Finite Group Databasebeta

← D3×#4726 #11857360

Subgroups — D3×#4726 #11857360

Order 1152.

2111 conjugacy classes of subgroups.

The subgroup lattice has 953 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D32C211yesmaximal, characteristic
2C2×D3×ΓL(1,𝔽25)C212yesmaximal, complemented
3#10592425C211yesmaximal, characteristic, complemented
4C3×#4726C211yesmaximal, characteristic, complemented
5C3×D3×C22⋊C8C211yesmaximal, characteristic, complemented
6#10591159C211yesmaximal, characteristic, complemented
7#10591154C211yesmaximal, characteristic, complemented
8D3×#830C211yesmaximal, characteristic, complemented
9#10590937C212yesmaximal, complemented
10#10590936C212yesmaximal, complemented
11D3×(C2×D3)⋊C8C212yesmaximal, complemented
12D3×#407—31nomaximal
13C2×#4726—31nomaximal
14C23×D32C411yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C22×#624C411yescharacteristic
19C22×D3×Dic3C411yescharacteristic
20C22×D3×Dic3C411yescharacteristic
21C2×C4×D32—28no—
22C2×C4×D32C411yescharacteristic
23C2×C4×D32C411yescharacteristic
24C2×C4×D32C411yescharacteristic
25C2×C4×D32C411yescharacteristic
26C2×C4×D32C2211yescharacteristic
27C2×C4×D32C2211yescharacteristic
28C2×C4×D32C2211yescharacteristic
29C2×C4×D32C2211yescharacteristic
30C2×#3743C2212yescomplemented
31C2×C3×ΓL(1,𝔽25)C2212yescomplemented
32C2×C3×D3×C8C2212yescomplemented
33C2×#3712C2212yescomplemented
34C2×#3711C2212yescomplemented
35C2×D3×C3⋊C8C2212yescomplemented
36D3×ΓL(1,𝔽25)—28no—
37C32×C22⋊C8C2211yescharacteristic, complemented
38#63657C2211yescharacteristic, complemented
39#63647C2212yescomplemented
40C3×#830C2211yescharacteristic, complemented
41C3×#830C2211yescharacteristic, complemented
42C3×(C2×D3)⋊C8C2212yescomplemented
43C3×(C2×D3)⋊C8C2212yescomplemented
44#63557C2212yescomplemented
45(C2×D3)⋊(C3⋊C8)C2212yescomplemented
46(C2×D3)⋊(C3⋊C8)C2212yescomplemented
47C23×C4×D3—31no—
48C23×C4×D3—31no—
49C2×D3×M16—32no—
50C22×ΓL(1,𝔽25)—32no—
51C3×#407—31no—
52C2×C3×C22⋊C8—31no—
53#5207—31no—
54C2×#830—31no—
55#5126—32no—
56C2×(C2×D3)⋊C8—32no—
57#4726—31no—
58#4726—32no—
59#4726—31no—
60#4726—31no—
61#4726—31no—
62#4726—31no—
63#4726—32no—
64#4726—32no—
65#4726—61no—
66#4726D311yescharacteristic, direct product factor
67D3×C22⋊C8—31no—
68D3×C22⋊C8—32no—
69D3×C22⋊C8D311yescharacteristic, complemented
70C23×C3⋊D3C2×C411yescharacteristic
71C23×C3×D3C2×C411yescharacteristic
72C23×C3×D3C2×C411yescharacteristic
73C22×D32—24no—
74C22×D32—24no—
75C22×D32—24no—
76C22×D32C2×C411yescharacteristic
77C22×D32C2×C411yescharacteristic
78C22×D32C2×C411yescharacteristic
79C22×D32C2×C411yescharacteristic
80C22×C32×C4C2311yescharacteristic
81C22×C3⋊Dic3C2×C411yescharacteristic
82C2×C4×C3⋊D3—24no—
