Finite Group Databasebeta

← C3×#10595064 #13174661

Subgroups — C3×#10595064 #13174661

Order 1728.

1742 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#235C211yesmaximal, characteristic, complemented
2C2×C3×D3×D12C211yesmaximal, characteristic, complemented
3C3×#64139C211yesmaximal, characteristic, complemented
4C32×#930C211yesmaximal, characteristic, complemented
5C3×#63983C212yesmaximal, complemented
6C3×#63979C212yesmaximal, complemented
7C3×#63922C212yesmaximal, complemented
8C3×#63909C211yesmaximal, characteristic, complemented
9C3×#63908C211yesmaximal, characteristic, complemented
10C3×#63907C212yesmaximal, complemented
11C3×#63841C211yesmaximal, characteristic, complemented
12C3×#5830—31nomaximal
13C3×#5607—31nomaximal
14#10595064C311yesmaximal, characteristic, direct product factor
15C22×C3×D32C2212yes—
16C22×C33×C4C2211yescharacteristic, complemented
17C2×C3×#638C2212yescomplemented
18C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×C32×#67C2211yescharacteristic
20C2×C32×#67C2211yescharacteristic, complemented
21C2×C32×#67C2212yescomplemented
22C32×#235—24no—
23C2×C32×D12C2211yescharacteristic
24C2×C32×D12C2211yescharacteristic
25C2×C32×C4×D3C2211yescharacteristic
26C2×C32×C4×D3C2211yescharacteristic, complemented
27C2×C32×Dic6C2211yescharacteristic, complemented
28C2×C3×#626C2212yes—
29C2×C3×#626C2212yescomplemented
30C2×C3×#625C2212yescomplemented
31C3×D3×D12—24no—
32C3×#3752C2212yescomplemented
33C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
34C32×(C2×D3)⋊C4C2212yescomplemented
35C32×C4⋊Dic3C2211yescharacteristic, complemented
36C3×#3722C2212yescomplemented
37C3×(C2×D3)⋊Dic3C2212yes—
38C3×(C2×D3)⋊Dic3C2212yescomplemented
39C3×Dic32C2212yescomplemented
40C2×C32×#41—31no—
41C2×C3×D3×D4—31no—
42C2×C3×#235—21no—
43C2×C3×#235D311yescharacteristic, complemented
44C2×C3×#235C2×C311yescharacteristic, complemented
45C22×C3×D12—31no—
46C2×D3×D12C2×C311yescharacteristic, complemented
47C32×#121—31no—
48#64139C2×C311yescharacteristic, complemented
49C3×#947—32no—
50C3×#940—32no—
51C3×#940—32no—
52C3×#938—31no—
53C3×#937—32no—
54C3×#937—32no—
55C3×#937—32no—
56C3×#930—21no—
57C3×#930—31no—
58C3×#930—31no—
59C3×#930—31no—
60C3×#930—31no—
61C3×#930—61no—
62C3×#930D311yescharacteristic, complemented
63C3×#930C2×C311yescharacteristic, complemented
64C3×#926—31no—
65C3×#895—31no—
66C3×#892—31no—
67C3×#885—32no—
68C3×#882—32no—
69#63983C2×C312yescomplemented
70#63979C2×C312yescomplemented
71#63922C2×C312yescomplemented
72#63909C2×C311yescharacteristic, complemented
73#63908C2×C311yescharacteristic, complemented
74#63907C2×C312yescomplemented
75#63841C2×C311yescharacteristic, complemented
76C23×C33C2311yescharacteristic
77C22×C3×C3⋊D3C2312yes—
78C22×C32×D3C2312yes—
79C22×C32×D3C2311yescharacteristic
80C22×C32×D3C2311yescharacteristic
81C2×C3×D32—24no—
82C2×C3×D32—42no—
83C2×C3×D32—42no—
84C2×C33×C4—22no—
85C2×C33×C4C2311yescharacteristic
86C2×C33×C4C2311yescharacteristic
87C3×#638—42no—
88C2×C3×C3⋊Dic3C2312yes—
89C3×C4⋊(C3⋊D3)—22no—
90C32×#67—22no—
