Finite Group Databasebeta

← C3×#25531 #10644138

Subgroups — C3×#25531 #10644138

Order 768.

1374 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#547C211yesmaximal, characteristic
2C2×C3×#483C211yesmaximal, characteristic, complemented
3C2×C3×#465C211yesmaximal, characteristic, complemented
4C3×#2417C211yesmaximal, characteristic, complemented
5C3×#2058C211yesmaximal, characteristic, complemented
6C3×#2034C211yesmaximal, characteristic, complemented
7C3×#2024C211yesmaximal, characteristic, complemented
8C3×#2000C211yesmaximal, characteristic, complemented
9C3×#1877C211yesmaximal, characteristic, complemented
10C3×#1874C211yesmaximal, characteristic, complemented
11C3×#1872C211yesmaximal, characteristic, complemented
12C3×#1869C211yesmaximal, characteristic, complemented
13C3×#1864C211yesmaximal, characteristic, complemented
14C3×#1853C211yesmaximal, characteristic, complemented
15C2×C3×#340C211yesmaximal, characteristic, complemented
16#25531C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41—21no—
18C22×C3×SD16C2211yescharacteristic
19C23×C3×C8C2211yescharacteristic
20C3×#547—24no—
21C3×#547—24no—
22C2×C3×C4⋊Q8C2211yescharacteristic
23C2×C3×#123—21no—
24C2×C3×#123—21no—
25C2×C3×C22⋊Q8—21no—
26C2×C3×C22⋊Q8C2211yescharacteristic
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×#121C2211yescharacteristic
29C2×C3×#121C2211yescharacteristic
30C2×C3×C4×D4C2211yescharacteristic
31C2×C3×C4×D4C2211yescharacteristic
32C22×C3×C4⋊C4C2211yescharacteristic
33C22×C3×C4⋊C4C2211yescharacteristic
34C22×C3×C4⋊C4C2211yescharacteristic
35C3×#483—24no—
36C3×#465—24no—
37C2×C3×#106C2211yescharacteristic
38C2×C3×#106C2211yescharacteristic
39C2×C3×#106C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×C22⋊C8C2211yescharacteristic
47C2×C3×C22⋊C8C2211yescharacteristic
48C2×C3×C22⋊C8C2211yescharacteristic
49C3×#398—21no—
50C3×#396—21no—
51C3×#391C2211yescharacteristic
52C3×#389C2211yescharacteristic
53C3×#386—21no—
54C3×#380—21no—
55C3×#380C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#547C2×C311yescharacteristic
65C2×#483C2×C311yescharacteristic, complemented
66C2×#465C2×C311yescharacteristic, complemented
67#2417C2×C311yescharacteristic, complemented
68#2058C2×C311yescharacteristic, complemented
69#2034C2×C311yescharacteristic, complemented
70#2024C2×C311yescharacteristic, complemented
71#2000C2×C311yescharacteristic, complemented
72#1877C2×C311yescharacteristic, complemented
73#1874C2×C311yescharacteristic, complemented
74#1872C2×C311yescharacteristic, complemented
75#1869C2×C311yescharacteristic, complemented
76#1864C2×C311yescharacteristic, complemented
77#1853C2×C311yescharacteristic, complemented
78C2×#340C2×C311yescharacteristic, complemented
79C2×C3×#41—28no—
80C2×C3×#41—44no—
81C2×C3×#41—44no—
82C22×C3×Q8—21no—
83C22×C3×Q8C2311yescharacteristic
84C22×C3×D4—21no—
85C22×C3×D4—21no—
86C22×C3×D4D411yescharacteristic
87C22×C3×D4C2311yescharacteristic
88C23×C3×C4—21no—
89C23×C3×C4—21no—
90C23×C3×C4—21no—
91C23×C3×C4—21no—
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C2×C3×SD16—22no—
95C2×C3×SD16—22no—
