Finite Group Databasebeta

← C3×#15095 #10633702

Subgroups — C3×#15095 #10633702

Order 768.

1378 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#388C211yesmaximal, characteristic
2C2×C3×C4×C4⋊C4C211yesmaximal, characteristic, complemented
3C3×#1445C211yesmaximal, characteristic, complemented
4C3×#1444C211yesmaximal, characteristic, complemented
5C3×#1442C211yesmaximal, characteristic, complemented
6C3×#1442C211yesmaximal, characteristic, complemented
7C3×#1439C211yesmaximal, characteristic
8C3×#1439C211yesmaximal, characteristic
9C3×#1439C211yesmaximal, characteristic
10C3×#1439C211yesmaximal, characteristic
11C3×#1437C211yesmaximal, characteristic
12C3×#1437C211yesmaximal, characteristic
13C3×#1436C211yesmaximal, characteristic, complemented
14C3×#1436C211yesmaximal, characteristic, complemented
15C3×#1434C211yesmaximal, characteristic, complemented
16#15095C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×C4⋊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×C22⋊C4C2211yescharacteristic
29C22×C3×C42C2211yescharacteristic
30C22×C3×C42C2211yescharacteristic
31C22×C3×C42C2211yescharacteristic
32C3×#388—24no—
33C3×C4×C4⋊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×#388C2×C311yescharacteristic
55C2×C4×C4⋊C4C2×C311yescharacteristic, complemented
56#1445C2×C311yescharacteristic, complemented
57#1444C2×C311yescharacteristic, complemented
58#1442C2×C311yescharacteristic, complemented
59#1442C2×C311yescharacteristic, complemented
60#1439C2×C311yescharacteristic
61#1439C2×C311yescharacteristic
62#1439C2×C311yescharacteristic
63#1439C2×C311yescharacteristic
64#1437C2×C311yescharacteristic
65#1437C2×C311yescharacteristic
66#1436C2×C311yescharacteristic, complemented
67#1436C2×C311yescharacteristic, complemented
68#1434C2×C311yescharacteristic, complemented
69C25×C3C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C2×C3×C4⋊C4—22no—
85C2×C3×C4⋊C4—22no—
86C2×C3×C4⋊C4—22no—
87C2×C3×C4⋊C4—22no—
88C2×C3×C4⋊C4—22no—
89C2×C3×C4⋊C4—22no—
90C2×C3×C4⋊C4—22no—
91C2×C3×C4⋊C4—22no—
92C2×C3×C4⋊C4—22no—
93C2×C3×C4⋊C4—22no—
94C2×C3×C4⋊C4—41no—
95C2×C3×C4⋊C4—41no—
96C2×C3×C4⋊C4—41no—
97C2×C3×C4⋊C4—41no—
98C2×C3×C4⋊C4—41no—
99C2×C3×C22⋊C4—22no—
100C2×C3×C22⋊C4—22no—
101C2×C3×C22⋊C4—22no—
102C2×C3×C22⋊C4—22no—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—22no—
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—41no—
112C2×C3×C22⋊C4—41no—
113C2×C3×C22⋊C4—41no—
114C2×C3×C22⋊C4—41no—
115C2×C3×C22⋊C4—41no—
116C2×C3×C22⋊C4—41no—
117C2×C3×C22⋊C4—41no—
118C2×C3×C22⋊C4—41no—
119C2×C3×C22⋊C4Q814yes—
120C2×C3×C42—22no—
121C2×C3×C42—22no—
122C2×C3×C42—22no—
123C2×C3×C42—22no—
124C2×C3×C42—41no—
125C2×C3×C42—41no—
126C2×C3×C42—41no—
127C2×C3×C42—41no—
128C2×C3×C42D414yes—
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—41no—
143C3×#95—41no—
144C3×#95—41no—
145C3×#95—41no—
146C3×#95—41no—
147C3×#95—41no—
148C3×#95—41no—
149C22×C4⋊C4C22×C311yescharacteristic
150C22×C4⋊C4C22×C311yescharacteristic
151C22×C4⋊C4C22×C311yescharacteristic
152C22×C4⋊C4C22×C311yescharacteristic
153C22×C4⋊C4C22×C311yescharacteristic
154C22×C22⋊C4C22×C311yescharacteristic
155C22×C22⋊C4C22×C311yescharacteristic
156C22×C22⋊C4C22×C311yescharacteristic
157C22×C22⋊C4C22×C311yescharacteristic
