Finite Group Databasebeta

← C3×#24220 #10642827

Subgroups — C3×#24220 #10642827

Order 768.

1556 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#535C211yesmaximal, characteristic
2C2×C3×#464C211yesmaximal, characteristic, complemented
3C2×C3×#460C211yesmaximal, characteristic, complemented
4C2×C3×#452C211yesmaximal, characteristic, complemented
5C2×C3×#450C211yesmaximal, characteristic, complemented
6C3×#2323C211yesmaximal, characteristic, complemented
7C3×#2042C211yesmaximal, characteristic, complemented
8C3×#2041C211yesmaximal, characteristic, complemented
9C3×#2015C211yesmaximal, characteristic, complemented
10C3×#2014C211yesmaximal, characteristic, complemented
11C3×#1983C211yesmaximal, characteristic, complemented
12C3×#1982C211yesmaximal, characteristic, complemented
13C3×#1798C211yesmaximal, characteristic, complemented
14C3×#1788C211yesmaximal, characteristic, complemented
15C3×#1786C211yesmaximal, characteristic, complemented
16#24220C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×C3×D4C2211yescharacteristic
19C22×C3×Q16C2211yescharacteristic, complemented
20C22×C3×SD16C2211yescharacteristic
21C22×C3×SD16C2211yescharacteristic
22C22×C3×SD16C2211yescharacteristic, complemented
23C3×#535—24no—
24C3×#535—24no—
25C2×C3×#127C2211yescharacteristic
26C2×C3×#127C2211yescharacteristic
27C2×C3×#124C2211yescharacteristic
28C2×C3×#124C2211yescharacteristic
29C2×C3×C22⋊Q8C2211yescharacteristic
30C2×C3×#121—21no—
31C2×C3×#121—21no—
32C2×C3×#120—21no—
33C2×C3×#120—21no—
34C2×C3×C4×Q8C2211yescharacteristic, complemented
35C2×C3×#117C2211yescharacteristic
36C3×#464—24no—
37C3×#460—24no—
38C3×#452—24no—
39C3×#450—24no—
40C2×C3×C4⋊C8C2211yescharacteristic, complemented
41C2×C3×C4⋊C8C2211yescharacteristic, complemented
42C2×C3×#103C2211yescharacteristic, complemented
43C2×C3×#103C2211yescharacteristic, complemented
44C2×C3×#103C2211yescharacteristic, complemented
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×#102C2211yescharacteristic
48C2×C3×#102C2211yescharacteristic
49C2×C3×#102C2211yescharacteristic
50C2×C3×#102C2211yescharacteristic
51C2×C3×#102C2211yescharacteristic, complemented
52C2×C3×#102C2211yescharacteristic, complemented
53C2×C3×#102C2211yescharacteristic, complemented
54C2×C3×C22⋊C8C2211yescharacteristic
55C2×C3×C22⋊C8C2211yescharacteristic
56C3×#391C2211yescharacteristic, complemented
57C3×#389—21no—
58C3×#389C2211yescharacteristic, complemented
59C3×#388—21no—
60C3×#388—21no—
61C3×#387—21no—
62C3×#380C2211yescharacteristic
63C3×C4×C4⋊C4C2211yescharacteristic, complemented
64C3×#336C2211yescharacteristic, complemented
65C3×#336C2211yescharacteristic, complemented
66C2×#535C2×C311yescharacteristic
67C2×#464C2×C311yescharacteristic, complemented
68C2×#460C2×C311yescharacteristic, complemented
69C2×#452C2×C311yescharacteristic, complemented
70C2×#450C2×C311yescharacteristic, complemented
71#2323C2×C311yescharacteristic, complemented
72#2042C2×C311yescharacteristic, complemented
73#2041C2×C311yescharacteristic, complemented
74#2015C2×C311yescharacteristic, complemented
75#2014C2×C311yescharacteristic, complemented
76#1983C2×C311yescharacteristic, complemented
77#1982C2×C311yescharacteristic, complemented
78#1798C2×C311yescharacteristic, complemented
