Finite Group Databasebeta

← #11819069

Subgroups — #11819069

Order 1152.

1113 conjugacy classes of subgroups.

The subgroup lattice has 623 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63918C211yesmaximal, characteristic, complemented
2C2×#63856C211yesmaximal, characteristic
3C4×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
4C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
5C3×#4929C211yesmaximal, characteristic, complemented
6#10591396C212yesmaximal, complemented
7#10591313C211yesmaximal, characteristic
8#10591293C212yesmaximal
9#10591286C212yesmaximal
10#10591220C211yesmaximal, characteristic, complemented
11#10591211C212yesmaximal, complemented
12#76632—31nomaximal
13#73508—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C22×#627C2212yes—
17C2×C32×C42C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C4×C3⋊Dic3C2212yes—
21C2×C3×(C2×D3)⋊C4C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×#3724C2212yes—
26C2×Dic3⋊Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×(C2×D3)⋊Dic3C2212yes—
29#63918—24no—
30#63856—24no—
31#63658C2212yes—
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2211yescharacteristic
35C3×C3⋊#95C2211yescharacteristic
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×#946—31no—
40C2×#924—31no—
41C2×#888—31no—
42C2×#869—31no—
43C3×#391—31no—
44C3×C4×C22⋊C4—31no—
45#5229—31no—
46#5212—31no—
47#4987—31no—
48#4951—32no—
49#4947—32no—
50C4×(C2×D3)⋊C4D311yescharacteristic
51C4×C4⋊Dic3—31no—
52C4×C4⋊Dic3—31no—
53C4×C4⋊Dic3—61no—
54#4929—31no—
55#4929D311yescharacteristic, complemented
56#4673—32no—
57#4669—32no—
58#4660—32no—
59#4658—32no—
60#4646—32no—
61#4646—32no—
62C23×C3×D3C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2312yes—
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3—22no—
76C2×C3×Dic6—22no—
77C2×C3×Dic6—22no—
78C2×C3×Dic6—22no—
79C2×#627—24no—
80C2×#627—24no—
81C2×#627—42no—
82C32×C42—22no—
83C4⋊(C3⋊Dic3)—22no—
84C4⋊(C3⋊Dic3)D414yes—
85C4×C3⋊Dic3—42no—
86C3×(C2×D3)⋊C4—22no—
87C3×(C2×D3)⋊C4Q814yescomplemented
88C3×C4⋊Dic3—22no—
89C3×C4×Dic3—22no—
90#3724—24no—
91Dic3⋊Dic3—24no—
92(C2×D3)⋊Dic3—24no—
93(C2×D3)⋊Dic3—42no—
94#2492—91noSylow
95C22×C3×Q8—31no—
96C23×C3×C4—31no—
97C22×C4×D3C2×D311yescharacteristic
98C22×Dic6—32no—
99C22×Dic6—32no—
100C22×Dic6C2×D311yescharacteristic
101C2×C3×C4⋊C4—31no—
102C2×C3×C22⋊C4—31no—
103C2×C3×C22⋊C4—31no—
104C2×C3×C42—21no—
105C2×C3×C42—31no—
106C2×C3×C42C2×D311yescharacteristic
107C2×C3×C42C2×D311yescharacteristic
108C2×#217—32no—
109C2×#217—32no—
110#946—64no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4C2×D311yescharacteristic
114C2×(C2×D3)⋊C4C2×D311yescharacteristic
115C2×C4⋊Dic3—31no—
116C2×C4⋊Dic3—31no—
117C2×C4⋊Dic3—31no—
118C2×C4⋊Dic3—31no—
119C2×C4⋊Dic3—32no—
120C2×C4⋊Dic3—61no—
121C2×C4⋊Dic3—61no—
122C2×C4⋊Dic3C2×D311yescharacteristic
123#924—64no—
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4—32no—
126C2×Dic3⋊C4—32no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3—62no—
130C2×C4×Dic3C2×D311yescharacteristic
131#888—64no—
132#869—64no—
133C3×#95—31no—
134C3×#95—32no—
135C3×#95—32no—
136C3×#95—31no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—62no—
