Finite Group Databasebeta

← #11803394

Subgroups — #11803394

Order 1152.

1477 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic
2C22×C3×Dic3⋊C4C211yesmaximal, characteristic, complemented
3C2×#63966C211yesmaximal, characteristic
4C3×C4×#217C211yesmaximal, characteristic, complemented
5#10591718C211yesmaximal, characteristic, complemented
6#10591711C211yesmaximal, characteristic
7#10591696C211yesmaximal, characteristic, complemented
8#10591334C212yesmaximal, complemented
9#10591330C212yesmaximal, complemented
10#10591290C212yesmaximal, complemented
11#10591289C212yesmaximal, complemented
12#82158—31nomaximal
13#73446—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×#638C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C23×C3×Dic3C2211yescharacteristic
19C2×#3757C2211yescharacteristic
20C4×#638—24no—
21C2×#3752C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C3×#217C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C2×C3×Dic3⋊C4—24no—
27C2×C3×Dic3⋊C4C2212yes—
28C2×C3×Dic3⋊C4C2212yes—
29C2×C3×C4×Dic3C2212yes—
30#63966C418yescomplemented
31C2×Dic3⋊Dic3C2212yes—
32C2×Dic3⋊Dic3C2212yes—
33C2×#3722C2212yes—
34C2×#3722C2212yes—
35C3×C3⋊#95C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C22×C3×C4⋊C4—31no—
41C2×#929—31no—
42C2×C4×#67—31no—
43C2×C4×#67—31no—
44C2×C4×#67—61no—
45C22×Dic3⋊C4D311yescharacteristic, complemented
46C2×#886—31no—
47C3×C4×C22⋊C4—31no—
48#5213—31no—
49#5211—31no—
50#5210—31no—
51C4×#217D311yescharacteristic, complemented
52#4990—32no—
53#4989—32no—
54#4978—32no—
55#4976—32no—
56#4958—31no—
57#4950—31no—
58#4943—31no—
59#4940—32no—
60#4928—32no—
61#4668—32no—
62#4653—32no—
63C24×C32C2311yescharacteristic
64C23×C3⋊D3C2311yescharacteristic
65C22×C32×C4—42no—
66C22×C32×C4D414yes—
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C2×#638—22no—
70C2×#638—22no—
71C2×#638C2×C414yes—
72C22×C3⋊Dic3C2311yescharacteristic
73C22×C3⋊Dic3C2311yescharacteristic
74C22×C3⋊Dic3C2311yescharacteristic
75C2×C4×C3⋊D3—22no—
76C2×C4×C3⋊D3—42no—
77C22×C3×Dic3—22no—
78C22×C3×Dic3—22no—
79C22×C3×Dic3—22no—
80C22×C3×Dic3—42no—
81C22×C3×Dic3C2×C414yescomplemented
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2312yes—
86#3757—22no—
87#3752—22no—
88#3750—22no—
89C4×C3⋊Dic3—22no—
90C3×#217—22no—
91C3×#217C2×C414yescomplemented
92C3×Dic3⋊C4—24no—
93C3×Dic3⋊C4—24no—
94C3×C4×Dic3—42no—
95Dic3⋊Dic3—42no—
96Dic3⋊Dic3C2×C418yescomplemented
97#3722—42no—
98#3722C2×C418yescomplemented
99#2322—91noSylow
100C23×C3×C4—21no—
101C23×C3×C4—31no—
102C23×C3×C4—31no—
103C23×C3×C4C2×D311yescharacteristic
104C23×C3×C4C2×D311yescharacteristic
105C22×#67—31no—
106C22×#67—31no—
107C22×#67—61no—
108C23×Dic3C2×D311yescharacteristic
109C23×Dic3C2×D311yescharacteristic
110C22×C4×D3—31no—
