Finite Group Databasebeta

← C3×#10591297 #13158271

Subgroups — C3×#10591297 #13158271

Order 1728.

1018 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×(C2×D3)⋊C4C211yesmaximal, characteristic
2C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
4C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
5C3×#63658C211yesmaximal, characteristic, complemented
6C32×C3⋊#95C211yesmaximal, characteristic, complemented
7C3×#63579C211yesmaximal, characteristic, complemented
8C3×#4953—31nomaximal
9C3×#4675—31nomaximal
10#10591297C311yesmaximal, 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
18C32×(C2×D3)⋊C4—22no—
19C3×Dic3⋊Dic3—22no—
20C3×(C2×D3)⋊Dic3—22no—
21C3×(C2×D3)⋊Dic3—22no—
22C2×C32×C22⋊C4—31no—
23C2×C3×#217—31no—
24C2×C3×#217—31no—
25C2×C3×(C2×D3)⋊C4—21no—
26C2×C3×(C2×D3)⋊C4—31no—
27C2×C3×(C2×D3)⋊C4—31no—
28C2×C3×(C2×D3)⋊C4D311yescharacteristic
29C2×C3×(C2×D3)⋊C4C2×C311yescharacteristic
30C2×C3×C4⋊Dic3—31no—
31C2×C3×Dic3⋊C4—31no—
32C2×Dic3⋊Dic3C2×C311yescharacteristic, complemented
33C2×(C2×D3)⋊Dic3C2×C311yescharacteristic
34C2×(C2×D3)⋊Dic3C2×C311yescharacteristic
35C32×#95—31no—
36#63658C2×C311yescharacteristic, complemented
37C3×C3⋊#95—21no—
38C3×C3⋊#95—31no—
39C3×C3⋊#95—31no—
40C3×C3⋊#95—31no—
41C3×C3⋊#95—31no—
42C3×C3⋊#95—61no—
43C3×C3⋊#95D311yescharacteristic, complemented
44C3×C3⋊#95C2×C311yescharacteristic, complemented
45#63579C2×C311yescharacteristic, complemented
46C23×C33C2311yescharacteristic
47C22×C32×D3—21no—
48C22×C32×D3—21no—
49C22×C32×D3—21no—
50C22×C32×D3—21no—
51C22×C32×D3—21no—
52C22×C32×D3—21no—
53C22×C32×D3D412yes—
54C2×C33×C4—21no—
55C2×C33×C4—21no—
56C2×C33×C4—21no—
57C2×C3×C3⋊Dic3—21no—
58C2×C3×C3⋊Dic3—21no—
59C2×C3×C3⋊Dic3—21no—
60C2×C3×C3⋊Dic3—21no—
61C2×C3×C3⋊Dic3—21no—
62C2×C3×C3⋊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×Dic3—21no—
71C2×C32×Dic3D412yes—
72C3×#397—91no—
73#4953—31no—
74#4675—31no—
75C24×C32—31no—
76C23×C3×D3—21no—
77C23×C3×D3C2×D311yescharacteristic
78C23×C3×D3C22×C311yescharacteristic
79C22×C32×C4—21no—
80C22×C32×C4—21no—
81C22×C32×C4—21no—
82C22×C32×C4—31no—
83C22×C32×C4—31no—
84C22×C32×C4—31no—
85C22×C32×C4—41no—
86C22×C32×C4C2×D311yescharacteristic
87C22×C32×C4C2×D311yescharacteristic
88C22×C32×C4C22×C311yescharacteristic
89C22×C3⋊Dic3C22×C311yescharacteristic
90C22×C3⋊Dic3C22×C311yescharacteristic
91C22×C3×Dic3—21no—
92C22×C3×Dic3—21no—
93C22×C3×Dic3—21no—
94C22×C3×Dic3—31no—
95C22×C3×Dic3—31no—
96C22×C3×Dic3—31no—
97C22×C3×Dic3—31no—
98C22×C3×Dic3—61no—
99C22×C3×Dic3—61no—
100C22×C3×Dic3C2×D311yescharacteristic
101C22×C3×Dic3C2×D311yescharacteristic
102C22×C3×Dic3C2×D311yescharacteristic
103C22×C3×Dic3C22×C311yescharacteristic
104C22×C3×Dic3C22×C311yescharacteristic
105C22×C3×Dic3C22×C311yescharacteristic
106C32×C22⋊C4—62no—
107C3×#217—62no—
108C3×#217—62no—
109C3×(C2×D3)⋊C4—24no—
