Finite Group Databasebeta

← #11794062

Subgroups — #11794062

Order 1152.

729 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3716C211yesmaximal, characteristic
2C2×#63643C211yesmaximal, characteristic, complemented
3C2×C3×#821C211yesmaximal, characteristic
4C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
5#10591318C211yesmaximal, characteristic
6#10591213C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#70482—31nomaximal
9#70217—31nomaximal
10C22×#634C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×(C2×D3)⋊Dic3—21no—
18C2×(C2×D3)⋊Dic3—21no—
19C2×#3716—22no—
20C2×#3716—22no—
21C2×#3716—22no—
22#63643—22no—
23C3×#821—22no—
24C3×Dic3⋊C8—22no—
25#63579—21no—
26#63579—21no—
27C22×#214—31no—
28C22×#204—31no—
29C2×C3×C4⋊C8—31no—
30C2×C3×#102—31no—
31#5221—31no—
32C2×#821D311yescharacteristic
33C2×#816—31no—
34C2×#816—31no—
35C2×#816—61no—
36C2×Dic3⋊C8D311yescharacteristic, complemented
37#4973—31no—
38#4939—31no—
39#4929—31no—
40#4551—31no—
41#4529—31no—
42C23×C3×D3—21no—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3—21no—
45C22×C3⋊Dic3—21no—
46C2×#634—21no—
47C2×#634—21no—
48C2×#634—21no—
49C2×#634—21no—
50C2×#634—21no—
51C2×#634D412yes—
52C22×C3×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C22×C3×Dic3D411yescharacteristic
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12D412yes—
61C2×C32×C8—21no—
62C2×C32×C8—21no—
63C2×C32×C8—21no—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4×Dic3—21no—
69C3×C4×Dic3—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8D412yes—
73(C2×D3)⋊Dic3—42no—
74(C2×D3)⋊Dic3—42no—
75#3716—28no—
76#2055—91noSylow
77C22×C3×D4—31no—
78C22×D12C2×D311yescharacteristic
79C22×Dic6—31no—
80C22×Dic6—31no—
81C22×Dic6—61no—
82C22×C3×C8—21no—
83C22×C3×C8—31no—
84C22×C3×C8C2×D311yescharacteristic
85C22×C3×C8C2×D311yescharacteristic
86C2×C3×C4⋊C4—31no—
87C2×C3×C42—31no—
88C2×#217—61no—
89C2×#217—61no—
90C2×#214—62no—
91C2×#214—62no—
92C2×#214—62no—
93C2×(C2×D3)⋊C4—61no—
94C2×(C2×D3)⋊C4—61no—
95C2×C4⋊Dic3—31no—
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—61no—
98C2×C4⋊Dic3C2×D311yescharacteristic
99C2×C4×Dic3C2×D311yescharacteristic
100C22×C3⋊C8C2×D311yescharacteristic
101C2×#204—62no—
102C2×#204—62no—
103C2×#204—62no—
104C3×C4⋊C8—62no—
105C3×#102—62no—
106C3⋊#95—61no—
107C3⋊#95—61no—
108C3⋊#95—61no—
109C3⋊#95—61no—
110#821—22no—
111#816—62no—
112#816—62no—
113#816—64no—
114Dic3⋊C8—22no—
115C23×C32C2×D411yescharacteristic
116C22×C3×D3—22no—
117C22×C3×D3—41no—
118C22×C3×D3—41no—
119C22×C3×D3—41no—
120C22×C3×D3—41no—
121C22×C3×D3—41no—
122C22×C3×D3—41no—
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C2×C32×C4#4111yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C3⋊Dic3—22no—
130C2×C3⋊Dic3—41no—
131C2×C3⋊Dic3—41no—
132C2×C3⋊Dic3—41no—
133C2×C3⋊Dic3—41no—
134C2×C3⋊Dic3—41no—
135#634—22no—
136#634—22no—
137#634—41no—
138#634—41no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3SD1612yescomplemented
148C3×D12—22no—
149C3×D12—22no—
150C3×D12—41no—
151C3×D12—41no—
