Finite Group Databasebeta

← C3×#76198 #11803549

Subgroups — C3×#76198 #11803549

Order 1152.

1421 conjugacy classes of subgroups.

The subgroup lattice has 703 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#895C211yesmaximal, characteristic
2C2×C3×#893C211yesmaximal, characteristic, complemented
3C2×C3×#872C211yesmaximal, characteristic, complemented
4C32×#389C211yesmaximal, characteristic, complemented
5C3×#4989C212yesmaximal, complemented
6C3×#4988C212yesmaximal, complemented
7C3×#4987C211yesmaximal, characteristic, complemented
8C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
9C3×#4939C211yesmaximal, characteristic, complemented
10C3×#4669C212yesmaximal, complemented
11C3×#4665C212yesmaximal, complemented
12C3×#2324—31nomaximal
13#76198C311yesmaximal, characteristic, direct product factor
14C22×C3×D12C2211yescharacteristic
15C22×C3×D12C2212yes—
16C22×C3×C4×D3C2211yescharacteristic
17C22×C3×C4×D3C2212yes—
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C32×C4⋊C4C2212yes—
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C32×C42C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×(C2×D3)⋊C4C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×C4×Dic3C2212yes—
33C2×C3×C4×Dic3C2211yescharacteristic
34C3×#895C418yescomplemented
35C3×#893—24no—
36C3×#872—24no—
37C32×#95C2212yes—
38C3×C3⋊#95C2212yes—
39C3×C3⋊#95C2212yes—
40C2×C3×#121—31no—
41C2×C3×C4×D4—31no—
42C2×C3×#117—31no—
43C2×#895C2×C311yescharacteristic
44C2×#893C2×C311yescharacteristic, complemented
45C2×#872C2×C311yescharacteristic, complemented
46C3×#390—32no—
47C3×#390—31no—
48C3×#389—21no—
49C3×#389D311yescharacteristic, complemented
50C3×#389C2×C311yescharacteristic, complemented
51C3×#388—32no—
52C3×#386—32no—
53C3×#385—32no—
54C3×#380—31no—
55C3×C4×C4⋊C4—31no—
56#4989C2×C312yescomplemented
57#4988C2×C312yescomplemented
58#4987C2×C311yescharacteristic, complemented
59Dic3×C4⋊C4C2×C311yescharacteristic, complemented
60#4939C2×C311yescharacteristic, complemented
61#4669C2×C312yescomplemented
62#4665C2×C312yescomplemented
63C23×C3×D3C2311yescharacteristic
64C23×C3×D3C2312yes—
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2312yes—
68C22×C32×C4C2312yes—
69C22×C32×C4C2311yescharacteristic
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C2×C3×D12—22no—
75C2×C3×D12—22no—
76C2×C3×D12—42no—
77C2×C3×D12—42no—
78C2×C3×D12C2×C414yes—
79C2×C3×D12C2×C418yescomplemented
80C2×C3×C4×D3—22no—
81C2×C3×C4×D3—22no—
82C2×C3×C4×D3—24no—
83C2×C3×C4×D3—42no—
84C2×C3×C4×D3—42no—
85C2×C3×C4×D3C2×C414yescomplemented
86C32×C4⋊C4—22no—
87C32×C4⋊C4—42no—
88C32×C4⋊C4C2×C414yescomplemented
89C32×C42—22no—
90C3×(C2×D3)⋊C4—24no—
91C3×(C2×D3)⋊C4—22no—
92C3×(C2×D3)⋊C4—22no—
93C3×(C2×D3)⋊C4—42no—
94C3×(C2×D3)⋊C4—42no—
95C3×(C2×D3)⋊C4—42no—
