Finite Group Databasebeta

← #11787220

Subgroups — #11787220

Order 1152.

901 conjugacy classes of subgroups.

The subgroup lattice has 567 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3748C211yesmaximal, characteristic, complemented
2C3×#5791C211yesmaximal, characteristic
3C3×C4×#217C211yesmaximal, characteristic, complemented
4C2×#63569C212yesmaximal, complemented
5#10589161C212yesmaximal, complemented
6#71713—31nomaximal
7#69453—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C2×C3×#235C2211yescharacteristic
10C2×#3748—21no—
11C2×#3748—24no—
12C2×#3748C2212yes—
13C22×C3⋊(C3⋊C8)—21no—
14C3×#953—21no—
15C2×C3×#217—21no—
16C3×#930C411yescharacteristic, complemented
17C3×#930C411yescharacteristic, complemented
18C3×#929—21no—
19C3×C4×#67—21no—
20C3×C4×#67—21no—
21C3×#926C2211yescharacteristic
22C3×#924C411yescharacteristic, complemented
23C3×#924C411yescharacteristic, complemented
24C2×C3×C4×Dic3C2212yes—
25C3×C3⋊#95—21no—
26#63569—24no—
27C3×#525—31no—
28#5791D311yescharacteristic
29C22×#208—31no—
30C22×#208—31no—
31C22×#208—61no—
32C3×C4×C22⋊C4—31no—
33C2×#837—32no—
34C4×#217D311yescharacteristic, complemented
35C2×#805—32no—
36#4532—32no—
37#4523—32no—
38C24×C32D411yescharacteristic
39C22×C32×C4—22no—
40C22×C32×C4—22no—
41C22×C32×C4C2×C411yescharacteristic
42C22×C32×C4C2×C411yescharacteristic
43C22×C32×C4D411yescharacteristic
44C22×C32×C4D411yescharacteristic
45C22×C32×C4D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C2×C3×#67—21no—
48C2×C3×#67—21no—
49C2×C3×#67—21no—
50C22×C3×Dic3—22no—
51C3×#235—22no—
52C3×#235—22no—
53C2×C3×D12C2×C411yescharacteristic
54C2×C3×C4×D3—21no—
55C2×C3×Dic6C2×C411yescharacteristic
56#3748—24no—
57#3748—22no—
58#3748D414yescomplemented
59C2×C3⋊(C3⋊C8)—24no—
60C2×C3⋊(C3⋊C8)—22no—
61C3×#217—24no—
62C3×#217—21no—
63C3×#217—21no—
64C3×#217—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×(C2×D3)⋊C4—21no—
67C3×C4⋊Dic3C2×C411yescharacteristic
68C3×C4⋊Dic3C2×C411yescharacteristic
69C3×Dic3⋊C4—21no—
70C3×Dic3⋊C4—21no—
71C3×C4×Dic3—21no—
72C3×C4×Dic3—22no—
73C3×C4×Dic3—22no—
74#1871—91noSylow
75C2×C3×#41—31no—
76C23×C3×C4—21no—
77C23×C3×C4C2×D311yescharacteristic
78C23×C3×C4C2×D311yescharacteristic
79C2×#235C2×D311yescharacteristic
80C3×#123—61no—
81C3×C22⋊Q8—31no—
82C3×C22⋊Q8—31no—
83C3×#121—31no—
84C3×#121—31no—
85C3×#120—61no—
86C3×C4×D4—61no—
87C3×C4×D4—61no—
88C3×#117—31no—
89C2×C3×C22⋊C4—61no—
90C2×C3×C42—32no—
91#953—21no—
92C2×#217—21no—
93#930Dic311yescharacteristic, complemented
94#930Dic311yescharacteristic, complemented
95#929—21no—
96C4×#67—21no—
97C4×#67—21no—
98#926C2×D311yescharacteristic
99#924Dic311yescharacteristic, complemented
100#924Dic311yescharacteristic, complemented
101C2×C4×Dic3C2×D312yes—
102C2×#208—32no—
103C2×#208—32no—
104C2×#208—62no—
105C2×#208—64no—
106C2×#208—64no—
107C2×#208—68no—
108C2×#208—62no—
109C2×#208—61no—
110C2×#208—61no—
111C22×C3⋊C8—62no—
112C22×C3⋊C8—61no—
113C22×C3⋊C8—61no—
114C3×#95—61no—
115#837—64no—
116C3⋊#95—21no—
117#805—64no—
118C23×C32—22no—
119C23×C32—22no—
120C23×C32—41no—