158C22×C22⋊C4C22×C311yescharacteristic
159C22×C22⋊C4C22×C311yescharacteristic
160C22×C22⋊C4C22×C311yescharacteristic
161C22×C42C22×C311yescharacteristic
162C22×C42C22×C311yescharacteristic
163C22×C42C22×C311yescharacteristic
164#388—24no—
165C4×C4⋊C4—24no—
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
182C2×#95C22×C311yescharacteristic
183C2×#95C22×C311yescharacteristic
184C2×#95C22×C311yescharacteristic
185C2×#95C22×C311yescharacteristic
186C24×C3—21no—
187C24×C3—21no—
188C24×C3—21no—
189C24×C3—21no—
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×C3C2×Q812yes—
201C24×C3C2411yescharacteristic
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×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4C2×D412yes—
287C22×C3×C4C2×D412yes—
288C22×C3×C4C2×D412yes—
289C22×C3×C4C2×Q812yes—
290C22×C3×C4C2×Q812yes—
291C22×C3×C4#4112yes—
292C22×C3×C4#4112yes—
293C22×C3×C4#4112yes—
294C22×C3×C4#4112yes—
295C22×C3×C4#4112yes—
296C22×C3×C4#4112yes—
297C22×C3×C4#4112yes—
298C22×C3×C4#4112yes—
299C22×C3×C4#4112yes—
300C3×C4⋊C4—28no—
301C3×C4⋊C4—28no—
302C3×C4⋊C4—44no—
303C3×C4⋊C4—44no—
304C3×C4⋊C4—44no—
305C3×C22⋊C4—28no—
306C3×C22⋊C4—44no—
307C3×C22⋊C4—44no—
308C3×C22⋊C4—44no—
309C3×C22⋊C4—44no—
310C3×C22⋊C4—44no—
311C3×C22⋊C4—44no—
312C3×C42—28no—
313C3×C42—44no—
314C3×C42—44no—
315C25C23×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
325C23×C4C23×C311yescharacteristic
326C23×C4C23×C311yescharacteristic
327C23×C4C23×C311yescharacteristic
328C23×C4C23×C311yescharacteristic
329C23×C4C23×C311yescharacteristic
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—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—41no—
341C2×C4⋊C4—41no—
342C2×C4⋊C4—41no—
343C2×C4⋊C4—41no—
344C2×C4⋊C4—41no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—41no—
358C2×C22⋊C4—41no—
359C2×C22⋊C4—41no—
360C2×C22⋊C4—41no—
361C2×C22⋊C4—41no—
362C2×C22⋊C4—41no—
363C2×C22⋊C4—41no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4C3×Q814yes—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—41no—
371C2×C42—41no—
372C2×C42—41no—
373C2×C42—41no—
374C2×C42C3×D414yes—
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—22no—
386#95—22no—
387#95—22no—
388#95—41no—
389#95—41no—
390#95—41no—
391#95—41no—
392#95—41no—
393#95—41no—
394#95—41no—
395C23×C3—22no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—41no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
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×C3C22×D411yescharacteristic
431C23×C3C22×Q811yescharacteristic
432C23×C3C2×#4111yescharacteristic
433C23×C3C2×#4111yescharacteristic
434C23×C3C2×#4111yescharacteristic
435C23×C3C2×#4111yescharacteristic
436C23×C3C2×#4111yescharacteristic
437C23×C3C2×#4111yescharacteristic
438C23×C3C2×#4111yescharacteristic
439C23×C3C2×#4111yescharacteristic
440C23×C3C2×#4111yescharacteristic
441C23×C3H(5,𝔽2)11yescharacteristic
442C23×C3H(5,𝔽2)11yescharacteristic
443C23×C3H(5,𝔽2)11yescharacteristic
444C23×C3H(5,𝔽2)11yescharacteristic
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—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—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×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×C4C22⋊Q814yes—
542C2×C3×C4#12614yes—
543C24—21no—
