Finite Group Databasebeta

← C3×#10595081 #13174678

Subgroups — C3×#10595081 #13174678

Order 1728.

2182 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3×#3811C212yesmaximal, complemented
3C2×C3×#3802C211yesmaximal, characteristic, complemented
4C32×#930C212yesmaximal, complemented
5C3×#63980C212yesmaximal, complemented
6C3×#63921C212yesmaximal, complemented
7C3×#63916C212yesmaximal, complemented
8C3×#63912C212yesmaximal, complemented
9C3×#63900C211yesmaximal, characteristic, complemented
10C3×D3×#121—32nomaximal
11#10595081C311yesmaximal, characteristic, direct product factor
12C23×C3×C3⋊D3C2211yescharacteristic
13C22×C3×D32C2212yes—
14C22×C33×C4C2211yescharacteristic, complemented
15C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
16C2×C3×C4×C3⋊D3—24no—
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×C3×C4×C3⋊D3C2211yescharacteristic
19C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
20C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
21C2×C32×#67C2214yescomplemented
22C2×C32×D12C2212yescomplemented
23C3×#3811—28no—
24C2×C3×#626C2214yescomplemented
25C2×C3×#625C2212yescomplemented
26C2×C3×#624C2212yes—
27C3×#3802—24no—
28C32×(C2×D3)⋊C4C2214yescomplemented
29C32×C4⋊Dic3C2212yescomplemented
30C3×#3724C2212yescomplemented
31C3×(C2×D3)⋊Dic3C2214yescomplemented
32C22×C4×C3⋊D3C2×C311yescharacteristic, complemented
33C2×C3×D3×D4—34no—
34C2×C3×D3×D4—32no—
35C22×C3×C4×D3—32no—
36C22×C3×C4×D3—61no—
37C2×#3811C2×C312yescomplemented
38C2×#3802C2×C311yescharacteristic, complemented
39C32×#121—32no—
40C3×#939—34no—
41C3×#938—32no—
42C3×#930—22no—
43C3×#930D312yescomplemented
44C3×#930C2×C312yescomplemented
45C3×#895—32no—
46C3×D3×C4⋊C4—32no—
47C3×#884—34no—
48C3×D3×C22⋊C4—34no—
49#63980C2×C312yescomplemented
50#63921C2×C312yescomplemented
51#63916C2×C312yescomplemented
52#63912C2×C312yescomplemented
53#63900C2×C311yescharacteristic, complemented
54C23×C33C2311yescharacteristic
55C22×C3×C3⋊D3—22no—
56C22×C3×C3⋊D3—22no—
57C22×C3×C3⋊D3D414yescomplemented
58C22×C3×C3⋊D3C2311yescharacteristic
59C22×C3×C3⋊D3C2311yescharacteristic
60C22×C32×D3C2314yes—
61C2×C3×D32—24no—
62C2×C3×D32—24no—
63C2×C3×D32—24no—
64C2×C33×C4—22no—
65C2×C33×C4C2311yescharacteristic
66C2×C33×C4C2311yescharacteristic
67C2×C3×C3⋊Dic3—22no—
68C2×C3×C3⋊Dic3C2311yescharacteristic
69C2×C3×C3⋊Dic3C2311yescharacteristic
70C3×C4×C3⋊D3—22no—
71C3×C4×C3⋊D3—22no—
72C3×C4×C3⋊D3—22no—
73C3×C4×C3⋊D3D414yescomplemented
74C32×#67—28no—
75C2×C32×Dic3C2314yes—
76C32×D12—24no—
77C3×#626—28no—
78C3×#625—24no—
79C3×#624—24no—
80C2×C3×#121—91no—
81D3×#121—32no—
