Finite Group Databasebeta

← #11785850

Subgroups — #11785850

Order 1152.

667 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#926C211yesmaximal, characteristic
2C3×#5126C211yesmaximal, characteristic
3C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic
4#10589421C211yesmaximal, characteristic, complemented
5C3×#4555C211yesmaximal, characteristic, complemented
6#10589162C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#69975—31nomaximal
9#68754—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17D3×#217—21no—
18C2×(C2×D3)⋊Dic3—21no—
19#63955—21no—
20D3×C4⋊Dic3C411yescharacteristic, complemented
21D3×C4⋊Dic3C411yescharacteristic, complemented
22C4×D3×Dic3—21no—
23#63855—21no—
24#63841C411yescharacteristic, complemented
25#63841C411yescharacteristic, complemented
26C3×(C2×D3)⋊C8—21no—
27C3×(C2×D3)⋊C8—21no—
28#63579—21no—
29C2×#926—31no—
30D3×#117—31no—
31C3×#407—31no—
32C4×#217—31no—
33#5126D311yescharacteristic
34C4×(C2×D3)⋊C4—31no—
35C3×#339—31no—
36#4555—31no—
37#4555—31no—
38#4555—31no—
39#4555—31no—
40#4555—61no—
41#4555D311yescharacteristic, complemented
42#4532—31no—
43#4523—31no—
44C23×C3×D3D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3D411yescharacteristic
49C2×C3×C4×D3—21no—
50C2×C3×C4×D3—21no—
51C2×C3×C4×D3—21no—
52C2×C3×C4×D3—21no—
53C2×C3×C4×D3C2×C411yescharacteristic
54C2×C3×C4×D3C2×C411yescharacteristic
55C2×C3×C4×D3D411yescharacteristic
56C2×C3×C4×D3D411yescharacteristic
57C2×D3×Dic3—21no—
58C2×D3×Dic3—21no—
59C32×M16—21no—
60C32×M16—21no—
61C2×C32×C8—21no—
62#3757—21no—
63C4⋊(C3⋊Dic3)C2×C411yescharacteristic
64C4⋊(C3⋊Dic3)C2×C411yescharacteristic
65C4×C3⋊Dic3—21no—
66C4×C3⋊Dic3—21no—
67C4×C3⋊Dic3—21no—
68C3×#217—21no—
69C3×C4⋊Dic3C2×C411yescharacteristic
70C3×C4⋊Dic3C2×C411yescharacteristic
71C3×C4×Dic3—21no—
72C3×C4×Dic3—21no—
73C3×C4×Dic3—21no—
74C3×#208—21no—
75C3×#208—21no—
76C2×C3×C3⋊C8—21no—
77Dic3⋊Dic3—21no—
78Dic3⋊Dic3—21no—
79(C2×D3)⋊Dic3—24no—
80(C2×D3)⋊Dic3—21no—
81(C2×D3)⋊Dic3—21no—
82Dic32—21no—
83Dic32—21no—
84#1826—91noSylow
85C23×C3×C4—31no—
86C22×C4×D3C2×D311yescharacteristic
87C2×C3×M16—21no—
88C2×C3×M16—31no—
89C2×C3×M16C2×D311yescharacteristic
90C2×C3×M16C2×D311yescharacteristic
91C3×#117—31no—
92C2×C3×C42—31no—
93C2×#217—61no—
94C2×#217—61no—
95C2×(C2×D3)⋊C4—61no—
96#926—31no—
97#926—31no—
98#926—31no—
99#926—31no—
100#926—61no—
101#926—61no—
102#926—61no—
103#926C2×D311yescharacteristic
104C2×C4⋊Dic3—31no—
105C2×C4⋊Dic3—31no—
106C2×C4×Dic3—31no—
107C2×C4×Dic3—31no—
108C2×C4×Dic3—61no—
109C2×C4×Dic3—61no—
110C2×C4×Dic3C2×D311yescharacteristic
111C2×#208C2×D311yescharacteristic
112#892—31no—
113#892—31no—
114D3×C4⋊C4—31no—
115D3×C4⋊C4—31no—
116D3×C22⋊C4—61no—
117#877—61no—
118#872—61no—
119C42×D3—61no—
120C3×C22⋊C8—61no—
121C3×C22⋊C8—61no—
122C3⋊#95—61no—
123C3⋊#95—61no—
124(C2×D3)⋊C8—21no—
125(C2×D3)⋊C8—21no—
126C23×C32C2×D411yescharacteristic
127C22×C3×D3—21no—
128C22×C3×D3—21no—
129C22×C3×D3—22no—
130C22×C3×D3—41no—
131C22×C3×D3C22⋊C411yescharacteristic
132C22×C3×D3C22⋊C411yescharacteristic
133C2×C32×C4C22×C411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C2×C32×C4#4111yescharacteristic
