Finite Group Databasebeta

← C3×#10594381 #13173938

Subgroups — C3×#10594381 #13173938

Order 1728.

1436 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3796C211yesmaximal, characteristic, complemented
2C2×C3×#3795C211yesmaximal, characteristic, complemented
3C3×#64106C211yesmaximal, characteristic, complemented
4C32×#897C211yesmaximal, characteristic, complemented
5C32×#893C211yesmaximal, characteristic, complemented
6C3×#63906C212yesmaximal, complemented
7C3×C4×#626C211yesmaximal, characteristic, complemented
8C3×#63891C212yesmaximal, complemented
9C3×#63890C212yesmaximal, complemented
10C3×D3×C4⋊Dic3C212yesmaximal, complemented
11C3×#63866C211yesmaximal, characteristic, complemented
12C3×#5631—31nomaximal
13C3×#5555—31nomaximal
14#10594381C311yesmaximal, characteristic, direct product factor
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C2×C32×D12C2211yescharacteristic
18C2×C32×C4×D3C2212yes—
19C2×C32×C4×D3C2211yescharacteristic
20C2×C32×Dic6C2211yescharacteristic
21C2×C3×#626C2212yes—
22C2×C3×#626C2211yescharacteristic
23C2×C3×#625C2212yes—
24C2×C3×D3×Dic3C2212yes—
25C2×C3×D3×Dic3C2212yes—
26C3×#3796—24no—
27C3×#3795—24no—
28C33×C4⋊C4C2211yescharacteristic
29C3×#3752C2212yes—
30C3×C4⋊(C3⋊Dic3)C2212yes—
31C32×(C2×D3)⋊C4C2212yes—
32C32×(C2×D3)⋊C4C2212yes—
33C32×C4⋊Dic3C2212yes—
34C32×C4×Dic3C2211yescharacteristic
35C3×Dic3⋊Dic3C2212yes—
36C3×Dic3⋊Dic3C2212yes—
37C3×Dic3⋊Dic3C2211yescharacteristic
38C3×#3722C2211yescharacteristic
39C3×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×C3×#239—31no—
41C2×C3×#237—31no—
42C2×C3×#237—31no—
43C2×C3×#235—31no—
44C2×#3796C2×C311yescharacteristic, complemented
45C2×#3795C2×C311yescharacteristic, complemented
46C32×C22⋊Q8—31no—
47C32×C4×D4—31no—
48#64106C2×C311yescharacteristic, complemented
49C3×#944—31no—
50C3×#930—32no—
51C3×C4×#67—31no—
52C2×C3×C4⋊Dic3—32no—
53C3×#897—21no—
54C3×#897—31no—
55C3×#897—31no—
56C3×#897—61no—
57C3×#897D311yescharacteristic, complemented
58C3×#897C2×C311yescharacteristic, complemented
59C3×#894—32no—
60C3×#893—21no—
61C3×#893D311yescharacteristic, complemented
62C3×#893C2×C311yescharacteristic, complemented
63C3×D3×C4⋊C4—32no—
64C3×#886—32no—
65C3×#886—32no—
66C3×#884—32no—
67C3×#883—32no—
68C3×C4×D12—31no—
69C3×#869—31no—
70#63906C2×C312yescomplemented
71C4×#626C2×C311yescharacteristic, complemented
72#63891C2×C312yescomplemented
73#63890C2×C312yescomplemented