96C2×C3×SD16—41no—
97C22×C3×C8—22no—
98C22×C3×C8—22no—
99C22×C3×C8—41no—
100C22×C3×C8C2311yescharacteristic
101C22×C3×C8C2311yescharacteristic
102C22×C3×C8C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C3×C4⋊Q8—22no—
105C3×C4⋊Q8—22no—
106C3×#123—28no—
107C3×#123—28no—
108C3×C22⋊Q8—28no—
109C3×C22⋊Q8—22no—
110C3×C22⋊Q8—22no—
111C3×C22⋊Q8—22no—
112C3×C22⋊Q8—41no—
113C3×#121—22no—
114C3×#121—22no—
115C3×#121—22no—
116C3×#121D414yes—
117C3×C4×D4—22no—
118C3×C4×D4—22no—
119C3×C4×D4—22no—
120C3×C4×D4—22no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—22no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4—22no—
126C2×C3×C4⋊C4—22no—
127C2×C3×C4⋊C4—22no—
128C2×C3×C4⋊C4—21no—
129C2×C3×C4⋊C4—21no—
130C2×C3×C4⋊C4—21no—
131C2×C3×C4⋊C4—21no—
132C2×C3×C4⋊C4—41no—
133C2×C3×C4⋊C4D411yescharacteristic
134C2×C3×C4⋊C4D414yes—
135C2×C3×C4⋊C4C2311yescharacteristic
136C2×C3×C4⋊C4C2311yescharacteristic
137C2×C3×C4⋊C4C2311yescharacteristic
138C2×C3×C4⋊C4C2311yescharacteristic
139C2×C3×C4⋊C4C2311yescharacteristic
140C2×C3×C4⋊C4C2311yescharacteristic
141C2×C3×C22⋊C4—21no—
142C2×C3×C22⋊C4—21no—
143C2×C3×C22⋊C4—21no—
144C2×C3×C22⋊C4—21no—
145C2×C3×C22⋊C4—21no—
146C2×C3×C22⋊C4—21no—
147C2×C3×C22⋊C4D411yescharacteristic
148C2×C3×C22⋊C4D411yescharacteristic
149C2×C3×C42C2311yescharacteristic
150C3×#106—22no—
151C3×#106—22no—
152C3×#106—22no—
153C3×#103—22no—
154C3×#103—22no—
155C3×#103—22no—
156C3×#102—22no—
157C3×#102—22no—
158C3×#102—41no—
159C3×C22⋊C8—22no—
160C3×C22⋊C8—22no—
161C3×C22⋊C8—41no—
162C3×#95—21no—
163C3×#95—21no—
164C3×#95—21no—
165C3×#95—21no—
166C22×#41—21no—
167C22×SD16C22×C311yescharacteristic
168C23×C8C22×C311yescharacteristic
169#547—24no—
170#547—24no—
171C2×C4⋊Q8C22×C311yescharacteristic
172C2×#123—21no—
173C2×#123—21no—
174C2×C22⋊Q8—21no—
175C2×C22⋊Q8C22×C311yescharacteristic
176C2×C22⋊Q8C22×C311yescharacteristic
177C2×#121C22×C311yescharacteristic
178C2×#121C22×C311yescharacteristic
179C2×C4×D4C22×C311yescharacteristic
180C2×C4×D4C22×C311yescharacteristic
181C22×C4⋊C4C22×C311yescharacteristic
182C22×C4⋊C4C22×C311yescharacteristic
183C22×C4⋊C4C22×C311yescharacteristic
184#483—24no—
185#465—24no—
186C2×#106C22×C311yescharacteristic
187C2×#106C22×C311yescharacteristic
188C2×#106C22×C311yescharacteristic
189C2×#103C22×C311yescharacteristic
190C2×#103C22×C311yescharacteristic
191C2×#103C22×C311yescharacteristic
192C2×#102C22×C311yescharacteristic
193C2×#102C22×C311yescharacteristic
194C2×#102C22×C311yescharacteristic
195C2×C22⋊C8C22×C311yescharacteristic
196C2×C22⋊C8C22×C311yescharacteristic
197C2×C22⋊C8C22×C311yescharacteristic
198#398—21no—
199#396—21no—
200#391C22×C311yescharacteristic
201#389C22×C311yescharacteristic
202#386—21no—
203#380—21no—
204#380C22×C311yescharacteristic
205#340C22×C311yescharacteristic
206#340C22×C311yescharacteristic
207#340C22×C311yescharacteristic
208#340C22×C311yescharacteristic
209#340C22×C311yescharacteristic
210#340C22×C311yescharacteristic
211#336C22×C311yescharacteristic
212#336C22×C311yescharacteristic
213C24×C3—21no—
214C24×C3C2×D411yescharacteristic