91C32×#67—22no—
92C32×#67—42no—
93C2×C32×Dic3C2312yes—
94C2×C32×Dic3C2311yescharacteristic
95C2×C32×Dic3C2311yescharacteristic
96C32×D12—22no—
97C32×D12—22no—
98C32×C4×D3—22no—
99C32×C4×D3D414yescomplemented
100C32×Dic6—22no—
101C3×#626—24no—
102C3×#626—42no—
103C3×#625—42no—
104C3×#535—91no—
105#5830—31no—
106#5607—31no—
107C23×C3×D3—32no—
108C23×C3×D3—32no—
109C22×D32C22×C312yes—
110C32×#41—64no—
111C2×C32×Q8—31no—
112C2×C32×D4—31no—
113C2×C32×D4—31no—
114C2×C32×D4—32no—
115C2×C32×D4—31no—
116C2×C32×D4—31no—
117C22×C32×C4—21no—
118C22×C32×C4—21no—
119C22×C32×C4—21no—
120C22×C32×C4—31no—
121C22×C32×C4—31no—
122C22×C32×C4—41no—
123C22×C32×C4C2×D311yescharacteristic, complemented
124C22×C32×C4C2×D311yescharacteristic, complemented
125C22×C32×C4C22×C311yescharacteristic, complemented
126C2×#638C22×C312yescomplemented
127C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
128C2×C3×#67—21no—
129C2×C3×#67—21no—
130C2×C3×#67—22no—
131C2×C3×#67—32no—
132C2×C3×#67—32no—
133C2×C3×#67—32no—
134C2×C3×#67—32no—
135C2×C3×#67—32no—
136C2×C3×#67—32no—
137C2×C3×#67—62no—
138C2×C3×#67C2×D311yescharacteristic
139C2×C3×#67C2×D311yescharacteristic, complemented
140C2×C3×#67C2×D312yescomplemented
141C2×C3×#67C22×C311yescharacteristic
142C2×C3×#67C22×C311yescharacteristic, complemented
143C2×C3×#67C22×C312yescomplemented
144C3×D3×D4—64no—
145C3×#235—28no—
146C3×#235—24no—
147C3×#235—24no—
148C2×C3×D12—21no—
149C2×C3×D12—21no—
150C2×C3×D12—32no—
151C2×C3×D12—31no—
152C2×C3×D12—31no—
153C2×C3×D12—32no—
154C2×C3×D12—64no—
155C2×C3×D12—61no—
156C2×C3×D12C2×D311yescharacteristic
157C2×C3×D12C2×D311yescharacteristic
158C2×C3×D12C22×C311yescharacteristic
159C2×C3×D12C22×C311yescharacteristic
160C2×C3×C4×D3—21no—
161C2×C3×C4×D3—21no—
162C2×C3×C4×D3C2×D311yescharacteristic
163C2×C3×C4×D3C2×D311yescharacteristic, complemented
164C2×C3×C4×D3C22×C311yescharacteristic
165C2×C3×C4×D3C22×C311yescharacteristic, complemented
166C2×C3×Dic6—21no—
167C2×C3×Dic6C2×D311yescharacteristic, complemented
168C2×C3×Dic6C22×C311yescharacteristic, complemented
169C2×#626C22×C312yes—
170C2×#626C22×C312yescomplemented
171C2×#625C22×C312yescomplemented
172D3×D12—24no—
173C32×C4⋊C4—31no—
174C32×C22⋊C4—32no—
175#3752C22×C312yescomplemented
176C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
177C3×#217—32no—
178C3×#217—32no—
179C3×(C2×D3)⋊C4—22no—
180C3×(C2×D3)⋊C4—32no—
181C3×(C2×D3)⋊C4—32no—
182C3×(C2×D3)⋊C4—32no—
183C3×(C2×D3)⋊C4—32no—
184C3×(C2×D3)⋊C4—32no—
185C3×(C2×D3)⋊C4—32no—
186C3×(C2×D3)⋊C4—62no—
187C3×(C2×D3)⋊C4C2×D312yescomplemented
188C3×(C2×D3)⋊C4C22×C312yescomplemented
189C3×C4⋊Dic3—21no—
190C3×C4⋊Dic3—31no—
191C3×C4⋊Dic3—31no—
192C3×C4⋊Dic3—61no—
193C3×C4⋊Dic3C2×D311yescharacteristic, complemented
194C3×C4⋊Dic3C22×C311yescharacteristic, complemented
195C3×C4×Dic3—32no—
196C3×C4×Dic3—32no—
197#3722C22×C312yescomplemented
198(C2×D3)⋊Dic3C22×C312yes—
199(C2×D3)⋊Dic3C22×C312yescomplemented
200Dic32C22×C312yescomplemented
201C22×C33—21no—
202C22×C33—21no—
203C22×C33—21no—
204C22×C33C2411yescharacteristic
205C2×C3×C3⋊D3—22no—
