Finite Group Databasebeta

← C3×#10591259 #13158212

Subgroups — C3×#10591259 #13158212

Order 1728.

1098 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3752C211yesmaximal, characteristic
2C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#3722C211yesmaximal, characteristic
4C2×C3×#3722C211yesmaximal, characteristic
5C2×C3×Dic32C211yesmaximal, characteristic, complemented
6C32×C3⋊#95C211yesmaximal, characteristic, complemented
7C32×C3⋊#95C211yesmaximal, characteristic, complemented
8C3×#4670—31nomaximal
9C3×#4669—31nomaximal
10#10591259C311yesmaximal, characteristic, direct product factor
11C23×C3×C3⋊D3C2211yescharacteristic
12C22×C33×C4C2211yescharacteristic
13C22×C3×C3⋊Dic3C2211yescharacteristic
14C22×C32×Dic3C2211yescharacteristic
15C22×C32×Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C3×#3752—22no—
19C3×Dic3⋊Dic3—22no—
20C3×#3722—22no—
21C3×#3722C414yescomplemented
22C3×Dic32—22no—
23C2×#3752C2×C311yescharacteristic
24C2×C3×(C2×D3)⋊C4—31no—
25C2×C3×(C2×D3)⋊C4—31no—
26C2×C3×(C2×D3)⋊C4—31no—
27C2×C3×(C2×D3)⋊C4—31no—
28C2×C3×(C2×D3)⋊C4—31no—
29C2×C3×(C2×D3)⋊C4—31no—
30C2×C3×(C2×D3)⋊C4—61no—
31C2×C3×C4⋊Dic3—31no—
32C2×C3×Dic3⋊C4—31no—
33C2×C3×C4×Dic3—31no—
34C2×C3×C4×Dic3—31no—
35C2×Dic3⋊Dic3C2×C311yescharacteristic, complemented
36C2×#3722C2×C311yescharacteristic
37C2×#3722C2×C311yescharacteristic
38C2×Dic32C2×C311yescharacteristic, complemented
39C32×#95—31no—
40C32×#95—31no—
41C3×C3⋊#95—21no—
42C3×C3⋊#95—21no—
43C3×C3⋊#95D311yescharacteristic, complemented
44C3×C3⋊#95D311yescharacteristic, complemented
45C3×C3⋊#95C2×C311yescharacteristic, complemented
46C3×C3⋊#95C2×C311yescharacteristic, complemented
47C23×C33C2311yescharacteristic
48C22×C3×C3⋊D3—21no—
49C22×C3×C3⋊D3—21no—
50C22×C3×C3⋊D3—21no—
51C22×C3×C3⋊D3—21no—
52C22×C3×C3⋊D3—21no—
53C22×C3×C3⋊D3—21no—
54C22×C3×C3⋊D3C2×C412yes—
55C2×C33×C4—21no—
56C2×C33×C4—21no—
57C2×C33×C4—21no—
58C2×C3×C3⋊Dic3—21no—
59C2×C3×C3⋊Dic3—21no—
60C2×C3×C3⋊Dic3D412yes—
61C2×C32×Dic3—21no—
62C2×C32×Dic3—21no—
63C2×C32×Dic3—21no—
64C2×C32×Dic3—21no—
65C2×C32×Dic3—21no—
66C2×C32×Dic3—21no—
67C2×C32×Dic3—21no—
68C2×C32×Dic3—21no—
69C2×C32×Dic3—21no—
70C2×C32×Dic3C2×C412yes—
71C2×C32×Dic3C2×C412yes—
72C2×C32×Dic3D412yes—
73C3×#388—91no—
74#4670—31no—
75#4669—31no—
76C23×C3⋊D3C22×C311yescharacteristic
77C23×C3×D3—31no—
78C23×C3×D3—31no—
79C23×C3×D3—61no—
80C22×C32×C4—21no—
81C22×C32×C4—21no—
82C22×C32×C4—21no—
83C22×C32×C4—31no—
84C22×C32×C4—31no—
85C22×C32×C4—31no—
86C22×C32×C4—31no—
87C22×C32×C4—41no—
88C22×C32×C4C2×D311yescharacteristic
89C22×C32×C4C2×D311yescharacteristic