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—21no—
141C2×C3⋊Dic3—21no—
142C2×C3⋊Dic3—41no—
143C2×C3⋊Dic3—41no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3C22⋊C411yescharacteristic
152C2×C3×Dic3C22⋊C411yescharacteristic
153C3×C4×D3—21no—
154C3×C4×D3—21no—
155C3×C4×D3—21no—
156C3×C4×D3—21no—
157C3×C4×D3—21no—
158C3×C4×D3—21no—
159C3×C4×D3—21no—
160C3×C4×D3—21no—
161D3×Dic3—42no—
162D3×Dic3—42no—
163C32×C8—41no—
164C3×C3⋊C8—41no—
165C2×#117—91no—
166#407—31no—
167C4×C22⋊C4—91no—
168#339—31no—
169#339—91no—
170#339—91no—
171#339—91no—
172C24×C3—31no—
173C23×D3D1211yescharacteristic
174C22×C3×C4—21no—
175C22×C3×C4—31no—
176C22×C3×C4—31no—
177C22×C3×C4—31no—
178C22×C3×C4—31no—
179C22×C3×C4—31no—
180C22×C3×C4—61no—
181C22×C3×C4—61no—
182C22×C3×C4—61no—
183C22×C3×C4—61no—
184C22×C3×C4—61no—
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C22×Dic3—21no—
188C22×Dic3—61no—
189C22×Dic3—61no—
190C22×Dic3—61no—
191C22×Dic3—61no—
192C22×Dic3—121no—
193C22×Dic3D1211yescharacteristic
194C2×C4×D3—21no—
195C2×C4×D3—21no—
196C2×C4×D3—21no—
197C2×C4×D3—21no—
198C2×C4×D3—61no—
199C2×C4×D3—61no—
200C2×C4×D3C4×D311yescharacteristic
201C2×C4×D3C4×D311yescharacteristic
202C2×C4×D3#6711yescharacteristic
203C2×C4×D3#6711yescharacteristic
204C3×M16—22no—
205C3×M16—21no—
206C3×M16—21no—
207C3×M16—21no—
208C3×M16—21no—
209C3×M16—41no—
210C3×M16—61no—
211C3×M16—61no—
212C2×C3×C8—21no—
213C2×C3×C8—21no—
214C2×C3×C8—41no—
215C2×C3×C8—61no—
216C3×C4⋊C4—31no—
217C3×C4⋊C4—31no—
218C3×C22⋊C4—61no—
219C3×C42—61no—
220C3×C42—61no—
221C3×C42—61no—
222#217—21no—
223#217—61no—
224#217—61no—
225#217—64no—
226#217—61no—
227#217—61no—
228#217—121no—
229(C2×D3)⋊C4—64no—
230(C2×D3)⋊C4—61no—
231(C2×D3)⋊C4—61no—
232C4⋊Dic3—31no—
233C4⋊Dic3—31no—
234C4⋊Dic3—31no—
235C4⋊Dic3—31no—
236C4⋊Dic3—61no—
237C4⋊Dic3—61no—
238C4⋊Dic3—61no—
239C4⋊Dic3—61no—
240C4⋊Dic3C4×D311yescharacteristic
241C4⋊Dic3C4×D311yescharacteristic
242Dic3⋊C4—61no—
243Dic3⋊C4—61no—
244C4×Dic3—21no—
245C4×Dic3—21no—
246C4×Dic3—21no—
247C4×Dic3—61no—
248C4×Dic3—61no—
249C4×Dic3—61no—
250C4×Dic3—61no—
251C4×Dic3—61no—
252C4×Dic3—61no—
253C4×Dic3—62no—
254C4×Dic3—61no—
255C4×Dic3—61no—
256C4×Dic3—61no—
257C4×Dic3—61no—
258C4×Dic3—121no—
259C4×Dic3—121no—
260#208—21no—
261#208—21no—
262C2×C3⋊C8—21no—
263C22×C32—21no—
264C22×C32—21no—
265C22×C32C2×C22⋊C411yescharacteristic
266C22×C32#12311yescharacteristic
267C22×C32#12311yescharacteristic
268C2×C3×D3—21no—
269C2×C3×D3—21no—
270C2×C3×D3—21no—
271C2×C3×D3—21no—
272C2×C3×D3—21no—
273C2×C3×D3—42no—
274C2×C3×D3—42no—
275C2×C3×D3#10412yes—
276C32×C4#11711yescharacteristic
277C32×C4#11711yescharacteristic
278C32×C4#12311yescharacteristic
279C32×C4#12311yescharacteristic
280C3⋊Dic3—42no—
281C3⋊Dic3—41no—
282C3⋊Dic3—41no—
283C3×Dic3—21no—
284C3×Dic3—21no—
285C3×Dic3—42no—
286C3×Dic3—41no—
287C3×Dic3—41no—
288C23×C4—31no—
289C2×M16—31no—
290C2×M16D3211yescharacteristic
291#117—31no—
292#117—91no—
293#117—91no—
294#117—91no—
295#117—181no—
296#117—181no—
297C2×C4⋊C4—91no—
298C2×C4⋊C4—91no—
299C2×C22⋊C4—181no—
