Finite Group Databasebeta

← C3×#25549 #10644156

Subgroups — C3×#25549 #10644156

Order 768.

1390 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#547C211yesmaximal, characteristic, complemented
2C2×C3×#481C211yesmaximal, characteristic, complemented
3C2×C3×#469C211yesmaximal, characteristic, complemented
4C3×#2414C211yesmaximal, characteristic, complemented
5C3×#2058C211yesmaximal, characteristic, complemented
6C3×#2034C211yesmaximal, characteristic, complemented
7C3×#2023C211yesmaximal, characteristic, complemented
8C3×#1999C211yesmaximal, characteristic, complemented
9C3×#1879C211yesmaximal, characteristic, complemented
10C3×#1875C211yesmaximal, characteristic, complemented
11C3×#1874C211yesmaximal, characteristic, complemented
12C3×#1870C211yesmaximal, characteristic, complemented
13C3×#1864C211yesmaximal, characteristic, complemented
14C3×#1853C211yesmaximal, characteristic, complemented
15C3×#1736C211yesmaximal, characteristic, complemented
16#25549C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41—21no—
18C22×C3×D8C2211yescharacteristic
19C22×C3×M16C2211yescharacteristic
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×#121C2211yescharacteristic
27C2×C3×#121C2211yescharacteristic
28C2×C3×#121C2211yescharacteristic
29C2×C3×#121C2211yescharacteristic
30C2×C3×C4×D4C2211yescharacteristic
31C2×C3×C4×D4C2211yescharacteristic
32C2×C3×#117C2211yescharacteristic
33C22×C3×C4⋊C4C2211yescharacteristic
34C22×C3×C4⋊C4C2211yescharacteristic
35C3×#481—24no—
36C3×#469—24no—
37C2×C3×#106C2211yescharacteristic
38C2×C3×#106C2211yescharacteristic
39C2×C3×#106C2211yescharacteristic
40C2×C3×#102C2211yescharacteristic
41C2×C3×#102C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×C22⋊C8C2211yescharacteristic
47C2×C3×C22⋊C8C2211yescharacteristic
48C2×C3×C22⋊C8C2211yescharacteristic
49C3×#394—21no—
50C3×#392—21no—
51C3×#390—21no—
52C3×#390C2211yescharacteristic
53C3×#389C2211yescharacteristic
54C3×#388—21no—
55C3×#380C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#547C2×C311yescharacteristic, complemented
65C2×#481C2×C311yescharacteristic, complemented
66C2×#469C2×C311yescharacteristic, complemented
67#2414C2×C311yescharacteristic, complemented
68#2058C2×C311yescharacteristic, complemented
69#2034C2×C311yescharacteristic, complemented
70#2023C2×C311yescharacteristic, complemented
71#1999C2×C311yescharacteristic, complemented
72#1879C2×C311yescharacteristic, complemented
73#1875C2×C311yescharacteristic, complemented
74#1874C2×C311yescharacteristic, complemented
75#1870C2×C311yescharacteristic, complemented
76#1864C2×C311yescharacteristic, complemented
77#1853C2×C311yescharacteristic, complemented
78#1736C2×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×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C2×C3×D8—22no—
96C2×C3×D8—22no—
97C2×C3×D8—41no—
98C2×C3×M16—22no—
99C2×C3×M16—22no—
100C2×C3×M16—41no—
101C22×C3×C8C2311yescharacteristic
102C22×C3×C8C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C22×C3×C8C2311yescharacteristic
105C3×C4⋊Q8—22no—
106C3×C4⋊Q8—22no—
107C3×#123—28no—
108C3×#123—28no—
109C3×C22⋊Q8—28no—
110C3×#121—22no—
111C3×#121—22no—
112C3×#121—22no—
113C3×#121—22no—
114C3×#121—22no—
115C3×#121—22no—
116C3×#121—41no—
117C3×#121D414yescomplemented
118C3×C4×D4—22no—
119C3×C4×D4—22no—
120C3×C4×D4—22no—
121C3×C4×D4—22no—
122C3×#117—22no—
123C3×#117—41no—
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—21no—
131C2×C3×C4⋊C4D411yescharacteristic
132C2×C3×C4⋊C4D414yescomplemented
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C4⋊C4C2311yescharacteristic
135C2×C3×C4⋊C4C2311yescharacteristic
136C2×C3×C4⋊C4C2311yescharacteristic
137C2×C3×C4⋊C4C2311yescharacteristic
