Finite Group Databasebeta

← #11859222

Subgroups — #11859222

Order 1152.

1277 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M16×C3⋊D3C211yesmaximal, characteristic, complemented
2C4×#3811C211yesmaximal, characteristic
3C2×D32×C8C211yesmaximal, characteristic, complemented
4C3×#5127C212yesmaximal, complemented
5#10591152C211yesmaximal, characteristic, complemented
6#10591151C212yesmaximal, complemented
7#10590935C211yesmaximal, characteristic, complemented
8#10590907C212yesmaximal, complemented
9#10590726C212yesmaximal, complemented
10#10590668C211yesmaximal, characteristic, complemented
11#10590658C211yesmaximal, characteristic, complemented
12D3×#435—32nomaximal
13C22×C4×C3⋊D3C2211yescharacteristic
14C2×#3811C411yescharacteristic
15C2×C4×D32C2211yescharacteristic
16C2×C32×M16C2211yescharacteristic, complemented
17C2×#3748C2211yescharacteristic, complemented
18M16×C3⋊D3—24no—
19C2×#3743C2211yescharacteristic, complemented
20C2×#3743C2211yescharacteristic, complemented
21C2×C8×C3⋊D3C2211yescharacteristic
22C2×C8×C3⋊D3C2211yescharacteristic
23C3×C4×#67C2212yes—
24C2×C3×D3×C8C2212yescomplemented
25#63974C411yescharacteristic
26#67⋊Dic3C412yes—
27#63921C411yescharacteristic
28C4×#626C2212yes—
29#63883C411yescharacteristic
30C4×#624C2211yescharacteristic
31#63881C412yes—
32C2×#3710C2211yescharacteristic
33C2×#3710C2211yescharacteristic
34C2×D3×C3⋊C8C2212yescomplemented
35D32×C8—24no—
36C3×#830C2212yescomplemented
37C3×(C2×D3)⋊C8C2212yescomplemented
38C3×#815C2212yescomplemented
39C3×Dic3⋊C8C2212yescomplemented
40Dic3⋊(C3⋊C8)C2212yescomplemented
41#63557C2212yescomplemented
42(C2×D3)⋊(C3⋊C8)C2212yescomplemented
43#63554C2212yescomplemented
44C2×D3×M16—32no—
45C2×D3×M16—61no—
46C22×D3×C8—32no—
47C4×D3×D4—32no—
48C3×#435—32no—
49#5127D312yescomplemented
50#5111—32no—
51#5011—32no—
52#4836—32no—
53D3×C4⋊C8—32no—
54#4730—32no—
55#4728—32no—
56D3×C22⋊C8—32no—
57D3×C22⋊C8—32no—
58#4706—32no—
59D3×#97—32no—
60C23×C3⋊D3C2×C411yescharacteristic
61C22×D32C2×C411yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C22×C3⋊Dic3C2×C411yescharacteristic
64C2×C4×C3⋊D3—22no—
65C2×C4×C3⋊D3—22no—
66C2×C4×C3⋊D3C2×C411yescharacteristic
67C2×C4×C3⋊D3C2×C411yescharacteristic
68C2×C4×C3⋊D3C2311yescharacteristic
69C2×C4×C3⋊D3C2311yescharacteristic
70C2×C3×#67C2×C412yes—
71C2×C3×C4×D3C2312yes—
72#3811—24no—
73C2×#626C2×C412yes—
74C2×#624C2×C411yescharacteristic
75C2×#624C2×C411yescharacteristic
76C2×#624C2×C411yescharacteristic
77C2×D3×Dic3C2×C412yes—
78C4×D32—22no—
79C4×D32—22no—
80C32×M16—22no—
81C2×C32×C8C2311yescharacteristic
82C2×C32×C8C2311yescharacteristic
83#3748—22no—
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86#3743—22no—
87#3743—22no—
88C8×C3⋊D3—22no—
