Finite Group Databasebeta

← #11773364

Subgroups — #11773364

Order 1152.

1337 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3750C211yesmaximal, characteristic
2C22×C3×C4⋊Dic3C211yesmaximal, characteristic
3C2×C3×C3⋊#95C211yesmaximal, characteristic
4C2×#63579C212yesmaximal
5C2×#63579C212yesmaximal
6#71566—31nomaximal
7#69410—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic
10C23×C3⋊Dic3C2211yescharacteristic
11C23×C3×Dic3C2212yes—
12C23×C3×Dic3C2212yes—
13C2×#3750—22no—
14C2×#3750—22no—
15C2×#3750C414yescomplemented
16C2×C3×C4⋊Dic3—22no—
17C2×C3×C4⋊Dic3—24no—
18C3×C3⋊#95—22no—
19#63579—24no—
20#63579—24no—
21C22×C3×C4⋊C4—31no—
22C22×C4⋊Dic3D311yescharacteristic
23C22×Dic3⋊C4—31no—
24C22×Dic3⋊C4—31no—
25C22×Dic3⋊C4—61no—
26C2×C3×#95—31no—
27C2×C3⋊#95—32no—
28C2×C3⋊#95—32no—
29C2×C3⋊#95—32no—
30C2×C3⋊#95—32no—
31C2×C3⋊#95D311yescharacteristic
32C24×C32C2311yescharacteristic
33C22×C32×C4—22no—
34C22×C32×C4—22no—
35C22×C32×C4C2×C412yes—
36C22×C32×C4D412yes—
37C22×C32×C4D412yes—
38C22×C3⋊Dic3—21no—
39C22×C3⋊Dic3—21no—
40C22×C3⋊Dic3—21no—
41C22×C3⋊Dic3—21no—
42C22×C3⋊Dic3—21no—
43C22×C3⋊Dic3—21no—
44C22×C3⋊Dic3—22no—
45C22×C3⋊Dic3—22no—
46C22×C3⋊Dic3C2×C412yes—
47C22×C3⋊Dic3C2×C412yes—
48C22×C3⋊Dic3D412yes—
49C22×C3⋊Dic3Q812yes—
50C22×C3×Dic3—22no—
51C22×C3×Dic3—22no—
52C22×C3×Dic3—22no—
53C22×C3×Dic3—22no—
54C22×C3×Dic3—22no—
55C22×C3×Dic3—22no—
56C22×C3×Dic3—22no—
57C22×C3×Dic3—22no—
58C22×C3×Dic3—22no—
59C22×C3×Dic3—22no—
60C22×C3×Dic3—22no—
61C22×C3×Dic3—22no—
62C22×C3×Dic3D414yes—
63C22×C3×Dic3Q814yes—
64#3750—28no—
65C3×C4⋊Dic3—28no—
66#1441—91noSylow
67C23×C3×C4—21no—
68C23×C3×C4—32no—
69C23×C3×C4—32no—
70C23×C3×C4C2×D311yescharacteristic
71C23×C3×C4C2×D311yescharacteristic
72C23×Dic3—31no—
73C23×Dic3—31no—
74C23×Dic3—31no—
75C23×Dic3—31no—
76C23×Dic3—61no—
77C23×Dic3—61no—
78C23×Dic3C2×D312yes—
79C23×Dic3C2×D312yes—
80C2×C3×C4⋊C4—64no—
81C2×C3×C4⋊C4—62no—
82C2×C4⋊Dic3—22no—
83C2×C4⋊Dic3—24no—
84C2×Dic3⋊C4—34no—
85C2×Dic3⋊C4—34no—
86C2×Dic3⋊C4—64no—
87C2×Dic3⋊C4—64no—
88C2×Dic3⋊C4—64no—
89C2×Dic3⋊C4—62no—
90C2×Dic3⋊C4—62no—
91C2×Dic3⋊C4—62no—
92C2×Dic3⋊C4—62no—
93C3×#95—62no—
94C3⋊#95—22no—
95C3⋊#95—64no—
96C3⋊#95—64no—
97C3⋊#95—64no—
98C3⋊#95—64no—
99C23×C32C22×C411yescharacteristic
100C23×C32C2×D411yescharacteristic
101C23×C32C2×D411yescharacteristic
102C23×C32C2×D411yescharacteristic
103C23×C32C2×D412yes—
104C23×C32C2×Q812yes—
105C23×C32C2×Q811yescharacteristic
106C23×C32#4112yes—
107C23×C32#4112yes—
108C23×C32#4111yescharacteristic
109C23×C32#4111yescharacteristic
110C2×C32×C4—24no—
111C2×C32×C4—22no—
112C2×C32×C4—24no—
113C2×C32×C4—22no—
114C2×C32×C4C22⋊C414yes—
115C2×C3⋊Dic3—22no—
116C2×C3⋊Dic3—22no—
117C2×C3⋊Dic3—22no—
118C2×C3⋊Dic3—22no—
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3—22no—
