Finite Group Databasebeta

← #11803407

Subgroups — #11803407

Order 1152.

1473 conjugacy classes of subgroups.

The subgroup lattice has 641 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3750C211yesmaximal, characteristic, complemented
2C2×#67⋊Dic3C211yesmaximal, characteristic
3C2×#63962C211yesmaximal, characteristic
4C3×#5213C211yesmaximal, characteristic
5C3×#5210C211yesmaximal, characteristic, complemented
6#10591705C211yesmaximal, characteristic, complemented
7#10591697C211yesmaximal, characteristic, complemented
8#10591372C212yesmaximal, complemented
9#10591281C212yesmaximal, complemented
10#10591251C212yesmaximal, complemented
11#10591234C212yesmaximal, complemented
12#74664—31nomaximal
13#74384—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C23×C3⋊Dic3C2211yescharacteristic
17C22×C3×#67C2211yescharacteristic
18C22×D3×Dic3C2211yescharacteristic
19C2×#3750—24no—
20C2×#3750C2212yes—
21C2×#3750C2212yes—
22C2×C3×#217C2211yescharacteristic
23C2×C3×#217C2211yescharacteristic
24C2×C3×#217C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×Dic3⋊C4C2212yes—
27#67⋊Dic3—24no—
28C2×Dic3⋊Dic3C2211yescharacteristic
29C2×Dic3⋊Dic3C2212yes—
30#63962C418yescomplemented
31C2×(C2×D3)⋊Dic3C2211yescharacteristic
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×Dic32C2211yescharacteristic
34C2×Dic32C2212yes—
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×#935—31no—
41C2×D4×Dic3—31no—
42C22×Dic3⋊C4—31no—
43C22×Dic3⋊C4—31no—
44C22×Dic3⋊C4—61no—
45C2×#886—31no—
46C2×#67⋊C4—31no—
47C3×#386—31no—
48C3×#385—31no—
49#5213D311yescharacteristic
50#5210D311yescharacteristic, complemented
51#4989—32no—
52#4972—32no—
53#4946—32no—
54#4944—32no—
55#4943—31no—
56#4943—31no—
57Dic3×C22⋊C4—31no—
58Dic3×C22⋊C4—31no—
59#4669—32no—
60#4654—32no—
61#4652—32no—
62#4647—32no—
63C24×C32C2311yescharacteristic
64C23×C3×D3C2311yescharacteristic
65C22×C32×C4—22no—
66C22×C32×C4—42no—
67C22×C32×C4C2312yes—
68C22×C3⋊Dic3—22no—
69C22×C3⋊Dic3—22no—
70C22×C3⋊Dic3—42no—
71C22×C3⋊Dic3C2×C414yescomplemented
72C22×C3⋊Dic3D414yes—
73C22×C3⋊Dic3C2312yes—
74C22×C3⋊Dic3C2311yescharacteristic
75C22×C3⋊Dic3C2311yescharacteristic
76C2×C3×#67—22no—
77C2×C3×#67—22no—
78C2×C3×#67C2×C414yes—
79C22×C3×Dic3C2311yescharacteristic
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2311yescharacteristic
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2311yescharacteristic
84C2×D3×Dic3—22no—
85C2×D3×Dic3—42no—
86#3750—24no—
87#3750—24no—
88C3×#217—22no—
89C3×#217—22no—
90C3×#217C2×C414yescomplemented
91C3×(C2×D3)⋊C4—42no—
92C3×Dic3⋊C4—42no—
93Dic3⋊Dic3—22no—
94Dic3⋊Dic3C2×C418yescomplemented
95(C2×D3)⋊Dic3—22no—
96(C2×D3)⋊Dic3C2×C418yescomplemented
97Dic32—22no—
98Dic32—42no—
