Finite Group Databasebeta

← C3×#15333 #10633940

Subgroups — C3×#15333 #10633940

Order 768.

1378 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#398C211yesmaximal, characteristic
2C2×C3×#391C211yesmaximal, characteristic
3C2×C3×#391C211yesmaximal, characteristic
4C2×C3×#389C211yesmaximal, characteristic
5C3×#1446C211yesmaximal, characteristic
6C3×#1444C211yesmaximal, characteristic
7C3×#1444C211yesmaximal, characteristic
8C3×#1444C211yesmaximal, characteristic
9C3×#1442C211yesmaximal, characteristic
10C3×#1441C211yesmaximal, characteristic
11C3×#1441C211yesmaximal, characteristic
12C3×#1441C211yesmaximal, characteristic
13C3×#1436C211yesmaximal, characteristic
14C3×#1436C211yesmaximal, characteristic
15C3×C4⋊#95C211yesmaximal, characteristic
16#15333C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×Q8C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C4⋊C4C2211yescharacteristic
26C22×C3×C4⋊C4C2211yescharacteristic
27C22×C3×C4⋊C4C2211yescharacteristic
28C22×C3×C42C2211yescharacteristic
29C22×C3×C42C2211yescharacteristic
30C3×#398—24no—
31C3×#391—24no—
32C3×#391—24no—
33C3×#389—24no—
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2211yescharacteristic
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42C2×C3×#95C2211yescharacteristic
43C2×C3×#95C2211yescharacteristic
44C2×C3×#95C2211yescharacteristic
45C2×C3×#95C2211yescharacteristic
46C2×C3×#95C2211yescharacteristic
47C2×C3×#95C2211yescharacteristic
48C2×C3×#95C2211yescharacteristic
49C2×C3×#95C2211yescharacteristic
50C2×C3×#95C2211yescharacteristic
51C2×C3×#95C2211yescharacteristic
52C2×C3×#95C2211yescharacteristic
53C2×C3×#95C2211yescharacteristic
54C2×C3×#95C2211yescharacteristic
55C2×C3×#95C2211yescharacteristic
56C2×#398C2×C311yescharacteristic
57C2×#391C2×C311yescharacteristic
58C2×#391C2×C311yescharacteristic
59C2×#389C2×C311yescharacteristic
60#1446C2×C311yescharacteristic
61#1444C2×C311yescharacteristic
62#1444C2×C311yescharacteristic
63#1444C2×C311yescharacteristic
64#1442C2×C311yescharacteristic
65#1441C2×C311yescharacteristic
66#1441C2×C311yescharacteristic
67#1441C2×C311yescharacteristic
68#1436C2×C311yescharacteristic
69#1436C2×C311yescharacteristic
70C4⋊#95C2×C311yescharacteristic
71C22×C3×Q8—22no—
72C22×C3×Q8—22no—
73C22×C3×Q8—22no—
74C22×C3×Q8—22no—
75C22×C3×Q8—41no—
76C22×C3×Q8—41no—
77C22×C3×Q8Q814yes—
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C2×C3×C4⋊C4—22no—
94C2×C3×C4⋊C4—22no—
95C2×C3×C4⋊C4—22no—
96C2×C3×C4⋊C4—22no—
97C2×C3×C4⋊C4—22no—
98C2×C3×C4⋊C4—22no—
99C2×C3×C4⋊C4—22no—
100C2×C3×C4⋊C4—22no—
101C2×C3×C4⋊C4—22no—
102C2×C3×C4⋊C4—22no—
103C2×C3×C4⋊C4—22no—
104C2×C3×C4⋊C4—22no—
105C2×C3×C4⋊C4—22no—
106C2×C3×C4⋊C4—22no—
107C2×C3×C4⋊C4—22no—
108C2×C3×C4⋊C4—22no—
