Finite Group Databasebeta

← #11787221

Subgroups — #11787221

Order 1152.

917 conjugacy classes of subgroups.

The subgroup lattice has 603 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596262C211yesmaximal, characteristic
2C22×C3×#208C211yesmaximal, characteristic, complemented
3C3×C4×#217C211yesmaximal, characteristic, complemented
4C2×#63570C212yesmaximal, complemented
5#10589162C212yesmaximal, complemented
6#71984—31nomaximal
7#69453—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C2×#3828C2211yescharacteristic
10#64162—21no—
11#64139C411yescharacteristic, complemented
12#64139C411yescharacteristic, complemented
13#64138—21no—
14C4×#638—21no—
15C4×#638—21no—
16#64135C2211yescharacteristic
17#64133C411yescharacteristic, complemented
18#64133C411yescharacteristic, complemented
19C2×C3×#217—21no—
20C2×C3×C4×Dic3C2212yes—
21C2×C3×#208—21no—
22C2×C3×#208—24no—
23C2×C3×#208C2212yes—
24C22×C3×C3⋊C8—21no—
25C3×C3⋊#95—21no—
26#63570—24no—
27C22×C3×M16—31no—
28#5791—31no—
29#5791—31no—
30#5791—61no—
31C22×#208D311yescharacteristic, complemented
32C3×C4×C22⋊C4—31no—
33C4×#217D311yescharacteristic, complemented
34C2×#825—32no—
35C2×#805—32no—
36#4555—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×#638—21no—
48C2×#638—21no—
49C2×#638—21no—
50#3828—22no—
51#3828—22no—
52C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
53C2×C4×C3⋊D3—21no—
54C2×#634C2×C411yescharacteristic
55C22×C3×Dic3—22no—
56#3757—21no—
57#3757—21no—
58#3757—21no—
59#3752—21no—
60#3752—21no—
61C4⋊(C3⋊Dic3)C2×C411yescharacteristic
62C4⋊(C3⋊Dic3)C2×C411yescharacteristic
63#3750—21no—
64#3750—21no—
65C4×C3⋊Dic3—21no—
66C3×#217—24no—
67C3×C4×Dic3—22no—
68C3×C4×Dic3—22no—
69C3×#208—24no—
70C3×#208—22no—
71C3×#208D414yescomplemented
72C2×C3×C3⋊C8—24no—
73C2×C3×C3⋊C8—22no—
74#1871—91noSylow
75C23×C3×C4—21no—
76C23×C3×C4C2×D311yescharacteristic
77C23×C3×C4C2×D311yescharacteristic
78C2×#235—31no—
79C2×#235—31no—
80C2×#235—61no—
81C2×C3×M16—32no—
82C2×C3×M16—64no—
83C2×C3×M16—61no—
84C22×C3×C8—61no—
85C2×C3×C22⋊C4—61no—
86C2×C3×C42—32no—
87#953—62no—
88#953—61no—
89#953—61no—
90C2×#217—21no—
91#930—31no—
92#930—31no—
93#930—31no—
94#930—31no—
95#930—61no—
96#930—61no—
97#929—62no—
98#929—61no—
99#929—61no—
100C4×#67—62no—
101C4×#67—62no—
102C4×#67—61no—
103C4×#67—61no—
104C4×#67—61no—
105C4×#67—61no—
106#926—31no—
107#926—31no—
108#926—61no—
109#924—31no—
110#924—31no—
111#924—31no—
112#924—31no—
113#924—61no—
114#924—61no—
115C2×C4×Dic3C2×D312yes—
116C2×#208—21no—
117C2×#208—24no—
118C2×#208C2×D312yes—
119C22×C3⋊C8—21no—
120C3×#95—61no—
121C3⋊#95—21no—
122#825—64no—
123#805—64no—
124C23×C32—22no—
125C23×C32—22no—
126C23×C32—41no—
127C23×C32C22⋊C411yescharacteristic
128C23×C32C22⋊C411yescharacteristic
129C23×C32C2×D411yescharacteristic
130C22×C3⋊D3—21no—
131C2×C32×C4—22no—
132C2×C32×C4—22no—
133C2×C32×C4—22no—
134C2×C32×C4—21no—
135C2×C32×C4—21no—
136C2×C32×C4—21no—
137C2×C32×C4—21no—
138C2×C32×C4C22⋊C411yescharacteristic
139C2×C32×C4C22⋊C411yescharacteristic
