Finite Group Databasebeta

← C3×#25506 #10644113

Subgroups — C3×#25506 #10644113

Order 768.

1202 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#529C211yesmaximal, characteristic, complemented
2C2×C3×#469C211yesmaximal, characteristic
3C2×C3×#468C211yesmaximal, characteristic, complemented
4C3×#2854C211yesmaximal, characteristic, complemented
5C3×#2059C211yesmaximal, characteristic, complemented
6C3×#2042C211yesmaximal, characteristic, complemented
7C3×#2025C211yesmaximal, characteristic, complemented
8C3×#2012C211yesmaximal, characteristic, complemented
9C3×#1895C211yesmaximal, characteristic, complemented
10C3×#1894C211yesmaximal, characteristic, complemented
11C3×#1880C211yesmaximal, characteristic, complemented
12C3×#1879C211yesmaximal, characteristic, complemented
13C3×#1865C211yesmaximal, characteristic, complemented
14C3×#1862C211yesmaximal, characteristic, complemented
15C3×#1728C211yesmaximal, characteristic, complemented
16#25506C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×D8C2211yescharacteristic
19C22×C3×M16C2211yescharacteristic
20C22×C3×M16C2211yescharacteristic
21C3×#529—24no—
22C3×#529—24no—
23C2×C3×#126—21no—
24C2×C3×#125C2211yescharacteristic
25C2×C3×#124C2211yescharacteristic
26C2×C3×#123—21no—
27C2×C3×#123—21no—
28C2×C3×C22⋊Q8C2211yescharacteristic
29C2×C3×#121C2211yescharacteristic
30C2×C3×#121C2211yescharacteristic
31C2×C3×C4×Q8C2211yescharacteristic
32C2×C3×C4×D4—21no—
33C2×C3×C4×D4C2211yescharacteristic
34C2×C3×#117—21no—
35C22×C3×C42C2211yescharacteristic
36C3×#469—24no—
37C3×#468—24no—
38C2×C3×#107C2211yescharacteristic
39C2×C3×#106C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×#102C2211yescharacteristic
48C3×#390C2211yescharacteristic
49C3×#390C2211yescharacteristic
50C3×#389C2211yescharacteristic
51C3×#389C2211yescharacteristic
52C3×#388—21no—
53C3×#388—21no—
54C3×#386—21no—
55C3×#380C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#529C2×C311yescharacteristic, complemented
65C2×#469C2×C311yescharacteristic
66C2×#468C2×C311yescharacteristic, complemented
67#2854C2×C311yescharacteristic, complemented
68#2059C2×C311yescharacteristic, complemented
69#2042C2×C311yescharacteristic, complemented
70#2025C2×C311yescharacteristic, complemented
71#2012C2×C311yescharacteristic, complemented
72#1895C2×C311yescharacteristic, complemented
73#1894C2×C311yescharacteristic, complemented
74#1880C2×C311yescharacteristic, complemented
75#1879C2×C311yescharacteristic, complemented
76#1865C2×C311yescharacteristic, complemented
77#1862C2×C311yescharacteristic, complemented
78#1728C2×C311yescharacteristic, complemented
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4—21no—
82C22×C3×D4C2311yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4—21no—
85C23×C3×C4D411yescharacteristic
86C23×C3×C4D411yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C2×C3×SD16—22no—
89C2×C3×SD16—22no—
90C2×C3×SD16—41no—
91C2×C3×D8—22no—
92C2×C3×D8—22no—
93C2×C3×D8—41no—
94C2×C3×M16—22no—
95C2×C3×M16—22no—
96C2×C3×M16—22no—
97C2×C3×M16—22no—
98C2×C3×M16—41no—
99C2×C3×M16—41no—
100C22×C3×C8C2311yescharacteristic
101C22×C3×C8C2311yescharacteristic
102C22×C3×C8C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C3×#126—28no—
105C3×#125—22no—
106C3×#125—22no—
107C3×#124—22no—
108C3×#124—22no—
109C3×#123—28no—
110C3×#123—44no—
111C3×C22⋊Q8—22no—
112C3×C22⋊Q8D414yes—
113C3×#121—22no—
114C3×#121—22no—
115C3×#121—22no—
116C3×#121D414yes—
117C3×C4×Q8—22no—
118C3×C4×Q8—22no—
119C3×C4×D4—28no—
120C3×C4×D4—22no—
121C3×C4×D4—22no—
122C3×#117—28no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4—21no—
127C2×C3×C4⋊C4—21no—
128C2×C3×C4⋊C4—21no—