138C2×C3×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
147C2×C3×C22⋊C4—21no—
148C2×C3×C22⋊C4D411yescharacteristic
149C2×C3×C22⋊C4D411yescharacteristic
150C2×C3×C42—21no—
151C2×C3×C42C2311yescharacteristic
152C3×#106—22no—
153C3×#106—22no—
154C3×#106—22no—
155C3×#102—22no—
156C3×#102—22no—
157C3×#102—22no—
158C3×#102—22no—
159C3×#102—22no—
160C3×#102—41no—
161C3×C22⋊C8—22no—
162C3×C22⋊C8—22no—
163C3×C22⋊C8—41no—
164C3×#95—21no—
165C3×#95—21no—
166C22×#41—21no—
167C22×D8C22×C311yescharacteristic
168C22×M16C22×C311yescharacteristic
169#547—24no—
170#547—24no—
171C2×C4⋊Q8C22×C311yescharacteristic
172C2×#123—21no—
173C2×#123—21no—
174C2×C22⋊Q8—21no—
175C2×#121C22×C311yescharacteristic
176C2×#121C22×C311yescharacteristic
177C2×#121C22×C311yescharacteristic
178C2×#121C22×C311yescharacteristic
179C2×C4×D4C22×C311yescharacteristic
180C2×C4×D4C22×C311yescharacteristic
181C2×#117C22×C311yescharacteristic
182C22×C4⋊C4C22×C311yescharacteristic
183C22×C4⋊C4C22×C311yescharacteristic
184#481—24no—
185#469—24no—
186C2×#106C22×C311yescharacteristic
187C2×#106C22×C311yescharacteristic
188C2×#106C22×C311yescharacteristic
189C2×#102C22×C311yescharacteristic
190C2×#102C22×C311yescharacteristic
191C2×#102C22×C311yescharacteristic
192C2×#102C22×C311yescharacteristic
193C2×#102C22×C311yescharacteristic
194C2×#102C22×C311yescharacteristic
195C2×C22⋊C8C22×C311yescharacteristic
196C2×C22⋊C8C22×C311yescharacteristic
197C2×C22⋊C8C22×C311yescharacteristic
198#394—21no—
199#392—21no—
200#390—21no—
201#390C22×C311yescharacteristic
202#389C22×C311yescharacteristic
203#388—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×C3—21no—
215C24×C3C2×D411yescharacteristic
216C24×C3C2×D411yescharacteristic
217C3×#41—432no—
218C2×C3×Q8—24no—
219C2×C3×Q8—42no—
220C2×C3×Q8—42no—
221C2×C3×D4—22no—
222C2×C3×D4—22no—
223C2×C3×D4—24no—
224C2×C3×D4—24no—
225C2×C3×D4—22no—
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—81no—
245C2×C3×D4—81no—
246C2×C3×D4—81no—
247C2×C3×D4C2×D412yes—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—24no—
253C22×C3×C4—24no—
254C22×C3×C4—24no—
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—42no—
268C22×C3×C4—42no—
269C22×C3×C4—42no—
270C22×C3×C4—42no—
271C22×C3×C4—42no—
272C22×C3×C4—42no—
273C22×C3×C4C2×D411yescharacteristic
274C22×C3×C4C2×D411yescharacteristic
275C22×C3×C4C2×D411yescharacteristic
276C22×C3×C4C2×D412yes—
277C22×C3×C4C2×D412yes—
278C22×C3×C4C2×D411yescharacteristic
279C22×C3×C4C2411yescharacteristic
280C3×D8—44no—
281C3×M16—44no—
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—21no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8#4112yescomplemented
294C3×C4⋊C4—24no—
295C3×C4⋊C4—24no—
296C3×C4⋊C4—24no—
297C3×C4⋊C4—22no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—21no—
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—42no—
319C3×C22⋊C4—42no—
320C3×C22⋊C4—81no—
321C3×C22⋊C4—81no—
322C3×C42—21no—
323C3×C42—21no—
324C3×C42—42no—
325C2×#41—28no—
326C2×#41—44no—
327C2×#41—44no—
328C22×Q8—21no—
329C22×D4—21no—
330C22×D4—21no—
331C22×D4—21no—
332C22×D4—21no—
333C22×D4C3×D411yescharacteristic
334C22×D4C23×C311yescharacteristic
335C22×D4C23×C311yescharacteristic
336C23×C4—21no—
337C23×C4—21no—
338C23×C4—21no—
339C23×C4C23×C311yescharacteristic
340C23×C4C23×C311yescharacteristic
341C2×D8—22no—
342C2×D8—22no—
343C2×D8—41no—
344C2×M16—22no—
345C2×M16—22no—
346C2×M16—41no—
347C22×C8C23×C311yescharacteristic
348C22×C8C23×C311yescharacteristic
349C22×C8C23×C311yescharacteristic
350C22×C8C23×C311yescharacteristic
351C4⋊Q8—22no—
352C4⋊Q8—22no—
353#123—28no—
354#123—28no—
355C22⋊Q8—28no—
356#121—22no—
357#121—22no—
358#121—22no—
359#121—22no—
