Finite Group Databasebeta

← #11808348

Subgroups — #11808348

Order 1152.

1549 conjugacy classes of subgroups.

The subgroup lattice has 597 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63900C211yesmaximal, characteristic
2C2×#63883C211yesmaximal, characteristic
3C2×#63883C211yesmaximal, characteristic
4C2×#63883C211yesmaximal, characteristic
5C3⋊D3×#95C211yesmaximal, characteristic
6C3×#4657C212yesmaximal, complemented
7#10591370C211yesmaximal, characteristic
8#10591370C211yesmaximal, characteristic
9#10591348C212yesmaximal, complemented
10#10591339C212yesmaximal, complemented
11#10591200C212yesmaximal, complemented
12D3×#398—32nomaximal
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×#624C2211yescharacteristic
17C22×#624C2211yescharacteristic
18C22×#624C2211yescharacteristic
19C22×#624C2211yescharacteristic
20C2×C3×C4⋊Dic3C2212yes—
21C2×C3×Dic3⋊C4C2212yes—
22C2×C3×Dic3⋊C4C2212yes—
23C2×C3×Dic3⋊C4C2212yes—
24C2×#3724C2212yes—
25C2×Dic3⋊Dic3C2212yes—
26C2×Dic3⋊Dic3C2212yes—
27C2×Dic3⋊Dic3C2212yes—
28#63900—24no—
29#63883—24no—
30#63883—24no—
31#63883—24no—
32C32×#95C2211yescharacteristic
33#63658C2211yescharacteristic
34#63658C2211yescharacteristic
35#63658C2211yescharacteristic
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×D3×C4⋊C4—32no—
41C2×D3×C4⋊C4—32no—
42C2×D3×C4⋊C4—32no—
43C2×D3×C4⋊C4—32no—
44C3×#398—32no—
45#4983—32no—
46#4982—32no—
47#4982—32no—
48#4981—32no—
49D3×#95—32no—
50D3×#95—32no—
51D3×#95—32no—
52D3×#95—61no—
53#4661—32no—
54#4657—32no—
55#4657D312yescomplemented
56C23×C3⋊D3C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3C2311yescharacteristic
61C22×C3⋊Dic3C2311yescharacteristic
62C22×C3⋊Dic3C2311yescharacteristic
63C2×C4×C3⋊D3—22no—
64C2×C4×C3⋊D3—22no—
65C2×C4×C3⋊D3—22no—
66C2×C4×C3⋊D3—22no—
67C2×C4×C3⋊D3—22no—
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3—22no—
70C2×C4×C3⋊D3—22no—
71C2×C4×C3⋊D3Q814yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C2×#624—22no—
77C2×#624—22no—
78C2×#624—22no—
79C2×#624—22no—
80C2×#624—22no—
81C2×#624—22no—
82C2×#624—22no—
83C2×#624—22no—
84C2×#624—22no—
85C2×#624D414yes—
86C2×#624D414yes—
87C2×#624Q814yes—
88C3×C4⋊Dic3—24no—
89C3×Dic3⋊C4—24no—
90C3×Dic3⋊C4—24no—
91C3×Dic3⋊C4—24no—
92#3724—24no—
93Dic3⋊Dic3—24no—
94Dic3⋊Dic3—24no—
95Dic3⋊Dic3—24no—
96C2×#398—91noSylow
97C22×C4×D3—32no—
98C22×C4×D3—32no—
99C22×C4×D3—32no—
100C22×C4×D3—32no—
101C22×C4×D3—32no—
102C22×C4×D3—32no—
103C22×C4×D3—32no—
104C22×C4×D3—61no—
105C22×C4×D3—61no—
106C22×C4×D3—61no—
107C2×C3×C4⋊C4—32no—
108C2×C3×C4⋊C4—32no—
109C2×C3×C4⋊C4—32no—
110C2×C3×C4⋊C4—32no—
111C2×C4⋊Dic3—32no—
112C2×C4⋊Dic3—32no—
113C2×C4⋊Dic3—32no—
114C2×C4⋊Dic3C2×D312yes—
115C2×Dic3⋊C4—32no—
116C2×Dic3⋊C4—32no—
117C2×Dic3⋊C4—32no—
118C2×Dic3⋊C4—32no—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4C2×D312yes—
121C2×Dic3⋊C4C2×D312yes—