152C32×C8—41no—
153C3×C3⋊C8—22no—
154C22×SD16—91no—
155C2×C4⋊C8—31no—
156C2×#103—91no—
157C2×#102—31no—
158#391—91no—
159#390—91no—
160#340—91no—
161C24×C3—61no—
162C23×D3—21no—
163C2×C3×D4—32no—
164C2×C3×D4—61no—
165C2×C3×D4—61no—
166C2×C3×D4—61no—
167C2×C3×D4—61no—
168C2×C3×D4—61no—
169C22×C3×C4—21no—
170C22×C3×C4—31no—
171C22×C3×C4—31no—
172C22×C3×C4—61no—
173C22×C3×C4C22×D311yescharacteristic
174C22×C3×C4C22×D311yescharacteristic
175C22×Dic3—21no—
176C22×Dic3—61no—
177C22×Dic3—61no—
178C22×Dic3—61no—
179C22×Dic3—61no—
180C22×Dic3—121no—
181C22×Dic3—121no—
182C22×Dic3D1211yescharacteristic
183C22×Dic3D1211yescharacteristic
184C2×D12—21no—
185C2×D12—21no—
186C2×D12—21no—
187C2×D12—21no—
188C2×D12—21no—
189C2×D12#6712yes—
190C2×Dic6—32no—
191C2×Dic6—32no—
192C2×Dic6—62no—
193C2×Dic6—62no—
194C2×Dic6—62no—
195C2×Dic6—61no—
196C2×Dic6—61no—
197C2×Dic6—61no—
198C2×Dic6—61no—
199C2×Dic6—61no—
200C2×Dic6—61no—
201C2×Dic6—61no—
202C2×Dic6—61no—
203C2×Dic6—61no—
204C2×Dic6—61no—
205C2×Dic6—121no—
206C2×Dic6—121no—
207C2×Dic6—121no—
208C2×C3×C8—22no—
209C2×C3×C8—21no—
210C2×C3×C8—21no—
211C2×C3×C8—21no—
212C2×C3×C8—21no—
213C2×C3×C8—21no—
214C2×C3×C8—21no—
215C2×C3×C8—32no—
216C2×C3×C8—41no—
217C2×C3×C8—41no—
218C2×C3×C8—61no—
219C2×C3×C8—61no—
220C3×C4⋊C4—61no—
221C3×C4⋊C4—61no—
222C3×C42—61no—
223C3×C42—61no—
224#217—122no—
225#217—122no—
226#214—68no—
227(C2×D3)⋊C4—122no—
228(C2×D3)⋊C4—122no—
229C4⋊Dic3—21no—
230C4⋊Dic3—21no—
231C4⋊Dic3—62no—
232C4⋊Dic3—61no—
233C4⋊Dic3—61no—
234C4⋊Dic3—61no—
235C4⋊Dic3—61no—
236C4⋊Dic3—121no—
237C4×Dic3—21no—
238C4×Dic3—21no—
239C2×C3⋊C8—21no—
240C2×C3⋊C8—21no—
241C2×C3⋊C8#6712yes—
242#204—68no—
243C22×C32#12111yescharacteristic
244C22×C32#12111yescharacteristic
245C22×C32#12111yescharacteristic
246C22×C32C2×SD1611yescharacteristic
247C22×C32#13511yescharacteristic
248C22×C32AGL(1,ℤ/8)11yescharacteristic
249C22×C32#13711yescharacteristic
250C2×C3×D3—42no—
251C2×C3×D3—42no—
252C2×C3×D3—42no—
253C2×C3×D3—81no—
254C2×C3×D3—81no—
255C2×C3×D3—81no—
256C2×C3×D3—81no—
257C32×C4#12011yescharacteristic
258C32×C4#12311yescharacteristic
259C32×C4#12311yescharacteristic
260C32×C4#12411yescharacteristic
261C3⋊Dic3—42no—
262C3⋊Dic3—81no—
263C3×Dic3—22no—
264C3×Dic3—41no—
265C3×Dic3—81no—
266C22×Q8—91no—
267C22×D4—31no—
268C2×SD16—182no—
269C2×SD16—182no—
270C2×SD16—182no—
271C22×C8—31no—
272C22×C8D3211yescharacteristic
273C2×C4⋊C4—31no—
274C2×C4⋊C4—91no—
275C2×C22⋊C4—181no—
276C2×C22⋊C4—181no—
277C2×C42—31no—
278C4⋊C8—62no—
279#103—182no—
280#102—62no—
281#95—181no—
282#95—181no—
283C23×C3—21no—
284C23×C3—62no—
285C23×C3—121no—
286C23×C3—121no—
287C23×C3—121no—
288C23×C3—121no—
289C23×C3—121no—
290C23×C3—121no—
291C23×C3C2×D1211yescharacteristic
292C23×C3D3×D411yescharacteristic
293C22×D3—22no—
294C22×D3—41no—
295C22×D3—41no—
296C22×D3—41no—
297C22×D3—41no—
298C22×D3—41no—
299C22×D3—41no—
300C3×D4—62no—
301C3×D4—62no—
302C3×D4—121no—
303C3×D4—121no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—32no—
311C2×C3×C4—61no—