206C2×C3×C3⋊D3—22no—
207C2×C3×C3⋊D3—22no—
208C2×C32×D3—21no—
209C2×C32×D3—21no—
210C2×C32×D3—21no—
211C2×C32×D3—22no—
212C2×C32×D3—21no—
213C2×C32×D3—22no—
214C2×C32×D3—21no—
215C2×C32×D3—22no—
216C2×C32×D3C2×D412yes—
217C3×D32—48no—
218C33×C4—21no—
219C33×C4C2×D412yes—
220C3×C3⋊Dic3—22no—
221C32×Dic3—21no—
222C32×Dic3—22no—
223C32×Dic3C2×D412yes—
224C2×C3×#41—31no—
225C2×C3×#41—31no—
226C2×C3×#41—61no—
227C22×C3×D4—91no—
228C2×D3×D4—31no—
229C2×#235C3×D311yescharacteristic, complemented
230C22×D12—31no—
231C3×#127—92no—
232C3×#124—92no—
233C3×#121—31no—
234C3×#121—31no—
235C3×#121—61no—
236C3×#121—91no—
237C3×#121—91no—
238C3×#121—91no—
239C3×#120—92no—
240C3×#120—92no—
241C3×#117—91no—
242#947—32no—
243#940—32no—
244#940—32no—
245#938—31no—
246#937—32no—
247#937—32no—
248#937—32no—
249#930—31no—
250#930—31no—
251#930—31no—
252#930—31no—
253#930—61no—
254#930C3×D311yescharacteristic, complemented
255#926—31no—
256#895—31no—
257#892—31no—
258#885—32no—
259#882—32no—
260C23×C32—21no—
261C23×C32—21no—
262C23×C32—21no—
263C23×C32—31no—
264C23×C32—32no—
265C23×C32—31no—
266C23×C32—41no—
267C23×C32C22×D311yescharacteristic
268C23×C32C22×D311yescharacteristic
269C23×C32C23×C311yescharacteristic
270C22×C3⋊D3C23×C312yes—
271C22×C3×D3—21no—
272C22×C3×D3—21no—
273C22×C3×D3—22no—
274C22×C3×D3—32no—
275C22×C3×D3—32no—
276C22×C3×D3—62no—
277C22×C3×D3—64no—
278C22×C3×D3—64no—
279C22×C3×D3—122no—
280C22×C3×D3—122no—
281C22×C3×D3—122no—
282C22×C3×D3—122no—
283C22×C3×D3C22×D312yes—
284C22×C3×D3C22×D311yescharacteristic
285C22×C3×D3C22×D311yescharacteristic
286C22×C3×D3C23×C312yes—
287C22×C3×D3C23×C311yescharacteristic
288C22×C3×D3C23×C311yescharacteristic
289C2×D32—24no—
290C2×D32—42no—
291C2×D32—42no—
292C32×Q8—62no—
293C32×D4—62no—
294C32×D4—62no—
295C32×D4—62no—
296C32×D4—62no—
297C32×D4—122no—
298C2×C32×C4—22no—
299C2×C32×C4—24no—
300C2×C32×C4—22no—
301C2×C32×C4—22no—
302C2×C32×C4—21no—
303C2×C32×C4—21no—
304C2×C32×C4—21no—
305C2×C32×C4—21no—
306C2×C32×C4—21no—
307C2×C32×C4—21no—
308C2×C32×C4—31no—
309C2×C32×C4—34no—
310C2×C32×C4—32no—
311C2×C32×C4—31no—
312C2×C32×C4—41no—
313C2×C32×C4—41no—
314C2×C32×C4—42no—
315C2×C32×C4—42no—
316C2×C32×C4—44no—
317C2×C32×C4—62no—
318C2×C32×C4C22×D311yescharacteristic
319C2×C32×C4C22×D311yescharacteristic
320C2×C32×C4C22×D311yescharacteristic
321C2×C32×C4C22×D311yescharacteristic
322C2×C32×C4C23×C311yescharacteristic
323C2×C32×C4C23×C311yescharacteristic
324#638—42no—
325C2×C3⋊Dic3C23×C312yes—
326C4⋊(C3⋊D3)—22no—
327C3×#67—24no—
328C3×#67—24no—
329C3×#67—22no—
330C3×#67—22no—
331C3×#67—22no—
332C3×#67—22no—
333C3×#67—42no—
334C3×#67—42no—
335C3×#67—44no—
336C3×#67—64no—
337C3×#67—122no—
338C3×#67—122no—
339C3×#67—122no—
340C3×#67—122no—
341C3×#67—122no—
342C3×#67—124no—
343C2×C3×Dic3—21no—
344C2×C3×Dic3—21no—
345C2×C3×Dic3—22no—
346C2×C3×Dic3—32no—
347C2×C3×Dic3—32no—
348C2×C3×Dic3—62no—
349C2×C3×Dic3C22×D312yes—
350C2×C3×Dic3C22×D311yescharacteristic
351C2×C3×Dic3C22×D311yescharacteristic
352C2×C3×Dic3C23×C312yes—
353C2×C3×Dic3C23×C311yescharacteristic
