Finite Group Databasebeta

← C3×#82604 #11808987

Subgroups — C3×#82604 #11808987

Order 1152.

3459 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×#67C211yesmaximal, characteristic, complemented
2C22×C3×D3×D4C211yesmaximal, characteristic, complemented
3C2×C32×#120C211yesmaximal, characteristic, complemented
4C2×C3×#953C211yesmaximal, characteristic, complemented
5C2×C3×#937C212yesmaximal, complemented
6C3×#5223C212yesmaximal, complemented
7C3×#5220C211yesmaximal, characteristic, complemented
8C3×#4960C212yesmaximal, complemented
9C3×#4958C211yesmaximal, characteristic, complemented
10C3×#4956C212yesmaximal, complemented
11C3×#4955C211yesmaximal, characteristic, complemented
12C3×#2403—31nomaximal
13#82604C311yesmaximal, characteristic, direct product factor
14C25×C32C2211yescharacteristic, complemented
15C24×C3×D3C2211yescharacteristic
16C24×C3×D3C2211yescharacteristic, complemented
17C22×C32×D4C2211yescharacteristic
18C22×C32×D4C2212yescomplemented
19C22×C3×#67—28no—
20C22×C3×#67—24no—
21C22×C3×#67C2212yes—
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2212yescomplemented
24C22×C3×#67C2211yescharacteristic, complemented
25C22×C3×#67C2212yescomplemented
26C23×C3×Dic3C2211yescharacteristic, complemented
27C2×C3×D3×D4—24no—
28C2×C3×D3×D4—24no—
29C2×C3×D3×D4—24no—
30C22×C3×D12C2211yescharacteristic, complemented
31C22×C3×C4×D3C2211yescharacteristic, complemented
32C32×#120—24no—
33C2×C32×C22⋊C4C2211yescharacteristic, complemented
34C2×C32×C22⋊C4C2212yescomplemented
35C3×#953—24no—
36C2×C3×#217C2211yescharacteristic, complemented
37C2×C3×#217C2212yescomplemented
38C2×C3×#217C2212yescomplemented
39C3×#937—28no—
40C2×C3×(C2×D3)⋊C4C2212yescomplemented
41C2×C3×(C2×D3)⋊C4C2212yescomplemented
42C2×C3×(C2×D3)⋊C4C2212yescomplemented
43C3×C3⋊#95C2212yescomplemented
44C3×C3⋊#95C2212yescomplemented
45C23×C3×D4—31no—
46C23×C3×D4—31no—
47C23×#67C2×C311yescharacteristic, complemented
48C22×D3×D4C2×C311yescharacteristic, complemented
49C2×C3×#120—21no—
50C2×C3×#120—32no—
51C2×C3×#120—31no—
52C2×C3×#120D311yescharacteristic, complemented
53C2×C3×#120C2×C311yescharacteristic, complemented
54C2×#953C2×C311yescharacteristic, complemented
55C2×#937C2×C312yescomplemented
56C3×#392—32no—
57C3×#392—32no—
58C3×#386—31no—
59C3×#386—32no—
60C3×#386—31no—
61C3×#379—31no—
62#5223C2×C312yescomplemented
63#5220C2×C311yescharacteristic, complemented
64#4960C2×C312yescomplemented
65#4958C2×C311yescharacteristic, complemented
66#4956C2×C312yescomplemented
67#4955C2×C311yescharacteristic, complemented
68C24×C32—22no—
69C24×C32—24no—
70C24×C32—22no—
71C24×C32—22no—
72C24×C32—42no—
73C24×C32C2311yescharacteristic
74C24×C32C2312yes—
75C24×C32C2311yescharacteristic
76C23×C3×D3—22no—
77C23×C3×D3—22no—
78C23×C3×D3—22no—
79C23×C3×D3—22no—
80C23×C3×D3—24no—
81C23×C3×D3—22no—
82C23×C3×D3—24no—
83C23×C3×D3—42no—
84C23×C3×D3—42no—
85C23×C3×D3D414yescomplemented
86C23×C3×D3C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C2×C32×D4—22no—
90C2×C32×D4—22no—
91C2×C32×D4—24no—
92C2×C32×D4—24no—
93C2×C32×D4—42no—
94C2×C32×D4D414yescomplemented
