Finite Group Databasebeta

← #11801837

Subgroups — #11801837

Order 1152.

1429 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#877C211yesmaximal, characteristic
2C2×#63955C211yesmaximal, characteristic
3C22×Dic32C211yesmaximal, characteristic
4#10592649C211yesmaximal, characteristic
5C3×#4950C211yesmaximal, characteristic
6#10591719C211yesmaximal, characteristic
7#10591718C211yesmaximal, characteristic
8#10591268C212yesmaximal, complemented
9Dic3×C4⋊Dic3C212yesmaximal, complemented
10#10591265C212yesmaximal, complemented
11#10591242C212yesmaximal, complemented
12#82227—31nomaximal
13#74378—31nomaximal
14C23×C3⋊Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C2×C32×C22⋊C4C2211yescharacteristic
18C2×#3757C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2212yes—
20C2×C3×#217C2211yescharacteristic
21C2×C3×#217C2211yescharacteristic
22C2×C3×C4⋊Dic3C2212yes—
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×C4×Dic3C2212yes—
25C3×#877C418yescomplemented
26C2×Dic3⋊Dic3C2212yes—
27C2×Dic3⋊Dic3C2212yes—
28C2×Dic3⋊Dic3C2211yescharacteristic
29C2×Dic3⋊Dic3C2211yescharacteristic
30#63955—24no—
31C2×Dic32—24no—
32C2×Dic32C2211yescharacteristic
33C2×Dic32C2212yes—
34C2×Dic32C2212yes—
35C2×Dic32C2211yescharacteristic
36#63658C2212yes—
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×#117—31no—
41C2×#926—31no—
42C22×C4×Dic3—31no—
43C22×C4×Dic3—31no—
44C2×#877—31no—
45C2×#877D311yescharacteristic
46C3×#385—31no—
47#5210—31no—
48#4984—32no—
49#4984—32no—
50#4976—32no—
51Dic3×C4⋊C4—32no—
52#4950—31no—
53#4950—31no—
54#4950—31no—
55#4950—31no—
56#4950—61no—
57#4950D311yescharacteristic
58#4946—31no—
59C4×C4⋊Dic3—32no—
60C4×C4⋊Dic3—32no—
61#4649—32no—
62#4647—32no—
63C24×C32C2311yescharacteristic
64C22×C32×C4C2312yes—
65C22×C3⋊Dic3—22no—
66C22×C3⋊Dic3—24no—
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3⋊Dic3C2312yes—
70C22×C3×Dic3—22no—
71C22×C3×Dic3—24no—
72C22×C3×Dic3C2×C414yes—
73C22×C3×Dic3D414yes—
74C22×C3×Dic3Q814yes—
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2311yescharacteristic
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2311yescharacteristic
80C22×C3×Dic3C2311yescharacteristic
81C32×C22⋊C4C2×C414yes—
82#3757—22no—
83C4⋊(C3⋊Dic3)—24no—
84C3×#217—22no—
85C3×#217C2×C414yes—
86C3×C4⋊Dic3—24no—
87C3×Dic3⋊C4C2×C418yescomplemented
88C3×C4×Dic3C2×C418yescomplemented
89Dic3⋊Dic3—24no—
90Dic3⋊Dic3—22no—
91Dic3⋊Dic3—22no—
92Dic3⋊Dic3—24no—
93Dic32—24no—
94Dic32—24no—
95Dic32—22no—
96Dic32—22no—
97#2296—91noSylow
98C23×C3×C4—31no—
99C23×C3×C4—31no—
100C23×Dic3—31no—
