Finite Group Databasebeta

← #11802740

Subgroups — #11802740

Order 1152.

1925 conjugacy classes of subgroups.

The subgroup lattice has 595 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3796C211yesmaximal, characteristic
2C2×#64081C211yesmaximal, characteristic, complemented
3C2×#63900C211yesmaximal, characteristic, complemented
4C3×#4939C211yesmaximal, characteristic, complemented
5C3×#4929C211yesmaximal, characteristic, complemented
6#10591369C214yesmaximal, complemented
7#10591323C211yesmaximal, characteristic, complemented
8#10591275C214yesmaximal, complemented
9#10591221C211yesmaximal, characteristic, complemented
10#76482—31nomaximal
11#76294—31nomaximal
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×#626C2212yes—
16C22×#624C2212yes—
17C22×D3×Dic3C2212yes—
18C2×#3796—24no—
19C2×#3796—24no—
20C2×#3796C418yescomplemented
21C2×C32×C42C2211yescharacteristic
22C2×#3752C2212yes—
23C2×#3750C2212yes—
24C2×C4×C3⋊Dic3C2211yescharacteristic
25#64081—24no—
26C2×C3×(C2×D3)⋊C4C2214yes—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×#3724C2212yes—
30C2×(C2×D3)⋊Dic3C2214yes—
31#63900—24no—
32C3×C3⋊#95C2214yes—
33#63579C2214yes—
34C22×#239—31no—
35C22×#237—31no—
36C2×D3×C4⋊C4—31no—
37C2×D3×C4⋊C4—31no—
38C2×#872—31no—
39C2×#872—31no—
40C2×#872—61no—
41C3×#391—31no—
42C3×#390—31no—
43#5229—31no—
44#5221—31no—
45#4988—31no—
46#4973—31no—
47#4956—34no—
48#4942—34no—
49#4939D311yescharacteristic, complemented
50#4929D311yescharacteristic, complemented
51#4667—34no—
52#4665—34no—
53C23×C3⋊D3C2311yescharacteristic
54C23×C3×D3C2312yes—
55C22×C32×C4C2312yes—
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3C2312yes—
58C22×C3⋊Dic3C2311yescharacteristic
59C2×C4×C3⋊D3C2×C414yes—
60C2×C4×C3⋊D3D414yes—
61C2×C4×C3⋊D3D414yes—
62C22×C3×Dic3C2312yes—
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2312yes—
65C2×C3×D12—22no—
66C2×C3×D12—22no—
67C2×C3×D12C2×C414yescomplemented
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—44no—
76C2×D3×Dic3—24no—
77C2×D3×Dic3—24no—
78C2×D3×Dic3C2×C418yescomplemented
79#3796—232no—
80C32×C42—22no—
81#3752—24no—
82#3750—24no—
83C4×C3⋊Dic3—22no—
84C3×(C2×D3)⋊C4—44no—
85C3×C4⋊Dic3—22no—
86C3×C4⋊Dic3—22no—
87#3724—24no—
88(C2×D3)⋊Dic3—44no—
89#2311—91noSylow
90C22×C3×Q8—31no—
91C22×C3×D4—31no—
92C22×#67—32no—
93C23×Dic3—32no—
94C2×#239—38no—
95C2×#239—64no—
96C2×#239—64no—
97C2×#237—38no—
98C2×#237—64no—
99C2×#237—64no—
100C22×D12—32no—
101C22×D12C2×D311yescharacteristic
102C22×C4×D3—31no—
103C22×C4×D3—31no—
104C22×C4×D3—32no—
105C22×C4×D3—32no—
106C22×C4×D3—32no—
107C22×C4×D3—61no—
108C22×Dic6C2×D311yescharacteristic
109C2×C3×C4⋊C4—31no—
110C2×C3×C4⋊C4—31no—
111C2×C3×C22⋊C4—34no—
112C2×C3×C42—21no—
113C2×C3×C42C2×D311yescharacteristic
114C2×C3×C42C2×D311yescharacteristic
115C2×#217—34no—
116C2×(C2×D3)⋊C4—32no—
117C2×(C2×D3)⋊C4—32no—
118C2×(C2×D3)⋊C4—34no—
119C2×(C2×D3)⋊C4—62no—
120C2×(C2×D3)⋊C4C2×D314yes—
121C2×C4⋊Dic3C2×D311yescharacteristic
122C2×C4⋊Dic3C2×D311yescharacteristic
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4—32no—
