Finite Group Databasebeta

← C3×#25533 #10644140

Subgroups — C3×#25533 #10644140

Order 768.

1444 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#547C211yesmaximal, characteristic, complemented
2C2×C3×#480C211yesmaximal, characteristic, complemented
3C2×C3×#466C211yesmaximal, characteristic, complemented
4C3×#2416C211yesmaximal, characteristic, complemented
5C3×#2057C211yesmaximal, characteristic, complemented
6C3×#2033C211yesmaximal, characteristic, complemented
7C3×#2023C211yesmaximal, characteristic, complemented
8C3×#1999C211yesmaximal, characteristic, complemented
9C3×#1879C211yesmaximal, characteristic, complemented
10C3×#1874C211yesmaximal, characteristic, complemented
11C3×#1874C211yesmaximal, characteristic, complemented
12C3×#1869C211yesmaximal, characteristic, complemented
13C3×#1862C211yesmaximal, characteristic, complemented
14C3×#1852C211yesmaximal, characteristic, complemented
15C2×C3×#340C211yesmaximal, characteristic, complemented
16#25533C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41—21no—
18C22×C3×D8C2211yescharacteristic
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×#121—21no—
27C2×C3×#121C2211yescharacteristic
28C2×C3×#121C2211yescharacteristic
29C2×C3×#121C2211yescharacteristic
30C2×C3×#121C2211yescharacteristic
31C2×C3×C4×D4C2211yescharacteristic
32C2×C3×C4×D4C2211yescharacteristic
33C22×C3×C4⋊C4C2211yescharacteristic
34C22×C3×C4⋊C4C2211yescharacteristic
35C22×C3×C4⋊C4C2211yescharacteristic
36C3×#480—24no—
37C3×#466—24no—
38C2×C3×#107C2211yescharacteristic
39C2×C3×#107C2211yescharacteristic
40C2×C3×#107C2211yescharacteristic
41C2×C3×#102C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
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×#547C2×C311yescharacteristic, complemented
65C2×#480C2×C311yescharacteristic, complemented
66C2×#466C2×C311yescharacteristic, complemented
67#2416C2×C311yescharacteristic, complemented
68#2057C2×C311yescharacteristic, complemented
69#2033C2×C311yescharacteristic, complemented
70#2023C2×C311yescharacteristic, complemented
71#1999C2×C311yescharacteristic, complemented
72#1879C2×C311yescharacteristic, complemented
73#1874C2×C311yescharacteristic, complemented
74#1874C2×C311yescharacteristic, complemented
75#1869C2×C311yescharacteristic, complemented
76#1862C2×C311yescharacteristic, complemented
77#1852C2×C311yescharacteristic, complemented
78C2×#340C2×C311yescharacteristic, complemented
79C2×C3×#41—28no—
80C2×C3×#41—44no—
81C2×C3×#41—44no—
82C22×C3×Q8—21no—
83C22×C3×D4—21no—
84C22×C3×D4—21no—
85C22×C3×D4—21no—
86C22×C3×D4—21no—
87C22×C3×D4D411yescharacteristic
88C22×C3×D4C2311yescharacteristic
89C22×C3×D4C2311yescharacteristic
90C23×C3×C4—21no—
91C23×C3×C4—21no—
92C23×C3×C4—21no—
93C23×C3×C4—21no—
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C2×C3×D8—22no—
97C2×C3×D8—22no—
98C2×C3×D8—41no—
99C22×C3×C8—22no—
100C22×C3×C8—22no—
101C22×C3×C8—41no—
102C22×C3×C8C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C22×C3×C8C2311yescharacteristic
105C22×C3×C8C2311yescharacteristic
106C3×C4⋊Q8—22no—
107C3×C4⋊Q8—22no—
108C3×#123—28no—
109C3×#123—28no—
110C3×C22⋊Q8—28no—