121C23×C32C22⋊C411yescharacteristic
122C23×C32C22⋊C411yescharacteristic
123C23×C32C2×D411yescharacteristic
124C22×C3×D3—21no—
125C2×C32×C4—22no—
126C2×C32×C4—22no—
127C2×C32×C4—22no—
128C2×C32×C4—21no—
129C2×C32×C4—21no—
130C2×C32×C4—21no—
131C2×C32×C4—21no—
132C2×C32×C4C22⋊C411yescharacteristic
133C2×C32×C4C22⋊C411yescharacteristic
134C2×C32×C4C22×C411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D412yes—
137C2×C32×C4#4112yes—
138C3×#67—42no—
139C3×#67—42no—
140C3×#67—42no—
141C2×C3×Dic3—24no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—42no—
146C2×C3×Dic3—42no—
147C3×D12—22no—
148C3×C4×D3—41no—
149C3×C4×D3—41no—
150C3×Dic6—22no—
151C3⋊(C3⋊C8)—24no—
152C22×M16—91no—
153#525—31no—
154C2×#104—92no—
155C4×C22⋊C4—31no—
156#339—92no—
157C24×C3—21no—
158C24×C3#6711yescharacteristic
159C24×C3#6711yescharacteristic
160C3×#41—62no—
161C3×#41—62no—
162C2×C3×Q8—31no—
163C2×C3×D4—31no—
164C2×C3×D4—61no—
165C2×C3×D4—61no—
166C2×C3×D4—61no—
167C22×C3×C4—24no—
168C22×C3×C4—24no—
169C22×C3×C4—22no—
170C22×C3×C4—22no—
171C22×C3×C4—22no—
172C22×C3×C4—22no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—62no—
180C22×C3×C4—61no—
181C22×C3×C4C4×D311yescharacteristic
182C22×C3×C4C4×D311yescharacteristic
183C22×C3×C4D1211yescharacteristic
184C22×C3×C4D1211yescharacteristic
185C22×C3×C4C2×Dic311yescharacteristic
186C22×C3×C4C2×Dic311yescharacteristic
187C22×C3×C4#6711yescharacteristic
188C22×C3×C4#6711yescharacteristic
189C22×C3×C4#6711yescharacteristic
190C22×C3×C4#6711yescharacteristic
191C22×C3×C4C22×D311yescharacteristic
192C22×C3×C4C22×D311yescharacteristic
193C2×#67—21no—
194C2×#67—21no—
195C2×#67—21no—
196C22×Dic3—22no—
197#235—22no—
198#235—22no—
199C2×D12C2×Dic311yescharacteristic
200C2×C4×D3—21no—
201C2×Dic6C2×Dic311yescharacteristic
202C3×C4⋊C4—31no—
203C3×C4⋊C4—31no—
204C3×C4⋊C4—61no—
205C3×C4⋊C4—61no—
206C3×C22⋊C4—64no—
207C3×C22⋊C4—61no—
208C3×C22⋊C4—61no—
209C3×C22⋊C4—61no—
210C3×C22⋊C4—61no—
211C3×C22⋊C4—61no—
212C3×C42—61no—
213C3×C42—62no—
214C3×C42—62no—
215#217—24no—
216#217—21no—
217#217—21no—
218#217—21no—
219(C2×D3)⋊C4—21no—
220(C2×D3)⋊C4—21no—
221C4⋊Dic3C2×Dic311yescharacteristic
222C4⋊Dic3C2×Dic311yescharacteristic
223Dic3⋊C4—21no—
224Dic3⋊C4—21no—
225C4×Dic3—21no—
226C4×Dic3—22no—
227C4×Dic3—22no—
228#208—34no—
229#208—34no—
230#208—64no—
231#208—68no—
232#208—64no—
233#208—64no—
234#208—64no—
235#208—62no—
236#208—62no—
237C2×C3⋊C8—68no—
238C2×C3⋊C8—64no—
239C2×C3⋊C8—64no—
240C2×C3⋊C8—64no—
241C2×C3⋊C8—62no—
242C2×C3⋊C8—62no—
243C22×C32—21no—
244C22×C32—21no—
245C22×C32—21no—
246C22×C32—21no—
247C22×C32—21no—
248C22×C32—21no—
249C22×C32—21no—
250C22×C32—44no—
251C22×C32#10412yescomplemented
252C22×C32C2×C22⋊C411yescharacteristic
253C22×C32#12112yes—
254C2×C3×D3—41no—
255C2×C3×D3—41no—
256C2×C3×D3—41no—
257C32×C4—21no—
258C32×C4—21no—
259C32×C4C4×D412yes—
260C32×C4#12011yescharacteristic
261C32×C4#12311yescharacteristic
262C3×Dic3—44no—
263C3×Dic3—41no—
264C3×Dic3—41no—
265C3×Dic3—41no—
266C2×#41—31no—
267C23×C4D3211yescharacteristic
268C2×M16—92no—
