Finite Group Databasebeta

← #11801899

Subgroups — #11801899

Order 1152.

2001 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3799C211yesmaximal, characteristic
2C2×C3×#892C211yesmaximal, characteristic, complemented
3C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
4#10592687C211yesmaximal, characteristic, complemented
5C3×#4973C211yesmaximal, characteristic, complemented
6#10591364C214yesmaximal, complemented
7#10591320C211yesmaximal, characteristic, complemented
8#10591233C214yesmaximal, complemented
9#10591221C211yesmaximal, characteristic, complemented
10#82228—31nomaximal
11#76478—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×#626C2212yes—
16C22×#624C2212yes—
17C22×D3×Dic3C2212yes—
18C2×#3799—24no—
19C2×#3799—24no—
20C2×#3799C418yescomplemented
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×#3752C2214yes—
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2212yes—
27C2×C3×C4×Dic3C2211yescharacteristic
28C3×#892—24no—
29C2×#3722C2214yes—
30C2×Dic32C2212yes—
31C4×D3×Dic3—24no—
32C3×C3⋊#95C2214yes—
33#63579C2214yes—
34C22×#239—31no—
35C22×#235—31no—
36C2×C3×#117—31no—
37C22×C4×Dic3—31no—
38C2×#892D311yescharacteristic, complemented
39C2×C42×D3—31no—
40C3×#391—31no—
41#5229—31no—
42#4988—31no—
43#4988—31no—
44#4988—31no—
45#4988—61no—
46#4973—31no—
47#4973D311yescharacteristic, complemented
48#4958—34no—
49#4939—31no—
50C4×(C2×D3)⋊C4—34no—
51#4666—34no—
52#4665—34no—
53C23×C3⋊D3C2312yes—
54C23×C3×D3C2311yescharacteristic
55C22×C32×C4C2312yes—
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3C2312yes—
58C2×C4⋊(C3⋊D3)—22no—
59C2×C4⋊(C3⋊D3)—22no—
60C2×C4⋊(C3⋊D3)C2×C414yescomplemented
61C22×C3×Dic3C2312yes—
62C22×C3×Dic3C2312yes—
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2311yescharacteristic
65C2×C3×C4×D3C2×C414yes—
66C2×C3×C4×D3D414yes—
67C2×C3×C4×D3D414yes—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6C2×C414yescomplemented
71C2×#626—24no—
72C2×#626—24no—
73C2×#626C2×C418yes—
74C2×#624—24no—
75C2×#624—24no—
76C2×#624C2×C418yescomplemented
77C2×D3×Dic3—24no—
78C2×D3×Dic3—24no—
79C2×D3×Dic3—24no—
80#3799—232no—
81C32×C4⋊C4—22no—
82#3752—28no—
83C4×C3⋊Dic3—22no—
84C3×(C2×D3)⋊C4—24no—
85C3×C4⋊Dic3—22no—
86C3×C4×Dic3—22no—
87C3×C4×Dic3—24no—
88#3722—28no—
89Dic32—24no—
90#2297—91noSylow
91C22×C3×Q8—31no—
92C23×C3×C4—31no—
93C22×#67—32no—
94C23×Dic3—32no—
95C2×#239—38no—
96C2×#239—64no—
97C2×#239—64no—
98C2×#235—38no—
99C2×#235—64no—
100C2×#235—64no—
101C22×D12—32no—
102C22×D12—31no—
103C22×D12—31no—
104C22×D12—61no—
105C22×C4×D3—32no—
