Finite Group Databasebeta

← #11775301

Subgroups — #11775301

Order 1152.

697 conjugacy classes of subgroups.

The subgroup lattice has 603 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#121C211yesmaximal, characteristic
2#10591294C211yesmaximal, characteristic, complemented
3#10591154C211yesmaximal, characteristic, complemented
4#10589403C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic, complemented
6#10589150C211yesmaximal, characteristic, complemented
7#10589149C211yesmaximal, characteristic, complemented
8#71674—31nomaximal
9#68304—31nomaximal
10C2×C3×D3×D4—21no—
11C2×C3×D3×D4C411yescharacteristic, complemented
12C22×C3×C4×D3C2211yescharacteristic
13C32×#121C2211yescharacteristic
14C3×#939—21no—
15C3×#938C411yescharacteristic, complemented
16C3×#930C2211yescharacteristic
17C3×#895C411yescharacteristic, complemented
18C3×D3×C4⋊C4C411yescharacteristic, complemented
19C3×#884—21no—
20C3×D3×C22⋊C4—21no—
21C2×(C2×D3)⋊Dic3—21no—
22C2×#3711—21no—
23#63658C2211yescharacteristic, complemented
24#63657C2211yescharacteristic, complemented
25C3×C3⋊#95C2211yescharacteristic, complemented
26C3×#830C2211yescharacteristic, complemented
27#63579—21no—
28(C2×D3)⋊(C3⋊C8)—21no—
29C2×C3×#121—31no—
30D3×#121D311yescharacteristic
31#5211—31no—
32#5207—31no—
33#4726—31no—
34#4664—31no—
35C3×#327—31no—
36#4537—31no—
37#4537—31no—
38#4537—31no—
39#4537—31no—
40#4537—61no—
41#4537D311yescharacteristic, complemented
42#4470—31no—
43#4451—31no—
44C23×C3×D3—21no—
45C23×C3×D3D411yescharacteristic
46C2×C32×D4—21no—
47C2×C32×D4C2×C411yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3—21no—
50C2×C3×#67—21no—
51C2×C3×#67—21no—
52C2×C3×#67—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C3×D3×D4—42no—
56C3×D3×D4—42no—
57C3×D3×D4—42no—
58C2×C3×D12—21no—
59C2×C3×D12C2×C411yescharacteristic
60C2×C3×C4×D3—21no—
61C2×C3×C4×D3—42no—
62C2×C3×C4×D3C2×C411yescharacteristic
63C2×C3×C4×D3C2×C411yescharacteristic
64C2×C3×C4×D3D411yescharacteristic
65C2×C3×C4×D3D411yescharacteristic
66C32×C4⋊C4C2×C411yescharacteristic
67C32×C22⋊C4—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C3×#217—21no—
70C3×(C2×D3)⋊C4—21no—
71C3×(C2×D3)⋊C4—21no—
72C3×C4⋊Dic3C2×C411yescharacteristic
73C3×Dic3⋊C4—21no—
74C2×C3×C3⋊C8—21no—
75(C2×D3)⋊Dic3—42no—
76#3711—42no—
77#1510—91noSylow
78C22×C3×D4—31no—
79C22×C3×D4—61no—
80C23×C3×C4—31no—
81C2×D3×D4—21no—
82C2×D3×D4Dic311yescharacteristic, complemented
83C22×C4×D3C2×D311yescharacteristic
84C3×#121—21no—
85C3×#121—31no—
86C3×#121—31no—
87C3×#121—31no—
88C3×#121—61no—
89C3×#121—61no—
90C3×#121C2×D311yescharacteristic
91C3×#121C2×D311yescharacteristic
