Finite Group Databasebeta

← C3×D3×#890 #13173984

Subgroups — C3×D3×#890 #13173984

Order 1728.

1134 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64099C211yesmaximal, characteristic, complemented
2C32×D3×C4⋊C4C211yesmaximal, characteristic
3C32×#890C211yesmaximal, characteristic, complemented
4C3×D3×C4⋊Dic3C212yesmaximal
5C3×D3×C4⋊Dic3C211yesmaximal, characteristic
6C3×D3×Dic3⋊C4C212yesmaximal
7C3×C4×D3×Dic3C211yesmaximal, characteristic
8C3×#63872C211yesmaximal, characteristic, complemented
9C3×#63869C211yesmaximal, characteristic, complemented
10C3×#63846C212yesmaximal, complemented
11C3×#63845C212yesmaximal, complemented
12C3×D3×#125—31nomaximal
13C2×C3×#890—31nomaximal
14D3×#890C311yesmaximal, characteristic, direct product factor
15C2×C32×C4×D3C2212yes—
16C2×C32×C4×D3C2211yescharacteristic
17C2×C3×D3×Dic3C2211yescharacteristic
18C2×C3×D3×Dic3C2211yescharacteristic
19C2×C3×D3×Dic3C2212yes—
20C33×C4⋊C4C2211yescharacteristic
21C3×C4⋊(C3⋊Dic3)C2212yes—
22C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C3×#3750C2212yes—
24C3×C4×C3⋊Dic3C2211yescharacteristic
25C32×C4⋊Dic3C2212yes—
26C32×C4⋊Dic3C2211yescharacteristic
27C32×C4⋊Dic3C2211yescharacteristic
28C32×Dic3⋊C4C2212yes—
29C32×Dic3⋊C4C2212yes—
30C32×C4×Dic3C2211yescharacteristic
31C3×#3724C2212yes—
32C3×Dic3⋊Dic3C2212yes—
33C3×Dic3⋊Dic3C2212yes—
34C3×Dic3⋊Dic3C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×Dic32C2211yescharacteristic
37C3×Dic32C2211yescharacteristic
38C32×#125—31no—
39C2×C32×C4⋊C4—31no—
40#64099C2×C311yescharacteristic, complemented
41C2×C3×C4⋊Dic3—32no—
42C2×C3×C4⋊Dic3—31no—
43C2×C3×Dic3⋊C4—32no—
44C2×C3×C4×Dic3—31no—
45C3×D3×C4⋊C4—21no—
46C3×D3×C4⋊C4—32no—
47C3×D3×C4⋊C4—31no—
48C3×D3×C4⋊C4—32no—
49C3×D3×C4⋊C4D311yescharacteristic
50C3×D3×C4⋊C4C2×C311yescharacteristic
51C3×#890—21no—
52C3×#890—31no—
53C3×#890—31no—
54C3×#890—32no—
55C3×#890—31no—
56C3×#890—31no—
57C3×#890—32no—
58C3×#890—31no—
59C3×#890—61no—
60C3×#890D311yescharacteristic, direct product factor
61C3×#890C2×C311yescharacteristic, complemented
62C3×#889—32no—
63C3×#889—32no—
64C3×C42×D3—31no—
65C3×#870—31no—
66D3×C4⋊Dic3C2×C311yescharacteristic
67D3×C4⋊Dic3C2×C312yes—
68D3×Dic3⋊C4C2×C312yes—
69C4×D3×Dic3C2×C311yescharacteristic
70#63872C2×C311yescharacteristic, complemented
71#63869C2×C311yescharacteristic, complemented
72#63846C2×C312yescomplemented
73#63845C2×C312yescomplemented
74C22×C32×D3C2311yescharacteristic
