Finite Group Databasebeta

← C3×#10591243 #13158177

Subgroups — C3×#10591243 #13158177

Order 1728.

1106 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3750C211yesmaximal, characteristic
2C2×C32×C4×Dic3C211yesmaximal, characteristic
3C2×C3×#3724C211yesmaximal, characteristic
4C2×C3×Dic32C211yesmaximal, characteristic
5C2×C3×Dic32C211yesmaximal, characteristic
6C32×C3⋊#95C211yesmaximal, characteristic
7C3×#63579C211yesmaximal, characteristic
8C3×C4×Dic3⋊C4—31nomaximal
9C3×#4649—31nomaximal
10#10591243C311yesmaximal, characteristic, direct product factor
11C22×C33×C4C2211yescharacteristic
12C22×C3×C3⋊Dic3C2211yescharacteristic
13C22×C3×C3⋊Dic3C2211yescharacteristic
14C22×C32×Dic3C2211yescharacteristic
15C22×C32×Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C3×#3750C414yescomplemented
19C32×C4×Dic3—22no—
20C3×#3724C414yescomplemented
21C3×Dic32—22no—
22C3×Dic32C414yescomplemented
23C2×C32×C42—31no—
24C2×#3750C2×C311yescharacteristic
25C2×C3×Dic3⋊C4—31no—
26C2×C3×Dic3⋊C4—31no—
27C2×C3×Dic3⋊C4—31no—
28C2×C3×Dic3⋊C4—31no—
29C2×C3×Dic3⋊C4—61no—
30C2×C3×C4×Dic3—21no—
31C2×C3×C4×Dic3—31no—
32C2×C3×C4×Dic3—31no—
33C2×C3×C4×Dic3—31no—
34C2×C3×C4×Dic3—31no—
35C2×C3×C4×Dic3D311yescharacteristic
36C2×C3×C4×Dic3C2×C311yescharacteristic
37C2×#3724C2×C311yescharacteristic
38C2×Dic32C2×C311yescharacteristic
39C2×Dic32C2×C311yescharacteristic
40C32×#95—31no—
41C3×C3⋊#95—21no—
42C3×C3⋊#95—31no—
43C3×C3⋊#95—31no—
44C3×C3⋊#95D311yescharacteristic
45C3×C3⋊#95C2×C311yescharacteristic
46#63579C2×C311yescharacteristic
47C23×C33C2311yescharacteristic
48C2×C33×C4—21no—
49C2×C33×C4—21no—
50C2×C33×C4C2×C412yes—
51C2×C3×C3⋊Dic3—21no—
52C2×C3×C3⋊Dic3—21no—
53C2×C3×C3⋊Dic3C2×C412yes—
54C2×C3×C3⋊Dic3C2×C412yes—
55C2×C3×C3⋊Dic3C2×C412yes—
56C2×C3×C3⋊Dic3C2×C412yes—
57C2×C32×Dic3—21no—
58C2×C32×Dic3—21no—
59C2×C32×Dic3—21no—
60C2×C32×Dic3—21no—
61C2×C32×Dic3—21no—
62C2×C32×Dic3—21no—
63C2×C32×Dic3C2×C412yes—
64C2×C32×Dic3C2×C412yes—
65C2×C32×Dic3C2×C412yes—
66C2×C32×Dic3C2×C412yes—
67C2×C32×Dic3D412yes—
68C2×C32×Dic3Q812yes—
69C3×C4×C4⋊C4—91no—
70C4×Dic3⋊C4—31no—
71#4649—31no—
72C22×C32×C4—21no—
73C22×C32×C4—21no—
74C22×C32×C4—21no—
75C22×C32×C4—31no—
76C22×C32×C4—31no—
77C22×C32×C4—31no—
78C22×C32×C4—31no—
79C22×C32×C4—41no—
80C22×C32×C4C2×D311yescharacteristic
81C22×C32×C4C2×D311yescharacteristic
82C22×C32×C4C22×C311yescharacteristic
83C22×C3⋊Dic3C22×C311yescharacteristic
84C22×C3⋊Dic3C22×C311yescharacteristic
85C22×C3×Dic3—21no—
86C22×C3×Dic3—21no—
87C22×C3×Dic3—21no—
