Finite Group Databasebeta

← #11775402

Subgroups — #11775402

Order 1152.

667 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5791C211yesmaximal, characteristic
2#10592906C211yesmaximal, characteristic, complemented
3C3×#5212C211yesmaximal, characteristic, complemented
4#10589153C212yesmaximal, complemented
5#10589149C212yesmaximal, complemented
6#71709—31nomaximal
7#69508—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C2×C3×#235C411yescharacteristic, complemented
10C2×#3748—21no—
11C3×#953—21no—
12C2×C3×#217—21no—
13C3×#930C411yescharacteristic, complemented
14C3×#930C2211yescharacteristic
15C3×#929—21no—
16C3×C4×#67—21no—
17C3×C4×#67—21no—
18C3×#926C411yescharacteristic, complemented
19C2×C3×C4⋊Dic3—21no—
20C3×#924C411yescharacteristic, complemented
21C3×#924C2211yescharacteristic
22#63657—21no—
23#63657C2212yes—
24C3×C3⋊#95C2212yes—
25C3×#525—31no—
26#5791D311yescharacteristic
27C3×#380—31no—
28#5212D311yescharacteristic, complemented
29#5207—31no—
30#5207—31no—
31#5207—61no—
32#4538—32no—
33#4537—32no—
34#4452—32no—
35#4451—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
44C2×C3×#67—21no—
45C2×C3×#67—21no—
46C2×C3×#67—21no—
47C22×C3×Dic3—22no—
48C3×#235—42no—
49C2×C3×D12C2×C411yescharacteristic
50C2×C3×C4×D3—21no—
51C2×C3×Dic6C2×C411yescharacteristic
52#3748—42no—
53C2×C3⋊(C3⋊C8)—22no—
54C3×#217—21no—
55C3×#217—21no—
56C3×#217—21no—
57C3×#217—42no—
58C3×(C2×D3)⋊C4—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3—42no—
61C3×C4⋊Dic3C2×C411yescharacteristic
62C3×C4⋊Dic3C2×C411yescharacteristic
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C3×C4×Dic3—21no—
66#1513—91noSylow
67C2×C3×#41—31no—
68C23×C3×C4—21no—
69C23×C3×C4C2×D311yescharacteristic
70C23×C3×C4C2×D311yescharacteristic
71C2×#235Dic311yescharacteristic, complemented
72C3×#123—61no—
73C3×C22⋊Q8—31no—
74C3×C22⋊Q8—31no—
75C3×#121—31no—
76C3×#121—31no—
77C3×#120—61no—
78C3×C4×D4—61no—
79C3×C4×D4—61no—
80C3×#117—31no—
81C2×C3×C4⋊C4—61no—
82C2×C3×C22⋊C4—61no—
83#953—21no—
84C2×#217—21no—
85#930Dic311yescharacteristic, complemented
86#930C2×D311yescharacteristic
87#929—21no—
88C4×#67—21no—
89C4×#67—21no—
90#926Dic311yescharacteristic, complemented
91C2×C4⋊Dic3—21no—
92#924Dic311yescharacteristic, complemented
93#924C2×D311yescharacteristic
94C2×#208—62no—
95C2×#208—61no—
96C2×#208—61no—
97C3×#95—32no—
98C3⋊#95C2×D312yes—
99#830—32no—
100#830—32no—
101#830—62no—
102#830—62no—
103#830—61no—
104#830—61no—
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
123C3×#67—42no—
124C3×#67—42no—
125C3×#67—41no—
126C3×#67—41no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—42no—
131C2×C3×Dic3—42no—
132C2×C3×Dic3—42no—
133C3×D12—41no—
134C3×C4×D3—42no—
135C3×Dic6—41no—
136C3⋊(C3⋊C8)—42no—
137#525—31no—
138#407—91no—
139#380—31no—
140#328—92no—
141#327—92no—
142C24×C3—21no—
143C24×C3#6711yescharacteristic
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×C4—62no—
162C22×C3×C4C4×D311yescharacteristic
163C22×C3×C4C4×D311yescharacteristic
164C22×C3×C4D1211yescharacteristic
165C22×C3×C4D1211yescharacteristic
166C22×C3×C4C2×Dic311yescharacteristic
167C22×C3×C4C2×Dic311yescharacteristic
168C22×C3×C4#6711yescharacteristic
169C22×C3×C4#6711yescharacteristic
170C22×C3×C4#6711yescharacteristic
171C22×C3×C4#6711yescharacteristic
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C22×D311yescharacteristic
174C2×#67—21no—
175C2×#67—21no—