354C2×C3×Dic3C23×C311yescharacteristic
355C3×D12—24no—
356C3×D12—22no—
357C3×D12—22no—
358C3×D12—22no—
359C3×D12—22no—
360C3×D12—42no—
361C3×D12—64no—
362C3×D12—62no—
363C3×D12—62no—
364C3×D12—122no—
365C3×D12—122no—
366C3×C4×D3—24no—
367C3×C4×D3—22no—
368C3×C4×D3—22no—
369C3×C4×D3—24no—
370C3×C4×D3#6714yescomplemented
371C3×C4×D3C3×D414yescomplemented
372C3×Dic6—24no—
373C3×Dic6—22no—
374C3×Dic6—22no—
375#626—24no—
376#626—42no—
377#625—42no—
378#535—91noSylow
379C2×C33—41no—
380C2×C33C22×D411yescharacteristic
381C2×C33H(5,𝔽2)11yescharacteristic
382C2×C33H(5,𝔽2)11yescharacteristic
383C3×C3⋊D3—42no—
384C32×D3—22no—
385C32×D3—41no—
386C32×D3—42no—
387C24×C3—92no—
388C23×D3—32no—
389C23×D3—32no—
390C3×#41—64no—
391C3×#41—64no—
392C3×#41—68no—
393C2×C3×Q8—31no—
394C2×C3×Q8—31no—
395C2×C3×Q8—61no—
396C2×C3×D4—31no—
397C2×C3×D4—31no—
398C2×C3×D4—31no—
399C2×C3×D4—31no—
400C2×C3×D4—32no—
401C2×C3×D4—32no—
402C2×C3×D4—31no—
403C2×C3×D4—31no—
404C2×C3×D4—31no—
405C2×C3×D4—31no—
406C2×C3×D4—61no—
407C2×C3×D4—61no—
408C2×C3×D4—61no—
409C2×C3×D4—61no—
410C2×C3×D4—62no—
411C2×C3×D4—92no—
412C2×C3×D4—92no—
413C2×C3×D4—92no—
414C2×C3×D4—92no—
415C2×C3×D4—91no—
416C2×C3×D4—184no—
417C22×C3×C4—21no—
418C22×C3×C4—21no—
419C22×C3×C4—21no—
420C22×C3×C4—31no—
421C22×C3×C4—31no—
422C22×C3×C4—31no—
423C22×C3×C4—31no—
424C22×C3×C4—41no—
425C22×C3×C4—61no—
426C22×C3×C4—61no—
427C22×C3×C4D3211yescharacteristic, complemented
428C22×C3×C4C2×C3×D311yescharacteristic, complemented
429C22×C3×C4C2×C3×D311yescharacteristic, complemented
430C2×#67—32no—
431C2×#67—32no—
432C2×#67—32no—
433C2×#67—32no—
434C2×#67—32no—
435C2×#67—32no—
436C2×#67—62no—
437C2×#67C2×C3×D311yescharacteristic
438C2×#67C2×C3×D311yescharacteristic, complemented
439C2×#67C2×C3×D312yescomplemented
440D3×D4—64no—
441#235—24no—
442C2×D12—32no—
443C2×D12—31no—
444C2×D12—31no—
445C2×D12—32no—
446C2×D12—61no—
447C2×D12—64no—
448C2×D12C2×C3×D311yescharacteristic
449C2×D12C2×C3×D311yescharacteristic
450C2×C4×D3C2×C3×D311yescharacteristic
451C2×C4×D3C2×C3×D311yescharacteristic, complemented
452C2×Dic6C2×C3×D311yescharacteristic, complemented
453C3×C4⋊C4—31no—
454C3×C4⋊C4—31no—
455C3×C4⋊C4—61no—
456C3×C4⋊C4—91no—
457C3×C22⋊C4—32no—
458C3×C22⋊C4—32no—
459C3×C22⋊C4—62no—
460C3×C22⋊C4—92no—
461C3×C22⋊C4—92no—
462C3×C22⋊C4—92no—
463C3×C22⋊C4—92no—
464C3×C42—92no—
465#217—32no—
466#217—32no—
467(C2×D3)⋊C4—32no—
468(C2×D3)⋊C4—32no—
469(C2×D3)⋊C4—32no—
470(C2×D3)⋊C4—32no—
471(C2×D3)⋊C4—32no—
472(C2×D3)⋊C4—32no—
473(C2×D3)⋊C4—62no—
474(C2×D3)⋊C4C2×C3×D312yescomplemented
475C4⋊Dic3—31no—
476C4⋊Dic3—31no—
477C4⋊Dic3—61no—
478C4⋊Dic3C2×C3×D311yescharacteristic, complemented
479C4×Dic3—32no—
480C4×Dic3—32no—
481C22×C32—21no—
482C22×C32—21no—
483C22×C32—21no—
484C22×C32—22no—
485C22×C32—22no—
486C22×C32—22no—
487C22×C32—21no—
488C22×C32—21no—
489C22×C32—21no—
490C22×C32—21no—
491C22×C32—21no—
492C22×C32—21no—
493C22×C32—21no—
494C22×C32—21no—
495C22×C32—21no—
496C22×C32—32no—
497C22×C32—41no—
498C22×C32—41no—
499C22×C32—41no—
500C22×C32—41no—
