Finite Group Databasebeta

← C3×#15336 #10633943

Subgroups — C3×#15336 #10633943

Order 768.

1290 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#400C211yesmaximal, characteristic
2C2×C3×#391C211yesmaximal, characteristic
3C2×C3×#391C211yesmaximal, characteristic
4C2×C3×#387C211yesmaximal, characteristic
5C3×#1446C211yesmaximal, characteristic
6C3×#1445C211yesmaximal, characteristic
7C3×#1444C211yesmaximal, characteristic
8C3×#1443C211yesmaximal, characteristic
9C3×#1442C211yesmaximal, characteristic
10C3×#1442C211yesmaximal, characteristic
11C3×#1441C211yesmaximal, characteristic
12C3×#1441C211yesmaximal, characteristic
13C3×#1436C211yesmaximal, characteristic
14C3×#1436C211yesmaximal, characteristic
15C3×#1434C211yesmaximal, characteristic
16#15336C311yesmaximal, 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×C42C2211yescharacteristic
25C22×C3×C42C2211yescharacteristic
26C3×#400—24no—
27C3×#391—24no—
28C3×#391—24no—
29C3×#387—24no—
30C2×C3×#95C2211yescharacteristic
31C2×C3×#95C2211yescharacteristic
32C2×C3×#95C2211yescharacteristic
33C2×C3×#95C2211yescharacteristic
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×#400C2×C311yescharacteristic
57C2×#391C2×C311yescharacteristic
58C2×#391C2×C311yescharacteristic
59C2×#387C2×C311yescharacteristic
60#1446C2×C311yescharacteristic
61#1445C2×C311yescharacteristic
62#1444C2×C311yescharacteristic
63#1443C2×C311yescharacteristic
64#1442C2×C311yescharacteristic
65#1442C2×C311yescharacteristic
66#1441C2×C311yescharacteristic
67#1441C2×C311yescharacteristic
68#1436C2×C311yescharacteristic
69#1436C2×C311yescharacteristic
70#1434C2×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—41no—
107C2×C3×C4⋊C4—41no—
108C2×C3×C4⋊C4—41no—
109C2×C3×C4⋊C4—41no—
110C2×C3×C4⋊C4—41no—
111C2×C3×C42—22no—
112C2×C3×C42—22no—
113C2×C3×C42—22no—
114C2×C3×C42—22no—
115C2×C3×C42—41no—
116C2×C3×C42—41no—
117C3×#95—22no—
118C3×#95—22no—
119C3×#95—22no—
120C3×#95—22no—
121C3×#95—22no—
122C3×#95—22no—
123C3×#95—22no—
124C3×#95—22no—
125C3×#95—22no—
126C3×#95—22no—
127C3×#95—22no—
128C3×#95—22no—
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—41no—
139C3×#95—41no—
140C3×#95—41no—
141C3×#95D414yes—
142C3×#95D414yes—
143C23×Q8C22×C311yescharacteristic
144C22×C4⋊C4C22×C311yescharacteristic
145C22×C4⋊C4C22×C311yescharacteristic
146C22×C4⋊C4C22×C311yescharacteristic
147C22×C4⋊C4C22×C311yescharacteristic
148C22×C4⋊C4C22×C311yescharacteristic
149C22×C4⋊C4C22×C311yescharacteristic
150C22×C42C22×C311yescharacteristic
151C22×C42C22×C311yescharacteristic
152#400—24no—
153#391—24no—
154#391—24no—
155#387—24no—
156C2×#95C22×C311yescharacteristic
157C2×#95C22×C311yescharacteristic
158C2×#95C22×C311yescharacteristic
159C2×#95C22×C311yescharacteristic
160C2×#95C22×C311yescharacteristic
161C2×#95C22×C311yescharacteristic
162C2×#95C22×C311yescharacteristic
163C2×#95C22×C311yescharacteristic
164C2×#95C22×C311yescharacteristic
165C2×#95C22×C311yescharacteristic
166C2×#95C22×C311yescharacteristic
167C2×#95C22×C311yescharacteristic
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
182C24×C3C2411yescharacteristic
183C2×C3×Q8—28no—
184C2×C3×Q8—28no—
185C2×C3×Q8—44no—
186C2×C3×Q8—44no—
187C2×C3×Q8—44no—
188C2×C3×Q8—44no—
189C2×C3×Q8—44no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
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×C4C2×D412yes—
281C22×C3×C4C2×D412yes—
282C22×C3×C4C2×D412yes—
283C22×C3×C4C2×D412yes—
284C22×C3×C4C2×D412yes—
285C22×C3×C4C2×D412yes—
286C22×C3×C4C2×Q812yes—
287C22×C3×C4C2×Q812yes—
288C22×C3×C4C2×Q812yes—
289C22×C3×C4#4112yes—
290C22×C3×C4#4112yes—
291C22×C3×C4#4112yes—
292C22×C3×C4#4112yes—
293C22×C3×C4#4112yes—
294C22×C3×C4#4112yes—
295C3×C4⋊C4—28no—
296C3×C4⋊C4—44no—
297C3×C4⋊C4—44no—
298C3×C4⋊C4—44no—
299C3×C4⋊C4—44no—
300C3×C4⋊C4—44no—
301C3×C42—44no—
