Finite Group Databasebeta

← #11794066

Subgroups — #11794066

Order 1152.

717 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#204C211yesmaximal, characteristic
2C2×#63641C211yesmaximal, characteristic, complemented
3#10591323C211yesmaximal, characteristic
4#10591221C211yesmaximal, characteristic, complemented
5C2×#63565C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic
7C3×#4551C211yesmaximal, characteristic, complemented
8#72051—31nomaximal
9#68863—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×#204—22no—
18C2×C3×#204—22no—
19C2×C3×#204—22no—
20C2×(C2×D3)⋊Dic3—21no—
21C2×(C2×D3)⋊Dic3—21no—
22#63641—22no—
23#63579—21no—
24#63579—21no—
25#63565—22no—
26#63562—22no—
27C22×C3×SD16—31no—
28C22×#204D311yescharacteristic
29#5229—31no—
30C2×#835—31no—
31#5221—31no—
32C2×#832—31no—
33C2×Dic3⋊C8—31no—
34C2×Dic3⋊C8—31no—
35C2×Dic3⋊C8—61no—
36#4988—31no—
37#4973—31no—
38C2×#810—31no—
39C2×#809—31no—
40C3×#340—31no—
41#4551D311yescharacteristic, complemented
42C23×C3×D3—21no—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3D411yescharacteristic
45C22×C3⋊Dic3D411yescharacteristic
46C22×C3×Dic3—21no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12D412yes—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6D412yes—
61C2×C32×C8—21no—
62C2×C32×C8—21no—
63C2×C32×C8D412yes—
64C4×C3⋊Dic3—21no—
65C4×C3⋊Dic3—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—21no—
73C3×#204—28no—
74(C2×D3)⋊Dic3—42no—
75(C2×D3)⋊Dic3—42no—
76#2055—91noSylow
77C22×C3×Q8—31no—
78C22×C3×D4—31no—
79C22×D12C2×D311yescharacteristic
80C22×Dic6C2×D311yescharacteristic
81C2×C3×SD16—62no—
82C2×C3×SD16—62no—
83C2×C3×SD16—62no—
84C22×C3×C8—21no—
85C22×C3×C8C2×D311yescharacteristic
86C22×C3×C8C2×D311yescharacteristic
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4—31no—
89C2×#217—61no—
90C2×#217—61no—
91C2×(C2×D3)⋊C4—61no—
92C2×(C2×D3)⋊C4—61no—
93C2×C4⋊Dic3C2×D311yescharacteristic
94C2×C4⋊Dic3C2×D311yescharacteristic
95C2×C4×Dic3—31no—
96C2×C4×Dic3—31no—
97C2×C4×Dic3—61no—
98C22×C3⋊C8—31no—
99C22×C3⋊C8—31no—
100C22×C3⋊C8—61no—
101C2×#204—22no—
102C2×#204—22no—
103C2×#204—22no—
104#835—62no—
105#832—62no—
106C3⋊#95—61no—
107C3⋊#95—61no—
108C3⋊#95—61no—
109C3⋊#95—61no—
110Dic3⋊C8—64no—
111Dic3⋊C8—62no—
112Dic3⋊C8—62no—
113#810—62no—
114#809—62no—
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—21no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3SD1612yescomplemented
135C2×C3×Dic3—22no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C3×D12—22no—
145C3×D12—22no—
146C3×D12—41no—
147C3×D12—41no—
148C3×Dic6—22no—
149C3×Dic6—22no—
150C3×Dic6—41no—
151C3×Dic6—41no—
152C32×C8—22no—
153C3⋊(C3⋊C8)—41no—
154C22×SD16—31no—
155C2×C4⋊C8—91no—
156C2×#103—91no—
157C2×#102—91no—
158#391—91no—
159#390—91no—
160#340—31no—
161C24×C3—61no—
162C23×D3—21no—
163C2×C3×Q8—32no—
164C2×C3×Q8—61no—
165C2×C3×Q8—61no—
