Finite Group Databasebeta

← #11800913

Subgroups — #11800913

Order 1152.

1689 conjugacy classes of subgroups.

The subgroup lattice has 621 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63904C212yesmaximal
2C2×C4×#626C211yesmaximal, characteristic
3#10592365C211yesmaximal, characteristic, complemented
4C3×D3×#95C211yesmaximal, characteristic, complemented
5C3×#4649C211yesmaximal, characteristic, complemented
6#10591370C211yesmaximal, characteristic, complemented
7C4×(C2×D3)⋊Dic3C212yesmaximal, complemented
8#10591241C212yesmaximal, complemented
9#10591239C211yesmaximal, characteristic, complemented
10#10591237C211yesmaximal, characteristic, complemented
11#10591233C212yesmaximal, complemented
12#73751—31nomaximal
13#73322—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C22×C3×C4×D3C2212yes—
17C22×#626C2211yescharacteristic
18C22×#624C2212yes—
19C2×#3752C2212yes—
20C2×C4×C3⋊Dic3C2212yes—
21C2×C3×Dic3⋊C4C2212yes—
22C2×C3×C4×Dic3C2212yes—
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×Dic3⋊Dic3C2211yescharacteristic
25C2×#3722C2211yescharacteristic
26C2×(C2×D3)⋊Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2211yescharacteristic
28C2×Dic32C2212yes—
29C2×Dic32C2212yes—
30#63904C4116yescomplemented
31C4×#626C418yescomplemented
32C32×#95C2211yescharacteristic
33#63658C2211yescharacteristic
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2211yescharacteristic
36C3×C3⋊#95C2211yescharacteristic
37#63579C2212yes—
38#63579C2212yes—
39C2×C4×#67—32no—
40C2×C4×#67—31no—
41C2×#893—32no—
42C2×C4×D12—31no—
43C3×C4×C4⋊C4—31no—
44C2×C3×#95—31no—
45C4×#217—32no—
46C4×#217—31no—
47Dic3×C4⋊C4—32no—
48C4×(C2×D3)⋊C4—32no—
49C4×(C2×D3)⋊C4—32no—
50#4932—31no—
51#4666—31no—
52#4666—32no—
53#4666—31no—
54#4666—31no—
55#4666—61no—
56D3×#95—31no—
57D3×#95—31no—
58D3×#95D311yescharacteristic, complemented
59#4649—32no—
60#4649D311yescharacteristic, complemented
61#4648—31no—
62C23×C3⋊D3C2311yescharacteristic
63C23×C3×D3C2311yescharacteristic
64C22×C32×C4C2312yes—
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2312yes—
68C2×C4×C3⋊D3—42no—
69C2×C4×C3⋊D3C2×C414yescomplemented
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C2×C3×C4×D3—42no—
76C2×C3×C4×D3—42no—
77C2×C3×C4×D3—42no—
78C2×C3×C4×D3C2×C414yescomplemented
79C2×C3×C4×D3C2×C418yescomplemented
80C2×#626C2×C414yes—
81C2×#626C2×C418yes—
82C2×#624—42no—
83C2×#624—42no—
84C2×#624C2×C418yescomplemented
85#3752C2×C418yescomplemented
86C4×C3⋊Dic3—42no—
87C3×Dic3⋊C4C2×C418yescomplemented
88C3×C4×Dic3—42no—
89C3×C4×Dic3C2×C414yescomplemented
90Dic3⋊Dic3C2×C414yescomplemented
91#3722C2×C414yescomplemented
92(C2×D3)⋊Dic3C2×C414yescomplemented
93(C2×D3)⋊Dic3C2×C418yescomplemented
94Dic32—42no—
95Dic32C2×C418yescomplemented
96#2275—91noSylow
97C23×C3×C4—32no—
