Finite Group Databasebeta

← C3×#14832 #10633439

Subgroups — C3×#14832 #10633439

Order 768.

1478 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#400C211yesmaximal, characteristic, complemented
2C2×C3×C4×C22⋊C4C211yesmaximal, characteristic
3C3×#1445C211yesmaximal, characteristic, complemented
4C3×#1443C211yesmaximal, characteristic, complemented
5C3×#1442C211yesmaximal, characteristic, complemented
6C3×#1439C211yesmaximal, characteristic
7C3×#1439C211yesmaximal, characteristic
8C3×#1439C211yesmaximal, characteristic
9C3×#1439C211yesmaximal, characteristic
10C3×#1436C211yesmaximal, characteristic, complemented
11C3×#1436C211yesmaximal, characteristic, complemented
12C3×C4⋊#95C211yesmaximal, characteristic, complemented
13C3×#1434C211yesmaximal, characteristic, complemented
14C3×C22⋊#95C211yesmaximal, characteristic
15C3×C22⋊#95C211yesmaximal, characteristic
16#14832C311yesmaximal, 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×#400—24no—
31C3×C4×C22⋊C4—24no—
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×#400C2×C311yescharacteristic, complemented
55C2×C4×C22⋊C4C2×C311yescharacteristic
56#1445C2×C311yescharacteristic, complemented
57#1443C2×C311yescharacteristic, complemented
58#1442C2×C311yescharacteristic, complemented
59#1439C2×C311yescharacteristic
60#1439C2×C311yescharacteristic
61#1439C2×C311yescharacteristic
62#1439C2×C311yescharacteristic
63#1436C2×C311yescharacteristic, complemented
64#1436C2×C311yescharacteristic, complemented
65C4⋊#95C2×C311yescharacteristic, complemented
66#1434C2×C311yescharacteristic, complemented
67C22⋊#95C2×C311yescharacteristic
68C22⋊#95C2×C311yescharacteristic
69C25×C3C2311yescharacteristic
70C23×C3×C4—22no—
71C23×C3×C4—22no—
72C23×C3×C4—22no—
73C23×C3×C4—22no—
74C23×C3×C4—22no—
75C23×C3×C4—41no—
76C23×C3×C4—41no—
77C23×C3×C4C2311yescharacteristic
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
91C2×C3×C4⋊C4—22no—
92C2×C3×C4⋊C4—22no—
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—41no—
99C2×C3×C4⋊C4—41no—
100C2×C3×C4⋊C4—41no—
101C2×C3×C4⋊C4—41no—
102C2×C3×C4⋊C4—41no—
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—22no—
112C2×C3×C22⋊C4—22no—
113C2×C3×C22⋊C4—22no—
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⋊C4—41no—
120C2×C3×C22⋊C4Q814yes—
121C2×C3×C42—22no—
122C2×C3×C42—22no—
123C2×C3×C42—22no—
124C2×C3×C42—22no—
125C2×C3×C42—41no—
126C2×C3×C42—41no—
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—22no—
139C3×#95—41no—
140C3×#95—41no—
141C3×#95—41no—
142C3×#95—41no—
143C3×#95—41no—
144C3×#95—41no—
145C3×#95—41no—
146C3×#95—41no—
147C3×#95—41no—
148C3×#95D414yes—
149C24×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×C42C22×C311yescharacteristic
161C22×C42C22×C311yescharacteristic
162#400—24no—
163C4×C22⋊C4—24no—
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
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×C3C2×Q812yes—
199C24×C3#4112yes—
200C24×C3#4112yes—
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—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—44no—
290C22×C3×C4—44no—
291C22×C3×C4—44no—
292C22×C3×C4—44no—
293C22×C3×C4—44no—
294C22×C3×C4—44no—
295C22×C3×C4C2×D412yes—
296C22×C3×C4C2×D412yes—
297C22×C3×C4C2×D412yes—
298C22×C3×C4C2×Q812yes—
299C22×C3×C4C2×Q812yes—
300C22×C3×C4#4112yes—
301C22×C3×C4#4112yes—
302C22×C3×C4#4112yes—
303C22×C3×C4#4112yes—
304C22×C3×C4#4112yes—
305C22×C3×C4#4112yes—
306C22×C3×C4#4112yes—
307C3×C4⋊C4—44no—
308C3×C4⋊C4—44no—
309C3×C4⋊C4—44no—
310C3×C4⋊C4—44no—
311C3×C22⋊C4—28no—
312C3×C22⋊C4—28no—
313C3×C22⋊C4—44no—
314C3×C22⋊C4—44no—
315C3×C22⋊C4—44no—
316C3×C22⋊C4—44no—
317C3×C42—44no—
318C3×C42—44no—
319C25C23×C311yescharacteristic
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—41no—
326C23×C4—41no—
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
337C23×C4C23×C311yescharacteristic
338C23×C4C23×C311yescharacteristic
339C23×C4C23×C311yescharacteristic
340C23×C4C23×C311yescharacteristic
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—41no—
349C2×C4⋊C4—41no—
350C2×C4⋊C4—41no—
351C2×C4⋊C4—41no—
