Finite Group Databasebeta

← #11792560

Subgroups — #11792560

Order 1152.

1049 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#204C211yesmaximal, characteristic, complemented
2C2×#63911C211yesmaximal, characteristic
3C22×#3717C211yesmaximal, characteristic, complemented
4C2×#63648C211yesmaximal, characteristic, complemented
5#10591220C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic, complemented
7C3×#4550C211yesmaximal, characteristic, complemented
8#72056—31nomaximal
9#68676—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×#626—22no—
14C22×C32×C8C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×C3×#204—22no—
19C2×C3×#204—22no—
20C2×C3×#204—22no—
21#63911—22no—
22#63911—22no—
23C2×#3717—22no—
24C2×#3717—22no—
25C2×#3717—22no—
26#63648—22no—
27#63579—22no—
28#63563—22no—
29C22×C3×SD16—31no—
30C22×#215—31no—
31C2×#940—31no—
32C22×#204—31no—
33C22×#204D311yescharacteristic, complemented
34C2×#874—31no—
35#5229—31no—
36C2×#832—31no—
37C2×#821—31no—
38C2×#821—31no—
39C2×#821—31no—
40C2×#821—61no—
41#4929—31no—
42C3×#336—31no—
43#4550D311yescharacteristic, complemented
44C23×C3⋊D3—21no—
45C23×C3×D3—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)D412yes—
54C22×C3×Dic3—21no—
55C22×C3×Dic3D412yes—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12D412yes—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6D412yescomplemented
68C2×#626—28no—
69C2×#626—44no—
70C2×#626—44no—
71C2×C32×C8—21no—
72C2×C32×C8—21no—
73C2×C32×C8D412yescomplemented
74C4⋊(C3⋊Dic3)—21no—
75C4⋊(C3⋊Dic3)—21no—
76C3×C4×Dic3—21no—
77C3×C4×Dic3—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8D412yescomplemented
81C3×#204—28no—
82#3717—28no—
83#2014—91noSylow
84C22×C3×Q8—31no—
85C22×C3×D4—31no—
86C22×#67—62no—
87C22×D12—31no—
88C22×D12—31no—
89C22×D12—61no—
90C22×D12—62no—
91C22×D12C2×D311yescharacteristic
92C22×Dic6C2×D311yescharacteristic
93C2×C3×SD16—62no—
94C2×C3×SD16—62no—
95C2×C3×SD16—62no—
96C22×C3×C8—21no—
97C22×C3×C8—31no—
98C22×C3×C8C2×D311yescharacteristic
99C22×C3×C8C2×D311yescharacteristic
100C2×C3×C42—31no—
101C2×#215—62no—
102C2×#215—62no—
103C2×#215—62no—
104#940—62no—
105#940—62no—
106C2×C4⋊Dic3—31no—
107C2×C4⋊Dic3—31no—
108C2×C4⋊Dic3—61no—
109C2×C4×Dic3C2×D311yescharacteristic
110C22×C3⋊C8C2×D311yescharacteristic
111C2×#204—22no—
112C2×#204—22no—
113C2×#204—22no—
114C2×#204—62no—
115C2×#204—62no—
116C2×#204—62no—
117#874—62no—
118#874—62no—
119#832—62no—
120C3⋊#95—62no—
121C3⋊#95—62no—
122#821—64no—
123#821—62no—
124#821—62no—
125#821—62no—
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—22no—
128C22×C3⋊D3—41no—
129C22×C3⋊D3—41no—
130C22×C3⋊D3—42no—
131C22×C3⋊D3—42no—
132C22×C3×D3—22no—
133C22×C3×D3—41no—
134C22×C3×D3—41no—
135C22×C3×D3—42no—
136C22×C3×D3—42no—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C3⋊Dic3—41no—
144C2×C3⋊Dic3—42no—
145C4⋊(C3⋊D3)—22no—
146C4⋊(C3⋊D3)—22no—
147C4⋊(C3⋊D3)—41no—
148C4⋊(C3⋊D3)—41no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3SD1614yescomplemented
155C3×D12—22no—
156C3×D12—22no—
