Finite Group Databasebeta

← #11805602

Subgroups — #11805602

Order 1152.

1189 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
1C2×C3×C4×Dic6C211yesmaximal, characteristic
2C2×Dic3×Dic6C211yesmaximal, characteristic
3C2×Dic3×Dic6C211yesmaximal, characteristic
4#10592627C211yesmaximal, characteristic
5C3×C4×Dic3⋊C4C211yesmaximal, characteristic
6#10591330C212yesmaximal
7#10591246C212yesmaximal
8#10591245C212yesmaximal
9#10591243C212yesmaximal
10#10591224C211yesmaximal, characteristic
11#10591212C211yesmaximal, characteristic
12#82461—31nomaximal
13#73637—31nomaximal
14C22×C3×Dic6C2211yescharacteristic
15C2×C32×C42C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×#3750C2212yes—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×Dic3⋊C4C2212yes—
21C2×C3×Dic3⋊C4C2211yescharacteristic
22C2×C3×Dic3⋊C4C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2212yes—
25C2×C3×C4×Dic3C2211yescharacteristic
26C3×C4×Dic6—24no—
27C2×#3724C2212yes—
28C2×Dic3⋊Dic3C2212yes—
29C2×Dic3⋊Dic3C2212yes—
30C2×Dic32C2212yes—
31C2×Dic32C2212yes—
32Dic3×Dic6—24no—
33Dic3×Dic6C418yescomplemented
34#63658C2212yes—
35C3×C3⋊#95C2211yescharacteristic
36C3×C3⋊#95C2211yescharacteristic
37#63579C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×C4×Q8—31no—
41C2×Q8×Dic3—31no—
42C2×Q8×Dic3—31no—
43C2×C4×Dic6—31no—
44C2×C4×Dic6—31no—
45C2×C4×Dic6D311yescharacteristic
46C3×C4×C4⋊C4—31no—
47#4977—31no—
48#4977—32no—
49#4976—32no—
50#4976—32no—
51#4972—32no—
52#4972—31no—
53#4936—31no—
54C4×Dic3⋊C4—32no—
55C4×Dic3⋊C4D311yescharacteristic
56#4928—31no—
57#4928—31no—
58#4928—31no—
59#4928—32no—
60#4928—61no—
61#4650—32no—
62#4649—32no—
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2312yes—
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2311yescharacteristic
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2312yes—
74C2×C3×Dic6C2×C414yes—
75C2×C3×Dic6D414yes—
76C2×C3×Dic6Q814yes—
77C32×C42—22no—
78C4⋊(C3⋊Dic3)—22no—
79C4⋊(C3⋊Dic3)C2×C414yes—
80#3750—24no—
81C3×C4⋊Dic3—22no—
82C3×Dic3⋊C4—22no—
83C3×Dic3⋊C4—24no—
84C3×Dic3⋊C4—22no—
85C3×C4×Dic3—22no—
86C3×C4×Dic3—24no—
87C3×C4×Dic3C2×C414yes—
88#3724—24no—
89Dic3⋊Dic3—24no—
90Dic3⋊Dic3C2×C418yes—
91Dic32—24no—
92Dic32C2×C418yes—
93#2351—91noSylow
94C22×C3×Q8—31no—
95C22×Dic6C2×D311yescharacteristic
96C3×C4×Q8—64no—
97C2×C3×C4⋊C4—32no—
98C2×C3×C4⋊C4—31no—
99C2×C3×C4⋊C4—31no—
100C2×C3×C4⋊C4—31no—
101C2×C3×C42—21no—
102C2×C3×C42—31no—
103C2×C3×C42—32no—
104C2×C3×C42—31no—
105C2×C3×C42C2×D311yescharacteristic
106C2×C3×C42C2×D311yescharacteristic
107Q8×Dic3—38no—
108Q8×Dic3—64no—
109C2×C4⋊Dic3—31no—
110C2×C4⋊Dic3—31no—
111C2×C4⋊Dic3—32no—
112C2×C4⋊Dic3—31no—
113C2×C4⋊Dic3—31no—
114C2×C4⋊Dic3—32no—
115C2×C4⋊Dic3—61no—
116C2×C4⋊Dic3—61no—
117C2×C4⋊Dic3C2×D311yescharacteristic
118C2×Dic3⋊C4—32no—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4—32no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—62no—
125C2×Dic3⋊C4C2×D312yes—