82C23×C3⋊D3C22×C311yescharacteristic
83C23×C3×D3—32no—
84C23×C3×D3—34no—
85C23×C3×D3—61no—
86C22×D32C22×C312yes—
87C2×C32×D4—34no—
88C2×C32×D4—32no—
89C22×C32×C4—21no—
90C22×C32×C4—22no—
91C22×C32×C4—41no—
92C22×C32×C4C2×D312yescomplemented
93C22×C32×C4C22×C311yescharacteristic, complemented
94C22×C3⋊Dic3C22×C311yescharacteristic, complemented
95C2×C4×C3⋊D3—24no—
96C2×C4×C3⋊D3C22×C311yescharacteristic
97C2×C4×C3⋊D3C22×C311yescharacteristic
98C2×C4×C3⋊D3C22×C311yescharacteristic, complemented
99C2×C4×C3⋊D3C22×C311yescharacteristic, complemented
100C2×C3×#67—24no—
101C2×C3×#67—34no—
102C2×C3×#67—34no—
103C2×C3×#67C2×D314yescomplemented
104C2×C3×#67C22×C314yescomplemented
105C22×C3×Dic3—32no—
106C22×C3×Dic3—61no—
107C3×D3×D4—68no—
108C3×D3×D4—616no—
109C2×C3×D12—22no—
110C2×C3×D12—34no—
111C2×C3×D12C2×D312yescomplemented
112C2×C3×D12C22×C312yescomplemented
113C2×C3×C4×D3—32no—
114C2×C3×C4×D3—32no—
115C2×C3×C4×D3—32no—
116C2×C3×C4×D3—32no—
117C2×C3×C4×D3—34no—
118C2×C3×C4×D3—68no—
119C2×C3×C4×D3—61no—
120C2×C3×C4×D3—61no—
121C2×C3×C4×D3—61no—
122C2×C3×C4×D3—61no—
123C2×C3×C4×D3—68no—
124#3811—28no—
125C2×#626C22×C314yescomplemented
126C2×#625C22×C312yescomplemented
127C2×#624C22×C312yes—
128#3802—24no—
129C32×C4⋊C4—32no—
130C32×C22⋊C4—34no—
131C3×#217—34no—
132C3×(C2×D3)⋊C4—24no—
133C3×(C2×D3)⋊C4—34no—
134C3×(C2×D3)⋊C4C2×D314yescomplemented
135C3×(C2×D3)⋊C4C22×C314yescomplemented
136C3×C4⋊Dic3—22no—
137C3×C4⋊Dic3C2×D312yescomplemented
138C3×C4⋊Dic3C22×C312yescomplemented
139C3×Dic3⋊C4—34no—
140#3724C22×C312yescomplemented
141(C2×D3)⋊Dic3C22×C314yescomplemented
142C22×C33—21no—
143C22×C33—21no—
144C22×C33C2×D412yescomplemented
145C22×C33C2411yescharacteristic
146C2×C3×C3⋊D3—21no—
147C2×C3×C3⋊D3—21no—
148C2×C3×C3⋊D3—28no—
149C2×C3×C3⋊D3C2×D412yes—
150C2×C3×C3⋊D3C2×D412yes—
151C2×C3×C3⋊D3C2×D412yescomplemented
152C2×C3×C3⋊D3#4112yes—
153C2×C32×D3—24no—
154C2×C32×D3—24no—
155C2×C32×D3—24no—
156C3×D32—48no—
157C33×C4—21no—
158C33×C4C2×D412yescomplemented
159C3×C3⋊Dic3—21no—
160C3×C3⋊Dic3C2×D412yescomplemented
161C32×Dic3—24no—
162C22×C3×D4—92no—
163C22×C3×D4—91no—
164C23×C3×C4—91no—
165C2×D3×D4—34no—
166C2×D3×D4—32no—
167C22×C4×D3—32no—
168C22×C4×D3—61no—
169C3×#121—32no—
170C3×#121—32no—
171C3×#121—62no—
172C3×#121—92no—
173C3×#121—92no—
174C3×#121—92no—
175C2×C3×C4⋊C4—91no—
176C2×C3×C22⋊C4—92no—
177#939—34no—
178#938—32no—
179#930C3×D312yescomplemented
180#895—32no—
181D3×C4⋊C4—32no—
182#884—34no—
183D3×C22⋊C4—34no—
184C23×C32—21no—
185C23×C32—22no—
186C23×C32—34no—
187C23×C32—41no—
188C23×C32C22×D312yes—
