Finite Group Databasebeta

← C3×#14740 #10633347

Subgroups — C3×#14740 #10633347

Order 768.

1534 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#397C211yesmaximal, characteristic
2C2×C3×#387C211yesmaximal, characteristic, complemented
3C2×C3×#385C211yesmaximal, characteristic
4C2×C3×C4×C22⋊C4C211yesmaximal, characteristic
5C3×#1445C211yesmaximal, characteristic, complemented
6C3×#1443C211yesmaximal, characteristic, complemented
7C3×#1442C211yesmaximal, characteristic, complemented
8C3×#1441C211yesmaximal, characteristic, complemented
9C3×#1440C211yesmaximal, characteristic
10C3×#1440C211yesmaximal, characteristic
11C3×#1439C211yesmaximal, characteristic
12C3×#1436C211yesmaximal, characteristic, complemented
13C3×#1436C211yesmaximal, characteristic, complemented
14C3×#1434C211yesmaximal, characteristic, complemented
15C3×C22⋊#95C211yesmaximal, characteristic
16#14740C311yesmaximal, characteristic, direct product factor, Sylow
17C24×C3×C4C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C42C2211yescharacteristic
29C22×C3×C42C2211yescharacteristic
30C3×#397—24no—
31C3×#387—24no—
32C3×#385—24no—
33C3×C4×C22⋊C4—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×#397C2×C311yescharacteristic
57C2×#387C2×C311yescharacteristic, complemented
58C2×#385C2×C311yescharacteristic
59C2×C4×C22⋊C4C2×C311yescharacteristic
60#1445C2×C311yescharacteristic, complemented
61#1443C2×C311yescharacteristic, complemented
62#1442C2×C311yescharacteristic, complemented
63#1441C2×C311yescharacteristic, complemented
64#1440C2×C311yescharacteristic
65#1440C2×C311yescharacteristic
66#1439C2×C311yescharacteristic
67#1436C2×C311yescharacteristic, complemented
68#1436C2×C311yescharacteristic, complemented
69#1434C2×C311yescharacteristic, complemented
70C22⋊#95C2×C311yescharacteristic
71C25×C3C2311yescharacteristic
72C23×C3×C4—22no—
73C23×C3×C4—22no—
74C23×C3×C4—22no—
75C23×C3×C4—22no—
76C23×C3×C4—22no—
77C23×C3×C4—41no—
78C23×C3×C4—41no—
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—41no—
102C2×C3×C4⋊C4—41no—
103C2×C3×C4⋊C4—41no—
104C2×C3×C4⋊C4D414yes—
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—22no—
108C2×C3×C22⋊C4—22no—
109C2×C3×C22⋊C4—22no—
110C2×C3×C22⋊C4—22no—
111C2×C3×C22⋊C4—22no—
112C2×C3×C22⋊C4—22no—
113C2×C3×C22⋊C4—22no—
114C2×C3×C22⋊C4—22no—
115C2×C3×C22⋊C4—22no—
116C2×C3×C22⋊C4—22no—
117C2×C3×C22⋊C4—22no—
118C2×C3×C22⋊C4—22no—
119C2×C3×C22⋊C4—22no—
120C2×C3×C22⋊C4—41no—
121C2×C3×C22⋊C4—41no—
122C2×C3×C22⋊C4D414yes—
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—22no—
142C3×#95—22no—
143C3×#95—22no—
144C3×#95—22no—
145C3×#95—22no—
146C3×#95—22no—
147C3×#95—22no—
148C3×#95—41no—
149C3×#95—41no—
150C3×#95—41no—
151C24×C4C22×C311yescharacteristic
152C22×C4⋊C4C22×C311yescharacteristic
153C22×C4⋊C4C22×C311yescharacteristic
154C22×C4⋊C4C22×C311yescharacteristic
155C22×C4⋊C4C22×C311yescharacteristic
156C22×C22⋊C4C22×C311yescharacteristic
157C22×C22⋊C4C22×C311yescharacteristic
158C22×C22⋊C4C22×C311yescharacteristic
159C22×C22⋊C4C22×C311yescharacteristic
160C22×C22⋊C4C22×C311yescharacteristic
161C22×C22⋊C4C22×C311yescharacteristic
162C22×C42C22×C311yescharacteristic
163C22×C42C22×C311yescharacteristic
164#397—24no—
165#387—24no—
166#385—24no—