74D3×C4⋊Dic3C2×C312yescomplemented
75#63866C2×C311yescharacteristic, complemented
76C22×C3×C3⋊D3C2311yescharacteristic
77C22×C32×D3C2311yescharacteristic
78C22×C32×D3C2312yes—
79C2×C33×C4C2312yes—
80C2×C33×C4C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2312yes—
83C3×C4×C3⋊D3—22no—
84C3×#634—22no—
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2312yes—
87C2×C32×Dic3C2311yescharacteristic
88C2×C32×Dic3C2311yescharacteristic
89C32×D12D414yescomplemented
90C32×C4×D3—22no—
91C32×C4×D3—24no—
92C32×Dic6—22no—
93C3×#626—24no—
94C3×#626—22no—
95C3×#625—24no—
96C3×D3×Dic3—24no—
97C3×D3×Dic3—24no—
98C3×#547—91no—
99#5631—31no—
100#5555—31no—
101C2×C32×Q8—31no—
102C2×C32×D4—31no—
103C22×C32×C4—32no—
104C22×C32×C4—31no—
105C2×C4×C3⋊D3C22×C311yescharacteristic
106C2×#634C22×C311yescharacteristic
107C2×C3×#67—32no—
108C2×C3×#67—32no—
109C2×C3×#67—31no—
110C2×C3×#67—32no—
111C22×C3×Dic3—32no—
112C22×C3×Dic3—32no—
113C3×#239—64no—
114C3×#237—64no—
115C3×#237—64no—
116C3×#235—64no—
117C2×C3×D12—21no—
118C2×C3×D12—32no—
119C2×C3×D12—31no—
120C2×C3×D12C2×D311yescharacteristic
121C2×C3×D12C22×C311yescharacteristic
122C2×C3×C4×D3—22no—
123C2×C3×C4×D3—21no—
124C2×C3×C4×D3—32no—
125C2×C3×C4×D3—32no—
126C2×C3×C4×D3—31no—
127C2×C3×C4×D3—31no—
128C2×C3×C4×D3—61no—
129C2×C3×C4×D3C2×D312yes—
130C2×C3×C4×D3C2×D311yescharacteristic
131C2×C3×C4×D3C22×C312yes—
132C2×C3×C4×D3C22×C311yescharacteristic
133C2×C3×Dic6—21no—
134C2×C3×Dic6—31no—
135C2×C3×Dic6—31no—
136C2×C3×Dic6—61no—
137C2×C3×Dic6C2×D311yescharacteristic
138C2×C3×Dic6C22×C311yescharacteristic
139C2×#626C22×C312yes—
140C2×#626C22×C311yescharacteristic
141C2×#625C22×C312yes—
142C2×D3×Dic3C22×C312yes—
143C2×D3×Dic3C22×C312yes—
144#3796—24no—
145#3795—24no—
146C32×C4⋊C4—21no—
147C32×C4⋊C4—21no—
148C32×C4⋊C4—21no—
149C32×C4⋊C4—32no—
150C32×C4⋊C4—41no—
151C32×C4⋊C4C2×D311yescharacteristic
152C32×C4⋊C4C2×D311yescharacteristic
153C32×C4⋊C4C22×C311yescharacteristic
154C32×C22⋊C4—32no—
155C32×C22⋊C4—32no—
156C32×C42—31no—
157#3752C22×C312yes—
158C4⋊(C3⋊Dic3)C22×C312yes—
159C3×#217—31no—
160C3×(C2×D3)⋊C4—22no—
161C3×(C2×D3)⋊C4—22no—
162C3×(C2×D3)⋊C4—31no—
163C3×(C2×D3)⋊C4—32no—
164C3×(C2×D3)⋊C4—32no—
165C3×(C2×D3)⋊C4—31no—
166C3×(C2×D3)⋊C4—31no—
167C3×(C2×D3)⋊C4—62no—
168C3×(C2×D3)⋊C4C2×D312yes—
169C3×(C2×D3)⋊C4C2×D312yes—
170C3×(C2×D3)⋊C4C22×C312yes—
171C3×(C2×D3)⋊C4C22×C312yes—
172C3×C4⋊Dic3—22no—
173C3×C4⋊Dic3—32no—
