Finite Group Databasebeta

← C3×#10594776 #13174411

Subgroups — C3×#10594776 #13174411

Order 1728.

1386 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#235C211yesmaximal, characteristic
2C2×C3×#3748C211yesmaximal, characteristic, complemented
3C2×C32×#208C211yesmaximal, characteristic, complemented
4C3×#63815C214yesmaximal, complemented
5C3×#63814C214yesmaximal, complemented
6C3×D3×#208C214yesmaximal, complemented
7C3×#5819—31nomaximal
8C3×#5745—31nomaximal
9#10594776C311yesmaximal, characteristic, direct product factor
10C22×C33×C4C2211yescharacteristic
11C2×C32×#67C412yes—
12C32×#235C412yes—
13C32×#235C412yes—
14C32×#235C2212yes—
15C32×#235C2212yes—
16C2×C32×D12C411yescharacteristic
17C2×C32×C4×D3C2212yes—
18C2×C32×Dic6C411yescharacteristic
19C3×#3748C2212yes—
20C3×#3748C2212yescomplemented
21C2×C3×C3⋊(C3⋊C8)C2212yescomplemented
22C32×#208C2212yes—
23C32×#208C2212yescomplemented
24C2×C32×C3⋊C8C2212yescomplemented
25C3×#3711C2218yescomplemented
26C3×D3×C3⋊C8C2218yescomplemented
27C2×C32×#41—31no—
28C2×C3×#235—21no—
29C2×C3×#235D311yescharacteristic
30C2×C3×#235C2×C311yescharacteristic
31C2×C32×M16—31no—
32C2×#3748C2×C311yescharacteristic, complemented
33C3×#948—34no—
34C3×#948—34no—
35C2×C3×#208—21no—
36C2×C3×#208—31no—
37C2×C3×#208—31no—
38C2×C3×#208—34no—
39C2×C3×#208—61no—
40C2×C3×#208D311yescharacteristic, complemented
41C2×C3×#208C2×C311yescharacteristic, complemented
42C3×#907—34no—
43C3×D3×M16—34no—
44C3×#901—34no—
45#63815C2×C314yescomplemented
46#63814C2×C314yescomplemented
47D3×#208C2×C314yescomplemented
48C23×C33C2×C411yescharacteristic
49C22×C32×D3C2×C412yes—
50C2×C33×C4C2×C411yescharacteristic
51C2×C33×C4C2×C411yescharacteristic
52C2×C33×C4C2×C411yescharacteristic
53C2×C33×C4C2311yescharacteristic
54C2×C33×C4C2311yescharacteristic
55C2×C33×C4C2311yescharacteristic
56C32×#67C2×C414yes—
57C32×#67C2×C414yes—
58C2×C32×Dic3C2×C412yes—
59C32×D12C2×C412yes—
60C32×D12C2×C412yes—
61C32×C4×D3C2×C414yes—
62C32×C4×D3C2314yes—
63C32×Dic6C2×C412yes—
64C32×Dic6C2×C412yes—
65C3×C3⋊(C3⋊C8)C2314yes—
66C32×C3⋊C8C2314yes—
67C3×#568—91no—
68#5819—31no—
69#5745—31no—
70C32×#41—32no—
71C32×#41—32no—
72C32×#41—32no—
73C32×#41—32no—
74C2×C32×Q8—31no—
75C2×C32×D4—32no—
76C2×C32×D4—31no—
77C22×C32×C4—21no—
78C22×C32×C4—21no—
79C22×C32×C4—21no—
80C22×C32×C4—32no—
81C22×C32×C4—41no—
82C22×C32×C4C2×D311yescharacteristic
83C22×C32×C4C2×D311yescharacteristic
84C22×C32×C4C22×C311yescharacteristic
85C2×C3×#67—22no—
86C2×C3×#67Dic312yes—
