Finite Group Databasebeta

← #11788351

Subgroups — #11788351

Order 1152.

749 conjugacy classes of subgroups.

The subgroup lattice has 591 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#946C211yesmaximal, characteristic
2C2×D3×#208C211yesmaximal, characteristic
3C2×#63663C211yesmaximal, characteristic, complemented
4C2×C3×#836C211yesmaximal, characteristic, complemented
5#10591069C211yesmaximal, characteristic
6#10589167C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#71698—31nomaximal
9#70115—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C22×C3×C4×D3C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#946—21no—
15C3×#946—21no—
16C3×#946—21no—
17C3×#946—21no—
18C2×C3×(C2×D3)⋊C4C412yes—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×Dic3⋊C4C412yes—
21C2×C3×#208C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23C2×#3711—21no—
24D3×#208—22no—
25D3×#208—22no—
26C2×D3×C3⋊C8—21no—
27#63663—22no—
28C3×#836—22no—
29(C2×D3)⋊(C3⋊C8)—21no—
30(C2×D3)⋊(C3⋊C8)—21no—
31C2×C3×C22⋊Q8—31no—
32C2×#946D311yescharacteristic
33C22×#208—31no—
34C2×D3×M16—31no—
35C2×C3×#101—31no—
36C2×#836—31no—
37C2×#836—31no—
38C2×#836—61no—
39C2×#836D311yescharacteristic, complemented
40#5207—31no—
41#5126—31no—
42#4554—31no—
43#4554—31no—
44#4530—31no—
45#4530—31no—
46C23×C3×D3C2×C411yescharacteristic
47C2×C32×Q8—21no—
48C2×C32×Q8—21no—
49C2×C32×Q8—21no—
50C2×C32×Q8—21no—
51C2×C32×Q8—21no—
52C2×C32×Q8—21no—
53C22×C32×C4C2×C412yes—
54C22×C32×C4C2311yescharacteristic
55C22×C3×Dic3C2×C411yescharacteristic
56C22×C3×Dic3C2×C412yes—
57C2×C3×C4×D3—21no—
58C2×C3×C4×D3—21no—
59C2×C3×C4×D3—21no—
60C2×C3×C4×D3—21no—
61C2×C3×C4×D3D411yescharacteristic
62C2×C3×C4×D3D411yescharacteristic
63C2×C3×C4×D3D411yescharacteristic
64C2×C3×C4×D3D411yescharacteristic
65#3748—21no—
66#3748—21no—
67#3748—21no—
68#3748D412yes—
69C2×C3⋊(C3⋊C8)—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C3×(C2×D3)⋊C4—22no—
72C3×(C2×D3)⋊C4—22no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75C3×Dic3⋊C4—22no—
76C3×Dic3⋊C4—22no—
77C3×#208—21no—
78C3×#208—21no—
79C3×#208—21no—
80C3×#208D412yes—
81C2×C3×C3⋊C8—21no—
82C2×C3×C3⋊C8—21no—
83#3711—24no—
84D3×C3⋊C8—24no—
85#1901—91noSylow
86C22×C3×Q8—21no—
87C22×C3×Q8C2×D311yescharacteristic
88C22×C3×Q8C2×D311yescharacteristic
89C23×C3×C4—31no—
90C22×C4×D3C2×D311yescharacteristic
91C2×C3×M16—31no—
92C2×C3×M16—31no—
93C3×C22⋊Q8—61no—
94C3×C22⋊Q8—61no—
95C3×C22⋊Q8—61no—
96C3×C22⋊Q8—61no—
97C2×C3×C4⋊C4—32no—
98C2×C3×C4⋊C4—31no—
99C2×C3×C22⋊C4—32no—
100#946—21no—
101#946—21no—
102#946—21no—
103#946—21no—
104C2×(C2×D3)⋊C4Dic312yes—
105C2×C4⋊Dic3C2×D311yescharacteristic
106C2×Dic3⋊C4Dic312yes—
107C2×#208—31no—
108C2×#208—31no—
109C2×#208—31no—
110C2×#208—31no—
111C2×#208—61no—
112C2×#208—61no—
113C2×#208—61no—
114C2×#208—62no—
115C2×#208—62no—
116C2×#208C2×D311yescharacteristic
117C2×#208C2×D311yescharacteristic
118C22×C3⋊C8—61no—
119D3×M16—62no—
120D3×M16—62no—
121C2×ΓL(1,𝔽25)—61no—
122C2×D3×C8—61no—
123C3×#101—62no—
