Finite Group Databasebeta

← #11805469

Subgroups — #11805469

Order 1152.

1649 conjugacy classes of subgroups.

The subgroup lattice has 587 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63902C211yesmaximal, characteristic
2C2×#63902C211yesmaximal, characteristic
3C2×C4×#625C211yesmaximal, characteristic
4C2×D3×Dic3⋊C4C212yesmaximal, complemented
5#10592348C211yesmaximal, characteristic, complemented
6C3×#4668C212yesmaximal, complemented
7#10591377C212yesmaximal, complemented
8#10591369C212yesmaximal, complemented
9#10591359C211yesmaximal, characteristic, complemented
10#10591337C211yesmaximal, characteristic, complemented
11#10591328C211yesmaximal, characteristic, complemented
12#74393—32nomaximal
13C22×C3×C4×D3C2212yes—
14C22×#625C2211yescharacteristic
15C22×D3×Dic3C2212yes—
16C22×D3×Dic3C2212yes—
17C2×#3750C2211yescharacteristic
18C2×#3750C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×(C2×D3)⋊C4C2212yes—
24C2×C3×C4⋊Dic3C2212yes—
25C2×C3×Dic3⋊C4C2212yes—
26C2×#3724C2212yes—
27C2×#3724C2211yescharacteristic
28C2×#3724C2211yescharacteristic
29C2×#3724C2211yescharacteristic
30C2×Dic3⋊Dic3C2212yes—
31C2×(C2×D3)⋊Dic3C2212yes—
32#63902—24no—
33#63902C418yescomplemented
34C4×#625—24no—
35D3×Dic3⋊C4—28no—
36C32×#95C2211yescharacteristic
37#63658C2211yescharacteristic
38C3×C3⋊#95C2212yes—
39#63579C2212yes—
40C2×C4×#67—32no—
41C22×Dic3⋊C4—32no—
42C2×D3×C4⋊C4—32no—
43C2×#67⋊C4—32no—
44C2×#67⋊C4—32no—
45C3×#385—32no—
46#4989—32no—
47#4976—32no—
48#4975—32no—
49#4950—32no—
50#4942—32no—
51#4668D312yescomplemented
52#4667—32no—
53#4649—32no—
54#4649—61no—
55#4647—32no—
56C23×C3×D3C2312yes—
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3C2311yescharacteristic
61C22×C3⋊Dic3C2311yescharacteristic
62C22×C3⋊Dic3C2311yescharacteristic
63C22×C3⋊Dic3C2311yescharacteristic
64C22×C3×Dic3C2312yes—
65C22×C3×Dic3C2312yes—
66C22×C3×Dic3C2312yes—
67C2×C3×C4×D3—24no—
68C2×C3×C4×D3—24no—
69C2×C3×C4×D3—42no—
70C2×#625C2×C414yes—
71C2×#625D414yes—
72C2×#625Q814yes—
73C2×D3×Dic3—24no—
74C2×D3×Dic3—24no—
75C2×D3×Dic3—24no—
76C2×D3×Dic3—24no—
77C2×D3×Dic3—42no—
78C2×D3×Dic3C2×C418yescomplemented
79#3750—22no—
80#3750D414yescomplemented
81C4×C3⋊Dic3—22no—
82C4×C3⋊Dic3—22no—
83C4×C3⋊Dic3C2×C414yescomplemented
84C3×(C2×D3)⋊C4—24no—
85C3×(C2×D3)⋊C4C2×C418yescomplemented
86C3×C4⋊Dic3—42no—
87C3×Dic3⋊C4—24no—
88#3724—24no—
89#3724—22no—
90#3724—22no—
91#3724C2×C414yescomplemented
92Dic3⋊Dic3—24no—
93(C2×D3)⋊Dic3—24no—
94D4×C4⋊C4—91noSylow
95C23×C3×C4—32no—
96C22×#67—32no—
97C23×Dic3—32no—
98C23×Dic3—32no—
99C22×C4×D3—32no—
100C22×C4×D3—32no—
101C22×C4×D3C2×D312yes—
102C2×C3×C4⋊C4—32no—
103C2×C3×C4⋊C4—32no—
104C2×C3×C22⋊C4—32no—
105C2×C3×C22⋊C4—32no—
106C2×#217—32no—
107C4×#67—68no—
108C2×(C2×D3)⋊C4—32no—
109C2×(C2×D3)⋊C4C2×D312yes—
110C2×(C2×D3)⋊C4C2×D312yes—
111C2×C4⋊Dic3—32no—
112C2×C4⋊Dic3C2×D312yes—
113C2×Dic3⋊C4—32no—
114C2×Dic3⋊C4—32no—
115C2×Dic3⋊C4—32no—
116C2×Dic3⋊C4—32no—
117C2×Dic3⋊C4—32no—
