Finite Group Databasebeta

← C3×#82633 #11803561

Subgroups — C3×#82633 #11803561

Order 1152.

1549 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#121C211yesmaximal, characteristic
2C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#926C211yesmaximal, characteristic, complemented
4C3×#5221C211yesmaximal, characteristic, complemented
5C3×#5221C212yesmaximal, complemented
6C3×#5220C212yesmaximal, complemented
7C3×#5212C211yesmaximal, characteristic, complemented
8C3×#4984C211yesmaximal, characteristic, complemented
9C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
10C3×#4951C212yesmaximal, complemented
11C3×#4950C212yesmaximal, complemented
12C3×#2324—31nomaximal
13#82633C311yesmaximal, characteristic, direct product factor
14C22×C32×D4C2211yescharacteristic
15C22×C32×D4C2212yes—
16C23×C32×C4C2211yescharacteristic
17C23×C3×Dic3C2212yes—
18C32×#121C418yescomplemented
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C32×C22⋊C4C2212yes—
21C2×C3×#217C2211yescharacteristic
22C2×C3×#217C2211yescharacteristic
23C2×C3×#217C2212yes—
24C2×C3×#217C2212yes—
25C2×C3×#217C2212yes—
26C2×C3×#217C2212yes—
27C3×D4×Dic3—24no—
28C3×#926—24no—
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×C4⋊Dic3C2212yes—
34C2×C3×C4×Dic3C2211yescharacteristic
35C2×C3×C4×Dic3C2212yes—
36C2×C3×C4×Dic3C2211yescharacteristic
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2212yes—
39C3×C3⋊#95C2212yes—
40C2×C3×#121—21no—
41C2×C3×#121D311yescharacteristic
42C2×C3×#121C2×C311yescharacteristic
43C2×C3×C4×D4—31no—
44C2×C3×#117—31no—
45C2×D4×Dic3C2×C311yescharacteristic, complemented
46C2×#926C2×C311yescharacteristic, complemented
47C3×#390—31no—
48C3×#390—32no—
49C3×#389—31no—
50C3×#388—32no—
51C3×#386—32no—
52C3×#385—32no—
53C3×#380—31no—
54C3×C4×C4⋊C4—31no—
55#5221C2×C311yescharacteristic, complemented
56#5221C2×C312yescomplemented
57#5220C2×C312yescomplemented
58#5212C2×C311yescharacteristic, complemented
59#4984C2×C311yescharacteristic, complemented
60Dic3×C4⋊C4C2×C311yescharacteristic, complemented
61#4951C2×C312yescomplemented
62#4950C2×C312yescomplemented
63C24×C32C2311yescharacteristic
64C24×C32C2312yes—
65C2×C32×D4—22no—
66C2×C32×D4—22no—
67C2×C32×D4—42no—
68C2×C32×D4—42no—
69C2×C32×D4C2×C414yes—
70C2×C32×D4C2×C418yescomplemented
71C22×C32×C4—22no—
72C22×C32×C4—22no—
73C22×C32×C4C2×C414yescomplemented
74C22×C32×C4C2312yes—
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C3×Dic3—24no—
78C22×C3×Dic3—42no—
79C22×C3×Dic3—42no—
80C22×C3×Dic3C2311yescharacteristic
81C22×C3×Dic3C2311yescharacteristic
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2311yescharacteristic
86C32×C4⋊C4C2×C414yescomplemented
87C32×C22⋊C4C2×C418yescomplemented
88C3×#217—22no—
89C3×#217—22no—
90C3×#217—24no—
91C3×#217—42no—
92C3×#217—42no—
93C3×#217—42no—
94C3×C4⋊Dic3—22no—
95C3×C4⋊Dic3—22no—
96C3×C4⋊Dic3—22no—
97C3×C4⋊Dic3—22no—
98C3×C4⋊Dic3—42no—
