Finite Group Databasebeta

← C3×#76430 #11803564

Subgroups — C3×#76430 #11803564

Order 1152.

1465 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#938C211yesmaximal, characteristic
2C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#872C211yesmaximal, characteristic, complemented
4C32×#390C211yesmaximal, characteristic, complemented
5C3×#4987C211yesmaximal, characteristic, complemented
6C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
7C3×#4958C212yesmaximal, complemented
8C3×#4957C212yesmaximal, complemented
9C3×#4946C212yesmaximal, complemented
10C3×#4944C212yesmaximal, complemented
11C3×#4928C211yesmaximal, characteristic, complemented
12C3×#2324—31nomaximal
13#76430C311yesmaximal, characteristic, direct product factor
14C22×C32×D4C2211yescharacteristic
15C22×C3×#67C2212yes—
16C23×C3×Dic3C2212yes—
17C22×C3×C4×D3C2211yescharacteristic
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C32×C22⋊C4C2212yes—
20C2×C32×C22⋊C4C2212yes—
21C2×C32×C42C2211yescharacteristic
22C2×C3×#217C2212yes—
23C2×C3×#217C2212yes—
24C3×#938C418yescomplemented
25C3×D4×Dic3—24no—
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2212yes—
34C2×C3×C4×Dic3C2212yes—
35C2×C3×C4×Dic3C2211yescharacteristic
36C3×#872—24no—
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2212yes—
39C3×C3⋊#95C2212yes—
40C2×C3×#121—31no—
41C2×C3×C4×D4—31no—
42C2×C3×#117—31no—
43C2×#938C2×C311yescharacteristic
44C2×D4×Dic3C2×C311yescharacteristic, complemented
45C2×#872C2×C311yescharacteristic, complemented
46C3×#390—21no—
47C3×#390—32no—
48C3×#390D311yescharacteristic, complemented
49C3×#390C2×C311yescharacteristic, complemented
50C3×#389—31no—
51C3×#388—32no—
52C3×#386—32no—
53C3×#385—32no—
54C3×#380—31no—
55C3×C4×C4⋊C4—31no—
56#4987C2×C311yescharacteristic, complemented
57Dic3×C4⋊C4C2×C311yescharacteristic, complemented
58#4958C2×C312yescomplemented
59#4957C2×C312yescomplemented
60#4946C2×C312yescomplemented
61#4944C2×C312yescomplemented
62#4928C2×C311yescharacteristic, complemented
63C24×C32C2312yes—
64C23×C3×D3C2311yescharacteristic
65C2×C32×D4—22no—
66C2×C32×D4—22no—
67C2×C32×D4C2×C414yes—
68C22×C32×C4C2312yes—
69C22×C32×C4C2311yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C2×C3×#67—42no—
73C2×C3×#67—42no—
74C2×C3×#67C2×C418yescomplemented
75C22×C3×Dic3—24no—
76C22×C3×Dic3—42no—
77C22×C3×Dic3—42no—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2311yescharacteristic
81C22×C3×Dic3C2311yescharacteristic
82C22×C3×Dic3C2311yescharacteristic
83C2×C3×C4×D3—22no—
84C2×C3×C4×D3—22no—
85C2×C3×C4×D3C2×C414yescomplemented
86C32×C4⋊C4—22no—
87C32×C22⋊C4—42no—
88C32×C22⋊C4—42no—
89C32×C42—22no—
90C3×#217—24no—
91C3×#217C2×C418yescomplemented
92C3×(C2×D3)⋊C4—22no—
93C3×(C2×D3)⋊C4—22no—
