Finite Group Databasebeta

← #11773403

Subgroups — #11773403

Order 1152.

1205 conjugacy classes of subgroups.

The subgroup lattice has 597 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4⋊Dic3C211yesmaximal, characteristic
2C2×#63658C211yesmaximal, characteristic
3C2×C3×C3⋊#95C211yesmaximal, characteristic
4C2×#63579C212yesmaximal
5C2×#63579C212yesmaximal
6#71567—31nomaximal
7#69412—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic
10C23×C3⋊Dic3C2211yescharacteristic
11C23×C3×Dic3C2212yes—
12C23×C3×Dic3C2212yes—
13C2×C3×C4⋊Dic3—22no—
14C2×C3×C4⋊Dic3—24no—
15#63658—22no—
16C3×C3⋊#95C414yescomplemented
17#63579—24no—
18#63579—24no—
19C22×C3×C4⋊C4—31no—
20C22×C4⋊Dic3D311yescharacteristic
21C2×C3×#95—31no—
22C2×C3⋊#95—31no—
23C2×C3⋊#95—31no—
24C2×C3⋊#95—32no—
25C2×C3⋊#95—32no—
26C2×C3⋊#95—32no—
27C2×C3⋊#95—32no—
28C2×C3⋊#95—61no—
29C2×C3⋊#95D311yescharacteristic
30C24×C32C2311yescharacteristic
31C22×C32×C4—22no—
32C22×C32×C4—22no—
33C22×C32×C4C2×C412yes—
34C22×C32×C4D412yes—
35C22×C32×C4Q812yes—
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3—21no—
38C22×C3⋊Dic3—22no—
39C22×C3⋊Dic3—21no—
40C22×C3⋊Dic3—21no—
41C22×C3⋊Dic3—22no—
42C22×C3⋊Dic3—22no—
43C22×C3⋊Dic3—22no—
44C22×C3⋊Dic3D412yes—
45C22×C3⋊Dic3Q812yes—
46C22×C3×Dic3—22no—
47C22×C3×Dic3—22no—
48C22×C3×Dic3—22no—
49C22×C3×Dic3—22no—
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×Dic3C2×C414yes—
59C22×C3×Dic3D414yes—
60C3×C4⋊Dic3—28no—
61#1442—91noSylow
62C23×C3×C4—21no—
63C23×C3×C4—32no—
64C23×C3×C4—32no—
65C23×C3×C4C2×D311yescharacteristic
66C23×C3×C4C2×D311yescharacteristic
67C23×Dic3—31no—
68C23×Dic3—31no—
69C23×Dic3—31no—
70C23×Dic3—31no—
71C23×Dic3—61no—
72C23×Dic3—61no—
73C23×Dic3C2×D312yes—
74C23×Dic3C2×D312yes—
75C2×C3×C4⋊C4—64no—
76C2×C3×C4⋊C4—62no—
77C2×C4⋊Dic3—22no—
78C2×C4⋊Dic3—24no—
79C3×#95—34no—
80C3⋊#95—64no—
81C3⋊#95—64no—
82C3⋊#95—64no—
83C3⋊#95—64no—
84C3⋊#95—62no—
85C3⋊#95—62no—
86C3⋊#95—64no—
87C3⋊#95Dic314yescomplemented
88C23×C32C22×C411yescharacteristic
89C23×C32C2×D411yescharacteristic
90C23×C32C2×D411yescharacteristic
91C23×C32C2×D412yes—
92C23×C32C2×Q811yescharacteristic
93C23×C32C2×Q811yescharacteristic
94C23×C32#4112yes—
95C23×C32#4112yes—
96C23×C32#4112yes—
97C23×C32#4111yescharacteristic
98C23×C32#4111yescharacteristic
99C2×C32×C4—24no—
100C2×C32×C4—22no—
101C2×C32×C4—24no—
102C2×C32×C4—22no—
103C2×C32×C4C4⋊C414yes—
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3—22no—
106C2×C3⋊Dic3—24no—
107C2×C3⋊Dic3—24no—
108C2×C3⋊Dic3—41no—
109C2×C3⋊Dic3—41no—
110C2×C3⋊Dic3—41no—
111C2×C3⋊Dic3—41no—
112C2×C3⋊Dic3—42no—
113C2×C3⋊Dic3—42no—
114C2×C3×Dic3—24no—
115C2×C3×Dic3—24no—
116C2×C3×Dic3—24no—
117C2×C3×Dic3—24no—
