Finite Group Databasebeta

← C3×#82380 #11824526

Subgroups — C3×#82380 #11824526

Order 1152.

1661 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic, complemented
2C2×C3×#939C212yesmaximal, complemented
3C2×C3×#930C211yesmaximal, characteristic, complemented
4C3×#5213C212yesmaximal, complemented
5C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
6C3×#4991C211yesmaximal, characteristic, complemented
7C3×#4981C211yesmaximal, characteristic, complemented
8C3×#4960C211yesmaximal, characteristic, complemented
9C3×#4958C212yesmaximal, complemented
10C3×#4953C211yesmaximal, characteristic, complemented
11C3×#4940C212yesmaximal, complemented
12C3×#2543—31nomaximal
13#82380C311yesmaximal, characteristic, direct product factor
14C22×C32×D4C2211yescharacteristic
15C23×C32×C4C2211yescharacteristic
16C23×C32×C4C2211yescharacteristic
17C22×C3×#67C2212yes—
18C22×C3×#67C2212yes—
19C23×C3×Dic3C2212yes—
20C22×C3×D12C2211yescharacteristic
21C32×C4×D4—24no—
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×C32×C42C2211yescharacteristic
26C2×C3×#217C2212yes—
27C3×#939—28no—
28C3×#930—24no—
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×(C2×D3)⋊C4C2212yes—
31C2×C3×(C2×D3)⋊C4C2212yes—
32C2×C3×(C2×D3)⋊C4C2212yes—
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×Dic3⋊C4C2212yes—
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2211yescharacteristic
38C3×C3⋊#95C2211yescharacteristic
39C3×C3⋊#95C2212yes—
40C2×C3×#121—32no—
41C2×C3×#121—31no—
42C2×C3×C4×D4—21no—
43C2×C3×C4×D4D311yescharacteristic, complemented
44C2×C3×C4×D4C2×C311yescharacteristic, complemented
45C2×#939C2×C312yescomplemented
46C2×#930C2×C311yescharacteristic, complemented
47C3×#398—31no—
48C3×#397—31no—
49C3×#394—31no—
50C3×#392—31no—
51C3×#388—32no—
52C3×#386—32no—
53C3×#386—32no—
54C2×C3×#95—31no—
55#5213C2×C312yescomplemented
56C2×C3⋊#95C2×C311yescharacteristic, complemented
57#4991C2×C311yescharacteristic, complemented
58#4981C2×C311yescharacteristic, complemented
59#4960C2×C311yescharacteristic, complemented
60#4958C2×C312yescomplemented
61#4953C2×C311yescharacteristic, complemented
62#4940C2×C312yescomplemented
63C24×C32C2311yescharacteristic
64C24×C32C2311yescharacteristic
65C23×C3×D3C2312yes—
66C2×C32×D4—22no—
67C2×C32×D4—22no—
68C2×C32×D4D414yescomplemented
69C22×C32×C4—22no—
70C22×C32×C4—42no—
71C22×C32×C4—42no—
72C22×C32×C4D414yescomplemented
73C22×C32×C4C2311yescharacteristic
74C22×C32×C4C2311yescharacteristic
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C2×C3×#67—24no—
79C2×C3×#67—24no—
80C2×C3×#67—24no—
81C2×C3×#67—24no—
82C2×C3×#67—24no—
83C2×C3×#67—42no—
84C22×C3×Dic3—24no—
85C22×C3×Dic3—24no—
86C22×C3×Dic3—42no—
