Finite Group Databasebeta

← #11794058

Subgroups — #11794058

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×C3×#215C211yesmaximal, characteristic
2#10592928C211yesmaximal, characteristic, complemented
3C2×C3×#835C211yesmaximal, characteristic, complemented
4#10591323C211yesmaximal, characteristic
5C2×#63572C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic
7#10589164C211yesmaximal, characteristic, complemented
8#72051—31nomaximal
9#70280—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×#215—22no—
15C2×C3×#215—22no—
16C2×C3×#215—22no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C2×(C2×D3)⋊Dic3—21no—
21C2×(C2×D3)⋊Dic3—21no—
22#63658—21no—
23#63658—21no—
24C3×#835—22no—
25#63572—22no—
26#63563—22no—
27C22×C3×SD16—31no—
28C22×#215D311yescharacteristic
29C2×C3×#103—31no—
30#5229—31no—
31#5229—31no—
32#5229—61no—
33C2×#835D311yescharacteristic, complemented
34#5221—31no—
35C2×#832—31no—
36C2×#821—31no—
37C2×Dic3⋊C8—31no—
38C2×Dic3⋊C8—31no—
39#4988—31no—
40#4551—31no—
41#4529—31no—
42C23×C3×D3—21no—
43C2×C32×Q8—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8—21no—
48C2×C32×Q8D412yes—
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—21no—
52C22×C3⋊Dic3D411yescharacteristic
53C22×C3⋊Dic3D411yescharacteristic
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—
61C4⋊(C3⋊Dic3)—21no—
62C4⋊(C3⋊Dic3)—21no—
63C4×C3⋊Dic3—21no—
64C4×C3⋊Dic3—21no—
65C3×#215—28no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8D412yes—
74(C2×D3)⋊Dic3—42no—
75(C2×D3)⋊Dic3—42no—
76#2055—91noSylow
77C22×C3×Q8—21no—
78C22×C3×Q8C2×D311yescharacteristic
79C22×C3×Q8C2×D311yescharacteristic
80C22×C3×D4—31no—
81C22×D12C2×D311yescharacteristic
82C2×C3×SD16—62no—
83C2×C3×SD16—62no—
84C2×C3×SD16—62no—
85C22×C3×C8—31no—
86C22×C3×C8—31no—
87C2×C3×C4⋊C4—31no—
88C2×#217—61no—
89C2×#217—61no—
90C2×#215—22no—
91C2×#215—22no—
92C2×#215—22no—
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×Dic3—31no—
100C2×C4×Dic3—31no—
101C2×C4×Dic3—61no—
102C22×C3⋊C8C2×D311yescharacteristic
103C22×C3⋊C8C2×D311yescharacteristic
104C3×#103—62no—
105#835—22no—
106#832—62no—
107C3⋊#95—61no—
108C3⋊#95—61no—
109C3⋊#95—61no—
110C3⋊#95—61no—
111C3⋊#95—62no—
112C3⋊#95—62no—
113#821—62no—
114Dic3⋊C8—62no—
115Dic3⋊C8—62no—
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—
124C32×Q8—22no—
125C32×Q8—22no—
126C32×Q8—41no—
127C32×Q8—41no—
128C2×C32×C4—22no—
129C2×C32×C4—41no—
130C2×C32×C4—41no—
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4#4111yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—21no—
141C2×C3⋊Dic3—21no—
142C2×C3⋊Dic3—41no—
143C2×C3⋊Dic3—41no—
144C2×C3⋊Dic3—41no—
145C2×C3⋊Dic3SD1612yescomplemented
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—31no—
156C2×C4⋊C8—91no—
157C2×#103—31no—
158C2×#102—91no—
159#391—91no—
160#390—91no—
161#340—91no—
162C24×C3—61no—
163C23×D3—21no—
164C2×C3×Q8—22no—
165C2×C3×Q8—21no—
166C2×C3×Q8—21no—
167C2×C3×Q8—21no—
168C2×C3×Q8—21no—
169C2×C3×Q8—21no—
170C2×C3×Q8—21no—
171C2×C3×Q8—21no—
172C2×C3×Q8—21no—
173C2×C3×Q8—21no—
174C2×C3×Q8—21no—
175C2×C3×Q8—22no—
176C2×C3×Q8—41no—
177C2×C3×Q8—41no—
178C2×C3×Q8—41no—
179C2×C3×Q8—41no—
180C2×C3×Q8#6712yes—
181C2×C3×Q8#6712yes—
182C2×C3×D4—32no—
183C2×C3×D4—61no—
184C2×C3×D4—61no—
185C2×C3×D4—61no—
186C2×C3×D4—61no—
187C2×C3×D4—61no—
188C22×C3×C4—22no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—61no—
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C22×Dic3—21no—
196C22×Dic3—31no—
197C22×Dic3—31no—
198C22×Dic3—31no—
199C22×Dic3—31no—
200C22×Dic3—61no—
