Finite Group Databasebeta

← C3×#10710712 #72252315

Subgroups — C3×#10710712 #72252315

Order 2304.

2812 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#87239C211yesmaximal, characteristic
2C3×#70015C214yesmaximal, complemented
3C3×#72129C211yesmaximal, characteristic, complemented
4C32×#1781C211yesmaximal, characteristic, complemented
5#10710712C311yesmaximal, characteristic, direct product factor
6C3×#12705—31nomaximal
7C23×C32×D4C2211yescharacteristic
8C2×C3×#1004C411yescharacteristic, complemented
9C2×C3×#953—21no—
10C2×C3×#953C412yescomplemented
11C3×#5806—24no—
12C3×#5805—21no—
13C3×#5804—21no—
14C3×#5804C2212yes—
15C3×D4×#67—24no—
16C3×#5798C411yescharacteristic, complemented
17C3×#5791—21no—
18C2×C32×#99—21no—
19C2×C32×#99C2212yescomplemented
20C32×#379—21no—
21C2×C3×#833—21no—
22C2×C3×#833C2212yescomplemented
23C3×#5207—21no—
24C3×#4472—24no—
25C3×#4471—24no—
26C3×#3484—31no—
27#87239C2×C311yescharacteristic
28C3×#2121—34no—
29C3×#1783—31no—
30C3×#1781—21no—
31C3×#1781D311yescharacteristic, complemented
32C3×#1781C2×C311yescharacteristic, complemented
33#72129C2×C311yescharacteristic, complemented
34#70015C2×C314yescomplemented
35C25×C32C2×C411yescharacteristic
36C25×C32D411yescharacteristic
37C22×C32×D4—24no—
38C22×C32×D4—42no—
39C22×C32×D4—42no—
40C22×C32×D4C2×C411yescharacteristic
41C22×C32×D4D411yescharacteristic
42C22×C32×D4D411yescharacteristic
43C22×C32×D4C2311yescharacteristic
44C23×C32×C4D411yescharacteristic
45C22×C3×#67—22no—
46C22×C3×#67—21no—
47C22×C3×#67—22no—
48C22×C3×#67C2×C412yes—
49C3×#1004—42no—
50C3×#1004—42no—
51C2×C3×#237—22no—
52C2×C3×D3×D4—22no—
53C2×C3×#235—21no—
54C2×C32×C22⋊C4—22no—
55C2×C32×C22⋊C4—42no—
56C3×#953—24no—
57C3×#953—24no—
58C3×#953—22no—
59C3×#953—22no—
60C3×#953—22no—
61C2×C3×#217—22no—
62C2×C3×#217—22no—
63C2×C3×#217—21no—
64C2×C3×#217C2×C412yes—
65C3×#940—22no—
66C3×#939—24no—
67C3×#939—24no—
68C3×#938—24no—
69C3×#937—22no—
70C3×#937D414yes—
71C3×#936—22no—
72C3×#935—22no—
73C3×#935D414yes—
74C3×D4×Dic3—24no—
75C3×#930—22no—
76C3×#929—22no—
77C3×C4×#67—24no—
78C3×#926—21no—
79C3×#924—22no—
80C2×C3×#208—22no—
81C32×#99—24no—
82C32×#99—42no—
83C3×#833—24no—
84C3×#833—42no—
85C3×#830—42no—
86#12705—31noSylow
87C2×C3×H(5,𝔽2)—31no—
88C23×C3×D4—21no—
89C23×C3×D4C2×D311yescharacteristic
90C23×C3×D4C22×C311yescharacteristic
91C2×#1004C3×C411yescharacteristic, complemented
92C3×#546—64no—
93C3×D42—64no—
94C3×#535—61no—
95C3×#534—32no—
96C3×#534—61no—
97C3×#525—61no—
98C2×C3×#120—32no—
99C2×C3×#120—61no—
100C3×#518—31no—
101C2×#953—21no—
102C2×#953C3×C412yescomplemented
103#5806—24no—
104#5805—21no—
105#5804—21no—
106#5804C22×C312yes—
107D4×#67—24no—
108#5798C3×C411yescharacteristic, complemented
109#5791—21no—
110C2×C3×#100—32no—
111C2×C3×#100—61no—
112C2×C3×#99—22no—
113C2×C3×#99—21no—
114C2×C3×#99—21no—
115C2×C3×#99—22no—
116C2×C3×#99C2×D312yescomplemented
117C2×C3×#99C22×C312yescomplemented
118C3×#407—61no—
119C3×#379—22no—
120C3×#379—21no—
121C3×#379—21no—
122C2×#833—21no—
123C2×#833C22×C312yescomplemented
