Finite Group Databasebeta

← C3×#69429 #11773330

Subgroups — C3×#69429 #11773330

Order 1152.

1637 conjugacy classes of subgroups.

The subgroup lattice has 1133 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic
2C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic
3C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic
4C2×C32×#95C211yesmaximal, characteristic, complemented
5C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
6C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
7C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
8C3×#1440—31nomaximal
9#69429C311yesmaximal, characteristic, direct product factor
10C24×C3×D3C2211yescharacteristic
11C23×C32×C4C2211yescharacteristic
12C23×C32×C4C2211yescharacteristic
13C23×C32×C4C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4—22no—
18C2×C3×(C2×D3)⋊C4—22no—
19C2×C3×(C2×D3)⋊C4—22no—
20C2×C3×(C2×D3)⋊C4—22no—
21C2×C3×(C2×D3)⋊C4—22no—
22C2×C3×(C2×D3)⋊C4—22no—
23C2×C3×(C2×D3)⋊C4—22no—
24C2×C3×(C2×D3)⋊C4—22no—
25C2×C3×(C2×D3)⋊C4C414yescomplemented
26C32×#95—22no—
27C3×C3⋊#95—22no—
28C3×C3⋊#95—22no—
29C3×C3⋊#95—22no—
30C22×C3×C22⋊C4—31no—
31C22×C3×C22⋊C4—31no—
32C22×C3×C22⋊C4—31no—
33C22×(C2×D3)⋊C4C2×C311yescharacteristic
34C22×(C2×D3)⋊C4C2×C311yescharacteristic
35C22×(C2×D3)⋊C4C2×C311yescharacteristic
36C2×C3×#95—21no—
37C2×C3×#95—31no—
38C2×C3×#95—31no—
39C2×C3×#95—31no—
40C2×C3×#95D311yescharacteristic, complemented
41C2×C3×#95C2×C311yescharacteristic, complemented
42C2×C3⋊#95C2×C311yescharacteristic, complemented
43C2×C3⋊#95C2×C311yescharacteristic, complemented
44C2×C3⋊#95C2×C311yescharacteristic, complemented
45C24×C32C2311yescharacteristic
46C23×C3×D3—21no—
47C23×C3×D3—21no—
48C23×C3×D3—21no—
49C23×C3×D3—21no—
50C23×C3×D3—21no—
51C23×C3×D3—21no—
52C23×C3×D3—21no—
53C23×C3×D3—21no—
54C23×C3×D3—21no—
55C23×C3×D3—21no—
56C23×C3×D3—21no—
57C23×C3×D3—21no—
58C23×C3×D3C2×C412yes—
59C23×C3×D3D412yes—
60C23×C3×D3D412yes—
61C22×C32×C4—21no—
62C22×C32×C4—21no—
63C22×C32×C4—21no—
64C22×C32×C4—21no—
65C22×C32×C4—21no—
66C22×C32×C4—21no—
67C22×C32×C4—21no—
68C22×C32×C4—21no—
69C22×C32×C4—21no—
70C22×C32×C4—21no—
71C22×C32×C4—21no—
72C22×C32×C4—21no—
73C22×C32×C4—21no—
74C22×C32×C4—21no—
75C22×C32×C4—21no—
76C22×C32×C4—21no—
77C22×C32×C4—21no—
78C22×C32×C4—21no—
79C22×C32×C4C2×C412yes—
80C22×C32×C4D412yes—
81C22×C32×C4D412yes—
82C22×C3×Dic3—21no—
83C22×C3×Dic3—21no—
84C22×C3×Dic3—21no—
85C22×C3×Dic3—21no—
86C22×C3×Dic3—21no—
87C22×C3×Dic3—21no—
88C22×C3×Dic3—21no—
89C22×C3×Dic3—21no—
90C22×C3×Dic3—21no—
91C22×C3×Dic3—21no—
92C22×C3×Dic3—21no—
93C22×C3×Dic3—21no—
94C22×C3×Dic3—21no—
95C22×C3×Dic3—21no—
96C22×C3×Dic3—21no—
97C22×C3×Dic3—21no—
98C22×C3×Dic3—21no—
99C22×C3×Dic3—21no—
100C22×C3×Dic3C2×C412yes—
101C22×C3×Dic3D412yes—
102C22×C3×Dic3D412yes—
103C3×(C2×D3)⋊C4—28no—
104C3×(C2×D3)⋊C4—28no—
105C3×(C2×D3)⋊C4—28no—
106#1440—31noSylow
107C25×C3—31no—
108C24×D3C22×C311yescharacteristic
109C23×C3×C4—21no—
110C23×C3×C4—21no—
111C23×C3×C4—21no—
112C23×C3×C4—31no—
113C23×C3×C4—31no—
114C23×C3×C4—31no—
115C23×C3×C4C2×D311yescharacteristic
116C23×C3×C4C2×D311yescharacteristic