360#121—22no—
361#121—22no—
362#121—41no—
363#121C3×D414yescomplemented
364C4×D4—22no—
365C4×D4—22no—
366C4×D4—22no—
367C4×D4—22no—
368#117—22no—
369#117—41no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4C3×D411yescharacteristic
378C2×C4⋊C4C3×D414yescomplemented
379C2×C4⋊C4C23×C311yescharacteristic
380C2×C4⋊C4C23×C311yescharacteristic
381C2×C4⋊C4C23×C311yescharacteristic
382C2×C4⋊C4C23×C311yescharacteristic
383C2×C4⋊C4C23×C311yescharacteristic
384C2×C4⋊C4C23×C311yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4C3×D411yescharacteristic
395C2×C22⋊C4C3×D411yescharacteristic
396C2×C42—21no—
397C2×C42C23×C311yescharacteristic
398#106—22no—
399#106—22no—
400#106—22no—
401#102—22no—
402#102—22no—
403#102—22no—
404#102—22no—
405#102—22no—
406#102—41no—
407C22⋊C8—22no—
408C22⋊C8—22no—
409C22⋊C8—41no—
410#95—21no—
411#95—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—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—22no—
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—41no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3—41no—
437C23×C3—41no—
438C23×C3#12012yes—
439C23×C3AGL(1,ℤ/8)12yes—
440C23×C3C22×D411yescharacteristic
441C3×Q8—48no—
442C3×D4—28no—
443C3×D4—22no—
444C3×D4—22no—
445C3×D4—48no—
446C3×D4—48no—
447C3×D4—41no—
448C3×D4—41no—
449C3×D4—41no—
450C3×D4—41no—
451C3×D4—41no—
452C3×D4—41no—
453C3×D4—84no—
454C3×D4—84no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—48no—
474C2×C3×C4—48no—
475C2×C3×C4—48no—
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—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#12012yes—
495C2×C3×C4AGL(1,ℤ/8)12yes—
496C2×C3×C4C22×D411yescharacteristic
497C2×C3×C4C22×D411yescharacteristic
498C2×C3×C4C2×#4111yescharacteristic
499C2×C3×C4C2×#4111yescharacteristic
500C2×C3×C4H(5,𝔽2)11yescharacteristic
501C2×C3×C42−1+411yescharacteristic
502C3×C8—22no—
503C3×C8—41no—
504C3×C8—41no—
505C3×C8—41no—
506C24—21no—
507C24—21no—
508C24C2×C3×D411yescharacteristic
509C24C2×C3×D411yescharacteristic
510#41—432no—
511C2×Q8—24no—
512C2×Q8—42no—
513C2×Q8—42no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—24no—
517C2×D4—24no—
518C2×D4—22no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—81no—
538C2×D4—81no—
539C2×D4—81no—
540C2×D4C2×C3×D412yes—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4C2×C3×D411yescharacteristic
567C22×C4C2×C3×D411yescharacteristic
568C22×C4C2×C3×D411yescharacteristic
569C22×C4C2×C3×D412yes—
570C22×C4C2×C3×D412yes—
571C22×C4C2×C3×D411yescharacteristic
572C22×C4C24×C311yescharacteristic
573D8—44no—
574M16—44no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8C3×#4112yescomplemented
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—22no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—81no—
600C4⋊C4C2×C3×D412yes—
601C4⋊C4C2×C3×D412yes—
602C4⋊C4C2×C3×D412yes—
603C4⋊C4C3×#4112yescomplemented
604C22⋊C4—24no—
605C22⋊C4—24no—
606C22⋊C4—22no—
607C22⋊C4—24no—
608C22⋊C4—22no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—81no—
614C22⋊C4—81no—
615C42—21no—
616C42—21no—
617C42—42no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—22no—
621C22×C3—22no—
622C22×C3—22no—
623C22×C3—22no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—42no—
633C22×C3—42no—
634C22×C3—42no—
635C22×C3—81no—
636C22×C3—81no—
637C22×C3—81no—
638C22×C3—81no—
639C22×C3—81no—
640C22×C3—81no—
641C22×C3—81no—
642C22×C3—81no—
643C22×C3—81no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3C2×#12011yescharacteristic
647C22×C3#54611yescharacteristic
648C22×C3#54711yescharacteristic
649C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
650C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
651C22×C3#57711yescharacteristic
