Finite Group Databasebeta

← C3×#24394 #10643001

Subgroups — C3×#24394 #10643001

Order 768.

1578 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#535C211yesmaximal, characteristic
2C2×C3×#468C211yesmaximal, characteristic, complemented
3C2×C3×#465C211yesmaximal, characteristic, complemented
4C2×C3×#450C211yesmaximal, characteristic, complemented
5C2×C3×#408C211yesmaximal, characteristic, complemented
6C3×#2616C211yesmaximal, characteristic, complemented
7C3×#2034C211yesmaximal, characteristic, complemented
8C3×#2033C211yesmaximal, characteristic, complemented
9C3×#2000C211yesmaximal, characteristic, complemented
10C3×#2000C211yesmaximal, characteristic, complemented
11C3×#1895C211yesmaximal, characteristic, complemented
12C3×#1893C211yesmaximal, characteristic, complemented
13C3×#1873C211yesmaximal, characteristic, complemented
14C3×#1854C211yesmaximal, characteristic, complemented
15C3×#1786C211yesmaximal, characteristic, complemented
16#24394C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×C3×D4C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×C3×SD16C2211yescharacteristic
21C22×C3×M16C2211yescharacteristic, complemented
22C23×C3×C8C2211yescharacteristic, complemented
23C3×#535—24no—
24C3×#535—24no—
25C2×C3×#127—21no—
26C2×C3×#124—21no—
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×C22⋊Q8C2211yescharacteristic, complemented
29C2×C3×C22⋊Q8C2211yescharacteristic, complemented
30C2×C3×#121C2211yescharacteristic
31C2×C3×#121C2211yescharacteristic
32C2×C3×#121C2211yescharacteristic
33C2×C3×#121C2211yescharacteristic
34C2×C3×#120—21no—
35C2×C3×#120—21no—
36C2×C3×#117C2211yescharacteristic
37C3×#468—24no—
38C3×#465—24no—
39C3×#450—24no—
40C2×C3×#107C2211yescharacteristic, complemented
41C2×C3×#106C2211yescharacteristic, complemented
42C2×C3×#103C2211yescharacteristic, complemented
43C2×C3×#103C2211yescharacteristic, complemented
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×#102C2211yescharacteristic
48C2×C3×#102C2211yescharacteristic
49C2×C3×#102C2211yescharacteristic
50C3×#408—24no—
51C2×C3×C22⋊C8C2211yescharacteristic
52C2×C3×C22⋊C8C2211yescharacteristic
53C2×C3×C22⋊C8C2211yescharacteristic, complemented
54C2×C3×C22⋊C8C2211yescharacteristic, complemented
55C3×#395—21no—
56C3×#394—21no—
57C3×#394—21no—
58C3×#394—21no—
59C3×#380C2211yescharacteristic
60C3×#380C2211yescharacteristic, complemented
61C3×#380C2211yescharacteristic, complemented
62C3×#340C2211yescharacteristic, complemented
63C3×#340C2211yescharacteristic, complemented
64C3×#340C2211yescharacteristic, complemented
65C3×#340C2211yescharacteristic, complemented
66C2×#535C2×C311yescharacteristic
67C2×#468C2×C311yescharacteristic, complemented
68C2×#465C2×C311yescharacteristic, complemented
69C2×#450C2×C311yescharacteristic, complemented
70C2×#408C2×C311yescharacteristic, complemented
71#2616C2×C311yescharacteristic, complemented
72#2034C2×C311yescharacteristic, complemented
73#2033C2×C311yescharacteristic, complemented
74#2000C2×C311yescharacteristic, complemented
75#2000C2×C311yescharacteristic, complemented
76#1895C2×C311yescharacteristic, complemented