96C3×(C2×D3)⋊C4C2×C418yescomplemented
97C3×C4⋊Dic3—22no—
98C3×Dic3⋊C4—22no—
99C3×Dic3⋊C4—22no—
100C3×C4×Dic3—42no—
101C3×C4×Dic3D414yescomplemented
102#2324—31noSylow
103C22×C3×D4—31no—
104C22×C3×D4—32no—
105C23×C3×C4—31no—
106C23×C3×C4—32no—
107C22×D12C22×C311yescharacteristic
108C22×D12C22×C312yes—
109C22×C4×D3C22×C311yescharacteristic
110C22×C4×D3C22×C312yes—
111C3×#121—38no—
112C3×C4×D4—64no—
113C3×#117—64no—
114C2×C3×C4⋊C4—21no—
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4—22no—
117C2×C3×C4⋊C4—31no—
118C2×C3×C4⋊C4—31no—
119C2×C3×C4⋊C4—31no—
120C2×C3×C4⋊C4C2×D311yescharacteristic
121C2×C3×C4⋊C4C2×D312yes—
122C2×C3×C4⋊C4C2×D311yescharacteristic
123C2×C3×C4⋊C4C22×C311yescharacteristic
124C2×C3×C4⋊C4C22×C312yes—
125C2×C3×C4⋊C4C22×C311yescharacteristic
126C2×C3×C22⋊C4—32no—
127C2×C3×C22⋊C4—31no—
128C2×C3×C22⋊C4—32no—
129C2×C3×C22⋊C4—31no—
130C2×C3×C22⋊C4—32no—
131C2×C3×C22⋊C4—32no—
132C2×C3×C22⋊C4—32no—
133C2×C3×C42—21no—
134C2×C3×C42—31no—
135C2×C3×C42—32no—
136C2×C3×C42C2×D311yescharacteristic
137C2×C3×C42C22×C311yescharacteristic
138C2×(C2×D3)⋊C4C22×C311yescharacteristic
139C2×(C2×D3)⋊C4C22×C312yes—
140C2×(C2×D3)⋊C4C22×C311yescharacteristic
141C2×(C2×D3)⋊C4C22×C312yes—
142C2×(C2×D3)⋊C4C22×C312yes—
143C2×(C2×D3)⋊C4C22×C312yes—
144C2×(C2×D3)⋊C4C22×C312yes—
145C2×C4⋊Dic3C22×C311yescharacteristic
146C2×Dic3⋊C4C22×C311yescharacteristic
147C2×Dic3⋊C4C22×C311yescharacteristic
148C2×C4×Dic3C22×C312yes—
149C2×C4×Dic3C22×C311yescharacteristic
150#895C3×C418yescomplemented
151#893—24no—
152#872—24no—
153C3×#95—22no—
154C3×#95—32no—
155C3×#95—32no—
156C3×#95C2×D312yes—
157C3×#95C22×C312yes—
158C3⋊#95C22×C312yes—
159C3⋊#95C22×C312yes—
160C23×C32C2411yescharacteristic
161C22×C3×D3—21no—
162C22×C3×D3—22no—
163C22×C3×D3—21no—
164C22×C3×D3—22no—
165C22×C3×D3—21no—
166C22×C3×D3—22no—
167C22×C3×D3—22no—
168C22×C3×D3—22no—
169C22×C3×D3—21no—
170C22×C3×D3—21no—
171C22×C3×D3—21no—
172C22×C3×D3—22no—
173C22×C3×D3C22×C414yes—
174C22×C3×D3C22×C412yes—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—22no—
178C2×C32×C4—22no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—22no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—22no—
185C2×C32×C4—22no—
186C2×C32×C4C22×C414yes—
187C2×C32×C4C22×C412yes—
188C2×C32×C4C2×D412yes—
189C2×C32×C4#4112yes—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3C22×C412yes—
200C2×C3×Dic3C2×D412yes—
201C2×C3×Dic3C2×D412yes—
202C3×D12—28no—
203C3×D12—48no—
204C3×C4×D3—28no—
205C3×C4×D3—48no—
206C2×#121—31no—
207C2×C4×D4—31no—
208C2×#117—31no—
209#390—32no—
210#390—31no—
211#389C3×D311yescharacteristic, complemented
212#388—32no—
213#386—32no—
214#385—32no—
215#380—31no—
216C4×C4⋊C4—31no—
217C24×C3—32no—
218C24×C3—31no—
219C23×D3C23×C311yescharacteristic
220C23×D3C23×C312yes—
221C2×C3×D4—34no—