99#2322—91noSylow
100C22×C3×D4—31no—
101C23×C3×C4—21no—
102C23×C3×C4C2×D311yescharacteristic
103C23×C3×C4C2×D311yescharacteristic
104C22×#67C2×D311yescharacteristic
105C23×Dic3—31no—
106C23×Dic3—31no—
107C23×Dic3—31no—
108C23×Dic3—31no—
109C23×Dic3—31no—
110C23×Dic3—61no—
111C23×Dic3—61no—
112C22×C4×D3—31no—
113C2×C3×C4⋊C4—32no—
114C2×C3×C22⋊C4—31no—
115C2×C3×C22⋊C4—31no—
116C2×C3×C22⋊C4—31no—
117C2×C3×C22⋊C4—32no—
118C2×#217—32no—
119C2×#217—31no—
120C2×#217C2×D311yescharacteristic
121C2×#217C2×D311yescharacteristic
122C2×#217C2×D311yescharacteristic
123#935—38no—
124D4×Dic3—64no—
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4—31no—
127C2×(C2×D3)⋊C4C2×D312yes—
128C2×C4⋊Dic3—32no—
129C2×C4⋊Dic3—31no—
130C2×Dic3⋊C4—32no—
131C2×Dic3⋊C4—32no—
132C2×Dic3⋊C4—32no—
133C2×Dic3⋊C4—32no—
134C2×Dic3⋊C4—32no—
135C2×Dic3⋊C4—31no—
136C2×Dic3⋊C4—62no—
137C2×Dic3⋊C4—62no—
138C2×Dic3⋊C4—64no—
139C2×Dic3⋊C4—64no—
140C2×Dic3⋊C4—68no—
141C2×Dic3⋊C4C2×D312yes—
142C2×C4×Dic3—31no—
143C2×C4×Dic3—31no—
144C2×C4×Dic3—32no—
145C2×C4×Dic3—32no—
146#886—38no—
147#67⋊C4—64no—
148C3×#95—32no—
149C3×#95—32no—
150C3⋊#95—32no—
151C3⋊#95—32no—
152C3⋊#95—32no—
153C3⋊#95—32no—
154C3⋊#95—32no—
155C3⋊#95—32no—
156C3⋊#95C2×D312yes—
157C3⋊#95C2×D312yes—
158C23×C32—22no—
159C23×C32—22no—
160C23×C32C22×C412yes—
161C23×C32C2×D412yes—
162C23×C32#4112yes—
163C23×C32C2411yescharacteristic
164C22×C3×D3—21no—
165C22×C3×D3—21no—
166C22×C3×D3—22no—
167C22×C3×D3—22no—
168C22×C3×D3C22×C412yes—
169C2×C32×C4—22no—
170C2×C32×C4—22no—
171C2×C32×C4—22no—
172C2×C32×C4—44no—
173C2×C3⋊Dic3—28no—
174C2×C3⋊Dic3—22no—
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3—22no—
177C2×C3⋊Dic3—22no—
178C2×C3⋊Dic3—44no—
179C2×C3⋊Dic3C22×C414yes—
180C2×C3⋊Dic3C2×D412yes—
181C2×C3⋊Dic3C2×D412yes—
182C3×#67—28no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3C22×C414yes—
195C2×C3×Dic3C22×C412yes—
196D3×Dic3—44no—
197C2×#123—91no—
198C2×C4×D4—91no—
199C22×C4⋊C4—91no—
200#389—92no—
201#388—92no—
202#387—92no—
203#386—31no—
204#385—31no—
205#385—92no—
206#381—91no—
207C4×C22⋊C4—91no—
208C24×C3—21no—
209C24×C3—31no—
210C24×C3C22×D311yescharacteristic
211C24×C3C22×D311yescharacteristic
212C23×D3C22×D311yescharacteristic
213C2×C3×D4—34no—
214C2×C3×D4—62no—
215C2×C3×D4—62no—
216C22×C3×C4—24no—
217C22×C3×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—32no—
221C22×C3×C4—31no—
222C22×C3×C4—32no—
223C22×C3×C4—31no—
224C22×C3×C4—31no—
225C22×C3×C4—42no—
226C22×C3×C4—42no—
227C22×C3×C4—44no—
228C22×C3×C4C22×D312yes—
229C22×C3×C4C22×D312yes—
230C2×#67—22no—
231C2×#67—22no—
232C2×#67C4×D314yes—
233C22×Dic3—34no—
234C22×Dic3—34no—
235C22×Dic3—31no—
236C22×Dic3—31no—
237C22×Dic3—32no—
238C22×Dic3—32no—
