Finite Group Databasebeta

← C3×#10591373 #13158199

Subgroups — C3×#10591373 #13158199

Order 1728.

1274 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×Dic3C211yesmaximal, characteristic
2C2×C32×(C2×D3)⋊C4C211yesmaximal, characteristic
3C2×C3×#3724C211yesmaximal, characteristic, complemented
4C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
6C3×#63658C211yesmaximal, characteristic, complemented
7C32×C3⋊#95C211yesmaximal, characteristic, complemented
8C3×#4946—31nomaximal
9C3×#4668—31nomaximal
10#10591373C311yesmaximal, characteristic, direct product factor
11C23×C32×D3C2211yescharacteristic
12C22×C33×C4C2211yescharacteristic
13C22×C3×C3⋊Dic3C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C32×Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C2×C3×D3×Dic3—22no—
19C2×C3×D3×Dic3—22no—
20C2×C3×D3×Dic3—22no—
21C32×(C2×D3)⋊C4—22no—
22C3×#3724—22no—
23C3×Dic3⋊Dic3—22no—
24C3×(C2×D3)⋊Dic3C414yescomplemented
25C23×C3×Dic3—31no—
26C22×C3×C4×D3—31no—
27C22×D3×Dic3C2×C311yescharacteristic
28C2×C32×C22⋊C4—31no—
29C2×C3×#217—31no—
30C2×C3×(C2×D3)⋊C4—21no—
31C2×C3×(C2×D3)⋊C4—31no—
32C2×C3×(C2×D3)⋊C4D311yescharacteristic
33C2×C3×(C2×D3)⋊C4C2×C311yescharacteristic
34C2×C3×C4⋊Dic3—31no—
35C2×C3×Dic3⋊C4—31no—
36C2×C3×Dic3⋊C4—31no—
37C2×C3×Dic3⋊C4—31no—
38C2×#3724C2×C311yescharacteristic, complemented
39C2×Dic3⋊Dic3C2×C311yescharacteristic, complemented
40C2×(C2×D3)⋊Dic3C2×C311yescharacteristic
41C32×#95—31no—
42#63658C2×C311yescharacteristic, complemented
43C3×C3⋊#95—21no—
44C3×C3⋊#95—31no—
45C3×C3⋊#95—31no—
46C3×C3⋊#95—61no—
47C3×C3⋊#95D311yescharacteristic, complemented
48C3×C3⋊#95C2×C311yescharacteristic, complemented
49C23×C33C2311yescharacteristic
50C22×C32×D3—21no—
51C22×C32×D3—21no—
52C22×C32×D3—21no—
53C22×C32×D3—21no—
54C22×C32×D3C2×C412yes—
55C22×C32×D3D412yes—
56C22×C32×D3Q812yes—
57C2×C33×C4—21no—
58C2×C33×C4—21no—
59C2×C33×C4—21no—
60C2×C3×C3⋊Dic3—21no—
61C2×C3×C3⋊Dic3—21no—
62C2×C3×C3⋊Dic3—21no—
63C2×C3×C3⋊Dic3—21no—
64C2×C3×C3⋊Dic3C2×C412yescomplemented
65C2×C3×C3⋊Dic3D412yes—
66C2×C32×Dic3—21no—
67C2×C32×Dic3—21no—
68C2×C32×Dic3—21no—
69C2×C32×Dic3—21no—
70C2×C32×Dic3—21no—
71C2×C32×Dic3—21no—
72C2×C32×Dic3—21no—
73C2×C32×Dic3C2×C412yescomplemented
74C2×C32×Dic3D412yes—
75C3×D3×Dic3—28no—
76C3×#385—91no—
77#4946—31no—
78#4668—31no—
79C24×C32—31no—
80C23×C3×D3—21no—
81C23×C3×D3C2×D311yescharacteristic
82C23×C3×D3C22×C311yescharacteristic
83C22×C32×C4—21no—
84C22×C32×C4—21no—
85C22×C32×C4—21no—
86C22×C32×C4—31no—
87C22×C32×C4—31no—
88C22×C32×C4—31no—
89C22×C32×C4—41no—
90C22×C32×C4C2×D311yescharacteristic
91C22×C32×C4C2×D311yescharacteristic
92C22×C32×C4C22×C311yescharacteristic
93C22×C3⋊Dic3C22×C311yescharacteristic
94C22×C3⋊Dic3C22×C311yescharacteristic
