Finite Group Databasebeta

← #11791488

Subgroups — #11791488

Order 1152.

757 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
1C2×#63863C211yesmaximal, characteristic
2C2×#63641C211yesmaximal, characteristic, complemented
3C2×C3×#821C211yesmaximal, characteristic
4C2×C3×#816C211yesmaximal, characteristic, complemented
5#10591274C211yesmaximal, characteristic, complemented
6C2×#63565C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic
8#70230—31nomaximal
9#70162—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×(C2×D3)⋊Dic3—21no—
18C2×(C2×D3)⋊Dic3—21no—
19C2×Dic32—21no—
20#63863—22no—
21#63863C414yescomplemented
22#63641—22no—
23C3×#821—22no—
24C3×#816—22no—
25#63579—21no—
26#63565—22no—
27#63562—22no—
28C2×#947—31no—
29C2×#936—31no—
30C2×C3×#103—31no—
31C2×C3×#102—31no—
32C2×#835—31no—
33C2×#832—31no—
34C2×#821D311yescharacteristic
35C2×#816D311yescharacteristic, complemented
36C2×Dic3⋊C8—31no—
37C2×Dic3⋊C8—31no—
38C2×Dic3⋊C8—61no—
39Dic3×C4⋊C4—31no—
40Dic3×C4⋊C4—31no—
41C2×#810—31no—
42C2×#809—31no—
43C23×C3×D3—21no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3D411yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12C2×C412yes—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6C2×C412yes—
62C2×C32×C8—21no—
63C2×C32×C8—21no—
64C2×C32×C8—21no—
65C4×C3⋊Dic3C2×C412yes—
66C4×C3⋊Dic3D412yes—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3D412yes—
73C3×C4⋊Dic3D412yes—
74(C2×D3)⋊Dic3—24no—
75(C2×D3)⋊Dic3—24no—
76Dic32—42no—
77#1983—91noSylow
78C22×C3×Q8—31no—
79C22×C3×D4—31no—
80C22×D12C2×D311yescharacteristic
81C22×Dic6C2×D311yescharacteristic
82C22×C3×C8—21no—
83C22×C3×C8C2×D311yescharacteristic
84C22×C3×C8C2×D311yescharacteristic
85C2×C3×C4⋊C4—31no—
86C2×C3×C4⋊C4—31no—
87C2×#217—61no—
88C2×#217—61no—
89#947—34no—
90#947—62no—
91#936—34no—
92#936—62no—
93C2×(C2×D3)⋊C4—61no—
94C2×(C2×D3)⋊C4—61no—
95C2×C4⋊Dic3C2×D311yescharacteristic
96C2×C4⋊Dic3C2×D311yescharacteristic
97C2×C4×Dic3—31no—
98C2×C4×Dic3—31no—
99C2×C4×Dic3—61no—
100C2×C4×Dic3—61no—
101C2×C4×Dic3—61no—
102C22×C3⋊C8—31no—
103C22×C3⋊C8—31no—
104C22×C3⋊C8—61no—
105C3×#103—62no—
106C3×#102—62no—
107#835—62no—
108#832—62no—
109C3⋊#95—61no—
110C3⋊#95—61no—
111#821—22no—
112#816—22no—
113Dic3⋊C8—62no—
114Dic3⋊C8—62no—
115Dic3⋊C8—64no—
116#810—62no—
117#809—62no—
118C23×C32C2×D411yescharacteristic
119C22×C3×D3—22no—
120C22×C3×D3—41no—
121C22×C3×D3—41no—
122C22×C3×D3—41no—
123C22×C3×D3—41no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C2×C32×C4C22×C411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3C22⋊C412yes—
137C2×C3⋊Dic3C22⋊C412yes—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C3×D12—22no—
148C3×D12—22no—
149C3×D12—41no—
150C3×D12—41no—
151C3×Dic6—22no—
152C3×Dic6—22no—
153C3×Dic6—41no—
154C3×Dic6—41no—
155C32×C8—41no—
156C3⋊(C3⋊C8)—41no—