352C2×C4⋊C4—41no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
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—41no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4—41no—
367C2×C22⋊C4—41no—
368C2×C22⋊C4—41no—
369C2×C22⋊C4—41no—
370C2×C22⋊C4C3×Q814yes—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—41no—
376C2×C42—41no—
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—22no—
389#95—41no—
390#95—41no—
391#95—41no—
392#95—41no—
393#95—41no—
394#95—41no—
395#95—41no—
396#95—41no—
397#95—41no—
398#95C3×D414yes—
399C23×C3—22no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—22no—
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—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×C3—41no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3#12514yes—
434C23×C3C22×D411yescharacteristic
435C23×C3C22×Q811yescharacteristic
436C23×C3C2×#4111yescharacteristic
437C23×C3C2×#4111yescharacteristic
438C23×C3C2×#4111yescharacteristic
439C23×C3C2×#4111yescharacteristic
440C23×C3C2×#4111yescharacteristic
441C23×C3C2×#4111yescharacteristic
442C23×C3C2×#4111yescharacteristic
443C23×C3C2×#4111yescharacteristic
444C23×C3C2×#4111yescharacteristic
445C23×C3H(5,𝔽2)11yescharacteristic
446C23×C3H(5,𝔽2)11yescharacteristic
447C23×C3H(5,𝔽2)11yescharacteristic
448C23×C3H(5,𝔽2)11yescharacteristic
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—416no—
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×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×C4C22⋊Q814yes—
547C2×C3×C4#12614yes—
548C24—21no—
549C24—21no—
550C24—21no—
551C24—21no—
552C24—21no—
553C24—21no—
554C24—21no—
555C24—21no—
556C24—21no—
557C24—21no—
558C24—21no—
559C24—21no—
560C24C2×C3×Q812yes—
561C24C3×#4112yes—
562C24C3×#4112yes—
563C24C24×C311yescharacteristic
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—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—44no—
652C22×C4—44no—
653C22×C4—44no—
654C22×C4—44no—
655C22×C4—44no—
656C22×C4—44no—
657C22×C4C2×C3×D412yes—
658C22×C4C2×C3×D412yes—
659C22×C4C2×C3×D412yes—
660C22×C4C2×C3×Q812yes—
661C22×C4C2×C3×Q812yes—
662C22×C4C3×#4112yes—
663C22×C4C3×#4112yes—
664C22×C4C3×#4112yes—
665C22×C4C3×#4112yes—
666C22×C4C3×#4112yes—
667C22×C4C3×#4112yes—
668C22×C4C3×#4112yes—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—44no—
672C4⋊C4—44no—
673C22⋊C4—28no—
674C22⋊C4—28no—
675C22⋊C4—44no—
676C22⋊C4—44no—
677C22⋊C4—44no—
678C22⋊C4—44no—
679C42—44no—
680C42—44no—
681C22×C3—24no—
682C22×C3—24no—
683C22×C3—24no—
684C22×C3—42no—
685C22×C3—42no—
686C22×C3—42no—
687C22×C3—42no—
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×C3C2×C22⋊Q811yescharacteristic
697C22×C3#52511yescharacteristic
698C22×C3#52511yescharacteristic
699C22×C3C2×#12511yescharacteristic
700C22×C3C2×#12611yescharacteristic
701C22×C3#52911yescharacteristic
702C22×C3#52911yescharacteristic
703C22×C3#52911yescharacteristic
704C22×C3#52911yescharacteristic
705C22×C3#52911yescharacteristic
706C22×C3#52911yescharacteristic
707C22×C3#52911yescharacteristic
708C22×C3#53311yescharacteristic
709C22×C3#53811yescharacteristic
710C22×C3#53811yescharacteristic
711C22×C3#53811yescharacteristic
712C22×C3#53811yescharacteristic
713C22×C3#54011yescharacteristic
714C22×C3#54011yescharacteristic
715C22×C3#54611yescharacteristic
716C22×C3#54611yescharacteristic
717C22×C3#54611yescharacteristic
718C22×C3#55011yescharacteristic
719C22×C3#55111yescharacteristic
720C22×C3#55111yescharacteristic
721C22×C3#55111yescharacteristic
722C22×C3#55111yescharacteristic
723C22×C3#55111yescharacteristic
724C22×C3#55311yescharacteristic
725C22×C3#55411yescharacteristic
726C22×C3#55411yescharacteristic
727C22×C3#55411yescharacteristic
728C22×C3#55411yescharacteristic
729C22×C3#55511yescharacteristic
730C22×C3#55911yescharacteristic
731C3×C4—24no—
732C3×C4—24no—
733C3×C4—42no—
734C3×C4—42no—
735C3×C4—42no—
736C3×C4—42no—
737C3×C4—42no—
738C3×C4—42no—
739C3×C4—81no—
740C3×C4—81no—
741C3×C4—81no—
742C3×C4—81no—
743C3×C4—81no—
744C3×C4—81no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