126C2×Dic3⋊C4C2×D311yescharacteristic
127C2×Dic3⋊C4C2×D311yescharacteristic
128C2×C4×Dic3—32no—
129C2×C4×Dic3—32no—
130C2×C4×Dic3—32no—
131C2×C4×Dic3—32no—
132C2×C4×Dic3C2×D312yes—
133C2×C4×Dic3C2×D311yescharacteristic
134C2×C4×Dic3C2×D311yescharacteristic
135C4×Dic6—24no—
136C4×Dic6—38no—
137C4×Dic6—64no—
138C3×#95—31no—
139C3×#95—31no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95—62no—
149C3⋊#95C2×D311yescharacteristic
150C3⋊#95C2×D311yescharacteristic
151C23×C32C2411yescharacteristic
152C2×C32×C4—21no—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4—21no—
156C2×C32×C4—21no—
157C2×C32×C4C22×C412yes—
158C2×C32×C4C2×D412yes—
159C2×C32×C4C2×Q812yes—
160C2×C32×C4#4112yes—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3C22×C414yes—
167C2×C3×Dic3—21no—
168C2×C3×Dic3—21no—
169C2×C3×Dic3—21no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3C22×C412yes—
180C2×C3×Dic3C22×C412yes—
181C2×C3×Dic3C22×C414yes—
182C2×C3×Dic3C2×D414yes—
183C2×C3×Dic3C2×Q814yes—
184C2×C3×Dic3#4112yes—
185C3×Dic6C4⋊C4116yescomplemented
186C2×C4×Q8—31no—
187C2×C4×Q8—91no—
188C2×C4×Q8—91no—
189#389—91no—
190#389—92no—
191#389—92no—
192#389—91no—
193#382—92no—
194#382—91no—
195C4×C4⋊C4—31no—
196C4×C4⋊C4—92no—
197C2×C3×Q8—34no—
198C2×C3×Q8—34no—
199C2×C3×Q8—34no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—32no—
204C22×C3×C4—31no—
205C22×C3×C4—31no—
206C22×C3×C4—31no—
207C22×C3×C4—32no—
208C22×C3×C4—31no—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C22×Dic3—32no—
216C22×Dic3—32no—
217C22×Dic3—32no—
218C22×Dic3—32no—
219C22×Dic3—62no—
220C22×Dic3—62no—
221C22×Dic3C22×D312yes—
222C22×Dic3C22×D311yescharacteristic
223C22×Dic3C22×D311yescharacteristic
224C22×Dic3C22×D311yescharacteristic
225C22×Dic3C22×D311yescharacteristic
226C22×Dic3C22×D312yes—
227C2×Dic6Dic614yes—
228C2×Dic6C4×D314yes—
229C2×Dic6#6714yes—
230C3×C4⋊C4—62no—
231C3×C4⋊C4—64no—
232C3×C4⋊C4—62no—
233C3×C4⋊C4—62no—
234C3×C42—22no—
235C3×C42—22no—
236C3×C42—34no—
237C3×C42—42no—
238C3×C42—64no—
239C3×C42—62no—
240C4⋊Dic3—22no—
241C4⋊Dic3—34no—
242C4⋊Dic3—34no—
243C4⋊Dic3—38no—
244C4⋊Dic3—64no—
245C4⋊Dic3—64no—
246C4⋊Dic3—62no—
247C4⋊Dic3—62no—
248C4⋊Dic3—122no—
249Dic3⋊C4—22no—
250Dic3⋊C4—22no—
251Dic3⋊C4—24no—
252Dic3⋊C4—38no—
253Dic3⋊C4—64no—
254Dic3⋊C4—64no—
255Dic3⋊C4—64no—
256Dic3⋊C4—64no—
257Dic3⋊C4—64no—
258Dic3⋊C4—124no—
259C4×Dic3—22no—
260C4×Dic3—24no—
261C4×Dic3—38no—
262C4×Dic3—38no—
263C4×Dic3—64no—
264C4×Dic3—64no—
265C4×Dic3C4×D314yes—
266C22×C32C23×C411yescharacteristic
267C22×C32C22×D411yescharacteristic
268C22×C32C22×Q811yescharacteristic
269C22×C32C2×#4111yescharacteristic
270C22×C32C2×#4111yescharacteristic
271C22×C322−1+411yescharacteristic
272C22×C322−1+411yescharacteristic
273C32×C4—22no—
274C32×C4—41no—
275C32×C4C2×C4⋊C414yes—
276C3⋊Dic3—24no—
277C3⋊Dic3—42no—
278C3×Dic3—22no—
279C3×Dic3—22no—
280C3×Dic3—22no—
281C3×Dic3—41no—
282C3×Dic3—42no—
283C3×Dic3C2×C4⋊C418yes—
284C22×Q8—31no—