122C2×Dic3⋊C4C2×D312yes—
123D3×C4⋊C4—68no—
124D3×C4⋊C4—68no—
125D3×C4⋊C4—68no—
126D3×C4⋊C4—68no—
127C3×#95—21no—
128C3×#95—32no—
129C3×#95—32no—
130C3×#95C2×D312yes—
131C3⋊#95—32no—
132C3⋊#95—32no—
133C3⋊#95—32no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—61no—
139C3⋊#95—61no—
140C3⋊#95—61no—
141C3⋊#95C2×D312yes—
142C3⋊#95C2×D312yes—
143C23×C32C2411yescharacteristic
144C22×C3⋊D3C2×D412yes—
145C22×C3⋊D3C2×D412yes—
146C22×C3⋊D3C2×Q812yes—
147C22×C3⋊D3C2×Q812yes—
148C22×C3⋊D3#4112yes—
149C22×C3⋊D3#4112yes—
150C22×C3⋊D3#4112yes—
151C2×C32×C4—21no—
152C2×C32×C4—21no—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4—21no—
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4C2×Q812yes—
160C2×C3⋊Dic3—21no—
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3—21no—
163C2×C3⋊Dic3—21no—
164C2×C3⋊Dic3—21no—
165C2×C3⋊Dic3—21no—
166C2×C3⋊Dic3—21no—
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3C2×Q812yes—
169C4×C3⋊D3—28no—
170C4×C3⋊D3—44no—
171C4×C3⋊D3—44no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3C2×D414yes—
182C2×C3×Dic3C2×D414yes—
183C2×C3×Dic3C2×Q814yes—
184#624—28no—
185#624—28no—
186#624—28no—
187#624—44no—
188C22×C4⋊C4—91no—
189C22×C4⋊C4—91no—
190C22×C4⋊C4—91no—
191C22×C4⋊C4—91no—
192#398—32no—
193#398—92no—
194#398—92no—
195#398—92no—
196C2×#95—91no—
197C2×#95—91no—
198C2×#95—91no—
199C23×D3—32no—
200C23×D3—61no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—32no—
205C22×C3×C4—32no—
206C22×C3×C4—32no—
207C22×C3×C4—32no—
208C22×C3×C4C22×D312yes—
209C22×C3×C4C22×D312yes—
210C22×C3×C4C22×D312yes—
211C22×Dic3—32no—
212C22×Dic3—32no—
213C22×Dic3—32no—
214C22×Dic3—61no—
215C22×Dic3—61no—
216C22×Dic3—61no—
217C22×Dic3C22×D312yes—
218C22×Dic3C22×D312yes—
219C22×Dic3C22×D312yes—
220C22×Dic3C22×D312yes—
221C2×C4×D3—38no—
222C2×C4×D3—38no—
223C2×C4×D3—38no—
224C2×C4×D3—38no—
225C2×C4×D3—64no—
226C2×C4×D3—64no—
227C2×C4×D3—64no—
228C2×C4×D3—64no—
229C2×C4×D3—64no—
230C2×C4×D3—64no—
231C2×C4×D3—64no—
232C2×C4×D3—64no—
233C2×C4×D3—64no—
234C2×C4×D3—64no—
235C2×C4×D3—64no—
236C2×C4×D3—64no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×C4×D3—64no—
240C2×C4×D3—64no—
241C2×C4×D3—64no—
242C2×C4×D3—64no—
243C2×C4×D3—64no—
244C2×C4×D3—64no—
245C2×C4×D3—122no—
246C2×C4×D3—122no—
247C2×C4×D3—122no—
248C2×C4×D3—122no—
249C2×C4×D3—122no—
250C2×C4×D3—122no—
251C3×C4⋊C4—64no—
252C3×C4⋊C4—64no—
253C3×C4⋊C4—64no—
254C3×C4⋊C4—64no—
255C4⋊Dic3—24no—
256C4⋊Dic3—64no—
257C4⋊Dic3—64no—
258C4⋊Dic3—64no—
259Dic3⋊C4—24no—
260Dic3⋊C4—24no—
261Dic3⋊C4—24no—
262Dic3⋊C4—64no—
263Dic3⋊C4—64no—
264Dic3⋊C4—64no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267C22×C32C22×D411yescharacteristic
268C22×C32C22×D411yescharacteristic
269C22×C32C22×Q811yescharacteristic
270C22×C32C22×Q811yescharacteristic
271C22×C32C2×#4111yescharacteristic