174C3×C4⋊Dic3—32no—
175C3×C4⋊Dic3—32no—
176C3×C4⋊Dic3—31no—
177C3×C4⋊Dic3—32no—
178C3×C4⋊Dic3—62no—
179C3×C4⋊Dic3C2×D312yes—
180C3×C4⋊Dic3C22×C312yes—
181C3×Dic3⋊C4—32no—
182C3×Dic3⋊C4—32no—
183C3×Dic3⋊C4—31no—
184C3×C4×Dic3—21no—
185C3×C4×Dic3C2×D311yescharacteristic
186C3×C4×Dic3C22×C311yescharacteristic
187Dic3⋊Dic3C22×C312yes—
188Dic3⋊Dic3C22×C312yes—
189Dic3⋊Dic3C22×C311yescharacteristic
190#3722C22×C311yescharacteristic
191(C2×D3)⋊Dic3C22×C311yescharacteristic
192C22×C33C2411yescharacteristic
193C2×C3×C3⋊D3—21no—
194C2×C3×C3⋊D3—21no—
195C2×C3×C3⋊D3—21no—
196C2×C32×D3—22no—
197C2×C32×D3—22no—
198C2×C32×D3—21no—
199C2×C32×D3—21no—
200C2×C32×D3—21no—
201C2×C32×D3C2×D414yes—
202C33×C4—22no—
203C33×C4C2×D412yes—
204C3×C3⋊Dic3—21no—
205C3×C3⋊Dic3—22no—
206C32×Dic3—21no—
207C32×Dic3—22no—
208C32×Dic3—21no—
209C32×Dic3#4112yescomplemented
210C2×C3×#41—91no—
211C2×C3×#41—91no—
212C2×#239—31no—
213C2×#237—31no—
214C2×#237—31no—
215C2×#235—31no—
216C3×C4⋊Q8—91no—
217C3×#123—92no—
218C3×#123—92no—
219C3×C22⋊Q8—31no—
220C3×C22⋊Q8—31no—
221C3×C22⋊Q8—61no—
222C3×C22⋊Q8—91no—
223C3×#121—92no—
224C3×C4×D4—31no—
225C3×C4×D4—31no—
226C3×C4×D4—61no—
227C3×C4×D4—91no—
228C2×C3×C4⋊C4—92no—
229#944—31no—
230#930—32no—
231C4×#67—31no—
232C2×C4⋊Dic3—32no—
233#897—31no—
234#897—31no—
235#897—61no—
236#897C3×D311yescharacteristic, complemented
237#894—32no—
238#893C3×D311yescharacteristic, complemented
239D3×C4⋊C4—32no—
240#886—32no—
241#886—32no—
242#884—32no—
243#883—32no—
244C4×D12—31no—
245#869—31no—
246C23×C32—32no—
247C23×C32—31no—
248C22×C3⋊D3C23×C311yescharacteristic
249C22×C3×D3—21no—
250C22×C3×D3—22no—
251C22×C3×D3—31no—
252C22×C3×D3—31no—
253C22×C3×D3—61no—
254C22×C3×D3C22×D311yescharacteristic
255C22×C3×D3C22×D312yes—
256C22×C3×D3C23×C311yescharacteristic
257C22×C3×D3C23×C312yes—
258C32×Q8—62no—
259C32×D4—34no—
260C2×C32×C4—21no—
261C2×C32×C4—22no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—22no—
265C2×C32×C4—22no—
266C2×C32×C4—31no—
267C2×C32×C4—32no—
268C2×C32×C4—31no—
269C2×C32×C4—31no—
270C2×C32×C4—41no—
271C2×C32×C4—42no—
272C2×C32×C4—64no—
273C2×C32×C4—62no—
274C2×C32×C4C22×D312yes—
275C2×C32×C4C22×D312yes—
276C2×C32×C4C22×D311yescharacteristic
277C2×C32×C4C22×D311yescharacteristic
278C2×C32×C4C23×C312yes—
279C2×C32×C4C23×C311yescharacteristic
280C2×C3⋊Dic3C23×C311yescharacteristic
281C2×C3⋊Dic3C23×C312yes—
282C4×C3⋊D3—22no—
283#634—22no—
284C3×#67—64no—
