Finite Group Databasebeta

← #11808400

Subgroups — #11808400

Order 1152.

1553 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#877C211yesmaximal, characteristic, complemented
2C2×#63952C212yesmaximal, complemented
3C2×#63894C211yesmaximal, characteristic, complemented
4#10592659C211yesmaximal, characteristic
5C3×#4953C211yesmaximal, characteristic, complemented
6#10591712C212yesmaximal, complemented
7#10591347C212yesmaximal, complemented
8#10591321C211yesmaximal, characteristic, complemented
9#10591242C211yesmaximal, characteristic, complemented
10#10591233C212yesmaximal, complemented
11#10591214C211yesmaximal, characteristic, complemented
12#82273—31nomaximal
13#77457—31nomaximal
14C22×#638C2212yes—
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C22×#624C2212yes—
18C2×C32×C22⋊C4C2211yescharacteristic
19C2×#3752C2212yes—
20C2×C3×#217C2212yes—
21C2×C3×#217C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×Dic3⋊C4C2211yescharacteristic
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C3×#877—24no—
28C2×#3724C2212yes—
29C2×Dic3⋊Dic3C2212yes—
30C2×#3722C2212yes—
31C2×#3722C2212yes—
32C2×#3722C2212yes—
33C2×Dic32C2212yes—
34#63952—28no—
35#63894—24no—
36#63658C2211yescharacteristic
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2211yescharacteristic
39#63579C2212yes—
40C2×C3×#117—31no—
41C2×C4×#67—32no—
42C2×#893—31no—
43C2×#67⋊C4—32no—
44C2×#877D311yescharacteristic, complemented
45C2×C4×D12—31no—
46C3×#397—31no—
47#4994—32no—
48#4991—31no—
49#4983—31no—
50#4981—31no—
51#4961—32no—
52#4960—31no—
53#4960—31no—
54#4960—61no—
55#4959—32no—
56#4953D311yescharacteristic, complemented
57C4×(C2×D3)⋊C4—32no—
58C4×C4⋊Dic3—31no—
59#4676—32no—
60#4672—31no—
61#4666—32no—
62#4649—31no—
63C24×C32C2311yescharacteristic
64C23×C3⋊D3C2312yes—
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C2×#638—24no—
68C2×#638—24no—
69C2×#638—24no—
70C22×C3⋊Dic3C2312yes—
71C2×C4⋊(C3⋊D3)—24no—
72C2×C4⋊(C3⋊D3)—22no—
73C22×C3×Dic3—22no—
74C22×C3×Dic3—22no—
75C22×C3×Dic3D414yescomplemented
76C22×C3×Dic3C2311yescharacteristic
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2311yescharacteristic
80C22×C3×Dic3C2311yescharacteristic
81C22×C3×Dic3C2311yescharacteristic
82C2×#624—24no—
83C2×#624—24no—
84C2×#624—24no—
85C32×C22⋊C4—22no—
86#3752—24no—
87C3×#217—24no—
88C3×#217—22no—
89C3×C4⋊Dic3—22no—
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4—22no—
92C3×C4×Dic3—22no—
93C3×C4×Dic3D414yescomplemented
94#3724—24no—
95Dic3⋊Dic3—24no—
96#3722—24no—
97#3722—24no—
98#3722—24no—
99Dic32—24no—
100#2392—91noSylow
101C23×C3×C4—31no—
102C22×#67—32no—
103C22×#67—32no—
104C22×#67—62no—
105C23×Dic3C2×D311yescharacteristic
106C22×D12—31no—
107C22×D12—31no—
108C22×D12—61no—
109C22×C4×D3—32no—
110C22×C4×D3—32no—