272C22×C32C2×#4111yescharacteristic
273C22×C32C2×#4111yescharacteristic
274C2×C3⋊D3#12114yes—
275C2×C3⋊D3C22⋊Q814yes—
276C2×C3⋊D3C22⋊Q814yes—
277C2×C3⋊D3#12314yes—
278C2×C3⋊D3#12514yes—
279C2×C3⋊D3#12514yes—
280C2×C3⋊D3C4⋊Q814yes—
281C32×C4—22no—
282C32×C4—41no—
283C32×C4—41no—
284C3⋊Dic3—22no—
285C3⋊Dic3—41no—
286C3⋊Dic3—41no—
287C3×Dic3—24no—
288C3×Dic3—24no—
289C3×Dic3—24no—
290C3×Dic3—42no—
291C23×C4—91no—
292C23×C4—91no—
293C23×C4—91no—
294C23×C4—91no—
295C23×C4—91no—
296C23×C4—91no—
297C23×C4—91no—
298C2×C4⋊C4—32no—
299C2×C4⋊C4—32no—
300C2×C4⋊C4—32no—
301C2×C4⋊C4—32no—
302C2×C4⋊C4—92no—
303C2×C4⋊C4—92no—
304C2×C4⋊C4—92no—
305C2×C4⋊C4—92no—
306C2×C4⋊C4—184no—
307C2×C4⋊C4—184no—
308C2×C4⋊C4—184no—
309C2×C4⋊C4—184no—
310#95—32no—
311#95—32no—
312#95—92no—
313#95—92no—
314#95—91no—
315#95—91no—
316#95—91no—
317#95D3211yescharacteristic
318C23×C3—21no—
319C23×C3C23×D312yes—
320C22×D3—34no—
321C22×D3—34no—
322C22×D3—34no—
323C22×D3—34no—
324C22×D3—34no—
325C22×D3—34no—
326C22×D3—34no—
327C22×D3—62no—
328C22×D3—62no—
329C22×D3—62no—
330C22×D3—62no—
331C22×D3—62no—
332C22×D3—62no—
333C22×D3—62no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
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—22no—
345C2×C3×C4—34no—
346C2×C3×C4—34no—
347C2×C3×C4—34no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—41no—
351C2×C3×C4—41no—
352C2×C3×C4—41no—
353C2×C3×C4—41no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4D3×Q814yes—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—34no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—121no—
386C2×Dic3—121no—
387C2×Dic3—121no—
388C2×Dic3—121no—
389C2×Dic3—121no—
390C2×Dic3—121no—
391C2×Dic3D3×D414yes—
392C2×Dic3D3×D414yes—
393C2×Dic3D3×Q814yes—
394C4×D3—616no—
395C4×D3—616no—
396C4×D3—616no—
397C4×D3—616no—
398C4×D3—128no—
399C4×D3—128no—
400C4×D3—128no—
401C4×D3—128no—
402C4×D3—128no—
403C4×D3—128no—
404C2×C32C2×#12111yescharacteristic
405C2×C32C2×C22⋊Q811yescharacteristic
406C2×C32C2×C22⋊Q811yescharacteristic
407C2×C32C2×#12311yescharacteristic
408C2×C32C2×#12511yescharacteristic
409C2×C32C2×#12511yescharacteristic
410C2×C32C2×C4⋊Q811yescharacteristic
411C3⋊D3#39818yescomplemented
412C24—91no—
413C22×C4—32no—
414C22×C4—32no—
415C22×C4—32no—
416C22×C4—32no—
417C22×C4—94no—
418C22×C4—94no—
419C22×C4—94no—
420C22×C4—91no—
421C22×C4—94no—
422C22×C4—91no—
423C22×C4—91no—
424C22×C4—182no—
425C22×C4—182no—
426C22×C4—182no—
427C22×C4—182no—
428C22×C4—182no—
429C22×C4—182no—
430C22×C4—182no—
431C22×C4—182no—
432C22×C4—182no—
433C22×C4—182no—
434C22×C4—182no—
435C22×C4—182no—
436C22×C4—182no—
437C22×C4—182no—
438C22×C4—182no—
439C22×C4—182no—
440C22×C4—182no—
441C22×C4C2×D3211yescharacteristic
442C22×C4C2×D3211yescharacteristic
443C22×C4C2×D3211yescharacteristic
444C4⋊C4—64no—
445C4⋊C4—64no—
446C4⋊C4—64no—
447C4⋊C4—64no—
448C4⋊C4—184no—