95C22×C3×Dic3—21no—
96C22×C3×Dic3—21no—
97C22×C3×Dic3—21no—
98C22×C3×Dic3—31no—
99C22×C3×Dic3—31no—
100C22×C3×Dic3—31no—
101C22×C3×Dic3—31no—
102C22×C3×Dic3—62no—
103C22×C3×Dic3—62no—
104C22×C3×Dic3—62no—
105C22×C3×Dic3—61no—
106C22×C3×Dic3—61no—
107C22×C3×Dic3C2×D311yescharacteristic
108C22×C3×Dic3C2×D311yescharacteristic
109C22×C3×Dic3C2×D311yescharacteristic
110C22×C3×Dic3C22×C311yescharacteristic
111C22×C3×Dic3C22×C311yescharacteristic
112C22×C3×Dic3C22×C311yescharacteristic
113C2×C3×C4×D3—62no—
114C2×C3×C4×D3—62no—
115C2×C3×C4×D3—62no—
116C2×D3×Dic3—22no—
117C2×D3×Dic3—22no—
118C2×D3×Dic3—22no—
119C32×C22⋊C4—62no—
120C3×#217—34no—
121C3×(C2×D3)⋊C4—24no—
122C3×(C2×D3)⋊C4—22no—
123C3×(C2×D3)⋊C4—22no—
124C3×(C2×D3)⋊C4—34no—
125C3×C4⋊Dic3—62no—
126C3×Dic3⋊C4—62no—
127C3×Dic3⋊C4—62no—
128C3×Dic3⋊C4—62no—
129#3724—22no—
130Dic3⋊Dic3—22no—
131(C2×D3)⋊Dic3C3×C414yescomplemented
132C22×C33C22×C411yescharacteristic
133C22×C33C2×D411yescharacteristic
134C22×C33C2×D411yescharacteristic
135C22×C33C2×D411yescharacteristic
136C22×C33C2×Q811yescharacteristic
137C22×C33#4111yescharacteristic
138C22×C33#4111yescharacteristic
139C2×C32×D3—22no—
140C2×C32×D3—22no—
141C2×C32×D3—22no—
142C2×C32×D3—22no—
143C2×C32×D3—22no—
144C2×C32×D3—22no—
145C2×C32×D3C4⋊C414yescomplemented
146C33×C4—41no—
147C3×C3⋊Dic3—22no—
148C3×C3⋊Dic3—22no—
149C32×Dic3—22no—
150C32×Dic3—22no—
151C32×Dic3—41no—
152C23×C3×C4—91no—
153C23×Dic3—31no—
154C22×C4×D3—31no—
155C2×C3×C4⋊C4—91no—
156C2×C3×C4⋊C4—91no—
157C2×C3×C22⋊C4—31no—
158C2×C3×C22⋊C4—31no—
159C2×C3×C22⋊C4—61no—
160C2×C3×C22⋊C4—91no—
161C2×#217—31no—
162C2×(C2×D3)⋊C4—31no—
163C2×(C2×D3)⋊C4C3×D311yescharacteristic
164C2×C4⋊Dic3—31no—
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—31no—
168C3×#95—31no—
169C3×#95—31no—
170C3×#95—61no—
171C3×#95—91no—
172C3⋊#95—31no—
173C3⋊#95—31no—
174C3⋊#95—61no—
175C3⋊#95C3×D311yescharacteristic, complemented
176C23×C32—21no—
177C23×C32—21no—
178C23×C32—21no—
179C23×C32—32no—
180C23×C32—32no—
181C23×C32—32no—
182C23×C32—41no—
183C23×C32—61no—
184C23×C32—61no—
185C23×C32—61no—
186C23×C32—61no—
187C23×C32C22×D311yescharacteristic
188C23×C32C22×D311yescharacteristic
189C23×C32C23×C311yescharacteristic
190C22×C3×D3—21no—
191C22×C3×D3—21no—
192C22×C3×D3—21no—
193C22×C3×D3—21no—
194C22×C3×D3—21no—
195C22×C3×D3—21no—
196C22×C3×D3—21no—
197C22×C3×D3—21no—
198C22×C3×D3—22no—
199C22×C3×D3—22no—
200C22×C3×D3—22no—
201C22×C3×D3—41no—
202C22×C3×D3—41no—
203C22×C3×D3—41no—
204C22×C3×D3—41no—
205C22×C3×D3Dic612yes—
206C22×C3×D3C4×D312yes—
207C22×C3×D3#6712yes—
208C22×C3×D3C2×C3×C412yes—
209C22×C3×D3C3×D412yes—
210C22×C3×D3C3×Q812yes—
211C2×C32×C4—21no—
212C2×C32×C4—21no—
213C2×C32×C4—21no—
214C2×C32×C4—22no—