166C2×C3×Q8—61no—
167C2×C3×Q8—61no—
168C2×C3×Q8—61no—
169C2×C3×D4—32no—
170C2×C3×D4—61no—
171C2×C3×D4—61no—
172C2×C3×D4—61no—
173C2×C3×D4—61no—
174C2×C3×D4—61no—
175C22×C3×C4—21no—
176C22×C3×C4—61no—
177C22×C3×C4—61no—
178C22×C3×C4—61no—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D311yescharacteristic
181C22×Dic3—21no—
182C22×Dic3—21no—
183C22×Dic3—21no—
184C22×Dic3—31no—
185C22×Dic3—31no—
186C22×Dic3—31no—
187C22×Dic3—31no—
188C22×Dic3—61no—
189C22×Dic3—61no—
190C2×D12—21no—
191C2×D12—21no—
192C2×D12—21no—
193C2×D12—21no—
194C2×D12—21no—
195C2×D12#6712yes—
196C2×Dic6—21no—
197C2×Dic6—21no—
198C2×Dic6—21no—
199C2×Dic6—21no—
200C2×Dic6—21no—
201C2×Dic6#6712yes—
202C3×SD16—68no—
203C2×C3×C8—21no—
204C2×C3×C8—21no—
205C2×C3×C8—21no—
206C2×C3×C8—21no—
207C2×C3×C8—22no—
208C2×C3×C8—41no—
209C2×C3×C8—41no—
210C2×C3×C8D1212yes—
211C2×C3×C8#6712yes—
212C3×C4⋊C4—61no—
213C3×C4⋊C4—61no—
214C3×C4⋊C4—61no—
215C3×C4⋊C4—61no—
216#217—122no—
217#217—122no—
218(C2×D3)⋊C4—122no—
219(C2×D3)⋊C4—122no—
220C4⋊Dic3—21no—
221C4⋊Dic3—21no—
222C4⋊Dic3—21no—
223C4⋊Dic3—21no—
224C4×Dic3—62no—
225C4×Dic3—62no—
226C4×Dic3—61no—
227C4×Dic3—61no—
228C4×Dic3—61no—
229C4×Dic3—61no—
230C2×C3⋊C8—62no—
231C2×C3⋊C8—61no—
232C2×C3⋊C8—61no—
233C2×C3⋊C8—61no—
234C2×C3⋊C8—61no—
235C2×C3⋊C8—61no—
236C2×C3⋊C8—61no—
237C2×C3⋊C8—121no—
238C2×C3⋊C8—121no—
239#204—28no—
240C22×C32#12111yescharacteristic
241C22×C32#12111yescharacteristic
242C22×C32#12111yescharacteristic
243C22×C32C2×SD1611yescharacteristic
244C22×C32#13511yescharacteristic
245C22×C32AGL(1,ℤ/8)11yescharacteristic
246C22×C32#13711yescharacteristic
247C2×C3×D3—42no—
248C2×C3×D3—42no—
249C2×C3×D3—42no—
250C2×C3×D3—81no—
251C2×C3×D3—81no—
252C2×C3×D3—81no—
253C2×C3×D3—81no—
254C32×C4#12011yescharacteristic
255C32×C4#12311yescharacteristic
256C32×C4#12311yescharacteristic
257C32×C4#12411yescharacteristic
258C3⋊Dic3—22no—
259C3⋊Dic3—41no—
260C3×Dic3—42no—
261C3×Dic3—81no—
262C3×Dic3—81no—
263C22×Q8—31no—
264C22×D4—31no—
265C2×SD16—62no—
266C2×SD16—62no—
267C2×SD16—62no—
268C22×C8—91no—
269C22×C8D3211yescharacteristic
270C2×C4⋊C4—31no—
271C2×C4⋊C4—31no—
272C2×C22⋊C4—181no—
273C2×C22⋊C4—181no—
274C2×C42—91no—
275C4⋊C8—182no—
276#103—182no—
277#102—182no—
278#95—181no—
279#95—181no—
280C23×C3—21no—
281C23×C3—62no—
282C23×C3—121no—
283C23×C3—121no—
284C23×C3—121no—
285C23×C3—121no—
286C23×C3—121no—
287C23×C3—121no—
288C23×C3D3×D411yescharacteristic
289C23×C3D3×D411yescharacteristic
290C22×D3—22no—
291C22×D3—41no—
292C22×D3—41no—
293C22×D3—41no—
294C22×D3—41no—
295C22×D3—41no—
296C22×D3—41no—
297C3×Q8—62no—
298C3×Q8—62no—
299C3×Q8—121no—
300C3×Q8—121no—
301C3×D4—62no—
302C3×D4—62no—
303C3×D4—121no—
304C3×D4—121no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—62no—
312C2×C3×C4—121no—
313C2×C3×C4—121no—
314C2×C3×C4—121no—
315C2×C3×C4—121no—
316C2×C3×C4—121no—
317C2×C3×C4—121no—