118C2×Dic3⋊C4—32no—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4—61no—
122C2×Dic3⋊C4—61no—
123C2×Dic3⋊C4—68no—
124C2×Dic3⋊C4C2×D312yes—
125C2×C4×Dic3—32no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—61no—
129C2×C4×Dic3—61no—
130C2×C4×Dic3—61no—
131D3×C4⋊C4—68no—
132#67⋊C4—316no—
133#67⋊C4—68no—
134C3×#95—21no—
135C3×#95—32no—
136C3×#95C2×D312yes—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—61no—
141C3⋊#95C2×D312yes—
142C23×C32C2411yescharacteristic
143C22×C3×D3—22no—
144C22×C3×D3—22no—
145C22×C3×D3—22no—
146C22×C3×D3—22no—
147C22×C3×D3C22×C414yes—
148C22×C3×D3C2×D414yes—
149C22×C3×D3C2×Q814yes—
150C2×C32×C4—21no—
151C2×C32×C4—21no—
152C2×C32×C4—21no—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4—21no—
156C2×C32×C4—21no—
157C2×C32×C4C22×C412yes—
158C2×C32×C4C2×D412yes—
159C2×C3⋊Dic3—21no—
160C2×C3⋊Dic3—21no—
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3—21no—
163C2×C3⋊Dic3—21no—
164C2×C3⋊Dic3C22×C412yes—
165C2×C3⋊Dic3C22×C412yes—
166C2×C3⋊Dic3C2×D412yes—
167C2×C3⋊Dic3C2×D412yes—
168C2×C3⋊Dic3C2×D412yes—
169C2×C3⋊Dic3C2×Q812yes—
170C2×C3⋊Dic3#4112yes—
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×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3C22×C414yes—
180C3×C4×D3—48no—
181#625C4⋊C4116yescomplemented
182D3×Dic3—216no—
183D3×Dic3—48no—
184C2×C4×D4—91no—
185C2×C4×D4—91no—
186C2×C4×D4—91no—
187C22×C4⋊C4—92no—
188#389—91no—
189#389—91no—
190#385—32no—
191#385—92no—
192#384—91no—
193#380—92no—
194C4×C4⋊C4—91no—
195C24×C3—32no—
196C23×D3C22×D312yes—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—32no—
201C22×C3×C4—32no—
202C22×C3×C4—32no—
203C22×C3×C4—64no—
204C22×C3×C4—64no—
205C22×C3×C4—122no—
206C22×C3×C4C22×D312yes—
207C22×C3×C4C22×D312yes—
208C22×C3×C4C22×D312yes—
209C2×#67—38no—
210C2×#67—38no—
211C2×#67—38no—
212C22×Dic3—32no—
213C22×Dic3—32no—
214C22×Dic3—32no—
215C22×Dic3—38no—
216C22×Dic3—32no—
217C22×Dic3—61no—
218C22×Dic3—61no—
219C22×Dic3—61no—
220C22×Dic3—61no—
221C22×Dic3—64no—
222C22×Dic3—64no—
223C22×Dic3—64no—
224C22×Dic3—64no—
225C22×Dic3—122no—
226C22×Dic3C22×D312yes—
227C22×Dic3C22×D312yes—
228C22×Dic3C22×D312yes—
229C2×C4×D3—24no—
230C2×C4×D3—24no—
231C2×C4×D3—38no—
232C2×C4×D3—42no—
233C2×C4×D3—64no—
234C2×C4×D3—64no—
235C2×C4×D3—64no—
236C2×C4×D3—64no—
237C2×C4×D3—122no—
238C3×C4⋊C4—64no—
239C3×C4⋊C4—122no—
240C3×C22⋊C4—38no—
241C3×C22⋊C4—64no—
242#217—64no—
243(C2×D3)⋊C4—24no—
244(C2×D3)⋊C4—64no—
245(C2×D3)⋊C4C4×D318yescomplemented
246C4⋊Dic3—42no—
247C4⋊Dic3—64no—
248Dic3⋊C4—24no—
249Dic3⋊C4—38no—
250Dic3⋊C4—38no—
251Dic3⋊C4—64no—
252Dic3⋊C4—64no—
253Dic3⋊C4—64no—
254Dic3⋊C4—64no—
255Dic3⋊C4—64no—
256Dic3⋊C4—64no—
257Dic3⋊C4—64no—
258Dic3⋊C4—64no—
259C4×Dic3—38no—
260C4×Dic3—64no—
261C4×Dic3—64no—
262C4×Dic3—64no—
263C4×Dic3—122no—
264C4×Dic3—122no—
265C22×C32C23×C411yescharacteristic
266C22×C32C22×D411yescharacteristic
267C22×C32C22×D411yescharacteristic
268C22×C32C22×Q811yescharacteristic
269C22×C32C2×#4111yescharacteristic
270C22×C32H(5,𝔽2)11yescharacteristic