124#5207—21no—
125C3×#352—64no—
126C3×AΣL(1,𝔽16)—64no—
127#4472—24no—
128#4471—24no—
129C24×C32—22no—
130C24×C32—22no—
131C24×C32—22no—
132C24×C32—41no—
133C24×C32—41no—
134C24×C32—41no—
135C24×C32—82no—
136C24×C32—82no—
137C24×C32C22⋊C411yescharacteristic
138C24×C32C22⋊C411yescharacteristic
139C24×C32C22⋊C411yescharacteristic
140C24×C32C22×C411yescharacteristic
141C24×C32C2×D411yescharacteristic
142C23×C3×D3—21no—
143C23×C3×D3C22⋊C412yescomplemented
144C2×C32×D4—22no—
145C2×C32×D4—22no—
146C2×C32×D4—22no—
147C2×C32×D4—22no—
148C2×C32×D4—22no—
149C2×C32×D4—22no—
150C2×C32×D4—22no—
151C2×C32×D4—41no—
152C2×C32×D4—41no—
153C2×C32×D4—41no—
154C2×C32×D4—41no—
155C2×C32×D4—416no—
156C2×C32×D4C2×D414yes—
157C22×C32×C4—22no—
158C22×C32×C4—22no—
159C22×C32×C4—41no—
160C22×C32×C4—42no—
161C22×C32×C4C22⋊C411yescharacteristic
162C22×C32×C4C2×D411yescharacteristic
163C2×C3×#67—24no—
164C2×C3×#67—22no—
165C2×C3×#67—22no—
166C2×C3×#67—22no—
167C2×C3×#67—24no—
168C2×C3×#67—24no—
169C2×C3×#67—42no—
170C2×C3×#67—42no—
171C2×C3×#67—42no—
172C2×C3×#67—42no—
173C2×C3×#67—84no—
174C2×C3×#67—84no—
175C22×C3×Dic3—21no—
176C22×C3×Dic3—22no—
177C22×C3×Dic3—22no—
178C22×C3×Dic3C22⋊C412yescomplemented
179C3×#237—48no—
180C3×D3×D4—48no—
181C3×#235—42no—
182C3×#235—42no—
183C2×C3×D12—21no—
184C2×C3×C4×D3—22no—
185C2×C3×Dic6—21no—
186C32×C22⋊C4—42no—
187C32×C22⋊C4—42no—
188C32×C22⋊C4—84no—
189C3×#217—24no—
190C3×#217—22no—
191C3×#217—24no—
192C3×#217—22no—
193C3×#217—24no—
194C3×#217C22⋊C414yescomplemented
195C3×(C2×D3)⋊C4—24no—
196C3×C4⋊Dic3—22no—
197C3×Dic3⋊C4—24no—
198C3×C4×Dic3—22no—
199C3×#208—42no—
200C3×#208—42no—
201C2×C3×C3⋊C8—42no—
202#3484—31no—
203#2121—34no—
204#1783—31no—
205#1781C3×D311yescharacteristic, complemented
206C25×C3—21no—
207C25×C3—21no—
208C25×C3C4×D311yescharacteristic
209C25×C3#6711yescharacteristic
210C25×C3C2×C3×C411yescharacteristic
211C25×C3C3×D411yescharacteristic
212C3×H(5,𝔽2)—122no—
213C3×H(5,𝔽2)—122no—
214C2×C3×#41—62no—
215C2×C3×#41—61no—
216C22×C3×D4—24no—
217C22×C3×D4—24no—
218C22×C3×D4—21no—
219C22×C3×D4—21no—
220C22×C3×D4—21no—
221C22×C3×D4—21no—
222C22×C3×D4—32no—
223C22×C3×D4—44no—
224C22×C3×D4—42no—
225C22×C3×D4—42no—
226C22×C3×D4—42no—
227C22×C3×D4—42no—
228C22×C3×D4—44no—
229C22×C3×D4—44no—
230C22×C3×D4—62no—
231C22×C3×D4—61no—
232C22×C3×D4—62no—
233C22×C3×D4—62no—
234C22×C3×D4C4×D311yescharacteristic
235C22×C3×D4D1211yescharacteristic
236C22×C3×D4#6711yescharacteristic
237C22×C3×D4C2×C3×C411yescharacteristic
238C22×C3×D4C3×D411yescharacteristic
239C22×C3×D4C3×D411yescharacteristic
240C22×C3×D4C22×D311yescharacteristic
241C22×C3×D4C23×C311yescharacteristic
242C23×C3×C4—21no—
243C23×C3×C4D1211yescharacteristic
244C23×C3×C4C3×D411yescharacteristic
245C22×#67—21no—
246C22×#67—22no—
247C22×#67—22no—
248C22×#67C2×C3×C412yes—
249#1004—42no—
250#1004—42no—
251C2×#237—22no—
252C2×D3×D4—22no—
253C2×#235—21no—
254C2×C3×M16—62no—
255C3×#127—62no—
256C3×#124—62no—
257C3×#123—34no—
258C3×#123—62no—
259C3×#123—62no—
260C3×C22⋊Q8—62no—