157C2×#124—91no—
158C2×C4⋊C8—91no—
159C2×#103—31no—
160C2×#103—91no—
161C2×#102—31no—
162C2×#102—91no—
163C4×C4⋊C4—91no—
164C24×C3—61no—
165C23×D3—21no—
166C2×C3×Q8—32no—
167C2×C3×Q8—61no—
168C2×C3×Q8—61no—
169C2×C3×Q8—61no—
170C2×C3×Q8—61no—
171C2×C3×Q8—61no—
172C2×C3×D4—32no—
173C2×C3×D4—61no—
174C2×C3×D4—61no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C22×C3×C4—21no—
179C22×C3×C4—61no—
180C22×C3×C4—61no—
181C22×C3×C4—61no—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C22×Dic3—21no—
185C22×Dic3—21no—
186C22×Dic3—21no—
187C22×Dic3—31no—
188C22×Dic3—31no—
189C22×Dic3—31no—
190C22×Dic3—31no—
191C22×Dic3—61no—
192C22×Dic3—61no—
193C2×D12—21no—
194C2×D12—21no—
195C2×D12—21no—
196C2×D12—21no—
197C2×D12—21no—
198C2×D12C4×D312yes—
199C2×Dic6—21no—
200C2×Dic6—21no—
201C2×Dic6—21no—
202C2×Dic6—21no—
203C2×Dic6—21no—
204C2×Dic6C4×D312yes—
205C2×C3×C8—22no—
206C2×C3×C8—21no—
207C2×C3×C8—21no—
208C2×C3×C8—21no—
209C2×C3×C8—21no—
210C2×C3×C8—21no—
211C2×C3×C8—21no—
212C2×C3×C8—41no—
213C2×C3×C8—41no—
214C3×C4⋊C4—32no—
215C3×C4⋊C4—32no—
216C3×C4⋊C4—61no—
217C3×C4⋊C4—61no—
218#217—64no—
219#217—64no—
220(C2×D3)⋊C4—64no—
221(C2×D3)⋊C4—64no—
222C4⋊Dic3—21no—
223C4⋊Dic3—21no—
224C4⋊Dic3#6712yes—
225C4⋊Dic3#6712yes—
226C4×Dic3—32no—
227C4×Dic3—32no—
228C4×Dic3—32no—
229C4×Dic3—32no—
230C4×Dic3—62no—
231C4×Dic3—62no—
232C4×Dic3—122no—
233C4×Dic3—122no—
234C2×C3⋊C8—62no—
235C2×C3⋊C8—61no—
236C2×C3⋊C8—61no—
237C2×C3⋊C8—61no—
238C2×C3⋊C8—61no—
239C2×C3⋊C8—61no—
240C2×C3⋊C8—61no—
241C2×C3⋊C8—121no—
242C2×C3⋊C8—121no—
243C22×C32C2×C22⋊C411yescharacteristic
244C22×C32#12111yescharacteristic
245C22×C32#12111yescharacteristic
246C22×C32#13511yescharacteristic
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×C4C4×D411yescharacteristic
258C32×C4C4×D411yescharacteristic
259C32×C4#12411yescharacteristic
260C32×C4#12711yescharacteristic
261C3⋊Dic3—22no—
262C3⋊Dic3—22no—
263C3×Dic3—42no—
264C3×Dic3—42no—
265C3×Dic3—42no—
266C22×Q8—31no—
267C22×D4—31no—
268C22×C8—91no—
269C22×C8D3211yescharacteristic
270#124—94no—
271#124—182no—
272C2×C4⋊C4—31no—
273C2×C4⋊C4—31no—
274C2×C22⋊C4—181no—
275C2×C22⋊C4—181no—
276C2×C42—91no—
277C2×C42—181no—
278C4⋊C8—182no—
279#103—62no—
280#103—182no—
281#102—62no—
282#102—182no—
283#95—181no—
284C23×C3—21no—
285C23×C3—62no—
286C23×C3—121no—
287C23×C3—121no—
288C23×C3—121no—
289C23×C3—121no—
290C23×C3—121no—
291C23×C3—121no—
292C23×C3D3×D411yescharacteristic
293C23×C3D3×D411yescharacteristic
294C22×D3—22no—
295C22×D3—41no—
296C22×D3—41no—
297C22×D3—41no—
298C22×D3—41no—
299C22×D3—41no—
300C22×D3—41no—
301C3×Q8—62no—
302C3×Q8—62no—
303C3×Q8—121no—
304C3×Q8—121no—
305C3×D4—62no—
306C3×D4—62no—
307C3×D4—121no—
308C3×D4—121no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—121no—
319C2×C3×C4—121no—
320C2×C3×C4—121no—