111C22×C4×D3—31no—
112C22×C4×D3—61no—
113C2×C3×C4⋊C4—32no—
114C2×C3×C4⋊C4—32no—
115C2×C3×C4⋊C4—64no—
116C2×C3×C22⋊C4—31no—
117C2×C3×C22⋊C4—31no—
118C2×C3×C42—32no—
119C2×#217—31no—
120C2×#217—31no—
121C2×#217—61no—
122C2×#217C2×D311yescharacteristic
123C2×#217C2×D311yescharacteristic
124#929—38no—
125C4×#67—68no—
126C4×#67—64no—
127C4×#67—64no—
128C2×(C2×D3)⋊C4—32no—
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—31no—
131C2×(C2×D3)⋊C4—31no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—32no—
134C2×(C2×D3)⋊C4—61no—
135C2×C4⋊Dic3—32no—
136C2×C4⋊Dic3—32no—
137C2×Dic3⋊C4—24no—
138C2×Dic3⋊C4—32no—
139C2×Dic3⋊C4—31no—
140C2×Dic3⋊C4—31no—
141C2×Dic3⋊C4—32no—
142C2×Dic3⋊C4—61no—
143C2×Dic3⋊C4C2×D312yes—
144C2×Dic3⋊C4C2×D312yes—
145C2×C4×Dic3—31no—
146C2×C4×Dic3—31no—
147C2×C4×Dic3—61no—
148C2×C4×Dic3C2×D312yes—
149#886—38no—
150C3×#95—32no—
151C3⋊#95—32no—
152C3⋊#95—32no—
153C3⋊#95—32no—
154C3⋊#95—32no—
155C3⋊#95—32no—
156C3⋊#95—32no—
157C3⋊#95—32no—
158C3⋊#95—32no—
159C3⋊#95C2×D312yes—
160C23×C32—22no—
161C23×C32—22no—
162C23×C32C22×C412yes—
163C23×C32C2×D412yes—
164C23×C32#4112yes—
165C23×C32C2411yescharacteristic
166C22×C3⋊D3—21no—
167C22×C3⋊D3—21no—
168C22×C3⋊D3—22no—
169C22×C3⋊D3—22no—
170C22×C3⋊D3C22×C412yes—
171C2×C32×C4—22no—
172C2×C32×C4—22no—
173C2×C32×C4—44no—
174C2×C32×C4C2×D412yes—
175C2×C32×C4C2×D412yes—
176#638—28no—
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—21no—
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—22no—
182C2×C3⋊Dic3—22no—
183C2×C3⋊Dic3C22×C412yes—
184C4×C3⋊D3—44no—
185C2×C3×Dic3—28no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
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—44no—
197C2×C3×Dic3C22×C414yes—
198C2×C3×Dic3C22×C414yes—
199C2×#123—91no—
200C2×C4×D4—91no—
201C22×C4⋊C4—31no—
202#389—92no—
203#388—92no—
204#387—92no—
205#386—91no—
206#385—92no—
207#385—91no—
208#381—91no—
209C4×C22⋊C4—31no—
210C24×C3—21no—
211C24×C3C22×D311yescharacteristic
212C24×C3C22×D311yescharacteristic
213C23×D3—31no—
214C23×D3—31no—
215C23×D3—61no—
216C22×C3×C4—24no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—34no—
220C22×C3×C4—32no—
221C22×C3×C4—32no—
222C22×C3×C4—32no—
223C22×C3×C4—32no—
224C22×C3×C4—42no—
225C22×C3×C4—42no—
226C22×C3×C4—44no—
227C22×C3×C4—62no—
228C22×C3×C4—62no—
229C22×C3×C4—62no—
230C22×C3×C4—122no—
231C22×C3×C4D1214yes—
232C22×C3×C4#6714yes—
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C22×C3×C4C22×D311yescharacteristic
236C22×C3×C4C22×D311yescharacteristic
237C2×#67—34no—
238C2×#67—34no—
239C2×#67—64no—
240C2×#67—64no—
241C2×#67—64no—
242C2×#67—62no—
243C2×#67—62no—
244C2×#67—62no—
245C2×#67—62no—
246C22×Dic3—22no—
247C22×Dic3—22no—
248C22×Dic3—22no—
249C22×Dic3—31no—
250C22×Dic3—31no—