189C23×C32C23×C311yescharacteristic
190C22×C3⋊D3—22no—
191C22×C3⋊D3—22no—
192C22×C3⋊D3C3×D414yescomplemented
193C22×C3⋊D3C23×C311yescharacteristic
194C22×C3⋊D3C23×C311yescharacteristic
195C22×C3×D3—24no—
196C22×C3×D3—32no—
197C22×C3×D3—38no—
198C22×C3×D3—32no—
199C22×C3×D3—64no—
200C22×C3×D3—61no—
201C22×C3×D3—61no—
202C22×C3×D3—68no—
203C22×C3×D3—68no—
204C22×C3×D3—68no—
205C22×C3×D3—64no—
206C22×C3×D3—64no—
207C22×C3×D3—64no—
208C22×C3×D3—64no—
209C22×C3×D3C22×D314yes—
210C22×C3×D3C23×C314yes—
211C2×D32—24no—
212C2×D32—24no—
213C2×D32—24no—
214C32×D4—68no—
215C32×D4—64no—
216C2×C32×C4—22no—
217C2×C32×C4—24no—
218C2×C32×C4—24no—
219C2×C32×C4—21no—
220C2×C32×C4—21no—
221C2×C32×C4—22no—
222C2×C32×C4—22no—
223C2×C32×C4—34no—
224C2×C32×C4—41no—
225C2×C32×C4—41no—
226C2×C32×C4—44no—
227C2×C32×C4—44no—
228C2×C32×C4C22×D312yes—
229C2×C32×C4C22×D312yes—
230C2×C32×C4C23×C311yescharacteristic
231C2×C32×C4C23×C311yescharacteristic
232C2×C3⋊Dic3—22no—
233C2×C3⋊Dic3C23×C311yescharacteristic
234C2×C3⋊Dic3C23×C311yescharacteristic
235C4×C3⋊D3—22no—
236C4×C3⋊D3—22no—
237C4×C3⋊D3—22no—
238C4×C3⋊D3C3×D414yescomplemented
239C3×#67—28no—
240C3×#67—28no—
241C3×#67—48no—
242C3×#67—68no—
243C3×#67—68no—
244C2×C3×Dic3—24no—
245C2×C3×Dic3—32no—
246C2×C3×Dic3—32no—
247C2×C3×Dic3—61no—
248C2×C3×Dic3—61no—
249C2×C3×Dic3—64no—
250C2×C3×Dic3—64no—
251C2×C3×Dic3C22×D314yes—
252C2×C3×Dic3C23×C314yes—
253C3×D12—24no—
254C3×D12—24no—
255C3×D12—44no—
256C3×D12—68no—
257C3×C4×D3—38no—
258C3×C4×D3—64no—
259C3×C4×D3—68no—
260C3×C4×D3—64no—
261C3×C4×D3—64no—
262C3×C4×D3—64no—
263C3×C4×D3—64no—
264C3×C4×D3—64no—
265C3×C4×D3—64no—
266#626—28no—
267#625—24no—
268#624—24no—
269C2×#121—91noSylow
270C2×C33—22no—
271C2×C33C22×D411yescharacteristic
272C2×C33C22×D411yescharacteristic
273C2×C33C2×#4111yescharacteristic
274C3×C3⋊D3—22no—
275C3×C3⋊D3#12114yescomplemented
276C32×D3—44no—
277C24×C3—92no—
278C24×C3—91no—
279C23×D3—32no—
280C23×D3—34no—
281C23×D3—61no—
282C2×C3×D4—34no—
283C2×C3×D4—34no—
284C2×C3×D4—32no—
285C2×C3×D4—32no—
286C2×C3×D4—62no—
287C2×C3×D4—64no—
288C2×C3×D4—94no—
289C2×C3×D4—92no—
290C2×C3×D4—184no—
291C2×C3×D4—188no—
292C22×C3×C4—21no—
293C22×C3×C4—22no—
294C22×C3×C4—41no—
295C22×C3×C4—92no—
296C22×C3×C4—91no—
297C22×C3×C4—91no—
298C22×C3×C4—91no—
299C22×C3×C4—91no—
300C22×C3×C4—91no—
301C22×C3×C4—184no—
302C22×C3×C4D3211yescharacteristic, complemented
303C22×C3×C4C2×C3×D312yescomplemented
304C2×#67—34no—
305C2×#67—34no—
306C2×#67C2×C3×D314yescomplemented
307C22×Dic3—32no—
308C22×Dic3—61no—
309D3×D4—68no—
310D3×D4—616no—
311C2×D12—34no—
