Finite Group Databasebeta

← #11775584

Subgroups — #11775584

Order 1152.

725 conjugacy classes of subgroups.

The subgroup lattice has 607 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#930C211yesmaximal, characteristic
2C3×D3×C22⋊C8C211yesmaximal, characteristic, complemented
3#10591295C211yesmaximal, characteristic, complemented
4#10589336C211yesmaximal, characteristic, complemented
5C3×#4470C211yesmaximal, characteristic, complemented
6#10589151C211yesmaximal, characteristic, complemented
7#10589150C211yesmaximal, characteristic, complemented
8#69944—31nomaximal
9#68307—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C2×D3×#67—21no—
12C2×D3×D12C411yescharacteristic, complemented
13#64139C2211yescharacteristic
14C3×#930C2211yescharacteristic
15C2×C3×D3×C8—21no—
16#63978—21no—
17C2×Dic3⋊Dic3—21no—
18C2×(C2×D3)⋊Dic3—21no—
19D3×(C2×D3)⋊C4—21no—
20#63909C411yescharacteristic, complemented
21#63908C411yescharacteristic, complemented
22#63906—21no—
23D3×C4⋊Dic3C411yescharacteristic, complemented
24C32×C22⋊C8C2211yescharacteristic, complemented
25#63658C2211yescharacteristic, complemented
26C3×C3⋊#95C2211yescharacteristic, complemented
27C3×#830C2211yescharacteristic, complemented
28C3×(C2×D3)⋊C8—21no—
29C2×#930—31no—
30D3×#121—31no—
31C2×C3×C22⋊C8—31no—
32#5212—31no—
33D3×C22⋊C8D311yescharacteristic, complemented
34#4667—31no—
35C3×#327—31no—
36#4537—31no—
37#4470—31no—
38#4470—31no—
39#4470—31no—
40#4470—31no—
41#4470—61no—
42#4470D311yescharacteristic, complemented
43#4451—31no—
44C23×C3×D3D411yescharacteristic
45C22×D32—21no—
46C22×C32×C4C2311yescharacteristic
47C2×#638—21no—
48C22×C3⋊Dic3—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—
66C2×C32×C8—21no—
67#3752—21no—
68C4⋊(C3⋊Dic3)C2×C411yescharacteristic
69C3×(C2×D3)⋊C4—21no—
70C3×C4⋊Dic3C2×C411yescharacteristic
71C2×C3×C3⋊C8—21no—
72C3×D3×C8—42no—
73Dic3⋊Dic3—21no—
74Dic3⋊Dic3—42no—
75#3722—21no—
76(C2×D3)⋊Dic3—21no—
77(C2×D3)⋊Dic3—42no—
78#1519—91noSylow
79C23×C3×C4—31no—
80C22×#67—61no—
81C2×D3×D4—31no—
82C2×D3×D4—61no—
83C22×D12—31no—
84C22×C4×D3C2×D311yescharacteristic
85C22×C3×C8—61no—
86C3×#121—31no—
87C2×#217—61no—
88#939—61no—
89#938—31no—
90#930—31no—
91#930—31no—
92#930—31no—
93#930—31no—
94#930—61no—
95#930—61no—
96#930—61no—
97#930C2×D311yescharacteristic
98C2×(C2×D3)⋊C4—61no—
99C2×(C2×D3)⋊C4—61no—
100C2×C4⋊Dic3—31no—
101C2×C4⋊Dic3—61no—
102C2×Dic3⋊C4—61no—
103C2×D3×C8—21no—
104#895—31no—
105D3×C4⋊C4—31no—
106#884—61no—
107D3×C22⋊C4—61no—
108C3×C22⋊C8—21no—
109C3×C22⋊C8—31no—
110C3×C22⋊C8—61no—
111C3×C22⋊C8C2×D311yescharacteristic, complemented
112C3×C22⋊C8C2×D311yescharacteristic, complemented
113C3×#95—31no—
114C3⋊#95—31no—
115C3⋊#95—31no—
116C3⋊#95—61no—
117C3⋊#95C2×D311yescharacteristic, complemented
118#830C2×D311yescharacteristic, complemented
119(C2×D3)⋊C8—21no—
120C23×C32C2×D411yescharacteristic
121C22×C3⋊D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3—41no—
124C22×C3×D3—41no—
125C22×C3×D3C22⋊C411yescharacteristic
126C22×C3×D3C22⋊C411yescharacteristic
127C22×C3×D3D812yes—
128C22×C3×D3SD1612yes—
129C2×D32—42no—
130C2×D32—42no—
131C2×D32—42no—
132C2×C32×C4—41no—