77#1893C2×C311yescharacteristic, complemented
78#1873C2×C311yescharacteristic, complemented
79#1854C2×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×Q8D411yescharacteristic
89C22×C3×Q8C2311yescharacteristic
90C22×C3×D4—21no—
91C22×C3×D4—21no—
92C22×C3×D4—21no—
93C22×C3×D4—21no—
94C22×C3×D4—22no—
95C22×C3×D4—22no—
96C22×C3×D4—21no—
97C22×C3×D4—22no—
98C22×C3×D4—22no—
99C22×C3×D4—41no—
100C22×C3×D4—41no—
101C22×C3×D4D411yescharacteristic
102C22×C3×D4D411yescharacteristic
103C22×C3×D4D411yescharacteristic
104C22×C3×D4C2311yescharacteristic
105C22×C3×D4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C2×C3×SD16—22no—
110C2×C3×SD16—22no—
111C2×C3×SD16—22no—
112C2×C3×SD16—22no—
113C2×C3×SD16—41no—
114C2×C3×SD16—41no—
115C2×C3×M16—22no—
116C2×C3×M16—22no—
117C2×C3×M16—41no—
118C22×C3×C8—22no—
119C22×C3×C8—22no—
120C22×C3×C8—41no—
121C22×C3×C8C2311yescharacteristic
122C22×C3×C8C2311yescharacteristic
123C22×C3×C8C2311yescharacteristic
124C22×C3×C8C2311yescharacteristic
125C3×#127—28no—
126C3×#124—28no—
127C3×C22⋊Q8—22no—
128C3×C22⋊Q8—22no—
129C3×C22⋊Q8—22no—
130C3×C22⋊Q8—22no—
131C3×C22⋊Q8—41no—
132C3×C22⋊Q8—41no—
133C3×#121—22no—
134C3×#121—22no—
135C3×#121—22no—
136C3×#121—22no—
137C3×#121—22no—
138C3×#121—22no—
139C3×#121D414yes—
140C3×#121D414yes—
141C3×#120—28no—
142C3×#120—28no—
143C3×#117—22no—
144C3×#117—22no—
145C2×C3×C4⋊C4—21no—
146C2×C3×C4⋊C4—21no—
147C2×C3×C4⋊C4—21no—
148C2×C3×C4⋊C4C2311yescharacteristic
149C2×C3×C4⋊C4C2311yescharacteristic
150C2×C3×C4⋊C4C2311yescharacteristic
151C2×C3×C4⋊C4C2311yescharacteristic
152C2×C3×C4⋊C4C2311yescharacteristic
153C2×C3×C22⋊C4—21no—
154C2×C3×C22⋊C4—21no—
155C2×C3×C22⋊C4—21no—
156C2×C3×C22⋊C4—21no—
157C2×C3×C22⋊C4—21no—
158C2×C3×C22⋊C4—21no—
159C2×C3×C22⋊C4—21no—
160C2×C3×C22⋊C4—21no—
161C2×C3×C22⋊C4—21no—
162C2×C3×C22⋊C4—21no—
163C2×C3×C22⋊C4—21no—
164C2×C3×C42—21no—
165C3×#107—22no—
166C3×#106—22no—
167C3×#103—22no—
168C3×#103—22no—
169C3×#102—22no—
170C3×#102—22no—
171C3×#102—22no—
172C3×#102—22no—
173C3×#102—41no—
174C3×#102—41no—
175C3×C22⋊C8—22no—
176C3×C22⋊C8—22no—
177C3×C22⋊C8—22no—
178C3×C22⋊C8D414yescomplemented
179C3×#95—21no—
180C3×#95—21no—
181C3×#95—21no—
182C22×#41C22×C311yescharacteristic
183C23×D4C22×C311yescharacteristic
184C22×SD16C22×C311yescharacteristic
185C22×SD16C22×C311yescharacteristic
186C22×M16C22×C311yescharacteristic, complemented
187C23×C8C22×C311yescharacteristic, complemented
188#535—24no—
189#535—24no—
190C2×#127—21no—
191C2×#124—21no—
192C2×C22⋊Q8C22×C311yescharacteristic
193C2×C22⋊Q8C22×C311yescharacteristic, complemented
194C2×C22⋊Q8C22×C311yescharacteristic, complemented
195C2×#121C22×C311yescharacteristic
196C2×#121C22×C311yescharacteristic
197C2×#121C22×C311yescharacteristic
198C2×#121C22×C311yescharacteristic
199C2×#120—21no—
200C2×#120—21no—
201C2×#117C22×C311yescharacteristic
202#468—24no—
203#465—24no—
204#450—24no—
205C2×#107C22×C311yescharacteristic, complemented
206C2×#106C22×C311yescharacteristic, complemented
207C2×#103C22×C311yescharacteristic, complemented
208C2×#103C22×C311yescharacteristic, complemented
209C2×#102C22×C311yescharacteristic
