Finite Group Databasebeta

← C3×#25539 #10644146

Subgroups — C3×#25539 #10644146

Order 768.

1190 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#552C211yesmaximal, characteristic, complemented
2C2×C3×#480C211yesmaximal, characteristic, complemented
3C2×C3×#465C211yesmaximal, characteristic, complemented
4C3×#2416C211yesmaximal, characteristic
5C3×#2059C211yesmaximal, characteristic, complemented
6C3×#2036C211yesmaximal, characteristic, complemented
7C3×#2025C211yesmaximal, characteristic, complemented
8C3×#2000C211yesmaximal, characteristic, complemented
9C3×#1880C211yesmaximal, characteristic, complemented
10C3×#1875C211yesmaximal, characteristic, complemented
11C3×#1872C211yesmaximal, characteristic, complemented
12C3×#1869C211yesmaximal, characteristic, complemented
13C3×#1863C211yesmaximal, characteristic, complemented
14C3×#1854C211yesmaximal, characteristic, complemented
15C2×C3×#340C211yesmaximal, characteristic, complemented
16#25539C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×SD16C2211yescharacteristic
18C23×C3×C8C2211yescharacteristic
19C3×#552—24no—
20C3×#552—24no—
21C2×C3×#126—21no—
22C2×C3×#125—21no—
23C2×C3×#125C2211yescharacteristic
24C2×C3×#123—21no—
25C2×C3×C22⋊Q8C2211yescharacteristic
26C2×C3×C22⋊Q8C2211yescharacteristic
27C2×C3×#121—21no—
28C2×C3×#121C2211yescharacteristic
29C2×C3×#121C2211yescharacteristic
30C2×C3×C4×Q8C2211yescharacteristic
31C2×C3×C4×D4C2211yescharacteristic
32C2×C3×#117—21no—
33C2×C3×#117C2211yescharacteristic
34C22×C3×C4⋊C4C2211yescharacteristic
35C22×C3×C4⋊C4C2211yescharacteristic
36C3×#480—24no—
37C3×#465—24no—
38C2×C3×#107C2211yescharacteristic
39C2×C3×#107C2211yescharacteristic
40C2×C3×#106C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#103C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×C22⋊C8C2211yescharacteristic
48C2×C3×C22⋊C8C2211yescharacteristic
49C2×C3×C22⋊C8C2211yescharacteristic
50C3×#396—21no—
51C3×#394—21no—
52C3×#390C2211yescharacteristic
53C3×#389C2211yescharacteristic
54C3×#386—21no—
55C3×#380C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#552C2×C311yescharacteristic, complemented
65C2×#480C2×C311yescharacteristic, complemented
66C2×#465C2×C311yescharacteristic, complemented
67#2416C2×C311yescharacteristic
68#2059C2×C311yescharacteristic, complemented
69#2036C2×C311yescharacteristic, complemented
70#2025C2×C311yescharacteristic, complemented
71#2000C2×C311yescharacteristic, complemented
72#1880C2×C311yescharacteristic, complemented
73#1875C2×C311yescharacteristic, complemented
74#1872C2×C311yescharacteristic, complemented
75#1869C2×C311yescharacteristic, complemented
76#1863C2×C311yescharacteristic, complemented
77#1854C2×C311yescharacteristic, complemented
78C2×#340C2×C311yescharacteristic, complemented
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4—21no—
82C22×C3×D4D411yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4—21no—
85C23×C3×C4—21no—
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C2×C3×SD16—22no—
89C2×C3×SD16—22no—
90C2×C3×SD16—41no—
91C22×C3×C8—22no—
92C22×C3×C8—22no—
93C22×C3×C8—41no—
94C22×C3×C8C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C3×#126—28no—
99C3×#125—28no—
100C3×#125—22no—
101C3×#125—22no—
102C3×#123—28no—
103C3×C22⋊Q8—22no—
104C3×C22⋊Q8—22no—
105C3×C22⋊Q8—22no—
106C3×C22⋊Q8D414yescomplemented
107C3×#121—22no—
108C3×#121—22no—
109C3×#121—22no—
110C3×#121—41no—
111C3×#121—44no—
112C3×C4×Q8—22no—
113C3×C4×Q8—22no—
114C3×C4×D4—22no—
115C3×C4×D4—22no—
116C3×#117—28no—
117C3×#117—22no—
118C3×#117—22no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—22no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4—22no—
127C2×C3×C4⋊C4—21no—