88C22×C3×Dic3—21no—
89C22×C3×Dic3—31no—
90C22×C3×Dic3—31no—
91C22×C3×Dic3—31no—
92C22×C3×Dic3—31no—
93C22×C3×Dic3—61no—
94C22×C3×Dic3—61no—
95C22×C3×Dic3C2×D311yescharacteristic
96C22×C3×Dic3C2×D311yescharacteristic
97C22×C3×Dic3C2×D311yescharacteristic
98C22×C3×Dic3C2×D311yescharacteristic
99C22×C3×Dic3C22×C311yescharacteristic
100C22×C3×Dic3C22×C311yescharacteristic
101C22×C3×Dic3C22×C311yescharacteristic
102C22×C3×Dic3C22×C311yescharacteristic
103C32×C42—62no—
104#3750C3×C414yescomplemented
105C3×Dic3⋊C4—34no—
106C3×Dic3⋊C4—34no—
107C3×Dic3⋊C4—34no—
108C3×Dic3⋊C4—34no—
109C3×Dic3⋊C4—64no—
110C3×C4×Dic3—24no—
111C3×C4×Dic3—22no—
112C3×C4×Dic3—22no—
113C3×C4×Dic3—34no—
114C3×C4×Dic3—34no—
115C3×C4×Dic3—62no—
116C3×C4×Dic3—62no—
117#3724C3×C414yescomplemented
118Dic32—22no—
119Dic32C3×C414yescomplemented
120C22×C33C22×C411yescharacteristic
121C22×C33C22×C411yescharacteristic
122C22×C33C22×C411yescharacteristic
123C22×C33C2×D411yescharacteristic
124C22×C33C2×Q811yescharacteristic
125C22×C33#4111yescharacteristic
126C22×C33#4111yescharacteristic
127C33×C4—22no—
128C3×C3⋊Dic3—22no—
129C3×C3⋊Dic3C4214yescomplemented
130C32×Dic3—22no—
131C32×Dic3—22no—
132C32×Dic3—22no—
133C32×Dic3C4⋊C414yescomplemented
134C2×C3×C4⋊C4—91no—
135C2×C3×C4⋊C4—91no—
136C2×C3×C42—31no—
137C2×C3×C42—31no—
138C2×C3×C42—61no—
139C2×C3×C42—91no—
140C2×C3×C42—91no—
141C2×Dic3⋊C4—31no—
142C2×Dic3⋊C4—31no—
143C2×Dic3⋊C4—31no—
144C2×Dic3⋊C4—31no—
145C2×Dic3⋊C4—61no—
146C2×C4×Dic3—31no—
147C2×C4×Dic3—31no—
148C2×C4×Dic3—31no—
149C2×C4×Dic3—31no—
150C2×C4×Dic3C3×D311yescharacteristic
151C3×#95—31no—
152C3×#95—31no—
153C3×#95—61no—
154C3×#95—91no—
155C3⋊#95—31no—
156C3⋊#95—31no—
157C3⋊#95C3×D311yescharacteristic
158C23×C32—21no—
159C23×C32—21no—
160C23×C32—21no—
161C23×C32—41no—
162C23×C32C22×D311yescharacteristic
163C23×C32C22×D311yescharacteristic
164C23×C32C23×C311yescharacteristic
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—22no—
168C2×C32×C4—22no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—22no—
174C2×C32×C4—22no—
175C2×C32×C4—22no—
176C2×C32×C4—32no—
177C2×C32×C4—32no—
178C2×C32×C4—32no—
179C2×C32×C4—32no—
180C2×C32×C4—32no—
181C2×C32×C4—32no—
182C2×C32×C4—42no—
183C2×C32×C4—41no—
184C2×C32×C4—41no—
185C2×C32×C4—41no—
186C2×C32×C4—41no—
187C2×C32×C4—42no—
188C2×C32×C4—42no—
189C2×C32×C4—61no—
190C2×C32×C4—61no—
191C2×C32×C4—61no—
192C2×C32×C4—61no—
193C2×C32×C4—61no—
194C2×C32×C4—61no—
195C2×C32×C4C4×D312yes—
196C2×C32×C4C4×D312yes—
