Finite Group Databasebeta

← #11808817

Subgroups — #11808817

Order 1152.

1225 conjugacy classes of subgroups.

The subgroup lattice has 583 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63898C211yesmaximal, characteristic
2C2×#63838C211yesmaximal, characteristic, complemented
3#10592347C211yesmaximal, characteristic, complemented
4C3×#4672C211yesmaximal, characteristic
5C3×#4659C211yesmaximal, characteristic, complemented
6#10591368C212yesmaximal, complemented
7#10591368C212yesmaximal, complemented
8#10591300C211yesmaximal, characteristic
9#10591299C212yesmaximal, complemented
10#10591293C212yesmaximal, complemented
11#10591225C211yesmaximal, characteristic, complemented
12#78131—31nomaximal
13#76893—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C22×#627C2211yescharacteristic
16C22×D3×Dic3C2212yes—
17C2×C4×C3⋊Dic3C2212yes—
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C3×(C2×D3)⋊C4C2212yes—
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×Dic3⋊C4C2211yescharacteristic
23C2×C3×Dic3⋊C4C2211yescharacteristic
24C2×#3724C2211yescharacteristic
25C2×(C2×D3)⋊Dic3C2212yes—
26C2×(C2×D3)⋊Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×Dic32C2211yescharacteristic
29C2×Dic32C2211yescharacteristic
30#63898—24no—
31#63838—24no—
32C32×#95C2211yescharacteristic
33#63658C2212yes—
34#63658C2211yescharacteristic
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×D4×Dic3—31no—
40C2×#893—31no—
41C2×#887—31no—
42C2×#887—31no—
43C3×#400—31no—
44C3×#394—31no—
45#5222—31no—
46#4991—31no—
47#4986—31no—
48#4985—31no—
49#4952—32no—
50#4947—32no—
51Dic3×C22⋊C4—32no—
52Dic3×C22⋊C4—32no—
53#4675—32no—
54#4673—32no—
55#4672D311yescharacteristic
56#4666—32no—
57#4666—32no—
58#4659D311yescharacteristic, complemented
59#4648—31no—
60#4648—31no—
61#4648—61no—
62C23×C3×D3C2312yes—
63C22×C32×C4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3C2312yes—
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3×Dic3C2311yescharacteristic
69C22×C3×Dic3C2311yescharacteristic
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C2×C3×D12—24no—
74C2×C3×D12—22no—
75C2×#627—22no—
76C2×#627—22no—
77C2×#627—22no—
78C2×D3×Dic3—24no—
79C2×D3×Dic3—24no—
80C2×D3×Dic3—24no—
81C4×C3⋊Dic3—24no—
82C4×C3⋊Dic3D414yes—
83C3×(C2×D3)⋊C4—24no—
84C3×(C2×D3)⋊C4—24no—
85C3×C4⋊Dic3—22no—
86C3×Dic3⋊C4—22no—
87C3×Dic3⋊C4—22no—
88#3724—22no—
89(C2×D3)⋊Dic3—24no—
90(C2×D3)⋊Dic3—24no—
91(C2×D3)⋊Dic3—24no—
92Dic32—22no—
93Dic32—22no—
94#2398—91noSylow
95C22×C3×D4—31no—
96C23×Dic3—32no—
97C22×D12C2×D311yescharacteristic
98C22×C4×D3—32no—
99C22×Dic6—31no—
100C22×Dic6—31no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C4⋊C4—31no—
103C2×C3×C4⋊C4—31no—
104C2×C3×C22⋊C4—32no—
105C2×C3×C22⋊C4—32no—
106C2×#217—32no—
107C2×#217—32no—
108C2×#217—32no—
109D4×Dic3—64no—
110C2×(C2×D3)⋊C4—32no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4C2×D312yes—
114C2×(C2×D3)⋊C4C2×D312yes—
115C2×C4⋊Dic3C2×D311yescharacteristic
116C2×Dic3⋊C4—31no—
117C2×Dic3⋊C4—31no—