128C2×C3×C4⋊C4—21no—
129C2×C3×C4⋊C4—41no—
130C2×C3×C4⋊C4D411yescharacteristic
131C2×C3×C4⋊C4D414yescomplemented
132C2×C3×C4⋊C4C2311yescharacteristic
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C4⋊C4C2311yescharacteristic
135C2×C3×C4⋊C4C2311yescharacteristic
136C2×C3×C4⋊C4C2311yescharacteristic
137C2×C3×C4⋊C4C2311yescharacteristic
138C2×C3×C22⋊C4—21no—
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4—21no—
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⋊C4D411yescharacteristic
147C2×C3×C22⋊C4D411yescharacteristic
148C2×C3×C42—21no—
149C2×C3×C42—21no—
150C2×C3×C42C2311yescharacteristic
151C3×#107—22no—
152C3×#107—22no—
153C3×#106—22no—
154C3×#103—22no—
155C3×#103—22no—
156C3×#103—41no—
157C3×#102—22no—
158C3×#102—22no—
159C3×#102—22no—
160C3×C22⋊C8—22no—
161C3×C22⋊C8—22no—
162C3×C22⋊C8—41no—
163C3×#95—21no—
164C3×#95—21no—
165C22×SD16C22×C311yescharacteristic
166C23×C8C22×C311yescharacteristic
167#552—24no—
168#552—24no—
169C2×#126—21no—
170C2×#125—21no—
171C2×#125C22×C311yescharacteristic
172C2×#123—21no—
173C2×C22⋊Q8C22×C311yescharacteristic
174C2×C22⋊Q8C22×C311yescharacteristic
175C2×#121—21no—
176C2×#121C22×C311yescharacteristic
177C2×#121C22×C311yescharacteristic
178C2×C4×Q8C22×C311yescharacteristic
179C2×C4×D4C22×C311yescharacteristic
180C2×#117—21no—
181C2×#117C22×C311yescharacteristic
182C22×C4⋊C4C22×C311yescharacteristic
183C22×C4⋊C4C22×C311yescharacteristic
184#480—24no—
185#465—24no—
186C2×#107C22×C311yescharacteristic
187C2×#107C22×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#396—21no—
199#394—21no—
200#390C22×C311yescharacteristic
201#389C22×C311yescharacteristic
202#386—21no—
203#380C22×C311yescharacteristic
204#340C22×C311yescharacteristic
205#340C22×C311yescharacteristic
206#340C22×C311yescharacteristic
207#340C22×C311yescharacteristic
208#340C22×C311yescharacteristic
209#340C22×C311yescharacteristic
210#336C22×C311yescharacteristic
211#336C22×C311yescharacteristic
212C24×C3—21no—
213C24×C3C2×D411yescharacteristic
214C24×C3C2×D411yescharacteristic
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8C2×D412yes—
221C2×C3×D4—22no—
222C2×C3×D4—22no—
223C2×C3×D4—22no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—42no—
231C2×C3×D4—42no—
232C2×C3×D4—42no—
233C2×C3×D4—42no—
234C2×C3×D4—42no—
235C2×C3×D4—81no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—24no—
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—42no—
255C22×C3×C4—42no—
256C22×C3×C4—42no—
257C22×C3×C4—42no—
258C22×C3×C4—81no—
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2×D411yescharacteristic
261C22×C3×C4C2×D411yescharacteristic
262C22×C3×C4C2×D411yescharacteristic
263C22×C3×C4C2×D412yes—
264C22×C3×C4C2×D412yes—
265C22×C3×C4C2411yescharacteristic
266C3×SD16—44no—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8—21no—
272C2×C3×C8—21no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—44no—
279C2×C3×C8#4112yes—
280C3×C4⋊C4—24no—
281C3×C4⋊C4—24no—
282C3×C4⋊C4—24no—
283C3×C4⋊C4—24no—
284C3×C4⋊C4—24no—
285C3×C4⋊C4—24no—
286C3×C4⋊C4—22no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4—21no—
292C3×C4⋊C4—21no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—42no—
296C3×C4⋊C4—42no—
297C3×C4⋊C4C2×D412yes—
298C3×C4⋊C4C2×D412yes—
299C3×C4⋊C4C2×D412yes—
300C3×C4⋊C4#4112yes—
301C3×C22⋊C4—24no—
302C3×C22⋊C4—24no—
303C3×C22⋊C4—24no—
304C3×C22⋊C4—22no—
305C3×C22⋊C4—22no—
306C3×C22⋊C4—42no—
307C3×C22⋊C4—42no—
308C3×C22⋊C4—42no—
309C3×C22⋊C4—42no—
310C3×C22⋊C4—81no—
311C3×C42—24no—
312C3×C42—24no—
313C3×C42—21no—
314C3×C42—21no—
315C22×Q8C23×C311yescharacteristic
316C22×D4—21no—
317C22×D4—21no—
318C22×D4C3×D411yescharacteristic