261C3×#121—62no—
262C3×#121—64no—
263C3×#121—64no—
264C3×#121—64no—
265C3×#120—34no—
266C3×#120—64no—
267C3×#120—62no—
268C3×#120—64no—
269C3×#120—62no—
270C3×#120—62no—
271C3×#120—62no—
272C3×C4×D4—64no—
273C3×C4×D4—64no—
274C3×#117—61no—
275C2×C3×C22⋊C4—24no—
276C2×C3×C22⋊C4—22no—
277C2×C3×C22⋊C4—22no—
278C2×C3×C22⋊C4—32no—
279C2×C3×C22⋊C4—44no—
280C2×C3×C22⋊C4—42no—
281C2×C3×C22⋊C4—42no—
282C2×C3×C22⋊C4—62no—
283C2×C3×C22⋊C4—62no—
284C2×C3×C22⋊C4—61no—
285#953—24no—
286#953—22no—
287#953—22no—
288#953—22no—
289#953—24no—
290C2×#217—22no—
291C2×#217—21no—
292C2×#217—22no—
293C2×#217C2×C3×C412yes—
294#940—22no—
295#939—24no—
296#939—24no—
297#938—24no—
298#937—22no—
299#937C3×D414yes—
300#936—22no—
301#935—22no—
302#935C3×D414yes—
303D4×Dic3—24no—
304#930—22no—
305#929—22no—
306C4×#67—24no—
307#926—21no—
308#924—22no—
309C2×#208—22no—
310C3×#100—64no—
311C3×#100—122no—
312C3×#99—24no—
313C3×#99—24no—
314C3×#99—44no—
315C3×#99—44no—
316C3×#99—42no—
317C3×#99—42no—
318C3×C22⋊C8—122no—
319#833—24no—
320#833—42no—
321#830—42no—
322C23×C32—21no—
323C23×C32—21no—
324C23×C32—21no—
325C23×C32—21no—
326C23×C32—21no—
327C23×C32—21no—
328C23×C32—21no—
329C23×C32—21no—
330C23×C32—21no—
331C23×C32—21no—
332C23×C32—21no—
333C23×C32—21no—
334C23×C32—42no—
335C23×C32—44no—
336C23×C32—44no—
337C23×C32—44no—
338C23×C32—44no—
339C23×C32—44no—
340C23×C32—82no—
341C23×C32—82no—
342C23×C32—82no—
343C23×C32—81no—
344C23×C32—81no—
345C23×C32—81no—
346C23×C32—81no—
347C23×C32—82no—
348C23×C32—82no—
349C23×C32—82no—
350C23×C32—82no—
351C23×C32—82no—
352C23×C32—82no—
353C23×C32#9912yes—
354C23×C32C2×C22⋊C412yes—
355C23×C32C2×C22⋊C411yescharacteristic
356C23×C32#12012yes—
357C22×C3×D3—22no—
358C22×C3×D3—42no—
359C22×C3×D3—42no—
360C22×C3×D3—82no—
361C22×C3×D3—82no—
362C32×D4—28no—
363C32×D4—44no—
364C32×D4—44no—
365C32×D4—44no—
366C2×C32×C4—21no—
367C2×C32×C4—21no—
368C2×C32×C4—21no—
369C2×C32×C4—21no—
370C2×C32×C4—44no—
371C2×C32×C4—82no—
372C2×C32×C4—84no—
373C2×C32×C4#9912yes—
374C2×C32×C4#12012yes—
375C3×#67—44no—
376C3×#67—44no—
377C3×#67—48no—
378C3×#67—42no—
379C3×#67—42no—
380C3×#67—84no—
381C3×#67—84no—
382C2×C3×Dic3—24no—
383C2×C3×Dic3—22no—
384C2×C3×Dic3—42no—
385C2×C3×Dic3—42no—
386C2×C3×Dic3—82no—
387C2×C3×Dic3—82no—
388C3×D12—42no—
389C3×C4×D3—44no—
390C3×Dic6—42no—
391C3×C3⋊C8—82no—
392C2×H(5,𝔽2)—31no—
393C23×D4C2×C3×D311yescharacteristic
394#546—64no—
395D42—64no—
396#535—61no—
397#534—32no—
398#534—61no—
399#525—61no—
400C2×#120—32no—
401C2×#120—61no—
402#518—31no—
403C2×#100—32no—
404C2×#100—61no—
405C2×#99—21no—
406C2×#99C2×C3×D312yescomplemented
407#407—61no—
408#379—21no—
409#352—64no—
410AΣL(1,𝔽16)—64no—
411C24×C3—24no—
412C24×C3—22no—
413C24×C3—22no—
414C24×C3—22no—
415C24×C3—22no—
416C24×C3—22no—
417C24×C3—22no—
418C24×C3—21no—
419C24×C3—21no—
420C24×C3—21no—
421C24×C3—21no—
422C24×C3—21no—
423C24×C3—32no—
424C24×C3—42no—
425C24×C3—42no—
426C24×C3—41no—
427C24×C3—41no—
428C24×C3—41no—
429C24×C3—41no—
430C24×C3—41no—
431C24×C3—41no—
432C24×C3—42no—
433C24×C3—42no—
