Finite Group Databasebeta

← C3×#10595074 #13174671

Subgroups — C3×#10595074 #13174671

Order 1728.

2190 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×C3×#3811C212yesmaximal, complemented
3C2×C3×D3×D12C211yesmaximal, characteristic, complemented
4C32×#930C211yesmaximal, characteristic, complemented
5C32×C4×#67C211yesmaximal, characteristic, complemented
6C3×#63981C212yesmaximal, complemented
7C3×#63923C212yesmaximal, complemented
8C3×#63911C211yesmaximal, characteristic, complemented
9C3×#63910C212yesmaximal, complemented
10C3×#63909C211yesmaximal, characteristic, complemented
11C3×#63894C211yesmaximal, characteristic, complemented
12C3×#5609—31nomaximal
13C3×D4×D12—31nomaximal
14#10595074C311yesmaximal, characteristic, direct product factor
15C23×C3×C3⋊D3C2212yescomplemented
16C22×C3×D32C2212yescomplemented
17C22×C33×C4C2211yescharacteristic, complemented
18C2×C3×C4⋊(C3⋊D3)—24no—
19C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
21C2×C3×C4⋊(C3⋊D3)C2212yescomplemented
22C2×C32×#67C2211yescharacteristic
23C2×C32×#67C2212yescomplemented
24C2×C32×D12C2211yescharacteristic, complemented
25C2×C32×C4×D3C2211yescharacteristic, complemented
26C3×#3811—28no—
27C2×C3×#626C2212yescomplemented
28C2×C3×#626C2212yescomplemented
29C2×C3×#626C2212yescomplemented
30C2×C3×#626C2212yescomplemented
31C2×C3×#624C2212yescomplemented
32C3×D3×D12—24no—
33C32×#217C2211yescharacteristic, complemented
34C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
35C32×(C2×D3)⋊C4C2212yescomplemented
36C32×C4⋊Dic3C2211yescharacteristic, complemented
37C32×Dic3⋊C4C2211yescharacteristic, complemented
38C32×C4×Dic3C2211yescharacteristic, complemented
39C3×#3722C2212yescomplemented
40C3×#3722C2212yescomplemented
41C22×C4⋊(C3⋊D3)C2×C311yescharacteristic, complemented
42C2×C3×D3×D4—32no—
43C2×C3×D3×D4—32no—
44C2×C3×D3×D4—31no—
45C22×C3×D12—31no—
46C22×C3×D12—31no—
47C22×C3×D12—31no—
48C22×C3×D12—61no—
49C2×#3811C2×C312yescomplemented
50C2×D3×D12C2×C311yescharacteristic, complemented
51C32×#121—31no—
52C32×C4×D4—31no—
53C3×#940—31no—
54C3×#937—32no—
55C3×#930—21no—
56C3×#930—31no—
57C3×#930D311yescharacteristic, complemented
58C3×#930C2×C311yescharacteristic, complemented
59C3×C4×#67—21no—
60C3×C4×#67D311yescharacteristic, complemented
61C3×C4×#67C2×C311yescharacteristic, complemented
62C3×#895—31no—
63C3×#895—32no—
64C3×#893—31no—
65C3×#884—32no—
66C3×#882—32no—
67C3×#882—32no—
68C3×#882—32no—
69C3×#874—31no—
70C3×C4×D12—31no—
71#63981C2×C312yescomplemented
72#63923C2×C312yescomplemented
73#63911C2×C311yescharacteristic, complemented
74#63910C2×C312yescomplemented
75#63909C2×C311yescharacteristic, complemented
76#63894C2×C311yescharacteristic, complemented
77C23×C33C2311yescharacteristic
78C22×C3×C3⋊D3—24no—
79C22×C3×C3⋊D3—24no—
80C22×C3×C3⋊D3—42no—
81C22×C3×C3⋊D3C2312yes—
82C22×C3×C3⋊D3C2312yes—
83C22×C32×D3C2312yes—
84C22×C32×D3C2311yescharacteristic
85C2×C3×D32—24no—
86C2×C3×D32—24no—
87C2×C3×D32—42no—
88C2×C33×C4—22no—
89C2×C33×C4C2311yescharacteristic
90C2×C33×C4C2311yescharacteristic
91C3×C4⋊(C3⋊D3)—24no—
92C3×C4⋊(C3⋊D3)—22no—
93C3×C4⋊(C3⋊D3)D414yescomplemented
94C32×#67—24no—
95C32×#67D414yescomplemented
96C2×C32×Dic3C2311yescharacteristic
97C2×C32×Dic3C2311yescharacteristic
98C2×C32×Dic3C2312yes—
99C2×C32×Dic3C2311yescharacteristic
100C32×D12—22no—
101C32×C4×D3—22no—
102C3×#626—24no—
103C3×#626—24no—
104C3×#626—24no—