167C4×C22⋊C4—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×C3—21no—
191C24×C3—21no—
192C24×C3—21no—
193C24×C3—21no—
194C24×C3—21no—
195C24×C3—21no—
196C24×C3—21no—
197C24×C3—21no—
198C24×C3—21no—
199C24×C3—21no—
200C24×C3—21no—
201C24×C3—21no—
202C24×C3C2×D412yes—
203C24×C3#4112yes—
204C24×C3#4112yes—
205C24×C3C2411yescharacteristic
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—28no—
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×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—44no—
294C22×C3×C4—44no—
295C22×C3×C4—44no—
296C22×C3×C4—44no—
297C22×C3×C4—44no—
298C22×C3×C4—44no—
299C22×C3×C4C2×D412yes—
300C22×C3×C4C2×D412yes—
301C22×C3×C4C2×D412yes—
302C22×C3×C4C2×D412yes—
303C22×C3×C4C2×D412yes—
304C22×C3×C4#4112yes—
305C22×C3×C4#4112yes—
306C22×C3×C4#4112yes—
307C22×C3×C4#4112yes—
308C22×C3×C4#4112yes—
309C22×C3×C4#4112yes—
310C22×C3×C4#4112yes—
311C3×C4⋊C4—28no—
312C3×C4⋊C4—44no—
313C3×C4⋊C4—44no—
314C3×C4⋊C4—44no—
315C3×C22⋊C4—28no—
316C3×C22⋊C4—28no—
317C3×C22⋊C4—28no—
318C3×C22⋊C4—44no—
319C3×C22⋊C4—44no—
320C3×C22⋊C4—44no—
321C3×C42—44no—
322C3×C42—44no—
323C25C23×C311yescharacteristic
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—41no—
330C23×C4—41no—
331C23×C4C23×C311yescharacteristic
332C23×C4C23×C311yescharacteristic
333C23×C4C23×C311yescharacteristic
334C23×C4C23×C311yescharacteristic
335C23×C4C23×C311yescharacteristic
336C23×C4C23×C311yescharacteristic
337C23×C4C23×C311yescharacteristic
338C23×C4C23×C311yescharacteristic
339C23×C4C23×C311yescharacteristic
340C23×C4C23×C311yescharacteristic
341C23×C4C23×C311yescharacteristic
342C23×C4C23×C311yescharacteristic
343C23×C4C23×C311yescharacteristic
344C23×C4C23×C311yescharacteristic
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⋊C4C3×D414yes—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—41no—
373C2×C22⋊C4—41no—
374C2×C22⋊C4C3×D414yes—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—41no—
380C2×C42—41no—
381#95—22no—
382#95—22no—
383#95—22no—
384#95—22no—
385#95—22no—
386#95—22no—
387#95—22no—
388#95—22no—
389#95—22no—
390#95—22no—
391#95—22no—
392#95—22no—
393#95—22no—
394#95—22no—
395#95—22no—
396#95—22no—
397#95—22no—
398#95—22no—
399#95—22no—
400#95—41no—
401#95—41no—
402#95—41no—
403C23×C3—22no—
404C23×C3—22no—
405C23×C3—22no—
406C23×C3—22no—
407C23×C3—22no—
408C23×C3—22no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—22no—
416C23×C3—22no—
417C23×C3—22no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3—41no—
437C23×C3#12314yes—
438C23×C3C22×D411yescharacteristic
439C23×C3C22×D411yescharacteristic
440C23×C3C2×#4111yescharacteristic
441C23×C3C2×#4111yescharacteristic
442C23×C3C2×#4111yescharacteristic
443C23×C3C2×#4111yescharacteristic
444C23×C3C2×#4111yescharacteristic
445C23×C3C2×#4111yescharacteristic
446C23×C3C2×#4111yescharacteristic
447C23×C3C2×#4111yescharacteristic
448C23×C3C2×#4111yescharacteristic
449C23×C3H(5,𝔽2)11yescharacteristic
450C23×C3H(5,𝔽2)11yescharacteristic
451C23×C32−1+411yescharacteristic
452C23×C32−1+411yescharacteristic
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—416no—
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×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4#12314yes—
552C24—21no—
553C24—21no—
554C24—21no—
555C24—21no—