239C22×Dic3—31no—
240C22×Dic3—31no—
241C22×Dic3—34no—
242C22×Dic3—34no—
243C22×Dic3—62no—
244C22×Dic3—64no—
245C22×Dic3—64no—
246C22×Dic3—61no—
247C22×Dic3—61no—
248C22×Dic3—62no—
249C22×Dic3—64no—
250C22×Dic3—64no—
251C22×Dic3—62no—
252C22×Dic3—62no—
253C22×Dic3—62no—
254C22×Dic3—62no—
255C22×Dic3—122no—
256C22×Dic3—122no—
257C22×Dic3—122no—
258C22×Dic3—124no—
259C22×Dic3C22×D312yes—
260C22×Dic3C22×D311yescharacteristic
261C22×Dic3C22×D311yescharacteristic
262C22×Dic3C22×D312yes—
263C22×Dic3C22×D311yescharacteristic
264C2×C4×D3—62no—
265C2×C4×D3—122no—
266C3×C4⋊C4—122no—
267C3×C22⋊C4—34no—
268C3×C22⋊C4—62no—
269C3×C22⋊C4—62no—
270C3×C22⋊C4—122no—
271#217—22no—
272#217—22no—
273#217—38no—
274#217—62no—
275#217C4×D314yescomplemented
276(C2×D3)⋊C4—38no—
277(C2×D3)⋊C4—42no—
278(C2×D3)⋊C4—62no—
279C4⋊Dic3—38no—
280C4⋊Dic3—62no—
281Dic3⋊C4—38no—
282Dic3⋊C4—42no—
283Dic3⋊C4—62no—
284Dic3⋊C4—64no—
285Dic3⋊C4—64no—
286Dic3⋊C4—64no—
287Dic3⋊C4—64no—
288Dic3⋊C4—68no—
289Dic3⋊C4—68no—
290C4×Dic3—62no—
291C4×Dic3—62no—
292C4×Dic3—122no—
293C4×Dic3—122no—
294C22×C32—24no—
295C22×C32—22no—
296C22×C32—22no—
297C22×C32—24no—
298C22×C32C4×D414yes—
299C22×C32C23×C411yescharacteristic
300C22×C32C22×D411yescharacteristic
301C22×C32C2×#4111yescharacteristic
302C22×C32H(5,𝔽2)12yes—
303C22×C322−1+412yes—
304C2×C3×D3—22no—
305C2×C3×D3—24no—
306C2×C3×D3—41no—
307C2×C3×D3—41no—
308C2×C3×D3—42no—
309C32×C4—42no—
310C3⋊Dic3—24no—
311C3⋊Dic3—22no—
312C3⋊Dic3—22no—
313C3×Dic3—22no—
314C3×Dic3—24no—
315C3×Dic3—41no—
316C3×Dic3—41no—
317C3×Dic3—42no—
318C22×D4—31no—
319C23×C4—91no—
320C23×C4—91no—
321C23×C4—91no—
322C23×C4D3211yescharacteristic
323#123—98no—
324C4×D4—184no—
325C2×C4⋊C4—32no—
326C2×C4⋊C4—92no—
327C2×C4⋊C4—91no—
328C2×C4⋊C4—92no—
329C2×C4⋊C4—92no—
330C2×C4⋊C4—184no—
331C2×C22⋊C4—31no—
332C2×C22⋊C4—31no—
333C2×C22⋊C4—31no—
334C2×C22⋊C4—32no—
335C2×C22⋊C4—92no—
336C2×C22⋊C4—91no—
337C2×C42—91no—
338C2×C42—92no—
339#95—32no—
340#95—32no—
341#95—92no—
342#95—92no—
343#95—92no—
344C23×C3—24no—
345C23×C3—24no—
346C23×C3—22no—
347C23×C3—22no—
348C23×C3—22no—
349C23×C3—22no—
350C23×C3—21no—
351C23×C3—22no—
352C23×C3—22no—
353C23×C3—22no—
354C23×C3—32no—
355C23×C3—61no—
356C23×C3—62no—
357C23×C3—61no—
358C23×C3—62no—
359C23×C3C2×C4×D312yes—
360C23×C3C2×C4×D312yes—
361C23×C3D3×D412yes—
362C23×C3D3×D412yes—
363C23×C3#23712yes—
364C23×C3#23912yes—
365C23×C3C23×D311yescharacteristic
366C23×C3C23×D311yescharacteristic
367C22×D3—21no—
368C22×D3—21no—
369C22×D3—22no—
370C22×D3—22no—
371C22×D3C2×C4×D312yes—
372C3×D4—68no—
373C2×C3×C4—24no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—32no—
381C2×C3×C4—34no—
382C2×C3×C4—42no—
383C2×C3×C4—42no—
384C2×C3×C4—48no—
385C2×C3×C4—44no—