109C2×C3×C4⋊C4—41no—
110C2×C3×C4⋊C4—41no—
111C2×C3×C4⋊C4—41no—
112C2×C3×C4⋊C4—41no—
113C2×C3×C4⋊C4—41no—
114C2×C3×C4⋊C4—41no—
115C2×C3×C4⋊C4—41no—
116C2×C3×C4⋊C4—41no—
117C2×C3×C4⋊C4—41no—
118C2×C3×C4⋊C4—41no—
119C2×C3×C4⋊C4—41no—
120C2×C3×C4⋊C4—41no—
121C2×C3×C4⋊C4—41no—
122C2×C3×C4⋊C4Q814yescomplemented
123C2×C3×C42—22no—
124C2×C3×C42—22no—
125C2×C3×C42—22no—
126C2×C3×C42—22no—
127C2×C3×C42—41no—
128C2×C3×C42—41no—
129C3×#95—22no—
130C3×#95—22no—
131C3×#95—22no—
132C3×#95—22no—
133C3×#95—22no—
134C3×#95—22no—
135C3×#95—22no—
136C3×#95—22no—
137C3×#95—22no—
138C3×#95—22no—
139C3×#95—22no—
140C3×#95—22no—
141C3×#95—41no—
142C3×#95—41no—
143C3×#95—41no—
144C3×#95—41no—
145C3×#95—41no—
146C3×#95—41no—
147C3×#95—41no—
148C3×#95D414yes—
149C3×#95D414yes—
150C3×#95Q814yescomplemented
151C23×Q8C22×C311yescharacteristic
152C22×C4⋊C4C22×C311yescharacteristic
153C22×C4⋊C4C22×C311yescharacteristic
154C22×C4⋊C4C22×C311yescharacteristic
155C22×C4⋊C4C22×C311yescharacteristic
156C22×C4⋊C4C22×C311yescharacteristic
157C22×C4⋊C4C22×C311yescharacteristic
158C22×C4⋊C4C22×C311yescharacteristic
159C22×C4⋊C4C22×C311yescharacteristic
160C22×C4⋊C4C22×C311yescharacteristic
161C22×C4⋊C4C22×C311yescharacteristic
162C22×C42C22×C311yescharacteristic
163C22×C42C22×C311yescharacteristic
164#398—24no—
165#391—24no—
166#391—24no—
167#389—24no—
168C2×#95C22×C311yescharacteristic
169C2×#95C22×C311yescharacteristic
170C2×#95C22×C311yescharacteristic
171C2×#95C22×C311yescharacteristic
172C2×#95C22×C311yescharacteristic
173C2×#95C22×C311yescharacteristic
174C2×#95C22×C311yescharacteristic
175C2×#95C22×C311yescharacteristic
176C2×#95C22×C311yescharacteristic
177C2×#95C22×C311yescharacteristic
178C2×#95C22×C311yescharacteristic
179C2×#95C22×C311yescharacteristic
180C2×#95C22×C311yescharacteristic
181C2×#95C22×C311yescharacteristic
182C2×#95C22×C311yescharacteristic
183C2×#95C22×C311yescharacteristic
184C2×#95C22×C311yescharacteristic
185C2×#95C22×C311yescharacteristic
186C2×#95C22×C311yescharacteristic
187C2×#95C22×C311yescharacteristic
188C2×#95C22×C311yescharacteristic
189C2×#95C22×C311yescharacteristic
190C24×C3C2411yescharacteristic
191C2×C3×Q8—28no—
192C2×C3×Q8—28no—
193C2×C3×Q8—44no—
194C2×C3×Q8—44no—
195C2×C3×Q8—44no—
196C2×C3×Q8—44no—
197C2×C3×Q8—44no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4C2×D412yes—
285C22×C3×C4C2×D412yes—
286C22×C3×C4C2×D412yes—
287C22×C3×C4C2×D412yes—
288C22×C3×C4C2×D412yes—
289C22×C3×C4C2×D412yes—
290C22×C3×C4C2×Q812yes—
291C22×C3×C4C2×Q812yes—
292C22×C3×C4C2×Q812yes—
293C22×C3×C4C2×Q812yes—
294C22×C3×C4C2×Q812yes—
295C22×C3×C4C2×Q812yes—
296C22×C3×C4C2×Q812yes—
297C22×C3×C4C2×Q812yes—
298C22×C3×C4C2×Q812yes—
299C22×C3×C4#4112yes—
300C22×C3×C4#4112yes—
301C22×C3×C4#4112yes—
