Finite Group Databasebeta

← C3×#10595154 #13174715

Subgroups — C3×#10595154 #13174715

Order 1728.

1746 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#237C211yesmaximal, characteristic, complemented
2C22×C3×D3×Dic3C211yesmaximal, characteristic, complemented
3C3×#64144C211yesmaximal, characteristic, complemented
4C32×#937C211yesmaximal, characteristic, complemented
5C3×#63976C211yesmaximal, characteristic, complemented
6C3×Dic3×#67C212yesmaximal, complemented
7C3×#63970C212yesmaximal, complemented
8C3×#63962C211yesmaximal, characteristic, complemented
9C3×#63955C211yesmaximal, characteristic, complemented
10C3×#63887C212yesmaximal, complemented
11C3×#63879C212yesmaximal, complemented
12C3×#5828—31nomaximal
13C3×#5586—31nomaximal
14#10595154C311yesmaximal, characteristic, direct product factor
15C23×C32×D3C2211yescharacteristic
16C2×C33×D4C2211yescharacteristic
17C22×C3×C3⋊Dic3C2211yescharacteristic
18C2×C32×#67C2211yescharacteristic
19C2×C32×#67C2212yes—
20C2×C32×#67C2211yescharacteristic, complemented
21C22×C32×Dic3C2211yescharacteristic
22C22×C32×Dic3C2211yescharacteristic, complemented
23C32×#237—24no—
24C2×C32×C4×D3C2211yescharacteristic, complemented
25C2×C32×Dic6C2211yescharacteristic, complemented
26C2×C3×#625C2212yes—
27C2×C3×D3×Dic3—24no—
28C2×C3×D3×Dic3C2212yes—
29C2×C3×D3×Dic3C2212yes—
30C3×#3757C2211yescharacteristic
31C3×#3757C2212yescomplemented
32C3×#3750C2212yescomplemented
33C32×#217C2211yescharacteristic
34C32×(C2×D3)⋊C4C2212yes—
35C3×Dic3⋊Dic3C2212yescomplemented
36C3×Dic3⋊Dic3C2212yescomplemented
37C3×(C2×D3)⋊Dic3C2212yes—
38C3×(C2×D3)⋊Dic3C2212yescomplemented
39C3×Dic32C2212yescomplemented
40C2×C32×#41—31no—
41C23×C3×Dic3—31no—
42C2×C3×#237—21no—
43C2×C3×#237D311yescharacteristic, complemented
44C2×C3×#237C2×C311yescharacteristic, complemented
45C22×C3×C4×D3—31no—
46C22×D3×Dic3C2×C311yescharacteristic, complemented
47C32×#120—31no—
48#64144C2×C311yescharacteristic, complemented
49C3×#953—31no—
50C3×#946—32no—
51C3×#939—32no—
52C3×#938—32no—
53C3×#937—21no—
54C3×#937—31no—
55C3×#937D311yescharacteristic, complemented
56C3×#937C2×C311yescharacteristic, complemented
57C3×#935—31no—
58C3×#935—31no—
59C3×#935—31no—
60C3×#935—61no—
61C3×D4×Dic3—32no—
62C3×C4×#67—32no—
63C3×C4×#67—32no—
64C3×#926—31no—
65C3×#886—31no—
66C3×#67⋊C4—32no—
67C3×#878—32no—
68C3×#877—31no—
69#63976C2×C311yescharacteristic, complemented
70Dic3×#67C2×C312yescomplemented
71#63970C2×C312yescomplemented
72#63962C2×C311yescharacteristic, complemented
73#63955C2×C311yescharacteristic, complemented
74#63887C2×C312yescomplemented
75#63879C2×C312yescomplemented
76C23×C33C2311yescharacteristic
77C23×C33C2311yescharacteristic
78C22×C32×D3—22no—
79C22×C32×D3—24no—