111C3×#117—64no—
112C2×C3×C4⋊C4—31no—
113C2×C3×C4⋊C4—31no—
114C2×C3×C4⋊C4—31no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—32no—
117C2×C3×C22⋊C4—31no—
118C2×C3×C22⋊C4C2×D311yescharacteristic
119C2×C3×C22⋊C4C2×D311yescharacteristic
120C2×C3×C42—31no—
121C2×C3×C42—31no—
122C2×#217C2×D312yes—
123C2×#217C2×D311yescharacteristic
124C4×#67—68no—
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4—32no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4—32no—
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—62no—
134C2×C4⋊Dic3—32no—
135C2×C4⋊Dic3C2×D311yescharacteristic
136C2×Dic3⋊C4—32no—
137C2×Dic3⋊C4—32no—
138C2×Dic3⋊C4—32no—
139C2×Dic3⋊C4C2×D311yescharacteristic
140C2×Dic3⋊C4C2×D311yescharacteristic
141C2×C4×Dic3—32no—
142C2×C4×Dic3—32no—
143C2×C4×Dic3C2×D311yescharacteristic
144C2×C4×Dic3C2×D311yescharacteristic
145#893—64no—
146#67⋊C4—68no—
147#877—24no—
148C4×D12—64no—
149C3×#95—31no—
150C3×#95—32no—
151C3⋊#95—31no—
152C3⋊#95—31no—
153C3⋊#95—32no—
154C3⋊#95—32no—
155C3⋊#95—61no—
156C3⋊#95C2×D311yescharacteristic
157C3⋊#95C2×D312yes—
158C23×C32—21no—
159C23×C32—21no—
160C23×C32—22no—
161C23×C32—22no—
162C23×C32C2×D412yes—
163C23×C32C2411yescharacteristic
164C22×C3⋊D3—22no—
165C22×C3⋊D3—22no—
166C22×C3⋊D3—22no—
167C22×C3⋊D3—22no—
168C22×C3⋊D3—22no—
169C22×C3⋊D3—22no—
170C22×C3⋊D3#4114yes—
171C2×C32×C4—22no—
172C2×C32×C4—21no—
173C2×C32×C4—22no—
174C2×C32×C4C2×D412yes—
175#638—216no—
176C2×C3⋊Dic3—22no—
177C2×C3⋊Dic3—22no—
178C2×C3⋊Dic3#4114yes—
179C4⋊(C3⋊D3)—28no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3—28no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3C2×D412yes—
193C2×C3×Dic3C2×D412yes—
194C2×C3×Dic3C2×D412yes—
195C2×C3×Dic3C2×D412yes—
196C2×C3×Dic3#4112yes—
197#624—48no—
198C2×C4×D4—91no—
199C2×C4×D4—92no—
200C2×#117—31no—
201#398—91no—
202#397—31no—
203#396—92no—
204#394—91no—
205#394—92no—
206#392—91no—
207C4×C4⋊C4—91no—
208C4×C22⋊C4—92no—
209C24×C3—21no—
210C24×C3C22×D311yescharacteristic
211C24×C3C22×D311yescharacteristic
212C23×D3—32no—
213C23×D3—32no—
214C23×D3—62no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—31no—
218C22×C3×C4—34no—
219C22×C3×C4—31no—
220C22×C3×C4—31no—
221C22×C3×C4—31no—
222C22×C3×C4—32no—
223C22×C3×C4—32no—
224C22×C3×C4—62no—
225C22×C3×C4—62no—
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C2×#67—64no—
231C2×#67—64no—
232C2×#67—64no—
233C2×#67—64no—
234C2×#67—64no—
235C2×#67—64no—
236C2×#67—124no—
237C2×#67—124no—
238C2×#67—124no—
239C22×Dic3—22no—
240C22×Dic3—22no—
241C22×Dic3—32no—
242C22×Dic3—32no—
243C22×Dic3—62no—
244C22×Dic3D1214yescomplemented
245C22×Dic3C22×D311yescharacteristic
246C22×Dic3C22×D312yes—
247C22×Dic3C22×D312yes—
248C22×Dic3C22×D311yescharacteristic
249C22×Dic3C22×D311yescharacteristic