312C2×C3×C4—61no—
313C2×C3×C4—61no—
314C2×C3×C4—61no—
315C2×C3×C4—61no—
316C2×C3×C4—121no—
317C2×C3×C4—121no—
318C2×C3×C4—121no—
319C2×C3×C4#23511yescharacteristic
320C2×C3×C4#23511yescharacteristic
321C2×C3×C4#23511yescharacteristic
322C2×C3×C4D3×D411yescharacteristic
323C2×C3×C4D3×D411yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4#23711yescharacteristic
327C2×C3×C4#23911yescharacteristic
328C2×C3×C4#23911yescharacteristic
329C2×C3×C4C2×#6711yescharacteristic
330C2×C3×C4C2×#6711yescharacteristic
331C2×Dic3—21no—
332C2×Dic3—21no—
333C2×Dic3—21no—
334C2×Dic3—21no—
335C2×Dic3—21no—
336C2×Dic3—41no—
337C2×Dic3—41no—
338C2×Dic3—41no—
339C2×Dic3—62no—
340C2×Dic3—62no—
341C2×Dic3—122no—
342C2×Dic3—122no—
343C2×Dic3—122no—
344C2×Dic3—121no—
345C2×Dic3—121no—
346C2×Dic3—121no—
347C2×Dic3—121no—
348C2×Dic3—122no—
349C2×Dic3—121no—
350C2×Dic3—121no—
351C2×Dic3—121no—
352C2×Dic3—121no—
353C2×Dic3—121no—
354C2×Dic3—121no—
355C2×Dic3—241no—
356C2×Dic3—241no—
357C2×Dic3#20412yescomplemented
358D12—22no—
359D12—22no—
360D12—41no—
361D12—41no—
362Dic6—64no—
363Dic6—62no—
364Dic6—62no—
365Dic6—62no—
366Dic6—62no—
367Dic6—122no—
368Dic6—122no—
369Dic6—122no—
370Dic6—121no—
371Dic6—121no—
372Dic6—121no—
373Dic6—121no—
374C3×C8—42no—
375C3×C8—41no—
376C3×C8—41no—
377C3×C8—62no—
378C3⋊C8—22no—
379C2×C32#39411yescharacteristic
380C2×C32#46011yescharacteristic
381C2×C32#46111yescharacteristic
382C2×C32#46311yescharacteristic
383C2×C32#46411yescharacteristic
384C2×C32#46511yescharacteristic
385C2×C32#46811yescharacteristic
386C3×D3—82no—
387C24—61no—
388C2×Q8—92no—
389C2×Q8—181no—
390C2×Q8—181no—
391C2×Q8—181no—
392C2×Q8—181no—
393C2×Q8—181no—
394C2×D4—32no—
395C2×D4—61no—
396C2×D4—61no—
397C2×D4—61no—
398C2×D4—61no—
399C2×D4—61no—
400C22×C4—31no—
401C22×C4—31no—
402C22×C4—61no—
403C22×C4—181no—
404C22×C4—181no—
405C22×C4C2×D3211yescharacteristic
406SD16—188no—
407C2×C8—21no—
408C2×C8—21no—
409C2×C8—21no—
410C2×C8—32no—
411C2×C8—61no—
412C2×C8—61no—
413C4⋊C4—61no—
414C4⋊C4—61no—
415C4⋊C4—181no—
416C4⋊C4—181no—
417C22⋊C4—362no—
418C22⋊C4—362no—
419C42—61no—
420C42—61no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—122no—
429C22×C3—122no—
430C22×C3—122no—
431C22×C3—241no—
432C22×C3—241no—
433C22×C3—241no—
434C22×C3—241no—
435C22×C3#88411yescharacteristic
436C22×C3#88411yescharacteristic
437C22×C3#89511yescharacteristic
438C22×C3#89511yescharacteristic
439C22×C3C2×#20411yescharacteristic
440C22×C3#90411yescharacteristic
441C22×C3#90811yescharacteristic
442C22×C3#90911yescharacteristic
443C22×C3#91111yescharacteristic
444C22×C3#91211yescharacteristic
445C22×C3D3×SD1611yescharacteristic
446C22×C3#91511yescharacteristic
447C22×C3#93011yescharacteristic
448C22×C3#93911yescharacteristic
449C2×D3—42no—
450C2×D3—42no—
451C2×D3—42no—
452C2×D3—81no—
453C2×D3—81no—
454C2×D3—81no—
455C2×D3—81no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—62no—
461C3×C4—121no—
462C3×C4—241no—
463C3×C4#88311yescharacteristic
464C3×C4#88511yescharacteristic
465C3×C4#89411yescharacteristic