80C22×C32×D3C2311yescharacteristic
81C22×C32×D3C2312yes—
82C33×D4—22no—
83C2×C33×C4C2311yescharacteristic
84C2×C3×C3⋊Dic3—22no—
85C2×C3×C3⋊Dic3C2312yes—
86C2×C3×C3⋊Dic3C2312yes—
87C32×#67—22no—
88C32×#67—24no—
89C32×#67—22no—
90C2×C32×Dic3—22no—
91C2×C32×Dic3D414yescomplemented
92C2×C32×Dic3C2312yes—
93C2×C32×Dic3C2311yescharacteristic
94C2×C32×Dic3C2311yescharacteristic
95C2×C32×Dic3C2311yescharacteristic
96C32×C4×D3—22no—
97C32×Dic6—22no—
98C3×#625—24no—
99C3×D3×Dic3—24no—
100C3×D3×Dic3—24no—
101C3×#525—91no—
102#5828—31no—
103#5586—31no—
104C24×C32—31no—
105C23×C3×D3—21no—
106C23×C3×D3C2×D311yescharacteristic
107C23×C3×D3C22×C311yescharacteristic
108C32×#41—64no—
109C2×C32×Q8—31no—
110C2×C32×D4—21no—
111C2×C32×D4—21no—
112C2×C32×D4—21no—
113C2×C32×D4—32no—
114C2×C32×D4—31no—
115C2×C32×D4—31no—
116C2×C32×D4—41no—
117C2×C32×D4C2×D311yescharacteristic
118C2×C32×D4C2×D311yescharacteristic
119C2×C32×D4C22×C311yescharacteristic
120C22×C32×C4—31no—
121C22×C32×C4—31no—
122C22×C32×C4—31no—
123C22×C3⋊Dic3C22×C311yescharacteristic
124C2×C3×#67—21no—
125C2×C3×#67—21no—
126C2×C3×#67—22no—
127C2×C3×#67—32no—
128C2×C3×#67—32no—
129C2×C3×#67C2×D311yescharacteristic
130C2×C3×#67C2×D312yes—
131C2×C3×#67C2×D311yescharacteristic, complemented
132C2×C3×#67C22×C312yes—
133C2×C3×#67C22×C311yescharacteristic
134C2×C3×#67C22×C311yescharacteristic, complemented
135C22×C3×Dic3—21no—
136C22×C3×Dic3—21no—
137C22×C3×Dic3—31no—
138C22×C3×Dic3—31no—
139C22×C3×Dic3—32no—
140C22×C3×Dic3—32no—
141C22×C3×Dic3—64no—
142C22×C3×Dic3—61no—
143C22×C3×Dic3C2×D311yescharacteristic
144C22×C3×Dic3C2×D311yescharacteristic, complemented
145C22×C3×Dic3C22×C311yescharacteristic
146C22×C3×Dic3C22×C311yescharacteristic, complemented
147C3×#237—28no—
148C3×#237—24no—
149C3×#237—24no—
150C2×C3×C4×D3—21no—
151C2×C3×C4×D3—32no—
152C2×C3×C4×D3—32no—
153C2×C3×C4×D3—64no—
154C2×C3×C4×D3C2×D311yescharacteristic, complemented
155C2×C3×C4×D3C22×C311yescharacteristic, complemented
156C2×C3×Dic6—21no—
157C2×C3×Dic6C2×D311yescharacteristic, complemented
158C2×C3×Dic6C22×C311yescharacteristic, complemented
159C2×#625C22×C312yes—
160C2×D3×Dic3—24no—
161C2×D3×Dic3C22×C312yes—
162C2×D3×Dic3C22×C312yes—
163C32×C22⋊C4—31no—
164C32×C22⋊C4—32no—
165#3757C22×C311yescharacteristic
166#3757C22×C312yescomplemented
167#3750C22×C312yescomplemented
168C3×#217—21no—
169C3×#217—31no—
170C3×#217—31no—
171C3×#217—32no—
172C3×#217—32no—
173C3×#217—32no—
174C3×#217—32no—
175C3×#217—61no—
176C3×#217—62no—
177C3×#217C2×D311yescharacteristic
178C3×#217C22×C311yescharacteristic
179C3×(C2×D3)⋊C4—22no—
180C3×(C2×D3)⋊C4—32no—
181C3×(C2×D3)⋊C4—32no—
182C3×(C2×D3)⋊C4C2×D312yes—
183C3×(C2×D3)⋊C4C22×C312yes—
184C3×C4⋊Dic3—32no—