302C3×C42—44no—
303C22×Q8—22no—
304C22×Q8—22no—
305C22×Q8—22no—
306C22×Q8—22no—
307C22×Q8—41no—
308C22×Q8—41no—
309C22×Q8C3×Q814yes—
310C23×C4C23×C311yescharacteristic
311C23×C4C23×C311yescharacteristic
312C23×C4C23×C311yescharacteristic
313C23×C4C23×C311yescharacteristic
314C23×C4C23×C311yescharacteristic
315C23×C4C23×C311yescharacteristic
316C23×C4C23×C311yescharacteristic
317C23×C4C23×C311yescharacteristic
318C23×C4C23×C311yescharacteristic
319C23×C4C23×C311yescharacteristic
320C23×C4C23×C311yescharacteristic
321C23×C4C23×C311yescharacteristic
322C23×C4C23×C311yescharacteristic
323C23×C4C23×C311yescharacteristic
324C23×C4C23×C311yescharacteristic
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—41no—
339C2×C4⋊C4—41no—
340C2×C4⋊C4—41no—
341C2×C4⋊C4—41no—
342C2×C4⋊C4—41no—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42—41no—
348C2×C42—41no—
349#95—22no—
350#95—22no—
351#95—22no—
352#95—22no—
353#95—22no—
354#95—22no—
355#95—22no—
356#95—22no—
357#95—22no—
358#95—22no—
359#95—22no—
360#95—22no—
361#95—22no—
362#95—22no—
363#95—22no—
364#95—22no—
365#95—22no—
366#95—22no—
367#95—22no—
368#95—22no—
369#95—22no—
370#95—41no—
371#95—41no—
372#95—41no—
373#95C3×D414yes—
374#95C3×D414yes—
375C23×C3C22×D411yescharacteristic
376C23×C3C22×D411yescharacteristic
377C23×C3C22×Q811yescharacteristic
378C23×C3C2×#4111yescharacteristic
379C23×C3C2×#4111yescharacteristic
380C23×C3C2×#4111yescharacteristic
381C23×C3C2×#4111yescharacteristic
382C23×C3C2×#4111yescharacteristic
383C23×C3C2×#4111yescharacteristic
384C23×C3H(5,𝔽2)11yescharacteristic
385C23×C3H(5,𝔽2)11yescharacteristic
386C23×C32−1+411yescharacteristic
387C23×C32−1+411yescharacteristic
388C23×C32−1+411yescharacteristic
389C23×C32−1+411yescharacteristic
390C3×Q8—416no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
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—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
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×C4C22⋊Q814yes—
495C2×C3×C4C22⋊Q814yes—
496C24C24×C311yescharacteristic
497C2×Q8—28no—
498C2×Q8—28no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×Q8—44no—
502C2×Q8—44no—
503C2×Q8—44no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
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×C4C2×C3×D412yes—
595C22×C4C2×C3×D412yes—
596C22×C4C2×C3×D412yes—
597C22×C4C2×C3×D412yes—
598C22×C4C2×C3×D412yes—
599C22×C4C2×C3×D412yes—
600C22×C4C2×C3×Q812yes—
601C22×C4C2×C3×Q812yes—
602C22×C4C2×C3×Q812yes—
603C22×C4C3×#4112yes—
604C22×C4C3×#4112yes—
605C22×C4C3×#4112yes—
606C22×C4C3×#4112yes—
607C22×C4C3×#4112yes—
608C22×C4C3×#4112yes—
609C4⋊C4—28no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—44no—
613C4⋊C4—44no—
614C4⋊C4—44no—
615C42—44no—
616C42—44no—
617C22×C3C2×C22⋊Q811yescharacteristic
618C22×C3C2×C22⋊Q811yescharacteristic
619C22×C3#52511yescharacteristic
620C22×C3#52911yescharacteristic
621C22×C3#52911yescharacteristic
622C22×C3#53211yescharacteristic
623C22×C3#53611yescharacteristic
624C22×C3#53611yescharacteristic
625C22×C3#54111yescharacteristic
626C22×C3#54111yescharacteristic
627C22×C3#54211yescharacteristic
628C22×C3#54211yescharacteristic
629C22×C3#54211yescharacteristic
630C22×C3#54211yescharacteristic
631C22×C3#54311yescharacteristic
632C22×C3D4211yescharacteristic
633C22×C3#54611yescharacteristic
634C22×C3#54611yescharacteristic
635C22×C3#54711yescharacteristic
636C22×C3#54711yescharacteristic
637C22×C3#54811yescharacteristic
638C22×C3#54811yescharacteristic
639C22×C3#55111yescharacteristic
640C22×C3#55111yescharacteristic
641C22×C3#55111yescharacteristic
642C22×C3#55211yescharacteristic
643C22×C3#55211yescharacteristic
644C22×C3#55611yescharacteristic
645C22×C3#55611yescharacteristic
646C22×C3#55711yescharacteristic
647C22×C3#55711yescharacteristic
648C22×C3#55711yescharacteristic