140C2×C32×C4C22×C411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D412yes—
143C2×C32×C4#4112yes—
144#638—42no—
145#638—42no—
146#638—42no—
147C2×C3⋊Dic3—21no—
148C2×C3⋊Dic3—21no—
149C2×C3⋊Dic3—21no—
150C4⋊(C3⋊D3)—22no—
151C4×C3⋊D3—41no—
152C4×C3⋊D3—41no—
153#634—22no—
154C2×C3×Dic3—24no—
155C2×C3×Dic3—42no—
156C2×C3×Dic3—42no—
157C3×C3⋊C8—24no—
158C22×M16—31no—
159#525—91no—
160C2×#104—92no—
161C4×C22⋊C4—31no—
162#339—92no—
163C24×C3—21no—
164C24×C3D1211yescharacteristic
165C24×C3#6711yescharacteristic
166C22×C3×C4—22no—
167C22×C3×C4—22no—
168C22×C3×C4—22no—
169C22×C3×C4—22no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—42no—
177C22×C3×C4—42no—
178C22×C3×C4—62no—
179C22×C3×C4C4×D311yescharacteristic
180C22×C3×C4C4×D311yescharacteristic
181C22×C3×C4C4×D311yescharacteristic
182C22×C3×C4C4×D311yescharacteristic
183C22×C3×C4D1211yescharacteristic
184C22×C3×C4D1211yescharacteristic
185C22×C3×C4D1211yescharacteristic
186C22×C3×C4#6711yescharacteristic
187C22×C3×C4#6711yescharacteristic
188C22×C3×C4#6711yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C2×#67—62no—
192C2×#67—62no—
193C2×#67—62no—
194C2×#67—61no—
195C2×#67—61no—
196C2×#67—61no—
197C2×#67—61no—
198C2×#67—61no—
199C2×#67—61no—
200C22×Dic3—22no—
201#235—62no—
202#235—62no—
203#235—62no—
204#235—62no—
205#235—122no—
206#235—122no—
207C2×D12—31no—
208C2×D12—31no—
209C2×D12—61no—
210C2×C4×D3—62no—
211C2×C4×D3—61no—
212C2×C4×D3—61no—
213C2×Dic6—31no—
214C2×Dic6—31no—
215C2×Dic6—61no—
216C3×M16—34no—
217C3×M16—64no—
218C3×M16—62no—
219C2×C3×C8—64no—
220C2×C3×C8—62no—
221C3×C22⋊C4—64no—
222C3×C42—62no—
223C3×C42—62no—
224#217—24no—
225#217—62no—
226#217—62no—
227#217—62no—
228#217—61no—
229#217—61no—
230#217—61no—
231#217—61no—
232#217—61no—
233#217—61no—
234(C2×D3)⋊C4—62no—
235(C2×D3)⋊C4—62no—
236(C2×D3)⋊C4—61no—
237(C2×D3)⋊C4—61no—
238(C2×D3)⋊C4—61no—
239(C2×D3)⋊C4—61no—
240C4⋊Dic3—31no—
241C4⋊Dic3—31no—
242C4⋊Dic3—31no—
243C4⋊Dic3—31no—
244C4⋊Dic3—61no—
245C4⋊Dic3—61no—
246Dic3⋊C4—62no—
247Dic3⋊C4—62no—
248Dic3⋊C4—61no—
249Dic3⋊C4—61no—
250Dic3⋊C4—61no—
251Dic3⋊C4—61no—
252C4×Dic3—22no—
253C4×Dic3—22no—
254C4×Dic3—62no—
255C4×Dic3—61no—
256C4×Dic3—61no—
257#208—24no—
258#208—22no—
259#208#6714yescomplemented
260C2×C3⋊C8—24no—
261C2×C3⋊C8—22no—
262C22×C32—21no—
263C22×C32—21no—
264C22×C32—21no—
265C22×C32—21no—
266C22×C32—21no—
267C22×C32—21no—
268C22×C32—21no—
269C22×C32—44no—
270C22×C32#10412yescomplemented
271C22×C32C2×C22⋊C411yescharacteristic
272C22×C32#12112yes—
273C2×C3⋊D3—41no—
274C2×C3⋊D3—41no—
275C2×C3⋊D3—41no—
276C32×C4—21no—
277C32×C4—21no—
278C32×C4C4×D412yes—
279C32×C4#12011yescharacteristic
280C32×C4#12311yescharacteristic
281C3⋊Dic3—41no—
282C3⋊Dic3—41no—
283C3⋊Dic3—41no—
284C3×Dic3—44no—
285C2×#41—91no—
286C23×C4D3211yescharacteristic
287C2×M16—32no—
288C2×M16—64no—
289C2×M16—61no—
290C22×C8—61no—
291#123—181no—
292C22⋊Q8—91no—
293C22⋊Q8—91no—
294#121—91no—
295#121—91no—
296#120—181no—
297C4×D4—181no—
298C4×D4—181no—
299#117—91no—
300C2×C22⋊C4—61no—
301C2×C42—32no—
302#104—184no—
303#95—61no—
304C23×C3—22no—