83C2×C4×C3⋊D3C2×C411yescharacteristic
84C2×C4×C3⋊D3C2×C411yescharacteristic
85C2×C4×C3⋊D3C2311yescharacteristic
86C2×C4×C3⋊D3C2311yescharacteristic
87C22×C3×Dic3C2×C411yescharacteristic
88C22×C3×Dic3C2×C411yescharacteristic
89C2×C3×C4×D3—24no—
90C2×C3×C4×D3—24no—
91C2×C3×C4×D3C2×C411yescharacteristic
92C2×C3×C4×D3C2×C411yescharacteristic
93C2×C3×C4×D3C2×C411yescharacteristic
94C2×C3×C4×D3C2×C411yescharacteristic
95C2×C3×C4×D3C2311yescharacteristic
96C2×C3×C4×D3C2311yescharacteristic
97C2×C3×C4×D3C2311yescharacteristic
98C2×C3×C4×D3C2311yescharacteristic
99C2×#624—24no—
100C2×#624C2×C411yescharacteristic
101C2×#624C2×C411yescharacteristic
102C2×#624C2×C411yescharacteristic
103C2×#624C2×C411yescharacteristic
104C2×D3×Dic3—24no—
105C2×D3×Dic3—24no—
106C2×D3×Dic3C2×C411yescharacteristic
107C2×D3×Dic3C2×C411yescharacteristic
108C2×D3×Dic3C2×C411yescharacteristic
109C2×D3×Dic3C2×C411yescharacteristic
110C2×D3×Dic3C2×C411yescharacteristic
111C2×D3×Dic3C2×C411yescharacteristic
112C2×D3×Dic3C2×C411yescharacteristic
113C2×D3×Dic3C2×C411yescharacteristic
114C4×D32—24no—
115C4×D32—24no—
116C4×D32—24no—
117C4×D32—24no—
118C4×D32—24no—
119C4×D32—24no—
120C4×D32—24no—
121C4×D32D418yes—
122C2×C32×C8C2312yescomplemented
123C2×C3⋊(C3⋊C8)C2312yescomplemented
124#3743—24no—
125C2×C3×C3⋊C8C2312yescomplemented
126C2×C3×C3⋊C8C2312yescomplemented
127C3×ΓL(1,𝔽25)—24no—
128C3×D3×C8—24no—
129#3712—24no—
130#3711—24no—
131D3×C3⋊C8—24no—
132C2×#407—91noSylow
133C24×D3—31no—
134C24×D3—31no—
135C23×C3×C4—31no—
136C23×C3×C4—31no—
137C23×Dic3—31no—
138C23×Dic3—31no—
139C22×C4×D3—31no—
140C22×C4×D3—31no—
141C22×C4×D3—31no—
142C22×C4×D3—31no—
143C22×C4×D3—31no—
144C22×C4×D3—31no—
145C22×C4×D3—31no—
146C22×C4×D3—31no—
147C22×C4×D3—31no—
148C22×C4×D3—31no—
149C22×C4×D3—31no—
150C22×C4×D3—31no—
151C22×C4×D3—31no—
152C22×C4×D3—31no—
153C22×C4×D3—31no—
154C22×C4×D3—31no—
155C22×C4×D3—31no—
156C22×C4×D3—31no—
157C22×C4×D3—31no—
158C22×C4×D3—31no—
159C22×C4×D3—31no—
160C22×C4×D3—31no—
161C22×C4×D3—61no—
162C22×C4×D3—68no—
163C22×C4×D3—68no—
164C22×C4×D3C2×D311yescharacteristic
165C22×C4×D3C2×D311yescharacteristic
166C2×C3×M16—32no—
167C22×C3×C8—32no—
168C2×#208—32no—
169C22×C3⋊C8—32no—
170D3×M16—68no—
171C2×ΓL(1,𝔽25)—32no—
172C2×ΓL(1,𝔽25)—32no—
173C2×ΓL(1,𝔽25)—32no—
174C2×ΓL(1,𝔽25)—32no—
175C2×ΓL(1,𝔽25)—32no—
176C2×ΓL(1,𝔽25)—62no—
177C2×ΓL(1,𝔽25)—68no—
178C2×ΓL(1,𝔽25)C2×D312yescomplemented
179C2×D3×C8—32no—
180C2×D3×C8C2×D312yescomplemented
181C3×C22⋊C8—21no—
182C3×C22⋊C8—31no—
183C3×C22⋊C8—31no—
184C3×C22⋊C8—32no—
185C3×C22⋊C8—32no—
186C3×C22⋊C8C2×D311yescharacteristic, complemented
187C3×C22⋊C8C2×D311yescharacteristic, complemented
188#830—31no—
189#830—31no—
190#830—32no—
191#830—32no—