466C3×C4#89411yescharacteristic
467C3×C4#92911yescharacteristic
468C3×C4#93711yescharacteristic
469C3×C4#93711yescharacteristic
470C3×C4#94711yescharacteristic
471Dic3—22no—
472Dic3—41no—
473Dic3—81no—
474Dic3—124no—
475Dic3—122no—
476Dic3—122no—
477Dic3—242no—
478Dic3—241no—
479Dic3—241no—
480C32#205511yescharacteristic, complemented, Sylow
481C23—62no—
482C23—121no—
483C23—121no—
484C23—121no—
485C23—121no—
486C23—121no—
487C23—121no—
488C23D3×D1211yescharacteristic
489Q8—182no—
490Q8—182no—
491Q8—361no—
492Q8—361no—
493D4—62no—
494D4—62no—
495D4—121no—
496D4—121no—
497C2×C4—32no—
498C2×C4—61no—
499C2×C4—61no—
500C2×C4—61no—
501C2×C4—61no—
502C2×C4—61no—
503C2×C4—121no—
504C2×C4—121no—
505C2×C4—121no—
506C2×C4—182no—
507C2×C4—361no—
508C2×C4—361no—
509C2×C4—361no—
510C2×C4—361no—
511C2×C4—361no—
512C2×C4#379611yescharacteristic
513C2×C4#379811yescharacteristic
514C2×C4#379911yescharacteristic
515C2×C4D3×#6711yescharacteristic
516C2×C4D3×#6711yescharacteristic
517C2×C4#381111yescharacteristic
518C8—41no—
519C8—62no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—242no—
528C2×C3#476211yescharacteristic
529C2×C3#476711yescharacteristic
530C2×C3#477811yescharacteristic
531C2×C3#478011yescharacteristic
532C2×C3#484111yescharacteristic
533C2×C3#484411yescharacteristic
534C2×C3#484511yescharacteristic
535C2×C3#484811yescharacteristic
536C2×C3#495911yescharacteristic
537C2×C3#499111yescharacteristic
538C2×C3#511411yescharacteristic
539C2×C3#513411yescharacteristic
540C2×C3#515311yescharacteristic
541C2×C3#516211yescharacteristic
542D3—82no—
543C22—122no—
544C22—122no—
545C22—122no—
546C22—241no—
547C22—241no—
548C22—241no—
549C22—241no—
550C22D3×#20411yescharacteristic
551C22#6379511yescharacteristic
552C22#6380011yescharacteristic
553C22#6380711yescharacteristic
554C22#6388611yescharacteristic
555C22#6390611yescharacteristic
556C22#6391011yescharacteristic
557C4—62no—
558C4—121no—
559C4—241no—
560C4—362no—
561C4—721no—
562C4#6385011yescharacteristic
563C4#6385311yescharacteristic
564C4#6390711yescharacteristic
565C4#6398311yescharacteristic
566C3—21no—
567C3#7021711yescharacteristic, complemented
568C3#7048211yescharacteristic, complemented
569C2—242no—
570C2#1059075211yescharacteristic
571C2#1059075511yescharacteristic
572C2#1059082511yescharacteristic
573C2#1059082811yescharacteristic
574C2#1059086111yescharacteristic
575C2#1059087911yescharacteristic
576C2#1059129111yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC22×C8D32
hypocenterC32#2055
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
2. C2×#63643C2semidirect
4. C2×C3×Dic3⋊C8C2semidirect
6. #10591213C2semidirect
7. #10589164C2semidirect
36. C2×Dic3⋊C8D3semidirect
147. C2×C3×Dic3SD16semidirect
357. C2×Dic3#204semidirect
480. C32#2055semidirect
567. C3#70217semidirect
568. C3#70482semidirect

Maximal subgroups

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

subgroupindex
C22×#37162
C2×#636432
C2×C3×#8212
C2×C3×Dic3⋊C82
#105913182
#105912132
#105891642
#704823
#702173