250C22×Dic3C22×D311yescharacteristic
251C2×D12—64no—
252C2×D12—64no—
253C2×D12—62no—
254C2×D12—62no—
255C2×D12—122no—
256C2×D12—124no—
257C2×C4×D3—64no—
258C2×C4×D3—64no—
259C2×C4×D3—64no—
260C2×C4×D3—64no—
261C2×C4×D3—64no—
262C2×C4×D3—64no—
263C3×C4⋊C4—62no—
264C3×C4⋊C4—62no—
265C3×C4⋊C4—62no—
266C3×C22⋊C4—22no—
267C3×C22⋊C4—22no—
268C3×C22⋊C4—42no—
269C3×C22⋊C4—62no—
270C3×C22⋊C4—64no—
271C3×C42—34no—
272C3×C42—62no—
273#217—24no—
274#217—22no—
275(C2×D3)⋊C4—64no—
276(C2×D3)⋊C4—64no—
277(C2×D3)⋊C4—64no—
278(C2×D3)⋊C4—64no—
279(C2×D3)⋊C4—64no—
280(C2×D3)⋊C4—64no—
281(C2×D3)⋊C4—64no—
282(C2×D3)⋊C4—64no—
283(C2×D3)⋊C4—124no—
284C4⋊Dic3—22no—
285C4⋊Dic3—64no—
286Dic3⋊C4—22no—
287Dic3⋊C4—22no—
288Dic3⋊C4—64no—
289Dic3⋊C4—64no—
290Dic3⋊C4—64no—
291C4×Dic3—22no—
292C4×Dic3—64no—
293C4×Dic3—64no—
294C4×Dic3#6714yescomplemented
295C22×C32—22no—
296C22×C32—24no—
297C22×C32—41no—
298C22×C32—42no—
299C22×C32—41no—
300C22×C32C22×D411yescharacteristic
301C22×C32C22×D411yescharacteristic
302C22×C32C2×#4111yescharacteristic
303C22×C32C2×#4112yes—
304C22×C32C2×#4112yes—
305C2×C3⋊D3—24no—
306C2×C3⋊D3—24no—
307C2×C3⋊D3—24no—
308C2×C3⋊D3—42no—
309C2×C3⋊D3—42no—
310C2×C3⋊D3—42no—
311C2×C3⋊D3—42no—
312C32×C4—22no—
313C32×C4—41no—
314C3⋊Dic3—24no—
315C3×Dic3—22no—
316C3×Dic3—22no—
317C3×Dic3—42no—
318C3×Dic3—42no—
319C3×Dic3—41no—
320C3×Dic3#12114yes—
321C22×D4—92no—
322C22×D4—91no—
323C23×C4—31no—
324C23×C4—92no—
325C4×D4—184no—
326C4×D4—188no—
327#117—64no—
328C2×C4⋊C4—31no—
329C2×C4⋊C4—31no—
330C2×C4⋊C4—31no—
331C2×C4⋊C4—92no—
332C2×C4⋊C4—92no—
333C2×C22⋊C4—31no—
334C2×C22⋊C4—32no—
335C2×C22⋊C4—92no—
336C2×C22⋊C4—92no—
337C2×C22⋊C4—92no—
338C2×C22⋊C4—92no—
339C2×C22⋊C4D3211yescharacteristic
340C2×C42—31no—
341C2×C42—31no—
342C2×C42—92no—
343#95—32no—
344#95—31no—
345#95—92no—
346#95—91no—
347C23×C3—21no—
348C23×C3—21no—
349C23×C3—22no—
350C23×C3—22no—
351C23×C3—22no—
352C23×C3—22no—
353C23×C3—21no—
354C23×C3—21no—
355C23×C3—21no—
356C23×C3—22no—
357C23×C3—41no—
358C23×C3—42no—
359C23×C3—42no—
360C23×C3—41no—
361C23×C3C2×D1212yes—
362C23×C3D3×D412yes—
363C23×C3C23×D311yescharacteristic
364C23×C3C23×D311yescharacteristic
365C22×D3—34no—
366C22×D3—34no—
367C22×D3—64no—
368C22×D3—62no—
369C22×D3—62no—
370C22×D3—62no—
371C22×D3—62no—
372C22×D3—62no—
373C22×D3—62no—
374C22×D3—62no—
375C22×D3—62no—
376C22×D3—62no—
377C22×D3—62no—
378C22×D3—62no—
379C22×D3—62no—
380C22×D3—122no—
381C22×D3—122no—
382C22×D3—122no—
383C22×D3—122no—
384C22×D3—122no—
385C22×D3—122no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—21no—
392C2×C3×C4—22no—
393C2×C3×C4—32no—
394C2×C3×C4—32no—
395C2×C3×C4—32no—
396C2×C3×C4—32no—
397C2×C3×C4—32no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—41no—
401C2×C3×C4—68no—
402C2×C3×C4—61no—
