Finite Group Databasebeta

← #11785857

Subgroups — #11785857

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×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
3#10591069C211yesmaximal, characteristic
4#10589389C211yesmaximal, characteristic, complemented
5C3×#4523C211yesmaximal, characteristic, complemented
6#10589162C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#69442—31nomaximal
9#68754—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4—21no—
15C3×#926C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18D3×#217—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×C3⋊#95—21no—
27(C2×D3)⋊(C3⋊C8)—21no—
28(C2×D3)⋊(C3⋊C8)—21no—
29C2×#926—31no—
30D3×#117—31no—
31C3×C4×C22⋊C4—31no—
32#5207—31no—
33#5126—31no—
34C4×(C2×D3)⋊C4D311yescharacteristic
35C3×#339—31no—
36#4555—31no—
37#4532—31no—
38#4523—31no—
39#4523—31no—
40#4523—31no—
41#4523—31no—
42#4523—61no—
43#4523D311yescharacteristic, complemented
44C23×C3×D3D411yescharacteristic
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
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×C42—21no—
60C32×C42—21no—
61#3757—21no—
62C4⋊(C3⋊Dic3)C2×C411yescharacteristic
63C4⋊(C3⋊Dic3)C2×C411yescharacteristic
64C4×C3⋊Dic3—21no—
65#3748—21no—
66#3748—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C3×#217—21no—
69C3×(C2×D3)⋊C4—24no—
70C3×C4⋊Dic3C2×C411yescharacteristic
71C3×C4⋊Dic3C2×C411yescharacteristic
72C3×C4×Dic3—21no—
73C3×C4×Dic3—21no—
74C3×C4×Dic3—21no—
75C3×#208—21no—
76C3×#208—21no—
77C2×C3×C3⋊C8—21no—
78Dic3⋊Dic3—21no—
79Dic3⋊Dic3—21no—
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—31no—
88C3×#117—31no—
89C2×C3×C22⋊C4—61no—
90C2×C3×C42—21no—
91C2×C3×C42—31no—
92C2×C3×C42C2×D311yescharacteristic
93C2×C3×C42C2×D311yescharacteristic
94C2×#217—61no—
95C2×(C2×D3)⋊C4—21no—
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—61no—
107C2×C4×Dic3C2×D311yescharacteristic
108C2×#208—31no—
109C2×#208—31no—
110C2×#208—61no—
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×#95—61no—
121C3⋊#95—21no—
122#830—61no—
123#830—61no—
124(C2×D3)⋊C8—61no—
125(C2×D3)⋊C8—61no—
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×C4—22no—
134C2×C32×C4—41no—
135C2×C32×C4—41no—
136C2×C32×C4C22×C411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4#4111yescharacteristic
139C2×C32×C4#4111yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3—21no—
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—
163C3⋊(C3⋊C8)—41no—
164C3×C3⋊C8—41no—
165C2×#117—91no—
166#407—91no—
167C4×C22⋊C4—31no—
168#339—31no—
169#339—91no—
170#339—91no—
171#339—91no—
172C24×C3—31no—
173C23×D3#6711yescharacteristic
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—31no—
178C22×C3×C4—31no—
179C22×C3×C4—31no—
180C22×C3×C4—31no—
181C22×C3×C4—31no—
182C22×C3×C4—41no—
183C22×C3×C4—61no—
184C22×C3×C4—61no—
185C22×C3×C4—61no—
186C22×C3×C4—61no—
187C22×C3×C4—61no—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C22×Dic3—21no—
191C22×Dic3—61no—
192C22×Dic3—61no—
193C22×Dic3#6711yescharacteristic
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×D3D1211yescharacteristic
203C2×C4×D3D1211yescharacteristic
204C3×M16—61no—
205C3×M16—61no—
206C2×C3×C8—61no—
207C3×C4⋊C4—31no—