75C2×C33×C4C2312yes—
76C2×C33×C4C2311yescharacteristic
77C2×C3×C3⋊Dic3C2311yescharacteristic
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2312yes—
80C2×C32×Dic3C2311yescharacteristic
81C2×C32×Dic3C2311yescharacteristic
82C2×C32×Dic3C2312yes—
83C2×C32×Dic3C2312yes—
84C2×C32×Dic3C2311yescharacteristic
85C32×C4×D3—24no—
86C32×C4×D3Q814yes—
87C3×D3×Dic3—22no—
88C3×D3×Dic3—22no—
89C3×D3×Dic3—24no—
90C2×C3×#125—91no—
91D3×#125—31no—
92C2×#890—31no—
93C22×C32×C4—31no—
94C22×C32×C4—32no—
95C22×C3×Dic3—31no—
96C22×C3×Dic3—31no—
97C22×C3×Dic3—32no—
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—22no—
100C2×C3×C4×D3—32no—
101C2×C3×C4×D3—31no—
102C2×C3×C4×D3—31no—
103C2×C3×C4×D3C2×D312yes—
104C2×C3×C4×D3C2×D311yescharacteristic
105C2×C3×C4×D3C22×C312yes—
106C2×C3×C4×D3C22×C311yescharacteristic
107C2×D3×Dic3C22×C311yescharacteristic
108C2×D3×Dic3C22×C311yescharacteristic
109C2×D3×Dic3C22×C312yes—
110C32×C4⋊C4—21no—
111C32×C4⋊C4—21no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4—32no—
114C32×C4⋊C4—32no—
115C32×C4⋊C4—32no—
116C32×C4⋊C4—31no—
117C32×C4⋊C4—31no—
118C32×C4⋊C4—41no—
119C32×C4⋊C4C2×D311yescharacteristic
120C32×C4⋊C4C2×D311yescharacteristic
121C32×C4⋊C4C22×C311yescharacteristic
122C32×C42—31no—
123C4⋊(C3⋊Dic3)C22×C312yes—
124C4⋊(C3⋊Dic3)C22×C311yescharacteristic
125#3750C22×C312yes—
126C4×C3⋊Dic3C22×C311yescharacteristic
127C3×C4⋊Dic3—22no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3—32no—
131C3×C4⋊Dic3—32no—
132C3×C4⋊Dic3—31no—
133C3×C4⋊Dic3—31no—
134C3×C4⋊Dic3—32no—
135C3×C4⋊Dic3—32no—
136C3×C4⋊Dic3—32no—
137C3×C4⋊Dic3—32no—
138C3×C4⋊Dic3—62no—
139C3×C4⋊Dic3—61no—
140C3×C4⋊Dic3C2×D312yes—
141C3×C4⋊Dic3C2×D311yescharacteristic
142C3×C4⋊Dic3C2×D311yescharacteristic
143C3×C4⋊Dic3C22×C312yes—
144C3×C4⋊Dic3C22×C311yescharacteristic
145C3×C4⋊Dic3C22×C311yescharacteristic
146C3×Dic3⋊C4—22no—
147C3×Dic3⋊C4—22no—
148C3×Dic3⋊C4—32no—
149C3×Dic3⋊C4—32no—
150C3×Dic3⋊C4—32no—
151C3×Dic3⋊C4—32no—
152C3×Dic3⋊C4—32no—
153C3×Dic3⋊C4—32no—
154C3×Dic3⋊C4—32no—
155C3×Dic3⋊C4—32no—
156C3×Dic3⋊C4—62no—
157C3×Dic3⋊C4C2×D312yes—
158C3×Dic3⋊C4C2×D312yes—
159C3×Dic3⋊C4C22×C312yes—
160C3×Dic3⋊C4C22×C312yes—
161C3×C4×Dic3—21no—
162C3×C4×Dic3—31no—
163C3×C4×Dic3—31no—
164C3×C4×Dic3—31no—
165C3×C4×Dic3—31no—
166C3×C4×Dic3—31no—
167C3×C4×Dic3—31no—
168C3×C4×Dic3—61no—
169C3×C4×Dic3C2×D311yescharacteristic
170C3×C4×Dic3C22×C311yescharacteristic
