Finite Group Databasebeta

← #11808401

Subgroups — #11808401

Order 1152.

1557 conjugacy classes of subgroups.

The subgroup lattice has 665 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64086C211yesmaximal, characteristic, complemented
2C2×#67⋊Dic3C212yesmaximal, complemented
3C2×#63898C211yesmaximal, characteristic, complemented
4C3×#4960C211yesmaximal, characteristic
5C3×#4953C211yesmaximal, characteristic, complemented
6#10591708C212yesmaximal, complemented
7#10591368C212yesmaximal, complemented
8#10591358C211yesmaximal, characteristic, complemented
9#10591309C212yesmaximal, complemented
10#10591302C211yesmaximal, characteristic, complemented
11#10591257C211yesmaximal, characteristic, complemented
12#77457—31nomaximal
13#76666—31nomaximal
14C23×C3⋊Dic3C2211yescharacteristic
15C22×C3×#67C2212yes—
16C22×C3×D12C2211yescharacteristic
17C22×D3×Dic3C2212yes—
18C2×C32×C22⋊C4C2211yescharacteristic
19C2×#3757C2211yescharacteristic
20C2×#3750C2211yescharacteristic
21C2×#3750C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24#64086—24no—
25C2×C3×#217C2212yes—
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28#67⋊Dic3—28no—
29C2×#3724C2212yes—
30C2×Dic3⋊Dic3C2212yes—
31C2×(C2×D3)⋊Dic3C2212yes—
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34C2×Dic32C2212yes—
35#63898—24no—
36C3×C3⋊#95C2211yescharacteristic
37C3×C3⋊#95C2211yescharacteristic
38C3×C3⋊#95C2212yes—
39#63579C2212yes—
40C2×D4×Dic3—32no—
41C2×D4×Dic3—31no—
42C2×#893—31no—
43C2×#67⋊C4—32no—
44C2×#877—31no—
45C2×#877—31no—
46C2×#877—61no—
47C3×#397—31no—
48C3×#392—31no—
49#5222—32no—
50#5222—31no—
51#4983—31no—
52#4960D311yescharacteristic
53#4959—32no—
54#4953D311yescharacteristic, complemented
55#4948—32no—
56Dic3×C22⋊C4—32no—
57#4676—32no—
58#4672—31no—
59#4666—32no—
60#4661—31no—
61#4649—31no—
62#4649—31no—
63C24×C32C2311yescharacteristic
64C23×C3×D3C2312yes—
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3—22no—
68C22×C3⋊Dic3—22no—
69C22×C3⋊Dic3D414yescomplemented
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2311yescharacteristic
73C22×C3⋊Dic3C2311yescharacteristic
74C2×C3×#67—24no—
75C2×C3×#67—24no—
76C2×C3×#67—24no—
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2312yes—
80C2×C3×D12—24no—
81C2×C3×D12—22no—
82C2×D3×Dic3—24no—
83C2×D3×Dic3—24no—
84C2×D3×Dic3—24no—
85C32×C22⋊C4—22no—
86#3757—22no—
87#3750—22no—
88#3750—22no—
89C4×C3⋊Dic3—22no—
90C4×C3⋊Dic3D414yescomplemented
91C3×#217—24no—
92C3×(C2×D3)⋊C4—24no—
93C3×C4⋊Dic3—22no—
94#3724—24no—
95Dic3⋊Dic3—24no—
96(C2×D3)⋊Dic3—24no—
97(C2×D3)⋊Dic3—24no—
98(C2×D3)⋊Dic3—24no—
99Dic32—24no—
100#2392—91noSylow
101C22×C3×D4—32no—
102C22×C3×D4—31no—
103C22×#67C2×D312yes—