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—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23C3×#12514yes—
780C23C22×C3×D411yescharacteristic
781C23C22×C3×Q811yescharacteristic
782C23C2×C3×#4111yescharacteristic
783C23C2×C3×#4111yescharacteristic
784C23C2×C3×#4111yescharacteristic
785C23C2×C3×#4111yescharacteristic
786C23C2×C3×#4111yescharacteristic
787C23C2×C3×#4111yescharacteristic
788C23C2×C3×#4111yescharacteristic
789C23C2×C3×#4111yescharacteristic
790C23C2×C3×#4111yescharacteristic
791C23C3×H(5,𝔽2)11yescharacteristic
792C23C3×H(5,𝔽2)11yescharacteristic
793C23C3×H(5,𝔽2)11yescharacteristic
794C23C3×H(5,𝔽2)11yescharacteristic
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—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—416no—
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×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×C4C3×C22⋊Q814yes—
893C2×C4C3×#12614yes—
894C2×C3—44no—
895C2×C3#240111yescharacteristic
896C2×C3#245011yescharacteristic
897C2×C3#245411yescharacteristic
898C2×C3#245911yescharacteristic
899C2×C3#246711yescharacteristic
900C2×C3#247111yescharacteristic
901C2×C3#248011yescharacteristic
902C2×C3#249711yescharacteristic
903C2×C3#250511yescharacteristic
904C2×C3#250511yescharacteristic
905C2×C3#251611yescharacteristic
906C2×C3#257211yescharacteristic
907C2×C3#258911yescharacteristic
908C2×C3#264811yescharacteristic
909C2×C3#285111yescharacteristic
910C22—24no—
911C22—24no—
912C22—24no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22C2×C3×C22⋊Q811yescharacteristic
926C22C3×#52511yescharacteristic
927C22C3×#52511yescharacteristic
928C22C2×C3×#12511yescharacteristic
929C22C2×C3×#12611yescharacteristic
930C22C3×#52911yescharacteristic
931C22C3×#52911yescharacteristic
932C22C3×#52911yescharacteristic
933C22C3×#52911yescharacteristic
934C22C3×#52911yescharacteristic
935C22C3×#52911yescharacteristic
936C22C3×#52911yescharacteristic
937C22C3×#53311yescharacteristic
938C22C3×#53811yescharacteristic
939C22C3×#53811yescharacteristic
940C22C3×#53811yescharacteristic
941C22C3×#53811yescharacteristic
942C22C3×#54011yescharacteristic
943C22C3×#54011yescharacteristic
944C22C3×#54611yescharacteristic
945C22C3×#54611yescharacteristic
946C22C3×#54611yescharacteristic
947C22C3×#55011yescharacteristic
948C22C3×#55111yescharacteristic
949C22C3×#55111yescharacteristic
950C22C3×#55111yescharacteristic
951C22C3×#55111yescharacteristic
952C22C3×#55111yescharacteristic
953C22C3×#55311yescharacteristic
954C22C3×#55411yescharacteristic
955C22C3×#55411yescharacteristic
956C22C3×#55411yescharacteristic
957C22C3×#55411yescharacteristic
958C22C3×#55511yescharacteristic
959C22C3×#55911yescharacteristic
960C4—24no—
961C4—24no—
962C4—42no—
963C4—42no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—81no—
969C4—81no—
970C4—81no—
971C4—81no—
972C4—81no—
973C4—81no—
974C3#1483211yescharacteristic, direct product factor, Sylow
975C2—44no—
976C2C3×#240111yescharacteristic
977C2C3×#245011yescharacteristic
978C2C3×#245411yescharacteristic
979C2C3×#245911yescharacteristic
980C2C3×#246711yescharacteristic
981C2C3×#247111yescharacteristic
982C2C3×#248011yescharacteristic
983C2C3×#249711yescharacteristic
984C2C3×#250511yescharacteristic
985C2C3×#250511yescharacteristic
986C2C3×#251611yescharacteristic
987C2C3×#257211yescharacteristic
988C2C3×#258911yescharacteristic
989C2C3×#264811yescharacteristic
990C2C3×#285111yescharacteristic
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
1. C2×C3×#400C2semidirect
3. C3×#1445C2semidirect
4. C3×#1443C2semidirect
5. C3×#1442C2semidirect
10. C3×#1436C2semidirect
11. C3×#1436C2semidirect
12. C3×C4⋊#95C2semidirect
13. C3×#1434C2semidirect
16. #14832C3direct (N × H)
54. C2×#400C2×C3semidirect
56. #1445C2×C3semidirect
57. #1443C2×C3semidirect
58. #1442C2×C3semidirect
63. #1436C2×C3semidirect
64. #1436C2×C3semidirect
65. C4⋊#95C2×C3semidirect
66. #1434C2×C3semidirect
974. C3#14832direct (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×C4×C22⋊C42
C3×#14452
C3×#14432
C3×#14422
C3×#14392
C3×#14362
C3×C4⋊#952
C3×#14342
C3×C22⋊#952
#148323