89C8×C3⋊D3D414yescomplemented
90C3×#217C2×C412yes—
91C3×(C2×D3)⋊C4C2×C412yes—
92C3×Dic3⋊C4C2×C412yes—
93C3×C4×Dic3C2312yes—
94C2×C3×C3⋊C8C2312yes—
95C2×C3×C3⋊C8C2312yes—
96C3×D3×C8—24no—
97Dic3⋊Dic3C2×C412yes—
98#3722C2×C412yes—
99(C2×D3)⋊Dic3C2×C412yes—
100Dic32C2×C412yes—
101#3710—22no—
102#3710—22no—
103D3×C3⋊C8—24no—
104C2×#435—91noSylow
105C2×D3×D4—32no—
106C22×C4×D3—32no—
107C22×C4×D3—32no—
108C22×C4×D3—61no—
109C2×C3×M16—21no—
110C2×C3×M16C2×D312yescomplemented
111C22×C3×C8—32no—
112C3×C4×D4—32no—
113D4×Dic3—32no—
114C4×#67—32no—
115C4×#67C2×D312yes—
116C2×#208—32no—
117C2×#208—61no—
118C22×C3⋊C8—32no—
119D3×M16—68no—
120D3×M16—68no—
121C2×ΓL(1,𝔽25)—32no—
122C2×ΓL(1,𝔽25)—32no—
123C2×ΓL(1,𝔽25)—61no—
124C2×ΓL(1,𝔽25)—61no—
125C2×D3×C8—32no—
126C2×D3×C8—32no—
127C2×D3×C8—32no—
128C2×D3×C8—32no—
129C2×D3×C8—32no—
130C2×D3×C8—61no—
131C2×D3×C8—61no—
132C2×D3×C8—68no—
133C2×D3×C8C2×D312yescomplemented
134#893—32no—
135D3×C4⋊C4—32no—
136#67⋊C4—32no—
137#67⋊C4—32no—
138D3×C22⋊C4—32no—
139D3×C22⋊C4—32no—
140C4×D12—32no—
141C42×D3—32no—
142C3×C4⋊C8—32no—
143C3×C22⋊C8—32no—
144C3×C22⋊C8—32no—
145C3×#97—32no—
146#830—32no—
147#830C2×D312yescomplemented
148(C2×D3)⋊C8—32no—
149(C2×D3)⋊C8—32no—
150(C2×D3)⋊C8—32no—
151(C2×D3)⋊C8C2×D312yescomplemented
152#815—32no—
153#815C2×D312yescomplemented
154Dic3⋊C8—32no—
155Dic3⋊C8C2×D312yescomplemented
156C4⋊(C3⋊C8)—32no—
157#803—32no—
158C23×C32C22×C411yescharacteristic
159C22×C3⋊D3—22no—
160C22×C3⋊D3—22no—
161C22×C3⋊D3—22no—
162C22×C3⋊D3C22×C411yescharacteristic
163C22×C3⋊D3C22×C411yescharacteristic
164C22×C3×D3C22×C412yes—
165C2×D32—22no—
166C2×D32—22no—
167C2×D32M1614yescomplemented
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4C22×C411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3C22×C411yescharacteristic
174C2×C3⋊Dic3C22×C411yescharacteristic
175C4×C3⋊D3—22no—
176C4×C3⋊D3—21no—
177C4×C3⋊D3—21no—
178C4×C3⋊D3—22no—
179C4×C3⋊D3C2×D412yes—
180C4×C3⋊D3#4112yes—
181C3×#67—24no—
182C2×C3×Dic3C22×C412yes—
183C2×C3×Dic3C22×C412yes—
184C2×C3×Dic3C22×C412yes—
185C3×C4×D3—22no—
186C3×C4×D3—22no—
187#626—24no—
188#624—22no—
189#624—22no—
190#624—22no—
191D3×Dic3—24no—
192C32×C8—21no—
193C32×C8C2×D412yescomplemented
194C3⋊(C3⋊C8)—21no—
195C3⋊(C3⋊C8)C2×D412yescomplemented
196C3×C3⋊C8—22no—
197C3×C3⋊C8—22no—
198C22×M16—91no—
199C23×C8—91no—
200C2×C4×D4—91no—
201#435—32no—
202#435—92no—
203#435—92no—
204#435—92no—
205C2×C4⋊C8—91no—
206C2×C22⋊C8—91no—
207C2×C22⋊C8—91no—
208C2×#97—91no—
209C23×D3—32no—
210C23×D3—32no—
211C23×D3—61no—
212C2×C3×D4—32no—
213C22×C3×C4—21no—
214C22×C3×C4—32no—
215C22×C3×C4C22×D312yes—
216C2×#67—32no—
217C2×#67C4×D312yes—
218C22×Dic3—32no—
219C22×Dic3—32no—
220C22×Dic3—61no—