146C3⋊#95C2×D311yescharacteristic
147C3⋊#95C2×D312yes—
148C3⋊#95C2×D311yescharacteristic
149C3⋊#95C2×D312yes—
150C23×C32C2411yescharacteristic
151C22×C3×D3—21no—
152C22×C3×D3—21no—
153C22×C3×D3—21no—
154C22×C3×D3—21no—
155C22×C3×D3—21no—
156C22×C3×D3—21no—
157C22×C3×D3C2×Q812yes—
158C2×C32×C4—21no—
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4—21no—
163C2×C32×C4C2×D412yes—
164C2×C32×C4C2×Q812yes—
165C2×C32×C4#4112yes—
166C2×C32×C4#4112yes—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3C2×D414yes—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3C2×Q812yes—
187C2×C3×Dic3#4112yes—
188C3×C4×D3—44no—
189C3×Dic6—44no—
190#627—48no—
191C2×C4⋊Q8—91no—
192C2×C22⋊Q8—91no—
193#400—92no—
194#393—92no—
195#391—31no—
196#391—92no—
197#391—91no—
198#388—92no—
199#380—91no—
200C4×C4⋊C4—91no—
201C4×C22⋊C4—31no—
202C24×C3—31no—
203C23×D3C22×D311yescharacteristic
204C2×C3×Q8—62no—
205C2×C3×Q8—62no—
206C2×C3×Q8—62no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—31no—
211C22×C3×C4—31no—
212C22×C3×C4—31no—
213C22×C3×C4—32no—
214C22×C3×C4—32no—
215C22×C3×C4—62no—
216C22×C3×C4—62no—
217C22×C3×C4—62no—
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C22×D311yescharacteristic
224C22×Dic3—32no—
225C22×Dic3—32no—
226C22×Dic3—32no—
227C22×Dic3—32no—
228C22×Dic3—62no—
229C22×Dic3—62no—
230C22×Dic3C22×D311yescharacteristic
231C22×Dic3C22×D312yes—
232C22×Dic3C22×D312yes—
233C22×Dic3C22×D311yescharacteristic
234C22×Dic3C22×D311yescharacteristic
235C2×C4×D3—22no—
236C2×C4×D3—22no—
237C2×C4×D3—22no—
238C2×Dic6—22no—
239C2×Dic6—22no—
240C2×Dic6—22no—
241C2×Dic6—64no—
242C2×Dic6—64no—
243C2×Dic6—64no—
244C2×Dic6—64no—
245C2×Dic6—122no—
246C2×Dic6—122no—
247C3×C4⋊C4—62no—
248C3×C22⋊C4—34no—
249C3×C22⋊C4—62no—
250C3×C42—24no—
251C3×C42—22no—
252C3×C42—22no—
253C3×C42—62no—
254#217—64no—
255#217—122no—
256(C2×D3)⋊C4—22no—
257(C2×D3)⋊C4—64no—
258(C2×D3)⋊C4—122no—
259(C2×D3)⋊C4Dic614yescomplemented
260C4⋊Dic3—22no—
261C4⋊Dic3—34no—
262C4⋊Dic3—34no—
263C4⋊Dic3—64no—
264C4⋊Dic3—64no—
265C4⋊Dic3—64no—
266C4⋊Dic3—62no—
267C4⋊Dic3—62no—
268Dic3⋊C4—64no—
269Dic3⋊C4—64no—
270Dic3⋊C4—64no—
271C4×Dic3—22no—
272C4×Dic3—122no—
273C4×Dic3—122no—
274C4×Dic3—124no—
275C22×C32C22×D411yescharacteristic
276C22×C32C22×Q811yescharacteristic
277C22×C32C2×#4111yescharacteristic
278C22×C32C2×#4111yescharacteristic
279C22×C32C2×#4111yescharacteristic
280C22×C32H(5,𝔽2)11yescharacteristic
281C22×C322−1+411yescharacteristic
282C2×C3×D3—22no—
283C2×C3×D3—22no—
284C2×C3×D3—22no—
285C2×C3×D3—41no—
286C2×C3×D3—41no—
287C2×C3×D3—41no—
288C2×C3×D3—41no—
289C32×C4—22no—
290C32×C4—41no—
291C32×C4#12414yes—
292C3⋊Dic3—24no—
293C3⋊Dic3—42no—
294C3×Dic3—22no—
295C3×Dic3—22no—
296C3×Dic3—42no—
297C3×Dic3—41no—
298C3×Dic3—42no—
299C22×Q8—31no—
300C22×Q8—92no—
301C23×C4—31no—
302C4⋊Q8—184no—
303C22⋊Q8—184no—
304C2×C4⋊C4—31no—
305C2×C4⋊C4—91no—
306C2×C4⋊C4—92no—
307C2×C4⋊C4—92no—
308C2×C4⋊C4—91no—
309C2×C22⋊C4—31no—
310C2×C22⋊C4—31no—
311C2×C22⋊C4—92no—
312C2×C22⋊C4—92no—
313C2×C42—31no—
314C2×C42—92no—
315C2×C42D3211yescharacteristic
316#95—31no—
317#95—31no—
318#95—32no—
319#95—32no—
320#95—92no—
321#95—92no—