171#3724C22×C312yes—
172Dic3⋊Dic3C22×C312yes—
173Dic3⋊Dic3C22×C312yes—
174Dic3⋊Dic3C22×C312yes—
175Dic3⋊Dic3C22×C312yes—
176Dic32C22×C311yescharacteristic
177Dic32C22×C311yescharacteristic
178C22×C33C2411yescharacteristic
179C2×C32×D3C2×Q812yes—
180C2×C32×D3#4112yes—
181C2×C32×D3#4112yes—
182C33×C4—22no—
183C33×C4C2×Q812yes—
184C3×C3⋊Dic3—21no—
185C3×C3⋊Dic3—21no—
186C3×C3⋊Dic3—22no—
187C32×Dic3—21no—
188C32×Dic3—21no—
189C32×Dic3—22no—
190C32×Dic3—22no—
191C32×Dic3C2×Q812yes—
192C3×#125—31no—
193C3×#125—31no—
194C3×#125—61no—
195C3×#125—91no—
196C3×#125—92no—
197C3×#125—92no—
198C3×#125—91no—
199C3×#125—91no—
200C2×C3×C4⋊C4—31no—
201C2×C3×C4⋊C4—31no—
202C2×C3×C4⋊C4—61no—
203C2×C3×C4⋊C4—92no—
204C2×C3×C4⋊C4—91no—
205C2×C3×C4⋊C4—92no—
206C2×C3×C42—91no—
207C2×C4⋊Dic3—32no—
208C2×C4⋊Dic3—31no—
209C2×Dic3⋊C4—32no—
210C2×C4×Dic3—31no—
211D3×C4⋊C4—32no—
212D3×C4⋊C4—32no—
213D3×C4⋊C4—31no—
214D3×C4⋊C4C3×D311yescharacteristic
215#890—31no—
216#890—31no—
217#890—31no—
218#890—32no—
219#890—31no—
220#890—32no—
221#890—31no—
222#890—61no—
223#890C3×D311yescharacteristic, direct product factor
224#889—32no—
225#889—32no—
226C42×D3—31no—
227#870—31no—
228C23×C32—31no—
229C22×C3×D3—21no—
230C22×C3×D3C22×D311yescharacteristic
231C22×C3×D3C23×C311yescharacteristic
232C2×C32×C4—21no—
233C2×C32×C4—22no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4—22no—
237C2×C32×C4—22no—
238C2×C32×C4—31no—
239C2×C32×C4—34no—
240C2×C32×C4—31no—
241C2×C32×C4—31no—
242C2×C32×C4—32no—
243C2×C32×C4—32no—
244C2×C32×C4—41no—
245C2×C32×C4—42no—
246C2×C32×C4—64no—
247C2×C32×C4C22×D312yes—
248C2×C32×C4C22×D312yes—
249C2×C32×C4C22×D311yescharacteristic
250C2×C32×C4C22×D311yescharacteristic
251C2×C32×C4C23×C312yes—
252C2×C32×C4C23×C311yescharacteristic
253C2×C3⋊Dic3C23×C311yescharacteristic
254C2×C3⋊Dic3C23×C311yescharacteristic
255C2×C3⋊Dic3C23×C312yes—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—22no—
260C2×C3×Dic3—22no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3—31no—
265C2×C3×Dic3—32no—
266C2×C3×Dic3—32no—
267C2×C3×Dic3—61no—
268C2×C3×Dic3—61no—
269C2×C3×Dic3—62no—
270C2×C3×Dic3—62no—
271C2×C3×Dic3—64no—
272C2×C3×Dic3—62no—
273C2×C3×Dic3C22×D311yescharacteristic
274C2×C3×Dic3C22×D311yescharacteristic
275C2×C3×Dic3C22×D312yes—
276C2×C3×Dic3C22×D312yes—
277C2×C3×Dic3C22×D311yescharacteristic
278C2×C3×Dic3C23×C311yescharacteristic
279C2×C3×Dic3C23×C311yescharacteristic
280C2×C3×Dic3C23×C312yes—