208C3×C4⋊C4—31no—
209C3×C22⋊C4—64no—
210C3×C22⋊C4—61no—
211C3×C42—22no—
212C3×C42—21no—
213C3×C42—21no—
214C3×C42—21no—
215C3×C42—21no—
216C3×C42—41no—
217C3×C42—61no—
218C3×C42—61no—
219C3×C42—61no—
220#217—21no—
221#217—61no—
222#217—61no—
223#217—61no—
224#217—61no—
225#217—121no—
226(C2×D3)⋊C4—24no—
227(C2×D3)⋊C4—61no—
228(C2×D3)⋊C4—61no—
229C4⋊Dic3—31no—
230C4⋊Dic3—31no—
231C4⋊Dic3—31no—
232C4⋊Dic3—31no—
233C4⋊Dic3—61no—
234C4⋊Dic3—61no—
235C4⋊Dic3—61no—
236C4⋊Dic3—61no—
237C4⋊Dic3C4×D311yescharacteristic
238C4⋊Dic3C4×D311yescharacteristic
239Dic3⋊C4—61no—
240Dic3⋊C4—61no—
241C4×Dic3—21no—
242C4×Dic3—21no—
243C4×Dic3—21no—
244C4×Dic3—61no—
245C4×Dic3—61no—
246C4×Dic3—61no—
247C4×Dic3—61no—
248C4×Dic3—61no—
249C4×Dic3—61no—
250C4×Dic3—121no—
251#208—21no—
252#208—21no—
253#208—62no—
254#208—61no—
255#208—61no—
256#208—61no—
257#208—61no—
258#208—121no—
259C2×C3⋊C8—21no—
260C2×C3⋊C8—61no—
261C2×C3⋊C8—61no—
262C2×C3⋊C8—121no—
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—42no—
277C32×C4#11711yescharacteristic
278C32×C4#11711yescharacteristic
279C32×C4#12311yescharacteristic
280C32×C4#12311yescharacteristic
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×M16—91no—
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—61no—
300C2×C22⋊C4—181no—
301C2×C42—31no—
302C2×C42—181no—
303C2×C42D3211yescharacteristic
304C22⋊C8—181no—
305C22⋊C8—181no—
306#95—61no—
307C23×C3—21no—
308C23×C3—31no—
309C23×C3—31no—
310C23×C3—62no—
311C23×C3—61no—
312C23×C3—61no—
313C23×C3—121no—
314C23×C3D3×D411yescharacteristic
315C23×C3C2×#6711yescharacteristic
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—22no—
323C2×C3×C4—22no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—31no—
331C2×C3×C4—31no—
332C2×C3×C4—42no—
333C2×C3×C4—42no—
334C2×C3×C4—41no—
335C2×C3×C4—41no—
336C2×C3×C4—42no—
337C2×C3×C4—41no—
338C2×C3×C4—41no—
339C2×C3×C4—61no—
340C2×C3×C4—61no—
341C2×C3×C4—61no—
342C2×C3×C4—61no—
343C2×C3×C4—61no—
344C2×C3×C4—61no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—61no—
348C2×C3×C4—61no—
349C2×C3×C4—62no—
350C2×C3×C4—61no—
351C2×C3×C4—61no—
352C2×C3×C4—121no—
353C2×C3×C4—121no—
354C2×C3×C4C2×C4×D311yescharacteristic
355C2×C3×C4C2×C4×D311yescharacteristic
356C2×C3×C4C2×D1211yescharacteristic
357C2×C3×C4#23511yescharacteristic
358C2×C3×C4#23511yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4#23711yescharacteristic
361C2×C3×C4#23711yescharacteristic
362C2×C3×C4#23711yescharacteristic
363C2×C3×C4#23711yescharacteristic
364C2×C3×C4#23711yescharacteristic
365C2×C3×C4#23911yescharacteristic
366C2×Dic3—21no—
367C2×Dic3—21no—
368C2×Dic3—22no—
369C2×Dic3—21no—
370C2×Dic3—21no—
371C2×Dic3—41no—
372C2×Dic3—41no—
373C2×Dic3—61no—
374C2×Dic3—61no—
375C2×Dic3—61no—
376C2×Dic3—61no—
377C2×Dic3—121no—
378C2×Dic3—121no—
379C2×Dic3—122no—
380C2×Dic3—122no—
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—121no—
394C3⋊C8—41no—
395C3⋊C8—122no—
396C3⋊C8—121no—
397C3⋊C8—121no—
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—21no—
407C22×C4—31no—
408C22×C4—31no—
409C22×C4—31no—
410C22×C4—31no—
411C22×C4—31no—
412C22×C4—61no—
413C22×C4—61no—
414C22×C4—61no—
415C22×C4—61no—
416C22×C4—61no—
417C22×C4—181no—
418C22×C4—181no—