271C22×C322−1+411yescharacteristic
272C2×C3×D3—24no—
273C2×C3×D3—24no—
274C2×C3×D3—24no—
275C2×C3×D3—24no—
276C2×C3×D3—24no—
277C2×C3×D3—24no—
278C2×C3×D3C2×C4⋊C418yescomplemented
279C32×C4—22no—
280C32×C4—22no—
281C32×C4—41no—
282C3⋊Dic3—22no—
283C3⋊Dic3—41no—
284C3⋊Dic3C2×C4⋊C414yescomplemented
285C3⋊Dic3C4×D414yescomplemented
286C3×Dic3—24no—
287C3×Dic3—42no—
288C3×Dic3—42no—
289C22×D4—91no—
290C23×C4—32no—
291C23×C4—92no—
292C23×C4—92no—
293C4×D4—98no—
294C4×D4—184no—
295C4×D4—184no—
296C2×C4⋊C4—32no—
297C2×C4⋊C4—32no—
298C2×C4⋊C4—91no—
299C2×C4⋊C4—91no—
300C2×C4⋊C4—92no—
301C2×C4⋊C4—92no—
302C2×C4⋊C4—91no—
303C2×C4⋊C4—91no—
304C2×C4⋊C4—91no—
305C2×C4⋊C4—188no—
306C2×C22⋊C4—32no—
307C2×C22⋊C4—32no—
308C2×C22⋊C4—92no—
309C2×C42—91no—
310C2×C42—91no—
311C2×C42—91no—
312#95—32no—
313#95—92no—
314#95—91no—
315#95D3211yescharacteristic
316C23×C3—21no—
317C23×C3—34no—
318C23×C3—34no—
319C23×C3—34no—
320C23×C3—62no—
321C23×C3—62no—
322C23×C3—62no—
323C23×C3—62no—
324C23×C3C23×D312yes—
325C22×D3—22no—
326C22×D3—22no—
327C22×D3—22no—
328C22×D3—22no—
329C22×D3C2×C4×D314yes—
330C22×D3D3×D414yes—
331C22×D3D3×Q814yes—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—34no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—128no—
358C2×C3×C4C2×C4×D314yes—
359C2×C3×C4D3×D414yes—
360#67—332no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—34no—
370C2×Dic3—34no—
371C2×Dic3—34no—
372C2×Dic3—34no—
373C2×Dic3—34no—
374C2×Dic3—34no—
375C2×Dic3—34no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—616no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390C2×Dic3—121no—
391C2×Dic3—121no—
392C2×Dic3—121no—
393C2×Dic3—121no—
394C2×Dic3—128no—
395C2×Dic3C2×C4×D314yes—
396C4×D3—48no—
397C4×D3—616no—
398C4×D3—128no—
399C2×C32C22×C4⋊C411yescharacteristic
400C2×C32C2×C4×D411yescharacteristic
401C2×C32#52011yescharacteristic
402C2×C32D4211yescharacteristic
403C2×C32#54711yescharacteristic
404C2×C32D4×Q811yescharacteristic
405C2×C32#55411yescharacteristic
406C3×D3—28no—
407C24—32no—
408C2×D4—94no—
409C2×D4—94no—
410C2×D4—94no—
411C22×C4—32no—
412C22×C4—32no—
413C22×C4—32no—
414C22×C4—64no—
415C22×C4—64no—
416C22×C4—98no—
417C22×C4—91no—
418C22×C4—91no—
419C22×C4—91no—
420C22×C4—91no—
421C22×C4—122no—
422C22×C4—184no—
423C22×C4—184no—
424C22×C4—184no—
425C22×C4—184no—
426C22×C4—362no—
427C22×C4C2×D3211yescharacteristic
428C22×C4C2×D3211yescharacteristic
429C22×C4C2×D3211yescharacteristic
430C4⋊C4—64no—
431C4⋊C4—94no—
432C4⋊C4—94no—
433C4⋊C4—122no—
434C4⋊C4—182no—
435C4⋊C4—184no—
436C4⋊C4—184no—
437C4⋊C4—182no—
438C4⋊C4—182no—
439C22⋊C4—38no—
440C22⋊C4—64no—
441C22⋊C4—184no—
442C42—94no—
443C42—182no—
444C42—182no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—38no—
453C22×C3—64no—
454C22×C3—64no—
455C22×C3—64no—
456C22×C3—64no—
457C22×C3—64no—
458C22×C3—64no—
459C22×C3C22×C4×D312yes—
460C22×C3C2×D3×D412yes—
461C22×C3C2×D3×D412yes—
462C22×C3#100412yes—
463C22×C3C2×D3×Q812yes—
464C22×C3D3×#4112yes—