124#836—22no—
125#836—62no—
126#836—62no—
127#836—64no—
128#830—61no—
129#830—61no—
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—41no—
137C22×C3×D3C22⋊C411yescharacteristic
138C22×C3×D3C22⋊C411yescharacteristic
139C32×Q8—41no—
140C32×Q8—41no—
141C32×Q8—41no—
142C32×Q8—41no—
143C2×C32×C4—22no—
144C2×C32×C4—22no—
145C2×C32×C4—22no—
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×Dic3—22no—
155C2×C3×Dic3—42no—
156C2×C3×Dic3C22⋊C411yescharacteristic
157C2×C3×Dic3C22⋊C411yescharacteristic
158C3×C4×D3—21no—
159C3×C4×D3—21no—
160C3×C4×D3—21no—
161C3×C4×D3—21no—
162C3×C4×D3—21no—
163C3×C4×D3—21no—
164C3×C4×D3—21no—
165C3×C4×D3—21no—
166C3⋊(C3⋊C8)—22no—
167C3⋊(C3⋊C8)—41no—
168C3×C3⋊C8—22no—
169C3×C3⋊C8—41no—
170C22×M16—91no—
171C2×C22⋊Q8—31no—
172C2×#101—31no—
173C2×#101—91no—
174#407—91no—
175#343—91no—
176#343—91no—
177C24×C3—31no—
178C23×D3C2×Dic311yescharacteristic
179C2×C3×Q8—22no—
180C2×C3×Q8—22no—
181C2×C3×Q8—21no—
182C2×C3×Q8—21no—
183C2×C3×Q8—21no—
184C2×C3×Q8—21no—
185C2×C3×Q8—21no—
186C2×C3×Q8—21no—
187C2×C3×Q8—21no—
188C2×C3×Q8—21no—
189C2×C3×Q8—21no—
190C2×C3×Q8—21no—
191C2×C3×Q8—21no—
192C2×C3×Q8—21no—
193C2×C3×Q8—41no—
194C2×C3×Q8—41no—
195C2×C3×Q8—41no—
196C2×C3×Q8—41no—
197C22×C3×C4—22no—
198C22×C3×C4—21no—
199C22×C3×C4—31no—
200C22×C3×C4—31no—
201C22×C3×C4—31no—
202C22×C3×C4—31no—
203C22×C3×C4—31no—
204C22×C3×C4—32no—
205C22×C3×C4—61no—
206C22×C3×C4—61no—
207C22×C3×C4—61no—
208C22×C3×C4—61no—
209C22×C3×C4C4×D312yes—
210C22×C3×C4C2×Dic312yes—
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×Dic3C2×Dic311yescharacteristic
214C22×Dic3C2×Dic312yes—
215C2×C4×D3—21no—
216C2×C4×D3—21no—
217C2×C4×D3—21no—
218C2×C4×D3—21no—
219C2×C4×D3#6711yescharacteristic
220C2×C4×D3#6711yescharacteristic
221C2×C4×D3#6711yescharacteristic
222C2×C4×D3#6711yescharacteristic
223C3×M16—32no—
224C3×M16—61no—
225C3×M16—61no—
226C3×M16—61no—
227C2×C3×C8—61no—
228C2×C3×C8—61no—
229C3×C4⋊C4—62no—
230C3×C4⋊C4—62no—
231C3×C4⋊C4—61no—
232C3×C4⋊C4—61no—
233C3×C22⋊C4—62no—
234C3×C22⋊C4—62no—
235(C2×D3)⋊C4—22no—
236(C2×D3)⋊C4—22no—
237C4⋊Dic3—21no—
238C4⋊Dic3—21no—
239Dic3⋊C4—22no—
240Dic3⋊C4—22no—
241#208—21no—
242#208—21no—
243#208—21no—
244#208—32no—
245#208—32no—
246#208—62no—
247#208—64no—
248#208—61no—
249#208—61no—
250#208—62no—
251#208—61no—
252#208—61no—
253#208—61no—
254#208—61no—
255#208—121no—
256#208—121no—
257#208#6712yes—
258C2×C3⋊C8—21no—
259C2×C3⋊C8—21no—
260C2×C3⋊C8—64no—
261C2×C3⋊C8—61no—
262C2×C3⋊C8—61no—
263C2×C3⋊C8—61no—
264C2×C3⋊C8—61no—
265C2×C3⋊C8—121no—
266C2×C3⋊C8—121no—
267ΓL(1,𝔽25)—64no—
268D3×C8—64no—
269C22×C32—21no—
270C22×C32—21no—
271C22×C32C2×C22⋊C411yescharacteristic
272C22×C32C4×D411yescharacteristic
273C22×C32C4×D411yescharacteristic
274C2×C3×D3—21no—
275C2×C3×D3—21no—
276C2×C3×D3—21no—
277C2×C3×D3—21no—
278C2×C3×D3—21no—
279C2×C3×D3—42no—
280C2×C3×D3—42no—
281C2×C3×D3#10112yescomplemented
282C32×C4—42no—
283C32×C4#12011yescharacteristic
284C32×C4#12111yescharacteristic
285C32×C4#12111yescharacteristic
