Finite Group Databasebeta

← #11819071

Subgroups — #11819071

Order 1152.

1109 conjugacy classes of subgroups.

The subgroup lattice has 625 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63918C211yesmaximal, characteristic, complemented
2C2×#63857C211yesmaximal, characteristic
3#10592628C211yesmaximal, characteristic, complemented
4C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
5C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
6#10591313C211yesmaximal, characteristic
7#10591305C212yesmaximal
8#10591293C212yesmaximal
9#10591213C211yesmaximal, characteristic, complemented
10#10591207C212yesmaximal, complemented
11#10591191C212yesmaximal, complemented
12#73789—31nomaximal
13#73508—31nomaximal
14C22×#634C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C22×#627C2212yes—
17C2×C32×C42C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C3×(C2×D3)⋊C4C2211yescharacteristic
20C2×C3×(C2×D3)⋊C4C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2212yes—
25C2×Dic3⋊Dic3C2212yes—
26C2×Dic3⋊Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×(C2×D3)⋊Dic3C2212yes—
29#63918—24no—
30#63857—24no—
31#63658C2212yes—
32#63658C2212yes—
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2211yescharacteristic
35C3×C3⋊#95C2211yescharacteristic
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×#924—31no—
40C2×#897—31no—
41C2×#888—31no—
42C2×#869—31no—
43C3×C4×C4⋊C4—31no—
44C3×C4×C22⋊C4—31no—
45#5212—31no—
46#4987—31no—
47#4973—31no—
48#4951—32no—
49#4947—32no—
50#4940—32no—
51C4×(C2×D3)⋊C4D311yescharacteristic
52C4×C4⋊Dic3D311yescharacteristic, complemented
53#4929—31no—
54#4929—31no—
55#4929—31no—
56#4929—32no—
57#4929—61no—
58#4673—32no—
59#4660—32no—
60#4659—32no—
61#4646—32no—
62C23×C3×D3C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2312yes—
68C2×#634—22no—
69C2×#634—22no—
70C2×#634—22no—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2311yescharacteristic
76C2×C3×C4×D3—22no—
77C2×C3×C4×D3—22no—
78C2×C3×C4×D3—22no—
79C2×#627—24no—
80C2×#627—24no—
81C2×#627—42no—
82C32×C42—22no—
83C4⋊(C3⋊Dic3)—22no—
84C3×(C2×D3)⋊C4—22no—
85C3×(C2×D3)⋊C4Q814yescomplemented
86C3×C4⋊Dic3—22no—
87C3×C4⋊Dic3D414yes—
88C3×C4×Dic3—22no—
89C3×C4×Dic3—42no—
90Dic3⋊Dic3—24no—
91Dic3⋊Dic3—24no—
92(C2×D3)⋊Dic3—24no—
93(C2×D3)⋊Dic3—42no—
94#2492—91noSylow
95C23×C3×C4—31no—
96C22×C4×D3C2×D311yescharacteristic
97C22×Dic6—31no—
98C22×Dic6—31no—
99C22×Dic6—32no—
100C22×Dic6—32no—
101C22×Dic6—61no—
102C2×C3×C4⋊C4—31no—
103C2×C3×C4⋊C4—31no—
104C2×C3×C22⋊C4—31no—
105C2×C3×C22⋊C4—31no—
106C2×C3×C42—21no—
107C2×C3×C42—31no—
108C2×C3×C42—32no—
109C2×C3×C42C2×D311yescharacteristic
110C2×C3×C42C2×D311yescharacteristic
111C2×#217—32no—
112C2×#217—32no—
113C2×(C2×D3)⋊C4—32no—
114C2×(C2×D3)⋊C4—32no—
115C2×(C2×D3)⋊C4C2×D311yescharacteristic
116C2×(C2×D3)⋊C4C2×D311yescharacteristic
117C2×C4⋊Dic3—31no—
118C2×C4⋊Dic3—31no—
119C2×C4⋊Dic3—32no—
120C2×C4⋊Dic3—32no—
121C2×C4⋊Dic3—61no—
122C2×C4⋊Dic3C2×D311yescharacteristic
123C2×C4⋊Dic3C2×D311yescharacteristic
124#924—64no—
125C2×Dic3⋊C4—32no—
126C2×Dic3⋊C4—32no—
127C2×C4×Dic3C2×D311yescharacteristic
128C2×C4×Dic3C2×D312yes—