87C2×C3×#67C3×C412yes—
88C3×#235—22no—
89C3×#235—22no—
90C3×#235—22no—
91C3×#235—22no—
92C3×#235Dic312yes—
93C3×#235Dic312yes—
94C3×#235C3×C412yes—
95C3×#235C3×C412yes—
96C3×#235C2×D312yes—
97C3×#235C2×D312yes—
98C3×#235C22×C312yes—
99C3×#235C22×C312yes—
100C2×C3×D12—21no—
101C2×C3×D12Dic311yescharacteristic
102C2×C3×D12C3×C411yescharacteristic
103C2×C3×C4×D3—22no—
104C2×C3×C4×D3C2×D312yes—
105C2×C3×C4×D3C22×C312yes—
106C2×C3×Dic6—21no—
107C2×C3×Dic6Dic311yescharacteristic
108C2×C3×Dic6C3×C411yescharacteristic
109C32×M16—32no—
110C32×M16—32no—
111C2×C32×C8—32no—
112#3748C22×C312yes—
113#3748C22×C312yescomplemented
114C2×C3⋊(C3⋊C8)C22×C312yescomplemented
115C3×#208—22no—
116C3×#208—22no—
117C3×#208—32no—
118C3×#208—32no—
119C3×#208—32no—
120C3×#208—32no—
121C3×#208—38no—
122C3×#208—62no—
123C3×#208—62no—
124C3×#208C2×D312yes—
125C3×#208C2×D312yescomplemented
126C3×#208C22×C312yes—
127C3×#208C22×C312yescomplemented
128C2×C3×C3⋊C8—22no—
129C2×C3×C3⋊C8—32no—
130C2×C3×C3⋊C8—32no—
131C2×C3×C3⋊C8—38no—
132C2×C3×C3⋊C8—62no—
133C2×C3×C3⋊C8C2×D312yescomplemented
134C2×C3×C3⋊C8C22×C312yescomplemented
135C3×ΓL(1,𝔽25)—38no—
136C3×D3×C8—38no—
137#3711C22×C318yescomplemented
138D3×C3⋊C8C22×C318yescomplemented
139C22×C33—41no—
140C22×C33C22×C411yescharacteristic
141C22×C33C22×C411yescharacteristic
142C22×C33C22×C411yescharacteristic
143C2×C32×D3—42no—
144C2×C32×D3C22×C414yes—
145C33×C4C22×C411yescharacteristic
146C33×C4C22×C411yescharacteristic
147C33×C4C22×C411yescharacteristic
148C33×C4C2411yescharacteristic
149C32×Dic3C22×C414yes—
150C2×C3×#41—31no—
151C2×C3×#41—31no—
152C2×C3×#41—61no—
153C2×#235C3×D311yescharacteristic
154C3×#131—94no—
155C3×#131—94no—
156C2×C3×M16—31no—
157C2×C3×M16—31no—
158C2×C3×M16—61no—
159C2×C3×M16—94no—
160C2×C3×M16—91no—
161#948—34no—
162#948—34no—
163C2×#208—31no—
164C2×#208—31no—
165C2×#208—34no—
166C2×#208—61no—
167C2×#208C3×D311yescharacteristic, complemented
168#907—34no—
169D3×M16—34no—
170#901—34no—
171C23×C32—21no—
172C23×C32—21no—
173C23×C32—21no—
174C23×C32—32no—
175C23×C32—41no—
176C23×C32C4×D311yescharacteristic
177C23×C32C2×Dic311yescharacteristic
178C23×C32C2×C3×C411yescharacteristic
179C22×C3×D3—22no—
180C22×C3×D3C2×Dic312yes—
181C22×C3×D3C2×C3×C412yes—
182C32×Q8—32no—
183C32×Q8—32no—
184C32×D4—34no—
185C32×D4—34no—
186C32×D4—32no—
187C32×D4—32no—
188C2×C32×C4—21no—
189C2×C32×C4—21no—
190C2×C32×C4—21no—
191C2×C32×C4—21no—
192C2×C32×C4—21no—
193C2×C32×C4—21no—
194C2×C32×C4—21no—