118C2×C3×Dic3—24no—
119C2×C3×Dic3—24no—
120C2×C3×Dic3—42no—
121C2×C3×Dic3—42no—
122C2×C3×Dic3—42no—
123C2×C3×Dic3—42no—
124C2×C3×Dic3—42no—
125C2×C3×Dic3—42no—
126C2×C3×Dic3—42no—
127C2×C3×Dic3—42no—
128C22×C4⋊C4—31no—
129C2×#95—31no—
130C2×#95—92no—
131C2×#95—92no—
132C2×#95—91no—
133C24×C3—21no—
134C24×C3C22×D311yescharacteristic
135C24×C3C22×D311yescharacteristic
136C22×C3×C4—22no—
137C22×C3×C4—22no—
138C22×C3×C4—22no—
139C22×C3×C4—22no—
140C22×C3×C4—22no—
141C22×C3×C4—22no—
142C22×C3×C4—22no—
143C22×C3×C4—34no—
144C22×C3×C4—34no—
145C22×C3×C4—42no—
146C22×C3×C4—42no—
147C22×C3×C4—62no—
148C22×C3×C4—62no—
149C22×C3×C4—62no—
150C22×C3×C4—62no—
151C22×C3×C4—62no—
152C22×C3×C4—62no—
153C22×C3×C4—62no—
154C22×C3×C4—62no—
155C22×C3×C4—62no—
156C22×C3×C4—62no—
157C22×C3×C4—62no—
158C22×C3×C4—62no—
159C22×C3×C4Dic612yes—
160C22×C3×C4Dic612yes—
161C22×C3×C4C4×D312yes—
162C22×C3×C4D1212yes—
163C22×C3×C4C2×Dic312yes—
164C22×C3×C4#6712yes—
165C22×Dic3—22no—
166C22×Dic3—22no—
167C22×Dic3—22no—
168C22×Dic3—22no—
169C22×Dic3—22no—
170C22×Dic3—22no—
171C22×Dic3—22no—
172C22×Dic3—22no—
173C22×Dic3—22no—
174C22×Dic3—22no—
175C22×Dic3—22no—
176C22×Dic3—22no—
177C22×Dic3—32no—
178C22×Dic3—32no—
179C22×Dic3—32no—
180C22×Dic3—32no—
181C22×Dic3—62no—
182C22×Dic3—62no—
183C22×Dic3—62no—
184C22×Dic3—62no—
185C22×Dic3—62no—
186C22×Dic3—62no—
187C22×Dic3—61no—
188C22×Dic3—61no—
189C22×Dic3—62no—
190C22×Dic3—62no—
191C22×Dic3—62no—
192C22×Dic3—62no—
193C22×Dic3—61no—
194C22×Dic3—61no—
195C22×Dic3—62no—
196C22×Dic3—61no—
197C22×Dic3—61no—
198C22×Dic3—62no—
199C22×Dic3—62no—
200C22×Dic3—61no—
201C22×Dic3—61no—
202C22×Dic3—62no—
203C22×Dic3—122no—
204C22×Dic3—122no—
205C22×Dic3—122no—
206C22×Dic3—122no—
207C22×Dic3C2×Dic314yes—
208C22×Dic3#6714yes—
209C3×C4⋊C4—68no—
210C4⋊Dic3—28no—
211C22×C32C2×C4⋊C411yescharacteristic
212C22×C32#11712yes—
213C22×C32C4×D411yescharacteristic
214C22×C32C4×D412yes—
215C22×C32C4×Q811yescharacteristic
216C22×C32#12011yescharacteristic
217C22×C32#12112yes—
218C22×C32#12111yescharacteristic
219C22×C32C22⋊Q812yes—
220C22×C32C22⋊Q812yes—
221C22×C32C22⋊Q811yescharacteristic
222C22×C32#12312yes—
223C22×C32#12311yescharacteristic
224C22×C32#12312yes—
225C22×C32#12411yescharacteristic
226C22×C32#12411yescharacteristic
227C22×C32#12412yes—
228C22×C32#12512yes—
229C22×C32#12512yes—
230C22×C32#12511yescharacteristic
231C22×C32#12612yes—
232C22×C32#12612yes—
233C22×C32C4⋊Q811yescharacteristic
234C32×C4—24no—
235C3⋊Dic3—42no—
236C3⋊Dic3—42no—
237C3×Dic3—44no—
238C3×Dic3—44no—
239C23×C4—32no—
240C23×C4—32no—
241C23×C4—91no—
242C23×C4—91no—
243C23×C4D3211yescharacteristic
244C2×C4⋊C4—64no—
245C2×C4⋊C4—62no—
246#95—34no—