98C23×C3×C4—31no—
99C22×#67—31no—
100C22×D12—31no—
101C22×C4×D3—31no—
102C22×C4×D3—31no—
103C22×C4×D3—32no—
104C22×C4×D3—32no—
105C22×C4×D3—61no—
106C22×C4×D3C2×D311yescharacteristic
107C22×C4×D3C2×D312yes—
108C2×C3×C4⋊C4—32no—
109C2×C3×C42—31no—
110C2×C3×C42—32no—
111C2×#217—32no—
112C2×#217—31no—
113C4×#67—316no—
114C4×#67—38no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4—31no—
117C2×(C2×D3)⋊C4—32no—
118C2×(C2×D3)⋊C4—32no—
119C2×(C2×D3)⋊C4—31no—
120C2×(C2×D3)⋊C4—31no—
121C2×(C2×D3)⋊C4—62no—
122C2×C4⋊Dic3—31no—
123C2×Dic3⋊C4—31no—
124C2×Dic3⋊C4C2×D312yes—
125C2×C4×Dic3—32no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3—32no—
130C2×C4×Dic3—32no—
131C2×C4×Dic3—62no—
132C2×C4×Dic3C2×D312yes—
133C2×C4×Dic3C2×D311yescharacteristic
134#893—316no—
135C4×D12—38no—
136C3×#95—21no—
137C3×#95—31no—
138C3×#95—32no—
139C3×#95—31no—
140C3×#95C2×D311yescharacteristic
141C3×#95C2×D311yescharacteristic
142C3⋊#95—31no—
143C3⋊#95—31no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95—61no—
149C3⋊#95C2×D311yescharacteristic
150C3⋊#95C2×D311yescharacteristic
151C3⋊#95C2×D312yes—
152C23×C32C2411yescharacteristic
153C22×C3⋊D3—21no—
154C22×C3⋊D3—22no—
155C22×C3⋊D3—21no—
156C22×C3⋊D3C22×C412yes—
157C22×C3⋊D3C22×C414yes—
158C22×C3×D3—21no—
159C22×C3×D3—22no—
160C22×C3×D3—21no—
161C22×C3×D3C22×C412yes—
162C22×C3×D3C22×C414yes—
163C2×C32×C4—22no—
164C2×C32×C4—22no—
165C2×C32×C4—22no—
166C2×C32×C4C22×C412yes—
167C2×C32×C4C22×C414yes—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3C22×C414yes—
172C2×C3⋊Dic3C22×C412yes—
173C4×C3⋊D3—44no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3C22×C414yes—
182C2×C3×Dic3C22×C412yes—
183C2×C3×Dic3C22×C414yes—
184C2×C3×Dic3C22×C412yes—
185C2×C3×Dic3C22×C414yes—
186C2×C3×Dic3C22×C412yes—
187C3×C4×D3—48no—
188C3×C4×D3—44no—
189#626C42116yescomplemented
190#624—48no—
191C2×C4×D4—91no—
192C2×C4×D4—92no—
193C4×C4⋊C4—31no—
194C4×C4⋊C4—92no—
195C4×C22⋊C4—92no—
196C4×C22⋊C4—91no—
197C4×C22⋊C4—92no—
198C4×C22⋊C4—91no—
199#376—91no—
200C2×#95—31no—
201C2×#95—91no—
202C24×C3—31no—
203C23×D3—31no—
204C23×D3—31no—
205C23×D3—61no—
206C23×D3C22×D311yescharacteristic
207C22×C3×C4—21no—
208C22×C3×C4—22no—
209C22×C3×C4—31no—
210C22×C3×C4—32no—
211C22×C3×C4—31no—
212C22×C3×C4—32no—
213C22×C3×C4—31no—
214C22×C3×C4—38no—
215C22×C3×C4—34no—
216C22×C3×C4—122no—
217C22×C3×C4—122no—
218C22×C3×C4—122no—
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C22×D312yes—
222C22×C3×C4C22×D312yes—
223C2×#67—38no—
224C2×#67—34no—
225C22×Dic3—32no—
226C22×Dic3—32no—
227C22×Dic3—31no—
228C22×Dic3—31no—
229C22×Dic3—61no—
230C22×Dic3—62no—
231C22×Dic3C22×D312yes—
232C22×Dic3C22×D311yescharacteristic
233C22×Dic3C22×D312yes—
234C22×Dic3C22×D311yescharacteristic
235C22×Dic3C22×D311yescharacteristic
236C2×D12—34no—