312C2×D12C2×C3×D312yescomplemented
313C2×C4×D3—32no—
314C2×C4×D3—32no—
315C2×C4×D3—32no—
316C2×C4×D3—32no—
317C2×C4×D3—34no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—68no—
323C2×C4×D3—68no—
324C3×C4⋊C4—32no—
325C3×C4⋊C4—32no—
326C3×C4⋊C4—62no—
327C3×C4⋊C4—92no—
328C3×C22⋊C4—34no—
329C3×C22⋊C4—34no—
330C3×C22⋊C4—64no—
331C3×C22⋊C4—94no—
332#217—34no—
333(C2×D3)⋊C4—34no—
334(C2×D3)⋊C4C2×C3×D314yescomplemented
335C4⋊Dic3C2×C3×D312yescomplemented
336Dic3⋊C4—34no—
337C22×C32—21no—
338C22×C32—21no—
339C22×C32—22no—
340C22×C32—22no—
341C22×C32—22no—
342C22×C32—22no—
343C22×C32—21no—
344C22×C32—22no—
345C22×C32—22no—
346C22×C32—24no—
347C22×C32—42no—
348C22×C32—41no—
349C22×C32—42no—
350C22×C32—42no—
351C22×C32—42no—
352C22×C32—42no—
353C22×C32—64no—
354C22×C32—64no—
355C22×C32—64no—
356C22×C32D3×D414yescomplemented
357C22×C32C2×C3×D412yescomplemented
358C22×C32C23×D312yes—
359C22×C32C24×C311yescharacteristic
360C2×C3⋊D3—21no—
361C2×C3⋊D3—21no—
362C2×C3⋊D3—28no—
363C2×C3⋊D3C2×C3×D412yes—
364C2×C3⋊D3C2×C3×D412yes—
365C2×C3⋊D3C2×C3×D412yescomplemented
366C2×C3⋊D3C3×#4112yes—
367C2×C3×D3—24no—
368C2×C3×D3—24no—
369C2×C3×D3—24no—
370C2×C3×D3—24no—
371C2×C3×D3—24no—
372C2×C3×D3—24no—
373C2×C3×D3—34no—
374C2×C3×D3—34no—
375C2×C3×D3—34no—
376C2×C3×D3—34no—
377C2×C3×D3—44no—
378C2×C3×D3—44no—
379C2×C3×D3—44no—
380C2×C3×D3—62no—
381C2×C3×D3—62no—
382C2×C3×D3—62no—
383C2×C3×D3—62no—
384C2×C3×D3—616no—
385C2×C3×D3—62no—
386C2×C3×D3—616no—
387C2×C3×D3—62no—
388C2×C3×D3—62no—
389C2×C3×D3—62no—
390C2×C3×D3—1216no—
391D32—48no—
392C32×C4—21no—
393C32×C4—22no—
394C32×C4—22no—
395C32×C4—22no—
396C32×C4—24no—
397C32×C4—42no—
398C32×C4—42no—
399C32×C4—42no—
400C32×C4—64no—
401C32×C4D3×D414yescomplemented
402C32×C4C2×C3×D412yescomplemented
403C3⋊Dic3—21no—
404C3⋊Dic3C2×C3×D412yescomplemented
405C3×Dic3—24no—
406C3×Dic3—24no—
407C3×Dic3—34no—
408C3×Dic3—44no—
409C3×Dic3—62no—
410C3×Dic3—62no—
411C3×Dic3—62no—
412C22×D4—92no—
413C22×D4—91no—
414C23×C4—91no—
415#121—32no—
416#121—92no—
417#121—92no—
418#121—92no—
419C2×C4⋊C4—91no—
420C2×C22⋊C4—92no—
421C33C2×#12111yescharacteristic, complemented, Sylow
422C23×C3—21no—
423C23×C3—22no—
424C23×C3—34no—
425C23×C3—34no—
426C23×C3—41no—
427C23×C3—64no—
428C23×C3—91no—
429C23×C3—91no—
430C23×C3—94no—
431C23×C3—182no—
432C23×C3—182no—
433C23×C3—184no—
434C23×C3—184no—
435C23×C3—184no—
436C23×C3C2×D3211yescharacteristic
437C23×C3C22×C3×D312yes—
438C22×D3—32no—
439C22×D3—32no—
440C22×D3—38no—
441C22×D3—64no—
442C22×D3—61no—
443C22×D3—61no—
444C22×D3—68no—
445C22×D3—68no—
446C22×D3—68no—
447C22×D3—64no—
448C22×D3—64no—