281C2×C3×Dic3C23×C312yes—
282C2×C3×Dic3C23×C311yescharacteristic
283C3×C4×D3—24no—
284C3×C4×D3—24no—
285C3×C4×D3—24no—
286C3×C4×D3—44no—
287C3×C4×D3—62no—
288C3×C4×D3—64no—
289C3×C4×D3—62no—
290C3×C4×D3Dic614yes—
291C3×C4×D3C3×Q814yes—
292D3×Dic3—22no—
293D3×Dic3—22no—
294D3×Dic3—24no—
295C2×#125—91noSylow
296C2×C33C22×Q811yescharacteristic
297C2×C33C2×#4111yescharacteristic
298C2×C33C2×#4111yescharacteristic
299C32×D3#12514yescomplemented
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—32no—
303C22×C3×C4—32no—
304C22×C3×C4—61no—
305C22×C3×C4—62no—
306C22×C3×C4—91no—
307C22×C3×C4—91no—
308C22×C3×C4—92no—
309C22×Dic3—31no—
310C22×Dic3—31no—
311C22×Dic3—32no—
312C2×C4×D3—31no—
313C2×C4×D3—31no—
314C2×C4×D3—32no—
315C2×C4×D3C2×C3×D312yes—
316C2×C4×D3C2×C3×D311yescharacteristic
317C3×C4⋊C4—21no—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—32no—
321C3×C4⋊C4—32no—
322C3×C4⋊C4—31no—
323C3×C4⋊C4—32no—
324C3×C4⋊C4—31no—
325C3×C4⋊C4—32no—
326C3×C4⋊C4—32no—
327C3×C4⋊C4—32no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—41no—
331C3×C4⋊C4—62no—
332C3×C4⋊C4—62no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—62no—
336C3×C4⋊C4—92no—
337C3×C4⋊C4—92no—
338C3×C4⋊C4—92no—
339C3×C4⋊C4—92no—
340C3×C4⋊C4—92no—
341C3×C4⋊C4—92no—
342C3×C4⋊C4—92no—
343C3×C4⋊C4—91no—
344C3×C4⋊C4D3211yescharacteristic
345C3×C4⋊C4C2×C3×D311yescharacteristic
346C3×C4⋊C4C2×C3×D311yescharacteristic
347C3×C42—31no—
348C3×C42—31no—
349C3×C42—61no—
350C3×C42—91no—
351C3×C42—91no—
352C3×C42—91no—
353C4⋊Dic3—31no—
354C4⋊Dic3—32no—
355C4⋊Dic3—32no—
356C4⋊Dic3—31no—
357C4⋊Dic3—32no—
358C4⋊Dic3—32no—
359C4⋊Dic3—32no—
360C4⋊Dic3—32no—
361C4⋊Dic3—62no—
362C4⋊Dic3—61no—
363C4⋊Dic3C2×C3×D311yescharacteristic
364C4⋊Dic3C2×C3×D312yes—
365C4⋊Dic3C2×C3×D311yescharacteristic
366Dic3⋊C4—32no—
367Dic3⋊C4—32no—
368Dic3⋊C4—32no—
369Dic3⋊C4—32no—
370Dic3⋊C4—32no—
371Dic3⋊C4—32no—
372Dic3⋊C4—32no—
373Dic3⋊C4—32no—
374Dic3⋊C4—62no—
375Dic3⋊C4C2×C3×D312yes—
376Dic3⋊C4C2×C3×D312yes—
377C4×Dic3—31no—
378C4×Dic3—31no—
379C4×Dic3—31no—
380C4×Dic3—31no—
381C4×Dic3—31no—
382C4×Dic3—31no—
383C4×Dic3—61no—
384C4×Dic3C2×C3×D311yescharacteristic
385C22×C32—21no—
386C22×C32—21no—
387C22×C32—21no—
388C22×C32—32no—
389C22×C32—32no—
390C22×C32—32no—
391C22×C32—41no—
392C22×C32C23×D311yescharacteristic
393C22×C32C23×D311yescharacteristic
394C22×C32C24×C311yescharacteristic
395C2×C3×D3—22no—
396C2×C3×D3—22no—
