Finite Group Databasebeta

← #11788318

Subgroups — #11788318

Order 1152.

829 conjugacy classes of subgroups.

The subgroup lattice has 621 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#895C211yesmaximal, characteristic
2C2×D3×#208C211yesmaximal, characteristic, complemented
3C2×#63558C211yesmaximal, characteristic, complemented
4C2×#63558C211yesmaximal, characteristic, complemented
5#10591069C211yesmaximal, characteristic, complemented
6#10589396C211yesmaximal, characteristic, complemented
7C3×#4530C211yesmaximal, characteristic, complemented
8#71683—31nomaximal
9#68992—31nomaximal
10C22×C3×D12C412yes—
11C22×C3×D12C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C2×C3×(C2×D3)⋊C4C412yes—
17C2×C3×#208C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C3×#895—21no—
20C3×#895—21no—
21C3×#895—21no—
22C3×#895—21no—
23C2×#3711—21no—
24D3×#208—22no—
25D3×#208—22no—
26C2×D3×C3⋊C8—21no—
27#63558—22no—
28#63558—22no—
29(C2×D3)⋊(C3⋊C8)—21no—
30(C2×D3)⋊(C3⋊C8)—21no—
31C2×C3×#121—31no—
32C22×#208—31no—
33C2×D3×M16—31no—
34C2×#895D311yescharacteristic
35C2×#833—31no—
36C2×#833—31no—
37#5207—31no—
38C2×#823—31no—
39C2×#823—31no—
40#5126—31no—
41C3×#343—31no—
42#4530—31no—
43#4530—31no—
44#4530—61no—
45#4530D311yescharacteristic, complemented
46C23×C3×D3C2×C411yescharacteristic
47C23×C3×D3C2×C412yes—
48C22×C32×C4C2×C412yes—
49C22×C32×C4C2311yescharacteristic
50C22×C3×Dic3C2×C411yescharacteristic
51C2×C3×D12—22no—
52C2×C3×D12—22no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—44no—
60C2×C3×C4×D3—21no—
61C2×C3×C4×D3—21no—
62C2×C3×C4×D3—21no—
63C2×C3×C4×D3—21no—
64C2×C3×C4×D3D411yescharacteristic
65C2×C3×C4×D3D411yescharacteristic
66C2×C3×C4×D3D411yescharacteristic
67C2×C3×C4×D3D411yescharacteristic
68C32×C4⋊C4—21no—
69C32×C4⋊C4—21no—
70#3748—21no—
71#3748—21no—
72#3748—21no—
73#3748D412yescomplemented
74C2×C3⋊(C3⋊C8)—21no—
75C2×C3⋊(C3⋊C8)—21no—
76C3×(C2×D3)⋊C4—22no—
77C3×(C2×D3)⋊C4—22no—
78C3×#208—21no—
79C3×#208—21no—
80C3×#208—21no—
81C3×#208D412yescomplemented
82C2×C3×C3⋊C8—21no—
83C2×C3×C3⋊C8—21no—
84#3711—24no—
85D3×C3⋊C8—24no—
86#1900—91noSylow
87C22×C3×D4—32no—
88C22×C3×D4—31no—
89C23×C3×C4—31no—
90C22×D12Dic312yes—
91C22×D12C2×D311yescharacteristic
92C22×C4×D3C2×D311yescharacteristic
93C2×C3×M16—31no—
94C2×C3×M16—31no—
95C3×#121—61no—
96C3×#121—61no—
97C3×#121—61no—
98C3×#121—61no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4C2×D311yescharacteristic
101C2×C3×C4⋊C4C2×D311yescharacteristic
102C2×C3×C22⋊C4—32no—
103C2×(C2×D3)⋊C4Dic312yes—
104C2×#208—31no—
105C2×#208—31no—
106C2×#208—31no—
107C2×#208—31no—
