Finite Group Databasebeta

← C3×#10595022 #13174598

Subgroups — C3×#10595022 #13174598

Order 1728.

1850 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#235C211yesmaximal, characteristic, complemented
2C22×C32×C4×D3C211yesmaximal, characteristic, complemented
3C3×#64135C211yesmaximal, characteristic, complemented
4C3×#63976C212yesmaximal, complemented
5C3×#63961C212yesmaximal, complemented
6C3×#63908C212yesmaximal, complemented
7C3×C4×#625C214yesmaximal, complemented
8C3×#63856C212yesmaximal, complemented
9C3×#5828—31nomaximal
10C3×#5791—31nomaximal
11#10595022C311yesmaximal, characteristic, direct product factor
12C23×C32×D3C2211yescharacteristic
13C22×C33×C4C2211yescharacteristic
14C2×C32×#67C2212yes—
15C22×C32×Dic3C2211yescharacteristic
16C32×#235—24no—
17C2×C32×D12C2211yescharacteristic, complemented
18C2×C32×C4×D3—24no—
19C2×C32×C4×D3C2212yes—
20C2×C32×C4×D3C2212yes—
21C2×C32×C4×D3C2212yescomplemented
22C2×C32×Dic6C2211yescharacteristic, complemented
23C2×C3×#625C2214yes—
24C3×#3757C2212yes—
25C3×C4⋊(C3⋊Dic3)C2212yescomplemented
26C3×C4×C3⋊Dic3C2212yescomplemented
27C3×#3724C2214yescomplemented
28C3×(C2×D3)⋊Dic3C2214yes—
29C3×(C2×D3)⋊Dic3C2214yescomplemented
30C2×C32×#41—31no—
31C23×C32×C4—31no—
32C2×C3×#235—21no—
33C2×C3×#235D311yescharacteristic, complemented
34C2×C3×#235C2×C311yescharacteristic, complemented
35C22×C3×C4×D3—21no—
36C22×C3×C4×D3D311yescharacteristic, complemented
37C22×C3×C4×D3C2×C311yescharacteristic, complemented
38#64135C2×C311yescharacteristic, complemented
39C3×#953—32no—
40C3×#946—32no—
41C3×#938—32no—
42C3×#937—32no—
43C3×#935—32no—
44C3×#930—32no—
45C3×#929—32no—
46C3×C4×#67—34no—
47C3×C4×#67—34no—
48C3×#926—31no—
49C3×#926—31no—
50C3×#926—61no—
51C3×#924—32no—
52#63976C2×C312yescomplemented
53#63961C2×C312yescomplemented
54#63908C2×C312yescomplemented
55C4×#625C2×C314yescomplemented
56#63856C2×C312yescomplemented
57C23×C33C2311yescharacteristic
58C22×C32×D3—22no—
59C22×C32×D3—24no—
60C22×C32×D3C2312yes—
61C22×C32×D3C2312yes—
62C2×C33×C4D414yescomplemented
63C2×C33×C4C2311yescharacteristic
64C2×C33×C4C2311yescharacteristic
65C2×C3×C3⋊Dic3C2314yes—
66C32×#67—24no—
67C2×C32×Dic3—22no—
68C2×C32×Dic3C2312yes—
69C2×C32×Dic3C2312yes—
70C32×D12—22no—
71C32×C4×D3—24no—
72C32×C4×D3—24no—
73C32×C4×D3—24no—
74C32×Dic6—22no—
75C3×#625—28no—
76C3×#525—91no—
77#5828—31no—
78#5791—31no—
79C24×C32—31no—
80C23×C3×D3—21no—
81C23×C3×D3C2×D311yescharacteristic
82C23×C3×D3C22×C311yescharacteristic
83C32×#41—64no—