126C2×Dic3⋊C4—32no—
127C2×Dic3⋊C4—62no—
128C2×C4×Dic3—31no—
129C2×C4×Dic3—31no—
130C2×C4×Dic3—61no—
131D3×C4⋊C4—64no—
132D3×C4⋊C4—64no—
133#872—64no—
134#872—64no—
135#872—68no—
136C3×#95—34no—
137C3⋊#95—34no—
138C3⋊#95—34no—
139C3⋊#95C2×D314yes—
140C23×C32C2411yescharacteristic
141C22×C3⋊D3—22no—
142C22×C3⋊D3—22no—
143C22×C3⋊D3C22×C412yes—
144C22×C3⋊D3C2×D412yes—
145C22×C3⋊D3C2×D412yes—
146C22×C3×D3—22no—
147C22×C3×D3—22no—
148C22×C3×D3—24no—
149C22×C3×D3—24no—
150C22×C3×D3C22×C414yes—
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4—22no—
154C2×C32×C4C22×C412yes—
155C2×C32×C4C2×D412yes—
156C2×C32×C4C2×D412yes—
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3C22×C412yes—
161C2×C3⋊Dic3C2×D412yes—
162C2×C3⋊Dic3C2×D412yes—
163C4×C3⋊D3C22⋊C4116yescomplemented
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—24no—
169C2×C3×Dic3—24no—
170C2×C3×Dic3C22×C414yes—
171C3×D12—28no—
172C3×Dic6—28no—
173#626—216no—
174#624—48no—
175D3×Dic3—216no—
176C22×#41—91no—
177C2×#117—91no—
178C22×C4⋊C4—91no—
179#391—31no—
180#391—91no—
181#390—31no—
182#390—91no—
183#386—94no—
184#380—94no—
185C24×C3—32no—
186C23×D3—31no—
187C23×D3—31no—
188C23×D3—61no—
189C23×D3C22×D312yes—
190C2×C3×Q8—34no—
191C2×C3×Q8—62no—
192C2×C3×Q8—62no—
193C2×C3×D4—34no—
194C2×C3×D4—62no—
195C2×C3×D4—62no—
196C22×C3×C4—21no—
197C22×C3×C4—22no—
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—31no—
209C22×Dic3—31no—
210C22×Dic3—38no—
211C22×Dic3—32no—
212C22×Dic3—32no—
213C22×Dic3—61no—
214C22×Dic3—62no—
215C22×Dic3—64no—
216C22×Dic3—64no—
217C22×Dic3C22×D312yes—
218C22×Dic3C22×D312yes—
219C22×Dic3C22×D312yes—
220#239—632no—
221#237—632no—
222C2×D12—22no—
223C2×D12—22no—
224C2×D12—38no—
225C2×D12—64no—
226C2×D12—64no—
227C2×D12C4×D314yescomplemented
228C2×C4×D3—34no—
229C2×C4×D3—34no—
230C2×C4×D3—34no—
231C2×C4×D3—34no—
232C2×C4×D3—34no—
233C2×C4×D3—34no—
234C2×C4×D3—38no—
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×D3—64no—
242C2×C4×D3—124no—
243C2×C4×D3—124no—
244C2×Dic6—22no—
245C2×Dic6—22no—
246C2×Dic6C4×D314yescomplemented
247C3×C4⋊C4—62no—
248C3×C4⋊C4—62no—
249C3×C22⋊C4—124no—
250C3×C42—24no—
251C3×C42—22no—
252C3×C42—22no—
253#217—124no—
254(C2×D3)⋊C4—44no—
255(C2×D3)⋊C4—64no—
256(C2×D3)⋊C4—64no—
257(C2×D3)⋊C4—68no—
258(C2×D3)⋊C4—124no—
259C4⋊Dic3—22no—
260C4⋊Dic3—22no—
261Dic3⋊C4—64no—
262Dic3⋊C4—64no—
263Dic3⋊C4—64no—
264Dic3⋊C4—64no—
265Dic3⋊C4—68no—
266C4×Dic3—64no—
267C4×Dic3—62no—
268C4×Dic3—62no—
269C22×C32C23×C411yescharacteristic
270C22×C32C22×D411yescharacteristic
271C22×C32C22×D411yescharacteristic
272C22×C32H(5,𝔽2)12yes—
273C22×C322−1+412yes—
274C2×C3⋊D3—24no—
275C2×C3⋊D3—22no—
276C2×C3⋊D3—22no—
277C2×C3⋊D3—24no—
278C2×C3⋊D3C2×C22⋊C414yes—
279C2×C3×D3—24no—
280C2×C3×D3—28no—
281C2×C3×D3—42no—
282C2×C3×D3—42no—
283C2×C3×D3—44no—
284C32×C4—42no—
285C32×C4C2×C22⋊C414yes—
286C3⋊Dic3—42no—
287C3⋊Dic3C2×C22⋊C414yes—
288C3×Dic3—24no—
289C3×Dic3—42no—
290C3×Dic3—42no—
291C2×#41—98no—
292C2×#41—184no—
293C2×#41—184no—
294C22×Q8—31no—
