Finite Group Databasebeta

← #11802741

Subgroups — #11802741

Order 1152.

1853 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×#3795C211yesmaximal, characteristic
2C2×C3×#872C211yesmaximal, characteristic, complemented
3C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
4#10592628C211yesmaximal, characteristic, complemented
5C3×#4939C211yesmaximal, characteristic, complemented
6#10591366C214yesmaximal, complemented
7#10591363C214yesmaximal, complemented
8#10591318C211yesmaximal, characteristic, complemented
9#10591213C211yesmaximal, characteristic, complemented
10#82270—31nomaximal
11#76294—31nomaximal
12C22×#634C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×C4×D3C2211yescharacteristic
15C22×#625C2212yes—
16C22×D3×Dic3C2212yes—
17C22×D3×Dic3C2212yes—
18C2×#3795—24no—
19C2×#3795—24no—
20C2×#3795C418yescomplemented
21C2×C32×C42C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×C3×(C2×D3)⋊C4C2212yes—
24C2×C3×(C2×D3)⋊C4C2214yes—
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×Dic3⋊C4C2212yes—
27C2×C3×C4×Dic3C2211yescharacteristic
28C3×#872—24no—
29C2×Dic3⋊Dic3C2212yes—
30C2×(C2×D3)⋊Dic3C2214yes—
31D3×C4⋊Dic3—24no—
32#63658C2214yes—
33#63579C2214yes—
34C22×#237—31no—
35C22×#235—31no—
36C2×C3×#117—31no—
37C22×C4⋊Dic3—31no—
38C2×D3×C4⋊C4—31no—
39C2×#872D311yescharacteristic, complemented
40C3×#390—31no—
41#5221—31no—
42#4987—34no—
43#4973—31no—
44#4958—34no—
45#4956—34no—
46#4942—34no—
47#4939—31no—
48#4939D311yescharacteristic, complemented
49#4929—31no—
50#4929—31no—
51#4929—31no—
52#4929—61no—
53C23×C3×D3C2312yes—
54C23×C3×D3C2311yescharacteristic
55C22×C32×C4C2312yes—
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3C2312yes—
58C22×C3⋊Dic3C2312yes—
59C2×#634—22no—
60C2×#634—22no—
61C2×#634C2×C414yescomplemented
62C22×C3×Dic3C2312yes—
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2311yescharacteristic
65C2×C3×D12—22no—
66C2×C3×D12—22no—
67C2×C3×D12C2×C414yescomplemented
68C2×C3×C4×D3C2×C414yes—
69C2×C3×C4×D3D414yes—
70C2×C3×C4×D3D414yes—
71C2×#625—24no—
72C2×#625—24no—
73C2×#625C2×C418yes—
74C2×D3×Dic3—24no—
75C2×D3×Dic3—24no—
76C2×D3×Dic3—24no—
77C2×D3×Dic3—44no—
78C2×D3×Dic3C2×C418yescomplemented
79#3795—232no—
80C32×C42—22no—
81C4⋊(C3⋊Dic3)—22no—
82C3×(C2×D3)⋊C4—24no—
83C3×(C2×D3)⋊C4—44no—
84C3×C4⋊Dic3—22no—
85C3×Dic3⋊C4—24no—
86C3×C4×Dic3—22no—
87Dic3⋊Dic3—24no—
88(C2×D3)⋊Dic3—44no—
89#2311—91noSylow
90C22×C3×D4—31no—
91C23×C3×C4—31no—
92C22×#67—32no—
93C22×#67—32no—
94C23×Dic3—32no—
95C23×Dic3—32no—