129#897—64no—
130#888—64no—
131#869—64no—
132C3×#95—31no—
133C3×#95—32no—
134C3×#95—31no—
135C3⋊#95—32no—
136C3⋊#95—32no—
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⋊#95—62no—
147C3⋊#95C2×D311yescharacteristic
148C3⋊#95C2×D312yes—
149C3⋊#95C2×D311yescharacteristic
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⋊Dic3—22no—
173#634—44no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3C2×D414yes—
187C2×C3×Dic3C2×Q812yes—
188C2×C3×Dic3#4112yes—
189C3×C4×D3—44no—
190#627—48no—
191C2×C4⋊Q8—91no—
192C2×C22⋊Q8—91no—
193#400—92no—
194#393—92no—
195#391—92no—
196#391—91no—
197#391—91no—
198#388—92no—
199#380—91no—
200C4×C4⋊C4—31no—
201C4×C22⋊C4—31no—
202C24×C3—31no—
203C23×D3C22×D311yescharacteristic
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—31no—
208C22×C3×C4—31no—
209C22×C3×C4—32no—
210C22×C3×C4—32no—
211C22×C3×C4—31no—
212C22×C3×C4—62no—
213C22×C3×C4—62no—
214C22×C3×C4—62no—
215C22×C3×C4C22×D311yescharacteristic
216C22×C3×C4C22×D311yescharacteristic
217C22×C3×C4C22×D311yescharacteristic
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C22×Dic3—32no—
222C22×Dic3—32no—
223C22×Dic3—32no—
224C22×Dic3—32no—
225C22×Dic3—62no—
226C22×Dic3—62no—
227C22×Dic3C22×D312yes—
228C22×Dic3C22×D311yescharacteristic
229C22×Dic3C22×D311yescharacteristic
230C22×Dic3C22×D312yes—
231C22×Dic3C22×D311yescharacteristic
232C2×C4×D3—22no—
233C2×C4×D3—22no—
234C2×C4×D3—22no—
235C2×Dic6—64no—
236C2×Dic6—64no—
237C2×Dic6—64no—
238C2×Dic6—62no—
239C2×Dic6—62no—
240C2×Dic6—62no—
241C2×Dic6—62no—
242C2×Dic6—62no—
243C2×Dic6—62no—
244C2×Dic6—64no—
245C2×Dic6—64no—
246C2×Dic6—122no—
247C2×Dic6—122no—
248C2×Dic6—122no—
249C2×Dic6—122no—
250C3×C4⋊C4—34no—
251C3×C4⋊C4—62no—
252C3×C22⋊C4—34no—
253C3×C22⋊C4—62no—
254C3×C42—22no—
255C3×C42—22no—
256C3×C42—42no—
257C3×C42—62no—
258C3×C42—122no—
259#217—64no—
260#217—122no—
261(C2×D3)⋊C4—22no—
262(C2×D3)⋊C4—64no—
263(C2×D3)⋊C4—122no—
264(C2×D3)⋊C4Dic614yescomplemented
265C4⋊Dic3—22no—
266C4⋊Dic3—64no—
267C4⋊Dic3—62no—
268C4⋊Dic3—62no—
269C4⋊Dic3—64no—
270C4⋊Dic3—122no—
271C4⋊Dic3D1214yes—
272Dic3⋊C4—64no—
273Dic3⋊C4—64no—
274C4×Dic3—22no—
275C4×Dic3—42no—
276C22×C32C22×D411yescharacteristic
277C22×C32C22×Q811yescharacteristic
278C22×C32C2×#4111yescharacteristic
279C22×C32C2×#4111yescharacteristic
280C22×C32C2×#4111yescharacteristic
281C22×C32H(5,𝔽2)11yescharacteristic
282C22×C322−1+411yescharacteristic
283C2×C3×D3—22no—
284C2×C3×D3—22no—
285C2×C3×D3—22no—
286C2×C3×D3—41no—
287C2×C3×D3—41no—
288C2×C3×D3—41no—
289C2×C3×D3—41no—
290C32×C4—22no—
291C32×C4—41no—
292C32×C4#12414yes—
293C3⋊Dic3—42no—
294C3⋊Dic3—42no—
295C3×Dic3—22no—
296C3×Dic3—24no—
297C3×Dic3—22no—
298C3×Dic3—41no—
299C3×Dic3—42no—
300C22×Q8—92no—
301C22×Q8—91no—
302C23×C4—31no—
303C4⋊Q8—184no—
304C22⋊Q8—184no—
305C2×C4⋊C4—31no—
306C2×C4⋊C4—31no—
307C2×C4⋊C4—92no—
308C2×C4⋊C4—92no—
309C2×C4⋊C4—91no—
310C2×C22⋊C4—31no—
311C2×C22⋊C4—31no—
312C2×C22⋊C4—92no—
313C2×C22⋊C4—92no—
314C2×C42—31no—
315C2×C42—32no—
316C2×C42D3211yescharacteristic
317#95—31no—
318#95—31no—
319#95—32no—
320#95—92no—
321#95—92no—
322#95—92no—
323#95—92no—
324#95—92no—