318C2×C3×C4—121no—
319C2×C3×C4—121no—
320C2×C3×C4C2×D1211yescharacteristic
321C2×C3×C4#23511yescharacteristic
322C2×C3×C4#23511yescharacteristic
323C2×C3×C4D3×D411yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4#23711yescharacteristic
326C2×C3×C4#23711yescharacteristic
327C2×C3×C4#23711yescharacteristic
328C2×C3×C4#23911yescharacteristic
329C2×C3×C4C2×#6711yescharacteristic
330C2×C3×C4C2×#6711yescharacteristic
331C2×C3×C4C2×#6711yescharacteristic
332C2×Dic3—22no—
333C2×Dic3—32no—
334C2×Dic3—32no—
335C2×Dic3—41no—
336C2×Dic3—41no—
337C2×Dic3—41no—
338C2×Dic3—41no—
339C2×Dic3—41no—
340C2×Dic3—41no—
341C2×Dic3—41no—
342C2×Dic3—41no—
343C2×Dic3—62no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—61no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349C2×Dic3—61no—
350C2×Dic3—62no—
351C2×Dic3—61no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357C2×Dic3—121no—
358C2×Dic3—121no—
359D12—22no—
360D12—22no—
361D12—41no—
362D12—41no—
363Dic6—22no—
364Dic6—22no—
365Dic6—41no—
366Dic6—41no—
367C3×C8—22no—
368C3×C8—22no—
369C3×C8—42no—
370C3⋊C8—122no—
371C3⋊C8—121no—
372C3⋊C8—121no—
373C2×C32#39411yescharacteristic
374C2×C32#46011yescharacteristic
375C2×C32#46111yescharacteristic
376C2×C32#46311yescharacteristic
377C2×C32#46411yescharacteristic
378C2×C32#46511yescharacteristic
379C2×C32#46811yescharacteristic
380C3×D3—82no—
381C24—61no—
382C2×Q8—32no—
383C2×Q8—61no—
384C2×Q8—61no—
385C2×Q8—61no—
386C2×Q8—61no—
387C2×Q8—61no—
388C2×D4—32no—
389C2×D4—61no—
390C2×D4—61no—
391C2×D4—61no—
392C2×D4—61no—
393C2×D4—61no—
394C22×C4—61no—
395C22×C4—61no—
396C22×C4—61no—
397C22×C4—91no—
398C22×C4—91no—
399C22×C4C2×D3211yescharacteristic
400SD16—68no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—181no—
404C2×C8—181no—
405C2×C8—181no—
406C2×C8#62612yes—
407C4⋊C4—61no—
408C4⋊C4—61no—
409C4⋊C4—61no—
410C4⋊C4—61no—
411C22⋊C4—362no—
412C22⋊C4—362no—
413C42—181no—
414C42—181no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—122no—
423C22×C3—122no—
424C22×C3—122no—
425C22×C3—241no—
426C22×C3—241no—
427C22×C3—241no—
428C22×C3—241no—
429C22×C3#88411yescharacteristic
430C22×C3#88411yescharacteristic
431C22×C3#89511yescharacteristic
432C22×C3#91111yescharacteristic
433C22×C3D3×SD1611yescharacteristic
434C22×C3D3×SD1611yescharacteristic
435C22×C3#91411yescharacteristic
436C22×C3#91511yescharacteristic
437C22×C3#91611yescharacteristic
438C22×C3#91611yescharacteristic
439C22×C3#91811yescharacteristic
440C22×C3#93811yescharacteristic
441C22×C3#93911yescharacteristic
442C22×C3#93911yescharacteristic
443C2×D3—42no—
444C2×D3—42no—
445C2×D3—42no—
446C2×D3—81no—
447C2×D3—81no—
448C2×D3—81no—
449C2×D3—81no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—122no—
455C3×C4—241no—
456C3×C4—241no—
457C3×C4#87511yescharacteristic
458C3×C4#88211yescharacteristic
459C3×C4#89411yescharacteristic
460C3×C4#89411yescharacteristic