295C22×D4—31no—
296C22×D4—92no—
297C23×C4—92no—
298C23×C4—92no—
299C23×C4—91no—
300#117—184no—
301C2×C4⋊C4—31no—
302C2×C4⋊C4—31no—
303C2×C4⋊C4—92no—
304C2×C4⋊C4—92no—
305C2×C4⋊C4—184no—
306C2×C22⋊C4—34no—
307C2×C22⋊C4—92no—
308C2×C22⋊C4—94no—
309C2×C42—91no—
310C2×C42D3211yescharacteristic
311#95—34no—
312#95—94no—
313C23×C3—21no—
314C23×C3—34no—
315C23×C3—62no—
316C23×C3—62no—
317C23×C3—64no—
318C23×C3—64no—
319C23×C3C23×D311yescharacteristic
320C23×C3C23×D311yescharacteristic
321C22×D3—22no—
322C22×D3—22no—
323C22×D3—24no—
324C22×D3—24no—
325C22×D3—32no—
326C22×D3—32no—
327C22×D3—32no—
328C22×D3—32no—
329C22×D3—32no—
330C22×D3—32no—
331C22×D3—62no—
332C22×D3—62no—
333C22×D3—62no—
334C22×D3—62no—
335C22×D3—62no—
336C22×D3—62no—
337C22×D3—62no—
338C22×D3—122no—
339C22×D3—122no—
340C22×D3C2×C4×D314yes—
341C3×Q8—68no—
342C3×D4—68no—
343C2×C3×C4—24no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—34no—
354C2×C3×C4—42no—
355C2×C3×C4—42no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—64no—
361C2×C3×C4—64no—
362C2×C3×C4C2×C4×D312yes—
363C2×C3×C4C2×C4×D312yes—
364C2×C3×C4D3×D412yes—
365C2×C3×C4D3×D412yes—
366C2×C3×C4D3×D412yes—
367C2×C3×C4D3×D412yes—
368#67—616no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—24no—
374C2×Dic3—24no—
375C2×Dic3—32no—
376C2×Dic3—32no—
377C2×Dic3—32no—
378C2×Dic3—32no—
379C2×Dic3—32no—
380C2×Dic3—32no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—616no—
385C2×Dic3—64no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—62no—
392C2×Dic3—122no—
393C2×Dic3—122no—
394C2×Dic3C2×C4×D314yes—
395D12—28no—
396D12—616no—
397C4×D3—316no—
398C4×D3—316no—
399C4×D3—616no—
400C4×D3—616no—
401C4×D3—128no—
402C4×D3—128no—
403Dic6—28no—
404C2×C32C22×C22⋊C411yescharacteristic
405C2×C32#52012yes—
406C2×C32#53511yescharacteristic
407C2×C32#53611yescharacteristic
408C2×C32#53712yes—
409C3⋊D3—24no—
410C3×D3—44no—
411C24—32no—
412C24—91no—
413#41—1832no—
414C2×Q8—34no—
415C2×Q8—62no—
416C2×Q8—62no—
417C2×D4—34no—
418C2×D4—62no—
419C2×D4—62no—
420C2×D4—98no—
421C2×D4—184no—
422C2×D4—184no—
423C22×C4—32no—
424C22×C4—32no—
425C22×C4—32no—
426C22×C4—98no—
427C22×C4—91no—
428C22×C4—94no—
429C22×C4—94no—
430C22×C4—94no—
431C22×C4—92no—
432C22×C4—184no—
433C22×C4—184no—
434C22×C4—184no—
435C22×C4—364no—
436C22×C4C2×D3212yes—
437C22×C4C2×D3211yescharacteristic
438C4⋊C4—62no—
439C4⋊C4—62no—
440C4⋊C4—184no—
441C4⋊C4—184no—
442C22⋊C4—124no—
443C22⋊C4—184no—
444C22⋊C4—364no—
445C42—22no—
446C42—182no—
447C22×C3—22no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—22no—
451C22×C3—21no—
452C22×C3—64no—
453C22×C3—68no—
454C22×C3—122no—
455C22×C3—122no—
456C22×C3—124no—
457C22×C3C22×C4×D311yescharacteristic
458C22×C3C22×C4×D311yescharacteristic
459C22×C3C2×D3×D411yescharacteristic
460C22×C3C2×D3×D411yescharacteristic
461C22×C3C2×D3×D411yescharacteristic
462C22×C3C2×D3×D411yescharacteristic
463C22×C3#100412yes—
464C22×C3#100712yes—
465C22×C3#100912yes—
466C22×C3#101012yes—
467C2×D3—24no—
468C2×D3—28no—
469C2×D3—34no—
470C2×D3—34no—
