Finite Group Databasebeta

← C3×#24397 #10643004

Subgroups — C3×#24397 #10643004

Order 768.

1508 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#537C211yesmaximal, characteristic, complemented
2C2×C3×#469C211yesmaximal, characteristic, complemented
3C2×C3×#465C211yesmaximal, characteristic, complemented
4C2×C3×#449C211yesmaximal, characteristic, complemented
5C2×C3×#408C211yesmaximal, characteristic, complemented
6C3×#2615C211yesmaximal, characteristic, complemented
7C3×#2035C211yesmaximal, characteristic, complemented
8C3×#2034C211yesmaximal, characteristic, complemented
9C3×#2000C211yesmaximal, characteristic, complemented
10C3×#1999C211yesmaximal, characteristic, complemented
11C3×#1894C211yesmaximal, characteristic, complemented
12C3×#1893C211yesmaximal, characteristic, complemented
13C3×#1874C211yesmaximal, characteristic, complemented
14C3×#1853C211yesmaximal, characteristic, complemented
15C3×#1788C211yesmaximal, characteristic, complemented
16#24397C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×#41C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×C3×D8C2211yescharacteristic
21C22×C3×M16C2211yescharacteristic
22C23×C3×C8C2211yescharacteristic
23C3×#537—24no—
24C3×#537—24no—
25C2×C3×C22⋊Q8—21no—
26C2×C3×C22⋊Q8C2211yescharacteristic
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×#121—21no—
29C2×C3×#121—21no—
30C2×C3×#121—21no—
31C2×C3×#121C2211yescharacteristic
32C2×C3×#121C2211yescharacteristic
33C2×C3×#121C2211yescharacteristic
34C2×C3×#121C2211yescharacteristic
35C2×C3×#121C2211yescharacteristic
36C22×C3×C4⋊C4C2211yescharacteristic
37C3×#469—24no—
38C3×#465—24no—
39C3×#449—24no—
40C2×C3×#106C2211yescharacteristic
41C2×C3×#106C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#103C2211yescharacteristic
44C2×C3×#103C2211yescharacteristic
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
54C2×C3×C22⋊C8C2211yescharacteristic
55C3×#393—21no—
56C3×#392—21no—
57C3×#392—21no—
58C3×#392—21no—
59C3×#380C2211yescharacteristic
60C3×#380C2211yescharacteristic
61C3×#380C2211yescharacteristic
62C3×#340C2211yescharacteristic
63C3×#340C2211yescharacteristic
64C3×#340C2211yescharacteristic
65C3×#340C2211yescharacteristic
66C2×#537C2×C311yescharacteristic, complemented
67C2×#469C2×C311yescharacteristic, complemented
68C2×#465C2×C311yescharacteristic, complemented
69C2×#449C2×C311yescharacteristic, complemented
70C2×#408C2×C311yescharacteristic, complemented
71#2615C2×C311yescharacteristic, complemented
72#2035C2×C311yescharacteristic, complemented
73#2034C2×C311yescharacteristic, complemented
74#2000C2×C311yescharacteristic, complemented
75#1999C2×C311yescharacteristic, complemented
76#1894C2×C311yescharacteristic, complemented
77#1893C2×C311yescharacteristic, complemented
78#1874C2×C311yescharacteristic, complemented
79#1853C2×C311yescharacteristic, complemented
80#1788C2×C311yescharacteristic, complemented
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41—22no—
87C2×C3×#41—22no—
88C2×C3×#41—22no—
89C2×C3×#41—41no—
90C2×C3×#41—41no—
91C2×C3×#41—41no—
92C2×C3×#41—41no—
93C22×C3×Q8D411yescharacteristic
94C22×C3×Q8C2311yescharacteristic
95C22×C3×D4—21no—
96C22×C3×D4—21no—
97C22×C3×D4—21no—
98C22×C3×D4—21no—
99C22×C3×D4—21no—
100C22×C3×D4—21no—
101C22×C3×D4D411yescharacteristic
102C22×C3×D4D411yescharacteristic
103C22×C3×D4D411yescharacteristic
104C22×C3×D4C2311yescharacteristic
105C22×C3×D4C2311yescharacteristic
106C23×C3×C4—21no—