105C3×#626—42no—
106C3×#624—24no—
107C3×D42—91no—
108#5609—31no—
109D4×D12—31no—
110C23×C3⋊D3C22×C312yescomplemented
111C23×C3×D3—32no—
112C23×C3×D3—32no—
113C23×C3×D3—32no—
114C23×C3×D3—32no—
115C23×C3×D3—62no—
116C22×D32C22×C312yescomplemented
117C2×C32×D4—31no—
118C2×C32×D4—32no—
119C2×C32×D4—31no—
120C22×C32×C4—21no—
121C22×C32×C4—21no—
122C22×C32×C4—21no—
123C22×C32×C4—31no—
124C22×C32×C4—41no—
125C22×C32×C4C2×D311yescharacteristic, complemented
126C22×C32×C4C2×D311yescharacteristic, complemented
127C22×C32×C4C22×C311yescharacteristic, complemented
128C2×C4⋊(C3⋊D3)—24no—
129C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
130C2×C4⋊(C3⋊D3)C22×C311yescharacteristic, complemented
131C2×C4⋊(C3⋊D3)C22×C312yescomplemented
132C2×C3×#67—21no—
133C2×C3×#67—22no—
134C2×C3×#67—32no—
135C2×C3×#67—32no—
136C2×C3×#67—32no—
137C2×C3×#67—32no—
138C2×C3×#67C2×D311yescharacteristic
139C2×C3×#67C2×D312yescomplemented
140C2×C3×#67C22×C311yescharacteristic
141C2×C3×#67C22×C312yescomplemented
142C3×D3×D4—64no—
143C3×D3×D4—68no—
144C3×D3×D4—68no—
145C2×C3×D12—21no—
146C2×C3×D12—31no—
147C2×C3×D12—31no—
148C2×C3×D12—32no—
149C2×C3×D12—32no—
150C2×C3×D12—32no—
151C2×C3×D12—32no—
152C2×C3×D12—32no—
153C2×C3×D12—31no—
154C2×C3×D12—31no—
155C2×C3×D12—32no—
156C2×C3×D12—64no—
157C2×C3×D12—64no—
158C2×C3×D12—64no—
159C2×C3×D12—61no—
160C2×C3×D12—62no—
161C2×C3×D12—61no—
162C2×C3×D12—68no—
163C2×C3×D12C2×D311yescharacteristic, complemented
164C2×C3×D12C22×C311yescharacteristic, complemented
165C2×C3×C4×D3—21no—
166C2×C3×C4×D3—32no—
167C2×C3×C4×D3—32no—
168C2×C3×C4×D3C2×D311yescharacteristic, complemented
169C2×C3×C4×D3C22×C311yescharacteristic, complemented
170#3811—28no—
171C2×#626C22×C312yescomplemented
172C2×#626C22×C312yescomplemented
173C2×#626C22×C312yescomplemented
174C2×#626C22×C312yescomplemented
175C2×#624C22×C312yescomplemented
176D3×D12—24no—
177C32×C4⋊C4—31no—
178C32×C4⋊C4—31no—
179C32×C22⋊C4—31no—
180C32×C22⋊C4—31no—
181C32×C22⋊C4—32no—
182C32×C42—31no—
183C3×#217—21no—
184C3×#217C2×D311yescharacteristic, complemented
185C3×#217C22×C311yescharacteristic, complemented
186C3×(C2×D3)⋊C4—21no—
187C3×(C2×D3)⋊C4—22no—
188C3×(C2×D3)⋊C4—32no—
189C3×(C2×D3)⋊C4—32no—
190C3×(C2×D3)⋊C4—32no—
191C3×(C2×D3)⋊C4—32no—
192C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
193C3×(C2×D3)⋊C4C2×D312yescomplemented
194C3×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
195C3×(C2×D3)⋊C4C22×C312yescomplemented
196C3×C4⋊Dic3—21no—
197C3×C4⋊Dic3C2×D311yescharacteristic, complemented
198C3×C4⋊Dic3C22×C311yescharacteristic, complemented
199C3×Dic3⋊C4—21no—
200C3×Dic3⋊C4C2×D311yescharacteristic, complemented
201C3×Dic3⋊C4C22×C311yescharacteristic, complemented
202C3×C4×Dic3—21no—
203C3×C4×Dic3C2×D311yescharacteristic, complemented
204C3×C4×Dic3C22×C311yescharacteristic, complemented
205#3722C22×C312yescomplemented
206#3722C22×C312yescomplemented
207C22×C33—21no—
208C22×C33—21no—
209C22×C33C2×D412yescomplemented
210C22×C33C2411yescharacteristic
211C2×C3×C3⋊D3—22no—
212C2×C3×C3⋊D3—22no—
213C2×C3×C3⋊D3—22no—
214C2×C3×C3⋊D3—22no—
215C2×C3×C3⋊D3—22no—
216C2×C3×C3⋊D3—48no—
217C2×C3×C3⋊D3C2×D414yescomplemented
218C2×C32×D3—21no—
219C2×C32×D3—21no—
220C2×C32×D3—22no—
221C2×C32×D3—22no—
222C2×C32×D3—22no—
223C2×C32×D3C2×D412yescomplemented
224C3×D32—48no—
225C33×C4—21no—
226C33×C4C2×D412yescomplemented
227C32×Dic3—22no—
