Finite Group Databasebeta

← C3×#25554 #10644161

Subgroups — C3×#25554 #10644161

Order 768.

1236 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#555C211yesmaximal, characteristic, complemented
2C2×C3×#482C211yesmaximal, characteristic, complemented
3C2×C3×#469C211yesmaximal, characteristic, complemented
4C3×#2416C211yesmaximal, 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×#1862C211yesmaximal, characteristic, complemented
14C3×#1854C211yesmaximal, characteristic, complemented
15C3×#1736C211yesmaximal, characteristic, complemented
16#25554C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×D8C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
19C3×#555—24no—
20C3×#555—24no—
21C2×C3×C4⋊Q8C2211yescharacteristic
22C2×C3×#124—21no—
23C2×C3×#124—21no—
24C2×C3×#121—21no—
25C2×C3×#121—21no—
26C2×C3×#121C2211yescharacteristic
27C2×C3×#121C2211yescharacteristic
28C2×C3×#121C2211yescharacteristic
29C2×C3×#121C2211yescharacteristic
30C2×C3×C4×D4C2211yescharacteristic
31C2×C3×C4×D4C2211yescharacteristic
32C2×C3×#117—21no—
33C2×C3×#117C2211yescharacteristic
34C2×C3×#117C2211yescharacteristic
35C22×C3×C4⋊C4C2211yescharacteristic
36C3×#482—24no—
37C3×#469—24no—
38C2×C3×#107C2211yescharacteristic
39C2×C3×#106C2211yescharacteristic
40C2×C3×#106C2211yescharacteristic
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×#555C2×C311yescharacteristic, complemented
65C2×#482C2×C311yescharacteristic, complemented
66C2×#469C2×C311yescharacteristic, complemented
67#2416C2×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#1862C2×C311yescharacteristic, complemented
77#1854C2×C311yescharacteristic, complemented
78#1736C2×C311yescharacteristic, complemented
79C22×C3×Q8—21no—
80C22×C3×D4—21no—
81C22×C3×D4—21no—
82C22×C3×D4—21no—
83C22×C3×D4—21no—
84C22×C3×D4D411yescharacteristic
85C22×C3×D4C2311yescharacteristic
86C22×C3×D4C2311yescharacteristic
87C23×C3×C4—21no—
88C23×C3×C4—21no—
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C2×C3×D8—22no—
92C2×C3×D8—22no—
93C2×C3×D8—41no—
94C2×C3×M16—22no—
95C2×C3×M16—22no—
96C2×C3×M16—41no—
97C22×C3×C8C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C22×C3×C8C2311yescharacteristic
101C3×C4⋊Q8—22no—
102C3×C4⋊Q8—22no—
103C3×#124—28no—
104C3×#124—28no—
105C3×#121—28no—
106C3×#121—22no—
107C3×#121—22no—
108C3×#121—22no—
109C3×#121—22no—
110C3×#121—22no—
111C3×#121—22no—
112C3×#121—41no—
113C3×#121—44no—
114C3×#121D414yescomplemented
115C3×C4×D4—22no—
116C3×C4×D4—22no—
117C3×C4×D4—22no—
118C3×C4×D4—22no—
119C3×#117—28no—
120C3×#117—22no—
121C3×#117—22no—
122C3×#117—22no—
123C3×#117D414yescomplemented
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4—22no—
126C2×C3×C4⋊C4—21no—
127C2×C3×C4⋊C4—21no—
128C2×C3×C4⋊C4—41no—
129C2×C3×C4⋊C4D411yescharacteristic
130C2×C3×C4⋊C4C2311yescharacteristic
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C4⋊C4C2311yescharacteristic
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C4⋊C4C2311yescharacteristic
135C2×C3×C4⋊C4C2311yescharacteristic
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×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×#106—22no—
153C3×#106—22no—
154C3×#102—22no—
155C3×#102—22no—
156C3×#102—22no—
157C3×#102—22no—
158C3×#102—22no—
159C3×#102—41no—
160C3×C22⋊C8—22no—
161C3×C22⋊C8—22no—
162C3×C22⋊C8—41no—
163C3×#95—21no—
164C3×#95—21no—