107C23×C3×C4—21no—
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2311yescharacteristic
110C23×C3×C4C2311yescharacteristic
111C2×C3×SD16—22no—
112C2×C3×SD16—22no—
113C2×C3×SD16—41no—
114C2×C3×D8—22no—
115C2×C3×D8—22no—
116C2×C3×D8—41no—
117C2×C3×M16—22no—
118C2×C3×M16—22no—
119C2×C3×M16—41no—
120C22×C3×C8—22no—
121C22×C3×C8—22no—
122C22×C3×C8—41no—
123C22×C3×C8C2311yescharacteristic
124C22×C3×C8C2311yescharacteristic
125C22×C3×C8C2311yescharacteristic
126C22×C3×C8C2311yescharacteristic
127C3×C22⋊Q8—28no—
128C3×C22⋊Q8—22no—
129C3×C22⋊Q8—22no—
130C3×C22⋊Q8—22no—
131C3×C22⋊Q8D414yescomplemented
132C3×#121—28no—
133C3×#121—28no—
134C3×#121—28no—
135C3×#121—22no—
136C3×#121—22no—
137C3×#121—22no—
138C3×#121—22no—
139C3×#121—22no—
140C3×#121—22no—
141C3×#121—22no—
142C3×#121—41no—
143C3×#121—41no—
144C3×#121D414yescomplemented
145C2×C3×C4⋊C4—21no—
146C2×C3×C4⋊C4—21no—
147C2×C3×C4⋊C4—21no—
148C2×C3×C4⋊C4—22no—
149C2×C3×C4⋊C4—22no—
150C2×C3×C4⋊C4C2311yescharacteristic
151C2×C3×C4⋊C4C2311yescharacteristic
152C2×C3×C4⋊C4C2311yescharacteristic
153C2×C3×C4⋊C4C2311yescharacteristic
154C2×C3×C4⋊C4C2311yescharacteristic
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×C22⋊C4—21no—
165C3×#106—22no—
166C3×#106—22no—
167C3×#103—22no—
168C3×#103—22no—
169C3×#103—41no—
170C3×#102—22no—
171C3×#102—22no—
172C3×#102—22no—
173C3×#102—22no—
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
183C22×#41C22×C311yescharacteristic
184C22×SD16C22×C311yescharacteristic
185C22×D8C22×C311yescharacteristic
186C22×M16C22×C311yescharacteristic
187C23×C8C22×C311yescharacteristic
188#537—24no—
189#537—24no—
190C2×C22⋊Q8—21no—
191C2×C22⋊Q8C22×C311yescharacteristic
192C2×C22⋊Q8C22×C311yescharacteristic
193C2×#121—21no—
194C2×#121—21no—
195C2×#121—21no—
196C2×#121C22×C311yescharacteristic
197C2×#121C22×C311yescharacteristic
198C2×#121C22×C311yescharacteristic
199C2×#121C22×C311yescharacteristic
200C2×#121C22×C311yescharacteristic
201C22×C4⋊C4C22×C311yescharacteristic
202#469—24no—
203#465—24no—
204#449—24no—
205C2×#106C22×C311yescharacteristic
206C2×#106C22×C311yescharacteristic
207C2×#103C22×C311yescharacteristic
208C2×#103C22×C311yescharacteristic
209C2×#103C22×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
219C2×C22⋊C8C22×C311yescharacteristic
220#393—21no—
221#392—21no—
222#392—21no—
223#392—21no—
224#380C22×C311yescharacteristic
225#380C22×C311yescharacteristic
226#380C22×C311yescharacteristic
227#340C22×C311yescharacteristic
228#340C22×C311yescharacteristic
229#340C22×C311yescharacteristic
230#340C22×C311yescharacteristic
231C24×C3—21no—
232C24×C3—21no—
233C24×C3C2×D411yescharacteristic
234C24×C3C2×D411yescharacteristic
235C24×C3C2×D411yescharacteristic
236C3×#41—44no—
237C3×#41—44no—
238C3×#41—44no—
239C3×#41—44no—
240C3×#41—44no—
241C3×#41—44no—
242C3×#41—44no—
243C3×#41—44no—
244C2×C3×Q8—22no—
245C2×C3×Q8—22no—
246C2×C3×Q8—21no—
247C2×C3×Q8—21no—
248C2×C3×Q8—21no—
249C2×C3×Q8—21no—
250C2×C3×Q8—21no—
251C2×C3×Q8—41no—
252C2×C3×Q8C2×D412yes—
253C2×C3×D4—24no—
254C2×C3×D4—22no—
255C2×C3×D4—22no—
256C2×C3×D4—22no—
257C2×C3×D4—22no—
258C2×C3×D4—24no—
259C2×C3×D4—24no—
260C2×C3×D4—22no—
261C2×C3×D4—22no—
262C2×C3×D4—21no—
263C2×C3×D4—21no—
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—41no—
274C2×C3×D4—41no—
275C2×C3×D4—41no—
276C2×C3×D4—42no—
277C2×C3×D4—42no—
278C2×C3×D4—42no—
279C2×C3×D4—42no—
280C2×C3×D4—42no—
281C2×C3×D4—81no—
282C2×C3×D4—81no—
283C2×C3×D4—81no—