84C2×C32×Q8—31no—
85C2×C32×D4—32no—
86C2×C32×D4—31no—
87C22×C32×C4—21no—
88C22×C32×C4—21no—
89C22×C32×C4—21no—
90C22×C32×C4—31no—
91C22×C32×C4—32no—
92C22×C32×C4—32no—
93C22×C32×C4—32no—
94C22×C32×C4—41no—
95C22×C32×C4—64no—
96C22×C32×C4C2×D311yescharacteristic
97C22×C32×C4C2×D311yescharacteristic
98C22×C32×C4C22×C311yescharacteristic
99C2×C3×#67—22no—
100C2×C3×#67—34no—
101C2×C3×#67—34no—
102C2×C3×#67C2×D312yes—
103C2×C3×#67C22×C312yes—
104C22×C3×Dic3—21no—
105C22×C3×Dic3C2×D311yescharacteristic
106C22×C3×Dic3C22×C311yescharacteristic
107C3×#235—28no—
108C3×#235—24no—
109C3×#235—24no—
110C2×C3×D12—21no—
111C2×C3×D12C2×D311yescharacteristic, complemented
112C2×C3×D12C22×C311yescharacteristic, complemented
113C2×C3×C4×D3—28no—
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3—22no—
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3—24no—
118C2×C3×C4×D3—24no—
119C2×C3×C4×D3C2×D312yes—
120C2×C3×C4×D3C2×D312yes—
121C2×C3×C4×D3C2×D312yescomplemented
122C2×C3×C4×D3C22×C312yes—
123C2×C3×C4×D3C22×C312yes—
124C2×C3×C4×D3C22×C312yescomplemented
125C2×C3×Dic6—21no—
126C2×C3×Dic6C2×D311yescharacteristic, complemented
127C2×C3×Dic6C22×C311yescharacteristic, complemented
128C2×#625C22×C314yes—
129#3757C22×C312yes—
130C4⋊(C3⋊Dic3)C22×C312yescomplemented
131C4×C3⋊Dic3C22×C312yescomplemented
132C3×#217—32no—
133C3×#217—32no—
134C3×#217—34no—
135C3×#217—34no—
136C3×#217—62no—
137C3×(C2×D3)⋊C4—34no—
138C3×(C2×D3)⋊C4—34no—
139C3×C4⋊Dic3—32no—
140C3×C4⋊Dic3—32no—
141C3×C4⋊Dic3—62no—
142C3×Dic3⋊C4—34no—
143C3×Dic3⋊C4—34no—
144C3×C4×Dic3—32no—
145C3×C4×Dic3—32no—
146C3×C4×Dic3—62no—
147#3724C22×C314yescomplemented
148(C2×D3)⋊Dic3C22×C314yes—
149(C2×D3)⋊Dic3C22×C314yescomplemented
150C22×C33—22no—
151C22×C33C2×D412yes—
152C22×C33C2411yescharacteristic
153C2×C32×D3—28no—
154C2×C32×D3—22no—
155C2×C32×D3—22no—
156C2×C32×D3—22no—
157C2×C32×D3—24no—
158C2×C32×D3#4114yescomplemented
159C33×C4C2×D412yes—
160C33×C4C2×D412yes—
161C3×C3⋊Dic3—24no—
162C32×Dic3—22no—
163C32×Dic3—22no—
164C2×C3×#41—31no—
165C2×C3×#41—31no—
166C2×C3×#41—61no—
167C23×C3×C4—31no—
168C23×C3×C4—31no—
169C23×C3×C4—61no—
170C2×#235C3×D311yescharacteristic, complemented
171C22×C4×D3C3×D311yescharacteristic, complemented
172C3×#123—92no—
173C3×C22⋊Q8—92no—
174C3×#121—92no—
175C3×#120—92no—
176C3×C4×D4—94no—
177C3×#117—91no—
178#953—32no—
179#946—32no—
180#938—32no—
181#937—32no—
182#935—32no—
183#930—32no—
184#929—32no—
185C4×#67—34no—
186C4×#67—34no—
187#926—31no—
188#926—31no—