228C32×Dic3—21no—
229C32×Dic3—21no—
230C32×Dic3C2×D412yescomplemented
231C22×C3×D4—91no—
232C22×C3×D4—92no—
233C22×C3×D4—91no—
234C2×D3×D4—32no—
235C2×D3×D4—32no—
236C2×D3×D4—31no—
237C22×D12—31no—
238C22×D12—31no—
239C22×D12—31no—
240C22×D12—61no—
241C3×#127—91no—
242C3×#121—31no—
243C3×#121—31no—
244C3×#121—61no—
245C3×#121—92no—
246C3×#121—91no—
247C3×#120—92no—
248C3×#120—92no—
249C3×C4×D4—31no—
250C3×C4×D4—31no—
251C3×C4×D4—61no—
252C3×C4×D4—91no—
253#940—31no—
254#937—32no—
255#930—31no—
256#930C3×D311yescharacteristic, complemented
257C4×#67C3×D311yescharacteristic, complemented
258#895—31no—
259#895—32no—
260#893—31no—
261#884—32no—
262#882—32no—
263#882—32no—
264#882—32no—
265#874—31no—
266C4×D12—31no—
267C23×C32—21no—
268C23×C32—21no—
269C23×C32—21no—
270C23×C32—31no—
271C23×C32—32no—
272C23×C32—41no—
273C23×C32C22×D311yescharacteristic
274C23×C32C22×D311yescharacteristic
275C23×C32C23×C311yescharacteristic
276C22×C3⋊D3—24no—
277C22×C3⋊D3—24no—
278C22×C3⋊D3—42no—
279C22×C3⋊D3C23×C312yes—
280C22×C3⋊D3C23×C312yes—
281C22×C3×D3—21no—
282C22×C3×D3—22no—
283C22×C3×D3—32no—
284C22×C3×D3—32no—
285C22×C3×D3—32no—
286C22×C3×D3—32no—
287C22×C3×D3—62no—
288C22×C3×D3—62no—
289C22×C3×D3—64no—
290C22×C3×D3—64no—
291C22×C3×D3—64no—
292C22×C3×D3—64no—
293C22×C3×D3—64no—
294C22×C3×D3—68no—
295C22×C3×D3—64no—
296C22×C3×D3—64no—
297C22×C3×D3—64no—
298C22×C3×D3—124no—
299C22×C3×D3—122no—
300C22×C3×D3—122no—
301C22×C3×D3—122no—
302C22×C3×D3—122no—
303C22×C3×D3—124no—
304C22×C3×D3C22×D312yes—
305C22×C3×D3C22×D311yescharacteristic
306C22×C3×D3C23×C312yes—
307C22×C3×D3C23×C311yescharacteristic
308C2×D32—24no—
309C2×D32—24no—
310C2×D32—42no—
311C32×D4—34no—
312C32×D4—64no—
313C32×D4—62no—
314C2×C32×C4—22no—
315C2×C32×C4—24no—
316C2×C32×C4—22no—
317C2×C32×C4—22no—
318C2×C32×C4—21no—
319C2×C32×C4—21no—
320C2×C32×C4—21no—
321C2×C32×C4—21no—
322C2×C32×C4—21no—
323C2×C32×C4—21no—
324C2×C32×C4—31no—
325C2×C32×C4—31no—
326C2×C32×C4—32no—
327C2×C32×C4—31no—
328C2×C32×C4—41no—
329C2×C32×C4—41no—
330C2×C32×C4—42no—
331C2×C32×C4—42no—
332C2×C32×C4—44no—
333C2×C32×C4—62no—
334C2×C32×C4C22×D311yescharacteristic
335C2×C32×C4C22×D311yescharacteristic
336C2×C32×C4C22×D311yescharacteristic
337C2×C32×C4C22×D311yescharacteristic
338C2×C32×C4C23×C311yescharacteristic
339C2×C32×C4C23×C311yescharacteristic
340C4⋊(C3⋊D3)—24no—
341C4⋊(C3⋊D3)—22no—
342C4⋊(C3⋊D3)C3×D414yescomplemented
343C3×#67—24no—
344C3×#67—24no—
345C3×#67—24no—
346C3×#67—44no—
347C3×#67—64no—
348C3×#67—64no—
349C3×#67—64no—
350C3×#67—122no—
351C3×#67D1214yescomplemented
352C3×#67C3×D414yescomplemented
353C2×C3×Dic3—21no—
354C2×C3×Dic3—21no—
355C2×C3×Dic3—21no—
356C2×C3×Dic3—22no—
357C2×C3×Dic3C22×D311yescharacteristic
358C2×C3×Dic3C22×D311yescharacteristic
359C2×C3×Dic3C22×D312yes—
360C2×C3×Dic3C22×D311yescharacteristic
361C2×C3×Dic3C23×C311yescharacteristic
362C2×C3×Dic3C23×C311yescharacteristic
363C2×C3×Dic3C23×C312yes—
364C2×C3×Dic3C23×C311yescharacteristic
365C3×D12—22no—
366C3×D12—22no—
367C3×D12—34no—
368C3×D12—34no—
369C3×D12—42no—
370C3×D12—64no—
371C3×D12—64no—
372C3×D12—64no—
373C3×D12—68no—
374C3×D12—64no—
375C3×D12—64no—
376C3×D12—64no—
377C3×D12—64no—
378C3×D12—62no—
379C3×D12—62no—
380C3×D12—122no—
381C3×C4×D3—22no—
382C3×C4×D3—22no—
383C3×C4×D3—42no—
384C3×C4×D3—64no—
385C3×C4×D3—64no—
386#626—24no—
387#626—24no—
388#626—24no—
389#626—42no—
390#624—24no—