215C2×C32×C4—22no—
216C2×C32×C4—22no—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—21no—
220C2×C32×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4—21no—
223C2×C32×C4—32no—
224C2×C32×C4—32no—
225C2×C32×C4—41no—
226C2×C32×C4—41no—
227C2×C32×C4—41no—
228C2×C32×C4—41no—
229C2×C32×C4—41no—
230C2×C32×C4—41no—
231C2×C32×C4—42no—
232C2×C32×C4—42no—
233C2×C32×C4—42no—
234C2×C32×C4—61no—
235C2×C32×C4—61no—
236C2×C32×C4—61no—
237C2×C32×C4—61no—
238C2×C32×C4—61no—
239C2×C32×C4—61no—
240C2×C32×C4—61no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3C2×C3×C412yescomplemented
246C2×C3⋊Dic3C3×D412yes—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—22no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—22no—
263C2×C3×Dic3—22no—
264C2×C3×Dic3—32no—
265C2×C3×Dic3—32no—
266C2×C3×Dic3—32no—
267C2×C3×Dic3—32no—
268C2×C3×Dic3—41no—
269C2×C3×Dic3—41no—
270C2×C3×Dic3—41no—
271C2×C3×Dic3—41no—
272C2×C3×Dic3—41no—
273C2×C3×Dic3—41no—
274C2×C3×Dic3—62no—
275C2×C3×Dic3—62no—
276C2×C3×Dic3—68no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—61no—
279C2×C3×Dic3—61no—
280C2×C3×Dic3—61no—
281C2×C3×Dic3—61no—
282C2×C3×Dic3—61no—
283C2×C3×Dic3—61no—
284C2×C3×Dic3—61no—
285C2×C3×Dic3—121no—
286C2×C3×Dic3—121no—
287C2×C3×Dic3—121no—
288C2×C3×Dic3—121no—
289C2×C3×Dic3C4×D312yescomplemented
290C2×C3×Dic3D1212yes—
291C2×C3×Dic3C2×C3×C412yescomplemented
292C2×C3×Dic3C3×D412yes—
293C3×C4×D3—68no—
294D3×Dic3—28no—
295#385—91noSylow
296C2×C33C2×C4⋊C411yescharacteristic
297C2×C33C4×D411yescharacteristic
298C2×C33C4×D411yescharacteristic
299C2×C33#12011yescharacteristic
300C2×C33C22⋊Q811yescharacteristic
301C2×C33C22⋊Q811yescharacteristic
302C2×C33#12311yescharacteristic
303C32×D3—24no—
304C24×C3—31no—
305C24×C3—31no—
306C24×C3—61no—
307C23×D3C2×C3×D311yescharacteristic
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—41no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C22×C3×C4—61no—
321C22×C3×C4—91no—
322C22×C3×C4—91no—
323C22×C3×C4—182no—
324C22×C3×C4—182no—
325C22×C3×C4—182no—
326C22×C3×C4D3211yescharacteristic
327C22×C3×C4C2×C3×D311yescharacteristic
328C22×C3×C4C2×C3×D311yescharacteristic
329C22×Dic3—31no—
330C22×Dic3—31no—
331C22×Dic3—31no—
332C22×Dic3—31no—
333C22×Dic3—61no—
334C22×Dic3—61no—
335C22×Dic3—62no—
336C22×Dic3—62no—
337C22×Dic3—62no—
338C22×Dic3C2×C3×D311yescharacteristic
339C22×Dic3C2×C3×D311yescharacteristic
340C22×Dic3C2×C3×D311yescharacteristic
341C2×C4×D3—62no—
342C2×C4×D3—62no—
343C2×C4×D3—62no—
344C3×C4⋊C4—182no—
345C3×C4⋊C4—182no—
346C3×C22⋊C4—62no—
347C3×C22⋊C4—62no—
348C3×C22⋊C4—64no—
349C3×C22⋊C4—94no—
350#217—34no—
351(C2×D3)⋊C4—22no—
352(C2×D3)⋊C4—34no—
353C4⋊Dic3—62no—
354Dic3⋊C4—62no—
355Dic3⋊C4—62no—
356Dic3⋊C4—62no—
357C22×C32—21no—
