Finite Group Databasebeta

← #11794076

Subgroups — #11794076

Order 1152.

741 conjugacy classes of subgroups.

The subgroup lattice has 587 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3716C211yesmaximal, characteristic
2#10592628C211yesmaximal, characteristic, complemented
3C3×#4939C211yesmaximal, characteristic
4C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
5C2×#63567C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic
7#10589164C211yesmaximal, characteristic, complemented
8#70482—31nomaximal
9#69651—31nomaximal
10C22×#634C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4—21no—
15C2×C3×(C2×D3)⋊C4—21no—
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×#3716—22no—
20C2×#3716—22no—
21C2×#3716—22no—
22#63658—21no—
23#63658—21no—
24C3×C4⋊(C3⋊C8)—22no—
25#63567—22no—
26#63563—22no—
27C22×#214—31no—
28C22×#204—31no—
29C2×C3×C4⋊C8—31no—
30C3×#390—31no—
31C2×#832—31no—
32C2×#821—31no—
33C2×#816—31no—
34C2×#810—31no—
35#4939D311yescharacteristic
36#4929—31no—
37#4929—31no—
38#4929—61no—
39C2×C4⋊(C3⋊C8)D311yescharacteristic, complemented
40#4551—31no—
41#4529—31no—
42C23×C3×D3—21no—
43C22×C32×C4D411yescharacteristic
44C22×C32×C4D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C22×C3⋊Dic3—21no—
48C2×#634—21no—
49C2×#634—21no—
50C2×#634—21no—
51C2×#634—21no—
52C2×#634—21no—
53C2×#634D412yes—
54C22×C3×Dic3—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12D412yes—
61C32×C42—21no—
62C32×C42—21no—
63C4⋊(C3⋊Dic3)—21no—
64C4⋊(C3⋊Dic3)—21no—
65C3×(C2×D3)⋊C4—42no—
66C3×(C2×D3)⋊C4—42no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8D412yes—
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—31no—
83C22×C3×C8—31no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C22⋊C4—61no—
86C2×C3×C22⋊C4—61no—
87C2×C3×C42—21no—
88C2×C3×C42C2×D311yescharacteristic
89C2×C3×C42C2×D311yescharacteristic
90C2×#214—62no—
91C2×#214—62no—
92C2×#214—62no—
93C2×(C2×D3)⋊C4—21no—
94C2×(C2×D3)⋊C4—21no—
95C2×C4⋊Dic3—31no—
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—61no—
98C2×C4⋊Dic3C2×D311yescharacteristic
99C22×C3⋊C8C2×D311yescharacteristic
100C22×C3⋊C8C2×D311yescharacteristic
101C2×#204—62no—
102C2×#204—62no—
103C2×#204—62no—
104C3×C4⋊C8—62no—
105#832—62no—
106C3⋊#95—62no—
107C3⋊#95—62no—
108C3⋊#95—61no—
109C3⋊#95—61no—
110C3⋊#95—61no—
111C3⋊#95—61no—
112#821—62no—
113#816—62no—
114#810—62no—
115C4⋊(C3⋊C8)—22no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3—22no—
118C22×C3×D3—41no—
119C22×C3×D3—41no—
120C22×C3×D3—41no—
121C22×C3×D3—41no—
122C22×C3×D3—41no—
123C22×C3×D3—41no—
124C2×C32×C4—21no—
125C2×C32×C4—21no—
126C2×C32×C4—21no—
127C2×C32×C4—21no—
128C2×C32×C4—21no—
129C2×C32×C4SD1612yescomplemented
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C2×C32×C4#4111yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—41no—
138C2×C3⋊Dic3—41no—
139C2×C3⋊Dic3—41no—
140C2×C3⋊Dic3—41no—
141C2×C3⋊Dic3—41no—
142#634—22no—
143#634—22no—
144#634—41no—
145#634—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C3×D12—22no—
150C3×D12—22no—