110C3×(C2×D3)⋊C4—22no—
111C3×(C2×D3)⋊C4—22no—
112C3×(C2×D3)⋊C4—62no—
113C3×(C2×D3)⋊C4—62no—
114C3×C4⋊Dic3—62no—
115C3×Dic3⋊C4—62no—
116Dic3⋊Dic3—22no—
117(C2×D3)⋊Dic3—22no—
118(C2×D3)⋊Dic3—22no—
119C22×C33C2×D411yescharacteristic
120C22×C33C2×D411yescharacteristic
121C22×C33#4111yescharacteristic
122C22×C33#4111yescharacteristic
123C22×C33#4111yescharacteristic
124C22×C33#4111yescharacteristic
125C22×C33#4111yescharacteristic
126C2×C32×D3—22no—
127C2×C32×D3—22no—
128C2×C32×D3—22no—
129C2×C32×D3—41no—
130C2×C32×D3—41no—
131C2×C32×D3—41no—
132C2×C32×D3—41no—
133C33×C4—41no—
134C3×C3⋊Dic3—41no—
135C3×C3⋊Dic3—41no—
136C32×Dic3—22no—
137C32×Dic3—41no—
138C32×Dic3—41no—
139C2×C3×C4⋊C4—91no—
140C2×C3×C22⋊C4—31no—
141C2×C3×C22⋊C4—31no—
142C2×C3×C22⋊C4—61no—
143C2×C3×C22⋊C4—91no—
144C2×C3×C22⋊C4—91no—
145C2×#217—31no—
146C2×#217—31no—
147C2×(C2×D3)⋊C4—31no—
148C2×(C2×D3)⋊C4—31no—
149C2×(C2×D3)⋊C4C3×D311yescharacteristic
150C2×C4⋊Dic3—31no—
151C2×Dic3⋊C4—31no—
152C3×#95—31no—
153C3×#95—31no—
154C3×#95—61no—
155C3×#95—91no—
156C3×#95—91no—
157C3⋊#95—31no—
158C3⋊#95—31no—
159C3⋊#95—31no—
160C3⋊#95—31no—
161C3⋊#95—61no—
162C3⋊#95C3×D311yescharacteristic, complemented
163C23×C32—21no—
164C23×C32—21no—
165C23×C32—21no—
166C23×C32—32no—
167C23×C32—41no—
168C23×C32—61no—
169C23×C32—61no—
170C23×C32—61no—
171C23×C32—61no—
172C23×C32—61no—
173C23×C32—61no—
174C23×C32C22×D311yescharacteristic
175C23×C32C22×D311yescharacteristic
176C23×C32C23×C311yescharacteristic
177C22×C3×D3—22no—
178C22×C3×D3—22no—
179C22×C3×D3—21no—
180C22×C3×D3—21no—
181C22×C3×D3—21no—
182C22×C3×D3—21no—
183C22×C3×D3—21no—
184C22×C3×D3—21no—
185C22×C3×D3—21no—
186C22×C3×D3—21no—
187C22×C3×D3—21no—
188C22×C3×D3—21no—
189C22×C3×D3—21no—
190C22×C3×D3—21no—
191C22×C3×D3—22no—
192C22×C3×D3—41no—
193C22×C3×D3—41no—
194C22×C3×D3—41no—
195C22×C3×D3—41no—
196C22×C3×D3D1212yes—
197C22×C3×D3C3×D412yes—
198C2×C32×C4—21no—
199C2×C32×C4—21no—
200C2×C32×C4—21no—
201C2×C32×C4—22no—
202C2×C32×C4—22no—
203C2×C32×C4—22no—
204C2×C32×C4—21no—
205C2×C32×C4—21no—
206C2×C32×C4—21no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4—21no—
210C2×C32×C4—32no—
211C2×C32×C4—41no—
212C2×C32×C4—41no—
213C2×C32×C4—41no—
214C2×C32×C4—41no—
215C2×C32×C4—41no—
216C2×C32×C4—41no—
217C2×C32×C4—42no—
218C2×C32×C4—42no—
219C2×C32×C4—42no—
220C2×C32×C4—61no—
221C2×C32×C4—61no—
222C2×C32×C4—61no—
223C2×C32×C4—61no—
224C2×C32×C4—61no—
225C2×C32×C4—61no—
226C2×C32×C4—61no—
227C2×C32×C4—61no—
228C2×C3⋊Dic3—21no—
229C2×C3⋊Dic3—21no—
230C2×C3⋊Dic3—21no—
231C2×C3⋊Dic3—21no—
232C2×C3⋊Dic3—21no—
233C2×C3⋊Dic3—21no—
234C2×C3×Dic3—21no—
235C2×C3×Dic3—21no—
236C2×C3×Dic3—21no—
237C2×C3×Dic3—21no—
238C2×C3×Dic3—22no—
239C2×C3×Dic3—22no—
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—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—22no—
253C2×C3×Dic3—41no—