92C2×C3×C4⋊C4—31no—
93C2×C3×C22⋊C4—61no—
94C2×#217—61no—
95#939—21no—
96#938Dic311yescharacteristic, complemented
97#930C2×D311yescharacteristic
98C2×(C2×D3)⋊C4—61no—
99C2×#208—61no—
100C2×ΓL(1,𝔽25)—61no—
101#895Dic311yescharacteristic, complemented
102D3×C4⋊C4Dic311yescharacteristic, complemented
103#884—21no—
104D3×C22⋊C4—21no—
105C3×C22⋊C8—31no—
106C3×#95—31no—
107C3⋊#95—31no—
108C3⋊#95—31no—
109C3⋊#95—61no—
110C3⋊#95—61no—
111C3⋊#95—61no—
112C3⋊#95C2×D311yescharacteristic, complemented
113#830—31no—
114#830—31no—
115#830—61no—
116#830—61no—
117#830C2×D311yescharacteristic, complemented
118(C2×D3)⋊C8—61no—
119C23×C32—21no—
120C23×C32C2×D411yescharacteristic
121C22×C3×D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3—22no—
124C22×C3×D3—21no—
125C22×C3×D3—41no—
126C22×C3×D3—42no—
127C22×C3×D3—42no—
128C22×C3×D3—42no—
129C22×C3×D3C22⋊C411yescharacteristic
130C22×C3×D3C22⋊C411yescharacteristic
131C32×D4—41no—
132C32×D4—41no—
133C32×D4—41no—
134C2×C32×C4—21no—
135C2×C32×C4—41no—
136C2×C32×C4C22×C411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C3⋊Dic3—41no—
139C2×C3⋊Dic3—41no—
140C2×C3⋊Dic3—41no—
141C3×#67—42no—
142C3×#67—42no—
143C3×#67—41no—
144C3×#67—41no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3C22⋊C411yescharacteristic
151C2×C3×Dic3C22⋊C411yescharacteristic
152C3×D12—41no—
153C3×D12—42no—
154C3×C4×D3—22no—
155C3×C4×D3—22no—
156C3×C4×D3—41no—
157C3×C4×D3—41no—
158C3×C4×D3—42no—
159C3⋊(C3⋊C8)—41no—
160C3×C3⋊C8—41no—
161C2×#121—31no—
162#407—91no—
163#381—91no—
164#327—31no—
165#327—91no—
166#327—91no—
167#327—91no—
168C24×C3—31no—
169C24×C3—61no—
170C23×D3—21no—
171C23×D3#6711yescharacteristic
172C2×C3×D4—21no—
173C2×C3×D4—21no—
174C2×C3×D4—21no—
175C2×C3×D4—31no—
176C2×C3×D4—41no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C2×C3×D4—61no—
180C2×C3×D4—61no—
181C2×C3×D4—122no—
182C2×C3×D4—122no—
183C2×C3×D4—122no—
184C2×C3×D4C4×D311yescharacteristic
185C2×C3×D4C2×Dic311yescharacteristic
186C22×C3×C4—21no—
187C22×C3×C4—31no—
188C22×C3×C4—31no—
189C22×C3×C4—31no—
190C22×C3×C4—31no—
191C22×C3×C4—31no—
192C22×C3×C4—61no—
193C22×C3×C4—61no—
194C22×C3×C4—122no—
195C22×C3×C4C22×D311yescharacteristic
196C22×C3×C4C22×D311yescharacteristic
197C2×#67—21no—
198C2×#67—21no—
199C2×#67—21no—
200C22×Dic3—21no—
201C22×Dic3—61no—
202C22×Dic3—61no—
203C22×Dic3—121no—
204C22×Dic3#6711yescharacteristic
205D3×D4—42no—
206D3×D4—42no—
207D3×D4—42no—
208C2×D12—21no—
209C2×D12C2×Dic311yescharacteristic
210C2×C4×D3—21no—
211C2×C4×D3—42no—
212C2×C4×D3C2×Dic311yescharacteristic
213C2×C4×D3C2×Dic311yescharacteristic
214C2×C4×D3#6711yescharacteristic