251C22×Dic3—31no—
252C22×Dic3—31no—
253C22×Dic3—31no—
254C22×Dic3—31no—
255C22×Dic3—42no—
256C22×Dic3—61no—
257C22×Dic3—61no—
258C22×Dic3—61no—
259C22×Dic3C4×D314yescomplemented
260C22×Dic3C22×D312yes—
261C22×Dic3C22×D312yes—
262C22×Dic3C22×D312yes—
263C22×Dic3C22×D312yes—
264C2×C4×D3—64no—
265C2×C4×D3—62no—
266C2×C4×D3—62no—
267C2×C4×D3—122no—
268C2×C4×D3—122no—
269C2×C4×D3—124no—
270C3×C4⋊C4—64no—
271C3×C4⋊C4—64no—
272C3×C22⋊C4—34no—
273C3×C22⋊C4—62no—
274C3×C42—122no—
275#217—22no—
276#217—64no—
277#217—62no—
278#217—62no—
279#217C4×D314yescomplemented
280(C2×D3)⋊C4—38no—
281(C2×D3)⋊C4—38no—
282(C2×D3)⋊C4—64no—
283(C2×D3)⋊C4—62no—
284(C2×D3)⋊C4—62no—
285(C2×D3)⋊C4—122no—
286(C2×D3)⋊C4—122no—
287C4⋊Dic3—38no—
288C4⋊Dic3—122no—
289Dic3⋊C4—24no—
290Dic3⋊C4—24no—
291Dic3⋊C4—38no—
292Dic3⋊C4—64no—
293Dic3⋊C4—62no—
294Dic3⋊C4—62no—
295Dic3⋊C4—122no—
296C4×Dic3—42no—
297C4×Dic3—64no—
298C4×Dic3—62no—
299C4×Dic3—62no—
300C22×C32—24no—
301C22×C32—22no—
302C22×C32—22no—
303C22×C32—24no—
304C22×C32C4×D414yes—
305C22×C32C23×C411yescharacteristic
306C22×C32C22×D411yescharacteristic
307C22×C32C2×#4111yescharacteristic
308C22×C32H(5,𝔽2)12yes—
309C22×C322−1+412yes—
310C2×C3⋊D3—22no—
311C2×C3⋊D3—24no—
312C2×C3⋊D3—41no—
313C2×C3⋊D3—41no—
314C2×C3⋊D3—42no—
315C32×C4—22no—
316C32×C4—22no—
317C3⋊Dic3—22no—
318C3⋊Dic3—41no—
319C3⋊Dic3—41no—
320C3×Dic3—24no—
321C3×Dic3—24no—
322C3×Dic3—42no—
323C3×Dic3—42no—
324C22×D4—91no—
325C23×C4—31no—
326C23×C4—31no—
327C23×C4—91no—
328C23×C4D3211yescharacteristic
329#123—98no—
330C4×D4—184no—
331C2×C4⋊C4—32no—
332C2×C4⋊C4—32no—
333C2×C4⋊C4—64no—
334C2×C4⋊C4—92no—
335C2×C4⋊C4—91no—
336C2×C4⋊C4—92no—
337C2×C22⋊C4—31no—
338C2×C22⋊C4—31no—
339C2×C22⋊C4—92no—
340C2×C22⋊C4—91no—
341C2×C22⋊C4—91no—
342C2×C22⋊C4—92no—
343C2×C42—32no—
344C2×C42—91no—
345#95—32no—
346#95—92no—
347#95—92no—
348#95—92no—
349#95—92no—
350C23×C3—22no—
351C23×C3—22no—
352C23×C3—22no—
353C23×C3—22no—
354C23×C3—21no—
355C23×C3—22no—
356C23×C3—22no—
357C23×C3—22no—
358C23×C3—42no—
359C23×C3—42no—
360C23×C3C2×C4×D312yes—
361C23×C3C2×C4×D312yes—
362C23×C3C2×D1212yes—
363C23×C3#23512yes—
364C23×C3#23512yes—
365C23×C3C2×#6712yes—
366C23×C3C23×D311yescharacteristic
367C23×C3C23×D311yescharacteristic
368C22×D3—32no—
369C22×D3—32no—
370C22×D3—62no—
371C22×D3—62no—
372C22×D3—62no—
373C22×D3—61no—
374C22×D3—61no—
375C22×D3—61no—
376C22×D3—62no—
377C22×D3—62no—
378C22×D3—62no—
379C22×D3—62no—
380C22×D3—61no—
381C22×D3—122no—
382C22×D3—122no—
383C2×C3×C4—24no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—34no—
391C2×C3×C4—34no—
392C2×C3×C4—42no—
393C2×C3×C4—44no—
394C2×C3×C4—44no—
395C2×C3×C4—48no—
396C2×C3×C4—68no—
397C2×C3×C4—62no—
398C2×C3×C4—62no—
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×C4—124no—