237C2×D12—38no—
238C2×C4×D3—34no—
239C2×C4×D3—34no—
240C2×C4×D3—38no—
241C2×C4×D3—38no—
242C2×C4×D3—42no—
243C2×C4×D3—42no—
244C2×C4×D3—42no—
245C2×C4×D3—64no—
246C2×C4×D3—122no—
247C2×C4×D3—122no—
248C2×C4×D3—122no—
249C2×C4×D3—122no—
250C2×C4×D3—122no—
251C2×C4×D3—122no—
252C2×C4×D3—124no—
253C2×C4×D3C4×D314yescomplemented
254C2×C4×D3C4×D318yescomplemented
255C3×C4⋊C4—38no—
256C3×C42—34no—
257C3×C42—122no—
258#217—38no—
259#217—34no—
260(C2×D3)⋊C4—34no—
261(C2×D3)⋊C4—38no—
262(C2×D3)⋊C4—38no—
263(C2×D3)⋊C4—38no—
264(C2×D3)⋊C4—34no—
265(C2×D3)⋊C4—34no—
266(C2×D3)⋊C4—68no—
267C4⋊Dic3—34no—
268Dic3⋊C4—34no—
269Dic3⋊C4C4×D318yescomplemented
270C4×Dic3—38no—
271C4×Dic3—38no—
272C4×Dic3—42no—
273C4×Dic3—122no—
274C4×Dic3—122no—
275C4×Dic3—122no—
276C4×Dic3—122no—
277C4×Dic3—124no—
278C4×Dic3C4×D314yescomplemented
279C22×C32C23×C411yescharacteristic
280C22×C32C23×C412yes—
281C22×C32H(5,𝔽2)11yescharacteristic
282C22×C32H(5,𝔽2)12yes—
283C22×C322−1+411yescharacteristic
284C2×C3⋊D3—24no—
285C2×C3⋊D3—22no—
286C2×C3⋊D3—22no—
287C2×C3⋊D3—24no—
288C2×C3⋊D3C2×C4214yes—
289C2×C3×D3—22no—
290C2×C3×D3—24no—
291C2×C3×D3—22no—
292C2×C3×D3—24no—
293C2×C3×D3C2×C4214yes—
294C32×C4—22no—
295C32×C4—24no—
296C3⋊Dic3—22no—
297C3⋊Dic3—24no—
298C3×Dic3—24no—
299C3×Dic3—24no—
300C3×Dic3—22no—
301C3×Dic3—22no—
302C3×Dic3C2×C4214yes—
303C22×D4—91no—
304C23×C4—32no—
305C23×C4—31no—
306C23×C4—92no—
307C23×C4—91no—
308C4×D4—98no—
309C4×D4—916no—
310C2×C4⋊C4—32no—
311C2×C4⋊C4—91no—
312C2×C22⋊C4—91no—
313C2×C22⋊C4—92no—
314C2×C22⋊C4—91no—
315C2×C22⋊C4—92no—
316C2×C42—31no—
317C2×C42—32no—
318C2×C42—92no—
319C2×C42—92no—
320C2×C42—92no—
321#95—31no—
322#95—32no—
323#95—31no—
324#95—92no—
325#95—92no—
326#95—91no—
327#95D3211yescharacteristic
328C23×C3—21no—
329C23×C3—32no—
330C23×C3—34no—
331C23×C3—61no—
332C23×C3—61no—
333C23×C3—62no—
334C23×C3C23×D311yescharacteristic
335C23×C3C23×D311yescharacteristic
336C22×D3—21no—
337C22×D3—22no—
338C22×D3—21no—
339C22×D3—32no—
340C22×D3—34no—
341C22×D3—32no—
342C22×D3—34no—
343C22×D3—64no—
344C22×D3—62no—
345C22×D3—61no—
346C22×D3—61no—
347C22×D3—62no—
348C22×D3—61no—
349C22×D3—61no—
350C22×D3—62no—
351C22×D3—122no—
352C22×D3—121no—
353C22×D3—121no—
354C22×D3C2×C4×D312yes—
355C22×D3C2×C4×D314yes—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—24no—
363C2×C3×C4—22no—
364C2×C3×C4—34no—
365C2×C3×C4—32no—
366C2×C3×C4—34no—
367C2×C3×C4—32no—
368C2×C3×C4—32no—
369C2×C3×C4—34no—
370C2×C3×C4—42no—
371C2×C3×C4—42no—
372C2×C3×C4—42no—
373C2×C3×C4—62no—
374C2×C3×C4—61no—
375C2×C3×C4—62no—
376C2×C3×C4—62no—
377C2×C3×C4—61no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—124no—
381C2×C3×C4—128no—
382C2×C3×C4C2×C4×D312yes—
383C2×C3×C4C2×C4×D314yes—
384C2×C3×C4C2×C4×D314yes—
385C2×C3×C4C2×C4×D312yes—
386#67—316no—
387C2×Dic3—21no—