101C23×Dic3—31no—
102C23×Dic3—61no—
103C23×Dic3C2×D311yescharacteristic
104C23×Dic3C2×D311yescharacteristic
105C3×#117—38no—
106C2×C3×C4⋊C4—32no—
107C2×C3×C4⋊C4—32no—
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—31no—
110C2×C3×C22⋊C4—31no—
111C2×C3×C22⋊C4C2×D311yescharacteristic
112C2×C3×C22⋊C4C2×D311yescharacteristic
113C2×C3×C42—32no—
114C2×#217—31no—
115C2×#217—31no—
116C2×#217—61no—
117C2×#217C2×D311yescharacteristic
118C2×#217C2×D311yescharacteristic
119#926—64no—
120C2×C4⋊Dic3—32no—
121C2×C4⋊Dic3—32no—
122C2×C4⋊Dic3—32no—
123C2×C4⋊Dic3—32no—
124C2×C4⋊Dic3—31no—
125C2×C4⋊Dic3—31no—
126C2×C4⋊Dic3—62no—
127C2×C4⋊Dic3C2×D312yes—
128C2×Dic3⋊C4—31no—
129C2×Dic3⋊C4—32no—
130C2×Dic3⋊C4—32no—
131C2×Dic3⋊C4—31no—
132C2×Dic3⋊C4C2×D312yes—
133C2×C4×Dic3—32no—
134C2×C4×Dic3—31no—
135C2×C4×Dic3—32no—
136C2×C4×Dic3—32no—
137C2×C4×Dic3—31no—
138C2×C4×Dic3—31no—
139C2×C4×Dic3—31no—
140C2×C4×Dic3—32no—
141C2×C4×Dic3—64no—
142C2×C4×Dic3—64no—
143C2×C4×Dic3C2×D312yes—
144#877—64no—
145#877Dic318yescomplemented
146C3×#95—32no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95—32no—
150C3⋊#95—32no—
151C3⋊#95—32no—
152C3⋊#95—32no—
153C3⋊#95—62no—
154C3⋊#95C2×D312yes—
155C23×C32—22no—
156C23×C32—22no—
157C23×C32C22×C412yes—
158C23×C32C2×D412yes—
159C23×C32C2×Q812yes—
160C23×C32C2411yescharacteristic
161C2×C32×C4—22no—
162C2×C32×C4—22no—
163C2×C32×C4C22×C414yes—
164C2×C3⋊Dic3—28no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3#4114yes—
172C2×C3×Dic3—28no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3C4⋊C4116yescomplemented
182C2×C3×Dic3C22×C414yes—
183C2×C3×Dic3C22×C412yes—
184C2×C3×Dic3C22×C412yes—
185C2×C3×Dic3C2×D412yes—
186C2×C3×Dic3C2×D412yes—
187C2×C3×Dic3C2×Q812yes—
188C2×C3×Dic3C2×Q812yes—
189C2×C3×Dic3#4114yes—
190C2×#117—31no—
191C2×#117—91no—
192C22×C42—91no—
193#389—92no—
194#389—92no—
195#385—31no—
196#385—91no—
197#385—91no—
198#385—91no—
199C4×C4⋊C4—92no—
200C4×C4⋊C4—92no—
201C24×C3—21no—
202C24×C3C22×D311yescharacteristic
203C24×C3C22×D311yescharacteristic
204C22×C3×C4—22no—
205C22×C3×C4—34no—
206C22×C3×C4—34no—
207C22×C3×C4—34no—
208C22×C3×C4—31no—
209C22×C3×C4—31no—
210C22×C3×C4—32no—
211C22×C3×C4—32no—
212C22×C3×C4—31no—
213C22×C3×C4—31no—
214C22×C3×C4—64no—
215C22×C3×C4—62no—
216C22×C3×C4C22×D312yes—
217C22×C3×C4C22×D312yes—
218C22×Dic3—22no—
219C22×Dic3—24no—
220C22×Dic3—32no—
221C22×Dic3—32no—
222C22×Dic3—31no—
223C22×Dic3—31no—
224C22×Dic3—31no—
225C22×Dic3—31no—
226C22×Dic3—62no—
227C22×Dic3—61no—
228C22×Dic3—61no—
229C22×Dic3—64no—
230C22×Dic3—64no—