221D3×D4—68no—
222C2×D12—32no—
223C2×C4×D3—32no—
224C2×C4×D3—32no—
225C2×C4×D3—32no—
226C2×C4×D3—32no—
227C2×C4×D3—32no—
228C2×C4×D3—32no—
229C2×C4×D3—32no—
230C2×C4×D3—32no—
231C2×C4×D3—61no—
232C2×C4×D3—61no—
233C2×C4×D3—61no—
234C2×C4×D3—61no—
235C2×C4×D3—64no—
236C2×C4×D3—64no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×C4×D3—64no—
240C2×C4×D3—64no—
241C2×C4×D3C22×D312yes—
242C3×M16—24no—
243C3×M16—24no—
244C2×C3×C8—21no—
245C2×C3×C8—21no—
246C2×C3×C8—32no—
247C2×C3×C8—32no—
248C2×C3×C8—64no—
249C2×C3×C8C22×D312yes—
250C2×C3×C8C22×D312yes—
251C3×C4⋊C4—32no—
252C3×C22⋊C4—32no—
253C3×C22⋊C4—32no—
254C3×C42—32no—
255#217—32no—
256#217C4×D312yes—
257(C2×D3)⋊C4—32no—
258(C2×D3)⋊C4—32no—
259(C2×D3)⋊C4—32no—
260(C2×D3)⋊C4C4×D312yes—
261C4⋊Dic3—32no—
262Dic3⋊C4—32no—
263Dic3⋊C4C4×D312yes—
264C4×Dic3—32no—
265C4×Dic3—32no—
266C4×Dic3C22×D312yes—
267#208—64no—
268#208—64no—
269C2×C3⋊C8—32no—
270C2×C3⋊C8—32no—
271C2×C3⋊C8—61no—
272C2×C3⋊C8—61no—
273C2×C3⋊C8—64no—
274C2×C3⋊C8C22×D312yes—
275C2×C3⋊C8C22×D312yes—
276ΓL(1,𝔽25)—64no—
277ΓL(1,𝔽25)—64no—
278ΓL(1,𝔽25)—64no—
279ΓL(1,𝔽25)—64no—
280D3×C8—24no—
281D3×C8—38no—
282D3×C8—64no—
283D3×C8—64no—
284D3×C8—64no—
285D3×C8—64no—
286D3×C8—64no—
287D3×C8—64no—
288C22×C32—21no—
289C22×C32—21no—
290C22×C32—21no—
291C22×C32C23×C411yescharacteristic
292C2×C3⋊D3—21no—
293C2×C3⋊D3—21no—
294C2×C3⋊D3—21no—
295C2×C3⋊D3—44no—
296C2×C3⋊D3C4×D412yes—
297C2×C3⋊D3C2×M1612yes—
298C2×C3⋊D3#13112yes—
299C2×C3×D3—22no—
300C2×C3×D3—22no—
301C2×C3×D3C2×M1614yescomplemented
302D32—28no—
303C32×C4—21no—
304C32×C4C22×D411yescharacteristic
305C32×C4C2×#4111yescharacteristic
306C3⋊Dic3—21no—
307C3⋊Dic3C4×D412yes—
308C3×Dic3—22no—
309C3×Dic3—22no—
310C3×Dic3—22no—
311C22×D4—91no—
312C23×C4—91no—
313C23×C4—91no—
314C2×M16—91no—
315C2×M16—91no—
316C2×M16—91no—
317C2×M16—184no—
318C2×M16D3211yescharacteristic, complemented
319C22×C8—32no—
320C22×C8—91no—
321C22×C8—91no—
322C22×C8—92no—
323C22×C8—91no—
324C22×C8—91no—
325C22×C8—184no—
326C4×D4—32no—
327C4×D4—92no—
328C4×D4—92no—
329C4×D4—92no—
330C2×C4⋊C4—91no—
331C2×C22⋊C4—91no—
332C2×C22⋊C4—91no—
333C2×C42—91no—
334C4⋊C8—32no—
335C4⋊C8—92no—
336C22⋊C8—32no—
337C22⋊C8—32no—
338C22⋊C8—92no—
339C22⋊C8—92no—
340#97—32no—
341#97—92no—
342C23×C3—21no—
343C23×C3—32no—
344C23×C3C2×C4×D312yes—
345C22×D3—32no—
346C22×D3—38no—
347C22×D3—32no—
348C22×D3—61no—
349C22×D3—61no—
350C22×D3—64no—
351C22×D3—64no—
352C22×D3—64no—
353C22×D3—64no—
354C22×D3—64no—
355C22×D3—64no—
356C22×D3—122no—
357C22×D3—122no—
358C22×D3C2×C4×D312yes—
359C3×D4—64no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—32no—
367C2×C3×C4—32no—
368C2×C3×C4—32no—
369C2×C3×C4—62no—
370C2×C3×C4—62no—
371C2×C3×C4C2×C4×D312yes—