300C2×C22⋊C4—181no—
301C2×C42—31no—
302C2×C42—91no—
303C2×C42—181no—
304C22⋊C8—61no—
305C22⋊C8—61no—
306#95—181no—
307C23×C3—21no—
308C23×C3—31no—
309C23×C3—31no—
310C23×C3—62no—
311C23×C3—61no—
312C23×C3—61no—
313C23×C3—121no—
314C23×C3C2×D1211yescharacteristic
315C23×C3D3×D411yescharacteristic
316C22×D3—21no—
317C22×D3—21no—
318C22×D3—22no—
319C22×D3—41no—
320C22×D3(C2×D3)⋊C411yescharacteristic
321C22×D3(C2×D3)⋊C411yescharacteristic
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—31no—
329C2×C3×C4—31no—
330C2×C3×C4—61no—
331C2×C3×C4—61no—
332C2×C3×C4—61no—
333C2×C3×C4—61no—
334C2×C3×C4—61no—
335C2×C3×C4—61no—
336C2×C3×C4—61no—
337C2×C3×C4—61no—
338C2×C3×C4—61no—
339C2×C3×C4—61no—
340C2×C3×C4—62no—
341C2×C3×C4—61no—
342C2×C3×C4—61no—
343C2×C3×C4—121no—
344C2×C3×C4—121no—
345C2×C3×C4C2×C4×D311yescharacteristic
346C2×C3×C4C2×C4×D311yescharacteristic
347C2×C3×C4#23511yescharacteristic
348C2×C3×C4#23511yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4#23711yescharacteristic
351C2×C3×C4#23711yescharacteristic
352C2×C3×C4#23711yescharacteristic
353C2×C3×C4#23711yescharacteristic
354C2×C3×C4#23711yescharacteristic
355C2×C3×C4#23911yescharacteristic
356C2×C3×C4C2×#6711yescharacteristic
357C2×Dic3—21no—
358C2×Dic3—21no—
359C2×Dic3—22no—
360C2×Dic3—21no—
361C2×Dic3—21no—
362C2×Dic3—41no—
363C2×Dic3—41no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—122no—
371C2×Dic3—121no—
372C2×Dic3—121no—
373C2×Dic3—122no—
374C2×Dic3—122no—
375C2×Dic3—122no—
376C2×Dic3—121no—
377C2×Dic3—121no—
378C2×Dic3—122no—
379C2×Dic3—121no—
380C2×Dic3—121no—
381C2×Dic3(C2×D3)⋊C411yescharacteristic
382C2×Dic3(C2×D3)⋊C411yescharacteristic
383C4×D3—21no—
384C4×D3—21no—
385C4×D3—21no—
386C4×D3—21no—
387C4×D3—21no—
388C4×D3—21no—
389C4×D3—21no—
390C4×D3—21no—
391C4×D3—122no—
392C4×D3—122no—
393C3×C8—42no—
394C3×C8—41no—
395C3×C8—41no—
396C3×C8—121no—
397C3⋊C8—41no—
398C2×C32—21no—
399C2×C32—21no—
400C2×C32#38111yescharacteristic
401C2×C32C2×#10411yescharacteristic
402C2×C32#42111yescharacteristic
403C3×D3—22no—
404C3×D3—41no—
405C24—31no—
406C22×C4—31no—
407C22×C4—31no—
408C22×C4—31no—
409C22×C4—31no—
410C22×C4—31no—
411C22×C4—61no—
412C22×C4—61no—
413C22×C4—61no—
414C22×C4—61no—
415C22×C4—61no—
416C22×C4—181no—
417C22×C4—181no—
418C22×C4—181no—
419C22×C4C2×D3211yescharacteristic
420M16—21no—
421M16—21no—
422M16—61no—
423M16—61no—
424C2×C8—21no—
425C2×C8—61no—
426C4⋊C4—31no—
427C4⋊C4—31no—
428C4⋊C4—91no—
429C4⋊C4—91no—
430C4⋊C4—181no—
431C4⋊C4—181no—
432C22⋊C4—61no—
433C22⋊C4—181no—
434C22⋊C4—181no—
435C22⋊C4—184no—
436C22⋊C4—181no—
437C42—61no—
438C42—61no—
439C42—61no—
440C42—181no—
441C42—181no—
442C42—181no—
443C42—181no—
444C42—181no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—32no—
453C22×C3—41no—
454C22×C3—41no—
455C22×C3—61no—
456C22×C3—61no—
457C22×C3—61no—
458C22×C3—61no—
459C22×C3—61no—
460C22×C3—122no—
461C22×C3—122no—
462C22×C3D3×C22⋊C411yescharacteristic
463C22×C3#88311yescharacteristic
464C22×C3#88611yescharacteristic
465C22×C3#88611yescharacteristic
466C22×C3#89411yescharacteristic
467C22×C3C2×(C2×D3)⋊C411yescharacteristic