122C2×C3⋊Dic3—24no—
123C2×C3⋊Dic3—41no—
124C2×C3⋊Dic3—42no—
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3C4⋊C414yescomplemented
127C2×C3×Dic3—24no—
128C2×C3×Dic3—24no—
129C2×C3×Dic3—24no—
130C2×C3×Dic3—24no—
131C2×C3×Dic3—24no—
132C2×C3×Dic3—24no—
133C2×C3×Dic3—42no—
134C2×C3×Dic3—42no—
135C2×C3×Dic3—42no—
136C2×C3×Dic3—42no—
137C2×C3×Dic3—42no—
138C2×C3×Dic3—42no—
139C2×C3×Dic3—42no—
140C2×C3×Dic3—42no—
141C22×C4⋊C4—31no—
142C22×C4⋊C4—91no—
143C2×#95—31no—
144C2×#95—92no—
145C2×#95—92no—
146C24×C3—21no—
147C24×C3C22×D311yescharacteristic
148C24×C3C22×D311yescharacteristic
149C22×C3×C4—22no—
150C22×C3×C4—22no—
151C22×C3×C4—22no—
152C22×C3×C4—22no—
153C22×C3×C4—22no—
154C22×C3×C4—22no—
155C22×C3×C4—22no—
156C22×C3×C4—34no—
157C22×C3×C4—34no—
158C22×C3×C4—42no—
159C22×C3×C4—42no—
160C22×C3×C4—62no—
161C22×C3×C4—62no—
162C22×C3×C4—62no—
163C22×C3×C4—62no—
164C22×C3×C4—62no—
165C22×C3×C4—62no—
166C22×C3×C4—62no—
167C22×C3×C4—62no—
168C22×C3×C4—62no—
169C22×C3×C4—62no—
170C22×C3×C4—62no—
171C22×C3×C4—62no—
172C22×C3×C4C4×D312yes—
173C22×C3×C4C4×D312yes—
174C22×C3×C4D1212yes—
175C22×C3×C4D1212yes—
176C22×C3×C4#6712yes—
177C22×C3×C4#6712yes—
178C22×Dic3—22no—
179C22×Dic3—22no—
180C22×Dic3—22no—
181C22×Dic3—22no—
182C22×Dic3—22no—
183C22×Dic3—22no—
184C22×Dic3—22no—
185C22×Dic3—22no—
186C22×Dic3—22no—
187C22×Dic3—22no—
188C22×Dic3—22no—
189C22×Dic3—22no—
190C22×Dic3—32no—
191C22×Dic3—32no—
192C22×Dic3—32no—
193C22×Dic3—32no—
194C22×Dic3—32no—
195C22×Dic3—32no—
196C22×Dic3—32no—
197C22×Dic3—32no—
198C22×Dic3—62no—
199C22×Dic3—62no—
200C22×Dic3—62no—
201C22×Dic3—62no—
202C22×Dic3—62no—
203C22×Dic3—62no—
204C22×Dic3—62no—
205C22×Dic3—62no—
206C22×Dic3—61no—
207C22×Dic3—61no—
208C22×Dic3—61no—
209C22×Dic3—61no—
210C22×Dic3—61no—
211C22×Dic3—61no—
212C22×Dic3—61no—
213C22×Dic3—61no—
214C22×Dic3—62no—
215C22×Dic3—62no—
216C22×Dic3—61no—
217C22×Dic3—61no—
218C22×Dic3—62no—
219C22×Dic3—62no—
220C22×Dic3—62no—
221C22×Dic3—62no—
222C22×Dic3—61no—
223C22×Dic3—61no—
224C22×Dic3—122no—
225C22×Dic3—122no—
226C22×Dic3Dic614yes—
227C22×Dic3#6714yes—
228C3×C4⋊C4—68no—
229C4⋊Dic3—28no—
230Dic3⋊C4—616no—
231Dic3⋊C4—68no—
232Dic3⋊C4—68no—
233C22×C32C2×C22⋊C411yescharacteristic
234C22×C32C2×C4⋊C411yescharacteristic
235C22×C32#11711yescharacteristic
236C22×C32C4×D412yes—
237C22×C32C4×Q812yes—
238C22×C32#12011yescharacteristic
239C22×C32#12112yes—
240C22×C32#12111yescharacteristic
241C22×C32#12111yescharacteristic
242C22×C32#12112yes—
243C22×C32C22⋊Q812yes—
244C22×C32C22⋊Q812yes—
245C22×C32C22⋊Q812yes—
246C22×C32C22⋊Q811yescharacteristic
247C22×C32C22⋊Q811yescharacteristic
248C22×C32#12311yescharacteristic
249C22×C32#12312yes—
250C22×C32#12411yescharacteristic
251C22×C32#12512yes—
252C22×C32#12512yes—
253C22×C32#12612yes—