189#926—61no—
190#924—32no—
191C23×C32—21no—
192C23×C32—21no—
193C23×C32—21no—
194C23×C32—32no—
195C23×C32—32no—
196C23×C32—41no—
197C23×C32—64no—
198C23×C32—62no—
199C23×C32C22×D311yescharacteristic
200C23×C32C22×D311yescharacteristic
201C23×C32C23×C311yescharacteristic
202C22×C3×D3—28no—
203C22×C3×D3—24no—
204C22×C3×D3—22no—
205C22×C3×D3—22no—
206C22×C3×D3—24no—
207C22×C3×D3—24no—
208C22×C3×D3—22no—
209C22×C3×D3—22no—
210C22×C3×D3C22×D312yes—
211C22×C3×D3C22×D312yes—
212C22×C3×D3C23×C312yes—
213C22×C3×D3C23×C312yes—
214C32×Q8—62no—
215C32×D4—64no—
216C32×D4—62no—
217C2×C32×C4—24no—
218C2×C32×C4—24no—
219C2×C32×C4—24no—
220C2×C32×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4—21no—
223C2×C32×C4—21no—
224C2×C32×C4—21no—
225C2×C32×C4—21no—
226C2×C32×C4—32no—
227C2×C32×C4—32no—
228C2×C32×C4—44no—
229C2×C32×C4—41no—
230C2×C32×C4—41no—
231C2×C32×C4—62no—
232C2×C32×C4—64no—
233C2×C32×C4—64no—
234C2×C32×C4—64no—
235C2×C32×C4#6714yescomplemented
236C2×C32×C4#6714yescomplemented
237C2×C32×C4C3×D414yescomplemented
238C2×C32×C4C22×D311yescharacteristic
239C2×C32×C4C22×D311yescharacteristic
240C2×C32×C4C22×D311yescharacteristic
241C2×C32×C4C22×D311yescharacteristic
242C2×C32×C4C23×C311yescharacteristic
243C2×C32×C4C23×C311yescharacteristic
244C2×C3⋊Dic3C23×C314yes—
245C3×#67—28no—
246C3×#67—24no—
247C3×#67—24no—
248C3×#67—68no—
249C3×#67—68no—
250C2×C3×Dic3—24no—
251C2×C3×Dic3—22no—
252C2×C3×Dic3—22no—
253C2×C3×Dic3—22no—
254C2×C3×Dic3—22no—
255C2×C3×Dic3—34no—
256C2×C3×Dic3—34no—
257C2×C3×Dic3—64no—
258C2×C3×Dic3C22×D312yes—
259C2×C3×Dic3C22×D312yes—
260C2×C3×Dic3C23×C312yes—
261C2×C3×Dic3C23×C312yes—
262C3×D12—24no—
263C3×D12—22no—
264C3×D12—22no—
265C3×C4×D3—28no—
266C3×C4×D3—28no—
267C3×C4×D3—28no—
268C3×C4×D3—24no—
269C3×C4×D3—24no—
270C3×C4×D3—24no—
271C3×C4×D3—24no—
272C3×C4×D3—24no—
273C3×C4×D3—24no—
274C3×Dic6—24no—
275C3×Dic6—22no—
276C3×Dic6—22no—
277#625—28no—
278#525—91noSylow
279C2×C33—22no—
280C2×C33C22×D411yescharacteristic
281C2×C33C2×#4112yes—
282C32×D3—24no—
283C32×D3—42no—
284C24×C3—31no—
285C24×C3—31no—
286C24×C3—61no—
287C23×D3C2×C3×D311yescharacteristic
288C3×#41—68no—
289C3×#41—64no—
290C3×#41—64no—
291C2×C3×Q8—31no—
292C2×C3×Q8—31no—
293C2×C3×Q8—61no—
294C2×C3×D4—32no—
295C2×C3×D4—32no—
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C2×C3×D4—61no—
299C2×C3×D4—62no—
300C2×C3×D4—94no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—32no—
307C22×C3×C4—32no—
308C22×C3×C4—32no—
309C22×C3×C4—32no—
310C22×C3×C4—32no—