465C22×C3#101012yes—
466C2×D3—24no—
467C2×D3—24no—
468C2×D3—24no—
469C2×D3—24no—
470C2×D3—24no—
471C2×D3—24no—
472C2×D3D3×C4⋊C418yescomplemented
473C3×C4—24no—
474C3×C4—24no—
475C3×C4—42no—
476C3×C4—42no—
477C3×C4—42no—
478C3×C4—42no—
479C3×C4—64no—
480C3×C4—122no—
481C3×C4—122no—
482Dic3—24no—
483Dic3—38no—
484Dic3—38no—
485Dic3—42no—
486Dic3—42no—
487Dic3—64no—
488Dic3—64no—
489Dic3—64no—
490Dic3—122no—
491Dic3—122no—
492Dic3—122no—
493C32D4×C4⋊C411yescharacteristic, complemented, Sylow
494C23—34no—
495C23—34no—
496C23—34no—
497C23—62no—
498C23—62no—
499C23—62no—
500C23—62no—
501C23C22×D3211yescharacteristic
502D4—916no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—34no—
511C2×C4—62no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—62no—
518C2×C4—62no—
519C2×C4—92no—
520C2×C4—92no—
521C2×C4—92no—
522C2×C4—92no—
523C2×C4—92no—
524C2×C4—92no—
525C2×C4—92no—
526C2×C4—128no—
527C2×C4—1816no—
528C2×C4—181no—
529C2×C4—181no—
530C2×C4—181no—
531C2×C4—181no—
532C2×C4—181no—
533C2×C4—368no—
534C2×C4C4×D3212yes—
535C2×C4#380212yes—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—68no—
544C2×C3C2×D3×C4⋊C412yes—
545C2×C3C4×D3×D412yes—
546C2×C3#554612yes—
547C2×C3#559012yes—
548C2×C3#563212yes—
549C2×C3#563612yes—
550C2×C3#565512yes—
551D3—28no—
552C22—38no—
553C22—64no—
554C22—64no—
555C22—64no—
556C22—64no—
557C22—64no—
558C22—64no—
559C22C2×C4×D3211yescharacteristic
560C22C2×#380211yescharacteristic
561C22#6430611yescharacteristic
562C22#6430911yescharacteristic
563C22D32×D411yescharacteristic
564C22#6431311yescharacteristic
565C22D32×Q811yescharacteristic
566C4—22no—
567C4—22no—
568C4—41no—
569C4—64no—
570C4—94no—
571C4—94no—
572C4—122no—
573C4—122no—
574C4—182no—
575C4—361no—
576C3—21no—
577C3#7439312yescomplemented
578C2—68no—
579C2C4×#380211yescharacteristic
580C2#1059405111yescharacteristic
581C2#1059418511yescharacteristic
582C2#1059427111yescharacteristic
583C2#1059452611yescharacteristic
584C2#1059453411yescharacteristic
585C2D32×C4⋊C411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#625C22
hypercenter#95D32
hypocenterC32D4×C4⋊C4
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
4. C2×D3×Dic3⋊C4C2semidirect
5. #10592348C2semidirect
6. C3×#4668C2semidirect
7. #10591377C2semidirect
8. #10591369C2semidirect
9. #10591359C2semidirect
10. #10591337C2semidirect
11. #10591328C2semidirect
33. #63902C4semidirect
51. #4668D3semidirect
78. C2×D3×Dic3C2×C4semidirect
80. #3750D4semidirect
83. C4×C3⋊Dic3C2×C4semidirect
85. C3×(C2×D3)⋊C4C2×C4semidirect
91. #3724C2×C4semidirect
181. #625C4⋊C4semidirect
245. (C2×D3)⋊C4C4×D3semidirect
278. C2×C3×D3C2×C4⋊C4semidirect
284. C3⋊Dic3C2×C4⋊C4semidirect
285. C3⋊Dic3C4×D4semidirect
472. C2×D3D3×C4⋊C4semidirect
493. C32D4×C4⋊C4semidirect
577. C3#74393semidirect

Maximal subgroups

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

subgroupindex
C2×#639022
C2×C4×#6252
C2×D3×Dic3⋊C42
#105923482
C3×#46682
#105913772
#105913692
#105913592
#105913372
#105913282
#743933