254C22×C32C4⋊Q811yescharacteristic
255C22×C32C4⋊Q812yes—
256C32×C4—24no—
257C3⋊Dic3—24no—
258C3⋊Dic3—42no—
259C3×Dic3—44no—
260C3×Dic3—44no—
261C23×C4—32no—
262C23×C4—32no—
263C23×C4—91no—
264C23×C4—91no—
265C23×C4D3211yescharacteristic
266C2×C4⋊C4—64no—
267C2×C4⋊C4—62no—
268C2×C4⋊C4—94no—
269C2×C4⋊C4—182no—
270C2×C4⋊C4—182no—
271#95—62no—
272#95—184no—
273#95—184no—
274C23×C3—22no—
275C23×C3—22no—
276C23×C3—21no—
277C23×C3—21no—
278C23×C3—21no—
279C23×C3—21no—
280C23×C3—22no—
281C23×C3—21no—
282C23×C3—21no—
283C23×C3—21no—
284C23×C3—22no—
285C23×C3C2×Dic612yes—
286C23×C3C2×C4×D311yescharacteristic
287C23×C3C2×C4×D311yescharacteristic
288C23×C3C2×D1211yescharacteristic
289C23×C3C2×D1211yescharacteristic
290C23×C3#23512yes—
291C23×C3#23512yes—
292C23×C3D3×D411yescharacteristic
293C23×C3D3×D411yescharacteristic
294C23×C3D3×D412yes—
295C23×C3#23712yes—
296C23×C3#23711yescharacteristic
297C23×C3#23711yescharacteristic
298C23×C3#23712yes—
299C23×C3D3×Q812yes—
300C23×C3D3×Q811yescharacteristic
301C23×C3D3×Q811yescharacteristic
302C23×C3#23911yescharacteristic
303C23×C3#23911yescharacteristic
304C23×C3C2×#6711yescharacteristic
305C23×C3C2×#6711yescharacteristic
306C23×C3C2×#6712yes—
307C2×C3×C4—24no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—24no—
311C2×C3×C4—22no—
312C2×C3×C4—24no—
313C2×C3×C4—24no—
314C2×C3×C4—22no—
315C2×C3×C4—24no—
316C2×C3×C4—44no—
317C2×C3×C4—42no—
318C2×C3×C4—42no—
319C2×C3×C4—44no—
320C2×C3×C4—64no—
321C2×C3×C4—64no—
322C2×C3×C4—64no—
323C2×C3×C4—64no—
324C2×C3×C4—64no—
325C2×C3×C4—64no—
326C2×C3×C4—122no—
327C2×C3×C4—122no—
328C2×C3×C4—122no—
329C2×C3×C4—122no—
330C2×C3×C4—122no—
331C2×C3×C4—122no—
332C2×C3×C4—122no—
333C2×C3×C4—122no—
334C2×C3×C4(C2×D3)⋊C414yes—
335C2×C3×C4(C2×D3)⋊C414yes—
336C2×Dic3—24no—
337C2×Dic3—24no—
338C2×Dic3—24no—
339C2×Dic3—24no—
340C2×Dic3—24no—
341C2×Dic3—24no—
342C2×Dic3—34no—
343C2×Dic3—34no—
344C2×Dic3—42no—
345C2×Dic3—42no—
346C2×Dic3—42no—
347C2×Dic3—42no—
348C2×Dic3—42no—
349C2×Dic3—42no—
350C2×Dic3—42no—
351C2×Dic3—42no—
352C2×Dic3—64no—
353C2×Dic3—64no—
354C2×Dic3—64no—
355C2×Dic3—64no—
356C2×Dic3—64no—
357C2×Dic3—64no—
358C2×Dic3—64no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—64no—
372C2×Dic3—64no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—64no—
376C2×Dic3—124no—
377C2×Dic3—122no—
378C2×Dic3—122no—
379C2×Dic3—124no—
380C2×Dic3—121no—
381C2×Dic3—121no—
382C2×Dic3—121no—
383C2×Dic3—122no—
384C2×Dic3—122no—
385C2×Dic3—121no—
386C2×C32#38011yescharacteristic
387C2×C32#38611yescharacteristic
388C2×C32#38712yes—
389C2×C32#38912yes—
390C2×C32#39111yescharacteristic
391C2×C32#39411yescharacteristic
392C2×C32#39511yescharacteristic
393C2×C32#39612yes—
394C2×C32#39811yescharacteristic
395C2×C32#39812yes—
396C2×C32#40011yescharacteristic