311C22×C3×C4—32no—
312C22×C3×C4—41no—
313C22×C3×C4—62no—
314C22×C3×C4—62no—
315C22×C3×C4—62no—
316C22×C3×C4—61no—
317C22×C3×C4—68no—
318C22×C3×C4—64no—
319C22×C3×C4—64no—
320C22×C3×C4D3211yescharacteristic
321C22×C3×C4C2×C3×D311yescharacteristic
322C22×C3×C4C2×C3×D311yescharacteristic
323C2×#67—34no—
324C2×#67—34no—
325C2×#67C2×C3×D312yes—
326C22×Dic3C2×C3×D311yescharacteristic
327#235—24no—
328C2×D12C2×C3×D311yescharacteristic, complemented
329C2×C4×D3—24no—
330C2×C4×D3C2×C3×D312yes—
331C2×C4×D3C2×C3×D312yes—
332C2×C4×D3C2×C3×D312yescomplemented
333C2×Dic6C2×C3×D311yescharacteristic, complemented
334C3×C4⋊C4—94no—
335C3×C4⋊C4—92no—
336C3×C22⋊C4—94no—
337C3×C22⋊C4—94no—
338C3×C22⋊C4—92no—
339C3×C42—92no—
340#217—32no—
341#217—32no—
342#217—34no—
343#217—34no—
344#217—62no—
345(C2×D3)⋊C4—34no—
346(C2×D3)⋊C4—34no—
347C4⋊Dic3—32no—
348C4⋊Dic3—32no—
349C4⋊Dic3—62no—
350Dic3⋊C4—34no—
351Dic3⋊C4—34no—
352C4×Dic3—32no—
353C4×Dic3—32no—
354C4×Dic3—62no—
355C22×C32—22no—
356C22×C32—24no—
357C22×C32—22no—
358C22×C32—22no—
359C22×C32—21no—
360C22×C32—21no—
361C22×C32—21no—
362C22×C32—22no—
363C22×C32—22no—
364C22×C32—22no—
365C22×C32—34no—
366C22×C32—42no—
367C22×C32—41no—
368C22×C32—42no—
369C22×C32—42no—
370C22×C32—44no—
371C22×C32—68no—
372C22×C32—62no—
373C22×C32—62no—
374C22×C32—62no—
375C22×C32—64no—
376C22×C32C2×#6712yes—
377C22×C32C2×#6712yes—
378C22×C32C2×C3×D412yes—
379C22×C32C23×D311yescharacteristic
380C22×C32C23×D311yescharacteristic
381C22×C32C24×C311yescharacteristic
382C2×C3×D3—24no—
383C2×C3×D3—216no—
384C2×C3×D3—28no—
385C2×C3×D3—28no—
386C2×C3×D3—24no—
387C2×C3×D3—22no—
388C2×C3×D3—22no—
389C2×C3×D3—22no—
390C2×C3×D3—22no—
391C2×C3×D3—24no—
392C2×C3×D3—24no—
393C2×C3×D3—22no—
394C2×C3×D3—22no—
395C2×C3×D3—24no—
396C2×C3×D3—24no—
397C2×C3×D3—44no—
398C2×C3×D3#23514yescomplemented
399C2×C3×D3C3×#4114yescomplemented
400C32×C4—22no—
401C32×C4—22no—
402C32×C4—22no—
403C32×C4—22no—
404C32×C4—22no—
405C32×C4—22no—
406C32×C4—42no—
407C32×C4—42no—
408C32×C4—62no—
409C32×C4—62no—
410C32×C4C2×#6712yes—
411C32×C4C2×#6712yes—
412C32×C4C2×#6712yes—
413C32×C4C2×#6712yes—
414C32×C4C2×C3×D412yes—
415C32×C4C2×C3×D412yes—
416C3⋊Dic3—24no—
417C3×Dic3—24no—
418C3×Dic3—24no—
419C3×Dic3—22no—
420C3×Dic3—22no—
421C3×Dic3—22no—
422C3×Dic3—22no—
423C3×Dic3—64no—
424C3×Dic3—64no—
425C3×Dic3—124no—
426C2×#41—31no—
427C23×C4—31no—
428#123—92no—
429C22⋊Q8—92no—
430#121—92no—
431#120—92no—
432C4×D4—94no—
433#117—91no—
434C33#52511yescharacteristic, complemented, Sylow