99C3×C4×Dic3—22no—
100C3×C4×Dic3—42no—
101C3×C4×Dic3D414yescomplemented
102#2324—31noSylow
103C22×C3×D4—21no—
104C22×C3×D4—22no—
105C22×C3×D4C2×D311yescharacteristic
106C22×C3×D4C2×D312yes—
107C22×C3×D4C22×C311yescharacteristic
108C22×C3×D4C22×C312yes—
109C23×C3×C4—21no—
110C23×C3×C4—32no—
111C23×C3×C4C2×D311yescharacteristic
112C23×C3×C4C22×C311yescharacteristic
113C23×Dic3C22×C312yes—
114C3×#121—28no—
115C3×#121Dic318yescomplemented
116C3×#121C3×C418yescomplemented
117C3×C4×D4—64no—
118C3×#117—64no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—31no—
121C2×C3×C4⋊C4—31no—
122C2×C3×C4⋊C4—31no—
123C2×C3×C4⋊C4—31no—
124C2×C3×C4⋊C4—32no—
125C2×C3×C4⋊C4C2×D311yescharacteristic
126C2×C3×C4⋊C4C22×C311yescharacteristic
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4—31no—
129C2×C3×C22⋊C4—32no—
130C2×C3×C22⋊C4—31no—
131C2×C3×C22⋊C4—32no—
132C2×C3×C22⋊C4—32no—
133C2×C3×C22⋊C4—32no—
134C2×C3×C22⋊C4C2×D312yes—
135C2×C3×C22⋊C4C22×C312yes—
136C2×C3×C42—31no—
137C2×C3×C42—31no—
138C2×C3×C42—32no—
139C2×#217C22×C312yes—
140C2×#217C22×C311yescharacteristic
141C2×#217C22×C311yescharacteristic
142C2×#217C22×C312yes—
143C2×#217C22×C312yes—
144C2×#217C22×C312yes—
145D4×Dic3—24no—
146#926—24no—
147C2×C4⋊Dic3C22×C311yescharacteristic
148C2×C4⋊Dic3C22×C311yescharacteristic
149C2×C4⋊Dic3C22×C311yescharacteristic
150C2×C4⋊Dic3C22×C311yescharacteristic
151C2×C4⋊Dic3C22×C312yes—
152C2×C4×Dic3C22×C311yescharacteristic
153C2×C4×Dic3C22×C312yes—
154C2×C4×Dic3C22×C311yescharacteristic
155C3×#95—32no—
156C3×#95—32no—
157C3×#95—32no—
158C3⋊#95C22×C312yes—
159C3⋊#95C22×C312yes—
160C3⋊#95C22×C312yes—
161C23×C32—21no—
162C23×C32—21no—
163C23×C32—21no—
164C23×C32—22no—
165C23×C32—21no—
166C23×C32—22no—
167C23×C32—21no—
168C23×C32—22no—
169C23×C32—22no—
170C23×C32—22no—
171C23×C32—21no—
172C23×C32—22no—
173C23×C32C22×C414yes—
174C23×C32C22×C412yes—
175C23×C32C2411yescharacteristic
176C32×D4—28no—
177C32×D4—48no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—22no—
181C2×C32×C4—22no—
182C2×C32×C4—28no—
183C2×C32×C4C22×C412yes—
184C2×C32×C4C22×C414yes—
185C2×C32×C4C22×C412yes—
186C2×C32×C4C2×D412yes—
187C2×C32×C4#4112yes—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—21no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—48no—
205C2×C3×Dic3C2×D412yes—
206C2×C3×Dic3C2×D412yes—
207C2×#121C3×D311yescharacteristic
208C2×C4×D4—31no—
209C2×#117—31no—
210#390—31no—
211#390—32no—
212#389—31no—
213#388—32no—
214#386—32no—
215#385—32no—
216#380—31no—
217C4×C4⋊C4—31no—
218C24×C3—21no—
219C24×C3—22no—
220C24×C3C22×D311yescharacteristic
221C24×C3C22×D312yes—
222C24×C3C23×C311yescharacteristic
223C24×C3C23×C312yes—
224C2×C3×D4—22no—
225C2×C3×D4—22no—
226C2×C3×D4—22no—
227C2×C3×D4—22no—
228C2×C3×D4—24no—
229C2×C3×D4—28no—
230C2×C3×D4—42no—
231C2×C3×D4—42no—
232C2×C3×D4—42no—
233C2×C3×D4—42no—
234C2×C3×D4—42no—
235C2×C3×D4—42no—