391D42—91noSylow
392C2×C33—22no—
393C2×C33C22×D411yescharacteristic
394C2×C33C22×D411yescharacteristic
395C2×C33H(5,𝔽2)11yescharacteristic
396C3×C3⋊D3—24no—
397C3×C3⋊D3—42no—
398C32×D3—22no—
399C32×D3—42no—
400C24×C3—92no—
401C24×C3—92no—
402C23×D3—32no—
403C23×D3—32no—
404C23×D3—32no—
405C23×D3—32no—
406C23×D3—62no—
407C2×C3×D4—31no—
408C2×C3×D4—31no—
409C2×C3×D4—32no—
410C2×C3×D4—32no—
411C2×C3×D4—31no—
412C2×C3×D4—31no—
413C2×C3×D4—61no—
414C2×C3×D4—61no—
415C2×C3×D4—62no—
416C2×C3×D4—92no—
417C2×C3×D4—92no—
418C2×C3×D4—92no—
419C2×C3×D4—92no—
420C2×C3×D4—91no—
421C2×C3×D4—92no—
422C2×C3×D4—91no—
423C2×C3×D4—184no—
424C2×C3×D4—184no—
425C2×C3×D4—188no—
426C22×C3×C4—21no—
427C22×C3×C4—21no—
428C22×C3×C4—21no—
429C22×C3×C4—31no—
430C22×C3×C4—31no—
431C22×C3×C4—41no—
432C22×C3×C4—61no—
433C22×C3×C4—92no—
434C22×C3×C4D3211yescharacteristic, complemented
435C22×C3×C4C2×C3×D311yescharacteristic, complemented
436C22×C3×C4C2×C3×D311yescharacteristic, complemented
437C2×#67—32no—
438C2×#67—32no—
439C2×#67—32no—
440C2×#67—32no—
441C2×#67C2×C3×D311yescharacteristic
442C2×#67C2×C3×D312yescomplemented
443D3×D4—64no—
444D3×D4—68no—
445D3×D4—68no—
446C2×D12—31no—
447C2×D12—31no—
448C2×D12—32no—
449C2×D12—32no—
450C2×D12—32no—
451C2×D12—31no—
452C2×D12—32no—
453C2×D12—32no—
454C2×D12—31no—
455C2×D12—32no—
456C2×D12—61no—
457C2×D12—62no—
458C2×D12—61no—
459C2×D12—64no—
460C2×D12—64no—
461C2×D12—64no—
462C2×D12—68no—
463C2×D12C2×C3×D311yescharacteristic, complemented
464C2×C4×D3—32no—
465C2×C4×D3—32no—
466C2×C4×D3C2×C3×D311yescharacteristic, complemented
467C3×C4⋊C4—31no—
468C3×C4⋊C4—31no—
469C3×C4⋊C4—31no—
470C3×C4⋊C4—31no—
471C3×C4⋊C4—61no—
472C3×C4⋊C4—61no—
473C3×C22⋊C4—31no—
474C3×C22⋊C4—31no—
475C3×C22⋊C4—31no—
476C3×C22⋊C4—32no—
477C3×C22⋊C4—31no—
478C3×C22⋊C4—32no—
479C3×C22⋊C4—61no—
480C3×C22⋊C4—62no—
481C3×C22⋊C4—61no—
482C3×C22⋊C4—92no—
483C3×C22⋊C4—92no—
484C3×C42—31no—
485C3×C42—31no—
486C3×C42—61no—
487#217C2×C3×D311yescharacteristic, complemented
488(C2×D3)⋊C4—32no—
489(C2×D3)⋊C4—32no—
490(C2×D3)⋊C4—32no—
491(C2×D3)⋊C4—32no—
492(C2×D3)⋊C4C2×C3×D311yescharacteristic, complemented
493(C2×D3)⋊C4C2×C3×D312yescomplemented
494C4⋊Dic3C2×C3×D311yescharacteristic, complemented
495Dic3⋊C4C2×C3×D311yescharacteristic, complemented
496C4×Dic3C2×C3×D311yescharacteristic, complemented
497C22×C32—21no—
498C22×C32—21no—
499C22×C32—22no—
500C22×C32—22no—
501C22×C32—21no—
502C22×C32—21no—
503C22×C32—21no—
504C22×C32—21no—
505C22×C32—21no—
506C22×C32—21no—
507C22×C32—21no—
508C22×C32—22no—
509C22×C32—22no—
510C22×C32—22no—
511C22×C32—32no—
512C22×C32—42no—
513C22×C32—41no—
514C22×C32—41no—
515C22×C32—41no—
516C22×C32—41no—
517C22×C32—41no—
518C22×C32—42no—
519C22×C32—42no—
520C22×C32—61no—
521C22×C32—61no—
522C22×C32—62no—
523C22×C32—62no—
524C22×C32—62no—
525C22×C32C2×D1212yescomplemented
526C22×C32D3×D412yescomplemented
527C22×C32C2×C3×D412yescomplemented
528C22×C32C23×D311yescharacteristic
529C22×C32C23×D311yescharacteristic
530C22×C32C24×C311yescharacteristic
531C2×C3⋊D3—22no—
532C2×C3⋊D3—22no—
533C2×C3⋊D3—22no—
534C2×C3⋊D3—22no—
535C2×C3⋊D3—22no—
536C2×C3⋊D3—48no—
537C2×C3⋊D3C2×C3×D414yescomplemented
538C2×C3×D3—21no—
539C2×C3×D3—21no—
540C2×C3×D3—21no—
541C2×C3×D3—21no—
542C2×C3×D3—22no—
543C2×C3×D3—22no—
544C2×C3×D3—22no—
545C2×C3×D3—22no—
546C2×C3×D3—22no—
547C2×C3×D3—22no—
548C2×C3×D3—22no—
549C2×C3×D3—34no—