305C23×C3—22no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—21no—
309C23×C3—21no—
310C23×C3—21no—
311C23×C3—42no—
312C23×C3—42no—
313C23×C3—41no—
314C23×C3—41no—
315C23×C3—42no—
316C23×C3(C2×D3)⋊C411yescharacteristic
317C23×C3(C2×D3)⋊C411yescharacteristic
318C23×C3(C2×D3)⋊C411yescharacteristic
319C23×C3(C2×D3)⋊C411yescharacteristic
320C23×C3C2×D1211yescharacteristic
321C23×C3C2×#6711yescharacteristic
322C22×D3—62no—
323C22×D3—61no—
324C22×D3—61no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—22no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—22no—
345C2×C3×C4—42no—
346C2×C3×C4—42no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—41no—
351C2×C3×C4—42no—
352C2×C3×C4—64no—
353C2×C3×C4—122no—
354C2×C3×C4—122no—
355C2×C3×C4(C2×D3)⋊C411yescharacteristic
356C2×C3×C4(C2×D3)⋊C411yescharacteristic
357C2×C3×C4(C2×D3)⋊C411yescharacteristic
358C2×C3×C4(C2×D3)⋊C411yescharacteristic
359C2×C3×C4C2×C4×D311yescharacteristic
360C2×C3×C4C2×C4×D311yescharacteristic
361C2×C3×C4C2×D1211yescharacteristic
362C2×C3×C4#23512yes—
363C2×C3×C4D3×D412yes—
364C2×C3×C4#23712yes—
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C2×#6712yes—
367#67—124no—
368#67—124no—
369#67—122no—
370#67—122no—
371#67—124no—
372#67—122no—
373#67—122no—
374#67—122no—
375#67—122no—
376C2×Dic3—24no—
377C2×Dic3—42no—
378C2×Dic3—42no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—61no—
383C2×Dic3—61no—
384C2×Dic3—61no—
385C2×Dic3—61no—
386C2×Dic3—61no—
387C2×Dic3—61no—
388D12—62no—
389D12—62no—
390D12—122no—
391C4×D3—122no—
392C4×D3—122no—
393C4×D3—121no—
394C4×D3—121no—
395C4×D3—121no—
396C4×D3—121no—
397Dic6—62no—
398Dic6—62no—
399Dic6—122no—
400C3×C8—64no—
401C3⋊C8—24no—
402C2×C32—22no—
403C2×C32—22no—
404C2×C32—41no—
405C2×C32#38611yescharacteristic
406C2×C32C2×#10411yescharacteristic
407C2×C32#42111yescharacteristic
408C3⋊D3—81no—
409C24#62611yescharacteristic
410#41—182no—
411#41—182no—
412C2×Q8—91no—
413C2×D4—91no—
414C2×D4—181no—
415C2×D4—181no—
416C2×D4—181no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—62no—
420C22×C4—181no—
421C22×C4#62411yescharacteristic
422C22×C4#62411yescharacteristic
423C22×C4#62611yescharacteristic
424C22×C4#62611yescharacteristic
425C22×C4#62611yescharacteristic
426C22×C4C2×D3211yescharacteristic
427M16—34no—
428M16—64no—
429M16—62no—
430C2×C8—64no—
431C2×C8—62no—
432C4⋊C4—91no—
433C4⋊C4—91no—
434C4⋊C4—181no—
435C4⋊C4—181no—
436C22⋊C4—64no—
437C22⋊C4—181no—
438C22⋊C4—181no—
439C22⋊C4—181no—
440C22⋊C4—181no—
441C22⋊C4—181no—
442C42—62no—
443C42—62no—
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—21no—
453C22×C3—22no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—22no—
461C22×C3—21no—
462C22×C3—22no—
463C22×C3—41no—
464C22×C3—41no—
465C22×C3—41no—
466C22×C3—41no—
467C22×C3—41no—
468C22×C3—41no—
469C22×C3—44no—
470C22×C3—44no—
471C22×C3—48no—
472C22×C3#80512yescomplemented
473C22×C3#82512yescomplemented
474C22×C3C2×(C2×D3)⋊C411yescharacteristic
475C22×C3C2×(C2×D3)⋊C411yescharacteristic
476C22×C3#93012yes—
477C22×C3#93912yes—