157C3×D12—41no—
158C3×D12—41no—
159C3×Dic6—22no—
160C3×Dic6—22no—
161C3×Dic6—41no—
162C3×Dic6—41no—
163#626—416no—
164C32×C8—22no—
165C3×C3⋊C8—22no—
166C22×SD16—31no—
167C22×SD16—91no—
168C2×#127—91no—
169C2×#102—91no—
170C2×#102—91no—
171#391—91no—
172#336—31no—
173C24×C3—61no—
174C23×D3—21no—
175C23×D3—61no—
176C23×D3—61no—
177C23×D3—121no—
178C2×C3×Q8—32no—
179C2×C3×Q8—61no—
180C2×C3×Q8—61no—
181C2×C3×Q8—61no—
182C2×C3×Q8—61no—
183C2×C3×Q8—61no—
184C2×C3×D4—32no—
185C2×C3×D4—61no—
186C2×C3×D4—61no—
187C2×C3×D4—61no—
188C2×C3×D4—61no—
189C2×C3×D4—61no—
190C22×C3×C4—21no—
191C22×C3×C4—32no—
192C22×C3×C4—61no—
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C2×#67—68no—
196C2×#67—124no—
197C2×#67—124no—
198C22×Dic3—21no—
199C22×Dic3—61no—
200C22×Dic3—61no—
201C22×Dic3—121no—
202C22×Dic3D1212yes—
203C2×D12—21no—
204C2×D12—21no—
205C2×D12—21no—
206C2×D12—21no—
207C2×D12—21no—
208C2×D12—32no—
209C2×D12—32no—
210C2×D12—62no—
211C2×D12—62no—
212C2×D12—62no—
213C2×D12—61no—
214C2×D12—61no—
215C2×D12—61no—
216C2×D12—61no—
217C2×D12—61no—
218C2×D12—61no—
219C2×D12—61no—
220C2×D12—61no—
221C2×D12—68no—
222C2×D12—61no—
223C2×D12—61no—
224C2×D12—121no—
225C2×D12—121no—
226C2×D12—121no—
227C2×D12—124no—
228C2×D12—124no—
229C2×D12#6712yes—
230C2×Dic6—21no—
231C2×Dic6—21no—
232C2×Dic6—21no—
233C2×Dic6—21no—
234C2×Dic6—21no—
235C2×Dic6#6712yescomplemented
236C3×SD16—68no—
237C2×C3×C8—21no—
238C2×C3×C8—21no—
239C2×C3×C8—21no—
240C2×C3×C8—21no—
241C2×C3×C8—22no—
242C2×C3×C8—32no—
243C2×C3×C8—41no—
244C2×C3×C8—41no—
245C2×C3×C8—61no—
246C2×C3×C8—61no—
247C2×C3×C8D1212yescomplemented
248C2×C3×C8#6712yescomplemented
249C3×C42—61no—
250C3×C42—61no—
251#215—68no—
252C4⋊Dic3—62no—
253C4⋊Dic3—61no—
254C4⋊Dic3—61no—
255C4⋊Dic3—61no—
256C4⋊Dic3—61no—
257C4⋊Dic3—121no—
258C4×Dic3—21no—
259C4×Dic3—21no—
260C2×C3⋊C8—21no—
261C2×C3⋊C8—21no—
262C2×C3⋊C8D1212yescomplemented
263#204—28no—
264#204—68no—
265C22×C32#12011yescharacteristic
266C22×C32#12111yescharacteristic
267C22×C32#12711yescharacteristic
268C22×C32C2×SD1612yes—
269C22×C32AGL(1,ℤ/8)12yes—
270C2×C3⋊D3—42no—
271C2×C3⋊D3—44no—
272C2×C3⋊D3—82no—
273C2×C3⋊D3—81no—
274C2×C3⋊D3—81no—
275C2×C3×D3—42no—
276C2×C3×D3—44no—
277C2×C3×D3—82no—
278C2×C3×D3—81no—
279C2×C3×D3—81no—
280C32×C4#12011yescharacteristic
281C32×C4#12011yescharacteristic
282C32×C4#12111yescharacteristic
283C32×C4#12111yescharacteristic
284C3⋊Dic3—81no—
285C3×Dic3—24no—
286C3×Dic3—42no—
287C22×Q8—31no—
288C22×D4—31no—
289C22×D4—91no—
290C22×D4—182no—
291C2×SD16—62no—
292C2×SD16—62no—
293C2×SD16—62no—
294C2×SD16—182no—
295C2×SD16—182no—
296C2×SD16—182no—
297C22×C8—31no—
298C22×C8D3211yescharacteristic
299#127—182no—
300#127—182no—
301C2×C4⋊C4—91no—
302C2×C42—31no—
303#102—182no—
304#102—182no—
305#95—182no—
306C23×C3—21no—
307C23×C3—62no—
308C23×C3—121no—
309C23×C3—121no—
310C23×C3—122no—
311C23×C3—122no—
312C23×C3C2×D1211yescharacteristic
313C23×C3D3×D411yescharacteristic
314C22×D3—22no—
315C22×D3—42no—
316C22×D3—42no—
317C22×D3—41no—
318C22×D3—41no—
319C22×D3—62no—