550C2×C3×D3—34no—
551C2×C3×D3—41no—
552C2×C3×D3—41no—
553C2×C3×D3—42no—
554C2×C3×D3—42no—
555C2×C3×D3—42no—
556C2×C3×D3—64no—
557C2×C3×D3—62no—
558C2×C3×D3—62no—
559C2×C3×D3—62no—
560C2×C3×D3—62no—
561C2×C3×D3—64no—
562C2×C3×D3—62no—
563C2×C3×D3—62no—
564C2×C3×D3—62no—
565C2×C3×D3—62no—
566C2×C3×D3—62no—
567C2×C3×D3—62no—
568C2×C3×D3—122no—
569C2×C3×D3—122no—
570C2×C3×D3—122no—
571C2×C3×D3—122no—
572C2×C3×D3—128no—
573C2×C3×D3—128no—
574C2×C3×D3—128no—
575C2×C3×D3—128no—
576C2×C3×D3—1216no—
577C2×C3×D3C2×D1212yescomplemented
578C2×C3×D3C2×C3×D412yescomplemented
579D32—48no—
580C32×C4—21no—
581C32×C4—22no—
582C32×C4—21no—
583C32×C4—21no—
584C32×C4—22no—
585C32×C4—22no—
586C32×C4—22no—
587C32×C4—32no—
588C32×C4—42no—
589C32×C4—41no—
590C32×C4—41no—
591C32×C4—42no—
592C32×C4—62no—
593C32×C4—61no—
594C32×C4—61no—
595C32×C4D3×D412yescomplemented
596C32×C4D3×D412yescomplemented
597C32×C4C2×C3×D412yescomplemented
598C3×Dic3—21no—
599C3×Dic3—22no—
600C3×Dic3—21no—
601C3×Dic3—22no—
602C3×Dic3—21no—
603C3×Dic3—21no—
604C3×Dic3—22no—
605C3×Dic3—41no—
606C3×Dic3—41no—
607C3×Dic3—42no—
608C3×Dic3C2×D1212yescomplemented
609C3×Dic3C2×C3×D412yescomplemented
610C22×D4—91no—
611C22×D4—92no—
612C22×D4—91no—
613#127—91no—
614#121—31no—
615#121—92no—
616#121—91no—
617#120—92no—
618#120—92no—
619C4×D4—31no—
620C4×D4—91no—
621C33D4211yescharacteristic, complemented, Sylow
622C23×C3—21no—
623C23×C3—21no—
624C23×C3—21no—
625C23×C3—31no—
626C23×C3—31no—
627C23×C3—32no—
628C23×C3—32no—
629C23×C3—41no—
630C23×C3—61no—
631C23×C3—62no—
632C23×C3—92no—
633C23×C3—92no—
634C23×C3—184no—
635C23×C3—184no—
636C23×C3—184no—
637C23×C3—184no—
638C23×C3—362no—
639C23×C3—362no—
640C23×C3C2×D3211yescharacteristic
641C23×C3C22×C3×D311yescharacteristic
642C23×C3C22×C3×D311yescharacteristic
643C22×D3—32no—
644C22×D3—32no—
645C22×D3—32no—
646C22×D3—32no—
647C22×D3—62no—
648C22×D3—62no—
649C22×D3—64no—
650C22×D3—64no—
651C22×D3—64no—
652C22×D3—64no—
653C22×D3—64no—
654C22×D3—68no—
655C22×D3—64no—
656C22×D3—64no—
657C22×D3—64no—
658C22×D3—124no—
659C22×D3—122no—
660C22×D3—122no—
661C22×D3—122no—
662C22×D3—122no—
663C22×D3—124no—
664C22×D3C22×C3×D312yes—
665C22×D3C22×C3×D311yescharacteristic
666C3×D4—34no—
667C3×D4—34no—
668C3×D4—64no—
669C3×D4—64no—
670C3×D4—64no—
671C3×D4—62no—
672C3×D4—62no—
673C3×D4—94no—
674C3×D4—122no—
675C3×D4—124no—
676C3×D4—184no—
677C3×D4—184no—
678C3×D4—184no—
679C3×D4—184no—
680C3×D4—182no—
681C3×D4—362no—
682C2×C3×C4—24no—
683C2×C3×C4—22no—
684C2×C3×C4—22no—
685C2×C3×C4—22no—
686C2×C3×C4—21no—
687C2×C3×C4—21no—
688C2×C3×C4—21no—
689C2×C3×C4—21no—
690C2×C3×C4—21no—
691C2×C3×C4—21no—
692C2×C3×C4—31no—
693C2×C3×C4—31no—
694C2×C3×C4—31no—
695C2×C3×C4—31no—
696C2×C3×C4—32no—
697C2×C3×C4—31no—
698C2×C3×C4—32no—
699C2×C3×C4—31no—
700C2×C3×C4—42no—
701C2×C3×C4—42no—
702C2×C3×C4—44no—
703C2×C3×C4—41no—
704C2×C3×C4—41no—
705C2×C3×C4—61no—
706C2×C3×C4—61no—
707C2×C3×C4—61no—
708C2×C3×C4—62no—
709C2×C3×C4—62no—
710C2×C3×C4—62no—
711C2×C3×C4—122no—
712C2×C3×C4—184no—
713C2×C3×C4C2×D3211yescharacteristic
714C2×C3×C4C2×D3211yescharacteristic
715C2×C3×C4C22×C3×D311yescharacteristic
716C2×C3×C4C22×C3×D311yescharacteristic
717C2×C3×C4C22×C3×D311yescharacteristic
718C2×C3×C4C22×C3×D311yescharacteristic
719#67—24no—
720#67—64no—
721#67—64no—
722#67—64no—
723#67—122no—
724#67C3×D1214yescomplemented
725C2×Dic3C22×C3×D311yescharacteristic