231C22×Dic3—62no—
232C22×Dic3—62no—
233C22×Dic3—124no—
234C22×Dic3—122no—
235C22×Dic3Dic614yes—
236C22×Dic3D1214yes—
237C22×Dic3C2×Dic314yes—
238C22×Dic3C22×D311yescharacteristic
239C22×Dic3C22×D311yescharacteristic
240C22×Dic3C22×D312yes—
241C22×Dic3C22×D312yes—
242C22×Dic3C22×D311yescharacteristic
243C22×Dic3C22×D311yescharacteristic
244C3×C4⋊C4—38no—
245C3×C4⋊C4—64no—
246C3×C22⋊C4—24no—
247C3×C22⋊C4—34no—
248C3×C22⋊C4—62no—
249C3×C22⋊C4C4×D314yes—
250C3×C22⋊C4C2×Dic314yes—
251C3×C42—38no—
252#217—22no—
253#217—62no—
254#217—62no—
255#217—122no—
256#217C2×Dic314yes—
257C4⋊Dic3—24no—
258C4⋊Dic3—64no—
259C4⋊Dic3—62no—
260C4⋊Dic3—62no—
261C4⋊Dic3—64no—
262C4⋊Dic3—64no—
263C4⋊Dic3—64no—
264C4⋊Dic3—124no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267Dic3⋊C4—62no—
268Dic3⋊C4—62no—
269Dic3⋊C4C2×Dic318yescomplemented
270C4×Dic3—64no—
271C4×Dic3—64no—
272C4×Dic3—62no—
273C4×Dic3—62no—
274C4×Dic3—62no—
275C4×Dic3—62no—
276C4×Dic3—64no—
277C4×Dic3—64no—
278C4×Dic3C2×Dic318yescomplemented
279C22×C32—24no—
280C22×C32—22no—
281C22×C32—22no—
282C22×C32—24no—
283C22×C32C2×C4⋊C414yes—
284C22×C32C23×C411yescharacteristic
285C22×C32C22×D411yescharacteristic
286C22×C32C22×Q811yescharacteristic
287C22×C32C2×#4112yes—
288C22×C32C2×#4112yes—
289C32×C4—24no—
290C3⋊Dic3—24no—
291C3⋊Dic3—41no—
292C3⋊Dic3—41no—
293C3×Dic3—24no—
294C3×Dic3—24no—
295C3×Dic3—41no—
296C3×Dic3—41no—
297C3×Dic3C2×C4⋊C414yes—
298C3×Dic3C2×C4⋊C414yes—
299C23×C4—31no—
300C23×C4—31no—
301C23×C4—91no—
302#117—38no—
303#117—184no—
304C2×C4⋊C4—32no—
305C2×C4⋊C4—32no—
306C2×C4⋊C4—91no—
307C2×C4⋊C4—91no—
308C2×C4⋊C4—92no—
309C2×C4⋊C4—92no—
310C2×C4⋊C4—92no—
311C2×C22⋊C4—31no—
312C2×C22⋊C4—31no—
313C2×C22⋊C4—91no—
314C2×C22⋊C4D3211yescharacteristic
315C2×C42—32no—
316C2×C42—91no—
317C2×C42—91no—
318C2×C42—92no—
319C2×C42—92no—
320C2×C42—184no—
321#95—32no—
322#95—92no—
323#95—92no—
324#95—92no—
325C23×C3—22no—
326C23×C3—22no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—21no—
330C23×C3—22no—
331C23×C3—22no—
332C23×C3—22no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3C2×Dic612yes—
336C23×C3C2×C4×D312yes—
337C23×C3C2×D1212yes—
338C23×C3D3×D412yes—
339C23×C3D3×Q812yes—
340C23×C3C22×Dic312yes—
341C23×C3C23×D311yescharacteristic
342C23×C3C23×D311yescharacteristic
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—24no—
348C2×C3×C4—316no—
349C2×C3×C4—32no—
350C2×C3×C4—32no—
351C2×C3×C4—32no—
352C2×C3×C4—32no—
353C2×C3×C4—32no—
354C2×C3×C4—32no—
355C2×C3×C4—34no—
356C2×C3×C4—34no—
357C2×C3×C4—42no—
358C2×C3×C4—42no—