215C2×C4×D3#6711yescharacteristic
216C2×C3×C8—61no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—31no—
219C3×C4⋊C4—61no—
220C3×C4⋊C4C4×D311yescharacteristic
221C3×C4⋊C4C2×Dic311yescharacteristic
222C3×C22⋊C4—21no—
223C3×C22⋊C4—21no—
224C3×C22⋊C4—41no—
225C3×C22⋊C4—61no—
226C3×C22⋊C4—61no—
227C3×C22⋊C4—61no—
228#217—21no—
229#217—122no—
230(C2×D3)⋊C4—21no—
231(C2×D3)⋊C4—21no—
232(C2×D3)⋊C4—122no—
233C4⋊Dic3C2×Dic311yescharacteristic
234Dic3⋊C4—21no—
235#208—122no—
236C2×C3⋊C8—21no—
237C2×C3⋊C8—61no—
238C2×C3⋊C8—61no—
239C2×C3⋊C8—121no—
240ΓL(1,𝔽25)—122no—
241C22×C32—21no—
242C22×C32—21no—
243C22×C32—41no—
244C22×C32—41no—
245C22×C32—41no—
246C22×C32C2×C22⋊C411yescharacteristic
247C22×C32AGL(1,ℤ/8)11yescharacteristic
248C22×C32AGL(1,ℤ/8)11yescharacteristic
249C2×C3×D3—21no—
250C2×C3×D3—21no—
251C2×C3×D3—21no—
252C2×C3×D3—21no—
253C2×C3×D3—21no—
254C2×C3×D3—42no—
255C2×C3×D3—42no—
256C2×C3×D3—41no—
257C2×C3×D3—41no—
258C2×C3×D3—41no—
259C2×C3×D3—84no—
260C2×C3×D3#9912yes—
261C32×C4—21no—
262C32×C4—21no—
263C32×C4—41no—
264C3⋊Dic3—81no—
265C3×Dic3—21no—
266C3×Dic3—21no—
267C3×Dic3—41no—
268C3×Dic3—81no—
269C22×D4—31no—
270C22×D4—61no—
271C23×C4—31no—
272C2×M16—181no—
273#121—31no—
274#121—31no—
275#121—31no—
276#121—61no—
277#121—61no—
278#121D3211yescharacteristic
279C2×C4⋊C4—31no—
280C2×C22⋊C4—61no—
281C2×C22⋊C4—181no—
282C22⋊C8—31no—
283C22⋊C8—91no—
284C22⋊C8—181no—
285#95—31no—
286#95—91no—
287#95—181no—
288C23×C3—21no—
289C23×C3—21no—
290C23×C3—21no—
291C23×C3—31no—
292C23×C3—31no—
293C23×C3—41no—
294C23×C3—62no—
295C23×C3—61no—
296C23×C3—61no—
297C23×C3—61no—
298C23×C3—121no—
299C23×C3—122no—
300C23×C3—122no—
301C23×C3—122no—
302C23×C3D3×D411yescharacteristic
303C23×C3C2×#6711yescharacteristic
304C22×D3—21no—
305C22×D3—21no—
306C22×D3—22no—
307C22×D3—21no—
308C22×D3—41no—
309C22×D3—42no—
310C22×D3—42no—
311C22×D3—42no—
312C22×D3#21711yescharacteristic
313C22×D3#21711yescharacteristic
314C3×D4—41no—
315C3×D4—41no—
316C3×D4—41no—
317C3×D4—41no—
318C3×D4—41no—
319C3×D4—41no—
320C3×D4—81no—
321C3×D4—81no—
322C3×D4—81no—
323C3×D4—121no—
324C3×D4—122no—
325C3×D4—122no—
326C3×D4—122no—
327C3×D4—121no—
328C3×D4—121no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—31no—
334C2×C3×C4—31no—
335C2×C3×C4—41no—
336C2×C3×C4—41no—
337C2×C3×C4—41no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
340C2×C3×C4—61no—
341C2×C3×C4—81no—
342C2×C3×C4—121no—
343C2×C3×C4—121no—
344C2×C3×C4—122no—
345C2×C3×C4—121no—
346C2×C3×C4—121no—
347C2×C3×C4—121no—
348C2×C3×C4—121no—
349C2×C3×C4C2×C4×D311yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4C22×Dic311yescharacteristic