165C22×D8C22×C311yescharacteristic
166C22×M16C22×C311yescharacteristic
167#555—24no—
168#555—24no—
169C2×C4⋊Q8C22×C311yescharacteristic
170C2×#124—21no—
171C2×#124—21no—
172C2×#121—21no—
173C2×#121—21no—
174C2×#121C22×C311yescharacteristic
175C2×#121C22×C311yescharacteristic
176C2×#121C22×C311yescharacteristic
177C2×#121C22×C311yescharacteristic
178C2×C4×D4C22×C311yescharacteristic
179C2×C4×D4C22×C311yescharacteristic
180C2×#117—21no—
181C2×#117C22×C311yescharacteristic
182C2×#117C22×C311yescharacteristic
183C22×C4⋊C4C22×C311yescharacteristic
184#482—24no—
185#469—24no—
186C2×#107C22×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#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×C3—21no—
214C24×C3C2×D411yescharacteristic
215C24×C3C2×D411yescharacteristic
216C2×C3×Q8—24no—
217C2×C3×Q8—81no—
218C2×C3×Q8—81no—
219C2×C3×D4—22no—
220C2×C3×D4—24no—
221C2×C3×D4—24no—
222C2×C3×D4—22no—
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—21no—
234C2×C3×D4—41no—
235C2×C3×D4—42no—
236C2×C3×D4—42no—
237C2×C3×D4—42no—
238C2×C3×D4—42no—
239C2×C3×D4—42no—
240C2×C3×D4—81no—
241C2×C3×D4—81no—
242C2×C3×D4—81no—
243C2×C3×D4—81no—
244C2×C3×D4—81no—
245C2×C3×D4C2×D412yes—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—24no—
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—21no—
262C22×C3×C4—21no—
263C22×C3×C4—42no—
264C22×C3×C4—42no—
265C22×C3×C4—42no—
266C22×C3×C4—42no—
267C22×C3×C4—81no—
268C22×C3×C4C2×D411yescharacteristic
269C22×C3×C4C2×D411yescharacteristic
270C22×C3×C4C2×D411yescharacteristic
271C22×C3×C4C2×D412yes—
272C22×C3×C4C2×D412yes—
273C22×C3×C4C2×D411yescharacteristic
274C22×C3×C4C2411yescharacteristic
275C3×D8—44no—
276C3×M16—44no—
277C2×C3×C8—21no—
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#4112yes—
289C3×C4⋊C4—24no—
290C3×C4⋊C4—22no—
291C3×C4⋊C4—21no—
292C3×C4⋊C4—21no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—42no—
300C3×C4⋊C4—42no—
301C3×C4⋊C4C2×D412yes—
302C3×C4⋊C4C2×D412yes—
303C3×C4⋊C4C2×D412yes—
304C3×C4⋊C4#4112yes—
305C3×C22⋊C4—24no—
306C3×C22⋊C4—24no—
307C3×C22⋊C4—24no—
308C3×C22⋊C4—24no—
309C3×C22⋊C4—22no—
310C3×C22⋊C4—24no—
311C3×C22⋊C4—22no—
312C3×C22⋊C4—42no—
313C3×C22⋊C4—42no—
314C3×C22⋊C4—42no—
315C3×C22⋊C4—42no—
316C3×C22⋊C4—81no—
317C3×C42—24no—
318C3×C42—24no—
319C3×C42—21no—
320C3×C42—21no—
321C22×Q8—21no—
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—21no—
325C22×D4—21no—
326C22×D4C3×D411yescharacteristic
327C22×D4C23×C311yescharacteristic
328C22×D4C23×C311yescharacteristic
329C23×C4—21no—
330C23×C4—21no—
331C23×C4C23×C311yescharacteristic
332C23×C4C23×C311yescharacteristic
333C2×D8—22no—
334C2×D8—22no—
335C2×D8—41no—
336C2×M16—22no—
337C2×M16—22no—
338C2×M16—41no—
339C22×C8C23×C311yescharacteristic
340C22×C8C23×C311yescharacteristic
341C22×C8C23×C311yescharacteristic
342C22×C8C23×C311yescharacteristic
343C4⋊Q8—22no—
344C4⋊Q8—22no—
345#124—28no—
346#124—28no—
347#121—28no—
348#121—22no—
349#121—22no—
350#121—22no—
351#121—22no—
352#121—22no—
353#121—22no—
354#121—41no—
355#121—44no—
356#121C3×D414yescomplemented
357C4×D4—22no—
358C4×D4—22no—
359C4×D4—22no—
360C4×D4—22no—
361#117—28no—
362#117—22no—
363#117—22no—
364#117—22no—
365#117C3×D414yescomplemented
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—41no—
371C2×C4⋊C4C3×D411yescharacteristic
372C2×C4⋊C4C23×C311yescharacteristic
373C2×C4⋊C4C23×C311yescharacteristic