192#830—61no—
193#830C2×D311yescharacteristic, complemented
194#830C2×D311yescharacteristic, complemented
195(C2×D3)⋊C8—32no—
196(C2×D3)⋊C8—32no—
197(C2×D3)⋊C8—32no—
198(C2×D3)⋊C8—32no—
199(C2×D3)⋊C8—32no—
200(C2×D3)⋊C8—32no—
201(C2×D3)⋊C8—62no—
202(C2×D3)⋊C8C2×D312yescomplemented
203(C2×D3)⋊C8C2×D312yescomplemented
204C23×C32C22×C411yescharacteristic
205C22×C3⋊D3—22no—
206C22×C3⋊D3—22no—
207C22×C3⋊D3—22no—
208C22×C3⋊D3C22×C411yescharacteristic
209C22×C3⋊D3C22×C411yescharacteristic
210C22×C3×D3—22no—
211C22×C3×D3—22no—
212C22×C3×D3—22no—
213C22×C3×D3—22no—
214C22×C3×D3—22no—
215C22×C3×D3M1614yescomplemented
216C22×C3×D3C22×C411yescharacteristic
217C22×C3×D3C22×C411yescharacteristic
218C22×C3×D3C22×C411yescharacteristic
219C22×C3×D3C22×C411yescharacteristic
220C2×D32—232no—
221C2×D32—22no—
222C2×D32—22no—
223C2×D32—22no—
224C2×D32—22no—
225C2×D32—22no—
226C2×D32—22no—
227C2×D32—22no—
228C2×D32—22no—
229C2×D32—22no—
230C2×D32—22no—
231C2×D32C22⋊C414yes—
232C2×D32M1614yescomplemented
233C2×C32×C4—22no—
234C2×C32×C4C22×C411yescharacteristic
235C2×C32×C4C2411yescharacteristic
236C2×C3⋊Dic3—22no—
237C2×C3⋊Dic3C22×C411yescharacteristic
238C2×C3⋊Dic3C22×C411yescharacteristic
239C4×C3⋊D3—22no—
240C4×C3⋊D3—22no—
241C4×C3⋊D3—22no—
242C4×C3⋊D3C2×D414yes—
243C2×C3×Dic3—22no—
244C2×C3×Dic3—22no—
245C2×C3×Dic3C22×C411yescharacteristic
246C2×C3×Dic3C22×C411yescharacteristic
247C2×C3×Dic3C22×C411yescharacteristic
248C2×C3×Dic3C22×C411yescharacteristic
249C3×C4×D3—22no—
250C3×C4×D3—22no—
251C3×C4×D3—22no—
252C3×C4×D3—22no—
253C3×C4×D3—22no—
254C3×C4×D3—22no—
255C3×C4×D3C2×D414yes—
256C3×C4×D3C2×D414yes—
257#624—22no—
258#624—22no—
259#624—22no—
260#624C22⋊C414yes—
261D3×Dic3—22no—
262D3×Dic3—22no—
263D3×Dic3—22no—
264D3×Dic3—22no—
265D3×Dic3—22no—
266D3×Dic3—22no—
267D3×Dic3C22⋊C414yes—
268D3×Dic3C22⋊C414yes—
269C32×C8—22no—
270C3⋊(C3⋊C8)—22no—
271C3×C3⋊C8—22no—
272C3×C3⋊C8—22no—
273C24×C4—91no—
274C22×M16—92no—
275#407—31no—
276#407—91no—
277#407—92no—
278#407—92no—
279#407—91no—
280#407—91no—
281C2×C22⋊C8—31no—
282C2×C22⋊C8—92no—
283C2×C22⋊C8—91no—
284C24×C3—31no—
285C24×C3—31no—
286C23×D3—31no—
287C23×D3—31no—
288C23×D3—31no—
289C23×D3—31no—
290C23×D3—31no—
291C23×D3—31no—
292C23×D3—31no—
293C23×D3—31no—
294C23×D3—31no—
295C23×D3—31no—
296C23×D3—61no—
297C23×D3—64no—
298C23×D3—64no—
299C23×D3—64no—
300C23×D3—64no—
301C23×D3—64no—
302C23×D3—64no—
303C23×D3C4×D311yescharacteristic
304C23×D3C4×D311yescharacteristic
305C22×C3×C4—21no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—64no—
317C22×C3×C4—64no—
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C22×Dic3—31no—
321C22×Dic3—31no—
322C22×Dic3—31no—
323C22×Dic3—31no—
324C22×Dic3—31no—
325C22×Dic3—31no—