108C2×#208—61no—
109C2×#208—61no—
110C2×#208—61no—
111C2×#208—62no—
112C2×#208—62no—
113C2×#208C2×D311yescharacteristic
114C2×#208C2×D311yescharacteristic
115C22×C3⋊C8—61no—
116D3×M16—62no—
117D3×M16—62no—
118C2×ΓL(1,𝔽25)—61no—
119C2×D3×C8—61no—
120#895—21no—
121#895—21no—
122#895—21no—
123#895—21no—
124#833—62no—
125#833—62no—
126#830—61no—
127#830—61no—
128#823—62no—
129#823—62no—
130(C2×D3)⋊C8—61no—
131(C2×D3)⋊C8—61no—
132C23×C32C22×C411yescharacteristic
133C22×C3×D3—21no—
134C22×C3×D3—21no—
135C22×C3×D3—22no—
136C22×C3×D3—22no—
137C22×C3×D3—22no—
138C22×C3×D3—22no—
139C22×C3×D3—41no—
140C22×C3×D3—42no—
141C22×C3×D3—42no—
142C22×C3×D3C22⋊C411yescharacteristic
143C22×C3×D3C22⋊C411yescharacteristic
144C2×C32×C4—22no—
145C2×C32×C4—42no—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4#4111yescharacteristic
151C2×C32×C4#4111yescharacteristic
152C2×C3×Dic3—21no—
153C2×C3×Dic3—21no—
154C2×C3×Dic3C22⋊C411yescharacteristic
155C2×C3×Dic3C22⋊C411yescharacteristic
156C3×D12—44no—
157C3×D12—44no—
158C3×D12—41no—
159C3×D12—41no—
160C3×D12—41no—
161C3×D12—41no—
162C3×C4×D3—21no—
163C3×C4×D3—21no—
164C3×C4×D3—21no—
165C3×C4×D3—21no—
166C3×C4×D3—21no—
167C3×C4×D3—21no—
168C3×C4×D3—21no—
169C3×C4×D3—21no—
170C3⋊(C3⋊C8)—22no—
171C3⋊(C3⋊C8)—41no—
172C3×C3⋊C8—22no—
173C3×C3⋊C8—41no—
174C22×M16—91no—
175C2×#121—31no—
176C2×#100—91no—
177C2×#100—91no—
178#407—91no—
179#343—31no—
180#343—91no—
181C24×C3—31no—
182C24×C3—32no—
183C23×D3C2×Dic311yescharacteristic
184C23×D3C2×Dic312yes—
185C2×C3×D4—62no—
186C2×C3×D4—62no—
187C2×C3×D4—61no—
188C2×C3×D4—61no—
189C2×C3×D4—61no—
190C2×C3×D4—61no—
191C2×C3×D4—61no—
192C2×C3×D4—61no—
193C2×C3×D4—124no—
194C22×C3×C4—22no—
195C22×C3×C4—21no—
196C22×C3×C4—31no—
197C22×C3×C4—31no—
198C22×C3×C4—31no—
199C22×C3×C4—31no—
200C22×C3×C4—31no—
201C22×C3×C4—61no—
202C22×C3×C4—61no—
203C22×C3×C4—61no—
204C22×C3×C4—61no—
205C22×C3×C4C4×D312yes—
206C22×C3×C4C2×Dic312yes—
207C22×C3×C4C22×D311yescharacteristic
208C22×C3×C4C22×D311yescharacteristic
209C22×Dic3C2×Dic311yescharacteristic
210C2×D12—22no—
211C2×D12—22no—
212C2×D12—21no—
213C2×D12—21no—
214C2×D12—21no—
215C2×D12—21no—
216C2×D12—21no—
217C2×D12—21no—
218C2×D12—44no—
219C2×C4×D3—21no—
220C2×C4×D3—21no—
221C2×C4×D3—21no—
222C2×C4×D3—21no—
223C2×C4×D3#6711yescharacteristic
224C2×C4×D3#6711yescharacteristic
225C2×C4×D3#6711yescharacteristic
226C2×C4×D3#6711yescharacteristic
227C3×M16—32no—
228C3×M16—61no—
229C3×M16—61no—
230C3×M16—61no—
231C2×C3×C8—61no—
232C2×C3×C8—61no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—41no—
238C3×C4⋊C4—41no—