359C2×C3×C4—68no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4—61no—
365C2×C3×C4—61no—
366C2×C3×C4—62no—
367C2×C3×C4—62no—
368C2×C3×C4C2×C4×D314yes—
369C2×C3×C4C22×Dic314yes—
370C2×Dic3—28no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—22no—
374C2×Dic3—22no—
375C2×Dic3—21no—
376C2×Dic3—21no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—34no—
380C2×Dic3—34no—
381C2×Dic3—64no—
382C2×Dic3—68no—
383C2×Dic3—68no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—61no—
389C2×Dic3—61no—
390C2×Dic3—61no—
391C2×Dic3—61no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—62no—
396C2×Dic3—122no—
397C2×Dic3—122no—
398C2×Dic3—128no—
399C2×Dic3—122no—
400C2×Dic3—121no—
401C2×Dic3—121no—
402C2×Dic3—122no—
403C2×Dic3C4⋊Dic3116yescomplemented
404C2×Dic3C2×Dic612yes—
405C2×Dic3C2×Dic612yes—
406C2×Dic3C2×D1212yes—
407C2×Dic3C2×D1212yes—
408C2×Dic3#23714yes—
409C2×Dic3C22×Dic314yes—
410C2×Dic3C22×Dic312yes—
411C2×Dic3C22×Dic312yes—
412C2×C32—24no—
413C2×C32C22×C4⋊C411yescharacteristic
414C2×C32C4×#4112yes—
415C2×C32#52511yescharacteristic
416C2×C32#52511yescharacteristic
417C2×C32#53312yes—
418C24C2×D3211yescharacteristic
419C22×C4—31no—
420C22×C4—31no—
421C22×C4—34no—
422C22×C4—34no—
423C22×C4—34no—
424C22×C4—32no—
425C22×C4—32no—
426C22×C4—31no—
427C22×C4—31no—
428C22×C4—64no—
429C22×C4—62no—
430C22×C4—92no—
431C22×C4—91no—
432C22×C4—91no—
433C22×C4—184no—
434C22×C4—182no—
435C22×C4C2×D3212yes—
436C4⋊C4—38no—
437C4⋊C4—64no—
438C4⋊C4—184no—
439C4⋊C4—182no—
440C4⋊C4—182no—
441C4⋊C4—184no—
442C4⋊C4—184no—
443C22⋊C4—34no—
444C22⋊C4—62no—
445C22⋊C4—182no—
446C22⋊C4D3×Dic314yes—
447C42—38no—
448C42—184no—
449C42—184no—
450C42—182no—
451C42—182no—
452C22×C3—22no—
453C22×C3—24no—
454C22×C3—22no—
455C22×C3—22no—
456C22×C3—24no—
457C22×C3—24no—
458C22×C3—22no—
459C22×C3—24no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—22no—
463C22×C3—22no—
464C22×C3—21no—
465C22×C3—24no—
466C22×C3—42no—
467C22×C3—42no—
468C22×C3—44no—
469C22×C3—44no—
470C22×C3D3×C4⋊C414yes—
471C22×C3C2×C4⋊Dic314yes—
472C22×C3C22×Dic611yescharacteristic
473C22×C3C22×C4×D311yescharacteristic
474C22×C3C22×D1211yescharacteristic
475C22×C3C2×D3×D411yescharacteristic
476C22×C3C2×#23712yes—
477C22×C3C2×D3×Q811yescharacteristic
478C22×C3D3×#4112yes—
479C22×C3D3×#4112yes—
480C22×C3D3×#4112yes—
481C22×C3C23×Dic311yescharacteristic
482C3×C4—24no—
483C3×C4—24no—
484C3×C4—34no—
485C3×C4—34no—
486C3×C4—44no—
487C3×C4—64no—
488C3×C4—64no—
489C3×C4—121no—
490C3×C4—121no—
491Dic3—24no—
492Dic3—24no—
493Dic3—41no—
494Dic3—41no—
495Dic3—64no—
