Finite Group Databasebeta

← #11824556

Subgroups — #11824556

Order 1152.

1533 conjugacy classes of subgroups.

The subgroup lattice has 699 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
2C2×#63970C212yesmaximal, complemented
3C2×#63908C211yesmaximal, characteristic, complemented
4#10592652C211yesmaximal, characteristic, complemented
5C3×#4960C211yesmaximal, characteristic, complemented
6#10591710C212yesmaximal, complemented
7#10591363C212yesmaximal, complemented
8D3×C3⋊#95C211yesmaximal, characteristic, complemented
9#10591353C211yesmaximal, characteristic, complemented
10#10591305C212yesmaximal, complemented
11#10591300C211yesmaximal, characteristic, complemented
12#82380—31nomaximal
13#76759—31nomaximal
14C22×C3×#67C2212yes—
15C22×C3×#67C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C22×C3×D12C2211yescharacteristic
18C22×C3×C4×D3C2211yescharacteristic
19C22×#625C2212yes—
20C22×D3×Dic3C2212yes—
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×#3757C2212yes—
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28C3×#67⋊C4—24no—
29#63970—28no—
30C2×Dic3⋊Dic3C2212yes—
31C2×(C2×D3)⋊Dic3C2212yes—
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34#63908—24no—
35#63658C2211yescharacteristic
36#63658C2212yes—
37C3×C3⋊#95C2211yescharacteristic
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×C4×D4—31no—
41C2×#939—32no—
42C2×#938—32no—
43C2×#938—31no—
44C2×#930—31no—
45C2×#67⋊C4D311yescharacteristic, complemented
46C3×#392—31no—
47#5222—31no—
48#5220—32no—
49#5213—32no—
50C2×C3⋊#95—31no—
51#4991—31no—
52#4981—31no—
53#4960D311yescharacteristic, complemented
54#4958—32no—
55#4956—32no—
56#4953—31no—
57#4953—31no—
58#4953—61no—
59#4951—32no—
60#4940—32no—
61D3×#95—31no—
62#4661—31no—
63C24×C32C2311yescharacteristic
64C23×C3×D3C2312yes—
65C23×C3×D3C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3C2312yes—
69C22×C3⋊Dic3C2312yes—
70C2×C3×#67—22no—
71C2×C3×#67—22no—
72C2×C3×#67—24no—
73C2×C3×#67—24no—
74C2×C3×#67—42no—
75C2×C3×#67D414yescomplemented
76C22×C3×Dic3—22no—
77C22×C3×Dic3—42no—
78C22×C3×Dic3C2311yescharacteristic
79C22×C3×Dic3C2311yescharacteristic
80C22×C3×Dic3C2311yescharacteristic
81C22×C3×Dic3C2312yes—
82C2×C3×D12—22no—
83C2×C3×D12—42no—
84C2×C3×C4×D3—42no—
85C2×C3×C4×D3D414yescomplemented
86C2×#625—24no—
87C2×#625—24no—
88C2×#625—24no—
89C2×D3×Dic3—24no—
90C2×D3×Dic3—24no—
91C2×D3×Dic3—42no—
92C32×C22⋊C4—22no—
93#3757—24no—
94C4⋊(C3⋊Dic3)—22no—
95C3×(C2×D3)⋊C4—22no—
96C3×(C2×D3)⋊C4—24no—
97C3×Dic3⋊C4—22no—
98C3×C4×Dic3—22no—
99Dic3⋊Dic3—24no—
100(C2×D3)⋊Dic3—24no—
101(C2×D3)⋊Dic3—24no—
102(C2×D3)⋊Dic3—42no—
103#2543—91noSylow
104C22×C3×D4—31no—
105C22×C3×D4—32no—
106C22×C3×D4—31no—
107C23×C3×C4—31no—
108C23×C3×C4—31no—
109C22×#67—32no—
110C22×#67—32no—
111C22×#67C2×D312yes—
112C22×#67C2×D311yescharacteristic
113C23×Dic3—32no—
114C23×Dic3C2×D311yescharacteristic