434C24×C3—42no—
435C24×C3—61no—
436C24×C3—82no—
437C24×C3—82no—
438C24×C3—82no—
439C24×C3—82no—
440C24×C3—84no—
441C24×C3—84no—
442C24×C3(C2×D3)⋊C411yescharacteristic
443C24×C3(C2×D3)⋊C411yescharacteristic
444C24×C3(C2×D3)⋊C411yescharacteristic
445C24×C3C3×C22⋊C411yescharacteristic
446C24×C3C3×C22⋊C411yescharacteristic
447C24×C3C3×C22⋊C411yescharacteristic
448C24×C3C2×C4×D311yescharacteristic
449C24×C3C2×#6711yescharacteristic
450C24×C3C22×C3×C411yescharacteristic
451C24×C3C2×C3×D411yescharacteristic
452C23×D3—21no—
453C23×D3C3×C22⋊C412yescomplemented
454C3×#41—122no—
455C3×#41—128no—
456C3×#41—122no—
457C2×C3×Q8—61no—
458C2×C3×D4—22no—
459C2×C3×D4—22no—
460C2×C3×D4—22no—
461C2×C3×D4—22no—
462C2×C3×D4—24no—
463C2×C3×D4—22no—
464C2×C3×D4—22no—
465C2×C3×D4—22no—
466C2×C3×D4—22no—
467C2×C3×D4—22no—
468C2×C3×D4—22no—
469C2×C3×D4—22no—
470C2×C3×D4—22no—
471C2×C3×D4—22no—
472C2×C3×D4—22no—
473C2×C3×D4—24no—
474C2×C3×D4—42no—
475C2×C3×D4—42no—
476C2×C3×D4—42no—
477C2×C3×D4—42no—
478C2×C3×D4—42no—
479C2×C3×D4—42no—
480C2×C3×D4—41no—
481C2×C3×D4—41no—
482C2×C3×D4—41no—
483C2×C3×D4—41no—
484C2×C3×D4—41no—
485C2×C3×D4—41no—
486C2×C3×D4—41no—
487C2×C3×D4—41no—
488C2×C3×D4—416no—
489C2×C3×D4—416no—
490C2×C3×D4—42no—
491C2×C3×D4—42no—
492C2×C3×D4—42no—
493C2×C3×D4—42no—
494C2×C3×D4—432no—
495C2×C3×D4—61no—
496C2×C3×D4—64no—
497C2×C3×D4—62no—
498C2×C3×D4—62no—
499C2×C3×D4—62no—
500C2×C3×D4—64no—
501C2×C3×D4—64no—
502C2×C3×D4—128no—
503C2×C3×D4—122no—
504C2×C3×D4—122no—
505C2×C3×D4—122no—
506C2×C3×D4—122no—
507C2×C3×D4—244no—
508C2×C3×D4—244no—
509C2×C3×D4D3×D414yes—
510C2×C3×D4C2×C3×D414yes—
511C22×C3×C4—22no—
512C22×C3×C4—22no—
513C22×C3×C4—22no—
514C22×C3×C4—22no—
515C22×C3×C4—21no—
516C22×C3×C4—21no—
517C22×C3×C4—32no—
518C22×C3×C4—42no—
519C22×C3×C4—42no—
520C22×C3×C4—41no—
521C22×C3×C4—41no—
522C22×C3×C4—42no—
523C22×C3×C4—44no—
524C22×C3×C4—42no—
525C22×C3×C4—42no—
526C22×C3×C4—62no—
527C22×C3×C4—61no—
528C22×C3×C4—62no—
529C22×C3×C4—62no—
530C22×C3×C4(C2×D3)⋊C411yescharacteristic
531C22×C3×C4C3×C22⋊C411yescharacteristic
532C22×C3×C4C2×D1211yescharacteristic
533C22×C3×C4C2×C3×D411yescharacteristic
534C2×#67—24no—
535C2×#67—22no—
536C2×#67—22no—
537C2×#67—22no—
538C2×#67—24no—
539C2×#67—24no—
540C2×#67—42no—
541C2×#67—42no—
542C2×#67—42no—
543C2×#67—42no—
544C2×#67—84no—
545C2×#67—84no—
546C22×Dic3—21no—
547C22×Dic3—22no—
548C22×Dic3—22no—
549C22×Dic3C3×C22⋊C412yescomplemented
550#237—48no—
551D3×D4—48no—
552#235—42no—
553#235—42no—
554C2×D12—21no—
555C2×C4×D3—22no—
556C2×Dic6—21no—
557C3×M16—122no—
558C3×M16—122no—
559C2×C3×C8—122no—
560C3×C4⋊C4—62no—
561C3×C4⋊C4—64no—
562C3×C22⋊C4—34no—
563C3×C22⋊C4—44no—
564C3×C22⋊C4—42no—
565C3×C22⋊C4—42no—
566C3×C22⋊C4—44no—
567C3×C22⋊C4—42no—
568C3×C22⋊C4—42no—
569C3×C22⋊C4—64no—
570C3×C22⋊C4—62no—
571C3×C22⋊C4—64no—
572C3×C22⋊C4—62no—
573C3×C22⋊C4—64no—
574C3×C22⋊C4—64no—
575C3×C22⋊C4—84no—
576C3×C22⋊C4—84no—
577C3×C22⋊C4—88no—
578C3×C42—62no—
579#217—24no—
580#217—22no—
581#217—24no—
582#217—22no—
583#217—24no—
