Finite Group Databasebeta

← #11805769

Subgroups — #11805769

Order 1152.

1341 conjugacy classes of subgroups.

The subgroup lattice has 603 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#626C211yesmaximal, characteristic
2C3⋊D3×#95C211yesmaximal, characteristic, complemented
3C3×#4666C211yesmaximal, characteristic, complemented
4C3×#4648C211yesmaximal, characteristic, complemented
5#10591387C212yesmaximal
6#10591355C211yesmaximal, characteristic, complemented
7#10591331C212yesmaximal, complemented
8#10591294C211yesmaximal, characteristic, complemented
9C4×#3722C212yesmaximal, complemented
10#10591279C212yesmaximal, complemented
11#10591223C211yesmaximal, characteristic, complemented
12#73576—31nomaximal
13#73417—31nomaximal
14C22×C4×C3⋊D3C2212yes—
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×#626C2211yescharacteristic
18C2×C3×(C2×D3)⋊C4C2212yes—
19C2×C3×C4×Dic3C2212yes—
20C2×C3×C4×Dic3C2212yes—
21C2×C3×C4×Dic3C2211yescharacteristic
22C2×#3724C2212yes—
23C2×Dic3⋊Dic3C2211yescharacteristic
24C2×#3722C2212yes—
25C2×#3722C2211yescharacteristic
26C2×(C2×D3)⋊Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2211yescharacteristic
28C4×#626C418yescomplemented
29C32×#95C2211yescharacteristic
30#63658C2212yes—
31#63658C2211yescharacteristic
32C3×C3⋊#95C2211yescharacteristic
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2211yescharacteristic
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×C4×#67—31no—
39C2×C4×D12—31no—
40C3×C4×C22⋊C4—31no—
41C3×#376—31no—
42#5211—31no—
43#4956—32no—
44#4944—32no—
45#4940—32no—
46C4×(C2×D3)⋊C4—32no—
47C4×(C2×D3)⋊C4—32no—
48#4937—31no—
49#4933—32no—
50#4667—31no—
51#4667—31no—
52#4666D311yescharacteristic, complemented
53#4665—32no—
54#4664—31no—
55D3×#95—31no—
56D3×#95—31no—
57D3×#95—61no—
58#4654—32no—
59#4651—31no—
60#4648D311yescharacteristic, complemented
61C23×C3⋊D3C2311yescharacteristic
62C23×C3×D3C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2312yes—
65C22×C3⋊Dic3C2312yes—
66C22×C3⋊Dic3C2311yescharacteristic
67C2×C4×C3⋊D3—24no—
68C2×C4×C3⋊D3—24no—
69C2×C4×C3⋊D3—42no—
70C2×C4×C3⋊D3—42no—
71C2×C4×C3⋊D3C2×C414yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2311yescharacteristic
77C2×C3×C4×D3—42no—
78C2×C3×C4×D3C2×C414yescomplemented
79C2×#626—22no—
80C2×#626—22no—
81C2×#626C2×C414yes—
82C3×(C2×D3)⋊C4—24no—
83C3×C4×Dic3—24no—
84C3×C4×Dic3—42no—
85C3×C4×Dic3C2×C414yescomplemented
86#3724—42no—
87Dic3⋊Dic3C2×C414yescomplemented
88#3722—24no—
89#3722C2×C414yes—
90(C2×D3)⋊Dic3—42no—
91(C2×D3)⋊Dic3C2×C414yescomplemented
92#2353—91noSylow
93C23×C3×C4—31no—
94C22×#67—31no—
95C22×D12—31no—
96C22×C4×D3—31no—
97C22×C4×D3—31no—
98C22×C4×D3—32no—
99C22×C4×D3—32no—
100C22×C4×D3—61no—
101C22×C4×D3—62no—
102C22×C4×D3C2×D311yescharacteristic
103C2×C3×C22⋊C4—32no—
104C2×C3×C42—31no—
105C2×C3×C42—32no—
106C2×C3×C42—32no—
107C2×#217—31no—
108C2×#217—32no—
109C4×#67—38no—
110C2×(C2×D3)⋊C4—31no—
111C2×(C2×D3)⋊C4—31no—
112C2×(C2×D3)⋊C4—31no—
113C2×(C2×D3)⋊C4—32no—
114C2×(C2×D3)⋊C4—32no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4C2×D312yes—
117C2×C4⋊Dic3—31no—
118C2×Dic3⋊C4—31no—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4—32no—
