Finite Group Databasebeta

← C3×#69428 #11773298

Subgroups — C3×#69428 #11773298

Order 1152.

1725 conjugacy classes of subgroups.

The subgroup lattice has 1145 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
4C22×C3×Dic3⋊C4C211yesmaximal, characteristic, complemented
5C2×C32×#95C211yesmaximal, characteristic, complemented
6C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
7C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
8C3×#1439—31nomaximal
9#69428C311yesmaximal, 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
26C2×C3×Dic3⋊C4—22no—
27C2×C3×Dic3⋊C4—22no—
28C2×C3×Dic3⋊C4—22no—
29C32×#95—22no—
30C3×C3⋊#95—22no—
31C3×C3⋊#95—22no—
32C22×C3×C4⋊C4—31no—
33C22×C3×C22⋊C4—31no—
34C22×C3×C22⋊C4—31no—
35C22×C3×C22⋊C4—31no—
36C22×(C2×D3)⋊C4C2×C311yescharacteristic
37C22×(C2×D3)⋊C4C2×C311yescharacteristic
38C22×(C2×D3)⋊C4C2×C311yescharacteristic
39C22×Dic3⋊C4C2×C311yescharacteristic, complemented
40C2×C3×#95—21no—
41C2×C3×#95—31no—
42C2×C3×#95—31no—
43C2×C3×#95D311yescharacteristic, complemented
44C2×C3×#95C2×C311yescharacteristic, complemented
45C2×C3⋊#95C2×C311yescharacteristic, complemented
46C2×C3⋊#95C2×C311yescharacteristic, complemented
47C24×C32C2311yescharacteristic
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×D3—21no—
59C23×C3×D3—21no—
60C23×C3×D3C2×C412yes—
61C23×C3×D3D412yes—
62C23×C3×D3Q812yes—
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×C4—21no—
80C22×C32×C4—21no—
81C22×C32×C4C2×C412yes—
82C22×C32×C4D412yes—
83C22×C32×C4D412yes—
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—
103C22×C3×Dic3D412yes—
104C22×C3×Dic3D412yes—
105C3×(C2×D3)⋊C4—28no—
106C3×(C2×D3)⋊C4—28no—
107C3×(C2×D3)⋊C4—28no—
108C3×Dic3⋊C4—28no—
109#1439—31noSylow
110C25×C3—31no—
111C24×D3C22×C311yescharacteristic
112C23×C3×C4—21no—
113C23×C3×C4—21no—
114C23×C3×C4—21no—
115C23×C3×C4—31no—
116C23×C3×C4—31no—
117C23×C3×C4—31no—
118C23×C3×C4C2×D311yescharacteristic
119C23×C3×C4C2×D311yescharacteristic
120C23×C3×C4C2×D311yescharacteristic
121C23×C3×C4C22×C311yescharacteristic
122C23×C3×C4C22×C311yescharacteristic
123C23×C3×C4C22×C311yescharacteristic
124C23×Dic3C22×C311yescharacteristic
125C23×Dic3C22×C311yescharacteristic
126C23×Dic3C22×C311yescharacteristic
127C2×C3×C4⋊C4—62no—
128C2×C3×C4⋊C4—62no—
129C2×C3×C4⋊C4—62no—
130C2×C3×C22⋊C4—34no—
131C2×C3×C22⋊C4—62no—
132C2×C3×C22⋊C4—62no—
133C2×C3×C22⋊C4—62no—
134C2×C3×C22⋊C4—62no—
135C2×C3×C22⋊C4—62no—
136C2×C3×C22⋊C4—62no—
137C2×C3×C22⋊C4—62no—
138C2×C3×C22⋊C4—62no—
139C2×(C2×D3)⋊C4—22no—
140C2×(C2×D3)⋊C4—22no—
141C2×(C2×D3)⋊C4—22no—
142C2×(C2×D3)⋊C4—22no—
143C2×(C2×D3)⋊C4—22no—
144C2×(C2×D3)⋊C4—22no—
145C2×(C2×D3)⋊C4—22no—
146C2×(C2×D3)⋊C4—22no—
147C2×(C2×D3)⋊C4C3×C414yescomplemented
148C2×Dic3⋊C4—22no—
149C2×Dic3⋊C4—22no—
150C2×Dic3⋊C4—22no—
151C3×#95—24no—
152C3×#95—22no—
153C3×#95—22no—
154C3×#95—62no—