652C22×C3#57711yescharacteristic
653C3×C4—22no—
654C3×C4—22no—
655C3×C4—41no—
656C3×C4—42no—
657C3×C4—42no—
658C3×C4—42no—
659C3×C4—41no—
660C3×C4—42no—
661C3×C4—81no—
662C3×C4—81no—
663C3×C4#53211yescharacteristic
664C3×C4#53711yescharacteristic
665C3×C4#54611yescharacteristic
666C3×C4#54711yescharacteristic
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—22no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23C3×#12012yes—
694C23C3×AGL(1,ℤ/8)12yes—
695C23C22×C3×D411yescharacteristic
696Q8—48no—
697D4—28no—
698D4—22no—
699D4—22no—
700D4—48no—
701D4—48no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—84no—
709D4—84no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—48no—
729C2×C4—48no—
730C2×C4—48no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
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—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4C3×#12012yes—
750C2×C4C3×AGL(1,ℤ/8)12yes—
751C2×C4C22×C3×D411yescharacteristic
752C2×C4C22×C3×D411yescharacteristic
753C2×C4C2×C3×#4111yescharacteristic
754C2×C4C2×C3×#4111yescharacteristic
755C2×C4C3×H(5,𝔽2)11yescharacteristic
756C2×C4C3×2−1+411yescharacteristic
757C8—22no—
758C8—41no—
759C8—41no—
760C8—41no—
761C2×C3—42no—
762C2×C3—42no—
763C2×C3—82no—
764C2×C3—161no—
765C2×C3#243011yescharacteristic
766C2×C3#300311yescharacteristic
767C2×C3#301011yescharacteristic
768C2×C3#330611yescharacteristic
769C2×C3#333211yescharacteristic
770C2×C3#334511yescharacteristic
771C2×C3#335411yescharacteristic
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22C2×C3×#12011yescharacteristic
801C22C3×#54611yescharacteristic
802C22C3×#54711yescharacteristic
803C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
804C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
805C22C3×#57711yescharacteristic
806C22C3×#57711yescharacteristic
807C4—22no—
808C4—22no—
809C4—41no—
810C4—42no—
811C4—42no—
812C4—42no—
813C4—41no—
814C4—42no—
815C4—81no—
816C4—81no—
817C4C3×#53211yescharacteristic
818C4C3×#53711yescharacteristic
819C4C3×#54611yescharacteristic
820C4C3×#54711yescharacteristic
821C3#2554911yescharacteristic, direct product factor, Sylow
822C2—42no—
823C2—42no—
824C2—82no—
825C2—161no—
826C2C3×#243011yescharacteristic
827C2C3×#300311yescharacteristic
828C2C3×#301011yescharacteristic
829C2C3×#330611yescharacteristic
830C2C3×#333211yescharacteristic
831C2C3×#334511yescharacteristic
832C2C3×#335411yescharacteristic
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×#481C2semidirect
3. C2×C3×#469C2semidirect
4. C3×#2414C2semidirect
5. C3×#2058C2semidirect
6. C3×#2034C2semidirect
7. C3×#2023C2semidirect
8. C3×#1999C2semidirect
9. C3×#1879C2semidirect
10. C3×#1875C2semidirect
11. C3×#1874C2semidirect
12. C3×#1870C2semidirect
13. C3×#1864C2semidirect
14. C3×#1853C2semidirect
15. C3×#1736C2semidirect
16. #25549C3direct (N × H)
64. C2×#547C2×C3semidirect
65. C2×#481C2×C3semidirect
66. C2×#469C2×C3semidirect
67. #2414C2×C3semidirect
68. #2058C2×C3semidirect
69. #2034C2×C3semidirect
70. #2023C2×C3semidirect
71. #1999C2×C3semidirect
72. #1879C2×C3semidirect
73. #1875C2×C3semidirect
74. #1874C2×C3semidirect
75. #1870C2×C3semidirect
76. #1864C2×C3semidirect
77. #1853C2×C3semidirect
78. #1736C2×C3semidirect
117. C3×#121D4semidirect
132. C2×C3×C4⋊C4D4semidirect
293. C2×C3×C8#41semidirect
310. C3×C4⋊C4#41semidirect
363. #121C3×D4semidirect
378. C2×C4⋊C4C3×D4semidirect
586. C2×C8C3×#41semidirect
603. C4⋊C4C3×#41semidirect
821. C3#25549direct (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×#4812
C2×C3×#4692
C3×#24142
C3×#20582
C3×#20342
C3×#20232
C3×#19992
C3×#18792
C3×#18752
C3×#18742
C3×#18702
C3×#18642
C3×#18532
C3×#17362
#255493