118C2×Dic3⋊C4C2×D311yescharacteristic
119C2×Dic3⋊C4C2×D311yescharacteristic
120C2×C4×Dic3—31no—
121C2×C4×Dic3—31no—
122C2×C4×Dic3—32no—
123C2×C4×Dic3—32no—
124C2×C4×Dic3—31no—
125C2×C4×Dic3—31no—
126C2×C4×Dic3—31no—
127C2×C4×Dic3—31no—
128C2×C4×Dic3—61no—
129C2×C4×Dic3—62no—
130#893—64no—
131#887—64no—
132#887—64no—
133C3×#95—21no—
134C3×#95—32no—
135C3×#95—32no—
136C3×#95C2×D311yescharacteristic
137C3×#95C2×D311yescharacteristic
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—31no—
141C3⋊#95—31no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—62no—
147C3⋊#95—61no—
148C3⋊#95C2×D312yes—
149C3⋊#95C2×D312yes—
150C23×C32C2411yescharacteristic
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3—22no—
155C22×C3×D3—22no—
156C22×C3×D3—22no—
157C22×C3×D3#4114yes—
158C2×C32×C4—22no—
159C2×C32×C4—22no—
160C2×C32×C4—22no—
161C2×C32×C4—22no—
162C2×C32×C4C2×D412yes—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—21no—
165C2×C3⋊Dic3—21no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3C2×D412yes—
169C2×C3⋊Dic3C2×D412yes—
170C2×C3⋊Dic3#4114yes—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3#4112yes—
183C2×C3×Dic3#4112yes—
184C3×D12—28no—
185#627—28no—
186D3×Dic3—48no—
187C2×C4×Q8—91no—
188C2×C4×D4—91no—
189#400—31no—
190#400—91no—
191#397—92no—
192#394—31no—
193#394—91no—
194#393—92no—
195C4×C22⋊C4—92no—
196C4×C22⋊C4—92no—
197#376—91no—
198C24×C3—32no—
199C23×D3C22×D312yes—
200C2×C3×D4—64no—
201C2×C3×D4—62no—
202C22×C3×C4—22no—
203C22×C3×C4—21no—
204C22×C3×C4—31no—
205C22×C3×C4—31no—
206C22×C3×C4—32no—
207C22×C3×C4—31no—
208C22×C3×C4—31no—
209C22×C3×C4C22×D312yes—
210C22×C3×C4C22×D312yes—
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×Dic3—31no—
214C22×Dic3—31no—
215C22×Dic3—31no—
216C22×Dic3—31no—
217C22×Dic3—32no—
218C22×Dic3—32no—
219C22×Dic3—61no—
220C22×Dic3—61no—
221C22×Dic3—62no—
222C22×Dic3—64no—
223C22×Dic3—64no—
224C22×Dic3—64no—
225C22×Dic3C22×D312yes—
226C22×Dic3C22×D311yescharacteristic
227C22×Dic3C22×D311yescharacteristic
228C22×Dic3C22×D311yescharacteristic
229C22×Dic3C22×D311yescharacteristic
230C2×D12—24no—
231C2×D12—22no—
232C2×C4×D3—64no—
233C2×C4×D3—64no—
234C2×C4×D3—64no—
235C2×Dic6—62no—
236C2×Dic6—62no—
237C2×Dic6—62no—
238C2×Dic6—62no—
239C2×Dic6—62no—
240C2×Dic6—62no—
241C3×C4⋊C4—62no—
242C3×C4⋊C4—62no—
243C3×C4⋊C4—62no—
244C3×C22⋊C4—64no—
245C3×C22⋊C4—64no—
246#217—64no—
247#217—64no—
248#217—64no—
249(C2×D3)⋊C4—24no—
250(C2×D3)⋊C4—24no—
251(C2×D3)⋊C4—64no—
252(C2×D3)⋊C4—64no—
253(C2×D3)⋊C4—64no—
254C4⋊Dic3—22no—
255Dic3⋊C4—22no—
256Dic3⋊C4—22no—
257Dic3⋊C4—62no—
258Dic3⋊C4—62no—
259C4×Dic3—34no—
260C4×Dic3—34no—
261C4×Dic3—64no—
262C4×Dic3—62no—
263C4×Dic3—62no—
264C4×Dic3—62no—
265C4×Dic3—62no—
266C4×Dic3—64no—
267C4×Dic3—64no—
268C4×Dic3—68no—
269C22×C32C22×D411yescharacteristic
270C22×C32C2×#4112yes—
271C22×C32C2×#4111yescharacteristic
272C22×C32C2×#4111yescharacteristic
273C22×C32C2×#4112yes—
274C2×C3×D3—24no—
275C2×C3×D3—24no—
276C2×C3×D3—24no—