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2312yes—
89C22×C3×Dic3C2312yes—
90C2×C3×D12—22no—
91C2×C3×D12—42no—
92C32×C4⋊C4—22no—
93C32×C22⋊C4—22no—
94C32×C22⋊C4—22no—
95C32×C42—22no—
96C3×#217—24no—
97C3×(C2×D3)⋊C4—24no—
98C3×(C2×D3)⋊C4—24no—
99C3×(C2×D3)⋊C4—24no—
100C3×(C2×D3)⋊C4—42no—
101C3×C4⋊Dic3—22no—
102C3×Dic3⋊C4—24no—
103#2543—31noSylow
104C22×C3×D4—21no—
105C22×C3×D4—32no—
106C22×C3×D4—32no—
107C22×C3×D4—31no—
108C22×C3×D4C2×D311yescharacteristic
109C22×C3×D4C22×C311yescharacteristic
110C23×C3×C4—21no—
111C23×C3×C4—21no—
112C23×C3×C4—32no—
113C23×C3×C4C2×D311yescharacteristic
114C23×C3×C4C2×D311yescharacteristic
115C23×C3×C4C22×C311yescharacteristic
116C23×C3×C4C22×C311yescharacteristic
117C22×#67C22×C312yes—
118C22×#67C22×C312yes—
119C23×Dic3C22×C312yes—
120C22×D12C22×C311yescharacteristic
121C3×#121—68no—
122C3×#121—64no—
123C3×C4×D4—28no—
124C3×C4×D4—24no—
125C3×C4×D4—24no—
126C2×C3×C4⋊C4—21no—
127C2×C3×C4⋊C4—32no—
128C2×C3×C4⋊C4—31no—
129C2×C3×C4⋊C4C2×D311yescharacteristic
130C2×C3×C4⋊C4C22×C311yescharacteristic
131C2×C3×C22⋊C4—21no—
132C2×C3×C22⋊C4—21no—
133C2×C3×C22⋊C4—32no—
134C2×C3×C22⋊C4—32no—
135C2×C3×C22⋊C4—32no—
136C2×C3×C22⋊C4—32no—
137C2×C3×C22⋊C4—32no—
138C2×C3×C22⋊C4C2×D311yescharacteristic
139C2×C3×C22⋊C4C2×D311yescharacteristic
140C2×C3×C22⋊C4C22×C311yescharacteristic
141C2×C3×C22⋊C4C22×C311yescharacteristic
142C2×C3×C42—21no—
143C2×C3×C42C2×D311yescharacteristic
144C2×C3×C42C22×C311yescharacteristic
145C2×#217C22×C312yes—
146#939—28no—
147#930—24no—
148C2×(C2×D3)⋊C4C22×C312yes—
149C2×(C2×D3)⋊C4C22×C312yes—
150C2×(C2×D3)⋊C4C22×C312yes—
151C2×(C2×D3)⋊C4C22×C312yes—
152C2×C4⋊Dic3C22×C311yescharacteristic
153C2×Dic3⋊C4C22×C312yes—
154C3×#95—32no—
155C3×#95—31no—
156C3×#95—31no—
157C3×#95—32no—
158C3×#95—32no—
159C3⋊#95C22×C312yes—
160C3⋊#95C22×C312yes—
161C3⋊#95C22×C311yescharacteristic
162C3⋊#95C22×C311yescharacteristic
163C3⋊#95C22×C312yes—
164C23×C32—21no—
165C23×C32—21no—
166C23×C32—22no—
167C23×C32—22no—
168C23×C32—22no—
169C23×C32—22no—
170C23×C32C2×D412yes—
171C23×C32C2×D412yes—
172C23×C32C2×D412yes—
173C23×C32#4112yes—
174C23×C32C2411yescharacteristic
175C22×C3×D3—22no—
176C22×C3×D3—22no—
177C22×C3×D3—22no—
178C22×C3×D3—22no—
179C22×C3×D3—22no—
180C22×C3×D3—22no—
181C22×C3×D3—22no—
182C32×D4—28no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—22no—
186C2×C32×C4—21no—
187C2×C32×C4—21no—
188C2×C32×C4—22no—
189C2×C32×C4—22no—
190C2×C32×C4—22no—
191C2×C32×C4—44no—
192C2×C32×C4—44no—
193C2×C32×C4C2×D412yes—
194C2×C32×C4C2×D412yes—
195C2×C32×C4C2×D412yes—
196C3×#67—48no—
197C3×#67—48no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—48no—
207C2×C3×Dic3#4114yes—
208C3×D12—44no—
209C2×#121—32no—
210C2×#121—31no—