284C2×C3×D4—81no—
285C2×C3×D4—81no—
286C2×C3×D4—81no—
287C2×C3×D4—81no—
288C2×C3×D4—81no—
289C2×C3×D4—81no—
290C2×C3×D4—81no—
291C2×C3×D4C2×D412yes—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—24no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—24no—
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—42no—
315C22×C3×C4—42no—
316C22×C3×C4—81no—
317C22×C3×C4—81no—
318C22×C3×C4C2×D411yescharacteristic
319C22×C3×C4C2×D411yescharacteristic
320C22×C3×C4C2×D412yes—
321C22×C3×C4C2×D412yes—
322C22×C3×C4C2×D411yescharacteristic
323C22×C3×C4C2×D412yes—
324C22×C3×C4#4112yes—
325C22×C3×C4C2411yescharacteristic
326C3×SD16—44no—
327C3×D8—44no—
328C3×M16—44no—
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—21no—
338C2×C3×C8—21no—
339C2×C3×C8—44no—
340C2×C3×C8C2×D412yes—
341C2×C3×C8C2×D412yes—
342C3×C4⋊C4—24no—
343C3×C4⋊C4—24no—
344C3×C4⋊C4—24no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4C2×D412yes—
354C3×C4⋊C4C2×D412yes—
355C3×C22⋊C4—24no—
356C3×C22⋊C4—24no—
357C3×C22⋊C4—24no—
358C3×C22⋊C4—24no—
359C3×C22⋊C4—42no—
360C3×C22⋊C4—42no—
361C3×C22⋊C4—42no—
362C3×C22⋊C4—81no—
363C3×C22⋊C4—81no—
364C3×C22⋊C4—81no—
365C2×#41—22no—
366C2×#41—22no—
367C2×#41—22no—
368C2×#41—22no—
369C2×#41—22no—
370C2×#41—22no—
371C2×#41—22no—
372C2×#41—22no—
373C2×#41—41no—
374C2×#41—41no—
375C2×#41—41no—
376C2×#41—41no—
377C22×Q8C3×D411yescharacteristic
378C22×Q8C23×C311yescharacteristic
379C22×D4—21no—
380C22×D4—21no—
381C22×D4—21no—
382C22×D4—21no—
383C22×D4—21no—
384C22×D4—21no—
385C22×D4C3×D411yescharacteristic
386C22×D4C3×D411yescharacteristic
387C22×D4C3×D411yescharacteristic
388C22×D4C23×C311yescharacteristic
389C22×D4C23×C311yescharacteristic
390C23×C4—21no—
391C23×C4—21no—
392C23×C4C23×C311yescharacteristic
393C23×C4C23×C311yescharacteristic
394C23×C4C23×C311yescharacteristic
395C2×SD16—22no—
396C2×SD16—22no—
397C2×SD16—41no—
398C2×D8—22no—
399C2×D8—22no—
400C2×D8—41no—
401C2×M16—22no—
402C2×M16—22no—
403C2×M16—41no—
404C22×C8—22no—
405C22×C8—22no—
406C22×C8—41no—
407C22×C8C23×C311yescharacteristic
408C22×C8C23×C311yescharacteristic
409C22×C8C23×C311yescharacteristic
410C22×C8C23×C311yescharacteristic
411C22⋊Q8—28no—
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414C22⋊Q8—22no—
415C22⋊Q8C3×D414yescomplemented
416#121—28no—
417#121—28no—
418#121—28no—
419#121—22no—
420#121—22no—
421#121—22no—
422#121—22no—
423#121—22no—
424#121—22no—
425#121—22no—
426#121—41no—
427#121—41no—
428#121C3×D414yescomplemented
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4C23×C311yescharacteristic
435C2×C4⋊C4C23×C311yescharacteristic
436C2×C4⋊C4C23×C311yescharacteristic
437C2×C4⋊C4C23×C311yescharacteristic
438C2×C4⋊C4C23×C311yescharacteristic
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×C22⋊C4—21no—
449#106—22no—
450#106—22no—
451#103—22no—
452#103—22no—
453#103—41no—
454#102—22no—
455#102—22no—
456#102—22no—
457#102—22no—
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—21no—
479C23×C3—22no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—41no—
487C23×C3—41no—
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#12012yes—
500C23×C3#12112yes—
501C23×C3C22×D411yescharacteristic
502C3×Q8—22no—
503C3×Q8—22no—
504C3×Q8—44no—
505C3×Q8—41no—
506C3×Q8—41no—
507C3×D4—22no—
508C3×D4—22no—
509C3×D4—44no—
510C3×D4—44no—
511C3×D4—44no—
512C3×D4—48no—
513C3×D4—41no—
514C3×D4—41no—
515C3×D4—41no—
516C3×D4—41no—
517C3×D4—41no—
518C3×D4—41no—
519C3×D4—84no—