151C3×D12—41no—
152C3×D12—41no—
153C3×C3⋊C8—22no—
154C3×C3⋊C8—41no—
155C22×SD16—91no—
156C2×C4⋊C8—31no—
157C2×#103—91no—
158C2×#102—91no—
159#391—91no—
160#390—31no—
161#340—91no—
162C24×C3—61no—
163C23×D3—21no—
164C2×C3×D4—32no—
165C2×C3×D4—61no—
166C2×C3×D4—61no—
167C2×C3×D4—61no—
168C2×C3×D4—61no—
169C2×C3×D4—61no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—61no—
174C22×C3×C4D1211yescharacteristic
175C22×C3×C4D1211yescharacteristic
176C22×C3×C4#6711yescharacteristic
177C22×C3×C4#6711yescharacteristic
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C22×D311yescharacteristic
180C22×Dic3—21no—
181C22×Dic3—62no—
182C22×Dic3—61no—
183C22×Dic3—61no—
184C22×Dic3—62no—
185C22×Dic3—61no—
186C22×Dic3—61no—
187C2×D12—21no—
188C2×D12—21no—
189C2×D12—21no—
190C2×D12—21no—
191C2×D12—21no—
192C2×D12D1212yes—
193C2×Dic6—32no—
194C2×Dic6—32no—
195C2×Dic6—62no—
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—62no—
205C2×Dic6—61no—
206C2×Dic6—61no—
207C2×Dic6—121no—
208C2×Dic6—121no—
209C2×Dic6—121no—
210C2×Dic6—121no—
211C2×C3×C8—32no—
212C2×C3×C8—61no—
213C2×C3×C8—61no—
214C2×C3×C8—61no—
215C2×C3×C8—61no—
216C2×C3×C8—61no—
217C3×C4⋊C4—61no—
218C3×C4⋊C4—61no—
219C3×C22⋊C4—122no—
220C3×C22⋊C4—122no—
221C3×C42—21no—
222C3×C42—21no—
223C3×C42—21no—
224C3×C42—21no—
225C3×C42—41no—
226C3×C42—41no—
227#214—68no—
228(C2×D3)⋊C4—42no—
229(C2×D3)⋊C4—42no—
230C4⋊Dic3—21no—
231C4⋊Dic3—21no—
232C4⋊Dic3—61no—
233C4⋊Dic3—61no—
234C4⋊Dic3—61no—
235C4⋊Dic3—61no—
236C4⋊Dic3—121no—
237C4⋊Dic3—121no—
238C2×C3⋊C8—21no—
239C2×C3⋊C8—21no—
240C2×C3⋊C8—21no—
241C2×C3⋊C8—21no—
242C2×C3⋊C8—21no—
243C2×C3⋊C8#6712yes—
244#204—68no—
245C22×C32#12111yescharacteristic
246C22×C32#12111yescharacteristic
247C22×C32#12111yescharacteristic
248C22×C32C2×SD1611yescharacteristic
249C22×C32#13511yescharacteristic
250C22×C32AGL(1,ℤ/8)11yescharacteristic
251C22×C32#13711yescharacteristic
252C2×C3×D3—42no—
253C2×C3×D3—42no—
254C2×C3×D3—42no—
255C2×C3×D3—81no—
256C2×C3×D3—81no—
257C2×C3×D3—81no—
258C2×C3×D3—81no—
259C32×C4—22no—
260C32×C4—41no—
261C32×C4#12011yescharacteristic
262C32×C4#12311yescharacteristic
263C32×C4#12311yescharacteristic
264C32×C4#12411yescharacteristic
265C3⋊Dic3—42no—
266C3⋊Dic3—81no—
267C3×Dic3—81no—
268C22×Q8—91no—
269C22×D4—31no—
270C2×SD16—182no—
271C2×SD16—182no—
272C2×SD16—182no—
273C22×C8—31no—
274C22×C8—31no—
275C2×C4⋊C4—31no—
276C2×C4⋊C4—91no—
277C2×C22⋊C4—61no—
278C2×C22⋊C4—61no—
279C2×C42D3211yescharacteristic
280C4⋊C8—62no—
281#103—182no—
282#102—182no—
283#95—181no—
284#95—181no—
285C23×C3—21no—
286C23×C3—62no—
287C23×C3—121no—
288C23×C3—121no—
289C23×C3—121no—
290C23×C3—121no—
291C23×C3—121no—
292C23×C3—121no—
293C23×C3C2×D1211yescharacteristic
294C23×C3C2×#6711yescharacteristic
295C22×D3—22no—
296C22×D3—41no—
297C22×D3—41no—
298C22×D3—41no—
299C22×D3—41no—
300C22×D3—41no—
301C22×D3—41no—
302C3×D4—62no—
303C3×D4—62no—
304C3×D4—121no—
305C3×D4—121no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—22no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—22no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—41no—
