Finite Group Databasebeta

← C3×#30468 #10649075

Subgroups — C3×#30468 #10649075

Order 768.

1330 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#496C211yesmaximal, characteristic, complemented
2C2×C3×#463C211yesmaximal, characteristic, complemented
3C2×C3×#447C211yesmaximal, characteristic, complemented
4C2×C3×#447C211yesmaximal, characteristic, complemented
5C3×#2435C211yesmaximal, characteristic, complemented
6C3×#2428C211yesmaximal, characteristic, complemented
7C3×#2054C211yesmaximal, characteristic, complemented
8C3×#2042C211yesmaximal, characteristic, complemented
9C3×#2012C211yesmaximal, characteristic, complemented
10C3×#2011C211yesmaximal, characteristic, complemented
11C3×#2000C211yesmaximal, characteristic, complemented
12C3×#2000C211yesmaximal, characteristic, complemented
13C3×#1936C211yesmaximal, characteristic, complemented
14C3×#1924C211yesmaximal, characteristic, complemented
15C3×#1879C211yesmaximal, characteristic, complemented
16#30468C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×D4C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic, complemented
19C22×C3×SD16C2211yescharacteristic, complemented
20C22×C3×D8C2211yescharacteristic
21C22×C3×D8C2211yescharacteristic
22C22×C3×D8C2211yescharacteristic
23C22×C3×D8C2211yescharacteristic
24C2×C3×#127C2211yescharacteristic, complemented
25C2×C3×#124C2211yescharacteristic
26C2×C3×#124C2211yescharacteristic
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×#121—21no—
29C2×C3×#121C2211yescharacteristic
30C2×C3×#121C2211yescharacteristic
31C2×C3×C4×D4C2211yescharacteristic, complemented
32C3×#496—24no—
33C3×#463—24no—
34C3×#447—24no—
35C3×#447—24no—
36C2×C3×C4⋊C8C2211yescharacteristic, complemented
37C2×C3×#103C2211yescharacteristic, complemented
38C2×C3×#103C2211yescharacteristic, complemented
39C2×C3×#102C2211yescharacteristic
40C2×C3×#102C2211yescharacteristic
41C2×C3×#102C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic, complemented
44C2×C3×#102C2211yescharacteristic, complemented
45C2×C3×C22⋊C8C2211yescharacteristic
46C2×C3×C22⋊C8C2211yescharacteristic
47C2×C3×#97C2211yescharacteristic, complemented
48C3×#394—21no—
49C3×#394—21no—
50C3×#394—21no—
51C3×#392—21no—
52C3×#390C2211yescharacteristic
53C3×#390C2211yescharacteristic
54C3×#390C2211yescharacteristic, complemented
55C3×#389C2211yescharacteristic, complemented
56C3×#386—21no—
57C3×#379—21no—
58C3×#379—21no—
59C3×C4×C22⋊C4C2211yescharacteristic
60C3×#340C2211yescharacteristic, complemented
61C3×#340C2211yescharacteristic, complemented
62C3×#336C2211yescharacteristic, complemented
63C3×#336C2211yescharacteristic, complemented
64C2×#496C2×C311yescharacteristic, complemented
65C2×#463C2×C311yescharacteristic, complemented
66C2×#447C2×C311yescharacteristic, complemented
67C2×#447C2×C311yescharacteristic, complemented
68#2435C2×C311yescharacteristic, complemented
69#2428C2×C311yescharacteristic, complemented
70#2054C2×C311yescharacteristic, complemented
71#2042C2×C311yescharacteristic, complemented
72#2012C2×C311yescharacteristic, complemented