397C2×C3×D3—22no—
398C2×C3×D3C2×Dic612yes—
399C2×C3×D3#23712yes—
400C2×C3×D3#23912yes—
401C2×C3×D3C2×C3×Q812yes—
402C2×C3×D3C3×#4112yes—
403C2×C3×D3C3×#4112yes—
404C32×C4—22no—
405C32×C4—22no—
406C32×C4—22no—
407C32×C4—22no—
408C32×C4—22no—
409C32×C4—22no—
410C32×C4—32no—
411C32×C4—42no—
412C32×C4—42no—
413C32×C4—42no—
414C32×C4—42no—
415C32×C4—61no—
416C32×C4—61no—
417C32×C4—62no—
418C32×C4—62no—
419C32×C4—82no—
420C32×C4C2×Dic612yes—
421C32×C4D3×Q812yes—
422C32×C4C2×C3×Q812yes—
423C3⋊Dic3—21no—
424C3⋊Dic3—21no—
425C3⋊Dic3—22no—
426C3×Dic3—22no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—22no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—22no—
433C3×Dic3—22no—
434C3×Dic3—22no—
435C3×Dic3—42no—
436C3×Dic3—41no—
437C3×Dic3—42no—
438C3×Dic3—41no—
439C3×Dic3—61no—
440C3×Dic3—61no—
441C3×Dic3—62no—
442C3×Dic3—61no—
443C3×Dic3—61no—
444C3×Dic3—62no—
445C3×Dic3—121no—
446C3×Dic3—121no—
447C3×Dic3—122no—
448C3×Dic3C2×Dic612yes—
449C3×Dic3C2×C3×Q812yes—
450#125—31no—
451#125—91no—
452#125—92no—
453#125—92no—
454#125—91no—
455#125—91no—
456C2×C4⋊C4—31no—
457C2×C4⋊C4—92no—
458C2×C4⋊C4—91no—
459C2×C4⋊C4—92no—
460C2×C42—91no—
461C33C2×#12511yescharacteristic, complemented, Sylow
462C23×C3—31no—
463C23×C3—31no—
464C23×C3—61no—
465C22×D3C22×C3×D311yescharacteristic
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—31no—
473C2×C3×C4—31no—
474C2×C3×C4—34no—
475C2×C3×C4—34no—
476C2×C3×C4—31no—
477C2×C3×C4—31no—
478C2×C3×C4—32no—
479C2×C3×C4—32no—
480C2×C3×C4—31no—
481C2×C3×C4—31no—
482C2×C3×C4—32no—
483C2×C3×C4—32no—
484C2×C3×C4—41no—
485C2×C3×C4—42no—
486C2×C3×C4—64no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—62no—
491C2×C3×C4—62no—
492C2×C3×C4—64no—
493C2×C3×C4—64no—
494C2×C3×C4—91no—
495C2×C3×C4—91no—
496C2×C3×C4—92no—
497C2×C3×C4—124no—
498C2×C3×C4—182no—
499C2×C3×C4—182no—
500C2×C3×C4—184no—
501C2×C3×C4C2×D3212yes—
502C2×C3×C4C2×D3211yescharacteristic
503C2×C3×C4C22×C3×D312yes—
504C2×C3×C4C22×C3×D312yes—
505C2×C3×C4C22×C3×D311yescharacteristic
506C2×C3×C4C22×C3×D311yescharacteristic
507C2×Dic3—31no—
508C2×Dic3—31no—
509C2×Dic3—31no—
510C2×Dic3—31no—
511C2×Dic3—32no—
512C2×Dic3—32no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—62no—
516C2×Dic3—62no—
517C2×Dic3—64no—
518C2×Dic3—62no—
519C2×Dic3C22×C3×D311yescharacteristic
520C2×Dic3C22×C3×D311yescharacteristic
521C2×Dic3C22×C3×D312yes—
522C2×Dic3C22×C3×D312yes—
523C2×Dic3C22×C3×D311yescharacteristic