176C2×#67—21no—
177C22×Dic3—22no—
178#235—42no—
179C2×D12C2×Dic311yescharacteristic
180C2×C4×D3—21no—
181C2×Dic6C2×Dic311yescharacteristic
182C3×C4⋊C4—31no—
183C3×C4⋊C4—31no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—122no—
187C3×C22⋊C4—61no—
188C3×C22⋊C4—61no—
189C3×C22⋊C4—61no—
190C3×C22⋊C4—61no—
191C3×C22⋊C4—61no—
192C3×C22⋊C4—122no—
193C3×C42—61no—
194#217—21no—
195#217—21no—
196#217—21no—
197#217—42no—
198(C2×D3)⋊C4—21no—
199(C2×D3)⋊C4—21no—
200C4⋊Dic3—42no—
201C4⋊Dic3C2×Dic311yescharacteristic
202C4⋊Dic3C2×Dic311yescharacteristic
203Dic3⋊C4—21no—
204Dic3⋊C4—21no—
205C4×Dic3—21no—
206#208—124no—
207#208—122no—
208#208—122no—
209C2×C3⋊C8—64no—
210C2×C3⋊C8—62no—
211C2×C3⋊C8—62no—
212C22×C32—21no—
213C22×C32—21no—
214C22×C32—21no—
215C22×C32—21no—
216C22×C32—21no—
217C22×C32—21no—
218C22×C32—21no—
219C22×C32—21no—
220C22×C32—42no—
221C22×C32—42no—
222C22×C32C2×C22⋊C411yescharacteristic
223C22×C32AGL(1,ℤ/8)11yescharacteristic
224C22×C32#13711yescharacteristic
225C2×C3×D3—41no—
226C2×C3×D3—41no—
227C2×C3×D3—41no—
228C32×C4—21no—
229C32×C4—21no—
230C32×C4—21no—
231C32×C4#9912yes—
232C3×Dic3—41no—
233C3×Dic3—41no—
234C3×Dic3—41no—
235C3×Dic3—82no—
236C2×#41—31no—
237C23×C4D3211yescharacteristic
238C2×M16—181no—
239#123—61no—
240C22⋊Q8—31no—
241C22⋊Q8—31no—
242#121—31no—
243#121—31no—
244#120—61no—
245C4×D4—61no—
246C4×D4—61no—
247#117—31no—
248C2×C4⋊C4—61no—
249C2×C22⋊C4—61no—
250C22⋊C8—92no—
251C22⋊C8—181no—
252#95—32no—
253C23×C3—21no—
254C23×C3—21no—
255C23×C3—21no—
256C23×C3—21no—
257C23×C3—21no—
258C23×C3—21no—
259C23×C3—21no—
260C23×C3—41no—
261C23×C3—41no—
262C23×C3—41no—
263C23×C3—41no—
264C23×C3—41no—
265C23×C3—41no—
266C23×C3—42no—
267C23×C3—42no—
268C23×C3—61no—
269C23×C3(C2×D3)⋊C411yescharacteristic
270C23×C3(C2×D3)⋊C411yescharacteristic
271C23×C3#21711yescharacteristic
272C23×C3#21711yescharacteristic
273C23×C3C2×#6711yescharacteristic
274C23×C3C2×#6711yescharacteristic
275C22×D3—21no—
276C3×Q8—121no—
277C3×D4—121no—
278C3×D4—122no—
279C3×D4—122no—
280C3×D4—121no—
281C3×D4—121no—
282C2×C3×C4—24no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—42no—
294C2×C3×C4—42no—
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—42no—
302C2×C3×C4—42no—
303C2×C3×C4—42no—
304C2×C3×C4—61no—
305C2×C3×C4—61no—
306C2×C3×C4—61no—
307C2×C3×C4—122no—
308C2×C3×C4—122no—
309C2×C3×C4—122no—
310C2×C3×C4—122no—
311C2×C3×C4(C2×D3)⋊C411yescharacteristic
312C2×C3×C4(C2×D3)⋊C411yescharacteristic
313C2×C3×C4#21711yescharacteristic
314C2×C3×C4#21711yescharacteristic
315C2×C3×C4C2×C4×D311yescharacteristic
316C2×C3×C4C2×D1211yescharacteristic
317C2×C3×C4C22×Dic311yescharacteristic
318C2×C3×C4C2×#6711yescharacteristic
319#67—42no—
320#67—42no—
321#67—41no—
322#67—41no—
323C2×Dic3—21no—
324C2×Dic3—21no—
325C2×Dic3—21no—
326C2×Dic3—42no—
327C2×Dic3—42no—
328C2×Dic3—42no—
329D12—41no—
330C4×D3—42no—
331Dic6—41no—
332C3⋊C8—124no—
333C3⋊C8—122no—
334C3⋊C8—122no—
335C2×C32—21no—
336C2×C32—21no—
337C2×C32—41no—
338C2×C32—41no—
339C2×C32C2×#9911yescharacteristic
340C2×C32#41711yescharacteristic
341C2×C32#42111yescharacteristic
342C3×D3—81no—
343C24#62511yescharacteristic
344#41—122no—
345C2×Q8—31no—
346C2×D4—31no—
347C2×D4—61no—
348C2×D4—61no—
349C2×D4—61no—
350C22×C4—42no—
351C22×C4—61no—
352C22×C4—62no—
353C22×C4D3×Dic311yescharacteristic
354C22×C4D3×Dic311yescharacteristic
355C22×C4#62511yescharacteristic