320C22×D3—62no—
321C22×D3—122no—
322C22×D3—122no—
323C22×D3—122no—
324C22×D3—121no—
325C22×D3—121no—
326C22×D3—122no—
327C22×D3—122no—
328C22×D3—122no—
329C22×D3—122no—
330C22×D3—121no—
331C22×D3—121no—
332C22×D3—242no—
333C22×D3—242no—
334C3×Q8—62no—
335C3×Q8—62no—
336C3×Q8—121no—
337C3×Q8—121no—
338C3×D4—62no—
339C3×D4—62no—
340C3×D4—121no—
341C3×D4—121no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—34no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4—121no—
353C2×C3×C4—121no—
354C2×C3×C4C2×D1211yescharacteristic
355C2×C3×C4C2×D1211yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4#23711yescharacteristic
362C2×C3×C4#23911yescharacteristic
363C2×C3×C4C2×#6711yescharacteristic
364C2×C3×C4C2×#6711yescharacteristic
365C2×C3×C4C2×#6711yescharacteristic
366#67—1216no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—41no—
371C2×Dic3—41no—
372C2×Dic3—122no—
373C2×Dic3—121no—
374C2×Dic3—122no—
375C2×Dic3—122no—
376C2×Dic3—121no—
377C2×Dic3—242no—
378C2×Dic3#20414yescomplemented
379D12—22no—
380D12—22no—
381D12—41no—
382D12—41no—
383D12—64no—
384D12—62no—
385D12—62no—
386D12—62no—
387D12—62no—
388D12—122no—
389D12—122no—
390D12—122no—
391D12—1216no—
392D12—121no—
393D12—121no—
394D12—121no—
395D12—121no—
396Dic6—22no—
397Dic6—22no—
398Dic6—41no—
399Dic6—41no—
400C3×C8—22no—
401C3×C8—22no—
402C3×C8—42no—
403C3×C8—62no—
404C3⋊C8—22no—
405C2×C32#39211yescharacteristic
406C2×C32#45012yes—
407C2×C32#46012yes—
408C2×C32#49211yescharacteristic
409C2×C32#49611yescharacteristic
410C3⋊D3—82no—
411C3×D3—82no—
412C24—61no—
413C24—181no—
414C2×Q8—32no—
415C2×Q8—61no—
416C2×Q8—61no—
417C2×Q8—61no—
418C2×Q8—61no—
419C2×Q8—61no—
420C2×D4—32no—
421C2×D4—61no—
422C2×D4—61no—
423C2×D4—61no—
424C2×D4—61no—
425C2×D4—61no—
426C2×D4—92no—
427C2×D4—188no—
428C2×D4—181no—
429C2×D4—181no—
430C2×D4—181no—
431C2×D4—181no—
432C2×D4—181no—
433C2×D4—364no—
434C2×D4—364no—
435C22×C4—32no—
436C22×C4—61no—
437C22×C4—181no—
438C22×C4C2×D3211yescharacteristic
439SD16—68no—
440SD16—188no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—32no—
444C2×C8—61no—
445C2×C8—61no—
446C2×C8#62612yescomplemented
447C4⋊C4—181no—
448C4⋊C4—181no—
449C42—61no—
450C42—61no—
451C22×C3—22no—
452C22×C3—22no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—122no—
457C22×C3—124no—
458C22×C3—241no—
459C22×C3—241no—
460C22×C3—242no—
461C22×C3#87411yescharacteristic
462C22×C3#88211yescharacteristic
463C22×C3#89511yescharacteristic
464C22×C3C2×#20412yes—
465C22×C3#90812yes—
466C22×C3D3×SD1612yes—
467C22×C3#91412yes—
468C22×C3#93711yescharacteristic
469C22×C3#93911yescharacteristic
470C22×C3#94011yescharacteristic
471C2×D3—44no—
472C2×D3—42no—
473C2×D3—82no—
474C2×D3—81no—
475C2×D3—81no—
476C2×D3—124no—
477C2×D3—124no—
478C2×D3—122no—
479C2×D3—122no—
480C2×D3—124no—
481C2×D3—244no—
482C2×D3—244no—
483C2×D3—242no—
484C2×D3—242no—
485C2×D3—242no—
486C2×D3—241no—
487C2×D3—241no—
488C2×D3—241no—
489C2×D3—241no—
490C2×D3—242no—
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—64no—
496C3×C4—122no—