185C3×C4⋊Dic3—32no—
186C3×Dic3⋊C4—32no—
187C3×Dic3⋊C4—32no—
188C3×Dic3⋊C4—32no—
189C3×Dic3⋊C4—32no—
190C3×Dic3⋊C4—62no—
191C3×C4×Dic3—32no—
192C3×C4×Dic3—32no—
193Dic3⋊Dic3C22×C312yescomplemented
194Dic3⋊Dic3C22×C312yescomplemented
195(C2×D3)⋊Dic3C22×C312yes—
196(C2×D3)⋊Dic3C22×C312yescomplemented
197Dic32C22×C312yescomplemented
198C22×C33—22no—
199C22×C33—21no—
200C22×C33—22no—
201C22×C33C2×D412yes—
202C22×C33C2411yescharacteristic
203C2×C32×D3—28no—
204C2×C32×D3—22no—
205C2×C32×D3—22no—
206C2×C32×D3—21no—
207C2×C32×D3—22no—
208C2×C32×D3#4114yescomplemented
209C33×C4—21no—
210C3×C3⋊Dic3—22no—
211C3×C3⋊Dic3—22no—
212C32×Dic3—21no—
213C32×Dic3—22no—
214C32×Dic3C2×D412yes—
215C32×Dic3C2×D412yes—
216C2×C3×#41—31no—
217C2×C3×#41—31no—
218C2×C3×#41—61no—
219C23×C3×C4—91no—
220C23×Dic3—31no—
221C2×#237C3×D311yescharacteristic, complemented
222C22×C4×D3—31no—
223C3×#123—91no—
224C3×#123—91no—
225C3×C22⋊Q8—92no—
226C3×#121—92no—
227C3×#120—31no—
228C3×#120—31no—
229C3×#120—61no—
230C3×#120—91no—
231C3×C4×D4—92no—
232C3×C4×D4—92no—
233C3×#117—91no—
234#953—31no—
235#946—32no—
236#939—32no—
237#938—32no—
238#937—31no—
239#937C3×D311yescharacteristic, complemented
240#935—31no—
241#935—31no—
242#935—31no—
243#935—61no—
244D4×Dic3—32no—
245C4×#67—32no—
246C4×#67—32no—
247#926—31no—
248#886—31no—
249#67⋊C4—32no—
250#878—32no—
251#877—31no—
252C23×C32—21no—
253C23×C32—21no—
254C23×C32—21no—
255C23×C32—21no—
256C23×C32—21no—
257C23×C32—21no—
258C23×C32—32no—
259C23×C32—31no—
260C23×C32—41no—
261C23×C32—41no—
262C23×C32—64no—
263C23×C32—62no—
264C23×C32C22×D311yescharacteristic
265C23×C32C22×D311yescharacteristic
266C23×C32C22×D311yescharacteristic
267C23×C32C22×D311yescharacteristic
268C23×C32C23×C311yescharacteristic
269C23×C32C23×C311yescharacteristic
270C22×C3×D3—22no—
271C22×C3×D3—22no—
272C22×C3×D3—24no—
273C22×C3×D3—24no—
274C22×C3×D3—22no—
275C22×C3×D3—21no—
276C22×C3×D3—44no—
277C22×C3×D3—42no—
278C22×C3×D3C22×D311yescharacteristic
279C22×C3×D3C22×D312yes—
280C22×C3×D3C23×C311yescharacteristic
281C22×C3×D3C23×C312yes—
282C32×Q8—62no—
283C32×D4—22no—
284C32×D4—24no—
285C32×D4—22no—
286C32×D4—22no—
287C32×D4—42no—
288C32×D4—42no—
289C32×D4—44no—
290C32×D4—62no—
291C32×D4—62no—
292C32×D4—64no—
293C2×C32×C4—21no—
294C2×C32×C4—21no—
295C2×C32×C4—21no—
296C2×C32×C4—34no—
297C2×C32×C4—31no—
298C2×C32×C4—31no—
299C2×C32×C4—32no—
300C2×C32×C4—31no—
301C2×C32×C4—41no—
302C2×C32×C4—62no—
303C2×C32×C4—62no—
304C2×C32×C4C22×D311yescharacteristic
305C2×C32×C4C22×D311yescharacteristic
306C2×C32×C4C23×C311yescharacteristic
307C2×C3⋊Dic3—22no—
308C2×C3⋊Dic3C23×C312yes—
309C2×C3⋊Dic3C23×C312yes—
310C3×#67—24no—
311C3×#67—24no—
312C3×#67—22no—
313C3×#67—22no—
314C3×#67—24no—