117C23×C3×C4C2×D311yescharacteristic
118C23×C3×C4C22×C311yescharacteristic
119C23×C3×C4C22×C311yescharacteristic
120C23×C3×C4C22×C311yescharacteristic
121C23×Dic3C22×C311yescharacteristic
122C23×Dic3C22×C311yescharacteristic
123C23×Dic3C22×C311yescharacteristic
124C2×C3×C22⋊C4—34no—
125C2×C3×C22⋊C4—62no—
126C2×C3×C22⋊C4—62no—
127C2×C3×C22⋊C4—62no—
128C2×C3×C22⋊C4—62no—
129C2×C3×C22⋊C4—62no—
130C2×C3×C22⋊C4—62no—
131C2×C3×C22⋊C4—62no—
132C2×C3×C22⋊C4—62no—
133C2×(C2×D3)⋊C4—22no—
134C2×(C2×D3)⋊C4—22no—
135C2×(C2×D3)⋊C4—22no—
136C2×(C2×D3)⋊C4—22no—
137C2×(C2×D3)⋊C4—22no—
138C2×(C2×D3)⋊C4—22no—
139C2×(C2×D3)⋊C4—22no—
140C2×(C2×D3)⋊C4—22no—
141C2×(C2×D3)⋊C4C3×C414yescomplemented
142C3×#95—24no—
143C3×#95—22no—
144C3×#95—22no—
145C3×#95—62no—
146C3×#95—62no—
147C3×#95—62no—
148C3⋊#95—22no—
149C3⋊#95—22no—
150C3⋊#95—22no—
151C23×C32C22×C411yescharacteristic
152C23×C32C2×D411yescharacteristic
153C23×C32C2×D411yescharacteristic
154C23×C32C2×D411yescharacteristic
155C23×C32C2×D411yescharacteristic
156C23×C32C2×D411yescharacteristic
157C23×C32C2×D411yescharacteristic
158C23×C32#4111yescharacteristic
159C23×C32#4111yescharacteristic
160C23×C32#4111yescharacteristic
161C23×C32#4111yescharacteristic
162C23×C32#4111yescharacteristic
163C23×C32#4111yescharacteristic
164C23×C32#4111yescharacteristic
165C23×C32#4111yescharacteristic
166C22×C3×D3—22no—
167C22×C3×D3—22no—
168C22×C3×D3—22no—
169C22×C3×D3—22no—
170C22×C3×D3—22no—
171C22×C3×D3—22no—
172C22×C3×D3—22no—
173C22×C3×D3—22no—
174C22×C3×D3—22no—
175C22×C3×D3—22no—
176C22×C3×D3—22no—
177C22×C3×D3—22no—
178C22×C3×D3—22no—
179C22×C3×D3—22no—
180C22×C3×D3—22no—
181C22×C3×D3—22no—
182C22×C3×D3—22no—
183C22×C3×D3—22no—
184C22×C3×D3—41no—
185C22×C3×D3—41no—
186C22×C3×D3—41no—
187C22×C3×D3—41no—
188C22×C3×D3—41no—
189C22×C3×D3—41no—
190C22×C3×D3—41no—
191C22×C3×D3—41no—
192C22×C3×D3—41no—
193C22×C3×D3—41no—
194C22×C3×D3—41no—
195C22×C3×D3—41no—
196C22×C3×D3—41no—
197C22×C3×D3—41no—
198C22×C3×D3—41no—
199C22×C3×D3—41no—
200C22×C3×D3C22⋊C414yes—
201C2×C32×C4—22no—
202C2×C32×C4—22no—
203C2×C32×C4—22no—
204C2×C32×C4—22no—
205C2×C32×C4—22no—
206C2×C32×C4—22no—
207C2×C32×C4—22no—
208C2×C32×C4—22no—
209C2×C32×C4—22no—
210C2×C32×C4—41no—
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—41no—
218C2×C32×C4—41no—
219C2×C32×C4—41no—
220C2×C32×C4—41no—
221C2×C32×C4—41no—
222C2×C3×Dic3—22no—
223C2×C3×Dic3—22no—
224C2×C3×Dic3—22no—
225C2×C3×Dic3—22no—
226C2×C3×Dic3—22no—
227C2×C3×Dic3—22no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3—22no—
230C2×C3×Dic3—22no—
231C2×C3×Dic3—41no—
232C2×C3×Dic3—41no—
233C2×C3×Dic3—41no—
234C2×C3×Dic3—41no—
235C2×C3×Dic3—41no—
236C2×C3×Dic3—41no—
237C2×C3×Dic3—41no—
238C2×C3×Dic3—41no—
239C2×C3×Dic3—41no—
240C2×C3×Dic3—41no—
241C2×C3×Dic3—41no—
242C2×C3×Dic3—41no—
243C22×C22⋊C4—31no—
244C22×C22⋊C4—31no—
245C22×C22⋊C4—31no—
246C2×#95—31no—
247C2×#95—31no—
248C2×#95—31no—
249C2×#95C3×D311yescharacteristic, complemented
250C24×C3—21no—
251C24×C3—32no—
252C24×C3—32no—
253C24×C3—32no—
254C24×C3—61no—
255C24×C3—61no—
256C24×C3—61no—
257C24×C3—61no—
258C24×C3—61no—