326C22×Dic3—31no—
327C22×Dic3—31no—
328C22×Dic3—31no—
329C22×Dic3—31no—
330C22×Dic3—61no—
331C22×Dic3—64no—
332C22×Dic3—64no—
333C22×Dic3C4×D311yescharacteristic
334C22×Dic3C4×D311yescharacteristic
335C2×C4×D3—24no—
336C2×C4×D3—24no—
337C2×C4×D3—31no—
338C2×C4×D3—31no—
339C2×C4×D3—31no—
340C2×C4×D3—31no—
341C2×C4×D3—31no—
342C2×C4×D3—31no—
343C2×C4×D3—38no—
344C2×C4×D3—38no—
345C2×C4×D3—31no—
346C2×C4×D3—31no—
347C2×C4×D3—31no—
348C2×C4×D3—31no—
349C2×C4×D3—31no—
350C2×C4×D3—31no—
351C2×C4×D3—31no—
352C2×C4×D3—31no—
353C2×C4×D3—31no—
354C2×C4×D3—31no—
355C2×C4×D3—31no—
356C2×C4×D3—31no—
357C2×C4×D3—31no—
358C2×C4×D3—31no—
359C2×C4×D3—31no—
360C2×C4×D3—31no—
361C2×C4×D3—31no—
362C2×C4×D3—31no—
363C2×C4×D3—61no—
364C2×C4×D3—61no—
365C2×C4×D3—61no—
366C2×C4×D3—61no—
367C2×C4×D3—64no—
368C2×C4×D3—64no—
369C2×C4×D3—64no—
370C2×C4×D3—64no—
371C2×C4×D3—64no—
372C2×C4×D3—64no—
373C2×C4×D3—64no—
374C2×C4×D3—64no—
375C2×C4×D3—64no—
376C2×C4×D3—64no—
377C2×C4×D3—64no—
378C2×C4×D3—64no—
379C2×C4×D3—64no—
380C2×C4×D3—64no—
381C2×C4×D3—64no—
382C2×C4×D3—64no—
383C2×C4×D3—64no—
384C2×C4×D3—64no—
385C2×C4×D3—64no—
386C2×C4×D3—64no—
387C2×C4×D3—124no—
388C2×C4×D3C4×D311yescharacteristic
389C2×C4×D3C4×D311yescharacteristic
390C2×C4×D3C4×D311yescharacteristic
391C2×C4×D3C4×D311yescharacteristic
392C2×C4×D3C22×D311yescharacteristic
393C2×C4×D3C22×D311yescharacteristic
394C2×C4×D3C22×D311yescharacteristic
395C2×C4×D3C22×D311yescharacteristic
396C3×M16—64no—
397C2×C3×C8—22no—
398C2×C3×C8—32no—
399C2×C3×C8—32no—
400C2×C3×C8—64no—
401C2×C3×C8C22×D312yescomplemented
402C2×C3×C8C22×D312yescomplemented
403#208—64no—
404C2×C3⋊C8—32no—
405C2×C3⋊C8—32no—
406C2×C3⋊C8—62no—
407C2×C3⋊C8—64no—
408C2×C3⋊C8C22×D312yescomplemented
409C2×C3⋊C8C22×D312yescomplemented
410ΓL(1,𝔽25)—24no—
411ΓL(1,𝔽25)—64no—
412ΓL(1,𝔽25)—64no—
413ΓL(1,𝔽25)—64no—
414ΓL(1,𝔽25)—64no—
415ΓL(1,𝔽25)—64no—
416ΓL(1,𝔽25)—124no—
417D3×C8—24no—
418D3×C8—64no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32C2×M1612yescomplemented
422C22×C32C23×C411yescharacteristic
423C2×C3⋊D3—28no—
424C2×C3⋊D3—21no—
425C2×C3⋊D3—21no—
426C2×C3⋊D3—21no—
427C2×C3⋊D3—21no—
428C2×C3⋊D3C2×C22⋊C412yes—
429C2×C3⋊D3C2×M1612yescomplemented
430C2×C3×D3—28no—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—21no—
436C2×C3×D3—21no—
437C2×C3×D3—28no—
438C2×C3×D3C2×C22⋊C412yes—
439C2×C3×D3C2×C22⋊C412yes—
440C2×C3×D3C2×M1612yes—
441C2×C3×D3C2×M1612yes—
442C2×C3×D3C2×M1612yescomplemented
443C2×C3×D3C2×M1612yescomplemented
444D32—28no—
445D32—28no—
446D32—28no—
447D32—28no—
448C32×C4—21no—
449C32×C4C22×D412yes—
450C3⋊Dic3—21no—
451C3⋊Dic3C2×C22⋊C412yes—
452C3×Dic3—21no—
453C3×Dic3—21no—
454C3×Dic3C2×C22⋊C412yes—
455C3×Dic3C2×C22⋊C412yes—