325C23×C3—21no—
326C23×C3—32no—
327C23×C3—61no—
328C23×C3—61no—
329C23×C3—61no—
330C23×C3—61no—
331C23×C3—61no—
332C23×C3—61no—
333C23×C3C23×D311yescharacteristic
334C23×C3C23×D311yescharacteristic
335C22×D3—21no—
336C22×D3—21no—
337C22×D3—21no—
338C22×D3—21no—
339C22×D3—21no—
340C22×D3—21no—
341C22×D3C2×Dic612yes—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—22no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—34no—
358C2×C3×C4—32no—
359C2×C3×C4—32no—
360C2×C3×C4—41no—
361C2×C3×C4—41no—
362C2×C3×C4—41no—
363C2×C3×C4—41no—
364C2×C3×C4—61no—
365C2×C3×C4—61no—
366C2×C3×C4—62no—
367C2×C3×C4—61no—
368C2×C3×C4—62no—
369C2×C3×C4—61no—
370C2×C3×C4—61no—
371C2×C3×C4—62no—
372C2×C3×C4—61no—
373C2×C3×C4—61no—
374C2×C3×C4—62no—
375C2×C3×C4—62no—
376C2×C3×C4—124no—
377C2×C3×C4C2×Dic612yes—
378C2×C3×C4C2×D1212yes—
379C2×C3×C4#23512yes—
380C2×C3×C4#23512yes—
381C2×C3×C4#23512yes—
382C2×C3×C4D3×D412yes—
383C2×C3×C4#23712yes—
384C2×C3×C4D3×Q812yes—
385C2×Dic3—21no—
386C2×Dic3—21no—
387C2×Dic3—22no—
388C2×Dic3—22no—
389C2×Dic3—21no—
390C2×Dic3—21no—
391C2×Dic3—22no—
392C2×Dic3—21no—
393C2×Dic3—21no—
394C2×Dic3—21no—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3—64no—
398C2×Dic3—62no—
399C2×Dic3—62no—
400C2×Dic3—62no—
401C2×Dic3—62no—
402C2×Dic3—62no—
403C2×Dic3—62no—
404C2×Dic3—62no—
405C2×Dic3—62no—
406C2×Dic3—62no—
407C2×Dic3—62no—
408C2×Dic3—62no—
409C2×Dic3—62no—
410C2×Dic3—122no—
411C2×Dic3—122no—
412C2×Dic3—122no—
413C2×Dic3—122no—
414C2×Dic3—122no—
415C2×Dic3C2×Dic612yes—
416C2×Dic3C2×D1214yes—
417C2×Dic3#23512yes—
418C4×D3—44no—
419Dic6—128no—
420Dic6—128no—
421Dic6—128no—
422Dic6—124no—
423Dic6—124no—
424C2×C32C2×#12411yescharacteristic
425C2×C32#53311yescharacteristic
426C2×C32#54211yescharacteristic
427C2×C32#54611yescharacteristic
428C2×C32D4×Q811yescharacteristic
429C2×C32#55411yescharacteristic
430C2×C32#55611yescharacteristic
431C3×D3—42no—
432C24—31no—
433C2×Q8—184no—
434C2×Q8—184no—
435C2×Q8—182no—
436C2×Q8—182no—
437C2×Q8—182no—
438C2×Q8—362no—
439C22×C4—31no—
440C22×C4—31no—
441C22×C4—32no—
442C22×C4—31no—
443C22×C4—32no—
444C22×C4—62no—
445C22×C4—62no—
446C22×C4—62no—
447C22×C4—92no—
448C22×C4—92no—
449C22×C4C2×D3211yescharacteristic
450C22×C4C2×D3211yescharacteristic
451C22×C4C2×D3211yescharacteristic
452C4⋊C4—34no—
453C4⋊C4—62no—
454C4⋊C4—184no—
455C4⋊C4—184no—
456C4⋊C4—182no—
457C22⋊C4—34no—
458C22⋊C4—62no—
459C22⋊C4—184no—
460C22⋊C4—362no—
461C42—22no—
462C42—62no—
463C42—122no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—62no—
472C22×C3—62no—
473C22×C3—62no—
474C22×C3—121no—
475C22×C3—121no—
476C22×C3—121no—
477C22×C3—121no—
478C22×C3C22×Dic611yescharacteristic
479C22×C3C22×D1211yescharacteristic
480C22×C3C2×#23511yescharacteristic
481C22×C3C2×#23511yescharacteristic
482C22×C3C2×#23511yescharacteristic
483C22×C3C2×#23511yescharacteristic
484C22×C3C2×D3×D411yescharacteristic
485C22×C3C2×#23711yescharacteristic
486C22×C3#100411yescharacteristic
487C22×C3C2×D3×Q811yescharacteristic
488C22×C3D3×#4111yescharacteristic
489C22×C3#100911yescharacteristic
490C22×C3#101011yescharacteristic
491C22×C3#101011yescharacteristic