259C24×C3—61no—
260C24×C3—61no—
261C24×C3—61no—
262C24×C3—61no—
263C24×C3—61no—
264C24×C3—61no—
265C24×C3—61no—
266C24×C3C22×D311yescharacteristic
267C24×C3C23×C311yescharacteristic
268C23×D3—21no—
269C23×D3—21no—
270C23×D3—21no—
271C23×D3—21no—
272C23×D3—21no—
273C23×D3—21no—
274C23×D3—21no—
275C23×D3—21no—
276C23×D3—21no—
277C23×D3—21no—
278C23×D3—21no—
279C23×D3—21no—
280C23×D3C2×C3×C412yes—
281C23×D3C3×D412yes—
282C23×D3C3×D412yes—
283C22×C3×C4—22no—
284C22×C3×C4—22no—
285C22×C3×C4—22no—
286C22×C3×C4—22no—
287C22×C3×C4—22no—
288C22×C3×C4—22no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—22no—
326C22×C3×C4—22no—
327C22×C3×C4—22no—
328C22×C3×C4—32no—
329C22×C3×C4—32no—
330C22×C3×C4—32no—
331C22×C3×C4—41no—
332C22×C3×C4—41no—
333C22×C3×C4—41no—
334C22×C3×C4—41no—
335C22×C3×C4—41no—
336C22×C3×C4—41no—
337C22×C3×C4—41no—
338C22×C3×C4—41no—
339C22×C3×C4—41no—
340C22×C3×C4—41no—
341C22×C3×C4—41no—
342C22×C3×C4—41no—
343C22×C3×C4—61no—
344C22×C3×C4—61no—
345C22×C3×C4—61no—
346C22×C3×C4—61no—
347C22×C3×C4—61no—
348C22×C3×C4—61no—
349C22×C3×C4—61no—
350C22×C3×C4—61no—
351C22×C3×C4—61no—
352C22×C3×C4—61no—
353C22×C3×C4—61no—
354C22×C3×C4—61no—
355C22×C3×C4—61no—
356C22×C3×C4—61no—
357C22×C3×C4—61no—
358C22×C3×C4—61no—
359C22×C3×C4—61no—
360C22×C3×C4—61no—
361C22×C3×C4C4×D312yes—
362C22×C3×C4D1212yes—
363C22×C3×C4#6712yes—
364C22×C3×C4C2×C3×C412yes—
365C22×C3×C4C3×D412yes—
366C22×C3×C4C3×D412yes—
367C22×Dic3—21no—
368C22×Dic3—21no—
369C22×Dic3—21no—
370C22×Dic3—21no—
371C22×Dic3—21no—
372C22×Dic3—21no—
373C22×Dic3—21no—
374C22×Dic3—21no—
375C22×Dic3—21no—
376C22×Dic3—21no—
377C22×Dic3—21no—
378C22×Dic3—21no—
379C22×Dic3—21no—
380C22×Dic3—21no—
381C22×Dic3—21no—
382C22×Dic3—21no—
383C22×Dic3—21no—
384C22×Dic3—21no—
385C22×Dic3C2×C3×C412yes—
386C22×Dic3C3×D412yes—
387C22×Dic3C3×D412yes—
388C3×C22⋊C4—68no—
389C3×C22⋊C4—68no—
390C3×C22⋊C4—68no—
391(C2×D3)⋊C4—28no—
392(C2×D3)⋊C4—28no—
393(C2×D3)⋊C4—28no—
394C22×C32C2×C22⋊C411yescharacteristic
395C22×C32#11711yescharacteristic
396C22×C32#11711yescharacteristic
397C22×C32C4×D411yescharacteristic
398C22×C32C4×D411yescharacteristic
399C22×C32C4×D411yescharacteristic
400C22×C32C4×D411yescharacteristic
401C22×C32#12011yescharacteristic
402C22×C32#12011yescharacteristic
403C22×C32#12111yescharacteristic
404C22×C32#12111yescharacteristic
405C22×C32#12111yescharacteristic
406C22×C32#12111yescharacteristic
407C22×C32#12111yescharacteristic
408C22×C32#12111yescharacteristic
409C22×C32#12111yescharacteristic
410C22×C32#12111yescharacteristic
411C22×C32#12311yescharacteristic
412C22×C32#12311yescharacteristic
413C22×C32#12311yescharacteristic
414C22×C32#12311yescharacteristic
415C22×C32#12311yescharacteristic
416C22×C32#12311yescharacteristic
417C22×C32#12311yescharacteristic
418C22×C32#12311yescharacteristic
419C22×C32#12311yescharacteristic
420C22×C32#12311yescharacteristic
421C22×C32#12411yescharacteristic
422C22×C32#12411yescharacteristic
423C22×C32#12411yescharacteristic
424C22×C32#12411yescharacteristic
425C22×C32#12611yescharacteristic
426C22×C32#12611yescharacteristic