195C2×C32×C4—21no—
196C2×C32×C4—21no—
197C2×C32×C4—21no—
198C2×C32×C4—21no—
199C2×C32×C4—21no—
200C2×C32×C4—21no—
201C2×C32×C4—21no—
202C2×C32×C4—21no—
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4—21no—
206C2×C32×C4—32no—
207C2×C32×C4—34no—
208C2×C32×C4—34no—
209C2×C32×C4—41no—
210C2×C32×C4—41no—
211C2×C32×C4—41no—
212C2×C32×C4—41no—
213C2×C32×C4—41no—
214C2×C32×C4—41no—
215C2×C32×C4C4×D311yescharacteristic
216C2×C32×C4C4×D311yescharacteristic
217C2×C32×C4C4×D311yescharacteristic
218C2×C32×C4C2×Dic311yescharacteristic
219C2×C32×C4C2×Dic311yescharacteristic
220C2×C32×C4C2×Dic311yescharacteristic
221C2×C32×C4C2×C3×C411yescharacteristic
222C2×C32×C4C2×C3×C411yescharacteristic
223C2×C32×C4C2×C3×C411yescharacteristic
224C2×C32×C4C22×D311yescharacteristic
225C2×C32×C4C22×D311yescharacteristic
226C2×C32×C4C22×D311yescharacteristic
227C2×C32×C4C22×D311yescharacteristic
228C2×C32×C4C22×D311yescharacteristic
229C2×C32×C4C22×D311yescharacteristic
230C2×C32×C4C23×C311yescharacteristic
231C2×C32×C4C23×C311yescharacteristic
232C2×C32×C4C23×C311yescharacteristic
233C3×#67—24no—
234C3×#67—24no—
235C3×#67C2×Dic314yes—
236C3×#67C2×Dic314yes—
237C3×#67C2×C3×C414yes—
238C3×#67C2×C3×C414yes—
239C2×C3×Dic3—22no—
240C2×C3×Dic3C2×Dic312yes—
241C2×C3×Dic3C2×C3×C412yes—
242C3×D12—22no—
243C3×D12—22no—
244C3×D12C2×Dic312yes—
245C3×D12C2×Dic312yes—
246C3×D12C2×C3×C412yes—
247C3×D12C2×C3×C412yes—
248C3×C4×D3—24no—
249C3×C4×D3—24no—
250C3×C4×D3C2×Dic314yes—
251C3×C4×D3C2×C3×C414yes—
252C3×C4×D3C22×D314yes—
253C3×C4×D3C23×C314yes—
254C3×Dic6—22no—
255C3×Dic6—22no—
256C3×Dic6C2×Dic312yes—
257C3×Dic6C2×Dic312yes—
258C3×Dic6C2×C3×C412yes—
259C3×Dic6C2×C3×C412yes—
260C32×C8—34no—
261C3⋊(C3⋊C8)C23×C314yes—
262C3×C3⋊C8—24no—
263C3×C3⋊C8—34no—
264C3×C3⋊C8—34no—
265C3×C3⋊C8—64no—
266C3×C3⋊C8C22×D314yes—
267C3×C3⋊C8C23×C314yes—
268#568—91noSylow
269C2×C33—21no—
270C2×C33—21no—
271C2×C33—21no—
272C2×C33C23×C411yescharacteristic
273C32×D3—24no—
274C3×#41—32no—
275C3×#41—32no—
276C3×#41—32no—
277C3×#41—32no—
278C3×#41—32no—
279C3×#41—32no—
280C3×#41—32no—
281C3×#41—32no—
282C3×#41—62no—
283C3×#41—62no—
284C3×#41—62no—
285C3×#41—62no—
286C2×C3×Q8—31no—
287C2×C3×Q8—31no—
288C2×C3×Q8—61no—
289C2×C3×D4—32no—
290C2×C3×D4—32no—
291C2×C3×D4—31no—
292C2×C3×D4—31no—
293C2×C3×D4—61no—
294C2×C3×D4—62no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—32no—
299C22×C3×C4—32no—
300C22×C3×C4—41no—
301C22×C3×C4—62no—
302C22×C3×C4D3211yescharacteristic