584#217C3×C22⋊C414yescomplemented
585(C2×D3)⋊C4—24no—
586C4⋊Dic3—22no—
587Dic3⋊C4—24no—
588C4×Dic3—22no—
589#208—42no—
590#208—42no—
591C2×C3⋊C8—42no—
592C22×C32—22no—
593C22×C32—22no—
594C22×C32—22no—
595C22×C32—22no—
596C22×C32—22no—
597C22×C32—22no—
598C22×C32—41no—
599C22×C32—42no—
600C22×C32—42no—
601C22×C32—41no—
602C22×C32—41no—
603C22×C32—41no—
604C22×C32—41no—
605C22×C32—41no—
606C22×C32—42no—
607C22×C32—42no—
608C22×C32—42no—
609C22×C32—42no—
610C22×C32—81no—
611C22×C32—81no—
612C22×C32—81no—
613C22×C32—81no—
614C22×C32—81no—
615C22×C32—81no—
616C22×C32—88no—
617C22×C32—88no—
618C22×C32#37911yescharacteristic
619C22×C32C2×#9911yescharacteristic
620C22×C32C2×#9911yescharacteristic
621C2×C3×D3—44no—
622C2×C3×D3—42no—
623C2×C3×D3—162no—
624C2×C3×D3—162no—
625C32×C4—22no—
626C32×C4—22no—
627C32×C4—162no—
628C3×Dic3—44no—
629C3×Dic3—42no—
630C25C3×C4×D311yescharacteristic
631C25C3×#6711yescharacteristic
632H(5,𝔽2)—122no—
633H(5,𝔽2)—122no—
634C2×#41—62no—
635C2×#41—61no—
636C22×D4—24no—
637C22×D4—32no—
638C22×D4—42no—
639C22×D4—42no—
640C22×D4—62no—
641C22×D4—61no—
642C22×D4—62no—
643C22×D4—62no—
644C22×D4C3×C4×D311yescharacteristic
645C22×D4C3×D1211yescharacteristic
646C22×D4C3×#6711yescharacteristic
647C22×D4C22×C3×D311yescharacteristic
648C23×C4C3×D1211yescharacteristic
649C2×M16—62no—
650#127—62no—
651#124—62no—
652#123—34no—
653#123—62no—
654#123—62no—
655C22⋊Q8—62no—
656#121—62no—
657#121—64no—
658#121—64no—
659#121—64no—
660#120—34no—
661#120—64no—
662#120—62no—
663#120—64no—
664#120—62no—
665#120—62no—
666#120—62no—
667C4×D4—64no—
668C4×D4—64no—
669#117—61no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—32no—
672C2×C22⋊C4—42no—
673C2×C22⋊C4—62no—
674C2×C22⋊C4—62no—
675C2×C22⋊C4—61no—
676#100—64no—
677#100—122no—
678#99—24no—
679#99—42no—
680C22⋊C8—122no—
681C23×C3—22no—
682C23×C3—22no—
683C23×C3—22no—
684C23×C3—21no—
685C23×C3—21no—
686C23×C3—21no—
687C23×C3—21no—
688C23×C3—21no—
689C23×C3—21no—
690C23×C3—21no—
691C23×C3—21no—
692C23×C3—21no—
693C23×C3—21no—
694C23×C3—21no—
695C23×C3—21no—
696C23×C3—21no—
697C23×C3—21no—
698C23×C3—21no—
699C23×C3—21no—
700C23×C3—21no—
701C23×C3—21no—
702C23×C3—22no—
703C23×C3—21no—
704C23×C3—21no—
705C23×C3—21no—
706C23×C3—21no—
707C23×C3—21no—
708C23×C3—21no—
709C23×C3—22no—
710C23×C3—21no—
711C23×C3—22no—
712C23×C3—22no—
713C23×C3—41no—
714C23×C3—41no—
715C23×C3—41no—
716C23×C3—41no—
717C23×C3—41no—
718C23×C3—41no—
719C23×C3—41no—
720C23×C3—41no—
721C23×C3—42no—
722C23×C3—42no—
723C23×C3—44no—
724C23×C3—44no—
725C23×C3—44no—
726C23×C3—44no—
727C23×C3—44no—
728C23×C3—48no—
729C23×C3—44no—
730C23×C3—44no—
731C23×C3—48no—
732C23×C3—44no—
733C23×C3—44no—
734C23×C3—44no—
735C23×C3—44no—
736C23×C3—48no—
737C23×C3—62no—
738C23×C3—84no—
739C23×C3—84no—
740C23×C3—82no—
741C23×C3—82no—
742C23×C3—84no—
743C23×C3—82no—
744C23×C3—82no—
745C23×C3—82no—
746C23×C3—82no—
747C23×C3—81no—
748C23×C3—81no—
749C23×C3—81no—
750C23×C3—81no—
751C23×C3—81no—
752C23×C3—81no—
753C23×C3—81no—
754C23×C3—81no—
755C23×C3—82no—