427C22×C32#12611yescharacteristic
428C22×C32#12611yescharacteristic
429C2×C3×D3—24no—
430C2×C3×D3—24no—
431C2×C3×D3—24no—
432C2×C3×D3—42no—
433C2×C3×D3—42no—
434C2×C3×D3—42no—
435C2×C3×D3—42no—
436C2×C3×D3—42no—
437C2×C3×D3—42no—
438C2×C3×D3—42no—
439C2×C3×D3—42no—
440C2×C3×D3—42no—
441C2×C3×D3—42no—
442C2×C3×D3—42no—
443C2×C3×D3—42no—
444C32×C4—42no—
445C32×C4—42no—
446C32×C4—42no—
447C3×Dic3—42no—
448C3×Dic3—42no—
449C3×Dic3—42no—
450C25—31no—
451C23×C4—31no—
452C23×C4—31no—
453C23×C4—31no—
454C23×C4C2×C3×D311yescharacteristic
455C23×C4C2×C3×D311yescharacteristic
456C23×C4C2×C3×D311yescharacteristic
457C2×C22⋊C4—34no—
458C2×C22⋊C4—62no—
459C2×C22⋊C4—62no—
460C2×C22⋊C4—62no—
461C2×C22⋊C4—62no—
462C2×C22⋊C4—62no—
463C2×C22⋊C4—62no—
464C2×C22⋊C4—62no—
465C2×C22⋊C4—62no—
466#95—22no—
467#95—62no—
468#95—62no—
469#95—62no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—34no—
486C23×C3—62no—
487C23×C3—62no—
488C23×C3—62no—
489C23×C3—62no—
490C23×C3—62no—
491C23×C3—62no—
492C23×C3—62no—
493C23×C3—62no—
494C23×C3—62no—
495C23×C3—62no—
496C23×C3—62no—
497C23×C3—62no—
498C23×C3—62no—
499C23×C3—62no—
500C23×C3—62no—
501C23×C3—62no—
502C23×C3—62no—
503C23×C3—62no—
504C23×C3—121no—
505C23×C3—121no—
506C23×C3—121no—
507C23×C3—121no—
508C23×C3—121no—
509C23×C3—121no—
510C23×C3—121no—
511C23×C3—121no—
512C23×C3—121no—
513C23×C3—121no—
514C23×C3—121no—
515C23×C3—121no—
516C23×C3—121no—
517C23×C3—121no—
518C23×C3—121no—
519C23×C3—121no—
520C23×C3C2×C4×D311yescharacteristic
521C23×C3C2×D1211yescharacteristic
522C23×C3#23511yescharacteristic
523C23×C3#23511yescharacteristic
524C23×C3#23511yescharacteristic
525C23×C3#23511yescharacteristic
526C23×C3D3×D411yescharacteristic
527C23×C3D3×D411yescharacteristic
528C23×C3D3×D411yescharacteristic
529C23×C3D3×D411yescharacteristic
530C23×C3#23711yescharacteristic
531C23×C3#23711yescharacteristic
532C23×C3#23911yescharacteristic
533C23×C3#23911yescharacteristic
534C23×C3C2×#6711yescharacteristic
535C23×C3C22×C3×C411yescharacteristic
536C23×C3C2×C3×D411yescharacteristic
537C23×C3C2×C3×D411yescharacteristic
538C23×C3C2×C3×D411yescharacteristic
539C23×C3C2×C3×D411yescharacteristic
540C23×C3C2×C3×D411yescharacteristic
541C23×C3C2×C3×D411yescharacteristic
542C23×C3C3×#4111yescharacteristic
543C23×C3C3×#4111yescharacteristic
544C23×C3C3×#4111yescharacteristic
545C23×C3C3×#4111yescharacteristic
546C23×C3C3×#4111yescharacteristic
547C23×C3C3×#4111yescharacteristic
548C23×C3C3×#4111yescharacteristic
549C23×C3C3×#4111yescharacteristic
550C22×D3—22no—
551C22×D3—22no—
552C22×D3—22no—
553C22×D3—22no—
554C22×D3—22no—
555C22×D3—22no—
556C22×D3—22no—
557C22×D3—22no—
558C22×D3—22no—
559C22×D3—22no—
560C22×D3—22no—
561C22×D3—22no—
562C22×D3—22no—
563C22×D3—22no—
564C22×D3—22no—
565C22×D3—22no—
566C22×D3—22no—
567C22×D3—22no—
568C22×D3—41no—
569C22×D3—41no—
570C22×D3—41no—
571C22×D3—41no—
572C22×D3—41no—
573C22×D3—41no—
574C22×D3—41no—
575C22×D3—41no—
576C22×D3—41no—
577C22×D3—41no—
578C22×D3—41no—
579C22×D3—41no—
580C22×D3—41no—
581C22×D3—41no—
582C22×D3—41no—
583C22×D3—41no—
584C22×D3C3×C22⋊C414yes—
585C2×C3×C4—24no—