315C3×#67—24no—
316C3×#67—22no—
317C3×#67—22no—
318C3×#67—44no—
319C3×#67—64no—
320C3×#67—64no—
321C2×C3×Dic3—24no—
322C2×C3×Dic3—22no—
323C2×C3×Dic3—22no—
324C2×C3×Dic3—24no—
325C2×C3×Dic3—21no—
326C2×C3×Dic3—21no—
327C2×C3×Dic3—21no—
328C2×C3×Dic3—22no—
329C2×C3×Dic3—32no—
330C2×C3×Dic3—32no—
331C2×C3×Dic3—32no—
332C2×C3×Dic3—32no—
333C2×C3×Dic3—62no—
334C2×C3×Dic3—62no—
335C2×C3×Dic3—62no—
336C2×C3×Dic3—62no—
337C2×C3×Dic3—64no—
338C2×C3×Dic3—64no—
339C2×C3×Dic3—122no—
340C2×C3×Dic3#6714yescomplemented
341C2×C3×Dic3C3×D414yescomplemented
342C2×C3×Dic3C22×D312yes—
343C2×C3×Dic3C22×D311yescharacteristic
344C2×C3×Dic3C22×D311yescharacteristic
345C2×C3×Dic3C22×D311yescharacteristic
346C2×C3×Dic3C23×C312yes—
347C2×C3×Dic3C23×C311yescharacteristic
348C2×C3×Dic3C23×C311yescharacteristic
349C2×C3×Dic3C23×C311yescharacteristic
350C3×C4×D3—24no—
351C3×C4×D3—22no—
352C3×C4×D3—22no—
353C3×C4×D3—64no—
354C3×C4×D3—64no—
355C3×Dic6—24no—
356C3×Dic6—22no—
357C3×Dic6—22no—
358#625—24no—
359D3×Dic3—24no—
360D3×Dic3—24no—
361#525—91noSylow
362C2×C33—22no—
363C2×C33—41no—
364C2×C33C22×D411yescharacteristic
365C2×C33C2×#4112yes—
366C32×D3—24no—
367C32×D3—41no—
368C24×C3—31no—
369C24×C3—31no—
370C24×C3—61no—
371C23×D3C2×C3×D311yescharacteristic
372C3×#41—64no—
373C3×#41—64no—
374C3×#41—68no—
375C2×C3×Q8—31no—
376C2×C3×Q8—31no—
377C2×C3×Q8—61no—
378C2×C3×D4—21no—
379C2×C3×D4—21no—
380C2×C3×D4—21no—
381C2×C3×D4—32no—
382C2×C3×D4—31no—
383C2×C3×D4—31no—
384C2×C3×D4—32no—
385C2×C3×D4—31no—
386C2×C3×D4—31no—
387C2×C3×D4—41no—
388C2×C3×D4—61no—
389C2×C3×D4—61no—
390C2×C3×D4—62no—
391C2×C3×D4—92no—
392C2×C3×D4D3211yescharacteristic
393C2×C3×D4C2×C3×D311yescharacteristic
394C2×C3×D4C2×C3×D311yescharacteristic
395C22×C3×C4—31no—
396C22×C3×C4—31no—
397C22×C3×C4—31no—
398C22×C3×C4—31no—
399C22×C3×C4—31no—
400C22×C3×C4—31no—
401C22×C3×C4—61no—
402C22×C3×C4—61no—
403C22×C3×C4—61no—
404C22×C3×C4—92no—
405C22×C3×C4—92no—
406C22×C3×C4—91no—
407C22×C3×C4—184no—
408C2×#67—32no—
409C2×#67—32no—
410C2×#67C2×C3×D311yescharacteristic
411C2×#67C2×C3×D312yes—
412C2×#67C2×C3×D311yescharacteristic, complemented
413C22×Dic3—31no—
414C22×Dic3—31no—
415C22×Dic3—32no—
416C22×Dic3—32no—
417C22×Dic3—61no—
418C22×Dic3—64no—
419C22×Dic3C2×C3×D311yescharacteristic
420C22×Dic3C2×C3×D311yescharacteristic, complemented
421#237—24no—
422C2×C4×D3—32no—
423C2×C4×D3—32no—
424C2×C4×D3—64no—
425C2×C4×D3C2×C3×D311yescharacteristic, complemented
426C2×Dic6C2×C3×D311yescharacteristic, complemented
427C3×C4⋊C4—92no—
428C3×C4⋊C4—92no—
429C3×C4⋊C4—92no—
430C3×C22⋊C4—31no—
431C3×C22⋊C4—31no—
432C3×C22⋊C4—32no—
433C3×C22⋊C4—32no—
434C3×C22⋊C4—62no—
435C3×C22⋊C4—61no—
436C3×C22⋊C4—92no—
437C3×C22⋊C4—92no—
438C3×C22⋊C4—91no—