319C22×D4C23×C311yescharacteristic
320C23×C4—21no—
321C23×C4—21no—
322C23×C4C23×C311yescharacteristic
323C23×C4C23×C311yescharacteristic
324C2×SD16—22no—
325C2×SD16—22no—
326C2×SD16—41no—
327C22×C8—22no—
328C22×C8—22no—
329C22×C8—41no—
330C22×C8C23×C311yescharacteristic
331C22×C8C23×C311yescharacteristic
332C22×C8C23×C311yescharacteristic
333C22×C8C23×C311yescharacteristic
334#126—28no—
335#125—28no—
336#125—22no—
337#125—22no—
338#123—28no—
339C22⋊Q8—22no—
340C22⋊Q8—22no—
341C22⋊Q8—22no—
342C22⋊Q8C3×D414yescomplemented
343#121—22no—
344#121—22no—
345#121—22no—
346#121—41no—
347#121—44no—
348C4×Q8—22no—
349C4×Q8—22no—
350C4×D4—22no—
351C4×D4—22no—
352#117—28no—
353#117—22no—
354#117—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—41no—
366C2×C4⋊C4C3×D411yescharacteristic
367C2×C4⋊C4C3×D414yescomplemented
368C2×C4⋊C4C23×C311yescharacteristic
369C2×C4⋊C4C23×C311yescharacteristic
370C2×C4⋊C4C23×C311yescharacteristic
371C2×C4⋊C4C23×C311yescharacteristic
372C2×C4⋊C4C23×C311yescharacteristic
373C2×C4⋊C4C23×C311yescharacteristic
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4C3×D411yescharacteristic
383C2×C22⋊C4C3×D411yescharacteristic
384C2×C42—21no—
385C2×C42—21no—
386C2×C42C23×C311yescharacteristic
387#107—22no—
388#107—22no—
389#106—22no—
390#103—22no—
391#103—22no—
392#103—41no—
393#102—22no—
394#102—22no—
395#102—22no—
396C22⋊C8—22no—
397C22⋊C8—22no—
398C22⋊C8—41no—
399#95—21no—
400#95—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3#12012yes—
420C23×C3#13512yes—
421C23×C3AGL(1,ℤ/8)12yes—
422C23×C3C22×D411yescharacteristic
423C3×Q8—22no—
424C3×Q8—22no—
425C3×Q8—41no—
426C3×Q8—41no—
427C3×D4—44no—
428C3×D4—41no—
429C3×D4—41no—
430C3×D4—41no—
431C3×D4—41no—
432C3×D4—84no—
433C3×D4—84no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—21no—
446C2×C3×C4—22no—
447C2×C3×C4—21no—
448C2×C3×C4—22no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
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—48no—
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—84no—
476C2×C3×C4#12012yes—
477C2×C3×C4C22×D411yescharacteristic
478C2×C3×C4C22×D411yescharacteristic
479C2×C3×C4C2×#4111yescharacteristic
480C2×C3×C4C2×#4111yescharacteristic
481C2×C3×C4H(5,𝔽2)11yescharacteristic
482C2×C3×C42−1+411yescharacteristic
483C3×C8—22no—
484C3×C8—41no—
485C3×C8—41no—
486C3×C8—41no—
487C24—21no—
488C24C2×C3×D411yescharacteristic
489C24C2×C3×D411yescharacteristic
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8C2×C3×D412yes—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—81no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—24no—
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—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—81no—
534C22×C4C2×C3×D411yescharacteristic
535C22×C4C2×C3×D411yescharacteristic
536C22×C4C2×C3×D411yescharacteristic
537C22×C4C2×C3×D411yescharacteristic
538C22×C4C2×C3×D412yes—
539C22×C4C2×C3×D412yes—
540C22×C4C24×C311yescharacteristic
541SD16—44no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—44no—
554C2×C8C3×#4112yes—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—22no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4C2×C3×D412yes—
573C4⋊C4C2×C3×D412yes—
574C4⋊C4C2×C3×D412yes—
575C4⋊C4C3×#4112yes—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—22no—
580C22⋊C4—22no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—81no—
586C42—24no—
587C42—24no—
588C42—21no—
589C42—21no—
590C22×C3—22no—
591C22×C3—22no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—41no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—81no—
604C22×C3—81no—
605C22×C3—81no—
606C22×C3—81no—
607C22×C3—81no—
608C22×C3—81no—
609C22×C3—81no—