222C2×C3×D4—38no—
223C2×C3×D4—62no—
224C2×C3×D4—62no—
225C2×C3×D4—122no—
226C2×C3×D4—122no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—22no—
230C22×C3×C4—21no—
231C22×C3×C4—22no—
232C22×C3×C4—31no—
233C22×C3×C4—31no—
234C22×C3×C4—31no—
235C22×C3×C4—34no—
236C22×C3×C4—32no—
237C22×C3×C4—64no—
238C22×C3×C4—62no—
239C22×C3×C4—62no—
240C22×C3×C4—122no—
241C22×C3×C4—122no—
242C22×C3×C4C22×D312yes—
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C22×D312yes—
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C23×C312yes—
248C22×C3×C4C23×C311yescharacteristic
249C22×C3×C4C23×C311yescharacteristic
250C22×C3×C4C23×C312yes—
251C22×C3×C4C23×C311yescharacteristic
252C22×Dic3C23×C312yes—
253C22×Dic3C23×C311yescharacteristic
254C22×Dic3C23×C311yescharacteristic
255C22×Dic3C23×C311yescharacteristic
256C2×D12—22no—
257C2×D12—22no—
258C2×D12—42no—
259C2×D12—42no—
260C2×D12C2×C3×C414yes—
261C2×D12C2×C3×C418yescomplemented
262C2×C4×D3—22no—
263C2×C4×D3—22no—
264C2×C4×D3—24no—
265C2×C4×D3—42no—
266C2×C4×D3—42no—
267C2×C4×D3C2×C3×C414yescomplemented
268C3×C4⋊C4—22no—
269C3×C4⋊C4—22no—
270C3×C4⋊C4—24no—
271C3×C4⋊C4—42no—
272C3×C4⋊C4—42no—
273C3×C4⋊C4—42no—
274C3×C4⋊C4—44no—
275C3×C4⋊C4—62no—
276C3×C4⋊C4—62no—
277C3×C4⋊C4—62no—
278C3×C4⋊C4C4×D314yescomplemented
279C3×C4⋊C4C2×C3×C414yescomplemented
280C3×C22⋊C4—38no—
281C3×C22⋊C4—62no—
282C3×C22⋊C4—62no—
283C3×C22⋊C4—64no—
284C3×C22⋊C4—122no—
285C3×C22⋊C4—122no—
286C3×C22⋊C4—122no—
287C3×C42—22no—
288C3×C42—22no—
289C3×C42—34no—
290C3×C42—42no—
291C3×C42—122no—
292(C2×D3)⋊C4—22no—
293(C2×D3)⋊C4—22no—
294(C2×D3)⋊C4—24no—
295(C2×D3)⋊C4—42no—
296(C2×D3)⋊C4—42no—
297(C2×D3)⋊C4—42no—
298(C2×D3)⋊C4C2×C3×C418yescomplemented
299C4⋊Dic3—22no—
300Dic3⋊C4—22no—
301Dic3⋊C4—22no—
302C4×Dic3—42no—
303C4×Dic3C3×D414yescomplemented
304C22×C32C23×C411yescharacteristic
305C22×C32C22×D411yescharacteristic
306C22×C32C2×#4111yescharacteristic
307C22×C32H(5,𝔽2)11yescharacteristic
308C22×C32H(5,𝔽2)11yescharacteristic
309C22×C32H(5,𝔽2)11yescharacteristic
310C22×C322−1+411yescharacteristic
311C2×C3×D3—22no—
312C2×C3×D3—24no—
313C2×C3×D3—22no—
314C2×C3×D3—24no—
315C2×C3×D3—22no—
316C2×C3×D3—24no—
317C2×C3×D3—42no—
318C2×C3×D3—41no—
319C2×C3×D3—41no—
320C2×C3×D3—42no—
321C2×C3×D3—41no—
322C2×C3×D3—42no—
323C2×C3×D3—41no—
324C2×C3×D3—42no—
325C32×C4—24no—
326C32×C4—41no—
327C32×C4—41no—
328C32×C4—42no—
329C32×C4C4×D414yes—
330C3×Dic3—22no—
331C3×Dic3—22no—
332C3×Dic3—22no—
333C3×Dic3—42no—
334C22×D4—31no—
335C22×D4—32no—
336C23×C4—31no—
337C23×C4—32no—
338#121—38no—
339C4×D4—64no—
340#117—64no—
341C2×C4⋊C4—31no—
342C2×C4⋊C4—31no—
343C2×C4⋊C4—31no—
344C2×C4⋊C4C2×C3×D311yescharacteristic
345C2×C4⋊C4C2×C3×D312yes—
346C2×C4⋊C4C2×C3×D311yescharacteristic
347C2×C22⋊C4—32no—
348C2×C22⋊C4—31no—
349C2×C22⋊C4—31no—
