Finite Group Databasebeta

← #11775400

Subgroups — #11775400

Order 1152.

689 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5791C211yesmaximal, characteristic
2#10592911C211yesmaximal, characteristic, complemented
3C3×#5207C211yesmaximal, characteristic, complemented
4#10589152C212yesmaximal, complemented
5#10589150C212yesmaximal, complemented
6#71709—31nomaximal
7#69979—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C2×C3×#235C411yescharacteristic, complemented
10C2×#3757—21no—
11C2×C4⋊(C3⋊Dic3)—21no—
12C3×#953—21no—
13C3×#930C411yescharacteristic, complemented
14C3×#930C2211yescharacteristic
15C3×#929—21no—
16C3×C4×#67—21no—
17C3×C4×#67—21no—
18C3×#926C411yescharacteristic, complemented
19C3×#924C411yescharacteristic, complemented
20C3×#924C2211yescharacteristic
21C2×C3×#208—21no—
22#63658C2212yes—
23C3×#830—21no—
24C3×#830C2212yes—
25C3×#525—31no—
26#5791D311yescharacteristic
27C3×#407—31no—
28#5212—31no—
29#5212—31no—
30#5212—61no—
31#5207D311yescharacteristic, complemented
32#4538—32no—
33#4537—32no—
34#4470—32no—
35#4467—32no—
36C24×C32D411yescharacteristic
37C22×C32×C4—42no—
38C22×C32×C4C2×C411yescharacteristic
39C22×C32×C4C2×C411yescharacteristic
40C22×C32×C4D411yescharacteristic
41C22×C32×C4D411yescharacteristic
42C22×C32×C4D411yescharacteristic
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3—22no—
45C2×C3×#67—21no—
46C2×C3×#67—21no—
47C2×C3×#67—21no—
48C3×#235—42no—
49C2×C3×D12C2×C411yescharacteristic
50C2×C3×C4×D3—21no—
51C2×C3×Dic6C2×C411yescharacteristic
52#3757—42no—
53C4⋊(C3⋊Dic3)—42no—
54C3×#217—21no—
55C3×#217—21no—
56C3×#217—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×C4⋊Dic3C2×C411yescharacteristic
60C3×C4⋊Dic3C2×C411yescharacteristic
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C3×C4×Dic3—21no—
64C3×#208—42no—
65C2×C3×C3⋊C8—22no—
66#1513—91noSylow
67C2×C3×#41—31no—
68C23×C3×C4—21no—
69C23×C3×C4C2×D311yescharacteristic
70C23×C3×C4C2×D311yescharacteristic
71C2×#235Dic311yescharacteristic, complemented
72C2×C3×M16—61no—
73C3×#123—61no—
74C3×C22⋊Q8—31no—
75C3×C22⋊Q8—31no—
76C3×#121—31no—
77C3×#121—31no—
78C3×#120—61no—
79C3×C4×D4—61no—
80C3×C4×D4—61no—
81C3×#117—31no—
82#953—21no—
83C2×#217—62no—
84C2×#217—61no—
85C2×#217—61no—
86#930Dic311yescharacteristic, complemented
87#930C2×D311yescharacteristic
88#929—21no—
89C4×#67—21no—
90C4×#67—21no—
91#926Dic311yescharacteristic, complemented
92C2×C4⋊Dic3—62no—
93C2×C4⋊Dic3—61no—
94C2×C4⋊Dic3—61no—
95#924Dic311yescharacteristic, complemented
96#924C2×D311yescharacteristic
97C2×#208—21no—
98C3×C22⋊C8—32no—
99C3×C22⋊C8—61no—
100C3⋊#95—32no—
101C3⋊#95—32no—
102C3⋊#95—62no—
103#830—21no—
104#830C2×D312yes—
105C23×C32—21no—
106C23×C32—21no—
107C23×C32—41no—
108C23×C32—41no—
109C23×C32C22⋊C411yescharacteristic
110C23×C32C22⋊C411yescharacteristic