79#1788C2×C311yescharacteristic, complemented
80#1786C2×C311yescharacteristic, complemented
81C25×C3—21no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41—41no—
87C2×C3×#41—41no—
88C22×C3×Q8C2311yescharacteristic
89C22×C3×Q8C2311yescharacteristic
90C22×C3×D4—21no—
91C22×C3×D4—22no—
92C22×C3×D4—22no—
93C22×C3×D4—21no—
94C22×C3×D4—21no—
95C22×C3×D4—21no—
96C22×C3×D4—21no—
97C22×C3×D4—21no—
98C22×C3×D4—22no—
99C22×C3×D4—22no—
100C22×C3×D4—41no—
101C22×C3×D4—41no—
102C22×C3×D4C2311yescharacteristic
103C22×C3×D4C2311yescharacteristic
104C22×C3×D4C2311yescharacteristic
105C23×C3×C4—21no—
106C23×C3×C4C2311yescharacteristic
107C2×C3×Q16—22no—
108C2×C3×Q16—22no—
109C2×C3×Q16—41no—
110C2×C3×SD16—22no—
111C2×C3×SD16—22no—
112C2×C3×SD16—22no—
113C2×C3×SD16—22no—
114C2×C3×SD16—22no—
115C2×C3×SD16—22no—
116C2×C3×SD16—41no—
117C2×C3×SD16—41no—
118C2×C3×SD16—41no—
119C22×C3×C8C2311yescharacteristic
120C22×C3×C8C2311yescharacteristic
121C22×C3×C8C2311yescharacteristic
122C22×C3×C8C2311yescharacteristic
123C3×#127—22no—
124C3×#127—22no—
125C3×#127—22no—
126C3×#127D414yes—
127C3×#124—22no—
128C3×#124—22no—
129C3×#124—22no—
130C3×#124D414yes—
131C3×C22⋊Q8—22no—
132C3×C22⋊Q8D414yescomplemented
133C3×#121—28no—
134C3×#121—28no—
135C3×#120—28no—
136C3×#120—28no—
137C3×C4×Q8—22no—
138C3×C4×Q8—22no—
139C3×#117—22no—
140C3×#117—22no—
141C2×C3×C4⋊C4—21no—
142C2×C3×C4⋊C4—21no—
143C2×C3×C4⋊C4—21no—
144C2×C3×C4⋊C4D411yescharacteristic
145C2×C3×C4⋊C4D411yescharacteristic
146C2×C3×C4⋊C4C2311yescharacteristic
147C2×C3×C4⋊C4C2311yescharacteristic
148C2×C3×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
155C2×C3×C22⋊C4D411yescharacteristic
156C2×C3×C22⋊C4D411yescharacteristic
157C2×C3×C42—21no—
158C2×C3×C42—21no—
159C2×C3×C42C2311yescharacteristic
160C2×C3×C42C2311yescharacteristic
161C3×C4⋊C8—22no—
162C3×C4⋊C8—22no—
163C3×#103—22no—
164C3×#103—22no—
165C3×#103—41no—
166C3×#102—22no—
167C3×#102—22no—
168C3×#102—22no—
169C3×#102—22no—
170C3×#102—22no—
171C3×#102—22no—
172C3×#102—41no—
173C3×#102—41no—
174C3×#102—41no—
175C3×C22⋊C8—22no—
176C3×C22⋊C8—22no—
177C3×#95—21no—
178C3×#95—21no—
179C3×#95—21no—
180C3×#95—21no—
181C3×#95—21no—
182C22×#41C22×C311yescharacteristic
183C23×D4C22×C311yescharacteristic
184C22×Q16C22×C311yescharacteristic, complemented
185C22×SD16C22×C311yescharacteristic
186C22×SD16C22×C311yescharacteristic
187C22×SD16C22×C311yescharacteristic, complemented
188#535—24no—
189#535—24no—
190C2×#127C22×C311yescharacteristic
191C2×#127C22×C311yescharacteristic
192C2×#124C22×C311yescharacteristic
193C2×#124C22×C311yescharacteristic
194C2×C22⋊Q8C22×C311yescharacteristic
195C2×#121—21no—
196C2×#121—21no—
197C2×#120—21no—
198C2×#120—21no—
199C2×C4×Q8C22×C311yescharacteristic, complemented
200C2×#117C22×C311yescharacteristic
201#464—24no—
202#460—24no—
203#452—24no—
204#450—24no—
205C2×C4⋊C8C22×C311yescharacteristic, complemented
206C2×C4⋊C8C22×C311yescharacteristic, complemented
207C2×#103C22×C311yescharacteristic, complemented
208C2×#103C22×C311yescharacteristic, complemented
209C2×#103C22×C311yescharacteristic, complemented
210C2×#102C22×C311yescharacteristic
211C2×#102C22×C311yescharacteristic
212C2×#102C22×C311yescharacteristic
213C2×#102C22×C311yescharacteristic