478C2×D3—122no—
479C2×D3—122no—
480C2×D3—122no—
481C2×D3—121no—
482C2×D3—121no—
483C2×D3—121no—
484C2×D3—121no—
485C2×D3—121no—
486C2×D3—121no—
487C3×C4—21no—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—21no—
491C3×C4—22no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—41no—
495C3×C4—41no—
496C3×C4—124no—
497C3×C4#67⋊C412yes—
498C3×C4#88211yescharacteristic
499C3×C4#88611yescharacteristic
500C3×C4C4×#6712yes—
501C3×C4#92911yescharacteristic
502C3×C4#95311yescharacteristic
503Dic3—44no—
504Dic3—122no—
505Dic3—122no—
506Dic3—122no—
507Dic3—121no—
508Dic3—121no—
509Dic3—121no—
510Dic3—121no—
511Dic3—121no—
512Dic3—121no—
513C32#187111yescharacteristic, complemented, Sylow
514C23—22no—
515C23—22no—
516C23—41no—
517C23—181no—
518C23#372211yescharacteristic
519C23#372211yescharacteristic
520C23C2×#62611yescharacteristic
521Q8—182no—
522D4—182no—
523D4—362no—
524D4—362no—
525D4—362no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—64no—
534C2×C4—122no—
535C2×C4—122no—
536C2×C4—181no—
537C2×C4—181no—
538C2×C4—181no—
539C2×C4—361no—
540C2×C4—361no—
541C2×C4#372211yescharacteristic
542C2×C4#372211yescharacteristic
543C2×C4#380412yes—
544C2×C4C2×#62411yescharacteristic
545C2×C4C2×#62611yescharacteristic
546C2×C4D3×#6712yes—
547C8—64no—
548C2×C3—22no—
549C2×C3—22no—
550C2×C3—22no—
551C2×C3—22no—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—42no—
556C2×C3—42no—
557C2×C3—42no—
558C2×C3—41no—
559C2×C3—41no—
560C2×C3C2×#80511yescharacteristic
561C2×C3#495811yescharacteristic
562C2×C3#500511yescharacteristic
563C2×C3C2×#82511yescharacteristic
564C2×C3#513911yescharacteristic
565C2×C3#521311yescharacteristic
566D3—242no—
567D3—241no—
568D3—241no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—44no—
577C22—361no—
578C22—361no—
579C22—361no—
580C22#6357012yescomplemented
581C22C2×#372211yescharacteristic
582C22#6397812yes—
583C4—21no—
584C4—21no—
585C4—124no—
586C4—361no—
587C4—361no—
588C4—361no—
589C4#6395212yes—
590C4#6396611yescharacteristic
591C4#6397711yescharacteristic
592C3—21no—
593C3#6945311yescharacteristic, complemented
594C3#7198411yescharacteristic, complemented
595C2—22no—
596C2—22no—
597C2—41no—
598C2—721no—
599C2C2×#6357011yescharacteristic
600C2#1059111311yescharacteristic
601C2#1059171111yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radical#10596262C2
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
2. C22×C3×#208C2semidirect
3. C3×C4×#217C2semidirect
4. C2×#63570C2semidirect
5. #10589162C2semidirect
11. #64139C4semidirect
12. #64139C4semidirect
17. #64133C4semidirect
18. #64133C4semidirect
31. C22×#208D3semidirect
33. C4×#217D3semidirect
71. C3×#208D4semidirect
259. #208#67semidirect
270. C22×C32#104semidirect
472. C22×C3#805semidirect
473. C22×C3#825semidirect
513. C32#1871semidirect
580. C22#63570semidirect
593. C3#69453semidirect
594. C3#71984semidirect

Maximal subgroups

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

subgroupindex
#105962622
C22×C3×#2082
C3×C4×#2172
C2×#635702
#105891622
#719843
#694533