556C24—21no—
557C24—21no—
558C24—21no—
559C24—21no—
560C24—21no—
561C24—21no—
562C24—21no—
563C24—21no—
564C24C2×C3×D412yes—
565C24C3×#4112yes—
566C24C3×#4112yes—
567C24C24×C311yescharacteristic
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—28no—
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×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—44no—
656C22×C4—44no—
657C22×C4—44no—
658C22×C4—44no—
659C22×C4—44no—
660C22×C4—44no—
661C22×C4C2×C3×D412yes—
662C22×C4C2×C3×D412yes—
663C22×C4C2×C3×D412yes—
664C22×C4C2×C3×D412yes—
665C22×C4C2×C3×D412yes—
666C22×C4C3×#4112yes—
667C22×C4C3×#4112yes—
668C22×C4C3×#4112yes—
669C22×C4C3×#4112yes—
670C22×C4C3×#4112yes—
671C22×C4C3×#4112yes—
672C22×C4C3×#4112yes—
673C4⋊C4—28no—
674C4⋊C4—44no—
675C4⋊C4—44no—
676C4⋊C4—44no—
677C22⋊C4—28no—
678C22⋊C4—28no—
679C22⋊C4—28no—
680C22⋊C4—44no—
681C22⋊C4—44no—
682C22⋊C4—44no—
683C42—44no—
684C42—44no—
685C22×C3—24no—
686C22×C3—24no—
687C22×C3—24no—
688C22×C3—42no—
689C22×C3—42no—
690C22×C3—42no—
691C22×C3—42no—
692C22×C3—42no—
693C22×C3—42no—
694C22×C3—42no—
695C22×C3—42no—
696C22×C3—42no—
697C22×C3—42no—
698C22×C3—42no—
699C22×C3—42no—
700C22×C3C2×#12311yescharacteristic
701C22×C3C2×#12311yescharacteristic
702C22×C3#52511yescharacteristic
703C22×C3#52511yescharacteristic
704C22×C3#52511yescharacteristic
705C22×C3#52911yescharacteristic
706C22×C3#52911yescharacteristic
707C22×C3#52911yescharacteristic
708C22×C3#52911yescharacteristic
709C22×C3#52911yescharacteristic
710C22×C3#52911yescharacteristic
711C22×C3#52911yescharacteristic
712C22×C3#53211yescharacteristic
713C22×C3#53811yescharacteristic
714C22×C3#53911yescharacteristic
715C22×C3#53911yescharacteristic
716C22×C3#53911yescharacteristic
717C22×C3#54111yescharacteristic
718C22×C3#54211yescharacteristic
719C22×C3D4211yescharacteristic
720C22×C3#54611yescharacteristic
721C22×C3#54611yescharacteristic
722C22×C3#54711yescharacteristic
723C22×C3#54711yescharacteristic
724C22×C3#54811yescharacteristic
725C22×C3#54811yescharacteristic
726C22×C3#55111yescharacteristic
727C22×C3#55111yescharacteristic
728C22×C3#55111yescharacteristic
729C22×C3#55211yescharacteristic
730C22×C3#55211yescharacteristic
731C22×C3#55311yescharacteristic
732C22×C3#55311yescharacteristic
733C22×C3#55611yescharacteristic
734C22×C3#55611yescharacteristic
735C3×C4—24no—
736C3×C4—42no—
737C3×C4—42no—
738C3×C4—42no—
739C3×C4—42no—
740C3×C4—42no—
741C3×C4—42no—
742C3×C4—42no—
743C3×C4—42no—
744C3×C4—42no—
745C3×C4—81no—
746C3×C4—81no—
747C3×C4—81no—
748C3×C4—81no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23C3×#12314yes—
784C23C22×C3×D411yescharacteristic
785C23C22×C3×D411yescharacteristic
786C23C2×C3×#4111yescharacteristic
787C23C2×C3×#4111yescharacteristic
788C23C2×C3×#4111yescharacteristic
789C23C2×C3×#4111yescharacteristic
790C23C2×C3×#4111yescharacteristic
791C23C2×C3×#4111yescharacteristic
792C23C2×C3×#4111yescharacteristic
793C23C2×C3×#4111yescharacteristic
794C23C2×C3×#4111yescharacteristic
795C23C3×H(5,𝔽2)11yescharacteristic
796C23C3×H(5,𝔽2)11yescharacteristic
797C23C3×2−1+411yescharacteristic
798C23C3×2−1+411yescharacteristic
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—416no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4C3×#12314yes—