285C3×#67—64no—
286C3×#67—64no—
287C3×#67—62no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—22no—
292C2×C3×Dic3—32no—
293C2×C3×Dic3—31no—
294C2×C3×Dic3—32no—
295C2×C3×Dic3—31no—
296C2×C3×Dic3—61no—
297C2×C3×Dic3—62no—
298C2×C3×Dic3—64no—
299C2×C3×Dic3—64no—
300C2×C3×Dic3C22×D311yescharacteristic
301C2×C3×Dic3C22×D312yes—
302C2×C3×Dic3C22×D311yescharacteristic
303C2×C3×Dic3C22×D311yescharacteristic
304C2×C3×Dic3C23×C311yescharacteristic
305C2×C3×Dic3C23×C311yescharacteristic
306C2×C3×Dic3C23×C312yes—
307C2×C3×Dic3C23×C311yescharacteristic
308C3×D12—24no—
309C3×D12—62no—
310C3×D12—64no—
311C3×D12D1214yescomplemented
312C3×D12C3×D414yescomplemented
313C3×C4×D3—22no—
314C3×C4×D3—22no—
315C3×C4×D3—24no—
316C3×C4×D3—24no—
317C3×C4×D3—44no—
318C3×C4×D3—42no—
319C3×C4×D3—64no—
320C3×C4×D3—64no—
321C3×C4×D3—62no—
322C3×C4×D3—62no—
323C3×C4×D3—122no—
324C3×Dic6—22no—
325C3×Dic6—22no—
326C3×Dic6—42no—
327C3×Dic6—62no—
328C3×Dic6—62no—
329C3×Dic6—122no—
330#626—24no—
331#626—22no—
332#625—24no—
333D3×Dic3—24no—
334D3×Dic3—24no—
335#547—91noSylow
336C2×C33C22×D411yescharacteristic
337C2×C33C2×#4111yescharacteristic
338C2×C332−1+411yescharacteristic
339C3×C3⋊D3—41no—
340C32×D3—24no—
341C32×D3—41no—
342C3×#41—184no—
343C3×#41—184no—
344C2×C3×Q8—31no—
345C2×C3×Q8—31no—
346C2×C3×Q8—61no—
347C2×C3×Q8—91no—
348C2×C3×D4—31no—
349C2×C3×D4—31no—
350C2×C3×D4—61no—
351C2×C3×D4—91no—
352C2×C3×D4—92no—
353C2×C3×D4—92no—
354C22×C3×C4—32no—
355C22×C3×C4—31no—
356C22×C3×C4—32no—
357C22×C3×C4—31no—
358C22×C3×C4—62no—
359C22×C3×C4—61no—
360C22×C3×C4—92no—
361C22×C3×C4—92no—
362C22×C3×C4—91no—
363C2×#67—32no—
364C2×#67—32no—
365C2×#67—31no—
366C2×#67—32no—
367C22×Dic3—32no—
368C22×Dic3—32no—
369#239—64no—
370#237—64no—
371#237—64no—
372#235—64no—
373C2×D12—31no—
374C2×D12—32no—
375C2×D12C2×C3×D311yescharacteristic
376C2×C4×D3—32no—
377C2×C4×D3—32no—
378C2×C4×D3—31no—
379C2×C4×D3—31no—
380C2×C4×D3—61no—
381C2×C4×D3C2×C3×D311yescharacteristic
382C2×C4×D3C2×C3×D312yes—
383C2×Dic6—31no—
384C2×Dic6—31no—
385C2×Dic6—61no—
386C2×Dic6C2×C3×D311yescharacteristic
387C3×C4⋊C4—21no—
388C3×C4⋊C4—21no—
389C3×C4⋊C4—21no—
390C3×C4⋊C4—32no—
391C3×C4⋊C4—32no—
392C3×C4⋊C4—41no—
393C3×C4⋊C4—62no—
394C3×C4⋊C4—91no—
395C3×C4⋊C4—92no—
396C3×C4⋊C4—92no—
397C3×C4⋊C4—92no—
398C3×C4⋊C4D3211yescharacteristic
399C3×C4⋊C4C2×C3×D311yescharacteristic
400C3×C4⋊C4C2×C3×D311yescharacteristic
401C3×C22⋊C4—32no—
402C3×C22⋊C4—32no—
