Finite Group Databasebeta

← #11802902

Subgroups — #11802902

Order 1152.

1749 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63921C211yesmaximal, characteristic
2C2×D3×(C2×D3)⋊C4C212yesmaximal
3#10592686C211yesmaximal, characteristic, complemented
4C3×#4989C212yesmaximal, complemented
5#10591379C212yesmaximal, complemented
6#10591373C212yesmaximal, complemented
7#10591367C212yesmaximal, complemented
8#10591355C211yesmaximal, characteristic, complemented
9#10591277C212yesmaximal, complemented
10#74591—32nomaximal
11C23×D32C2211yescharacteristic
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×C3×C4×D3C2212yes—
14C22×#624C2211yescharacteristic
15C22×D3×Dic3C2212yes—
16C2×C32×C4⋊C4C2211yescharacteristic, complemented
17C2×#3752C2212yes—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
19C2×C3×(C2×D3)⋊C4C2212yes—
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×C3×Dic3⋊C4C2212yescomplemented
22C2×#3724C2211yescharacteristic, complemented
23C2×#3724C2211yescharacteristic, complemented
24C2×Dic3⋊Dic3C2212yescomplemented
25C2×#3722C2212yes—
26C2×(C2×D3)⋊Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2212yes—
28#63921C418yescomplemented
29D3×(C2×D3)⋊C4—28no—
30#63658C2212yescomplemented
31C3×C3⋊#95C2212yescomplemented
32C3×C3⋊#95C2212yescomplemented
33#63579C2212yescomplemented
34C22×(C2×D3)⋊C4—32no—
35C2×D3×C22⋊C4—32no—
36C2×D3×C22⋊C4—32no—
37C3×#385—32no—
38#5210—32no—
39#4989—32no—
40#4989D312yescomplemented
41#4987—32no—
42#4987—32no—
43#4987—61no—
44#4950—32no—
45#4946—32no—
46#4668—32no—
47#4668—32no—
48#4667—32no—
49#4667—32no—
50C23×C3⋊D3C2311yescharacteristic
51C23×C3×D3C2312yes—
52C22×D32—41no—
53C22×D32—41no—
54C22×D32—41no—
55C22×D32—41no—
56C22×D32C2×C414yes—
57C22×D32D414yes—
58C22×D32Q814yes—
59C22×C32×C4C2312yes—
60C22×C32×C4C2311yescharacteristic
61C22×C3⋊Dic3C2312yes—
62C22×C3⋊Dic3C2311yescharacteristic
63C2×C4×C3⋊D3—41no—
64C2×C4×C3⋊D3—41no—
65C2×C4×C3⋊D3C2×C414yescomplemented
66C22×C3×Dic3C2312yes—
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2312yes—
69C2×C3×C4×D3—24no—
70C2×C3×C4×D3—42no—
71C2×C3×C4×D3—42no—
72C2×#624—41no—
73C2×#624—41no—
74C2×#624C2×C414yescomplemented
75C2×D3×Dic3—24no—
76C2×D3×Dic3—42no—
77C2×D3×Dic3—42no—
78C32×C4⋊C4—41no—
79#3752—24no—
80C4⋊(C3⋊Dic3)—41no—
81C3×(C2×D3)⋊C4—24no—
82C3×(C2×D3)⋊C4C2×C418yescomplemented
83C3×Dic3⋊C4—42no—
84#3724—41no—
85#3724—41no—
86Dic3⋊Dic3—42no—
87#3722—24no—
88(C2×D3)⋊Dic3—24no—
89(C2×D3)⋊Dic3C2×C418yescomplemented
90#2315—91noSylow
91C24×D3—32no—
92C23×C3×C4—32no—
93C23×Dic3—32no—
94C22×C4×D3—32no—
95C22×C4×D3—32no—
96C22×C4×D3—32no—