121C2×C4×Dic3C2×D312yes—
122C2×C4×Dic3C2×D312yes—
123C2×C4×Dic3C2×D311yescharacteristic
124C4×D12—38no—
125C3×#95—21no—
126C3×#95—31no—
127C3×#95—32no—
128C3×#95—31no—
129C3×#95C2×D311yescharacteristic
130C3×#95C2×D311yescharacteristic
131C3⋊#95—31no—
132C3⋊#95—32no—
133C3⋊#95—31no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—61no—
142C3⋊#95—62no—
143C3⋊#95C2×D311yescharacteristic
144C3⋊#95C2×D312yes—
145C3⋊#95C2×D311yescharacteristic
146C23×C32C2411yescharacteristic
147C22×C3⋊D3—22no—
148C22×C3⋊D3—22no—
149C22×C3⋊D3C22×C412yes—
150C22×C3⋊D3#4112yes—
151C22×C3⋊D3#4112yes—
152C22×C3×D3—22no—
153C22×C3×D3—21no—
154C22×C3×D3—21no—
155C22×C3×D3—22no—
156C22×C3×D3C22×C412yes—
157C2×C32×C4—22no—
158C2×C32×C4—22no—
159C2×C32×C4—22no—
160C2×C32×C4C22×C412yes—
161C2×C32×C4#4114yes—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3C22×C412yes—
167C4×C3⋊D3—44no—
168C4×C3⋊D3—48no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—21no—
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×Dic3C22×C412yes—
180C2×C3×Dic3C22×C412yes—
181C2×C3×Dic3C22×C412yes—
182C3×C4×D3—44no—
183#626—28no—
184C2×C4×D4—91no—
185#388—92no—
186#387—92no—
187#386—92no—
188#383—91no—
189#381—91no—
190#380—91no—
191C4×C22⋊C4—31no—
192C4×C22⋊C4—92no—
193#376—31no—
194C2×#95—91no—
195C24×C3—31no—
196C23×D3—31no—
197C23×D3—31no—
198C23×D3—61no—
199C23×D3C22×D311yescharacteristic
200C22×C3×C4—22no—
201C22×C3×C4—21no—
202C22×C3×C4—31no—
203C22×C3×C4—31no—
204C22×C3×C4—31no—
205C22×C3×C4—34no—
206C22×C3×C4—32no—
207C22×C3×C4—32no—
208C22×C3×C4—122no—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D312yes—
212C22×C3×C4C22×D312yes—
213C2×#67—34no—
214C2×#67—62no—
215C2×#67—62no—
216C22×Dic3—31no—
217C22×Dic3—31no—
218C22×Dic3—32no—
219C22×Dic3—32no—
220C22×Dic3—61no—
221C22×Dic3—62no—
222C22×Dic3C22×D312yes—
223C22×Dic3C22×D312yes—
224C22×Dic3C22×D311yescharacteristic
225C22×Dic3C22×D311yescharacteristic
226C22×Dic3C22×D311yescharacteristic
227C2×D12—34no—
228C2×D12—62no—
229C2×D12—62no—
230C2×C4×D3—34no—
231C2×C4×D3—34no—
232C2×C4×D3—42no—
233C2×C4×D3—64no—
234C2×C4×D3—64no—
235C2×C4×D3—64no—
236C2×C4×D3—68no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×C4×D3—124no—
240C2×C4×D3—122no—
241C2×C4×D3—122no—
242C2×C4×D3—122no—
243C2×C4×D3—122no—
244C2×C4×D3—124no—
245C2×C4×D3—124no—
246C2×C4×D3C4×D314yescomplemented
247C3×C22⋊C4—64no—
248C3×C42—34no—
249C3×C42—64no—
250C3×C42—122no—
251#217—34no—
252#217—122no—
253(C2×D3)⋊C4—24no—
254(C2×D3)⋊C4—34no—
255(C2×D3)⋊C4—34no—
256(C2×D3)⋊C4—34no—
257(C2×D3)⋊C4—64no—
258(C2×D3)⋊C4—64no—
259(C2×D3)⋊C4—122no—
260C4⋊Dic3—34no—
261Dic3⋊C4—34no—
262Dic3⋊C4—122no—
263Dic3⋊C4—122no—
264C4×Dic3—24no—
265C4×Dic3—42no—
266C4×Dic3C4×D314yescomplemented
267C22×C32C23×C411yescharacteristic
268C22×C32C2×#4112yes—
269C22×C32C2×#4111yescharacteristic
270C22×C32C2×#4111yescharacteristic
271C22×C32H(5,𝔽2)12yes—
272C2×C3⋊D3—22no—
273C2×C3⋊D3—22no—
274C2×C3⋊D3—24no—
275C2×C3⋊D3—24no—
276C2×C3⋊D3#11714yes—
277C2×C3×D3—22no—
278C2×C3×D3—22no—
279C2×C3×D3—22no—
280C2×C3×D3—42no—
281C2×C3×D3—42no—
282C32×C4—22no—
283C32×C4—24no—
284C3⋊Dic3—22no—
285C3⋊Dic3—42no—
286C3×Dic3—22no—