94C3×(C2×D3)⋊C4—42no—
95C3×C4⋊Dic3—22no—
96C3×C4⋊Dic3C2×C414yescomplemented
97C3×Dic3⋊C4—22no—
98C3×Dic3⋊C4—22no—
99C3×Dic3⋊C4—42no—
100C3×C4×Dic3—42no—
101C3×C4×Dic3D414yescomplemented
102#2324—31noSylow
103C22×C3×D4—21no—
104C22×C3×D4—32no—
105C22×C3×D4C2×D311yescharacteristic
106C22×C3×D4C22×C311yescharacteristic
107C23×C3×C4—31no—
108C23×C3×C4—32no—
109C22×#67C22×C312yes—
110C23×Dic3C22×C312yes—
111C22×C4×D3C22×C311yescharacteristic
112C3×#121—38no—
113C3×C4×D4—64no—
114C3×#117—64no—
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4—31no—
117C2×C3×C4⋊C4—31no—
118C2×C3×C4⋊C4—31no—
119C2×C3×C4⋊C4—31no—
120C2×C3×C4⋊C4—32no—
121C2×C3×C4⋊C4C2×D311yescharacteristic
122C2×C3×C4⋊C4C22×C311yescharacteristic
123C2×C3×C22⋊C4—22no—
124C2×C3×C22⋊C4—22no—
125C2×C3×C22⋊C4—32no—
126C2×C3×C22⋊C4—32no—
127C2×C3×C22⋊C4—31no—
128C2×C3×C22⋊C4—31no—
129C2×C3×C22⋊C4—32no—
130C2×C3×C22⋊C4C2×D312yes—
131C2×C3×C22⋊C4C2×D312yes—
132C2×C3×C22⋊C4C22×C312yes—
133C2×C3×C22⋊C4C22×C312yes—
134C2×C3×C42—21no—
135C2×C3×C42—31no—
136C2×C3×C42—32no—
137C2×C3×C42C2×D311yescharacteristic
138C2×C3×C42C22×C311yescharacteristic
139C2×#217C22×C312yes—
140C2×#217C22×C312yes—
141#938C3×C418yescomplemented
142D4×Dic3—24no—
143C2×(C2×D3)⋊C4C22×C311yescharacteristic
144C2×(C2×D3)⋊C4C22×C311yescharacteristic
145C2×(C2×D3)⋊C4C22×C312yes—
146C2×C4⋊Dic3C22×C311yescharacteristic
147C2×C4⋊Dic3C22×C311yescharacteristic
148C2×Dic3⋊C4C22×C311yescharacteristic
149C2×Dic3⋊C4C22×C311yescharacteristic
150C2×Dic3⋊C4C22×C312yes—
151C2×C4×Dic3C22×C312yes—
152C2×C4×Dic3C22×C311yescharacteristic
153#872—24no—
154C3×#95—32no—
155C3×#95—32no—
156C3×#95—32no—
157C3⋊#95C22×C312yes—
158C3⋊#95C22×C312yes—
159C3⋊#95C22×C312yes—
160C23×C32—22no—
161C23×C32—22no—
162C23×C32—22no—
163C23×C32—22no—
164C23×C32—22no—
165C23×C32—22no—
166C23×C32C22×C414yes—
167C23×C32C2411yescharacteristic
168C22×C3×D3—21no—
169C22×C3×D3—21no—
170C22×C3×D3—21no—
171C22×C3×D3—21no—
172C22×C3×D3—21no—
173C22×C3×D3—21no—
174C22×C3×D3C22×C412yes—
175C32×D4—28no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—22no—
181C2×C32×C4—22no—
182C2×C32×C4—21no—
183C2×C32×C4—22no—
184C2×C32×C4—21no—
185C2×C32×C4C22×C412yes—
186C2×C32×C4C2×D412yes—
187C2×C32×C4#4112yes—
188C3×#67—48no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—48no—
201C2×C3×Dic3C22×C414yes—
202C2×C3×Dic3C22×C412yes—
203C2×C3×Dic3C2×D412yes—
204C2×C3×Dic3C2×D412yes—
205C3×C4×D3—28no—
206C2×#121—31no—
207C2×C4×D4—31no—
208C2×#117—31no—
209#390—32no—
210#390C3×D311yescharacteristic, complemented
211#389—31no—
212#388—32no—
213#386—32no—
214#385—32no—
215#380—31no—
216C4×C4⋊C4—31no—
217C24×C3—22no—
218C24×C3—31no—
219C24×C3C22×D312yes—
220C24×C3C23×C312yes—
221C23×D3C23×C311yescharacteristic