95C22×C32×C4C2312yes—
96C22×C32×C4C2311yescharacteristic
97C2×C3×#67—232no—
98C2×C3×#67—22no—
99C2×C3×#67—22no—
100C2×C3×#67—22no—
101C2×C3×#67—24no—
102C2×C3×#67—22no—
103C2×C3×#67—24no—
104C2×C3×#67—24no—
105C2×C3×#67—24no—
106C2×C3×#67—24no—
107C2×C3×#67—24no—
108C2×C3×#67—22no—
109C2×C3×#67—24no—
110C2×C3×#67—42no—
111C2×C3×#67D418yescomplemented
112C2×C3×#67D414yescomplemented
113C22×C3×Dic3—22no—
114C22×C3×Dic3—24no—
115C22×C3×Dic3C2312yes—
116C22×C3×Dic3C2312yes—
117C22×C3×Dic3C2311yescharacteristic
118C3×D3×D4—232no—
119C2×C3×D12—22no—
120C2×C3×D12—22no—
121C2×C3×D12—22no—
122C2×C3×C4×D3—22no—
123C2×C3×C4×D3—22no—
124C2×C3×C4×D3—22no—
125C32×C22⋊C4—22no—
126C32×C22⋊C4—24no—
127C3×#217—22no—
128C3×#217—24no—
129C3×#217—24no—
130C3×(C2×D3)⋊C4—24no—
131C3×(C2×D3)⋊C4—24no—
132C3×(C2×D3)⋊C4—42no—
133#2403—31noSylow
134C25×C3—21no—
135C25×C3—31no—
136C25×C3—31no—
137C25×C3C2×D311yescharacteristic, complemented
138C25×C3C22×C311yescharacteristic, complemented
139C24×D3C22×C311yescharacteristic
140C24×D3C22×C311yescharacteristic, complemented
141C22×C3×D4—21no—
142C22×C3×D4—22no—
143C22×C3×D4—31no—
144C22×C3×D4—32no—
145C22×C3×D4—32no—
146C22×C3×D4—31no—
147C22×C3×D4—32no—
148C22×C3×D4—31no—
149C22×C3×D4—64no—
150C22×C3×D4—64no—
151C22×C3×D4—68no—
152C22×C3×D4—64no—
153C22×C3×D4—64no—
154C22×C3×D4C2×D311yescharacteristic
155C22×C3×D4C2×D312yescomplemented
156C22×C3×D4C22×C311yescharacteristic
157C22×C3×D4C22×C312yescomplemented
158C23×C3×C4—31no—
159C23×C3×C4—31no—
160C22×#67—24no—
161C22×#67—28no—
162C22×#67C22×C311yescharacteristic
163C22×#67C22×C312yes—
164C22×#67C22×C311yescharacteristic, complemented
165C22×#67C22×C312yescomplemented
166C22×#67C22×C312yescomplemented
167C23×Dic3C22×C311yescharacteristic, complemented
168C2×D3×D4—24no—
169C2×D3×D4—24no—
170C2×D3×D4—24no—
171C22×D12C22×C311yescharacteristic, complemented
172C22×C4×D3C22×C311yescharacteristic, complemented
173C3×#120—28no—
174C3×#120—24no—
175C3×#120—24no—
176C3×#120—68no—
177C3×#120—64no—
178C2×C3×C22⋊C4—21no—
179C2×C3×C22⋊C4—22no—
180C2×C3×C22⋊C4—31no—
181C2×C3×C22⋊C4—32no—
182C2×C3×C22⋊C4—32no—
183C2×C3×C22⋊C4—32no—
184C2×C3×C22⋊C4—32no—
185C2×C3×C22⋊C4—32no—
186C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
187C2×C3×C22⋊C4C2×D312yescomplemented
188C2×C3×C22⋊C4C22×C311yescharacteristic, complemented
189C2×C3×C22⋊C4C22×C312yescomplemented
190#953—24no—
191C2×#217C22×C311yescharacteristic, complemented
192C2×#217C22×C312yescomplemented
193C2×#217C22×C312yescomplemented
194#937—28no—
195C2×(C2×D3)⋊C4C22×C312yescomplemented
196C2×(C2×D3)⋊C4C22×C312yescomplemented
197C2×(C2×D3)⋊C4C22×C312yescomplemented
198C3×#95—32no—
199C3×#95—32no—
200C3⋊#95C22×C312yescomplemented
201C3⋊#95C22×C312yescomplemented
202C23×C32—22no—
203C23×C32—22no—
204C23×C32—22no—
205C23×C32—22no—
206C23×C32—28no—
207C23×C32—22no—
208C23×C32—21no—
209C23×C32—21no—
210C23×C32—22no—
211C23×C32—22no—
212C23×C32—22no—
213C23×C32—22no—
214C23×C32—22no—
215C23×C32—48no—
216C23×C32—48no—
217C23×C32—44no—
218C23×C32—44no—
219C23×C32C2×D412yes—