449C22×D3—64no—
450C22×D3—64no—
451C22×D3C22×C3×D314yes—
452C3×D4—68no—
453C3×D4—68no—
454C3×D4—64no—
455C3×D4—64no—
456C3×D4—124no—
457C3×D4—128no—
458C3×D4—188no—
459C3×D4—184no—
460C2×C3×C4—24no—
461C2×C3×C4—22no—
462C2×C3×C4—24no—
463C2×C3×C4—22no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—22no—
467C2×C3×C4—34no—
468C2×C3×C4—34no—
469C2×C3×C4—44no—
470C2×C3×C4—44no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—64no—
474C2×C3×C4—91no—
475C2×C3×C4—94no—
476C2×C3×C4—91no—
477C2×C3×C4—182no—
478C2×C3×C4—182no—
479C2×C3×C4—184no—
480C2×C3×C4—182no—
481C2×C3×C4—182no—
482C2×C3×C4C2×D3211yescharacteristic
483C2×C3×C4C2×D3211yescharacteristic
484C2×C3×C4C22×C3×D312yes—
485C2×C3×C4C22×C3×D312yes—
486#67—28no—
487#67—68no—
488#67—68no—
489C2×Dic3—32no—
490C2×Dic3—32no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—64no—
494C2×Dic3—64no—
495C2×Dic3C22×C3×D314yes—
496D12—24no—
497D12—68no—
498C4×D3—38no—
499C4×D3—64no—
500C4×D3—68no—
501C4×D3—64no—
502C4×D3—64no—
503C4×D3—64no—
504C4×D3—64no—
505C4×D3—64no—
506C4×D3—64no—
507C2×C32—22no—
508C2×C32—24no—
509C2×C32—24no—
510C2×C32—21no—
511C2×C32—21no—
512C2×C32—21no—
513C2×C32—22no—
514C2×C32—22no—
515C2×C32—22no—
516C2×C32—41no—
517C2×C32—41no—
518C2×C32—41no—
519C2×C32—44no—
520C2×C32—44no—
521C2×C32—124no—
522C2×C32C2×D3×D412yes—
523C2×C32C2×D3×D412yes—
524C2×C32D3×#4112yes—
525C2×C32C22×C3×D411yescharacteristic
526C2×C32C22×C3×D411yescharacteristic
527C2×C32C2×C3×#4111yescharacteristic
528C3⋊D3—22no—
529C3⋊D3C3×#12114yescomplemented
530C3×D3—38no—
531C3×D3—44no—
532C3×D3—44no—
533C3×D3—64no—
534C3×D3—64no—
535C3×D3—64no—
536C3×D3—84no—
537C24—92no—
538C24—91no—
539C2×D4—34no—
540C2×D4—32no—
541C2×D4—94no—
542C2×D4—92no—
543C2×D4—184no—
544C2×D4—188no—
545C22×C4—92no—
546C22×C4—91no—
547C22×C4—91no—
548C22×C4—91no—
549C22×C4—91no—
550C22×C4—91no—
551C22×C4—184no—
552C22×C4C3×D3211yescharacteristic, complemented
553C4⋊C4—32no—
554C4⋊C4—92no—
555C22⋊C4—34no—
556C22⋊C4—94no—
557C22×C3—22no—
558C22×C3—22no—
559C22×C3—21no—
560C22×C3—21no—
561C22×C3—22no—
562C22×C3—22no—
563C22×C3—21no—
564C22×C3—22no—
565C22×C3—22no—
566C22×C3—24no—
567C22×C3—42no—
568C22×C3—42no—
569C22×C3—42no—
570C22×C3—42no—
571C22×C3—41no—
572C22×C3—42no—
573C22×C3—64no—
574C22×C3—64no—
575C22×C3—64no—
576C22×C3—64no—
577C22×C3—64no—
578C22×C3—64no—
579C22×C3—92no—
580C22×C3—92no—
581C22×C3—92no—
582C22×C3—92no—
583C22×C3—124no—
584C22×C3—124no—
585C22×C3—124no—
586C22×C3—188no—
587C22×C3—181no—
588C22×C3—181no—
589C22×C3—368no—
590C22×C3#380212yescomplemented