287C3×Dic3—22no—
288C3×Dic3—22no—
289C3×Dic3—42no—
290C3×Dic3—42no—
291C22×D4—91no—
292C23×C4—31no—
293C23×C4—91no—
294C23×C4—92no—
295C4×D4—98no—
296C2×C4⋊C4—91no—
297C2×C4⋊C4—92no—
298C2×C22⋊C4—32no—
299C2×C22⋊C4—91no—
300C2×C22⋊C4—91no—
301C2×C22⋊C4—92no—
302C2×C22⋊C4—92no—
303C2×C42—31no—
304C2×C42—32no—
305C2×C42—32no—
306#95—31no—
307#95—32no—
308#95—31no—
309#95—92no—
310#95—92no—
311#95—92no—
312#95—91no—
313#95—92no—
314#95D3211yescharacteristic
315C23×C3—21no—
316C23×C3—32no—
317C23×C3—62no—
318C23×C3—61no—
319C23×C3—61no—
320C23×C3—62no—
321C23×C3C23×D311yescharacteristic
322C23×C3C23×D311yescharacteristic
323C22×D3—22no—
324C22×D3—22no—
325C22×D3—21no—
326C22×D3—21no—
327C22×D3—32no—
328C22×D3—32no—
329C22×D3—32no—
330C22×D3—32no—
331C22×D3—32no—
332C22×D3—32no—
333C22×D3—62no—
334C22×D3—62no—
335C22×D3—62no—
336C22×D3—64no—
337C22×D3—64no—
338C22×D3—62no—
339C22×D3—62no—
340C22×D3—62no—
341C22×D3—62no—
342C22×D3C2×C4×D312yes—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—24no—
350C2×C3×C4—22no—
351C2×C3×C4—32no—
352C2×C3×C4—32no—
353C2×C3×C4—32no—
354C2×C3×C4—42no—
355C2×C3×C4—42no—
356C2×C3×C4—42no—
357C2×C3×C4—62no—
358C2×C3×C4—61no—
359C2×C3×C4—61no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4—124no—
368C2×C3×C4C2×C4×D312yes—
369C2×C3×C4C2×C4×D312yes—
370C2×C3×C4#23514yes—
371C2×C3×C4#23514yes—
372#67—68no—
373C2×Dic3—22no—
374C2×Dic3—22no—
375C2×Dic3—21no—
376C2×Dic3—21no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—22no—
383C2×Dic3—32no—
384C2×Dic3—32no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—64no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—62no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—122no—
396C2×Dic3—122no—
397C2×Dic3—122no—
398C2×Dic3C2×C4×D312yes—
399C2×Dic3C2×C4×D312yes—
400C2×Dic3C2×C4×D312yes—
401D12—68no—
402C4×D3—44no—
403C4×D3—124no—
404C4×D3—124no—
405C4×D3—128no—
406C4×D3—128no—
407C4×D3—128no—
408C4×D3—1216no—
409C2×C32C2×#11711yescharacteristic
410C2×C32C4×#4111yescharacteristic
411C2×C32#51811yescharacteristic
412C2×C32#55112yes—
413C2×C32#55312yes—
414C3⋊D3—24no—
415C3×D3—42no—
416C24—31no—
417C24—91no—
418C2×D4—94no—
419C2×D4—182no—
420C2×D4—182no—
421C22×C4—31no—
422C22×C4—31no—
423C22×C4—31no—
424C22×C4—34no—
425C22×C4—32no—
426C22×C4—32no—
427C22×C4—91no—
428C22×C4—94no—
429C22×C4—92no—
430C22×C4—122no—
431C22×C4—184no—
432C22×C4—184no—
433C22×C4—362no—
434C22×C4—362no—
435C22×C4C2×D3212yes—
436C22×C4C2×D3211yescharacteristic
437C4⋊C4—94no—
438C4⋊C4—362no—
439C22⋊C4—64no—
440C22⋊C4—94no—
441C22⋊C4—94no—
442C22⋊C4—184no—
443C22⋊C4—362no—
444C42—34no—
445C42—64no—
446C42—122no—
447C22×C3—22no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—22no—
451C22×C3—21no—
452C22×C3—62no—
453C22×C3—62no—
454C22×C3—62no—
455C22×C3—122no—
456C22×C3—122no—
457C22×C3C22×C4×D311yescharacteristic
458C22×C3C22×C4×D311yescharacteristic
459C22×C3C2×#23512yes—
460C22×C3C2×#23512yes—
461C22×C3#100412yes—
462C22×C3D3×#4111yescharacteristic
463C22×C3D3×#4111yescharacteristic
464C22×C3D3×#4111yescharacteristic
465C22×C3D3×#4111yescharacteristic
466C22×C3#100912yes—
467C2×D3—22no—
468C2×D3—22no—
469C2×D3—22no—