269C2×M16—184no—
270C2×M16—181no—
271C22×C8—181no—
272#123—61no—
273C22⋊Q8—31no—
274C22⋊Q8—31no—
275#121—31no—
276#121—31no—
277#120—61no—
278C4×D4—61no—
279C4×D4—61no—
280#117—31no—
281C2×C22⋊C4—61no—
282C2×C42—32no—
283#104—184no—
284#95—61no—
285C23×C3—24no—
286C23×C3—22no—
287C23×C3—22no—
288C23×C3—22no—
289C23×C3—22no—
290C23×C3—21no—
291C23×C3—21no—
292C23×C3—21no—
293C23×C3—42no—
294C23×C3—41no—
295C23×C3—41no—
296C23×C3—42no—
297C23×C3—61no—
298C23×C3(C2×D3)⋊C411yescharacteristic
299C23×C3(C2×D3)⋊C411yescharacteristic
300C23×C3#21711yescharacteristic
301C23×C3#21711yescharacteristic
302C23×C3C2×#6711yescharacteristic
303C23×C3C2×#6711yescharacteristic
304C22×D3—21no—
305C3×Q8—62no—
306C3×D4—62no—
307C3×D4—122no—
308C3×D4—122no—
309C3×D4—122no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—24no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—24no—
316C2×C3×C4—24no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—22no—
335C2×C3×C4—21no—
336C2×C3×C4—22no—
337C2×C3×C4—64no—
338C2×C3×C4—61no—
339C2×C3×C4—61no—
340C2×C3×C4—61no—
341C2×C3×C4—122no—
342C2×C3×C4—122no—
343C2×C3×C4—121no—
344C2×C3×C4—121no—
345C2×C3×C4(C2×D3)⋊C411yescharacteristic
346C2×C3×C4(C2×D3)⋊C411yescharacteristic
347C2×C3×C4#21711yescharacteristic
348C2×C3×C4#21711yescharacteristic
349C2×C3×C4C2×C4×D311yescharacteristic
350C2×C3×C4C2×D1211yescharacteristic
351C2×C3×C4D3×D412yes—
352C2×C3×C4D3×D412yes—
353C2×C3×C4#23712yes—
354C2×C3×C4#23712yes—
355C2×C3×C4C22×Dic311yescharacteristic
356C2×C3×C4C2×#6711yescharacteristic
357#67—42no—
358#67—42no—
359#67—42no—
360C2×Dic3—24no—
361C2×Dic3—21no—
362C2×Dic3—21no—
363C2×Dic3—21no—
364C2×Dic3—42no—
365C2×Dic3—42no—
366D12—22no—
367C4×D3—41no—
368C4×D3—41no—
369Dic6—22no—
370C3⋊C8—68no—
371C3⋊C8—64no—
372C3⋊C8—64no—
373C2×C32—22no—
374C2×C32—22no—
375C2×C32—41no—
376C2×C32#38611yescharacteristic
377C2×C32C2×#10411yescharacteristic
378C2×C32#42111yescharacteristic
379C3×D3—81no—
380C24#62511yescharacteristic
381#41—62no—
382#41—62no—
383C2×Q8—31no—
384C2×D4—31no—
385C2×D4—61no—
386C2×D4—61no—
387C2×D4—61no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—62no—
391C22×C4—61no—
392C22×C4D3×Dic311yescharacteristic
393C22×C4D3×Dic311yescharacteristic
394C22×C4#62511yescharacteristic
395C22×C4#62611yescharacteristic
396C22×C4#62611yescharacteristic
397C22×C4C2×D3211yescharacteristic
398M16—94no—
399M16—184no—
400M16—182no—
401C2×C8—184no—
402C2×C8—182no—
403C4⋊C4—31no—
404C4⋊C4—31no—
405C4⋊C4—61no—
406C4⋊C4—61no—
407C22⋊C4—64no—
408C22⋊C4—61no—
409C22⋊C4—61no—
410C22⋊C4—61no—
411C22⋊C4—61no—
412C22⋊C4—61no—
413C42—61no—
414C42—62no—
415C42—62no—
416C22×C3—22no—
417C22×C3—22no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—22no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—22no—
434C22×C3—21no—
435C22×C3—22no—
436C22×C3—41no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—44no—
441C22×C3—44no—
442C22×C3—48no—
443C22×C3—121no—
444C22×C3—121no—
445C22×C3—121no—
446C22×C3#80512yescomplemented
447C22×C3#83712yescomplemented