285C4×Q8—64no—
286C4×Q8—98no—
287C4×Q8—184no—
288C2×C4⋊C4—32no—
289C2×C4⋊C4—31no—
290C2×C4⋊C4—31no—
291C2×C4⋊C4—31no—
292C2×C4⋊C4—92no—
293C2×C4⋊C4—91no—
294C2×C4⋊C4—92no—
295C2×C4⋊C4—92no—
296C2×C4⋊C4—91no—
297C2×C4⋊C4—92no—
298C2×C42—31no—
299C2×C42—32no—
300C2×C42—31no—
301C2×C42—92no—
302C2×C42—92no—
303C2×C42D3211yescharacteristic
304#95—31no—
305#95—31no—
306#95—92no—
307#95—92no—
308#95—92no—
309#95—92no—
310C23×C3—21no—
311C23×C3C23×D311yescharacteristic
312C23×C3C23×D311yescharacteristic
313C3×Q8—316no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—22no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
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—22no—
328C2×C3×C4—22no—
329C2×C3×C4—34no—
330C2×C3×C4—34no—
331C2×C3×C4—34no—
332C2×C3×C4—32no—
333C2×C3×C4—32no—
334C2×C3×C4—32no—
335C2×C3×C4—41no—
336C2×C3×C4—41no—
337C2×C3×C4—41no—
338C2×C3×C4—41no—
339C2×C3×C4—61no—
340C2×C3×C4—61no—
341C2×C3×C4—61no—
342C2×C3×C4—61no—
343C2×C3×C4—61no—
344C2×C3×C4—61no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—61no—
348C2×C3×C4—61no—
349C2×C3×C4—62no—
350C2×C3×C4—61no—
351C2×C3×C4C2×Dic612yes—
352C2×C3×C4C2×C4×D312yes—
353C2×C3×C4C2×C4×D312yes—
354C2×C3×C4#23512yes—
355C2×C3×C4D3×D412yes—
356C2×C3×C4D3×Q812yes—
357C2×C3×C4#23912yes—
358C2×C3×C4C2×#6712yes—
359C2×Dic3—21no—
360C2×Dic3—21no—
361C2×Dic3—21no—
362C2×Dic3—21no—
363C2×Dic3—21no—
364C2×Dic3—21no—
365C2×Dic3—21no—
366C2×Dic3—21no—
367C2×Dic3—22no—
368C2×Dic3—21no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—34no—
372C2×Dic3—34no—
373C2×Dic3—64no—
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—122no—
385C2×Dic3—122no—
386C2×Dic3—122no—
387C2×Dic3—122no—
388C2×Dic3—122no—
389C2×Dic3C2×Dic614yes—
390C2×Dic3C2×C4×D312yes—
391C2×Dic3C2×C4×D312yes—
392C2×Dic3C2×C4×D314yes—
393C2×Dic3#23512yes—
394C2×Dic3C2×#6714yes—
395Dic6Dic3⋊C4116yescomplemented
396C2×C32C22×C4⋊C411yescharacteristic
397C2×C32C4×#4111yescharacteristic
398C2×C32#51911yescharacteristic
399C2×C32#54811yescharacteristic
400C2×C32#54811yescharacteristic
401C2×C32#55711yescharacteristic
402C2×C32#55711yescharacteristic
403C2×Q8—34no—
404C2×Q8—34no—
405C2×Q8—34no—
406C22×C4—32no—
407C22×C4—31no—
408C22×C4—31no—
409C22×C4—31no—
410C22×C4—31no—
411C22×C4—32no—
412C22×C4—92no—
413C22×C4—92no—
414C22×C4C2×D3211yescharacteristic
415C22×C4C2×D3211yescharacteristic
416C22×C4C2×D3211yescharacteristic
417C4⋊C4—64no—
418C4⋊C4—62no—
419C4⋊C4—62no—
420C4⋊C4—62no—
421C4⋊C4—98no—
422C4⋊C4—94no—
423C4⋊C4—184no—
424C4⋊C4—184no—
425C4⋊C4—184no—
426C4⋊C4—182no—
427C42—22no—
428C42—34no—
429C42—64no—
430C42—62no—
431C42—98no—
432C42—184no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3C22×Dic611yescharacteristic
441C22×C3C22×C4×D311yescharacteristic
442C22×C3C22×C4×D311yescharacteristic
443C22×C3C2×#23511yescharacteristic
444C22×C3C2×#23511yescharacteristic
445C22×C3C2×D3×D411yescharacteristic
446C22×C3C2×D3×Q811yescharacteristic