403C3×C22⋊C4—32no—
404C3×C22⋊C4—32no—
405C3×C22⋊C4—62no—
406C3×C22⋊C4—62no—
407C3×C22⋊C4—91no—
408C3×C22⋊C4—91no—
409C3×C22⋊C4—92no—
410C3×C42—31no—
411C3×C42—31no—
412C3×C42—61no—
413#217—31no—
414(C2×D3)⋊C4—31no—
415(C2×D3)⋊C4—32no—
416(C2×D3)⋊C4—32no—
417(C2×D3)⋊C4—31no—
418(C2×D3)⋊C4—31no—
419(C2×D3)⋊C4—62no—
420(C2×D3)⋊C4C2×C3×D312yes—
421(C2×D3)⋊C4C2×C3×D312yes—
422C4⋊Dic3—32no—
423C4⋊Dic3—32no—
424C4⋊Dic3—32no—
425C4⋊Dic3—32no—
426C4⋊Dic3—31no—
427C4⋊Dic3—62no—
428C4⋊Dic3C2×C3×D312yes—
429Dic3⋊C4—32no—
430Dic3⋊C4—32no—
431Dic3⋊C4—31no—
432C4×Dic3C2×C3×D311yescharacteristic
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—21no—
436C22×C32—34no—
437C22×C32—41no—
438C22×C32—61no—
439C22×C32—62no—
440C22×C32—62no—
441C22×C32—61no—
442C22×C32—61no—
443C22×C32C23×D311yescharacteristic
444C22×C32C23×D311yescharacteristic
445C22×C32C24×C311yescharacteristic
446C2×C3⋊D3—21no—
447C2×C3⋊D3—21no—
448C2×C3⋊D3—21no—
449C2×C3×D3—22no—
450C2×C3×D3—22no—
451C2×C3×D3—22no—
452C2×C3×D3—22no—
453C2×C3×D3—22no—
454C2×C3×D3—21no—
455C2×C3×D3—21no—
456C2×C3×D3—21no—
457C2×C3×D3—21no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—24no—
461C2×C3×D3—42no—
462C2×C3×D3—41no—
463C2×C3×D3—42no—
464C2×C3×D3—41no—
465C2×C3×D3—62no—
466C2×C3×D3—61no—
467C2×C3×D3—61no—
468C2×C3×D3—61no—
469C2×C3×D3—61no—
470C2×C3×D3—61no—
471C2×C3×D3—61no—
472C2×C3×D3—121no—
473C2×C3×D3—121no—
474C2×C3×D3C2×D1214yes—
475C2×C3×D3C2×C3×D414yes—
476C32×C4—22no—
477C32×C4—22no—
478C32×C4—22no—
479C32×C4—22no—
480C32×C4—22no—
481C32×C4—22no—
482C32×C4—32no—
483C32×C4—42no—
484C32×C4—42no—
485C32×C4—42no—
486C32×C4—42no—
487C32×C4—61no—
488C32×C4—62no—
489C32×C4—61no—
490C32×C4—82no—
491C32×C4C2×D1212yes—
492C32×C4D3×D412yes—
493C32×C4C2×C3×D412yes—
494C3⋊Dic3—21no—
495C3⋊Dic3—22no—
496C3×Dic3—22no—
497C3×Dic3—21no—
498C3×Dic3—21no—
499C3×Dic3—21no—
500C3×Dic3—22no—
501C3×Dic3—21no—
502C3×Dic3—22no—
503C3×Dic3—42no—
504C3×Dic3—41no—
505C3×Dic3—41no—
506C3×Dic3—62no—
507C3×Dic3—61no—
508C3×Dic3—62no—
509C3×Dic3—61no—
510C3×Dic3—122no—
511C3×Dic3—121no—
512C3×Dic3#23712yescomplemented
513C3×Dic3C3×#4112yescomplemented
514C2×#41—91no—
515C2×#41—91no—
516C4⋊Q8—91no—
517#123—92no—
518#123—92no—
519C22⋊Q8—31no—
520C22⋊Q8—91no—
521#121—92no—
522C4×D4—31no—
523C4×D4—91no—
524C2×C4⋊C4—92no—
525C33#54711yescharacteristic, complemented, Sylow
526C23×C3—32no—
527C23×C3—32no—
528C23×C3—31no—