322#95—92no—
323#95—92no—
324C23×C3—21no—
325C23×C3—32no—
326C23×C3—61no—
327C23×C3—61no—
328C23×C3—61no—
329C23×C3—61no—
330C23×C3—61no—
331C23×C3—61no—
332C23×C3C23×D311yescharacteristic
333C23×C3C23×D311yescharacteristic
334C22×D3—21no—
335C22×D3—21no—
336C22×D3—21no—
337C22×D3—21no—
338C22×D3—21no—
339C22×D3—21no—
340C22×D3C2×Dic612yes—
341C3×Q8—124no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—22no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—32no—
360C2×C3×C4—32no—
361C2×C3×C4—41no—
362C2×C3×C4—41no—
363C2×C3×C4—61no—
364C2×C3×C4—61no—
365C2×C3×C4—61no—
366C2×C3×C4—61no—
367C2×C3×C4—62no—
368C2×C3×C4—61no—
369C2×C3×C4—62no—
370C2×C3×C4—61no—
371C2×C3×C4—62no—
372C2×C3×C4—62no—
373C2×C3×C4—61no—
374C2×C3×C4—62no—
375C2×C3×C4—62no—
376C2×C3×C4—124no—
377C2×C3×C4C2×Dic612yes—
378C2×C3×C4#23512yes—
379C2×C3×C4#23512yes—
380C2×C3×C4D3×D412yes—
381C2×C3×C4D3×D412yes—
382C2×C3×C4#23712yes—
383C2×C3×C4#23712yes—
384C2×C3×C4D3×Q812yes—
385C2×Dic3—21no—
386C2×Dic3—21no—
387C2×Dic3—21no—
388C2×Dic3—21no—
389C2×Dic3—22no—
390C2×Dic3—21no—
391C2×Dic3—21no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—21no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—34no—
399C2×Dic3—34no—
400C2×Dic3—64no—
401C2×Dic3—62no—
402C2×Dic3—62no—
403C2×Dic3—62no—
404C2×Dic3—62no—
405C2×Dic3—64no—
406C2×Dic3—62no—
407C2×Dic3—62no—
408C2×Dic3—62no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—62no—
412C2×Dic3—122no—
413C2×Dic3—122no—
414C2×Dic3—122no—
415C2×Dic3—122no—
416C2×Dic3C2×Dic612yes—
417C2×Dic3#23512yes—
418C4×D3—44no—
419Dic6—44no—
420Dic6—128no—
421Dic6—128no—
422C2×C32C2×#12411yescharacteristic
423C2×C32#53311yescharacteristic
424C2×C32#54211yescharacteristic
425C2×C32#54611yescharacteristic
426C2×C32D4×Q811yescharacteristic
427C2×C32#55411yescharacteristic
428C2×C32#55611yescharacteristic
429C3×D3—42no—
430C24—31no—
431C2×Q8—62no—
432C2×Q8—62no—
433C2×Q8—62no—
434C2×Q8—184no—
435C2×Q8—184no—
436C2×Q8—362no—
437C22×C4—31no—
438C22×C4—31no—
439C22×C4—32no—
440C22×C4—31no—
441C22×C4—32no—
442C22×C4—62no—
443C22×C4—62no—
444C22×C4—62no—
445C22×C4—92no—
446C22×C4—92no—
447C22×C4C2×D3211yescharacteristic
448C22×C4C2×D3211yescharacteristic
449C22×C4C2×D3211yescharacteristic
450C4⋊C4—62no—
451C4⋊C4—94no—
452C4⋊C4—184no—
453C4⋊C4—184no—
454C4⋊C4—182no—
455C22⋊C4—34no—
456C22⋊C4—62no—
457C22⋊C4—184no—
458C22⋊C4—362no—
459C42—22no—
460C42—62no—
461C42—362no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—62no—
470C22×C3—62no—
471C22×C3—62no—
472C22×C3—121no—
473C22×C3—121no—
474C22×C3—121no—
475C22×C3—121no—
476C22×C3C22×Dic611yescharacteristic
477C22×C3C2×#23511yescharacteristic
478C22×C3C2×#23511yescharacteristic
479C22×C3C2×#23511yescharacteristic
480C22×C3C2×D3×D411yescharacteristic
481C22×C3C2×D3×D411yescharacteristic
482C22×C3C2×#23711yescharacteristic
483C22×C3C2×#23711yescharacteristic
484C22×C3C2×D3×Q811yescharacteristic
485C22×C3#100711yescharacteristic
486C22×C3D3×#4111yescharacteristic
487C22×C3#100911yescharacteristic
488C22×C3#100911yescharacteristic
489C22×C3#101011yescharacteristic
490C2×D3—22no—
491C2×D3—22no—
492C2×D3—22no—
493C2×D3—41no—
494C2×D3—41no—