386C2×C3×C4—44no—
387C2×C3×C4—61no—
388C2×C3×C4—62no—
389C2×C3×C4—61no—
390C2×C3×C4—62no—
391C2×C3×C4—61no—
392C2×C3×C4—61no—
393C2×C3×C4—62no—
394C2×C3×C4—62no—
395C2×C3×C4—62no—
396C2×C3×C4—62no—
397C2×C3×C4—62no—
398#67—28no—
399C2×Dic3—21no—
400C2×Dic3—21no—
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3—21no—
404C2×Dic3—21no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—34no—
411C2×Dic3—34no—
412C2×Dic3—32no—
413C2×Dic3—32no—
414C2×Dic3—32no—
415C2×Dic3—32no—
416C2×Dic3—64no—
417C2×Dic3—62no—
418C2×Dic3—62no—
419C2×Dic3—64no—
420C2×Dic3—64no—
421C2×Dic3—616no—
422C2×Dic3—68no—
423C2×Dic3—68no—
424C2×Dic3—62no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427C2×Dic3—62no—
428C2×Dic3—62no—
429C2×Dic3—62no—
430C2×Dic3—62no—
431C2×Dic3—62no—
432C2×Dic3—122no—
433C2×Dic3—122no—
434C2×Dic3—124no—
435C2×Dic3—124no—
436C2×Dic3—124no—
437C2×Dic3—128no—
438C2×Dic3C2×C4×D314yes—
439C2×Dic3C2×C4×D312yes—
440C4×D3—124no—
441C2×C32—24no—
442C2×C32C2×C4×D411yescharacteristic
443C2×C32#52012yes—
444C2×C32#53411yescharacteristic
445C2×C32#53611yescharacteristic
446C2×C32#53912yes—
447C3×D3—42no—
448C24—31no—
449C24C2×D3211yescharacteristic
450C2×D4—34no—
451C2×D4—62no—
452C2×D4—62no—
453C22×C4—22no—
454C22×C4—31no—
455C22×C4—32no—
456C22×C4—31no—
457C22×C4—32no—
458C22×C4—31no—
459C22×C4—42no—
460C22×C4—91no—
461C22×C4—92no—
462C22×C4—91no—
463C22×C4—94no—
464C22×C4—94no—
465C22×C4—182no—
466C22×C4—182no—
467C22×C4—182no—
468C22×C4—362no—
469C22×C4—362no—
470C22×C4C2×D3212yes—
471C4⋊C4—98no—
472C4⋊C4—122no—
473C4⋊C4—184no—
474C4⋊C4—184no—
475C4⋊C4—182no—
476C22⋊C4—34no—
477C22⋊C4—62no—
478C22⋊C4—62no—
479C22⋊C4—98no—
480C22⋊C4—122no—
481C22⋊C4—182no—
482C42—182no—
483C42—362no—
484C22×C3—24no—
485C22×C3—28no—
486C22×C3—24no—
487C22×C3—28no—
488C22×C3—24no—
489C22×C3—22no—
490C22×C3—22no—
491C22×C3—24no—
492C22×C3—24no—
493C22×C3—22no—
494C22×C3—22no—
495C22×C3—24no—
496C22×C3—21no—
497C22×C3—22no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—22no—
501C22×C3—24no—
502C22×C3—62no—
503C22×C3—64no—
504C22×C3—122no—
505C22×C3—121no—
506C22×C3—121no—
507C22×C3#67⋊C414yes—
508C22×C3#89314yes—
509C22×C3C22×C4×D311yescharacteristic
510C22×C3C22×C4×D311yescharacteristic
511C22×C3C2×D3×D411yescharacteristic
512C22×C3C2×D3×D411yescharacteristic
513C22×C3C2×#23711yescharacteristic
514C22×C3#100412yes—
515C22×C3#100412yes—
516C22×C3C2×#23911yescharacteristic
517C22×C3#101012yes—
518C22×C3#101012yes—
519C2×D3—22no—
520C2×D3—24no—
521C2×D3—41no—
522C2×D3—41no—
523C2×D3—42no—
524C3×C4—44no—
525C3×C4—42no—
526C3×C4—42no—
527C3×C4—62no—
528C3×C4—64no—
529C3×C4—122no—
530C3×C4—121no—
531C3×C4—121no—
532Dic3—22no—
533Dic3—24no—
534Dic3—41no—