90C22×C32×C4C22×C311yescharacteristic
91C22×C3⋊Dic3C22×C311yescharacteristic
92C22×C3×Dic3—21no—
93C22×C3×Dic3—21no—
94C22×C3×Dic3—21no—
95C22×C3×Dic3—21no—
96C22×C3×Dic3—31no—
97C22×C3×Dic3—31no—
98C22×C3×Dic3—61no—
99C22×C3×Dic3C2×D311yescharacteristic
100C22×C3×Dic3C2×D311yescharacteristic
101C22×C3×Dic3C2×D311yescharacteristic
102C22×C3×Dic3C2×D311yescharacteristic
103C22×C3×Dic3C22×C311yescharacteristic
104C22×C3×Dic3C22×C311yescharacteristic
105C22×C3×Dic3C22×C311yescharacteristic
106C22×C3×Dic3C22×C311yescharacteristic
107#3752—22no—
108C3×(C2×D3)⋊C4—34no—
109C3×(C2×D3)⋊C4—34no—
110C3×(C2×D3)⋊C4—62no—
111C3×(C2×D3)⋊C4—62no—
112C3×(C2×D3)⋊C4—62no—
113C3×(C2×D3)⋊C4—64no—
114C3×(C2×D3)⋊C4—62no—
115C3×C4⋊Dic3—62no—
116C3×Dic3⋊C4—62no—
117C3×C4×Dic3—62no—
118C3×C4×Dic3—62no—
119Dic3⋊Dic3—22no—
120#3722—22no—
121#3722C3×C414yescomplemented
122Dic32—22no—
123C22×C33C22×C411yescharacteristic
124C22×C33C2×D411yescharacteristic
125C22×C33C2×D411yescharacteristic
126C22×C33#4111yescharacteristic
127C22×C33#4111yescharacteristic
128C22×C33#4111yescharacteristic
129C22×C33#4111yescharacteristic
130C2×C3×C3⋊D3—22no—
131C2×C3×C3⋊D3—22no—
132C2×C3×C3⋊D3—22no—
133C2×C3×C3⋊D3—41no—
134C2×C3×C3⋊D3—41no—
135C2×C3×C3⋊D3—41no—
136C2×C3×C3⋊D3—41no—
137C33×C4—41no—
138C3×C3⋊Dic3—22no—
139C32×Dic3—22no—
140C32×Dic3—22no—
141C32×Dic3—22no—
142C32×Dic3—41no—
143C2×C3×C4⋊C4—91no—
144C2×C3×C22⋊C4—91no—
145C2×C3×C22⋊C4—91no—
146C2×C3×C22⋊C4—91no—
147C2×C3×C42—91no—
148C2×(C2×D3)⋊C4—31no—
149C2×(C2×D3)⋊C4—31no—
150C2×(C2×D3)⋊C4—31no—
151C2×(C2×D3)⋊C4—31no—
152C2×(C2×D3)⋊C4—31no—
153C2×(C2×D3)⋊C4—31no—
154C2×(C2×D3)⋊C4—61no—
155C2×C4⋊Dic3—31no—
156C2×Dic3⋊C4—31no—
157C2×C4×Dic3—31no—
158C2×C4×Dic3—31no—
159C3×#95—31no—
160C3×#95—31no—
161C3×#95—31no—
162C3×#95—31no—
163C3×#95—61no—
164C3×#95—61no—
165C3⋊#95C3×D311yescharacteristic, complemented
166C3⋊#95C3×D311yescharacteristic, complemented
167C23×C32—21no—
168C23×C32—21no—
169C23×C32—21no—
170C23×C32—41no—
171C23×C32C22×D311yescharacteristic
172C23×C32C22×D311yescharacteristic
173C23×C32C23×C311yescharacteristic
174C22×C3⋊D3—21no—
175C22×C3⋊D3—21no—
176C22×C3⋊D3—21no—
177C22×C3⋊D3—21no—
178C22×C3⋊D3—21no—
179C22×C3⋊D3—21no—
180C22×C3⋊D3C2×C3×C412yes—
181C22×C3×D3—32no—
182C22×C3×D3—32no—
183C22×C3×D3—62no—
184C22×C3×D3—62no—
185C22×C3×D3—62no—
186C22×C3×D3—61no—
187C22×C3×D3—61no—
188C22×C3×D3—61no—
189C22×C3×D3—61no—
190C22×C3×D3—61no—
191C22×C3×D3—61no—
192C22×C3×D3—61no—
193C22×C3×D3—61no—
194C22×C3×D3—61no—
195C22×C3×D3—61no—
196C22×C3×D3—61no—
197C22×C3×D3—61no—
198C22×C3×D3—121no—
199C22×C3×D3—121no—
