Finite Group Databasebeta

← C3×#10594427 #13173986

Subgroups — C3×#10594427 #13173986

Order 1728.

1182 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64096C211yesmaximal, characteristic, complemented
2C32×#895C211yesmaximal, characteristic
3C32×#890C211yesmaximal, characteristic, complemented
4C3×#63898C211yesmaximal, characteristic, complemented
5C3×#63898C212yesmaximal, complemented
6C3×#63884C212yesmaximal, complemented
7C3×#63878C212yesmaximal, complemented
8C3×C4×D3×Dic3C211yesmaximal, characteristic, complemented
9C3×#63860C211yesmaximal, characteristic, complemented
10C3×#63858C212yesmaximal, complemented
11C3×#63857C211yesmaximal, characteristic, complemented
12C3×#5691—31nomaximal
13C3×#5600—31nomaximal
14#10594427C311yesmaximal, characteristic, direct product factor
15C2×C3×#634C2211yescharacteristic
16C2×C32×D12C2211yescharacteristic
17C2×C32×D12C2212yes—
18C2×C32×C4×D3C2211yescharacteristic
19C2×C3×D3×Dic3C2211yescharacteristic
20C2×C3×D3×Dic3C2211yescharacteristic
21C2×C3×D3×Dic3C2212yes—
22C33×C4⋊C4C2211yescharacteristic
23C3×#3750C2212yes—
24C3×C4×C3⋊Dic3C2211yescharacteristic
25C3×C4×C3⋊Dic3C2212yes—
26C32×(C2×D3)⋊C4C2212yes—
27C32×C4⋊Dic3C2211yescharacteristic
28C32×C4⋊Dic3C2212yes—
29C32×Dic3⋊C4C2212yes—
30C32×C4×Dic3C2211yescharacteristic
31C3×Dic3⋊Dic3C2212yes—
32C3×(C2×D3)⋊Dic3C2212yes—
33C3×(C2×D3)⋊Dic3C2212yes—
34C3×(C2×D3)⋊Dic3C2212yes—
35C3×(C2×D3)⋊Dic3C2212yes—
36C3×Dic32C2211yescharacteristic
37C3×Dic32C2211yescharacteristic
38C32×#125—31no—
39C32×#121—31no—
40#64096C2×C311yescharacteristic, complemented
41C3×#936—31no—
42C3×#935—32no—
43C3×D4×Dic3—32no—
44C3×D4×Dic3—31no—
45C3×#924—31no—
46C2×C3×C4×Dic3—31no—
47C3×#898—32no—
48C3×#897—31no—
49C3×#895—21no—
50C3×#895D311yescharacteristic
51C3×#895C2×C311yescharacteristic
52C3×#894—32no—
53C3×#893—32no—
54C3×#893—31no—
55C3×#892—32no—
56C3×#890—21no—
57C3×#890D311yescharacteristic, complemented
58C3×#890C2×C311yescharacteristic, complemented
59C3×#887—31no—
60C3×#887—31no—
61C3×#887—61no—
62C3×#879—32no—
63C3×#877—32no—
64C3×#875—31no—
65C3×C42×D3—31no—
66#63898C2×C312yescomplemented
67#63898C2×C311yescharacteristic, complemented
68#63884C2×C312yescomplemented
69#63878C2×C312yescomplemented
70C4×D3×Dic3C2×C311yescharacteristic, complemented
71#63860C2×C311yescharacteristic, complemented
72#63858C2×C312yescomplemented
73#63857C2×C311yescharacteristic, complemented
74C22×C32×D3C2312yes—
75C22×C32×D3C2311yescharacteristic
76C2×C33×C4C2312yes—
77C2×C33×C4C2311yescharacteristic
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2312yes—
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C3×#634—22no—
82C2×C32×Dic3C2311yescharacteristic
83C2×C32×Dic3C2311yescharacteristic
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2311yescharacteristic
86C32×D12—24no—
87C32×D12—22no—
88C32×C4×D3—22no—
89C3×D3×Dic3—22no—