529C23×C3—31no—
530C23×C3—61no—
531C23×C3—62no—
532C23×C3—91no—
533C22×D3—31no—
534C22×D3—31no—
535C22×D3—61no—
536C22×D3C22×C3×D311yescharacteristic
537C22×D3C22×C3×D312yes—
538C3×Q8—62no—
539C3×Q8—62no—
540C3×Q8—122no—
541C3×Q8—182no—
542C3×D4—34no—
543C3×D4—34no—
544C3×D4—64no—
545C3×D4—182no—
546C3×D4—184no—
547C3×D4—184no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—31no—
555C2×C3×C4—31no—
556C2×C3×C4—31no—
557C2×C3×C4—32no—
558C2×C3×C4—31no—
559C2×C3×C4—32no—
560C2×C3×C4—31no—
561C2×C3×C4—31no—
562C2×C3×C4—41no—
563C2×C3×C4—42no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—62no—
567C2×C3×C4—61no—
568C2×C3×C4—64no—
569C2×C3×C4—64no—
570C2×C3×C4—62no—
571C2×C3×C4—62no—
572C2×C3×C4—91no—
573C2×C3×C4—92no—
574C2×C3×C4—122no—
575C2×C3×C4—124no—
576C2×C3×C4—184no—
577C2×C3×C4—184no—
578C2×C3×C4—182no—
579C2×C3×C4C2×D3212yes—
580C2×C3×C4C2×D3211yescharacteristic
581C2×C3×C4C22×C3×D312yes—
582C2×C3×C4C22×C3×D312yes—
583C2×C3×C4C22×C3×D311yescharacteristic
584C2×C3×C4C22×C3×D311yescharacteristic
585#67—64no—
586#67—64no—
587#67—64no—
588#67—62no—
589C2×Dic3—32no—
590C2×Dic3—31no—
591C2×Dic3—32no—
592C2×Dic3—31no—
593C2×Dic3—61no—
594C2×Dic3—62no—
595C2×Dic3—64no—
596C2×Dic3—64no—
597C2×Dic3C22×C3×D311yescharacteristic
598C2×Dic3C22×C3×D312yes—
599C2×Dic3C22×C3×D311yescharacteristic
600C2×Dic3C22×C3×D311yescharacteristic
601D12—62no—
602D12—64no—
603D12C3×D1214yescomplemented
604C4×D3—22no—
605C4×D3—24no—
606C4×D3—64no—
607C4×D3—64no—
608C4×D3—62no—
609C4×D3—62no—
610C4×D3—122no—
611Dic6—22no—
612Dic6—62no—
613Dic6—62no—
614Dic6—122no—
615C2×C32—21no—
616C2×C32—21no—
617C2×C32—21no—
618C2×C32—21no—
619C2×C32—21no—
620C2×C32—21no—
621C2×C32—21no—
622C2×C32—21no—
623C2×C32—21no—
624C2×C32—41no—
625C2×C32—41no—
626C2×C32—41no—
627C2×C32—64no—
628C2×C32—121no—
629C2×C32C22×D1211yescharacteristic
630C2×C32C2×D3×D411yescharacteristic
631C2×C32C2×#23711yescharacteristic
632C2×C32#100711yescharacteristic
633C2×C32D3×#4111yescharacteristic
634C2×C32#101011yescharacteristic
635C2×C32C22×C3×D411yescharacteristic
636C2×C32C2×C3×#4111yescharacteristic
637C2×C32C3×2−1+411yescharacteristic
638C3⋊D3—41no—
639C3×D3—24no—
640C3×D3—24no—
641C3×D3—44no—
642C3×D3—42no—
643C3×D3—41no—
644C3×D3—41no—
645C3×D3—122no—
646C3×D3—121no—
647C3×D3—121no—
648#41—184no—
649#41—184no—
650C2×Q8—31no—
651C2×Q8—91no—
652C2×D4—31no—
653C2×D4—91no—
654C2×D4—92no—
655C2×D4—92no—
656C22×C4—32no—
