Finite Group Databasebeta

← #11803372

Subgroups — #11803372

Order 1152.

1477 conjugacy classes of subgroups.

The subgroup lattice has 577 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64090C211yesmaximal, characteristic
2C2×#63975C211yesmaximal, characteristic
3C2×#63883C211yesmaximal, characteristic, complemented
4C3×#4945C212yesmaximal, complemented
5#10591722C211yesmaximal, characteristic
6#10591719C212yesmaximal, complemented
7#10591375C211yesmaximal, characteristic, complemented
8#10591371C211yesmaximal, characteristic, complemented
9#10591335C212yesmaximal, complemented
10#10591330C212yesmaximal, complemented
11C4×#3722C211yesmaximal, characteristic, complemented
12#75828—32nomaximal
13C22×#638C2211yescharacteristic
14C23×C3⋊Dic3C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×#624C2211yescharacteristic
17C22×#624C2211yescharacteristic
18C2×C32×C22⋊C4C2211yescharacteristic
19C2×#3752C2211yescharacteristic
20C2×#3750C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22#64090—24no—
23C2×C3×#217C2212yes—
24C2×C3×#217C2212yes—
25C2×C3×Dic3⋊C4C2212yes—
26C2×C3×C4×Dic3C2212yes—
27#63975C418yescomplemented
28C2×Dic3⋊Dic3C2212yes—
29C2×Dic3⋊Dic3C2212yes—
30C2×Dic3⋊Dic3C2212yes—
31C2×#3722C2211yescharacteristic
32C2×#3722C2211yescharacteristic
33#63883—24no—
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×D3×C4⋊C4—32no—
40C2×#883—32no—
41C2×#67⋊C4—32no—
42C2×#67⋊C4—61no—
43C3×#388—32no—
44#4976—32no—
45#4956—32no—
46#4950—32no—
47#4946—32no—
48#4945D312yescomplemented
49C4×(C2×D3)⋊C4—32no—
50#4928—32no—
51#4668—32no—
52#4664—32no—
53#4655—32no—
54#4654—32no—
55C24×C32C2311yescharacteristic
56C23×C3⋊D3C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C2×#638—22no—
60C2×#638—22no—
61C2×#638C2×C414yes—
62C22×C3⋊Dic3—22no—
63C22×C3⋊Dic3—42no—
64C22×C3⋊Dic3C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C2×C4×C3⋊D3—42no—
68C2×C4×C3⋊D3D414yes—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C2×#624—22no—
74C2×#624—22no—
75C2×#624—22no—
76C2×#624—42no—
77C2×#624C2×C414yescomplemented
78C32×C22⋊C4—22no—
79#3752—22no—
80#3750—22no—
81C4×C3⋊Dic3—22no—
82C3×#217—42no—
83C3×#217C2×C418yescomplemented
84C3×Dic3⋊C4—24no—
85C3×C4×Dic3—42no—
86Dic3⋊Dic3—24no—
87Dic3⋊Dic3—42no—
88Dic3⋊Dic3C2×C418yescomplemented
89#3722—22no—
90#3722C2×C414yescomplemented
91#2322—91noSylow
92C22×#67—32no—
93C22×#67—61no—
94C23×Dic3—32no—
95C23×Dic3—61no—
96C22×C4×D3—32no—
97C22×C4×D3—32no—
98C22×C4×D3—32no—
99C22×C4×D3—61no—
100C2×C3×C4⋊C4—32no—
101C2×C3×C22⋊C4—21no—
102C2×C3×C22⋊C4—32no—
103C2×C3×C22⋊C4—32no—
104C2×C3×C22⋊C4C2×D312yes—
105C2×C3×C42—32no—
106C2×#217C2×D312yes—
107C2×#217C2×D312yes—
108C2×(C2×D3)⋊C4—32no—
109C2×(C2×D3)⋊C4—32no—
110C2×(C2×D3)⋊C4—32no—
111C2×(C2×D3)⋊C4—61no—
112C2×C4⋊Dic3—32no—
113C2×C4⋊Dic3—32no—
114C2×C4⋊Dic3—32no—
115C2×Dic3⋊C4—32no—