649C22×C3#55711yescharacteristic
650C22×C3#56311yescharacteristic
651C22×C3#56311yescharacteristic
652C3×C4—24no—
653C3×C4—24no—
654C3×C4—42no—
655C3×C4—42no—
656C3×C4—42no—
657C3×C4—42no—
658C3×C4—42no—
659C3×C4—42no—
660C3×C4—42no—
661C3×C4—42no—
662C3×C4—42no—
663C3×C4—81no—
664C3×C4—81no—
665C3×C4—81no—
666C3×C4—81no—
667C23C22×C3×D411yescharacteristic
668C23C22×C3×D411yescharacteristic
669C23C22×C3×Q811yescharacteristic
670C23C2×C3×#4111yescharacteristic
671C23C2×C3×#4111yescharacteristic
672C23C2×C3×#4111yescharacteristic
673C23C2×C3×#4111yescharacteristic
674C23C2×C3×#4111yescharacteristic
675C23C2×C3×#4111yescharacteristic
676C23C3×H(5,𝔽2)11yescharacteristic
677C23C3×H(5,𝔽2)11yescharacteristic
678C23C3×2−1+411yescharacteristic
679C23C3×2−1+411yescharacteristic
680C23C3×2−1+411yescharacteristic
681C23C3×2−1+411yescharacteristic
682Q8—416no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
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—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
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×C4C3×C22⋊Q814yes—
787C2×C4C3×C22⋊Q814yes—
788C2×C3#243711yescharacteristic
789C2×C3#245311yescharacteristic
790C2×C3#245311yescharacteristic
791C2×C3#246111yescharacteristic
792C2×C3#247711yescharacteristic
793C2×C3#252111yescharacteristic
794C2×C3#252711yescharacteristic
795C2×C3#256511yescharacteristic
796C2×C3#258111yescharacteristic
797C2×C3#267411yescharacteristic
798C2×C3#269811yescharacteristic
799C2×C3#271611yescharacteristic
800C2×C3#275811yescharacteristic
801C2×C3#279911yescharacteristic
802C2×C3#279911yescharacteristic
803C22C2×C3×C22⋊Q811yescharacteristic
804C22C2×C3×C22⋊Q811yescharacteristic
805C22C3×#52511yescharacteristic
806C22C3×#52911yescharacteristic
807C22C3×#52911yescharacteristic
808C22C3×#53211yescharacteristic
809C22C3×#53611yescharacteristic
810C22C3×#53611yescharacteristic
811C22C3×#54111yescharacteristic
812C22C3×#54111yescharacteristic
813C22C3×#54211yescharacteristic
814C22C3×#54211yescharacteristic
815C22C3×#54211yescharacteristic
816C22C3×#54211yescharacteristic
817C22C3×#54311yescharacteristic
818C22C3×D4211yescharacteristic
819C22C3×#54611yescharacteristic
820C22C3×#54611yescharacteristic
821C22C3×#54711yescharacteristic
822C22C3×#54711yescharacteristic
823C22C3×#54811yescharacteristic
824C22C3×#54811yescharacteristic
825C22C3×#55111yescharacteristic
826C22C3×#55111yescharacteristic
827C22C3×#55111yescharacteristic
828C22C3×#55211yescharacteristic
829C22C3×#55211yescharacteristic
830C22C3×#55611yescharacteristic
831C22C3×#55611yescharacteristic
832C22C3×#55711yescharacteristic
833C22C3×#55711yescharacteristic
834C22C3×#55711yescharacteristic
835C22C3×#55711yescharacteristic
836C22C3×#56311yescharacteristic
837C22C3×#56311yescharacteristic
838C4—24no—
839C4—24no—
840C4—42no—
841C4—42no—
842C4—42no—
843C4—42no—
844C4—42no—
845C4—42no—
846C4—42no—
847C4—42no—
848C4—42no—
849C4—81no—
850C4—81no—
851C4—81no—
852C4—81no—
853C3#1533611yescharacteristic, direct product factor, Sylow
854C2C3×#243711yescharacteristic
855C2C3×#245311yescharacteristic
856C2C3×#245311yescharacteristic
857C2C3×#246111yescharacteristic
858C2C3×#247711yescharacteristic
859C2C3×#252111yescharacteristic
860C2C3×#252711yescharacteristic
861C2C3×#256511yescharacteristic
862C2C3×#258111yescharacteristic
863C2C3×#267411yescharacteristic
864C2C3×#269811yescharacteristic
865C2C3×#271611yescharacteristic
866C2C3×#275811yescharacteristic
867C2C3×#279911yescharacteristic
868C2C3×#279911yescharacteristic
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. #15336C3direct (N × H)
853. C3#15336direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4002
C2×C3×#3912
C2×C3×#3872
C3×#14462
C3×#14452
C3×#14442
C3×#14432
C3×#14422
C3×#14412
C3×#14362
C3×#14342
#153363