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C4⋊C4C2311yescharacteristic
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C4⋊C4C2311yescharacteristic
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C22⋊C4—21no—
135C2×C3×C22⋊C4—21no—
136C2×C3×C22⋊C4—21no—
137C2×C3×C22⋊C4—21no—
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×C42—22no—
146C2×C3×C42—22no—
147C2×C3×C42—21no—
148C2×C3×C42D411yescharacteristic
149C2×C3×C42D411yescharacteristic
150C2×C3×C42C2311yescharacteristic
151C2×C3×C42C2311yescharacteristic
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×#102—22no—
161C3×#102—41no—
162C3×#95—21no—
163C3×#95—21no—
164C3×#95—21no—
165C22×SD16C22×C311yescharacteristic
166C22×D8C22×C311yescharacteristic
167C22×M16C22×C311yescharacteristic
168C22×M16C22×C311yescharacteristic
169#529—24no—
170#529—24no—
171C2×#126—21no—
172C2×#125C22×C311yescharacteristic
173C2×#124C22×C311yescharacteristic
174C2×#123—21no—
175C2×#123—21no—
176C2×C22⋊Q8C22×C311yescharacteristic
177C2×#121C22×C311yescharacteristic
178C2×#121C22×C311yescharacteristic
179C2×C4×Q8C22×C311yescharacteristic
180C2×C4×D4—21no—
181C2×C4×D4C22×C311yescharacteristic
182C2×#117—21no—
183C22×C42C22×C311yescharacteristic
184#469—24no—
185#468—24no—
186C2×#107C22×C311yescharacteristic
187C2×#106C22×C311yescharacteristic
188C2×#103C22×C311yescharacteristic
189C2×#103C22×C311yescharacteristic
190C2×#103C22×C311yescharacteristic
191C2×#102C22×C311yescharacteristic
192C2×#102C22×C311yescharacteristic
193C2×#102C22×C311yescharacteristic
194C2×#102C22×C311yescharacteristic
195C2×#102C22×C311yescharacteristic
196#390C22×C311yescharacteristic
197#390C22×C311yescharacteristic
198#389C22×C311yescharacteristic
199#389C22×C311yescharacteristic
200#388—21no—
201#388—21no—
202#386—21no—
203#380C22×C311yescharacteristic
204#340C22×C311yescharacteristic
205#340C22×C311yescharacteristic
206#340C22×C311yescharacteristic
207#340C22×C311yescharacteristic
208#336C22×C311yescharacteristic
209#336C22×C311yescharacteristic
210#336C22×C311yescharacteristic
211#336C22×C311yescharacteristic
212C24×C3—21no—
213C24×C3—21no—
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—24no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
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—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—42no—
234C2×C3×D4—42no—
235C2×C3×D4—42no—
236C2×C3×D4—42no—
237C2×C3×D4—42no—
238C2×C3×D4C2×D412yes—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—24no—
244C22×C3×C4—22no—
245C22×C3×C4—22no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—22no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—41no—
254C22×C3×C4—41no—
255C22×C3×C4—41no—
256C22×C3×C4—42no—
257C22×C3×C4—42no—
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2×D411yescharacteristic
261C22×C3×C4C2×D411yescharacteristic
262C22×C3×C4C2×D412yes—
263C22×C3×C4C2×D412yes—
264C22×C3×C4C2×D411yescharacteristic
265C22×C3×C4C2411yescharacteristic
266C3×SD16—44no—
267C3×D8—44no—
268C3×M16—44no—
269C3×M16—44no—
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—21no—
279C2×C3×C8—21no—
280C2×C3×C8#4112yes—
281C2×C3×C8#4112yes—
282C3×C4⋊C4—24no—
283C3×C4⋊C4—24no—
284C3×C4⋊C4—24no—
285C3×C4⋊C4—24no—
286C3×C4⋊C4—21no—
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—42no—
295C3×C4⋊C4—42no—
296C3×C4⋊C4C2×D412yes—
297C3×C4⋊C4C2×D412yes—
298C3×C22⋊C4—24no—
299C3×C22⋊C4—24no—
300C3×C22⋊C4—24no—
301C3×C22⋊C4—24no—
302C3×C22⋊C4—24no—
303C3×C22⋊C4—42no—
304C3×C22⋊C4—42no—
305C3×C22⋊C4—42no—
306C3×C22⋊C4—42no—
307C3×C22⋊C4—42no—
308C3×C22⋊C4—42no—
309C3×C42—24no—
310C3×C42—22no—
311C3×C42—22no—