155C3×#95—62no—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C23×C32C22×C411yescharacteristic
159C23×C32C2×D411yescharacteristic
160C23×C32C2×D411yescharacteristic
161C23×C32C2×D411yescharacteristic
162C23×C32C2×D411yescharacteristic
163C23×C32C2×D411yescharacteristic
164C23×C32C2×D411yescharacteristic
165C23×C32C2×D411yescharacteristic
166C23×C32C2×Q811yescharacteristic
167C23×C32#4111yescharacteristic
168C23×C32#4111yescharacteristic
169C23×C32#4111yescharacteristic
170C23×C32#4111yescharacteristic
171C23×C32#4111yescharacteristic
172C23×C32#4111yescharacteristic
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—22no—
185C22×C3×D3—22no—
186C22×C3×D3—22no—
187C22×C3×D3—22no—
188C22×C3×D3—22no—
189C22×C3×D3—22no—
190C22×C3×D3—22no—
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×D3—41no—
201C22×C3×D3—41no—
202C22×C3×D3—41no—
203C22×C3×D3—41no—
204C22×C3×D3—41no—
205C22×C3×D3—41no—
206C22×C3×D3—41no—
207C22×C3×D3C4⋊C414yescomplemented
208C2×C32×C4—22no—
209C2×C32×C4—22no—
210C2×C32×C4—22no—
211C2×C32×C4—22no—
212C2×C32×C4—22no—
213C2×C32×C4—22no—
214C2×C32×C4—22no—
215C2×C32×C4—22no—
216C2×C32×C4—22no—
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—41no—
224C2×C32×C4—41no—
225C2×C32×C4—41no—
226C2×C32×C4—41no—
227C2×C32×C4—41no—
228C2×C32×C4—41no—
229C2×C3×Dic3—22no—
230C2×C3×Dic3—22no—
231C2×C3×Dic3—22no—
232C2×C3×Dic3—22no—
233C2×C3×Dic3—22no—
234C2×C3×Dic3—22no—
235C2×C3×Dic3—22no—
236C2×C3×Dic3—22no—
237C2×C3×Dic3—22no—
238C2×C3×Dic3—22no—
239C2×C3×Dic3—22no—
240C2×C3×Dic3—22no—
241C2×C3×Dic3—41no—
242C2×C3×Dic3—41no—
243C2×C3×Dic3—41no—
244C2×C3×Dic3—41no—
245C2×C3×Dic3—41no—
246C2×C3×Dic3—41no—
247C2×C3×Dic3—41no—
248C2×C3×Dic3—41no—
249C2×C3×Dic3C22⋊C414yescomplemented
250C22×C4⋊C4—31no—
251C22×C22⋊C4—31no—
252C22×C22⋊C4—31no—
253C22×C22⋊C4—31no—
254C2×#95—31no—
255C2×#95—31no—
256C2×#95C3×D311yescharacteristic, complemented
257C24×C3—21no—
258C24×C3—32no—
259C24×C3—32no—
260C24×C3—32no—
261C24×C3—61no—
262C24×C3—61no—
263C24×C3—61no—
264C24×C3—61no—
265C24×C3—61no—
266C24×C3—61no—
267C24×C3—61no—
268C24×C3—61no—
269C24×C3—61no—
270C24×C3—61no—
271C24×C3—61no—
272C24×C3—61no—
273C24×C3C22×D311yescharacteristic
274C24×C3C23×C311yescharacteristic
275C23×D3—21no—
276C23×D3—21no—
277C23×D3—21no—
278C23×D3—21no—
279C23×D3—21no—
280C23×D3—21no—
281C23×D3—21no—
282C23×D3—21no—
283C23×D3—21no—
284C23×D3—21no—
285C23×D3—21no—
286C23×D3—21no—
287C23×D3C2×C3×C412yes—
288C23×D3C3×D412yes—
289C23×D3C3×Q812yes—
290C22×C3×C4—22no—
291C22×C3×C4—22no—
292C22×C3×C4—22no—
293C22×C3×C4—22no—
294C22×C3×C4—22no—
295C22×C3×C4—22no—
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—21no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—21no—
332C22×C3×C4—22no—
333C22×C3×C4—22no—
334C22×C3×C4—22no—
335C22×C3×C4—32no—
336C22×C3×C4—32no—
337C22×C3×C4—32no—
338C22×C3×C4—32no—
339C22×C3×C4—32no—