222C2×C3×D4—22no—
223C2×C3×D4—22no—
224C2×C3×D4—22no—
225C2×C3×D4—22no—
226C2×C3×D4—24no—
227C2×C3×D4—38no—
228C2×C3×D4—42no—
229C2×C3×D4—42no—
230C2×C3×D4—122no—
231C2×C3×D4—122no—
232C2×C3×D4C4×D314yes—
233C2×C3×D4C2×C3×C414yes—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—22no—
238C22×C3×C4—32no—
239C22×C3×C4—31no—
240C22×C3×C4—31no—
241C22×C3×C4—31no—
242C22×C3×C4—34no—
243C22×C3×C4—32no—
244C22×C3×C4—64no—
245C22×C3×C4—62no—
246C22×C3×C4—62no—
247C22×C3×C4—122no—
248C22×C3×C4—122no—
249C22×C3×C4C22×D312yes—
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C23×C312yes—
254C22×C3×C4C23×C311yescharacteristic
255C22×C3×C4C23×C311yescharacteristic
256C22×C3×C4C23×C311yescharacteristic
257C2×#67—42no—
258C2×#67—42no—
259C2×#67C2×C3×C418yescomplemented
260C22×Dic3—24no—
261C22×Dic3—42no—
262C22×Dic3—42no—
263C22×Dic3C23×C312yes—
264C22×Dic3C23×C312yes—
265C22×Dic3C23×C311yescharacteristic
266C22×Dic3C23×C311yescharacteristic
267C22×Dic3C23×C311yescharacteristic
268C2×C4×D3—22no—
269C2×C4×D3—22no—
270C2×C4×D3C2×C3×C414yescomplemented
271C3×C4⋊C4—22no—
272C3×C4⋊C4—22no—
273C3×C4⋊C4—34no—
274C3×C4⋊C4—42no—
275C3×C4⋊C4—62no—
276C3×C4⋊C4—62no—
277C3×C4⋊C4—62no—
278C3×C4⋊C4—122no—
279C3×C22⋊C4—38no—
280C3×C22⋊C4—42no—
281C3×C22⋊C4—42no—
282C3×C22⋊C4—42no—
283C3×C22⋊C4—42no—
284C3×C22⋊C4—44no—
285C3×C22⋊C4—44no—
286C3×C22⋊C4—62no—
287C3×C22⋊C4—62no—
288C3×C22⋊C4—64no—
289C3×C22⋊C4—122no—
290C3×C42—22no—
291C3×C42—22no—
292C3×C42—34no—
293C3×C42—42no—
294C3×C42—122no—
295#217—24no—
296#217C2×C3×C418yescomplemented
297(C2×D3)⋊C4—22no—
298(C2×D3)⋊C4—22no—
299(C2×D3)⋊C4—42no—
300C4⋊Dic3—22no—
301C4⋊Dic3C2×C3×C414yescomplemented
302Dic3⋊C4—22no—
303Dic3⋊C4—22no—
304Dic3⋊C4—42no—
305C4×Dic3—42no—
306C4×Dic3C3×D414yescomplemented
307C22×C32—24no—
308C22×C32—24no—
309C22×C32—24no—
310C22×C32—42no—
311C22×C32—42no—
312C22×C32—42no—
313C22×C32—42no—
314C22×C32C23×C411yescharacteristic
315C22×C32C22×D411yescharacteristic
316C22×C32C2×#4111yescharacteristic
317C22×C32H(5,𝔽2)11yescharacteristic
318C22×C32H(5,𝔽2)11yescharacteristic
319C22×C32H(5,𝔽2)11yescharacteristic
320C22×C322−1+411yescharacteristic
321C2×C3×D3—22no—
322C2×C3×D3—22no—
323C2×C3×D3—22no—
324C2×C3×D3—41no—
325C2×C3×D3—41no—
326C2×C3×D3—41no—
327C2×C3×D3—41no—
328C32×C4—41no—
329C32×C4—41no—
330C32×C4—42no—
331C32×C4C4×D414yes—
332C3×Dic3—22no—
333C3×Dic3—24no—
334C3×Dic3—22no—
335C3×Dic3—22no—
336C3×Dic3—42no—
337C22×D4—32no—
338C22×D4C2×C3×D311yescharacteristic
339C23×C4—31no—
340C23×C4—32no—
341#121—38no—
342C4×D4—64no—
343#117—64no—
344C2×C4⋊C4—31no—
345C2×C4⋊C4—31no—
346C2×C4⋊C4—31no—
347C2×C4⋊C4—31no—
348C2×C4⋊C4—32no—
349C2×C4⋊C4C2×C3×D311yescharacteristic
350C2×C22⋊C4—32no—
351C2×C22⋊C4—32no—
352C2×C22⋊C4—31no—