544C24—21no—
545C24—21no—
546C24—21no—
547C24—21no—
548C24—21no—
549C24—21no—
550C24—21no—
551C24—21no—
552C24—21no—
553C24—21no—
554C24—21no—
555C24—21no—
556C24—21no—
557C24C2×C3×Q812yes—
558C24C24×C311yescharacteristic
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×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×C4C2×C3×D412yes—
644C22×C4C2×C3×D412yes—
645C22×C4C2×C3×D412yes—
646C22×C4C2×C3×Q812yes—
647C22×C4C2×C3×Q812yes—
648C22×C4C3×#4112yes—
649C22×C4C3×#4112yes—
650C22×C4C3×#4112yes—
651C22×C4C3×#4112yes—
652C22×C4C3×#4112yes—
653C22×C4C3×#4112yes—
654C22×C4C3×#4112yes—
655C22×C4C3×#4112yes—
656C22×C4C3×#4112yes—
657C4⋊C4—28no—
658C4⋊C4—28no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C4⋊C4—44no—
662C22⋊C4—28no—
663C22⋊C4—44no—
664C22⋊C4—44no—
665C22⋊C4—44no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C22⋊C4—44no—
669C42—28no—
670C42—44no—
671C42—44no—
672C22×C3—42no—
673C22×C3—42no—
674C22×C3—42no—
675C22×C3—42no—
676C22×C3—42no—
677C22×C3—42no—
678C22×C3—42no—
679C22×C3—81no—
680C22×C3—81no—
681C22×C3—81no—
682C22×C3—81no—
683C22×C3—81no—
684C22×C3—81no—
685C22×C3—81no—
686C22×C3—81no—
687C22×C3C2×C22⋊Q811yescharacteristic
688C22×C3#52511yescharacteristic
689C22×C3#52511yescharacteristic
690C22×C3#52511yescharacteristic
691C22×C3C2×#12611yescharacteristic
692C22×C3#52911yescharacteristic
693C22×C3#52911yescharacteristic
694C22×C3#52911yescharacteristic
695C22×C3#52911yescharacteristic
696C22×C3#52911yescharacteristic
697C22×C3#53211yescharacteristic
698C22×C3#53311yescharacteristic
699C22×C3#53311yescharacteristic
700C22×C3#53411yescharacteristic
701C22×C3#53511yescharacteristic
702C22×C3#53811yescharacteristic
703C22×C3#53811yescharacteristic
704C22×C3#54011yescharacteristic
705C22×C3#54011yescharacteristic
706C22×C3#55111yescharacteristic
707C22×C3#55111yescharacteristic
708C22×C3#55111yescharacteristic
709C22×C3#55311yescharacteristic
710C22×C3#55311yescharacteristic
711C22×C3#55311yescharacteristic
712C22×C3#55311yescharacteristic
713C22×C3#55411yescharacteristic
714C22×C3#55411yescharacteristic
715C22×C3#55411yescharacteristic
716C22×C3#55411yescharacteristic
717C22×C3#55511yescharacteristic
718C22×C3#55511yescharacteristic
719C22×C3#55911yescharacteristic
720C22×C3#55911yescharacteristic
721C22×C3#55911yescharacteristic
722C3×C4—24no—
723C3×C4—24no—
724C3×C4—42no—
725C3×C4—42no—
726C3×C4—42no—
727C3×C4—42no—
728C3×C4—42no—
729C3×C4—42no—
730C3×C4—42no—
731C3×C4—42no—
732C3×C4—81no—
733C3×C4—81no—
734C3×C4—81no—
735C3×C4—81no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23C22×C3×D411yescharacteristic
772C23C22×C3×Q811yescharacteristic
773C23C2×C3×#4111yescharacteristic
774C23C2×C3×#4111yescharacteristic
775C23C2×C3×#4111yescharacteristic
776C23C2×C3×#4111yescharacteristic
777C23C2×C3×#4111yescharacteristic
778C23C2×C3×#4111yescharacteristic
779C23C2×C3×#4111yescharacteristic
780C23C2×C3×#4111yescharacteristic
781C23C2×C3×#4111yescharacteristic
782C23C3×H(5,𝔽2)11yescharacteristic
783C23C3×H(5,𝔽2)11yescharacteristic
784C23C3×H(5,𝔽2)11yescharacteristic
785C23C3×H(5,𝔽2)11yescharacteristic
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
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—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