610C22×C3#44914yes—
611C22×C3C2×#12011yescharacteristic
612C22×C3#54611yescharacteristic
613C22×C3#54711yescharacteristic
614C22×C3C2×#13511yescharacteristic
615C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
616C22×C3#57711yescharacteristic
617C22×C3#57811yescharacteristic
618C3×C4—22no—
619C3×C4—41no—
620C3×C4—42no—
621C3×C4—41no—
622C3×C4—42no—
623C3×C4—42no—
624C3×C4—41no—
625C3×C4—42no—
626C3×C4—42no—
627C3×C4—81no—
628C3×C4—81no—
629C3×C4#53211yescharacteristic
630C3×C4#53711yescharacteristic
631C3×C4#54611yescharacteristic
632C3×C4#54711yescharacteristic
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23C3×#12012yes—
652C23C3×#13512yes—
653C23C3×AGL(1,ℤ/8)12yes—
654C23C22×C3×D411yescharacteristic
655Q8—22no—
656Q8—22no—
657Q8—41no—
658Q8—41no—
659D4—44no—
660D4—41no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—84no—
665D4—84no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—48no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—84no—
708C2×C4C3×#12012yes—
709C2×C4C22×C3×D411yescharacteristic
710C2×C4C22×C3×D411yescharacteristic
711C2×C4C2×C3×#4111yescharacteristic
712C2×C4C2×C3×#4111yescharacteristic
713C2×C4C3×H(5,𝔽2)11yescharacteristic
714C2×C4C3×2−1+411yescharacteristic
715C8—22no—
716C8—41no—
717C8—41no—
718C8—41no—
719C2×C3—24no—
720C2×C3—81no—
721C2×C3—161no—
722C2×C3#243011yescharacteristic
723C2×C3C2×#44911yescharacteristic
724C2×C3#301311yescharacteristic
725C2×C3#330011yescharacteristic
726C2×C3#331011yescharacteristic
727C2×C3#333711yescharacteristic
728C2×C3#334311yescharacteristic
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22C3×#44914yes—
750C22C2×C3×#12011yescharacteristic
751C22C3×#54611yescharacteristic
752C22C3×#54711yescharacteristic
753C22C2×C3×#13511yescharacteristic
754C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
755C22C3×#57711yescharacteristic
756C22C3×#57811yescharacteristic
757C4—22no—
758C4—41no—
759C4—42no—
760C4—41no—
761C4—42no—
762C4—42no—
763C4—41no—
764C4—42no—
765C4—42no—
766C4—81no—
767C4—81no—
768C4C3×#53211yescharacteristic
769C4C3×#53711yescharacteristic
770C4C3×#54611yescharacteristic
771C4C3×#54711yescharacteristic
772C3#2553911yescharacteristic, direct product factor, Sylow
773C2—24no—
774C2—81no—
775C2—161no—
776C2C3×#243011yescharacteristic
777C2C2×C3×#44911yescharacteristic
778C2C3×#301311yescharacteristic
779C2C3×#330011yescharacteristic
780C2C3×#331011yescharacteristic
781C2C3×#333711yescharacteristic
782C2C3×#334311yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#2416C2
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
1. C2×C3×#552C2semidirect
2. C2×C3×#480C2semidirect
3. C2×C3×#465C2semidirect
5. C3×#2059C2semidirect
6. C3×#2036C2semidirect
7. C3×#2025C2semidirect
8. C3×#2000C2semidirect
9. C3×#1880C2semidirect
10. C3×#1875C2semidirect
11. C3×#1872C2semidirect
12. C3×#1869C2semidirect
13. C3×#1863C2semidirect
14. C3×#1854C2semidirect
15. C2×C3×#340C2semidirect
16. #25539C3direct (N × H)
64. C2×#552C2×C3semidirect
65. C2×#480C2×C3semidirect
66. C2×#465C2×C3semidirect
68. #2059C2×C3semidirect
69. #2036C2×C3semidirect
70. #2025C2×C3semidirect
71. #2000C2×C3semidirect
72. #1880C2×C3semidirect
73. #1875C2×C3semidirect
74. #1872C2×C3semidirect
75. #1869C2×C3semidirect
76. #1863C2×C3semidirect
77. #1854C2×C3semidirect
78. C2×#340C2×C3semidirect
106. C3×C22⋊Q8D4semidirect
131. C2×C3×C4⋊C4D4semidirect
342. C22⋊Q8C3×D4semidirect
367. C2×C4⋊C4C3×D4semidirect
772. C3#25539direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5522
C2×C3×#4802
C2×C3×#4652
C3×#24162
C3×#20592
C3×#20362
C3×#20252
C3×#20002
C3×#18802
C3×#18752
C3×#18722
C3×#18692
C3×#18632
C3×#18542
C2×C3×#3402
#255393