215C24×C3C2×D411yescharacteristic
216C3×#41—432no—
217C2×C3×Q8—24no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—42no—
225C2×C3×Q8—42no—
226C2×C3×D4—22no—
227C2×C3×D4—22no—
228C2×C3×D4—24no—
229C2×C3×D4—24no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—42no—
236C2×C3×D4—42no—
237C2×C3×D4—42no—
238C2×C3×D4—42no—
239C2×C3×D4SD1614yescomplemented
240C2×C3×D4C2×D412yes—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—24no—
246C22×C3×C4—24no—
247C22×C3×C4—24no—
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—42no—
262C22×C3×C4—42no—
263C22×C3×C4—42no—
264C22×C3×C4—42no—
265C22×C3×C4—42no—
266C22×C3×C4—42no—
267C22×C3×C4—42no—
268C22×C3×C4—42no—
269C22×C3×C4—81no—
270C22×C3×C4C2×D411yescharacteristic
271C22×C3×C4C2×D411yescharacteristic
272C22×C3×C4C2×D411yescharacteristic
273C22×C3×C4C2×D412yes—
274C22×C3×C4C2×D412yes—
275C22×C3×C4C2×D411yescharacteristic
276C22×C3×C4C2411yescharacteristic
277C3×SD16—44no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C2×C3×C8—21no—
288C2×C3×C8—21no—
289C2×C3×C8—44no—
290C2×C3×C8#4112yescomplemented
291C3×C4⋊C4—24no—
292C3×C4⋊C4—24no—
293C3×C4⋊C4—24no—
294C3×C4⋊C4—22no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—42no—
304C3×C4⋊C4—42no—
305C3×C4⋊C4—42no—
306C3×C4⋊C4—81no—
307C3×C4⋊C4C2×D412yes—
308C3×C4⋊C4C2×D412yes—
309C3×C4⋊C4C2×D412yes—
310C3×C4⋊C4#4112yescomplemented
311C3×C22⋊C4—24no—
312C3×C22⋊C4—24no—
313C3×C22⋊C4—22no—
314C3×C22⋊C4—24no—
315C3×C22⋊C4—22no—
316C3×C22⋊C4—42no—
317C3×C22⋊C4—42no—
318C3×C22⋊C4—81no—
319C3×C42—21no—
320C3×C42—21no—
321C2×#41—28no—
322C2×#41—44no—
323C2×#41—44no—
324C22×Q8—21no—
325C22×Q8C23×C311yescharacteristic
326C22×D4—21no—
327C22×D4—21no—
328C22×D4C3×D411yescharacteristic
329C22×D4C23×C311yescharacteristic
330C23×C4—21no—
331C23×C4—21no—
332C23×C4—21no—
333C23×C4—21no—
334C23×C4C23×C311yescharacteristic
335C23×C4C23×C311yescharacteristic
336C2×SD16—22no—
337C2×SD16—22no—
338C2×SD16—41no—
339C22×C8—22no—
340C22×C8—22no—
341C22×C8—41no—
342C22×C8C23×C311yescharacteristic
343C22×C8C23×C311yescharacteristic
344C22×C8C23×C311yescharacteristic
345C22×C8C23×C311yescharacteristic
346C4⋊Q8—22no—
347C4⋊Q8—22no—
348#123—28no—
349#123—28no—
350C22⋊Q8—28no—
351C22⋊Q8—22no—
352C22⋊Q8—22no—
353C22⋊Q8—22no—
354C22⋊Q8—41no—
355#121—22no—
356#121—22no—
357#121—22no—
358#121C3×D414yes—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—22no—
362C4×D4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—41no—
375C2×C4⋊C4C3×D411yescharacteristic
376C2×C4⋊C4C3×D414yes—
377C2×C4⋊C4C23×C311yescharacteristic
378C2×C4⋊C4C23×C311yescharacteristic
379C2×C4⋊C4C23×C311yescharacteristic
380C2×C4⋊C4C23×C311yescharacteristic
381C2×C4⋊C4C23×C311yescharacteristic
382C2×C4⋊C4C23×C311yescharacteristic
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4C3×D411yescharacteristic
390C2×C22⋊C4C3×D411yescharacteristic
391C2×C42C23×C311yescharacteristic
392#106—22no—
393#106—22no—
394#106—22no—
395#103—22no—
396#103—22no—
397#103—22no—
398#102—22no—
399#102—22no—
400#102—41no—
401C22⋊C8—22no—
402C22⋊C8—22no—