340C22×C3×C4—41no—
341C22×C3×C4—41no—
342C22×C3×C4—41no—
343C22×C3×C4—41no—
344C22×C3×C4—41no—
345C22×C3×C4—41no—
346C22×C3×C4—41no—
347C22×C3×C4—41no—
348C22×C3×C4—41no—
349C22×C3×C4—41no—
350C22×C3×C4—41no—
351C22×C3×C4—41no—
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×C4—61no—
362C22×C3×C4—61no—
363C22×C3×C4—61no—
364C22×C3×C4—61no—
365C22×C3×C4—61no—
366C22×C3×C4—61no—
367C22×C3×C4—61no—
368C22×C3×C4C4×D312yes—
369C22×C3×C4D1212yes—
370C22×C3×C4#6712yes—
371C22×C3×C4C2×C3×C412yes—
372C22×C3×C4C3×D412yes—
373C22×C3×C4C3×D412yes—
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×Dic3—21no—
386C22×Dic3—21no—
387C22×Dic3—21no—
388C22×Dic3—21no—
389C22×Dic3—21no—
390C22×Dic3C2×C3×C412yes—
391C22×Dic3C3×D412yes—
392C22×Dic3C3×D412yes—
393C22×Dic3C3×D412yes—
394C22×Dic3C3×D412yes—
395C3×C4⋊C4—68no—
396C3×C22⋊C4—68no—
397C3×C22⋊C4—68no—
398C3×C22⋊C4—68no—
399(C2×D3)⋊C4—28no—
400(C2×D3)⋊C4—28no—
401(C2×D3)⋊C4—28no—
402Dic3⋊C4—28no—
403C22×C32C2×C22⋊C411yescharacteristic
404C22×C32C2×C4⋊C411yescharacteristic
405C22×C32#11711yescharacteristic
406C22×C32C4×D411yescharacteristic
407C22×C32C4×D411yescharacteristic
408C22×C32C4×D411yescharacteristic
409C22×C32C4×D411yescharacteristic
410C22×C32#12011yescharacteristic
411C22×C32#12011yescharacteristic
412C22×C32#12011yescharacteristic
413C22×C32#12111yescharacteristic
414C22×C32#12111yescharacteristic
415C22×C32#12111yescharacteristic
416C22×C32#12111yescharacteristic
417C22×C32#12111yescharacteristic
418C22×C32#12111yescharacteristic
419C22×C32#12111yescharacteristic
420C22×C32#12111yescharacteristic
421C22×C32C22⋊Q811yescharacteristic
422C22×C32C22⋊Q811yescharacteristic
423C22×C32C22⋊Q811yescharacteristic
424C22×C32C22⋊Q811yescharacteristic
425C22×C32C22⋊Q811yescharacteristic
426C22×C32C22⋊Q811yescharacteristic
427C22×C32#12311yescharacteristic
428C22×C32#12311yescharacteristic
429C22×C32#12311yescharacteristic
430C22×C32#12311yescharacteristic
431C22×C32#12311yescharacteristic
432C22×C32#12411yescharacteristic
433C22×C32#12411yescharacteristic
434C22×C32#12411yescharacteristic
435C22×C32#12611yescharacteristic
436C22×C32#12611yescharacteristic
437C22×C32#12711yescharacteristic
438C2×C3×D3—24no—
439C2×C3×D3—24no—
440C2×C3×D3—24no—
441C2×C3×D3—42no—
442C2×C3×D3—42no—
443C2×C3×D3—42no—
444C2×C3×D3—42no—
445C2×C3×D3—42no—
446C2×C3×D3—42no—
447C2×C3×D3—42no—
448C2×C3×D3—42no—
449C2×C3×D3—42no—
450C2×C3×D3—42no—
451C2×C3×D3—42no—
452C2×C3×D3—42no—
453C32×C4—42no—
454C32×C4—42no—
455C32×C4—42no—
456C3×Dic3—24no—
457C3×Dic3—42no—
458C3×Dic3—42no—
459C25—31no—
460C23×C4—31no—
461C23×C4—31no—
462C23×C4—31no—
463C23×C4C2×C3×D311yescharacteristic
464C23×C4C2×C3×D311yescharacteristic
465C23×C4C2×C3×D311yescharacteristic
466C2×C4⋊C4—62no—
467C2×C4⋊C4—62no—
468C2×C4⋊C4—62no—
469C2×C22⋊C4—34no—
470C2×C22⋊C4—62no—
471C2×C22⋊C4—62no—
472C2×C22⋊C4—62no—