286C32×C4#12311yescharacteristic
287C3×Dic3—21no—
288C3×Dic3—21no—
289C3×Dic3—42no—
290C22×Q8D3211yescharacteristic
291C23×C4—31no—
292C2×M16—31no—
293C2×M16—31no—
294C2×M16—91no—
295C2×M16—91no—
296C2×M16—181no—
297C2×M16—182no—
298C2×M16—182no—
299C22×C8—181no—
300C22⋊Q8—61no—
301C22⋊Q8—61no—
302C22⋊Q8—61no—
303C22⋊Q8—61no—
304C2×C4⋊C4—32no—
305C2×C4⋊C4—31no—
306C2×C22⋊C4—32no—
307#101—62no—
308#101—182no—
309C22⋊C8—181no—
310C22⋊C8—181no—
311C23×C3—21no—
312C23×C3—31no—
313C23×C3—31no—
314C23×C3—62no—
315C23×C3—61no—
316C23×C3—61no—
317C23×C3—121no—
318C23×C3C2×C4×D311yescharacteristic
319C23×C3C22×Dic311yescharacteristic
320C22×D3—21no—
321C22×D3—21no—
322C22×D3—22no—
323C22×D3—41no—
324C22×D3#21711yescharacteristic
325C22×D3#21711yescharacteristic
326C3×Q8—42no—
327C3×Q8—42no—
328C3×Q8—42no—
329C3×Q8—42no—
330C3×Q8—41no—
331C3×Q8—41no—
332C3×Q8—41no—
333C3×Q8—41no—
334C3×Q8—41no—
335C3×Q8—41no—
336C3×Q8—41no—
337C3×Q8—41no—
338C2×C3×C4—24no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—31no—
352C2×C3×C4—31no—
353C2×C3×C4—42no—
354C2×C3×C4—42no—
355C2×C3×C4—61no—
356C2×C3×C4—61no—
357C2×C3×C4—61no—
358C2×C3×C4—61no—
359C2×C3×C4—61no—
360C2×C3×C4—61no—
361C2×C3×C4—61no—
362C2×C3×C4—61no—
363C2×C3×C4—61no—
364C2×C3×C4—61no—
365C2×C3×C4—62no—
366C2×C3×C4—122no—
367C2×C3×C4#23511yescharacteristic
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4#23711yescharacteristic
374C2×C3×C4#23711yescharacteristic
375C2×C3×C4#23711yescharacteristic
376C2×C3×C4C2×#6711yescharacteristic
377C2×C3×C4C2×#6711yescharacteristic
378C2×C3×C4C2×#6711yescharacteristic
379C2×Dic3—21no—
380C2×Dic3—21no—
381C2×Dic3—22no—
382C2×Dic3—42no—
383C2×Dic3#21711yescharacteristic
384C2×Dic3#21711yescharacteristic
385C4×D3—21no—
386C4×D3—21no—
387C4×D3—21no—
388C4×D3—21no—
389C4×D3—21no—
390C4×D3—21no—
391C4×D3—21no—
392C4×D3—21no—
393C3×C8—62no—
394C3×C8—121no—
395C3⋊C8—22no—
396C3⋊C8—41no—
397C3⋊C8—62no—
398C3⋊C8—62no—
399C3⋊C8—122no—
400C3⋊C8—122no—
401C3⋊C8—121no—
402C3⋊C8—121no—
403C2×C32—21no—
404C2×C32—21no—
405C2×C32#38611yescharacteristic
406C2×C32C2×#10111yescharacteristic
407C2×C32#41311yescharacteristic
408C3×D3—22no—
409C3×D3—41no—
410C24—31no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C22×C4—31no—
418C22×C4—31no—
419C22×C4—31no—
420C22×C4—31no—
421C22×C4—31no—
422C22×C4—32no—
423C22×C4—61no—
424C22×C4—61no—
425C22×C4—61no—
426C22×C4—61no—
427C22×C4D3×Dic312yes—
428C22×C4C2×D3211yescharacteristic
429M16—32no—
430M16—61no—
431M16—61no—
432M16—61no—
433M16—92no—
434M16—184no—
435M16—181no—
436M16—181no—
437M16—181no—
438C2×C8—61no—
439C2×C8—61no—
440C2×C8—184no—
441C2×C8—181no—
442C2×C8—181no—
443C4⋊C4—62no—
444C4⋊C4—62no—
445C4⋊C4—61no—
446C4⋊C4—61no—
447C22⋊C4—62no—
448C22⋊C4—62no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—32no—
457C22×C3—41no—
458C22×C3—41no—
459C22×C3—61no—
460C22×C3—61no—
461C22×C3—61no—
462C22×C3—61no—
463C22×C3—61no—
464C22×C3—122no—
465C22×C3—122no—
466C22×C3D3×C22⋊C411yescharacteristic