358C22×C32—21no—
359C22×C32—21no—
360C22×C32—21no—
361C22×C32—21no—
362C22×C32—21no—
363C22×C32—21no—
364C22×C32—21no—
365C22×C32—21no—
366C22×C32—21no—
367C22×C32—21no—
368C22×C32—21no—
369C22×C32—21no—
370C22×C32—21no—
371C22×C32—21no—
372C22×C32—21no—
373C22×C32—21no—
374C22×C32—21no—
375C22×C32—21no—
376C22×C32—21no—
377C22×C32—21no—
378C22×C32—34no—
379C22×C32—41no—
380C22×C32—41no—
381C22×C32—41no—
382C22×C32—41no—
383C22×C32—41no—
384C22×C32—41no—
385C22×C32—41no—
386C22×C32—62no—
387C22×C32—62no—
388C22×C32—62no—
389C22×C32—62no—
390C22×C32—62no—
391C22×C32—62no—
392C22×C32C2×Dic611yescharacteristic
393C22×C32C2×C4×D311yescharacteristic
394C22×C32C2×C4×D311yescharacteristic
395C22×C32C2×D1211yescharacteristic
396C22×C32#23511yescharacteristic
397C22×C32D3×D411yescharacteristic
398C22×C32D3×D411yescharacteristic
399C22×C32D3×D411yescharacteristic
400C22×C32D3×D411yescharacteristic
401C22×C32#23711yescharacteristic
402C22×C32#23711yescharacteristic
403C22×C32#23711yescharacteristic
404C22×C32D3×Q811yescharacteristic
405C22×C32C2×#6711yescharacteristic
406C22×C32C22×C3×C411yescharacteristic
407C22×C32C2×C3×D411yescharacteristic
408C22×C32C2×C3×D411yescharacteristic
409C22×C32C2×C3×D411yescharacteristic
410C22×C32C2×C3×Q811yescharacteristic
411C22×C32C3×#4111yescharacteristic
412C22×C32C3×#4111yescharacteristic
413C2×C3×D3—22no—
414C2×C3×D3—22no—
415C2×C3×D3—22no—
416C2×C3×D3—22no—
417C2×C3×D3—22no—
418C2×C3×D3—22no—
419C2×C3×D3—22no—
420C2×C3×D3—22no—
421C2×C3×D3—22no—
422C2×C3×D3—22no—
423C2×C3×D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—24no—
426C2×C3×D3—42no—
427C2×C3×D3—42no—
428C2×C3×D3—42no—
429C2×C3×D3—42no—
430C2×C3×D3—42no—
431C2×C3×D3—42no—
432C2×C3×D3Dic3⋊C414yescomplemented
433C2×C3×D3C3×C4⋊C414yescomplemented
434C32×C4—42no—
435C32×C4—42no—
436C32×C4—42no—
437C32×C4—44no—
438C32×C4—41no—
439C32×C4—41no—
440C32×C4—41no—
441C32×C4—62no—
442C32×C4—62no—
443C32×C4—121no—
444C3⋊Dic3—22no—
445C3⋊Dic3—22no—
446C3×Dic3—22no—
447C3×Dic3—22no—
448C3×Dic3—22no—
449C3×Dic3—22no—
450C3×Dic3—42no—
451C3×Dic3—42no—
452C3×Dic3—42no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C3×Dic3—62no—
456C3×Dic3—62no—
457C3×Dic3—62no—
458C3×Dic3—62no—
459C3×Dic3—122no—
460C3×Dic3—122no—
461C23×C4—91no—
462C2×C4⋊C4—91no—
463C2×C4⋊C4—91no—
464C2×C22⋊C4—31no—
465C2×C22⋊C4—91no—
466#95—31no—
467#95—91no—
468C33#38511yescharacteristic, complemented, Sylow
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—32no—
473C23×C3—32no—
474C23×C3—32no—
475C23×C3—32no—
476C23×C3—32no—
477C23×C3—32no—
478C23×C3—41no—
479C23×C3—62no—
480C23×C3—62no—
481C23×C3—62no—
482C23×C3—61no—
483C23×C3—61no—
484C23×C3—61no—
485C23×C3—61no—
486C23×C3—61no—
487C23×C3—61no—
488C23×C3—61no—