111C23×C32C2×D411yescharacteristic
112C22×C3×D3—21no—
113C2×C32×C4—22no—
114C2×C32×C4—22no—
115C2×C32×C4—22no—
116C2×C32×C4—41no—
117C2×C32×C4—41no—
118C2×C32×C4—41no—
119C2×C32×C4C22⋊C411yescharacteristic
120C2×C32×C4C22⋊C411yescharacteristic
121C2×C32×C4C22×C411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C3⋊Dic3—42no—
124C2×C3⋊Dic3—42no—
125C2×C3⋊Dic3—42no—
126C3×#67—42no—
127C3×#67—42no—
128C3×#67—41no—
129C3×#67—41no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C3×D12—41no—
134C3×C4×D3—42no—
135C3×Dic6—41no—
136C3×C3⋊C8—42no—
137#525—31no—
138#407—31no—
139#380—91no—
140#328—92no—
141#327—92no—
142C24×C3—21no—
143C24×C3D1211yescharacteristic
144C24×C3#6711yescharacteristic
145C3×#41—122no—
146C2×C3×Q8—31no—
147C2×C3×D4—31no—
148C2×C3×D4—61no—
149C2×C3×D4—61no—
150C2×C3×D4—61no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—42no—
158C22×C3×C4—42no—
159C22×C3×C4—44no—
160C22×C3×C4—61no—
161C22×C3×C4C4×D311yescharacteristic
162C22×C3×C4C4×D311yescharacteristic
163C22×C3×C4D1211yescharacteristic
164C22×C3×C4C2×Dic311yescharacteristic
165C22×C3×C4C2×Dic311yescharacteristic
166C22×C3×C4#6711yescharacteristic
167C22×C3×C4#6711yescharacteristic
168C22×C3×C4#6711yescharacteristic
169C22×C3×C4#6711yescharacteristic
170C22×C3×C4#6711yescharacteristic
171C22×C3×C4C22×D311yescharacteristic
172C22×C3×C4C22×D311yescharacteristic
173C2×#67—21no—
174C2×#67—21no—
175C2×#67—21no—
176C22×Dic3—64no—
177C22×Dic3—62no—
178C22×Dic3—62no—
179#235—42no—
180C2×D12C2×Dic311yescharacteristic
181C2×C4×D3—21no—
182C2×Dic6C2×Dic311yescharacteristic
183C3×M16—122no—
184C2×C3×C8—62no—
185C3×C4⋊C4—31no—
186C3×C4⋊C4—31no—
187C3×C4⋊C4—61no—
188C3×C4⋊C4—61no—
189C3×C22⋊C4—61no—
190C3×C22⋊C4—61no—
191C3×C22⋊C4—61no—
192C3×C22⋊C4—61no—
193C3×C22⋊C4—61no—
194C3×C42—61no—
195#217—21no—
196#217—21no—
197#217—21no—
198#217—124no—
199#217—122no—
200#217—122no—
201(C2×D3)⋊C4—21no—
202(C2×D3)⋊C4—21no—
203C4⋊Dic3—124no—
204C4⋊Dic3—122no—
205C4⋊Dic3—122no—
206C4⋊Dic3C2×Dic311yescharacteristic
207C4⋊Dic3C2×Dic311yescharacteristic
208Dic3⋊C4—21no—
209Dic3⋊C4—21no—
210C4×Dic3—21no—
211#208—42no—
212C2×C3⋊C8—22no—
213C22×C32—21no—
214C22×C32—21no—
215C22×C32—21no—
216C22×C32—21no—
217C22×C32—21no—
218C22×C32—21no—
219C22×C32—21no—
220C22×C32—21no—
221C22×C32—42no—
222C22×C32—42no—
223C22×C32C2×C22⋊C411yescharacteristic
224C22×C32AGL(1,ℤ/8)11yescharacteristic
225C22×C32#13711yescharacteristic
226C2×C3×D3—41no—
227C2×C3×D3—41no—
228C2×C3×D3—41no—
229C32×C4—21no—
230C32×C4—21no—
231C32×C4—21no—
232C32×C4#9912yes—
233C3⋊Dic3—82no—
234C3×Dic3—41no—
235C3×Dic3—41no—
236C3×Dic3—41no—
237C2×#41—31no—
238C23×C4D3211yescharacteristic
239C2×M16—61no—
240#123—61no—
241C22⋊Q8—31no—
242C22⋊Q8—31no—
243#121—31no—
244#121—31no—
245#120—61no—
246C4×D4—61no—
247C4×D4—61no—
248#117—31no—