90C3×D3×Dic3—22no—
91C3×D3×Dic3—24no—
92C3×#529—91no—
93#5691—31no—
94#5600—31no—
95C2×C32×D4—32no—
96C2×C32×D4—31no—
97C22×C32×C4—31no—
98C2×#634C22×C311yescharacteristic
99C22×C3×Dic3—32no—
100C22×C3×Dic3—31no—
101C22×C3×Dic3—31no—
102C2×C3×D12—21no—
103C2×C3×D12—22no—
104C2×C3×D12C2×D312yes—
105C2×C3×D12C2×D311yescharacteristic
106C2×C3×D12C22×C311yescharacteristic
107C2×C3×D12C22×C312yes—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—32no—
110C2×C3×C4×D3—31no—
111C2×C3×C4×D3—31no—
112C2×C3×C4×D3C2×D311yescharacteristic
113C2×C3×C4×D3C22×C311yescharacteristic
114C2×C3×Dic6—31no—
115C2×C3×Dic6—31no—
116C2×C3×Dic6—61no—
117C2×D3×Dic3C22×C311yescharacteristic
118C2×D3×Dic3C22×C311yescharacteristic
119C2×D3×Dic3C22×C312yes—
120C32×C4⋊C4—21no—
121C32×C4⋊C4—21no—
122C32×C4⋊C4—21no—
123C32×C4⋊C4—32no—
124C32×C4⋊C4—31no—
125C32×C4⋊C4—32no—
126C32×C4⋊C4—41no—
127C32×C4⋊C4C2×D311yescharacteristic
128C32×C4⋊C4C2×D311yescharacteristic
129C32×C4⋊C4C22×C311yescharacteristic
130C32×C22⋊C4—32no—
131C32×C42—31no—
132#3750C22×C312yes—
133C4×C3⋊Dic3C22×C311yescharacteristic
134C4×C3⋊Dic3C22×C312yes—
135C3×#217—32no—
136C3×#217—32no—
137C3×#217—32no—
138C3×#217—32no—
139C3×(C2×D3)⋊C4—22no—
140C3×(C2×D3)⋊C4—32no—
141C3×(C2×D3)⋊C4—32no—
142C3×(C2×D3)⋊C4—32no—
143C3×(C2×D3)⋊C4—32no—
144C3×(C2×D3)⋊C4C2×D312yes—
145C3×(C2×D3)⋊C4C22×C312yes—
146C3×C4⋊Dic3—22no—
147C3×C4⋊Dic3—21no—
148C3×C4⋊Dic3—32no—
149C3×C4⋊Dic3C2×D312yes—
150C3×C4⋊Dic3C2×D311yescharacteristic
151C3×C4⋊Dic3C22×C311yescharacteristic
152C3×C4⋊Dic3C22×C312yes—
153C3×Dic3⋊C4—22no—
154C3×Dic3⋊C4—32no—
155C3×Dic3⋊C4—32no—
156C3×Dic3⋊C4—32no—
157C3×Dic3⋊C4—62no—
158C3×Dic3⋊C4C2×D312yes—
159C3×Dic3⋊C4C22×C312yes—
160C3×C4×Dic3—21no—
161C3×C4×Dic3—32no—
162C3×C4×Dic3—32no—
163C3×C4×Dic3—31no—
164C3×C4×Dic3—31no—
165C3×C4×Dic3—31no—
166C3×C4×Dic3—31no—
167C3×C4×Dic3—31no—
168C3×C4×Dic3—31no—
169C3×C4×Dic3—62no—
170C3×C4×Dic3—61no—
171C3×C4×Dic3C2×D311yescharacteristic
172C3×C4×Dic3C22×C311yescharacteristic
173Dic3⋊Dic3C22×C312yes—
174(C2×D3)⋊Dic3C22×C312yes—
175(C2×D3)⋊Dic3C22×C312yes—
176(C2×D3)⋊Dic3C22×C312yes—
177(C2×D3)⋊Dic3C22×C312yes—
178Dic32C22×C311yescharacteristic
179Dic32C22×C311yescharacteristic
180C22×C33C2411yescharacteristic
181C2×C32×D3—21no—
182C2×C32×D3—21no—
183C2×C32×D3—22no—
184C2×C32×D3—22no—
185C2×C32×D3—22no—
186C2×C32×D3#4112yes—
187C33×C4—22no—
188C33×C4#4112yes—
189C3×C3⋊Dic3—22no—
190C3×C3⋊Dic3—21no—
191C3×C3⋊Dic3#4112yes—
192C32×Dic3—21no—
193C32×Dic3—21no—
194C32×Dic3—22no—
195C32×Dic3—21no—
196C3×#126—92no—
197C3×#125—31no—
198C3×#125—31no—
199C3×#125—61no—
200C3×#124—91no—
201C3×#123—92no—
202C3×C22⋊Q8—91no—
203C3×#121—31no—
204C3×#121—31no—
205C3×#121—61no—
206C3×C4×Q8—91no—
207C3×C4×D4—91no—
208C3×C4×D4—92no—
209C3×#117—92no—
210C2×C3×C42—91no—
211#936—31no—
212#935—32no—
213D4×Dic3—32no—
214D4×Dic3—31no—
215#924—31no—