220C23×C32C2×D412yes—
221C23×C32C2×D412yes—
222C23×C32C2×D414yescomplemented
223C23×C32C2×D412yescomplemented
224C23×C32C2411yescharacteristic
225C22×C3×D3—21no—
226C22×C3×D3—21no—
227C22×C3×D3—22no—
228C22×C3×D3—28no—
229C22×C3×D3—28no—
230C22×C3×D3—22no—
231C22×C3×D3—21no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C22×C3×D3—22no—
236C22×C3×D3—22no—
237C22×C3×D3—22no—
238C22×C3×D3—28no—
239C22×C3×D3—44no—
240C22×C3×D3—48no—
241C22×C3×D3—48no—
242C22×C3×D3—48no—
243C22×C3×D3—48no—
244C22×C3×D3—44no—
245C22×C3×D3—44no—
246C22×C3×D3C2×D412yes—
247C22×C3×D3C2×D414yes—
248C22×C3×D3C2×D412yes—
249C22×C3×D3C2×D412yescomplemented
250C32×D4—28no—
251C32×D4—48no—
252C2×C32×C4—22no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—22no—
256C2×C32×C4—22no—
257C2×C32×C4C2×D412yescomplemented
258C3×#67—28no—
259C3×#67—216no—
260C3×#67—28no—
261C3×#67—216no—
262C3×#67—48no—
263C2×C3×Dic3—28no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—22no—
267C2×C3×Dic3—22no—
268C2×C3×Dic3—22no—
269C2×C3×Dic3—22no—
270C2×C3×Dic3—22no—
271C2×C3×Dic3C2×D414yescomplemented
272C2×C3×Dic3C2×D412yescomplemented
273C3×D12—28no—
274C3×C4×D3—28no—
275C23×D4—31no—
276C23×D4—31no—
277C2×#120—31no—
278C2×#120—32no—
279C2×#120C3×D311yescharacteristic, complemented
280#392—32no—
281#392—32no—
282#386—31no—
283#386—32no—
284#386—31no—
285#379—31no—
286C24×C3—22no—
287C24×C3—24no—
288C24×C3—22no—
289C24×C3—24no—
290C24×C3—24no—
291C24×C3—22no—
292C24×C3—22no—
293C24×C3—22no—
294C24×C3—22no—
295C24×C3—22no—
296C24×C3—21no—
297C24×C3—21no—
298C24×C3—31no—
299C24×C3—31no—
300C24×C3—31no—
301C24×C3—34no—
302C24×C3—42no—
303C24×C3—44no—
304C24×C3—42no—
305C24×C3—42no—
306C24×C3—42no—
307C24×C3—44no—
308C24×C3—64no—
309C24×C3—62no—
310C24×C3—62no—
311C24×C3—64no—
312C24×C3—62no—
313C24×C3—62no—
314C24×C3—62no—
315C24×C3—122no—
316C24×C3—122no—
317C24×C3C22×D312yes—
318C24×C3C22×D311yescharacteristic
319C24×C3C22×D311yescharacteristic
320C24×C3C23×C312yes—
321C24×C3C23×C311yescharacteristic
322C24×C3C23×C311yescharacteristic
323C23×D3—22no—
324C23×D3—22no—
325C23×D3—22no—
326C23×D3—22no—
327C23×D3—24no—
328C23×D3—22no—
329C23×D3—24no—
330C23×D3—42no—
331C23×D3—42no—
332C23×D3C3×D414yescomplemented
333C23×D3C23×C311yescharacteristic
334C23×D3C23×C311yescharacteristic
335C23×D3C23×C311yescharacteristic
336C2×C3×D4—22no—
337C2×C3×D4—22no—
338C2×C3×D4—22no—
339C2×C3×D4—22no—
340C2×C3×D4—28no—
341C2×C3×D4—24no—
342C2×C3×D4—24no—
343C2×C3×D4—24no—
344C2×C3×D4—24no—
345C2×C3×D4—24no—
346C2×C3×D4—34no—
347C2×C3×D4—38no—
348C2×C3×D4—42no—
349C2×C3×D4—42no—
350C2×C3×D4—44no—
351C2×C3×D4—42no—
352C2×C3×D4—42no—
353C2×C3×D4—44no—
354C2×C3×D4—62no—
355C2×C3×D4—62no—
356C2×C3×D4—62no—
357C2×C3×D4—64no—
358C2×C3×D4—632no—
359C2×C3×D4—64no—
360C2×C3×D4—64no—
361C2×C3×D4—62no—
362C2×C3×D4—64no—
363C2×C3×D4—632no—
364C2×C3×D4—62no—
365C2×C3×D4—64no—
366C2×C3×D4—62no—
367C2×C3×D4—62no—
368C2×C3×D4—64no—
369C2×C3×D4—64no—
370C2×C3×D4—62no—
371C2×C3×D4—122no—
372C2×C3×D4#6714yescomplemented
373C2×C3×D4C3×D414yescomplemented
374C22×C3×C4—22no—