106C22×C4×D3—32no—
107C22×C4×D3—32no—
108C22×C4×D3C2×D311yescharacteristic
109C22×Dic6C2×D311yescharacteristic
110C3×#117—64no—
111C2×C3×C4⋊C4—21no—
112C2×C3×C4⋊C4—31no—
113C2×C3×C4⋊C4C2×D311yescharacteristic
114C2×C3×C4⋊C4C2×D311yescharacteristic
115C2×C3×C22⋊C4—32no—
116C2×C3×C42—32no—
117C2×C3×C42—31no—
118C2×(C2×D3)⋊C4—34no—
119C2×(C2×D3)⋊C4—34no—
120C2×(C2×D3)⋊C4—34no—
121C2×(C2×D3)⋊C4—34no—
122C2×(C2×D3)⋊C4—64no—
123C2×(C2×D3)⋊C4C2×D312yes—
124C2×C4⋊Dic3C2×D311yescharacteristic
125C2×C4×Dic3—31no—
126C2×C4×Dic3—31no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3—61no—
130C2×C4×Dic3—64no—
131C2×C4×Dic3C2×D312yes—
132C2×C4×Dic3C2×D311yescharacteristic
133#892—24no—
134C42×D3—64no—
135C3×#95—34no—
136C3⋊#95—34no—
137C3⋊#95—34no—
138C3⋊#95C2×D314yes—
139C23×C32C2411yescharacteristic
140C22×C3⋊D3—22no—
141C22×C3⋊D3—22no—
142C22×C3⋊D3—24no—
143C22×C3⋊D3—24no—
144C22×C3⋊D3C22×C414yes—
145C22×C3×D3—22no—
146C22×C3×D3—22no—
147C22×C3×D3C22×C412yes—
148C22×C3×D3C2×D412yes—
149C22×C3×D3C2×D412yes—
150C2×C32×C4—22no—
151C2×C32×C4—24no—
152C2×C32×C4C22×C412yes—
153C2×C32×C4C2×D412yes—
154C2×C32×C4C2×D412yes—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3#4114yescomplemented
158C4⋊(C3⋊D3)—28no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—24no—
165C2×C3×Dic3C22×C414yes—
166C2×C3×Dic3C22×C412yes—
167C2×C3×Dic3C2×D412yes—
168C2×C3×Dic3C2×D412yes—
169C2×C3×Dic3#4114yescomplemented
170C3×C4×D3C22⋊C4116yescomplemented
171C3×Dic6—28no—
172#626—216no—
173#624—216no—
174D3×Dic3—216no—
175C22×#41—91no—
176C2×#117—31no—
177C22×C42—91no—
178#391—31no—
179#391—91no—
180#390—91no—
181#390—91no—
182#386—94no—
183C4×C22⋊C4—94no—
184C24×C3—31no—
185C23×D3—32no—
186C23×D3—32no—
187C23×D3—62no—
188C23×D3C22×D311yescharacteristic
189C2×C3×Q8—34no—
190C2×C3×Q8—62no—
191C2×C3×Q8—62no—
192C22×C3×C4—21no—
193C22×C3×C4—22no—
194C22×C3×C4—31no—
195C22×C3×C4—34no—
196C22×C3×C4—34no—
197C22×C3×C4—34no—
198C22×C3×C4—32no—
199C22×C3×C4—32no—
200C22×C3×C4—32no—
201C22×C3×C4C22×D312yes—
202C22×C3×C4C22×D312yes—
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D311yescharacteristic
205C2×#67—38no—
206C2×#67—64no—
207C2×#67—64no—
208C22×Dic3—32no—
209C22×Dic3—32no—
210C22×Dic3—62no—
211C22×Dic3—64no—
212C22×Dic3—64no—
213C22×Dic3—64no—
214C22×Dic3C22×D312yes—
215C22×Dic3C22×D312yes—
216C22×Dic3C22×D312yes—
217C22×Dic3C22×D311yescharacteristic
218#239—632no—
219#235—632no—
220C2×D12—38no—
221C2×D12—34no—
222C2×D12—34no—
223C2×D12—64no—
224C2×D12—64no—
225C2×D12—64no—
226C2×D12—62no—
227C2×D12—62no—