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—21no—
438C23×C3—32no—
439C23×C3—32no—
440C23×C3—32no—
441C23×C3—32no—
442C23×C3—41no—
443C23×C3—62no—
444C23×C3—62no—
445C23×C3—64no—
446C23×C3—64no—
447C23×C3—64no—
448C23×C3—68no—
449C23×C3—62no—
450C23×C3—62no—
451C23×C3C2×D3211yescharacteristic
452C23×C3C22×C3×D311yescharacteristic
453C23×C3C22×C3×D311yescharacteristic
454C22×D3—22no—
455C22×D3—24no—
456C22×D3C22×C3×D312yes—
457C22×D3C22×C3×D312yes—
458C3×Q8—64no—
459C3×Q8—62no—
460C3×Q8—62no—
461C3×D4—64no—
462C3×D4—68no—
463C3×D4—64no—
464C3×D4—64no—
465C3×D4—62no—
466C3×D4—62no—
467C3×D4—188no—
468C2×C3×C4—24no—
469C2×C3×C4—24no—
470C2×C3×C4—24no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—32no—
478C2×C3×C4—32no—
479C2×C3×C4—32no—
480C2×C3×C4—32no—
481C2×C3×C4—44no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—62no—
485C2×C3×C4—62no—
486C2×C3×C4—68no—
487C2×C3×C4—68no—
488C2×C3×C4—68no—
489C2×C3×C4—64no—
490C2×C3×C4—62no—
491C2×C3×C4—62no—
492C2×C3×C4—64no—
493C2×C3×C4—64no—
494C2×C3×C4—64no—
495C2×C3×C4—64no—
496C2×C3×C4—64no—
497C2×C3×C4—64no—
498C2×C3×C4—94no—
499C2×C3×C4#62514yescomplemented
500C2×C3×C4C3×#6714yescomplemented
501C2×C3×C4C3×#6714yescomplemented
502C2×C3×C4C2×D3211yescharacteristic
503C2×C3×C4C2×D3211yescharacteristic
504C2×C3×C4C22×C3×D311yescharacteristic
505C2×C3×C4C22×C3×D311yescharacteristic
506C2×C3×C4C22×C3×D311yescharacteristic
507C2×C3×C4C22×C3×D311yescharacteristic
508#67—24no—
509#67—68no—
510#67—68no—
511C2×Dic3—22no—
512C2×Dic3—34no—
513C2×Dic3—34no—
514C2×Dic3—64no—
515C2×Dic3C22×C3×D312yes—
516C2×Dic3C22×C3×D312yes—
517D12—22no—
518C4×D3—24no—
519C4×D3—24no—
520C4×D3—24no—
521Dic6—22no—
522C2×C32—22no—
523C2×C32—24no—
524C2×C32—22no—
525C2×C32—22no—
526C2×C32—22no—
527C2×C32—21no—
528C2×C32—22no—
529C2×C32—22no—
530C2×C32—21no—
531C2×C32—21no—
532C2×C32—41no—
533C2×C32—42no—
534C2×C32—42no—
535C2×C32—42no—
536C2×C32—44no—
537C2×C32—64no—
538C2×C32—122no—
539C2×C32C2×#23512yes—
540C2×C32D3×#4112yes—
541C2×C32C22×#6711yescharacteristic
542C2×C32C22×#6711yescharacteristic
543C2×C32C22×C3×D411yescharacteristic
544C2×C32C2×C3×#4112yes—
545C3×D3—28no—
546C3×D3—24no—
547C3×D3—24no—
548C3×D3—44no—
549C3×D3—42no—
550C3×D3—42no—
551C24—31no—
552#41—64no—
553C2×Q8—31no—
554C2×D4—32no—
555C2×D4—31no—
556C2×D4—94no—
557C22×C4—31no—
558C22×C4—32no—
559C22×C4—32no—
560C22×C4—32no—
561C22×C4—64no—
562C22×C4C3×D3211yescharacteristic
563C4⋊C4—94no—
564C4⋊C4—92no—