216C2×C4×Dic3—31no—
217#898—32no—
218#897—31no—
219#895C3×D311yescharacteristic
220#894—32no—
221#893—31no—
222#893—32no—
223#892—32no—
224#890C3×D311yescharacteristic, complemented
225#887—31no—
226#887—31no—
227#887—61no—
228#879—32no—
229#877—32no—
230#875—31no—
231C42×D3—31no—
232C23×C32—31no—
233C23×C32—32no—
234C22×C3×D3—21no—
235C22×C3×D3—22no—
236C22×C3×D3C22×D312yes—
237C22×C3×D3C22×D311yescharacteristic
238C22×C3×D3C23×C312yes—
239C22×C3×D3C23×C311yescharacteristic
240C32×D4—64no—
241C32×D4—62no—
242C2×C32×C4—21no—
243C2×C32×C4—22no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—22no—
247C2×C32×C4—22no—
248C2×C32×C4—31no—
249C2×C32×C4—31no—
250C2×C32×C4—31no—
251C2×C32×C4—32no—
252C2×C32×C4—41no—
253C2×C32×C4—42no—
254C2×C32×C4—62no—
255C2×C32×C4C22×D312yes—
256C2×C32×C4C22×D312yes—
257C2×C32×C4C22×D311yescharacteristic
258C2×C32×C4C22×D311yescharacteristic
259C2×C32×C4C23×C312yes—
260C2×C32×C4C23×C311yescharacteristic
261C2×C3⋊Dic3C23×C311yescharacteristic
262C2×C3⋊Dic3C23×C312yes—
263C2×C3⋊Dic3C23×C311yescharacteristic
264#634—22no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—22no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—32no—
274C2×C3×Dic3—32no—
275C2×C3×Dic3—61no—
276C2×C3×Dic3—62no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—62no—
279C2×C3×Dic3—64no—
280C2×C3×Dic3—62no—
281C2×C3×Dic3C22×D311yescharacteristic
282C2×C3×Dic3C22×D311yescharacteristic
283C2×C3×Dic3C22×D311yescharacteristic
284C2×C3×Dic3C22×D312yes—
285C2×C3×Dic3C23×C311yescharacteristic
286C2×C3×Dic3C23×C311yescharacteristic
287C2×C3×Dic3C23×C311yescharacteristic
288C2×C3×Dic3C23×C312yes—
289C3×D12—24no—
290C3×D12—24no—
291C3×D12—22no—
292C3×D12—22no—
293C3×D12—42no—
294C3×D12—44no—
295C3×C4×D3—22no—
296C3×C4×D3—22no—
297C3×C4×D3—42no—
298C3×C4×D3—62no—
299C3×C4×D3—64no—
300C3×C4×D3—62no—
301C3×Dic6—64no—
302C3×Dic6—62no—
303C3×Dic6—62no—
304D3×Dic3—22no—
305D3×Dic3—22no—
306D3×Dic3—24no—
307#529—91noSylow
308C2×C33C2×#4111yescharacteristic
309C2×C33C2×#4111yescharacteristic
310C2×C33C2×#4111yescharacteristic
311C32×D3—22no—
312C32×D3—42no—
313C2×C3×Q8—91no—
314C2×C3×D4—32no—
315C2×C3×D4—31no—
316C2×C3×D4—32no—
317C2×C3×D4—31no—
318C2×C3×D4—62no—
319C2×C3×D4—61no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—61no—
323C22×C3×C4—91no—
324C22×C3×C4—91no—
325C22×C3×C4—92no—
326C22×Dic3—32no—
327C22×Dic3—31no—
328C22×Dic3—31no—
329C2×D12C2×C3×D311yescharacteristic
330C2×D12C2×C3×D312yes—
331C2×C4×D3—31no—
332C2×C4×D3—31no—
333C2×C4×D3—32no—
334C2×C4×D3C2×C3×D311yescharacteristic
335C2×Dic6—31no—
336C2×Dic6—31no—
337C2×Dic6—61no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—32no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—32no—
344C3×C4⋊C4—32no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—32no—
347C3×C4⋊C4—41no—
348C3×C4⋊C4—62no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—62no—
