Finite Group Databasebeta

← #11775299

Subgroups — #11775299

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
1D3×#930C211yesmaximal, characteristic
2C3×#4664C211yesmaximal, characteristic, complemented
3#10591154C211yesmaximal, characteristic, complemented
4#10589317C211yesmaximal, characteristic, complemented
5C3×#4451C211yesmaximal, characteristic, complemented
6#10589151C211yesmaximal, characteristic, complemented
7#10589149C211yesmaximal, characteristic, complemented
8#69531—31nomaximal
9#68304—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C2×D3×#67—21no—
12C2×D3×D12C411yescharacteristic, complemented
13#64139C2211yescharacteristic
14C3×#930C2211yescharacteristic
15C2×C3×(C2×D3)⋊C4—21no—
16#63978—21no—
17D3×(C2×D3)⋊C4—21no—
18#63909C411yescharacteristic, complemented
19#63908C411yescharacteristic, complemented
20#63906—21no—
21D3×C4⋊Dic3C411yescharacteristic, complemented
22C2×#3711—21no—
23C32×#95C2211yescharacteristic, complemented
24#63657C2211yescharacteristic, complemented
25C3×C3⋊#95—21no—
26C3×C3⋊#95C2211yescharacteristic, complemented
27C3×#830C2211yescharacteristic, complemented
28(C2×D3)⋊(C3⋊C8)—21no—
29C2×#930—31no—
30D3×#121—31no—
31C3×#381—31no—
32#5207—31no—
33#4726—31no—
34#4664D311yescharacteristic, complemented
35C3×#327—31no—
36#4537—31no—
37#4470—31no—
38#4451—31no—
39#4451—31no—
40#4451—31no—
41#4451—31no—
42#4451—61no—
43#4451D311yescharacteristic, complemented
44C23×C3×D3D411yescharacteristic
45C22×D32—21no—
46C22×C32×C4—21no—
47C22×C32×C4C2311yescharacteristic
48C2×#638—21no—
49C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
50C2×C3×#67—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3D411yescharacteristic
53C2×C3×D12C2×C411yescharacteristic
54C2×C3×C4×D3—42no—
55C2×C3×C4×D3C2×C411yescharacteristic
56C2×C3×C4×D3C2×C411yescharacteristic
57C2×C3×C4×D3D411yescharacteristic
58C2×C3×C4×D3D411yescharacteristic
59D3×#67—42no—
60D3×#67—42no—
61C2×#626—21no—
62C2×#626—21no—
63C2×#625—21no—
64C2×D3×Dic3—21no—
65D3×D12—42no—
66#3752—21no—
67C4⋊(C3⋊Dic3)C2×C411yescharacteristic
68C2×C3⋊(C3⋊C8)—21no—
69C3×(C2×D3)⋊C4—21no—
70C3×(C2×D3)⋊C4—42no—
71C3×C4⋊Dic3C2×C411yescharacteristic
72C2×C3×C3⋊C8—21no—
73Dic3⋊Dic3—21no—
74#3722—21no—
75(C2×D3)⋊Dic3—21no—
76#3711—42no—
77#1510—91noSylow
78C23×C3×C4—31no—
79C22×#67—61no—
80C2×D3×D4—31no—
81C2×D3×D4—61no—
82C22×D12—31no—
83C22×C4×D3C2×D311yescharacteristic
84C3×#121—31no—
85C2×C3×C22⋊C4—61no—
86#939—61no—
87#938—31no—
88#930—31no—
89#930—31no—
90#930—31no—
91#930—31no—
92#930—61no—
93#930—61no—
94#930—61no—
95#930C2×D311yescharacteristic
96C2×(C2×D3)⋊C4—21no—
97C2×(C2×D3)⋊C4—61no—
98C2×C4⋊Dic3—31no—
99C2×#208—61no—
100C2×ΓL(1,𝔽25)—61no—
101#895—31no—
102D3×C4⋊C4—31no—
103#884—61no—
104D3×C22⋊C4—61no—
105C3×C22⋊C8—31no—
106C3×#95—21no—
107C3×#95—31no—
108C3×#95—61no—
109C3×#95C2×D311yescharacteristic, complemented
110C3×#95C2×D311yescharacteristic, complemented
111C3⋊#95—21no—
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×C32C2×D411yescharacteristic
120C22×C3⋊D3—21no—