200C22×C3×D3—121no—
201C22×C3×D3—121no—
202C2×C32×C4—21no—
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4—22no—
206C2×C32×C4—22no—
207C2×C32×C4—22no—
208C2×C32×C4—21no—
209C2×C32×C4—21no—
210C2×C32×C4—21no—
211C2×C32×C4—21no—
212C2×C32×C4—21no—
213C2×C32×C4—21no—
214C2×C32×C4—32no—
215C2×C32×C4—32no—
216C2×C32×C4—32no—
217C2×C32×C4—41no—
218C2×C32×C4—41no—
219C2×C32×C4—41no—
220C2×C32×C4—41no—
221C2×C32×C4—41no—
222C2×C32×C4—41no—
223C2×C32×C4—42no—
224C2×C32×C4—42no—
225C2×C32×C4—42no—
226C2×C32×C4—61no—
227C2×C32×C4—61no—
228C2×C32×C4—61no—
229C2×C32×C4—61no—
230C2×C32×C4—61no—
231C2×C32×C4—61no—
232C2×C32×C4—61no—
233C2×C32×C4—61no—
234C2×C32×C4—61no—
235C2×C3⋊Dic3—21no—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3C3×D412yes—
238C2×C3×Dic3—21no—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—22no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—22no—
258C2×C3×Dic3—22no—
259C2×C3×Dic3—22no—
260C2×C3×Dic3—32no—
261C2×C3×Dic3—32no—
262C2×C3×Dic3—41no—
263C2×C3×Dic3—41no—
264C2×C3×Dic3—41no—
265C2×C3×Dic3—41no—
266C2×C3×Dic3—41no—
267C2×C3×Dic3—41no—
268C2×C3×Dic3—41no—
269C2×C3×Dic3—41no—
270C2×C3×Dic3—62no—
271C2×C3×Dic3—61no—
272C2×C3×Dic3—61no—
273C2×C3×Dic3—61no—
274C2×C3×Dic3—61no—
275C2×C3×Dic3—121no—
276C2×C3×Dic3—121no—
277C2×C3×Dic3C4×D312yes—
278C2×C3×Dic3C4×D312yes—
279C2×C3×Dic3D1212yes—
280C2×C3×Dic3C2×C3×C412yes—
281C2×C3×Dic3C2×C3×C412yes—
282C2×C3×Dic3C3×D412yes—
283#388—91noSylow
284C2×C33#11711yescharacteristic
285C2×C33C4×D411yescharacteristic
286C2×C33C4×D411yescharacteristic
287C2×C33#12111yescharacteristic
288C2×C33#12311yescharacteristic
289C2×C33#12411yescharacteristic
290C2×C33#12611yescharacteristic
291C3×C3⋊D3—42no—
292C24×C3—91no—
293C23×D3—31no—
294C23×D3—31no—
295C23×D3—61no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—41no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C22×C3×C4—91no—
313C22×C3×C4D3211yescharacteristic
314C22×C3×C4C2×C3×D311yescharacteristic
315C22×C3×C4C2×C3×D311yescharacteristic
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—61no—
319C22×Dic3C2×C3×D311yescharacteristic
320C22×Dic3C2×C3×D311yescharacteristic
321C22×Dic3C2×C3×D311yescharacteristic
322C22×Dic3C2×C3×D311yescharacteristic
323C3×C4⋊C4—182no—
324C3×C22⋊C4—94no—
325C3×C22⋊C4—182no—
326C3×C22⋊C4—182no—
327C3×C42—182no—
328(C2×D3)⋊C4—34no—
329(C2×D3)⋊C4—34no—
330(C2×D3)⋊C4—62no—
331(C2×D3)⋊C4—62no—
332(C2×D3)⋊C4—62no—
333(C2×D3)⋊C4—64no—
334(C2×D3)⋊C4—62no—
335C4⋊Dic3—62no—
336Dic3⋊C4—62no—
337C4×Dic3—62no—
338C4×Dic3—62no—
339C22×C32—21no—
340C22×C32—21no—
341C22×C32—21no—