388C2×Dic3—22no—
389C2×Dic3—22no—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—21no—
393C2×Dic3—22no—
394C2×Dic3—34no—
395C2×Dic3—34no—
396C2×Dic3—32no—
397C2×Dic3—32no—
398C2×Dic3—62no—
399C2×Dic3—64no—
400C2×Dic3—64no—
401C2×Dic3—62no—
402C2×Dic3—62no—
403C2×Dic3—62no—
404C2×Dic3—62no—
405C2×Dic3—62no—
406C2×Dic3—62no—
407C2×Dic3—122no—
408C2×Dic3—122no—
409C2×Dic3C2×C4×D314yes—
410C2×Dic3C2×C4×D312yes—
411C2×Dic3C2×C4×D314yes—
412C2×Dic3C2×C4×D312yes—
413C2×Dic3C2×C4×D314yes—
414C2×Dic3C2×C4×D312yes—
415D12—316no—
416C4×D3—48no—
417C4×D3—44no—
418C4×D3—128no—
419C4×D3—128no—
420C4×D3—124no—
421C4×D3—124no—
422C4×D3—128no—
423C2×C32C22×C4211yescharacteristic
424C2×C32#51811yescharacteristic
425C2×C32#51812yes—
426C2×C32#52011yescharacteristic
427C2×C32#52012yes—
428C3⋊D3—24no—
429C3×D3—24no—
430C24—31no—
431C24—91no—
432C2×D4—94no—
433C2×D4—98no—
434C22×C4—31no—
435C22×C4—32no—
436C22×C4—31no—
437C22×C4—32no—
438C22×C4—31no—
439C22×C4—38no—
440C22×C4—34no—
441C22×C4—98no—
442C22×C4—92no—
443C22×C4—91no—
444C22×C4—94no—
445C22×C4—122no—
446C22×C4—122no—
447C22×C4—122no—
448C22×C4—362no—
449C22×C4—362no—
450C22×C4—362no—
451C22×C4C2×D3211yescharacteristic
452C22×C4C2×D3212yes—
453C4⋊C4—38no—
454C4⋊C4—94no—
455C22⋊C4—94no—
456C22⋊C4—94no—
457C22⋊C4—98no—
458C22⋊C4—98no—
459C42—34no—
460C42—98no—
461C42—122no—
462C42—362no—
463C42—362no—
464C22×C3—22no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—22no—
468C22×C3—21no—
469C22×C3—34no—
470C22×C3—62no—
471C22×C3—62no—
472C22×C3—64no—
473C22×C3—64no—
474C22×C3C22×C4×D312yes—
475C22×C3C22×C4×D311yescharacteristic
476C22×C3C22×C4×D311yescharacteristic
477C22×C3C22×C4×D312yes—
478C22×C3#100411yescharacteristic
479C22×C3#100411yescharacteristic
480C22×C3#100412yes—
481C22×C3#100711yescharacteristic
482C22×C3#100711yescharacteristic
483C22×C3#100912yes—
484C2×D3—22no—
485C2×D3—24no—
486C2×D3—24no—
487C2×D3—22no—
488C2×D3—34no—
489C2×D3—34no—
490C2×D3—64no—
491C2×D3—62no—
492C2×D3—64no—
493C2×D3—64no—
494C2×D3—62no—
495C2×D3—62no—
496C2×D3—62no—
497C2×D3—64no—
498C2×D3—64no—
499C2×D3—122no—
500C2×D3—124no—
501C2×D3—122no—
502C2×D3—124no—
503C2×D3C42×D314yes—
504C3×C4—22no—
505C3×C4—24no—
506C3×C4—22no—
507C3×C4—24no—
508C3×C4—34no—
509C3×C4—42no—
510C3×C4—44no—
511C3×C4—64no—
512C3×C4—62no—
513C3×C4—62no—
514C3×C4—64no—
515Dic3—24no—
516Dic3—22no—
517Dic3—22no—
518Dic3—24no—
519Dic3—64no—
520Dic3—62no—
521Dic3—64no—
522Dic3—62no—
523Dic3—64no—
524Dic3—124no—
525Dic3C42×D314yes—
526C32#227511yescharacteristic, complemented, Sylow
527C23—34no—
528C23—32no—
529C23—61no—
530C23—62no—
531C23—61no—
532C23—94no—
533C23—92no—
534C23—181no—
535C23—182no—
536C23—181no—
537C23C22×D3211yescharacteristic
538D4—916no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—32no—