473C2×C22⋊C4—62no—
474C2×C22⋊C4—62no—
475C2×C22⋊C4—62no—
476C2×C22⋊C4—62no—
477C2×C22⋊C4—62no—
478#95—22no—
479#95—62no—
480#95—62no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—21no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—34no—
497C23×C3—62no—
498C23×C3—62no—
499C23×C3—62no—
500C23×C3—62no—
501C23×C3—62no—
502C23×C3—62no—
503C23×C3—62no—
504C23×C3—62no—
505C23×C3—62no—
506C23×C3—62no—
507C23×C3—62no—
508C23×C3—62no—
509C23×C3—62no—
510C23×C3—62no—
511C23×C3—62no—
512C23×C3—62no—
513C23×C3—62no—
514C23×C3—62no—
515C23×C3—121no—
516C23×C3—121no—
517C23×C3—121no—
518C23×C3—121no—
519C23×C3—121no—
520C23×C3—121no—
521C23×C3—121no—
522C23×C3—121no—
523C23×C3—121no—
524C23×C3—121no—
525C23×C3—121no—
526C23×C3—121no—
527C23×C3—121no—
528C23×C3—121no—
529C23×C3—121no—
530C23×C3—121no—
531C23×C3C2×C4×D311yescharacteristic
532C23×C3C2×D1211yescharacteristic
533C23×C3#23511yescharacteristic
534C23×C3#23511yescharacteristic
535C23×C3#23511yescharacteristic
536C23×C3#23511yescharacteristic
537C23×C3D3×D411yescharacteristic
538C23×C3D3×D411yescharacteristic
539C23×C3D3×D411yescharacteristic
540C23×C3D3×D411yescharacteristic
541C23×C3D3×D411yescharacteristic
542C23×C3#23711yescharacteristic
543C23×C3D3×Q811yescharacteristic
544C23×C3#23911yescharacteristic
545C23×C3C2×#6711yescharacteristic
546C23×C3C22×C3×C411yescharacteristic
547C23×C3C2×C3×D411yescharacteristic
548C23×C3C2×C3×D411yescharacteristic
549C23×C3C2×C3×D411yescharacteristic
550C23×C3C2×C3×D411yescharacteristic
551C23×C3C2×C3×D411yescharacteristic
552C23×C3C2×C3×D411yescharacteristic
553C23×C3C2×C3×D411yescharacteristic
554C23×C3C2×C3×Q811yescharacteristic
555C23×C3C3×#4111yescharacteristic
556C23×C3C3×#4111yescharacteristic
557C23×C3C3×#4111yescharacteristic
558C23×C3C3×#4111yescharacteristic
559C23×C3C3×#4111yescharacteristic
560C23×C3C3×#4111yescharacteristic
561C22×D3—22no—
562C22×D3—22no—
563C22×D3—22no—
564C22×D3—22no—
565C22×D3—22no—
566C22×D3—22no—
567C22×D3—22no—
568C22×D3—22no—
569C22×D3—22no—
570C22×D3—22no—
571C22×D3—22no—
572C22×D3—22no—
573C22×D3—22no—
574C22×D3—22no—
575C22×D3—22no—
576C22×D3—22no—
577C22×D3—22no—
578C22×D3—22no—
579C22×D3—41no—
580C22×D3—41no—
581C22×D3—41no—
582C22×D3—41no—
583C22×D3—41no—
584C22×D3—41no—
585C22×D3—41no—
586C22×D3—41no—
587C22×D3—41no—
588C22×D3—41no—
589C22×D3—41no—
590C22×D3—41no—
591C22×D3—41no—
592C22×D3—41no—
593C22×D3—41no—
594C22×D3—41no—
595C22×D3C3×C4⋊C414yescomplemented
596C2×C3×C4—24no—
597C2×C3×C4—24no—
598C2×C3×C4—24no—
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—22no—
607C2×C3×C4—22no—
608C2×C3×C4—22no—
609C2×C3×C4—22no—
610C2×C3×C4—22no—
611C2×C3×C4—22no—
612C2×C3×C4—22no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—22no—
617C2×C3×C4—34no—
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—42no—
625C2×C3×C4—42no—
626C2×C3×C4—42no—
627C2×C3×C4—42no—
