Finite Group Databasebeta

← #11792606

Subgroups — #11792606

Order 1152.

929 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3744C211yesmaximal, characteristic
2C2×#63864C211yesmaximal, characteristic
3C22×#3719C211yesmaximal, characteristic, complemented
4C2×C3×#816C211yesmaximal, characteristic, complemented
5#10591213C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic
7C3×#4550C211yesmaximal, characteristic, complemented
8#70278—31nomaximal
9#68677—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C2×#3744—22no—
15C2×#3744—22no—
16C2×#3744—22no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C2×#3722—22no—
21#63864—22no—
22#63864—22no—
23C2×#3719—22no—
24C2×#3719—22no—
25C2×#3719—22no—
26C3×#816—22no—
27#63579—22no—
28#63564—22no—
29C2×#947—31no—
30C22×#216—31no—
31C22×Dic12—31no—
32C22×#204—31no—
33C22×#204—31no—
34C22×#204—61no—
35C2×#875—31no—
36C2×C3×#103—31no—
37C2×#821—31no—
38C2×#816D311yescharacteristic, complemented
39#4973—31no—
40C2×#809—31no—
41#4929—31no—
42C3×#336—31no—
43#4550D311yescharacteristic, complemented
44C23×C3⋊D3—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C2×C4⋊(C3⋊D3)—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)D412yes—
53C2×#634—21no—
54C2×#634—21no—
55C2×#634—21no—
56C2×#634—21no—
57C2×#634—21no—
58C2×#634D412yes—
59C22×C3×Dic3—21no—
60C22×C3×Dic3—21no—
61C22×C3×Dic3D412yes—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6D412yes—
68C2×C32×C8—21no—
69C2×C32×C8—21no—
70C2×C32×C8D412yes—
71#3744—28no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3—21no—
74C3×C4×Dic3—21no—
75C3×C4×Dic3—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8D412yes—
79#3722—28no—
80#3719—28no—
81#2015—91noSylow
82C22×C3×Q8—31no—
83C22×D12—31no—
84C22×D12—31no—
85C22×D12—61no—
86C22×Dic6—31no—
87C22×Dic6—31no—
88C22×Dic6—61no—
89C22×Dic6C2×D311yescharacteristic
90C22×C3×C8—21no—
91C22×C3×C8—31no—
92C22×C3×C8C2×D311yescharacteristic
93C22×C3×C8C2×D311yescharacteristic
94C2×C3×C4⋊C4—31no—
95C2×C3×C42—31no—
96#947—62no—
97#947—62no—
98C2×#216—62no—
99C2×#216—62no—
100C2×#216—62no—
101C2×(C2×D3)⋊C4—62no—
102C2×(C2×D3)⋊C4—62no—
103C2×C4⋊Dic3C2×D311yescharacteristic
104C2×C4×Dic3C2×D311yescharacteristic
105C22×C3⋊C8C2×D311yescharacteristic
106C2×Dic12—62no—
107C2×Dic12—62no—
108C2×Dic12—62no—
109C2×#204—62no—
110C2×#204—62no—
111C2×#204—62no—
112C2×#204—62no—
113C2×#204—64no—
114C2×#204—64no—
115C2×#204—64no—
116C2×#204—62no—
117C2×#204—62no—
118#875—62no—
119#875—62no—
120C3×#103—62no—
121C3⋊#95—62no—
122C3⋊#95—62no—
123#821—62no—
124#816—22no—
125#809—62no—
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—22no—
128C22×C3⋊D3—41no—
129C22×C3⋊D3—41no—
130C22×C3⋊D3—42no—
131C22×C3⋊D3—42no—
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—41no—
140C2×C3⋊Dic3—41no—
141C4⋊(C3⋊D3)—22no—