375C22×C3×C4—21no—
376C22×C3×C4—32no—
377C22×C3×C4—31no—
378C22×C3×C4—32no—
379C22×C3×C4—62no—
380C22×C3×C4—62no—
381C22×C3×C4—64no—
382C22×C3×C4—62no—
383C22×C3×C4—62no—
384C22×C3×C4C22×D312yes—
385C22×C3×C4C22×D311yescharacteristic
386C22×C3×C4C23×C312yes—
387C22×C3×C4C23×C311yescharacteristic
388C2×#67—232no—
389C2×#67—22no—
390C2×#67—22no—
391C2×#67—22no—
392C2×#67—24no—
393C2×#67—22no—
394C2×#67—24no—
395C2×#67—24no—
396C2×#67—24no—
397C2×#67—24no—
398C2×#67—24no—
399C2×#67—22no—
400C2×#67—24no—
401C2×#67—42no—
402C2×#67C3×D418yescomplemented
403C2×#67C3×D414yescomplemented
404C22×Dic3—22no—
405C22×Dic3—24no—
406C22×Dic3C23×C312yes—
407C22×Dic3C23×C312yes—
408C22×Dic3C23×C311yescharacteristic
409D3×D4—232no—
410C2×D12—22no—
411C2×D12—22no—
412C2×D12—22no—
413C2×C4×D3—22no—
414C2×C4×D3—22no—
415C2×C4×D3—22no—
416C3×C22⋊C4—24no—
417C3×C22⋊C4—28no—
418C3×C22⋊C4—22no—
419C3×C22⋊C4—22no—
420C3×C22⋊C4—24no—
421C3×C22⋊C4—24no—
422C3×C22⋊C4—64no—
423C3×C22⋊C4—64no—
424C3×C22⋊C4—64no—
425C3×C22⋊C4—64no—
426C3×C22⋊C4—62no—
427C3×C22⋊C4—122no—
428#217—22no—
429#217—24no—
430#217—24no—
431(C2×D3)⋊C4—24no—
432(C2×D3)⋊C4—24no—
433(C2×D3)⋊C4—42no—
434C22×C32—24no—
435C22×C32—22no—
436C22×C32—22no—
437C22×C32—24no—
438C22×C32—24no—
439C22×C32—24no—
440C22×C32—22no—
441C22×C32—24no—
442C22×C32—24no—
443C22×C32—416no—
444C22×C32—42no—
445C22×C32—42no—
446C22×C32—42no—
447C22×C32—42no—
448C22×C32—41no—
449C22×C32—41no—
450C22×C32—42no—
451C22×C32#12014yescomplemented
452C22×C32C22×D411yescharacteristic
453C22×C32C22×D412yes—
454C22×C32C22×D411yescharacteristic
455C22×C32C22×D411yescharacteristic
456C22×C32H(5,𝔽2)12yes—
457C2×C3×D3—22no—
458C2×C3×D3—22no—
459C2×C3×D3—24no—
460C2×C3×D3—24no—
461C2×C3×D3—22no—
462C2×C3×D3—22no—
463C2×C3×D3—22no—
464C2×C3×D3—22no—
465C2×C3×D3—24no—
466C2×C3×D3—416no—
467C2×C3×D3—416no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—42no—
471C2×C3×D3—42no—
472C2×C3×D3—42no—
473C2×C3×D3#12014yescomplemented
474C32×C4—22no—
475C32×C4—42no—
476C3×Dic3—22no—
477C3×Dic3—24no—
478C3×Dic3—42no—
479C25—31no—
480C25—31no—
481C25C2×C3×D311yescharacteristic, complemented
482C22×D4—31no—
483C22×D4—32no—
484C22×D4—32no—
485C22×D4—31no—
486C22×D4—32no—
487C22×D4—31no—
488C22×D4—64no—
489C22×D4—64no—
490C22×D4—68no—
491C22×D4—64no—
492C22×D4—64no—
493C22×D4C2×C3×D311yescharacteristic
494C22×D4C2×C3×D312yescomplemented
495C23×C4—31no—
496C23×C4—31no—
497#120—24no—
498#120—68no—
499#120—64no—
500C2×C22⋊C4—31no—
501C2×C22⋊C4—32no—
502C2×C22⋊C4—32no—
503C2×C22⋊C4—32no—
504C2×C22⋊C4—32no—
505C2×C22⋊C4—32no—
506C2×C22⋊C4C2×C3×D311yescharacteristic, complemented
507C2×C22⋊C4C2×C3×D312yescomplemented
508#95—32no—
509#95—32no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—22no—
514C23×C3—24no—
515C23×C3—28no—
516C23×C3—24no—
517C23×C3—28no—
518C23×C3—22no—
519C23×C3—22no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—22no—
532C23×C3—22no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—22no—
536C23×C3—22no—
537C23×C3—22no—
538C23×C3—21no—
539C23×C3—22no—
540C23×C3—22no—
541C23×C3—24no—