501C22×C32—41no—
502C22×C32—41no—
503C22×C32—41no—
504C22×C32—42no—
505C22×C32—42no—
506C22×C32—42no—
507C22×C32—61no—
508C22×C32—61no—
509C22×C32—61no—
510C22×C32—61no—
511C22×C32—61no—
512C22×C32—62no—
513C22×C32—62no—
514C22×C32—62no—
515C22×C32C23×D311yescharacteristic
516C22×C32C23×D311yescharacteristic
517C22×C32C24×C311yescharacteristic
518C2×C3⋊D3—22no—
519C2×C3⋊D3—22no—
520C2×C3⋊D3—22no—
521C2×C3×D3—21no—
522C2×C3×D3—21no—
523C2×C3×D3—21no—
524C2×C3×D3—21no—
525C2×C3×D3—22no—
526C2×C3×D3—22no—
527C2×C3×D3—22no—
528C2×C3×D3—21no—
529C2×C3×D3—21no—
530C2×C3×D3—22no—
531C2×C3×D3—21no—
532C2×C3×D3—22no—
533C2×C3×D3—21no—
534C2×C3×D3—21no—
535C2×C3×D3—22no—
536C2×C3×D3—21no—
537C2×C3×D3—22no—
538C2×C3×D3—22no—
539C2×C3×D3—41no—
540C2×C3×D3—41no—
541C2×C3×D3—41no—
542C2×C3×D3—41no—
543C2×C3×D3—42no—
544C2×C3×D3—42no—
545C2×C3×D3—42no—
546C2×C3×D3—62no—
547C2×C3×D3—62no—
548C2×C3×D3—62no—
549C2×C3×D3—62no—
550C2×C3×D3—62no—
551C2×C3×D3—62no—
552C2×C3×D3—122no—
553C2×C3×D3—122no—
554C2×C3×D3—122no—
555C2×C3×D3—128no—
556C2×C3×D3—128no—
557C2×C3×D3C2×#6712yes—
558C2×C3×D3C2×C3×D412yes—
559D32—48no—
560C32×C4—21no—
561C32×C4—22no—
562C32×C4—21no—
563C32×C4—21no—
564C32×C4—22no—
565C32×C4—22no—
566C32×C4—22no—
567C32×C4—32no—
568C32×C4—42no—
569C32×C4—41no—
570C32×C4—41no—
571C32×C4—42no—
572C32×C4—61no—
573C32×C4—62no—
574C32×C4D3×D412yes—
575C32×C4C2×#6712yes—
576C32×C4C2×C3×D412yes—
577C3⋊Dic3—22no—
578C3×Dic3—22no—
579C3×Dic3—22no—
580C3×Dic3—21no—
581C3×Dic3—21no—
582C3×Dic3—22no—
583C3×Dic3—22no—
584C3×Dic3—42no—
585C3×Dic3—62no—
586C3×Dic3—62no—
587C3×Dic3—122no—
588C3×Dic3C2×#6712yes—
589C3×Dic3C2×C3×D412yes—
590C2×#41—31no—
591C22×D4—91no—
592#127—92no—
593#124—92no—
594#121—31no—
595#121—91no—
596#121—91no—
597#121—91no—
598#120—92no—
599#120—92no—
600#117—91no—
601C33#53511yescharacteristic, complemented, Sylow
602C23×C3—21no—
603C23×C3—21no—
604C23×C3—21no—
605C23×C3—31no—
606C23×C3—31no—
607C23×C3—32no—
608C23×C3—31no—
609C23×C3—32no—
610C23×C3—31no—
611C23×C3—41no—
612C23×C3—61no—
613C23×C3—61no—
614C23×C3—62no—
615C23×C3—92no—
616C23×C3—184no—
617C23×C3—362no—
618C23×C3—362no—
619C23×C3C2×D3211yescharacteristic
620C23×C3C22×C3×D311yescharacteristic
621C23×C3C22×C3×D311yescharacteristic
622C22×D3—32no—
623C22×D3—32no—
624C22×D3—62no—
625C22×D3—64no—
626C22×D3—64no—
627C22×D3—122no—
628C22×D3—122no—
629C22×D3—122no—
630C22×D3—122no—
631C22×D3C22×C3×D312yes—
632C22×D3C22×C3×D311yescharacteristic
633C22×D3C22×C3×D311yescharacteristic
634C3×Q8—62no—
635C3×Q8—62no—
636C3×Q8—64no—
637C3×D4—62no—
638C3×D4—62no—
639C3×D4—64no—
640C3×D4—62no—
641C3×D4—62no—
642C3×D4—62no—
643C3×D4—62no—
644C3×D4—64no—
645C3×D4—64no—
646C3×D4—62no—
647C3×D4—62no—
648C3×D4—122no—
649C3×D4—122no—
650C3×D4—122no—
651C3×D4—124no—
652C3×D4—184no—
653C3×D4—182no—
654C3×D4—362no—
655C3×D4—362no—
656C3×D4—362no—
657C2×C3×C4—24no—
658C2×C3×C4—22no—
659C2×C3×C4—22no—
660C2×C3×C4—22no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—31no—
668C2×C3×C4—31no—
669C2×C3×C4—34no—
670C2×C3×C4—34no—