97C22×C4×D3—61no—
98C22×C4×D3C2×D312yes—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4—32no—
101C2×C3×C4⋊C4C2×D312yescomplemented
102C2×C3×C22⋊C4—32no—
103C2×C3×C22⋊C4—32no—
104C2×#217—32no—
105C2×#217—32no—
106C2×(C2×D3)⋊C4—32no—
107C2×(C2×D3)⋊C4—32no—
108C2×(C2×D3)⋊C4—32no—
109C2×(C2×D3)⋊C4—32no—
110C2×(C2×D3)⋊C4—32no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—62no—
113C2×(C2×D3)⋊C4—68no—
114C2×(C2×D3)⋊C4C2×D312yes—
115C2×(C2×D3)⋊C4C2×D312yes—
116C2×C4⋊Dic3—32no—
117C2×C4⋊Dic3—32no—
118C2×C4⋊Dic3—61no—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4C2×D312yescomplemented
123D3×C22⋊C4—316no—
124D3×C22⋊C4—68no—
125C3×#95—32no—
126C3×#95—32no—
127C3⋊#95—32no—
128C3⋊#95—32no—
129C3⋊#95—32no—
130C3⋊#95—32no—
131C3⋊#95—62no—
132C3⋊#95C2×D312yescomplemented
133C3⋊#95C2×D312yescomplemented
134C23×C32C2411yescharacteristic
135C22×C3⋊D3—21no—
136C22×C3⋊D3—21no—
137C22×C3⋊D3—21no—
138C22×C3⋊D3—21no—
139C22×C3⋊D3C22×C412yes—
140C22×C3⋊D3C2×D412yes—
141C22×C3⋊D3C2×Q812yes—
142C22×C3×D3—22no—
143C22×C3×D3—22no—
144C22×C3×D3—22no—
145C22×C3×D3—22no—
146C22×C3×D3C22×C414yes—
147C22×C3×D3C2×D414yes—
148C22×C3×D3C2×Q814yes—
149C2×D32—44no—
150C2×D32—44no—
151C2×D32—44no—
152C2×D32—44no—
153C2×D32—44no—
154C2×D32—44no—
155C2×D32C4⋊C4116yescomplemented
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4—22no—
159C2×C32×C4—22no—
160C2×C32×C4—22no—
161C2×C32×C4C22×C412yes—
162C2×C3⋊Dic3—21no—
163C2×C3⋊Dic3—21no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3C22×C412yes—
168C4×C3⋊D3—44no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3C22×C414yes—
178C3×C4×D3—48no—
179#624—44no—
180D3×Dic3—48no—
181C22×C22⋊C4—91no—
182C22×C22⋊C4—92no—
183#385—32no—
184#385—92no—
185#385—92no—
186#385—92no—
187#380—91no—
188#380—92no—
189#380—91no—
190C24×C3—32no—
191C23×D3—32no—
192C23×D3—38no—
193C23×D3—38no—
194C23×D3—38no—
195C23×D3—61no—
196C23×D3—122no—
197C23×D3—122no—
198C23×D3—122no—
199C23×D3—122no—
200C23×D3C22×D312yes—
201C22×C3×C4—21no—
202C22×C3×C4—22no—
203C22×C3×C4—32no—
204C22×C3×C4—32no—
205C22×C3×C4—32no—
206C22×C3×C4—64no—
207C22×C3×C4—122no—
208C22×C3×C4—122no—
209C22×C3×C4C22×D312yes—
210C22×C3×C4C22×D312yes—
211C22×C3×C4C22×D312yes—
212C22×Dic3—32no—
213C22×Dic3—32no—
214C22×Dic3—32no—
215C22×Dic3—61no—
216C22×Dic3—62no—
217C22×Dic3—64no—
218C22×Dic3—122no—
219C22×Dic3—122no—
220C22×Dic3C22×D312yes—
221C22×Dic3C22×D312yes—
222C22×Dic3C22×D312yes—
223C2×C4×D3—24no—
224C2×C4×D3—38no—
225C2×C4×D3—38no—
226C2×C4×D3—42no—
227C2×C4×D3—42no—
228C2×C4×D3—64no—
229C2×C4×D3—64no—
230C2×C4×D3—122no—
231C2×C4×D3—122no—
232C2×C4×D3—122no—