439C3×C22⋊C4—92no—
440C3×C42—92no—
441#217—31no—
442#217—31no—
443#217—32no—
444#217—32no—
445#217—32no—
446#217—32no—
447#217—61no—
448#217—62no—
449#217C2×C3×D311yescharacteristic
450(C2×D3)⋊C4—32no—
451(C2×D3)⋊C4—32no—
452(C2×D3)⋊C4C2×C3×D312yes—
453C4⋊Dic3—32no—
454C4⋊Dic3—32no—
455Dic3⋊C4—32no—
456Dic3⋊C4—32no—
457Dic3⋊C4—32no—
458Dic3⋊C4—32no—
459Dic3⋊C4—62no—
460C4×Dic3—32no—
461C4×Dic3—32no—
462C22×C32—21no—
463C22×C32—22no—
464C22×C32—22no—
465C22×C32—22no—
466C22×C32—22no—
467C22×C32—22no—
468C22×C32—22no—
469C22×C32—21no—
470C22×C32—21no—
471C22×C32—22no—
472C22×C32—21no—
473C22×C32—21no—
474C22×C32—21no—
475C22×C32—22no—
476C22×C32—22no—
477C22×C32—22no—
478C22×C32—34no—
479C22×C32—41no—
480C22×C32—42no—
481C22×C32—41no—
482C22×C32—41no—
483C22×C32—42no—
484C22×C32—42no—
485C22×C32—42no—
486C22×C32—42no—
487C22×C32—42no—
488C22×C32—42no—
489C22×C32—42no—
490C22×C32—61no—
491C22×C32—68no—
492C22×C32—62no—
493C22×C32—62no—
494C22×C32—62no—
495C22×C32—82no—
496C22×C32—82no—
497C22×C32D3×D412yes—
498C22×C32C2×#6712yes—
499C22×C32C2×C3×D412yes—
500C22×C32C23×D311yescharacteristic
501C22×C32C23×D311yescharacteristic
502C22×C32C24×C311yescharacteristic
503C2×C3×D3—28no—
504C2×C3×D3—28no—
505C2×C3×D3—22no—
506C2×C3×D3—22no—
507C2×C3×D3—22no—
508C2×C3×D3—22no—
509C2×C3×D3—22no—
510C2×C3×D3—22no—
511C2×C3×D3—21no—
512C2×C3×D3—21no—
513C2×C3×D3—22no—
514C2×C3×D3—24no—
515C2×C3×D3—42no—
516C2×C3×D3—42no—
517C2×C3×D3—42no—
518C2×C3×D3—48no—
519C2×C3×D3#23714yescomplemented
520C2×C3×D3C3×#4114yescomplemented
521C32×C4—21no—
522C32×C4—22no—
523C32×C4—21no—
524C32×C4—21no—
525C32×C4—32no—
526C32×C4—32no—
527C32×C4—41no—
528C32×C4—41no—
529C32×C4—42no—
530C32×C4—61no—
531C32×C4—62no—
532C3⋊Dic3—22no—
533C3⋊Dic3—22no—
534C3×Dic3—22no—
535C3×Dic3—22no—
536C3×Dic3—21no—
537C3×Dic3—21no—
538C3×Dic3—22no—
539C3×Dic3—22no—
540C3×Dic3—22no—
541C3×Dic3—42no—
542C3×Dic3—62no—
543C3×Dic3—62no—
544C3×Dic3—62no—
545C3×Dic3—62no—
546C3×Dic3—122no—
547C3×Dic3—122no—
548C3×Dic3C2×#6712yes—
549C3×Dic3C2×#6712yes—
550C3×Dic3C2×C3×D412yes—
551C3×Dic3C2×C3×D412yes—
552C2×#41—31no—
553C23×C4—91no—
554#123—91no—
555#123—91no—
556C22⋊Q8—92no—
557#121—92no—
558#120—31no—
559#120—91no—
560C4×D4—92no—
561C4×D4—92no—
562#117—91no—
563C33#52511yescharacteristic, complemented, Sylow
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—21no—
570C23×C3—32no—
571C23×C3—32no—
572C23×C3—31no—
573C23×C3—31no—
574C23×C3—41no—
575C23×C3—41no—
576C23×C3—62no—
577C23×C3—61no—
578C23×C3—64no—
579C23×C3—64no—
580C23×C3—62no—
581C23×C3—62no—
582C23×C3—122no—
583C23×C3—124no—
584C23×C3C2×D3211yescharacteristic
585C23×C3C2×D3211yescharacteristic
586C23×C3C22×C3×D311yescharacteristic