197C2×C32×C4C2×C3×C412yes—
198C2×C3⋊Dic3—21no—
199C2×C3⋊Dic3—21no—
200C2×C3⋊Dic3C2×C3×C412yes—
201C2×C3⋊Dic3C2×C3×C412yes—
202C2×C3⋊Dic3C2×C3×C412yes—
203C2×C3⋊Dic3C2×C3×C412yes—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—21no—
207C2×C3×Dic3—21no—
208C2×C3×Dic3—21no—
209C2×C3×Dic3—21no—
210C2×C3×Dic3—21no—
211C2×C3×Dic3—21no—
212C2×C3×Dic3—21no—
213C2×C3×Dic3—21no—
214C2×C3×Dic3—21no—
215C2×C3×Dic3—21no—
216C2×C3×Dic3—21no—
217C2×C3×Dic3—21no—
218C2×C3×Dic3—22no—
219C2×C3×Dic3—22no—
220C2×C3×Dic3—22no—
221C2×C3×Dic3—22no—
222C2×C3×Dic3—22no—
223C2×C3×Dic3—22no—
224C2×C3×Dic3—32no—
225C2×C3×Dic3—32no—
226C2×C3×Dic3—32no—
227C2×C3×Dic3—32no—
228C2×C3×Dic3—32no—
229C2×C3×Dic3—32no—
230C2×C3×Dic3—32no—
231C2×C3×Dic3—32no—
232C2×C3×Dic3—41no—
233C2×C3×Dic3—41no—
234C2×C3×Dic3—41no—
235C2×C3×Dic3—41no—
236C2×C3×Dic3—62no—
237C2×C3×Dic3—62no—
238C2×C3×Dic3—62no—
239C2×C3×Dic3—62no—
240C2×C3×Dic3—61no—
241C2×C3×Dic3—61no—
242C2×C3×Dic3—61no—
243C2×C3×Dic3—61no—
244C2×C3×Dic3—121no—
245C2×C3×Dic3—121no—
246C2×C3×Dic3Dic612yes—
247C2×C3×Dic3C4×D312yes—
248C2×C3×Dic3C4×D312yes—
249C2×C3×Dic3C4×D312yes—
250C2×C3×Dic3C4×D312yes—
251C2×C3×Dic3#6712yes—
252C2×C3×Dic3C2×C3×C412yes—
253C2×C3×Dic3C2×C3×C412yes—
254C2×C3×Dic3C2×C3×C412yes—
255C2×C3×Dic3C2×C3×C412yes—
256C2×C3×Dic3C3×D412yes—
257C2×C3×Dic3C3×Q812yes—
258C4×C4⋊C4—91noSylow
259C2×C33C2×C4211yescharacteristic
260C2×C33C2×C4⋊C411yescharacteristic
261C2×C33#11711yescharacteristic
262C2×C33C4×D411yescharacteristic
263C2×C33C4×D411yescharacteristic
264C2×C33C4×Q811yescharacteristic
265C2×C33C4×Q811yescharacteristic
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—31no—
270C22×C3×C4—31no—
271C22×C3×C4—31no—
272C22×C3×C4—31no—
273C22×C3×C4—31no—
274C22×C3×C4—31no—
275C22×C3×C4—31no—
276C22×C3×C4—31no—
277C22×C3×C4—41no—
278C22×C3×C4—61no—
279C22×C3×C4—61no—
280C22×C3×C4—61no—
281C22×C3×C4—61no—
282C22×C3×C4—91no—
283C22×C3×C4—91no—
284C22×C3×C4D3211yescharacteristic
285C22×C3×C4C2×C3×D311yescharacteristic
286C22×C3×C4C2×C3×D311yescharacteristic
287C22×Dic3—31no—
288C22×Dic3—31no—
289C22×Dic3—31no—
290C22×Dic3—31no—
291C22×Dic3—61no—
292C22×Dic3—61no—
293C22×Dic3C2×C3×D311yescharacteristic
294C22×Dic3C2×C3×D311yescharacteristic
295C22×Dic3C2×C3×D311yescharacteristic
296C22×Dic3C2×C3×D311yescharacteristic
297C3×C4⋊C4—94no—
298C3×C4⋊C4—94no—
299C3×C42—62no—
300C3×C42—62no—
301C3×C42—64no—
302C3×C42—94no—
303C3×C42—182no—
304Dic3⋊C4—34no—
305Dic3⋊C4—34no—
306Dic3⋊C4—34no—
307Dic3⋊C4—34no—
308Dic3⋊C4—64no—