489C23×C3—61no—
490C23×C3—121no—
491C23×C3—121no—
492C23×C3—121no—
493C23×C3—121no—
494C23×C3C2×D3211yescharacteristic
495C23×C3C22×C3×D311yescharacteristic
496C23×C3C22×C3×D311yescharacteristic
497C22×D3—21no—
498C22×D3—21no—
499C22×D3—21no—
500C22×D3—21no—
501C22×D3C3×Dic612yes—
502C22×D3C3×C4×D312yes—
503C22×D3C3×#6712yes—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—32no—
517C2×C3×C4—32no—
518C2×C3×C4—32no—
519C2×C3×C4—32no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—42no—
527C2×C3×C4—42no—
528C2×C3×C4—42no—
529C2×C3×C4—62no—
530C2×C3×C4—62no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—62no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—92no—
547C2×C3×C4—92no—
548C2×C3×C4—121no—
549C2×C3×C4—121no—
550C2×C3×C4—121no—
551C2×C3×C4—121no—
552C2×C3×C4—121no—
553C2×C3×C4—121no—
554C2×C3×C4—188no—
555C2×C3×C4—181no—
556C2×C3×C4—181no—
557C2×C3×C4—181no—
558C2×C3×C4—181no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—32no—
567C2×Dic3—32no—
568C2×Dic3—32no—
569C2×Dic3—32no—
570C2×Dic3—62no—
571C2×Dic3—62no—
572C2×Dic3—68no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—121no—
582C2×Dic3—121no—
583C2×Dic3—121no—
584C2×Dic3—121no—
585C2×Dic3C3×C4×D312yescomplemented
586C2×Dic3C3×D1212yes—
587C4×D3—68no—
588C2×C32—21no—
589C2×C32—21no—
590C2×C32—21no—
591C2×C32—21no—
592C2×C32—21no—
593C2×C32—21no—
594C2×C32—21no—
595C2×C32—21no—
596C2×C32—21no—
597C2×C32—21no—
598C2×C32—21no—
599C2×C32—21no—
600C2×C32—21no—
601C2×C32—21no—
602C2×C32—21no—
603C2×C32—21no—
604C2×C32—21no—
605C2×C32—21no—
606C2×C32—21no—
607C2×C32—21no—
608C2×C32—21no—
609C2×C32—41no—
610C2×C32—41no—
611C2×C32—41no—
612C2×C32—41no—
613C2×C32—41no—
614C2×C32—41no—
615C2×C32—41no—
616C2×C32—64no—
617C2×C32C4×D1211yescharacteristic
618C2×C32#87811yescharacteristic
619C2×C32#87811yescharacteristic
620C2×C32#67⋊C411yescharacteristic
621C2×C32#67⋊C411yescharacteristic
622C2×C32#67⋊C411yescharacteristic
623C2×C32#88211yescharacteristic
624C2×C32#88311yescharacteristic
625C2×C32D3×C4⋊C411yescharacteristic
626C2×C32#89611yescharacteristic
627C2×C32#89711yescharacteristic
628C2×C32C2×Dic3⋊C411yescharacteristic
629C2×C32#93511yescharacteristic
630C2×C32#93711yescharacteristic
631C2×C32C2×C3×C4⋊C411yescharacteristic
632C2×C32C3×C4×D411yescharacteristic
633C2×C32C3×C4×D411yescharacteristic
634C2×C32C3×#12011yescharacteristic
635C2×C32C3×C22⋊Q811yescharacteristic
636C2×C32C3×C22⋊Q811yescharacteristic
637C2×C32C3×#12311yescharacteristic
638C3×D3—24no—
639C3×D3—24no—
640C3×D3—44no—
641C24—31no—
642C22×C4—31no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—91no—
646C22×C4—91no—
647C22×C4—182no—
648C22×C4—182no—
649C22×C4—182no—
650C22×C4C3×D3211yescharacteristic
651C4⋊C4—182no—