303C22×C3×C4C2×C3×D311yescharacteristic
304C22×C3×C4C2×C3×D311yescharacteristic
305C2×#67C3×Dic312yes—
306#235C3×Dic312yes—
307#235C3×Dic312yes—
308#235C2×C3×D312yes—
309#235C2×C3×D312yes—
310C2×D12C3×Dic311yescharacteristic
311C2×C4×D3C2×C3×D312yes—
312C2×Dic6C3×Dic311yescharacteristic
313C3×M16—32no—
314C3×M16—32no—
315C3×M16—32no—
316C3×M16—32no—
317C3×M16—62no—
318C3×M16—62no—
319C3×M16—98no—
320C3×M16—92no—
321C3×M16—92no—
322C2×C3×C8—32no—
323C2×C3×C8—32no—
324C2×C3×C8—62no—
325C2×C3×C8—98no—
326C2×C3×C8—92no—
327#208—32no—
328#208—32no—
329#208—32no—
330#208—32no—
331#208—38no—
332#208—62no—
333#208—62no—
334#208C2×C3×D312yes—
335#208C2×C3×D312yescomplemented
336C2×C3⋊C8—32no—
337C2×C3⋊C8—32no—
338C2×C3⋊C8—38no—
339C2×C3⋊C8—62no—
340C2×C3⋊C8C2×C3×D312yescomplemented
341ΓL(1,𝔽25)—38no—
342D3×C8—38no—
343C22×C32—21no—
344C22×C32—21no—
345C22×C32—21no—
346C22×C32—21no—
347C22×C32—21no—
348C22×C32—21no—
349C22×C32—21no—
350C22×C32—21no—
351C22×C32—21no—
352C22×C32—34no—
353C22×C32—41no—
354C22×C32—41no—
355C22×C32—41no—
356C22×C32—41no—
357C22×C32—41no—
358C22×C32—41no—
359C22×C32—42no—
360C22×C32—42no—
361C22×C32—42no—
362C22×C32—44no—
363C22×C32—122no—
364C22×C32C2×C4×D311yescharacteristic
365C22×C32C2×C4×D311yescharacteristic
366C22×C32C2×C4×D311yescharacteristic
367C22×C32C22×Dic311yescharacteristic
368C22×C32C22×Dic311yescharacteristic
369C22×C32C22×Dic311yescharacteristic
370C22×C32C22×C3×C411yescharacteristic
371C22×C32C22×C3×C411yescharacteristic
372C22×C32C22×C3×C411yescharacteristic
373C2×C3×D3—24no—
374C2×C3×D3—42no—
375C2×C3×D3—42no—
376C2×C3×D3—44no—
377C2×C3×D3C22×Dic314yes—
378C2×C3×D3C22×C3×C414yes—
379C32×C4—21no—
380C32×C4—21no—
381C32×C4—21no—
382C32×C4—21no—
383C32×C4—21no—
384C32×C4—21no—
385C32×C4—21no—
386C32×C4—21no—
387C32×C4—21no—
388C32×C4—21no—
389C32×C4—21no—
390C32×C4—21no—
391C32×C4—34no—
392C32×C4—41no—
393C32×C4—41no—
394C32×C4—41no—
395C32×C4—41no—
396C32×C4C2×C4×D311yescharacteristic
397C32×C4C2×C4×D311yescharacteristic
398C32×C4C2×C4×D311yescharacteristic
399C32×C4C22×Dic311yescharacteristic
400C32×C4C22×Dic311yescharacteristic
401C32×C4C22×Dic311yescharacteristic
402C32×C4C22×C3×C411yescharacteristic
403C32×C4C22×C3×C411yescharacteristic
404C32×C4C22×C3×C411yescharacteristic
405C32×C4C23×D311yescharacteristic
406C32×C4C23×D311yescharacteristic
407C32×C4C24×C311yescharacteristic
408C3×Dic3—24no—
409C3×Dic3C22×Dic314yes—
410C3×Dic3C22×C3×C414yes—
411C2×#41—31no—
412#131—94no—
413#131—94no—