352C2×C3×C4C2×#6711yescharacteristic
353#67—42no—
354#67—42no—
355#67—41no—
356#67—41no—
357C2×Dic3—21no—
358C2×Dic3—41no—
359C2×Dic3—41no—
360C2×Dic3—41no—
361C2×Dic3—41no—
362C2×Dic3—121no—
363C2×Dic3—121no—
364C2×Dic3—121no—
365C2×Dic3—121no—
366C2×Dic3—122no—
367C2×Dic3—121no—
368C2×Dic3—121no—
369C2×Dic3—241no—
370C2×Dic3—241no—
371C2×Dic3#21711yescharacteristic
372C2×Dic3#21711yescharacteristic
373D12—41no—
374D12—42no—
375C4×D3—22no—
376C4×D3—22no—
377C4×D3—41no—
378C4×D3—41no—
379C4×D3—42no—
380C3×C8—121no—
381C3⋊C8—41no—
382C3⋊C8—121no—
383C3⋊C8—121no—
384C3⋊C8—241no—
385C2×C32—21no—
386C2×C32—21no—
387C2×C32—81no—
388C2×C32C2×#9911yescharacteristic
389C2×C32#41811yescharacteristic
390C2×C32#42111yescharacteristic
391C3×D3—22no—
392C3×D3—41no—
393C3×D3—81no—
394C24—31no—
395C24—61no—
396C2×D4—21no—
397C2×D4—31no—
398C2×D4—61no—
399C2×D4—61no—
400C2×D4—61no—
401C2×D4—61no—
402C2×D4—122no—
403C2×D4—122no—
404C2×D4—122no—
405C2×D4D3×Dic311yescharacteristic
406C22×C4—31no—
407C22×C4—31no—
408C22×C4—31no—
409C22×C4—31no—
410C22×C4—31no—
411C22×C4—61no—
412C22×C4—61no—
413C22×C4—122no—
414C22×C4—181no—
415C22×C4C2×D3211yescharacteristic
416M16—362no—
417C2×C8—61no—
418C2×C8—181no—
419C4⋊C4—31no—
420C4⋊C4—61no—
421C4⋊C4D3×Dic311yescharacteristic
422C22⋊C4—21no—
423C22⋊C4—61no—
424C22⋊C4—61no—
425C22⋊C4—61no—
426C22⋊C4—362no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—32no—
435C22×C3—41no—
436C22×C3—41no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3—41no—
442C22×C3—41no—
443C22×C3—61no—
444C22×C3—61no—
445C22×C3—61no—
446C22×C3—61no—
447C22×C3—61no—
448C22×C3—81no—
449C22×C3—81no—
450C22×C3—81no—
451C22×C3—122no—
452C22×C3—122no—
453C22×C3—121no—
454C22×C3—121no—
455C22×C3—121no—
456C22×C3—244no—
457C22×C3D3×C22⋊C411yescharacteristic
458C22×C3#91111yescharacteristic
459C22×C3#91411yescharacteristic
460C22×C3#93211yescharacteristic
461C22×C3#93211yescharacteristic
462C22×C3C2×#21711yescharacteristic
463C2×D3—21no—
464C2×D3—21no—
465C2×D3—21no—
466C2×D3—21no—
467C2×D3—21no—
468C2×D3—42no—
469C2×D3—42no—
470C2×D3—41no—
471C2×D3—41no—
472C2×D3—41no—
473C2×D3—84no—
474C2×D3#83412yes—
475C3×C4—21no—
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—21no—
479C3×C4—41no—
480C3×C4—41no—
481C3×C4—41no—
482C3×C4—41no—
483C3×C4—61no—
484C3×C4—61no—
485C3×C4—81no—
486C3×C4—121no—
487C3×C4—241no—
488Dic3—21no—
489Dic3—21no—
490Dic3—41no—
491Dic3—81no—
492Dic3—241no—
493Dic3—241no—
494Dic3—242no—
495C32#151011yescharacteristic, complemented, Sylow
496C23—21no—
497C23—31no—
498C23—31no—
499C23—62no—
500C23—61no—
501C23—61no—
502C23—61no—
503C23—121no—