350C2×C22⋊C4—32no—
351C2×C22⋊C4—32no—
352C2×C22⋊C4—32no—
353C2×C22⋊C4—32no—
354C2×C42—31no—
355C2×C42—32no—
356C2×C42C2×C3×D311yescharacteristic
357#95—32no—
358#95—32no—
359#95C2×C3×D312yes—
360C23×C3—21no—
361C23×C3—34no—
362C23×C3—32no—
363C23×C3—61no—
364C23×C3—62no—
365C23×C3—62no—
366C23×C3—61no—
367C23×C3—61no—
368C23×C3—62no—
369C23×C3—62no—
370C23×C3—61no—
371C23×C3—61no—
372C23×C3—62no—
373C23×C3—62no—
374C23×C3—61no—
375C23×C3C23×D311yescharacteristic
376C23×C3C24×C311yescharacteristic
377C22×D3—21no—
378C22×D3—22no—
379C22×D3—21no—
380C22×D3—22no—
381C22×D3—21no—
382C22×D3—22no—
383C22×D3—22no—
384C22×D3—22no—
385C22×D3—21no—
386C22×D3—21no—
387C22×D3—21no—
388C22×D3—22no—
389C22×D3C22×C3×C414yes—
390C22×D3C22×C3×C412yes—
391C3×D4—68no—
392C3×D4—128no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—22no—
402C2×C3×C4—21no—
403C2×C3×C4—22no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—22no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—22no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—22no—
414C2×C3×C4—21no—
415C2×C3×C4—22no—
416C2×C3×C4—21no—
417C2×C3×C4—22no—
418C2×C3×C4—24no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—32no—
422C2×C3×C4—32no—
423C2×C3×C4—32no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—42no—
427C2×C3×C4—42no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—42no—
431C2×C3×C4—42no—
432C2×C3×C4—42no—
433C2×C3×C4—61no—
434C2×C3×C4—61no—
435C2×C3×C4—61no—
436C2×C3×C4—61no—
437C2×C3×C4—61no—
438C2×C3×C4—61no—
439C2×C3×C4—68no—
440C2×C3×C4—62no—
441C2×C3×C4—62no—
442C2×C3×C4—62no—
443C2×C3×C4—128no—
444C2×C3×C4C2×C4×D314yes—
445C2×C3×C4C2×C4×D312yes—
446C2×C3×C4D3×D412yes—
447C2×C3×C4#23912yes—
448C2×C3×C4C22×C3×C414yes—
449C2×C3×C4C22×C3×C412yes—
450C2×C3×C4C2×C3×D412yes—
451C2×C3×C4C3×#4112yes—
452C2×Dic3—21no—
453C2×Dic3—21no—
454C2×Dic3—21no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—22no—
459C2×Dic3—22no—
460C2×Dic3—22no—
461C2×Dic3C22×C3×C412yes—
462C2×Dic3C2×C3×D412yes—
463C2×Dic3C2×C3×D412yes—
464D12—28no—
465D12—48no—
466C4×D3—28no—
467C4×D3—48no—
468C2×C32C2×C4×D411yescharacteristic
469C2×C32#51811yescharacteristic
470C2×C32#52011yescharacteristic
471C2×C32#53511yescharacteristic
472C2×C32#53711yescharacteristic
473C2×C32#54011yescharacteristic
474C2×C32#54211yescharacteristic
475C3×D3—42no—
476C3×D3—44no—
477C24—32no—
478C24—31no—
479C2×D4—34no—
480C2×D4—38no—
481C2×D4—62no—
482C2×D4—62no—
483C2×D4—122no—
484C2×D4—122no—
485C22×C4—31no—
486C22×C4—31no—
487C22×C4—31no—
488C22×C4—34no—
489C22×C4—32no—
490C22×C4—64no—
491C22×C4—62no—
492C22×C4—62no—
493C22×C4—122no—
494C22×C4—122no—
495C22×C4C22×C3×D312yes—
496C22×C4C22×C3×D311yescharacteristic
497C22×C4C22×C3×D311yescharacteristic
498C22×C4C22×C3×D312yes—
499C22×C4C22×C3×D311yescharacteristic