247#95—184no—
248#95—184no—
249#95—182no—
250C23×C3—22no—
251C23×C3—21no—
252C23×C3—21no—
253C23×C3—21no—
254C23×C3—22no—
255C23×C3—21no—
256C23×C3—21no—
257C23×C3—22no—
258C23×C3—21no—
259C23×C3—21no—
260C23×C3—22no—
261C23×C3C2×Dic611yescharacteristic
262C23×C3C2×Dic611yescharacteristic
263C23×C3C2×C4×D311yescharacteristic
264C23×C3C2×D1211yescharacteristic
265C23×C3#23512yes—
266C23×C3#23512yes—
267C23×C3#23512yes—
268C23×C3D3×D411yescharacteristic
269C23×C3D3×D411yescharacteristic
270C23×C3D3×D412yes—
271C23×C3#23712yes—
272C23×C3#23711yescharacteristic
273C23×C3#23711yescharacteristic
274C23×C3#23712yes—
275C23×C3D3×Q811yescharacteristic
276C23×C3D3×Q811yescharacteristic
277C23×C3#23911yescharacteristic
278C23×C3#23911yescharacteristic
279C23×C3#23912yes—
280C23×C3C22×Dic311yescharacteristic
281C23×C3C2×#6711yescharacteristic
282C23×C3C2×#6712yes—
283C2×C3×C4—24no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—24no—
287C2×C3×C4—24no—
288C2×C3×C4—22no—
289C2×C3×C4—24no—
290C2×C3×C4—22no—
291C2×C3×C4—24no—
292C2×C3×C4—44no—
293C2×C3×C4—42no—
294C2×C3×C4—44no—
295C2×C3×C4—42no—
296C2×C3×C4—64no—
297C2×C3×C4—64no—
298C2×C3×C4—64no—
299C2×C3×C4—64no—
300C2×C3×C4—64no—
301C2×C3×C4—64no—
302C2×C3×C4—122no—
303C2×C3×C4—122no—
304C2×C3×C4—122no—
305C2×C3×C4—122no—
306C2×C3×C4—122no—
307C2×C3×C4—122no—
308C2×C3×C4—122no—
309C2×C3×C4—122no—
310C2×C3×C4Dic3⋊C414yes—
311C2×C3×C4C4⋊Dic314yes—
312C2×Dic3—24no—
313C2×Dic3—24no—
314C2×Dic3—24no—
315C2×Dic3—24no—
316C2×Dic3—24no—
317C2×Dic3—24no—
318C2×Dic3—42no—
319C2×Dic3—42no—
320C2×Dic3—42no—
321C2×Dic3—42no—
322C2×Dic3—42no—
323C2×Dic3—42no—
324C2×Dic3—42no—
325C2×Dic3—42no—
326C2×Dic3—64no—
327C2×Dic3—64no—
328C2×Dic3—64no—
329C2×Dic3—64no—
330C2×Dic3—62no—
331C2×Dic3—64no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—64no—
336C2×Dic3—124no—
337C2×Dic3—124no—
338C2×Dic3—124no—
339C2×Dic3—122no—
340C2×Dic3—122no—
341C2×Dic3—124no—
342C2×Dic3—122no—
343C2×Dic3—122no—
344C2×Dic3—121no—
345C2×Dic3—121no—
346C2×Dic3—121no—
347C2×Dic3—122no—
348C2×Dic3—121no—
349C2×Dic3—122no—
350C2×Dic3—122no—
351C2×Dic3—121no—
352C2×Dic3—121no—
353C2×Dic3—121no—
354C2×Dic3—122no—
355C2×Dic3—121no—
356C2×C32#38211yescharacteristic
357C2×C32#38511yescharacteristic
358C2×C32#38712yes—
359C2×C32#38812yes—
360C2×C32#38911yescharacteristic
361C2×C32#39311yescharacteristic
362C2×C32#39411yescharacteristic
363C2×C32#39711yescharacteristic
364C2×C32#39812yes—
365C2×C32#40011yescharacteristic
366C2×C32#40012yes—
367C24C2×D3211yescharacteristic
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—34no—
371C22×C4—34no—
372C22×C4—62no—
373C22×C4—62no—
374C22×C4—62no—
375C22×C4—62no—