520C3×D4—84no—
521C3×D4—84no—
522C3×D4—84no—
523C3×D4—84no—
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—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—48no—
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—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—84no—
563C2×C3×C4#12012yes—
564C2×C3×C4#12112yes—
565C2×C3×C4C22×D411yescharacteristic
566C2×C3×C4C22×D411yescharacteristic
567C2×C3×C4C22×D411yescharacteristic
568C2×C3×C4C2×#4111yescharacteristic
569C2×C3×C4H(5,𝔽2)11yescharacteristic
570C2×C3×C4H(5,𝔽2)11yescharacteristic
571C3×C8—22no—
572C3×C8—22no—
573C3×C8—41no—
574C3×C8—41no—
575C24—21no—
576C24—21no—
577C24C2×C3×D411yescharacteristic
578C24C2×C3×D411yescharacteristic
579C24C2×C3×D411yescharacteristic
580#41—44no—
581#41—44no—
582#41—44no—
583#41—44no—
584#41—44no—
585#41—44no—
586#41—44no—
587#41—44no—
588C2×Q8—22no—
589C2×Q8—22no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—41no—
596C2×Q8C2×C3×D412yes—
597C2×D4—24no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—24no—
603C2×D4—24no—
604C2×D4—22no—
605C2×D4—22no—
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—21no—
616C2×D4—21no—
617C2×D4—41no—
618C2×D4—41no—
619C2×D4—41no—
620C2×D4—42no—
621C2×D4—42no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—81no—
626C2×D4—81no—
627C2×D4—81no—
628C2×D4—81no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4C2×C3×D412yes—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—24no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—24no—
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—42no—
659C22×C4—42no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4C2×C3×D411yescharacteristic
663C22×C4C2×C3×D411yescharacteristic
664C22×C4C2×C3×D412yes—
665C22×C4C2×C3×D412yes—
666C22×C4C2×C3×D411yescharacteristic
667C22×C4C2×C3×D412yes—
668C22×C4C3×#4112yes—
669C22×C4C24×C311yescharacteristic
670SD16—44no—
671D8—44no—
672M16—44no—
673C2×C8—21no—
674C2×C8—21no—
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—44no—
684C2×C8C2×C3×D412yes—
685C2×C8C2×C3×D412yes—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4C2×C3×D412yes—
698C4⋊C4C2×C3×D412yes—
699C22⋊C4—24no—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—81no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C22×C3—22no—
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—22no—
713C22×C3—22no—
714C22×C3—22no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—42no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—42no—
729C22×C3—41no—
730C22×C3—42no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—81no—
734C22×C3—81no—
735C22×C3—81no—
736C22×C3—81no—
737C22×C3—81no—
738C22×C3—81no—
739C22×C3—81no—
740C22×C3—81no—
741C22×C3—81no—
742C22×C3—81no—
743C22×C3—81no—
744C22×C3C2×#12011yescharacteristic
745C22×C3C2×#12111yescharacteristic
746C22×C3#53411yescharacteristic
747C22×C3#57611yescharacteristic
748C22×C3#57711yescharacteristic
749C22×C3#57711yescharacteristic
750C22×C3#57711yescharacteristic
751C3×C4—22no—
752C3×C4—22no—
753C3×C4—41no—
754C3×C4—42no—
755C3×C4—42no—
756C3×C4—42no—
757C3×C4—81no—
758C3×C4—81no—
759C3×C4—81no—
760C3×C4D4211yescharacteristic
761C3×C4D4211yescharacteristic
762C3×C4#54611yescharacteristic
763C3×C4#54611yescharacteristic
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
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—22no—
782C23—21no—
783C23—21no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23C3×#12012yes—