133C2×C32×C4C22×C411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135#638—41no—
136#638—41no—
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—41no—
139C2×C3⋊Dic3—41no—
140C2×C3⋊Dic3—41no—
141C4⋊(C3⋊D3)—41no—
142C3×#67—41no—
143C3×#67—41no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3C22⋊C411yescharacteristic
150C2×C3×Dic3C22⋊C411yescharacteristic
151C3×D12—41no—
152C3×C4×D3—22no—
153C3×C4×D3—22no—
154C3×C4×D3—41no—
155C3×C4×D3—41no—
156#626—42no—
157#626—42no—
158#625—42no—
159D3×Dic3—42no—
160C32×C8—41no—
161C3×C3⋊C8—41no—
162C2×#121—91no—
163C2×C22⋊C8—31no—
164#380—91no—
165#327—31no—
166#327—91no—
167#327—91no—
168#327—91no—
169C24×C3—31no—
170C23×D3—61no—
171C23×D3—61no—
172C23×D3D1211yescharacteristic
173C2×C3×D4—31no—
174C2×C3×D4—61no—
175C22×C3×C4—21no—
176C22×C3×C4—31no—
177C22×C3×C4—31no—
178C22×C3×C4—31no—
179C22×C3×C4—31no—
180C22×C3×C4—31no—
181C22×C3×C4—61no—
182C22×C3×C4—122no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C2×#67—21no—
186C2×#67—61no—
187C2×#67—61no—
188C2×#67—61no—
189C2×#67—61no—
190C2×#67—61no—
191C2×#67—61no—
192C2×#67—121no—
193C2×#67—122no—
194C2×#67—122no—
195C22×Dic3—21no—
196C22×Dic3—61no—
197C22×Dic3—61no—
198C22×Dic3—61no—
199C22×Dic3—121no—
200C22×Dic3D1211yescharacteristic
201D3×D4—122no—
202D3×D4—122no—
203D3×D4—122no—
204C2×D12—31no—
205C2×D12—31no—
206C2×D12—61no—
207C2×D12—61no—
208C2×D12—61no—
209C2×D12—122no—
210C2×D12C4×D311yescharacteristic
211C2×C4×D3—42no—
212C2×C4×D3—61no—
213C2×C4×D3C4×D311yescharacteristic
214C2×C4×D3C4×D311yescharacteristic
215C2×C4×D3#6711yescharacteristic
216C2×C4×D3#6711yescharacteristic
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—41no—
220C2×C3×C8—61no—
221C2×C3×C8—122no—
222C3×C4⋊C4—31no—
223C3×C22⋊C4—61no—
224#217—61no—
225#217—122no—
226(C2×D3)⋊C4—21no—
227(C2×D3)⋊C4—61no—
228(C2×D3)⋊C4—61no—
229(C2×D3)⋊C4—61no—
230(C2×D3)⋊C4—61no—
231(C2×D3)⋊C4—61no—
232(C2×D3)⋊C4—121no—
233(C2×D3)⋊C4—122no—
234C4⋊Dic3—31no—
235C4⋊Dic3—31no—
236C4⋊Dic3—61no—
237C4⋊Dic3—61no—
238C4⋊Dic3—122no—
239C4⋊Dic3C4×D311yescharacteristic
240Dic3⋊C4—61no—
241Dic3⋊C4—122no—
242C2×C3⋊C8—21no—
243D3×C8—42no—
244C22×C32—21no—
245C22×C32—21no—
246C22×C32C2×C22⋊C411yescharacteristic
247C22×C32C2×D811yescharacteristic
248C22×C32C2×SD1611yescharacteristic
249C2×C3⋊D3—41no—
250C2×C3⋊D3—41no—
251C2×C3⋊D3—41no—
252C2×C3×D3—21no—
253C2×C3×D3—21no—
254C2×C3×D3—21no—
255C2×C3×D3—21no—
256C2×C3×D3—42no—
257C2×C3×D3—42no—
258C2×C3×D3—41no—
259C2×C3×D3—41no—
260C2×C3×D3—41no—
261C2×C3×D3#10212yes—
262C2×C3×D3#10212yes—
263D32—84no—
264C32×C4—21no—
265C32×C4—21no—
266C3⋊Dic3—41no—
267C3⋊Dic3—81no—
268C3×Dic3—21no—
269C3×Dic3—41no—
270C3×Dic3—81no—
271C3×Dic3#9912yes—
272C22×D4—91no—
273C22×D4—181no—
274C23×C4—31no—
275C22×C8—61no—
276#121—31no—
277#121—91no—
278#121—91no—
279#121—91no—
280#121—181no—
281#121—181no—
282C2×C4⋊C4—91no—
283C2×C4⋊C4—181no—
284C2×C22⋊C4—181no—
285C2×C22⋊C4—181no—
286C22⋊C8—31no—
287C22⋊C8—61no—
288C22⋊C8D3211yescharacteristic, complemented
289#95—31no—
290#95—91no—
291C23×C3—21no—
292C23×C3—31no—
293C23×C3—31no—
294C23×C3—32no—
295C23×C3—32no—
296C23×C3—61no—
297C23×C3—121no—
298C23×C3—121no—
299C23×C3C2×D1211yescharacteristic