277C2×C3×D3—42no—
278C2×C3×D3—42no—
279C2×C3×D3—42no—
280C2×C3×D3—42no—
281C32×C4—22no—
282C32×C4—42no—
283C3⋊Dic3—22no—
284C3⋊Dic3—42no—
285C3⋊Dic3#12414yes—
286C3×Dic3—22no—
287C3×Dic3—22no—
288C3×Dic3—41no—
289C3×Dic3—41no—
290C3×Dic3—42no—
291C22×Q8—91no—
292C22×D4—31no—
293C23×C4—92no—
294C4×Q8—184no—
295C4×D4—184no—
296C2×C4⋊C4—31no—
297C2×C4⋊C4—31no—
298C2×C4⋊C4—31no—
299C2×C4⋊C4—91no—
300C2×C22⋊C4—32no—
301C2×C22⋊C4—32no—
302C2×C22⋊C4—92no—
303C2×C22⋊C4—92no—
304C2×C22⋊C4—92no—
305C2×C42—91no—
306C2×C42—91no—
307C2×C42—91no—
308C2×C42—92no—
309#95—32no—
310#95—32no—
311#95—92no—
312#95—92no—
313#95—92no—
314#95—91no—
315#95D3211yescharacteristic
316C23×C3—21no—
317C23×C3—34no—
318C23×C3—62no—
319C23×C3—62no—
320C23×C3—62no—
321C23×C3—62no—
322C23×C3—62no—
323C23×C3—62no—
324C23×C3C23×D311yescharacteristic
325C23×C3C23×D311yescharacteristic
326C22×D3—22no—
327C22×D3—22no—
328C22×D3—22no—
329C22×D3—22no—
330C22×D3—22no—
331C22×D3—22no—
332C22×D3#23714yes—
333C3×D4—68no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—24no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—32no—
345C2×C3×C4—32no—
346C2×C3×C4—42no—
347C2×C3×C4—42no—
348C2×C3×C4—42no—
349C2×C3×C4—61no—
350C2×C3×C4—61no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—61no—
354C2×C3×C4—61no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4D3×D412yes—
361C2×C3×C4D3×D412yes—
362C2×Dic3—21no—
363C2×Dic3—21no—
364C2×Dic3—21no—
365C2×Dic3—21no—
366C2×Dic3—21no—
367C2×Dic3—21no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—32no—
374C2×Dic3—32no—
375C2×Dic3—34no—
376C2×Dic3—34no—
377C2×Dic3—32no—
378C2×Dic3—32no—
379C2×Dic3—62no—
380C2×Dic3—64no—
381C2×Dic3—62no—
382C2×Dic3—61no—
383C2×Dic3—61no—
384C2×Dic3—61no—
385C2×Dic3—61no—
386C2×Dic3—64no—
387C2×Dic3—62no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—62no—
392C2×Dic3—62no—
393C2×Dic3—121no—
394C2×Dic3—121no—
395C2×Dic3—122no—
396C2×Dic3—122no—
397C2×Dic3—128no—
398C2×Dic3#23712yes—
399C2×Dic3#23912yes—
400D12—28no—
401C4×D3—128no—
402Dic6—68no—
403Dic6—68no—
404C2×C32#52511yescharacteristic
405C2×C32#52511yescharacteristic
406C2×C32C2×#12411yescharacteristic
407C2×C32#52912yes—
408C2×C32#52912yes—
409C3×D3—44no—
410C24—32no—
411C2×Q8—182no—
412C2×Q8—182no—
413C2×Q8—182no—
414C2×D4—64no—
415C2×D4—62no—
416C22×C4—31no—
417C22×C4—31no—
418C22×C4—32no—
419C22×C4—31no—
420C22×C4—31no—
421C22×C4—91no—
422C22×C4—91no—
423C22×C4—92no—
424C22×C4—184no—
425C22×C4—184no—
426C22×C4—184no—
427C22×C4C2×D3212yes—
428C22×C4C2×D3211yescharacteristic
429C4⋊C4—62no—
430C4⋊C4—62no—
431C4⋊C4—62no—
432C4⋊C4—182no—
433C22⋊C4—64no—
434C22⋊C4—64no—
435C22⋊C4—184no—
436C22⋊C4—184no—
437C22⋊C4—184no—
438C42—94no—
439C42—184no—
440C42—182no—
441C42—182no—
442C22×C3—21no—
443C22×C3—22no—
444C22×C3—22no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—64no—
448C22×C3—64no—
449C22×C3—64no—
450C22×C3—122no—
451C22×C3—122no—
452C22×C3—122no—
453C22×C3—122no—
454C22×C3C2×D3×D411yescharacteristic