116C2×Dic3⋊C4—32no—
117C2×Dic3⋊C4—32no—
118C2×Dic3⋊C4—32no—
119C2×Dic3⋊C4—61no—
120C2×Dic3⋊C4C2×D312yes—
121C2×C4×Dic3—32no—
122C2×C4×Dic3—61no—
123C2×C4×Dic3C2×D312yes—
124D3×C4⋊C4—68no—
125#883—316no—
126#67⋊C4—68no—
127#67⋊C4—68no—
128C3×#95—32no—
129C3×#95—32no—
130C3⋊#95—32no—
131C3⋊#95—32no—
132C3⋊#95—32no—
133C3⋊#95—32no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95C2×D312yes—
137C3⋊#95C2×D312yes—
138C23×C32—21no—
139C23×C32—21no—
140C23×C32—22no—
141C23×C32—22no—
142C23×C32C22×C412yes—
143C23×C32C2411yescharacteristic
144C22×C3⋊D3—22no—
145C22×C3⋊D3—22no—
146C22×C3⋊D3C22×C412yes—
147C22×C3⋊D3C2×D412yes—
148C22×C3⋊D3#4112yes—
149C2×C32×C4—21no—
150C2×C32×C4—22no—
151C2×C32×C4—22no—
152C2×C32×C4C2×D412yes—
153#638—28no—
154C2×C3⋊Dic3—21no—
155C2×C3⋊Dic3—21no—
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3—21no—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—44no—
160C2×C3⋊Dic3C22×C412yes—
161C2×C3⋊Dic3C2×D412yes—
162C4×C3⋊D3—44no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3C22×C414yes—
174C2×C3×Dic3C22×C414yes—
175#624—28no—
176#624—44no—
177C2×#123—91no—
178C2×C4×D4—91no—
179C22×C4⋊C4—91no—
180#389—92no—
181#388—32no—
182#387—92no—
183#386—91no—
184#385—91no—
185#385—92no—
186#381—91no—
187C4×C22⋊C4—91no—
188C24×C3—21no—
189C24×C3C22×D312yes—
190C23×D3—32no—
191C23×D3—61no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—32no—
195C22×C3×C4—32no—
196C22×C3×C4—32no—
197C22×C3×C4—32no—
198C22×C3×C4C22×D312yes—
199C22×C3×C4C22×D312yes—
200C2×#67—38no—
201C2×#67—64no—
202C2×#67—64no—
203C2×#67—64no—
204C2×#67—64no—
205C2×#67—64no—
206C22×Dic3—32no—
207C22×Dic3—32no—
208C22×Dic3—32no—
209C22×Dic3—61no—
210C22×Dic3—61no—
211C22×Dic3—61no—
212C22×Dic3—64no—
213C22×Dic3—64no—
214C22×Dic3—122no—
215C22×Dic3—122no—
216C22×Dic3—124no—
217C22×Dic3C22×D312yes—
218C22×Dic3C22×D312yes—
219C22×Dic3C22×D312yes—
220C22×Dic3C22×D312yes—
221C2×C4×D3—38no—
222C2×C4×D3—38no—
223C2×C4×D3—64no—
224C2×C4×D3—64no—
225C2×C4×D3—64no—
226C2×C4×D3—64no—
227C2×C4×D3—122no—
228C2×C4×D3—122no—
229C2×C4×D3—122no—
230C2×C4×D3—122no—
231C2×C4×D3—124no—
232C3×C4⋊C4—64no—
233C3×C22⋊C4—24no—
234C3×C22⋊C4—24no—
235C3×C22⋊C4—38no—
236C3×C22⋊C4—122no—
237C3×C42—122no—
238#217—42no—
239#217C4×D318yescomplemented
240(C2×D3)⋊C4—38no—
241(C2×D3)⋊C4—64no—
242(C2×D3)⋊C4—64no—
243(C2×D3)⋊C4—64no—
244C4⋊Dic3—38no—
245C4⋊Dic3—64no—
246C4⋊Dic3—122no—
247Dic3⋊C4—24no—
248Dic3⋊C4—38no—
249Dic3⋊C4—64no—
250Dic3⋊C4—64no—
251Dic3⋊C4—64no—
252Dic3⋊C4—122no—
253C4×Dic3—42no—
254C4×Dic3—64no—
255C4×Dic3—64no—
256C22×C32—22no—
257C22×C32—24no—
258C22×C32—41no—
259C22×C32—41no—
260C22×C32—42no—
261C22×C32C23×C411yescharacteristic
262C22×C32C22×D411yescharacteristic
263C22×C32C2×#4111yescharacteristic
264C22×C32H(5,𝔽2)12yes—
265C22×C322−1+412yes—
266C2×C3⋊D3—24no—
267C2×C3⋊D3—22no—
268C2×C3⋊D3—22no—