756C23×C3—82no—
757C23×C3—82no—
758C23×C3—82no—
759C23×C3—82no—
760C23×C3—82no—
761C23×C3—82no—
762C23×C3—82no—
763C23×C3—84no—
764C23×C3—82no—
765C23×C3—82no—
766C23×C3—84no—
767C23×C3—84no—
768C23×C3—84no—
769C23×C3—84no—
770C23×C3—82no—
771C23×C3—82no—
772C23×C3—82no—
773C23×C3—82no—
774C23×C3—82no—
775C23×C3—82no—
776C23×C3—84no—
777C23×C3—84no—
778C23×C3—84no—
779C23×C3—122no—
780C23×C3—122no—
781C23×C3—242no—
782C23×C3—242no—
783C23×C3#80612yes—
784C23×C3C3×#9912yes—
785C23×C3D3×C22⋊C412yes—
786C23×C3C2×(C2×D3)⋊C411yescharacteristic
787C23×C3#93712yes—
788C23×C3C2×C3×C22⋊C412yes—
789C23×C3C2×C3×C22⋊C411yescharacteristic
790C23×C3C3×#12012yes—
791C22×D3—22no—
792C22×D3—42no—
793C22×D3—42no—
794C22×D3—82no—
795C22×D3—82no—
796C3×Q8—122no—
797C3×D4—28no—
798C3×D4—28no—
799C3×D4—48no—
800C3×D4—44no—
801C3×D4—44no—
802C3×D4—44no—
803C3×D4—44no—
804C3×D4—44no—
805C3×D4—44no—
806C3×D4—48no—
807C3×D4—48no—
808C3×D4—48no—
809C3×D4—122no—
810C3×D4—124no—
811C3×D4—124no—
812C3×D4—128no—
813C3×D4—122no—
814C3×D4—122no—
815C3×D4—244no—
816C3×D4—244no—
817C2×C3×C4—21no—
818C2×C3×C4—21no—
819C2×C3×C4—21no—
820C2×C3×C4—21no—
821C2×C3×C4—21no—
822C2×C3×C4—21no—
823C2×C3×C4—21no—
824C2×C3×C4—21no—
825C2×C3×C4—22no—
826C2×C3×C4—22no—
827C2×C3×C4—41no—
828C2×C3×C4—41no—
829C2×C3×C4—41no—
830C2×C3×C4—41no—
831C2×C3×C4—44no—
832C2×C3×C4—44no—
833C2×C3×C4—48no—
834C2×C3×C4—64no—
835C2×C3×C4—62no—
836C2×C3×C4—84no—
837C2×C3×C4—82no—
838C2×C3×C4—82no—
839C2×C3×C4—88no—
840C2×C3×C4—84no—
841C2×C3×C4—84no—
842C2×C3×C4—124no—
843C2×C3×C4—122no—
844C2×C3×C4—122no—
845C2×C3×C4—242no—
846C2×C3×C4—242no—
847C2×C3×C4#80612yes—
848C2×C3×C4C3×#9912yes—
849C2×C3×C4#88212yes—
850C2×C3×C4C3×#12012yes—
851#67—44no—
852#67—44no—
853#67—48no—
854#67—42no—
855#67—42no—
856#67—84no—
857#67—84no—
858C2×Dic3—24no—
859C2×Dic3—22no—
860C2×Dic3—42no—
861C2×Dic3—42no—
862C2×Dic3—82no—
863C2×Dic3—82no—
864D12—42no—
865C4×D3—44no—
866Dic6—42no—
867C3×C8—242no—
868C3⋊C8—82no—
869C2×C32—21no—
870C2×C32—21no—
871C2×C32—21no—
872C2×C32—42no—
873C2×C32—42no—
874C2×C32—42no—
875C2×C32—42no—
876C2×C32—81no—
877C2×C32#178111yescharacteristic
878C3×D3—82no—
879C24—22no—
880C24—22no—
881C24—22no—
882C24—32no—
883C24—41no—
884C24—41no—
885C24—41no—
886C24—61no—
887C24—82no—
888C24—82no—
889C24C3×(C2×D3)⋊C411yescharacteristic
890C24C3×(C2×D3)⋊C411yescharacteristic
891C24C3×(C2×D3)⋊C411yescharacteristic
892C24C2×C3×C4×D311yescharacteristic
893C24C2×C3×#6711yescharacteristic
894#41—122no—
895#41—128no—
896#41—122no—
897C2×Q8—61no—
898C2×D4—22no—
899C2×D4—22no—
900C2×D4—22no—
901C2×D4—22no—
902C2×D4—22no—
903C2×D4—22no—
904C2×D4—22no—
905C2×D4—41no—
906C2×D4—41no—
907C2×D4—41no—
908C2×D4—41no—
909C2×D4—416no—
910C2×D4—61no—
911C2×D4—64no—
912C2×D4—62no—
913C2×D4—62no—
914C2×D4—62no—
915C2×D4—64no—
916C2×D4—64no—
917C2×D4—128no—
918C2×D4—122no—
919C2×D4—122no—
920C2×D4—122no—
921C2×D4—122no—
922C2×D4—244no—
923C2×D4—244no—
924C2×D4C3×D3×D414yes—
925C22×C4—22no—
926C22×C4—22no—
927C22×C4—32no—
928C22×C4—41no—