111C3×#121—22no—
112C3×#121—22no—
113C3×#121—22no—
114C3×#121—22no—
115C3×#121—22no—
116C3×#121—22no—
117C3×#121—41no—
118C3×#121—44no—
119C3×#121D414yescomplemented
120C3×C4×D4—22no—
121C3×C4×D4—22no—
122C3×C4×D4—22no—
123C3×C4×D4—22no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4—22no—
127C2×C3×C4⋊C4—21no—
128C2×C3×C4⋊C4—22no—
129C2×C3×C4⋊C4—22no—
130C2×C3×C4⋊C4—22no—
131C2×C3×C4⋊C4—21no—
132C2×C3×C4⋊C4—21no—
133C2×C3×C4⋊C4—41no—
134C2×C3×C4⋊C4D411yescharacteristic
135C2×C3×C4⋊C4D414yescomplemented
136C2×C3×C4⋊C4C2311yescharacteristic
137C2×C3×C4⋊C4C2311yescharacteristic
138C2×C3×C4⋊C4C2311yescharacteristic
139C2×C3×C4⋊C4C2311yescharacteristic
140C2×C3×C4⋊C4C2311yescharacteristic
141C2×C3×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
148C2×C3×C22⋊C4—21no—
149C2×C3×C22⋊C4—21no—
150C2×C3×C22⋊C4D411yescharacteristic
151C2×C3×C22⋊C4D411yescharacteristic
152C2×C3×C42C2311yescharacteristic
153C3×#107—22no—
154C3×#107—22no—
155C3×#107—22no—
156C3×#102—22no—
157C3×#102—22no—
158C3×#102—22no—
159C3×#102—22no—
160C3×#102—22no—
161C3×#102—41no—
162C3×C22⋊C8—22no—
163C3×C22⋊C8—22no—
164C3×C22⋊C8—41no—
165C3×#95—21no—
166C3×#95—21no—
167C22×#41—21no—
168C22×D8C22×C311yescharacteristic
169C23×C8C22×C311yescharacteristic
170#547—24no—
171#547—24no—
172C2×C4⋊Q8C22×C311yescharacteristic
173C2×#123—21no—
174C2×#123—21no—
175C2×C22⋊Q8—21no—
176C2×#121—21no—
177C2×#121C22×C311yescharacteristic
178C2×#121C22×C311yescharacteristic
179C2×#121C22×C311yescharacteristic
180C2×#121C22×C311yescharacteristic
181C2×C4×D4C22×C311yescharacteristic
182C2×C4×D4C22×C311yescharacteristic
183C22×C4⋊C4C22×C311yescharacteristic
184C22×C4⋊C4C22×C311yescharacteristic
185C22×C4⋊C4C22×C311yescharacteristic
186#480—24no—
187#466—24no—
188C2×#107C22×C311yescharacteristic
189C2×#107C22×C311yescharacteristic
190C2×#107C22×C311yescharacteristic
191C2×#102C22×C311yescharacteristic
192C2×#102C22×C311yescharacteristic
193C2×#102C22×C311yescharacteristic
194C2×#102C22×C311yescharacteristic
195C2×#102C22×C311yescharacteristic
196C2×#102C22×C311yescharacteristic
197C2×C22⋊C8C22×C311yescharacteristic
198C2×C22⋊C8C22×C311yescharacteristic
199C2×C22⋊C8C22×C311yescharacteristic
200#396—21no—
201#394—21no—
202#390C22×C311yescharacteristic
203#389C22×C311yescharacteristic
204#386—21no—
205#380C22×C311yescharacteristic
206#340C22×C311yescharacteristic
207#340C22×C311yescharacteristic
208#340C22×C311yescharacteristic
209#340C22×C311yescharacteristic
210#340C22×C311yescharacteristic
211#340C22×C311yescharacteristic
212#336C22×C311yescharacteristic
213#336C22×C311yescharacteristic
214C24×C3—21no—
215C24×C3—21no—
216C24×C3C2×D411yescharacteristic
217C24×C3C2×D411yescharacteristic
218C3×#41—432no—
219C2×C3×Q8—24no—
220C2×C3×Q8—42no—
221C2×C3×Q8—42no—
222C2×C3×D4—22no—
223C2×C3×D4—22no—
224C2×C3×D4—24no—
225C2×C3×D4—24no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—42no—
238C2×C3×D4—42no—
239C2×C3×D4—42no—
240C2×C3×D4—42no—
241C2×C3×D4—42no—
242C2×C3×D4—42no—
243C2×C3×D4—42no—
244C2×C3×D4—42no—
245C2×C3×D4—42no—
246C2×C3×D4—81no—
247C2×C3×D4D814yescomplemented
248C2×C3×D4C2×D412yes—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—24no—