115C22×D12C2×D311yescharacteristic
116C22×C4×D3—32no—
117C22×C4×D3C2×D311yescharacteristic
118C3×C4×D4—64no—
119C2×C3×C4⋊C4—31no—
120C2×C3×C22⋊C4—21no—
121C2×C3×C22⋊C4—32no—
122C2×C3×C22⋊C4—31no—
123C2×C3×C22⋊C4C2×D311yescharacteristic
124C2×C3×C22⋊C4C2×D311yescharacteristic
125C2×C3×C42—31no—
126C2×#217—32no—
127C2×#217—32no—
128C2×#217—32no—
129C2×#217—32no—
130C2×#217—32no—
131C2×#217—62no—
132#939—68no—
133#938—68no—
134#938—64no—
135#930—64no—
136C2×(C2×D3)⋊C4—32no—
137C2×(C2×D3)⋊C4—32no—
138C2×(C2×D3)⋊C4—32no—
139C2×(C2×D3)⋊C4C2×D312yes—
140C2×(C2×D3)⋊C4C2×D311yescharacteristic
141C2×C4⋊Dic3—31no—
142C2×C4⋊Dic3—31no—
143C2×C4⋊Dic3—32no—
144C2×C4⋊Dic3—61no—
145C2×Dic3⋊C4—32no—
146C2×Dic3⋊C4C2×D311yescharacteristic
147C2×C4×Dic3C2×D311yescharacteristic
148#67⋊C4—24no—
149C3×#95—31no—
150C3⋊#95—31no—
151C3⋊#95—32no—
152C3⋊#95—32no—
153C3⋊#95—31no—
154C3⋊#95—32no—
155C3⋊#95—32no—
156C3⋊#95—32no—
157C3⋊#95—32no—
158C3⋊#95—61no—
159C3⋊#95—62no—
160C3⋊#95C2×D311yescharacteristic
161C23×C32—21no—
162C23×C32—21no—
163C23×C32—22no—
164C23×C32—22no—
165C23×C32C2×D412yes—
166C23×C32C2411yescharacteristic
167C22×C3×D3—22no—
168C22×C3×D3—22no—
169C22×C3×D3—22no—
170C22×C3×D3—22no—
171C22×C3×D3—22no—
172C22×C3×D3—22no—
173C22×C3×D3—22no—
174C22×C3×D3—22no—
175C22×C3×D3—22no—
176C22×C3×D3C2×D412yes—
177C22×C3×D3C2×D412yes—
178C22×C3×D3#4112yes—
179C2×C32×C4—22no—
180C2×C32×C4—21no—
181C2×C32×C4—22no—
182C2×C32×C4C2×D412yes—
183C2×C3⋊Dic3—22no—
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3—22no—
187C2×C3⋊Dic3—22no—
188C2×C3⋊Dic3—22no—
189C3×#67—28no—
190C3×#67—48no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—44no—
199C2×C3×Dic3C2×D412yes—
200C2×C3×Dic3C2×D412yes—
201C2×C3×Dic3#4114yes—
202C3×D12—44no—
203C3×C4×D3—44no—
204#625—48no—
205D3×Dic3—48no—
206C2×#121—91no—
207C2×#121—92no—
208C2×C4×D4—31no—
209#398—91no—
210#397—91no—
211#394—91no—
212#392—31no—
213#388—92no—
214#386—92no—
215#386—92no—
216C2×#95—91no—
217C24×C3—21no—
218C24×C3—31no—
219C24×C3—32no—
220C24×C3C22×D311yescharacteristic
221C24×C3C22×D311yescharacteristic
222C23×D3C22×D312yes—
223C23×D3C22×D311yescharacteristic
224C2×C3×D4—34no—
225C2×C3×D4—64no—
226C2×C3×D4—62no—
227C2×C3×D4—62no—
228C2×C3×D4—64no—
229C2×C3×D4—62no—
230C2×C3×D4—122no—
231C2×C3×D4—122no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—32no—
235C22×C3×C4—31no—
236C22×C3×C4—31no—
237C22×C3×C4—34no—
238C22×C3×C4—31no—
239C22×C3×C4—62no—
240C22×C3×C4—122no—
241C22×C3×C4—122no—
242C22×C3×C4C22×D311yescharacteristic
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C22×D311yescharacteristic
246C2×#67—22no—
247C2×#67—22no—
248C2×#67—24no—
249C2×#67—24no—
250C2×#67—42no—
251C2×#67—64no—
252C2×#67—64no—
253C2×#67—64no—
254C2×#67—64no—
255C2×#67—64no—
256C2×#67—64no—
257C2×#67D1214yescomplemented
258C22×Dic3—22no—
259C22×Dic3—32no—
260C22×Dic3—32no—
261C22×Dic3—32no—
262C22×Dic3—32no—