587C23×C3C22×C3×D311yescharacteristic
588C23×C3C22×C3×D311yescharacteristic
589C23×C3C22×C3×D311yescharacteristic
590C22×D3—22no—
591C22×D3—24no—
592C22×D3C22×C3×D311yescharacteristic
593C22×D3C22×C3×D312yes—
594C3×Q8—62no—
595C3×Q8—62no—
596C3×Q8—64no—
597C3×D4—24no—
598C3×D4—22no—
599C3×D4—22no—
600C3×D4—22no—
601C3×D4—42no—
602C3×D4—42no—
603C3×D4—44no—
604C3×D4—62no—
605C3×D4—62no—
606C3×D4—64no—
607C3×D4—64no—
608C3×D4—64no—
609C3×D4—64no—
610C3×D4—62no—
611C3×D4—62no—
612C3×D4—124no—
613C3×D4—184no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—31no—
618C2×C3×C4—31no—
619C2×C3×C4—31no—
620C2×C3×C4—31no—
621C2×C3×C4—34no—
622C2×C3×C4—34no—
623C2×C3×C4—32no—
624C2×C3×C4—31no—
625C2×C3×C4—32no—
626C2×C3×C4—31no—
627C2×C3×C4—41no—
628C2×C3×C4—61no—
629C2×C3×C4—61no—
630C2×C3×C4—61no—
631C2×C3×C4—64no—
632C2×C3×C4—62no—
633C2×C3×C4—62no—
634C2×C3×C4—62no—
635C2×C3×C4—64no—
636C2×C3×C4—62no—
637C2×C3×C4—62no—
638C2×C3×C4—64no—
639C2×C3×C4—92no—
640C2×C3×C4—92no—
641C2×C3×C4—184no—
642C2×C3×C4—184no—
643C2×C3×C4—182no—
644C2×C3×C4C2×D3211yescharacteristic
645C2×C3×C4C22×C3×D311yescharacteristic
646C2×C3×C4C22×C3×D311yescharacteristic
647#67—22no—
648#67—24no—
649#67—22no—
650#67—64no—
651#67—64no—
652C2×Dic3—22no—
653C2×Dic3—32no—
654C2×Dic3—32no—
655C2×Dic3—32no—
656C2×Dic3—32no—
657C2×Dic3—62no—
658C2×Dic3—62no—
659C2×Dic3—62no—
660C2×Dic3—62no—
661C2×Dic3—64no—
662C2×Dic3—64no—
663C2×Dic3—122no—
664C2×Dic3C3×#6714yescomplemented
665C2×Dic3C22×C3×D312yes—
666C2×Dic3C22×C3×D311yescharacteristic
667C2×Dic3C22×C3×D311yescharacteristic
668C2×Dic3C22×C3×D311yescharacteristic
669C4×D3—22no—
670C4×D3—64no—
671C4×D3—64no—
672Dic6—22no—
673C2×C32—22no—
674C2×C32—22no—
675C2×C32—22no—
676C2×C32—22no—
677C2×C32—21no—
678C2×C32—21no—
679C2×C32—22no—
680C2×C32—22no—
681C2×C32—21no—
682C2×C32—41no—
683C2×C32—42no—
684C2×C32—42no—
685C2×C32—42no—
686C2×C32—42no—
687C2×C32—41no—
688C2×C32—42no—
689C2×C32—41no—
690C2×C32—41no—
691C2×C32—64no—
692C2×C32—82no—
693C2×C32—81no—
694C2×C32—81no—
695C2×C32—82no—
696C2×C32—121no—
697C2×C32C2×D3×D411yescharacteristic
698C2×C32C2×#23712yes—
699C2×C32D3×#4112yes—
700C2×C32C22×#6711yescharacteristic
701C2×C32C22×C3×D411yescharacteristic
702C2×C32C2×C3×#4112yes—
703C3×D3—24no—
704C3×D3—24no—
705C3×D3—44no—
706C3×D3—42no—
707C3×D3—41no—
708C3×D3—41no—
709C24—31no—
710#41—64no—
711C2×Q8—31no—
712C2×D4—32no—
713C2×D4—31no—
714C2×D4—31no—
715C2×D4—92no—
716C2×D4C3×D3211yescharacteristic
717C22×C4—31no—
718C22×C4—31no—
719C22×C4—31no—
720C22×C4—92no—
721C22×C4—92no—
722C22×C4—91no—
723C22×C4—184no—
724C4⋊C4—92no—
725C4⋊C4—92no—
726C4⋊C4—92no—
727C22⋊C4—31no—
728C22⋊C4—32no—
729C22⋊C4—92no—
730C22⋊C4—92no—
731C22⋊C4—91no—