239C3×C22⋊C4—62no—
240C3×C22⋊C4—62no—
241(C2×D3)⋊C4—22no—
242(C2×D3)⋊C4—22no—
243#208—21no—
244#208—21no—
245#208—21no—
246#208—32no—
247#208—32no—
248#208—62no—
249#208—64no—
250#208—61no—
251#208—61no—
252#208—62no—
253#208—61no—
254#208—61no—
255#208—61no—
256#208—61no—
257#208—121no—
258#208—121no—
259#208D1212yescomplemented
260C2×C3⋊C8—21no—
261C2×C3⋊C8—21no—
262C2×C3⋊C8—64no—
263C2×C3⋊C8—61no—
264C2×C3⋊C8—61no—
265C2×C3⋊C8—61no—
266C2×C3⋊C8—61no—
267C2×C3⋊C8—121no—
268C2×C3⋊C8—121no—
269ΓL(1,𝔽25)—64no—
270D3×C8—64no—
271C22×C32—21no—
272C22×C32—21no—
273C22×C32C2×C22⋊C411yescharacteristic
274C22×C32C4×D411yescharacteristic
275C22×C32C4×D411yescharacteristic
276C2×C3×D3—21no—
277C2×C3×D3—21no—
278C2×C3×D3—21no—
279C2×C3×D3—21no—
280C2×C3×D3—21no—
281C2×C3×D3—42no—
282C2×C3×D3—42no—
283C2×C3×D3—42no—
284C2×C3×D3—42no—
285C2×C3×D3—42no—
286C2×C3×D3—82no—
287C2×C3×D3—82no—
288C2×C3×D3#10012yescomplemented
289C32×C4—42no—
290C32×C4#12011yescharacteristic
291C32×C4#12111yescharacteristic
292C32×C4#12111yescharacteristic
293C32×C4#12311yescharacteristic
294C3×Dic3—21no—
295C3×Dic3—21no—
296C22×D4—32no—
297C22×D4—31no—
298C23×C4—31no—
299C2×M16—31no—
300C2×M16—31no—
301C2×M16—91no—
302C2×M16—91no—
303C2×M16—181no—
304C2×M16—182no—
305C2×M16—182no—
306C22×C8—181no—
307#121—61no—
308#121—61no—
309#121—61no—
310#121—61no—
311C2×C4⋊C4D3211yescharacteristic
312C2×C22⋊C4—32no—
313#100—182no—
314#100—182no—
315C22⋊C8—181no—
316C22⋊C8—181no—
317C23×C3—21no—
318C23×C3—31no—
319C23×C3—31no—
320C23×C3—62no—
321C23×C3—61no—
322C23×C3—61no—
323C23×C3—62no—
324C23×C3—62no—
325C23×C3—62no—
326C23×C3—121no—
327C23×C3—122no—
328C23×C3—122no—
329C23×C3C2×C4×D311yescharacteristic
330C23×C3C22×Dic311yescharacteristic
331C22×D3—21no—
332C22×D3—21no—
333C22×D3—22no—
334C22×D3—22no—
335C22×D3—22no—
336C22×D3—22no—
337C22×D3—41no—
338C22×D3—42no—
339C22×D3—42no—
340C22×D3#21711yescharacteristic
341C22×D3#21711yescharacteristic
342C3×D4—124no—
343C3×D4—124no—
344C3×D4—121no—
345C3×D4—121no—
346C3×D4—121no—
347C3×D4—121no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—31no—
357C2×C3×C4—31no—
358C2×C3×C4—42no—
359C2×C3×C4—42no—
360C2×C3×C4—42no—
361C2×C3×C4—61no—
362C2×C3×C4—61no—
363C2×C3×C4—61no—
364C2×C3×C4—61no—
365C2×C3×C4—61no—
366C2×C3×C4—61no—
367C2×C3×C4—61no—
368C2×C3×C4—61no—
369C2×C3×C4—61no—
370C2×C3×C4—61no—
371C2×C3×C4—82no—
372C2×C3×C4C2×D1211yescharacteristic
373C2×C3×C4#23511yescharacteristic
374C2×C3×C4D3×D411yescharacteristic
375C2×C3×C4D3×D411yescharacteristic
376C2×C3×C4D3×D411yescharacteristic
377C2×C3×C4D3×D411yescharacteristic