524C4×D3—24no—
525C4×D3—62no—
526C4×D3—62no—
527C4×D3—64no—
528C4×D3C3×Dic614yes—
529C2×C32—21no—
530C2×C32—21no—
531C2×C32—21no—
532C2×C32—21no—
533C2×C32—21no—
534C2×C32—21no—
535C2×C32—21no—
536C2×C32—21no—
537C2×C32—21no—
538C2×C32—34no—
539C2×C32—41no—
540C2×C32—41no—
541C2×C32—41no—
542C2×C32C22×Dic611yescharacteristic
543C2×C32C2×#23711yescharacteristic
544C2×C32C2×D3×Q811yescharacteristic
545C2×C32C2×#23911yescharacteristic
546C2×C32D3×#4111yescharacteristic
547C2×C32D3×#4111yescharacteristic
548C2×C32C22×C3×Q811yescharacteristic
549C2×C32C2×C3×#4111yescharacteristic
550C2×C32C2×C3×#4111yescharacteristic
551C3×D3—24no—
552C3×D3#89014yesdirect product factor
553C3×D3C3×#12514yescomplemented
554C22×C4—31no—
555C22×C4—32no—
556C22×C4—91no—
557C22×C4—91no—
558C22×C4—92no—
559C4⋊C4—32no—
560C4⋊C4—31no—
561C4⋊C4—32no—
562C4⋊C4—32no—
563C4⋊C4—31no—
564C4⋊C4—92no—
565C4⋊C4—92no—
566C4⋊C4—92no—
567C4⋊C4—92no—
568C4⋊C4—92no—
569C4⋊C4—92no—
570C4⋊C4—92no—
571C4⋊C4—91no—
572C4⋊C4C3×D3211yescharacteristic
573C42—31no—
574C42—91no—
575C42—91no—
576C42—91no—
577C22×C3—21no—
578C22×C3—21no—
579C22×C3—21no—
580C22×C3—32no—
581C22×C3—32no—
582C22×C3—32no—
583C22×C3—32no—
584C22×C3—32no—
585C22×C3—32no—
586C22×C3—41no—
587C22×C3—62no—
588C22×C3—62no—
589C22×C3—62no—
590C22×C3C22×D3211yescharacteristic
591C22×C3C23×C3×D311yescharacteristic
592C22×C3C23×C3×D311yescharacteristic
593C2×D3C2×C3×Dic612yes—
594C2×D3C3×#23712yes—
595C2×D3C3×#23912yes—
596C3×C4—22no—
597C3×C4—22no—
598C3×C4—22no—
599C3×C4—22no—
600C3×C4—22no—
601C3×C4—22no—
602C3×C4—32no—
603C3×C4—32no—
604C3×C4—42no—
605C3×C4—42no—
606C3×C4—42no—
607C3×C4—42no—
608C3×C4—62no—
609C3×C4—62no—
610C3×C4—61no—
611C3×C4—61no—
612C3×C4—62no—
613C3×C4—61no—
614C3×C4—61no—
615C3×C4—62no—
616C3×C4—62no—
617C3×C4—82no—
618C3×C4—122no—
619C3×C4—121no—
620C3×C4—122no—
621C3×C4—121no—
622C3×C4—181no—
623C3×C4—181no—
624C3×C4—182no—
625C3×C4D3×Dic612yes—
626C3×C4C2×C3×Dic612yes—
627C3×C4C3×D3×Q812yes—
628Dic3—22no—
629Dic3—21no—
630Dic3—22no—
631Dic3—21no—
632Dic3—61no—
633Dic3—61no—
634Dic3—62no—
635Dic3—61no—
636Dic3—62no—
637Dic3—61no—
638Dic3—121no—
639Dic3—122no—
640Dic3—121no—
641Dic3C2×C3×Dic612yes—
642C32—21no—
643C32—21no—
644C32—21no—
645C32—41no—
646C32C2×#89011yescharacteristic, complemented
647C32D3×#12511yescharacteristic, complemented
648C32C2×C3×#12511yescharacteristic, complemented
649C23—31no—