300C23×C3D3×D411yescharacteristic
301C22×D3—21no—
302C22×D3—41no—
303C22×D3—41no—
304C22×D3—61no—
305C22×D3—61no—
306C22×D3—121no—
307C22×D3—122no—
308C22×D3—122no—
309C22×D3—122no—
310C22×D3—122no—
311C22×D3—122no—
312C22×D3—122no—
313C22×D3#20412yes—
314C22×D3D2412yes—
315C22×D3(C2×D3)⋊C411yescharacteristic
316C22×D3(C2×D3)⋊C411yescharacteristic
317C3×D4—121no—
318C3×D4—121no—
319C3×D4—121no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—31no—
323C2×C3×C4—31no—
324C2×C3×C4—41no—
325C2×C3×C4—41no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4—61no—
330C2×C3×C4—81no—
331C2×C3×C4—121no—
332C2×C3×C4—121no—
333C2×C3×C4—121no—
334C2×C3×C4—121no—
335C2×C3×C4—121no—
336C2×C3×C4C2×C4×D311yescharacteristic
337C2×C3×C4C2×C4×D311yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4C2×#6711yescharacteristic
340#67—41no—
341#67—41no—
342#67—122no—
343#67—122no—
344#67—121no—
345#67—121no—
346#67—121no—
347#67—121no—
348#67—122no—
349#67—122no—
350#67—241no—
351#67—241no—
352C2×Dic3—22no—
353C2×Dic3—21no—
354C2×Dic3—41no—
355C2×Dic3—41no—
356C2×Dic3—41no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—121no—
360C2×Dic3—122no—
361C2×Dic3—121no—
362C2×Dic3—121no—
363C2×Dic3—121no—
364C2×Dic3—121no—
365C2×Dic3—122no—
366C2×Dic3—121no—
367C2×Dic3—121no—
368C2×Dic3—241no—
369C2×Dic3—241no—
370C2×Dic3(C2×D3)⋊C411yescharacteristic
371C2×Dic3(C2×D3)⋊C411yescharacteristic
372D12—41no—
373D12—121no—
374D12—121no—
375D12—122no—
376D12—122no—
377D12—241no—
378C4×D3—22no—
379C4×D3—22no—
380C4×D3—41no—
381C4×D3—41no—
382C4×D3—122no—
383C3×C8—41no—
384C3×C8—41no—
385C3×C8—81no—
386C3×C8—121no—
387C3⋊C8—41no—
388C2×C32—21no—
389C2×C32—21no—
390C2×C32C2×#9911yescharacteristic
391C2×C32C2×#10211yescharacteristic
392C2×C32#42111yescharacteristic
393C3⋊D3—81no—
394C3×D3—22no—
395C3×D3—22no—
396C3×D3—81no—
397C24—31no—
398C24—181no—
399C2×D4—31no—
400C2×D4—61no—
401C2×D4—91no—
402C2×D4—181no—
403C2×D4—181no—
404C2×D4—181no—
405C2×D4—181no—
406C2×D4—362no—
407C2×D4—362no—
408C2×D4—362no—
409C22×C4—31no—
410C22×C4—31no—
411C22×C4—31no—
412C22×C4—31no—
413C22×C4—31no—
414C22×C4—61no—
415C22×C4—122no—
416C22×C4—181no—
417C22×C4—181no—
418C22×C4C2×D3211yescharacteristic
419C2×C8—21no—
420C2×C8—61no—
421C2×C8—122no—
422C4⋊C4—31no—
423C4⋊C4—91no—
424C4⋊C4—181no—
425C4⋊C4—362no—
426C22⋊C4—61no—
427C22⋊C4—181no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22⋊C4—362no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—32no—
439C22×C3—32no—
440C22×C3—41no—
441C22×C3—41no—
442C22×C3—61no—
443C22×C3—61no—
444C22×C3—61no—
445C22×C3—61no—
446C22×C3—122no—
447C22×C3—122no—
448C22×C3—121no—
449C22×C3—121no—
450C22×C3—121no—
451C22×C3D3×C22⋊C411yescharacteristic
452C22×C3C2×#20411yescharacteristic
453C22×C3C2×D2411yescharacteristic
454C22×C3D3×D811yescharacteristic
455C22×C3D3×SD1611yescharacteristic
456C22×C3C2×(C2×D3)⋊C411yescharacteristic
457C2×D3—21no—
458C2×D3—21no—
459C2×D3—21no—
460C2×D3—21no—
461C2×D3—42no—
462C2×D3—42no—
463C2×D3—41no—
464C2×D3—41no—
465C2×D3—41no—
466C2×D3—121no—
467C2×D3—121no—
468C2×D3—121no—
469C2×D3—121no—
470C2×D3—121no—
471C2×D3—121no—
472C2×D3—241no—
473C2×D3—241no—