73#2011C2×C311yescharacteristic, complemented
74#2000C2×C311yescharacteristic, complemented
75#2000C2×C311yescharacteristic, complemented
76#1936C2×C311yescharacteristic, complemented
77#1924C2×C311yescharacteristic, complemented
78#1879C2×C311yescharacteristic, complemented
79C25×C3—21no—
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4—22no—
82C22×C3×D4—22no—
83C22×C3×D4—21no—
84C22×C3×D4—21no—
85C22×C3×D4—21no—
86C22×C3×D4—21no—
87C22×C3×D4—21no—
88C22×C3×D4—41no—
89C22×C3×D4—41no—
90C22×C3×D4—41no—
91C22×C3×D4—41no—
92C22×C3×D4C2311yescharacteristic
93C22×C3×D4C2311yescharacteristic
94C22×C3×D4C2311yescharacteristic
95C22×C3×D4C2311yescharacteristic
96C23×C3×C4—21no—
97C23×C3×C4C2311yescharacteristic
98C2×C3×SD16—22no—
99C2×C3×SD16—22no—
100C2×C3×SD16—22no—
101C2×C3×SD16—41no—
102C2×C3×SD16—41no—
103C2×C3×SD16—41no—
104C2×C3×D8—22no—
105C2×C3×D8—22no—
106C2×C3×D8—22no—
107C2×C3×D8—22no—
108C2×C3×D8—22no—
109C2×C3×D8—41no—
110C2×C3×D8—41no—
111C2×C3×D8—41no—
112C2×C3×D8—41no—
113C2×C3×D8—41no—
114C2×C3×D8—41no—
115C2×C3×D8D414yescomplemented
116C22×C3×C8C2311yescharacteristic
117C22×C3×C8C2311yescharacteristic
118C22×C3×C8C2311yescharacteristic
119C22×C3×C8C2311yescharacteristic
120C3×#127—22no—
121C3×#127—41no—
122C3×#124—22no—
123C3×#124—22no—
124C3×#124—41no—
125C3×#124—41no—
126C3×C22⋊Q8—41no—
127C3×C22⋊Q8—41no—
128C3×#121—22no—
129C3×#121—22no—
130C3×#121—44no—
131C3×#121—41no—
132C3×#121—41no—
133C3×C4×D4—22no—
134C3×C4×D4—41no—
135C2×C3×C4⋊C4—21no—
136C2×C3×C4⋊C4—21no—
137C2×C3×C4⋊C4C2311yescharacteristic
138C2×C3×C4⋊C4C2311yescharacteristic
139C2×C3×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
149C2×C3×C22⋊C4—21no—
150C2×C3×C22⋊C4—21no—
151C2×C3×C22⋊C4—21no—
152C2×C3×C22⋊C4—21no—
153C2×C3×C22⋊C4—21no—
154C2×C3×C22⋊C4D411yescharacteristic
155C2×C3×C22⋊C4D411yescharacteristic
156C2×C3×C42C2311yescharacteristic
157C2×C3×C42C2311yescharacteristic
158C3×C4⋊C8—22no—
159C3×#103—22no—
160C3×#103—41no—
161C3×#102—22no—
162C3×#102—22no—
163C3×#102—22no—
164C3×#102—41no—
165C3×#102—41no—
166C3×#102D414yescomplemented
167C3×C22⋊C8—22no—
168C3×C22⋊C8—22no—
169C3×#97—22no—
170C3×#95—21no—
171C3×#95D411yescharacteristic
172C3×#95D411yescharacteristic
173C23×D4C22×C311yescharacteristic
174C22×SD16C22×C311yescharacteristic, complemented
175C22×SD16C22×C311yescharacteristic, complemented
176C22×D8C22×C311yescharacteristic
177C22×D8C22×C311yescharacteristic
178C22×D8C22×C311yescharacteristic
179C22×D8C22×C311yescharacteristic
180C2×#127C22×C311yescharacteristic, complemented
181C2×#124C22×C311yescharacteristic
182C2×#124C22×C311yescharacteristic
183C2×C22⋊Q8C22×C311yescharacteristic
184C2×#121—21no—
185C2×#121C22×C311yescharacteristic
186C2×#121C22×C311yescharacteristic
187C2×C4×D4C22×C311yescharacteristic, complemented
188#496—24no—
189#463—24no—
190#447—24no—
191#447—24no—
192C2×C4⋊C8C22×C311yescharacteristic, complemented
193C2×#103C22×C311yescharacteristic, complemented
194C2×#103C22×C311yescharacteristic, complemented
195C2×#102C22×C311yescharacteristic
196C2×#102C22×C311yescharacteristic