456C25—91no—
457C23×C4—31no—
458C23×C4—31no—
459C23×C4—91no—
460C23×C4—91no—
461C23×C4—91no—
462C23×C4—91no—
463C23×C4—91no—
464C23×C4—91no—
465C23×C4—91no—
466C23×C4—91no—
467C23×C4—91no—
468C23×C4—91no—
469C23×C4—91no—
470C23×C4—91no—
471C23×C4—188no—
472C2×M16—32no—
473C2×M16—92no—
474C2×M16—92no—
475C2×M16—92no—
476C2×M16—188no—
477C22×C8—32no—
478C22×C8—92no—
479C22⋊C8—31no—
480C22⋊C8—31no—
481C22⋊C8—32no—
482C22⋊C8—32no—
483C22⋊C8—92no—
484C22⋊C8—92no—
485C22⋊C8—92no—
486C22⋊C8—91no—
487C22⋊C8—92no—
488C22⋊C8D3211yescharacteristic, complemented
489C23×C3—21no—
490C23×C3—31no—
491C23×C3—34no—
492C23×C3—31no—
493C23×C3—31no—
494C23×C3—31no—
495C23×C3—62no—
496C23×C3—62no—
497C23×C3—62no—
498C23×C3—62no—
499C23×C3—62no—
500C23×C3C2×C4×D311yescharacteristic
501C23×C3C2×C4×D311yescharacteristic
502C22×D3—22no—
503C22×D3—22no—
504C22×D3—22no—
505C22×D3—22no—
506C22×D3—22no—
507C22×D3—31no—
508C22×D3—31no—
509C22×D3—31no—
510C22×D3—31no—
511C22×D3—34no—
512C22×D3—34no—
513C22×D3—34no—
514C22×D3—34no—
515C22×D3—61no—
516C22×D3—61no—
517C22×D3—62no—
518C22×D3—62no—
519C22×D3—62no—
520C22×D3—62no—
521C22×D3—62no—
522C22×D3—62no—
523C22×D3—62no—
524C22×D3—62no—
525C22×D3—62no—
526C22×D3—62no—
527C22×D3—62no—
528C22×D3—62no—
529C22×D3—632no—
530C22×D3—632no—
531C22×D3—62no—
532C22×D3—62no—
533C22×D3—62no—
534C22×D3—62no—
535C22×D3—62no—
536C22×D3—62no—
537C22×D3—62no—
538C22×D3—62no—
539C22×D3—62no—
540C22×D3—62no—
541C22×D3—62no—
542C22×D3—62no—
543C22×D3—62no—
544C22×D3—62no—
545C22×D3—122no—
546C22×D3—122no—
547C22×D3—122no—
548C22×D3ΓL(1,𝔽25)14yescomplemented
549C22×D3C2×C4×D311yescharacteristic
550C22×D3C2×C4×D311yescharacteristic
551C22×D3C2×C4×D311yescharacteristic
552C22×D3C2×C4×D311yescharacteristic
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—31no—
558C2×C3×C4—31no—
559C2×C3×C4—34no—
560C2×C3×C4—34no—
561C2×C3×C4—31no—
562C2×C3×C4—31no—
563C2×C3×C4—42no—
564C2×C3×C4—62no—
565C2×C3×C4—62no—
566C2×C3×C4—62no—
567C2×C3×C4—62no—
568C2×C3×C4—62no—
569C2×C3×C4—62no—
570C2×C3×C4—62no—
571C2×C3×C4—62no—
572C2×C3×C4C2×C4×D311yescharacteristic
573C2×C3×C4C2×C4×D311yescharacteristic
574C2×C3×C4C23×D311yescharacteristic
575C2×C3×C4C23×D311yescharacteristic
576C2×Dic3—22no—
577C2×Dic3—22no—
578C2×Dic3—31no—
579C2×Dic3—31no—
580C2×Dic3—34no—
581C2×Dic3—34no—
582C2×Dic3—31no—
583C2×Dic3—31no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—62no—
587C2×Dic3—62no—
588C2×Dic3—62no—
589C2×Dic3—62no—
590C2×Dic3—62no—
591C2×Dic3—62no—
592C2×Dic3—62no—
593C2×Dic3—62no—
594C2×Dic3—122no—
595C2×Dic3C2×C4×D311yescharacteristic
596C2×Dic3C2×C4×D311yescharacteristic
597C2×Dic3C2×C4×D311yescharacteristic
598C2×Dic3C2×C4×D311yescharacteristic
599C4×D3—22no—