403C2×C3×C4—62no—
404C2×C3×C4—61no—
405C2×C3×C4—62no—
406C2×C3×C4—62no—
407C2×C3×C4—62no—
408C2×C3×C4—61no—
409C2×C3×C4—62no—
410C2×C3×C4—62no—
411C2×C3×C4—62no—
412C2×C3×C4—62no—
413C2×C3×C4D3×D412yes—
414C2×C3×C4C2×#6712yes—
415#67—616no—
416#67—616no—
417#67—1216no—
418C2×Dic3—21no—
419C2×Dic3—22no—
420C2×Dic3—21no—
421C2×Dic3—28no—
422C2×Dic3—22no—
423C2×Dic3—22no—
424C2×Dic3—22no—
425C2×Dic3—22no—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—22no—
429C2×Dic3—21no—
430C2×Dic3—34no—
431C2×Dic3—34no—
432C2×Dic3—64no—
433C2×Dic3—62no—
434C2×Dic3—62no—
435C2×Dic3—62no—
436C2×Dic3—62no—
437C2×Dic3—122no—
438C2×Dic3—122no—
439C2×Dic3C2×D1212yes—
440C2×Dic3C2×D1212yes—
441C2×Dic3#23512yes—
442C2×Dic3C2×#6712yes—
443C2×Dic3C2×#6712yes—
444D12—68no—
445D12—68no—
446D12—128no—
447C4×D3—128no—
448C4×D3—128no—
449C2×C32—42no—
450C2×C32C2×#12111yescharacteristic
451C2×C32#52512yes—
452C2×C32#52511yescharacteristic
453C2×C32#52912yes—
454C2×C32#53211yescharacteristic
455C3⋊D3—44no—
456C24—92no—
457C24C2×D3211yescharacteristic
458C2×D4—184no—
459C2×D4—184no—
460C2×D4—184no—
461C2×D4—184no—
462C2×D4—182no—
463C22×C4—31no—
464C22×C4—31no—
465C22×C4—31no—
466C22×C4—34no—
467C22×C4—32no—
468C22×C4—32no—
469C22×C4—31no—
470C22×C4—62no—
471C22×C4—62no—
472C22×C4—92no—
473C22×C4—184no—
474C22×C4—184no—
475C22×C4—184no—
476C22×C4C2×D3211yescharacteristic
477C22×C4C2×D3211yescharacteristic
478C4⋊C4—62no—
479C4⋊C4—62no—
480C4⋊C4—62no—
481C4⋊C4—184no—
482C4⋊C4—184no—
483C22⋊C4—22no—
484C22⋊C4—62no—
485C22⋊C4—64no—
486C22⋊C4—184no—
487C22⋊C4—184no—
488C22⋊C4—184no—
489C22⋊C4—184no—
490C42—34no—
491C42—62no—
492C42—184no—
493C22×C3—24no—
494C22×C3—24no—
495C22×C3—22no—
496C22×C3—22no—
497C22×C3—21no—
498C22×C3—21no—
499C22×C3—22no—
500C22×C3—22no—
501C22×C3—21no—
502C22×C3—44no—
503C22×C3—42no—
504C22×C3—41no—
505C22×C3—41no—
506C22×C3—42no—
507C22×C3—42no—
508C22×C3—41no—
509C22×C3—41no—
510C22×C3—82no—
511C22×C3—81no—
512C22×C3—81no—
513C22×C3C22×D1211yescharacteristic
514C22×C3C2×#23511yescharacteristic
515C22×C3C2×D3×D411yescharacteristic
516C22×C3C2×D3×D411yescharacteristic
517C22×C3D3×#4111yescharacteristic
518C22×C3D3×#4112yes—
519C22×C3D3×#4112yes—
520C22×C3D3×#4112yes—
521C22×C3D3×#4112yes—
522C22×C3C22×#6711yescharacteristic
523C2×D3—64no—
524C2×D3—64no—
525C2×D3—64no—
526C2×D3—64no—
527C2×D3—64no—
528C2×D3—64no—
529C2×D3—124no—
530C2×D3—124no—
531C2×D3—124no—
532C2×D3—122no—
533C2×D3—122no—
534C2×D3—122no—
535C2×D3—122no—
536C2×D3—122no—
537C2×D3—122no—
538C2×D3—122no—
539C2×D3—122no—
540C2×D3—242no—
541C2×D3—242no—
542C2×D3—242no—
543C2×D3—242no—
544C3×C4—22no—
545C3×C4—22no—
546C3×C4—34no—
547C3×C4—42no—
548C3×C4—41no—
549C3×C4—41no—
550C3×C4—62no—
551C3×C4—62no—
552C3×C4—81no—
553C3×C4—121no—
554C3×C4—122no—