96C2×#237—38no—
97C2×#237—64no—
98C2×#237—64no—
99C2×#235—38no—
100C2×#235—64no—
101C2×#235—64no—
102C22×D12C2×D311yescharacteristic
103C22×C4×D3—32no—
104C22×C4×D3—32no—
105C22×C4×D3C2×D311yescharacteristic
106C22×Dic6—31no—
107C22×Dic6—31no—
108C22×Dic6—61no—
109C3×#117—64no—
110C2×C3×C4⋊C4—32no—
111C2×C3×C4⋊C4—31no—
112C2×C3×C22⋊C4—32no—
113C2×C3×C22⋊C4—34no—
114C2×C3×C42—21no—
115C2×C3×C42—31no—
116C2×C3×C42C2×D311yescharacteristic
117C2×C3×C42C2×D311yescharacteristic
118C2×#217—34no—
119C2×(C2×D3)⋊C4—34no—
120C2×(C2×D3)⋊C4C2×D312yes—
121C2×(C2×D3)⋊C4C2×D314yes—
122C2×C4⋊Dic3—31no—
123C2×C4⋊Dic3—31no—
124C2×C4⋊Dic3—32no—
125C2×C4⋊Dic3—61no—
126C2×C4⋊Dic3—64no—
127C2×C4⋊Dic3C2×D311yescharacteristic
128C2×Dic3⋊C4—32no—
129C2×Dic3⋊C4C2×D312yes—
130C2×C4×Dic3C2×D311yescharacteristic
131D3×C4⋊C4—64no—
132#872—24no—
133C3⋊#95—34no—
134C3⋊#95—34no—
135C3⋊#95—34no—
136C3⋊#95—34no—
137C3⋊#95—64no—
138C23×C32C2411yescharacteristic
139C22×C3×D3—22no—
140C22×C3×D3—22no—
141C22×C3×D3—22no—
142C22×C3×D3—22no—
143C22×C3×D3—24no—
144C22×C3×D3—24no—
145C22×C3×D3C22×C414yes—
146C22×C3×D3C22×C412yes—
147C22×C3×D3C2×D412yes—
148C22×C3×D3C2×D412yes—
149C2×C32×C4—22no—
150C2×C32×C4—22no—
151C2×C32×C4—22no—
152C2×C32×C4C22×C412yes—
153C2×C32×C4C2×D412yes—
154C2×C32×C4C2×D412yes—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—24no—
159C2×C3⋊Dic3C22×C414yes—
160#634—28no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—24no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3C22×C412yes—
167C2×C3×Dic3C2×D412yes—
168C2×C3×Dic3C2×D412yes—
169C3×D12—28no—
170C3×C4×D3C22⋊C4116yescomplemented
171#625—216no—
172D3×Dic3—216no—
173D3×Dic3—48no—
174C22×#41—91no—
175C2×#117—31no—
176C22×C4⋊C4—91no—
177#391—91no—
178#391—91no—
179#390—31no—
180#390—91no—
181#386—94no—
182#380—94no—
183C24×C3—31no—
184C24×C3—32no—
185C23×D3C22×D312yes—
186C23×D3C22×D311yescharacteristic
187C2×C3×D4—34no—
188C2×C3×D4—62no—
189C2×C3×D4—62no—
190C22×C3×C4—21no—
191C22×C3×C4—22no—
192C22×C3×C4—31no—
193C22×C3×C4—34no—
194C22×C3×C4—34no—
195C22×C3×C4—34no—
196C22×C3×C4—32no—
197C22×C3×C4—32no—
198C22×C3×C4C22×D312yes—
199C22×C3×C4C22×D312yes—
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C2×#67—38no—
203C2×#67—38no—
204C2×#67—64no—
205C2×#67—64no—
206C2×#67—64no—
207C2×#67—64no—
208C22×Dic3—32no—
209C22×Dic3—32no—
210C22×Dic3—38no—
211C22×Dic3—32no—
212C22×Dic3—32no—
213C22×Dic3—62no—
214C22×Dic3—62no—
215C22×Dic3—64no—
216C22×Dic3—64no—
217C22×Dic3—64no—
218C22×Dic3—124no—