726C2×Dic3C22×C3×D311yescharacteristic
727C2×Dic3C22×C3×D312yes—
728C2×Dic3C22×C3×D311yescharacteristic
729D12—22no—
730D12—34no—
731D12—34no—
732D12—64no—
733D12—64no—
734D12—64no—
735D12—68no—
736D12—64no—
737D12—64no—
738D12—64no—
739D12—64no—
740D12—62no—
741D12—62no—
742D12—122no—
743C4×D3—22no—
744C4×D3—64no—
745C4×D3—64no—
746C2×C32—22no—
747C2×C32—24no—
748C2×C32—22no—
749C2×C32—22no—
750C2×C32—21no—
751C2×C32—21no—
752C2×C32—21no—
753C2×C32—21no—
754C2×C32—21no—
755C2×C32—21no—
756C2×C32—21no—
757C2×C32—21no—
758C2×C32—21no—
759C2×C32—41no—
760C2×C32—41no—
761C2×C32—41no—
762C2×C32—42no—
763C2×C32—42no—
764C2×C32—44no—
765C2×C32—62no—
766C2×C32—122no—
767C2×C32C22×D1211yescharacteristic
768C2×C32C2×D3×D411yescharacteristic
769C2×C32C2×D3×D411yescharacteristic
770C2×C32C2×D3×D411yescharacteristic
771C2×C32#100911yescharacteristic
772C2×C32#100911yescharacteristic
773C2×C32C22×C3×D411yescharacteristic
774C2×C32C22×C3×D411yescharacteristic
775C2×C32C3×H(5,𝔽2)11yescharacteristic
776C3⋊D3—24no—
777C3⋊D3—42no—
778C3×D3—22no—
779C3×D3—22no—
780C3×D3—42no—
781C3×D3—42no—
782C3×D3—42no—
783C3×D3—64no—
784C3×D3—64no—
785C3×D3—82no—
786C3×D3—124no—
787C3×D3—124no—
788C3×D3—122no—
789C3×D3—122no—
790C24—92no—
791C24—92no—
792C2×D4—31no—
793C2×D4—32no—
794C2×D4—31no—
795C2×D4—92no—
796C2×D4—92no—
797C2×D4—92no—
798C2×D4—92no—
799C2×D4—91no—
800C2×D4—92no—
801C2×D4—91no—
802C2×D4—184no—
803C2×D4—184no—
804C2×D4—188no—
805C22×C4—31no—
806C22×C4—92no—
807C22×C4C3×D3211yescharacteristic, complemented
808C4⋊C4—31no—
809C4⋊C4—31no—
810C22⋊C4—31no—
811C22⋊C4—31no—
812C22⋊C4—32no—
813C22⋊C4—92no—
814C22⋊C4—92no—
815C42—31no—
816C22×C3—22no—
817C22×C3—22no—
818C22×C3—21no—
819C22×C3—21no—
820C22×C3—21no—
821C22×C3—21no—
822C22×C3—21no—
823C22×C3—21no—
824C22×C3—21no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—22no—
830C22×C3—32no—
831C22×C3—32no—
832C22×C3—41no—
833C22×C3—41no—
834C22×C3—41no—
835C22×C3—41no—
836C22×C3—42no—
837C22×C3—42no—
838C22×C3—41no—
839C22×C3—42no—
840C22×C3—62no—
841C22×C3—61no—
842C22×C3—61no—
843C22×C3—61no—
844C22×C3—61no—
845C22×C3—62no—
846C22×C3—62no—
847C22×C3—62no—
848C22×C3—62no—
849C22×C3—62no—
850C22×C3—62no—
851C22×C3—94no—
852C22×C3—121no—
853C22×C3—121no—
854C22×C3—122no—
855C22×C3—122no—
856C22×C3—122no—
857C22×C3—182no—
858C22×C3—182no—
859C22×C3—182no—
860C22×C3—182no—
861C22×C3—182no—
862C22×C3—368no—
863C22×C3—368no—
864C22×C3D3×D1212yescomplemented
865C22×C3C2×C3×D1212yescomplemented
866C22×C3C3×D3×D412yescomplemented
867C22×C3C22×D3211yescharacteristic
868C22×C3C23×C3×D311yescharacteristic
869C22×C3C23×C3×D311yescharacteristic
870C2×D3—21no—
871C2×D3—21no—
872C2×D3—22no—
873C2×D3—22no—
874C2×D3—22no—
875C2×D3—34no—
876C2×D3—34no—
877C2×D3—64no—
878C2×D3—62no—
879C2×D3—62no—
880C2×D3—62no—
881C2×D3—62no—
882C2×D3—64no—
883C2×D3—62no—
884C2×D3—62no—
885C2×D3—62no—
886C2×D3—62no—
887C2×D3—62no—
888C2×D3—62no—
889C2×D3—122no—
890C2×D3—122no—
891C2×D3—122no—
892C2×D3—122no—
893C2×D3—128no—
894C2×D3—128no—
895C2×D3—128no—
896C2×D3—128no—
897C2×D3—1216no—
898C2×D3C2×C3×D1212yescomplemented
899C3×C4—22no—
900C3×C4—21no—
901C3×C4—21no—
902C3×C4—21no—
903C3×C4—22no—
904C3×C4—22no—
905C3×C4—22no—
906C3×C4—32no—
907C3×C4—32no—
908C3×C4—41no—
909C3×C4—41no—
910C3×C4—42no—
911C3×C4—42no—
912C3×C4—62no—
913C3×C4—62no—
914C3×C4—61no—
915C3×C4—61no—
916C3×C4—62no—