356C22×C4#62611yescharacteristic
357C22×C4#62611yescharacteristic
358C22×C4C2×D3211yescharacteristic
359M16—362no—
360C2×C8—182no—
361C4⋊C4—31no—
362C4⋊C4—31no—
363C4⋊C4—61no—
364C4⋊C4—61no—
365C4⋊C4—122no—
366C22⋊C4—61no—
367C22⋊C4—61no—
368C22⋊C4—61no—
369C22⋊C4—61no—
370C22⋊C4—61no—
371C22⋊C4—122no—
372C42—61no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—22no—
378C22×C3—22no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
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—41no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—42no—
401C22×C3—42no—
402C22×C3—42no—
403C22×C3—42no—
404C22×C3—44no—
405C22×C3—44no—
406C22×C3—121no—
407C22×C3—121no—
408C22×C3—121no—
409C22×C3C2×(C2×D3)⋊C411yescharacteristic
410C22×C3#93211yescharacteristic
411C22×C3#94211yescharacteristic
412C22×C3#94911yescharacteristic
413C22×C3#95111yescharacteristic
414C22×C3C2×#21711yescharacteristic
415C2×D3—41no—
416C2×D3—41no—
417C2×D3—41no—
418C3×C4—22no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—22no—
426C3×C4—41no—
427C3×C4—41no—
428C3×C4—121no—
429C3×C4—121no—
430C3×C4—121no—
431C3×C4—242no—
432C3×C4#80612yes—
433C3×C4#83412yes—
434Dic3—41no—
435Dic3—41no—
436Dic3—41no—
437Dic3—82no—
438C32#151311yescharacteristic, complemented, Sylow
439C23—21no—
440C23—21no—
441C23—41no—
442C23—41no—
443C23—61no—
444C23(C2×D3)⋊Dic311yescharacteristic
445C23(C2×D3)⋊Dic311yescharacteristic
446C23C2×#62511yescharacteristic
447Q8—121no—
448D4—121no—
449D4—122no—
450D4—122no—
451D4—121no—
452D4—121no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—61no—
460C2×C4—61no—
461C2×C4—61no—
462C2×C4—122no—
463C2×C4—122no—
464C2×C4—122no—
465C2×C4—122no—
466C2×C4(C2×D3)⋊Dic311yescharacteristic
467C2×C4(C2×D3)⋊Dic311yescharacteristic
468C2×C4C2×D3×Dic311yescharacteristic
469C2×C4C2×#62611yescharacteristic
470C8—362no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—41no—
479C2×C3—41no—
480C2×C3—42no—
481C2×C3—42no—
482C2×C3—41no—
483C2×C3—41no—
484C2×C3—41no—
485C2×C3—41no—
486C2×C3—241no—
487C2×C3C2×#80611yescharacteristic
488C2×C3#496611yescharacteristic
489C2×C3#500511yescharacteristic
490C2×C3C2×#83411yescharacteristic
491C2×C3#523211yescharacteristic
492C2×C3#523611yescharacteristic
493D3—81no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—42no—
503C22—42no—
504C22—121no—
505C22—121no—
506C22—121no—
507C22#6382311yescharacteristic
508C22#6382711yescharacteristic
509C22C2×(C2×D3)⋊Dic311yescharacteristic
510C4—21no—
511C4—21no—
512C4—21no—
513C4—121no—
514C4—121no—
515C4—121no—
516C4—242no—
517C4#6358012yes—
518C3—21no—
519C3#6950811yescharacteristic, complemented
520C3#7170911yescharacteristic, complemented
521C2—21no—
522C2—21no—
523C2—41no—
524C2—41no—
525C2—241no—
526C2#1059108711yescharacteristic
527C2#1059111111yescharacteristic
528C2C2×#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. #10592906C2semidirect
3. C3×#5212C2semidirect
4. #10589153C2semidirect
5. #10589149C2semidirect
9. C2×C3×#235C4semidirect
13. C3×#930C4semidirect
18. C3×#926C4semidirect
20. C3×#924C4semidirect
28. #5212D3semidirect
71. C2×#235Dic3semidirect
85. #930Dic3semidirect
90. #926Dic3semidirect
92. #924Dic3semidirect
438. C32#1513semidirect
519. C3#69508semidirect
520. C3#71709semidirect

Maximal subgroups

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

subgroupindex
C3×#57912
#105929062
C3×#52122
#105891532
#105891492
#717093
#695083