732C22⋊C4—92no—
733C42—92no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—34no—
751C22×C3—34no—
752C22×C3—42no—
753C22×C3—42no—
754C22×C3—42no—
755C22×C3—42no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—42no—
759C22×C3—42no—
760C22×C3—42no—
761C22×C3—41no—
762C22×C3—42no—
763C22×C3—64no—
764C22×C3—68no—
765C22×C3—68no—
766C22×C3—62no—
767C22×C3—62no—
768C22×C3—62no—
769C22×C3—62no—
770C22×C3—62no—
771C22×C3—62no—
772C22×C3—61no—
773C22×C3—61no—
774C22×C3—62no—
775C22×C3—82no—
776C22×C3—82no—
777C22×C3—122no—
778C22×C3—122no—
779C22×C3—122no—
780C22×C3—128no—
781C22×C3D3×#6712yes—
782C22×C3C3×D3×D412yes—
783C22×C3C2×C3×#6712yes—
784C22×C3C22×D3211yescharacteristic
785C22×C3C23×C3×D311yescharacteristic
786C22×C3C23×C3×D311yescharacteristic
787C2×D3—28no—
788C2×D3—22no—
789C2×D3—22no—
790C2×D3—22no—
791C2×D3—21no—
792C2×D3C3×#23714yescomplemented
793C3×C4—22no—
794C3×C4—21no—
795C3×C4—21no—
796C3×C4—21no—
797C3×C4—32no—
798C3×C4—32no—
799C3×C4—32no—
800C3×C4—32no—
801C3×C4—41no—
802C3×C4—41no—
803C3×C4—42no—
804C3×C4—62no—
805C3×C4—62no—
806C3×C4—62no—
807C3×C4—62no—
808C3×C4—61no—
809C3×C4—61no—
810C3×C4—62no—
811C3×C4—122no—
812C3×C4—182no—
813C3×C4—182no—
814Dic3—22no—
815Dic3—21no—
816Dic3—62no—
817Dic3—62no—
818Dic3—62no—
819Dic3—62no—
820Dic3—122no—
821Dic3—122no—
822Dic3C2×C3×#6712yes—
823Dic3C2×C3×#6712yes—
824C32—21no—
825C32—21no—
826C32—21no—
827C32—41no—
828C32#558611yescharacteristic, complemented
829C32#582811yescharacteristic, complemented
830C32C3×#52511yescharacteristic, complemented
831C23—32no—
832C23—31no—
833C23—64no—
834C23—62no—
835C23C2×C3×D3211yescharacteristic
836C23C2×C3×D3211yescharacteristic
837Q8—62no—
838D4—22no—
839D4—62no—
840D4—64no—
841D4—62no—
842D4—184no—
843C2×C4—31no—
844C2×C4—31no—
845C2×C4—34no—
846C2×C4—32no—
847C2×C4—31no—
848C2×C4—62no—
849C2×C4—62no—
850C2×C4—92no—
851C2×C4—92no—
852C2×C4—184no—
853C2×C4—184no—
854C2×C4—182no—
855C2×C4C2×C3×D3211yescharacteristic
856C2×C3—22no—
857C2×C3—22no—
858C2×C3—22no—
859C2×C3—21no—
860C2×C3—21no—
861C2×C3—21no—
862C2×C3—22no—
863C2×C3—22no—
864C2×C3—22no—
865C2×C3—42no—
866C2×C3—42no—
867C2×C3—42no—
868C2×C3—42no—
869C2×C3—41no—
870C2×C3—41no—
871C2×C3—41no—
872C2×C3—41no—
873C2×C3—42no—
874C2×C3—64no—
875C2×C3—64no—
876C2×C3—82no—
877C2×C3—81no—
878C2×C3—81no—
879C2×C3—82no—
880C2×C3—124no—
881C2×C3—122no—
882C2×C3—121no—
883C2×C3—121no—
884C2×C3D3×#23712yes—
885C2×C3C2×D3×#6711yescharacteristic
886C2×C3C2×C3×D3×D411yescharacteristic
887C2×C3C2×C3×#23712yes—
888C2×C3C3×D3×#4112yes—
889C2×C3C22×C3×#6711yescharacteristic
890D3—24no—
891D3—41no—
892C22—22no—
893C22—21no—
894C22—22no—
895C22—34no—
896C22—68no—
897C22—62no—
898C22—62no—
899C22—61no—
900C22—62no—