233C2×C4×D3—122no—
234C2×C4×D3—122no—
235C2×C4×D3—122no—
236C2×C4×D3—122no—
237C2×C4×D3—122no—
238C3×C4⋊C4—42no—
239C3×C4⋊C4—42no—
240C3×C4⋊C4—122no—
241C3×C22⋊C4—38no—
242C3×C22⋊C4—64no—
243#217—38no—
244#217—64no—
245(C2×D3)⋊C4—24no—
246(C2×D3)⋊C4—38no—
247(C2×D3)⋊C4—64no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—64no—
250(C2×D3)⋊C4—64no—
251(C2×D3)⋊C4—64no—
252(C2×D3)⋊C4—124no—
253(C2×D3)⋊C4C4×D318yescomplemented
254C4⋊Dic3—122no—
255C4⋊Dic3—122no—
256C4⋊Dic3—122no—
257Dic3⋊C4—42no—
258Dic3⋊C4—122no—
259Dic3⋊C4—122no—
260Dic3⋊C4—122no—
261C22×C32C23×C411yescharacteristic
262C22×C32C22×D411yescharacteristic
263C22×C32C22×Q811yescharacteristic
264C22×C32H(5,𝔽2)11yescharacteristic
265C22×C32H(5,𝔽2)11yescharacteristic
266C22×C32H(5,𝔽2)11yescharacteristic
267C22×C32H(5,𝔽2)11yescharacteristic
268C2×C3⋊D3—22no—
269C2×C3⋊D3—22no—
270C2×C3⋊D3—22no—
271C2×C3⋊D3—22no—
272C2×C3⋊D3—22no—
273C2×C3⋊D3—22no—
274C2×C3⋊D3C2×C4⋊C414yes—
275C2×C3×D3—24no—
276C2×C3×D3—24no—
277C2×C3×D3—24no—
278C2×C3×D3—24no—
279C2×C3×D3—24no—
280C2×C3×D3—24no—
281C2×C3×D3C2×C4⋊C418yes—
282D32—416no—
283C32×C4—22no—
284C32×C4—42no—
285C3⋊Dic3—22no—
286C3⋊Dic3—42no—
287C3×Dic3—24no—
288C3×Dic3—42no—
289C3×Dic3—42no—
290C25—91no—
291C23×C4—32no—
292C23×C4—91no—
293C23×C4—92no—
294C23×C4—91no—
295C2×C4⋊C4—32no—
296C2×C4⋊C4—91no—
297C2×C4⋊C4—91no—
298C2×C4⋊C4—92no—
299C2×C4⋊C4—91no—
300C2×C4⋊C4D3211yescharacteristic, complemented
301C2×C22⋊C4—32no—
302C2×C22⋊C4—32no—
303C2×C22⋊C4—98no—
304C2×C22⋊C4—92no—
305C2×C22⋊C4—92no—
306C2×C22⋊C4—92no—
307C2×C22⋊C4—92no—
308C2×C22⋊C4—188no—
309#95—32no—
310#95—32no—
311#95—92no—
312#95—92no—
313C23×C3—21no—
314C23×C3—34no—
315C23×C3—34no—
316C23×C3—34no—
317C23×C3—62no—
318C23×C3—62no—
319C23×C3—62no—
320C23×C3—62no—
321C23×C3C23×D312yes—
322C22×D3—22no—
323C22×D3—22no—
324C22×D3—22no—
325C22×D3—22no—
326C22×D3—34no—
327C22×D3—34no—
328C22×D3—34no—
329C22×D3—332no—
330C22×D3—62no—
331C22×D3—62no—
332C22×D3—62no—
333C22×D3—62no—
334C22×D3—62no—
335C22×D3—62no—
336C22×D3—62no—
337C22×D3—121no—
338C22×D3—121no—
339C22×D3—121no—
340C22×D3—121no—
341C22×D3—128no—
342C22×D3—128no—
343C22×D3—128no—
344C22×D3—128no—
345C22×D3—128no—
346C22×D3—128no—
347C22×D3C2×C4×D314yes—
348C22×D3D3×D414yes—
349C22×D3D3×Q814yes—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—34no—
362C2×C3×C4—42no—
363C2×C3×C4—42no—
364C2×C3×C4—42no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4—62no—
368C2×C3×C4—62no—
369C2×C3×C4—62no—
370C2×C3×C4—62no—
371C2×C3×C4—62no—
372C2×C3×C4—62no—
373C2×C3×C4—128no—
374C2×C3×C4C2×C4×D314yes—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—22no—