449C4⋊C4—184no—
450C4⋊C4—184no—
451C4⋊C4—184no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3C2×D3×D412yes—
460C22×C3C2×D3×D412yes—
461C22×C3C2×D3×Q812yes—
462C22×C3C2×D3×Q812yes—
463C22×C3D3×#4112yes—
464C22×C3D3×#4112yes—
465C22×C3D3×#4112yes—
466C2×D3—38no—
467C2×D3—38no—
468C2×D3—38no—
469C2×D3—38no—
470C2×D3—38no—
471C2×D3—38no—
472C2×D3—38no—
473C2×D3—64no—
474C2×D3—64no—
475C2×D3—64no—
476C2×D3—64no—
477C2×D3—64no—
478C2×D3—64no—
479C2×D3—64no—
480C3×C4—24no—
481C3×C4—42no—
482C3×C4—42no—
483C3×C4—42no—
484C3×C4—42no—
485C3×C4—42no—
486C3×C4—64no—
487C3×C4—64no—
488C3×C4—64no—
489C3×C4—122no—
490Dic3—24no—
491Dic3—24no—
492Dic3—24no—
493Dic3—42no—
494Dic3—64no—
495Dic3—122no—
496Dic3—122no—
497Dic3—122no—
498Dic3—122no—
499Dic3—122no—
500C32C2×#39811yescharacteristic, complemented, Sylow
501C23—92no—
502C23—92no—
503C23—92no—
504C23—92no—
505C23—92no—
506C23—92no—
507C23—92no—
508C23C22×D3211yescharacteristic
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—34no—
518C2×C4—34no—
519C2×C4—34no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—62no—
528C2×C4—62no—
529C2×C4—92no—
530C2×C4—188no—
531C2×C4—188no—
532C2×C4—188no—
533C2×C4—188no—
534C2×C4—181no—
535C2×C4—181no—
536C2×C4—181no—
537C2×C4—181no—
538C2×C4—181no—
539C2×C4—181no—
540C2×C4—181no—
541C2×C4—181no—
542C2×C4—364no—
543C2×C4—364no—
544C2×C4—364no—
545C2×C4#379712yes—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3D3×#12112yes—
554C2×C3D3×C22⋊Q812yes—
555C2×C3D3×C22⋊Q812yes—
556C2×C3D3×#12312yes—
557C2×C3D3×#12512yes—
558C2×C3D3×#12512yes—
559C2×C3D3×C4⋊Q812yes—
560D3—316no—
561D3—68no—
562C22—94no—
563C22—94no—
564C22—94no—
565C22—94no—
566C22—94no—
567C22—94no—
568C22—94no—
569C22C2×#379711yescharacteristic
570C22#6430611yescharacteristic
571C22#6430611yescharacteristic
572C22D32×D411yescharacteristic
573C22D32×D411yescharacteristic
574C22#6431211yescharacteristic
575C22D32×Q811yescharacteristic
576C4—22no—
577C4—41no—
578C4—41no—
579C4—64no—
580C4—64no—
581C4—64no—
582C4—122no—
583C4—182no—
584C4—361no—
585C4—361no—
586C3—21no—
587C3D3×#39812yescomplemented
588C2—98no—
589C2#1059394811yescharacteristic
590C2#1059406711yescharacteristic
591C2#1059426011yescharacteristic
592C2#1059426511yescharacteristic
593C2#1059437411yescharacteristic
594C2#1059439911yescharacteristic
595C2#1059462411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32C2×#398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
6. C3×#4657C2semidirect
9. #10591348C2semidirect
10. #10591339C2semidirect
11. #10591200C2semidirect
55. #4657D3semidirect
411. C3⋊D3#398semidirect
500. C32C2×#398semidirect
587. C3D3×#398semidirect

Maximal subgroups

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

subgroupindex
C2×#639002
C2×#638832
C3⋊D3×#952
C3×#46572
#105913702
#105913482
#105913392
#105912002
D3×#3983