254C22×C3×C4—24no—
255C22×C3×C4—24no—
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—42no—
269C22×C3×C4—42no—
270C22×C3×C4—42no—
271C22×C3×C4—42no—
272C22×C3×C4—42no—
273C22×C3×C4—42no—
274C22×C3×C4—42no—
275C22×C3×C4—42no—
276C22×C3×C4—81no—
277C22×C3×C4C2×D411yescharacteristic
278C22×C3×C4C2×D411yescharacteristic
279C22×C3×C4C2×D411yescharacteristic
280C22×C3×C4C2×D412yes—
281C22×C3×C4C2×D412yes—
282C22×C3×C4C2×D411yescharacteristic
283C22×C3×C4C2411yescharacteristic
284C3×D8—44no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C2×C3×C8—21no—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8—44no—
297C2×C3×C8#4112yescomplemented
298C3×C4⋊C4—24no—
299C3×C4⋊C4—24no—
300C3×C4⋊C4—24no—
301C3×C4⋊C4—22no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4—21no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—42no—
311C3×C4⋊C4—42no—
312C3×C4⋊C4C2×D412yes—
313C3×C4⋊C4C2×D412yes—
314C3×C4⋊C4C2×D412yes—
315C3×C4⋊C4#4112yescomplemented
316C3×C22⋊C4—24no—
317C3×C22⋊C4—24no—
318C3×C22⋊C4—22no—
319C3×C22⋊C4—24no—
320C3×C22⋊C4—22no—
321C3×C22⋊C4—42no—
322C3×C22⋊C4—42no—
323C3×C22⋊C4—42no—
324C3×C22⋊C4—42no—
325C3×C22⋊C4—81no—
326C3×C42—21no—
327C3×C42—21no—
328C2×#41—28no—
329C2×#41—44no—
330C2×#41—44no—
331C22×Q8—21no—
332C22×D4—21no—
333C22×D4—21no—
334C22×D4—21no—
335C22×D4—21no—
336C22×D4C3×D411yescharacteristic
337C22×D4C23×C311yescharacteristic
338C22×D4C23×C311yescharacteristic
339C23×C4—21no—
340C23×C4—21no—
341C23×C4—21no—
342C23×C4—21no—
343C23×C4C23×C311yescharacteristic
344C23×C4C23×C311yescharacteristic
345C2×D8—22no—
346C2×D8—22no—
347C2×D8—41no—
348C22×C8—22no—
349C22×C8—22no—
350C22×C8—41no—
351C22×C8C23×C311yescharacteristic
352C22×C8C23×C311yescharacteristic
353C22×C8C23×C311yescharacteristic
354C22×C8C23×C311yescharacteristic
355C4⋊Q8—22no—
356C4⋊Q8—22no—
357#123—28no—
358#123—28no—
359C22⋊Q8—28no—
360#121—22no—
361#121—22no—
362#121—22no—
363#121—22no—
364#121—22no—
365#121—22no—
366#121—41no—
367#121—44no—
368#121C3×D414yescomplemented
369C4×D4—22no—
370C4×D4—22no—
371C4×D4—22no—
372C4×D4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—41no—
383C2×C4⋊C4C3×D411yescharacteristic
384C2×C4⋊C4C3×D414yescomplemented
385C2×C4⋊C4C23×C311yescharacteristic
386C2×C4⋊C4C23×C311yescharacteristic
387C2×C4⋊C4C23×C311yescharacteristic
388C2×C4⋊C4C23×C311yescharacteristic
389C2×C4⋊C4C23×C311yescharacteristic
390C2×C4⋊C4C23×C311yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4C3×D411yescharacteristic
400C2×C22⋊C4C3×D411yescharacteristic
401C2×C42C23×C311yescharacteristic
402#107—22no—
403#107—22no—
404#107—22no—
405#102—22no—
406#102—22no—
407#102—22no—
408#102—22no—
409#102—22no—
410#102—41no—
411C22⋊C8—22no—
412C22⋊C8—22no—
413C22⋊C8—41no—
414#95—21no—
415#95—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—21no—
426C23×C3—22no—
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—41no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3#12012yes—
441C23×C3C2×D812yes—
442C23×C3C2×D812yes—
443C23×C3AGL(1,ℤ/8)12yes—
444C23×C3C22×D411yescharacteristic
445C3×Q8—48no—
446C3×D4—28no—
447C3×D4—22no—