197C2×#102C22×C311yescharacteristic
198C2×#102C22×C311yescharacteristic
199C2×#102C22×C311yescharacteristic, complemented
200C2×#102C22×C311yescharacteristic, complemented
201C2×C22⋊C8C22×C311yescharacteristic
202C2×C22⋊C8C22×C311yescharacteristic
203C2×#97C22×C311yescharacteristic, complemented
204#394—21no—
205#394—21no—
206#394—21no—
207#392—21no—
208#390C22×C311yescharacteristic
209#390C22×C311yescharacteristic
210#390C22×C311yescharacteristic, complemented
211#389C22×C311yescharacteristic, complemented
212#386—21no—
213#379—21no—
214#379—21no—
215C4×C22⋊C4C22×C311yescharacteristic
216#340C22×C311yescharacteristic, complemented
217#340C22×C311yescharacteristic, complemented
218#336C22×C311yescharacteristic, complemented
219#336C22×C311yescharacteristic, complemented
220C24×C3—21no—
221C24×C3—21no—
222C24×C3—21no—
223C24×C3—21no—
224C24×C3—42no—
225C24×C3—42no—
226C24×C3—42no—
227C24×C3—42no—
228C24×C3—42no—
229C24×C3—81no—
230C24×C3—81no—
231C24×C3C2×D411yescharacteristic
232C2×C3×Q8—21no—
233C2×C3×Q8—21no—
234C2×C3×Q8—21no—
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4—21no—
252C2×C3×D4—21no—
253C2×C3×D4—21no—
254C2×C3×D4—21no—
255C2×C3×D4—21no—
256C2×C3×D4—21no—
257C2×C3×D4—21no—
258C2×C3×D4—21no—
259C2×C3×D4—42no—
260C2×C3×D4—42no—
261C2×C3×D4—42no—
262C2×C3×D4—42no—
263C2×C3×D4—42no—
264C2×C3×D4—42no—
265C2×C3×D4—42no—
266C2×C3×D4—42no—
267C2×C3×D4—44no—
268C2×C3×D4—44no—
269C2×C3×D4—44no—
270C2×C3×D4—44no—
271C2×C3×D4—42no—
272C2×C3×D4—42no—
273C2×C3×D4—42no—
274C2×C3×D4—81no—
275C2×C3×D4—81no—
276C2×C3×D4—81no—
277C2×C3×D4—81no—
278C2×C3×D4C2×D412yes—
279C2×C3×D4C2×D412yes—
280C2×C3×D4C2×D412yes—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—42no—
292C22×C3×C4—42no—
293C22×C3×C4—81no—
294C22×C3×C4C2×D411yescharacteristic
295C22×C3×C4C2×D411yescharacteristic
296C22×C3×C4C2×D411yescharacteristic
297C22×C3×C4C2×D411yescharacteristic
298C22×C3×C4C2×D411yescharacteristic
299C22×C3×C4C2411yescharacteristic
300C3×SD16—44no—
301C3×SD16—44no—
302C3×D8—44no—
303C3×D8—44no—
304C3×D8—44no—
305C3×D8—44no—
306C2×C3×C8—21no—
307C2×C3×C8—21no—
308C2×C3×C8—21no—
309C2×C3×C8—21no—
310C2×C3×C8—21no—
311C2×C3×C8—21no—
312C2×C3×C8—21no—
313C2×C3×C8—21no—
314C2×C3×C8—21no—
315C2×C3×C8—21no—
316C2×C3×C8C2×D412yes—
317C2×C3×C8C2×D412yes—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—21no—
321C3×C4⋊C4—21no—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—42no—
324C3×C4⋊C4—42no—
325C3×C4⋊C4C2×D412yes—
326C3×C22⋊C4—22no—
327C3×C22⋊C4—41no—
328C3×C22⋊C4—42no—
329C3×C22⋊C4—42no—
330C3×C22⋊C4—42no—
331C3×C22⋊C4—42no—
332C3×C22⋊C4—42no—
333C3×C22⋊C4—42no—
334C3×C22⋊C4—42no—
335C3×C22⋊C4—42no—
336C3×C22⋊C4—42no—
337C3×C22⋊C4—81no—
338C3×C22⋊C4—81no—
339C3×C22⋊C4—81no—
340C3×C22⋊C4—81no—
341C3×C22⋊C4—81no—
342C3×C42—21no—
343C3×C42—21no—
344C3×C42—21no—
345C3×C42—21no—
346C25—21no—
347C22×Q8C23×C311yescharacteristic
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—21no—
351C22×D4—21no—
352C22×D4—21no—
353C22×D4—21no—
354C22×D4—21no—
355C22×D4—41no—
356C22×D4—41no—
357C22×D4—41no—
358C22×D4—41no—