403C22⋊C8—41no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—22no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3#12012yes—
426C23×C3C2×SD1612yes—
427C23×C3C2×SD1612yes—
428C23×C3AGL(1,ℤ/8)12yes—
429C23×C3C22×D411yescharacteristic
430C3×Q8—48no—
431C3×Q8—41no—
432C3×Q8—41no—
433C3×Q8—41no—
434C3×Q8—41no—
435C3×D4—28no—
436C3×D4—22no—
437C3×D4—22no—
438C3×D4—48no—
439C3×D4—48no—
440C3×D4—41no—
441C3×D4—41no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—48no—
461C2×C3×C4—48no—
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—48no—
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—84no—
485C2×C3×C4#12012yes—
486C2×C3×C4C2×SD1612yes—
487C2×C3×C4C22×D411yescharacteristic
488C2×C3×C4C22×D411yescharacteristic
489C2×C3×C4C2×#4111yescharacteristic
490C2×C3×C4C2×#4111yescharacteristic
491C2×C3×C4H(5,𝔽2)11yescharacteristic
492C2×C3×C42−1+411yescharacteristic
493C3×C8—22no—
494C3×C8—41no—
495C3×C8—41no—
496C3×C8—41no—
497C24—21no—
498C24C2×C3×D411yescharacteristic
499C24C2×C3×D411yescharacteristic
500#41—432no—
501C2×Q8—24no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—24no—
513C2×D4—24no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4C3×SD1614yescomplemented
524C2×D4C2×C3×D412yes—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
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—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—81no—
554C22×C4C2×C3×D411yescharacteristic
555C22×C4C2×C3×D411yescharacteristic
556C22×C4C2×C3×D411yescharacteristic
557C22×C4C2×C3×D412yes—
558C22×C4C2×C3×D412yes—
559C22×C4C2×C3×D411yescharacteristic
560C22×C4C24×C311yescharacteristic
561SD16—44no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—44no—
574C2×C8C3×#4112yescomplemented
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—22no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—81no—
591C4⋊C4C2×C3×D412yes—
592C4⋊C4C2×C3×D412yes—
593C4⋊C4C2×C3×D412yes—
594C4⋊C4C3×#4112yescomplemented
595C22⋊C4—24no—
596C22⋊C4—24no—
597C22⋊C4—22no—
598C22⋊C4—24no—
599C22⋊C4—22no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—81no—
603C42—21no—
604C42—21no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—22no—
610C22×C3—22no—
611C22×C3—22no—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—42no—
619C22×C3—42no—
620C22×C3—42no—
621C22×C3—81no—
622C22×C3—81no—
623C22×C3—81no—
624C22×C3—81no—
625C22×C3#45014yes—
626C22×C3C2×#12011yescharacteristic
627C22×C3#54611yescharacteristic
628C22×C3#54711yescharacteristic
629C22×C3C22×SD1611yescharacteristic
630C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
631C22×C3#57711yescharacteristic
632C22×C3#57811yescharacteristic
633C3×C4—22no—
634C3×C4—22no—
635C3×C4—41no—
636C3×C4—42no—
637C3×C4—42no—
638C3×C4—42no—
639C3×C4—41no—
640C3×C4—42no—
641C3×C4—81no—
642C3×C4—81no—
643C3×C4—81no—
644C3×C4#53211yescharacteristic
645C3×C4#53711yescharacteristic
646C3×C4#54611yescharacteristic
647C3×C4#54711yescharacteristic
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23C3×#12012yes—
666C23C2×C3×SD1612yes—
667C23C2×C3×SD1612yes—
668C23C3×AGL(1,ℤ/8)12yes—
669C23C22×C3×D411yescharacteristic