586C2×C3×C4—24no—
587C2×C3×C4—24no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—22no—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
605C2×C3×C4—22no—
606C2×C3×C4—42no—
607C2×C3×C4—42no—
608C2×C3×C4—42no—
609C2×C3×C4—42no—
610C2×C3×C4—42no—
611C2×C3×C4—42no—
612C2×C3×C4—42no—
613C2×C3×C4—42no—
614C2×C3×C4—42no—
615C2×C3×C4—42no—
616C2×C3×C4—42no—
617C2×C3×C4—42no—
618C2×C3×C4—42no—
619C2×C3×C4—42no—
620C2×C3×C4—42no—
621C2×C3×C4—42no—
622C2×C3×C4—42no—
623C2×C3×C4—42no—
624C2×C3×C4—41no—
625C2×C3×C4—41no—
626C2×C3×C4—41no—
627C2×C3×C4—41no—
628C2×C3×C4—41no—
629C2×C3×C4—41no—
630C2×C3×C4—41no—
631C2×C3×C4—41no—
632C2×C3×C4—41no—
633C2×C3×C4—41no—
634C2×C3×C4—41no—
635C2×C3×C4—41no—
636C2×C3×C4—41no—
637C2×C3×C4—41no—
638C2×C3×C4—41no—
639C2×C3×C4—41no—
640C2×C3×C4—41no—
641C2×C3×C4—41no—
642C2×C3×C4—41no—
643C2×C3×C4—41no—
644C2×C3×C4—41no—
645C2×C3×C4—41no—
646C2×C3×C4—41no—
647C2×C3×C4—41no—
648C2×C3×C4—62no—
649C2×C3×C4—62no—
650C2×C3×C4—62no—
651C2×C3×C4—62no—
652C2×C3×C4—62no—
653C2×C3×C4—62no—
654C2×C3×C4—62no—
655C2×C3×C4—62no—
656C2×C3×C4—62no—
657C2×C3×C4—121no—
658C2×C3×C4—121no—
659C2×C3×C4—121no—
660C2×C3×C4—121no—
661C2×C3×C4—121no—
662C2×C3×C4—121no—
663C2×C3×C4—121no—
664C2×C3×C4—121no—
665C2×C3×C4—121no—
666C2×C3×C4—121no—
667C2×C3×C4—121no—
668C2×C3×C4—121no—
669C2×Dic3—22no—
670C2×Dic3—22no—
671C2×Dic3—22no—
672C2×Dic3—22no—
673C2×Dic3—22no—
674C2×Dic3—22no—
675C2×Dic3—22no—
676C2×Dic3—22no—
677C2×Dic3—22no—
678C2×Dic3—41no—
679C2×Dic3—41no—
680C2×Dic3—41no—
681C2×Dic3—41no—
682C2×Dic3—41no—
683C2×Dic3—41no—
684C2×Dic3—41no—
685C2×Dic3—41no—
686C2×Dic3—41no—
687C2×Dic3—41no—
688C2×Dic3—41no—
689C2×Dic3—41no—
690C2×C32#38111yescharacteristic
691C2×C32#38611yescharacteristic
692C2×C32#38611yescharacteristic
693C2×C32#38811yescharacteristic
694C2×C32#38811yescharacteristic
695C2×C32#38811yescharacteristic
696C2×C32#38811yescharacteristic
697C2×C32#39411yescharacteristic
698C2×C32#39411yescharacteristic
699C2×C32#39411yescharacteristic
700C2×C32#39411yescharacteristic
701C2×C32#39711yescharacteristic
702C2×C32#39711yescharacteristic
703C2×C32#39711yescharacteristic
704C2×C32#39711yescharacteristic
705C3×D3—44no—
706C24—32no—
707C24—32no—
708C24—32no—
709C24—61no—
710C24—61no—
711C24—61no—
712C24—61no—
713C24—61no—
714C24—61no—
715C24—61no—
716C24—61no—
717C24—61no—
718C24—61no—
719C24—61no—
720C24—61no—
721C24C22×C3×D311yescharacteristic
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—32no—
741C22×C4—32no—
742C22×C4—32no—
743C22×C4—61no—
744C22×C4—61no—
745C22×C4—61no—
746C22×C4—61no—
747C22×C4—61no—
748C22×C4—61no—
749C22×C4—61no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—61no—
761C22×C4C3×C4×D312yes—
762C22×C4C3×D1212yes—
763C22×C4C3×#6712yes—
764C22⋊C4—68no—
765C22⋊C4—68no—
766C22⋊C4—68no—
767C22×C3—21no—
768C22×C3—21no—
769C22×C3—21no—
770C22×C3—21no—
771C22×C3—21no—
772C22×C3—21no—
773C22×C3—21no—
774C22×C3—21no—
775C22×C3—21no—
776C22×C3—21no—
777C22×C3—21no—
778C22×C3—21no—
779C22×C3—21no—
780C22×C3—21no—
781C22×C3—21no—
782C22×C3—21no—
783C22×C3—21no—
784C22×C3—21no—
785C22×C3—21no—