628C2×C3×C4—42no—
629C2×C3×C4—42no—
630C2×C3×C4—42no—
631C2×C3×C4—42no—
632C2×C3×C4—42no—
633C2×C3×C4—42no—
634C2×C3×C4—42no—
635C2×C3×C4—42no—
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—41no—
649C2×C3×C4—41no—
650C2×C3×C4—41no—
651C2×C3×C4—41no—
652C2×C3×C4—41no—
653C2×C3×C4—41no—
654C2×C3×C4—41no—
655C2×C3×C4—41no—
656C2×C3×C4—41no—
657C2×C3×C4—41no—
658C2×C3×C4—41no—
659C2×C3×C4—41no—
660C2×C3×C4—62no—
661C2×C3×C4—62no—
662C2×C3×C4—62no—
663C2×C3×C4—62no—
664C2×C3×C4—62no—
665C2×C3×C4—62no—
666C2×C3×C4—62no—
667C2×C3×C4—62no—
668C2×C3×C4—62no—
669C2×C3×C4—62no—
670C2×C3×C4—62no—
671C2×C3×C4—62no—
672C2×C3×C4—121no—
673C2×C3×C4—121no—
674C2×C3×C4—121no—
675C2×C3×C4—121no—
676C2×C3×C4—121no—
677C2×C3×C4—121no—
678C2×C3×C4—121no—
679C2×C3×C4—121no—
680C2×Dic3—22no—
681C2×Dic3—22no—
682C2×Dic3—22no—
683C2×Dic3—22no—
684C2×Dic3—22no—
685C2×Dic3—22no—
686C2×Dic3—22no—
687C2×Dic3—22no—
688C2×Dic3—22no—
689C2×Dic3—22no—
690C2×Dic3—22no—
691C2×Dic3—22no—
692C2×Dic3—41no—
693C2×Dic3—41no—
694C2×Dic3—41no—
695C2×Dic3—41no—
696C2×Dic3—41no—
697C2×Dic3—41no—
698C2×Dic3—41no—
699C2×Dic3—41no—
700C2×Dic3C3×C22⋊C414yescomplemented
701C2×C32#38011yescharacteristic
702C2×C32#38511yescharacteristic
703C2×C32#38511yescharacteristic
704C2×C32#38611yescharacteristic
705C2×C32#38811yescharacteristic
706C2×C32#38811yescharacteristic
707C2×C32#39011yescharacteristic
708C2×C32#39211yescharacteristic
709C2×C32#39311yescharacteristic
710C2×C32#39411yescharacteristic
711C2×C32#39411yescharacteristic
712C2×C32#39611yescharacteristic
713C2×C32#39611yescharacteristic
714C2×C32#39711yescharacteristic
715C2×C32#39911yescharacteristic
716C3×D3—44no—
717C24—32no—
718C24—32no—
719C24—32no—
720C24—61no—
721C24—61no—
722C24—61no—
723C24—61no—
724C24—61no—
725C24—61no—
726C24—61no—
727C24—61no—
728C24—61no—
729C24—61no—
730C24—61no—
731C24—61no—
732C24C22×C3×D311yescharacteristic
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—32no—
752C22×C4—32no—
753C22×C4—32no—
754C22×C4—32no—
755C22×C4—32no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—61no—
761C22×C4—61no—
762C22×C4—61no—
763C22×C4—61no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4—61no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—61no—
772C22×C4C3×C4×D312yes—
773C22×C4C3×D1212yes—
774C22×C4C3×#6712yes—
775C4⋊C4—68no—
776C22⋊C4—68no—
777C22⋊C4—68no—
778C22⋊C4—68no—
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—21no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—64no—
815C22×C3—64no—
816C22×C3—64no—
817C22×C3—122no—
818C22×C3—122no—
819C22×C3—122no—
820C22×C3—122no—
821C22×C3—122no—
822C22×C3—122no—
823C22×C3—122no—
824C22×C3—122no—
825C22×C3—122no—
826C22×C3—122no—
827C22×C3—122no—
828C22×C3—122no—
829C22×C3#87211yescharacteristic
830C22×C3C4×D1211yescharacteristic
831C22×C3#87511yescharacteristic