142C4⋊(C3⋊D3)—22no—
143C4⋊(C3⋊D3)—41no—
144C4⋊(C3⋊D3)—41no—
145#634—22no—
146#634—22no—
147#634—41no—
148#634—41no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—42no—
157C3×Dic6—22no—
158C3×Dic6—22no—
159C3×Dic6—41no—
160C3×Dic6—41no—
161C32×C8—22no—
162C3×C3⋊C8—22no—
163C22×Q16—91no—
164C22×SD16—91no—
165C2×#124—91no—
166C2×#103—31no—
167C2×#102—91no—
168#391—91no—
169#336—31no—
170C23×D3—61no—
171C23×D3—61no—
172C23×D3—121no—
173C2×C3×Q8—32no—
174C2×C3×Q8—61no—
175C2×C3×Q8—61no—
176C2×C3×Q8—61no—
177C2×C3×Q8—61no—
178C2×C3×Q8—61no—
179C22×C3×C4—21no—
180C22×C3×C4—32no—
181C22×C3×C4—61no—
182C22×C3×C4—61no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C22×Dic3—21no—
186C22×Dic3—21no—
187C22×Dic3—61no—
188C22×Dic3—61no—
189C22×Dic3—121no—
190C22×Dic3D1212yes—
191C2×D12—32no—
192C2×D12—32no—
193C2×D12—62no—
194C2×D12—62no—
195C2×D12—62no—
196C2×D12—61no—
197C2×D12—61no—
198C2×D12—61no—
199C2×D12—61no—
200C2×D12—61no—
201C2×D12—61no—
202C2×D12—61no—
203C2×D12—61no—
204C2×D12—61no—
205C2×D12—61no—
206C2×D12—121no—
207C2×D12—121no—
208C2×D12—121no—
209C2×Dic6—21no—
210C2×Dic6—21no—
211C2×Dic6—21no—
212C2×Dic6—21no—
213C2×Dic6—21no—
214C2×Dic6—32no—
215C2×Dic6—32no—
216C2×Dic6—62no—
217C2×Dic6—62no—
218C2×Dic6—62no—
219C2×Dic6—61no—
220C2×Dic6—61no—
221C2×Dic6—61no—
222C2×Dic6—61no—
223C2×Dic6—61no—
224C2×Dic6—61no—
225C2×Dic6—61no—
226C2×Dic6—61no—
227C2×Dic6—61no—
228C2×Dic6—61no—
229C2×Dic6—121no—
230C2×Dic6—121no—
231C2×Dic6—121no—
232C2×Dic6D1212yes—
233C2×C3×C8—22no—
234C2×C3×C8—22no—
235C2×C3×C8—21no—
236C2×C3×C8—21no—
237C2×C3×C8—21no—
238C2×C3×C8—21no—
239C2×C3×C8—22no—
240C2×C3×C8—32no—
241C2×C3×C8—61no—
242C2×C3×C8—61no—
243C2×C3×C8D1212yes—
244C2×C3×C8#6712yes—
245C3×C4⋊C4—61no—
246C3×C4⋊C4—61no—
247C3×C42—61no—
248C3×C42—61no—
249#216—68no—
250(C2×D3)⋊C4—68no—
251(C2×D3)⋊C4—68no—
252C4⋊Dic3—21no—
253C4⋊Dic3—21no—
254C4×Dic3—21no—
255C4×Dic3—21no—
256C2×C3⋊C8—21no—
257C2×C3⋊C8—21no—
258C2×C3⋊C8D1212yes—
259Dic12—68no—
260#204—616no—
261#204—68no—
262#204—68no—
263C22×C32#12011yescharacteristic
264C22×C32#12111yescharacteristic
265C22×C32#12711yescharacteristic
266C22×C32#13512yes—
267C22×C32#13712yes—
268C2×C3⋊D3—42no—
269C2×C3⋊D3—44no—
270C2×C3⋊D3—82no—
271C2×C3⋊D3—81no—
272C2×C3⋊D3—81no—
273C32×C4#12011yescharacteristic
274C32×C4#12011yescharacteristic
275C32×C4#12111yescharacteristic
276C32×C4#12111yescharacteristic
277C3⋊Dic3—42no—
278C3×Dic3—42no—
279C3×Dic3—42no—
280C3×Dic3—81no—
281C22×Q8—31no—
282C22×Q8—91no—
283C22×D4—91no—
284C2×Q16—182no—
285C2×Q16—182no—
286C2×Q16—182no—
287C2×SD16—182no—
288C2×SD16—182no—
289C2×SD16—182no—
290C22×C8—31no—
291C22×C8D3211yescharacteristic
292#124—182no—
293#124—182no—
294C2×C4⋊C4—31no—
295C2×C22⋊C4—182no—
296C2×C42—31no—
297#103—62no—
298#102—182no—
299#95—182no—