309C4×Dic3—22no—
310C4×Dic3—34no—
311C4×Dic3—34no—
312C4×Dic3—62no—
313C4×Dic3—62no—
314C22×C32—21no—
315C22×C32—21no—
316C22×C32—21no—
317C22×C32—21no—
318C22×C32—21no—
319C22×C32—21no—
320C22×C32—21no—
321C22×C32—21no—
322C22×C32—21no—
323C22×C32—21no—
324C22×C32—21no—
325C22×C32—21no—
326C22×C32—21no—
327C22×C32—21no—
328C22×C32—21no—
329C22×C32—21no—
330C22×C32—21no—
331C22×C32—21no—
332C22×C32—21no—
333C22×C32—21no—
334C22×C32—21no—
335C22×C32—41no—
336C22×C32—41no—
337C22×C32—41no—
338C22×C32—41no—
339C22×C32—41no—
340C22×C32—41no—
341C22×C32—41no—
342C22×C32C2×Dic611yescharacteristic
343C22×C32C2×C4×D311yescharacteristic
344C22×C32C2×C4×D311yescharacteristic
345C22×C32C2×C4×D311yescharacteristic
346C22×C32C2×C4×D311yescharacteristic
347C22×C32C2×C4×D311yescharacteristic
348C22×C32C2×C4×D311yescharacteristic
349C22×C32#23511yescharacteristic
350C22×C32#23511yescharacteristic
351C22×C32D3×D411yescharacteristic
352C22×C32#23711yescharacteristic
353C22×C32#23711yescharacteristic
354C22×C32D3×Q811yescharacteristic
355C22×C32C2×#6711yescharacteristic
356C22×C32C22×C3×C411yescharacteristic
357C22×C32C22×C3×C411yescharacteristic
358C22×C32C22×C3×C411yescharacteristic
359C22×C32C2×C3×D411yescharacteristic
360C22×C32C2×C3×Q811yescharacteristic
361C22×C32C3×#4111yescharacteristic
362C22×C32C3×#4111yescharacteristic
363C32×C4—22no—
364C32×C4—24no—
365C32×C4—22no—
366C32×C4—22no—
367C32×C4—34no—
368C32×C4—42no—
369C32×C4—42no—
370C32×C4—44no—
371C32×C4—62no—
372C32×C4—62no—
373C32×C4—62no—
374C3⋊Dic3—22no—
375C3⋊Dic3C3×C4214yescomplemented
376C3×Dic3—24no—
377C3×Dic3—22no—
378C3×Dic3—22no—
379C3×Dic3—22no—
380C3×Dic3—22no—
381C3×Dic3—22no—
382C3×Dic3—22no—
383C3×Dic3—24no—
384C3×Dic3—34no—
385C3×Dic3—34no—
386C3×Dic3—42no—
387C3×Dic3—42no—
388C3×Dic3—64no—
389C3×Dic3—62no—
390C3×Dic3—62no—
391C3×Dic3—122no—
392C3×Dic3Dic3⋊C414yescomplemented
393C3×Dic3C3×C4⋊C414yescomplemented
394C2×C4⋊C4—91no—
395C2×C4⋊C4—91no—
396C2×C42—31no—
397C2×C42—91no—
398C2×C42—91no—
399#95—31no—
400#95—91no—
401C33C4×C4⋊C411yescharacteristic, complemented, Sylow
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—41no—
406C23×C3C2×D3211yescharacteristic
407C23×C3C22×C3×D311yescharacteristic
408C23×C3C22×C3×D311yescharacteristic
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—32no—
421C2×C3×C4—32no—
422C2×C3×C4—32no—
423C2×C3×C4—32no—
424C2×C3×C4—32no—
425C2×C3×C4—32no—
426C2×C3×C4—32no—
427C2×C3×C4—32no—
428C2×C3×C4—32no—
429C2×C3×C4—32no—
430C2×C3×C4—32no—