670Q8—48no—
671Q8—41no—
672Q8—41no—
673Q8—41no—
674Q8—41no—
675D4—28no—
676D4—22no—
677D4—22no—
678D4—48no—
679D4—48no—
680D4—41no—
681D4—41no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—48no—
701C2×C4—48no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—48no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—84no—
725C2×C4C3×#12012yes—
726C2×C4C2×C3×SD1612yes—
727C2×C4C22×C3×D411yescharacteristic
728C2×C4C22×C3×D411yescharacteristic
729C2×C4C2×C3×#4111yescharacteristic
730C2×C4C2×C3×#4111yescharacteristic
731C2×C4C3×H(5,𝔽2)11yescharacteristic
732C2×C4C3×2−1+411yescharacteristic
733C8—22no—
734C8—41no—
735C8—41no—
736C8—41no—
737C2×C3—24no—
738C2×C3—42no—
739C2×C3—82no—
740C2×C3#243011yescharacteristic
741C2×C3C2×#45011yescharacteristic
742C2×C3#301311yescharacteristic
743C2×C3#329811yescharacteristic
744C2×C3#330611yescharacteristic
745C2×C3#333511yescharacteristic
746C2×C3#334311yescharacteristic
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22C3×#45014yes—
768C22C2×C3×#12011yescharacteristic
769C22C3×#54611yescharacteristic
770C22C3×#54711yescharacteristic
771C22C22×C3×SD1611yescharacteristic
772C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
773C22C3×#57711yescharacteristic
774C22C3×#57811yescharacteristic
775C4—22no—
776C4—22no—
777C4—41no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—41no—
782C4—42no—
783C4—81no—
784C4—81no—
785C4—81no—
786C4C3×#53211yescharacteristic
787C4C3×#53711yescharacteristic
788C4C3×#54611yescharacteristic
789C4C3×#54711yescharacteristic
790C3#2553111yescharacteristic, direct product factor, Sylow
791C2—24no—
792C2—42no—
793C2—82no—
794C2C3×#243011yescharacteristic
795C2C2×C3×#45011yescharacteristic
796C2C3×#301311yescharacteristic
797C2C3×#329811yescharacteristic
798C2C3×#330611yescharacteristic
799C2C3×#333511yescharacteristic
800C2C3×#334311yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#547C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#483C2semidirect
3. C2×C3×#465C2semidirect
4. C3×#2417C2semidirect
5. C3×#2058C2semidirect
6. C3×#2034C2semidirect
7. C3×#2024C2semidirect
8. C3×#2000C2semidirect
9. C3×#1877C2semidirect
10. C3×#1874C2semidirect
11. C3×#1872C2semidirect
12. C3×#1869C2semidirect
13. C3×#1864C2semidirect
14. C3×#1853C2semidirect
15. C2×C3×#340C2semidirect
16. #25531C3direct (N × H)
65. C2×#483C2×C3semidirect
66. C2×#465C2×C3semidirect
67. #2417C2×C3semidirect
68. #2058C2×C3semidirect
69. #2034C2×C3semidirect
70. #2024C2×C3semidirect
71. #2000C2×C3semidirect
72. #1877C2×C3semidirect
73. #1874C2×C3semidirect
74. #1872C2×C3semidirect
75. #1869C2×C3semidirect
76. #1864C2×C3semidirect
77. #1853C2×C3semidirect
78. C2×#340C2×C3semidirect
239. C2×C3×D4SD16semidirect
290. C2×C3×C8#41semidirect
310. C3×C4⋊C4#41semidirect
523. C2×D4C3×SD16semidirect
574. C2×C8C3×#41semidirect
594. C4⋊C4C3×#41semidirect
790. C3#25531direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5472
C2×C3×#4832
C2×C3×#4652
C3×#24172
C3×#20582
C3×#20342
C3×#20242
C3×#20002
C3×#18772
C3×#18742
C3×#18722
C3×#18692
C3×#18642
C3×#18532
C2×C3×#3402
#255313