300C23×C3—21no—
301C23×C3C2×D1211yescharacteristic
302C23×C3D3×D411yescharacteristic
303C22×D3—62no—
304C22×D3—62no—
305C22×D3—122no—
306C22×D3—122no—
307C22×D3—122no—
308C22×D3—121no—
309C22×D3—121no—
310C22×D3—121no—
311C22×D3—122no—
312C22×D3—122no—
313C22×D3—122no—
314C22×D3—122no—
315C22×D3—121no—
316C22×D3—242no—
317C22×D3—242no—
318C3×Q8—62no—
319C3×Q8—62no—
320C3×Q8—121no—
321C3×Q8—121no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—121no—
333C2×C3×C4—121no—
334C2×C3×C4—121no—
335C2×C3×C4—122no—
336C2×C3×C4C2×D1211yescharacteristic
337C2×C3×C4C2×D1211yescharacteristic
338C2×C3×C4C2×D1211yescharacteristic
339C2×C3×C4#23511yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4#23911yescharacteristic
347C2×C3×C4C2×#6711yescharacteristic
348C2×Dic3—22no—
349C2×Dic3—22no—
350C2×Dic3—22no—
351C2×Dic3—22no—
352C2×Dic3—41no—
353C2×Dic3—41no—
354C2×Dic3—42no—
355C2×Dic3—41no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—122no—
359C2×Dic3—122no—
360C2×Dic3—122no—
361C2×Dic3—121no—
362C2×Dic3—121no—
363C2×Dic3—121no—
364C2×Dic3—121no—
365D12—64no—
366D12—62no—
367D12—62no—
368D12—62no—
369D12—62no—
370D12—122no—
371D12—122no—
372D12—122no—
373D12—121no—
374D12—121no—
375D12—121no—
376D12—121no—
377Dic6—22no—
378Dic6—22no—
379Dic6—41no—
380Dic6—41no—
381Dic6—64no—
382Dic6—62no—
383Dic6—62no—
384Dic6—62no—
385Dic6—62no—
386Dic6—122no—
387Dic6—122no—
388Dic6—122no—
389Dic6—121no—
390Dic6—121no—
391Dic6—121no—
392Dic6—121no—
393C3×C8—24no—
394C3×C8—22no—
395C3×C8—22no—
396C3×C8—62no—
397C3⋊C8—22no—
398C2×C32#39211yescharacteristic
399C2×C32#45212yes—
400C2×C32#46412yes—
401C2×C32#49511yescharacteristic
402C2×C32#49711yescharacteristic
403C3⋊D3—82no—
404C24—181no—
405C2×Q8—32no—
406C2×Q8—61no—
407C2×Q8—61no—
408C2×Q8—61no—
409C2×Q8—61no—
410C2×Q8—61no—
411C2×Q8—92no—
412C2×Q8—181no—
413C2×Q8—181no—
414C2×Q8—181no—
415C2×Q8—181no—
416C2×Q8—181no—
417C2×D4—92no—
418C2×D4—181no—
419C2×D4—181no—
420C2×D4—181no—
421C2×D4—181no—
422C2×D4—181no—
423C22×C4—32no—
424C22×C4—61no—
425C22×C4—61no—
426C22×C4—181no—
427C22×C4C2×D3211yescharacteristic
428Q16—188no—
429SD16—188no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—32no—
433C2×C8—61no—
434C2×C8—61no—
435C2×C8#62612yes—
436C4⋊C4—61no—
437C4⋊C4—61no—
438C22⋊C4—188no—
439C42—61no—
440C42—61no—
441C22×C3—22no—
442C22×C3—22no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3#87411yescharacteristic
447C22×C3#88211yescharacteristic
448C22×C3#88211yescharacteristic
449C22×C3#88411yescharacteristic
450C22×C3#89511yescharacteristic
451C22×C3#90412yes—
452C22×C3#90912yes—
453C22×C3#91612yes—
454C22×C3#91812yes—
455C22×C3#94011yescharacteristic
456C2×D3—124no—
457C2×D3—122no—
458C2×D3—122no—
459C2×D3—124no—
460C2×D3—124no—
461C2×D3—244no—
462C2×D3—244no—
463C2×D3—242no—
464C2×D3—242no—