652C4⋊C4—182no—
653C22⋊C4—62no—
654C22⋊C4—94no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—34no—
677C22×C3—34no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—64no—
686C22×C3—62no—
687C22×C3—62no—
688C22×C3—62no—
689C22×C3—62no—
690C22×C3—62no—
691C22×C3—62no—
692C22×C3—62no—
693C22×C3—62no—
694C22×C3—62no—
695C22×C3—62no—
696C22×C3—62no—
697C22×C3—62no—
698C22×C3—122no—
699C22×C3—122no—
700C22×C3—122no—
701C22×C3—122no—
702C22×C3—122no—
703C22×C3—122no—
704C22×C3D3×Dic611yescharacteristic
705C22×C3C4×D3211yescharacteristic
706C22×C3D3×D1211yescharacteristic
707C22×C3#380211yescharacteristic
708C22×C3#380411yescharacteristic
709C22×C3#380511yescharacteristic
710C22×C3D3×#6711yescharacteristic
711C22×C3C2×C3×Dic611yescharacteristic
712C22×C3C2×C3×C4×D311yescharacteristic
713C22×C3C2×C3×C4×D311yescharacteristic
714C22×C3C2×C3×D1211yescharacteristic
715C22×C3C3×#23511yescharacteristic
716C22×C3C3×D3×D411yescharacteristic
717C22×C3C3×D3×D411yescharacteristic
718C22×C3C3×D3×D411yescharacteristic
719C22×C3C3×D3×D411yescharacteristic
720C22×C3C3×#23711yescharacteristic
721C22×C3C3×#23711yescharacteristic
722C22×C3C3×#23711yescharacteristic
723C22×C3C3×D3×Q811yescharacteristic
724C22×C3C2×C3×#6711yescharacteristic
725C2×D3—22no—
726C2×D3—22no—
727C2×D3—22no—
728C2×D3—22no—
729C2×D3—22no—
730C2×D3—22no—
731C2×D3C3×Dic3⋊C414yescomplemented
732C3×C4—42no—
733C3×C4—42no—
734C3×C4—42no—
735C3×C4—44no—
736C3×C4—41no—
737C3×C4—41no—
738C3×C4—41no—
739C3×C4—62no—
740C3×C4—62no—
741C3×C4—62no—
742C3×C4—62no—
743C3×C4—122no—
744C3×C4—122no—
745C3×C4—122no—
746C3×C4—121no—
747C3×C4—121no—
748C3×C4—182no—
749C3×C4—182no—
750Dic3—22no—
751Dic3—22no—
752Dic3—41no—
753Dic3—62no—
754Dic3—62no—
755Dic3—62no—
756Dic3—62no—
757Dic3—122no—
758Dic3—122no—
759C32—21no—
760C32—21no—
761C32—21no—
762C32—41no—
763C32#466811yescharacteristic, complemented
764C32#494611yescharacteristic, complemented
765C32C3×#38511yescharacteristic, complemented
766C23—32no—
767C23—32no—
768C23—32no—
769C23—61no—
770C23—61no—
771C23—61no—
772C23—61no—
773C23C2×C3×D3211yescharacteristic
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—32no—
778C2×C4—32no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—92no—
787C2×C4—92no—
788C2×C4—188no—
789C2×C4—181no—
790C2×C4—181no—
791C2×C4—181no—
792C2×C4—181no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—41no—
815C2×C3—41no—
816C2×C3—41no—
817C2×C3—41no—
818C2×C3—41no—
819C2×C3—41no—
820C2×C3—41no—
821C2×C3—64no—
822C2×C3—64no—
823C2×C3—124no—
824C2×C3D3×Dic3⋊C411yescharacteristic
825C2×C3#6388011yescharacteristic
826C2×C3#6389311yescharacteristic
827C2×C3#6389911yescharacteristic
828C2×C3#6390211yescharacteristic
829C2×C3#6392211yescharacteristic