376C22×C4—62no—
377C22×C4—62no—
378C22×C4—62no—
379C22×C4—62no—
380C22×C4—62no—
381C22×C4—62no—
382C22×C4—62no—
383C22×C4—62no—
384C22×C4—92no—
385C22×C4—92no—
386C22×C4—181no—
387C22×C4—181no—
388C22×C4—182no—
389C22×C4—182no—
390C22×C4—182no—
391C22×C4—181no—
392C22×C4—181no—
393C22×C4—182no—
394C22×C4D3×Dic312yes—
395C22×C4#62612yes—
396C22×C4#62712yes—
397C4⋊C4—68no—
398C22×C3—22no—
399C22×C3—21no—
400C22×C3—22no—
401C22×C3—22no—
402C22×C3—22no—
403C22×C3—22no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—22no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—22no—
410C22×C3—22no—
411C22×C3—22no—
412C22×C3—21no—
413C22×C3—22no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—22no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—22no—
420C22×C3—21no—
421C22×C3#87012yes—
422C22×C3#87511yescharacteristic
423C22×C3#87511yescharacteristic
424C22×C3#87812yes—
425C22×C3#87912yes—
426C22×C3#88211yescharacteristic
427C22×C3#88312yes—
428C22×C3#88412yes—
429C22×C3#88512yes—
430C22×C3#88611yescharacteristic
431C22×C3#88711yescharacteristic
432C22×C3#88811yescharacteristic
433C22×C3#88811yescharacteristic
434C22×C3#88912yes—
435C22×C3#88912yes—
436C22×C3#89012yes—
437C22×C3#89011yescharacteristic
438C22×C3#89011yescharacteristic
439C22×C3#89212yes—
440C22×C3#89311yescharacteristic
441C22×C3#89412yes—
442C22×C3#89412yes—
443C22×C3#89511yescharacteristic
444C22×C3#89612yes—
445C22×C3#89711yescharacteristic
446C22×C3#89812yes—
447C22×C3#89812yes—
448C22×C3#89812yes—
449C22×C3C2×Dic3⋊C411yescharacteristic
450C22×C3#92412yes—
451C22×C3C2×C4⋊Dic311yescharacteristic
452C22×C3#92612yes—
453C22×C3C4×#6712yes—
454C22×C3#92911yescharacteristic
455C22×C3D4×Dic311yescharacteristic
456C22×C3D4×Dic312yes—
457C22×C3#93512yes—
458C22×C3#93611yescharacteristic
459C22×C3#93811yescharacteristic
460C22×C3#93912yes—
461C22×C3Q8×Dic311yescharacteristic
462C22×C3#94611yescharacteristic
463C22×C3#94612yes—
464C22×C3#94711yescharacteristic
465C22×C3#94712yes—
466C22×C3#95311yescharacteristic
467C3×C4—24no—
468C3×C4—24no—
469C3×C4—44no—
470C3×C4—124no—
471C3×C4—124no—
472Dic3—44no—
473Dic3—44no—
474Dic3—124no—
475Dic3—124no—
476Dic3—122no—
477Dic3—122no—
478Dic3—122no—
479Dic3—122no—
480C32#144211yescharacteristic, complemented, Sylow
481C23#379512yes—
482C23#379611yescharacteristic
483C23#379611yescharacteristic
484C23#379711yescharacteristic
485C23#379912yes—
486C23#380211yescharacteristic
487C23C2×D3×Dic311yescharacteristic
488C23#380412yes—
489C23C2×#62611yescharacteristic
490C23C2×#62711yescharacteristic
491C23D3×#6712yes—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—22no—
496C2×C4—64no—
497C2×C4—64no—
498C2×C4—64no—