565C22⋊C4—94no—
566C22⋊C4—94no—
567C22⋊C4—92no—
568C42—92no—
569C22×C3—24no—
570C22×C3—22no—
571C22×C3—22no—
572C22×C3—22no—
573C22×C3—21no—
574C22×C3—21no—
575C22×C3—21no—
576C22×C3—22no—
577C22×C3—22no—
578C22×C3—22no—
579C22×C3—34no—
580C22×C3—34no—
581C22×C3—42no—
582C22×C3—42no—
583C22×C3—44no—
584C22×C3—41no—
585C22×C3—42no—
586C22×C3—64no—
587C22×C3—64no—
588C22×C3—616no—
589C22×C3—68no—
590C22×C3—68no—
591C22×C3—64no—
592C22×C3—64no—
593C22×C3—62no—
594C22×C3—62no—
595C22×C3—62no—
596C22×C3—62no—
597C22×C3—64no—
598C22×C3—62no—
599C22×C3—64no—
600C22×C3—62no—
601C22×C3—124no—
602C22×C3C2×#62512yes—
603C22×C3C2×C3×#6712yes—
604C22×C3C2×C3×#6712yes—
605C22×C3C22×D3211yescharacteristic
606C22×C3C23×C3×D311yescharacteristic
607C22×C3C23×C3×D311yescharacteristic
608C2×D3—28no—
609C2×D3—22no—
610C2×D3—22no—
611C2×D3—24no—
612C2×D3—22no—
613C2×D3C3×#23514yescomplemented
614C3×C4—22no—
615C3×C4—22no—
616C3×C4—22no—
617C3×C4—22no—
618C3×C4—22no—
619C3×C4—22no—
620C3×C4—42no—
621C3×C4—42no—
622C3×C4—64no—
623C3×C4—64no—
624C3×C4—62no—
625C3×C4—62no—
626C3×C4—62no—
627C3×C4—62no—
628C3×C4—184no—
629C3×C4C2×#62512yes—
630C3×C4C2×#62512yes—
631C3×C4C2×C3×#6712yes—
632C3×C4C2×C3×#6712yes—
633C3×C4C2×C3×#6712yes—
634C3×C4C2×C3×#6712yes—
635Dic3—22no—
636Dic3—22no—
637Dic3—64no—
638Dic3—64no—
639Dic3—124no—
640C32—21no—
641C32—21no—
642C32—21no—
643C32—41no—
644C32#579111yescharacteristic, complemented
645C32#582811yescharacteristic, complemented
646C32C3×#52511yescharacteristic, complemented
647C23—32no—
648C23—32no—
649C23—64no—
650C23—62no—
651C23C2×C3×D3211yescharacteristic
652Q8—62no—
653D4—64no—
654D4—62no—
655D4—188no—
656C2×C4—32no—
657C2×C4—32no—
658C2×C4—62no—
659C2×C4—64no—
660C2×C4—64no—
661C2×C4—64no—
662C2×C4—94no—
663C2×C4C3×#62514yescomplemented
664C2×C4C2×C3×D3211yescharacteristic
665C2×C4C2×C3×D3211yescharacteristic
666C2×C3—24no—
667C2×C3—22no—
668C2×C3—22no—
669C2×C3—22no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—22no—
674C2×C3—22no—
675C2×C3—22no—
676C2×C3—42no—
677C2×C3—42no—
678C2×C3—44no—
679C2×C3—41no—
680C2×C3—42no—
681C2×C3—68no—
682C2×C3—64no—
683C2×C3—64no—
684C2×C3—124no—
685C2×C3—122no—
686C2×C3—122no—
687C2×C3D3×#23512yes—
688C2×C3C22×#62511yescharacteristic
689C2×C3C2×C3×#23512yes—
690C2×C3C3×D3×#4112yes—
691C2×C3C22×C3×#6711yescharacteristic
692C2×C3C22×C3×#6711yescharacteristic
693D3—24no—
694D3—42no—
695C22—22no—
696C22—34no—
697C22—68no—
698C22—62no—
699C22—62no—
700C22—62no—
701C22—64no—