504C23—122no—
505C23—122no—
506C23—122no—
507C23D3×#6711yescharacteristic
508D4—41no—
509D4—41no—
510D4—41no—
511D4—121no—
512D4—122no—
513D4—122no—
514D4—122no—
515D4—121no—
516D4—121no—
517C2×C4—21no—
518C2×C4—31no—
519C2×C4—31no—
520C2×C4—41no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—61no—
524C2×C4—121no—
525C2×C4—121no—
526C2×C4—122no—
527C2×C4—121no—
528C2×C4—121no—
529C2×C4—121no—
530C2×C4—121no—
531C2×C4—361no—
532C2×C4—361no—
533C2×C4—361no—
534C2×C4C2×D3×Dic311yescharacteristic
535C2×C4D3×#6711yescharacteristic
536C8—121no—
537C8—361no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—41no—
546C2×C3—41no—
547C2×C3—62no—
548C2×C3—81no—
549C2×C3—81no—
550C2×C3—121no—
551C2×C3—161no—
552C2×C3—241no—
553C2×C3D3×#9911yescharacteristic
554C2×C3#477011yescharacteristic
555C2×C3#482111yescharacteristic
556C2×C3#521511yescharacteristic
557C2×C3C2×#83411yescharacteristic
558C2×C3#523611yescharacteristic
559D3—22no—
560D3—41no—
561D3—81no—
562C22—21no—
563C22—21no—
564C22—32no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—61no—
569C22—61no—
570C22—61no—
571C22—61no—
572C22—61no—
573C22—122no—
574C22—122no—
575C22—121no—
576C22—121no—
577C22—121no—
578C22—244no—
579C22#6393211yescharacteristic
580C22#6393411yescharacteristic
581C22D3×#21711yescharacteristic
582C4—21no—
583C4—21no—
584C4—41no—
585C4—61no—
586C4—61no—
587C4—121no—
588C4—241no—
589C4—721no—
590C3—21no—
591C3#6830411yescharacteristic, complemented
592C3#7167411yescharacteristic, complemented
593C2—21no—
594C2—21no—
595C2—62no—
596C2—81no—
597C2—121no—
598C2—241no—
599C2#1059142111yescharacteristic
600C2D3×#83411yescharacteristic
601C2#1059167011yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#121C22
socleC22×C32C2×C22⋊C4
prime radicalC3×D3×#121C2
cosocleC22×C32×C4C23
hypercenter#121D32
hypocenterC32#1510
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #10591294C2semidirect
3. #10591154C2semidirect
4. #10589403C2semidirect
5. C3×#4537C2semidirect
6. #10589150C2semidirect
7. #10589149C2semidirect
11. C2×C3×D3×D4C4semidirect
15. C3×#938C4semidirect
17. C3×#895C4semidirect
18. C3×D3×C4⋊C4C4semidirect
23. #63658C22semidirect
24. #63657C22semidirect
25. C3×C3⋊#95C22semidirect
26. C3×#830C22semidirect
41. #4537D3semidirect
82. C2×D3×D4Dic3semidirect
96. #938Dic3semidirect
101. #895Dic3semidirect
102. D3×C4⋊C4Dic3semidirect
112. C3⋊#95C2×D3semidirect
117. #830C2×D3semidirect
495. C32#1510semidirect
591. C3#68304semidirect
592. C3#71674semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1212
#105912942
#105911542
#105894032
C3×#45372
#105891502
#105891492
#716743
#683043