671C2×C3×C4—32no—
672C2×C3×C4—31no—
673C2×C3×C4—32no—
674C2×C3×C4—31no—
675C2×C3×C4—42no—
676C2×C3×C4—42no—
677C2×C3×C4—44no—
678C2×C3×C4—41no—
679C2×C3×C4—41no—
680C2×C3×C4—64no—
681C2×C3×C4—61no—
682C2×C3×C4—61no—
683C2×C3×C4—62no—
684C2×C3×C4—64no—
685C2×C3×C4—62no—
686C2×C3×C4—62no—
687C2×C3×C4—92no—
688C2×C3×C4C2×D3211yescharacteristic
689C2×C3×C4C2×D3211yescharacteristic
690C2×C3×C4C22×C3×D311yescharacteristic
691C2×C3×C4C22×C3×D311yescharacteristic
692C2×C3×C4C22×C3×D311yescharacteristic
693C2×C3×C4C22×C3×D311yescharacteristic
694#67—22no—
695#67—22no—
696#67—42no—
697#67—64no—
698#67—122no—
699#67—122no—
700#67—122no—
701#67—122no—
702#67—122no—
703#67—124no—
704C2×Dic3—32no—
705C2×Dic3—32no—
706C2×Dic3—62no—
707C2×Dic3C22×C3×D312yes—
708C2×Dic3C22×C3×D311yescharacteristic
709C2×Dic3C22×C3×D311yescharacteristic
710D12—22no—
711D12—22no—
712D12—64no—
713D12—62no—
714D12—62no—
715D12—122no—
716D12—122no—
717C4×D3—22no—
718C4×D3C3×#6714yescomplemented
719Dic6—22no—
720C2×C32—21no—
721C2×C32—21no—
722C2×C32—21no—
723C2×C32—21no—
724C2×C32—21no—
725C2×C32—21no—
726C2×C32—21no—
727C2×C32—21no—
728C2×C32—21no—
729C2×C32—41no—
730C2×C32—41no—
731C2×C32—41no—
732C2×C32—42no—
733C2×C32—42no—
734C2×C32—42no—
735C2×C32—44no—
736C2×C32—41no—
737C2×C32—41no—
738C2×C32—41no—
739C2×C32—62no—
740C2×C32—121no—
741C2×C32—122no—
742C2×C32C2×D3×D411yescharacteristic
743C2×C32#100411yescharacteristic
744C2×C32#100911yescharacteristic
745C2×C32#100911yescharacteristic
746C2×C32#100911yescharacteristic
747C2×C32C22×#6711yescharacteristic
748C2×C32C22×C3×D411yescharacteristic
749C2×C32C3×H(5,𝔽2)11yescharacteristic
750C2×C32C3×H(5,𝔽2)11yescharacteristic
751C3⋊D3—42no—
752C3×D3—22no—
753C3×D3—22no—
754C3×D3—42no—
755C3×D3—42no—
756C3×D3—41no—
757C3×D3—42no—
758C3×D3—42no—
759C3×D3—41no—
760C3×D3—82no—
761C3×D3—122no—
762C3×D3—122no—
763C3×D3—242no—
764C24—92no—
765#41—64no—
766C2×Q8—31no—
767C2×D4—31no—
768C2×D4—31no—
769C2×D4—32no—
770C2×D4—31no—
771C2×D4—31no—
772C2×D4—92no—
773C2×D4—92no—
774C2×D4—92no—
775C2×D4—92no—
776C2×D4—91no—
777C2×D4—184no—
778C22×C4—31no—
779C22×C4—31no—
780C22×C4C3×D3211yescharacteristic, complemented
781C4⋊C4—31no—
782C4⋊C4—91no—
783C22⋊C4—32no—
784C22⋊C4—92no—
785C22⋊C4—92no—
786C22⋊C4—92no—
787C22⋊C4—92no—
788C42—92no—
789C22×C3—22no—
790C22×C3—22no—
791C22×C3—22no—
792C22×C3—21no—
793C22×C3—21no—
794C22×C3—21no—
795C22×C3—21no—
796C22×C3—21no—
797C22×C3—21no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—21no—
801C22×C3—21no—
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—32no—
805C22×C3—32no—
806C22×C3—41no—
807C22×C3—41no—
808C22×C3—41no—
809C22×C3—41no—
810C22×C3—41no—
811C22×C3—41no—
812C22×C3—42no—
813C22×C3—42no—
814C22×C3—42no—
815C22×C3—41no—
816C22×C3—62no—
817C22×C3—62no—
818C22×C3—61no—
819C22×C3—61no—
820C22×C3—61no—
821C22×C3—61no—
822C22×C3—62no—
823C22×C3—61no—
824C22×C3—61no—
825C22×C3—62no—
826C22×C3—61no—
827C22×C3—62no—
828C22×C3—61no—
829C22×C3—61no—
830C22×C3—61no—
831C22×C3—62no—
832C22×C3—62no—
833C22×C3—62no—
834C22×C3—121no—