832C22×C3#87611yescharacteristic
833C22×C3D3×C22⋊C411yescharacteristic
834C22×C3#67⋊C411yescharacteristic
835C22×C3#88211yescharacteristic
836C22×C3#88211yescharacteristic
837C22×C3#88311yescharacteristic
838C22×C3#88411yescharacteristic
839C22×C3#88411yescharacteristic
840C22×C3#88411yescharacteristic
841C22×C3#88411yescharacteristic
842C22×C3#88411yescharacteristic
843C22×C3#88511yescharacteristic
844C22×C3#88511yescharacteristic
845C22×C3D3×C4⋊C411yescharacteristic
846C22×C3#89311yescharacteristic
847C22×C3#89411yescharacteristic
848C22×C3#89411yescharacteristic
849C22×C3#89411yescharacteristic
850C22×C3#89511yescharacteristic
851C22×C3#89611yescharacteristic
852C22×C3#89611yescharacteristic
853C22×C3#89611yescharacteristic
854C22×C3#89611yescharacteristic
855C22×C3#89711yescharacteristic
856C22×C3#89811yescharacteristic
857C22×C3C4×#6711yescharacteristic
858C22×C3#92911yescharacteristic
859C22×C3#93011yescharacteristic
860C22×C3#93711yescharacteristic
861C22×C3#93911yescharacteristic
862C22×C3#94011yescharacteristic
863C22×C3#94611yescharacteristic
864C22×C3C2×C3×C22⋊C411yescharacteristic
865C22×C3C2×C3×C4⋊C411yescharacteristic
866C22×C3C3×#11711yescharacteristic
867C22×C3C3×C4×D411yescharacteristic
868C22×C3C3×C4×D411yescharacteristic
869C22×C3C3×C4×D411yescharacteristic
870C22×C3C3×C4×D411yescharacteristic
871C22×C3C3×#12011yescharacteristic
872C22×C3C3×#12011yescharacteristic
873C22×C3C3×#12011yescharacteristic
874C22×C3C3×#12111yescharacteristic
875C22×C3C3×#12111yescharacteristic
876C22×C3C3×#12111yescharacteristic
877C22×C3C3×#12111yescharacteristic
878C22×C3C3×#12111yescharacteristic
879C22×C3C3×#12111yescharacteristic
880C22×C3C3×#12111yescharacteristic
881C22×C3C3×#12111yescharacteristic
882C22×C3C3×C22⋊Q811yescharacteristic
883C22×C3C3×C22⋊Q811yescharacteristic
884C22×C3C3×C22⋊Q811yescharacteristic
885C22×C3C3×C22⋊Q811yescharacteristic
886C22×C3C3×C22⋊Q811yescharacteristic
887C22×C3C3×C22⋊Q811yescharacteristic
888C22×C3C3×#12311yescharacteristic
889C22×C3C3×#12311yescharacteristic
890C22×C3C3×#12311yescharacteristic
891C22×C3C3×#12311yescharacteristic
892C22×C3C3×#12311yescharacteristic
893C22×C3C3×#12411yescharacteristic
894C22×C3C3×#12411yescharacteristic
895C22×C3C3×#12411yescharacteristic
896C22×C3C3×#12611yescharacteristic
897C22×C3C3×#12611yescharacteristic
898C22×C3C3×#12711yescharacteristic
899C2×D3—24no—
900C2×D3—24no—
901C2×D3—24no—
902C2×D3—42no—
903C2×D3—42no—
904C2×D3—42no—
905C2×D3—42no—
906C2×D3—42no—
907C2×D3—42no—
908C2×D3—42no—
909C2×D3—42no—
910C2×D3—42no—
911C2×D3—42no—
912C2×D3—42no—
913C2×D3—42no—
914C3×C4—44no—
915C3×C4—44no—
916C3×C4—44no—
917C3×C4—42no—
918C3×C4—42no—
919C3×C4—42no—
920C3×C4—42no—
921C3×C4—42no—
922C3×C4—42no—
923C3×C4—64no—
924C3×C4—122no—
925C3×C4—122no—
926Dic3—24no—
927Dic3—42no—
928Dic3—42no—
929C32#143911yescharacteristic, complemented, Sylow