702C22C2×C3×#62512yes—
703C22C22×C3×D3211yescharacteristic
704C4—62no—
705C4—62no—
706C4—184no—
707C4C2×C3×#62512yes—
708C4C2×C3×#62512yes—
709C3—21no—
710C3—21no—
711C3—21no—
712C3—41no—
713C3#1059502211yescharacteristic, direct product factor
714C3C3×#579111yescharacteristic, complemented
715C3C3×#582811yescharacteristic, complemented
716C2—22no—
717C2—64no—
718C2—122no—
719C2C3×D3×#23512yes—
720C2C22×C3×#62511yescharacteristic
subgroupG/H
centerC2×C3×C4C2×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
hypercenterC22×C3×C4D32
hypocenterC32C3×#525
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C2×C32×#235C2semidirect
2. C22×C32×C4×D3C2semidirect
3. C3×#64135C2semidirect
4. C3×#63976C2semidirect
5. C3×#63961C2semidirect
6. C3×#63908C2semidirect
7. C3×C4×#625C2semidirect
8. C3×#63856C2semidirect
11. #10595022C3direct (N × H)
17. C2×C32×D12C22semidirect
21. C2×C32×C4×D3C22semidirect
22. C2×C32×Dic6C22semidirect
25. C3×C4⋊(C3⋊Dic3)C22semidirect
26. C3×C4×C3⋊Dic3C22semidirect
27. C3×#3724C22semidirect
29. C3×(C2×D3)⋊Dic3C22semidirect
33. C2×C3×#235D3semidirect
34. C2×C3×#235C2×C3semidirect
36. C22×C3×C4×D3D3semidirect
37. C22×C3×C4×D3C2×C3semidirect
38. #64135C2×C3semidirect
52. #63976C2×C3semidirect
53. #63961C2×C3semidirect
54. #63908C2×C3semidirect
55. C4×#625C2×C3semidirect
56. #63856C2×C3semidirect
62. C2×C33×C4D4semidirect
111. C2×C3×D12C2×D3semidirect
112. C2×C3×D12C22×C3semidirect
121. C2×C3×C4×D3C2×D3semidirect
124. C2×C3×C4×D3C22×C3semidirect
126. C2×C3×Dic6C2×D3semidirect
127. C2×C3×Dic6C22×C3semidirect
130. C4⋊(C3⋊Dic3)C22×C3semidirect
131. C4×C3⋊Dic3C22×C3semidirect
147. #3724C22×C3semidirect
149. (C2×D3)⋊Dic3C22×C3semidirect
158. C2×C32×D3#41semidirect
170. C2×#235C3×D3semidirect
171. C22×C4×D3C3×D3semidirect
235. C2×C32×C4#67semidirect
236. C2×C32×C4#67semidirect
237. C2×C32×C4C3×D4semidirect
328. C2×D12C2×C3×D3semidirect
332. C2×C4×D3C2×C3×D3semidirect
333. C2×Dic6C2×C3×D3semidirect
398. C2×C3×D3#235semidirect
399. C2×C3×D3C3×#41semidirect
434. C33#525semidirect
499. C2×C3×C4#625semidirect
500. C2×C3×C4C3×#67semidirect
501. C2×C3×C4C3×#67semidirect
613. C2×D3C3×#235semidirect
644. C32#5791semidirect
645. C32#5828semidirect
646. C32C3×#525semidirect
663. C2×C4C3×#625semidirect
713. C3#10595022direct (N × H)
714. C3C3×#5791semidirect
715. C3C3×#5828semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#2352
C22×C32×C4×D32
C3×#641352
C3×#639762
C3×#639612
C3×#639082
C3×C4×#6252
C3×#638562
C3×#58283
C3×#57913
#105950223