228C2×D12—62no—
229C2×D12—62no—
230C2×D12—122no—
231C2×D12—122no—
232C2×C4×D3—38no—
233C2×C4×D3—38no—
234C2×C4×D3—64no—
235C2×C4×D3—64no—
236C2×C4×D3—64no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×C4×D3—64no—
240C2×C4×D3—64no—
241C2×C4×D3C4×D314yes—
242C2×C4×D3D1214yes—
243C2×C4×D3#6714yes—
244C2×Dic6—22no—
245C2×Dic6—22no—
246C2×Dic6C4×D314yescomplemented
247C3×C4⋊C4—22no—
248C3×C4⋊C4—22no—
249C3×C4⋊C4—42no—
250C3×C4⋊C4—62no—
251C3×C22⋊C4—64no—
252C3×C42—64no—
253C3×C42—62no—
254(C2×D3)⋊C4—24no—
255(C2×D3)⋊C4—68no—
256(C2×D3)⋊C4—68no—
257(C2×D3)⋊C4—68no—
258(C2×D3)⋊C4—68no—
259(C2×D3)⋊C4—128no—
260C4⋊Dic3—22no—
261C4×Dic3—22no—
262C4×Dic3—24no—
263C4×Dic3—64no—
264C4×Dic3—62no—
265C4×Dic3—62no—
266C4×Dic3—64no—
267C4×Dic3—122no—
268C22×C32C23×C411yescharacteristic
269C22×C32C22×D411yescharacteristic
270C22×C32C22×D411yescharacteristic
271C22×C32C2×#4112yes—
272C22×C32C2×#4112yes—
273C2×C3⋊D3—24no—
274C2×C3⋊D3—28no—
275C2×C3⋊D3—44no—
276C2×C3⋊D3—42no—
277C2×C3⋊D3—42no—
278C2×C3×D3—24no—
279C2×C3×D3—24no—
280C2×C3×D3—22no—
281C2×C3×D3—22no—
282C2×C3×D3C2×C22⋊C414yes—
283C32×C4—42no—
284C32×C4C2×C22⋊C414yes—
285C3⋊Dic3—24no—
286C3×Dic3—24no—
287C3×Dic3—24no—
288C3×Dic3—42no—
289C3×Dic3C2×C22⋊C414yes—
290C2×#41—98no—
291C2×#41—184no—
292C2×#41—184no—
293C22×Q8—31no—
294C22×D4—92no—
295C22×D4—91no—
296C23×C4—31no—
297C23×C4—92no—
298C23×C4—92no—
299#117—64no—
300C2×C4⋊C4—31no—
301C2×C4⋊C4D3211yescharacteristic
302C2×C22⋊C4—32no—
303C2×C22⋊C4—94no—
304C2×C22⋊C4—94no—
305C2×C42—32no—
306C2×C42—31no—
307C2×C42—92no—
308C2×C42—91no—
309C2×C42—184no—
310#95—34no—
311#95—94no—
312C23×C3—21no—
313C23×C3—32no—
314C23×C3—32no—
315C23×C3—32no—
316C23×C3—62no—
317C23×C3—62no—
318C23×C3C23×D311yescharacteristic
319C23×C3C23×D311yescharacteristic
320C22×D3—22no—
321C22×D3—22no—
322C22×D3—34no—
323C22×D3—34no—
324C22×D3—64no—
325C22×D3—62no—
326C22×D3—62no—
327C22×D3—62no—
328C22×D3—64no—
329C22×D3—64no—
330C22×D3—64no—
331C22×D3—64no—
332C22×D3—62no—
333C22×D3—124no—
334C22×D3—122no—
335C22×D3—122no—
336C22×D3—124no—
337C22×D3C2×C4×D312yes—
338C22×D3C2×D1212yes—
339C22×D3C2×#6712yes—
340C3×Q8—68no—
341C2×C3×C4—22no—
342C2×C3×C4—24no—
343C2×C3×C4—24no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—32no—
351C2×C3×C4—316no—
352C2×C3×C4—34no—
353C2×C3×C4—34no—
354C2×C3×C4—44no—
355C2×C3×C4—42no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—64no—
362C2×C3×C4C2×C4×D312yes—
363C2×C3×C4C2×C4×D312yes—
364C2×C3×C4C2×D1212yes—
365C2×C3×C4D3×D412yes—
366C2×C3×C4D3×D412yes—
367C2×C3×C4C2×#6712yes—