236C2×C3×D4—44no—
237C2×C3×D4—44no—
238C2×C3×D4C2×Dic314yes—
239C2×C3×D4C2×Dic318yescomplemented
240C2×C3×D4C2×C3×C414yes—
241C2×C3×D4C2×C3×C418yescomplemented
242C22×C3×C4—22no—
243C22×C3×C4—22no—
244C22×C3×C4—22no—
245C22×C3×C4—22no—
246C22×C3×C4—24no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—22no—
250C22×C3×C4—31no—
251C22×C3×C4—31no—
252C22×C3×C4—31no—
253C22×C3×C4—32no—
254C22×C3×C4—32no—
255C22×C3×C4—31no—
256C22×C3×C4—42no—
257C22×C3×C4—42no—
258C22×C3×C4—64no—
259C22×C3×C4—122no—
260C22×C3×C4—122no—
261C22×C3×C4C2×Dic314yescomplemented
262C22×C3×C4C2×C3×C414yescomplemented
263C22×C3×C4C22×D312yes—
264C22×C3×C4C22×D311yescharacteristic
265C22×C3×C4C22×D311yescharacteristic
266C22×C3×C4C23×C312yes—
267C22×C3×C4C23×C311yescharacteristic
268C22×C3×C4C23×C311yescharacteristic
269C22×Dic3—24no—
270C22×Dic3—42no—
271C22×Dic3—42no—
272C22×Dic3C23×C311yescharacteristic
273C22×Dic3C23×C312yes—
274C22×Dic3C23×C312yes—
275C22×Dic3C23×C311yescharacteristic
276C22×Dic3C23×C311yescharacteristic
277C22×Dic3C23×C311yescharacteristic
278C3×C4⋊C4—24no—
279C3×C4⋊C4—62no—
280C3×C4⋊C4—62no—
281C3×C4⋊C4—62no—
282C3×C4⋊C4—62no—
283C3×C4⋊C4—122no—
284C3×C4⋊C4C2×Dic314yescomplemented
285C3×C4⋊C4C2×C3×C414yescomplemented
286C3×C22⋊C4—28no—
287C3×C22⋊C4—62no—
288C3×C22⋊C4—62no—
289C3×C22⋊C4—64no—
290C3×C22⋊C4—122no—
291C3×C22⋊C4—122no—
292C3×C22⋊C4—122no—
293C3×C22⋊C4C2×Dic318yescomplemented
294C3×C22⋊C4C2×C3×C418yescomplemented
295C3×C42—34no—
296C3×C42—62no—
297C3×C42—122no—
298#217—22no—
299#217—22no—
300#217—24no—
301#217—42no—
302#217—42no—
303#217—42no—
304C4⋊Dic3—22no—
305C4⋊Dic3—22no—
306C4⋊Dic3—22no—
307C4⋊Dic3—22no—
308C4⋊Dic3—42no—
309C4×Dic3—22no—
310C4×Dic3—42no—
311C4×Dic3C3×D414yescomplemented
312C22×C32—22no—
313C22×C32—22no—
314C22×C32—24no—
315C22×C32—24no—
316C22×C32—22no—
317C22×C32—24no—
318C22×C32—41no—
319C22×C32—41no—
320C22×C32—41no—
321C22×C32—41no—
322C22×C32—42no—
323C22×C32—42no—
324C22×C32—42no—
325C22×C32—42no—
326C22×C32C23×C411yescharacteristic
327C22×C32C22×D411yescharacteristic
328C22×C32C2×#4111yescharacteristic
329C22×C32H(5,𝔽2)11yescharacteristic
330C22×C32H(5,𝔽2)11yescharacteristic
331C22×C32H(5,𝔽2)11yescharacteristic
332C22×C322−1+411yescharacteristic
333C32×C4—22no—
334C32×C4—24no—
335C32×C4C4×D414yes—
336C3×Dic3—22no—
337C3×Dic3—22no—
338C3×Dic3—41no—
339C3×Dic3—42no—
340C3×Dic3—41no—
341C3×Dic3—42no—
342C22×D4C2×C3×D311yescharacteristic
343C22×D4C2×C3×D312yes—
344C23×C4—32no—
345C23×C4C2×C3×D311yescharacteristic
346#121C3×Dic318yescomplemented
347C4×D4—64no—
348#117—64no—
349C2×C4⋊C4—31no—
350C2×C4⋊C4—31no—
351C2×C4⋊C4—31no—
352C2×C4⋊C4—31no—
353C2×C4⋊C4—32no—
354C2×C4⋊C4C2×C3×D311yescharacteristic
355C2×C22⋊C4—31no—
356C2×C22⋊C4—31no—
357C2×C22⋊C4—32no—
358C2×C22⋊C4—32no—
359C2×C22⋊C4—32no—
360C2×C22⋊C4—32no—
361C2×C22⋊C4C2×C3×D312yes—
362C2×C42—31no—
363C2×C42—31no—
364C2×C42—32no—