786C22×C3—21no—
787C22×C3—21no—
788C22×C3—21no—
789C22×C3—21no—
790C22×C3—21no—
791C22×C3—21no—
792C22×C3—21no—
793C22×C3—21no—
794C22×C3—21no—
795C22×C3—21no—
796C22×C3—21no—
797C22×C3—21no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—21no—
801C22×C3—21no—
802C22×C3—64no—
803C22×C3—64no—
804C22×C3—64no—
805C22×C3—122no—
806C22×C3—122no—
807C22×C3—122no—
808C22×C3—122no—
809C22×C3—122no—
810C22×C3—122no—
811C22×C3—122no—
812C22×C3—122no—
813C22×C3—122no—
814C22×C3—122no—
815C22×C3—122no—
816C22×C3—122no—
817C22×C3#87211yescharacteristic
818C22×C3C4×D1211yescharacteristic
819C22×C3#87511yescharacteristic
820C22×C3#87611yescharacteristic
821C22×C3D3×C22⋊C411yescharacteristic
822C22×C3#67⋊C411yescharacteristic
823C22×C3#88211yescharacteristic
824C22×C3#88311yescharacteristic
825C22×C3#88311yescharacteristic
826C22×C3#88311yescharacteristic
827C22×C3#88411yescharacteristic
828C22×C3#88411yescharacteristic
829C22×C3#88411yescharacteristic
830C22×C3#88511yescharacteristic
831C22×C3#88511yescharacteristic
832C22×C3#88611yescharacteristic
833C22×C3#89211yescharacteristic
834C22×C3#89311yescharacteristic
835C22×C3#89411yescharacteristic
836C22×C3#89411yescharacteristic
837C22×C3#89411yescharacteristic
838C22×C3#89411yescharacteristic
839C22×C3#89411yescharacteristic
840C22×C3#89511yescharacteristic
841C22×C3#89511yescharacteristic
842C22×C3#89811yescharacteristic
843C22×C3#89811yescharacteristic
844C22×C3#89811yescharacteristic
845C22×C3C4×#6711yescharacteristic
846C22×C3#92911yescharacteristic
847C22×C3#93011yescharacteristic
848C22×C3#93711yescharacteristic
849C22×C3#93811yescharacteristic
850C22×C3#93911yescharacteristic
851C22×C3#94711yescharacteristic
852C22×C3C2×C3×C22⋊C411yescharacteristic
853C22×C3C3×#11711yescharacteristic
854C22×C3C3×#11711yescharacteristic
855C22×C3C3×C4×D411yescharacteristic
856C22×C3C3×C4×D411yescharacteristic
857C22×C3C3×C4×D411yescharacteristic
858C22×C3C3×C4×D411yescharacteristic
859C22×C3C3×#12011yescharacteristic
860C22×C3C3×#12011yescharacteristic
861C22×C3C3×#12111yescharacteristic
862C22×C3C3×#12111yescharacteristic
863C22×C3C3×#12111yescharacteristic
864C22×C3C3×#12111yescharacteristic
865C22×C3C3×#12111yescharacteristic
866C22×C3C3×#12111yescharacteristic
867C22×C3C3×#12111yescharacteristic
868C22×C3C3×#12111yescharacteristic
869C22×C3C3×#12311yescharacteristic
870C22×C3C3×#12311yescharacteristic
871C22×C3C3×#12311yescharacteristic
872C22×C3C3×#12311yescharacteristic
873C22×C3C3×#12311yescharacteristic
874C22×C3C3×#12311yescharacteristic
875C22×C3C3×#12311yescharacteristic
876C22×C3C3×#12311yescharacteristic
877C22×C3C3×#12311yescharacteristic
878C22×C3C3×#12311yescharacteristic
879C22×C3C3×#12411yescharacteristic
880C22×C3C3×#12411yescharacteristic
881C22×C3C3×#12411yescharacteristic
882C22×C3C3×#12411yescharacteristic
883C22×C3C3×#12611yescharacteristic
884C22×C3C3×#12611yescharacteristic
885C22×C3C3×#12611yescharacteristic
886C22×C3C3×#12611yescharacteristic
887C2×D3—24no—
888C2×D3—24no—
889C2×D3—24no—
890C2×D3—42no—
891C2×D3—42no—
892C2×D3—42no—
893C2×D3—42no—
894C2×D3—42no—