448C3×D4—22no—
449C3×D4—48no—
450C3×D4—48no—
451C3×D4—41no—
452C3×D4—41no—
453C3×D4—41no—
454C3×D4—41no—
455C3×D4—41no—
456C3×D4—41no—
457C3×D4—84no—
458C3×D4—84no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—21no—
473C2×C3×C4—22no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—48no—
478C2×C3×C4—48no—
479C2×C3×C4—41no—
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—48no—
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—84no—
499C2×C3×C4#12012yes—
500C2×C3×C4C2×D812yes—
501C2×C3×C4C22×D411yescharacteristic
502C2×C3×C4C22×D411yescharacteristic
503C2×C3×C4C2×#4111yescharacteristic
504C2×C3×C4C2×#4111yescharacteristic
505C2×C3×C4H(5,𝔽2)11yescharacteristic
506C2×C3×C42−1+411yescharacteristic
507C3×C8—22no—
508C3×C8—41no—
509C3×C8—41no—
510C3×C8—41no—
511C24—21no—
512C24—21no—
513C24C2×C3×D411yescharacteristic
514C24C2×C3×D411yescharacteristic
515#41—432no—
516C2×Q8—24no—
517C2×Q8—42no—
518C2×Q8—42no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—24no—
522C2×D4—24no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—81no—
544C2×D4C3×D814yescomplemented
545C2×D4C2×C3×D412yes—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—81no—
574C22×C4C2×C3×D411yescharacteristic
575C22×C4C2×C3×D411yescharacteristic
576C22×C4C2×C3×D411yescharacteristic
577C22×C4C2×C3×D412yes—
578C22×C4C2×C3×D412yes—
579C22×C4C2×C3×D411yescharacteristic
580C22×C4C24×C311yescharacteristic
581D8—44no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—44no—
594C2×C8C3×#4112yescomplemented
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—22no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4C2×C3×D412yes—
610C4⋊C4C2×C3×D412yes—
611C4⋊C4C2×C3×D412yes—
612C4⋊C4C3×#4112yescomplemented
613C22⋊C4—24no—
614C22⋊C4—24no—
615C22⋊C4—22no—
616C22⋊C4—24no—
617C22⋊C4—22no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—81no—
623C42—21no—
624C42—21no—
625C22×C3—22no—
626C22×C3—22no—
627C22×C3—22no—
628C22×C3—22no—
629C22×C3—22no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—42no—
639C22×C3—42no—
640C22×C3—42no—
641C22×C3—81no—
642C22×C3—81no—
643C22×C3—81no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3—81no—
647C22×C3—81no—
648C22×C3—81no—
649C22×C3—81no—
650C22×C3—81no—
651C22×C3—81no—
652C22×C3#44714yes—
653C22×C3C2×#12011yescharacteristic
654C22×C3#54611yescharacteristic
655C22×C3#54711yescharacteristic
656C22×C3C22×D811yescharacteristic
657C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
658C22×C3#57711yescharacteristic
659C22×C3#57811yescharacteristic
660C3×C4—22no—
661C3×C4—22no—
662C3×C4—41no—
663C3×C4—42no—
664C3×C4—42no—
665C3×C4—42no—
666C3×C4—41no—
667C3×C4—42no—
668C3×C4—81no—
669C3×C4—81no—
670C3×C4#53211yescharacteristic
671C3×C4#53711yescharacteristic
672C3×C4#54611yescharacteristic
673C3×C4#54711yescharacteristic
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—22no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23C3×#12012yes—
699C23C2×C3×D812yes—
700C23C2×C3×D812yes—
701C23C3×AGL(1,ℤ/8)12yes—
702C23C22×C3×D411yescharacteristic
703Q8—48no—
704D4—28no—
705D4—22no—
706D4—22no—
707D4—48no—
708D4—48no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—84no—