471C2×D3—42no—
472C2×D3—42no—
473C2×D3—44no—
474C2×D3—64no—
475C2×D3—62no—
476C2×D3—62no—
477C2×D3—62no—
478C2×D3—62no—
479C2×D3—64no—
480C2×D3—64no—
481C2×D3—64no—
482C2×D3—64no—
483C2×D3—124no—
484C2×D3—124no—
485C2×D3—122no—
486C2×D3—122no—
487C3×C4—24no—
488C3×C4—44no—
489C3×C4—42no—
490C3×C4—42no—
491C3×C4—64no—
492C3×C4—122no—
493C3×C4—122no—
494C3×C4D3×C22⋊C414yes—
495C3×C4D3×C22⋊C414yes—
496Dic3—24no—
497Dic3—34no—
498Dic3—34no—
499Dic3—42no—
500Dic3—42no—
501Dic3—64no—
502Dic3—124no—
503Dic3—122no—
504Dic3—122no—
505C32#231111yescharacteristic, complemented, Sylow
506C23—34no—
507C23—64no—
508C23—62no—
509C23—64no—
510C23—62no—
511C23—92no—
512C23—92no—
513C23—92no—
514C23—182no—
515C23—182no—
516C23C22×D3211yescharacteristic
517Q8—68no—
518D4—68no—
519D4—1816no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—34no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—62no—
528C2×C4—64no—
529C2×C4—64no—
530C2×C4—92no—
531C2×C4—92no—
532C2×C4—92no—
533C2×C4—916no—
534C2×C4—1816no—
535C2×C4—182no—
536C2×C4—182no—
537C2×C4—182no—
538C2×C4—368no—
539C2×C4C4×D3212yes—
540C2×C4#380212yes—
541C2×C4#381112yes—
542C2×C3—22no—
543C2×C3—22no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—124no—
548C2×C3C2×D3×C22⋊C411yescharacteristic
549C2×C3C2×D3×C22⋊C411yescharacteristic
550C2×C3#554612yes—
551C2×C3#557412yes—
552C2×C3#560812yes—
553C2×C3#562912yes—
554C2×C3#567411yescharacteristic
555C2×C3#567511yescharacteristic
556C2×C3#571511yescharacteristic
557C2×C3#572411yescharacteristic
558D3—44no—
559D3—64no—
560D3—64no—
561D3—124no—
562C22—68no—
563C22—64no—
564C22—94no—
565C22—124no—
566C22—122no—
567C22—122no—
568C22—184no—
569C22—184no—
570C22—182no—
571C22—182no—
572C22#6429712yes—
573C22C2×C4×D3211yescharacteristic
574C22C2×#380211yescharacteristic
575C22#6430712yes—
576C22C2×#381111yescharacteristic
577C4—42no—
578C4—64no—
579C4—94no—
580C4—122no—
581C4—122no—
582C4—362no—
583C4#6392114yes—
584C3—21no—
585C3#7629411yescharacteristic, complemented
586C3#7648211yescharacteristic, complemented
587C2—124no—
588C2—184no—
589C2#1059388912yes—
590C2#1059390811yescharacteristic
591C2#1059401011yescharacteristic
592C2#1059492312yes—
593C2C2×#6392111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC22×#3796C2
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×#64081C2semidirect
3. C2×#63900C2semidirect
4. C3×#4939C2semidirect
5. C3×#4929C2semidirect
6. #10591369C2semidirect
7. #10591323C2semidirect
8. #10591275C2semidirect
9. #10591221C2semidirect
20. C2×#3796C4semidirect
49. #4939D3semidirect
50. #4929D3semidirect
67. C2×C3×D12C2×C4semidirect
70. C2×C3×Dic6C2×C4semidirect
78. C2×D3×Dic3C2×C4semidirect
163. C4×C3⋊D3C22⋊C4semidirect
227. C2×D12C4×D3semidirect
246. C2×Dic6C4×D3semidirect
505. C32#2311semidirect
585. C3#76294semidirect
586. C3#76482semidirect

Maximal subgroups

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

subgroupindex
C22×#37962
C2×#640812
C2×#639002
C3×#49392
C3×#49292
#105913692
#105913232
#105912752
#105912212
#764823
#762943