543C2×C4—34no—
544C2×C4—32no—
545C2×C4—34no—
546C2×C4—34no—
547C2×C4—32no—
548C2×C4—61no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—62no—
552C2×C4—62no—
553C2×C4—62no—
554C2×C4—61no—
555C2×C4—94no—
556C2×C4—92no—
557C2×C4—124no—
558C2×C4—128no—
559C2×C4—182no—
560C2×C4—182no—
561C2×C4—182no—
562C2×C4—364no—
563C2×C4—368no—
564C2×C4C4×D3212yes—
565C2×C4C4×D3214yes—
566C2×C3—22no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—22no—
571C2×C3—64no—
572C2×C3C2×C42×D311yescharacteristic
573C2×C3C2×C42×D311yescharacteristic
574C2×C3#548611yescharacteristic
575C2×C3#548612yes—
576C2×C3#550412yes—
577C2×C3#550411yescharacteristic
578C2×C3#550411yescharacteristic
579C2×C3#552111yescharacteristic
580C2×C3#554512yes—
581C2×C3#557412yes—
582D3—24no—
583D3—64no—
584D3—64no—
585D3—124no—
586C22—34no—
587C22—64no—
588C22—62no—
589C22—62no—
590C22—64no—
591C22—94no—
592C22—184no—
593C22—182no—
594C22—182no—
595C22—184no—
596C22C2×C4×D3212yes—
597C22C2×C4×D3211yescharacteristic
598C22#6431311yescharacteristic
599C22#6431412yes—
600C22#6431611yescharacteristic
601C4—22no—
602C4—24no—
603C4—34no—
604C4—62no—
605C4—62no—
606C4—64no—
607C4—64no—
608C4—184no—
609C4—182no—
610C3—21no—
611C3#7332211yescharacteristic, complemented
612C3#7375111yescharacteristic, complemented
613C2—64no—
614C2—184no—
615C2C42×D3211yescharacteristic
616C2#1059418211yescharacteristic
617C2#1059425412yes—
618C2#1059432712yes—
619C2#1059450911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC2×C32C22×C42
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#626C22
hypercenter#95D32
hypocenterC32#2275
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. #10592365C2semidirect
4. C3×D3×#95C2semidirect
5. C3×#4649C2semidirect
6. #10591370C2semidirect
7. C4×(C2×D3)⋊Dic3C2semidirect
8. #10591241C2semidirect
9. #10591239C2semidirect
10. #10591237C2semidirect
11. #10591233C2semidirect
30. #63904C4semidirect
31. C4×#626C4semidirect
58. D3×#95D3semidirect
60. #4649D3semidirect
69. C2×C4×C3⋊D3C2×C4semidirect
78. C2×C3×C4×D3C2×C4semidirect
79. C2×C3×C4×D3C2×C4semidirect
84. C2×#624C2×C4semidirect
85. #3752C2×C4semidirect
87. C3×Dic3⋊C4C2×C4semidirect
89. C3×C4×Dic3C2×C4semidirect
90. Dic3⋊Dic3C2×C4semidirect
91. #3722C2×C4semidirect
92. (C2×D3)⋊Dic3C2×C4semidirect
93. (C2×D3)⋊Dic3C2×C4semidirect
95. Dic32C2×C4semidirect
189. #626C42semidirect
253. C2×C4×D3C4×D3semidirect
254. C2×C4×D3C4×D3semidirect
269. Dic3⋊C4C4×D3semidirect
278. C4×Dic3C4×D3semidirect
526. C32#2275semidirect
611. C3#73322semidirect
612. C3#73751semidirect

Maximal subgroups

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

subgroupindex
C2×#639042
C2×C4×#6262
#105923652
C3×D3×#952
C3×#46492
#105913702
C4×(C2×D3)⋊Dic32
#105912412
#105912392
#105912372
#105912332
#737513
#733223