353C2×C22⋊C4—31no—
354C2×C22⋊C4—32no—
355C2×C22⋊C4C2×C3×D312yes—
356C2×C22⋊C4C2×C3×D312yes—
357C2×C42—31no—
358C2×C42—32no—
359C2×C42C2×C3×D311yescharacteristic
360#95—32no—
361#95—32no—
362#95—32no—
363C23×C3—22no—
364C23×C3—22no—
365C23×C3—22no—
366C23×C3—22no—
367C23×C3—22no—
368C23×C3—22no—
369C23×C3—22no—
370C23×C3—22no—
371C23×C3—22no—
372C23×C3—22no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3—21no—
376C23×C3—24no—
377C23×C3—32no—
378C23×C3—42no—
379C23×C3—42no—
380C23×C3—42no—
381C23×C3—42no—
382C23×C3—42no—
383C23×C3—42no—
384C23×C3—61no—
385C23×C3—61no—
386C23×C3—61no—
387C23×C3—61no—
388C23×C3—61no—
389C23×C3—61no—
390C23×C3C2×C4×D314yes—
391C23×C3C22×C3×C414yes—
392C23×C3C23×D311yescharacteristic
393C23×C3C24×C311yescharacteristic
394C22×D3—21no—
395C22×D3—21no—
396C22×D3—21no—
397C22×D3—21no—
398C22×D3—21no—
399C22×D3—21no—
400C22×D3C22×C3×C412yes—
401C3×D4—28no—
402C3×D4—28no—
403C3×D4—48no—
404C3×D4—128no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—22no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—21no—
421C2×C3×C4—22no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—32no—
429C2×C3×C4—34no—
430C2×C3×C4—32no—
431C2×C3×C4—32no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—42no—
437C2×C3×C4—42no—
438C2×C3×C4—42no—
439C2×C3×C4—61no—
440C2×C3×C4—61no—
441C2×C3×C4—61no—
442C2×C3×C4—62no—
443C2×C3×C4—61no—
444C2×C3×C4—62no—
445C2×C3×C4—61no—
446C2×C3×C4—61no—
447C2×C3×C4—68no—
448C2×C3×C4—62no—
449C2×C3×C4—62no—
450C2×C3×C4—62no—
451C2×C3×C4—128no—
452C2×C3×C4C2×C4×D312yes—
453C2×C3×C4D3×D412yes—
454C2×C3×C4#23712yes—
455C2×C3×C4C22×C3×C412yes—
456C2×C3×C4C2×C3×D412yes—
457C2×C3×C4C3×#4112yes—
458#67—48no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—22no—
463C2×Dic3—22no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—22no—
470C2×Dic3—48no—
471C2×Dic3C22×C3×C414yes—
472C2×Dic3C22×C3×C412yes—
473C2×Dic3C2×C3×D412yes—
474C2×Dic3C2×C3×D412yes—
475C4×D3—28no—
476C2×C32—44no—
477C2×C32C2×C4×D411yescharacteristic
478C2×C32#51811yescharacteristic
479C2×C32#52011yescharacteristic
480C2×C32#53511yescharacteristic
481C2×C32#53711yescharacteristic
482C2×C32#54011yescharacteristic
483C2×C32#54211yescharacteristic
484C3×D3—42no—
485C24—31no—
486C24C22×C3×D312yes—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—38no—
490C2×D4—122no—
491C2×D4—122no—
492C2×D4C3×C4×D314yes—
493C22×C4—32no—
494C22×C4—31no—
495C22×C4—31no—
496C22×C4—31no—
497C22×C4—34no—
498C22×C4—32no—
499C22×C4—64no—
500C22×C4—62no—
501C22×C4—62no—
502C22×C4—122no—
503C22×C4—122no—
504C22×C4C22×C3×D312yes—
505C22×C4C22×C3×D311yescharacteristic
506C22×C4C22×C3×D311yescharacteristic
507C22×C4C22×C3×D311yescharacteristic
508C4⋊C4—22no—
509C4⋊C4—34no—