321C2×C3×C4—121no—
322C2×C3×C4—121no—
323C2×C3×C4—121no—
324C2×C3×C4C2×C4×D311yescharacteristic
325C2×C3×C4C2×C4×D311yescharacteristic
326C2×C3×C4#23511yescharacteristic
327C2×C3×C4#23511yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4#23711yescharacteristic
333C2×C3×C4#23711yescharacteristic
334C2×C3×C4C2×#6711yescharacteristic
335C2×C3×C4C2×#6711yescharacteristic
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—32no—
340C2×Dic3—32no—
341C2×Dic3—32no—
342C2×Dic3—32no—
343C2×Dic3—41no—
344C2×Dic3—41no—
345C2×Dic3—41no—
346C2×Dic3—41no—
347C2×Dic3—41no—
348C2×Dic3—41no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—62no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—121no—
362C2×Dic3—121no—
363D12—22no—
364D12—22no—
365D12—41no—
366D12—41no—
367Dic6—22no—
368Dic6—22no—
369Dic6—41no—
370Dic6—41no—
371C3×C8—42no—
372C3×C8—41no—
373C3×C8—41no—
374C3⋊C8—122no—
375C3⋊C8—121no—
376C3⋊C8—121no—
377C2×C32#39011yescharacteristic
378C2×C32#41611yescharacteristic
379C2×C32#41711yescharacteristic
380C2×C32#46311yescharacteristic
381C2×C32#46311yescharacteristic
382C2×C32#46411yescharacteristic
383C2×C32#46411yescharacteristic
384C3×D3—82no—
385C24—61no—
386C2×Q8—32no—
387C2×Q8—61no—
388C2×Q8—61no—
389C2×Q8—61no—
390C2×Q8—61no—
391C2×Q8—61no—
392C2×D4—32no—
393C2×D4—61no—
394C2×D4—61no—
395C2×D4—61no—
396C2×D4—61no—
397C2×D4—61no—
398C22×C4—61no—
399C22×C4—61no—
400C22×C4—61no—
401C22×C4—91no—
402C22×C4—91no—
403C22×C4C2×D3211yescharacteristic
404C2×C8—21no—
405C2×C8—21no—
406C2×C8—21no—
407C2×C8—181no—
408C2×C8—181no—
409C2×C8—181no—
410C4⋊C4—32no—
411C4⋊C4—32no—
412C4⋊C4—61no—
413C4⋊C4—61no—
414C22⋊C4—184no—
415C22⋊C4—184no—
416C42—92no—
417C42—92no—
418C42—362no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—122no—
427C22×C3—122no—
428C22×C3—122no—
429C22×C3—241no—
430C22×C3—241no—
431C22×C3—241no—
432C22×C3—241no—
433C22×C3D3×C22⋊C411yescharacteristic
434C22×C3D3×C22⋊C411yescharacteristic
435C22×C3#88411yescharacteristic
436C22×C3#88411yescharacteristic
437C22×C3#91111yescharacteristic
438C22×C3#91211yescharacteristic
439C22×C3#91411yescharacteristic
440C22×C3#91511yescharacteristic
441C22×C3#91611yescharacteristic
442C22×C3#91611yescharacteristic
443C22×C3#91811yescharacteristic
444C22×C3#91911yescharacteristic
445C22×C3#93911yescharacteristic
446C22×C3#93911yescharacteristic
447C2×D3—42no—
448C2×D3—42no—
449C2×D3—42no—
450C2×D3—81no—
451C2×D3—81no—
452C2×D3—81no—
453C2×D3—81no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—122no—
459C3×C4—122no—
460C3×C4—122no—
461C3×C4#67⋊C411yescharacteristic
462C3×C4#67⋊C411yescharacteristic
463C3×C4#88511yescharacteristic
464C3×C4#88511yescharacteristic
465C3×C4C4×#6711yescharacteristic
466C3×C4C4×#6711yescharacteristic
467C3×C4#94011yescharacteristic
468C3×C4#94011yescharacteristic