263C22×Dic3—42no—
264C22×Dic3—62no—
265C22×Dic3—62no—
266C22×Dic3—64no—
267C22×Dic3—64no—
268C22×Dic3—122no—
269C22×Dic3C22×D311yescharacteristic
270C22×Dic3C22×D311yescharacteristic
271C22×Dic3C22×D312yes—
272C22×Dic3C22×D311yescharacteristic
273C2×D12—22no—
274C2×D12—42no—
275C2×C4×D3—42no—
276C2×C4×D3—64no—
277C2×C4×D3—64no—
278C2×C4×D3—122no—
279C2×C4×D3#6714yescomplemented
280C3×C4⋊C4—62no—
281C3×C22⋊C4—22no—
282C3×C22⋊C4—22no—
283C3×C22⋊C4—42no—
284C3×C22⋊C4—64no—
285C3×C22⋊C4—62no—
286C3×C42—62no—
287#217—64no—
288#217—64no—
289#217—64no—
290#217—64no—
291#217—124no—
292#217—122no—
293(C2×D3)⋊C4—22no—
294(C2×D3)⋊C4—24no—
295(C2×D3)⋊C4—64no—
296(C2×D3)⋊C4—64no—
297(C2×D3)⋊C4—122no—
298C4⋊Dic3—62no—
299C4⋊Dic3—62no—
300C4⋊Dic3—64no—
301C4⋊Dic3—122no—
302Dic3⋊C4—22no—
303Dic3⋊C4—64no—
304C4×Dic3—22no—
305C22×C32—22no—
306C22×C32—24no—
307C22×C32—41no—
308C22×C32—41no—
309C22×C32—42no—
310C22×C32C22×D411yescharacteristic
311C22×C32C22×D411yescharacteristic
312C22×C32C2×#4111yescharacteristic
313C22×C32C2×#4112yes—
314C22×C32H(5,𝔽2)12yes—
315C2×C3×D3—22no—
316C2×C3×D3—22no—
317C2×C3×D3—24no—
318C2×C3×D3—24no—
319C2×C3×D3—42no—
320C2×C3×D3—42no—
321C2×C3×D3—42no—
322C2×C3×D3—42no—
323C2×C3×D3—42no—
324C2×C3×D3—42no—
325C2×C3×D3—42no—
326C2×C3×D3#12114yes—
327C32×C4—22no—
328C32×C4—41no—
329C3⋊Dic3—42no—
330C3⋊Dic3—42no—
331C3×Dic3—22no—
332C3×Dic3—22no—
333C3×Dic3—24no—
334C3×Dic3—41no—
335C22×D4—31no—
336C22×D4—32no—
337C22×D4—31no—
338C22×D4—92no—
339C23×C4—31no—
340C23×C4—31no—
341C23×C4—92no—
342#121—184no—
343#121—188no—
344C4×D4—64no—
345C2×C4⋊C4—31no—
346C2×C4⋊C4—92no—
347C2×C4⋊C4—91no—
348C2×C22⋊C4—31no—
349C2×C22⋊C4—32no—
350C2×C22⋊C4—92no—
351C2×C22⋊C4—92no—
352C2×C22⋊C4—92no—
353C2×C22⋊C4—92no—
354C2×C22⋊C4D3211yescharacteristic
355C2×C42—31no—
356#95—31no—
357#95—92no—
358#95—92no—
359#95—91no—
360#95—92no—
361C23×C3—21no—
362C23×C3—21no—
363C23×C3—22no—
364C23×C3—22no—
365C23×C3—22no—
366C23×C3—21no—
367C23×C3—22no—
368C23×C3—21no—
369C23×C3—21no—
370C23×C3—22no—
371C23×C3—32no—
372C23×C3—32no—
373C23×C3—32no—
374C23×C3—41no—
375C23×C3—41no—
376C23×C3—42no—
377C23×C3—42no—
378C23×C3—62no—
379C23×C3—62no—
380C23×C3—62no—
381C23×C3—62no—
382C23×C3—62no—
383C23×C3—62no—
384C23×C3—62no—
385C23×C3—62no—
386C23×C3—62no—
387C23×C3C2×D1212yes—
388C23×C3D3×D412yes—
389C23×C3C23×D311yescharacteristic
390C23×C3C23×D311yescharacteristic
391C22×D3—22no—
392C22×D3—22no—
393C22×D3—22no—
394C22×D3—22no—
395C22×D3—22no—
396C22×D3—22no—
397C22×D3—22no—
398C22×D3—22no—
399C22×D3—22no—
400C22×D3C2×D1212yes—
401C22×D3#23512yes—
402C22×D3C2×#6712yes—
403C3×D4—68no—
404C3×D4—124no—
405C3×D4—128no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—21no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—21no—
412C2×C3×C4—22no—
413C2×C3×C4—32no—
414C2×C3×C4—32no—
415C2×C3×C4—34no—
416C2×C3×C4—42no—
417C2×C3×C4—41no—
418C2×C3×C4—42no—