368#67—616no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—24no—
374C2×Dic3—22no—
375C2×Dic3—34no—
376C2×Dic3—34no—
377C2×Dic3—64no—
378C2×Dic3—616no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—122no—
384C2×Dic3—122no—
385C2×Dic3C2×C4×D314yes—
386C2×Dic3C2×C4×D312yes—
387C2×Dic3C2×D1212yes—
388C2×Dic3#23914yescomplemented
389C2×Dic3C2×#6712yes—
390D12—616no—
391D12—68no—
392D12—68no—
393D12—128no—
394C4×D3—616no—
395C4×D3—616no—
396C4×D3—616no—
397C4×D3(C2×D3)⋊C4116yescomplemented
398Dic6—28no—
399C2×C32C22×C22⋊C411yescharacteristic
400C2×C32C4×#4112yes—
401C2×C32#52512yes—
402C2×C32#53211yescharacteristic
403C2×C32#53211yescharacteristic
404C3⋊D3—44no—
405C3×D3—24no—
406C24—31no—
407C24—92no—
408#41—1832no—
409C2×Q8—34no—
410C2×Q8—62no—
411C2×Q8—62no—
412C2×D4—98no—
413C2×D4—94no—
414C2×D4—184no—
415C2×D4—184no—
416C2×D4—182no—
417C2×D4—182no—
418C22×C4—31no—
419C22×C4—34no—
420C22×C4—34no—
421C22×C4—34no—
422C22×C4—32no—
423C22×C4—32no—
424C22×C4—32no—
425C22×C4—98no—
426C22×C4—92no—
427C22×C4—184no—
428C22×C4—184no—
429C22×C4—184no—
430C22×C4—184no—
431C22×C4—184no—
432C22×C4C2×D3212yes—
433C22×C4C2×D3211yescharacteristic
434C4⋊C4—22no—
435C4⋊C4—62no—
436C22⋊C4—64no—
437C22⋊C4—188no—
438C22⋊C4—188no—
439C42—64no—
440C42—62no—
441C42—184no—
442C42—182no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—22no—
446C22×C3—22no—
447C22×C3—21no—
448C22×C3—34no—
449C22×C3—62no—
450C22×C3—62no—
451C22×C3—64no—
452C22×C3—64no—
453C22×C3C22×C4×D311yescharacteristic
454C22×C3C22×C4×D311yescharacteristic
455C22×C3C22×D1211yescharacteristic
456C22×C3C2×D3×D411yescharacteristic
457C22×C3C2×D3×D411yescharacteristic
458C22×C3C2×#23912yes—
459C22×C3D3×#4112yes—
460C22×C3D3×#4112yes—
461C22×C3D3×#4112yes—
462C22×C3C22×#6711yescharacteristic
463C2×D3—24no—
464C2×D3—24no—
465C2×D3—22no—
466C2×D3—22no—
467C2×D3—64no—
468C2×D3—68no—
469C2×D3—64no—
470C2×D3—68no—
471C2×D3—124no—
472C2×D3—128no—
473C2×D3—122no—
474C2×D3—122no—
475C2×D3—124no—
476C2×D3—122no—
477C2×D3—122no—
478C2×D3—124no—
479C2×D3—242no—
480C2×D3—244no—
481C2×D3—242no—
482C2×D3C2×(C2×D3)⋊C414yes—
483C3×C4—24no—
484C3×C4—34no—
485C3×C4—42no—
486C3×C4—42no—
487C3×C4—64no—
488C3×C4—64no—
489C3×C4—82no—
490C3×C4—122no—
491C3×C4D3×C22⋊C414yes—
492C3×C4C2×(C2×D3)⋊C414yes—
493Dic3—24no—
494Dic3—24no—
495Dic3—42no—
496Dic3—64no—
497Dic3—64no—
498Dic3—124no—
499Dic3C2×(C2×D3)⋊C414yes—
500C32#229711yescharacteristic, complemented, Sylow
501C23—32no—
502C23—32no—
503C23—32no—
504C23—62no—
505C23—62no—
506C23—94no—
507C23—182no—