591C22×C3C3×D3×D414yescomplemented
592C22×C3C22×D3211yescharacteristic
593C22×C3C23×C3×D312yes—
594C2×D3—24no—
595C2×D3—24no—
596C2×D3—24no—
597C2×D3—34no—
598C2×D3—34no—
599C2×D3—34no—
600C2×D3—34no—
601C2×D3—62no—
602C2×D3—62no—
603C2×D3—62no—
604C2×D3—62no—
605C2×D3—616no—
606C2×D3—62no—
607C2×D3—616no—
608C2×D3—62no—
609C2×D3—62no—
610C2×D3—62no—
611C2×D3—1216no—
612C3×C4—22no—
613C3×C4—21no—
614C3×C4—22no—
615C3×C4—22no—
616C3×C4—24no—
617C3×C4—42no—
618C3×C4—42no—
619C3×C4—42no—
620C3×C4—64no—
621C3×C4—64no—
622C3×C4—92no—
623C3×C4—124no—
624C3×C4—181no—
625C3×C4#381112yescomplemented
626C3×C4C3×D3×D414yescomplemented
627Dic3—24no—
628Dic3—34no—
629Dic3—62no—
630Dic3—62no—
631Dic3—62no—
632C32—21no—
633C32—22no—
634C32—41no—
635C32D3×#12112yescomplemented
636C32C2×C3×#12111yescharacteristic, complemented
637C23—34no—
638C23—91no—
639C23—91no—
640C23—94no—
641C23—182no—
642C23—182no—
643C23—184no—
644C23—184no—
645C23—184no—
646C23C2×C3×D3211yescharacteristic
647D4—68no—
648D4—64no—
649D4—188no—
650D4—184no—
651C2×C4—22no—
652C2×C4—34no—
653C2×C4—91no—
654C2×C4—94no—
655C2×C4—91no—
656C2×C4—182no—
657C2×C4—182no—
658C2×C4—184no—
659C2×C4—182no—
660C2×C4—182no—
661C2×C4C2×C3×D3211yescharacteristic
662C2×C4C2×C3×D3211yescharacteristic
663C2×C3—24no—
664C2×C3—22no—
665C2×C3—24no—
666C2×C3—21no—
667C2×C3—22no—
668C2×C3—22no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—22no—
672C2×C3—44no—
673C2×C3—44no—
674C2×C3—41no—
675C2×C3—41no—
676C2×C3—41no—
677C2×C3—94no—
678C2×C3—124no—
679C2×C3—124no—
680C2×C3—182no—
681C2×C3—244no—
682C2×C3C2×#380211yescharacteristic
683C2×C3#6430611yescharacteristic
684C2×C3C2×#381111yescharacteristic
685C2×C3C2×C3×D3×D412yes—
686C2×C3C2×C3×D3×D412yes—
687C2×C3C3×D3×#4112yes—
688D3—38no—
689D3—44no—
690D3—64no—
691D3—64no—
692D3—64no—
693C22—21no—
694C22—21no—
695C22—64no—
696C22—64no—
697C22—64no—
698C22—92no—
699C22—92no—
700C22—92no—
701C22—92no—
702C22—188no—
703C22—181no—
704C22—181no—
705C22—368no—
706C22C3×#380212yescomplemented
707C22C22×C3×D3211yescharacteristic
708C4—21no—
709C4—64no—
710C4—92no—
711C4—181no—
712C4C3×#381112yescomplemented
713C3—21no—
714C3—22no—
715C3—41no—
716C3#1059508111yescharacteristic, direct product factor
717C3C3×D3×#12112yescomplemented
718C2—22no—
719C2—94no—
720C2—124no—
721C2—182no—
722C2C2×C3×#380211yescharacteristic
723C2C3×#6430611yescharacteristic
724C2C2×C3×#381111yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
hypercenterC22×C3×C4D32
hypocenterC32C2×C3×#121
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. C22×C3×C4×C3⋊D3C2semidirect