419C2×C3×C4—62no—
420C2×C3×C4—61no—
421C2×C3×C4—62no—
422C2×C3×C4—62no—
423C2×C3×C4—61no—
424C2×C3×C4—61no—
425C2×C3×C4—62no—
426C2×C3×C4—124no—
427C2×C3×C4—124no—
428C2×C3×C4D3×D412yes—
429C2×C3×C4C2×#6712yes—
430#67—28no—
431#67—48no—
432#67—128no—
433#67—128no—
434C2×Dic3—21no—
435C2×Dic3—22no—
436C2×Dic3—22no—
437C2×Dic3—22no—
438C2×Dic3—21no—
439C2×Dic3—22no—
440C2×Dic3—21no—
441C2×Dic3—44no—
442C2×Dic3—62no—
443C2×Dic3—62no—
444C2×Dic3—62no—
445C2×Dic3—62no—
446C2×Dic3—62no—
447C2×Dic3—62no—
448C2×Dic3—62no—
449C2×Dic3—62no—
450C2×Dic3—62no—
451C2×Dic3—62no—
452C2×Dic3—62no—
453C2×Dic3—62no—
454C2×Dic3—122no—
455C2×Dic3—122no—
456C2×Dic3—122no—
457C2×Dic3—122no—
458C2×Dic3—122no—
459C2×Dic3—122no—
460C2×Dic3—128no—
461C2×Dic3C2×D1212yes—
462C2×Dic3#23714yes—
463C2×Dic3C2×#6712yes—
464D12—44no—
465C4×D3—44no—
466C4×D3—128no—
467C2×C32—42no—
468C2×C32C2×#12111yescharacteristic
469C2×C32#53211yescharacteristic
470C2×C32#53411yescharacteristic
471C2×C32#54612yes—
472C2×C32#55312yes—
473C3×D3—24no—
474C3×D3—82no—
475C24—31no—
476C24—32no—
477C24C2×D3211yescharacteristic
478C2×D4—34no—
479C2×D4—64no—
480C2×D4—62no—
481C2×D4—62no—
482C2×D4—64no—
483C2×D4—62no—
484C2×D4—122no—
485C2×D4—122no—
486C2×D4—184no—
487C2×D4—184no—
488C2×D4—184no—
489C22×C4—32no—
490C22×C4—31no—
491C22×C4—31no—
492C22×C4—34no—
493C22×C4—31no—
494C22×C4—62no—
495C22×C4—92no—
496C22×C4—92no—
497C22×C4—122no—
498C22×C4—122no—
499C22×C4—184no—
500C22×C4—184no—
501C22×C4—362no—
502C22×C4C2×D3211yescharacteristic
503C22×C4C2×D3211yescharacteristic
504C4⋊C4—62no—
505C4⋊C4—184no—
506C4⋊C4—182no—
507C22⋊C4—22no—
508C22⋊C4—64no—
509C22⋊C4—62no—
510C22⋊C4—184no—
511C22⋊C4—184no—
512C22⋊C4—184no—
513C22⋊C4—362no—
514C42—62no—
515C22×C3—22no—
516C22×C3—24no—
517C22×C3—24no—
518C22×C3—22no—
519C22×C3—21no—
520C22×C3—21no—
521C22×C3—22no—
522C22×C3—22no—
523C22×C3—21no—
524C22×C3—34no—
525C22×C3—44no—
526C22×C3—42no—
527C22×C3—41no—
528C22×C3—42no—
529C22×C3—41no—
530C22×C3—41no—
531C22×C3—41no—
532C22×C3—42no—
533C22×C3—62no—
534C22×C3—62no—
535C22×C3—64no—
536C22×C3—64no—
537C22×C3—81no—
538C22×C3—82no—
539C22×C3—81no—
540C22×C3—122no—
541C22×C3—122no—
542C22×C3—122no—
543C22×C3—122no—
544C22×C3—122no—
545C22×C3—122no—
546C22×C3—122no—
547C22×C3C22×D1211yescharacteristic
548C22×C3C2×#23511yescharacteristic
549C22×C3C2×D3×D411yescharacteristic
550C22×C3C2×D3×D411yescharacteristic
551C22×C3C2×#23712yes—
552C22×C3#100412yes—
553C22×C3#100412yes—
554C22×C3D3×#4111yescharacteristic
555C22×C3D3×#4112yes—
556C22×C3C22×#6711yescharacteristic
557C2×D3—24no—
558C2×D3—22no—
559C2×D3—24no—
560C2×D3—22no—
561C2×D3—42no—
562C2×D3—42no—
563C2×D3—42no—
564C2×D3—42no—
565C2×D3—42no—
566C2×D3—42no—
567C2×D3—42no—
568C2×D3#93014yes—
569C3×C4—22no—
570C3×C4—22no—
571C3×C4—42no—
572C3×C4—41no—
573C3×C4—41no—
574C3×C4—64no—
575C3×C4—62no—
576C3×C4—62no—
577C3×C4—81no—