372C2×C3×C4C23×D312yes—
373#67—24no—
374#67—64no—
375C2×Dic3—32no—
376C2×Dic3—32no—
377C2×Dic3—61no—
378C2×Dic3—61no—
379C2×Dic3—64no—
380C2×Dic3—64no—
381C2×Dic3—64no—
382C2×Dic3C2×C4×D312yes—
383C2×Dic3C2×C4×D312yes—
384C2×Dic3C2×C4×D312yes—
385D12—64no—
386C4×D3—22no—
387C4×D3—22no—
388C4×D3—34no—
389C4×D3—34no—
390C4×D3—62no—
391C4×D3—62no—
392C4×D3—64no—
393C4×D3—64no—
394C4×D3—64no—
395C4×D3—64no—
396C4×D3—64no—
397C4×D3—64no—
398C4×D3—62no—
399C4×D3—64no—
400C4×D3—64no—
401C4×D3—62no—
402C4×D3—62no—
403C4×D3—62no—
404C3×C8—22no—
405C3×C8—22no—
406C3×C8—22no—
407C3×C8—62no—
408C3×C8—62no—
409C3×C8D3×D414yescomplemented
410C3⋊C8—22no—
411C3⋊C8—22no—
412C3⋊C8—34no—
413C3⋊C8—62no—
414C3⋊C8—62no—
415C3⋊C8—62no—
416C2×C32—41no—
417C2×C32C2×C4×D411yescharacteristic
418C2×C32C22×M1611yescharacteristic
419C2×C32C2×#13111yescharacteristic
420C3⋊D3—41no—
421C3⋊D3#43514yescomplemented
422C3×D3—24no—
423C24—91no—
424C24—91no—
425C2×D4—32no—
426C2×D4—92no—
427C2×D4—184no—
428C22×C4—32no—
429C22×C4—91no—
430C22×C4—91no—
431C22×C4—91no—
432C22×C4—92no—
433C22×C4—91no—
434C22×C4—91no—
435C22×C4—91no—
436C22×C4—91no—
437C22×C4—91no—
438C22×C4—182no—
439C22×C4—182no—
440C22×C4—182no—
441C22×C4—182no—
442C22×C4C2×D3211yescharacteristic
443M16—22no—
444M16—182no—
445M16—182no—
446M16—182no—
447C2×C8—32no—
448C2×C8—32no—
449C2×C8—64no—
450C2×C8—91no—
451C2×C8—94no—
452C2×C8—91no—
453C2×C8—182no—
454C2×C8—182no—
455C2×C8—182no—
456C2×C8—184no—
457C2×C8C2×D3211yescharacteristic
458C2×C8C2×D3211yescharacteristic
459C4⋊C4—32no—
460C4⋊C4—92no—
461C22⋊C4—32no—
462C22⋊C4—32no—
463C22⋊C4—92no—
464C22⋊C4—92no—
465C42—32no—
466C42—92no—
467C22×C3—22no—
468C22×C3—22no—
469C22×C3—22no—
470C22×C3—22no—
471C22×C3—21no—
472C22×C3—34no—
473C22×C3—41no—
474C22×C3—41no—
475C22×C3—62no—
476C22×C3—62no—
477C22×C3C22×C4×D312yes—
478C2×D3—22no—
479C2×D3—22no—
480C2×D3—34no—
481C2×D3—34no—
482C2×D3—34no—
483C2×D3—62no—
484C2×D3—62no—
485C2×D3—62no—
486C2×D3—616no—
487C2×D3—62no—
488C2×D3—62no—
489C2×D3—62no—
490C2×D3—62no—
491C2×D3—121no—
492C2×D3—121no—
493C2×D3—128no—
494C2×D3—128no—
495C2×D3D3×M1614yescomplemented
496C3×C4—22no—
497C3×C4—22no—
498C3×C4—21no—
499C3×C4—21no—
500C3×C4—62no—
501C3×C4—62no—
502C3×C4—62no—
503C3×C4C2×D3×D412yes—
504C3×C4D3×#4112yes—
505Dic3—22no—
506Dic3—22no—
507Dic3—22no—
508Dic3—34no—
509Dic3—62no—
510Dic3—62no—
511Dic3—62no—
512C32C2×#43511yescharacteristic, complemented, Sylow
513C23—32no—
514C23—94no—
515C23—91no—
516C23—91no—
517C23—182no—
518C23—182no—
519C23—182no—
520C23—182no—
521C23—182no—
522C23C4×D3211yescharacteristic
523D4—64no—
524D4—184no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—32no—
528C2×C4—32no—
529C2×C4—32no—
530C2×C4—62no—