929C22×C4—42no—
930C22×C4—62no—
931C22×C4—61no—
932C22×C4—62no—
933C22×C4—62no—
934C22×C4C3×(C2×D3)⋊C411yescharacteristic
935C22×C4C2×C3×D1211yescharacteristic
936M16—122no—
937M16—122no—
938C2×C8—122no—
939C4⋊C4—62no—
940C4⋊C4—64no—
941C22⋊C4—34no—
942C22⋊C4—42no—
943C22⋊C4—42no—
944C22⋊C4—64no—
945C22⋊C4—62no—
946C22⋊C4—64no—
947C22⋊C4—62no—
948C22⋊C4—64no—
949C22⋊C4—64no—
950C22⋊C4—84no—
951C42—62no—
952C22×C3—22no—
953C22×C3—24no—
954C22×C3—22no—
955C22×C3—24no—
956C22×C3—22no—
957C22×C3—22no—
958C22×C3—22no—
959C22×C3—22no—
960C22×C3—22no—
961C22×C3—22no—
962C22×C3—22no—
963C22×C3—22no—
964C22×C3—22no—
965C22×C3—22no—
966C22×C3—21no—
967C22×C3—21no—
968C22×C3—21no—
969C22×C3—42no—
970C22×C3—42no—
971C22×C3—42no—
972C22×C3—42no—
973C22×C3—41no—
974C22×C3—41no—
975C22×C3—42no—
976C22×C3—42no—
977C22×C3—42no—
978C22×C3—42no—
979C22×C3—42no—
980C22×C3—42no—
981C22×C3—42no—
982C22×C3—42no—
983C22×C3—44no—
984C22×C3—42no—
985C22×C3—42no—
986C22×C3—42no—
987C22×C3—42no—
988C22×C3—42no—
989C22×C3—41no—
990C22×C3—41no—
991C22×C3—41no—
992C22×C3—41no—
993C22×C3—41no—
994C22×C3—41no—
995C22×C3—42no—
996C22×C3—42no—
997C22×C3—42no—
998C22×C3—44no—
999C22×C3—42no—
1000C22×C3—42no—
1001C22×C3—41no—
1002C22×C3—41no—
1003C22×C3—41no—
1004C22×C3—41no—
1005C22×C3—82no—
1006C22×C3—82no—
1007C22×C3—82no—
1008C22×C3—82no—
1009C22×C3—81no—
1010C22×C3—81no—
1011C22×C3—81no—
1012C22×C3—81no—
1013C22×C3—81no—
1014C22×C3—81no—
1015C22×C3—81no—
1016C22×C3—81no—
1017C22×C3—81no—
1018C22×C3—81no—
1019C22×C3—81no—
1020C22×C3—81no—
1021C22×C3—82no—
1022C22×C3—82no—
1023C22×C3—82no—
1024C22×C3—88no—
1025C22×C3—88no—
1026C22×C3—816no—
1027C22×C3—88no—
1028C22×C3—88no—
1029C22×C3—82no—
1030C22×C3—82no—
1031C22×C3—82no—
1032C22×C3—816no—
1033C22×C3—124no—
1034C22×C3—122no—
1035C22×C3—482no—
1036C22×C3—482no—
1037C22×C3C2×#80611yescharacteristic
1038C22×C3C2×#80611yescharacteristic
1039C22×C3#495511yescharacteristic
1040C22×C3C3×#37911yescharacteristic
1041C22×C3C2×C3×#9911yescharacteristic
1042C22×C3C2×C3×#9911yescharacteristic
1043C2×D3—44no—
1044C2×D3—42no—
1045C2×D3—162no—
1046C2×D3—162no—
1047C3×C4—22no—
1048C3×C4—22no—
1049C3×C4—22no—
1050C3×C4—22no—
1051C3×C4—42no—
1052C3×C4—42no—
1053C3×C4—124no—
1054C3×C4—122no—
1055C3×C4—164no—
1056C3×C4—162no—
1057C3×C4—162no—
1058Dic3—44no—
1059Dic3—42no—
1060C32#1270511yescharacteristic, complemented, Sylow
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—42no—
1074C23—44no—
1075C23—44no—
1076C23—44no—
1077C23—44no—
1078C23—44no—
1079C23—62no—
1080C23—82no—
1081C23—82no—
1082C23—82no—
1083C23—81no—
1084C23—81no—
1085C23—81no—
1086C23—81no—
1087C23—82no—
1088C23—82no—
1089C23—82no—
1090C23—82no—
1091C23—82no—
1092C23—82no—
1093C23—122no—
1094C23—122no—
1095C23—242no—
1096C23—242no—
1097C23C3×#80612yes—
1098C23C3×D3×C22⋊C412yes—
1099C23C2×C3×(C2×D3)⋊C411yescharacteristic
1100C23C3×#93712yes—
1101Q8—122no—
1102D4—28no—
1103D4—44no—
1104D4—44no—
1105D4—44no—
1106D4—122no—
1107D4—124no—
1108D4—124no—
1109D4—128no—
1110D4—122no—
1111D4—122no—