104C23×Dic3—31no—
105C23×Dic3—31no—
106C23×Dic3—32no—
107C23×Dic3—61no—
108C22×D12C2×D311yescharacteristic
109C22×C4×D3—32no—
110C2×C3×C4⋊C4—31no—
111C2×C3×C22⋊C4—21no—
112C2×C3×C22⋊C4—32no—
113C2×C3×C22⋊C4—32no—
114C2×C3×C22⋊C4C2×D311yescharacteristic
115C2×C3×C22⋊C4C2×D311yescharacteristic
116C2×#217—31no—
117C2×#217—31no—
118C2×#217—32no—
119C2×#217—32no—
120C2×#217—32no—
121C2×#217—61no—
122C2×#217C2×D312yes—
123D4×Dic3—64no—
124D4×Dic3—68no—
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4—32no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4C2×D312yes—
129C2×C4⋊Dic3—32no—
130C2×C4⋊Dic3C2×D311yescharacteristic
131C2×Dic3⋊C4—31no—
132C2×Dic3⋊C4—31no—
133C2×Dic3⋊C4—31no—
134C2×Dic3⋊C4—31no—
135C2×Dic3⋊C4—32no—
136C2×Dic3⋊C4—32no—
137C2×Dic3⋊C4—32no—
138C2×Dic3⋊C4—61no—
139C2×Dic3⋊C4—61no—
140C2×C4×Dic3—31no—
141C2×C4×Dic3—31no—
142C2×C4×Dic3—31no—
143C2×C4×Dic3—31no—
144C2×C4×Dic3—32no—
145C2×C4×Dic3—32no—
146C2×C4×Dic3—61no—
147C2×C4×Dic3—61no—
148#893—64no—
149#67⋊C4—68no—
150#877—64no—
151#877—64no—
152#877—68no—
153C3×#95—31no—
154C3×#95—31no—
155C3×#95—32no—
156C3⋊#95—32no—
157C3⋊#95—32no—
158C3⋊#95C2×D311yescharacteristic
159C3⋊#95C2×D311yescharacteristic
160C3⋊#95C2×D312yes—
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#4114yes—
174C2×C32×C4—21no—
175C2×C32×C4—22no—
176C2×C32×C4—22no—
177C2×C32×C4C2×D412yes—
178C2×C3⋊Dic3—21no—
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3—28no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—22no—
183C2×C3⋊Dic3—22no—
184C2×C3⋊Dic3C2×D412yes—
185C2×C3⋊Dic3C2×D412yes—
186C2×C3⋊Dic3C2×D412yes—
187C2×C3⋊Dic3C2×D412yes—
188C2×C3⋊Dic3#4112yes—
189C3×#67—216no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3#4114yes—
199C3×D12—28no—
200D3×Dic3—48no—
201C2×C4×D4—92no—
202C2×C4×D4—91no—
203C2×#117—91no—
204#398—91no—
205#397—31no—
206#396—92no—
207#394—91no—
208#394—92no—
209#392—31no—
210C4×C4⋊C4—91no—
211C4×C22⋊C4—92no—
212C24×C3—21no—
213C24×C3—32no—
214C24×C3C22×D311yescharacteristic
215C24×C3C22×D311yescharacteristic
216C23×D3C22×D312yes—
217C2×C3×D4—64no—
218C2×C3×D4—64no—
219C2×C3×D4—64no—
220C2×C3×D4—64no—
221C2×C3×D4—62no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—32no—
225C22×C3×C4—32no—
226C22×C3×C4—32no—
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C2×#67—24no—
232C2×#67—24no—
233C2×#67—24no—
234C22×Dic3—31no—
235C22×Dic3—31no—
236C22×Dic3—34no—
237C22×Dic3—34no—
238C22×Dic3—31no—
239C22×Dic3—31no—
240C22×Dic3—31no—
241C22×Dic3—31no—
242C22×Dic3—31no—
243C22×Dic3—31no—
244C22×Dic3—61no—
245C22×Dic3—61no—
246C22×Dic3—64no—
247C22×Dic3—61no—
248C22×Dic3—61no—
249C22×Dic3—64no—
250C22×Dic3—64no—
251C22×Dic3—64no—
252C22×Dic3—62no—