214C2×#102C22×C311yescharacteristic
215C2×#102C22×C311yescharacteristic
216C2×#102C22×C311yescharacteristic, complemented
217C2×#102C22×C311yescharacteristic, complemented
218C2×#102C22×C311yescharacteristic, complemented
219C2×C22⋊C8C22×C311yescharacteristic
220C2×C22⋊C8C22×C311yescharacteristic
221#391C22×C311yescharacteristic, complemented
222#389—21no—
223#389C22×C311yescharacteristic, complemented
224#388—21no—
225#388—21no—
226#387—21no—
227#380C22×C311yescharacteristic
228C4×C4⋊C4C22×C311yescharacteristic, complemented
229#336C22×C311yescharacteristic, complemented
230#336C22×C311yescharacteristic, complemented
231C24×C3—24no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3—42no—
236C24×C3—42no—
237C24×C3—81no—
238C24×C3—81no—
239C24×C3—81no—
240C24×C3—81no—
241C24×C3C2×D411yescharacteristic
242C3×#41—44no—
243C3×#41—44no—
244C3×#41—44no—
245C3×#41—44no—
246C2×C3×Q8—21no—
247C2×C3×Q8—21no—
248C2×C3×Q8—21no—
249C2×C3×Q8—21no—
250C2×C3×Q8—21no—
251C2×C3×Q8—21no—
252C2×C3×Q8—21no—
253C2×C3×Q8—21no—
254C2×C3×Q8—21no—
255C2×C3×Q8—21no—
256C2×C3×Q8C2×D412yes—
257C2×C3×Q8C2×D412yes—
258C2×C3×D4—24no—
259C2×C3×D4—24no—
260C2×C3×D4—24no—
261C2×C3×D4—24no—
262C2×C3×D4—24no—
263C2×C3×D4—24no—
264C2×C3×D4—21no—
265C2×C3×D4—21no—
266C2×C3×D4—21no—
267C2×C3×D4—21no—
268C2×C3×D4—21no—
269C2×C3×D4—21no—
270C2×C3×D4—21no—
271C2×C3×D4—21no—
272C2×C3×D4—21no—
273C2×C3×D4—21no—
274C2×C3×D4—21no—
275C2×C3×D4—21no—
276C2×C3×D4—21no—
277C2×C3×D4—21no—
278C2×C3×D4—21no—
279C2×C3×D4—44no—
280C2×C3×D4—44no—
281C2×C3×D4—44no—
282C2×C3×D4—44no—
283C2×C3×D4—42no—
284C2×C3×D4—42no—
285C2×C3×D4—42no—
286C2×C3×D4—42no—
287C2×C3×D4—81no—
288C2×C3×D4—81no—
289C2×C3×D4—81no—
290C2×C3×D4—81no—
291C2×C3×D4—81no—
292C2×C3×D4—81no—
293C2×C3×D4—81no—
294C2×C3×D4—81no—
295C2×C3×D4C2×D412yes—
296C2×C3×D4C2×D412yes—
297C2×C3×D4C2×D412yes—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—24no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—42no—
309C22×C3×C4—42no—
310C22×C3×C4C2×D411yescharacteristic
311C22×C3×C4C2×D411yescharacteristic
312C22×C3×C4C2×D411yescharacteristic
313C22×C3×C4C2×D411yescharacteristic
314C22×C3×C4C2×D411yescharacteristic
315C22×C3×C4C2×D412yes—
316C22×C3×C4#4112yes—
317C22×C3×C4C2411yescharacteristic
318C3×Q16—44no—
319C3×SD16—44no—
320C3×SD16—44no—
321C3×SD16—44no—
322C2×C3×C8—21no—
323C2×C3×C8—21no—
324C2×C3×C8—21no—
325C2×C3×C8—21no—
326C2×C3×C8—21no—
327C2×C3×C8—21no—
328C2×C3×C8—21no—
329C2×C3×C8—21no—
330C2×C3×C8—21no—
331C2×C3×C8—21no—
332C2×C3×C8—21no—
333C2×C3×C8—21no—
334C3×C4⋊C4—22no—
335C3×C4⋊C4—22no—
336C3×C4⋊C4—24no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—42no—
343C3×C4⋊C4—81no—
344C3×C4⋊C4C2×D412yes—
345C3×C22⋊C4—24no—
346C3×C22⋊C4—24no—
347C3×C22⋊C4—24no—
348C3×C22⋊C4—24no—
349C3×C22⋊C4—24no—
350C3×C22⋊C4—22no—
351C3×C22⋊C4—22no—
352C3×C22⋊C4—81no—
353C3×C42—21no—
354C3×C42—21no—
355C3×C42—42no—
356C3×C42—81no—
357C3×C42C2×D412yes—
358C3×C42C2×D412yes—
359C25—21no—
360C2×#41—22no—
361C2×#41—22no—
362C2×#41—22no—
363C2×#41—22no—
364C2×#41—41no—
365C2×#41—41no—
366C22×Q8C23×C311yescharacteristic
367C22×Q8C23×C311yescharacteristic
368C22×D4—21no—
369C22×D4—22no—
370C22×D4—22no—
371C22×D4—21no—
372C22×D4—21no—
373C22×D4—21no—