431C2×C3×C4—32no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—42no—
437C2×C3×C4—42no—
438C2×C3×C4—42no—
439C2×C3×C4—62no—
440C2×C3×C4—62no—
441C2×C3×C4—62no—
442C2×C3×C4—62no—
443C2×C3×C4—62no—
444C2×C3×C4—62no—
445C2×C3×C4—62no—
446C2×C3×C4—62no—
447C2×C3×C4—61no—
448C2×C3×C4—61no—
449C2×C3×C4—61no—
450C2×C3×C4—61no—
451C2×C3×C4—61no—
452C2×C3×C4—61no—
453C2×C3×C4—61no—
454C2×C3×C4—61no—
455C2×C3×C4—61no—
456C2×C3×C4—61no—
457C2×C3×C4—61no—
458C2×C3×C4—61no—
459C2×C3×C4—92no—
460C2×C3×C4—92no—
461C2×C3×C4—92no—
462C2×C3×C4—92no—
463C2×C3×C4—121no—
464C2×C3×C4—121no—
465C2×C3×C4—121no—
466C2×C3×C4—121no—
467C2×C3×C4—181no—
468C2×C3×C4—181no—
469C2×C3×C4#62412yes—
470C2×C3×C4C3×C4×D312yes—
471C2×C3×C4C3×C4×D312yes—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—32no—
479C2×Dic3—32no—
480C2×Dic3—32no—
481C2×Dic3—32no—
482C2×Dic3—32no—
483C2×Dic3—32no—
484C2×Dic3—32no—
485C2×Dic3—32no—
486C2×Dic3—62no—
487C2×Dic3—62no—
488C2×Dic3—62no—
489C2×Dic3—62no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—61no—
494C2×Dic3—121no—
495C2×Dic3—121no—
496C2×Dic3C3×Dic612yes—
497C2×Dic3C3×C4×D312yes—
498C2×Dic3C3×C4×D312yes—
499C2×Dic3C3×C4×D312yes—
500C2×Dic3C3×C4×D312yes—
501C2×Dic3C3×#6712yes—
502C2×C32—21no—
503C2×C32—21no—
504C2×C32—21no—
505C2×C32—21no—
506C2×C32—21no—
507C2×C32—21no—
508C2×C32—21no—
509C2×C32—21no—
510C2×C32—21no—
511C2×C32—21no—
512C2×C32—21no—
513C2×C32—21no—
514C2×C32—21no—
515C2×C32—21no—
516C2×C32—21no—
517C2×C32—21no—
518C2×C32—21no—
519C2×C32—21no—
520C2×C32—21no—
521C2×C32—21no—
522C2×C32—21no—
523C2×C32—41no—
524C2×C32—41no—
525C2×C32—41no—
526C2×C32—41no—
527C2×C32—41no—
528C2×C32—41no—
529C2×C32—41no—
530C2×C32C4×Dic611yescharacteristic
531C2×C32C4×Dic611yescharacteristic
532C2×C32C42×D311yescharacteristic
533C2×C32C42×D311yescharacteristic
534C2×C32#87211yescharacteristic
535C2×C32#87711yescharacteristic
536C2×C32#67⋊C411yescharacteristic
537C2×C32#67⋊C411yescharacteristic
538C2×C32#88711yescharacteristic
539C2×C32#88711yescharacteristic
540C2×C32D3×C4⋊C411yescharacteristic
541C2×C32C2×Dic3⋊C411yescharacteristic
542C2×C32C4×#6711yescharacteristic
543C2×C32C4×#6711yescharacteristic
544C2×C32C2×C3×C4211yescharacteristic
545C2×C32C2×C3×C4⋊C411yescharacteristic
546C2×C32C3×#11711yescharacteristic
547C2×C32C3×C4×D411yescharacteristic
548C2×C32C3×C4×D411yescharacteristic
549C2×C32C3×C4×Q811yescharacteristic
550C2×C32C3×C4×Q811yescharacteristic
551C22×C4—31no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—91no—