253C22×Dic3—62no—
254C22×Dic3—62no—
255C22×Dic3—62no—
256C22×Dic3—64no—
257C22×Dic3—64no—
258C22×Dic3C22×D312yes—
259C22×Dic3C22×D312yes—
260C22×Dic3C22×D312yes—
261C2×D12—24no—
262C2×D12—22no—
263C2×C4×D3—64no—
264C2×C4×D3—64no—
265C2×C4×D3—64no—
266C3×C4⋊C4—62no—
267C3×C22⋊C4—24no—
268C3×C22⋊C4—22no—
269C3×C22⋊C4—22no—
270C3×C22⋊C4—64no—
271C3×C22⋊C4—64no—
272#217—24no—
273#217—64no—
274#217—64no—
275#217—64no—
276#217—62no—
277#217—62no—
278#217—64no—
279(C2×D3)⋊C4—24no—
280(C2×D3)⋊C4—64no—
281(C2×D3)⋊C4—64no—
282(C2×D3)⋊C4—64no—
283C4⋊Dic3—22no—
284C4⋊Dic3—64no—
285Dic3⋊C4—64no—
286Dic3⋊C4—64no—
287Dic3⋊C4—62no—
288Dic3⋊C4—62no—
289Dic3⋊C4—64no—
290Dic3⋊C4—64no—
291Dic3⋊C4—62no—
292Dic3⋊C4—62no—
293Dic3⋊C4—64no—
294C4×Dic3—34no—
295C4×Dic3—34no—
296C4×Dic3—64no—
297C4×Dic3—64no—
298C4×Dic3—64no—
299C4×Dic3—62no—
300C4×Dic3—62no—
301C4×Dic3—64no—
302C22×C32—22no—
303C22×C32—24no—
304C22×C32—41no—
305C22×C32—42no—
306C22×C32—41no—
307C22×C32C22×D411yescharacteristic
308C22×C32C22×D411yescharacteristic
309C22×C32C2×#4112yes—
310C22×C32C2×#4112yes—
311C22×C32C2×#4111yescharacteristic
312C2×C3×D3—24no—
313C2×C3×D3—24no—
314C2×C3×D3—24no—
315C2×C3×D3—42no—
316C2×C3×D3—42no—
317C2×C3×D3—42no—
318C2×C3×D3—42no—
319C32×C4—22no—
320C32×C4—41no—
321C3⋊Dic3—22no—
322C3⋊Dic3—22no—
323C3⋊Dic3—41no—
324C3⋊Dic3#12114yes—
325C3×Dic3—24no—
326C3×Dic3—42no—
327C3×Dic3—42no—
328C22×D4—32no—
329C22×D4—31no—
330C23×C4—92no—
331C23×C4—91no—
332C4×D4—184no—
333C4×D4—188no—
334#117—184no—
335C2×C4⋊C4—31no—
336C2×C4⋊C4—92no—
337C2×C4⋊C4—92no—
338C2×C4⋊C4—91no—
339C2×C4⋊C4—91no—
340C2×C22⋊C4—32no—
341C2×C22⋊C4—32no—
342C2×C22⋊C4—92no—
343C2×C22⋊C4—92no—
344C2×C22⋊C4—92no—
345C2×C22⋊C4—91no—
346C2×C22⋊C4D3211yescharacteristic
347C2×C42—91no—
348C2×C42—92no—
349C2×C42—91no—
350#95—32no—
351#95—31no—
352#95—31no—
353#95—92no—
354C23×C3—22no—
355C23×C3—22no—
356C23×C3—21no—
357C23×C3—21no—
358C23×C3—22no—
359C23×C3—22no—
360C23×C3—21no—
361C23×C3—21no—
362C23×C3—22no—
363C23×C3—22no—
364C23×C3—21no—
365C23×C3—22no—
366C23×C3—34no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—62no—
370C23×C3—62no—
371C23×C3—62no—
372C23×C3—62no—
373C23×C3—62no—
374C23×C3—62no—
375C23×C3D3×D412yes—
376C23×C3D3×D412yes—
377C23×C3C23×D311yescharacteristic
378C23×C3C23×D311yescharacteristic
379C22×D3—22no—
380C22×D3—22no—
381C22×D3—22no—
382C22×D3—22no—
383C22×D3—22no—
384C22×D3—22no—
385C22×D3#23714yes—
386C3×D4—68no—
387C3×D4—616no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—34no—
397C2×C3×C4—42no—
398C2×C3×C4—42no—
399C2×C3×C4—62no—
400C2×C3×C4—62no—
401C2×C3×C4—62no—
402C2×C3×C4—62no—
403C2×C3×C4—62no—
404C2×C3×C4—62no—
405C2×C3×C4—62no—
406C2×C3×C4—62no—