508C23—184no—
509C23—184no—
510C23—182no—
511C23C22×D3211yescharacteristic
512Q8—68no—
513D4—1816no—
514D4—188no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—32no—
518C2×C4—32no—
519C2×C4—32no—
520C2×C4—316no—
521C2×C4—34no—
522C2×C4—34no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—64no—
528C2×C4—62no—
529C2×C4—94no—
530C2×C4—1816no—
531C2×C4—1816no—
532C2×C4—182no—
533C2×C4—182no—
534C2×C4C4×D3212yes—
535C2×C4D3×D1212yes—
536C2×C4D3×#6712yes—
537C2×C3—21no—
538C2×C3—22no—
539C2×C3—22no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—64no—
543C2×C3C2×D3×C22⋊C411yescharacteristic
544C2×C3#552212yes—
545C2×C3#552412yes—
546C2×C3C4×#23912yes—
547C2×C3#562712yes—
548C2×C3#566811yescharacteristic
549C2×C3#572511yescharacteristic
550C2×C3C22×(C2×D3)⋊C411yescharacteristic
551C2×C3#583211yescharacteristic
552C2×C3#583211yescharacteristic
553D3—24no—
554D3—124no—
555D3—124no—
556D3—244no—
557C22—34no—
558C22—62no—
559C22—64no—
560C22—64no—
561C22—62no—
562C22—188no—
563C22—184no—
564C22—362no—
565C22—364no—
566C22—362no—
567C22C2×C4×D3211yescharacteristic
568C22C2×D3×D1211yescharacteristic
569C22#6431212yes—
570C22D3×#23912yes—
571C22C2×D3×#6711yescharacteristic
572C4—34no—
573C4—42no—
574C4—64no—
575C4—64no—
576C4—122no—
577C4—184no—
578C4D3×(C2×D3)⋊C414yes—
579C3—21no—
580C3#7647811yescharacteristic, complemented
581C3#8222811yescharacteristic, complemented
582C2—64no—
583C2—364no—
584C2#1059436212yes—
585C2#1059462712yes—
586C2C2×D3×(C2×D3)⋊C411yescharacteristic
587C2#1059515311yescharacteristic
588C2#1059536011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×#3799C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2297
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#892C2semidirect
3. C2×C4×D3×Dic3C2semidirect
4. #10592687C2semidirect
5. C3×#4973C2semidirect
6. #10591364C2semidirect
7. #10591320C2semidirect
8. #10591233C2semidirect
9. #10591221C2semidirect
20. C2×#3799C4semidirect
38. C2×#892D3semidirect
47. #4973D3semidirect
60. C2×C4⋊(C3⋊D3)C2×C4semidirect
70. C2×C3×Dic6C2×C4semidirect
76. C2×#624C2×C4semidirect
157. C2×C3⋊Dic3#41semidirect
169. C2×C3×Dic3#41semidirect
170. C3×C4×D3C22⋊C4semidirect
246. C2×Dic6C4×D3semidirect
388. C2×Dic3#239semidirect
397. C4×D3(C2×D3)⋊C4semidirect
500. C32#2297semidirect
580. C3#76478semidirect
581. C3#82228semidirect

Maximal subgroups

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

subgroupindex
C22×#37992
C2×C3×#8922
C2×C4×D3×Dic32
#105926872
C3×#49732
#105913642
#105913202
#105912332
#105912212
#822283
#764783