374C2×C4⋊C4C23×C311yescharacteristic
375C2×C4⋊C4C23×C311yescharacteristic
376C2×C4⋊C4C23×C311yescharacteristic
377C2×C4⋊C4C23×C311yescharacteristic
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4C3×D411yescharacteristic
389C2×C22⋊C4C3×D411yescharacteristic
390C2×C42—21no—
391C2×C42—21no—
392C2×C42C23×C311yescharacteristic
393#107—22no—
394#106—22no—
395#106—22no—
396#102—22no—
397#102—22no—
398#102—22no—
399#102—22no—
400#102—22no—
401#102—41no—
402C22⋊C8—22no—
403C22⋊C8—22no—
404C22⋊C8—41no—
405#95—21no—
406#95—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—22no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
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#12012yes—
435C23×C3C22×D411yescharacteristic
436C3×Q8—84no—
437C3×D4—22no—
438C3×D4—22no—
439C3×D4—44no—
440C3×D4—41no—
441C3×D4—41no—
442C3×D4—41no—
443C3×D4—41no—
444C3×D4—41no—
445C3×D4—41no—
446C3×D4—84no—
447C3×D4—84no—
448C3×D4—84no—
449C3×D4—84no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—21no—
459C2×C3×C4—22no—
460C2×C3×C4—21no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—21no—
464C2×C3×C4—22no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—48no—
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—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—84no—
488C2×C3×C4#12012yes—
489C2×C3×C4AGL(1,ℤ/8)12yes—
490C2×C3×C4C22×D411yescharacteristic
491C2×C3×C4C22×D411yescharacteristic
492C2×C3×C4C2×#4111yescharacteristic
493C2×C3×C4C2×#4111yescharacteristic
494C2×C3×C4H(5,𝔽2)11yescharacteristic
495C2×C3×C42−1+411yescharacteristic
496C3×C8—22no—
497C3×C8—41no—
498C3×C8—41no—
499C3×C8—41no—
500C24—21no—
501C24—21no—
502C24C2×C3×D411yescharacteristic
503C24C2×C3×D411yescharacteristic
504C2×Q8—24no—
505C2×Q8—81no—
506C2×Q8—81no—
507C2×D4—22no—
508C2×D4—24no—
509C2×D4—24no—
510C2×D4—22no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—41no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—81no—
529C2×D4—81no—
530C2×D4—81no—
531C2×D4—81no—
532C2×D4—81no—
533C2×D4C2×C3×D412yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—24no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—81no—
556C22×C4C2×C3×D411yescharacteristic
557C22×C4C2×C3×D411yescharacteristic
558C22×C4C2×C3×D411yescharacteristic
559C22×C4C2×C3×D412yes—
560C22×C4C2×C3×D412yes—
561C22×C4C2×C3×D411yescharacteristic
562C22×C4C24×C311yescharacteristic
563D8—44no—
564M16—44no—
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—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8C3×#4112yes—
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⋊C4C2×C3×D412yes—
590C4⋊C4C2×C3×D412yes—
591C4⋊C4C2×C3×D412yes—
592C4⋊C4C3×#4112yes—
593C22⋊C4—24no—
594C22⋊C4—24no—
595C22⋊C4—24no—
596C22⋊C4—24no—
597C22⋊C4—22no—
598C22⋊C4—24no—
599C22⋊C4—22no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—81no—
605C42—24no—
606C42—24no—
607C42—21no—
608C42—21no—
609C22×C3—22no—
610C22×C3—22no—
611C22×C3—22no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—42no—
620C22×C3—42no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—42no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—81no—
627C22×C3—81no—
628C22×C3—81no—
629C22×C3—81no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3—81no—
635C22×C3—81no—
636C22×C3—81no—
637C22×C3C2×#12011yescharacteristic
638C22×C3#54611yescharacteristic