302C22×C3×C4#4112yes—
303C3×C4⋊C4—28no—
304C3×C4⋊C4—44no—
305C3×C4⋊C4—44no—
306C3×C4⋊C4—44no—
307C3×C4⋊C4—44no—
308C3×C4⋊C4—44no—
309C3×C4⋊C4—44no—
310C3×C4⋊C4—44no—
311C3×C4⋊C4—44no—
312C3×C4⋊C4—44no—
313C3×C42—44no—
314C3×C42—44no—
315C22×Q8—22no—
316C22×Q8—22no—
317C22×Q8—22no—
318C22×Q8—22no—
319C22×Q8—41no—
320C22×Q8—41no—
321C22×Q8C3×Q814yes—
322C23×C4C23×C311yescharacteristic
323C23×C4C23×C311yescharacteristic
324C23×C4C23×C311yescharacteristic
325C23×C4C23×C311yescharacteristic
326C23×C4C23×C311yescharacteristic
327C23×C4C23×C311yescharacteristic
328C23×C4C23×C311yescharacteristic
329C23×C4C23×C311yescharacteristic
330C23×C4C23×C311yescharacteristic
331C23×C4C23×C311yescharacteristic
332C23×C4C23×C311yescharacteristic
333C23×C4C23×C311yescharacteristic
334C23×C4C23×C311yescharacteristic
335C23×C4C23×C311yescharacteristic
336C23×C4C23×C311yescharacteristic
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—41no—
354C2×C4⋊C4—41no—
355C2×C4⋊C4—41no—
356C2×C4⋊C4—41no—
357C2×C4⋊C4—41no—
358C2×C4⋊C4—41no—
359C2×C4⋊C4—41no—
360C2×C4⋊C4—41no—
361C2×C4⋊C4—41no—
362C2×C4⋊C4—41no—
363C2×C4⋊C4—41no—
364C2×C4⋊C4—41no—
365C2×C4⋊C4—41no—
366C2×C4⋊C4C3×Q814yescomplemented
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—41no—
372C2×C42—41no—
373#95—22no—
374#95—22no—
375#95—22no—
376#95—22no—
377#95—22no—
378#95—22no—
379#95—22no—
380#95—22no—
381#95—22no—
382#95—22no—
383#95—22no—
384#95—22no—
385#95—41no—
386#95—41no—
387#95—41no—
388#95—41no—
389#95—41no—
390#95—41no—
391#95—41no—
392#95C3×D414yes—
393#95C3×D414yes—
394#95C3×Q814yescomplemented
395C23×C3C22×D411yescharacteristic
396C23×C3C22×D411yescharacteristic
397C23×C3C22×Q811yescharacteristic
398C23×C3C22×Q811yescharacteristic
399C23×C3C22×Q811yescharacteristic
400C23×C3C2×#4111yescharacteristic
401C23×C3C2×#4111yescharacteristic
402C23×C3C2×#4111yescharacteristic
403C23×C3C2×#4111yescharacteristic
404C23×C3H(5,𝔽2)11yescharacteristic
405C23×C3H(5,𝔽2)11yescharacteristic
406C23×C3H(5,𝔽2)11yescharacteristic
407C23×C3H(5,𝔽2)11yescharacteristic
408C23×C32−1+411yescharacteristic
409C23×C32−1+411yescharacteristic
410C3×Q8—416no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
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—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
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—41no—
511C2×C3×C4—41no—
512C2×C3×C4C22⋊Q814yes—
513C2×C3×C4C22⋊Q814yes—
514C2×C3×C4C22⋊Q814yes—
515C2×C3×C4C4⋊Q814yes—
516C24C24×C311yescharacteristic
517C2×Q8—28no—
518C2×Q8—28no—
519C2×Q8—44no—
520C2×Q8—44no—
521C2×Q8—44no—
522C2×Q8—44no—
523C2×Q8—44no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4C2×C3×D412yes—
611C22×C4C2×C3×D412yes—
612C22×C4C2×C3×D412yes—