2. C2×C3×#3811C2semidirect
3. C2×C3×#3802C2semidirect
4. C32×#930C2semidirect
5. C3×#63980C2semidirect
6. C3×#63921C2semidirect
7. C3×#63916C2semidirect
8. C3×#63912C2semidirect
9. C3×#63900C2semidirect
11. #10595081C3direct (N × H)
14. C22×C33×C4C22semidirect
15. C22×C3×C3⋊Dic3C22semidirect
19. C2×C3×C4×C3⋊D3C22semidirect
20. C2×C3×C4×C3⋊D3C22semidirect
21. C2×C32×#67C22semidirect
22. C2×C32×D12C22semidirect
24. C2×C3×#626C22semidirect
25. C2×C3×#625C22semidirect
28. C32×(C2×D3)⋊C4C22semidirect
29. C32×C4⋊Dic3C22semidirect
30. C3×#3724C22semidirect
31. C3×(C2×D3)⋊Dic3C22semidirect
32. C22×C4×C3⋊D3C2×C3semidirect
37. C2×#3811C2×C3semidirect
38. C2×#3802C2×C3semidirect
43. C3×#930D3semidirect
44. C3×#930C2×C3semidirect
49. #63980C2×C3semidirect
50. #63921C2×C3semidirect
51. #63916C2×C3semidirect
52. #63912C2×C3semidirect
53. #63900C2×C3semidirect
57. C22×C3×C3⋊D3D4semidirect
73. C3×C4×C3⋊D3D4semidirect
92. C22×C32×C4C2×D3semidirect
93. C22×C32×C4C22×C3semidirect
94. C22×C3⋊Dic3C22×C3semidirect
98. C2×C4×C3⋊D3C22×C3semidirect
99. C2×C4×C3⋊D3C22×C3semidirect
103. C2×C3×#67C2×D3semidirect
104. C2×C3×#67C22×C3semidirect
111. C2×C3×D12C2×D3semidirect
112. C2×C3×D12C22×C3semidirect
125. C2×#626C22×C3semidirect
126. C2×#625C22×C3semidirect
134. C3×(C2×D3)⋊C4C2×D3semidirect
135. C3×(C2×D3)⋊C4C22×C3semidirect
137. C3×C4⋊Dic3C2×D3semidirect
138. C3×C4⋊Dic3C22×C3semidirect
140. #3724C22×C3semidirect
141. (C2×D3)⋊Dic3C22×C3semidirect
144. C22×C33C2×D4semidirect
151. C2×C3×C3⋊D3C2×D4semidirect
158. C33×C4C2×D4semidirect
160. C3×C3⋊Dic3C2×D4semidirect
179. #930C3×D3semidirect
192. C22×C3⋊D3C3×D4semidirect
238. C4×C3⋊D3C3×D4semidirect
275. C3×C3⋊D3#121semidirect
302. C22×C3×C4D32semidirect
303. C22×C3×C4C2×C3×D3semidirect
306. C2×#67C2×C3×D3semidirect
312. C2×D12C2×C3×D3semidirect
334. (C2×D3)⋊C4C2×C3×D3semidirect
335. C4⋊Dic3C2×C3×D3semidirect
356. C22×C32D3×D4semidirect
357. C22×C32C2×C3×D4semidirect
365. C2×C3⋊D3C2×C3×D4semidirect
401. C32×C4D3×D4semidirect
402. C32×C4C2×C3×D4semidirect
404. C3⋊Dic3C2×C3×D4semidirect
421. C33C2×#121semidirect
529. C3⋊D3C3×#121semidirect
552. C22×C4C3×D32semidirect
590. C22×C3#3802semidirect
591. C22×C3C3×D3×D4semidirect
625. C3×C4#3811semidirect
626. C3×C4C3×D3×D4semidirect
635. C32D3×#121semidirect
636. C32C2×C3×#121semidirect
706. C22C3×#3802semidirect
712. C4C3×#3811semidirect
716. C3#10595081direct (N × H)
717. C3C3×D3×#121semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4×C3⋊D32
C2×C3×#38112
C2×C3×#38022
C32×#9302
C3×#639802
C3×#639212
C3×#639162
C3×#639122
C3×#639002
C3×D3×#1213
#105950813