383C2×Dic3—34no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—62no—
392C2×Dic3—62no—
393C2×Dic3—121no—
394C2×Dic3—121no—
395C2×Dic3—122no—
396C2×Dic3—122no—
397C2×Dic3—122no—
398C2×Dic3—128no—
399C2×Dic3C2×C4×D314yes—
400C4×D3—48no—
401C4×D3—128no—
402C4×D3—128no—
403C4×D3—128no—
404C4×D3—128no—
405C2×C32C22×C4⋊C411yescharacteristic
406C2×C32#51811yescharacteristic
407C2×C32#51811yescharacteristic
408C2×C32#53411yescharacteristic
409C2×C32#53411yescharacteristic
410C2×C32#54311yescharacteristic
411C2×C32#54311yescharacteristic
412C3⋊D3—24no—
413C3×D3—28no—
414C24—32no—
415C24—94no—
416C24—94no—
417C24—94no—
418C24—91no—
419C24—361no—
420C24—361no—
421C24—361no—
422C24—361no—
423C22×C4—32no—
424C22×C4—32no—
425C22×C4—32no—
426C22×C4—64no—
427C22×C4—94no—
428C22×C4—91no—
429C22×C4—94no—
430C22×C4—92no—
431C22×C4—122no—
432C22×C4—122no—
433C22×C4—184no—
434C22×C4—361no—
435C22×C4—361no—
436C22×C4—361no—
437C22×C4—361no—
438C22×C4—362no—
439C22×C4—362no—
440C22×C4C2×D3212yes—
441C22×C4C2×D3211yescharacteristic
442C4⋊C4—41no—
443C4⋊C4—122no—
444C4⋊C4—361no—
445C4⋊C4—361no—
446C4⋊C4—361no—
447C4⋊C4—362no—
448C22⋊C4—38no—
449C22⋊C4—64no—
450C22⋊C4—98no—
451C22⋊C4—184no—
452C22⋊C4—184no—
453C22⋊C4—184no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—38no—
462C22×C3—64no—
463C22×C3—64no—
464C22×C3—64no—
465C22×C3—64no—
466C22×C3—64no—
467C22×C3—64no—
468C22×C3C22×C4×D312yes—
469C22×C3C2×D3×D412yes—
470C22×C3#100412yes—
471C22×C3#100412yes—
472C22×C3C2×D3×Q812yes—
473C22×C3#100912yes—
474C22×C3#100912yes—
475C2×D3—24no—
476C2×D3—24no—
477C2×D3—24no—
478C2×D3—24no—
479C2×D3—24no—
480C2×D3—24no—
481C2×D3—38no—
482C2×D3—64no—
483C2×D3—64no—
484C2×D3—64no—
485C2×D3—64no—
486C2×D3—64no—
487C2×D3—64no—
488C2×D3—64no—
489C2×D3—122no—
490C2×D3—122no—
491C2×D3—122no—
492C2×D3—122no—
493C2×D3—122no—
494C2×D3—122no—
495C2×D3—1232no—
496C2×D3D3×C4⋊C418yes—
497C3×C4—24no—
498C3×C4—24no—
499C3×C4—42no—
500C3×C4—42no—
501C3×C4—64no—
502C3×C4—82no—
503C3×C4—122no—
504C3×C4—122no—
505Dic3—24no—
506Dic3—42no—
507Dic3—42no—
508Dic3—64no—
509Dic3—122no—
510Dic3—122no—
511Dic3—122no—
512Dic3—242no—
513C32#231511yescharacteristic, complemented, Sylow
514C23—34no—
515C23—34no—
516C23—34no—
517C23—62no—
518C23—62no—
519C23—62no—
520C23—62no—
521C23—916no—
522C23—92no—
523C23—92no—
524C23—92no—
525C23—181no—
526C23—181no—
527C23—181no—
528C23—181no—
529C23—364no—
530C23—364no—
531C23—364no—
532C23—364no—
533C23—364no—
534C23—364no—
535C23C22×D3211yescharacteristic
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—34no—
542C2×C4—62no—