542C23×C3—22no—
543C23×C3—22no—
544C23×C3—34no—
545C23×C3—32no—
546C23×C3—32no—
547C23×C3—32no—
548C23×C3—42no—
549C23×C3—42no—
550C23×C3—42no—
551C23×C3—42no—
552C23×C3—42no—
553C23×C3—42no—
554C23×C3—42no—
555C23×C3—41no—
556C23×C3—41no—
557C23×C3—42no—
558C23×C3—48no—
559C23×C3—48no—
560C23×C3—48no—
561C23×C3—48no—
562C23×C3—48no—
563C23×C3—416no—
564C23×C3—44no—
565C23×C3—44no—
566C23×C3—48no—
567C23×C3—416no—
568C23×C3—48no—
569C23×C3—44no—
570C23×C3—44no—
571C23×C3—68no—
572C23×C3—68no—
573C23×C3—61no—
574C23×C3—62no—
575C23×C3—61no—
576C23×C3—68no—
577C23×C3—62no—
578C23×C3—61no—
579C23×C3—61no—
580C23×C3—62no—
581C23×C3—62no—
582C23×C3—62no—
583C23×C3—61no—
584C23×C3—61no—
585C23×C3—124no—
586C23×C3—128no—
587C23×C3—128no—
588C23×C3—128no—
589C23×C3—124no—
590C23×C3—128no—
591C23×C3—124no—
592C23×C3D3×D412yes—
593C23×C3D3×D412yes—
594C23×C3D3×D414yescomplemented
595C23×C3C2×#6712yes—
596C23×C3C2×#6712yescomplemented
597C23×C3C2×C3×D412yes—
598C23×C3C2×C3×D412yes—
599C23×C3C2×C3×D412yes—
600C23×C3C2×C3×D414yescomplemented
601C23×C3C2×C3×D412yescomplemented
602C23×C3C23×D311yescharacteristic
603C23×C3C24×C311yescharacteristic
604C22×D3—21no—
605C22×D3—21no—
606C22×D3—22no—
607C22×D3—28no—
608C22×D3—28no—
609C22×D3—22no—
610C22×D3—21no—
611C22×D3—21no—
612C22×D3—21no—
613C22×D3—21no—
614C22×D3—22no—
615C22×D3—22no—
616C22×D3—22no—
617C22×D3—28no—
618C22×D3—44no—
619C22×D3—48no—
620C22×D3—48no—
621C22×D3—48no—
622C22×D3—48no—
623C22×D3—44no—
624C22×D3—44no—
625C22×D3C2×C3×D412yes—
626C22×D3C2×C3×D414yes—
627C22×D3C2×C3×D412yes—
628C22×D3C2×C3×D412yescomplemented
629C3×D4—28no—
630C3×D4—28no—
631C3×D4—48no—
632C3×D4—48no—
633C3×D4—48no—
634C3×D4—416no—
635C3×D4—68no—
636C3×D4—616no—
637C3×D4—68no—
638C3×D4—616no—
639C3×D4—68no—
640C3×D4—128no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—24no—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—22no—
652C2×C3×C4—22no—
653C2×C3×C4—32no—
654C2×C3×C4—34no—
655C2×C3×C4—41no—
656C2×C3×C4—41no—
657C2×C3×C4—42no—
658C2×C3×C4—42no—
659C2×C3×C4—68no—
660C2×C3×C4—68no—
661C2×C3×C4—61no—
662C2×C3×C4—62no—
663C2×C3×C4—62no—
664C2×C3×C4—61no—
665C2×C3×C4—62no—
666C2×C3×C4—62no—
667C2×C3×C4—62no—
668C2×C3×C4C2×#6712yescomplemented
669C2×C3×C4C2×C3×D412yescomplemented
670#67—28no—
671#67—216no—
672#67—28no—
673#67—216no—
674#67—48no—
675C2×Dic3—28no—
676C2×Dic3—21no—
677C2×Dic3—21no—
678C2×Dic3—22no—
679C2×Dic3—22no—
680C2×Dic3—22no—
681C2×Dic3—22no—
682C2×Dic3—22no—
683C2×Dic3C2×C3×D414yescomplemented
684C2×Dic3C2×C3×D412yescomplemented
685D12—28no—
686C4×D3—28no—
687C2×C32—24no—
688C2×C32—44no—
689C2×C32—42no—
690C2×C32C2×#12011yescharacteristic
691C2×C32C2×#12011yescharacteristic
692C2×C32#53411yescharacteristic
693C2×C32D4212yes—
694C2×C32D4212yes—
695C3×D3—24no—
696C3×D3—42no—
697C3×D3—42no—
698C24—22no—
699C24—24no—
700C24—22no—
701C24—22no—
702C24—31no—
703C24—31no—
704C24—31no—
705C24—34no—
706C24—42no—
707C24—64no—
708C24—62no—
709C24—62no—
710C24—64no—
711C24—62no—
712C24—62no—
713C24—62no—
714C24—122no—
715C24—122no—
716C24C22×C3×D312yes—