496Dic3—64no—
497Dic3—124no—
498Dic3—121no—
499Dic3—121no—
500Dic3—121no—
501Dic3—121no—
502Dic3—241no—
503Dic3—241no—
504Dic3C2×C4⋊Dic314yes—
505Dic3C2×C4⋊Dic314yes—
506C32#229611yescharacteristic, complemented, Sylow
507C23—22no—
508C23—22no—
509C23D3×Dic612yes—
510C23D3×D1212yes—
511C23C2×D3×Dic312yes—
512C23C22×D3211yescharacteristic
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—32no—
516C2×C4—32no—
517C2×C4—32no—
518C2×C4—32no—
519C2×C4—32no—
520C2×C4—32no—
521C2×C4—316no—
522C2×C4—34no—
523C2×C4—34no—
524C2×C4—68no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—62no—
528C2×C4—62no—
529C2×C4—61no—
530C2×C4—61no—
531C2×C4—62no—
532C2×C4—62no—
533C2×C4—94no—
534C2×C4—188no—
535C2×C4—182no—
536C2×C4—182no—
537C2×C4—181no—
538C2×C4—181no—
539C2×C4—182no—
540C2×C4—182no—
541C2×C4C2×D3×Dic314yes—
542C2×C3—24no—
543C2×C3—24no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—22no—
548C2×C3—22no—
549C2×C3—44no—
550C2×C3C2×D3×C4⋊C411yescharacteristic
551C2×C3#551712yes—
552C2×C3#552411yescharacteristic
553C2×C3#552411yescharacteristic
554C2×C3C4×#23712yes—
555C2×C3#558611yescharacteristic
556C2×C3#562212yes—
557C2×C3#565611yescharacteristic
558C2×C3C22×C4⋊Dic311yescharacteristic
559C2×C3Dic3×#4112yes—
560C22—22no—
561C22—22no—
562C22—24no—
563C22—24no—
564C22D3×C4⋊Dic314yes—
565C22C2×D3×Dic611yescharacteristic
566C22C2×D3×D1211yescharacteristic
567C22D3×#23712yes—
568C22#6431212yes—
569C22C22×D3×Dic311yescharacteristic
570C4—24no—
571C4—34no—
572C4—34no—
573C4—64no—
574C4—64no—
575C4—121no—
576C4—121no—
577C4—184no—
578C4—361no—
579C4—361no—
580C3—21no—
581C3#7437811yescharacteristic, complemented
582C3#8222711yescharacteristic, complemented
583C2—24no—
584C2#1059402912yes—
585C2#1059407811yescharacteristic
586C2#1059407911yescharacteristic
587C2C2×D3×C4⋊Dic311yescharacteristic
588C2Dic3×#23712yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#2296
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. #10591268C2semidirect
9. Dic3×C4⋊Dic3C2semidirect
10. #10591265C2semidirect
11. #10591242C2semidirect
25. C3×#877C4semidirect
87. C3×Dic3⋊C4C2×C4semidirect
88. C3×C4×Dic3C2×C4semidirect
145. #877Dic3semidirect
181. C2×C3×Dic3C4⋊C4semidirect
269. Dic3⋊C4C2×Dic3semidirect
278. C4×Dic3C2×Dic3semidirect
403. C2×Dic3C4⋊Dic3semidirect
506. C32#2296semidirect
581. C3#74378semidirect
582. C3#82227semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8772
C2×#639552
C22×Dic322
#105926492
C3×#49502
#105917192
#105917182
#105912682
Dic3×C4⋊Dic32
#105912652
#105912422
#822273
#743783