249C2×C4⋊C4—181no—
250C2×C22⋊C4—181no—
251C22⋊C8—32no—
252C22⋊C8—61no—
253#95—92no—
254C23×C3—22no—
255C23×C3—22no—
256C23×C3—21no—
257C23×C3—21no—
258C23×C3—21no—
259C23×C3—21no—
260C23×C3—21no—
261C23×C3—21no—
262C23×C3—21no—
263C23×C3—41no—
264C23×C3—41no—
265C23×C3—41no—
266C23×C3—41no—
267C23×C3—42no—
268C23×C3—42no—
269C23×C3—61no—
270C23×C3(C2×D3)⋊C411yescharacteristic
271C23×C3(C2×D3)⋊C411yescharacteristic
272C23×C3#21711yescharacteristic
273C23×C3#21711yescharacteristic
274C23×C3C2×D1211yescharacteristic
275C23×C3C2×#6711yescharacteristic
276C22×D3—21no—
277C3×Q8—121no—
278C3×D4—121no—
279C3×D4—122no—
280C3×D4—122no—
281C3×D4—121no—
282C3×D4—121no—
283C2×C3×C4—24no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—42no—
295C2×C3×C4—42no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—41no—
302C2×C3×C4—42no—
303C2×C3×C4—42no—
304C2×C3×C4—42no—
305C2×C3×C4—61no—
306C2×C3×C4—61no—
307C2×C3×C4—61no—
308C2×C3×C4—122no—
309C2×C3×C4(C2×D3)⋊C411yescharacteristic
310C2×C3×C4(C2×D3)⋊C411yescharacteristic
311C2×C3×C4#21711yescharacteristic
312C2×C3×C4#21711yescharacteristic
313C2×C3×C4C2×C4×D311yescharacteristic
314C2×C3×C4C22×Dic311yescharacteristic
315C2×C3×C4C2×#6711yescharacteristic
316C2×C3×C4C2×#6711yescharacteristic
317#67—42no—
318#67—42no—
319#67—41no—
320#67—41no—
321C2×Dic3—21no—
322C2×Dic3—21no—
323C2×Dic3—21no—
324C2×Dic3—124no—
325C2×Dic3—122no—
326C2×Dic3—122no—
327C2×Dic3—124no—
328C2×Dic3—124no—
329C2×Dic3—122no—
330C2×Dic3—122no—
331C2×Dic3—122no—
332C2×Dic3—122no—
333D12—41no—
334C4×D3—42no—
335Dic6—41no—
336C3×C8—122no—
337C3⋊C8—42no—
338C2×C32—21no—
339C2×C32—21no—
340C2×C32—41no—
341C2×C32—41no—
342C2×C32C2×#9911yescharacteristic
343C2×C32#41711yescharacteristic
344C2×C32#42111yescharacteristic
345C3×D3—81no—
346C24#62611yescharacteristic
347#41—122no—
348C2×Q8—31no—
349C2×D4—31no—
350C2×D4—61no—
351C2×D4—61no—
352C2×D4—61no—
353C22×C4—42no—
354C22×C4—61no—
355C22×C4—182no—
356C22×C4D3×Dic311yescharacteristic
357C22×C4D3×Dic311yescharacteristic
358C22×C4#62511yescharacteristic
359C22×C4#62511yescharacteristic
360C22×C4#62611yescharacteristic
361C22×C4C2×D3211yescharacteristic
362M16—122no—
363C2×C8—62no—
364C4⋊C4—31no—
365C4⋊C4—31no—
366C4⋊C4—61no—
367C4⋊C4—61no—
368C4⋊C4—362no—
369C22⋊C4—61no—
370C22⋊C4—61no—
371C22⋊C4—61no—
372C22⋊C4—61no—
373C22⋊C4—61no—
374C22⋊C4—362no—
375C42—61no—
376C22×C3—22no—
377C22×C3—22no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—22no—
383C22×C3—22no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—41no—
400C22×C3—41no—
401C22×C3—41no—
402C22×C3—41no—
403C22×C3—44no—
404C22×C3—44no—
405C22×C3—42no—
406C22×C3—42no—
407C22×C3—42no—
408C22×C3—42no—
409C22×C3—121no—
410C22×C3—121no—
411C22×C3—121no—
412C22×C3#90811yescharacteristic
413C22×C3#90911yescharacteristic
414C22×C3C2×(C2×D3)⋊C411yescharacteristic