397C24C2×D3211yescharacteristic
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—34no—
401C22×C4—34no—
402C22×C4—62no—
403C22×C4—62no—
404C22×C4—62no—
405C22×C4—62no—
406C22×C4—62no—
407C22×C4—62no—
408C22×C4—62no—
409C22×C4—62no—
410C22×C4—62no—
411C22×C4—62no—
412C22×C4—62no—
413C22×C4—62no—
414C22×C4—92no—
415C22×C4—92no—
416C22×C4—92no—
417C22×C4—92no—
418C22×C4—181no—
419C22×C4—181no—
420C22×C4—181no—
421C22×C4—181no—
422C22×C4—182no—
423C22×C4—181no—
424C22×C4—181no—
425C22×C4—182no—
426C22×C4#62412yes—
427C22×C4#62612yes—
428C22×C4#62612yes—
429C4⋊C4—68no—
430C4⋊C4—188no—
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3—22no—
435C22×C3—21no—
436C22×C3—22no—
437C22×C3—22no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—22no—
443C22×C3—22no—
444C22×C3—22no—
445C22×C3—22no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—22no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—22no—
454C22×C3C4×Dic612yes—
455C22×C3#86911yescharacteristic
456C22×C3#87511yescharacteristic
457C22×C3#87812yes—
458C22×C3#87812yes—
459C22×C3#87912yes—
460C22×C3#67⋊C412yes—
461C22×C3#88211yescharacteristic
462C22×C3#88412yes—
463C22×C3#88611yescharacteristic
464C22×C3#88712yes—
465C22×C3#88812yes—
466C22×C3#88912yes—
467C22×C3#88912yes—
468C22×C3#88912yes—
469C22×C3#89012yes—
470C22×C3D3×C4⋊C411yescharacteristic
471C22×C3D3×C4⋊C411yescharacteristic
472C22×C3#89211yescharacteristic
473C22×C3#89211yescharacteristic
474C22×C3#89412yes—
475C22×C3#89511yescharacteristic
476C22×C3#89511yescharacteristic
477C22×C3#89612yes—
478C22×C3#89712yes—
479C22×C3#89711yescharacteristic
480C22×C3#89711yescharacteristic
481C22×C3#89812yes—
482C22×C3#92412yes—
483C22×C3C2×(C2×D3)⋊C411yescharacteristic
484C22×C3C2×(C2×D3)⋊C411yescharacteristic
485C22×C3C4×#6712yes—
486C22×C3#92911yescharacteristic
487C22×C3#93012yes—
488C22×C3#93512yes—
489C22×C3#93611yescharacteristic
490C22×C3#93811yescharacteristic
491C22×C3#93811yescharacteristic
492C22×C3#93912yes—
493C22×C3#93912yes—
494C22×C3#94412yes—
495C22×C3#94411yescharacteristic
496C22×C3#94611yescharacteristic
497C22×C3#94611yescharacteristic
498C22×C3#94612yes—
499C22×C3#95311yescharacteristic
500C3×C4—24no—
501C3×C4—24no—
502C3×C4—44no—
503C3×C4—124no—
504C3×C4—124no—
505Dic3—44no—
506Dic3—44no—
507Dic3—68no—
508Dic3—64no—
509Dic3—64no—
510Dic3—124no—
511Dic3—122no—
512Dic3—122no—
513C32#144111yescharacteristic, complemented, Sylow
514C23D3×Dic612yes—
515C23#379512yes—
516C23#379611yescharacteristic
517C23#379611yescharacteristic
518C23#379711yescharacteristic
519C23#380211yescharacteristic
520C23#380412yes—
521C23C2×#62411yescharacteristic
522C23C2×#62611yescharacteristic
523C23C2×#62611yescharacteristic
524C23D3×#6712yes—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—64no—