219C22×Dic3C22×D312yes—
220C22×Dic3C22×D312yes—
221C22×Dic3C22×D311yescharacteristic
222#237—632no—
223#235—632no—
224C2×D12—22no—
225C2×D12—22no—
226C2×D12C4×D314yescomplemented
227C2×C4×D3—38no—
228C2×C4×D3—64no—
229C2×C4×D3—64no—
230C2×C4×D3—64no—
231C2×C4×D3—124no—
232C2×C4×D3C4×D314yes—
233C2×C4×D3D1214yes—
234C2×C4×D3#6714yes—
235C2×Dic6—34no—
236C2×Dic6—34no—
237C2×Dic6—64no—
238C2×Dic6—62no—
239C2×Dic6—62no—
240C2×Dic6—62no—
241C2×Dic6—62no—
242C2×Dic6—122no—
243C2×Dic6—122no—
244C3×C4⋊C4—64no—
245C3×C4⋊C4—62no—
246C3×C22⋊C4—64no—
247C3×C22⋊C4—124no—
248C3×C42—22no—
249C3×C42—22no—
250C3×C42—42no—
251C3×C42—62no—
252#217—124no—
253(C2×D3)⋊C4—24no—
254(C2×D3)⋊C4—44no—
255(C2×D3)⋊C4—124no—
256C4⋊Dic3—22no—
257C4⋊Dic3—64no—
258C4⋊Dic3—62no—
259C4⋊Dic3—62no—
260C4⋊Dic3—122no—
261Dic3⋊C4—24no—
262Dic3⋊C4—64no—
263C4×Dic3—22no—
264C22×C32C23×C411yescharacteristic
265C22×C32C22×D411yescharacteristic
266C22×C32C22×D411yescharacteristic
267C22×C32H(5,𝔽2)12yes—
268C22×C322−1+412yes—
269C2×C3×D3—24no—
270C2×C3×D3—22no—
271C2×C3×D3—22no—
272C2×C3×D3—24no—
273C2×C3×D3—24no—
274C2×C3×D3—28no—
275C2×C3×D3—42no—
276C2×C3×D3—42no—
277C2×C3×D3—44no—
278C2×C3×D3C2×C22⋊C414yes—
279C32×C4—42no—
280C32×C4C2×C22⋊C414yes—
281C3⋊Dic3—24no—
282C3⋊Dic3—42no—
283C3×Dic3—42no—
284C3×Dic3—42no—
285C3×Dic3C2×C22⋊C414yes—
286C2×#41—98no—
287C2×#41—184no—
288C2×#41—184no—
289C22×Q8—91no—
290C22×D4—31no—
291C22×D4—92no—
292C23×C4—31no—
293C23×C4—92no—
294C23×C4—92no—
295#117—64no—
296C2×C4⋊C4—31no—
297C2×C4⋊C4—32no—
298C2×C4⋊C4—92no—
299C2×C4⋊C4—91no—
300C2×C4⋊C4—184no—
301C2×C22⋊C4—32no—
302C2×C22⋊C4—34no—
303C2×C22⋊C4—94no—
304C2×C42—31no—
305C2×C42D3211yescharacteristic
306#95—94no—
307#95—94no—
308C23×C3—21no—
309C23×C3—32no—
310C23×C3—32no—
311C23×C3—32no—
312C23×C3—34no—
313C23×C3—62no—
314C23×C3—62no—
315C23×C3—62no—
316C23×C3—64no—
317C23×C3—64no—
318C23×C3—62no—
319C23×C3C23×D311yescharacteristic
320C23×C3C23×D311yescharacteristic
321C22×D3—22no—
322C22×D3—22no—
323C22×D3—22no—
324C22×D3—22no—
325C22×D3—24no—
326C22×D3—24no—
327C22×D3C2×C4×D314yes—
328C22×D3C2×C4×D312yes—
329C22×D3C2×D1212yes—
330C22×D3C2×#6712yes—
331C3×D4—68no—
332C2×C3×C4—24no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—32no—
343C2×C3×C4—32no—
344C2×C3×C4—32no—
345C2×C3×C4—316no—
346C2×C3×C4—42no—
347C2×C3×C4—42no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4—64no—
352C2×C3×C4—62no—
353C2×C3×C4C2×C4×D312yes—
354C2×C3×C4C2×C4×D312yes—
355C2×C3×C4C2×D1212yes—
356C2×C3×C4D3×D412yes—