930C23—34no—
931C23—62no—
932C23—62no—
933C23—62no—
934C23—62no—
935C23—62no—
936C23—62no—
937C23—62no—
938C23—62no—
939C23—62no—
940C23—62no—
941C23—62no—
942C23—62no—
943C23—62no—
944C23—62no—
945C23—62no—
946C23—62no—
947C23—62no—
948C23—62no—
949C23—121no—
950C23—121no—
951C23—121no—
952C23—121no—
953C23—121no—
954C23—121no—
955C23—121no—
956C23—121no—
957C23—121no—
958C23—121no—
959C23—121no—
960C23—121no—
961C23—121no—
962C23—121no—
963C23—121no—
964C23—121no—
965C23C2×C3×C4×D311yescharacteristic
966C23C2×C3×D1211yescharacteristic
967C23C3×#23511yescharacteristic
968C23C3×#23511yescharacteristic
969C23C3×#23511yescharacteristic
970C23C3×#23511yescharacteristic
971C23C3×D3×D411yescharacteristic
972C23C3×D3×D411yescharacteristic
973C23C3×D3×D411yescharacteristic
974C23C3×D3×D411yescharacteristic
975C23C3×D3×D411yescharacteristic
976C23C3×#23711yescharacteristic
977C23C3×D3×Q811yescharacteristic
978C23C3×#23911yescharacteristic
979C23C2×C3×#6711yescharacteristic
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—34no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—62no—
1003C2×C4—62no—
1004C2×C4—62no—
1005C2×C4—62no—
1006C2×C4—62no—
1007C2×C4—62no—
1008C2×C4—62no—
1009C2×C4—62no—
1010C2×C4—62no—
1011C2×C4—62no—
1012C2×C4—62no—
1013C2×C4—62no—
1014C2×C4—121no—
1015C2×C4—121no—
1016C2×C4—121no—
1017C2×C4—121no—
1018C2×C4—121no—
1019C2×C4—121no—
1020C2×C4—121no—
1021C2×C4—121no—
1022C2×C3—21no—
1023C2×C3—21no—
1024C2×C3—21no—
1025C2×C3—21no—
1026C2×C3—21no—
1027C2×C3—21no—
1028C2×C3—21no—
1029C2×C3—21no—
1030C2×C3—21no—
1031C2×C3—21no—
1032C2×C3—21no—
1033C2×C3—21no—
1034C2×C3—21no—
1035C2×C3—21no—
1036C2×C3—21no—
1037C2×C3—124no—
1038C2×C3#466511yescharacteristic
1039C2×C3#466711yescharacteristic
1040C2×C3#466811yescharacteristic
1041C2×C3#466911yescharacteristic
1042C2×C3#467211yescharacteristic
1043C2×C3#467311yescharacteristic
1044C2×C3#467511yescharacteristic
1045C2×C3#467611yescharacteristic
1046C2×C3#494011yescharacteristic
1047C2×C3#495711yescharacteristic
1048C2×C3#495911yescharacteristic
1049C2×C3#496011yescharacteristic
1050C2×C3#498911yescharacteristic
1051C2×C3#499311yescharacteristic
1052C2×C3#499411yescharacteristic
1053C2×C3C3×#38011yescharacteristic
1054C2×C3C3×#38511yescharacteristic
1055C2×C3C3×#38511yescharacteristic
1056C2×C3C3×#38611yescharacteristic
1057C2×C3C3×#38811yescharacteristic
1058C2×C3C3×#38811yescharacteristic
1059C2×C3C3×#39011yescharacteristic
1060C2×C3C3×#39211yescharacteristic
1061C2×C3C3×#39311yescharacteristic
1062C2×C3C3×#39411yescharacteristic
1063C2×C3C3×#39411yescharacteristic
1064C2×C3C3×#39611yescharacteristic
1065C2×C3C3×#39611yescharacteristic
1066C2×C3C3×#39711yescharacteristic
1067C2×C3C3×#39911yescharacteristic
1068D3—44no—
1069C22—64no—
1070C22—64no—
1071C22—64no—
1072C22—122no—
1073C22—122no—
1074C22—122no—
1075C22—122no—
1076C22—122no—