374C22×D4—21no—
375C22×D4—21no—
376C22×D4—22no—
377C22×D4—22no—
378C22×D4—41no—
379C22×D4—41no—
380C22×D4C23×C311yescharacteristic
381C22×D4C23×C311yescharacteristic
382C22×D4C23×C311yescharacteristic
383C23×C4—21no—
384C23×C4C23×C311yescharacteristic
385C2×Q16—22no—
386C2×Q16—22no—
387C2×Q16—41no—
388C2×SD16—22no—
389C2×SD16—22no—
390C2×SD16—22no—
391C2×SD16—22no—
392C2×SD16—22no—
393C2×SD16—22no—
394C2×SD16—41no—
395C2×SD16—41no—
396C2×SD16—41no—
397C22×C8C23×C311yescharacteristic
398C22×C8C23×C311yescharacteristic
399C22×C8C23×C311yescharacteristic
400C22×C8C23×C311yescharacteristic
401#127—22no—
402#127—22no—
403#127—22no—
404#127C3×D414yes—
405#124—22no—
406#124—22no—
407#124—22no—
408#124C3×D414yes—
409C22⋊Q8—22no—
410C22⋊Q8C3×D414yescomplemented
411#121—28no—
412#121—28no—
413#120—28no—
414#120—28no—
415C4×Q8—22no—
416C4×Q8—22no—
417#117—22no—
418#117—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4C3×D411yescharacteristic
423C2×C4⋊C4C3×D411yescharacteristic
424C2×C4⋊C4C23×C311yescharacteristic
425C2×C4⋊C4C23×C311yescharacteristic
426C2×C4⋊C4C23×C311yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4C3×D411yescharacteristic
434C2×C22⋊C4C3×D411yescharacteristic
435C2×C42—21no—
436C2×C42—21no—
437C2×C42C23×C311yescharacteristic
438C2×C42C23×C311yescharacteristic
439C4⋊C8—22no—
440C4⋊C8—22no—
441#103—22no—
442#103—22no—
443#103—41no—
444#102—22no—
445#102—22no—
446#102—22no—
447#102—22no—
448#102—22no—
449#102—22no—
450#102—41no—
451#102—41no—
452#102—41no—
453C22⋊C8—22no—
454C22⋊C8—22no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460C23×C3—21no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—48no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—41no—
487C23×C3—41no—
488C23×C3—84no—
489C23×C3—84no—
490C23×C3—84no—
491C23×C3—84no—
492C23×C3—84no—
493C23×C3—84no—
494C23×C3#12112yes—
495C23×C3C22×D411yescharacteristic
496C3×Q8—22no—
497C3×Q8—22no—
498C3×Q8—22no—
499C3×Q8—22no—
500C3×Q8—41no—
501C3×Q8—41no—
502C3×Q8—41no—
503C3×Q8—41no—
504C3×D4—22no—
505C3×D4—22no—
506C3×D4—22no—
507C3×D4—22no—
508C3×D4—22no—
509C3×D4—22no—
510C3×D4—48no—
511C3×D4—48no—
512C3×D4—41no—
513C3×D4—41no—
514C3×D4—41no—
515C3×D4—41no—
516C3×D4—41no—
517C3×D4—41no—
518C3×D4—84no—
519C3×D4—84no—
520C3×D4—84no—
521C3×D4—84no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—22no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—48no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4#12012yes—
555C2×C3×C4#12012yes—
556C2×C3×C4#12112yes—
557C2×C3×C4C22×D411yescharacteristic
558C2×C3×C4C22×D411yescharacteristic
559C2×C3×C4C22×D411yescharacteristic
560C2×C3×C4C2×#4111yescharacteristic
561C2×C3×C4H(5,𝔽2)11yescharacteristic
562C2×C3×C4H(5,𝔽2)11yescharacteristic
563C3×C8—41no—
564C3×C8—41no—
565C3×C8—41no—
566C3×C8—41no—
567C24—24no—
568C24—21no—
569C24—21no—
570C24—21no—
571C24—42no—
572C24—42no—
573C24—81no—
574C24—81no—
575C24—81no—
576C24—81no—
577C24C2×C3×D411yescharacteristic
578#41—44no—
579#41—44no—
580#41—44no—
581#41—44no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8C2×C3×D412yes—
593C2×Q8C2×C3×D412yes—
594C2×D4—24no—
595C2×D4—24no—
596C2×D4—24no—
597C2×D4—24no—
598C2×D4—24no—
599C2×D4—24no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—44no—