351C3×C4⋊C4—92no—
352C3×C4⋊C4—92no—
353C3×C4⋊C4D3211yescharacteristic
354C3×C4⋊C4C2×C3×D311yescharacteristic
355C3×C4⋊C4C2×C3×D311yescharacteristic
356C3×C22⋊C4—32no—
357C3×C22⋊C4—32no—
358C3×C22⋊C4—62no—
359C3×C22⋊C4—92no—
360C3×C22⋊C4—92no—
361C3×C22⋊C4—92no—
362C3×C22⋊C4—92no—
363C3×C42—31no—
364C3×C42—31no—
365C3×C42—61no—
366C3×C42—91no—
367C3×C42—91no—
368C3×C42—91no—
369C3×C42—92no—
370#217—32no—
371#217—32no—
372#217—32no—
373#217—32no—
374(C2×D3)⋊C4—32no—
375(C2×D3)⋊C4—32no—
376(C2×D3)⋊C4—32no—
377(C2×D3)⋊C4—32no—
378(C2×D3)⋊C4C2×C3×D312yes—
379C4⋊Dic3—32no—
380C4⋊Dic3C2×C3×D312yes—
381C4⋊Dic3C2×C3×D311yescharacteristic
382Dic3⋊C4—32no—
383Dic3⋊C4—32no—
384Dic3⋊C4—32no—
385Dic3⋊C4—62no—
386Dic3⋊C4C2×C3×D312yes—
387C4×Dic3—31no—
388C4×Dic3—32no—
389C4×Dic3—32no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—31no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—61no—
396C4×Dic3—62no—
397C4×Dic3C2×C3×D311yescharacteristic
398C22×C32—21no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—32no—
402C22×C32—41no—
403C22×C32—61no—
404C22×C32—61no—
405C22×C32—62no—
406C22×C32—62no—
407C22×C32—62no—
408C22×C32C23×D311yescharacteristic
409C22×C32C23×D311yescharacteristic
410C22×C32C24×C311yescharacteristic
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—22no—
416C2×C3×D3—22no—
417C2×C3×D3—22no—
418C2×C3×D3—22no—
419C2×C3×D3—22no—
420C2×C3×D3—22no—
421C2×C3×D3—22no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—42no—
425C2×C3×D3—42no—
426C2×C3×D3—42no—
427C2×C3×D3#23712yes—
428C2×C3×D3C3×#4112yes—
429C32×C4—22no—
430C32×C4—22no—
431C32×C4—22no—
432C32×C4—22no—
433C32×C4—22no—
434C32×C4—22no—
435C32×C4—42no—
436C32×C4—42no—
437C32×C4—42no—
438C32×C4—42no—
439C32×C4—61no—
440C32×C4—61no—
441C32×C4—61no—
442C32×C4—62no—
443C32×C4—82no—
444C32×C4#23712yes—
445C32×C4#23912yes—
446C32×C4C3×#4112yes—
447C3⋊Dic3—22no—
448C3⋊Dic3—21no—
449C3⋊Dic3C3×#4112yes—
450C3×Dic3—21no—
451C3×Dic3—21no—
452C3×Dic3—21no—
453C3×Dic3—22no—
454C3×Dic3—21no—
455C3×Dic3—21no—
456C3×Dic3—22no—
457C3×Dic3—21no—
458C3×Dic3—32no—
459C3×Dic3—32no—
460C3×Dic3—41no—
461C3×Dic3—41no—
462C3×Dic3—42no—
463C3×Dic3—41no—
464C3×Dic3—62no—
465C3×Dic3—64no—
466C3×Dic3—62no—
467C3×Dic3—61no—
468C3×Dic3—62no—
469C3×Dic3—61no—
470C3×Dic3—121no—
471#126—92no—
472#125—31no—
473#124—91no—
474#123—92no—
475C22⋊Q8—91no—
476#121—31no—
477C4×Q8—91no—
478C4×D4—91no—
479C4×D4—92no—
480#117—92no—
481C2×C42—91no—
482C33#52911yescharacteristic, complemented, Sylow
483C23×C3—31no—
484C23×C3—31no—
485C23×C3—32no—
486C23×C3—32no—
487C23×C3—61no—
488C23×C3—62no—
489C22×D3C22×C3×D312yes—
490C22×D3C22×C3×D311yescharacteristic
491C3×Q8—182no—
492C3×D4—64no—
493C3×D4—64no—
494C3×D4—62no—
495C3×D4—62no—
496C3×D4—122no—
497C3×D4—124no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—32no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—32no—