798C23C3×#12112yes—
799C23C22×C3×D411yescharacteristic
800Q8—22no—
801Q8—22no—
802Q8—44no—
803Q8—41no—
804Q8—41no—
805D4—22no—
806D4—22no—
807D4—44no—
808D4—44no—
809D4—44no—
810D4—48no—
811D4—41no—
812D4—41no—
813D4—41no—
814D4—41no—
815D4—41no—
816D4—41no—
817D4—84no—
818D4—84no—
819D4—84no—
820D4—84no—
821D4—84no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—48no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
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—84no—
861C2×C4C3×#12012yes—
862C2×C4C3×#12112yes—
863C2×C4C22×C3×D411yescharacteristic
864C2×C4C22×C3×D411yescharacteristic
865C2×C4C22×C3×D411yescharacteristic
866C2×C4C2×C3×#4111yescharacteristic
867C2×C4C3×H(5,𝔽2)11yescharacteristic
868C2×C4C3×H(5,𝔽2)11yescharacteristic
869C8—22no—
870C8—22no—
871C8—41no—
872C8—41no—
873C2×C3—42no—
874C2×C3—42no—
875C2×C3—81no—
876C2×C3—82no—
877C2×C3—161no—
878C2×C3#241011yescharacteristic
879C2×C3#301011yescharacteristic
880C2×C3#301211yescharacteristic
881C2×C3#306011yescharacteristic
882C2×C3#306211yescharacteristic
883C2×C3#319811yescharacteristic
884C2×C3#320411yescharacteristic
885C22—22no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—42no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—42no—
907C22—41no—
908C22—41no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22C2×C3×#12011yescharacteristic
921C22C2×C3×#12111yescharacteristic
922C22C3×#53411yescharacteristic
923C22C3×#57611yescharacteristic
924C22C3×#57711yescharacteristic
925C22C3×#57711yescharacteristic
926C22C3×#57711yescharacteristic
927C4—22no—
928C4—22no—
929C4—41no—
930C4—42no—
931C4—42no—
932C4—42no—
933C4—81no—
934C4—81no—
935C4—81no—
936C4C3×D4211yescharacteristic
937C4C3×D4211yescharacteristic
938C4C3×#54611yescharacteristic
939C4C3×#54611yescharacteristic
940C3#2439711yescharacteristic, direct product factor, Sylow
941C2—42no—
942C2—42no—
943C2—81no—
944C2—82no—
945C2—161no—
946C2C3×#241011yescharacteristic
947C2C3×#301011yescharacteristic
948C2C3×#301211yescharacteristic
949C2C3×#306011yescharacteristic
950C2C3×#306211yescharacteristic
951C2C3×#319811yescharacteristic
952C2C3×#320411yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
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
1. C2×C3×#537C2semidirect
2. C2×C3×#469C2semidirect
3. C2×C3×#465C2semidirect
4. C2×C3×#449C2semidirect
5. C2×C3×#408C2semidirect
6. C3×#2615C2semidirect
7. C3×#2035C2semidirect
8. C3×#2034C2semidirect
9. C3×#2000C2semidirect
10. C3×#1999C2semidirect
11. C3×#1894C2semidirect
12. C3×#1893C2semidirect
13. C3×#1874C2semidirect
14. C3×#1853C2semidirect
15. C3×#1788C2semidirect
16. #24397C3direct (N × H)
66. C2×#537C2×C3semidirect
67. C2×#469C2×C3semidirect
68. C2×#465C2×C3semidirect
69. C2×#449C2×C3semidirect
70. C2×#408C2×C3semidirect
71. #2615C2×C3semidirect
72. #2035C2×C3semidirect
73. #2034C2×C3semidirect
74. #2000C2×C3semidirect
75. #1999C2×C3semidirect
76. #1894C2×C3semidirect
77. #1893C2×C3semidirect
78. #1874C2×C3semidirect
79. #1853C2×C3semidirect
80. #1788C2×C3semidirect
131. C3×C22⋊Q8D4semidirect
144. C3×#121D4semidirect
178. C3×C22⋊C8D4semidirect
415. C22⋊Q8C3×D4semidirect
428. #121C3×D4semidirect
462. C22⋊C8C3×D4semidirect
940. C3#24397direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5372
C2×C3×#4692
C2×C3×#4652
C2×C3×#4492
C2×C3×#4082
C3×#26152
C3×#20352
C3×#20342
C3×#20002
C3×#19992
C3×#18942
C3×#18932
C3×#18742
C3×#18532
C3×#17882
#243973