365#95—32no—
366#95—32no—
367#95—32no—
368C23×C3—22no—
369C23×C3—22no—
370C23×C3—21no—
371C23×C3—22no—
372C23×C3—21no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3—22no—
376C23×C3—21no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—22no—
380C23×C3—21no—
381C23×C3—22no—
382C23×C3—21no—
383C23×C3—22no—
384C23×C3—21no—
385C23×C3—22no—
386C23×C3—21no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—21no—
393C23×C3—22no—
394C23×C3—21no—
395C23×C3—22no—
396C23×C3—24no—
397C23×C3—41no—
398C23×C3—41no—
399C23×C3—41no—
400C23×C3—41no—
401C23×C3—42no—
402C23×C3—42no—
403C23×C3—42no—
404C23×C3—42no—
405C23×C3—42no—
406C23×C3—42no—
407C23×C3C22×Dic314yes—
408C23×C3C22×Dic312yes—
409C23×C3C22×C3×C414yes—
410C23×C3C22×C3×C412yes—
411C23×C3C23×D311yescharacteristic
412C23×C3C24×C311yescharacteristic
413C3×D4—28no—
414C3×D4—28no—
415C3×D4—48no—
416C3×D4—48no—
417C3×D4—48no—
418C3×D4—416no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—28no—
428C2×C3×C4—28no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—24no—
434C2×C3×C4—32no—
435C2×C3×C4—32no—
436C2×C3×C4—48no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—42no—
440C2×C3×C4—42no—
441C2×C3×C4—61no—
442C2×C3×C4—61no—
443C2×C3×C4—61no—
444C2×C3×C4—61no—
445C2×C3×C4—61no—
446C2×C3×C4—61no—
447C2×C3×C4—62no—
448C2×C3×C4—62no—
449C2×C3×C4—62no—
450C2×C3×C4—61no—
451C2×C3×C4—61no—
452C2×C3×C4—62no—
453C2×C3×C4—61no—
454C2×C3×C4—62no—
455C2×C3×C4—62no—
456C2×C3×C4—61no—
457C2×C3×C4—128no—
458C2×C3×C4D3×D412yes—
459C2×C3×C4#23712yes—
460C2×C3×C4C22×Dic312yes—
461C2×C3×C4C22×Dic314yes—
462C2×C3×C4C22×Dic312yes—
463C2×C3×C4C22×C3×C412yes—
464C2×C3×C4C22×C3×C414yes—
465C2×C3×C4C22×C3×C412yes—
466C2×C3×C4C2×C3×D412yes—
467C2×C3×C4C3×#4112yes—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—21no—
478C2×Dic3—22no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—21no—
484C2×Dic3—48no—
485C2×Dic3C2×C3×D412yes—
486C2×Dic3C2×C3×D412yes—
487C2×C32—42no—
488C2×C32—44no—
489C2×C32C2×C4×D411yescharacteristic
490C2×C32#51811yescharacteristic
491C2×C32#52011yescharacteristic
492C2×C32#53511yescharacteristic
493C2×C32#53711yescharacteristic
494C2×C32#54011yescharacteristic
495C2×C32#54211yescharacteristic
496C24C22×C3×D311yescharacteristic
497C24C22×C3×D312yes—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4C2×C3×Dic314yes—
503C2×D4C2×C3×Dic318yescomplemented
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—31no—
507C22×C4—31no—
508C22×C4—31no—
509C22×C4—32no—
510C22×C4—32no—
511C22×C4—31no—
512C22×C4—64no—
513C22×C4—122no—
514C22×C4—122no—
515C22×C4C2×C3×Dic314yescomplemented
516C22×C4C22×C3×D312yes—
517C22×C4C22×C3×D311yescharacteristic
518C22×C4C22×C3×D311yescharacteristic
519C4⋊C4—62no—
520C4⋊C4—62no—
521C4⋊C4—62no—
522C4⋊C4—62no—
523C4⋊C4—122no—
524C4⋊C4C2×C3×Dic314yescomplemented
525C22⋊C4—62no—
526C22⋊C4—62no—
527C22⋊C4—64no—
528C22⋊C4—122no—