312C3×C42—21no—
313C3×C42—21no—
314C3×C42—21no—
315C3×C42—21no—
316C22×Q8C23×C311yescharacteristic
317C22×D4—21no—
318C22×D4—21no—
319C22×D4C23×C311yescharacteristic
320C22×D4C23×C311yescharacteristic
321C23×C4—21no—
322C23×C4C3×D411yescharacteristic
323C23×C4C3×D411yescharacteristic
324C23×C4C23×C311yescharacteristic
325C2×SD16—22no—
326C2×SD16—22no—
327C2×SD16—41no—
328C2×D8—22no—
329C2×D8—22no—
330C2×D8—41no—
331C2×M16—22no—
332C2×M16—22no—
333C2×M16—22no—
334C2×M16—22no—
335C2×M16—41no—
336C2×M16—41no—
337C22×C8C23×C311yescharacteristic
338C22×C8C23×C311yescharacteristic
339C22×C8C23×C311yescharacteristic
340C22×C8C23×C311yescharacteristic
341#126—28no—
342#125—22no—
343#125—22no—
344#124—22no—
345#124—22no—
346#123—28no—
347#123—44no—
348C22⋊Q8—22no—
349C22⋊Q8C3×D414yes—
350#121—22no—
351#121—22no—
352#121—22no—
353#121C3×D414yes—
354C4×Q8—22no—
355C4×Q8—22no—
356C4×D4—28no—
357C4×D4—22no—
358C4×D4—22no—
359#117—28no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4C23×C311yescharacteristic
367C2×C4⋊C4C23×C311yescharacteristic
368C2×C4⋊C4C23×C311yescharacteristic
369C2×C4⋊C4C23×C311yescharacteristic
370C2×C4⋊C4C23×C311yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
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×C42—21no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42C3×D411yescharacteristic
386C2×C42C3×D411yescharacteristic
387C2×C42C23×C311yescharacteristic
388C2×C42C23×C311yescharacteristic
389#107—22no—
390#106—22no—
391#103—22no—
392#103—22no—
393#103—41no—
394#102—22no—
395#102—22no—
396#102—22no—
397#102—22no—
398#102—41no—
399#95—21no—
400#95—21no—
401#95—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—22no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3#12012yes—
423C23×C3C22×D411yescharacteristic
424C3×Q8—22no—
425C3×Q8—22no—
426C3×Q8—41no—
427C3×Q8—41no—
428C3×D4—22no—
429C3×D4—22no—
430C3×D4—48no—
431C3×D4—41no—
432C3×D4—41no—
433C3×D4—41no—
434C3×D4—41no—
435C3×D4—41no—
436C3×D4—41no—
437C3×D4—84no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—44no—
459C2×C3×C4—48no—
460C2×C3×C4—44no—
461C2×C3×C4—41no—
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—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4#12012yes—
477C2×C3×C4AGL(1,ℤ/8)12yes—
478C2×C3×C4C22×D411yescharacteristic
479C2×C3×C4C22×D411yescharacteristic
480C2×C3×C4C2×#4111yescharacteristic
481C2×C3×C4C2×#4111yescharacteristic
482C2×C3×C4H(5,𝔽2)11yescharacteristic
483C2×C3×C42−1+411yescharacteristic
484C3×C8—22no—
485C3×C8—22no—
486C3×C8—41no—
487C3×C8—41no—
488C24—21no—
489C24—21no—
490C24C2×C3×D411yescharacteristic
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8C2×C3×D412yes—
497C2×D4—24no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4C2×C3×D412yes—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—42no—
533C22×C4—42no—
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×C4C2×C3×D411yescharacteristic
541C22×C4C24×C311yescharacteristic
542SD16—44no—
543D8—44no—
544M16—44no—
545M16—44no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8C3×#4112yes—
557C2×C8C3×#4112yes—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—24no—
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—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C42—24no—
586C42—22no—
587C42—22no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—41no—
596C22×C3—41no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—42no—
600C22×C3—42no—
601C22×C3—42no—
602C22×C3—81no—
603C22×C3—81no—
604C22×C3—81no—
605C22×C3—81no—
606C22×C3—81no—
607C22×C3—81no—
608C22×C3—81no—
609C22×C3—81no—
610C22×C3—81no—
611C22×C3—81no—
612C22×C3—81no—