613C22×C4C2×C3×D412yes—
614C22×C4C2×C3×D412yes—
615C22×C4C2×C3×D412yes—
616C22×C4C2×C3×Q812yes—
617C22×C4C2×C3×Q812yes—
618C22×C4C2×C3×Q812yes—
619C22×C4C2×C3×Q812yes—
620C22×C4C2×C3×Q812yes—
621C22×C4C2×C3×Q812yes—
622C22×C4C2×C3×Q812yes—
623C22×C4C2×C3×Q812yes—
624C22×C4C2×C3×Q812yes—
625C22×C4C3×#4112yes—
626C22×C4C3×#4112yes—
627C22×C4C3×#4112yes—
628C22×C4C3×#4112yes—
629C4⋊C4—28no—
630C4⋊C4—44no—
631C4⋊C4—44no—
632C4⋊C4—44no—
633C4⋊C4—44no—
634C4⋊C4—44no—
635C4⋊C4—44no—
636C4⋊C4—44no—
637C4⋊C4—44no—
638C4⋊C4—44no—
639C42—44no—
640C42—44no—
641C22×C3C2×C22⋊Q811yescharacteristic
642C22×C3C2×C22⋊Q811yescharacteristic
643C22×C3C2×C22⋊Q811yescharacteristic
644C22×C3#52911yescharacteristic
645C22×C3C2×C4⋊Q811yescharacteristic
646C22×C3#53311yescharacteristic
647C22×C3#53511yescharacteristic
648C22×C3#53711yescharacteristic
649C22×C3#53811yescharacteristic
650C22×C3#53811yescharacteristic
651C22×C3#54111yescharacteristic
652C22×C3#54211yescharacteristic
653C22×C3#54311yescharacteristic
654C22×C3#54411yescharacteristic
655C22×C3#54411yescharacteristic
656C22×C3D4211yescharacteristic
657C22×C3#54611yescharacteristic
658C22×C3#54611yescharacteristic
659C22×C3#54611yescharacteristic
660C22×C3#54711yescharacteristic
661C22×C3#54811yescharacteristic
662C22×C3D4×Q811yescharacteristic
663C22×C3#55111yescharacteristic
664C22×C3#55411yescharacteristic
665C22×C3#55411yescharacteristic
666C22×C3#55411yescharacteristic
667C22×C3#55411yescharacteristic
668C22×C3#55711yescharacteristic
669C22×C3#55711yescharacteristic
670C22×C3#55711yescharacteristic
671C22×C3Q8211yescharacteristic
672C22×C3Q8211yescharacteristic
673C22×C3#55911yescharacteristic
674C22×C3#56211yescharacteristic
675C22×C3#56211yescharacteristic
676C3×C4—24no—
677C3×C4—24no—
678C3×C4—24no—
679C3×C4—24no—
680C3×C4—42no—
681C3×C4—42no—
682C3×C4—42no—
683C3×C4—42no—
684C3×C4—42no—
685C3×C4—42no—
686C3×C4—42no—
687C3×C4—81no—
688C3×C4—81no—
689C3×C4—81no—
690C3×C4—81no—
691C23C22×C3×D411yescharacteristic
692C23C22×C3×D411yescharacteristic
693C23C22×C3×Q811yescharacteristic
694C23C22×C3×Q811yescharacteristic
695C23C22×C3×Q811yescharacteristic
696C23C2×C3×#4111yescharacteristic
697C23C2×C3×#4111yescharacteristic
698C23C2×C3×#4111yescharacteristic
699C23C2×C3×#4111yescharacteristic
700C23C3×H(5,𝔽2)11yescharacteristic
701C23C3×H(5,𝔽2)11yescharacteristic
702C23C3×H(5,𝔽2)11yescharacteristic
703C23C3×H(5,𝔽2)11yescharacteristic
704C23C3×2−1+411yescharacteristic
705C23C3×2−1+411yescharacteristic
706Q8—416no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4C3×C22⋊Q814yes—
809C2×C4C3×C22⋊Q814yes—
810C2×C4C3×C22⋊Q814yes—
811C2×C4C3×C4⋊Q814yes—
812C2×C3#243711yescharacteristic
813C2×C3#244011yescharacteristic
814C2×C3#245011yescharacteristic