414C2×M16—31no—
415C2×M16—94no—
416C2×M16—91no—
417C33#56811yescharacteristic, complemented, Sylow
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—32no—
422C23×C3—32no—
423C23×C3—41no—
424C23×C3—62no—
425C23×C3D3×Dic311yescharacteristic
426C23×C3C3×C4×D311yescharacteristic
427C23×C3C2×C3×Dic311yescharacteristic
428C22×D3C2×C3×Dic312yes—
429C3×Q8—32no—
430C3×Q8—32no—
431C3×Q8—32no—
432C3×Q8—32no—
433C3×Q8—62no—
434C3×Q8—62no—
435C3×D4—34no—
436C3×D4—34no—
437C3×D4—34no—
438C3×D4—34no—
439C3×D4—32no—
440C3×D4—32no—
441C3×D4—32no—
442C3×D4—32no—
443C3×D4—62no—
444C3×D4—62no—
445C3×D4—64no—
446C3×D4—64no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—32no—
466C2×C3×C4—32no—
467C2×C3×C4—34no—
468C2×C3×C4—34no—
469C2×C3×C4—34no—
470C2×C3×C4—34no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—64no—
478C2×C3×C4—64no—
479C2×C3×C4—62no—
480C2×C3×C4D3×Dic311yescharacteristic
481C2×C3×C4D3×Dic311yescharacteristic
482C2×C3×C4D3×Dic311yescharacteristic
483C2×C3×C4C3×C4×D311yescharacteristic
484C2×C3×C4C3×C4×D311yescharacteristic
485C2×C3×C4C3×C4×D311yescharacteristic
486C2×C3×C4C2×C3×Dic311yescharacteristic
487C2×C3×C4C2×C3×Dic311yescharacteristic
488C2×C3×C4C2×C3×Dic311yescharacteristic
489C2×C3×C4C2×D3211yescharacteristic
490C2×C3×C4C2×D3211yescharacteristic
491C2×C3×C4C2×D3211yescharacteristic
492C2×C3×C4C22×C3×D311yescharacteristic
493C2×C3×C4C22×C3×D311yescharacteristic
494C2×C3×C4C22×C3×D311yescharacteristic
495C2×C3×C4C22×C3×D311yescharacteristic
496C2×C3×C4C22×C3×D311yescharacteristic
497C2×C3×C4C22×C3×D311yescharacteristic
498#67C2×C3×Dic314yes—
499#67C2×C3×Dic314yes—
500C2×Dic3C2×C3×Dic312yes—
501D12C2×C3×Dic312yes—
502D12C2×C3×Dic312yes—
503C4×D3C2×C3×Dic314yes—
504C4×D3C22×C3×D314yes—
505Dic6C2×C3×Dic312yes—
506Dic6C2×C3×Dic312yes—
507C3×C8—34no—
508C3×C8—34no—
509C3×C8—64no—
510C3×C8—94no—
511C3⋊C8—34no—
512C3⋊C8—34no—
513C3⋊C8—64no—
514C3⋊C8C22×C3×D314yes—
515C2×C32—21no—
516C2×C32—21no—
517C2×C32—21no—
518C2×C32—22no—
519C2×C32—22no—
520C2×C32—22no—
521C2×C32—21no—
522C2×C32—21no—
523C2×C32—21no—
524C2×C32—21no—
525C2×C32—21no—
526C2×C32—21no—
527C2×C32—21no—
528C2×C32—21no—
529C2×C32—21no—
530C2×C32—41no—
531C2×C32—41no—
532C2×C32—41no—
533C2×C32—41no—
534C2×C32—41no—
535C2×C32—41no—
536C2×C32—41no—
537C2×C32—42no—
538C2×C32—42no—
539C2×C32—42no—
540C2×C32—64no—
541C2×C32C22×C4×D311yescharacteristic
542C2×C32C23×Dic311yescharacteristic
543C2×C32C23×C3×C411yescharacteristic
544C3×D3—24no—