378C2×C3×C4D3×D411yescharacteristic
379C2×C3×C4#23711yescharacteristic
380C2×C3×C4#23711yescharacteristic
381C2×C3×C4#23911yescharacteristic
382C2×C3×C4C2×#6711yescharacteristic
383C2×C3×C4C2×#6711yescharacteristic
384C2×Dic3—21no—
385C2×Dic3—21no—
386C2×Dic3#21711yescharacteristic
387C2×Dic3#21711yescharacteristic
388D12—44no—
389D12—44no—
390D12—41no—
391D12—41no—
392D12—41no—
393D12—41no—
394C4×D3—21no—
395C4×D3—21no—
396C4×D3—21no—
397C4×D3—21no—
398C4×D3—21no—
399C4×D3—21no—
400C4×D3—21no—
401C4×D3—21no—
402C3×C8—62no—
403C3×C8—121no—
404C3⋊C8—22no—
405C3⋊C8—41no—
406C3⋊C8—62no—
407C3⋊C8—62no—
408C3⋊C8—122no—
409C3⋊C8—122no—
410C3⋊C8—121no—
411C3⋊C8—121no—
412C2×C32—21no—
413C2×C32—21no—
414C2×C32#38611yescharacteristic
415C2×C32C2×#10011yescharacteristic
416C2×C32#41311yescharacteristic
417C3×D3—22no—
418C3×D3—41no—
419C3×D3—82no—
420C24—31no—
421C24—32no—
422C2×D4—62no—
423C2×D4—62no—
424C2×D4—61no—
425C2×D4—61no—
426C2×D4—61no—
427C2×D4—61no—
428C2×D4—61no—
429C2×D4—61no—
430C2×D4—124no—
431C22×C4—31no—
432C22×C4—31no—
433C22×C4—31no—
434C22×C4—31no—
435C22×C4—31no—
436C22×C4—61no—
437C22×C4—61no—
438C22×C4—61no—
439C22×C4—61no—
440C22×C4D3×Dic312yes—
441C22×C4C2×D3211yescharacteristic
442M16—32no—
443M16—61no—
444M16—61no—
445M16—61no—
446M16—92no—
447M16—184no—
448M16—181no—
449M16—181no—
450M16—181no—
451C2×C8—61no—
452C2×C8—61no—
453C2×C8—184no—
454C2×C8—181no—
455C2×C8—181no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C22⋊C4—62no—
459C22⋊C4—62no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—32no—
468C22×C3—41no—
469C22×C3—41no—
470C22×C3—61no—
471C22×C3—61no—
472C22×C3—61no—
473C22×C3—61no—
474C22×C3—61no—
475C22×C3—122no—
476C22×C3—122no—
477C22×C3—122no—
478C22×C3—122no—
479C22×C3—122no—
480C22×C3—242no—
481C22×C3—242no—
482C22×C3C4×D1211yescharacteristic
483C22×C3D3×C22⋊C411yescharacteristic
484C22×C3#89311yescharacteristic
485C22×C3D4×Dic311yescharacteristic
486C22×C3D4×Dic311yescharacteristic
487C22×C3C2×#21711yescharacteristic
488C2×D3—21no—
489C2×D3—21no—
490C2×D3—21no—
491C2×D3—21no—
492C2×D3—21no—
493C2×D3—42no—
494C2×D3—42no—
495C2×D3—42no—
496C2×D3—42no—
497C2×D3—42no—
498C2×D3—82no—
499C2×D3—82no—
500C2×D3#83312yescomplemented
501C3×C4—21no—
502C3×C4—21no—
503C3×C4—21no—
504C3×C4—21no—
505C3×C4—42no—
506C3×C4—42no—
507C3×C4—61no—
508C3×C4—61no—
509C3×C4—82no—
510C3×C4#88211yescharacteristic
511C3×C4#88411yescharacteristic
512C3×C4#89411yescharacteristic
513C3×C4#89511yescharacteristic
514C3×C4#93511yescharacteristic
515C3×C4#93711yescharacteristic
516C3×C4#93911yescharacteristic