269C2×C3⋊D3—24no—
270C2×C3⋊D3C4×D414yes—
271C32×C4—22no—
272C32×C4—41no—
273C3⋊Dic3—22no—
274C3⋊Dic3—22no—
275C3⋊Dic3—41no—
276C3×Dic3—24no—
277C3×Dic3—24no—
278C3×Dic3—42no—
279C3×Dic3—42no—
280C22×D4—91no—
281C23×C4—91no—
282C23×C4—91no—
283C23×C4—91no—
284C23×C4—91no—
285#123—98no—
286C4×D4—184no—
287C2×C4⋊C4—32no—
288C2×C4⋊C4—92no—
289C2×C4⋊C4—92no—
290C2×C4⋊C4—91no—
291C2×C4⋊C4—92no—
292C2×C4⋊C4—184no—
293C2×C22⋊C4—32no—
294C2×C22⋊C4—32no—
295C2×C22⋊C4—91no—
296C2×C22⋊C4—91no—
297C2×C22⋊C4—91no—
298C2×C22⋊C4D3211yescharacteristic
299C2×C42—32no—
300C2×C42—91no—
301#95—32no—
302#95—32no—
303#95—92no—
304#95—92no—
305#95—92no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—22no—
309C23×C3—22no—
310C23×C3—22no—
311C23×C3—22no—
312C23×C3—22no—
313C23×C3—22no—
314C23×C3—21no—
315C23×C3—22no—
316C23×C3—42no—
317C23×C3—42no—
318C23×C3C2×C4×D314yes—
319C23×C3C23×D312yes—
320C22×D3—34no—
321C22×D3—34no—
322C22×D3—34no—
323C22×D3—62no—
324C22×D3—62no—
325C22×D3—62no—
326C22×D3—62no—
327C22×D3—62no—
328C22×D3—62no—
329C22×D3—62no—
330C22×D3—122no—
331C22×D3—122no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—34no—
340C2×C3×C4—34no—
341C2×C3×C4—42no—
342C2×C3×C4—42no—
343C2×C3×C4—62no—
344C2×C3×C4—62no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4D3×D414yes—
354#67—616no—
355#67—616no—
356C2×Dic3—22no—
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—34no—
367C2×Dic3—34no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—64no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—122no—
382C2×Dic3—128no—
383C2×Dic3—128no—
384C2×Dic3C2×C4×D314yes—
385C2×Dic3C2×C4×D314yes—
386C4×D3—616no—
387C4×D3—128no—
388C4×D3—128no—
389C4×D3—128no—
390C2×C32—42no—
391C2×C32C2×C4×D411yescharacteristic
392C2×C32#52012yes—
393C2×C32#53411yescharacteristic
394C2×C32#53611yescharacteristic
395C2×C32#53912yes—
396C3⋊D3—24no—
397C24—91no—
398C24C2×D3211yescharacteristic
399C2×D4—94no—
400C2×D4—182no—
401C2×D4—182no—
402C22×C4—32no—
403C22×C4—32no—
404C22×C4—32no—
405C22×C4—32no—
406C22×C4—94no—
407C22×C4—91no—
408C22×C4—91no—
409C22×C4—94no—
410C22×C4—91no—
411C22×C4—182no—
412C22×C4—182no—
413C22×C4—182no—
414C22×C4—182no—
415C22×C4—362no—
416C22×C4—362no—
417C22×C4—362no—
418C22×C4C2×D3211yescharacteristic
419C22×C4C2×D3211yescharacteristic
420C4⋊C4—64no—
421C4⋊C4—98no—
422C4⋊C4—184no—
423C4⋊C4—182no—
424C4⋊C4—362no—
425C22⋊C4—22no—
426C22⋊C4—38no—
427C22⋊C4—94no—
428C22⋊C4—122no—
429C22⋊C4—182no—
430C22⋊C4—182no—
431C42—122no—
432C42—182no—
433C22×C3—24no—
434C22×C3—24no—
435C22×C3—24no—
436C22×C3—24no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—22no—
440C22×C3—22no—
441C22×C3—21no—
442C22×C3—44no—
443C22×C3—42no—
444C22×C3—42no—
445C22×C3—44no—
446C22×C3—42no—
447C22×C3—42no—
448C22×C3—42no—
449C22×C3—42no—
450C22×C3C22×C4×D312yes—
451C22×C3C2×D3×D412yes—