835C22×C3—121no—
836C22×C3—121no—
837C22×C3—121no—
838C22×C3—122no—
839C22×C3—122no—
840C22×C3—122no—
841C22×C3—182no—
842C22×C3—182no—
843C22×C3—182no—
844C22×C3—368no—
845C22×C3C22×D3211yescharacteristic
846C22×C3C23×C3×D311yescharacteristic
847C22×C3C23×C3×D311yescharacteristic
848C2×D3—21no—
849C2×D3—21no—
850C2×D3—22no—
851C2×D3—22no—
852C2×D3—21no—
853C2×D3—21no—
854C2×D3—22no—
855C2×D3—21no—
856C2×D3—62no—
857C2×D3—62no—
858C2×D3—62no—
859C2×D3—62no—
860C2×D3—62no—
861C2×D3—62no—
862C2×D3—122no—
863C2×D3—122no—
864C2×D3—122no—
865C2×D3—128no—
866C2×D3—128no—
867C2×D3C2×C3×#6712yes—
868C3×C4—22no—
869C3×C4—21no—
870C3×C4—21no—
871C3×C4—21no—
872C3×C4—22no—
873C3×C4—22no—
874C3×C4—22no—
875C3×C4—32no—
876C3×C4—32no—
877C3×C4—41no—
878C3×C4—41no—
879C3×C4—42no—
880C3×C4—42no—
881C3×C4—62no—
882C3×C4—62no—
883C3×C4—62no—
884C3×C4—61no—
885C3×C4—61no—
886C3×C4—62no—
887C3×C4—122no—
888C3×C4—182no—
889C3×C4D3×#6712yes—
890C3×C4C3×D3×D412yes—
891C3×C4C2×C3×#6712yes—
892Dic3—22no—
893Dic3—21no—
894Dic3—62no—
895Dic3—62no—
896Dic3—122no—
897Dic3C2×C3×#6712yes—
898C32—21no—
899C32—21no—
900C32—21no—
901C32—41no—
902C32#560711yescharacteristic, complemented
903C32#583011yescharacteristic, complemented
904C32C3×#53511yescharacteristic, complemented
905C23—31no—
906C23—32no—
907C23—31no—
908C23—92no—
909C23—184no—
910C23—362no—
911C23—362no—
912C23C2×C3×D3211yescharacteristic
913Q8—62no—
914D4—62no—
915D4—62no—
916D4—62no—
917D4—62no—
918D4—122no—
919D4—184no—
920D4—182no—
921D4—362no—
922D4—362no—
923D4—362no—
924C2×C4—22no—
925C2×C4—31no—
926C2×C4—34no—
927C2×C4—32no—
928C2×C4—31no—
929C2×C4—62no—
930C2×C4—92no—
931C2×C4C2×C3×D3211yescharacteristic
932C2×C4C2×C3×D3211yescharacteristic
933C2×C3—21no—
934C2×C3—21no—
935C2×C3—21no—
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—21no—
939C2×C3—21no—
940C2×C3—21no—
941C2×C3—21no—
942C2×C3—42no—
943C2×C3—42no—
944C2×C3—42no—
945C2×C3—44no—
946C2×C3—41no—
947C2×C3—41no—
948C2×C3—41no—
949C2×C3—41no—
950C2×C3—41no—
951C2×C3—41no—
952C2×C3—62no—
953C2×C3—62no—
954C2×C3—122no—
955C2×C3—122no—
956C2×C3—122no—
957C2×C3—121no—
958C2×C3—122no—
959C2×C3—121no—
960C2×C3—242no—
961C2×C3—362no—
962C2×C3#6430711yescharacteristic
963C2×C3#6430811yescharacteristic
964C2×C3C2×D3×#6711yescharacteristic
965C2×C3C2×C3×D3×D411yescharacteristic
966C2×C3C3×#100411yescharacteristic
967C2×C3C3×#100911yescharacteristic
968C2×C3C3×#100911yescharacteristic
969C2×C3C3×#100911yescharacteristic
970C2×C3C22×C3×#6711yescharacteristic
971D3—22no—
972D3—41no—
973D3—42no—
974D3—122no—
975D3—122no—
976D3—242no—
977C22—21no—
978C22—21no—
979C22—21no—
980C22—32no—
981C22—61no—
982C22—61no—
983C22—61no—
984C22—62no—
985C22—62no—
986C22—61no—
987C22—61no—
988C22—62no—
989C22—182no—
990C22—182no—
991C22—182no—
992C22—368no—
993C22C22×C3×D3211yescharacteristic
994C4—21no—
995C4—32no—
996C4—61no—
997C4—62no—
998C4—182no—
999C4C3×D3×#6712yes—
1000C3—21no—
1001C3—21no—
1002C3—21no—
1003C3—41no—
1004C3#1059506411yescharacteristic, direct product factor