600C4×D3—22no—
601C4×D3—22no—
602C4×D3—22no—
603C4×D3—22no—
604C4×D3—22no—
605C4×D3—34no—
606C4×D3—34no—
607C4×D3—34no—
608C4×D3—34no—
609C4×D3—34no—
610C4×D3—34no—
611C4×D3—64no—
612C4×D3—62no—
613C4×D3—62no—
614C4×D3—62no—
615C4×D3—62no—
616C4×D3—62no—
617C4×D3—62no—
618C4×D3—62no—
619C4×D3—62no—
620C4×D3—62no—
621C4×D3—62no—
622C4×D3—62no—
623C4×D3—62no—
624C4×D3—62no—
625C4×D3—62no—
626C4×D3—62no—
627C4×D3—62no—
628C4×D3—62no—
629C4×D3—62no—
630C4×D3—122no—
631C4×D3—122no—
632C4×D3—122no—
633C4×D3D3×D414yes—
634C4×D3D3×D414yes—
635C3×C8—22no—
636C3×C8—22no—
637C3×C8—42no—
638C3×C8—62no—
639C3×C8—62no—
640C3⋊C8—22no—
641C3⋊C8—22no—
642C3⋊C8—62no—
643C3⋊C8—62no—
644C3⋊C8—122no—
645C2×C32—22no—
646C2×C32C22×C22⋊C411yescharacteristic
647C2×C32C22×M1611yescharacteristic
648C2×C32C22×M1611yescharacteristic
649C3⋊D3—22no—
650C3⋊D3—22no—
651C3×D3—22no—
652C3×D3—22no—
653C3×D3—22no—
654C3×D3#40714yescomplemented
655C24—31no—
656C24—31no—
657C24—91no—
658C24—91no—
659C24—91no—
660C24—91no—
661C24—91no—
662C24—184no—
663C24—184no—
664C24—184no—
665C22×C4—31no—
666C22×C4—31no—
667C22×C4—31no—
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—31no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—31no—
674C22×C4—31no—
675C22×C4—64no—
676C22×C4—64no—
677C22×C4—98no—
678C22×C4—91no—
679C22×C4—91no—
680C22×C4—91no—
681C22×C4—91no—
682C22×C4—91no—
683C22×C4—91no—
684C22×C4—91no—
685C22×C4—91no—
686C22×C4—91no—
687C22×C4—91no—
688C22×C4—91no—
689C22×C4—91no—
690C22×C4—91no—
691C22×C4—91no—
692C22×C4—91no—
693C22×C4—91no—
694C22×C4—91no—
695C22×C4—184no—
696C22×C4—184no—
697C22×C4—184no—
698C22×C4—184no—
699C22×C4—184no—
700C22×C4—184no—
701C22×C4—184no—
702C22×C4—184no—
703C22×C4—184no—
704C22×C4—184no—
705C22×C4—184no—
706C22×C4C2×D3211yescharacteristic
707M16—64no—
708M16—184no—
709M16—184no—
710M16—184no—
711C2×C8—32no—
712C2×C8—32no—
713C2×C8—64no—
714C2×C8—92no—
715C2×C8—184no—
716C2×C8C2×D3212yescomplemented
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—22no—
722C22×C3—21no—
723C22×C3—32no—
724C22×C3—32no—
725C22×C3—32no—
726C22×C3—32no—
727C22×C3—32no—
728C22×C3—32no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—68no—
732C22×C3—68no—
733C22×C3—61no—
734C22×C3—61no—
735C22×C3—61no—
736C22×C3—61no—
737C22×C3—61no—
738C22×C3—61no—
739C22×C3C2×ΓL(1,𝔽25)12yescomplemented
740C22×C3D3×M1612yescomplemented
741C22×C3C22×C4×D311yescharacteristic
742C22×C3C22×C4×D311yescharacteristic
743C2×D3—28no—
744C2×D3—21no—
745C2×D3—21no—
746C2×D3—21no—
747C2×D3—21no—
748C2×D3—21no—
749C2×D3—21no—
750C2×D3—28no—
751C2×D3—32no—
752C2×D3—32no—
753C2×D3—32no—
754C2×D3—32no—
755C2×D3—62no—
756C2×D3—62no—
757C2×D3—68no—
758C2×D3—68no—
759C2×D3—68no—