556C22×C4—91no—
557C22×C4C3×D3211yescharacteristic
558C4⋊C4—94no—
559C4⋊C4—94no—
560C42—62no—
561C42—94no—
562C42—182no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—21no—
566C22×C3—21no—
567C22×C3—21no—
568C22×C3—21no—
569C22×C3—21no—
570C22×C3—21no—
571C22×C3—21no—
572C22×C3—21no—
573C22×C3—21no—
574C22×C3—21no—
575C22×C3—21no—
576C22×C3—21no—
577C22×C3—21no—
578C22×C3—21no—
579C22×C3—21no—
580C22×C3—21no—
581C22×C3—21no—
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3D3×Dic611yescharacteristic
592C22×C3#379511yescharacteristic
593C22×C3C4×D3211yescharacteristic
594C22×C3C4×D3211yescharacteristic
595C22×C3#380411yescharacteristic
596C22×C3C2×#62411yescharacteristic
597C22×C3D3×#6711yescharacteristic
598C22×C3C2×C3×Dic611yescharacteristic
599C22×C3C2×C3×C4×D311yescharacteristic
600C22×C3C2×C3×C4×D311yescharacteristic
601C22×C3C2×C3×C4×D311yescharacteristic
602C22×C3C2×C3×C4×D311yescharacteristic
603C22×C3C2×C3×C4×D311yescharacteristic
604C22×C3C2×C3×C4×D311yescharacteristic
605C22×C3C3×#23511yescharacteristic
606C22×C3C3×#23511yescharacteristic
607C22×C3C3×D3×D411yescharacteristic
608C22×C3C3×#23711yescharacteristic
609C22×C3C3×#23711yescharacteristic
610C22×C3C3×D3×Q811yescharacteristic
611C22×C3C2×C3×#6711yescharacteristic
612C3×C4—24no—
613C3×C4—22no—
614C3×C4—22no—
615C3×C4—22no—
616C3×C4—34no—
617C3×C4—34no—
618C3×C4—42no—
619C3×C4—42no—
620C3×C4—44no—
621C3×C4—64no—
622C3×C4—64no—
623C3×C4—62no—
624C3×C4—62no—
625C3×C4—62no—
626C3×C4—62no—
627C3×C4—62no—
628C3×C4—62no—
629C3×C4—94no—
630C3×C4—122no—
631C3×C4—122no—
632C3×C4—182no—
633Dic3—22no—
634Dic3—22no—
635Dic3—22no—
636Dic3—34no—
637Dic3—34no—
638Dic3—64no—
639Dic3—62no—
640Dic3—62no—
641Dic3—122no—
642Dic3C3×Dic3⋊C414yescomplemented
643C32—21no—
644C32—21no—
645C32—21no—
646C32—41no—
647C32#464911yescharacteristic, complemented
648C32C4×Dic3⋊C411yescharacteristic, complemented
649C32C3×C4×C4⋊C411yescharacteristic, complemented
650C23C2×C3×D3211yescharacteristic
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—32no—
654C2×C4—32no—
655C2×C4—32no—
656C2×C4—32no—
657C2×C4—32no—
658C2×C4—32no—
659C2×C4—61no—
660C2×C4—61no—
661C2×C4—61no—
662C2×C4—61no—
663C2×C4—61no—
664C2×C4—61no—
665C2×C4—92no—
666C2×C4—92no—
667C2×C4—92no—
668C2×C4—92no—
669C2×C4—181no—
670C2×C4—181no—
671C2×C4C3×#62412yes—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—41no—
694C2×C3—41no—
695C2×C3—41no—
696C2×C3—41no—
697C2×C3—41no—
698C2×C3—41no—
699C2×C3—41no—
700C2×C3#6383711yescharacteristic