419C22×C4C2×D3211yescharacteristic
420M16—61no—
421M16—61no—
422M16—181no—
423M16—181no—
424C2×C8—61no—
425C2×C8—181no—
426C4⋊C4—31no—
427C4⋊C4—31no—
428C4⋊C4—91no—
429C4⋊C4—91no—
430C4⋊C4—181no—
431C4⋊C4—181no—
432C22⋊C4—64no—
433C22⋊C4—61no—
434C22⋊C4—181no—
435C22⋊C4—181no—
436C22⋊C4—181no—
437C42—21no—
438C42—21no—
439C42—61no—
440C42—61no—
441C42—61no—
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#89411yescharacteristic
465C22×C3C2×(C2×D3)⋊C411yescharacteristic
466C22×C3#93511yescharacteristic
467C22×C3#93511yescharacteristic
468C2×D3—21no—
469C2×D3—21no—
470C2×D3—21no—
471C2×D3—21no—
472C2×D3—21no—
473C2×D3—42no—
474C2×D3—42no—
475C2×D3#80512yes—
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—21no—
479C3×C4—21no—
480C3×C4—42no—
481C3×C4—42no—
482C3×C4—44no—
483C3×C4—61no—
484C3×C4—61no—
485C3×C4—122no—
486C3×C4—121no—
487C3×C4—121no—
488C3×C4#87211yescharacteristic
489C3×C4#87711yescharacteristic
490C3×C4#87711yescharacteristic
491C3×C4#88311yescharacteristic
492C3×C4#88611yescharacteristic
493C3×C4#88611yescharacteristic
494C3×C4#89211yescharacteristic
495C3×C4#89411yescharacteristic
496Dic3—21no—
497Dic3—21no—
498Dic3—42no—
499Dic3—41no—
500Dic3—41no—
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×#6711yescharacteristic
515C2×C4—22no—
516C2×C4—31no—
517C2×C4—31no—
518C2×C4—41no—
519C2×C4—41no—
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—61no—
529C2×C4—61no—
530C2×C4—62no—
531C2×C4—61no—
532C2×C4—61no—
533C2×C4—121no—
534C2×C4—121no—
535C2×C4—181no—
536C2×C4—181no—
537C2×C4—362no—
538C2×C4—362no—
539C2×C4#379511yescharacteristic
540C2×C4#379611yescharacteristic
541C2×C4C4×D3211yescharacteristic
542C2×C4D3×D1211yescharacteristic
543C2×C4#380411yescharacteristic
544C2×C4#380511yescharacteristic
545C8—121no—
546C8—361no—
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×C3C2×#80511yescharacteristic
562C2×C3#494311yescharacteristic
563C2×C3#500511yescharacteristic
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#6388411yescharacteristic
577C22D3×(C2×D3)⋊C411yescharacteristic
578C22#6396911yescharacteristic
579C4—42no—
580C4—61no—
581C4—61no—
582C4—122no—
583C4—121no—
584C4—121no—
585C4—361no—
586C4—361no—
587C4#6387711yescharacteristic
588C4#6387811yescharacteristic
589C4#6389011yescharacteristic
590C4#6389111yescharacteristic
591C3—21no—
592C3#6875411yescharacteristic, complemented
593C3#6944211yescharacteristic, complemented
594C2—21no—
595C2—21no—
596C2—62no—
597C2—121no—
598C2D3×#80511yescharacteristic
599C2#1059039211yescharacteristic
600C2#1059136211yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3×D3D4
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1826
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. #10589389C2semidirect
5. C3×#4523C2semidirect
6. #10589162C2semidirect
7. #10589161C2semidirect
20. D3×C4⋊Dic3C4semidirect
21. D3×C4⋊Dic3C4semidirect
24. #63841C4semidirect
25. #63841C4semidirect
43. #4523D3semidirect
507. C32#1826semidirect
592. C3#68754semidirect
593. C3#69442semidirect

Maximal subgroups

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

subgroupindex
D3×#9262
C3×C4×(C2×D3)⋊C42
#105910692
#105893892
C3×#45232
#105891622
#105891612
#694423
#687543