760C2×D3—68no—
761C2×D3—68no—
762C2×D3—68no—
763C2×D3—68no—
764C2×D3—68no—
765C2×D3—61no—
766C2×D3—61no—
767C2×D3—61no—
768C2×D3—61no—
769C2×D3—61no—
770C2×D3—61no—
771C2×D3—61no—
772C2×D3—61no—
773C2×D3—68no—
774C2×D3—68no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—128no—
780C2×D3D3×C22⋊C412yes—
781C2×D3D3×C22⋊C412yes—
782C2×D3C2×ΓL(1,𝔽25)12yes—
783C2×D3C2×ΓL(1,𝔽25)12yescomplemented
784C2×D3D3×M1612yes—
785C2×D3D3×M1612yescomplemented
786C3×C4—21no—
787C3×C4—21no—
788C3×C4—22no—
789C3×C4—32no—
790C3×C4—32no—
791C3×C4—41no—
792C3×C4—61no—
793C3×C4—61no—
794C3×C4C2×D3×D412yes—
795C3×C4C2×D3×D412yes—
796Dic3—21no—
797Dic3—21no—
798Dic3—32no—
799Dic3—32no—
800Dic3—62no—
801Dic3—61no—
802Dic3—61no—
803Dic3—121no—
804Dic3D3×C22⋊C412yes—
805Dic3D3×C22⋊C412yes—
806C32C2×#40711yescharacteristic, complemented, Sylow
807C23—31no—
808C23—34no—
809C23—31no—
810C23—31no—
811C23—31no—
812C23—62no—
813C23—62no—
814C23—62no—
815C23—62no—
816C23—62no—
817C23—94no—
818C23—94no—
819C23—91no—
820C23—91no—
821C23—182no—
822C23—182no—
823C23—182no—
824C23—182no—
825C23—182no—
826C23—182no—
827C23—182no—
828C23—182no—
829C23—182no—
830C23—182no—
831C23—182no—
832C23—182no—
833C23—1832no—
834C23—182no—
835C23C4×D3211yescharacteristic
836C2×C4—22no—
837C2×C4—31no—
838C2×C4—31no—
839C2×C4—34no—
840C2×C4—34no—
841C2×C4—31no—
842C2×C4—31no—
843C2×C4—62no—
844C2×C4—62no—
845C2×C4—62no—
846C2×C4—62no—
847C2×C4—62no—
848C2×C4—62no—
849C2×C4—62no—
850C2×C4—62no—
851C2×C4—94no—
852C2×C4—94no—
853C2×C4—94no—
854C2×C4—91no—
855C2×C4—94no—
856C2×C4—91no—
857C2×C4—182no—
858C2×C4—182no—
859C2×C4—182no—
860C2×C4—182no—
861C2×C4—182no—
862C2×C4—182no—
863C2×C4—182no—
864C2×C4—182no—
865C2×C4—182no—
866C2×C4—182no—
867C2×C4—182no—
868C2×C4—182no—
869C2×C4—182no—
870C2×C4C4×D3211yescharacteristic
871C2×C4C22×D3211yescharacteristic
872C8—22no—
873C8—62no—
874C8—62no—
875C8—182no—
876C2×C3—22no—
877C2×C3—22no—
878C2×C3—21no—
879C2×C3—21no—
880C2×C3—21no—
881C2×C3—34no—
882C2×C3—42no—
883C2×C3—62no—
884C2×C3—62no—
885C2×C3—62no—
886C2×C3C2×D3×C22⋊C411yescharacteristic
887C2×C3C2×D3×C22⋊C411yescharacteristic
888C2×C3C22×ΓL(1,𝔽25)11yescharacteristic
889C2×C3C2×D3×M1611yescharacteristic
890C2×C3C2×D3×M1611yescharacteristic
891C2×C3C2×D3×M1611yescharacteristic
892D3—22no—
893D3—22no—
894D3—22no—
895D3—62no—
896D3—62no—
897D3—62no—
898D3—62no—
899D3—122no—
900D3—122no—
901D3#472614yesdirect product factor
902C22—21no—
903C22—21no—
904C22—32no—
905C22—32no—
906C22—32no—
907C22—32no—
908C22—32no—
909C22—32no—
910C22—68no—
911C22—68no—
912C22—61no—
913C22—61no—
914C22—61no—
915C22—61no—
916C22—61no—
917C22—61no—
918C22—92no—
919C22—92no—
920C22—188no—
921C22—188no—
922C22—188no—