468C2×D3—21no—
469C2×D3—21no—
470C2×D3—21no—
471C2×D3—21no—
472C2×D3—21no—
473C2×D3—42no—
474C2×D3—42no—
475C2×D3#82512yes—
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—21no—
479C3×C4—21no—
480C3×C4—61no—
481C3×C4—61no—
482C3×C4—122no—
483C3×C4—121no—
484C3×C4—121no—
485C3×C4#87211yescharacteristic
486C3×C4#87711yescharacteristic
487C3×C4#87711yescharacteristic
488C3×C4#88311yescharacteristic
489C3×C4#89211yescharacteristic
490C3×C4#89411yescharacteristic
491C3×C4#93511yescharacteristic
492C3×C4#93511yescharacteristic
493Dic3—21no—
494Dic3—21no—
495Dic3—42no—
496Dic3—41no—
497Dic3—41no—
498Dic3—122no—
499Dic3—122no—
500Dic3—124no—
501Dic3—121no—
502Dic3—121no—
503Dic3—121no—
504Dic3—121no—
505Dic3—241no—
506Dic3—241no—
507C32#182611yescharacteristic, complemented, Sylow
508C23—31no—
509C23—31no—
510C23—62no—
511C23—61no—
512C23—61no—
513C23—121no—
514C23D3×D1211yescharacteristic
515C2×C4—31no—
516C2×C4—31no—
517C2×C4—61no—
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—62no—
528C2×C4—61no—
529C2×C4—61no—
530C2×C4—121no—
531C2×C4—121no—
532C2×C4—182no—
533C2×C4—181no—
534C2×C4—181no—
535C2×C4—362no—
536C2×C4—362no—
537C2×C4—361no—
538C2×C4—361no—
539C2×C4#379511yescharacteristic
540C2×C4#379611yescharacteristic
541C2×C4C4×D3211yescharacteristic
542C2×C4#380411yescharacteristic
543C2×C4#380511yescharacteristic
544C2×C4D3×#6711yescharacteristic
545C8—41no—
546C8—121no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—41no—
555C2×C3—41no—
556C2×C3—62no—
557C2×C3—121no—
558C2×C3#466411yescharacteristic
559C2×C3D3×#10411yescharacteristic
560C2×C3#482111yescharacteristic
561C2×C3#494311yescharacteristic
562C2×C3C2×#82511yescharacteristic
563C2×C3#513911yescharacteristic
564D3—22no—
565D3—41no—
566C22—21no—
567C22—21no—
568C22—32no—
569C22—61no—
570C22—61no—
571C22—61no—
572C22—61no—
573C22—61no—
574C22—122no—
575C22—122no—
576C22#6389011yescharacteristic
577C22#6389111yescharacteristic
578C22D3×(C2×D3)⋊C411yescharacteristic
579C4—61no—
580C4—61no—
581C4—122no—
582C4—121no—
583C4—121no—
584C4—362no—
585C4—361no—
586C4—361no—
587C4#6387711yescharacteristic
588C4#6387811yescharacteristic
589C4#6388411yescharacteristic
590C4#6396911yescharacteristic
591C3—21no—
592C3#6875411yescharacteristic, complemented
593C3#6997511yescharacteristic, complemented
594C2—21no—
595C2—21no—
596C2—62no—
597C2—121no—
598C2D3×#82511yescharacteristic
599C2#1059100511yescharacteristic
600C2#1059136211yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3×D3D4
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1826
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. #10589421C2semidirect
5. C3×#4555C2semidirect
6. #10589162C2semidirect
7. #10589160C2semidirect
20. D3×C4⋊Dic3C4semidirect
21. D3×C4⋊Dic3C4semidirect
24. #63841C4semidirect
25. #63841C4semidirect
41. #4555D3semidirect
507. C32#1826semidirect
592. C3#68754semidirect
593. C3#69975semidirect

Maximal subgroups

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

subgroupindex
D3×#9262
C3×#51262
C4×(C2×D3)⋊Dic32
#105894212
C3×#45552
#105891622
#105891602
#699753
#687543