717C24C22×C3×D311yescharacteristic
718C24C22×C3×D311yescharacteristic
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—24no—
722C2×D4—24no—
723C2×D4—34no—
724C2×D4—38no—
725C2×D4—42no—
726C2×D4—62no—
727C2×D4—62no—
728C2×D4—62no—
729C2×D4—64no—
730C2×D4—632no—
731C2×D4—64no—
732C2×D4—64no—
733C2×D4—62no—
734C2×D4—64no—
735C2×D4—632no—
736C2×D4—62no—
737C2×D4—64no—
738C2×D4—62no—
739C2×D4—62no—
740C2×D4—64no—
741C2×D4—64no—
742C2×D4—62no—
743C2×D4—122no—
744C2×D4C3×#6714yescomplemented
745C22×C4—32no—
746C22×C4—31no—
747C22×C4—32no—
748C22×C4—62no—
749C22×C4—62no—
750C22×C4—64no—
751C22×C4—62no—
752C22×C4—62no—
753C22×C4C22×C3×D312yes—
754C22×C4C22×C3×D311yescharacteristic
755C22⋊C4—22no—
756C22⋊C4—24no—
757C22⋊C4—64no—
758C22⋊C4—64no—
759C22⋊C4—64no—
760C22⋊C4—64no—
761C22⋊C4—62no—
762C22⋊C4—122no—
763C22×C3—24no—
764C22×C3—22no—
765C22×C3—22no—
766C22×C3—24no—
767C22×C3—22no—
768C22×C3—22no—
769C22×C3—24no—
770C22×C3—24no—
771C22×C3—28no—
772C22×C3—22no—
773C22×C3—24no—
774C22×C3—24no—
775C22×C3—24no—
776C22×C3—24no—
777C22×C3—24no—
778C22×C3—22no—
779C22×C3—24no—
780C22×C3—24no—
781C22×C3—24no—
782C22×C3—24no—
783C22×C3—21no—
784C22×C3—21no—
785C22×C3—22no—
786C22×C3—22no—
787C22×C3—21no—
788C22×C3—34no—
789C22×C3—44no—
790C22×C3—42no—
791C22×C3—42no—
792C22×C3—44no—
793C22×C3—44no—
794C22×C3—44no—
795C22×C3—42no—
796C22×C3—44no—
797C22×C3—416no—
798C22×C3—416no—
799C22×C3—44no—
800C22×C3—44no—
801C22×C3—44no—
802C22×C3—44no—
803C22×C3—432no—
804C22×C3—42no—
805C22×C3—42no—
806C22×C3—41no—
807C22×C3—42no—
808C22×C3—41no—
809C22×C3—42no—
810C22×C3—42no—
811C22×C3—41no—
812C22×C3—42no—
813C22×C3—41no—
814C22×C3—42no—
815C22×C3—42no—
816C22×C3—42no—
817C22×C3—42no—
818C22×C3—62no—
819C22×C3—64no—
820C22×C3—62no—
821C22×C3—64no—
822C22×C3—62no—
823C22×C3—62no—
824C22×C3—62no—
825C22×C3—62no—
826C22×C3—64no—
827C22×C3—81no—
828C22×C3—81no—
829C22×C3—82no—
830C22×C3—1216no—
831C22×C3—1216no—
832C22×C3—122no—
833C22×C3—122no—
834C22×C3—121no—
835C22×C3—121no—
836C22×C3—122no—
837C22×C3#93714yescomplemented
838C22×C3C3×#12014yescomplemented
839C22×C3C2×D3×D411yescharacteristic
840C22×C3C2×D3×D411yescharacteristic
841C22×C3C2×D3×D412yes—
842C22×C3#100412yes—
843C22×C3C22×#6711yescharacteristic
844C22×C3C22×C3×D411yescharacteristic
845C22×C3C22×C3×D412yes—
846C22×C3C22×C3×D411yescharacteristic
847C22×C3C22×C3×D411yescharacteristic
848C22×C3C3×H(5,𝔽2)12yes—
849C2×D3—22no—
850C2×D3—22no—
851C2×D3—24no—
852C2×D3—24no—
853C2×D3—22no—
854C2×D3—22no—
855C2×D3—22no—
856C2×D3—22no—
857C2×D3—24no—
858C2×D3—416no—
859C2×D3—416no—
860C2×D3—41no—
861C2×D3—41no—
862C2×D3—42no—
863C2×D3—42no—
864C2×D3—42no—
865C2×D3C3×#12014yescomplemented
866C3×C4—22no—
867C3×C4—22no—
868C3×C4—42no—
869C3×C4—44no—
870C3×C4—42no—
871C3×C4—42no—
872C3×C4—62no—
873C3×C4—64no—
874C3×C4—122no—
875Dic3—22no—
876Dic3—24no—
877Dic3—42no—
878C32#240311yescharacteristic, complemented, Sylow
879C23—22no—
880C23—22no—
881C23—28no—
882C23—22no—
883C23—22no—
884C23—21no—
885C23—21no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—34no—