474C2×D3—241no—
475C2×D3—244no—
476C2×D3—244no—
477C2×D3#82112yes—
478C2×D3#82112yes—
479C3×C4—21no—
480C3×C4—21no—
481C3×C4—21no—
482C3×C4—21no—
483C3×C4—32no—
484C3×C4—41no—
485C3×C4—41no—
486C3×C4—61no—
487C3×C4—121no—
488C3×C4—241no—
489Dic3—21no—
490Dic3—41no—
491Dic3—81no—
492Dic3—121no—
493Dic3—121no—
494Dic3—241no—
495Dic3—241no—
496Dic3—241no—
497Dic3—242no—
498Dic3#80612yes—
499C32#151911yescharacteristic, complemented, Sylow
500C23—31no—
501C23—31no—
502C23—32no—
503C23—32no—
504C23—61no—
505C23—121no—
506C23—121no—
507C23—181no—
508C23—362no—
509C23—362no—
510C23—362no—
511C23D3×D1211yescharacteristic
512D4—121no—
513D4—121no—
514D4—121no—
515D4—361no—
516D4—362no—
517D4—362no—
518D4—362no—
519D4—361no—
520D4—361no—
521C2×C4—31no—
522C2×C4—31no—
523C2×C4—41no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—61no—
528C2×C4—121no—
529C2×C4—121no—
530C2×C4—121no—
531C2×C4—121no—
532C2×C4—121no—
533C2×C4—181no—
534C2×C4—362no—
535C2×C4—361no—
536C2×C4—361no—
537C2×C4—361no—
538C2×C4C4×D3211yescharacteristic
539C2×C4D3×#6711yescharacteristic
540C8—41no—
541C8—121no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—41no—
550C2×C3—41no—
551C2×C3—62no—
552C2×C3—62no—
553C2×C3—241no—
554C2×C3D3×#9911yescharacteristic
555C2×C3D3×#10211yescharacteristic
556C2×C3#482111yescharacteristic
557C2×C3C2×#80611yescharacteristic
558C2×C3C2×#82111yescharacteristic
559C2×C3#513911yescharacteristic
560D3—22no—
561D3—22no—
562D3—81no—
563D3—241no—
564D3—241no—
565D3—481no—
566C22—21no—
567C22—21no—
568C22—32no—
569C22—32no—
570C22—61no—
571C22—61no—
572C22—61no—
573C22—61no—
574C22—122no—
575C22—122no—
576C22—121no—
577C22—121no—
578C22—121no—
579C22—361no—
580C22—361no—
581C22—361no—
582C22—724no—
583C22D3×#20411yescharacteristic
584C22D3×D2411yescharacteristic
585C22D3×(C2×D3)⋊C411yescharacteristic
586C4—21no—
587C4—21no—
588C4—32no—
589C4—61no—
590C4—121no—
591C4—241no—
592C4—361no—
593C4—721no—
594C3—21no—
595C3#6830711yescharacteristic, complemented
596C3#6994411yescharacteristic, complemented
597C2—21no—
598C2—21no—
599C2—62no—
600C2—62no—
601C2—241no—
602C2—721no—
603C2D3×#80611yescharacteristic
604C2D3×#82111yescharacteristic
605C2#1059100511yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalD3×#930C2
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1519
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×D3×C22⋊C8C2semidirect
3. #10591295C2semidirect
4. #10589336C2semidirect
5. C3×#4470C2semidirect
6. #10589151C2semidirect
7. #10589150C2semidirect
12. C2×D3×D12C4semidirect
20. #63909C4semidirect
21. #63908C4semidirect
23. D3×C4⋊Dic3C4semidirect
24. C32×C22⋊C8C22semidirect
25. #63658C22semidirect
26. C3×C3⋊#95C22semidirect
27. C3×#830C22semidirect
33. D3×C22⋊C8D3semidirect
42. #4470D3semidirect
111. C3×C22⋊C8C2×D3semidirect
112. C3×C22⋊C8C2×D3semidirect
117. C3⋊#95C2×D3semidirect
118. #830C2×D3semidirect
288. C22⋊C8D32semidirect
499. C32#1519semidirect
595. C3#68307semidirect
596. C3#69944semidirect

Maximal subgroups

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

subgroupindex
D3×#9302
C3×D3×C22⋊C82
#105912952
#105893362
C3×#44702
#105891512
#105891502
#699443
#683073