210C2×#102C22×C311yescharacteristic
211C2×#102C22×C311yescharacteristic
212C2×#102C22×C311yescharacteristic
213C2×#102C22×C311yescharacteristic
214C2×#102C22×C311yescharacteristic
215#408—24no—
216C2×C22⋊C8C22×C311yescharacteristic
217C2×C22⋊C8C22×C311yescharacteristic
218C2×C22⋊C8C22×C311yescharacteristic, complemented
219C2×C22⋊C8C22×C311yescharacteristic, complemented
220#395—21no—
221#394—21no—
222#394—21no—
223#394—21no—
224#380C22×C311yescharacteristic
225#380C22×C311yescharacteristic, complemented
226#380C22×C311yescharacteristic, complemented
227#340C22×C311yescharacteristic, complemented
228#340C22×C311yescharacteristic, complemented
229#340C22×C311yescharacteristic, complemented
230#340C22×C311yescharacteristic, complemented
231C24×C3—24no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—42no—
235C24×C3—42no—
236C24×C3—81no—
237C24×C3—81no—
238C24×C3—81no—
239C24×C3—81no—
240C24×C3C2×D411yescharacteristic
241C24×C3C2×D411yescharacteristic
242C24×C3C2×D411yescharacteristic
243C3×#41—44no—
244C3×#41—44no—
245C3×#41—44no—
246C3×#41—44no—
247C2×C3×Q8—22no—
248C2×C3×Q8—22no—
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—41no—
256C2×C3×D4—24no—
257C2×C3×D4—22no—
258C2×C3×D4—22no—
259C2×C3×D4—22no—
260C2×C3×D4—22no—
261C2×C3×D4—24no—
262C2×C3×D4—24no—
263C2×C3×D4—24no—
264C2×C3×D4—24no—
265C2×C3×D4—22no—
266C2×C3×D4—22no—
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—44no—
278C2×C3×D4—44no—
279C2×C3×D4—44no—
280C2×C3×D4—44no—
281C2×C3×D4—41no—
282C2×C3×D4—41no—
283C2×C3×D4—41no—
284C2×C3×D4—42no—
285C2×C3×D4—42no—
286C2×C3×D4—81no—
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×D4C2×D412yes—
295C2×C3×D4C2×D412yes—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4C2×D411yescharacteristic
317C22×C3×C4C2×D411yescharacteristic
318C22×C3×C4C2×D412yes—
319C22×C3×C4C2×D412yes—
320C22×C3×C4C2×D411yescharacteristic
321C22×C3×C4C2×D412yes—
322C22×C3×C4#4112yes—
323C22×C3×C4C2411yescharacteristic
324C3×SD16—44no—
325C3×SD16—44no—
326C3×M16—44no—
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—
334C2×C3×C8—21no—
335C2×C3×C8—21no—
336C2×C3×C8—21no—
337C2×C3×C8—44no—
338C2×C3×C8C2×D412yes—
339C2×C3×C8C2×D412yes—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—42no—
349C3×C4⋊C4—42no—
350C3×C4⋊C4—42no—
351C3×C4⋊C4C2×D412yes—
352C3×C4⋊C4C2×D412yes—
353C3×C22⋊C4—24no—
354C3×C22⋊C4—24no—
355C3×C22⋊C4—24no—
356C3×C22⋊C4—24no—
357C3×C22⋊C4—24no—
358C3×C22⋊C4—42no—
359C3×C22⋊C4—42no—
360C3×C22⋊C4—42no—
361C3×C22⋊C4—81no—
362C3×C22⋊C4—81no—
363C3×C22⋊C4—81no—
364C3×C42—24no—
365C25—21no—
366C2×#41—22no—
367C2×#41—22no—
368C2×#41—22no—
369C2×#41—22no—
370C2×#41—41no—
371C2×#41—41no—
372C22×Q8C3×D411yescharacteristic
373C22×Q8C23×C311yescharacteristic
374C22×D4—21no—
375C22×D4—21no—
376C22×D4—21no—
377C22×D4—21no—
378C22×D4—22no—
379C22×D4—22no—
380C22×D4—21no—
381C22×D4—22no—
382C22×D4—22no—
383C22×D4—41no—
384C22×D4—41no—
385C22×D4C3×D411yescharacteristic
386C22×D4C3×D411yescharacteristic
387C22×D4C3×D411yescharacteristic
388C22×D4C23×C311yescharacteristic
389C22×D4C23×C311yescharacteristic
390C23×C4C23×C311yescharacteristic