201C22×Dic3—61no—
202C22×Dic3—62no—
203C22×Dic3—61no—
204C22×Dic3—61no—
205C2×D12—21no—
206C2×D12—21no—
207C2×D12—21no—
208C2×D12—21no—
209C2×D12—21no—
210C2×D12#6712yes—
211C3×SD16—68no—
212C2×C3×C8—32no—
213C2×C3×C8—61no—
214C2×C3×C8—61no—
215C2×C3×C8—61no—
216C2×C3×C8—61no—
217C2×C3×C8—61no—
218C3×C4⋊C4—61no—
219C3×C4⋊C4—61no—
220#217—122no—
221#217—122no—
222#215—28no—
223(C2×D3)⋊C4—122no—
224(C2×D3)⋊C4—122no—
225C4⋊Dic3—21no—
226C4⋊Dic3—21no—
227C4⋊Dic3—61no—
228C4⋊Dic3—61no—
229C4⋊Dic3—61no—
230C4⋊Dic3—61no—
231C4⋊Dic3—121no—
232C4⋊Dic3—121no—
233C4×Dic3—61no—
234C4×Dic3—61no—
235C4×Dic3—61no—
236C4×Dic3—61no—
237C4×Dic3—121no—
238C4×Dic3—121no—
239C2×C3⋊C8—21no—
240C2×C3⋊C8—21no—
241C2×C3⋊C8—21no—
242C2×C3⋊C8—21no—
243C2×C3⋊C8—21no—
244C2×C3⋊C8#6712yes—
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—42no—
260C32×C4#12011yescharacteristic
261C32×C4#12311yescharacteristic
262C32×C4#12311yescharacteristic
263C32×C4#12411yescharacteristic
264C3⋊Dic3—22no—
265C3⋊Dic3—41no—
266C3⋊Dic3—81no—
267C3×Dic3—81no—
268C22×Q8D3211yescharacteristic
269C22×D4—31no—
270C2×SD16—62no—
271C2×SD16—62no—
272C2×SD16—62no—
273C22×C8—31no—
274C22×C8—31no—
275C2×C4⋊C4—31no—
276C2×C4⋊C4—91no—
277C2×C22⋊C4—181no—
278C2×C22⋊C4—181no—
279C2×C42—91no—
280C4⋊C8—182no—
281#103—62no—
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×C3D3×D411yescharacteristic
294C23×C3D3×D411yescharacteristic
295C22×D3—22no—
296C22×D3—41no—
297C22×D3—41no—
298C22×D3—41no—
299C22×D3—41no—
300C22×D3—41no—
301C22×D3—41no—
302C3×Q8—22no—
303C3×Q8—22no—
304C3×Q8—22no—
305C3×Q8—22no—
306C3×Q8—42no—
307C3×Q8—42no—
308C3×Q8—42no—
309C3×Q8—42no—
310C3×Q8—41no—
311C3×Q8—41no—
312C3×Q8—41no—
313C3×Q8—41no—
314C3×D4—62no—
315C3×D4—62no—
316C3×D4—121no—
317C3×D4—121no—
318C2×C3×C4—24no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—42no—
328C2×C3×C4—42no—
329C2×C3×C4—41no—
330C2×C3×C4—41no—
331C2×C3×C4—41no—
332C2×C3×C4—41no—
333C2×C3×C4—121no—
334C2×C3×C4—121no—
335C2×C3×C4—121no—
336C2×C3×C4#23511yescharacteristic
337C2×C3×C4#23511yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4#23711yescharacteristic
341C2×C3×C4#23711yescharacteristic
342C2×C3×C4#23711yescharacteristic
343C2×C3×C4#23711yescharacteristic
344C2×C3×C4C2×#6711yescharacteristic
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347C2×C3×C4C2×#6711yescharacteristic
348C2×Dic3—32no—
349C2×Dic3—32no—
350C2×Dic3—41no—
351C2×Dic3—41no—
352C2×Dic3—41no—
353C2×Dic3—62no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357C2×Dic3—61no—
358C2×Dic3—62no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—121no—
366C2×Dic3—121no—
367C2×Dic3—121no—
368C2×Dic3—121no—
369C2×Dic3—122no—
370C2×Dic3—122no—
371C2×Dic3—122no—
372C2×Dic3—121no—
373C2×Dic3—121no—
374C2×Dic3—121no—
375C2×Dic3—121no—
376C2×Dic3—121no—
377C2×Dic3—121no—
378D12—22no—
379D12—22no—
380D12—41no—
381D12—41no—
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—21no—
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8#62512yes—
401C2×D4—32no—
402C2×D4—61no—
403C2×D4—61no—
404C2×D4—61no—
405C2×D4—61no—
406C2×D4—61no—
407C22×C4—21no—
408C22×C4—61no—
409C22×C4—91no—
410C22×C4—91no—
411C22×C4—181no—
412C22×C4C2×D3211yescharacteristic
413SD16—68no—
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—362no—
425C22⋊C4—362no—
426C42—181no—
427C42—181no—
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#88411yescharacteristic
443C22×C3#88411yescharacteristic
444C22×C3D3×SD1611yescharacteristic
445C22×C3D3×SD1611yescharacteristic