500C4⋊C4—22no—
501C4⋊C4—42no—
502C4⋊C4—62no—
503C4⋊C4—62no—
504C4⋊C4—62no—
505C4⋊C4C3×C4×D314yescomplemented
506C22⋊C4—38no—
507C22⋊C4—62no—
508C22⋊C4—62no—
509C22⋊C4—64no—
510C22⋊C4—122no—
511C22⋊C4—122no—
512C22⋊C4—122no—
513C42—22no—
514C42—34no—
515C42—122no—
516C22×C3—21no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—21no—
520C22×C3—21no—
521C22×C3—21no—
522C22×C3—21no—
523C22×C3—62no—
524C22×C3—64no—
525C22×C3—62no—
526C22×C3—64no—
527C22×C3—64no—
528C22×C3—62no—
529C22×C3—121no—
530C22×C3—122no—
531C22×C3—122no—
532C22×C3—121no—
533C22×C3—122no—
534C22×C3—121no—
535C22×C3—121no—
536C22×C3—122no—
537C22×C3C22×C4×D311yescharacteristic
538C22×C3C2×D3×D411yescharacteristic
539C22×C3#100411yescharacteristic
540C22×C3C2×#23911yescharacteristic
541C22×C3#100711yescharacteristic
542C22×C3#100911yescharacteristic
543C22×C3#100911yescharacteristic
544C22×C3C23×C3×C411yescharacteristic
545C22×C3C22×C3×D411yescharacteristic
546C22×C3C2×C3×#4111yescharacteristic
547C22×C3C3×H(5,𝔽2)11yescharacteristic
548C22×C3C3×H(5,𝔽2)11yescharacteristic
549C22×C3C3×H(5,𝔽2)11yescharacteristic
550C22×C3C3×2−1+411yescharacteristic
551C2×D3—22no—
552C2×D3—24no—
553C2×D3—22no—
554C2×D3—24no—
555C2×D3—22no—
556C2×D3—24no—
557C2×D3—42no—
558C2×D3—41no—
559C2×D3—41no—
560C2×D3—42no—
561C2×D3—41no—
562C2×D3—42no—
563C2×D3—41no—
564C2×D3—42no—
565C3×C4—24no—
566C3×C4—24no—
567C3×C4—24no—
568C3×C4—44no—
569C3×C4—42no—
570C3×C4—42no—
571C3×C4—42no—
572C3×C4—41no—
573C3×C4—42no—
574C3×C4—41no—
575C3×C4—41no—
576C3×C4—41no—
577C3×C4—62no—
578C3×C4—62no—
579C3×C4—62no—
580C3×C4—82no—
581C3×C4—122no—
582C3×C4#89314yes—
583C3×C4C3×C4×D414yes—
584Dic3—22no—
585Dic3—22no—
586Dic3—22no—
587Dic3—42no—
588C32#232411yescharacteristic, complemented, Sylow
589C23—34no—
590C23—32no—
591C23—61no—
592C23—62no—
593C23—62no—
594C23—61no—
595C23—61no—
596C23—62no—
597C23—62no—
598C23—61no—
599C23—61no—
600C23—62no—
601C23—62no—
602C23—61no—
603C23C23×C3×D311yescharacteristic
604D4—68no—
605D4—128no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—22no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—32no—
618C2×C4—32no—
619C2×C4—32no—
620C2×C4—61no—
621C2×C4—61no—
622C2×C4—61no—
623C2×C4—61no—
624C2×C4—61no—
625C2×C4—61no—
626C2×C4—68no—
627C2×C4—62no—
628C2×C4—62no—
629C2×C4—62no—
630C2×C4—128no—
631C2×C4C2×C3×C4×D314yes—
632C2×C4C2×C3×C4×D312yes—
633C2×C4C3×D3×D412yes—
634C2×C4C3×#23912yes—
635C2×C3—21no—
636C2×C3—21no—
637C2×C3—21no—
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—21no—
641C2×C3—21no—
642C2×C3—122no—
643C2×C3—124no—
644C2×C3C2×#89311yescharacteristic
645C2×C3#554511yescharacteristic
646C2×C3#557411yescharacteristic
647C2×C3#560711yescharacteristic
648C2×C3#562911yescharacteristic
649C2×C3#569711yescharacteristic