211C2×C4×D4C3×D311yescharacteristic, complemented
212#398—31no—
213#397—31no—
214#394—31no—
215#392—31no—
216#388—32no—
217#386—32no—
218#386—32no—
219C2×#95—31no—
220C24×C3—21no—
221C24×C3—21no—
222C24×C3—32no—
223C24×C3C22×D311yescharacteristic
224C24×C3C22×D311yescharacteristic
225C24×C3C23×C311yescharacteristic
226C24×C3C23×C311yescharacteristic
227C23×D3C23×C312yes—
228C2×C3×D4—24no—
229C2×C3×D4—24no—
230C2×C3×D4—22no—
231C2×C3×D4—22no—
232C2×C3×D4—22no—
233C2×C3×D4—22no—
234C2×C3×D4—24no—
235C2×C3×D4—64no—
236C2×C3×D4—64no—
237C2×C3×D4—64no—
238C2×C3×D4—64no—
239C2×C3×D4—64no—
240C2×C3×D4—62no—
241C2×C3×D4—122no—
242C2×C3×D4—122no—
243C2×C3×D4D1214yescomplemented
244C2×C3×D4C3×D414yescomplemented
245C22×C3×C4—24no—
246C22×C3×C4—22no—
247C22×C3×C4—22no—
248C22×C3×C4—24no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—32no—
255C22×C3×C4—32no—
256C22×C3×C4—32no—
257C22×C3×C4—42no—
258C22×C3×C4—42no—
259C22×C3×C4—42no—
260C22×C3×C4—42no—
261C22×C3×C4—44no—
262C22×C3×C4—44no—
263C22×C3×C4—64no—
264C22×C3×C4—64no—
265C22×C3×C4—122no—
266C22×C3×C4#6714yescomplemented
267C22×C3×C4C3×D414yescomplemented
268C22×C3×C4C22×D311yescharacteristic
269C22×C3×C4C22×D311yescharacteristic
270C22×C3×C4C22×D311yescharacteristic
271C22×C3×C4C22×D311yescharacteristic
272C22×C3×C4C22×D311yescharacteristic
273C22×C3×C4C23×C311yescharacteristic
274C22×C3×C4C23×C311yescharacteristic
275C22×C3×C4C23×C311yescharacteristic
276C22×C3×C4C23×C311yescharacteristic
277C22×C3×C4C23×C311yescharacteristic
278C2×#67—24no—
279C2×#67—24no—
280C2×#67—24no—
281C2×#67—24no—
282C2×#67—24no—
283C2×#67—42no—
284C22×Dic3—24no—
285C22×Dic3—24no—
286C22×Dic3—42no—
287C22×Dic3C23×C312yes—
288C22×Dic3C23×C312yes—
289C22×Dic3C23×C312yes—
290C2×D12—22no—
291C2×D12—42no—
292C3×C4⋊C4—24no—
293C3×C4⋊C4—22no—
294C3×C4⋊C4—22no—
295C3×C4⋊C4—64no—
296C3×C4⋊C4—62no—
297C3×C22⋊C4—24no—
298C3×C22⋊C4—24no—
299C3×C22⋊C4—22no—
300C3×C22⋊C4—22no—
301C3×C22⋊C4—22no—
302C3×C22⋊C4—22no—
303C3×C22⋊C4—64no—
304C3×C22⋊C4—64no—
305C3×C22⋊C4—64no—
306C3×C22⋊C4—64no—
307C3×C22⋊C4—122no—
308C3×C42—24no—
309C3×C42—22no—
310C3×C42—22no—
311#217—24no—
312(C2×D3)⋊C4—24no—
313(C2×D3)⋊C4—24no—
314(C2×D3)⋊C4—24no—
315(C2×D3)⋊C4—42no—
316C4⋊Dic3—22no—
317Dic3⋊C4—24no—
318C22×C32—22no—
319C22×C32—22no—
320C22×C32—22no—
321C22×C32—24no—
322C22×C32—24no—
323C22×C32—24no—
324C22×C32—41no—
325C22×C32—41no—
326C22×C32—42no—
327C22×C32#12114yes—
328C22×C32C22×D411yescharacteristic
329C22×C32C22×D411yescharacteristic
330C22×C32C2×#4111yescharacteristic
331C22×C32C2×#4112yes—
332C22×C32H(5,𝔽2)12yes—
333C2×C3×D3—42no—
334C2×C3×D3—42no—
335C2×C3×D3—42no—
336C2×C3×D3—42no—
337C2×C3×D3—42no—
338C2×C3×D3—42no—
339C2×C3×D3—42no—