618C2×D4—44no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4—42no—
622C2×D4—42no—
623C2×D4—81no—
624C2×D4—81no—
625C2×D4—81no—
626C2×D4—81no—
627C2×D4—81no—
628C2×D4—81no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4C2×C3×D412yes—
632C2×D4C2×C3×D412yes—
633C2×D4C2×C3×D412yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—24no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—42no—
645C22×C4—42no—
646C22×C4C2×C3×D411yescharacteristic
647C22×C4C2×C3×D411yescharacteristic
648C22×C4C2×C3×D411yescharacteristic
649C22×C4C2×C3×D411yescharacteristic
650C22×C4C2×C3×D411yescharacteristic
651C22×C4C2×C3×D412yes—
652C22×C4C3×#4112yes—
653C22×C4C24×C311yescharacteristic
654Q16—44no—
655SD16—44no—
656SD16—44no—
657SD16—44no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—24no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—42no—
679C4⋊C4—81no—
680C4⋊C4C2×C3×D412yes—
681C22⋊C4—24no—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—22no—
687C22⋊C4—22no—
688C22⋊C4—81no—
689C42—21no—
690C42—21no—
691C42—42no—
692C42—81no—
693C42C2×C3×D412yes—
694C42C2×C3×D412yes—
695C22×C3—22no—
696C22×C3—22no—
697C22×C3—22no—
698C22×C3—41no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—42no—
703C22×C3—42no—
704C22×C3—42no—
705C22×C3—42no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3—42no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—816no—
712C22×C3—81no—
713C22×C3—81no—
714C22×C3—81no—
715C22×C3—81no—
716C22×C3—81no—
717C22×C3—81no—
718C22×C3—81no—
719C22×C3—81no—
720C22×C3—81no—
721C22×C3—81no—
722C22×C3—81no—
723C22×C3—81no—
724C22×C3C2×#12011yescharacteristic
725C22×C3C2×#12111yescharacteristic
726C22×C3#53511yescharacteristic
727C22×C3#57611yescharacteristic
728C22×C3#57711yescharacteristic
729C22×C3#57711yescharacteristic
730C22×C3#57711yescharacteristic
731C3×C4—22no—
732C3×C4—22no—
733C3×C4—22no—
734C3×C4—42no—
735C3×C4—42no—
736C3×C4—41no—
737C3×C4—41no—
738C3×C4—42no—
739C3×C4—81no—
740C3×C4—81no—
741C3×C4D4211yescharacteristic
742C3×C4D4211yescharacteristic
743C3×C4#54611yescharacteristic
744C3×C4#54611yescharacteristic
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—48no—
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—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—84no—
774C23—84no—
775C23—84no—
776C23—84no—
777C23—84no—
778C23—84no—
779C23C3×#12112yes—
780C23C22×C3×D411yescharacteristic
781Q8—22no—
782Q8—22no—
783Q8—22no—
784Q8—22no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789D4—22no—
790D4—22no—
791D4—22no—
792D4—22no—
793D4—22no—
794D4—22no—
795D4—48no—
796D4—48no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—41no—
803D4—84no—
804D4—84no—
805D4—84no—
806D4—84no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—48no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4C3×#12012yes—
840C2×C4C3×#12012yes—
841C2×C4C3×#12112yes—
842C2×C4C22×C3×D411yescharacteristic
843C2×C4C22×C3×D411yescharacteristic
844C2×C4C22×C3×D411yescharacteristic
845C2×C4C2×C3×#4111yescharacteristic
846C2×C4C3×H(5,𝔽2)11yescharacteristic
847C2×C4C3×H(5,𝔽2)11yescharacteristic
848C8—41no—
849C8—41no—
850C8—41no—
851C8—41no—
852C2×C3—42no—
853C2×C3—82no—
854C2×C3—82no—
855C2×C3—82no—