917C3×C4—61no—
918C3×C4—61no—
919C3×C4—121no—
920C3×C4—122no—
921C3×C4—121no—
922C3×C4#381112yescomplemented
923C3×C4C3×D3×D412yescomplemented
924C3×C4C3×D3×D412yescomplemented
925Dic3—21no—
926Dic3—22no—
927Dic3—21no—
928Dic3C2×C3×D1212yescomplemented
929C32—21no—
930C32—21no—
931C32—21no—
932C32—41no—
933C32D4×D1211yescharacteristic, complemented
934C32#560911yescharacteristic, complemented
935C32C3×D4211yescharacteristic, complemented
936C23—31no—
937C23—32no—
938C23—92no—
939C23—92no—
940C23—184no—
941C23—184no—
942C23—184no—
943C23—184no—
944C23—362no—
945C23—362no—
946C23C2×C3×D3211yescharacteristic
947D4—34no—
948D4—64no—
949D4—62no—
950D4—94no—
951D4—184no—
952D4—184no—
953D4—184no—
954D4—184no—
955D4—182no—
956D4—362no—
957C2×C4—22no—
958C2×C4—31no—
959C2×C4—31no—
960C2×C4—31no—
961C2×C4—32no—
962C2×C4—62no—
963C2×C4—184no—
964C2×C4C2×C3×D3211yescharacteristic
965C2×C4C2×C3×D3211yescharacteristic
966C2×C3—24no—
967C2×C3—22no—
968C2×C3—22no—
969C2×C3—22no—
970C2×C3—21no—
971C2×C3—21no—
972C2×C3—21no—
973C2×C3—21no—
974C2×C3—21no—
975C2×C3—21no—
976C2×C3—21no—
977C2×C3—21no—
978C2×C3—21no—
979C2×C3—42no—
980C2×C3—42no—
981C2×C3—44no—
982C2×C3—41no—
983C2×C3—41no—
984C2×C3—41no—
985C2×C3—62no—
986C2×C3—62no—
987C2×C3—122no—
988C2×C3—122no—
989C2×C3—122no—
990C2×C3—184no—
991C2×C3—242no—
992C2×C3—362no—
993C2×C3C2×D3×D1211yescharacteristic
994C2×C3#6430811yescharacteristic
995C2×C3C2×#381111yescharacteristic
996C2×C3C22×C3×D1211yescharacteristic
997C2×C3C2×C3×D3×D411yescharacteristic
998C2×C3C2×C3×D3×D411yescharacteristic
999C2×C3C2×C3×D3×D411yescharacteristic
1000C2×C3C3×#100911yescharacteristic
1001C2×C3C3×#100911yescharacteristic
1002D3—22no—
1003D3—42no—
1004D3—64no—
1005D3—64no—
1006D3—124no—
1007D3—124no—
1008D3—122no—
1009D3—122no—
1010C22—21no—
1011C22—21no—
1012C22—32no—
1013C22—61no—
1014C22—61no—
1015C22—62no—
1016C22—62no—
1017C22—62no—
1018C22—94no—
1019C22—182no—
1020C22—182no—
1021C22—182no—
1022C22—182no—
1023C22—182no—
1024C22—368no—
1025C22—368no—
1026C22C3×D3×D1212yescomplemented
1027C22C22×C3×D3211yescharacteristic
1028C4—21no—
1029C4—32no—
1030C4—61no—
1031C4—62no—
1032C4—61no—
1033C4C3×#381112yescomplemented
1034C3—21no—
1035C3—21no—
1036C3—21no—
1037C3—41no—
1038C3#1059507411yescharacteristic, direct product factor
1039C3C3×D4×D1211yescharacteristic, complemented
1040C3C3×#560911yescharacteristic, complemented
1041C2—22no—
1042C2—62no—
1043C2—122no—
1044C2—184no—
1045C2—362no—
1046C2C2×C3×D3×D1211yescharacteristic
1047C2C3×#6430811yescharacteristic
1048C2C2×C3×#381111yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
hypercenterC22×C3×C4D32
hypocenterC32C3×D42
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C4⋊(C3⋊D3)C2semidirect
2. C2×C3×#3811C2semidirect
3. C2×C3×D3×D12C2semidirect
4. C32×#930C2semidirect
5. C32×C4×#67C2semidirect
6. C3×#63981C2semidirect
7. C3×#63923C2semidirect
8. C3×#63911C2semidirect
9. C3×#63910C2semidirect
10. C3×#63909C2semidirect
11. C3×#63894C2semidirect
14. #10595074C3direct (N × H)
15. C23×C3×C3⋊D3C22semidirect
16. C22×C3×D32C22semidirect
17. C22×C33×C4C22semidirect
20. C2×C3×C4⋊(C3⋊D3)C22semidirect
21. C2×C3×C4⋊(C3⋊D3)C22semidirect
23. C2×C32×#67C22semidirect
24. C2×C32×D12C22semidirect
25. C2×C32×C4×D3C22semidirect
27. C2×C3×#626C22semidirect
28. C2×C3×#626C22semidirect
29. C2×C3×#626C22semidirect
30. C2×C3×#626C22semidirect