340C32×C4—22no—
341C32×C4—22no—
342C32×C4—22no—
343C32×C4—41no—
344C32×C4—41no—
345C3×Dic3—24no—
346C3×Dic3—42no—
347C3×Dic3—42no—
348C22×D4—32no—
349C22×D4—32no—
350C22×D4—31no—
351C22×D4C2×C3×D311yescharacteristic
352C23×C4—32no—
353C23×C4C2×C3×D311yescharacteristic
354C23×C4C2×C3×D311yescharacteristic
355#121—68no—
356#121—64no—
357C4×D4—24no—
358C2×C4⋊C4—32no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4C2×C3×D311yescharacteristic
361C2×C22⋊C4—32no—
362C2×C22⋊C4—32no—
363C2×C22⋊C4—32no—
364C2×C22⋊C4—32no—
365C2×C22⋊C4—32no—
366C2×C22⋊C4C2×C3×D311yescharacteristic
367C2×C22⋊C4C2×C3×D311yescharacteristic
368C2×C42C2×C3×D311yescharacteristic
369#95—32no—
370#95—31no—
371#95—31no—
372#95—32no—
373#95—32no—
374C23×C3—22no—
375C23×C3—22no—
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—21no—
381C23×C3—22no—
382C23×C3—22no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3—22no—
386C23×C3—21no—
387C23×C3—22no—
388C23×C3—21no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—42no—
394C23×C3—42no—
395C23×C3—42no—
396C23×C3—42no—
397C23×C3—62no—
398C23×C3—62no—
399C23×C3—62no—
400C23×C3—62no—
401C23×C3—62no—
402C23×C3—62no—
403C23×C3—62no—
404C23×C3C2×D1212yes—
405C23×C3C2×D1212yes—
406C23×C3#23512yes—
407C23×C3C2×#6712yes—
408C23×C3C2×C3×D412yes—
409C23×C3C2×C3×D412yes—
410C23×C3C2×C3×D412yes—
411C23×C3C3×#4112yes—
412C23×C3C23×D311yescharacteristic
413C23×C3C24×C311yescharacteristic
414C22×D3—22no—
415C22×D3—22no—
416C22×D3—22no—
417C22×D3—22no—
418C22×D3—22no—
419C22×D3—22no—
420C22×D3—22no—
421C3×D4—216no—
422C3×D4—28no—
423C3×D4—28no—
424C3×D4—124no—
425C3×D4—128no—
426C3×D4—128no—
427C2×C3×C4—22no—
428C2×C3×C4—24no—
429C2×C3×C4—22no—
430C2×C3×C4—21no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—34no—
452C2×C3×C4—42no—
453C2×C3×C4—42no—
454C2×C3×C4—42no—
455C2×C3×C4—44no—
456C2×C3×C4—44no—
457C2×C3×C4—48no—
458C2×C3×C4—48no—
459C2×C3×C4—44no—
460C2×C3×C4—44no—
461C2×C3×C4—62no—
462C2×C3×C4—62no—
463C2×C3×C4—62no—
464C2×C3×C4—62no—
465C2×C3×C4—62no—
466C2×C3×C4—62no—
467C2×C3×C4—62no—
468C2×C3×C4—62no—
469C2×C3×C4—128no—
470C2×C3×C4C2×D1212yes—
471C2×C3×C4C2×#6712yes—
472C2×C3×C4C2×#6712yes—
473C2×C3×C4C2×C3×D412yes—
474C2×C3×C4C2×C3×D412yes—
475C2×C3×C4C2×C3×D412yes—
476#67—48no—
477#67—48no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—48no—
487C2×Dic3C3×#4114yes—
488D12—44no—
489C2×C32—24no—
490C2×C32—42no—
491C2×C32C2×#12111yescharacteristic
492C2×C32#53211yescharacteristic
493C2×C32#53411yescharacteristic
494C2×C32#54612yes—
495C2×C32#55312yes—
496C3×D3—82no—
497C24—32no—
498C24C22×C3×D311yescharacteristic
499C24C22×C3×D311yescharacteristic
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—64no—