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×C4C3×C22⋊Q814yes—
883C2×C4C3×#12614yes—
884C2×C3—82no—
885C2×C3#239611yescharacteristic
886C2×C3#249711yescharacteristic
887C2×C3#251311yescharacteristic
888C2×C3#251611yescharacteristic
889C2×C3#252211yescharacteristic
890C2×C3#257411yescharacteristic
891C2×C3#257911yescharacteristic
892C2×C3#258011yescharacteristic
893C2×C3#258911yescharacteristic
894C2×C3#259311yescharacteristic
895C2×C3#259711yescharacteristic
896C2×C3#260211yescharacteristic
897C2×C3#261011yescharacteristic
898C2×C3#263511yescharacteristic
899C2×C3#285211yescharacteristic
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22C2×C3×C22⋊Q811yescharacteristic
916C22C3×#52511yescharacteristic
917C22C3×#52511yescharacteristic
918C22C3×#52511yescharacteristic
919C22C2×C3×#12611yescharacteristic
920C22C3×#52911yescharacteristic
921C22C3×#52911yescharacteristic
922C22C3×#52911yescharacteristic
923C22C3×#52911yescharacteristic
924C22C3×#52911yescharacteristic
925C22C3×#53211yescharacteristic
926C22C3×#53311yescharacteristic
927C22C3×#53311yescharacteristic
928C22C3×#53411yescharacteristic
929C22C3×#53511yescharacteristic
930C22C3×#53811yescharacteristic
931C22C3×#53811yescharacteristic
932C22C3×#54011yescharacteristic
933C22C3×#54011yescharacteristic
934C22C3×#55111yescharacteristic
935C22C3×#55111yescharacteristic
936C22C3×#55111yescharacteristic
937C22C3×#55311yescharacteristic
938C22C3×#55311yescharacteristic
939C22C3×#55311yescharacteristic
940C22C3×#55311yescharacteristic
941C22C3×#55411yescharacteristic
942C22C3×#55411yescharacteristic
943C22C3×#55411yescharacteristic
944C22C3×#55411yescharacteristic
945C22C3×#55511yescharacteristic
946C22C3×#55511yescharacteristic
947C22C3×#55911yescharacteristic
948C22C3×#55911yescharacteristic
949C22C3×#55911yescharacteristic
950C4—24no—
951C4—24no—
952C4—42no—
953C4—42no—
954C4—42no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—42no—
959C4—42no—
960C4—81no—
961C4—81no—
962C4—81no—
963C4—81no—
964C3#1509511yescharacteristic, direct product factor, Sylow
965C2—82no—
966C2C3×#239611yescharacteristic
967C2C3×#249711yescharacteristic
968C2C3×#251311yescharacteristic
969C2C3×#251611yescharacteristic
970C2C3×#252211yescharacteristic
971C2C3×#257411yescharacteristic
972C2C3×#257911yescharacteristic
973C2C3×#258011yescharacteristic
974C2C3×#258911yescharacteristic
975C2C3×#259311yescharacteristic
976C2C3×#259711yescharacteristic
977C2C3×#260211yescharacteristic
978C2C3×#261011yescharacteristic
979C2C3×#263511yescharacteristic
980C2C3×#285211yescharacteristic
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×C4×C4⋊C4C2semidirect
3. C3×#1445C2semidirect
4. C3×#1444C2semidirect
5. C3×#1442C2semidirect
6. C3×#1442C2semidirect
13. C3×#1436C2semidirect
14. C3×#1436C2semidirect
15. C3×#1434C2semidirect
16. #15095C3direct (N × H)
55. C2×C4×C4⋊C4C2×C3semidirect
56. #1445C2×C3semidirect
57. #1444C2×C3semidirect
58. #1442C2×C3semidirect
59. #1442C2×C3semidirect
66. #1436C2×C3semidirect
67. #1436C2×C3semidirect
68. #1434C2×C3semidirect
964. C3#15095direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3882
C2×C3×C4×C4⋊C42
C3×#14452
C3×#14442
C3×#14422
C3×#14392
C3×#14372
C3×#14362
C3×#14342
#150953