923C22—188no—
924C22—188no—
925C22—181no—
926C22—181no—
927C22—181no—
928C22—181no—
929C22D3×ΓL(1,𝔽25)12yescomplemented
930C22C2×C4×D3211yescharacteristic
931C4—21no—
932C4—32no—
933C4—32no—
934C4—61no—
935C4—61no—
936C4—92no—
937C4—181no—
938C4D32×D412yes—
939C3—21no—
940C3C2×#472611yescharacteristic, complemented
941C3D3×#40711yescharacteristic, complemented
942C2—22no—
943C2—34no—
944C2—62no—
945C2—62no—
946C2—62no—
947C2—182no—
948C2—182no—
949C2D32×C22⋊C411yescharacteristic
950C2C2×D3×ΓL(1,𝔽25)11yescharacteristic
951C2D32×M1611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C22⋊C8C22
prime radicalC23×D32C4
cosocleC2×C32×C4C24
hypercenterC22⋊C8D32
hypocenterC32C2×#407
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×D3×ΓL(1,𝔽25)C2semidirect
3. #10592425C2semidirect
4. C3×#4726C2semidirect
5. C3×D3×C22⋊C8C2semidirect
6. #10591159C2semidirect
7. #10591154C2semidirect
8. D3×#830C2semidirect
9. #10590937C2semidirect
10. #10590936C2semidirect
11. D3×(C2×D3)⋊C8C2semidirect
30. C2×#3743C22semidirect
31. C2×C3×ΓL(1,𝔽25)C22semidirect
32. C2×C3×D3×C8C22semidirect
33. C2×#3712C22semidirect
34. C2×#3711C22semidirect
35. C2×D3×C3⋊C8C22semidirect
37. C32×C22⋊C8C22semidirect
38. #63657C22semidirect
39. #63647C22semidirect
40. C3×#830C22semidirect
41. C3×#830C22semidirect
42. C3×(C2×D3)⋊C8C22semidirect
43. C3×(C2×D3)⋊C8C22semidirect
44. #63557C22semidirect
45. (C2×D3)⋊(C3⋊C8)C22semidirect
46. (C2×D3)⋊(C3⋊C8)C22semidirect
66. #4726D3direct (N × H)
69. D3×C22⋊C8D3semidirect
122. C2×C32×C8C23semidirect
123. C2×C3⋊(C3⋊C8)C23semidirect
125. C2×C3×C3⋊C8C23semidirect
126. C2×C3×C3⋊C8C23semidirect
178. C2×ΓL(1,𝔽25)C2×D3semidirect
180. C2×D3×C8C2×D3semidirect
186. C3×C22⋊C8C2×D3semidirect
187. C3×C22⋊C8C2×D3semidirect
193. #830C2×D3semidirect
194. #830C2×D3semidirect
202. (C2×D3)⋊C8C2×D3semidirect
203. (C2×D3)⋊C8C2×D3semidirect
215. C22×C3×D3M16semidirect
232. C2×D32M16semidirect
401. C2×C3×C8C22×D3semidirect
402. C2×C3×C8C22×D3semidirect
408. C2×C3⋊C8C22×D3semidirect
409. C2×C3⋊C8C22×D3semidirect
421. C22×C32C2×M16semidirect
429. C2×C3⋊D3C2×M16semidirect
442. C2×C3×D3C2×M16semidirect
443. C2×C3×D3C2×M16semidirect
488. C22⋊C8D32semidirect
548. C22×D3ΓL(1,𝔽25)semidirect
654. C3×D3#407semidirect
716. C2×C8C2×D32semidirect
739. C22×C3C2×ΓL(1,𝔽25)semidirect
740. C22×C3D3×M16semidirect
783. C2×D3C2×ΓL(1,𝔽25)semidirect
785. C2×D3D3×M16semidirect
806. C32C2×#407semidirect
901. D3#4726direct (N × H)
929. C22D3×ΓL(1,𝔽25)semidirect
940. C3C2×#4726semidirect
941. C3D3×#407semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D322
C2×D3×ΓL(1,𝔽25)2
#105924252
C3×#47262
C3×D3×C22⋊C82
#105911592
#105911542
D3×#8302
#105909372
#105909362
D3×(C2×D3)⋊C82
D3×#4073
C2×#47263