495C2×D3—41no—
496C2×D3—41no—
497C3×C4—24no—
498C3×C4—22no—
499C3×C4—22no—
500C3×C4—24no—
501C3×C4—42no—
502C3×C4—41no—
503C3×C4—41no—
504C3×C4—62no—
505C3×C4—62no—
506C3×C4—121no—
507C3×C4—122no—
508C3×C4—122no—
509C3×C4#88514yes—
510C3×C4#88514yes—
511Dic3—22no—
512Dic3—22no—
513Dic3—42no—
514Dic3—42no—
515Dic3—41no—
516Dic3—64no—
517Dic3—64no—
518Dic3—124no—
519Dic3—124no—
520Dic3—122no—
521Dic3—122no—
522C32#249211yescharacteristic, complemented, Sylow
523C23—32no—
524C23—61no—
525C23—61no—
526C23—61no—
527C23—61no—
528C23—61no—
529C23—61no—
530C23C22×D3211yescharacteristic
531Q8—124no—
532Q8—368no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—32no—
539C2×C4—32no—
540C2×C4—61no—
541C2×C4—61no—
542C2×C4—61no—
543C2×C4—61no—
544C2×C4—61no—
545C2×C4—62no—
546C2×C4—62no—
547C2×C4—62no—
548C2×C4—61no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—61no—
552C2×C4—62no—
553C2×C4—94no—
554C2×C4—124no—
555C2×C4—182no—
556C2×C4—182no—
557C2×C4—182no—
558C2×C4—182no—
559C2×C4—182no—
560C2×C4D3×Dic612yes—
561C2×C4#379812yes—
562C2×C4#380212yes—
563C2×C4#380512yes—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—122no—
572C2×C3#547011yescharacteristic
573C2×C3C2×#88511yescharacteristic
574C2×C3C2×#88511yescharacteristic
575C2×C3#553411yescharacteristic
576C2×C3D4×Dic611yescharacteristic
577C2×C3#554211yescharacteristic
578C2×C3#554311yescharacteristic
579C2×C3#555011yescharacteristic
580C2×C3#557811yescharacteristic
581C2×C3#558211yescharacteristic
582C2×C3#563511yescharacteristic
583C2×C3#564111yescharacteristic
584C2×C3#567611yescharacteristic
585C2×C3#572711yescharacteristic
586D3—42no—
587C22—62no—
588C22—62no—
589C22—62no—
590C22—121no—
591C22—121no—
592C22—121no—
593C22—121no—
594C22C2×D3×Dic611yescharacteristic
595C22#6429711yescharacteristic
596C22C2×#379811yescharacteristic
597C22C2×#380211yescharacteristic
598C22D3×#23511yescharacteristic
599C22#6430811yescharacteristic
600C22C2×#380511yescharacteristic
601C4—22no—
602C4—41no—
603C4—62no—
604C4—62no—
605C4—121no—
606C4—122no—
607C4—122no—
608C4—184no—
609C4—362no—
610C4#6391514yes—
611C3—21no—
612C3#7350811yescharacteristic, complemented
613C3#7663211yescharacteristic, complemented
614C2—122no—
615C2#1059387311yescharacteristic
616C2#1059387811yescharacteristic
617C2#1059390411yescharacteristic
618C2#1059400711yescharacteristic
619C2#1059484111yescharacteristic
620C2#1059499311yescharacteristic
621C2C2×#6391511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C42C22
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32#2492
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#63918C2semidirect
3. C4×C4⋊(C3⋊Dic3)C2semidirect
5. C3×#4929C2semidirect
6. #10591396C2semidirect
10. #10591220C2semidirect
11. #10591211C2semidirect
55. #4929D3semidirect
87. C3×(C2×D3)⋊C4Q8semidirect
259. (C2×D3)⋊C4Dic6semidirect
522. C32#2492semidirect
612. C3#73508semidirect
613. C3#76632semidirect

Maximal subgroups

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

subgroupindex
C2×#639182
C2×#638562
C4×C4⋊(C3⋊Dic3)2
C3×C4×(C2×D3)⋊C42
C3×#49292
#105913962
#105913132
#105912932
#105912862
#105912202
#105912112
#766323
#735083