650C2×C4—31no—
651C2×C4—34no—
652C2×C4—31no—
653C2×C4—31no—
654C2×C4—32no—
655C2×C4—32no—
656C2×C4—64no—
657C2×C4—91no—
658C2×C4—91no—
659C2×C4—92no—
660C2×C4—182no—
661C2×C4—184no—
662C2×C4—182no—
663C2×C4C2×C3×D3212yes—
664C2×C4C2×C3×D3211yescharacteristic
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—34no—
675C2×C3—34no—
676C2×C3—41no—
677C2×C3—41no—
678C2×C3—41no—
679C2×C3—64no—
680C2×C3C2×D3×Dic611yescharacteristic
681C2×C3D3×#23711yescharacteristic
682C2×C3D3×#23911yescharacteristic
683C2×C3C22×C3×Dic611yescharacteristic
684C2×C3C2×C3×#23711yescharacteristic
685C2×C3C2×C3×D3×Q811yescharacteristic
686C2×C3C2×C3×#23911yescharacteristic
687C2×C3C3×D3×#4111yescharacteristic
688C2×C3C3×D3×#4111yescharacteristic
689D3C3×#89014yesdirect product factor
690C22—32no—
691C22—32no—
692C22—32no—
693C22C22×C3×D3211yescharacteristic
694C4—22no—
695C4—32no—
696C4—61no—
697C4—62no—
698C4—62no—
699C4—61no—
700C4—181no—
701C4—182no—
702C4—181no—
703C4C3×D3×Dic612yes—
704C3—21no—
705C3—21no—
706C3—21no—
707C3—41no—
708C3D3×#89011yescharacteristic, direct product factor
709C3C2×C3×#89011yescharacteristic, complemented
710C3C3×D3×#12511yescharacteristic, complemented
711C2—34no—
712C2C2×C3×D3×Dic611yescharacteristic
713C2C3×D3×#23711yescharacteristic
714C2C3×D3×#23911yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C24
prime radicalC22×C32×D3C23
hypercenterC3×C4⋊C4D32
hypocenterC32C2×C3×#125
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. C3×#64099C2semidirect
3. C32×#890C2semidirect
8. C3×#63872C2semidirect
9. C3×#63869C2semidirect
10. C3×#63846C2semidirect
11. C3×#63845C2semidirect
14. D3×#890C3direct (N × H)
40. #64099C2×C3semidirect
60. C3×#890D3direct (N × H)
61. C3×#890C2×C3semidirect
70. #63872C2×C3semidirect
71. #63869C2×C3semidirect
72. #63846C2×C3semidirect
73. #63845C2×C3semidirect
223. #890C3×D3direct (N × H)
299. C32×D3#125semidirect
461. C33C2×#125semidirect
552. C3×D3#890direct (N × H)
553. C3×D3C3×#125semidirect
646. C32C2×#890semidirect
647. C32D3×#125semidirect
648. C32C2×C3×#125semidirect
689. D3C3×#890direct (N × H)
708. C3D3×#890direct (N × H)
709. C3C2×C3×#890semidirect
710. C3C3×D3×#125semidirect

Maximal subgroups

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

subgroupindex
C3×#640992
C32×D3×C4⋊C42
C32×#8902
C3×D3×C4⋊Dic32
C3×D3×Dic3⋊C42
C3×C4×D3×Dic32
C3×#638722
C3×#638692
C3×#638462
C3×#638452
C3×D3×#1253
C2×C3×#8903
D3×#8903