254C2×C3×Dic3—41no—
255C2×C3×Dic3—41no—
256C2×C3×Dic3—41no—
257C2×C3×Dic3—41no—
258C2×C3×Dic3—41no—
259C2×C3×Dic3—62no—
260C2×C3×Dic3—62no—
261C2×C3×Dic3—61no—
262C2×C3×Dic3—61no—
263C2×C3×Dic3—61no—
264C2×C3×Dic3—61no—
265C2×C3×Dic3—61no—
266C2×C3×Dic3—61no—
267C2×C3×Dic3—61no—
268C2×C3×Dic3—61no—
269C2×C3×Dic3—61no—
270C2×C3×Dic3—61no—
271C2×C3×Dic3—61no—
272C2×C3×Dic3—61no—
273C2×C3×Dic3—121no—
274C2×C3×Dic3—121no—
275C2×C3×Dic3—121no—
276C2×C3×Dic3—121no—
277C2×C3×Dic3#6712yes—
278C2×C3×Dic3C3×D412yes—
279#397—91noSylow
280C2×C33#12111yescharacteristic
281C2×C33#12311yescharacteristic
282C2×C33#12311yescharacteristic
283C2×C33#12311yescharacteristic
284C2×C33#12411yescharacteristic
285C2×C33#12611yescharacteristic
286C2×C33#12611yescharacteristic
287C32×D3—42no—
288C24×C3—31no—
289C24×C3—31no—
290C24×C3—61no—
291C23×D3C2×C3×D311yescharacteristic
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—41no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C22×C3×C4—61no—
305C22×C3×C4—91no—
306C22×C3×C4—91no—
307C22×C3×C4D3211yescharacteristic
308C22×C3×C4C2×C3×D311yescharacteristic
309C22×C3×C4C2×C3×D311yescharacteristic
310C22×Dic3—31no—
311C22×Dic3—31no—
312C22×Dic3—31no—
313C22×Dic3—31no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3C2×C3×D311yescharacteristic
317C22×Dic3C2×C3×D311yescharacteristic
318C22×Dic3C2×C3×D311yescharacteristic
319C3×C4⋊C4—182no—
320C3×C22⋊C4—62no—
321C3×C22⋊C4—62no—
322C3×C22⋊C4—64no—
323C3×C22⋊C4—182no—
324C3×C22⋊C4—182no—
325#217—62no—
326#217—62no—
327(C2×D3)⋊C4—22no—
328(C2×D3)⋊C4—62no—
329(C2×D3)⋊C4—62no—
330C4⋊Dic3—62no—
331Dic3⋊C4—62no—
332C22×C32—21no—
333C22×C32—21no—
334C22×C32—21no—
335C22×C32—21no—
336C22×C32—21no—
337C22×C32—21no—
338C22×C32—21no—
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—41no—
354C22×C32—41no—
355C22×C32—41no—
356C22×C32—41no—
357C22×C32—41no—
358C22×C32—41no—
359C22×C32—41no—
360C22×C32—62no—
361C22×C32—62no—
362C22×C32—62no—
363C22×C32—121no—
364C22×C32—121no—
365C22×C32—121no—
366C22×C32—121no—
367C22×C32C2×D1211yescharacteristic
368C22×C32#23511yescharacteristic
369C22×C32#23511yescharacteristic
370C22×C32#23511yescharacteristic
371C22×C32#23511yescharacteristic
372C22×C32D3×D411yescharacteristic
373C22×C32D3×D411yescharacteristic
374C22×C32#23711yescharacteristic
375C22×C32#23711yescharacteristic
376C22×C32#23711yescharacteristic
377C22×C32#23711yescharacteristic
378C22×C32#23711yescharacteristic
379C22×C32#23911yescharacteristic
380C22×C32C2×#6711yescharacteristic
381C22×C32C2×C3×D411yescharacteristic
382C22×C32C2×C3×D411yescharacteristic
383C22×C32C3×#4111yescharacteristic
384C22×C32C3×#4111yescharacteristic
385C22×C32C3×#4111yescharacteristic
386C22×C32C3×#4111yescharacteristic
387C22×C32C3×#4111yescharacteristic
388C2×C3×D3—24no—
389C2×C3×D3—22no—
390C2×C3×D3—22no—
391C2×C3×D3—22no—