545C3×D3—24no—
546C3×D3—44no—
547#41—32no—
548#41—32no—
549#41—32no—
550#41—32no—
551C2×Q8—31no—
552C2×D4—32no—
553C2×D4—31no—
554C22×C4—32no—
555C22×C4C3×D3211yescharacteristic
556M16—32no—
557M16—32no—
558M16—98no—
559M16—92no—
560M16—92no—
561C2×C8—32no—
562C2×C8—98no—
563C2×C8—92no—
564C22×C3—21no—
565C22×C3—21no—
566C22×C3—21no—
567C22×C3—21no—
568C22×C3—21no—
569C22×C3—21no—
570C22×C3—21no—
571C22×C3—21no—
572C22×C3—21no—
573C22×C3—34no—
574C22×C3—34no—
575C22×C3—41no—
576C22×C3—41no—
577C22×C3—41no—
578C22×C3—42no—
579C22×C3—42no—
580C22×C3—42no—
581C22×C3—44no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3—64no—
586C22×C3—122no—
587C22×C3—122no—
588C22×C3—124no—
589C22×C3C2×D3×Dic311yescharacteristic
590C22×C3C2×D3×Dic311yescharacteristic
591C22×C3C2×D3×Dic311yescharacteristic
592C22×C3C2×C3×C4×D311yescharacteristic
593C22×C3C2×C3×C4×D311yescharacteristic
594C22×C3C2×C3×C4×D311yescharacteristic
595C22×C3C22×C3×Dic311yescharacteristic
596C22×C3C22×C3×Dic311yescharacteristic
597C22×C3C22×C3×Dic311yescharacteristic
598C2×D3—42no—
599C2×D3C22×C3×Dic314yes—
600C3×C4—21no—
601C3×C4—21no—
602C3×C4—21no—
603C3×C4—21no—
604C3×C4—21no—
605C3×C4—21no—
606C3×C4—21no—
607C3×C4—21no—
608C3×C4—21no—
609C3×C4—21no—
610C3×C4—21no—
611C3×C4—21no—
612C3×C4—34no—
613C3×C4—34no—
614C3×C4—41no—
615C3×C4—41no—
616C3×C4—41no—
617C3×C4—41no—
618C3×C4—64no—
619C3×C4C2×D3×Dic311yescharacteristic
620C3×C4C2×D3×Dic311yescharacteristic
621C3×C4C2×D3×Dic311yescharacteristic
622C3×C4C2×C3×C4×D311yescharacteristic
623C3×C4C2×C3×C4×D311yescharacteristic
624C3×C4C2×C3×C4×D311yescharacteristic
625C3×C4C22×C3×Dic311yescharacteristic
626C3×C4C22×C3×Dic311yescharacteristic
627C3×C4C22×C3×Dic311yescharacteristic
628C3×C4C22×D3211yescharacteristic
629C3×C4C23×C3×D311yescharacteristic
630C3×C4C23×C3×D311yescharacteristic
631Dic3C22×C3×Dic314yes—
632C32—21no—
633C32—21no—
634C32—21no—
635C32—41no—
636C32#574511yescharacteristic, complemented
637C32#581911yescharacteristic, complemented
638C32C3×#56811yescharacteristic, complemented
639C23—32no—
640C23C3×D3×Dic311yescharacteristic
641Q8—32no—
642Q8—32no—
643D4—34no—
644D4—34no—
645D4—32no—
646D4—32no—
647C2×C4—32no—
648C2×C4—34no—
649C2×C4—34no—
650C2×C4C3×D3×Dic311yescharacteristic
651C2×C4C3×D3×Dic311yescharacteristic
652C2×C4C3×D3×Dic311yescharacteristic
653C2×C4C2×C3×D3211yescharacteristic
654C2×C4C2×C3×D3211yescharacteristic
655C2×C4C2×C3×D3211yescharacteristic
656C8—34no—
657C8—94no—
658C2×C3—22no—