895C2×D3—42no—
896C2×D3—42no—
897C2×D3—42no—
898C2×D3—42no—
899C2×D3—42no—
900C2×D3—42no—
901C2×D3—42no—
902C3×C4—44no—
903C3×C4—44no—
904C3×C4—44no—
905C3×C4—42no—
906C3×C4—42no—
907C3×C4—42no—
908C3×C4—42no—
909C3×C4—42no—
910C3×C4—42no—
911C3×C4—122no—
912C3×C4—122no—
913C3×C4—122no—
914Dic3—42no—
915Dic3—42no—
916Dic3—42no—
917C32#144011yescharacteristic, complemented, Sylow
918C23—34no—
919C23—62no—
920C23—62no—
921C23—62no—
922C23—62no—
923C23—62no—
924C23—62no—
925C23—62no—
926C23—62no—
927C23—62no—
928C23—62no—
929C23—62no—
930C23—62no—
931C23—62no—
932C23—62no—
933C23—62no—
934C23—62no—
935C23—62no—
936C23—62no—
937C23—121no—
938C23—121no—
939C23—121no—
940C23—121no—
941C23—121no—
942C23—121no—
943C23—121no—
944C23—121no—
945C23—121no—
946C23—121no—
947C23—121no—
948C23—121no—
949C23—121no—
950C23—121no—
951C23—121no—
952C23—121no—
953C23C2×C3×C4×D311yescharacteristic
954C23C2×C3×D1211yescharacteristic
955C23C3×#23511yescharacteristic
956C23C3×#23511yescharacteristic
957C23C3×#23511yescharacteristic
958C23C3×#23511yescharacteristic
959C23C3×D3×D411yescharacteristic
960C23C3×D3×D411yescharacteristic
961C23C3×D3×D411yescharacteristic
962C23C3×D3×D411yescharacteristic
963C23C3×#23711yescharacteristic
964C23C3×#23711yescharacteristic
965C23C3×#23911yescharacteristic
966C23C3×#23911yescharacteristic
967C23C2×C3×#6711yescharacteristic
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—62no—
990C2×C4—62no—
991C2×C4—62no—
992C2×C4—62no—
993C2×C4—62no—
994C2×C4—62no—
995C2×C4—62no—
996C2×C4—62no—
997C2×C4—62no—
998C2×C4—121no—
999C2×C4—121no—
1000C2×C4—121no—
1001C2×C4—121no—
1002C2×C4—121no—
1003C2×C4—121no—
1004C2×C4—121no—
1005C2×C4—121no—
1006C2×C4—121no—
1007C2×C4—121no—
1008C2×C4—121no—
1009C2×C4—121no—
1010C2×C3—21no—
1011C2×C3—21no—
1012C2×C3—21no—
1013C2×C3—21no—
1014C2×C3—21no—
1015C2×C3—21no—
1016C2×C3—21no—
1017C2×C3—21no—
1018C2×C3—21no—
1019C2×C3—21no—
1020C2×C3—21no—
1021C2×C3—21no—
1022C2×C3—21no—
1023C2×C3—21no—
1024C2×C3—21no—
1025C2×C3—124no—
1026C2×C3#466411yescharacteristic
1027C2×C3#466511yescharacteristic
1028C2×C3#466911yescharacteristic
1029C2×C3#467011yescharacteristic
1030C2×C3#467211yescharacteristic
1031C2×C3#467411yescharacteristic
1032C2×C3#467511yescharacteristic
1033C2×C3#467511yescharacteristic
1034C2×C3#494011yescharacteristic
1035C2×C3#495611yescharacteristic
1036C2×C3#495911yescharacteristic
1037C2×C3#496111yescharacteristic
1038C2×C3#499011yescharacteristic
1039C2×C3#499111yescharacteristic
1040C2×C3#499211yescharacteristic
1041C2×C3C3×#38111yescharacteristic
1042C2×C3C3×#38611yescharacteristic
1043C2×C3C3×#38611yescharacteristic
1044C2×C3C3×#38811yescharacteristic
1045C2×C3C3×#38811yescharacteristic
1046C2×C3C3×#38811yescharacteristic
1047C2×C3C3×#38811yescharacteristic
1048C2×C3C3×#39411yescharacteristic
1049C2×C3C3×#39411yescharacteristic
1050C2×C3C3×#39411yescharacteristic
1051C2×C3C3×#39411yescharacteristic
1052C2×C3C3×#39711yescharacteristic
1053C2×C3C3×#39711yescharacteristic
1054C2×C3C3×#39711yescharacteristic
1055C2×C3C3×#39711yescharacteristic
1056D3—44no—
1057C22—64no—