467C22×C3#67⋊C411yescharacteristic
468C22×C3C4×#6711yescharacteristic
469C22×C3D4×Dic311yescharacteristic
470C22×C3D4×Dic311yescharacteristic
471C22×C3C2×#21711yescharacteristic
472C2×D3—21no—
473C2×D3—21no—
474C2×D3—21no—
475C2×D3—21no—
476C2×D3—21no—
477C2×D3—42no—
478C2×D3—42no—
479C2×D3#83612yescomplemented
480C3×C4—21no—
481C3×C4—21no—
482C3×C4—21no—
483C3×C4—21no—
484C3×C4—44no—
485C3×C4—42no—
486C3×C4—42no—
487C3×C4—61no—
488C3×C4—61no—
489C3×C4—122no—
490C3×C4#88311yescharacteristic
491C3×C4#88411yescharacteristic
492C3×C4#93511yescharacteristic
493C3×C4#93711yescharacteristic
494C3×C4#93711yescharacteristic
495C3×C4#93811yescharacteristic
496C3×C4#93911yescharacteristic
497C3×C4#93911yescharacteristic
498Dic3—21no—
499Dic3—21no—
500Dic3—42no—
501C32#190111yescharacteristic, complemented, Sylow
502C23—31no—
503C23—31no—
504C23—62no—
505C23—61no—
506C23—61no—
507C23—121no—
508C23C2×D3×Dic311yescharacteristic
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—31no—
517C2×C4—31no—
518C2×C4—61no—
519C2×C4—61no—
520C2×C4—61no—
521C2×C4—61no—
522C2×C4—61no—
523C2×C4—61no—
524C2×C4—61no—
525C2×C4—61no—
526C2×C4—61no—
527C2×C4—61no—
528C2×C4—62no—
529C2×C4—122no—
530C2×C4#380411yescharacteristic
531C2×C4#380511yescharacteristic
532C2×C4D3×#6711yescharacteristic
533C2×C4D3×#6711yescharacteristic
534C2×C4D3×#6711yescharacteristic
535C2×C4#381111yescharacteristic
536C8—62no—
537C8—121no—
538C8—182no—
539C8—361no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—41no—
548C2×C3—41no—
549C2×C3—62no—
550C2×C3—121no—
551C2×C3D3×#10111yescharacteristic
552C2×C3#475111yescharacteristic
553C2×C3#495611yescharacteristic
554C2×C3#522011yescharacteristic
555C2×C3C2×#83611yescharacteristic
556C2×C3#523711yescharacteristic
557D3—22no—
558D3—41no—
559C22—21no—
560C22—21no—
561C22—32no—
562C22—61no—
563C22—61no—
564C22—61no—
565C22—61no—
566C22—61no—
567C22—122no—
568C22—122no—
569C22D3×#21711yescharacteristic
570C22Dic3×#6711yescharacteristic
571C22#67⋊Dic311yescharacteristic
572C4—42no—
573C4—61no—
574C4—61no—
575C4—122no—
576C4#6396911yescharacteristic
577C4#6397011yescharacteristic
578C4#6397111yescharacteristic
579C4#6398311yescharacteristic
580C3—21no—
581C3#7011511yescharacteristic, complemented
582C3#7169811yescharacteristic, complemented
583C2—21no—
584C2—21no—
585C2—62no—
586C2—121no—
587C2D3×#83611yescharacteristic
588C2#1059163711yescharacteristic
589C2#1059172111yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3×D3C2×C4
cosocleC22×C32×C4C23
hypercenterC22×Q8D32
hypocenterC32#1901
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. C2×#63663C2semidirect
4. C2×C3×#836C2semidirect
6. #10589167C2semidirect
7. #10589167C2semidirect
39. C2×#836D3semidirect
281. C2×C3×D3#101semidirect
479. C2×D3#836semidirect
501. C32#1901semidirect
581. C3#70115semidirect
582. C3#71698semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9462
C2×D3×#2082
C2×#636632
C2×C3×#8362
#105910692
#105891672
#716983
#701153