856C2×C3#240811yescharacteristic
857C2×C3#300911yescharacteristic
858C2×C3#301211yescharacteristic
859C2×C3#304311yescharacteristic
860C2×C3#304511yescharacteristic
861C2×C3#322211yescharacteristic
862C2×C3#322411yescharacteristic
863C22—22no—
864C22—22no—
865C22—22no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—816no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22—81no—
891C22—81no—
892C22C2×C3×#12011yescharacteristic
893C22C2×C3×#12111yescharacteristic
894C22C3×#53511yescharacteristic
895C22C3×#57611yescharacteristic
896C22C3×#57711yescharacteristic
897C22C3×#57711yescharacteristic
898C22C3×#57711yescharacteristic
899C4—22no—
900C4—22no—
901C4—22no—
902C4—42no—
903C4—42no—
904C4—41no—
905C4—41no—
906C4—42no—
907C4—81no—
908C4—81no—
909C4C3×D4211yescharacteristic
910C4C3×D4211yescharacteristic
911C4C3×#54611yescharacteristic
912C4C3×#54611yescharacteristic
913C3#2422011yescharacteristic, direct product factor, Sylow
914C2—42no—
915C2—82no—
916C2—82no—
917C2—82no—
918C2C3×#240811yescharacteristic
919C2C3×#300911yescharacteristic
920C2C3×#301211yescharacteristic
921C2C3×#304311yescharacteristic
922C2C3×#304511yescharacteristic
923C2C3×#322211yescharacteristic
924C2C3×#322411yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#535C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#464C2semidirect
3. C2×C3×#460C2semidirect
4. C2×C3×#452C2semidirect
5. C2×C3×#450C2semidirect
6. C3×#2323C2semidirect
7. C3×#2042C2semidirect
8. C3×#2041C2semidirect
9. C3×#2015C2semidirect
10. C3×#2014C2semidirect
11. C3×#1983C2semidirect
12. C3×#1982C2semidirect
13. C3×#1798C2semidirect
14. C3×#1788C2semidirect
15. C3×#1786C2semidirect
16. #24220C3direct (N × H)
19. C22×C3×Q16C22semidirect
22. C22×C3×SD16C22semidirect
34. C2×C3×C4×Q8C22semidirect
40. C2×C3×C4⋊C8C22semidirect
41. C2×C3×C4⋊C8C22semidirect
42. C2×C3×#103C22semidirect
43. C2×C3×#103C22semidirect
44. C2×C3×#103C22semidirect
51. C2×C3×#102C22semidirect
52. C2×C3×#102C22semidirect
53. C2×C3×#102C22semidirect
56. C3×#391C22semidirect
58. C3×#389C22semidirect
63. C3×C4×C4⋊C4C22semidirect
64. C3×#336C22semidirect
65. C3×#336C22semidirect
67. C2×#464C2×C3semidirect
68. C2×#460C2×C3semidirect
69. C2×#452C2×C3semidirect
70. C2×#450C2×C3semidirect
71. #2323C2×C3semidirect
72. #2042C2×C3semidirect
73. #2041C2×C3semidirect
74. #2015C2×C3semidirect
75. #2014C2×C3semidirect
76. #1983C2×C3semidirect
77. #1982C2×C3semidirect
78. #1798C2×C3semidirect
79. #1788C2×C3semidirect
80. #1786C2×C3semidirect
132. C3×C22⋊Q8D4semidirect
184. C22×Q16C22×C3semidirect
187. C22×SD16C22×C3semidirect
199. C2×C4×Q8C22×C3semidirect
205. C2×C4⋊C8C22×C3semidirect
206. C2×C4⋊C8C22×C3semidirect
207. C2×#103C22×C3semidirect
208. C2×#103C22×C3semidirect
209. C2×#103C22×C3semidirect
216. C2×#102C22×C3semidirect
217. C2×#102C22×C3semidirect
218. C2×#102C22×C3semidirect
221. #391C22×C3semidirect
223. #389C22×C3semidirect
228. C4×C4⋊C4C22×C3semidirect
229. #336C22×C3semidirect
230. #336C22×C3semidirect
410. C22⋊Q8C3×D4semidirect
913. C3#24220direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5352
C2×C3×#4642
C2×C3×#4602
C2×C3×#4522
C2×C3×#4502
C3×#23232
C3×#20422
C3×#20412
C3×#20152
C3×#20142
C3×#19832
C3×#19822
C3×#17982
C3×#17882
C3×#17862
#242203