342C22×C32—21no—
343C22×C32—21no—
344C22×C32—21no—
345C22×C32—21no—
346C22×C32—21no—
347C22×C32—21no—
348C22×C32—21no—
349C22×C32—21no—
350C22×C32—21no—
351C22×C32—21no—
352C22×C32—21no—
353C22×C32—21no—
354C22×C32—21no—
355C22×C32—21no—
356C22×C32—21no—
357C22×C32—21no—
358C22×C32—21no—
359C22×C32—21no—
360C22×C32—41no—
361C22×C32—41no—
362C22×C32—41no—
363C22×C32—41no—
364C22×C32—41no—
365C22×C32—41no—
366C22×C32—41no—
367C22×C32C2×C4×D311yescharacteristic
368C22×C32C2×C4×D311yescharacteristic
369C22×C32C2×D1211yescharacteristic
370C22×C32#23511yescharacteristic
371C22×C32#23511yescharacteristic
372C22×C32#23511yescharacteristic
373C22×C32D3×D411yescharacteristic
374C22×C32D3×D411yescharacteristic
375C22×C32D3×D411yescharacteristic
376C22×C32#23711yescharacteristic
377C22×C32#23711yescharacteristic
378C22×C32#23711yescharacteristic
379C22×C32#23911yescharacteristic
380C22×C32#23911yescharacteristic
381C22×C32C22×C3×C411yescharacteristic
382C22×C32C2×C3×D411yescharacteristic
383C22×C32C2×C3×D411yescharacteristic
384C22×C32C3×#4111yescharacteristic
385C22×C32C3×#4111yescharacteristic
386C22×C32C3×#4111yescharacteristic
387C22×C32C3×#4111yescharacteristic
388C2×C3⋊D3—22no—
389C2×C3⋊D3—22no—
390C2×C3⋊D3—22no—
391C2×C3⋊D3—41no—
392C2×C3⋊D3—41no—
393C2×C3⋊D3—41no—
394C2×C3⋊D3—41no—
395C2×C3×D3—64no—
396C2×C3×D3—62no—
397C2×C3×D3—62no—
398C2×C3×D3—62no—
399C2×C3×D3—62no—
400C2×C3×D3—62no—
401C2×C3×D3—62no—
402C2×C3×D3—122no—
403C2×C3×D3—122no—
404C2×C3×D3—122no—
405C2×C3×D3—122no—
406C2×C3×D3—122no—
407C2×C3×D3—122no—
408C2×C3×D3—121no—
409C2×C3×D3—121no—
410C2×C3×D3—121no—
411C2×C3×D3—121no—
412C2×C3×D3—121no—
413C2×C3×D3—121no—
414C2×C3×D3—121no—
415C2×C3×D3—121no—
416C32×C4—42no—
417C32×C4—42no—
418C32×C4—42no—
419C32×C4—44no—
420C32×C4—41no—
421C32×C4—41no—
422C32×C4—41no—
423C32×C4—62no—
424C32×C4—62no—
425C32×C4—62no—
426C32×C4—121no—
427C3⋊Dic3—22no—
428C3×Dic3—22no—
429C3×Dic3—22no—
430C3×Dic3—22no—
431C3×Dic3—22no—
432C3×Dic3—22no—
433C3×Dic3—22no—
434C3×Dic3—42no—
435C3×Dic3—42no—
436C3×Dic3—42no—
437C3×Dic3—42no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3—62no—
441C3×Dic3—62no—
442C3×Dic3—122no—
443C2×C4⋊C4—91no—
444C2×C22⋊C4—91no—
445C2×C22⋊C4—91no—
446C2×C22⋊C4—91no—
447C2×C42—91no—
448#95—31no—
449#95—31no—
450C33#38811yescharacteristic, complemented, Sylow
451C23×C3—21no—
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—41no—
455C23×C3—92no—
456C23×C3—181no—
457C23×C3—181no—
458C23×C3—181no—
459C23×C3—181no—
460C23×C3—181no—
461C23×C3—181no—
462C23×C3C2×D3211yescharacteristic
463C23×C3C22×C3×D311yescharacteristic