578C3×C4—121no—
579Dic3—22no—
580Dic3—22no—
581Dic3—24no—
582Dic3—41no—
583Dic3—122no—
584Dic3—122no—
585Dic3—122no—
586Dic3—122no—
587Dic3—242no—
588Dic3—242no—
589C32#254311yescharacteristic, complemented, Sylow
590C23—21no—
591C23—22no—
592C23—22no—
593C23—21no—
594C23—32no—
595C23—32no—
596C23—32no—
597C23—62no—
598C23—62no—
599C23—62no—
600C23—62no—
601C23—62no—
602C23—62no—
603C23—62no—
604C23—62no—
605C23—62no—
606C23D3×D1212yes—
607C23C22×D3211yescharacteristic
608D4—68no—
609D4—124no—
610D4—128no—
611D4—368no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—21no—
615C2×C4—32no—
616C2×C4—34no—
617C2×C4—32no—
618C2×C4—62no—
619C2×C4—61no—
620C2×C4—62no—
621C2×C4—62no—
622C2×C4—61no—
623C2×C4—62no—
624C2×C4—61no—
625C2×C4—124no—
626C2×C4—124no—
627C2×C4—182no—
628C2×C4—182no—
629C2×C4—182no—
630C2×C4—182no—
631C2×C4—182no—
632C2×C4—182no—
633C2×C4—368no—
634C2×C4D3×#6712yes—
635C2×C3—21no—
636C2×C3—22no—
637C2×C3—21no—
638C2×C3—22no—
639C2×C3—21no—
640C2×C3—42no—
641C2×C3—42no—
642C2×C3—64no—
643C2×C3—82no—
644C2×C3—242no—
645C2×C3#554012yes—
646C2×C3#555412yes—
647C2×C3#558911yescharacteristic
648C2×C3#559112yes—
649C2×C3D3×#12111yescharacteristic
650C2×C3#561412yes—
651C2×C3#571611yescharacteristic
652C2×C3C2×#93011yescharacteristic
653C2×C3#580411yescharacteristic
654C2×C3#583211yescharacteristic
655D3—24no—
656D3—82no—
657C22—24no—
658C22—22no—
659C22—34no—
660C22—41no—
661C22—42no—
662C22—41no—
663C22—62no—
664C22—64no—
665C22—62no—
666C22—64no—
667C22—122no—
668C22—122no—
669C22—122no—
670C22—122no—
671C22—122no—
672C22—122no—
673C22—122no—
674C22C2×D3×D1211yescharacteristic
675C22D3×#23511yescharacteristic
676C22D3×#23712yes—
677C22#6431312yes—
678C22C2×D3×#6711yescharacteristic
679C4—22no—
680C4—41no—
681C4—62no—
682C4—64no—
683C4—62no—
684C4—121no—
685C4—362no—
686C4—362no—
687C3—21no—
688C3#7675911yescharacteristic, complemented
689C3#8238011yescharacteristic, complemented
690C2—42no—
691C2—64no—
692C2—242no—
693C2#1059419812yes—
694C2#1059429212yes—
695C2D3×#93011yescharacteristic
696C2#1059515211yescharacteristic
697C2#1059523011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2543
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#67⋊C4C2semidirect
2. C2×#63970C2semidirect
3. C2×#63908C2semidirect
4. #10592652C2semidirect
5. C3×#4960C2semidirect
6. #10591710C2semidirect
7. #10591363C2semidirect
8. D3×C3⋊#95C2semidirect
9. #10591353C2semidirect
10. #10591305C2semidirect
11. #10591300C2semidirect
45. C2×#67⋊C4D3semidirect
53. #4960D3semidirect
75. C2×C3×#67D4semidirect
85. C2×C3×C4×D3D4semidirect
257. C2×#67D12semidirect
279. C2×C4×D3#67semidirect
589. C32#2543semidirect
688. C3#76759semidirect
689. C3#82380semidirect

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×#639702
C2×#639082
#105926522
C3×#49602
#105917102
#105913632
D3×C3⋊#952
#105913532
#105913052
#105913002
#823803
#767593