447C22×C3C2×#23911yescharacteristic
448C22×C3#100711yescharacteristic
449C22×C3D3×#4111yescharacteristic
450C22×C3#101011yescharacteristic
451C22×C3#101011yescharacteristic
452C22×C3#101011yescharacteristic
453C22×C3C22×#6711yescharacteristic
454C3×C4—22no—
455C3×C4—22no—
456C3×C4—24no—
457C3×C4—38no—
458C3×C4—42no—
459C3×C4—42no—
460C3×C4—41no—
461C3×C4—41no—
462C3×C4—62no—
463C3×C4—62no—
464C3×C4—62no—
465C3×C4—122no—
466C3×C4—121no—
467C3×C4D3×C4⋊C414yes—
468C3×C4C2×Dic3⋊C414yes—
469Dic3—22no—
470Dic3—22no—
471Dic3—22no—
472Dic3—41no—
473Dic3—42no—
474Dic3—64no—
475Dic3—64no—
476Dic3—124no—
477Dic3—122no—
478Dic3—122no—
479Dic3—242no—
480Dic3C2×Dic3⋊C418yes—
481C32#235111yescharacteristic, complemented, Sylow
482C23C22×D3211yescharacteristic
483Q8—316no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—34no—
490C2×C4—34no—
491C2×C4—34no—
492C2×C4—32no—
493C2×C4—32no—
494C2×C4—32no—
495C2×C4—61no—
496C2×C4—61no—
497C2×C4—61no—
498C2×C4—61no—
499C2×C4—61no—
500C2×C4—61no—
501C2×C4—61no—
502C2×C4—62no—
503C2×C4—61no—
504C2×C4—62no—
505C2×C4—62no—
506C2×C4—61no—
507C2×C4—94no—
508C2×C4—182no—
509C2×C4—182no—
510C2×C4—182no—
511C2×C4—182no—
512C2×C4—182no—
513C2×C4D3×Dic612yes—
514C2×C4#379912yes—
515C2×C4C4×D3212yes—
516C2×C4D3×#6712yes—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3C4×#23511yescharacteristic
525C2×C3C2×D3×C4⋊C411yescharacteristic
526C2×C3#551611yescharacteristic
527C2×C3#555211yescharacteristic
528C2×C3#555211yescharacteristic
529C2×C3#556711yescharacteristic
530C2×C3#556711yescharacteristic
531C2×C3#556911yescharacteristic
532C2×C3#557011yescharacteristic
533C2×C3#557211yescharacteristic
534C2×C3C4×#23911yescharacteristic
535C2×C3C22×Dic3⋊C411yescharacteristic
536C2×C3#581711yescharacteristic
537C2×C3#583111yescharacteristic
538C22C2×D3×Dic611yescharacteristic
539C22#6429711yescharacteristic
540C22#6429811yescharacteristic
541C22C2×#379911yescharacteristic
542C22C2×C4×D3211yescharacteristic
543C22D3×#23511yescharacteristic
544C22C2×D3×#6711yescharacteristic
545C4—22no—
546C4—38no—
547C4—41no—
548C4—62no—
549C4—62no—
550C4—62no—
551C4—122no—
552C4—121no—
553C4—184no—
554C4—362no—
555C4D3×Dic3⋊C414yes—
556C3—21no—
557C3#7363711yescharacteristic, complemented
558C3#8246111yescharacteristic, complemented
559C2#1059385111yescharacteristic
560C2#1059386011yescharacteristic
561C2#1059388511yescharacteristic
562C2C4×#379911yescharacteristic
563C2C2×D3×Dic3⋊C411yescharacteristic
564C2#1059489911yescharacteristic
565C2#1059490211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2351
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
33. Dic3×Dic6C4semidirect
185. C3×Dic6C4⋊C4semidirect
395. Dic6Dic3⋊C4semidirect
481. C32#2351semidirect
557. C3#73637semidirect
558. C3#82461semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×Dic62
C2×Dic3×Dic62
#105926272
C3×C4×Dic3⋊C42
#105913302
#105912462
#105912452
#105912432
#105912242
#105912122
#824613
#736373