407C2×C3×C4D3×D412yes—
408C2×C3×C4D3×D412yes—
409#67—216no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—22no—
413C2×Dic3—22no—
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—32no—
419C2×Dic3—32no—
420C2×Dic3—32no—
421C2×Dic3—32no—
422C2×Dic3—32no—
423C2×Dic3—32no—
424C2×Dic3—32no—
425C2×Dic3—32no—
426C2×Dic3—32no—
427C2×Dic3—32no—
428C2×Dic3—62no—
429C2×Dic3—62no—
430C2×Dic3—62no—
431C2×Dic3—62no—
432C2×Dic3—62no—
433C2×Dic3—68no—
434C2×Dic3—68no—
435C2×Dic3—62no—
436C2×Dic3—616no—
437C2×Dic3—62no—
438C2×Dic3—61no—
439C2×Dic3—61no—
440C2×Dic3—62no—
441C2×Dic3—62no—
442C2×Dic3—61no—
443C2×Dic3—61no—
444C2×Dic3—62no—
445C2×Dic3—61no—
446C2×Dic3—61no—
447C2×Dic3—62no—
448C2×Dic3—62no—
449C2×Dic3—122no—
450C2×Dic3—122no—
451C2×Dic3—128no—
452C2×Dic3#23714yes—
453D12—28no—
454C4×D3—128no—
455C2×C32—42no—
456C2×C32C2×#12111yescharacteristic
457C2×C32#52512yes—
458C2×C32#52511yescharacteristic
459C2×C32#52912yes—
460C2×C32#53211yescharacteristic
461C3×D3—44no—
462C24—32no—
463C24C2×D3211yescharacteristic
464C2×D4—64no—
465C2×D4—64no—
466C2×D4—64no—
467C2×D4—64no—
468C2×D4—62no—
469C22×C4—32no—
470C22×C4—32no—
471C22×C4—32no—
472C22×C4—91no—
473C22×C4—91no—
474C22×C4—91no—
475C22×C4—94no—
476C22×C4—91no—
477C22×C4—184no—
478C22×C4—184no—
479C22×C4—184no—
480C22×C4—182no—
481C22×C4—182no—
482C22×C4C2×D3211yescharacteristic
483C22×C4C2×D3211yescharacteristic
484C4⋊C4—62no—
485C4⋊C4—182no—
486C4⋊C4—184no—
487C4⋊C4—184no—
488C4⋊C4—182no—
489C22⋊C4—22no—
490C22⋊C4—64no—
491C22⋊C4—64no—
492C22⋊C4—184no—
493C22⋊C4—184no—
494C22⋊C4—184no—
495C22⋊C4—182no—
496C42—94no—
497C42—182no—
498C42—184no—
499C22×C3—24no—
500C22×C3—24no—
501C22×C3—24no—
502C22×C3—22no—
503C22×C3—22no—
504C22×C3—21no—
505C22×C3—21no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—21no—
509C22×C3—44no—
510C22×C3—44no—
511C22×C3—42no—
512C22×C3—42no—
513C22×C3—41no—
514C22×C3—41no—
515C22×C3—42no—
516C22×C3—41no—
517C22×C3—41no—
518C22×C3—42no—
519C22×C3—64no—
520C22×C3—64no—
521C22×C3—64no—
522C22×C3—122no—
523C22×C3—122no—
524C22×C3—122no—
525C22×C3—122no—
526C22×C3C2×D3×D411yescharacteristic
527C22×C3C2×D3×D411yescharacteristic
528C22×C3C2×D3×D411yescharacteristic
529C22×C3C2×D3×D411yescharacteristic
530C22×C3C2×#23712yes—
531C22×C3C2×#23712yes—
532C22×C3D3×#4111yescharacteristic
533C22×C3D3×#4111yescharacteristic
534C22×C3D3×#4112yes—
535C22×C3D3×#4112yes—
536C2×D3—24no—
537C2×D3—24no—
538C2×D3—24no—
539C2×D3—42no—
540C2×D3—42no—
541C2×D3—42no—
542C2×D3—42no—
543C3×C4—22no—
544C3×C4—22no—
545C3×C4—42no—
546C3×C4—42no—
547C3×C4—41no—
548C3×C4—41no—
549C3×C4—64no—
550C3×C4—122no—
551C3×C4—122no—
552Dic3—24no—
553Dic3—34no—
554Dic3—34no—