391C23×C4C23×C311yescharacteristic
392C23×C4C23×C311yescharacteristic
393C2×SD16—22no—
394C2×SD16—22no—
395C2×SD16—22no—
396C2×SD16—22no—
397C2×SD16—41no—
398C2×SD16—41no—
399C2×M16—22no—
400C2×M16—22no—
401C2×M16—41no—
402C22×C8—22no—
403C22×C8—22no—
404C22×C8—41no—
405C22×C8C23×C311yescharacteristic
406C22×C8C23×C311yescharacteristic
407C22×C8C23×C311yescharacteristic
408C22×C8C23×C311yescharacteristic
409#127—28no—
410#124—28no—
411C22⋊Q8—22no—
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414C22⋊Q8—22no—
415C22⋊Q8—41no—
416C22⋊Q8—41no—
417#121—22no—
418#121—22no—
419#121—22no—
420#121—22no—
421#121—22no—
422#121—22no—
423#121C3×D414yes—
424#121C3×D414yes—
425#120—28no—
426#120—28no—
427#117—22no—
428#117—22no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4C23×C311yescharacteristic
433C2×C4⋊C4C23×C311yescharacteristic
434C2×C4⋊C4C23×C311yescharacteristic
435C2×C4⋊C4C23×C311yescharacteristic
436C2×C4⋊C4C23×C311yescharacteristic
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C42—21no—
449#107—22no—
450#106—22no—
451#103—22no—
452#103—22no—
453#102—22no—
454#102—22no—
455#102—22no—
456#102—22no—
457#102—41no—
458#102—41no—
459C22⋊C8—22no—
460C22⋊C8—22no—
461C22⋊C8—22no—
462C22⋊C8C3×D414yescomplemented
463#95—21no—
464#95—21no—
465#95—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—48no—
488C23×C3—41no—
489C23×C3—41no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3—41no—
493C23×C3—41no—
494C23×C3—41no—
495C23×C3—41no—
496C23×C3—41no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3—41no—
500C23×C3—84no—
501C23×C3—84no—
502C23×C3—84no—
503C23×C3—84no—
504C23×C3—84no—
505C23×C3—84no—
506C23×C3#12012yes—
507C23×C3#12112yes—
508C23×C3C22×D411yescharacteristic
509C3×Q8—44no—
510C3×Q8—41no—
511C3×Q8—41no—
512C3×Q8—41no—
513C3×Q8—41no—
514C3×D4—22no—
515C3×D4—22no—
516C3×D4—22no—
517C3×D4—22no—
518C3×D4—44no—
519C3×D4—44no—
520C3×D4—48no—
521C3×D4—44no—
522C3×D4—41no—
523C3×D4—41no—
524C3×D4—41no—
525C3×D4—41no—
526C3×D4—84no—
527C3×D4—84no—
528C3×D4—84no—
529C3×D4—84no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—22no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
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—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4#12012yes—
568C2×C3×C4#12112yes—
569C2×C3×C4C22×D411yescharacteristic
570C2×C3×C4C22×D411yescharacteristic
571C2×C3×C4C22×D411yescharacteristic
572C2×C3×C4C2×#4111yescharacteristic
573C2×C3×C4H(5,𝔽2)11yescharacteristic
574C2×C3×C4H(5,𝔽2)11yescharacteristic
575C3×C8—22no—
576C3×C8—22no—
577C3×C8—41no—
578C3×C8—41no—
579C24—24no—
580C24—21no—
581C24—21no—
582C24—42no—
583C24—42no—
584C24—81no—
585C24—81no—
586C24—81no—
587C24—81no—
588C24C2×C3×D411yescharacteristic
589C24C2×C3×D411yescharacteristic
590C24C2×C3×D411yescharacteristic
591#41—44no—
592#41—44no—
593#41—44no—
594#41—44no—
595C2×Q8—22no—
596C2×Q8—22no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—41no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—44no—
626C2×D4—44no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—41no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—81no—