446C22×C3#91411yescharacteristic
447C22×C3#91411yescharacteristic
448C22×C3#91511yescharacteristic
449C22×C3#91611yescharacteristic
450C22×C3#91811yescharacteristic
451C22×C3#91911yescharacteristic
452C22×C3#93811yescharacteristic
453C22×C3#93911yescharacteristic
454C22×C3#93911yescharacteristic
455C22×C3#93911yescharacteristic
456C2×D3—42no—
457C2×D3—42no—
458C2×D3—42no—
459C2×D3—81no—
460C2×D3—81no—
461C2×D3—81no—
462C2×D3—81no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—44no—
468C3×C4—42no—
469C3×C4—42no—
470C3×C4—241no—
471C3×C4#88311yescharacteristic
472C3×C4#88511yescharacteristic
473C3×C4#92911yescharacteristic
474C3×C4#93511yescharacteristic
475C3×C4#93511yescharacteristic
476C3×C4#93611yescharacteristic
477C3×C4#93711yescharacteristic
478C3×C4#95311yescharacteristic
479Dic3—62no—
480Dic3—62no—
481Dic3—81no—
482Dic3—122no—
483Dic3—122no—
484Dic3—121no—
485Dic3—121no—
486Dic3—242no—
487Dic3—241no—
488Dic3—241no—
489C32#205511yescharacteristic, complemented, Sylow
490C23—62no—
491C23—121no—
492C23—121no—
493C23—121no—
494C23—121no—
495C23—121no—
496C23—121no—
497C23#381111yescharacteristic
498Q8—22no—
499Q8—22no—
500Q8—41no—
501Q8—41no—
502D4—62no—
503D4—62no—
504D4—121no—
505D4—121no—
506C2×C4—22no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—92no—
510C2×C4—121no—
511C2×C4—121no—
512C2×C4—121no—
513C2×C4—181no—
514C2×C4—181no—
515C2×C4—181no—
516C2×C4—181no—
517C2×C4—181no—
518C2×C4—361no—
519C2×C4—361no—
520C2×C4—361no—
521C2×C4#380411yescharacteristic
522C2×C4#380411yescharacteristic
523C2×C4#380511yescharacteristic
524C2×C4C2×#62511yescharacteristic
525C2×C4D3×#6711yescharacteristic
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#480711yescharacteristic
538C2×C3#481211yescharacteristic
539C2×C3#481811yescharacteristic
540C2×C3#481911yescharacteristic
541C2×C3#495911yescharacteristic
542C2×C3#516211yescharacteristic
543C2×C3#516311yescharacteristic
544C2×C3#516311yescharacteristic
545C2×C3#516511yescharacteristic
546C2×C3#516611yescharacteristic
547C2×C3#517111yescharacteristic
548C2×C3#517411yescharacteristic
549C2×C3#518511yescharacteristic
550C2×C3#522211yescharacteristic
551D3—82no—
552C22—122no—
553C22—122no—
554C22—122no—
555C22—241no—
556C22—241no—
557C22—241no—
558C22—241no—
559C22#6394011yescharacteristic
560C22#6394111yescharacteristic
561C22#6395011yescharacteristic
562C22#6395111yescharacteristic
563C22#6395811yescharacteristic
564C22#6397111yescharacteristic
565C22#6398011yescharacteristic
566C4—42no—
567C4—182no—
568C4—241no—
569C4—361no—
570C4—721no—
571C4#6395911yescharacteristic
572C4#6396111yescharacteristic
573C4#6396911yescharacteristic
574C4#6397611yescharacteristic
575C3—21no—
576C3#7028011yescharacteristic, complemented
577C3#7205111yescharacteristic, complemented
578C2—242no—
579C2#1059156911yescharacteristic
580C2#1059157011yescharacteristic
581C2#1059159011yescharacteristic
582C2#1059159111yescharacteristic
583C2#1059161211yescharacteristic
584C2#1059162211yescharacteristic
585C2#1059170811yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC22×Q8D32
hypocenterC32#2055
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. #10592928C2semidirect
3. C2×C3×#835C2semidirect
5. C2×#63572C2semidirect
7. #10589164C2semidirect
33. C2×#835D3semidirect
145. C2×C3⋊Dic3SD16semidirect
489. C32#2055semidirect
576. C3#70280semidirect
577. C3#72051semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2152
#105929282
C2×C3×#8352
#105913232
C2×#635722
C2×#635632
#105891642
#720513
#702803