555Dic3—42no—
556Dic3—42no—
557Dic3—64no—
558Dic3—64no—
559Dic3—62no—
560Dic3—62no—
561Dic3—62no—
562Dic3—62no—
563Dic3—122no—
564Dic3—122no—
565Dic3—121no—
566Dic3—121no—
567C32#239211yescharacteristic, complemented, Sylow
568C23—21no—
569C23—22no—
570C23—22no—
571C23—21no—
572C23—34no—
573C23—62no—
574C23—62no—
575C23—62no—
576C23—62no—
577C23—62no—
578C23—62no—
579C23#380212yes—
580C23C22×D3211yescharacteristic
581D4—68no—
582D4—616no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—34no—
587C2×C4—62no—
588C2×C4—62no—
589C2×C4—62no—
590C2×C4—62no—
591C2×C4—62no—
592C2×C4—62no—
593C2×C4—62no—
594C2×C4—62no—
595C2×C4—92no—
596C2×C4—92no—
597C2×C4—92no—
598C2×C4—92no—
599C2×C4—92no—
600C2×C4—188no—
601C2×C4—181no—
602C2×C4—182no—
603C2×C4—181no—
604C2×C4—182no—
605C2×C4—181no—
606C2×C4—368no—
607C2×C4#381112yes—
608C2×C3—21no—
609C2×C3—22no—
610C2×C3—22no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—44no—
614C2×C3—42no—
615C2×C3—42no—
616C2×C3—124no—
617C2×C3#558612yes—
618C2×C3#558611yescharacteristic
619C2×C3#560012yes—
620C2×C3D3×#12111yescharacteristic
621C2×C3D3×#12111yescharacteristic
622C2×C3#565612yes—
623C2×C3#565611yescharacteristic
624C2×C3#566811yescharacteristic
625C2×C3#570612yes—
626C2×C3#571611yescharacteristic
627D3—44no—
628C22—22no—
629C22—24no—
630C22—42no—
631C22—41no—
632C22—41no—
633C22—64no—
634C22—64no—
635C22—64no—
636C22—122no—
637C22—122no—
638C22—122no—
639C22—122no—
640C22C2×#380211yescharacteristic
641C22#6430611yescharacteristic
642C22D3×#23712yes—
643C22D3×#23712yes—
644C22C2×#381111yescharacteristic
645C4—22no—
646C4—41no—
647C4—64no—
648C4—94no—
649C4—122no—
650C4—122no—
651C4—182no—
652C4—182no—
653C4—361no—
654C3—21no—
655C3#7666611yescharacteristic, complemented
656C3#7745711yescharacteristic, complemented
657C2—42no—
658C2—124no—
659C2#1059408212yes—
660C2#1059411212yes—
661C2#1059508111yescharacteristic
662C2#1059516011yescharacteristic
663C2#1059516711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC3×#4960C2
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×#64086C2semidirect
2. C2×#67⋊Dic3C2semidirect
3. C2×#63898C2semidirect
5. C3×#4953C2semidirect
6. #10591708C2semidirect
7. #10591368C2semidirect
8. #10591358C2semidirect
9. #10591309C2semidirect
10. #10591302C2semidirect
11. #10591257C2semidirect
54. #4953D3semidirect
69. C22×C3⋊Dic3D4semidirect
90. C4×C3⋊Dic3D4semidirect
567. C32#2392semidirect
655. C3#76666semidirect
656. C3#77457semidirect

Maximal subgroups

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

subgroupindex
C2×#640862
C2×#67⋊Dic32
C2×#638982
C3×#49602
C3×#49532
#105917082
#105913682
#105913582
#105913092
#105913022
#105912572
#774573
#766663