1077C22—122no—
1078C22—122no—
1079C22—122no—
1080C22—122no—
1081C22—122no—
1082C22—122no—
1083C22—122no—
1084C22C3×#87211yescharacteristic
1085C22C3×C4×D1211yescharacteristic
1086C22C3×#87511yescharacteristic
1087C22C3×#87611yescharacteristic
1088C22C3×D3×C22⋊C411yescharacteristic
1089C22C3×#67⋊C411yescharacteristic
1090C22C3×#88211yescharacteristic
1091C22C3×#88211yescharacteristic
1092C22C3×#88311yescharacteristic
1093C22C3×#88411yescharacteristic
1094C22C3×#88411yescharacteristic
1095C22C3×#88411yescharacteristic
1096C22C3×#88411yescharacteristic
1097C22C3×#88411yescharacteristic
1098C22C3×#88511yescharacteristic
1099C22C3×#88511yescharacteristic
1100C22C3×D3×C4⋊C411yescharacteristic
1101C22C3×#89311yescharacteristic
1102C22C3×#89411yescharacteristic
1103C22C3×#89411yescharacteristic
1104C22C3×#89411yescharacteristic
1105C22C3×#89511yescharacteristic
1106C22C3×#89611yescharacteristic
1107C22C3×#89611yescharacteristic
1108C22C3×#89611yescharacteristic
1109C22C3×#89611yescharacteristic
1110C22C3×#89711yescharacteristic
1111C22C3×#89811yescharacteristic
1112C22C3×C4×#6711yescharacteristic
1113C22C3×#92911yescharacteristic
1114C22C3×#93011yescharacteristic
1115C22C3×#93711yescharacteristic
1116C22C3×#93911yescharacteristic
1117C22C3×#94011yescharacteristic
1118C22C3×#94611yescharacteristic
1119C4—42no—
1120C4—42no—
1121C4—42no—
1122C4—64no—
1123C4—122no—
1124C4—122no—
1125C3—21no—
1126C3#6942811yescharacteristic, direct product factor
1127C3C3×#143911yescharacteristic, complemented
1128C2—124no—
1129C2C3×#466511yescharacteristic
1130C2C3×#466711yescharacteristic
1131C2C3×#466811yescharacteristic
1132C2C3×#466911yescharacteristic
1133C2C3×#467211yescharacteristic
1134C2C3×#467311yescharacteristic
1135C2C3×#467511yescharacteristic
1136C2C3×#467611yescharacteristic
1137C2C3×#494011yescharacteristic
1138C2C3×#495711yescharacteristic
1139C2C3×#495911yescharacteristic
1140C2C3×#496011yescharacteristic
1141C2C3×#498911yescharacteristic
1142C2C3×#499311yescharacteristic
1143C2C3×#499411yescharacteristic
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×#1439
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. C22×C3×Dic3⋊C4C2semidirect
5. C2×C32×#95C2semidirect
6. C2×C3×C3⋊#95C2semidirect
7. C2×C3×C3⋊#95C2semidirect
9. #69428C3direct (N × H)
25. C2×C3×(C2×D3)⋊C4C4semidirect
39. C22×Dic3⋊C4C2×C3semidirect
43. C2×C3×#95D3semidirect
44. C2×C3×#95C2×C3semidirect
45. C2×C3⋊#95C2×C3semidirect
46. C2×C3⋊#95C2×C3semidirect
147. C2×(C2×D3)⋊C4C3×C4semidirect
207. C22×C3×D3C4⋊C4semidirect
249. C2×C3×Dic3C22⋊C4semidirect
256. C2×#95C3×D3semidirect
595. C22×D3C3×C4⋊C4semidirect
700. C2×Dic3C3×C22⋊C4semidirect
929. C32#1439semidirect
1126. C3#69428direct (N × H)
1127. C3C3×#1439semidirect

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
C22×C3×Dic3⋊C42
C2×C32×#952
C2×C3×C3⋊#952
C3×#14393
#694283