1005C3C3×#560711yescharacteristic, complemented
1006C3C3×#583011yescharacteristic, complemented
1007C2—41no—
1008C2—62no—
1009C2—122no—
1010C2—121no—
1011C2—362no—
1012C2C3×#6430711yescharacteristic
1013C2C3×#6430811yescharacteristic
1014C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
hypercenterC22×C3×C4D32
hypocenterC32C3×#535
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C2×C32×#235C2semidirect
2. C2×C3×D3×D12C2semidirect
3. C3×#64139C2semidirect
4. C32×#930C2semidirect
5. C3×#63983C2semidirect
6. C3×#63979C2semidirect
7. C3×#63922C2semidirect
8. C3×#63909C2semidirect
9. C3×#63908C2semidirect
10. C3×#63907C2semidirect
11. C3×#63841C2semidirect
14. #10595064C3direct (N × H)
16. C22×C33×C4C22semidirect
17. C2×C3×#638C22semidirect
20. C2×C32×#67C22semidirect
21. C2×C32×#67C22semidirect
26. C2×C32×C4×D3C22semidirect
27. C2×C32×Dic6C22semidirect
29. C2×C3×#626C22semidirect
30. C2×C3×#625C22semidirect
32. C3×#3752C22semidirect
33. C3×C4⋊(C3⋊Dic3)C22semidirect
34. C32×(C2×D3)⋊C4C22semidirect
35. C32×C4⋊Dic3C22semidirect
36. C3×#3722C22semidirect
38. C3×(C2×D3)⋊Dic3C22semidirect
39. C3×Dic32C22semidirect
43. C2×C3×#235D3semidirect
44. C2×C3×#235C2×C3semidirect
46. C2×D3×D12C2×C3semidirect
48. #64139C2×C3semidirect
62. C3×#930D3semidirect
63. C3×#930C2×C3semidirect
69. #63983C2×C3semidirect
70. #63979C2×C3semidirect
71. #63922C2×C3semidirect
72. #63909C2×C3semidirect
73. #63908C2×C3semidirect
74. #63907C2×C3semidirect
75. #63841C2×C3semidirect
99. C32×C4×D3D4semidirect
123. C22×C32×C4C2×D3semidirect
124. C22×C32×C4C2×D3semidirect
125. C22×C32×C4C22×C3semidirect
126. C2×#638C22×C3semidirect
139. C2×C3×#67C2×D3semidirect
140. C2×C3×#67C2×D3semidirect
142. C2×C3×#67C22×C3semidirect
143. C2×C3×#67C22×C3semidirect
163. C2×C3×C4×D3C2×D3semidirect
165. C2×C3×C4×D3C22×C3semidirect
167. C2×C3×Dic6C2×D3semidirect
168. C2×C3×Dic6C22×C3semidirect
170. C2×#626C22×C3semidirect
171. C2×#625C22×C3semidirect
175. #3752C22×C3semidirect
176. C4⋊(C3⋊Dic3)C22×C3semidirect
187. C3×(C2×D3)⋊C4C2×D3semidirect
188. C3×(C2×D3)⋊C4C22×C3semidirect
193. C3×C4⋊Dic3C2×D3semidirect
194. C3×C4⋊Dic3C22×C3semidirect
197. #3722C22×C3semidirect
199. (C2×D3)⋊Dic3C22×C3semidirect
200. Dic32C22×C3semidirect
229. C2×#235C3×D3semidirect
254. #930C3×D3semidirect
370. C3×C4×D3#67semidirect
371. C3×C4×D3C3×D4semidirect
427. C22×C3×C4D32semidirect
428. C22×C3×C4C2×C3×D3semidirect
429. C22×C3×C4C2×C3×D3semidirect
438. C2×#67C2×C3×D3semidirect
439. C2×#67C2×C3×D3semidirect
451. C2×C4×D3C2×C3×D3semidirect
452. C2×Dic6C2×C3×D3semidirect
474. (C2×D3)⋊C4C2×C3×D3semidirect
478. C4⋊Dic3C2×C3×D3semidirect
601. C33#535semidirect
718. C4×D3C3×#67semidirect
780. C22×C4C3×D32semidirect
902. C32#5607semidirect
903. C32#5830semidirect
904. C32C3×#535semidirect
1004. C3#10595064direct (N × H)
1005. C3C3×#5607semidirect
1006. C3C3×#5830semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#2352
C2×C3×D3×D122
C3×#641392
C32×#9302
C3×#639832
C3×#639792
C3×#639222
C3×#639092
C3×#639082
C3×#639072
C3×#638412
C3×#58303
C3×#56073
#105950643