499C2×C4—64no—
500C2×C4—64no—
501C2×C4—64no—
502C2×C4—122no—
503C2×C4—122no—
504C2×C4—122no—
505C2×C4—122no—
506C2×C4—122no—
507C2×C4—122no—
508C2×C4—122no—
509C2×C4—122no—
510C2×C4—184no—
511C2×C4—182no—
512C2×C4—184no—
513C2×C4—182no—
514C2×C4—362no—
515C2×C4—361no—
516C2×C4—361no—
517C2×C4—362no—
518C2×C4—361no—
519C2×C4—361no—
520C2×C4Dic3⋊Dic314yes—
521C2×C3—22no—
522C2×C3—21no—
523C2×C3—22no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—22no—
527C2×C3—22no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3#465712yes—
533C2×C3#465911yescharacteristic
534C2×C3#466012yes—
535C2×C3#467211yescharacteristic
536C2×C3#467311yescharacteristic
537C2×C3#467411yescharacteristic
538C2×C3#493611yescharacteristic
539C2×C3#495011yescharacteristic
540C2×C3#495112yes—
541C2×C3#497211yescharacteristic
542C2×C3#497711yescharacteristic
543C2×C3#497812yes—
544C2×C3#498012yes—
545C2×C3#498212yes—
546C2×C3#498411yescharacteristic
547C2×C3#498511yescharacteristic
548C2×C3#498612yes—
549C2×C3#499012yes—
550C2×C3#499211yescharacteristic
551C2×C3#521011yescharacteristic
552C2×C3#522211yescharacteristic
553C2×C3#523111yescharacteristic
554C22#6384112yes—
555C22#6384311yescharacteristic
556C22#6384712yes—
557C22#6384812yes—
558C22#6385412yes—
559C22#6385812yes—
560C22#6386011yescharacteristic
561C22#6386411yescharacteristic
562C22#6386912yes—
563C22#6387111yescharacteristic
564C22#6387211yescharacteristic
565C22#6388412yes—
566C22#6388512yes—
567C22#6388812yes—
568C22#6389811yescharacteristic
569C22#6390712yes—
570C22#6391611yescharacteristic
571C22#6391911yescharacteristic
572C22#6396412yes—
573C22C2×Dic3⋊Dic311yescharacteristic
574C22#6396611yescharacteristic
575C22Dic3×#6712yes—
576C22#6397711yescharacteristic
577C4—24no—
578C4—124no—
579C4—124no—
580C4—362no—
581C4—362no—
582C3—21no—
583C3#6941211yescharacteristic, complemented
584C3#7156711yescharacteristic, complemented
585C2#1059122411yescharacteristic
586C2#1059122711yescharacteristic
587C2#1059126212yes—
588C2#1059130211yescharacteristic
589C2#1059130712yes—
590C2#1059131011yescharacteristic
591C2#1059132611yescharacteristic
592C2#1059134312yes—
593C2#1059134512yes—
594C2#1059135711yescharacteristic
595C2#1059171811yescharacteristic
subgroupG/H
center, FrattiniC24C2×D32
commutatorC23×C32C22×C4
FittingC23×C32×C4C22
socle, prime radical, cosocleC24×C32C23
hypercenterC23×C4D32
hypocenterC32#1442
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
16. C3×C3⋊#95C4semidirect
87. C3⋊#95Dic3semidirect
480. C32#1442semidirect
583. C3#69412semidirect
584. C3#71567semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4⋊Dic32
C2×#636582
C2×C3×C3⋊#952
C2×#635792
#715673
#694123