415C22×C3#94911yescharacteristic
416C22×C3#95111yescharacteristic
417C22×C3C2×#21711yescharacteristic
418C2×D3—41no—
419C2×D3—41no—
420C2×D3—41no—
421C3×C4—22no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—22no—
429C3×C4—41no—
430C3×C4—41no—
431C3×C4—121no—
432C3×C4—121no—
433C3×C4—121no—
434C3×C4#80612yes—
435C3×C4#83412yes—
436Dic3—41no—
437Dic3—41no—
438Dic3—41no—
439Dic3—244no—
440Dic3—242no—
441Dic3—242no—
442C32#151311yescharacteristic, complemented, Sylow
443C23—21no—
444C23—21no—
445C23—41no—
446C23—41no—
447C23—61no—
448C23(C2×D3)⋊Dic311yescharacteristic
449C23(C2×D3)⋊Dic311yescharacteristic
450C23C2×#62611yescharacteristic
451Q8—121no—
452D4—121no—
453D4—122no—
454D4—122no—
455D4—121no—
456D4—121no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—61no—
464C2×C4—61no—
465C2×C4—61no—
466C2×C4—122no—
467C2×C4—362no—
468C2×C4—362no—
469C2×C4—362no—
470C2×C4(C2×D3)⋊Dic311yescharacteristic
471C2×C4(C2×D3)⋊Dic311yescharacteristic
472C2×C4C2×D3×Dic311yescharacteristic
473C2×C4C2×#62511yescharacteristic
474C8—122no—
475C2×C3—22no—
476C2×C3—22no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—42no—
485C2×C3—42no—
486C2×C3—41no—
487C2×C3—41no—
488C2×C3—41no—
489C2×C3—41no—
490C2×C3—241no—
491C2×C3C2×#80611yescharacteristic
492C2×C3#513311yescharacteristic
493C2×C3#513911yescharacteristic
494C2×C3C2×#83411yescharacteristic
495C2×C3#523211yescharacteristic
496C2×C3#523611yescharacteristic
497D3—81no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—42no—
507C22—42no—
508C22—121no—
509C22—121no—
510C22—121no—
511C22#6382511yescharacteristic
512C22#6383111yescharacteristic
513C22C2×(C2×D3)⋊Dic311yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—121no—
518C4—121no—
519C4—121no—
520C4—722no—
521C4#6358012yes—
522C3—21no—
523C3#6997911yescharacteristic, complemented
524C3#7170911yescharacteristic, complemented
525C2—21no—
526C2—21no—
527C2—41no—
528C2—41no—
529C2—241no—
530C2#1059108811yescharacteristic
531C2#1059111011yescharacteristic
532C2C2×#6358011yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊Dic3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#5791C2
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1513
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #10592911C2semidirect
3. C3×#5207C2semidirect
4. #10589152C2semidirect
5. #10589150C2semidirect
9. C2×C3×#235C4semidirect
13. C3×#930C4semidirect
18. C3×#926C4semidirect
19. C3×#924C4semidirect
31. #5207D3semidirect
71. C2×#235Dic3semidirect
86. #930Dic3semidirect
91. #926Dic3semidirect
95. #924Dic3semidirect
442. C32#1513semidirect
523. C3#69979semidirect
524. C3#71709semidirect

Maximal subgroups

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

subgroupindex
C3×#57912
#105929112
C3×#52072
#105891522
#105891502
#717093
#699793