659C2×C3—22no—
660C2×C3—22no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—41no—
674C2×C3—41no—
675C2×C3—41no—
676C2×C3—41no—
677C2×C3—41no—
678C2×C3—41no—
679C2×C3—42no—
680C2×C3—42no—
681C2×C3—42no—
682C2×C3—41no—
683C2×C3—64no—
684C2×C3—64no—
685C2×C3—124no—
686C2×C3C22×D3×Dic311yescharacteristic
687C2×C3C22×C3×C4×D311yescharacteristic
688C2×C3C23×C3×Dic311yescharacteristic
689D3—24no—
690C22—34no—
691C22—41no—
692C22—122no—
693C22C2×C3×D3×Dic311yescharacteristic
694C22C2×C3×D3×Dic311yescharacteristic
695C22C2×C3×D3×Dic311yescharacteristic
696C4—34no—
697C4C2×C3×D3×Dic311yescharacteristic
698C4C2×C3×D3×Dic311yescharacteristic
699C4C2×C3×D3×Dic311yescharacteristic
700C4C22×C3×D3211yescharacteristic
701C3—21no—
702C3—21no—
703C3—21no—
704C3—41no—
705C3#1059477611yescharacteristic, direct product factor
706C3C3×#574511yescharacteristic, complemented
707C3C3×#581911yescharacteristic, complemented
708C2—21no—
709C2—21no—
710C2—21no—
711C2—64no—
712C2C22×C3×D3×Dic311yescharacteristic
subgroupG/H
centerC3×C4C22×D32
commutatorC2×C32C23×C3×C4
FrattiniC4C22×C3×D32
FittingC22×C33×C4C22
socleC2×C33C23×C4
prime radicalC2×C32×#235C2
cosocleC32×C4C24×C3
hypercenterC22×C3×C4D32
hypocenterC32C3×#568
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C3×C4 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#3748C2semidirect
3. C2×C32×#208C2semidirect
4. C3×#63815C2semidirect
5. C3×#63814C2semidirect
6. C3×D3×#208C2semidirect
9. #10594776C3direct (N × H)
20. C3×#3748C22semidirect
21. C2×C3×C3⋊(C3⋊C8)C22semidirect
23. C32×#208C22semidirect
24. C2×C32×C3⋊C8C22semidirect
25. C3×#3711C22semidirect
26. C3×D3×C3⋊C8C22semidirect
32. C2×#3748C2×C3semidirect
40. C2×C3×#208D3semidirect
41. C2×C3×#208C2×C3semidirect
45. #63815C2×C3semidirect
46. #63814C2×C3semidirect
47. D3×#208C2×C3semidirect
113. #3748C22×C3semidirect
114. C2×C3⋊(C3⋊C8)C22×C3semidirect
125. C3×#208C2×D3semidirect
127. C3×#208C22×C3semidirect
133. C2×C3×C3⋊C8C2×D3semidirect
134. C2×C3×C3⋊C8C22×C3semidirect
137. #3711C22×C3semidirect
138. D3×C3⋊C8C22×C3semidirect
167. C2×#208C3×D3semidirect
335. #208C2×C3×D3semidirect
340. C2×C3⋊C8C2×C3×D3semidirect
417. C33#568semidirect
636. C32#5745semidirect
637. C32#5819semidirect
638. C32C3×#568semidirect
705. C3#10594776direct (N × H)
706. C3C3×#5745semidirect
707. C3C3×#5819semidirect

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×#37482
C2×C32×#2082
C3×#638152
C3×#638142
C3×D3×#2082
C3×#58193
C3×#57453
#105947763