121C22×C3×D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3—22no—
124C22×C3×D3—21no—
125C22×C3×D3—41no—
126C22×C3×D3C22⋊C411yescharacteristic
127C22×C3×D3C22⋊C411yescharacteristic
128C2×D32—42no—
129C2×D32—42no—
130C2×D32—42no—
131C2×C32×C4—41no—
132C2×C32×C4—41no—
133C2×C32×C4—41no—
134C2×C32×C4—41no—
135C2×C32×C4C22×C411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137#638—41no—
138#638—41no—
139C2×C3⋊Dic3—21no—
140C4⋊(C3⋊D3)—41no—
141C3×#67—41no—
142C3×#67—41no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3C22⋊C411yescharacteristic
149C2×C3×Dic3C22⋊C411yescharacteristic
150C3×D12—41no—
151C3×C4×D3—22no—
152C3×C4×D3—22no—
153C3×C4×D3—41no—
154C3×C4×D3—41no—
155#626—42no—
156#626—42no—
157#625—42no—
158D3×Dic3—42no—
159C3⋊(C3⋊C8)—41no—
160C3×C3⋊C8—41no—
161C2×#121—91no—
162#407—91no—
163#381—31no—
164#327—31no—
165#327—91no—
166#327—91no—
167#327—91no—
168C24×C3—31no—
169C23×D3—61no—
170C23×D3—61no—
171C23×D3#6711yescharacteristic
172C2×C3×D4—31no—
173C2×C3×D4—61no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—31no—
178C22×C3×C4—31no—
179C22×C3×C4—31no—
180C22×C3×C4—31no—
181C22×C3×C4—31no—
182C22×C3×C4—41no—
183C22×C3×C4—61no—
184C22×C3×C4—122no—
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C2×#67—21no—
188C2×#67—61no—
189C2×#67—61no—
190C2×#67—61no—
191C2×#67—61no—
192C2×#67—61no—
193C2×#67—61no—
194C2×#67—121no—
195C2×#67—122no—
196C2×#67—122no—
197C22×Dic3—21no—
198C22×Dic3—61no—
199C22×Dic3#6711yescharacteristic
200D3×D4—122no—
201D3×D4—122no—
202D3×D4—122no—
203C2×D12—31no—
204C2×D12—31no—
205C2×D12—61no—
206C2×D12—61no—
207C2×D12—61no—
208C2×D12—122no—
209C2×D12C4×D311yescharacteristic
210C2×C4×D3—42no—
211C2×C4×D3—61no—
212C2×C4×D3C4×D311yescharacteristic
213C2×C4×D3C4×D311yescharacteristic
214C2×C4×D3D1211yescharacteristic
215C2×C4×D3D1211yescharacteristic
216C2×C3×C8—61no—
217C3×C4⋊C4—31no—
218C3×C22⋊C4—61no—
219C3×C22⋊C4—122no—
220#217—61no—
221(C2×D3)⋊C4—21no—
222(C2×D3)⋊C4—42no—
223(C2×D3)⋊C4—61no—
224(C2×D3)⋊C4—61no—
225(C2×D3)⋊C4—61no—
226(C2×D3)⋊C4—61no—
227(C2×D3)⋊C4—61no—
228(C2×D3)⋊C4—121no—
229C4⋊Dic3—31no—
230C4⋊Dic3—31no—
231C4⋊Dic3—61no—
232C4⋊Dic3—61no—
233C4⋊Dic3C4×D311yescharacteristic
234Dic3⋊C4—61no—
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×C32C2×C22⋊C411yescharacteristic
244C22×C32AGL(1,ℤ/8)11yescharacteristic
245C22×C32AGL(1,ℤ/8)11yescharacteristic
246C2×C3⋊D3—41no—
247C2×C3⋊D3—41no—
248C2×C3⋊D3—41no—
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#9912yes—
260D32—84no—
261C32×C4—21no—
262C32×C4—21no—
263C32×C4—81no—
264C3⋊Dic3—41no—
265C3×Dic3—21no—
266C3×Dic3—21no—
267C3×Dic3—41no—
268C3×Dic3—81no—
269C22×D4—91no—
270C22×D4—181no—
271C23×C4—31no—
272C2×M16—181no—
273#121—31no—
274#121—91no—
275#121—91no—
276#121—91no—
277#121—181no—
278#121—181no—
279C2×C4⋊C4—91no—
280C2×C22⋊C4—61no—
281C2×C22⋊C4—181no—
282C22⋊C8—31no—
283C22⋊C8—91no—
284C22⋊C8—181no—
285#95—31no—
286#95—61no—
287#95D3211yescharacteristic, complemented
288C23×C3—21no—
289C23×C3—31no—
290C23×C3—31no—
291C23×C3—62no—
292C23×C3—61no—
293C23×C3—61no—