448C22×C3C2×(C2×D3)⋊C411yescharacteristic
449C22×C3#93912yes—
450C22×C3#93912yes—
451C22×C3C2×#21711yescharacteristic
452C2×D3—41no—
453C2×D3—41no—
454C2×D3—41no—
455C3×C4—22no—
456C3×C4—22no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—22no—
463C3×C4—21no—
464C3×C4—124no—
465C3×C4—121no—
466C3×C4—121no—
467C3×C4—121no—
468C3×C4#67⋊C412yes—
469C3×C4#88211yescharacteristic
470C3×C4#88611yescharacteristic
471C3×C4D4×Dic312yes—
472C3×C4#93511yescharacteristic
473C3×C4#93711yescharacteristic
474Dic3—44no—
475Dic3—41no—
476Dic3—41no—
477Dic3—41no—
478C32#187111yescharacteristic, complemented, Sylow
479C23—22no—
480C23—22no—
481C23—41no—
482C23—61no—
483C23(C2×D3)⋊Dic311yescharacteristic
484C23(C2×D3)⋊Dic311yescharacteristic
485C23C2×#62511yescharacteristic
486Q8—62no—
487D4—62no—
488D4—122no—
489D4—122no—
490D4—122no—
491C2×C4—22no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—64no—
499C2×C4—61no—
500C2×C4—61no—
501C2×C4—61no—
502C2×C4—122no—
503C2×C4—122no—
504C2×C4—121no—
505C2×C4—121no—
506C2×C4(C2×D3)⋊Dic311yescharacteristic
507C2×C4(C2×D3)⋊Dic311yescharacteristic
508C2×C4C2×D3×Dic311yescharacteristic
509C2×C4#380512yes—
510C2×C4C2×#62611yescharacteristic
511C2×C4#381112yes—
512C8—184no—
513C2×C3—24no—
514C2×C3—22no—
515C2×C3—22no—
516C2×C3—22no—
517C2×C3—22no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—42no—
522C2×C3—42no—
523C2×C3—41no—
524C2×C3—41no—
525C2×C3—241no—
526C2×C3C2×#80511yescharacteristic
527C2×C3#495811yescharacteristic
528C2×C3#500511yescharacteristic
529C2×C3#522011yescharacteristic
530C2×C3C2×#83711yescharacteristic
531C2×C3#523611yescharacteristic
532D3—81no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—44no—
541C22—121no—
542C22—121no—
543C22—121no—
544C22#6356912yescomplemented
545C22C2×(C2×D3)⋊Dic311yescharacteristic
546C22#6398012yes—
547C4—21no—
548C4—21no—
549C4—124no—
550C4—121no—
551C4—121no—
552C4—121no—
553C4#6396211yescharacteristic
554C4#67⋊Dic312yes—
555C4#6398111yescharacteristic
556C3—21no—
557C3#6945311yescharacteristic, complemented
558C3#7171311yescharacteristic, complemented
559C2—22no—
560C2—22no—
561C2—41no—
562C2—241no—
563C2C2×#6356911yescharacteristic
564C2#1059111111yescharacteristic
565C2#1059171311yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#5791C2
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1871
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3748C2semidirect
3. C3×C4×#217C2semidirect
4. C2×#63569C2semidirect
5. #10589161C2semidirect
16. C3×#930C4semidirect
17. C3×#930C4semidirect
22. C3×#924C4semidirect
23. C3×#924C4semidirect
34. C4×#217D3semidirect
58. #3748D4semidirect
93. #930Dic3semidirect
94. #930Dic3semidirect
99. #924Dic3semidirect
100. #924Dic3semidirect
251. C22×C32#104semidirect
446. C22×C3#805semidirect
447. C22×C3#837semidirect
478. C32#1871semidirect
544. C22#63569semidirect
557. C3#69453semidirect
558. C3#71713semidirect

Maximal subgroups

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

subgroupindex
C22×#37482
C3×#57912
C3×C4×#2172
C2×#635692
#105891612
#717133
#694533