893C23—32no—
894C23—32no—
895C23—32no—
896C23—48no—
897C23—48no—
898C23—44no—
899C23—44no—
900C23—68no—
901C23—68no—
902C23—61no—
903C23—62no—
904C23—61no—
905C23—68no—
906C23—62no—
907C23—61no—
908C23—61no—
909C23—62no—
910C23—62no—
911C23—62no—
912C23—61no—
913C23—61no—
914C23—124no—
915C23—128no—
916C23—128no—
917C23—128no—
918C23—124no—
919C23—128no—
920C23—124no—
921C23C3×D3×D412yes—
922C23C3×D3×D412yes—
923C23C3×D3×D414yescomplemented
924C23C2×C3×#6712yes—
925C23C2×C3×#6712yescomplemented
926C23C23×C3×D311yescharacteristic
927D4—28no—
928D4—48no—
929D4—68no—
930D4—616no—
931D4—68no—
932D4—616no—
933D4—68no—
934D4—128no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—32no—
941C2×C4—34no—
942C2×C4—68no—
943C2×C4—68no—
944C2×C4—61no—
945C2×C4—62no—
946C2×C4—62no—
947C2×C4—61no—
948C2×C4—62no—
949C2×C4—62no—
950C2×C4—62no—
951C2×C4C2×C3×#6712yescomplemented
952C2×C3—24no—
953C2×C3—24no—
954C2×C3—21no—
955C2×C3—22no—
956C2×C3—21no—
957C2×C3—21no—
958C2×C3—22no—
959C2×C3—44no—
960C2×C3—48no—
961C2×C3—42no—
962C2×C3—44no—
963C2×C3—44no—
964C2×C3—42no—
965C2×C3—64no—
966C2×C3—82no—
967C2×C3—122no—
968C2×C3—122no—
969C2×C3D3×#12011yescharacteristic
970C2×C3#558911yescharacteristic
971C2×C3#559012yes—
972C2×C3C2×#93711yescharacteristic
973C2×C3D4×#6712yes—
974C2×C3C2×C3×#12011yescharacteristic
975C2×C3C2×C3×#12011yescharacteristic
976C2×C3C3×#53411yescharacteristic
977C2×C3C3×D4212yes—
978C2×C3C3×D4212yes—
979D3—24no—
980D3—42no—
981D3—42no—
982C22—24no—
983C22—22no—
984C22—22no—
985C22—24no—
986C22—22no—
987C22—24no—
988C22—24no—
989C22—24no—
990C22—24no—
991C22—34no—
992C22—416no—
993C22—42no—
994C22—42no—
995C22—41no—
996C22—42no—
997C22—41no—
998C22—42no—
999C22—42no—
1000C22—62no—
1001C22—64no—
1002C22—62no—
1003C22—64no—
1004C22—62no—
1005C22—62no—
1006C22—62no—
1007C22—62no—
1008C22—64no—
1009C22—1216no—
1010C22—1216no—
1011C22—122no—
1012C22—122no—
1013C22—121no—
1014C22—121no—
1015C22—122no—
1016C22C3×#93714yescomplemented
1017C22C2×C3×D3×D411yescharacteristic
1018C22C2×C3×D3×D411yescharacteristic
1019C22C2×C3×D3×D412yes—
1020C22C3×#100412yes—
1021C22C22×C3×#6711yescharacteristic
1022C4—22no—
1023C4—42no—
1024C4—62no—
1025C4—64no—
1026C4—122no—
1027C3—21no—
1028C3#8260411yescharacteristic, direct product factor
1029C3C3×#240311yescharacteristic, complemented
1030C2—24no—
1031C2—44no—
1032C2—42no—
1033C2—64no—
1034C2—122no—
1035C2—122no—
1036C2C3×D3×#12011yescharacteristic
1037C2C3×#558911yescharacteristic
1038C2C3×#559012yes—
1039C2C2×C3×#93711yescharacteristic
1040C2C3×D4×#6712yes—
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×#120C2
socleC23×C32C24
hypercenterC2×C3×#120D3
hypocenterC3C3×#2403
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#120

Complements

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

NH ≅ G/Ntype
1. C23×C3×#67C2semidirect
2. C22×C3×D3×D4C2semidirect
3. C2×C32×#120C2semidirect
4. C2×C3×#953C2semidirect
5. C2×C3×#937C2semidirect
6. C3×#5223C2semidirect
7. C3×#5220C2semidirect
8. C3×#4960C2semidirect
9. C3×#4958C2semidirect
10. C3×#4956C2semidirect