408C2×C3×C4C2×D1212yes—
409C2×C3×C4C2×D1212yes—
410C2×C3×C4C2×#6712yes—
411C2×C3×C4C2×#6712yes—
412#67—616no—
413#67—68no—
414#67—68no—
415C2×Dic3—28no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—22no—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3—22no—
423C2×Dic3—22no—
424C2×Dic3—22no—
425C2×Dic3—22no—
426C2×Dic3—32no—
427C2×Dic3—32no—
428C2×Dic3—44no—
429C2×Dic3—62no—
430C2×Dic3—62no—
431C2×Dic3—62no—
432C2×Dic3—61no—
433C2×Dic3—61no—
434C2×Dic3—61no—
435C2×Dic3—61no—
436C2×Dic3—62no—
437C2×Dic3—62no—
438C2×Dic3—61no—
439C2×Dic3—61no—
440C2×Dic3—62no—
441C2×Dic3—62no—
442C2×Dic3—62no—
443C2×Dic3—62no—
444C2×Dic3—61no—
445C2×Dic3—61no—
446C2×Dic3—122no—
447C2×Dic3—122no—
448C2×Dic3C2×C4×D314yes—
449C2×Dic3C2×C4×D314yes—
450C4×D3—128no—
451C4×D3—124no—
452C4×D3—124no—
453C2×C32—24no—
454C2×C32C2×C4×D411yescharacteristic
455C2×C32#52012yes—
456C2×C32#53411yescharacteristic
457C2×C32#53611yescharacteristic
458C2×C32#53912yes—
459C3⋊D3—42no—
460C24—91no—
461C24C2×D3211yescharacteristic
462C2×D4—94no—
463C2×D4—182no—
464C2×D4—182no—
465C22×C4—32no—
466C22×C4—32no—
467C22×C4—34no—
468C22×C4—32no—
469C22×C4—32no—
470C22×C4—42no—
471C22×C4—62no—
472C22×C4—62no—
473C22×C4—62no—
474C22×C4—91no—
475C22×C4—91no—
476C22×C4—91no—
477C22×C4—122no—
478C22×C4—182no—
479C22×C4—362no—
480C22×C4#62614yes—
481C22×C4C2×D3211yescharacteristic
482C22×C4C2×D3211yescharacteristic
483C4⋊C4—64no—
484C4⋊C4—64no—
485C4⋊C4—98no—
486C4⋊C4—182no—
487C4⋊C4—362no—
488C22⋊C4—34no—
489C22⋊C4—62no—
490C22⋊C4—98no—
491C22⋊C4—182no—
492C22⋊C4—182no—
493C22⋊C4—362no—
494C42—122no—
495C42—182no—
496C22×C3—22no—
497C22×C3—24no—
498C22×C3—24no—
499C22×C3—22no—
500C22×C3—24no—
501C22×C3—22no—
502C22×C3—22no—
503C22×C3—24no—
504C22×C3—22no—
505C22×C3—21no—
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—22no—
509C22×C3—24no—
510C22×C3—42no—
511C22×C3—44no—
512C22×C3—42no—
513C22×C3—44no—
514C22×C3C4×D1214yes—
515C22×C3C4×#6714yes—
516C22×C3C22×C4×D311yescharacteristic
517C22×C3C22×C4×D311yescharacteristic
518C22×C3C22×D1211yescharacteristic
519C22×C3C2×#23511yescharacteristic
520C22×C3C2×#23511yescharacteristic
521C22×C3#100412yes—
522C22×C3#100412yes—
523C22×C3#100712yes—
524C22×C3#101012yes—
525C22×C3C22×#6711yescharacteristic
526C2×D3—64no—
527C2×D3—62no—
528C2×D3—64no—
529C2×D3—62no—
530C2×D3—64no—
531C2×D3—124no—
532C2×D3—122no—
533C2×D3—124no—
534C2×D3—122no—
535C2×D3—121no—
536C2×D3—122no—
537C2×D3—121no—
538C2×D3—121no—
539C2×D3—121no—
540C2×D3—122no—
541C3×C4—24no—
542C3×C4—22no—
543C3×C4—22no—
544C3×C4—22no—
545C3×C4—22no—
546C3×C4—42no—
547C3×C4—64no—
548C3×C4—64no—
549C3×C4—122no—
550C3×C4—122no—
551Dic3—24no—
552Dic3—24no—
553Dic3—42no—
554Dic3—42no—
555Dic3—64no—
556Dic3—62no—