1112D4—244no—
1113D4—244no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—44no—
1119C2×C4—64no—
1120C2×C4—62no—
1121C2×C4—82no—
1122C2×C4—84no—
1123C2×C4—124no—
1124C2×C4—122no—
1125C2×C4—122no—
1126C2×C4—242no—
1127C2×C4—242no—
1128C2×C4C3×#80612yes—
1129C2×C4C3×#88212yes—
1130C8—242no—
1131C2×C3—22no—
1132C2×C3—21no—
1133C2×C3—21no—
1134C2×C3—21no—
1135C2×C3—21no—
1136C2×C3—21no—
1137C2×C3—21no—
1138C2×C3—21no—
1139C2×C3—41no—
1140C2×C3—41no—
1141C2×C3—44no—
1142C2×C3—44no—
1143C2×C3—42no—
1144C2×C3—42no—
1145C2×C3—42no—
1146C2×C3—42no—
1147C2×C3—42no—
1148C2×C3—42no—
1149C2×C3—42no—
1150C2×C3—42no—
1151C2×C3—82no—
1152C2×C3—82no—
1153C2×C3—82no—
1154C2×C3—81no—
1155C2×C3—81no—
1156C2×C3—242no—
1157C2×C3#6949811yescharacteristic
1158C2×C3C3×#178111yescharacteristic
1159D3—82no—
1160C22—22no—
1161C22—22no—
1162C22—22no—
1163C22—22no—
1164C22—22no—
1165C22—22no—
1166C22—41no—
1167C22—42no—
1168C22—42no—
1169C22—42no—
1170C22—42no—
1171C22—42no—
1172C22—41no—
1173C22—41no—
1174C22—41no—
1175C22—42no—
1176C22—41no—
1177C22—41no—
1178C22—81no—
1179C22—81no—
1180C22—81no—
1181C22—81no—
1182C22—81no—
1183C22—81no—
1184C22—88no—
1185C22—88no—
1186C22—124no—
1187C22—122no—
1188C22—482no—
1189C22—482no—
1190C22C2×C3×#80611yescharacteristic
1191C22C2×C3×#80611yescharacteristic
1192C22C3×#495511yescharacteristic
1193C4—22no—
1194C4—22no—
1195C4—124no—
1196C4—122no—
1197C4—162no—
1198C3—21no—
1199C3C3×#1270511yescharacteristic, complemented
1200C3#1071071211yescharacteristic, direct product factor
1201C2—21no—
1202C2—21no—
1203C2—21no—
1204C2—42no—
1205C2—42no—
1206C2—42no—
1207C2—42no—
1208C2—81no—
1209C2—242no—
1210C2C3×#6949811yescharacteristic
subgroupG/H
centerC2×C3#69498
commutatorC24×C3C22×C3×C4
FrattiniC22×D4C22×C3×D3
FittingC32×#1781C2
socleC2×C32#1781
prime radicalC3×#87239C2
cosocleC22×C3×D4C23×C3
hypercenterC3×#1781D3
hypocenterC3C3×#12705
LCSG ▷ C24×C3 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C23×C3 ◁ C23×C3×D4 ◁ C3×#1781

Complements

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

NH ≅ G/Ntype
2. C3×#70015C2semidirect
3. C3×#72129C2semidirect
4. C32×#1781C2semidirect
5. #10710712C3direct (N × H)
8. C2×C3×#1004C4semidirect
10. C2×C3×#953C4semidirect
16. C3×#5798C4semidirect
19. C2×C32×#99C22semidirect
22. C2×C3×#833C22semidirect
31. C3×#1781D3semidirect
32. C3×#1781C2×C3semidirect
33. #72129C2×C3semidirect
34. #70015C2×C3semidirect
91. C2×#1004C3×C4semidirect
102. C2×#953C3×C4semidirect
108. #5798C3×C4semidirect
116. C2×C3×#99C2×D3semidirect
117. C2×C3×#99C22×C3semidirect
123. C2×#833C22×C3semidirect
143. C23×C3×D3C22⋊C4semidirect
178. C22×C3×Dic3C22⋊C4semidirect
194. C3×#217C22⋊C4semidirect
205. #1781C3×D3semidirect
406. C2×#99C2×C3×D3semidirect
453. C23×D3C3×C22⋊C4semidirect
549. C22×Dic3C3×C22⋊C4semidirect
584. #217C3×C22⋊C4semidirect
1060. C32#12705semidirect
1199. C3C3×#12705semidirect
1200. C3#10710712direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#872392
C3×#700152
C3×#721292
C32×#17812
#107107123
C3×#127053