657C22×C4—31no—
658C22×C4—92no—
659C22×C4—92no—
660C22×C4—91no—
661C4⋊C4—32no—
662C4⋊C4—91no—
663C4⋊C4—92no—
664C4⋊C4—92no—
665C4⋊C4—92no—
666C4⋊C4C3×D3211yescharacteristic
667C22⋊C4—32no—
668C22⋊C4—32no—
669C22⋊C4—91no—
670C22⋊C4—91no—
671C22⋊C4—92no—
672C42—31no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—34no—
677C22×C3—34no—
678C22×C3—41no—
679C22×C3—64no—
680C22×C3—62no—
681C22×C3—62no—
682C22×C3—62no—
683C22×C3—62no—
684C22×C3—62no—
685C22×C3—61no—
686C22×C3—61no—
687C22×C3—61no—
688C22×C3—61no—
689C22×C3—61no—
690C22×C3—61no—
691C22×C3—122no—
692C22×C3—121no—
693C22×C3—122no—
694C22×C3—121no—
695C22×C3—181no—
696C22×C3—181no—
697C22×C3—181no—
698C22×C3C22×D3211yescharacteristic
699C22×C3C23×C3×D311yescharacteristic
700C22×C3C23×C3×D311yescharacteristic
701C2×D3—22no—
702C2×D3—22no—
703C2×D3—21no—
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—62no—
707C2×D3—61no—
708C2×D3—61no—
709C2×D3—61no—
710C2×D3—61no—
711C2×D3—61no—
712C2×D3—61no—
713C2×D3—121no—
714C2×D3—121no—
715C2×D3C2×C3×D1214yes—
716C3×C4—22no—
717C3×C4—22no—
718C3×C4—22no—
719C3×C4—22no—
720C3×C4—22no—
721C3×C4—22no—
722C3×C4—32no—
723C3×C4—32no—
724C3×C4—42no—
725C3×C4—42no—
726C3×C4—42no—
727C3×C4—42no—
728C3×C4—62no—
729C3×C4—61no—
730C3×C4—62no—
731C3×C4—61no—
732C3×C4—61no—
733C3×C4—62no—
734C3×C4—61no—
735C3×C4—82no—
736C3×C4—121no—
737C3×C4—122no—
738C3×C4—121no—
739C3×C4—181no—
740C3×C4—182no—
741C3×C4D3×D1212yes—
742C3×C4C2×C3×D1212yes—
743C3×C4C3×D3×D412yes—
744Dic3—22no—
745Dic3—21no—
746Dic3—21no—
747Dic3—62no—
748Dic3—61no—
749Dic3—62no—
750Dic3—61no—
751Dic3—122no—
752Dic3—121no—
753Dic3C3×#23712yescomplemented
754C32—21no—
755C32—21no—
756C32—21no—
757C32—41no—
758C32#555511yescharacteristic, complemented
759C32#563111yescharacteristic, complemented
760C32C3×#54711yescharacteristic, complemented
761C23—32no—
762C23—31no—
763C23—91no—
764Q8—62no—
765Q8—182no—
766D4—34no—
767D4—182no—
768D4—184no—
769D4—184no—
770C2×C4—31no—
771C2×C4—31no—
772C2×C4—32no—
773C2×C4—31no—
774C2×C4—64no—
775C2×C4—62no—
776C2×C4—91no—
777C2×C4—92no—
778C2×C4—184no—
779C2×C4—184no—
780C2×C4—182no—
781C2×C4C2×C3×D3212yes—
782C2×C4C2×C3×D3211yescharacteristic
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—41no—
793C2×C3—41no—
794C2×C3—41no—
795C2×C3—64no—
796C2×C3—64no—
797C2×C3—124no—
798C2×C3—122no—
799C2×C3—121no—
800C2×C3—121no—
801C2×C3—361no—
802C2×C3C2×D3×D1211yescharacteristic