465C2×D3—241no—
466C2×D3—241no—
467C2×D3—241no—
468C2×D3—241no—
469C2×D3—242no—
470C2×D3—242no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—122no—
476C3×C4—122no—
477C3×C4—241no—
478C3×C4#88211yescharacteristic
479C3×C4#88211yescharacteristic
480C3×C4#88211yescharacteristic
481C3×C4#88411yescharacteristic
482C3×C4#89511yescharacteristic
483C3×C4#89511yescharacteristic
484C3×C4#93011yescharacteristic
485C3×C4#93711yescharacteristic
486Dic3—42no—
487Dic3—42no—
488Dic3—81no—
489Dic3—124no—
490Dic3—122no—
491Dic3—122no—
492C32#201511yescharacteristic, complemented, Sylow
493C23—182no—
494C23—362no—
495C23—362no—
496C23—361no—
497C23—361no—
498C23D3×D1211yescharacteristic
499Q8—62no—
500Q8—62no—
501Q8—121no—
502Q8—121no—
503Q8—182no—
504Q8—182no—
505Q8—361no—
506Q8—361no—
507D4—182no—
508D4—182no—
509D4—361no—
510D4—361no—
511C2×C4—62no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—62no—
515C2×C4—121no—
516C2×C4—121no—
517C2×C4—122no—
518C2×C4—121no—
519C2×C4—182no—
520C2×C4—361no—
521C2×C4—361no—
522C2×C4#379911yescharacteristic
523C2×C4D3×D1211yescharacteristic
524C2×C4D3×D1211yescharacteristic
525C2×C4C2×#62611yescharacteristic
526C2×C4#381111yescharacteristic
527C2×C4#381111yescharacteristic
528C8—22no—
529C8—62no—
530C2×C3—22no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—22no—
535C2×C3#467111yescharacteristic
536C2×C3#469611yescharacteristic
537C2×C3#471511yescharacteristic
538C2×C3#473312yes—
539C2×C3#479812yes—
540C2×C3#480812yes—
541C2×C3#484512yes—
542C2×C3#496011yescharacteristic
543C2×C3#516811yescharacteristic
544C2×C3#519011yescharacteristic
545D3—244no—
546D3—242no—
547D3—242no—
548C22—362no—
549C22—364no—
550C22—722no—
551C22—721no—
552C22—721no—
553C22#6380112yes—
554C22#6380612yes—
555C22#6391011yescharacteristic
556C22#6391111yescharacteristic
557C22#6392311yescharacteristic
558C4—122no—
559C4—122no—
560C4—241no—
561C4—362no—
562C4#6390911yescharacteristic
563C4#6391011yescharacteristic
564C4#6392311yescharacteristic
565C4#6398111yescharacteristic
566C3—21no—
567C3#6867711yescharacteristic, complemented
568C3#7027811yescharacteristic, complemented
569C2—722no—
570C2#1059081312yes—
571C2#1059086211yescharacteristic
572C2#1059089911yescharacteristic
573C2#1059097012yes—
574C2#1059139511yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC22×C8D32
hypocenterC32#2015
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
3. C22×#3719C2semidirect
4. C2×C3×#816C2semidirect
5. #10591213C2semidirect
7. C3×#4550C2semidirect
38. C2×#816D3semidirect
43. #4550D3semidirect
492. C32#2015semidirect
567. C3#68677semidirect
568. C3#70278semidirect

Maximal subgroups

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

subgroupindex
C22×#37442
C2×#638642
C22×#37192
C2×C3×#8162
#105912132
C2×#635642
C3×#45502
#702783
#686773