898C2×C3—44no—
899C2×C3#239511yescharacteristic
900C2×C3#241811yescharacteristic
901C2×C3#241911yescharacteristic
902C2×C3#242111yescharacteristic
903C2×C3#244311yescharacteristic
904C2×C3#246011yescharacteristic
905C2×C3#246111yescharacteristic
906C2×C3#246611yescharacteristic
907C2×C3#247811yescharacteristic
908C2×C3#252311yescharacteristic
909C2×C3#253011yescharacteristic
910C2×C3#256011yescharacteristic
911C2×C3#257611yescharacteristic
912C2×C3#265211yescharacteristic
913C2×C3#285311yescharacteristic
914C22—24no—
915C22—24no—
916C22—24no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22C2×C3×#12311yescharacteristic
930C22C2×C3×#12311yescharacteristic
931C22C3×#52511yescharacteristic
932C22C3×#52511yescharacteristic
933C22C3×#52511yescharacteristic
934C22C3×#52911yescharacteristic
935C22C3×#52911yescharacteristic
936C22C3×#52911yescharacteristic
937C22C3×#52911yescharacteristic
938C22C3×#52911yescharacteristic
939C22C3×#52911yescharacteristic
940C22C3×#52911yescharacteristic
941C22C3×#53211yescharacteristic
942C22C3×#53811yescharacteristic
943C22C3×#53911yescharacteristic
944C22C3×#53911yescharacteristic
945C22C3×#53911yescharacteristic
946C22C3×#54111yescharacteristic
947C22C3×#54211yescharacteristic
948C22C3×D4211yescharacteristic
949C22C3×#54611yescharacteristic
950C22C3×#54611yescharacteristic
951C22C3×#54711yescharacteristic
952C22C3×#54711yescharacteristic
953C22C3×#54811yescharacteristic
954C22C3×#54811yescharacteristic
955C22C3×#55111yescharacteristic
956C22C3×#55111yescharacteristic
957C22C3×#55111yescharacteristic
958C22C3×#55211yescharacteristic
959C22C3×#55211yescharacteristic
960C22C3×#55311yescharacteristic
961C22C3×#55311yescharacteristic
962C22C3×#55611yescharacteristic
963C22C3×#55611yescharacteristic
964C4—24no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—42no—
970C4—42no—
971C4—42no—
972C4—42no—
973C4—42no—
974C4—81no—
975C4—81no—
976C4—81no—
977C4—81no—
978C3#1474011yescharacteristic, direct product factor, Sylow
979C2—44no—
980C2C3×#239511yescharacteristic
981C2C3×#241811yescharacteristic
982C2C3×#241911yescharacteristic
983C2C3×#242111yescharacteristic
984C2C3×#244311yescharacteristic
985C2C3×#246011yescharacteristic
986C2C3×#246111yescharacteristic
987C2C3×#246611yescharacteristic
988C2C3×#247811yescharacteristic
989C2C3×#252311yescharacteristic
990C2C3×#253011yescharacteristic
991C2C3×#256011yescharacteristic
992C2C3×#257611yescharacteristic
993C2C3×#265211yescharacteristic
994C2C3×#285311yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
prime radicalC25×C3C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#387C2semidirect
5. C3×#1445C2semidirect
6. C3×#1443C2semidirect
7. C3×#1442C2semidirect
8. C3×#1441C2semidirect
12. C3×#1436C2semidirect
13. C3×#1436C2semidirect
14. C3×#1434C2semidirect
16. #14740C3direct (N × H)
57. C2×#387C2×C3semidirect
60. #1445C2×C3semidirect
61. #1443C2×C3semidirect
62. #1442C2×C3semidirect
63. #1441C2×C3semidirect
67. #1436C2×C3semidirect
68. #1436C2×C3semidirect
69. #1434C2×C3semidirect
978. C3#14740direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3972
C2×C3×#3872
C2×C3×#3852
C2×C3×C4×C22⋊C42
C3×#14452
C3×#14432
C3×#14422
C3×#14412
C3×#14402
C3×#14392
C3×#14362
C3×#14342
C3×C22⋊#952
#147403