650C2×C3#573311yescharacteristic
651C2×C3C2×C3×C4×D411yescharacteristic
652C2×C3C3×#51811yescharacteristic
653C2×C3C3×#52011yescharacteristic
654C2×C3C3×#53511yescharacteristic
655C2×C3C3×#53711yescharacteristic
656C2×C3C3×#54011yescharacteristic
657C2×C3C3×#54211yescharacteristic
658D3—42no—
659D3—44no—
660C22—62no—
661C22—64no—
662C22—62no—
663C22—64no—
664C22—64no—
665C22—62no—
666C22—122no—
667C22—121no—
668C22—121no—
669C22—122no—
670C22—121no—
671C22—122no—
672C22—122no—
673C22—121no—
674C22C22×C3×C4×D311yescharacteristic
675C22C2×C3×D3×D411yescharacteristic
676C22C3×#100411yescharacteristic
677C22C2×C3×#23911yescharacteristic
678C22C3×#100711yescharacteristic
679C22C3×#100911yescharacteristic
680C22C3×#100911yescharacteristic
681C4—24no—
682C4—42no—
683C4—41no—
684C4—41no—
685C4—62no—
686C4—62no—
687C4—62no—
688C4—122no—
689C4C3×#89314yes—
690C3—21no—
691C3#7619811yescharacteristic, direct product factor
692C3C3×#232411yescharacteristic, complemented
693C2—122no—
694C2—124no—
695C2C2×C3×#89311yescharacteristic
696C2C3×#554511yescharacteristic
697C2C3×#557411yescharacteristic
698C2C3×#560711yescharacteristic
699C2C3×#562911yescharacteristic
700C2C3×#569711yescharacteristic
701C2C3×#573311yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#389C2
socleC23×C32C24
prime radicalC2×C3×#895C2
cosocleC23×C3C24×C3
hypercenterC3×#389D3
hypocenterC3C3×#2324
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#389

Complements

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

NH ≅ G/Ntype
2. C2×C3×#893C2semidirect
3. C2×C3×#872C2semidirect
4. C32×#389C2semidirect
5. C3×#4989C2semidirect
6. C3×#4988C2semidirect
7. C3×#4987C2semidirect
8. C3×Dic3×C4⋊C4C2semidirect
9. C3×#4939C2semidirect
10. C3×#4669C2semidirect
11. C3×#4665C2semidirect
13. #76198C3direct (N × H)
34. C3×#895C4semidirect
44. C2×#893C2×C3semidirect
45. C2×#872C2×C3semidirect
49. C3×#389D3semidirect
50. C3×#389C2×C3semidirect
56. #4989C2×C3semidirect
57. #4988C2×C3semidirect
58. #4987C2×C3semidirect
59. Dic3×C4⋊C4C2×C3semidirect
60. #4939C2×C3semidirect
61. #4669C2×C3semidirect
62. #4665C2×C3semidirect
79. C2×C3×D12C2×C4semidirect
85. C2×C3×C4×D3C2×C4semidirect
88. C32×C4⋊C4C2×C4semidirect
96. C3×(C2×D3)⋊C4C2×C4semidirect
101. C3×C4×Dic3D4semidirect
150. #895C3×C4semidirect
211. #389C3×D3semidirect
261. C2×D12C2×C3×C4semidirect
267. C2×C4×D3C2×C3×C4semidirect
278. C3×C4⋊C4C4×D3semidirect
279. C3×C4⋊C4C2×C3×C4semidirect
298. (C2×D3)⋊C4C2×C3×C4semidirect
303. C4×Dic3C3×D4semidirect
505. C4⋊C4C3×C4×D3semidirect
588. C32#2324semidirect
691. C3#76198direct (N × H)
692. C3C3×#2324semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8952
C2×C3×#8932
C2×C3×#8722
C32×#3892
C3×#49892
C3×#49882
C3×#49872
C3×Dic3×C4⋊C42
C3×#49392
C3×#46692
C3×#46652
C3×#23243
#761983