531C2×C4—62no—
532C2×C4—91no—
533C2×C4—92no—
534C2×C4—92no—
535C2×C4—91no—
536C2×C4—182no—
537C2×C4—182no—
538C2×C4—182no—
539C2×C4—182no—
540C2×C4—182no—
541C2×C4—184no—
542C2×C4—182no—
543C2×C4—181no—
544C2×C4—181no—
545C2×C4C4×D3211yescharacteristic
546C2×C4C22×D3211yescharacteristic
547C8—21no—
548C8—62no—
549C8—62no—
550C8—92no—
551C8—181no—
552C8#381112yescomplemented
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—42no—
557C2×C3—42no—
558C2×C3—64no—
559C2×C3C4×D3×D412yes—
560C2×C3C2×D3×M1612yes—
561C2×C3D3×#13112yes—
562D3—24no—
563D3—38no—
564D3—64no—
565D3—122no—
566D3—122no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—34no—
571C22—62no—
572C22—62no—
573C22—92no—
574C22—92no—
575C22—92no—
576C22—188no—
577C22—181no—
578C22—181no—
579C22—181no—
580C22—364no—
581C22C2×C4×D3211yescharacteristic
582C4—21no—
583C4—62no—
584C4—62no—
585C4—62no—
586C4—92no—
587C4—181no—
588C4#6430611yescharacteristic
589C4C2×#381111yescharacteristic
590C3—21no—
591C3D3×#43512yescomplemented
592C2—41no—
593C2—64no—
594C2—94no—
595C2—361no—
596C2D32×M1611yescharacteristic
597C2#1059470711yescharacteristic
598C2C4×#381111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC2×C32×M16C22
prime radicalC2×#3811C4
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32C2×#435
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×M16×C3⋊D3C2semidirect
3. C2×D32×C8C2semidirect
4. C3×#5127C2semidirect
5. #10591152C2semidirect
6. #10591151C2semidirect
7. #10590935C2semidirect
8. #10590907C2semidirect
9. #10590726C2semidirect
10. #10590668C2semidirect
11. #10590658C2semidirect
16. C2×C32×M16C22semidirect
17. C2×#3748C22semidirect
19. C2×#3743C22semidirect
20. C2×#3743C22semidirect
24. C2×C3×D3×C8C22semidirect
34. C2×D3×C3⋊C8C22semidirect
36. C3×#830C22semidirect
37. C3×(C2×D3)⋊C8C22semidirect
38. C3×#815C22semidirect
39. C3×Dic3⋊C8C22semidirect
40. Dic3⋊(C3⋊C8)C22semidirect
41. #63557C22semidirect
42. (C2×D3)⋊(C3⋊C8)C22semidirect
43. #63554C22semidirect
49. #5127D3semidirect
89. C8×C3⋊D3D4semidirect
110. C2×C3×M16C2×D3semidirect
133. C2×D3×C8C2×D3semidirect
147. #830C2×D3semidirect
151. (C2×D3)⋊C8C2×D3semidirect
153. #815C2×D3semidirect
155. Dic3⋊C8C2×D3semidirect
167. C2×D32M16semidirect
193. C32×C8C2×D4semidirect
195. C3⋊(C3⋊C8)C2×D4semidirect
301. C2×C3×D3C2×M16semidirect
318. C2×M16D32semidirect
409. C3×C8D3×D4semidirect
421. C3⋊D3#435semidirect
495. C2×D3D3×M16semidirect
512. C32C2×#435semidirect
552. C8#3811semidirect
591. C3D3×#435semidirect

Maximal subgroups

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

subgroupindex
C2×M16×C3⋊D32
C4×#38112
C2×D32×C82
C3×#51272
#105911522
#105911512
#105909352
#105909072
#105907262
#105906682
#105906582
D3×#4353