1058C22—64no—
1059C22—64no—
1060C22—122no—
1061C22—122no—
1062C22—122no—
1063C22—122no—
1064C22—122no—
1065C22—122no—
1066C22—122no—
1067C22—122no—
1068C22—122no—
1069C22—122no—
1070C22—122no—
1071C22—122no—
1072C22C3×#87211yescharacteristic
1073C22C3×C4×D1211yescharacteristic
1074C22C3×#87511yescharacteristic
1075C22C3×#87611yescharacteristic
1076C22C3×D3×C22⋊C411yescharacteristic
1077C22C3×#67⋊C411yescharacteristic
1078C22C3×#88211yescharacteristic
1079C22C3×#88311yescharacteristic
1080C22C3×#88311yescharacteristic
1081C22C3×#88311yescharacteristic
1082C22C3×#88411yescharacteristic
1083C22C3×#88411yescharacteristic
1084C22C3×#88411yescharacteristic
1085C22C3×#88511yescharacteristic
1086C22C3×#88511yescharacteristic
1087C22C3×#88611yescharacteristic
1088C22C3×#89211yescharacteristic
1089C22C3×#89311yescharacteristic
1090C22C3×#89411yescharacteristic
1091C22C3×#89411yescharacteristic
1092C22C3×#89411yescharacteristic
1093C22C3×#89411yescharacteristic
1094C22C3×#89411yescharacteristic
1095C22C3×#89511yescharacteristic
1096C22C3×#89511yescharacteristic
1097C22C3×#89811yescharacteristic
1098C22C3×#89811yescharacteristic
1099C22C3×#89811yescharacteristic
1100C22C3×C4×#6711yescharacteristic
1101C22C3×#92911yescharacteristic
1102C22C3×#93011yescharacteristic
1103C22C3×#93711yescharacteristic
1104C22C3×#93811yescharacteristic
1105C22C3×#93911yescharacteristic
1106C22C3×#94711yescharacteristic
1107C4—42no—
1108C4—42no—
1109C4—42no—
1110C4—122no—
1111C4—122no—
1112C4—122no—
1113C3—21no—
1114C3#6942911yescharacteristic, direct product factor
1115C3C3×#144011yescharacteristic, complemented
1116C2—124no—
1117C2C3×#466411yescharacteristic
1118C2C3×#466511yescharacteristic
1119C2C3×#466911yescharacteristic
1120C2C3×#467011yescharacteristic
1121C2C3×#467211yescharacteristic
1122C2C3×#467411yescharacteristic
1123C2C3×#467511yescharacteristic
1124C2C3×#467511yescharacteristic
1125C2C3×#494011yescharacteristic
1126C2C3×#495611yescharacteristic
1127C2C3×#495911yescharacteristic
1128C2C3×#496111yescharacteristic
1129C2C3×#499011yescharacteristic
1130C2C3×#499111yescharacteristic
1131C2C3×#499211yescharacteristic
subgroupG/H
centerC24×C3C22×D3
commutatorC23×C3C22×C3×C4
FrattiniC24C22×C3×D3
FittingC2×C32×#95C2
socleC24×C32C23
prime radicalC24×C3×D3C22
cosocleC24×C3C23×C3
hypercenterC2×C3×#95D3
hypocenterC3C3×#1440
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C2×C3×#95

Complements

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

NH ≅ G/Ntype
4. C2×C32×#95C2semidirect
5. C2×C3×C3⋊#95C2semidirect
6. C2×C3×C3⋊#95C2semidirect
7. C2×C3×C3⋊#95C2semidirect
9. #69429C3direct (N × H)
25. C2×C3×(C2×D3)⋊C4C4semidirect
40. C2×C3×#95D3semidirect
41. C2×C3×#95C2×C3semidirect
42. C2×C3⋊#95C2×C3semidirect
43. C2×C3⋊#95C2×C3semidirect
44. C2×C3⋊#95C2×C3semidirect
141. C2×(C2×D3)⋊C4C3×C4semidirect
249. C2×#95C3×D3semidirect
917. C32#1440semidirect
1114. C3#69429direct (N × H)
1115. C3C3×#1440semidirect

Maximal subgroups

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

subgroupindex
C22×C3×(C2×D3)⋊C42
C2×C32×#952
C2×C3×C3⋊#952
C3×#14403
#694293