392C2×C3×D3—22no—
393C2×C3×D3—22no—
394C2×C3×D3—22no—
395C2×C3×D3—42no—
396C2×C3×D3—42no—
397C2×C3×D3—42no—
398C2×C3×D3—42no—
399C2×C3×D3—42no—
400C2×C3×D3—42no—
401C2×C3×D3—41no—
402C2×C3×D3—41no—
403C2×C3×D3—41no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408C2×C3×D3—41no—
409C32×C4—42no—
410C32×C4—42no—
411C32×C4—42no—
412C32×C4—44no—
413C32×C4—41no—
414C32×C4—41no—
415C32×C4—41no—
416C32×C4—62no—
417C32×C4—121no—
418C32×C4—121no—
419C3⋊Dic3—41no—
420C3⋊Dic3—41no—
421C3×Dic3—22no—
422C3×Dic3—22no—
423C3×Dic3—42no—
424C3×Dic3—42no—
425C3×Dic3—42no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3—122no—
431C3×Dic3—122no—
432C3×Dic3—121no—
433C3×Dic3—121no—
434C3×Dic3—121no—
435C3×Dic3—121no—
436C2×C4⋊C4—91no—
437C2×C22⋊C4—31no—
438C2×C22⋊C4—91no—
439C2×C22⋊C4—91no—
440#95—31no—
441#95—91no—
442#95—91no—
443C33#39711yescharacteristic, complemented, Sylow
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—32no—
448C23×C3—32no—
449C23×C3—41no—
450C23×C3—62no—
451C23×C3—62no—
452C23×C3—62no—
453C23×C3—61no—
454C23×C3—61no—
455C23×C3—61no—
456C23×C3—61no—
457C23×C3—61no—
458C23×C3—61no—
459C23×C3—61no—
460C23×C3—61no—
461C23×C3—61no—
462C23×C3—61no—
463C23×C3—61no—
464C23×C3—61no—
465C23×C3—121no—
466C23×C3—121no—
467C23×C3—121no—
468C23×C3—121no—
469C23×C3C2×D3211yescharacteristic
470C23×C3C22×C3×D311yescharacteristic
471C23×C3C22×C3×D311yescharacteristic
472C22×D3—21no—
473C22×D3—21no—
474C22×D3—21no—
475C22×D3—21no—
476C22×D3—21no—
477C22×D3—21no—
478C22×D3C3×D1212yes—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—32no—
492C2×C3×C4—32no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—42no—
500C2×C3×C4—42no—
501C2×C3×C4—42no—
502C2×C3×C4—62no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—62no—
508C2×C3×C4—62no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—121no—
522C2×C3×C4—121no—
523C2×C3×C4—121no—
524C2×C3×C4—121no—
525C2×C3×C4—121no—
526C2×C3×C4—121no—
527C2×C3×C4—181no—
528C2×C3×C4—181no—
529C2×C3×C4—181no—
530C2×C3×C4—181no—
531C2×C3×C4—181no—
532C2×C3×C4—181no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—62no—
542C2×Dic3—62no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—121no—
556C2×Dic3—121no—
557C2×Dic3—121no—
558C2×Dic3—121no—
559C2×Dic3C3×#6712yes—
560C2×C32—21no—
561C2×C32—21no—
562C2×C32—21no—
563C2×C32—21no—
564C2×C32—21no—
565C2×C32—21no—
566C2×C32—21no—
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—41no—
582C2×C32—41no—
583C2×C32—41no—
584C2×C32—41no—
585C2×C32—41no—
586C2×C32—41no—
587C2×C32—41no—
588C2×C32—122no—
589C2×C32#87611yescharacteristic
590C2×C32#87911yescharacteristic
591C2×C32#87911yescharacteristic
592C2×C32#88311yescharacteristic
593C2×C32#88411yescharacteristic
594C2×C32#88511yescharacteristic
595C2×C32#88611yescharacteristic
596C2×C32#88611yescharacteristic