470C2×D3—34no—
471C2×D3—34no—
472C2×D3—42no—
473C2×D3—42no—
474C2×D3—64no—
475C2×D3—64no—
476C2×D3—68no—
477C2×D3—68no—
478C2×D3—64no—
479C2×D3—62no—
480C2×D3—62no—
481C2×D3—62no—
482C2×D3—62no—
483C2×D3—64no—
484C2×D3—64no—
485C2×D3—64no—
486C2×D3—64no—
487C3×C4—22no—
488C3×C4—22no—
489C3×C4—24no—
490C3×C4—24no—
491C3×C4—42no—
492C3×C4—44no—
493C3×C4—62no—
494C3×C4—62no—
495C3×C4—62no—
496C3×C4—122no—
497C3×C4—122no—
498Dic3—22no—
499Dic3—22no—
500Dic3—22no—
501Dic3—42no—
502Dic3—42no—
503Dic3—62no—
504Dic3—62no—
505Dic3—122no—
506Dic3—124no—
507Dic3—122no—
508Dic3—122no—
509C32#235311yescharacteristic, complemented, Sylow
510C23—32no—
511C23—62no—
512C23—61no—
513C23—62no—
514C23—61no—
515C23—92no—
516C23—92no—
517C23—92no—
518C23—182no—
519C23—182no—
520C23C22×D3211yescharacteristic
521D4—188no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—32no—
526C2×C4—32no—
527C2×C4—32no—
528C2×C4—62no—
529C2×C4—61no—
530C2×C4—62no—
531C2×C4—61no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—62no—
536C2×C4—62no—
537C2×C4—62no—
538C2×C4—92no—
539C2×C4—124no—
540C2×C4—182no—
541C2×C4—182no—
542C2×C4—182no—
543C2×C4—182no—
544C2×C4—364no—
545C2×C4—368no—
546C2×C4#379814yes—
547C2×C4C4×D3212yes—
548C2×C3—22no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—22no—
553C2×C3—122no—
554C2×C3C4×#23511yescharacteristic
555C2×C3C4×#23511yescharacteristic
556C2×C3#548611yescharacteristic
557C2×C3D3×#11711yescharacteristic
558C2×C3D3×#11711yescharacteristic
559C2×C3#552111yescharacteristic
560C2×C3#552712yes—
561C2×C3#553012yes—
562C2×C3#555612yes—
563C2×C3#555812yes—
564D3—42no—
565D3—68no—
566D3—64no—
567D3—64no—
568C22—62no—
569C22—62no—
570C22—62no—
571C22—94no—
572C22—122no—
573C22—122no—
574C22—184no—
575C22—182no—
576C22—182no—
577C22—184no—
578C22C2×#379812yes—
579C22C2×C4×D3211yescharacteristic
580C22#6431211yescharacteristic
581C22#6431412yes—
582C22#6431911yescharacteristic
583C4—22no—
584C4—24no—
585C4—62no—
586C4—62no—
587C4—62no—
588C4—122no—
589C4—122no—
590C4—182no—
591C4—362no—
592C3—21no—
593C3#7341711yescharacteristic, complemented
594C3#7357611yescharacteristic, complemented
595C2—122no—
596C2—184no—
597C2C4×#379811yescharacteristic
598C2#1059404012yes—
599C2#1059418211yescharacteristic
600C2#1059458312yes—
601C2#1059460211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#626C22
hypercenter#95D32
hypocenterC32#2353
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×#95C2semidirect
3. C3×#4666C2semidirect
4. C3×#4648C2semidirect
6. #10591355C2semidirect
7. #10591331C2semidirect
8. #10591294C2semidirect
9. C4×#3722C2semidirect
10. #10591279C2semidirect
11. #10591223C2semidirect
28. C4×#626C4semidirect
52. #4666D3semidirect
60. #4648D3semidirect
78. C2×C3×C4×D3C2×C4semidirect
85. C3×C4×Dic3C2×C4semidirect
87. Dic3⋊Dic3C2×C4semidirect
91. (C2×D3)⋊Dic3C2×C4semidirect
246. C2×C4×D3C4×D3semidirect
266. C4×Dic3C4×D3semidirect
509. C32#2353semidirect
593. C3#73417semidirect
594. C3#73576semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6262
C3⋊D3×#952
C3×#46662
C3×#46482
#105913872
#105913552
#105913312
#105912942
C4×#37222
#105912792
#105912232
#735763
#734173