639C22×C3#54711yescharacteristic
640C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
641C22×C3#57511yescharacteristic
642C22×C3#57611yescharacteristic
643C22×C3#57711yescharacteristic
644C3×C4—22no—
645C3×C4—22no—
646C3×C4—41no—
647C3×C4—42no—
648C3×C4—41no—
649C3×C4—42no—
650C3×C4—42no—
651C3×C4—42no—
652C3×C4—81no—
653C3×C4—81no—
654C3×C4#53211yescharacteristic
655C3×C4#53711yescharacteristic
656C3×C4#54611yescharacteristic
657C3×C4#54711yescharacteristic
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23C3×#12012yes—
686C23C22×C3×D411yescharacteristic
687Q8—84no—
688D4—22no—
689D4—22no—
690D4—44no—
691D4—41no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—84no—
698D4—84no—
699D4—84no—
700D4—84no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—48no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—84no—
739C2×C4C3×#12012yes—
740C2×C4C3×AGL(1,ℤ/8)12yes—
741C2×C4C22×C3×D411yescharacteristic
742C2×C4C22×C3×D411yescharacteristic
743C2×C4C2×C3×#4111yescharacteristic
744C2×C4C2×C3×#4111yescharacteristic
745C2×C4C3×H(5,𝔽2)11yescharacteristic
746C2×C4C3×2−1+411yescharacteristic
747C8—22no—
748C8—41no—
749C8—41no—
750C8—41no—
751C2×C3—42no—
752C2×C3—81no—
753C2×C3—82no—
754C2×C3—161no—
755C2×C3#243011yescharacteristic
756C2×C3#300611yescharacteristic
757C2×C3#301211yescharacteristic
758C2×C3#332111yescharacteristic
759C2×C3#332511yescharacteristic
760C2×C3#334711yescharacteristic
761C2×C3#335411yescharacteristic
762C22—22no—
763C22—22no—
764C22—22no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—42no—
771C22—42no—
772C22—41no—
773C22—41no—
774C22—42no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22C2×C3×#12011yescharacteristic
791C22C3×#54611yescharacteristic
792C22C3×#54711yescharacteristic
793C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
794C22C3×#57511yescharacteristic
795C22C3×#57611yescharacteristic
796C22C3×#57711yescharacteristic
797C4—22no—
798C4—22no—
799C4—41no—
800C4—42no—
801C4—41no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—81no—
806C4—81no—
807C4C3×#53211yescharacteristic
808C4C3×#53711yescharacteristic
809C4C3×#54611yescharacteristic
810C4C3×#54711yescharacteristic
811C3#2555411yescharacteristic, direct product factor, Sylow
812C2—42no—
813C2—81no—
814C2—82no—
815C2—161no—
816C2C3×#243011yescharacteristic
817C2C3×#300611yescharacteristic
818C2C3×#301211yescharacteristic
819C2C3×#332111yescharacteristic
820C2C3×#332511yescharacteristic
821C2C3×#334711yescharacteristic
822C2C3×#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×#555C2semidirect
2. C2×C3×#482C2semidirect
3. C2×C3×#469C2semidirect
4. C3×#2416C2semidirect
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×#1862C2semidirect
14. C3×#1854C2semidirect
15. C3×#1736C2semidirect
16. #25554C3direct (N × H)
64. C2×#555C2×C3semidirect
65. C2×#482C2×C3semidirect
66. C2×#469C2×C3semidirect
67. #2416C2×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. #1862C2×C3semidirect
77. #1854C2×C3semidirect
78. #1736C2×C3semidirect
114. C3×#121D4semidirect
123. C3×#117D4semidirect
356. #121C3×D4semidirect
365. #117C3×D4semidirect
811. C3#25554direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5552
C2×C3×#4822
C2×C3×#4692
C3×#24162
C3×#20582
C3×#20342
C3×#20232
C3×#19992
C3×#18792
C3×#18752
C3×#18742
C3×#18702
C3×#18622
C3×#18542
C3×#17362
#255543