597C2×C32#89411yescharacteristic
598C2×C32#89411yescharacteristic
599C2×C32#89811yescharacteristic
600C2×C32#93011yescharacteristic
601C2×C32#93511yescharacteristic
602C2×C32#93611yescharacteristic
603C2×C32C3×#12111yescharacteristic
604C2×C32C3×#12311yescharacteristic
605C2×C32C3×#12311yescharacteristic
606C2×C32C3×#12311yescharacteristic
607C2×C32C3×#12411yescharacteristic
608C2×C32C3×#12611yescharacteristic
609C2×C32C3×#12611yescharacteristic
610C3×D3—44no—
611C3×D3—42no—
612C3×D3—42no—
613C24—31no—
614C22×C4—31no—
615C22×C4—31no—
616C22×C4—31no—
617C22×C4—91no—
618C22×C4—91no—
619C22×C4C3×D3211yescharacteristic
620C4⋊C4—182no—
621C22⋊C4—62no—
622C22⋊C4—182no—
623C22⋊C4—182no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
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—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—64no—
653C22×C3—62no—
654C22×C3—62no—
655C22×C3—62no—
656C22×C3—62no—
657C22×C3—62no—
658C22×C3—62no—
659C22×C3—122no—
660C22×C3—122no—
661C22×C3—122no—
662C22×C3—122no—
663C22×C3—122no—
664C22×C3—122no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3#379511yescharacteristic
674C22×C3#379611yescharacteristic
675C22×C3#379811yescharacteristic
676C22×C3D3×D1211yescharacteristic
677C22×C3#380411yescharacteristic
678C22×C3#380511yescharacteristic
679C22×C3D3×#6711yescharacteristic
680C22×C3C2×C3×D1211yescharacteristic
681C22×C3C3×#23511yescharacteristic
682C22×C3C3×#23511yescharacteristic
683C22×C3C3×#23511yescharacteristic
684C22×C3C3×#23511yescharacteristic
685C22×C3C3×D3×D411yescharacteristic
686C22×C3C3×D3×D411yescharacteristic
687C22×C3C3×#23711yescharacteristic
688C22×C3C3×#23711yescharacteristic
689C22×C3C3×#23711yescharacteristic
690C22×C3C3×#23711yescharacteristic
691C22×C3C3×#23711yescharacteristic
692C22×C3C3×#23911yescharacteristic
693C22×C3C2×C3×#6711yescharacteristic
694C2×D3—22no—
695C2×D3—22no—
696C2×D3—22no—
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—41no—
701C3×C4—42no—
702C3×C4—42no—
703C3×C4—42no—
704C3×C4—44no—
705C3×C4—41no—
706C3×C4—41no—
707C3×C4—41no—
708C3×C4—62no—
709C3×C4—62no—
710C3×C4—122no—
711C3×C4—122no—
712C3×C4—122no—
713C3×C4—121no—
714C3×C4—121no—
715C3×C4—121no—
716C3×C4—121no—
717C3×C4—361no—
718C3×C4—361no—
719Dic3—22no—
720Dic3—41no—
721Dic3—41no—
722Dic3—122no—
723Dic3—122no—
724Dic3—121no—
725Dic3—121no—
726Dic3—121no—
727Dic3—121no—
728C32—21no—
729C32—21no—
730C32—21no—
731C32—41no—
732C32#467511yescharacteristic, complemented
733C32#495311yescharacteristic, complemented
734C32C3×#39711yescharacteristic, complemented
735C23—32no—
736C23—61no—
737C23—61no—
738C23—61no—
739C23—61no—
740C23—61no—
741C23—61no—
742C23C2×C3×D3211yescharacteristic
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—32no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—181no—
756C2×C4—181no—
