122no—
602C2—362no—
603C2D3×#87511yescharacteristic
604C2#1059407911yescharacteristic
605C2#1059408812yes—
606C2#1059441712yes—
607C2#1059462611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC22×#626C22
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×#63844C2semidirect
3. #10592372C2semidirect
4. C3×#4674C2semidirect
5. C3×#4648C2semidirect
6. Dic3×(C2×D3)⋊C4C2semidirect
7. #10591326C2semidirect
8. #10591322C2semidirect
10. #10591233C2semidirect
11. #10591209C2semidirect
52. #4674D3semidirect
61. #4648D3semidirect
515. C32#2398semidirect
599. C3#73419semidirect
600. C3#77460semidirect

Maximal subgroups

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

subgroupindex
C2×#638802
C2×#638442
#105923722
C3×#46742
C3×#46482
Dic3×(C2×D3)⋊C42
#105913262
#105913222
#105912922
#105912332
#105912092
#774603
#734193