543C2×C4—62no—
544C2×C4—62no—
545C2×C4—62no—
546C2×C4—62no—
547C2×C4—62no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—92no—
551C2×C4—128no—
552C2×C4—181no—
553C2×C4—181no—
554C2×C4—182no—
555C2×C4—182no—
556C2×C4—182no—
557C2×C4—364no—
558C2×C4—364no—
559C2×C4—368no—
560C2×C4C4×D3212yes—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—68no—
569C2×C3C2×D3×C4⋊C412yes—
570C2×C3#554512yes—
571C2×C3#554512yes—
572C2×C3#558912yes—
573C2×C3#563412yes—
574C2×C3#563412yes—
575C2×C3#565312yes—
576D3—28no—
577D3—68no—
578D3—124no—
579C22—38no—
580C22—64no—
581C22—64no—
582C22—64no—
583C22—64no—
584C22—64no—
585C22—64no—
586C22—94no—
587C22—182no—
588C22—182no—
589C22—182no—
590C22—182no—
591C22—182no—
592C22—182no—
593C22—3616no—
594C22C2×C4×D3211yescharacteristic
595C22#6430811yescharacteristic
596C22D32×D411yescharacteristic
597C22#6431311yescharacteristic
598C22D32×Q811yescharacteristic
599C22#6432011yescharacteristic
600C22#6433011yescharacteristic
601C4—22no—
602C4—42no—
603C4—64no—
604C4—122no—
605C4—122no—
606C4—182no—
607C4—362no—
608C3—21no—
609C3#7459112yescomplemented
610C2—68no—
611C2—184no—
612C2D32×C4⋊C411yescharacteristic
613C2#1059460611yescharacteristic
614C2#1059461011yescharacteristic
615C2#1059463611yescharacteristic
616C2#1059505811yescharacteristic
617C2#1059528011yescharacteristic
618C2#1059543411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC23×D32C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2315
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #10592686C2semidirect
4. C3×#4989C2semidirect
5. #10591379C2semidirect
6. #10591373C2semidirect
7. #10591367C2semidirect
8. #10591355C2semidirect
9. #10591277C2semidirect
16. C2×C32×C4⋊C4C22semidirect
18. C2×C4⋊(C3⋊Dic3)C22semidirect
21. C2×C3×Dic3⋊C4C22semidirect
22. C2×#3724C22semidirect
23. C2×#3724C22semidirect
24. C2×Dic3⋊Dic3C22semidirect
28. #63921C4semidirect
30. #63658C22semidirect
31. C3×C3⋊#95C22semidirect
32. C3×C3⋊#95C22semidirect
33. #63579C22semidirect
40. #4989D3semidirect
65. C2×C4×C3⋊D3C2×C4semidirect
74. C2×#624C2×C4semidirect
82. C3×(C2×D3)⋊C4C2×C4semidirect
89. (C2×D3)⋊Dic3C2×C4semidirect
101. C2×C3×C4⋊C4C2×D3semidirect
122. C2×Dic3⋊C4C2×D3semidirect
132. C3⋊#95C2×D3semidirect
133. C3⋊#95C2×D3semidirect
155. C2×D32C4⋊C4semidirect
253. (C2×D3)⋊C4C4×D3semidirect
300. C2×C4⋊C4D32semidirect
513. C32#2315semidirect
609. C3#74591semidirect

Maximal subgroups

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

subgroupindex
C2×#639212
C2×D3×(C2×D3)⋊C42
#105926862
C3×#49892
#105913792
#105913732
#105913672
#105913552
#105912772
#745913