492C2×D3—22no—
493C2×D3—22no—
494C2×D3—22no—
495C2×D3—41no—
496C2×D3—41no—
497C2×D3—41no—
498C2×D3—41no—
499C3×C4—22no—
500C3×C4—22no—
501C3×C4—24no—
502C3×C4—42no—
503C3×C4—42no—
504C3×C4—41no—
505C3×C4—41no—
506C3×C4—64no—
507C3×C4—62no—
508C3×C4—62no—
509C3×C4—121no—
510C3×C4—122no—
511C3×C4#87514yes—
512C3×C4#88514yes—
513Dic3—22no—
514Dic3—22no—
515Dic3—24no—
516Dic3—41no—
517Dic3—42no—
518Dic3—124no—
519Dic3—122no—
520Dic3—122no—
521Dic3—122no—
522Dic3—122no—
523Dic3—242no—
524C32#249211yescharacteristic, complemented, Sylow
525C23—32no—
526C23—61no—
527C23—61no—
528C23—61no—
529C23—61no—
530C23—61no—
531C23—61no—
532C23C22×D3211yescharacteristic
533Q8—368no—
534Q8—364no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—32no—
541C2×C4—34no—
542C2×C4—32no—
543C2×C4—61no—
544C2×C4—61no—
545C2×C4—61no—
546C2×C4—62no—
547C2×C4—62no—
548C2×C4—61no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—61no—
552C2×C4—61no—
553C2×C4—62no—
554C2×C4—61no—
555C2×C4—124no—
556C2×C4—182no—
557C2×C4—182no—
558C2×C4—182no—
559C2×C4—182no—
560C2×C4—182no—
561C2×C4—182no—
562C2×C4D3×Dic612yes—
563C2×C4#379812yes—
564C2×C4D3×D1212yes—
565C2×C4#380412yes—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—122no—
574C2×C3#547011yescharacteristic
575C2×C3C2×#87511yescharacteristic
576C2×C3C2×#88511yescharacteristic
577C2×C3#551111yescharacteristic
578C2×C3#553311yescharacteristic
579C2×C3#553411yescharacteristic
580C2×C3D4×Dic611yescharacteristic
581C2×C3#554211yescharacteristic
582C2×C3#554311yescharacteristic
583C2×C3#555011yescharacteristic
584C2×C3#555411yescharacteristic
585C2×C3#556111yescharacteristic
586C2×C3Q8×D1211yescharacteristic
587C2×C3#557811yescharacteristic
588D3—42no—
589C22—62no—
590C22—62no—
591C22—62no—
592C22—121no—
593C22—121no—
594C22—121no—
595C22—121no—
596C22C2×D3×Dic611yescharacteristic
597C22#6429811yescharacteristic
598C22C2×#379811yescharacteristic
599C22C2×D3×D1211yescharacteristic
600C22D3×#23511yescharacteristic
601C22#6430711yescharacteristic
602C22C2×#380411yescharacteristic
603C4—22no—
604C4—41no—
605C4—62no—
606C4—62no—
607C4—64no—
608C4—121no—
609C4—122no—
610C4—362no—
611C4—362no—
612C4#6385214yes—
613C3—21no—
614C3#7350811yescharacteristic, complemented
615C3#7378911yescharacteristic, complemented
616C2—122no—
617C2#1059387311yescharacteristic
618C2Dic6×D1211yescharacteristic
619C2#1059398311yescharacteristic
620C2#1059400311yescharacteristic
621C2C2×#6385211yescharacteristic
622C2#1059484011yescharacteristic
623C2#1059498811yescharacteristic
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. #10592628C2semidirect
5. C3×C4×C4⋊Dic3C2semidirect
9. #10591213C2semidirect
10. #10591207C2semidirect
11. #10591191C2semidirect
52. C4×C4⋊Dic3D3semidirect
85. C3×(C2×D3)⋊C4Q8semidirect
264. (C2×D3)⋊C4Dic6semidirect
524. C32#2492semidirect
614. C3#73508semidirect
615. C3#73789semidirect

Maximal subgroups

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

subgroupindex
C2×#639182
C2×#638572
#105926282
C3×C4×(C2×D3)⋊C42
C3×C4×C4⋊Dic32
#105913132
#105913052
#105912932
#105912132
#105912072
#105911912
#737893
#735083