757C2×C4—181no—
758C2×C4—181no—
759C2×C4—181no—
760C2×C4—181no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
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—41no—
783C2×C3—41no—
784C2×C3—41no—
785C2×C3—41no—
786C2×C3—41no—
787C2×C3—41no—
788C2×C3—41no—
789C2×C3—124no—
790C2×C3—122no—
791C2×C3—122no—
792C2×C3#6385911yescharacteristic
793C2×C3#6386211yescharacteristic
794C2×C3#6388411yescharacteristic
795C2×C3#6389011yescharacteristic
796C2×C3#6389111yescharacteristic
797C2×C3#6390611yescharacteristic
798C2×C3#6395911yescharacteristic
799C2×C3C3×#87611yescharacteristic
800C2×C3C3×#87911yescharacteristic
801C2×C3C3×#87911yescharacteristic
802C2×C3C3×#88311yescharacteristic
803C2×C3C3×#88411yescharacteristic
804C2×C3C3×#88511yescharacteristic
805C2×C3C3×#88611yescharacteristic
806C2×C3C3×#88611yescharacteristic
807C2×C3C3×#89411yescharacteristic
808C2×C3C3×#89411yescharacteristic
809C2×C3C3×#89811yescharacteristic
810C2×C3C3×#93011yescharacteristic
811C2×C3C3×#93511yescharacteristic
812C2×C3C3×#93611yescharacteristic
813D3—42no—
814C22—62no—
815C22—62no—
816C22—62no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22—121no—
821C22C3×#379511yescharacteristic
822C22C3×#379611yescharacteristic
823C22C3×#379811yescharacteristic
824C22C3×D3×D1211yescharacteristic
825C22C3×#380411yescharacteristic
826C22C3×#380511yescharacteristic
827C22C3×D3×#6711yescharacteristic
828C4—41no—
829C4—62no—
830C4—121no—
831C4—121no—
832C4—361no—
833C4—361no—
834C3—21no—
835C3—21no—
836C3—21no—
837C3—41no—
838C3#1059129711yescharacteristic, direct product factor
839C3C3×#467511yescharacteristic, complemented
840C3C3×#495311yescharacteristic, complemented
841C2—122no—
842C2C3×#6385911yescharacteristic
843C2C3×#6386211yescharacteristic
844C2C3×#6388411yescharacteristic
845C2C3×#6389011yescharacteristic
846C2C3×#6389111yescharacteristic
847C2C3×#6390611yescharacteristic
848C2C3×#6395911yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutator, cosocleC23×C32C23×C3
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC23×C32×D3C22
hypercenterC22×C3×C4D32
hypocenterC32C3×#397
LCSG ▷ C23×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. C3×#63658C2semidirect
6. C32×C3⋊#95C2semidirect
7. C3×#63579C2semidirect
10. #10591297C3direct (N × H)
32. C2×Dic3⋊Dic3C2×C3semidirect
36. #63658C2×C3semidirect
43. C3×C3⋊#95D3semidirect
44. C3×C3⋊#95C2×C3semidirect
45. #63579C2×C3semidirect
162. C3⋊#95C3×D3semidirect
443. C33#397semidirect
732. C32#4675semidirect
733. C32#4953semidirect
734. C32C3×#397semidirect
838. C3#10591297direct (N × H)
839. C3C3×#4675semidirect
840. C3C3×#4953semidirect

Maximal subgroups

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

subgroupindex
C2×C32×(C2×D3)⋊C42
C2×C3×Dic3⋊Dic32
C2×C3×(C2×D3)⋊Dic32
C3×#636582
C32×C3⋊#952
C3×#635792
C3×#49533
C3×#46753
#105912973