325C2×C3×C4—41no—
326C2×C3×C4—41no—
327C2×C3×C4—41no—
328C2×C3×C4—121no—
329C2×C3×C4—121no—
330C2×C3×C4—121no—
331C2×C3×C4#20412yescomplemented
332C2×C3×C4#21412yescomplemented
333C2×C3×C4C2×D1211yescharacteristic
334C2×C3×C4#23511yescharacteristic
335C2×C3×C4#23511yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4#23711yescharacteristic
341C2×C3×C4#23711yescharacteristic
342C2×C3×C4#23911yescharacteristic
343C2×C3×C4#23911yescharacteristic
344C2×C3×C4C2×#6711yescharacteristic
345C2×Dic3—41no—
346C2×Dic3—41no—
347C2×Dic3—41no—
348C2×Dic3—64no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—122no—
352C2×Dic3—122no—
353C2×Dic3—121no—
354C2×Dic3—121no—
355C2×Dic3—121no—
356C2×Dic3—121no—
357C2×Dic3—122no—
358C2×Dic3—122no—
359C2×Dic3—122no—
360C2×Dic3—121no—
361C2×Dic3—121no—
362C2×Dic3—121no—
363C2×Dic3—121no—
364C2×Dic3—121no—
365C2×Dic3—121no—
366D12—22no—
367D12—22no—
368D12—41no—
369D12—41no—
370Dic6—62no—
371Dic6—62no—
372Dic6—62no—
373Dic6—62no—
374Dic6—122no—
375Dic6—122no—
376Dic6—122no—
377Dic6—122no—
378Dic6—121no—
379Dic6—121no—
380Dic6—121no—
381Dic6—121no—
382C3×C8—62no—
383C3×C8—121no—
384C3⋊C8—22no—
385C3⋊C8—41no—
386C2×C32#39411yescharacteristic
387C2×C32#46011yescharacteristic
388C2×C32#46111yescharacteristic
389C2×C32#46311yescharacteristic
390C2×C32#46411yescharacteristic
391C2×C32#46511yescharacteristic
392C2×C32#46811yescharacteristic
393C3×D3—82no—
394C24—61no—
395C2×Q8—92no—
396C2×Q8—181no—
397C2×Q8—181no—
398C2×Q8—181no—
399C2×Q8—181no—
400C2×Q8—181no—
401C2×D4—32no—
402C2×D4—61no—
403C2×D4—61no—
404C2×D4—61no—
405C2×D4—61no—
406C2×D4—61no—
407C22×C4—61no—
408C22×C4—181no—
409C22×C4—181no—
410C22×C4#62611yescharacteristic
411C22×C4#62611yescharacteristic
412C22×C4C2×D3211yescharacteristic
413SD16—188no—
414C2×C8—32no—
415C2×C8—61no—
416C2×C8—61no—
417C2×C8—61no—
418C2×C8—61no—
419C2×C8—61no—
420C4⋊C4—61no—
421C4⋊C4—61no—
422C4⋊C4—181no—
423C4⋊C4—181no—
424C22⋊C4—122no—
425C22⋊C4—122no—
426C42—21no—
427C42—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—122no—
436C22×C3—122no—
437C22×C3—122no—
438C22×C3—241no—
439C22×C3—241no—
440C22×C3—241no—
441C22×C3—241no—
442C22×C3#89511yescharacteristic
443C22×C3#89511yescharacteristic
444C22×C3C2×#20411yescharacteristic
445C22×C3#90411yescharacteristic
446C22×C3#90811yescharacteristic
447C22×C3#90911yescharacteristic
448C22×C3#93011yescharacteristic
449C22×C3#93011yescharacteristic
450C22×C3#93211yescharacteristic
451C22×C3C2×#21411yescharacteristic
452C22×C3#93811yescharacteristic
453C22×C3#93911yescharacteristic
454C22×C3#95011yescharacteristic
455C22×C3#95111yescharacteristic
456C2×D3—42no—
457C2×D3—42no—
458C2×D3—42no—
459C2×D3—81no—
460C2×D3—81no—
461C2×D3—81no—
462C2×D3—81no—
463C3×C4—22no—
464C3×C4—22no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—21no—
469C3×C4—42no—
470C3×C4—42no—
471C3×C4—41no—
472C3×C4—41no—
473C3×C4—241no—
474C3×C4#88211yescharacteristic
475C3×C4#88311yescharacteristic