294C23×C3—61no—
295C23×C3—121no—
296C23×C3D3×D411yescharacteristic
297C23×C3C2×#6711yescharacteristic
298C22×D3—21no—
299C22×D3—21no—
300C22×D3—22no—
301C22×D3—21no—
302C22×D3—41no—
303C22×D3—61no—
304C22×D3—61no—
305C22×D3—121no—
306C22×D3—122no—
307C22×D3—122no—
308C22×D3—122no—
309C22×D3—122no—
310C22×D3—122no—
311C22×D3—122no—
312C22×D3(C2×D3)⋊C411yescharacteristic
313C22×D3(C2×D3)⋊C411yescharacteristic
314C3×D4—121no—
315C3×D4—121no—
316C3×D4—121no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—31no—
320C2×C3×C4—31no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4—41no—
325C2×C3×C4—41no—
326C2×C3×C4—41no—
327C2×C3×C4—42no—
328C2×C3×C4—41no—
329C2×C3×C4—41no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—61no—
333C2×C3×C4—81no—
334C2×C3×C4—81no—
335C2×C3×C4—81no—
336C2×C3×C4—121no—
337C2×C3×C4—121no—
338C2×C3×C4—121no—
339C2×C3×C4—121no—
340C2×C3×C4—121no—
341C2×C3×C4—121no—
342C2×C3×C4C2×C4×D311yescharacteristic
343C2×C3×C4C2×C4×D311yescharacteristic
344C2×C3×C4C2×D1211yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346#67—41no—
347#67—41no—
348#67—122no—
349#67—122no—
350#67—122no—
351#67—122no—
352#67—121no—
353#67—121no—
354#67—121no—
355#67—121no—
356#67—241no—
357#67—241no—
358C2×Dic3—21no—
359C2×Dic3—41no—
360C2×Dic3—41no—
361C2×Dic3—41no—
362C2×Dic3—41no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—121no—
366C2×Dic3—122no—
367C2×Dic3(C2×D3)⋊C411yescharacteristic
368C2×Dic3(C2×D3)⋊C411yescharacteristic
369D12—41no—
370D12—121no—
371D12—121no—
372D12—122no—
373D12—122no—
374D12—241no—
375C4×D3—22no—
376C4×D3—22no—
377C4×D3—41no—
378C4×D3—41no—
379C4×D3—122no—
380C3×C8—121no—
381C3⋊C8—41no—
382C3⋊C8—121no—
383C3⋊C8—121no—
384C3⋊C8—241no—
385C2×C32—21no—
386C2×C32—21no—
387C2×C32C2×#9911yescharacteristic
388C2×C32#41811yescharacteristic
389C2×C32#42111yescharacteristic
390C3⋊D3—81no—
391C3×D3—22no—
392C3×D3—41no—
393C3×D3—81no—
394C24—31no—
395C24—181no—
396C2×D4—31no—
397C2×D4—61no—
398C2×D4—91no—
399C2×D4—181no—
400C2×D4—181no—
401C2×D4—181no—
402C2×D4—181no—
403C2×D4—362no—
404C2×D4—362no—
405C2×D4—362no—
406C22×C4—21no—
407C22×C4—31no—
408C22×C4—31no—
409C22×C4—31no—
410C22×C4—31no—
411C22×C4—31no—
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—91no—
421C4⋊C4—181no—
422C22⋊C4—61no—
423C22⋊C4—122no—
424C22⋊C4—181no—
425C22⋊C4—181no—
426C22⋊C4—181no—
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—61no—
438C22×C3—61no—
439C22×C3—61no—
440C22×C3—61no—
441C22×C3—61no—
442C22×C3—122no—
443C22×C3—122no—
444C22×C3—121no—
445C22×C3—121no—
446C22×C3—121no—
447C22×C3D3×C22⋊C411yescharacteristic
448C22×C3#91111yescharacteristic
449C22×C3#91411yescharacteristic
450C22×C3C2×(C2×D3)⋊C411yescharacteristic
451C22×C3#94911yescharacteristic
452C22×C3#94911yescharacteristic
453C2×D3—21no—
454C2×D3—21no—
455C2×D3—21no—
456C2×D3—21no—
457C2×D3—21no—
458C2×D3—42no—
459C2×D3—42no—
460C2×D3—41no—
461C2×D3—41no—
462C2×D3—41no—
463C2×D3—121no—
464C2×D3—121no—
465C2×D3—121no—
466C2×D3—121no—
467C2×D3—121no—
468C2×D3—121no—
469C2×D3—241no—