11. C3×#4955C2semidirect
13. #82604C3direct (N × H)
14. C25×C32C22semidirect
16. C24×C3×D3C22semidirect
18. C22×C32×D4C22semidirect
23. C22×C3×#67C22semidirect
24. C22×C3×#67C22semidirect
25. C22×C3×#67C22semidirect
26. C23×C3×Dic3C22semidirect
30. C22×C3×D12C22semidirect
31. C22×C3×C4×D3C22semidirect
33. C2×C32×C22⋊C4C22semidirect
34. C2×C32×C22⋊C4C22semidirect
36. C2×C3×#217C22semidirect
37. C2×C3×#217C22semidirect
38. C2×C3×#217C22semidirect
40. C2×C3×(C2×D3)⋊C4C22semidirect
41. C2×C3×(C2×D3)⋊C4C22semidirect
42. C2×C3×(C2×D3)⋊C4C22semidirect
43. C3×C3⋊#95C22semidirect
44. C3×C3⋊#95C22semidirect
47. C23×#67C2×C3semidirect
48. C22×D3×D4C2×C3semidirect
52. C2×C3×#120D3semidirect
53. C2×C3×#120C2×C3semidirect
54. C2×#953C2×C3semidirect
55. C2×#937C2×C3semidirect
62. #5223C2×C3semidirect
63. #5220C2×C3semidirect
64. #4960C2×C3semidirect
65. #4958C2×C3semidirect
66. #4956C2×C3semidirect
67. #4955C2×C3semidirect
85. C23×C3×D3D4semidirect
94. C2×C32×D4D4semidirect
111. C2×C3×#67D4semidirect
112. C2×C3×#67D4semidirect
137. C25×C3C2×D3semidirect
138. C25×C3C22×C3semidirect
140. C24×D3C22×C3semidirect
155. C22×C3×D4C2×D3semidirect
157. C22×C3×D4C22×C3semidirect
164. C22×#67C22×C3semidirect
165. C22×#67C22×C3semidirect
166. C22×#67C22×C3semidirect
167. C23×Dic3C22×C3semidirect
171. C22×D12C22×C3semidirect
172. C22×C4×D3C22×C3semidirect
186. C2×C3×C22⋊C4C2×D3semidirect
187. C2×C3×C22⋊C4C2×D3semidirect
188. C2×C3×C22⋊C4C22×C3semidirect
189. C2×C3×C22⋊C4C22×C3semidirect
191. C2×#217C22×C3semidirect
192. C2×#217C22×C3semidirect
193. C2×#217C22×C3semidirect
195. C2×(C2×D3)⋊C4C22×C3semidirect
196. C2×(C2×D3)⋊C4C22×C3semidirect
197. C2×(C2×D3)⋊C4C22×C3semidirect
200. C3⋊#95C22×C3semidirect
201. C3⋊#95C22×C3semidirect
222. C23×C32C2×D4semidirect
223. C23×C32C2×D4semidirect
249. C22×C3×D3C2×D4semidirect
257. C2×C32×C4C2×D4semidirect
271. C2×C3×Dic3C2×D4semidirect
272. C2×C3×Dic3C2×D4semidirect
279. C2×#120C3×D3semidirect
332. C23×D3C3×D4semidirect
372. C2×C3×D4#67semidirect
373. C2×C3×D4C3×D4semidirect
402. C2×#67C3×D4semidirect
403. C2×#67C3×D4semidirect
451. C22×C32#120semidirect
473. C2×C3×D3#120semidirect
481. C25C2×C3×D3semidirect
494. C22×D4C2×C3×D3semidirect
506. C2×C22⋊C4C2×C3×D3semidirect
507. C2×C22⋊C4C2×C3×D3semidirect
594. C23×C3D3×D4semidirect
596. C23×C3C2×#67semidirect
600. C23×C3C2×C3×D4semidirect
601. C23×C3C2×C3×D4semidirect
628. C22×D3C2×C3×D4semidirect
668. C2×C3×C4C2×#67semidirect
669. C2×C3×C4C2×C3×D4semidirect
683. C2×Dic3C2×C3×D4semidirect
684. C2×Dic3C2×C3×D4semidirect
744. C2×D4C3×#67semidirect
837. C22×C3#937semidirect
838. C22×C3C3×#120semidirect
865. C2×D3C3×#120semidirect
878. C32#2403semidirect
923. C23C3×D3×D4semidirect
925. C23C2×C3×#67semidirect
951. C2×C4C2×C3×#67semidirect
1016. C22C3×#937semidirect
1028. C3#82604direct (N × H)
1029. C3C3×#2403semidirect

Maximal subgroups

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

subgroupindex
C23×C3×#672
C22×C3×D3×D42
C2×C32×#1202
C2×C3×#9532
C2×C3×#9372
C3×#52232
C3×#52202
C3×#49602
C3×#49582
C3×#49562
C3×#49552
C3×#24033
#826043