476C3×C4#88511yescharacteristic
477C3×C4#88611yescharacteristic
478C3×C4#89411yescharacteristic
479C3×C4#89411yescharacteristic
480C3×C4#93711yescharacteristic
481C3×C4#94711yescharacteristic
482Dic3—81no—
483Dic3—124no—
484Dic3—122no—
485Dic3—122no—
486Dic3—242no—
487Dic3—241no—
488Dic3—241no—
489C32#205511yescharacteristic, complemented, Sylow
490C23—62no—
491C23—121no—
492C23—121no—
493C23—121no—
494C23—121no—
495C23—121no—
496C23—121no—
497C23C2×#62611yescharacteristic
498Q8—182no—
499Q8—182no—
500Q8—361no—
501Q8—361no—
502D4—62no—
503D4—62no—
504D4—121no—
505D4—121no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—121no—
512C2×C4—121no—
513C2×C4—121no—
514C2×C4—182no—
515C2×C4—361no—
516C2×C4—361no—
517C2×C4—361no—
518C2×C4—361no—
519C2×C4—361no—
520C2×C4#371612yescomplemented
521C2×C4#379611yescharacteristic
522C2×C4#379911yescharacteristic
523C2×C4D3×D1211yescharacteristic
524C2×C4#380211yescharacteristic
525C2×C4#380411yescharacteristic
526C2×C4D3×#6711yescharacteristic
527C8—62no—
528C8—121no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—242no—
537C2×C3#484111yescharacteristic
538C2×C3#484411yescharacteristic
539C2×C3#484511yescharacteristic
540C2×C3#484811yescharacteristic
541C2×C3#496111yescharacteristic
542C2×C3#499111yescharacteristic
543C2×C3#501611yescharacteristic
544C2×C3#501911yescharacteristic
545C2×C3#504111yescharacteristic
546C2×C3#504211yescharacteristic
547C2×C3#505411yescharacteristic
548C2×C3#507511yescharacteristic
549C2×C3#511411yescharacteristic
550C2×C3#513411yescharacteristic
551D3—82no—
552C22—122no—
553C22—122no—
554C22—122no—
555C22—241no—
556C22—241no—
557C22—241no—
558C22—241no—
559C22C2×#371611yescharacteristic
560C22#6382911yescharacteristic
561C22#6383011yescharacteristic
562C22#6383111yescharacteristic
563C22#6390911yescharacteristic
564C22#6391611yescharacteristic
565C22#6397811yescharacteristic
566C4—22no—
567C4—41no—
568C4—241no—
569C4—362no—
570C4—721no—
571C4#6385411yescharacteristic
572C4#6389011yescharacteristic
573C4#6390711yescharacteristic
574C4#6392211yescharacteristic
575C3—21no—
576C3#6965111yescharacteristic, complemented
577C3#7048211yescharacteristic, complemented
578C2—242no—
579C2#1059036511yescharacteristic
580C2#1059036611yescharacteristic
581C2#1059037711yescharacteristic
582C2#1059037811yescharacteristic
583C2#1059117511yescharacteristic
584C2#1059117611yescharacteristic
585C2#1059139211yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32#2055
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #10592628C2semidirect
4. C2×C3×C4⋊(C3⋊C8)C2semidirect
5. C2×#63567C2semidirect
7. #10589164C2semidirect
39. C2×C4⋊(C3⋊C8)D3semidirect
129. C2×C32×C4SD16semidirect
331. C2×C3×C4#204semidirect
332. C2×C3×C4#214semidirect
489. C32#2055semidirect
520. C2×C4#3716semidirect
576. C3#69651semidirect
577. C3#70482semidirect

Maximal subgroups

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

subgroupindex
C22×#37162
#105926282
C3×#49392
C2×C3×C4⋊(C3⋊C8)2
C2×#635672
C2×#635632
#105891642
#704823
#696513