464C23×C3C22×C3×D311yescharacteristic
465C22×D3—32no—
466C22×D3—32no—
467C22×D3—62no—
468C22×D3—62no—
469C22×D3—62no—
470C22×D3—61no—
471C22×D3—61no—
472C22×D3—61no—
473C22×D3—61no—
474C22×D3—61no—
475C22×D3—61no—
476C22×D3—61no—
477C22×D3—61no—
478C22×D3—61no—
479C22×D3—61no—
480C22×D3—61no—
481C22×D3—61no—
482C22×D3—121no—
483C22×D3—121no—
484C22×D3—121no—
485C22×D3—121no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—32no—
499C2×C3×C4—32no—
500C2×C3×C4—32no—
501C2×C3×C4—32no—
502C2×C3×C4—32no—
503C2×C3×C4—32no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—42no—
511C2×C3×C4—42no—
512C2×C3×C4—42no—
513C2×C3×C4—62no—
514C2×C3×C4—62no—
515C2×C3×C4—62no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—62no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—92no—
536C2×C3×C4—121no—
537C2×C3×C4—121no—
538C2×C3×C4—121no—
539C2×C3×C4—121no—
540C2×C3×C4—121no—
541C2×C3×C4—121no—
542C2×C3×C4—121no—
543C2×C3×C4—121no—
544C2×C3×C4—181no—
545C2×C3×C4—181no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—32no—
556C2×Dic3—32no—
557C2×Dic3—62no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—121no—
563C2×Dic3—121no—
564C2×Dic3C3×C4×D312yes—
565C2×Dic3C3×C4×D312yes—
566C2×Dic3C3×D1212yes—
567C2×C32—21no—
568C2×C32—21no—
569C2×C32—21no—
570C2×C32—21no—
571C2×C32—21no—
572C2×C32—21no—
573C2×C32—21no—
574C2×C32—21no—
575C2×C32—21no—
576C2×C32—21no—
577C2×C32—21no—
578C2×C32—21no—
579C2×C32—21no—
580C2×C32—21no—
581C2×C32—21no—
582C2×C32—21no—
583C2×C32—21no—
584C2×C32—21no—
585C2×C32—21no—
586C2×C32—21no—
587C2×C32—21no—
588C2×C32—41no—
589C2×C32—41no—
590C2×C32—41no—
591C2×C32—41no—
592C2×C32—41no—
593C2×C32—41no—
594C2×C32—41no—
595C2×C32#87211yescharacteristic
596C2×C32C4×D1211yescharacteristic
597C2×C32#67⋊C411yescharacteristic
598C2×C32#67⋊C411yescharacteristic
599C2×C32#88411yescharacteristic
600C2×C32#88511yescharacteristic
601C2×C32#88511yescharacteristic
602C2×C32#88611yescharacteristic
603C2×C32#89211yescharacteristic
604C2×C32#89311yescharacteristic
605C2×C32#89411yescharacteristic
606C2×C32#89511yescharacteristic
607C2×C32#89811yescharacteristic
608C2×C32#89811yescharacteristic
609C2×C32C3×#11711yescharacteristic
610C2×C32C3×C4×D411yescharacteristic
611C2×C32C3×C4×D411yescharacteristic
612C2×C32C3×#12111yescharacteristic
613C2×C32C3×#12311yescharacteristic
614C2×C32C3×#12411yescharacteristic
615C2×C32C3×#12611yescharacteristic
616C3⋊D3—42no—
617C3×D3—124no—
618C3×D3—122no—
619C3×D3—122no—
620C24—91no—
621C22×C4—31no—
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—31no—
625C22×C4—91no—