461C3×C4#93511yescharacteristic
462C3×C4#93511yescharacteristic
463C3×C4#93611yescharacteristic
464C3×C4#95311yescharacteristic
465Dic3—42no—
466Dic3—64no—
467Dic3—62no—
468Dic3—62no—
469Dic3—81no—
470Dic3—81no—
471Dic3—122no—
472Dic3—121no—
473Dic3—121no—
474C32#205511yescharacteristic, complemented, Sylow
475C23—62no—
476C23—121no—
477C23—121no—
478C23—121no—
479C23—121no—
480C23—121no—
481C23—121no—
482C23#380211yescharacteristic
483Q8—62no—
484Q8—62no—
485Q8—121no—
486Q8—121no—
487D4—62no—
488D4—62no—
489D4—121no—
490D4—121no—
491C2×C4—62no—
492C2×C4—92no—
493C2×C4—121no—
494C2×C4—121no—
495C2×C4—121no—
496C2×C4—121no—
497C2×C4—121no—
498C2×C4—121no—
499C2×C4—121no—
500C2×C4—121no—
501C2×C4—181no—
502C2×C4—181no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—181no—
506C2×C4#379511yescharacteristic
507C2×C4#379511yescharacteristic
508C2×C4#379611yescharacteristic
509C2×C4C2×#62611yescharacteristic
510C2×C4D3×#6711yescharacteristic
511C2×C4D3×#6711yescharacteristic
512C8—22no—
513C8—361no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—242no—
522C2×C3#467211yescharacteristic
523C2×C3#476211yescharacteristic
524C2×C3#478711yescharacteristic
525C2×C3#479811yescharacteristic
526C2×C3#481811yescharacteristic
527C2×C3#486411yescharacteristic
528C2×C3#488611yescharacteristic
529C2×C3#516211yescharacteristic
530C2×C3#516311yescharacteristic
531C2×C3#516511yescharacteristic
532C2×C3#516611yescharacteristic
533C2×C3#517111yescharacteristic
534C2×C3#517411yescharacteristic
535C2×C3#522211yescharacteristic
536D3—82no—
537C22—122no—
538C22—122no—
539C22—122no—
540C22—241no—
541C22—241no—
542C22—241no—
543C22—241no—
544C22#6379611yescharacteristic
545C22#6379811yescharacteristic
546C22#6380911yescharacteristic
547C22#6381111yescharacteristic
548C22#6388511yescharacteristic
549C22#6388511yescharacteristic
550C22#6391611yescharacteristic
551C4—122no—
552C4—182no—
553C4—241no—
554C4—241no—
555C4—361no—
556C4#6386011yescharacteristic
557C4#6388411yescharacteristic
558C4#6388411yescharacteristic
559C4#6397711yescharacteristic
560C3—21no—
561C3#6886311yescharacteristic, complemented
562C3#7205111yescharacteristic, complemented
563C2—242no—
564C2#1059074811yescharacteristic
565C2#1059075011yescharacteristic
566C2#1059079611yescharacteristic
567C2#1059084311yescharacteristic
568C2#1059084511yescharacteristic
569C2#1059087611yescharacteristic
570C2#1059130211yescharacteristic
subgroupG/H
centerC23#3802
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×#63641C2semidirect
4. #10591221C2semidirect
5. C2×#63565C2semidirect
7. C3×#4551C2semidirect
41. #4551D3semidirect
134. C2×C3⋊Dic3SD16semidirect
474. C32#2055semidirect
561. C3#68863semidirect
562. C3#72051semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2042
C2×#636412
#105913232
#105912212
C2×#635652
C2×#635622
C3×#45512
#720513
#688633