510C4⋊C4—62no—
511C4⋊C4—62no—
512C4⋊C4—62no—
513C4⋊C4—122no—
514C22⋊C4—38no—
515C22⋊C4—42no—
516C22⋊C4—42no—
517C22⋊C4—62no—
518C22⋊C4—62no—
519C22⋊C4—64no—
520C22⋊C4—122no—
521C42—22no—
522C42—34no—
523C42—122no—
524C22×C3—24no—
525C22×C3—24no—
526C22×C3—24no—
527C22×C3—24no—
528C22×C3—24no—
529C22×C3—24no—
530C22×C3—21no—
531C22×C3—21no—
532C22×C3—21no—
533C22×C3—21no—
534C22×C3—21no—
535C22×C3—21no—
536C22×C3—21no—
537C22×C3—44no—
538C22×C3—44no—
539C22×C3—44no—
540C22×C3—42no—
541C22×C3—42no—
542C22×C3—42no—
543C22×C3—42no—
544C22×C3—42no—
545C22×C3—42no—
546C22×C3—42no—
547C22×C3—42no—
548C22×C3—62no—
549C22×C3—62no—
550C22×C3—62no—
551C22×C3—82no—
552C22×C3—82no—
553C22×C3—82no—
554C22×C3—82no—
555C22×C3—121no—
556C22×C3—121no—
557C22×C3—121no—
558C22×C3—121no—
559C22×C3C22×C4×D311yescharacteristic
560C22×C3C2×D3×D411yescharacteristic
561C22×C3C2×#23711yescharacteristic
562C22×C3#100411yescharacteristic
563C22×C3#100411yescharacteristic
564C22×C3#100911yescharacteristic
565C22×C3#101011yescharacteristic
566C22×C3C23×C3×C411yescharacteristic
567C22×C3C22×C3×D411yescharacteristic
568C22×C3C2×C3×#4111yescharacteristic
569C22×C3C3×H(5,𝔽2)11yescharacteristic
570C22×C3C3×H(5,𝔽2)11yescharacteristic
571C22×C3C3×H(5,𝔽2)11yescharacteristic
572C22×C3C3×2−1+411yescharacteristic
573C2×D3—22no—
574C2×D3—22no—
575C2×D3—22no—
576C2×D3—41no—
577C2×D3—41no—
578C2×D3—41no—
579C2×D3—41no—
580C3×C4—24no—
581C3×C4—42no—
582C3×C4—42no—
583C3×C4—42no—
584C3×C4—41no—
585C3×C4—41no—
586C3×C4—41no—
587C3×C4—41no—
588C3×C4—42no—
589C3×C4—62no—
590C3×C4—64no—
591C3×C4—62no—
592C3×C4—62no—
593C3×C4—82no—
594C3×C4—122no—
595C3×C4#67⋊C414yes—
596C3×C4C3×C4×D414yes—
597Dic3—22no—
598Dic3—24no—
599Dic3—22no—
600Dic3—22no—
601Dic3—42no—
602C32#232411yescharacteristic, complemented, Sylow
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—32no—
610C23—61no—
611C23—61no—
612C23—61no—
613C23—61no—
614C23—61no—
615C23—61no—
616C23C2×C3×C4×D314yes—
617C23C23×C3×D311yescharacteristic
618D4—28no—
619D4—128no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—32no—
630C2×C4—34no—
631C2×C4—32no—
632C2×C4—32no—
633C2×C4—61no—
634C2×C4—61no—
635C2×C4—61no—
636C2×C4—62no—
637C2×C4—61no—
638C2×C4—62no—
639C2×C4—61no—
640C2×C4—61no—
641C2×C4—68no—
642C2×C4—62no—
643C2×C4—62no—
644C2×C4—62no—
645C2×C4—128no—
646C2×C4C2×C3×C4×D312yes—
647C2×C4C3×D3×D412yes—
648C2×C4C3×#23712yes—
649C2×C3—21no—
650C2×C3—21no—
651C2×C3—21no—
652C2×C3—21no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—44no—
657C2×C3—44no—
658C2×C3—84no—
659C2×C3—122no—
660C2×C3C2×#67⋊C411yescharacteristic
661C2×C3#554511yescharacteristic
662C2×C3#554611yescharacteristic
663C2×C3#560711yescharacteristic
664C2×C3#560811yescharacteristic