626C22×C4C3×D3211yescharacteristic
627C4⋊C4—182no—
628C22⋊C4—94no—
629C22⋊C4—182no—
630C22⋊C4—182no—
631C42—182no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—182no—
661C22×C3—182no—
662C22×C3—182no—
663C22×C3—361no—
664C22×C3—361no—
665C22×C3—361no—
666C22×C3—361no—
667C22×C3#379611yescharacteristic
668C22×C3#379911yescharacteristic
669C22×C3C4×D3211yescharacteristic
670C22×C3D3×D1211yescharacteristic
671C22×C3#380411yescharacteristic
672C22×C3#380411yescharacteristic
673C22×C3#381111yescharacteristic
674C22×C3C2×C3×C4×D311yescharacteristic
675C22×C3C2×C3×C4×D311yescharacteristic
676C22×C3C2×C3×D1211yescharacteristic
677C22×C3C3×#23511yescharacteristic
678C22×C3C3×#23511yescharacteristic
679C22×C3C3×#23511yescharacteristic
680C22×C3C3×D3×D411yescharacteristic
681C22×C3C3×D3×D411yescharacteristic
682C22×C3C3×D3×D411yescharacteristic
683C22×C3C3×#23711yescharacteristic
684C22×C3C3×#23711yescharacteristic
685C22×C3C3×#23711yescharacteristic
686C22×C3C3×#23911yescharacteristic
687C22×C3C3×#23911yescharacteristic
688C2×D3—64no—
689C2×D3—62no—
690C2×D3—62no—
691C2×D3—62no—
692C2×D3—62no—
693C2×D3—62no—
694C2×D3—62no—
695C2×D3—122no—
696C2×D3—122no—
697C2×D3—122no—
698C2×D3—122no—
699C2×D3—122no—
700C2×D3—122no—
701C2×D3—121no—
702C2×D3—121no—
703C2×D3—121no—
704C2×D3—121no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—121no—
709C3×C4—42no—
710C3×C4—42no—
711C3×C4—42no—
712C3×C4—44no—
713C3×C4—41no—
714C3×C4—41no—
715C3×C4—41no—
716C3×C4—62no—
717C3×C4—62no—
718C3×C4—62no—
719C3×C4—62no—
720C3×C4—62no—
721C3×C4—62no—
722C3×C4—122no—
723C3×C4—122no—
724C3×C4—122no—
725C3×C4—122no—
726C3×C4—121no—
727C3×C4—121no—
728C3×C4—182no—
729Dic3—22no—
730Dic3—22no—
731Dic3—22no—
732Dic3—41no—
733Dic3—62no—
734Dic3—62no—
735Dic3—122no—
736C32—21no—
737C32—21no—
738C32—21no—
739C32—41no—
740C32#466911yescharacteristic, complemented
741C32#467011yescharacteristic, complemented
742C32C3×#38811yescharacteristic, complemented
743C23—92no—
744C23—181no—
745C23—181no—
746C23—181no—
747C23—181no—
748C23—181no—
749C23—181no—
750C23C2×C3×D3211yescharacteristic
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—32no—
755C2×C4—32no—
756C2×C4—32no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—92no—
767C2×C4—181no—
768C2×C4—181no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—21no—
774C2×C3—21no—
775C2×C3—21no—
776C2×C3—21no—
777C2×C3—21no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—41no—
791C2×C3—41no—
792C2×C3—41no—
793C2×C3—41no—
794C2×C3—41no—
795C2×C3—41no—
796C2×C3—41no—
797C2×C3—362no—
798C2×C3#6383611yescharacteristic