901C22C3×D3×#6712yes—
902C22C22×C3×D3211yescharacteristic
903C4—21no—
904C4—32no—
905C4—32no—
906C4—61no—
907C4—62no—
908C4—182no—
909C4—182no—
910C3—21no—
911C3—21no—
912C3—21no—
913C3—41no—
914C3#1059515411yescharacteristic, direct product factor
915C3C3×#558611yescharacteristic, complemented
916C3C3×#582811yescharacteristic, complemented
917C2—22no—
918C2—41no—
919C2—64no—
920C2—121no—
921C2C3×D3×#23712yes—
922C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C3×#525
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×#237C2semidirect
2. C22×C3×D3×Dic3C2semidirect
3. C3×#64144C2semidirect
4. C32×#937C2semidirect
5. C3×#63976C2semidirect
6. C3×Dic3×#67C2semidirect
7. C3×#63970C2semidirect
8. C3×#63962C2semidirect
9. C3×#63955C2semidirect
10. C3×#63887C2semidirect
11. C3×#63879C2semidirect
14. #10595154C3direct (N × H)
20. C2×C32×#67C22semidirect
22. C22×C32×Dic3C22semidirect
24. C2×C32×C4×D3C22semidirect
25. C2×C32×Dic6C22semidirect
31. C3×#3757C22semidirect
32. C3×#3750C22semidirect
35. C3×Dic3⋊Dic3C22semidirect
36. C3×Dic3⋊Dic3C22semidirect
38. C3×(C2×D3)⋊Dic3C22semidirect
39. C3×Dic32C22semidirect
43. C2×C3×#237D3semidirect
44. C2×C3×#237C2×C3semidirect
46. C22×D3×Dic3C2×C3semidirect
48. #64144C2×C3semidirect
55. C3×#937D3semidirect
56. C3×#937C2×C3semidirect
69. #63976C2×C3semidirect
70. Dic3×#67C2×C3semidirect
71. #63970C2×C3semidirect
72. #63962C2×C3semidirect
73. #63955C2×C3semidirect
74. #63887C2×C3semidirect
75. #63879C2×C3semidirect
91. C2×C32×Dic3D4semidirect
131. C2×C3×#67C2×D3semidirect
134. C2×C3×#67C22×C3semidirect
144. C22×C3×Dic3C2×D3semidirect
146. C22×C3×Dic3C22×C3semidirect
154. C2×C3×C4×D3C2×D3semidirect
155. C2×C3×C4×D3C22×C3semidirect
157. C2×C3×Dic6C2×D3semidirect
158. C2×C3×Dic6C22×C3semidirect
166. #3757C22×C3semidirect
167. #3750C22×C3semidirect
193. Dic3⋊Dic3C22×C3semidirect
194. Dic3⋊Dic3C22×C3semidirect
196. (C2×D3)⋊Dic3C22×C3semidirect
197. Dic32C22×C3semidirect
208. C2×C32×D3#41semidirect
221. C2×#237C3×D3semidirect
239. #937C3×D3semidirect
340. C2×C3×Dic3#67semidirect
341. C2×C3×Dic3C3×D4semidirect
412. C2×#67C2×C3×D3semidirect
420. C22×Dic3C2×C3×D3semidirect
425. C2×C4×D3C2×C3×D3semidirect
426. C2×Dic6C2×C3×D3semidirect
519. C2×C3×D3#237semidirect
520. C2×C3×D3C3×#41semidirect
563. C33#525semidirect
664. C2×Dic3C3×#67semidirect
792. C2×D3C3×#237semidirect
828. C32#5586semidirect
829. C32#5828semidirect
830. C32C3×#525semidirect
914. C3#10595154direct (N × H)
915. C3C3×#5586semidirect
916. C3C3×#5828semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#2372
C22×C3×D3×Dic32
C3×#641442
C32×#9372
C3×#639762
C3×Dic3×#672
C3×#639702
C3×#639622
C3×#639552
C3×#638872
C3×#638792
C3×#58283
C3×#55863
#105951543