357C2×C3×C4D3×D412yes—
358C2×C3×C4C2×#6712yes—
359#67—616no—
360#67—616no—
361C2×Dic3—22no—
362C2×Dic3—24no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—34no—
367C2×Dic3—34no—
368C2×Dic3—64no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—616no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—64no—
377C2×Dic3—64no—
378C2×Dic3—122no—
379C2×Dic3—122no—
380C2×Dic3—122no—
381C2×Dic3—124no—
382C2×Dic3—128no—
383C2×Dic3C2×C4×D312yes—
384C2×Dic3C2×D1212yes—
385C2×Dic3C2×#6712yes—
386D12—28no—
387C4×D3—616no—
388C4×D3—128no—
389C4×D3(C2×D3)⋊C4116yescomplemented
390Dic6—68no—
391Dic6—68no—
392Dic6—128no—
393C2×C32C22×C22⋊C411yescharacteristic
394C2×C32#52012yes—
395C2×C32#53511yescharacteristic
396C2×C32#53611yescharacteristic
397C2×C32#53712yes—
398C3×D3—24no—
399C3×D3—44no—
400C24—31no—
401C24—32no—
402#41—1832no—
403C2×Q8—94no—
404C2×Q8—182no—
405C2×Q8—182no—
406C2×D4—34no—
407C2×D4—62no—
408C2×D4—62no—
409C2×D4—98no—
410C2×D4—184no—
411C2×D4—184no—
412C22×C4—31no—
413C22×C4—34no—
414C22×C4—34no—
415C22×C4—34no—
416C22×C4—32no—
417C22×C4—32no—
418C22×C4—98no—
419C22×C4—92no—
420C22×C4—92no—
421C22×C4—184no—
422C22×C4—184no—
423C22×C4—184no—
424C22×C4—364no—
425C22×C4C2×D3212yes—
426C22×C4C2×D3211yescharacteristic
427C4⋊C4—64no—
428C4⋊C4—62no—
429C4⋊C4—184no—
430C4⋊C4—182no—
431C22⋊C4—64no—
432C22⋊C4—124no—
433C22⋊C4—364no—
434C42—22no—
435C42—62no—
436C22×C3—22no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—22no—
440C22×C3—21no—
441C22×C3—34no—
442C22×C3—62no—
443C22×C3—62no—
444C22×C3—64no—
445C22×C3—64no—
446C22×C3—68no—
447C22×C3—64no—
448C22×C3—122no—
449C22×C3—122no—
450C22×C3—124no—
451C22×C3C22×C4×D311yescharacteristic
452C22×C3C22×C4×D311yescharacteristic
453C22×C3C22×D1211yescharacteristic
454C22×C3C2×D3×D411yescharacteristic
455C22×C3C2×D3×D411yescharacteristic
456C22×C3#100412yes—
457C22×C3#100912yes—
458C22×C3#101012yes—
459C22×C3#101012yes—
460C22×C3C22×#6711yescharacteristic
461C2×D3—24no—
462C2×D3—22no—
463C2×D3—22no—
464C2×D3—24no—
465C2×D3—24no—
466C2×D3—28no—
467C2×D3—42no—
468C2×D3—42no—
469C2×D3—44no—
470C2×D3C2×(C2×D3)⋊C414yes—
471C3×C4—24no—
472C3×C4—34no—
473C3×C4—44no—
474C3×C4—42no—
475C3×C4—42no—
476C3×C4—122no—
477C3×C4—122no—
478C3×C4D3×C22⋊C414yes—
479C3×C4C2×(C2×D3)⋊C414yes—
480Dic3—42no—
481Dic3—42no—
482Dic3—64no—
483Dic3—64no—
484Dic3—124no—
485Dic3—122no—
486Dic3—122no—
487Dic3—242no—
488Dic3C2×(C2×D3)⋊C414yes—
489C32#231111yescharacteristic, complemented, Sylow
490C23—32no—
491C23—32no—