497C3×C4#88211yescharacteristic
498C3×C4#88211yescharacteristic
499C3×C4#89511yescharacteristic
500C3×C4#89511yescharacteristic
501C3×C4#93711yescharacteristic
502C3×C4#93811yescharacteristic
503C3×C4#93911yescharacteristic
504C3×C4#95311yescharacteristic
505Dic3—24no—
506Dic3—42no—
507Dic3—242no—
508Dic3—241no—
509Dic3—241no—
510C32#201411yescharacteristic, complemented, Sylow
511C23—62no—
512C23—122no—
513C23—122no—
514C23—121no—
515C23—121no—
516C23—182no—
517C23—362no—
518C23—362no—
519C23—361no—
520C23—361no—
521C23D3×D1211yescharacteristic
522Q8—62no—
523Q8—62no—
524Q8—121no—
525Q8—121no—
526D4—62no—
527D4—62no—
528D4—121no—
529D4—121no—
530D4—182no—
531D4—182no—
532D4—3616no—
533D4—361no—
534D4—361no—
535C2×C4—34no—
536C2×C4—62no—
537C2×C4—62no—
538C2×C4—62no—
539C2×C4—121no—
540C2×C4—121no—
541C2×C4—362no—
542C2×C4—361no—
543C2×C4#379611yescharacteristic
544C2×C4D3×D1211yescharacteristic
545C2×C4#380211yescharacteristic
546C2×C4C2×#62611yescharacteristic
547C2×C4D3×#6711yescharacteristic
548C2×C4D3×#6711yescharacteristic
549C8—22no—
550C8—62no—
551C2×C3—22no—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—22no—
556C2×C3—242no—
557C2×C3#467111yescharacteristic
558C2×C3#469311yescharacteristic
559C2×C3#471211yescharacteristic
560C2×C3#473112yes—
561C2×C3#484812yes—
562C2×C3#516312yes—
563C2×C3#516912yes—
564C2×C3#517511yescharacteristic
565C2×C3#517611yescharacteristic
566C2×C3#522311yescharacteristic
567D3—82no—
568D3—244no—
569D3—242no—
570D3—242no—
571C22—122no—
572C22—124no—
573C22—242no—
574C22—241no—
575C22—241no—
576C22—362no—
577C22—364no—
578C22—722no—
579C22—721no—
580C22—721no—
581C22D3×#20412yes—
582C22#6379412yes—
583C22#6388611yescharacteristic
584C22#6391111yescharacteristic
585C22#6392211yescharacteristic
586C4—64no—
587C4—122no—
588C4—721no—
589C4#6388611yescharacteristic
590C4#6391611yescharacteristic
591C4#6392211yescharacteristic
592C4#6397711yescharacteristic
593C3—21no—
594C3#6867611yescharacteristic, complemented
595C3#7205611yescharacteristic, complemented
596C2—242no—
597C2—722no—
598C2#1059079912yes—
599C2#1059087711yescharacteristic
600C2#1059088111yescharacteristic
601C2#1059094212yes—
602C2#1059139111yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC2×#63911C2
hypercenterC22×C8D32
hypocenterC32#2014
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C3×#204C2semidirect
3. C22×#3717C2semidirect
4. C2×#63648C2semidirect
5. #10591220C2semidirect
6. C2×#63563C2semidirect
7. C3×#4550C2semidirect
33. C22×#204D3semidirect
43. #4550D3semidirect
67. C2×C3×Dic6D4semidirect
73. C2×C32×C8D4semidirect
80. C2×C3×C3⋊C8D4semidirect
154. C2×C3×Dic3SD16semidirect
235. C2×Dic6#67semidirect
247. C2×C3×C8D12semidirect
248. C2×C3×C8#67semidirect
262. C2×C3⋊C8D12semidirect
378. C2×Dic3#204semidirect
446. C2×C8#626semidirect
510. C32#2014semidirect
594. C3#68676semidirect
595. C3#72056semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2042
C2×#639112
C22×#37172
C2×#636482
#105912202
C2×#635632
C3×#45502
#720563
#686763