503C2×D4—64no—
504C2×D4—64no—
505C2×D4—64no—
506C2×D4—64no—
507C2×D4—62no—
508C2×D4—122no—
509C2×D4—122no—
510C2×D4C3×D1214yescomplemented
511C22×C4—22no—
512C22×C4—32no—
513C22×C4—32no—
514C22×C4—32no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—64no—
518C22×C4—64no—
519C22×C4—122no—
520C22×C4C3×#6714yescomplemented
521C22×C4C22×C3×D311yescharacteristic
522C22×C4C22×C3×D311yescharacteristic
523C22×C4C22×C3×D311yescharacteristic
524C22×C4C22×C3×D311yescharacteristic
525C22×C4C22×C3×D311yescharacteristic
526C4⋊C4—22no—
527C4⋊C4—64no—
528C4⋊C4—62no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—64no—
532C22⋊C4—64no—
533C22⋊C4—64no—
534C22⋊C4—64no—
535C22⋊C4—122no—
536C42—22no—
537C22×C3—24no—
538C22×C3—22no—
539C22×C3—24no—
540C22×C3—22no—
541C22×C3—22no—
542C22×C3—22no—
543C22×C3—24no—
544C22×C3—24no—
545C22×C3—24no—
546C22×C3—22no—
547C22×C3—24no—
548C22×C3—22no—
549C22×C3—24no—
550C22×C3—24no—
551C22×C3—21no—
552C22×C3—21no—
553C22×C3—22no—
554C22×C3—22no—
555C22×C3—21no—
556C22×C3—42no—
557C22×C3—44no—
558C22×C3—44no—
559C22×C3—42no—
560C22×C3—44no—
561C22×C3—42no—
562C22×C3—44no—
563C22×C3—42no—
564C22×C3—42no—
565C22×C3—41no—
566C22×C3—41no—
567C22×C3—41no—
568C22×C3—41no—
569C22×C3—42no—
570C22×C3—122no—
571C22×C3—122no—
572C22×C3—122no—
573C22×C3—122no—
574C22×C3—122no—
575C22×C3—122no—
576C22×C3—122no—
577C22×C3#93014yes—
578C22×C3C3×#12114yes—
579C22×C3C22×D1211yescharacteristic
580C22×C3C2×#23511yescharacteristic
581C22×C3#100412yes—
582C22×C3D3×#4112yes—
583C22×C3C22×#6711yescharacteristic
584C22×C3C22×C3×D411yescharacteristic
585C22×C3C22×C3×D411yescharacteristic
586C22×C3C2×C3×#4111yescharacteristic
587C22×C3C2×C3×#4112yes—
588C22×C3C3×H(5,𝔽2)12yes—
589C2×D3—42no—
590C2×D3—42no—
591C2×D3—42no—
592C2×D3—42no—
593C2×D3—42no—
594C2×D3—42no—
595C2×D3—42no—
596C3×C4—24no—
597C3×C4—24no—
598C3×C4—22no—
599C3×C4—22no—
600C3×C4—22no—
601C3×C4—22no—
602C3×C4—22no—
603C3×C4—22no—
604C3×C4—42no—
605C3×C4—42no—
606C3×C4—42no—
607C3×C4—41no—
608C3×C4—41no—
609C3×C4—41no—
610C3×C4—41no—
611C3×C4—64no—
612C3×C4—122no—
613C3×C4—122no—
614Dic3—24no—
615Dic3—42no—
616Dic3—42no—
617C32#254311yescharacteristic, complemented, Sylow
618C23—22no—
619C23—22no—
620C23—21no—
621C23—22no—
622C23—22no—
623C23—21no—
624C23—62no—
625C23—62no—
626C23—62no—
627C23—62no—
628C23—62no—
629C23—62no—
630C23—62no—
631C23C2×C3×D1212yes—
632C23C2×C3×D1212yes—
633C23C3×#23512yes—
634C23C2×C3×#6712yes—
635C23C23×C3×D311yescharacteristic
636D4—28no—
637D4—124no—
638D4—128no—
639D4—128no—
640C2×C4—21no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—34no—
649C2×C4—44no—
650C2×C4—44no—
651C2×C4—62no—
652C2×C4—62no—
653C2×C4—62no—
654C2×C4—62no—