492C23—32no—
493C23—34no—
494C23—62no—
495C23—62no—
496C23—64no—
497C23—62no—
498C23—64no—
499C23—62no—
500C23C22×D3211yescharacteristic
501Q8—188no—
502D4—68no—
503D4—1816no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—32no—
508C2×C4—32no—
509C2×C4—32no—
510C2×C4—316no—
511C2×C4—62no—
512C2×C4—62no—
513C2×C4—64no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—94no—
517C2×C4—1816no—
518C2×C4—182no—
519C2×C4—182no—
520C2×C4—182no—
521C2×C4—184no—
522C2×C4—368no—
523C2×C4C4×D3212yes—
524C2×C4D3×D1212yes—
525C2×C4D3×#6712yes—
526C2×C3—22no—
527C2×C3—21no—
528C2×C3—22no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—64no—
532C2×C3—124no—
533C2×C3C2×D3×C22⋊C411yescharacteristic
534C2×C3#552312yes—
535C2×C3#552511yescharacteristic
536C2×C3#552611yescharacteristic
537C2×C3#554612yes—
538C2×C3#560812yes—
539C2×C3#567511yescharacteristic
540C2×C3#571511yescharacteristic
541C2×C3C22×(C2×D3)⋊C411yescharacteristic
542C2×C3#583312yes—
543D3—24no—
544D3—44no—
545C22—34no—
546C22—64no—
547C22—62no—
548C22—64no—
549C22—62no—
550C22—68no—
551C22—64no—
552C22—122no—
553C22—124no—
554C22—122no—
555C22#6429812yes—
556C22C2×C4×D3211yescharacteristic
557C22C2×D3×D1211yescharacteristic
558C22#6430712yes—
559C22C2×D3×#6711yescharacteristic
560C4—34no—
561C4—42no—
562C4—122no—
563C4—122no—
564C4—184no—
565C4—362no—
566C4D3×(C2×D3)⋊C414yes—
567C3—21no—
568C3#7629411yescharacteristic, complemented
569C3#8227011yescharacteristic, complemented
570C2—64no—
571C2—124no—
572C2#1059388712yes—
573C2#1059389411yescharacteristic
574C2#1059400011yescharacteristic
575C2#1059500412yes—
576C2C2×D3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC22×#3795C2
hypercenterC2×C42D32
hypocenterC32#2311
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×#872C2semidirect
3. C2×D3×C4⋊Dic3C2semidirect
4. #10592628C2semidirect
5. C3×#4939C2semidirect
6. #10591366C2semidirect
7. #10591363C2semidirect
8. #10591318C2semidirect
9. #10591213C2semidirect
20. C2×#3795C4semidirect
39. C2×#872D3semidirect
48. #4939D3semidirect
61. C2×#634C2×C4semidirect
67. C2×C3×D12C2×C4semidirect
78. C2×D3×Dic3C2×C4semidirect
170. C3×C4×D3C22⋊C4semidirect
226. C2×D12C4×D3semidirect
389. C4×D3(C2×D3)⋊C4semidirect
489. C32#2311semidirect
568. C3#76294semidirect
569. C3#82270semidirect

Maximal subgroups

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

subgroupindex
C22×#37952
C2×C3×#8722
C2×D3×C4⋊Dic32
#105926282
C3×#49392
#105913662
#105913632
#105913182
#105912132
#822703
#762943