635C2×D4—81no—
636C2×D4—81no—
637C2×D4—81no—
638C2×D4—81no—
639C2×D4—81no—
640C2×D4—81no—
641C2×D4—81no—
642C2×D4C2×C3×D412yes—
643C2×D4C2×C3×D412yes—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4C2×C3×D411yescharacteristic
665C22×C4C2×C3×D411yescharacteristic
666C22×C4C2×C3×D412yes—
667C22×C4C2×C3×D412yes—
668C22×C4C2×C3×D411yescharacteristic
669C22×C4C2×C3×D412yes—
670C22×C4C3×#4112yes—
671C22×C4C24×C311yescharacteristic
672SD16—44no—
673SD16—44no—
674M16—44no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—44no—
686C2×C8C2×C3×D412yes—
687C2×C8C2×C3×D412yes—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—42no—
697C4⋊C4—42no—
698C4⋊C4—42no—
699C4⋊C4C2×C3×D412yes—
700C4⋊C4C2×C3×D412yes—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—81no—
710C22⋊C4—81no—
711C22⋊C4—81no—
712C42—24no—
713C22×C3—22no—
714C22×C3—22no—
715C22×C3—22no—
716C22×C3—22no—
717C22×C3—22no—
718C22×C3—22no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—42no—
729C22×C3—42no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—42no—
734C22×C3—42no—
735C22×C3—41no—
736C22×C3—42no—
737C22×C3—42no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—816no—
741C22×C3—81no—
742C22×C3—81no—
743C22×C3—81no—
744C22×C3—81no—
745C22×C3—81no—
746C22×C3—81no—
747C22×C3—81no—
748C22×C3—81no—
749C22×C3C2×#12011yescharacteristic
750C22×C3C2×#12111yescharacteristic
751C22×C3#53411yescharacteristic
752C22×C3#57611yescharacteristic
753C22×C3#57711yescharacteristic
754C22×C3#57711yescharacteristic
755C22×C3#57711yescharacteristic
756C3×C4—22no—
757C3×C4—22no—
758C3×C4—41no—
759C3×C4—42no—
760C3×C4—42no—
761C3×C4—81no—
762C3×C4—81no—
763C3×C4—81no—
764C3×C4—81no—
765C3×C4D4211yescharacteristic
766C3×C4D4211yescharacteristic
767C3×C4#54611yescharacteristic
768C3×C4#54611yescharacteristic
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—22no—
786C23—22no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—48no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—84no—
804C23—84no—
805C23—84no—
806C23—84no—
807C23—84no—
808C23—84no—
809C23C3×#12012yes—
810C23C3×#12112yes—
811C23C22×C3×D411yescharacteristic
812Q8—44no—
813Q8—41no—
814Q8—41no—
815Q8—41no—
816Q8—41no—
817D4—22no—
818D4—22no—
819D4—22no—
820D4—22no—
821D4—44no—
822D4—44no—
823D4—48no—
824D4—44no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—84no—
830D4—84no—
831D4—84no—
832D4—84no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4C3×#12012yes—
871C2×C4C3×#12112yes—
872C2×C4C22×C3×D411yescharacteristic
873C2×C4C22×C3×D411yescharacteristic
874C2×C4C22×C3×D411yescharacteristic
875C2×C4C2×C3×#4111yescharacteristic
876C2×C4C3×H(5,𝔽2)11yescharacteristic
877C2×C4C3×H(5,𝔽2)11yescharacteristic
878C8—22no—
879C8—22no—
880C8—41no—
881C8—41no—
882C2×C3—42no—
883C2×C3—42no—
884C2×C3—81no—
885C2×C3—82no—
886C2×C3—82no—
887C2×C3#241011yescharacteristic
888C2×C3#300911yescharacteristic
889C2×C3#301211yescharacteristic
890C2×C3#305711yescharacteristic
891C2×C3#306211yescharacteristic
892C2×C3#319811yescharacteristic
893C2×C3#320011yescharacteristic
894C22—22no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—42no—