359C22×D4C23×C311yescharacteristic
360C22×D4C23×C311yescharacteristic
361C22×D4C23×C311yescharacteristic
362C22×D4C23×C311yescharacteristic
363C23×C4—21no—
364C23×C4C23×C311yescharacteristic
365C2×SD16—22no—
366C2×SD16—22no—
367C2×SD16—22no—
368C2×SD16—41no—
369C2×SD16—41no—
370C2×SD16—41no—
371C2×D8—22no—
372C2×D8—22no—
373C2×D8—22no—
374C2×D8—22no—
375C2×D8—22no—
376C2×D8—41no—
377C2×D8—41no—
378C2×D8—41no—
379C2×D8—41no—
380C2×D8—41no—
381C2×D8—41no—
382C2×D8C3×D414yescomplemented
383C22×C8C23×C311yescharacteristic
384C22×C8C23×C311yescharacteristic
385C22×C8C23×C311yescharacteristic
386C22×C8C23×C311yescharacteristic
387#127—22no—
388#127—41no—
389#124—22no—
390#124—22no—
391#124—41no—
392#124—41no—
393C22⋊Q8—41no—
394C22⋊Q8—41no—
395#121—22no—
396#121—22no—
397#121—44no—
398#121—41no—
399#121—41no—
400C4×D4—22no—
401C4×D4—41no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4C23×C311yescharacteristic
405C2×C4⋊C4C23×C311yescharacteristic
406C2×C4⋊C4C23×C311yescharacteristic
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4C3×D411yescharacteristic
422C2×C22⋊C4C3×D411yescharacteristic
423C2×C42C23×C311yescharacteristic
424C2×C42C23×C311yescharacteristic
425C4⋊C8—22no—
426#103—22no—
427#103—41no—
428#102—22no—
429#102—22no—
430#102—22no—
431#102—41no—
432#102—41no—
433#102C3×D414yescomplemented
434C22⋊C8—22no—
435C22⋊C8—22no—
436#97—22no—
437#95—21no—
438#95C3×D411yescharacteristic
439#95C3×D411yescharacteristic
440C23×C3—21no—
441C23×C3—21no—
442C23×C3—21no—
443C23×C3—21no—
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—48no—
450C23×C3—41no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3—41no—
456C23×C3—41no—
457C23×C3—41no—
458C23×C3—41no—
459C23×C3—41no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3—41no—
465C23×C3—41no—
466C23×C3—41no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—84no—
476C23×C3—84no—
477C23×C3—84no—
478C23×C3—84no—
479C23×C3—84no—
480C23×C3—84no—
481C23×C3AGL(1,ℤ/8)12yes—
482C23×C3C22×D411yescharacteristic
483C3×Q8—41no—
484C3×Q8—41no—
485C3×Q8—41no—
486C3×Q8—41no—
487C3×D4—22no—
488C3×D4—22no—
489C3×D4—22no—
490C3×D4—22no—
491C3×D4—22no—
492C3×D4—22no—
493C3×D4—48no—
494C3×D4—41no—
495C3×D4—41no—
496C3×D4—41no—
497C3×D4—41no—
498C3×D4—41no—
499C3×D4—41no—
500C3×D4—41no—
501C3×D4—41no—
502C3×D4—41no—
503C3×D4—41no—
504C3×D4—84no—
505C3×D4—84no—
506C3×D4—84no—
507C3×D4—84no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—22no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—84no—
540C2×C3×C4C22×D411yescharacteristic
541C2×C3×C4C22×D411yescharacteristic
542C2×C3×C4H(5,𝔽2)11yescharacteristic
543C2×C3×C4H(5,𝔽2)11yescharacteristic
544C2×C3×C4H(5,𝔽2)11yescharacteristic
545C2×C3×C4H(5,𝔽2)11yescharacteristic
546C3×C8—22no—
547C3×C8—22no—
548C3×C8—41no—
549C3×C8—41no—
550C24—21no—
551C24—21no—
552C24—21no—
553C24—21no—
554C24—42no—
555C24—42no—
556C24—42no—
557C24—42no—
558C24—42no—
559C24—81no—
560C24—81no—
561C24C2×C3×D411yescharacteristic
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—44no—
598C2×D4—44no—
599C2×D4—44no—