455C22×C3C2×D3×D411yescharacteristic
456C22×C3C2×#23712yes—
457C22×C3C2×#23711yescharacteristic
458C22×C3C2×#23911yescharacteristic
459C22×C3D3×#4112yes—
460C22×C3D3×#4112yes—
461C22×C3D3×#4112yes—
462C22×C3D3×#4111yescharacteristic
463C22×C3D3×#4111yescharacteristic
464C2×D3—24no—
465C2×D3—24no—
466C2×D3—24no—
467C2×D3—42no—
468C2×D3—42no—
469C2×D3—42no—
470C2×D3—42no—
471C3×C4—22no—
472C3×C4—22no—
473C3×C4—42no—
474C3×C4—44no—
475C3×C4—42no—
476C3×C4—42no—
477C3×C4—62no—
478C3×C4—62no—
479C3×C4—121no—
480C3×C4—122no—
481C3×C4—121no—
482Dic3—22no—
483Dic3—22no—
484Dic3—34no—
485Dic3—34no—
486Dic3—41no—
487Dic3—42no—
488Dic3—41no—
489Dic3—64no—
490Dic3—62no—
491Dic3—62no—
492Dic3—122no—
493Dic3—124no—
494Dic3—122no—
495Dic3—122no—
496C32#239811yescharacteristic, complemented, Sylow
497C23—34no—
498C23—62no—
499C23—62no—
500C23—62no—
501C23—62no—
502C23—62no—
503C23—62no—
504C23C22×D3211yescharacteristic
505Q8—188no—
506D4—68no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—32no—
512C2×C4—32no—
513C2×C4—61no—
514C2×C4—61no—
515C2×C4—61no—
516C2×C4—61no—
517C2×C4—61no—
518C2×C4—61no—
519C2×C4—62no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—92no—
525C2×C4—94no—
526C2×C4—92no—
527C2×C4—181no—
528C2×C4—181no—
529C2×C4—182no—
530C2×C4—182no—
531C2×C4—182no—
532C2×C4—368no—
533C2×C4#380212yes—
534C2×C3—21no—
535C2×C3—22no—
536C2×C3—21no—
537C2×C3—22no—
538C2×C3—21no—
539C2×C3—124no—
540C2×C3#558611yescharacteristic
541C2×C3#560012yes—
542C2×C3#560611yescharacteristic
543C2×C3#562711yescharacteristic
544C2×C3#564912yes—
545C2×C3#565611yescharacteristic
546C2×C3D3×#12411yescharacteristic
547C2×C3D3×#12411yescharacteristic
548C2×C3#569112yes—
549C2×C3#570612yes—
550D3—44no—
551C22—64no—
552C22—64no—
553C22—64no—
554C22—122no—
555C22—122no—
556C22—122no—
557C22—122no—
558C22C2×#380211yescharacteristic
559C22#6430612yes—
560C22D3×#23712yes—
561C22D3×#23711yescharacteristic
562C22D3×#23911yescharacteristic
563C4—22no—
564C4—42no—
565C4—62no—
566C4—62no—
567C4—94no—
568C4—121no—
569C4—121no—
570C4—122no—
571C4—182no—
572C4—362no—
573C3—21no—
574C3#7689311yescharacteristic, complemented
575C3#7813111yescharacteristic, complemented
576C2—124no—
577C2#1059400911yescharacteristic
578C2#1059408211yescharacteristic
579C2#1059411212yes—
580C2#1059444112yes—
581C2#1059463211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC22×C3×D12C22
hypercenter#95D32
hypocenterC32#2398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#63838C2semidirect
3. #10592347C2semidirect
5. C3×#4659C2semidirect
6. #10591368C2semidirect
7. #10591368C2semidirect
9. #10591299C2semidirect
10. #10591293C2semidirect
11. #10591225C2semidirect
58. #4659D3semidirect
496. C32#2398semidirect
574. C3#76893semidirect
575. C3#78131semidirect

Maximal subgroups

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

subgroupindex
C2×#638982
C2×#638382
#105923472
C3×#46722
C3×#46592
#105913682
#105913002
#105912992
#105912932
#105912252
#781313
#768933