557Dic3—62no—
558Dic3—122no—
559Dic3—122no—
560Dic3—121no—
561Dic3—121no—
562Dic3—121no—
563Dic3—121no—
564C32#232211yescharacteristic, complemented, Sylow
565C23—22no—
566C23—22no—
567C23—92no—
568C23—182no—
569C23—181no—
570C23—181no—
571C23—182no—
572C23#379812yes—
573C23C4×D3212yes—
574C23C2×#62612yes—
575C23C22×D3211yescharacteristic
576D4—188no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—34no—
580C2×C4—34no—
581C2×C4—44no—
582C2×C4—62no—
583C2×C4—62no—
584C2×C4—62no—
585C2×C4—62no—
586C2×C4—68no—
587C2×C4—62no—
588C2×C4—62no—
589C2×C4—62no—
590C2×C4—62no—
591C2×C4—62no—
592C2×C4—62no—
593C2×C4—92no—
594C2×C4—124no—
595C2×C4—181no—
596C2×C4—181no—
597C2×C4—182no—
598C2×C4—181no—
599C2×C4—181no—
600C2×C4—182no—
601C2×C4—364no—
602C2×C4C2×#62612yes—
603C2×C4C2×#62612yes—
604C2×C3—24no—
605C2×C3—24no—
606C2×C3—22no—
607C2×C3—21no—
608C2×C3—22no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—44no—
612C2×C3C2×C4×D1211yescharacteristic
613C2×C3#549311yescharacteristic
614C2×C3#550412yes—
615C2×C3#551512yes—
616C2×C3#552611yescharacteristic
617C2×C3#554612yes—
618C2×C3#556412yes—
619C2×C3C2×C4×#6711yescharacteristic
620C2×C3#580411yescharacteristic
621C2×C3#581611yescharacteristic
622D3—124no—
623D3—122no—
624D3—122no—
625C22—24no—
626C22—22no—
627C22—24no—
628C22—22no—
629C22—184no—
630C22—182no—
631C22—362no—
632C22—361no—
633C22—361no—
634C22C4×#62614yes—
635C22#6429712yes—
636C22C2×#379811yescharacteristic
637C22C2×C4×D3211yescharacteristic
638C22C22×#62611yescharacteristic
639C22#6433012yes—
640C4—22no—
641C4—22no—
642C4—64no—
643C4—64no—
644C4—122no—
645C4—122no—
646C4—182no—
647C4—361no—
648C4—361no—
649C3—21no—
650C3#7344611yescharacteristic, complemented
651C3#8215811yescharacteristic, complemented
652C2—24no—
653C2—362no—
654C2#1059484212yes—
655C2#1059486611yescharacteristic
656C2#1059487412yes—
657C2C2×C4×#62611yescharacteristic
658C2#1059551911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC23×C4D32
hypocenterC32#2322
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×Dic3⋊C4C2semidirect
4. C3×C4×#217C2semidirect
5. #10591718C2semidirect
7. #10591696C2semidirect
8. #10591334C2semidirect
9. #10591330C2semidirect
10. #10591290C2semidirect
11. #10591289C2semidirect
30. #63966C4semidirect
45. C22×Dic3⋊C4D3semidirect
51. C4×#217D3semidirect
81. C22×C3×Dic3C2×C4semidirect
91. C3×#217C2×C4semidirect
96. Dic3⋊Dic3C2×C4semidirect
98. #3722C2×C4semidirect
259. C22×Dic3C4×D3semidirect
279. #217C4×D3semidirect
564. C32#2322semidirect
650. C3#73446semidirect
651. C3#82158semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C22×C3×Dic3⋊C42
C2×#639662
C3×C4×#2172
#105917182
#105917112
#105916962
#105913342
#105913302
#105912902
#105912892
#821583
#734463