470C2×D3—241no—
471C2×D3—241no—
472C2×D3—244no—
473C2×D3—244no—
474C2×D3#80612yes—
475C3×C4—21no—
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—21no—
479C3×C4—41no—
480C3×C4—41no—
481C3×C4—61no—
482C3×C4—61no—
483C3×C4—81no—
484C3×C4—81no—
485C3×C4—82no—
486C3×C4—121no—
487C3×C4—241no—
488Dic3—21no—
489Dic3—21no—
490Dic3—41no—
491Dic3—81no—
492Dic3—121no—
493Dic3—121no—
494Dic3—241no—
495C32#151011yescharacteristic, complemented, Sylow
496C23—31no—
497C23—31no—
498C23—62no—
499C23—61no—
500C23—61no—
501C23—61no—
502C23—121no—
503C23—181no—
504C23—362no—
505C23—362no—
506C23—362no—
507C23D3×#6711yescharacteristic
508D4—121no—
509D4—121no—
510D4—121no—
511D4—361no—
512D4—362no—
513D4—362no—
514D4—362no—
515D4—361no—
516D4—361no—
517C2×C4—31no—
518C2×C4—31no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—61no—
526C2×C4—121no—
527C2×C4—121no—
528C2×C4—121no—
529C2×C4—121no—
530C2×C4—121no—
531C2×C4—121no—
532C2×C4—181no—
533C2×C4—362no—
534C2×C4C4×D3211yescharacteristic
535C2×C4D3×D1211yescharacteristic
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—121no—
549C2×C3—241no—
550C2×C3D3×#9911yescharacteristic
551C2×C3#477011yescharacteristic
552C2×C3#482111yescharacteristic
553C2×C3C2×#80611yescharacteristic
554C2×C3#500111yescharacteristic
555C2×C3#500511yescharacteristic
556D3—22no—
557D3—41no—
558D3—81no—
559D3—241no—
560D3—241no—
561D3—481no—
562C22—21no—
563C22—21no—
564C22—32no—
565C22—61no—
566C22—61no—
567C22—61no—
568C22—61no—
569C22—61no—
570C22—122no—
571C22—122no—
572C22—121no—
573C22—121no—
574C22—121no—
575C22—361no—
576C22—361no—
577C22—361no—
578C22—724no—
579C22D3×(C2×D3)⋊C411yescharacteristic
580C22#6392511yescharacteristic
581C22#6393911yescharacteristic
582C4—21no—
583C4—21no—
584C4—61no—
585C4—61no—
586C4—81no—
587C4—121no—
588C4—241no—
589C4—361no—
590C3—21no—
591C3#6830411yescharacteristic, complemented
592C3#6953111yescharacteristic, complemented
593C2—21no—
594C2—21no—
595C2—62no—
596C2—121no—
597C2—241no—
598C2—721no—
599C2#1059039211yescharacteristic
600C2D3×#80611yescharacteristic
601C2#1059059211yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32C2×C22⋊C4
prime radicalD3×#930C2
cosocleC22×C32×C4C23
hypercenter#95D32
hypocenterC32#1510
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C3×#4664C2semidirect
3. #10591154C2semidirect
4. #10589317C2semidirect
5. C3×#4451C2semidirect
6. #10589151C2semidirect
7. #10589149C2semidirect
12. C2×D3×D12C4semidirect
18. #63909C4semidirect
19. #63908C4semidirect
21. D3×C4⋊Dic3C4semidirect
23. C32×#95C22semidirect
24. #63657C22semidirect
26. C3×C3⋊#95C22semidirect
27. C3×#830C22semidirect
34. #4664D3semidirect
43. #4451D3semidirect
109. C3×#95C2×D3semidirect
110. C3×#95C2×D3semidirect
112. C3⋊#95C2×D3semidirect
117. #830C2×D3semidirect
287. #95D32semidirect
495. C32#1510semidirect
591. C3#68304semidirect
592. C3#69531semidirect

Maximal subgroups

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

subgroupindex
D3×#9302
C3×#46642
#105911542
#105893172
C3×#44512
#105891512
#105891492
#695313
#683043