665C2×C3#568211yescharacteristic
666C2×C3#571911yescharacteristic
667C2×C3C2×C3×C4×D411yescharacteristic
668C2×C3C3×#51811yescharacteristic
669C2×C3C3×#52011yescharacteristic
670C2×C3C3×#53511yescharacteristic
671C2×C3C3×#53711yescharacteristic
672C2×C3C3×#54011yescharacteristic
673C2×C3C3×#54211yescharacteristic
674D3—42no—
675C22—24no—
676C22—24no—
677C22—24no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22—62no—
683C22—62no—
684C22—62no—
685C22—121no—
686C22—121no—
687C22—121no—
688C22—121no—
689C22C22×C3×C4×D311yescharacteristic
690C22C2×C3×D3×D411yescharacteristic
691C22C2×C3×#23711yescharacteristic
692C22C3×#100411yescharacteristic
693C22C3×#100411yescharacteristic
694C22C3×#100911yescharacteristic
695C22C3×#101011yescharacteristic
696C4—41no—
697C4—41no—
698C4—42no—
699C4—64no—
700C4—62no—
701C4—62no—
702C4—62no—
703C4—122no—
704C4C3×#67⋊C414yes—
705C3—21no—
706C3#7643011yescharacteristic, direct product factor
707C3C3×#232411yescharacteristic, complemented
708C2—44no—
709C2—122no—
710C2C2×C3×#67⋊C411yescharacteristic
711C2C3×#554511yescharacteristic
712C2C3×#554611yescharacteristic
713C2C3×#560711yescharacteristic
714C2C3×#560811yescharacteristic
715C2C3×#568211yescharacteristic
716C2C3×#571911yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#390C2
socleC23×C32C24
prime radicalC2×C3×#938C2
cosocleC23×C3C24×C3
hypercenterC3×#390D3
hypocenterC3C3×#2324
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#390

Complements

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

NH ≅ G/Ntype
2. C2×C3×D4×Dic3C2semidirect
3. C2×C3×#872C2semidirect
4. C32×#390C2semidirect
5. C3×#4987C2semidirect
6. C3×Dic3×C4⋊C4C2semidirect
7. C3×#4958C2semidirect
8. C3×#4957C2semidirect
9. C3×#4946C2semidirect
10. C3×#4944C2semidirect
11. C3×#4928C2semidirect
13. #76430C3direct (N × H)
24. C3×#938C4semidirect
44. C2×D4×Dic3C2×C3semidirect
45. C2×#872C2×C3semidirect
48. C3×#390D3semidirect
49. C3×#390C2×C3semidirect
56. #4987C2×C3semidirect
57. Dic3×C4⋊C4C2×C3semidirect
58. #4958C2×C3semidirect
59. #4957C2×C3semidirect
60. #4946C2×C3semidirect
61. #4944C2×C3semidirect
62. #4928C2×C3semidirect
74. C2×C3×#67C2×C4semidirect
85. C2×C3×C4×D3C2×C4semidirect
91. C3×#217C2×C4semidirect
96. C3×C4⋊Dic3C2×C4semidirect
101. C3×C4×Dic3D4semidirect
141. #938C3×C4semidirect
210. #390C3×D3semidirect
259. C2×#67C2×C3×C4semidirect
270. C2×C4×D3C2×C3×C4semidirect
296. #217C2×C3×C4semidirect
301. C4⋊Dic3C2×C3×C4semidirect
306. C4×Dic3C3×D4semidirect
602. C32#2324semidirect
706. C3#76430direct (N × H)
707. C3C3×#2324semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9382
C2×C3×D4×Dic32
C2×C3×#8722
C32×#3902
C3×#49872
C3×Dic3×C4⋊C42
C3×#49582
C3×#49572
C3×#49462
C3×#49442
C3×#49282
C3×#23243
#764303