517C3×C4#93911yescharacteristic
518Dic3—21no—
519Dic3—21no—
520C32#190011yescharacteristic, complemented, Sylow
521C23—31no—
522C23—31no—
523C23—62no—
524C23—61no—
525C23—61no—
526C23—62no—
527C23—62no—
528C23—62no—
529C23—121no—
530C23—122no—
531C23—122no—
532C23C2×D3×Dic311yescharacteristic
533D4—124no—
534D4—124no—
535D4—121no—
536D4—121no—
537D4—121no—
538D4—121no—
539C2×C4—22no—
540C2×C4—31no—
541C2×C4—31no—
542C2×C4—42no—
543C2×C4—61no—
544C2×C4—61no—
545C2×C4—61no—
546C2×C4—61no—
547C2×C4—61no—
548C2×C4—61no—
549C2×C4—61no—
550C2×C4—61no—
551C2×C4—61no—
552C2×C4—61no—
553C2×C4#379511yescharacteristic
554C2×C4#379611yescharacteristic
555C2×C4D3×D1211yescharacteristic
556C2×C4#380211yescharacteristic
557C2×C4D3×#6711yescharacteristic
558C2×C4D3×#6711yescharacteristic
559C8—62no—
560C8—121no—
561C8—182no—
562C8—361no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—41no—
571C2×C3—41no—
572C2×C3—62no—
573C2×C3—121no—
574C2×C3—242no—
575C2×C3#466511yescharacteristic
576C2×C3D3×#10011yescharacteristic
577C2×C3#475111yescharacteristic
578C2×C3C2×#83311yescharacteristic
579C2×C3#522011yescharacteristic
580C2×C3#523711yescharacteristic
581D3—22no—
582D3—41no—
583D3—82no—
584C22—21no—
585C22—21no—
586C22—32no—
587C22—61no—
588C22—61no—
589C22—61no—
590C22—61no—
591C22—61no—
592C22—122no—
593C22—122no—
594C22—122no—
595C22—122no—
596C22—122no—
597C22—242no—
598C22—242no—
599C22Dic3×D1211yescharacteristic
600C22#6389811yescharacteristic
601C22D3×#21711yescharacteristic
602C4—42no—
603C4—61no—
604C4—61no—
605C4#6388411yescharacteristic
606C4#6388511yescharacteristic
607C4#6388611yescharacteristic
608C4#6392211yescharacteristic
609C3—21no—
610C3#6899211yescharacteristic, complemented
611C3#7168311yescharacteristic, complemented
612C2—21no—
613C2—21no—
614C2—62no—
615C2—121no—
616C2—242no—
617C2#1059137611yescharacteristic
618C2D3×#83311yescharacteristic
619C2#1059163711yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#895C2
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1900
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×D3×#208C2semidirect
3. C2×#63558C2semidirect
4. C2×#63558C2semidirect
5. #10591069C2semidirect
6. #10589396C2semidirect
7. C3×#4530C2semidirect
45. #4530D3semidirect
73. #3748D4semidirect
81. C3×#208D4semidirect
259. #208D12semidirect
288. C2×C3×D3#100semidirect
500. C2×D3#833semidirect
520. C32#1900semidirect
610. C3#68992semidirect
611. C3#71683semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8952
C2×D3×#2082
C2×#635582
#105910692
#105893962
C3×#45302
#716833
#689923