469Dic3—42no—
470Dic3—42no—
471Dic3—42no—
472Dic3—64no—
473Dic3—62no—
474Dic3—62no—
475Dic3—62no—
476Dic3—62no—
477Dic3—122no—
478C32#198311yescharacteristic, complemented, Sylow
479C23—62no—
480C23—121no—
481C23—121no—
482C23—121no—
483C23—121no—
484C23—121no—
485C23—121no—
486C23#380211yescharacteristic
487Q8—62no—
488Q8—62no—
489Q8—121no—
490Q8—121no—
491D4—62no—
492D4—62no—
493D4—121no—
494D4—121no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—92no—
499C2×C4—92no—
500C2×C4—121no—
501C2×C4—121no—
502C2×C4—121no—
503C2×C4—121no—
504C2×C4—121no—
505C2×C4—121no—
506C2×C4—181no—
507C2×C4—181no—
508C2×C4—181no—
509C2×C4—181no—
510C2×C4#379511yescharacteristic
511C2×C4#379511yescharacteristic
512C2×C4C4×D3211yescharacteristic
513C2×C4D3×#6711yescharacteristic
514C2×C4D3×#6711yescharacteristic
515C2×C4#381111yescharacteristic
516C8—41no—
517C8—361no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—242no—
526C2×C3#476711yescharacteristic
527C2×C3#477111yescharacteristic
528C2×C3#477211yescharacteristic
529C2×C3#478711yescharacteristic
530C2×C3#479811yescharacteristic
531C2×C3#480311yescharacteristic
532C2×C3#480411yescharacteristic
533C2×C3#481911yescharacteristic
534C2×C3#495711yescharacteristic
535C2×C3#495711yescharacteristic
536C2×C3#515311yescharacteristic
537C2×C3#516511yescharacteristic
538C2×C3#516611yescharacteristic
539C2×C3#518511yescharacteristic
540D3—82no—
541C22—122no—
542C22—122no—
543C22—122no—
544C22—241no—
545C22—241no—
546C22—241no—
547C22—241no—
548C22#6379811yescharacteristic
549C22#6380911yescharacteristic
550C22#6381011yescharacteristic
551C22#6381111yescharacteristic
552C22#6388511yescharacteristic
553C22#6388511yescharacteristic
554C22#6392111yescharacteristic
555C4—122no—
556C4—122no—
557C4—122no—
558C4—182no—
559C4—182no—
560C4#6387911yescharacteristic
561C4#6387911yescharacteristic
562C4#6391311yescharacteristic
563C4#6397911yescharacteristic
564C3—21no—
565C3#7016211yescharacteristic, complemented
566C3#7023011yescharacteristic, complemented
567C2—242no—
568C2#1059075011yescharacteristic
569C2#1059075111yescharacteristic
570C2#1059079611yescharacteristic
571C2#1059079711yescharacteristic
572C2#1059095611yescharacteristic
573C2#1059095711yescharacteristic
574C2#1059138611yescharacteristic
subgroupG/H
centerC23#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1983
LCSG ▷ C2×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. C2×C3×#816C2semidirect
5. #10591274C2semidirect
6. C2×#63565C2semidirect
21. #63863C4semidirect
35. C2×#816D3semidirect
478. C32#1983semidirect
565. C3#70162semidirect
566. C3#70230semidirect

Maximal subgroups

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

subgroupindex
C2×#638632
C2×#636412
C2×C3×#8212
C2×C3×#8162
#105912742
C2×#635652
C2×#635622
#702303
#701623