799C2×C3#6384811yescharacteristic
800C2×C3#6388011yescharacteristic
801C2×C3#6388111yescharacteristic
802C2×C3#6389011yescharacteristic
803C2×C3#6391011yescharacteristic
804C2×C3#6395311yescharacteristic
805C2×C3C3×#87211yescharacteristic
806C2×C3C3×C4×D1211yescharacteristic
807C2×C3C3×#67⋊C411yescharacteristic
808C2×C3C3×#67⋊C411yescharacteristic
809C2×C3C3×#88411yescharacteristic
810C2×C3C3×#88511yescharacteristic
811C2×C3C3×#88511yescharacteristic
812C2×C3C3×#88611yescharacteristic
813C2×C3C3×#89211yescharacteristic
814C2×C3C3×#89311yescharacteristic
815C2×C3C3×#89411yescharacteristic
816C2×C3C3×#89511yescharacteristic
817C2×C3C3×#89811yescharacteristic
818C2×C3C3×#89811yescharacteristic
819D3—124no—
820D3—122no—
821D3—122no—
822C22—182no—
823C22—182no—
824C22—182no—
825C22—361no—
826C22—361no—
827C22—361no—
828C22—361no—
829C22C3×#379611yescharacteristic
830C22C3×#379911yescharacteristic
831C22C3×C4×D3211yescharacteristic
832C22C3×D3×D1211yescharacteristic
833C22C3×#380411yescharacteristic
834C22C3×#380411yescharacteristic
835C22C3×#381111yescharacteristic
836C4—41no—
837C4—62no—
838C4—62no—
839C4—62no—
840C4—121no—
841C4—182no—
842C3—21no—
843C3—21no—
844C3—21no—
845C3—41no—
846C3#1059125911yescharacteristic, direct product factor
847C3C3×#466911yescharacteristic, complemented
848C3C3×#467011yescharacteristic, complemented
849C2—362no—
850C2C3×#6383611yescharacteristic
851C2C3×#6384811yescharacteristic
852C2C3×#6388011yescharacteristic
853C2C3×#6388111yescharacteristic
854C2C3×#6389011yescharacteristic
855C2C3×#6391011yescharacteristic
856C2C3×#6395311yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutatorC22×C32C22×C3×C4
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC23×C3×C3⋊D3C22
cosocleC23×C32C23×C3
hypercenterC22×C3×C4D32
hypocenterC32C3×#388
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×Dic3⋊Dic3C2semidirect
5. C2×C3×Dic32C2semidirect
6. C32×C3⋊#95C2semidirect
7. C32×C3⋊#95C2semidirect
10. #10591259C3direct (N × H)
21. C3×#3722C4semidirect
35. C2×Dic3⋊Dic3C2×C3semidirect
38. C2×Dic32C2×C3semidirect
43. C3×C3⋊#95D3semidirect
44. C3×C3⋊#95D3semidirect
45. C3×C3⋊#95C2×C3semidirect
46. C3×C3⋊#95C2×C3semidirect
121. #3722C3×C4semidirect
165. C3⋊#95C3×D3semidirect
166. C3⋊#95C3×D3semidirect
450. C33#388semidirect
740. C32#4669semidirect
741. C32#4670semidirect
742. C32C3×#388semidirect
846. C3#10591259direct (N × H)
847. C3C3×#4669semidirect
848. C3C3×#4670semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37522
C2×C3×Dic3⋊Dic32
C2×C3×#37222
C2×C3×Dic322
C32×C3⋊#952
C3×#46703
C3×#46693
#105912593