613C22×C3C2×#12011yescharacteristic
614C22×C3#53211yescharacteristic
615C22×C3#53711yescharacteristic
616C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
617C22×C3#57511yescharacteristic
618C22×C3#57511yescharacteristic
619C22×C3#57511yescharacteristic
620C3×C4—22no—
621C3×C4—22no—
622C3×C4—42no—
623C3×C4—41no—
624C3×C4—41no—
625C3×C4—42no—
626C3×C4—41no—
627C3×C4—42no—
628C3×C4—81no—
629C3×C4—81no—
630C3×C4—81no—
631C3×C4#54611yescharacteristic
632C3×C4#54611yescharacteristic
633C3×C4#54711yescharacteristic
634C3×C4#54711yescharacteristic
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23C3×#12012yes—
656C23C22×C3×D411yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—41no—
660Q8—41no—
661D4—22no—
662D4—22no—
663D4—48no—
664D4—41no—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—84no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—44no—
692C2×C4—48no—
693C2×C4—44no—
694C2×C4—41no—
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—41no—
708C2×C4—41no—
709C2×C4C3×#12012yes—
710C2×C4C3×AGL(1,ℤ/8)12yes—
711C2×C4C22×C3×D411yescharacteristic
712C2×C4C22×C3×D411yescharacteristic
713C2×C4C2×C3×#4111yescharacteristic
714C2×C4C2×C3×#4111yescharacteristic
715C2×C4C3×H(5,𝔽2)11yescharacteristic
716C2×C4C3×2−1+411yescharacteristic
717C8—22no—
718C8—22no—
719C8—41no—
720C8—41no—
721C2×C3—42no—
722C2×C3—82no—
723C2×C3—161no—
724C2×C3#243011yescharacteristic
725C2×C3#300511yescharacteristic
726C2×C3#300611yescharacteristic
727C2×C3#317111yescharacteristic
728C2×C3#318311yescharacteristic
729C2×C3#325111yescharacteristic
730C2×C3#325611yescharacteristic
731C22—22no—
732C22—22no—
733C22—22no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22C2×C3×#12011yescharacteristic
753C22C3×#53211yescharacteristic
754C22C3×#53711yescharacteristic
755C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
756C22C3×#57511yescharacteristic
757C22C3×#57511yescharacteristic
758C22C3×#57511yescharacteristic
759C4—22no—
760C4—22no—
761C4—42no—
762C4—41no—
763C4—41no—
764C4—42no—
765C4—41no—
766C4—42no—
767C4—81no—
768C4—81no—
769C4—81no—
770C4C3×#54611yescharacteristic
771C4C3×#54611yescharacteristic
772C4C3×#54711yescharacteristic
773C4C3×#54711yescharacteristic
774C3#2550611yescharacteristic, direct product factor, Sylow
775C2—42no—
776C2—82no—
777C2—161no—
778C2C3×#243011yescharacteristic
779C2C3×#300511yescharacteristic
780C2C3×#300611yescharacteristic
781C2C3×#317111yescharacteristic
782C2C3×#318311yescharacteristic
783C2C3×#325111yescharacteristic
784C2C3×#325611yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#469C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C22×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#529C2semidirect
3. C2×C3×#468C2semidirect
4. C3×#2854C2semidirect
5. C3×#2059C2semidirect
6. C3×#2042C2semidirect
7. C3×#2025C2semidirect
8. C3×#2012C2semidirect
9. C3×#1895C2semidirect
10. C3×#1894C2semidirect
11. C3×#1880C2semidirect
12. C3×#1879C2semidirect
13. C3×#1865C2semidirect
14. C3×#1862C2semidirect
15. C3×#1728C2semidirect
16. #25506C3direct (N × H)
64. C2×#529C2×C3semidirect
66. C2×#468C2×C3semidirect
67. #2854C2×C3semidirect
68. #2059C2×C3semidirect
69. #2042C2×C3semidirect
70. #2025C2×C3semidirect
71. #2012C2×C3semidirect
72. #1895C2×C3semidirect
73. #1894C2×C3semidirect
74. #1880C2×C3semidirect
75. #1879C2×C3semidirect
76. #1865C2×C3semidirect
77. #1862C2×C3semidirect
78. #1728C2×C3semidirect
774. C3#25506direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5292
C2×C3×#4692
C2×C3×#4682
C3×#28542
C3×#20592
C3×#20422
C3×#20252
C3×#20122
C3×#18952
C3×#18942
C3×#18802
C3×#18792
C3×#18652
C3×#18622
C3×#17282
#255063