716D4—84no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—48no—
736C2×C4—48no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—48no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—84no—
757C2×C4C3×#12012yes—
758C2×C4C2×C3×D812yes—
759C2×C4C22×C3×D411yescharacteristic
760C2×C4C22×C3×D411yescharacteristic
761C2×C4C2×C3×#4111yescharacteristic
762C2×C4C2×C3×#4111yescharacteristic
763C2×C4C3×H(5,𝔽2)11yescharacteristic
764C2×C4C3×2−1+411yescharacteristic
765C8—22no—
766C8—41no—
767C8—41no—
768C8—41no—
769C2×C3—24no—
770C2×C3—42no—
771C2×C3—82no—
772C2×C3—161no—
773C2×C3#243011yescharacteristic
774C2×C3C2×#44711yescharacteristic
775C2×C3#301311yescharacteristic
776C2×C3#329411yescharacteristic
777C2×C3#330811yescharacteristic
778C2×C3#333411yescharacteristic
779C2×C3#334511yescharacteristic
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22C3×#44714yes—
808C22C2×C3×#12011yescharacteristic
809C22C3×#54611yescharacteristic
810C22C3×#54711yescharacteristic
811C22C22×C3×D811yescharacteristic
812C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
813C22C3×#57711yescharacteristic
814C22C3×#57811yescharacteristic
815C4—22no—
816C4—22no—
817C4—41no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—41no—
822C4—42no—
823C4—81no—
824C4—81no—
825C4C3×#53211yescharacteristic
826C4C3×#53711yescharacteristic
827C4C3×#54611yescharacteristic
828C4C3×#54711yescharacteristic
829C3#2553311yescharacteristic, direct product factor, Sylow
830C2—24no—
831C2—42no—
832C2—82no—
833C2—161no—
834C2C3×#243011yescharacteristic
835C2C2×C3×#44711yescharacteristic
836C2C3×#301311yescharacteristic
837C2C3×#329411yescharacteristic
838C2C3×#330811yescharacteristic
839C2C3×#333411yescharacteristic
840C2C3×#334511yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
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×#547C2semidirect
2. C2×C3×#480C2semidirect
3. C2×C3×#466C2semidirect
4. C3×#2416C2semidirect
5. C3×#2057C2semidirect
6. C3×#2033C2semidirect
7. C3×#2023C2semidirect
8. C3×#1999C2semidirect
9. C3×#1879C2semidirect
10. C3×#1874C2semidirect
11. C3×#1874C2semidirect
12. C3×#1869C2semidirect
13. C3×#1862C2semidirect
14. C3×#1852C2semidirect
15. C2×C3×#340C2semidirect
16. #25533C3direct (N × H)
64. C2×#547C2×C3semidirect
65. C2×#480C2×C3semidirect
66. C2×#466C2×C3semidirect
67. #2416C2×C3semidirect
68. #2057C2×C3semidirect
69. #2033C2×C3semidirect
70. #2023C2×C3semidirect
71. #1999C2×C3semidirect
72. #1879C2×C3semidirect
73. #1874C2×C3semidirect
74. #1874C2×C3semidirect
75. #1869C2×C3semidirect
76. #1862C2×C3semidirect
77. #1852C2×C3semidirect
78. C2×#340C2×C3semidirect
119. C3×#121D4semidirect
135. C2×C3×C4⋊C4D4semidirect
247. C2×C3×D4D8semidirect
297. C2×C3×C8#41semidirect
315. C3×C4⋊C4#41semidirect
368. #121C3×D4semidirect
384. C2×C4⋊C4C3×D4semidirect
544. C2×D4C3×D8semidirect
594. C2×C8C3×#41semidirect
612. C4⋊C4C3×#41semidirect
829. C3#25533direct (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×#4802
C2×C3×#4662
C3×#24162
C3×#20572
C3×#20332
C3×#20232
C3×#19992
C3×#18792
C3×#18742
C3×#18692
C3×#18622
C3×#18522
C2×C3×#3402
#255333