529C22⋊C4—122no—
530C22⋊C4—122no—
531C22⋊C4C2×C3×Dic318yescomplemented
532C42—34no—
533C42—62no—
534C42—122no—
535C22×C3—24no—
536C22×C3—22no—
537C22×C3—24no—
538C22×C3—22no—
539C22×C3—24no—
540C22×C3—22no—
541C22×C3—24no—
542C22×C3—22no—
543C22×C3—24no—
544C22×C3—22no—
545C22×C3—24no—
546C22×C3—22no—
547C22×C3—24no—
548C22×C3—21no—
549C22×C3—21no—
550C22×C3—21no—
551C22×C3—21no—
552C22×C3—21no—
553C22×C3—21no—
554C22×C3—21no—
555C22×C3—42no—
556C22×C3—42no—
557C22×C3—44no—
558C22×C3—44no—
559C22×C3—44no—
560C22×C3—42no—
561C22×C3—42no—
562C22×C3—42no—
563C22×C3—42no—
564C22×C3—41no—
565C22×C3—42no—
566C22×C3—42no—
567C22×C3—41no—
568C22×C3—41no—
569C22×C3—42no—
570C22×C3—42no—
571C22×C3—41no—
572C22×C3—41no—
573C22×C3—42no—
574C22×C3—41no—
575C22×C3—42no—
576C22×C3—41no—
577C22×C3—42no—
578C22×C3—41no—
579C22×C3—42no—
580C22×C3—82no—
581C22×C3—82no—
582C22×C3—82no—
583C22×C3—82no—
584C22×C3C2×D3×D411yescharacteristic
585C22×C3C2×#23711yescharacteristic
586C22×C3#100411yescharacteristic
587C22×C3#100411yescharacteristic
588C22×C3#100911yescharacteristic
589C22×C3#101011yescharacteristic
590C22×C3C23×Dic311yescharacteristic
591C22×C3C23×C3×C411yescharacteristic
592C22×C3C22×C3×D411yescharacteristic
593C22×C3C2×C3×#4111yescharacteristic
594C22×C3C3×H(5,𝔽2)11yescharacteristic
595C22×C3C3×H(5,𝔽2)11yescharacteristic
596C22×C3C3×H(5,𝔽2)11yescharacteristic
597C22×C3C3×2−1+411yescharacteristic
598C3×C4—22no—
599C3×C4—24no—
600C3×C4—22no—
601C3×C4—24no—
602C3×C4—24no—
603C3×C4—42no—
604C3×C4—44no—
605C3×C4—62no—
606C3×C4—62no—
607C3×C4—122no—
608C3×C4—121no—
609C3×C4—121no—
610C3×C4—122no—
611C3×C4D4×Dic314yes—
612C3×C4C3×C4×D414yes—
613Dic3—22no—
614Dic3—22no—
615Dic3—42no—
616Dic3—41no—
617Dic3—41no—
618Dic3—42no—
619C32#232411yescharacteristic, complemented, Sylow
620C23—21no—
621C23—22no—
622C23—21no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—22no—
630C23—21no—
631C23—22no—
632C23C22×C3×Dic314yes—
633C23C22×C3×Dic312yes—
634C23C23×C3×D311yescharacteristic
635D4—28no—
636D4—48no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—28no—
642C2×C4—32no—
643C2×C4—32no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—62no—
651C2×C4—62no—
652C2×C4—62no—
653C2×C4—61no—
654C2×C4—61no—
655C2×C4—62no—
656C2×C4—61no—
657C2×C4—62no—
658C2×C4—62no—
659C2×C4—61no—
660C2×C4—128no—
661C2×C4C3×D3×D412yes—
662C2×C4C3×#23712yes—
663C2×C4C22×C3×Dic312yes—
664C2×C4C22×C3×Dic314yes—
665C2×C4C22×C3×Dic312yes—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—44no—
674C2×C3—42no—
675C2×C3—44no—
676C2×C3—42no—
677C2×C3—44no—
678C2×C3—84no—
679C2×C3#560311yescharacteristic
680C2×C3#560711yescharacteristic
681C2×C3#560811yescharacteristic
682C2×C3#561911yescharacteristic
683C2×C3C2×D4×Dic311yescharacteristic
684C2×C3#579811yescharacteristic
685C2×C3#582711yescharacteristic
686C2×C3C2×C3×C4×D411yescharacteristic