555C3×C4—122no—
556Dic3—22no—
557Dic3—22no—
558Dic3—42no—
559Dic3—41no—
560Dic3—42no—
561Dic3—64no—
562Dic3—64no—
563Dic3—124no—
564Dic3#93014yes—
565C32#239211yescharacteristic, complemented, Sylow
566C23—21no—
567C23—22no—
568C23—22no—
569C23—21no—
570C23—94no—
571C23—182no—
572C23—182no—
573C23—182no—
574C23—182no—
575C23—182no—
576C23—182no—
577C23D3×D1212yes—
578C23C22×D3211yescharacteristic
579D4—188no—
580D4—1816no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—32no—
585C2×C4—32no—
586C2×C4—32no—
587C2×C4—32no—
588C2×C4—32no—
589C2×C4—68no—
590C2×C4—61no—
591C2×C4—62no—
592C2×C4—61no—
593C2×C4—62no—
594C2×C4—62no—
595C2×C4—62no—
596C2×C4—62no—
597C2×C4—62no—
598C2×C4—62no—
599C2×C4—61no—
600C2×C4—62no—
601C2×C4—94no—
602C2×C4—182no—
603C2×C4—182no—
604C2×C4—368no—
605C2×C4D3×#6712yes—
606C2×C3—22no—
607C2×C3—22no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—42no—
612C2×C3—42no—
613C2×C3—82no—
614C2×C3#552412yes—
615C2×C3#552812yes—
616C2×C3D3×#12111yescharacteristic
617C2×C3#565612yes—
618C2×C3#565611yescharacteristic
619C2×C3#566811yescharacteristic
620C2×C3#570612yes—
621C2×C3C2×#93011yescharacteristic
622C2×C3#582811yescharacteristic
623C2×C3#583211yescharacteristic
624D3—124no—
625D3—124no—
626D3—244no—
627C22—24no—
628C22—22no—
629C22—42no—
630C22—41no—
631C22—41no—
632C22—184no—
633C22—184no—
634C22—184no—
635C22—362no—
636C22—362no—
637C22—362no—
638C22—362no—
639C22C2×D3×D1211yescharacteristic
640C22D3×#23511yescharacteristic
641C22#6431212yes—
642C22#6431212yes—
643C22C2×D3×#6711yescharacteristic
644C4—22no—
645C4—34no—
646C4—41no—
647C4—62no—
648C4—62no—
649C4—122no—
650C4—121no—
651C4—122no—
652C4—184no—
653C3—21no—
654C3#7745711yescharacteristic, complemented
655C3#8227311yescharacteristic, complemented
656C2—42no—
657C2—364no—
658C2#1059407912yes—
659C2#1059410612yes—
660C2D3×#93011yescharacteristic
661C2#1059515311yescharacteristic
662C2#1059515911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radical#10592659C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2392
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×#877C2semidirect
2. C2×#63952C2semidirect
3. C2×#63894C2semidirect
5. C3×#4953C2semidirect
6. #10591712C2semidirect
7. #10591347C2semidirect
8. #10591321C2semidirect
9. #10591242C2semidirect
10. #10591233C2semidirect
11. #10591214C2semidirect
44. C2×#877D3semidirect
56. #4953D3semidirect
75. C22×C3×Dic3D4semidirect
93. C3×C4×Dic3D4semidirect
244. C22×Dic3D12semidirect
294. C4×Dic3#67semidirect
565. C32#2392semidirect
654. C3#77457semidirect
655. C3#82273semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8772
C2×#639522
C2×#638942
#105926592
C3×#49532
#105917122
#105913472
#105913212
#105912422
#105912332
#105912142
#822733
#774573