803C2×C3D3×#23711yescharacteristic
804C2×C3#6431511yescharacteristic
805C2×C3C22×C3×D1211yescharacteristic
806C2×C3C2×C3×D3×D411yescharacteristic
807C2×C3C2×C3×#23711yescharacteristic
808C2×C3C3×#100711yescharacteristic
809C2×C3C3×D3×#4111yescharacteristic
810C2×C3C3×#101011yescharacteristic
811D3—24no—
812D3—41no—
813D3—122no—
814D3—121no—
815D3—121no—
816C22—34no—
817C22—62no—
818C22—62no—
819C22—61no—
820C22—61no—
821C22—61no—
822C22—181no—
823C22—181no—
824C22—181no—
825C22C22×C3×D3211yescharacteristic
826C4—22no—
827C4—32no—
828C4—61no—
829C4—62no—
830C4—61no—
831C4—181no—
832C4—182no—
833C4C3×D3×D1212yes—
834C3—21no—
835C3—21no—
836C3—21no—
837C3—41no—
838C3#1059438111yescharacteristic, direct product factor
839C3C3×#555511yescharacteristic, complemented
840C3C3×#563111yescharacteristic, complemented
841C2—64no—
842C2—121no—
843C2—361no—
844C2C2×C3×D3×D1211yescharacteristic
845C2C3×D3×#23711yescharacteristic
846C2C3×#6431511yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C24
hypercenterC3×C4⋊C4D32
hypocenterC32C3×#547
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3796C2semidirect
2. C2×C3×#3795C2semidirect
3. C3×#64106C2semidirect
4. C32×#897C2semidirect
5. C32×#893C2semidirect
6. C3×#63906C2semidirect
7. C3×C4×#626C2semidirect
8. C3×#63891C2semidirect
9. C3×#63890C2semidirect
10. C3×D3×C4⋊Dic3C2semidirect
11. C3×#63866C2semidirect
14. #10594381C3direct (N × H)
44. C2×#3796C2×C3semidirect
45. C2×#3795C2×C3semidirect
48. #64106C2×C3semidirect
57. C3×#897D3semidirect
58. C3×#897C2×C3semidirect
61. C3×#893D3semidirect
62. C3×#893C2×C3semidirect
70. #63906C2×C3semidirect
71. C4×#626C2×C3semidirect
72. #63891C2×C3semidirect
73. #63890C2×C3semidirect
74. D3×C4⋊Dic3C2×C3semidirect
75. #63866C2×C3semidirect
89. C32×D12D4semidirect
209. C32×Dic3#41semidirect
236. #897C3×D3semidirect
238. #893C3×D3semidirect
311. C3×D12D12semidirect
312. C3×D12C3×D4semidirect
512. C3×Dic3#237semidirect
513. C3×Dic3C3×#41semidirect
525. C33#547semidirect
603. D12C3×D12semidirect
753. Dic3C3×#237semidirect
758. C32#5555semidirect
759. C32#5631semidirect
760. C32C3×#547semidirect
838. C3#10594381direct (N × H)
839. C3C3×#5555semidirect
840. C3C3×#5631semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37962
C2×C3×#37952
C3×#641062
C32×#8972
C32×#8932
C3×#639062
C3×C4×#6262
C3×#638912
C3×#638902
C3×D3×C4⋊Dic32
C3×#638662
C3×#56313
C3×#55553
#105943813