830C2×C3#6396911yescharacteristic
831C2×C3C3×C4×D1211yescharacteristic
832C2×C3C3×#87811yescharacteristic
833C2×C3C3×#87811yescharacteristic
834C2×C3C3×#67⋊C411yescharacteristic
835C2×C3C3×#67⋊C411yescharacteristic
836C2×C3C3×#67⋊C411yescharacteristic
837C2×C3C3×#88211yescharacteristic
838C2×C3C3×#88311yescharacteristic
839C2×C3C3×D3×C4⋊C411yescharacteristic
840C2×C3C3×#89611yescharacteristic
841C2×C3C3×#89711yescharacteristic
842C2×C3C2×C3×Dic3⋊C411yescharacteristic
843C2×C3C3×#93511yescharacteristic
844C2×C3C3×#93711yescharacteristic
845D3—24no—
846C22—34no—
847C22—62no—
848C22—62no—
849C22—62no—
850C22—62no—
851C22—62no—
852C22—62no—
853C22C3×D3×Dic611yescharacteristic
854C22C3×C4×D3211yescharacteristic
855C22C3×D3×D1211yescharacteristic
856C22C3×#380211yescharacteristic
857C22C3×#380411yescharacteristic
858C22C3×#380511yescharacteristic
859C22C3×D3×#6711yescharacteristic
860C4—41no—
861C4—62no—
862C4—62no—
863C4—121no—
864C4—182no—
865C4—182no—
866C3—21no—
867C3—21no—
868C3—21no—
869C3—41no—
870C3#1059137311yescharacteristic, direct product factor
871C3C3×#466811yescharacteristic, complemented
872C3C3×#494611yescharacteristic, complemented
873C2—64no—
874C2C3×D3×Dic3⋊C411yescharacteristic
875C2C3×#6388011yescharacteristic
876C2C3×#6389311yescharacteristic
877C2C3×#6389911yescharacteristic
878C2C3×#6390211yescharacteristic
879C2C3×#6392211yescharacteristic
880C2C3×#6396911yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutatorC22×C32C22×C3×C4
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC23×C32×D3C22
cosocleC23×C32C23×C3
hypercenterC22×C3×C4D32
hypocenterC32C3×#385
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
3. C2×C3×#3724C2semidirect
4. C2×C3×Dic3⋊Dic3C2semidirect
6. C3×#63658C2semidirect
7. C32×C3⋊#95C2semidirect
10. #10591373C3direct (N × H)
24. C3×(C2×D3)⋊Dic3C4semidirect
38. C2×#3724C2×C3semidirect
39. C2×Dic3⋊Dic3C2×C3semidirect
42. #63658C2×C3semidirect
47. C3×C3⋊#95D3semidirect
48. C3×C3⋊#95C2×C3semidirect
64. C2×C3×C3⋊Dic3C2×C4semidirect
73. C2×C32×Dic3C2×C4semidirect
131. (C2×D3)⋊Dic3C3×C4semidirect
145. C2×C32×D3C4⋊C4semidirect
175. C3⋊#95C3×D3semidirect
245. C2×C3⋊Dic3C2×C3×C4semidirect
289. C2×C3×Dic3C4×D3semidirect
291. C2×C3×Dic3C2×C3×C4semidirect
432. C2×C3×D3Dic3⋊C4semidirect
433. C2×C3×D3C3×C4⋊C4semidirect
468. C33#385semidirect
585. C2×Dic3C3×C4×D3semidirect
731. C2×D3C3×Dic3⋊C4semidirect
763. C32#4668semidirect
764. C32#4946semidirect
765. C32C3×#385semidirect
870. C3#10591373direct (N × H)
871. C3C3×#4668semidirect
872. C3C3×#4946semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×Dic32
C2×C32×(C2×D3)⋊C42
C2×C3×#37242
C2×C3×Dic3⋊Dic32
C2×C3×(C2×D3)⋊Dic32
C3×#636582
C32×C3⋊#952
C3×#49463
C3×#46683
#105913733