530C2×C4—64no—
531C2×C4—64no—
532C2×C4—64no—
533C2×C4—64no—
534C2×C4—64no—
535C2×C4—94no—
536C2×C4—122no—
537C2×C4—122no—
538C2×C4—122no—
539C2×C4—122no—
540C2×C4—122no—
541C2×C4—122no—
542C2×C4—122no—
543C2×C4—122no—
544C2×C4—182no—
545C2×C4—182no—
546C2×C4—182no—
547C2×C4—182no—
548C2×C4—182no—
549C2×C4—182no—
550C2×C4—184no—
551C2×C4—182no—
552C2×C4—361no—
553C2×C4—361no—
554C2×C4—362no—
555C2×C4#372214yes—
556C2×C3—22no—
557C2×C3—22no—
558C2×C3—21no—
559C2×C3—22no—
560C2×C3—21no—
561C2×C3—22no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3#464712yes—
568C2×C3#465512yes—
569C2×C3#465611yescharacteristic
570C2×C3#465911yescharacteristic
571C2×C3#466111yescharacteristic
572C2×C3#467211yescharacteristic
573C2×C3#492911yescharacteristic
574C2×C3#494812yes—
575C2×C3#495811yescharacteristic
576C2×C3#497311yescharacteristic
577C2×C3#497612yes—
578C2×C3#497812yes—
579C2×C3#498112yes—
580C2×C3#498212yes—
581C2×C3#498311yescharacteristic
582C2×C3#498511yescharacteristic
583C2×C3#498711yescharacteristic
584C2×C3#498711yescharacteristic
585C2×C3#499412yes—
586C2×C3#521311yescharacteristic
587C2×C3#522211yescharacteristic
588C2×C3#523011yescharacteristic
589C22#6383912yes—
590C22#6384412yes—
591C22#6384612yes—
592C22#6384712yes—
593C22#6384911yescharacteristic
594C22#6385712yes—
595C22#6385812yes—
596C22#6386011yescharacteristic
597C22#6386611yescharacteristic
598C22#6387111yescharacteristic
599C22#6387111yescharacteristic
600C22#6388412yes—
601C22#6388512yes—
602C22#6388712yes—
603C22#6389912yes—
604C22#6390011yescharacteristic
605C22#6391611yescharacteristic
606C22#6391611yescharacteristic
607C22#6395212yes—
608C22C2×#372211yescharacteristic
609C22#6396611yescharacteristic
610C22#6397711yescharacteristic
611C22#6397812yes—
612C4—24no—
613C4—124no—
614C4—124no—
615C4—184no—
616C4—362no—
617C3—21no—
618C3#6941011yescharacteristic, complemented
619C3#7156611yescharacteristic, complemented
620C2#1059121311yescharacteristic
621C2#1059122711yescharacteristic
622C2#1059126312yes—
623C2#1059126412yes—
624C2#1059130211yescharacteristic
625C2#1059130812yes—
626C2#1059132511yescharacteristic
627C2#1059134212yes—
628C2#1059134611yescharacteristic
629C2#1059135811yescharacteristic
630C2#1059171111yescharacteristic
subgroupG/H
center, FrattiniC24C2×D32
commutatorC23×C32C22×C4
FittingC23×C32×C4C22
socle, prime radical, cosocleC24×C32C23
hypercenterC23×C4D32
hypocenterC32#1441
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
15. C2×#3750C4semidirect
126. C2×C3⋊Dic3C4⋊C4semidirect
513. C32#1441semidirect
618. C3#69410semidirect
619. C3#71566semidirect

Maximal subgroups

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

subgroupindex
C22×#37502
C22×C3×C4⋊Dic32
C2×C3×C3⋊#952
C2×#635792
#715663
#694103