600C2×D4—44no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—81no—
605C2×D4—81no—
606C2×D4—81no—
607C2×D4—81no—
608C2×D4C2×C3×D412yes—
609C2×D4C2×C3×D412yes—
610C2×D4C2×C3×D412yes—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—81no—
624C22×C4C2×C3×D411yescharacteristic
625C22×C4C2×C3×D411yescharacteristic
626C22×C4C2×C3×D411yescharacteristic
627C22×C4C2×C3×D411yescharacteristic
628C22×C4C2×C3×D411yescharacteristic
629C22×C4C24×C311yescharacteristic
630SD16—44no—
631SD16—44no—
632D8—44no—
633D8—44no—
634D8—44no—
635D8—44no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8C2×C3×D412yes—
647C2×C8C2×C3×D412yes—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4C2×C3×D412yes—
656C22⋊C4—22no—
657C22⋊C4—41no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—81no—
668C22⋊C4—81no—
669C22⋊C4—81no—
670C22⋊C4—81no—
671C22⋊C4—81no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—21no—
676C22×C3—22no—
677C22×C3—22no—
678C22×C3—22no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—42no—
684C22×C3—42no—
685C22×C3—42no—
686C22×C3—42no—
687C22×C3—42no—
688C22×C3—42no—
689C22×C3—42no—
690C22×C3—42no—
691C22×C3—42no—
692C22×C3—816no—
693C22×C3—81no—
694C22×C3—81no—
695C22×C3—81no—
696C22×C3—81no—
697C22×C3—81no—
698C22×C3—81no—
699C22×C3—81no—
700C22×C3—81no—
701C22×C3—81no—
702C22×C3—81no—
703C22×C3—81no—
704C22×C3—81no—
705C22×C3—81no—
706C22×C3—81no—
707C22×C3—81no—
708C22×C3—81no—
709C22×C3—81no—
710C22×C3—81no—
711C22×C3—81no—
712C22×C3#53511yescharacteristic
713C22×C3D4211yescharacteristic
714C22×C3D4211yescharacteristic
715C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
716C22×C3#57511yescharacteristic
717C22×C3#57611yescharacteristic
718C22×C3#57611yescharacteristic
719C3×C4—41no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—42no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—81no—
726C3×C4—81no—
727C3×C4—81no—
728C3×C4#53411yescharacteristic
729C3×C4#53511yescharacteristic
730C3×C4D4211yescharacteristic
731C3×C4#56011yescharacteristic
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—48no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—84no—
768C23—84no—
769C23—84no—
770C23—84no—
771C23—84no—
772C23—84no—
773C23C3×AGL(1,ℤ/8)12yes—
774C23C22×C3×D411yescharacteristic
775Q8—41no—
776Q8—41no—
777Q8—41no—
778Q8—41no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—22no—
785D4—48no—
786D4—41no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—84no—
797D4—84no—
798D4—84no—
799D4—84no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—84no—
832C2×C4C22×C3×D411yescharacteristic
833C2×C4C22×C3×D411yescharacteristic
834C2×C4C3×H(5,𝔽2)11yescharacteristic
835C2×C4C3×H(5,𝔽2)11yescharacteristic
836C2×C4C3×H(5,𝔽2)11yescharacteristic
837C2×C4C3×H(5,𝔽2)11yescharacteristic
838C8—22no—
839C8—22no—
840C8—41no—
841C8—41no—
842C2×C3—42no—
843C2×C3—82no—
844C2×C3—82no—
845C2×C3—82no—
846C2×C3—161no—
847C2×C3#266911yescharacteristic
848C2×C3#321311yescharacteristic
849C2×C3#322011yescharacteristic
850C2×C3#326411yescharacteristic
851C2×C3#326411yescharacteristic