910C22—42no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—42no—
915C22—42no—
916C22—41no—
917C22—42no—
918C22—42no—
919C22—41no—
920C22—41no—
921C22—816no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22C2×C3×#12011yescharacteristic
931C22C2×C3×#12111yescharacteristic
932C22C3×#53411yescharacteristic
933C22C3×#57611yescharacteristic
934C22C3×#57711yescharacteristic
935C22C3×#57711yescharacteristic
936C22C3×#57711yescharacteristic
937C4—22no—
938C4—22no—
939C4—41no—
940C4—42no—
941C4—42no—
942C4—81no—
943C4—81no—
944C4—81no—
945C4—81no—
946C4C3×D4211yescharacteristic
947C4C3×D4211yescharacteristic
948C4C3×#54611yescharacteristic
949C4C3×#54611yescharacteristic
950C3#2439411yescharacteristic, direct product factor, Sylow
951C2—42no—
952C2—42no—
953C2—81no—
954C2—82no—
955C2—82no—
956C2C3×#241011yescharacteristic
957C2C3×#300911yescharacteristic
958C2C3×#301211yescharacteristic
959C2C3×#305711yescharacteristic
960C2C3×#306211yescharacteristic
961C2C3×#319811yescharacteristic
962C2C3×#320011yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#535C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C22×C3×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#468C2semidirect
3. C2×C3×#465C2semidirect
4. C2×C3×#450C2semidirect
5. C2×C3×#408C2semidirect
6. C3×#2616C2semidirect
7. C3×#2034C2semidirect
8. C3×#2033C2semidirect
9. C3×#2000C2semidirect
10. C3×#2000C2semidirect
11. C3×#1895C2semidirect
12. C3×#1893C2semidirect
13. C3×#1873C2semidirect
14. C3×#1854C2semidirect
15. C3×#1786C2semidirect
16. #24394C3direct (N × H)
21. C22×C3×M16C22semidirect
22. C23×C3×C8C22semidirect
28. C2×C3×C22⋊Q8C22semidirect
29. C2×C3×C22⋊Q8C22semidirect
40. C2×C3×#107C22semidirect
41. C2×C3×#106C22semidirect
42. C2×C3×#103C22semidirect
43. C2×C3×#103C22semidirect
53. C2×C3×C22⋊C8C22semidirect
54. C2×C3×C22⋊C8C22semidirect
60. C3×#380C22semidirect
61. C3×#380C22semidirect
62. C3×#340C22semidirect
63. C3×#340C22semidirect
64. C3×#340C22semidirect
65. C3×#340C22semidirect
67. C2×#468C2×C3semidirect
68. C2×#465C2×C3semidirect
69. C2×#450C2×C3semidirect
70. C2×#408C2×C3semidirect
71. #2616C2×C3semidirect
72. #2034C2×C3semidirect
73. #2033C2×C3semidirect
74. #2000C2×C3semidirect
75. #2000C2×C3semidirect
76. #1895C2×C3semidirect
77. #1893C2×C3semidirect
78. #1873C2×C3semidirect
79. #1854C2×C3semidirect
80. #1786C2×C3semidirect
178. C3×C22⋊C8D4semidirect
186. C22×M16C22×C3semidirect
187. C23×C8C22×C3semidirect
193. C2×C22⋊Q8C22×C3semidirect
194. C2×C22⋊Q8C22×C3semidirect
205. C2×#107C22×C3semidirect
206. C2×#106C22×C3semidirect
207. C2×#103C22×C3semidirect
208. C2×#103C22×C3semidirect
218. C2×C22⋊C8C22×C3semidirect
219. C2×C22⋊C8C22×C3semidirect
225. #380C22×C3semidirect
226. #380C22×C3semidirect
227. #340C22×C3semidirect
228. #340C22×C3semidirect
229. #340C22×C3semidirect
230. #340C22×C3semidirect
462. C22⋊C8C3×D4semidirect
950. C3#24394direct (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×#4682
C2×C3×#4652
C2×C3×#4502
C2×C3×#4082
C3×#26162
C3×#20342
C3×#20332
C3×#20002
C3×#18952
C3×#18932
C3×#18732
C3×#18542
C3×#17862
#243943