31. C2×C3×#624C22semidirect
33. C32×#217C22semidirect
34. C32×(C2×D3)⋊C4C22semidirect
35. C32×(C2×D3)⋊C4C22semidirect
36. C32×C4⋊Dic3C22semidirect
37. C32×Dic3⋊C4C22semidirect
38. C32×C4×Dic3C22semidirect
39. C3×#3722C22semidirect
40. C3×#3722C22semidirect
41. C22×C4⋊(C3⋊D3)C2×C3semidirect
49. C2×#3811C2×C3semidirect
50. C2×D3×D12C2×C3semidirect
57. C3×#930D3semidirect
58. C3×#930C2×C3semidirect
60. C3×C4×#67D3semidirect
61. C3×C4×#67C2×C3semidirect
71. #63981C2×C3semidirect
72. #63923C2×C3semidirect
73. #63911C2×C3semidirect
74. #63910C2×C3semidirect
75. #63909C2×C3semidirect
76. #63894C2×C3semidirect
93. C3×C4⋊(C3⋊D3)D4semidirect
95. C32×#67D4semidirect
110. C23×C3⋊D3C22×C3semidirect
116. C22×D32C22×C3semidirect
125. C22×C32×C4C2×D3semidirect
126. C22×C32×C4C2×D3semidirect
127. C22×C32×C4C22×C3semidirect
130. C2×C4⋊(C3⋊D3)C22×C3semidirect
131. C2×C4⋊(C3⋊D3)C22×C3semidirect
139. C2×C3×#67C2×D3semidirect
141. C2×C3×#67C22×C3semidirect
163. C2×C3×D12C2×D3semidirect
164. C2×C3×D12C22×C3semidirect
168. C2×C3×C4×D3C2×D3semidirect
169. C2×C3×C4×D3C22×C3semidirect
171. C2×#626C22×C3semidirect
172. C2×#626C22×C3semidirect
173. C2×#626C22×C3semidirect
174. C2×#626C22×C3semidirect
175. C2×#624C22×C3semidirect
184. C3×#217C2×D3semidirect
185. C3×#217C22×C3semidirect
192. C3×(C2×D3)⋊C4C2×D3semidirect
193. C3×(C2×D3)⋊C4C2×D3semidirect
194. C3×(C2×D3)⋊C4C22×C3semidirect
195. C3×(C2×D3)⋊C4C22×C3semidirect
197. C3×C4⋊Dic3C2×D3semidirect
198. C3×C4⋊Dic3C22×C3semidirect
200. C3×Dic3⋊C4C2×D3semidirect
201. C3×Dic3⋊C4C22×C3semidirect
203. C3×C4×Dic3C2×D3semidirect
204. C3×C4×Dic3C22×C3semidirect
205. #3722C22×C3semidirect
206. #3722C22×C3semidirect
209. C22×C33C2×D4semidirect
217. C2×C3×C3⋊D3C2×D4semidirect
223. C2×C32×D3C2×D4semidirect
226. C33×C4C2×D4semidirect
230. C32×Dic3C2×D4semidirect
256. #930C3×D3semidirect
257. C4×#67C3×D3semidirect
342. C4⋊(C3⋊D3)C3×D4semidirect
351. C3×#67D12semidirect
352. C3×#67C3×D4semidirect
434. C22×C3×C4D32semidirect
435. C22×C3×C4C2×C3×D3semidirect
436. C22×C3×C4C2×C3×D3semidirect
442. C2×#67C2×C3×D3semidirect
463. C2×D12C2×C3×D3semidirect
466. C2×C4×D3C2×C3×D3semidirect
487. #217C2×C3×D3semidirect
492. (C2×D3)⋊C4C2×C3×D3semidirect
493. (C2×D3)⋊C4C2×C3×D3semidirect
494. C4⋊Dic3C2×C3×D3semidirect
495. Dic3⋊C4C2×C3×D3semidirect
496. C4×Dic3C2×C3×D3semidirect
525. C22×C32C2×D12semidirect
526. C22×C32D3×D4semidirect
527. C22×C32C2×C3×D4semidirect
537. C2×C3⋊D3C2×C3×D4semidirect
577. C2×C3×D3C2×D12semidirect
578. C2×C3×D3C2×C3×D4semidirect
595. C32×C4D3×D4semidirect
596. C32×C4D3×D4semidirect
597. C32×C4C2×C3×D4semidirect
608. C3×Dic3C2×D12semidirect
609. C3×Dic3C2×C3×D4semidirect
621. C33D42semidirect
724. #67C3×D12semidirect
807. C22×C4C3×D32semidirect
864. C22×C3D3×D12semidirect
865. C22×C3C2×C3×D12semidirect
866. C22×C3C3×D3×D4semidirect
898. C2×D3C2×C3×D12semidirect
922. C3×C4#3811semidirect
923. C3×C4C3×D3×D4semidirect
924. C3×C4C3×D3×D4semidirect
928. Dic3C2×C3×D12semidirect
933. C32D4×D12semidirect
934. C32#5609semidirect
935. C32C3×D42semidirect
1026. C22C3×D3×D12semidirect
1033. C4C3×#3811semidirect
1038. C3#10595074direct (N × H)
1039. C3C3×D4×D12semidirect
1040. C3C3×#5609semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4⋊(C3⋊D3)2
C2×C3×#38112
C2×C3×D3×D122
C32×#9302
C32×C4×#672
C3×#639812
C3×#639232
C3×#639112
C3×#639102
C3×#639092
C3×#638942
C3×#56093
C3×D4×D123
#105950743