815C2×C3#245111yescharacteristic
816C2×C3#245311yescharacteristic
817C2×C3#255011yescharacteristic
818C2×C3#256711yescharacteristic
819C2×C3#258211yescharacteristic
820C2×C3#258911yescharacteristic
821C2×C3#267611yescharacteristic
822C2×C3#270411yescharacteristic
823C2×C3#271011yescharacteristic
824C2×C3#275511yescharacteristic
825C2×C3#280611yescharacteristic
826C2×C3#280611yescharacteristic
827C22C2×C3×C22⋊Q811yescharacteristic
828C22C2×C3×C22⋊Q811yescharacteristic
829C22C2×C3×C22⋊Q811yescharacteristic
830C22C3×#52911yescharacteristic
831C22C2×C3×C4⋊Q811yescharacteristic
832C22C3×#53311yescharacteristic
833C22C3×#53511yescharacteristic
834C22C3×#53711yescharacteristic
835C22C3×#53811yescharacteristic
836C22C3×#53811yescharacteristic
837C22C3×#54111yescharacteristic
838C22C3×#54211yescharacteristic
839C22C3×#54311yescharacteristic
840C22C3×#54411yescharacteristic
841C22C3×#54411yescharacteristic
842C22C3×D4211yescharacteristic
843C22C3×#54611yescharacteristic
844C22C3×#54611yescharacteristic
845C22C3×#54611yescharacteristic
846C22C3×#54711yescharacteristic
847C22C3×#54811yescharacteristic
848C22C3×D4×Q811yescharacteristic
849C22C3×#55111yescharacteristic
850C22C3×#55411yescharacteristic
851C22C3×#55411yescharacteristic
852C22C3×#55411yescharacteristic
853C22C3×#55411yescharacteristic
854C22C3×#55711yescharacteristic
855C22C3×#55711yescharacteristic
856C22C3×#55711yescharacteristic
857C22C3×Q8211yescharacteristic
858C22C3×Q8211yescharacteristic
859C22C3×#55911yescharacteristic
860C22C3×#56211yescharacteristic
861C22C3×#56211yescharacteristic
862C4—24no—
863C4—24no—
864C4—24no—
865C4—24no—
866C4—42no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—81no—
874C4—81no—
875C4—81no—
876C4—81no—
877C3#1533311yescharacteristic, direct product factor, Sylow
878C2C3×#243711yescharacteristic
879C2C3×#244011yescharacteristic
880C2C3×#245011yescharacteristic
881C2C3×#245111yescharacteristic
882C2C3×#245311yescharacteristic
883C2C3×#255011yescharacteristic
884C2C3×#256711yescharacteristic
885C2C3×#258211yescharacteristic
886C2C3×#258911yescharacteristic
887C2C3×#267611yescharacteristic
888C2C3×#270411yescharacteristic
889C2C3×#271011yescharacteristic
890C2C3×#275511yescharacteristic
891C2C3×#280611yescharacteristic
892C2C3×#280611yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C3C24
commutator, Frattini, cosocleC24C24×C3
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
16. #15333C3direct (N × H)
122. C2×C3×C4⋊C4Q8semidirect
150. C3×#95Q8semidirect
366. C2×C4⋊C4C3×Q8semidirect
394. #95C3×Q8semidirect
877. C3#15333direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3982
C2×C3×#3912
C2×C3×#3892
C3×#14462
C3×#14442
C3×#14422
C3×#14412
C3×#14362
C3×C4⋊#952
#153333