701C2×C3#6384411yescharacteristic
702C2×C3D3×Dic3⋊C411yescharacteristic
703C2×C3#6387711yescharacteristic
704C2×C3#6387911yescharacteristic
705C2×C3C4×#62411yescharacteristic
706C2×C3#6395211yescharacteristic
707C2×C3C3×C4×Dic611yescharacteristic
708C2×C3C3×C4×Dic611yescharacteristic
709C2×C3C3×C42×D311yescharacteristic
710C2×C3C3×C42×D311yescharacteristic
711C2×C3C3×#87211yescharacteristic
712C2×C3C3×#87711yescharacteristic
713C2×C3C3×#67⋊C411yescharacteristic
714C2×C3C3×#67⋊C411yescharacteristic
715C2×C3C3×#88711yescharacteristic
716C2×C3C3×#88711yescharacteristic
717C2×C3C3×D3×C4⋊C411yescharacteristic
718C2×C3C2×C3×Dic3⋊C411yescharacteristic
719C2×C3C3×C4×#6711yescharacteristic
720C2×C3C3×C4×#6711yescharacteristic
721C22C3×D3×Dic611yescharacteristic
722C22C3×#379511yescharacteristic
723C22C3×C4×D3211yescharacteristic
724C22C3×C4×D3211yescharacteristic
725C22C3×#380411yescharacteristic
726C22C2×C3×#62411yescharacteristic
727C22C3×D3×#6711yescharacteristic
728C4—22no—
729C4—34no—
730C4—62no—
731C4—62no—
732C4—62no—
733C4—94no—
734C4—182no—
735C3—21no—
736C3—21no—
737C3—21no—
738C3—41no—
739C3#1059124311yescharacteristic, direct product factor
740C3C3×#464911yescharacteristic, complemented
741C3C3×C4×Dic3⋊C411yescharacteristic, complemented
742C2C3×#6383711yescharacteristic
743C2C3×#6384411yescharacteristic
744C2C3×D3×Dic3⋊C411yescharacteristic
745C2C3×#6387711yescharacteristic
746C2C3×#6387911yescharacteristic
747C2C3×C4×#62411yescharacteristic
748C2C3×#6395211yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutatorC2×C32C2×C3×C42
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socle, prime radicalC23×C33C23
cosocleC23×C32C23×C3
hypercenterC22×C3×C4D32
hypocenterC32C3×C4×C4⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
10. #10591243C3direct (N × H)
18. C3×#3750C4semidirect
20. C3×#3724C4semidirect
22. C3×Dic32C4semidirect
104. #3750C3×C4semidirect
117. #3724C3×C4semidirect
119. Dic32C3×C4semidirect
129. C3×C3⋊Dic3C42semidirect
133. C32×Dic3C4⋊C4semidirect
375. C3⋊Dic3C3×C42semidirect
392. C3×Dic3Dic3⋊C4semidirect
393. C3×Dic3C3×C4⋊C4semidirect
401. C33C4×C4⋊C4semidirect
642. Dic3C3×Dic3⋊C4semidirect
647. C32#4649semidirect
648. C32C4×Dic3⋊C4semidirect
649. C32C3×C4×C4⋊C4semidirect
739. C3#10591243direct (N × H)
740. C3C3×#4649semidirect
741. C3C3×C4×Dic3⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37502
C2×C32×C4×Dic32
C2×C3×#37242
C2×C3×Dic322
C32×C3⋊#952
C3×#635792
C3×C4×Dic3⋊C43
C3×#46493
#105912433