852C2×C3#326811yescharacteristic
853C2×C3#327311yescharacteristic
854C22—22no—
855C22—22no—
856C22—22no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—816no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22C3×#53511yescharacteristic
891C22C3×D4211yescharacteristic
892C22C3×D4211yescharacteristic
893C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
894C22C3×#57511yescharacteristic
895C22C3×#57611yescharacteristic
896C22C3×#57611yescharacteristic
897C4—41no—
898C4—41no—
899C4—41no—
900C4—42no—
901C4—41no—
902C4—41no—
903C4—81no—
904C4—81no—
905C4—81no—
906C4C3×#53411yescharacteristic
907C4C3×#53511yescharacteristic
908C4C3×D4211yescharacteristic
909C4C3×#56011yescharacteristic
910C3#3046811yescharacteristic, direct product factor, Sylow
911C2—42no—
912C2—82no—
913C2—82no—
914C2—82no—
915C2—161no—
916C2C3×#266911yescharacteristic
917C2C3×#321311yescharacteristic
918C2C3×#322011yescharacteristic
919C2C3×#326411yescharacteristic
920C2C3×#326411yescharacteristic
921C2C3×#326811yescharacteristic
922C2C3×#327311yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#496C2semidirect
2. C2×C3×#463C2semidirect
3. C2×C3×#447C2semidirect
4. C2×C3×#447C2semidirect
5. C3×#2435C2semidirect
6. C3×#2428C2semidirect
7. C3×#2054C2semidirect
8. C3×#2042C2semidirect
9. C3×#2012C2semidirect
10. C3×#2011C2semidirect
11. C3×#2000C2semidirect
12. C3×#2000C2semidirect
13. C3×#1936C2semidirect
14. C3×#1924C2semidirect
15. C3×#1879C2semidirect
16. #30468C3direct (N × H)
18. C22×C3×SD16C22semidirect
19. C22×C3×SD16C22semidirect
24. C2×C3×#127C22semidirect
31. C2×C3×C4×D4C22semidirect
36. C2×C3×C4⋊C8C22semidirect
37. C2×C3×#103C22semidirect
38. C2×C3×#103C22semidirect
43. C2×C3×#102C22semidirect
44. C2×C3×#102C22semidirect
47. C2×C3×#97C22semidirect
54. C3×#390C22semidirect
55. C3×#389C22semidirect
60. C3×#340C22semidirect
61. C3×#340C22semidirect
62. C3×#336C22semidirect
63. C3×#336C22semidirect
64. C2×#496C2×C3semidirect
65. C2×#463C2×C3semidirect
66. C2×#447C2×C3semidirect
67. C2×#447C2×C3semidirect
68. #2435C2×C3semidirect
69. #2428C2×C3semidirect
70. #2054C2×C3semidirect
71. #2042C2×C3semidirect
72. #2012C2×C3semidirect
73. #2011C2×C3semidirect
74. #2000C2×C3semidirect
75. #2000C2×C3semidirect
76. #1936C2×C3semidirect
77. #1924C2×C3semidirect
78. #1879C2×C3semidirect
115. C2×C3×D8D4semidirect
166. C3×#102D4semidirect
174. C22×SD16C22×C3semidirect
175. C22×SD16C22×C3semidirect
180. C2×#127C22×C3semidirect
187. C2×C4×D4C22×C3semidirect
192. C2×C4⋊C8C22×C3semidirect
193. C2×#103C22×C3semidirect
194. C2×#103C22×C3semidirect
199. C2×#102C22×C3semidirect
200. C2×#102C22×C3semidirect
203. C2×#97C22×C3semidirect
210. #390C22×C3semidirect
211. #389C22×C3semidirect
216. #340C22×C3semidirect
217. #340C22×C3semidirect
218. #336C22×C3semidirect
219. #336C22×C3semidirect
382. C2×D8C3×D4semidirect
433. #102C3×D4semidirect
910. C3#30468direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4962
C2×C3×#4632
C2×C3×#4472
C3×#24352
C3×#24282
C3×#20542
C3×#20422
C3×#20122
C3×#20112
C3×#20002
C3×#19362
C3×#19242
C3×#18792
#304683