687C2×C3C3×#51811yescharacteristic
688C2×C3C3×#52011yescharacteristic
689C2×C3C3×#53511yescharacteristic
690C2×C3C3×#53711yescharacteristic
691C2×C3C3×#54011yescharacteristic
692C2×C3C3×#54211yescharacteristic
693C22—22no—
694C22—24no—
695C22—22no—
696C22—24no—
697C22—22no—
698C22—24no—
699C22—41no—
700C22—42no—
701C22—42no—
702C22—41no—
703C22—41no—
704C22—42no—
705C22—41no—
706C22—42no—
707C22C2×C3×D3×D411yescharacteristic
708C22C2×C3×#23711yescharacteristic
709C22C3×#100411yescharacteristic
710C22C3×#100411yescharacteristic
711C22C3×#100911yescharacteristic
712C22C3×#101011yescharacteristic
713C22C23×C3×Dic311yescharacteristic
714C4—22no—
715C4—24no—
716C4—62no—
717C4—62no—
718C4—122no—
719C4—121no—
720C4—121no—
721C4—122no—
722C4C3×D4×Dic314yes—
723C3—21no—
724C3#8263311yescharacteristic, direct product factor
725C3C3×#232411yescharacteristic, complemented
726C2—42no—
727C2—44no—
728C2C3×#560311yescharacteristic
729C2C3×#560711yescharacteristic
730C2C3×#560811yescharacteristic
731C2C3×#561911yescharacteristic
732C2C2×C3×D4×Dic311yescharacteristic
733C2C3×#579811yescharacteristic
734C2C3×#582711yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
Fitting, prime radicalC2×C32×#121C2
socleC23×C32C24
cosocleC23×C3C24×C3
hypercenterC2×C3×#121D3
hypocenterC3C3×#2324
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#121

Complements

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

NH ≅ G/Ntype
2. C2×C3×D4×Dic3C2semidirect
3. C2×C3×#926C2semidirect
4. C3×#5221C2semidirect
5. C3×#5221C2semidirect
6. C3×#5220C2semidirect
7. C3×#5212C2semidirect
8. C3×#4984C2semidirect
9. C3×Dic3×C4⋊C4C2semidirect
10. C3×#4951C2semidirect
11. C3×#4950C2semidirect
13. #82633C3direct (N × H)
18. C32×#121C4semidirect
45. C2×D4×Dic3C2×C3semidirect
46. C2×#926C2×C3semidirect
55. #5221C2×C3semidirect
56. #5221C2×C3semidirect
57. #5220C2×C3semidirect
58. #5212C2×C3semidirect
59. #4984C2×C3semidirect
60. Dic3×C4⋊C4C2×C3semidirect
61. #4951C2×C3semidirect
62. #4950C2×C3semidirect
70. C2×C32×D4C2×C4semidirect
73. C22×C32×C4C2×C4semidirect
86. C32×C4⋊C4C2×C4semidirect
87. C32×C22⋊C4C2×C4semidirect
101. C3×C4×Dic3D4semidirect
115. C3×#121Dic3semidirect
116. C3×#121C3×C4semidirect
239. C2×C3×D4C2×Dic3semidirect
241. C2×C3×D4C2×C3×C4semidirect
261. C22×C3×C4C2×Dic3semidirect
262. C22×C3×C4C2×C3×C4semidirect
284. C3×C4⋊C4C2×Dic3semidirect
285. C3×C4⋊C4C2×C3×C4semidirect
293. C3×C22⋊C4C2×Dic3semidirect
294. C3×C22⋊C4C2×C3×C4semidirect
311. C4×Dic3C3×D4semidirect
346. #121C3×Dic3semidirect
503. C2×D4C2×C3×Dic3semidirect
515. C22×C4C2×C3×Dic3semidirect
524. C4⋊C4C2×C3×Dic3semidirect
531. C22⋊C4C2×C3×Dic3semidirect
619. C32#2324semidirect
724. C3#82633direct (N × H)
725. C3C3×#2324semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1212
C2×C3×D4×Dic32
C2×C3×#9262
C3×#52212
C3×#52202
C3×#52122
C3×#49842
C3×Dic3×C4⋊C42
C3×#49512
C3×#49502
C3×#23243
#826333