452C22×C3#100412yes—
453C22×C3D3×#4112yes—
454C22×C3#100912yes—
455C22×C3#101012yes—
456C22×C3#101012yes—
457C2×D3—38no—
458C2×D3—64no—
459C2×D3—64no—
460C2×D3—64no—
461C2×D3—64no—
462C2×D3—64no—
463C2×D3—64no—
464C2×D3—64no—
465C2×D3—122no—
466C2×D3—124no—
467C2×D3—122no—
468C2×D3—124no—
469C3×C4—24no—
470C3×C4—42no—
471C3×C4—42no—
472C3×C4—42no—
473C3×C4—64no—
474C3×C4—64no—
475C3×C4—122no—
476C3×C4—122no—
477Dic3—24no—
478Dic3—24no—
479Dic3—42no—
480Dic3—42no—
481Dic3—64no—
482Dic3—64no—
483Dic3—64no—
484Dic3—64no—
485Dic3—122no—
486Dic3—122no—
487C32#232211yescharacteristic, complemented, Sylow
488C23—21no—
489C23—22no—
490C23—22no—
491C23—21no—
492C23—92no—
493C23—92no—
494C23—92no—
495C23—182no—
496C23—182no—
497C23C4×D3212yes—
498C23C22×D3211yescharacteristic
499D4—188no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—34no—
504C2×C4—34no—
505C2×C4—62no—
506C2×C4—62no—
507C2×C4—62no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—62no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—62no—
515C2×C4—92no—
516C2×C4—92no—
517C2×C4—188no—
518C2×C4—181no—
519C2×C4—182no—
520C2×C4—181no—
521C2×C4—182no—
522C2×C4—181no—
523C2×C4—364no—
524C2×C4—364no—
525C2×C4—364no—
526C2×C4#381112yes—
527C2×C3—22no—
528C2×C3—21no—
529C2×C3—22no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—44no—
533C2×C3—44no—
534C2×C3#552312yes—
535C2×C3C4×D3×D412yes—
536C2×C3#554612yes—
537C2×C3#560512yes—
538C2×C3#566012yes—
539C2×C3#567512yes—
540C2×C3#570712yes—
541D3—68no—
542D3—124no—
543C22—24no—
544C22—22no—
545C22—41no—
546C22—42no—
547C22—41no—
548C22—94no—
549C22—184no—
550C22—182no—
551C22—184no—
552C22—182no—
553C22C2×C4×D3211yescharacteristic
554C22#6430611yescharacteristic
555C22#6430912yes—
556C22#6431412yes—
557C22C2×#381111yescharacteristic
558C4—22no—
559C4—41no—
560C4—64no—
561C4—64no—
562C4—122no—
563C4—122no—
564C4—182no—
565C4—182no—
566C4—361no—
567C3—21no—
568C3#7582812yescomplemented
569C2—42no—
570C2—184no—
571C2#1059404912yes—
572C2#1059422712yes—
573C2C4×#381111yescharacteristic
574C2#1059517111yescharacteristic
575C2#1059530811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2322
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#63883C2semidirect
4. C3×#4945C2semidirect
6. #10591719C2semidirect
7. #10591375C2semidirect
8. #10591371C2semidirect
9. #10591335C2semidirect
10. #10591330C2semidirect
11. C4×#3722C2semidirect
27. #63975C4semidirect
48. #4945D3semidirect
77. C2×#624C2×C4semidirect
83. C3×#217C2×C4semidirect
88. Dic3⋊Dic3C2×C4semidirect
90. #3722C2×C4semidirect
239. #217C4×D3semidirect
487. C32#2322semidirect
568. C3#75828semidirect

Maximal subgroups

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

subgroupindex
C2×#640902
C2×#639752
C2×#638832
C3×#49452
#105917222
#105917192
#105913752
#105913712
#105913352
#105913302
C4×#37222
#758283