655C2×C4—62no—
656C2×C4—62no—
657C2×C4—62no—
658C2×C4—62no—
659C2×C4—128no—
660C2×C4C2×C3×D1212yes—
661C2×C4C2×C3×#6712yes—
662C2×C4C2×C3×#6712yes—
663C2×C3—24no—
664C2×C3—24no—
665C2×C3—21no—
666C2×C3—22no—
667C2×C3—21no—
668C2×C3—22no—
669C2×C3—21no—
670C2×C3—44no—
671C2×C3—44no—
672C2×C3—42no—
673C2×C3—42no—
674C2×C3—242no—
675C2×C3#554012yes—
676C2×C3#555412yes—
677C2×C3C2×#93011yescharacteristic
678C2×C3#580411yescharacteristic
679C2×C3#583211yescharacteristic
680C2×C3C2×C3×#12111yescharacteristic
681C2×C3C3×#53211yescharacteristic
682C2×C3C3×#53411yescharacteristic
683C2×C3C3×#54612yes—
684C2×C3C3×#55312yes—
685D3—82no—
686C22—24no—
687C22—22no—
688C22—24no—
689C22—22no—
690C22—22no—
691C22—24no—
692C22—42no—
693C22—41no—
694C22—41no—
695C22—122no—
696C22—122no—
697C22—122no—
698C22—122no—
699C22—122no—
700C22—122no—
701C22—122no—
702C22C3×#93014yes—
703C22C22×C3×D1211yescharacteristic
704C22C2×C3×#23511yescharacteristic
705C22C3×#100412yes—
706C22C3×D3×#4112yes—
707C22C22×C3×#6711yescharacteristic
708C4—22no—
709C4—22no—
710C4—22no—
711C4—41no—
712C4—41no—
713C4—64no—
714C4—122no—
715C4—122no—
716C3—21no—
717C3#8238011yescharacteristic, direct product factor
718C3C3×#254311yescharacteristic, complemented
719C2—24no—
720C2—42no—
721C2—242no—
722C2C3×#554012yes—
723C2C3×#555412yes—
724C2C2×C3×#93011yescharacteristic
725C2C3×#580411yescharacteristic
726C2C3×#583211yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×C4×D4C2
socleC23×C32C24
hypercenterC2×C3×C4×D4D3
hypocenterC3C3×#2543
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×D4C2semidirect
2. C2×C3×#939C2semidirect
3. C2×C3×#930C2semidirect
4. C3×#5213C2semidirect
5. C2×C3×C3⋊#95C2semidirect
6. C3×#4991C2semidirect
7. C3×#4981C2semidirect
8. C3×#4960C2semidirect
9. C3×#4958C2semidirect
10. C3×#4953C2semidirect
11. C3×#4940C2semidirect
13. #82380C3direct (N × H)
43. C2×C3×C4×D4D3semidirect
44. C2×C3×C4×D4C2×C3semidirect
45. C2×#939C2×C3semidirect
46. C2×#930C2×C3semidirect
55. #5213C2×C3semidirect
56. C2×C3⋊#95C2×C3semidirect
57. #4991C2×C3semidirect
58. #4981C2×C3semidirect
59. #4960C2×C3semidirect
60. #4958C2×C3semidirect
61. #4953C2×C3semidirect
62. #4940C2×C3semidirect
68. C2×C32×D4D4semidirect
72. C22×C32×C4D4semidirect
211. C2×C4×D4C3×D3semidirect
243. C2×C3×D4D12semidirect
244. C2×C3×D4C3×D4semidirect
266. C22×C3×C4#67semidirect
267. C22×C3×C4C3×D4semidirect
510. C2×D4C3×D12semidirect
520. C22×C4C3×#67semidirect
617. C32#2543semidirect
717. C3#82380direct (N × H)
718. C3C3×#2543semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×C3×#9392
C2×C3×#9302
C3×#52132
C2×C3×C3⋊#952
C3×#49912
C3×#49812
C3×#49602
C3×#49582
C3×#49532
C3×#49402
C3×#25433
#823803