535Dic3—41no—
536Dic3—42no—
537Dic3—68no—
538Dic3—64no—
539Dic3—64no—
540Dic3—62no—
541Dic3—62no—
542Dic3—62no—
543Dic3—62no—
544Dic3—122no—
545Dic3—122no—
546C32#232211yescharacteristic, complemented, Sylow
547C23—22no—
548C23—22no—
549C23—32no—
550C23—61no—
551C23—62no—
552C23—61no—
553C23—62no—
554C23#379612yes—
555C23C4×D3212yes—
556C23#381112yes—
557C23C22×D3211yescharacteristic
558D4—68no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—34no—
563C2×C4—32no—
564C2×C4—44no—
565C2×C4—61no—
566C2×C4—62no—
567C2×C4—61no—
568C2×C4—62no—
569C2×C4—62no—
570C2×C4—62no—
571C2×C4—62no—
572C2×C4—61no—
573C2×C4—61no—
574C2×C4—62no—
575C2×C4—62no—
576C2×C4—94no—
577C2×C4—92no—
578C2×C4—92no—
579C2×C4—182no—
580C2×C4—182no—
581C2×C4—182no—
582C2×C4—182no—
583C2×C4—188no—
584C2×C4—364no—
585C2×C4—364no—
586C2×C3—28no—
587C2×C3—24no—
588C2×C3—24no—
589C2×C3—22no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—22no—
593C2×C3—21no—
594C2×C3—122no—
595C2×C3C2×#67⋊C411yescharacteristic
596C2×C3C2×#89311yescharacteristic
597C2×C3#554612yes—
598C2×C3#554612yes—
599C2×C3#558911yescharacteristic
600C2×C3#558911yescharacteristic
601C2×C3#560212yes—
602C2×C3#564512yes—
603C2×C3#564811yescharacteristic
604C2×C3#564811yescharacteristic
605D3—42no—
606C22—24no—
607C22—22no—
608C22—24no—
609C22—22no—
610C22—64no—
611C22—62no—
612C22—121no—
613C22—122no—
614C22—121no—
615C22#6388114yes—
616C22C2×#379611yescharacteristic
617C22#6429812yes—
618C22C2×C4×D3211yescharacteristic
619C22C2×#381111yescharacteristic
620C22#6433012yes—
621C4—42no—
622C4—64no—
623C4—62no—
624C4—121no—
625C4—122no—
626C4—121no—
627C4—184no—
628C4—182no—
629C4—182no—
630C3—21no—
631C3#7438411yescharacteristic, complemented
632C3#7466411yescharacteristic, complemented
633C2—24no—
634C2—122no—
635C2#1059487612yes—
636C2C2×#6388111yescharacteristic
637C2#1059492111yescharacteristic
638C2#1059497412yes—
639C2#1059552811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32#2322
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3750C2semidirect
5. C3×#5210C2semidirect
6. #10591705C2semidirect
7. #10591697C2semidirect
8. #10591372C2semidirect
9. #10591281C2semidirect
10. #10591251C2semidirect
11. #10591234C2semidirect
30. #63962C4semidirect
50. #5210D3semidirect
71. C22×C3⋊Dic3C2×C4semidirect
90. C3×#217C2×C4semidirect
94. Dic3⋊Dic3C2×C4semidirect
96. (C2×D3)⋊Dic3C2×C4semidirect
275. #217C4×D3semidirect
546. C32#2322semidirect
631. C3#74384semidirect
632. C3#74664semidirect

Maximal subgroups

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

subgroupindex
C22×#37502
C2×#67⋊Dic32
C2×#639622
C3×#52132
C3×#52102
#105917052
#105916972
#105913722
#105912812
#105912512
#105912342
#746643
#743843