512C2×C3×C4—41no—
513C2×C3×C4—42no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—62no—
518C2×C3×C4—62no—
519C2×C3×C4—62no—
520C2×C3×C4—91no—
521C2×C3×C4—91no—
522C2×C3×C4—92no—
523C2×C3×C4—122no—
524C2×C3×C4—182no—
525C2×C3×C4—184no—
526C2×C3×C4—182no—
527C2×C3×C4C2×D3212yes—
528C2×C3×C4C2×D3211yescharacteristic
529C2×C3×C4C22×C3×D312yes—
530C2×C3×C4C22×C3×D312yes—
531C2×C3×C4C22×C3×D311yescharacteristic
532C2×C3×C4C22×C3×D311yescharacteristic
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—32no—
538C2×Dic3—32no—
539C2×Dic3—61no—
540C2×Dic3—62no—
541C2×Dic3—61no—
542C2×Dic3—62no—
543C2×Dic3—64no—
544C2×Dic3—62no—
545C2×Dic3C22×C3×D311yescharacteristic
546C2×Dic3C22×C3×D311yescharacteristic
547C2×Dic3C22×C3×D311yescharacteristic
548C2×Dic3C22×C3×D312yes—
549D12—24no—
550D12—22no—
551C4×D3—22no—
552C4×D3—62no—
553C4×D3—64no—
554C4×D3—62no—
555Dic6—64no—
556Dic6—62no—
557Dic6—62no—
558C2×C32—21no—
559C2×C32—21no—
560C2×C32—21no—
561C2×C32—21no—
562C2×C32—21no—
563C2×C32—21no—
564C2×C32—21no—
565C2×C32—21no—
566C2×C32—21no—
567C2×C32—41no—
568C2×C32—41no—
569C2×C32—41no—
570C2×C32—62no—
571C2×C32—122no—
572C2×C32C2×#23711yescharacteristic
573C2×C32C2×#23711yescharacteristic
574C2×C32C2×#23911yescharacteristic
575C2×C32D3×#4111yescharacteristic
576C2×C32D3×#4111yescharacteristic
577C2×C32D3×#4111yescharacteristic
578C2×C32C2×C3×#4111yescharacteristic
579C2×C32C2×C3×#4111yescharacteristic
580C2×C32C2×C3×#4111yescharacteristic
581C3×D3—22no—
582C3×D3—22no—
583C3×D3—42no—
584C3×D3—42no—
585C3×D3—42no—
586C3×D3—82no—
587C2×Q8—91no—
588C2×D4—32no—
589C2×D4—31no—
590C22×C4—31no—
591C22×C4—91no—
592C22×C4—91no—
593C22×C4—92no—
594C4⋊C4—32no—
595C4⋊C4—31no—
596C4⋊C4—32no—
597C4⋊C4—92no—
598C4⋊C4—92no—
599C4⋊C4C3×D3211yescharacteristic
600C22⋊C4—32no—
601C22⋊C4—92no—
602C22⋊C4—92no—
603C22⋊C4—92no—
604C22⋊C4—92no—
605C42—31no—
606C42—91no—
607C42—91no—
608C42—91no—
609C42—92no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—32no—
614C22×C3—32no—
615C22×C3—41no—
616C22×C3—62no—
617C22×C3—61no—
618C22×C3—61no—
619C22×C3—61no—
620C22×C3—61no—
621C22×C3—62no—
622C22×C3—62no—
623C22×C3—62no—
624C22×C3—62no—
625C22×C3—62no—
626C22×C3—62no—
627C22×C3—121no—
628C22×C3—121no—
629C22×C3—122no—
630C22×C3—122no—
631C22×C3—122no—
632C22×C3C22×D3211yescharacteristic
633C22×C3C23×C3×D311yescharacteristic
634C22×C3C23×C3×D311yescharacteristic
635C2×D3—21no—
636C2×D3—21no—
637C2×D3—22no—
638C2×D3—22no—
639C2×D3—22no—
640C2×D3C3×#23712yes—
641C3×C4—22no—
642C3×C4—22no—
643C3×C4—22no—
644C3×C4—22no—
645C3×C4—22no—
646C3×C4—22no—
647C3×C4—42no—
648C3×C4—42no—
649C3×C4—42no—
650C3×C4—42no—
651C3×C4—61no—
652C3×C4—61no—
653C3×C4—61no—
654C3×C4—62no—
655C3×C4—61no—
656C3×C4—61no—
657C3×C4—61no—
658C3×C4—62no—
659C3×C4—82no—
660C3×C4—92no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4—122no—
664C3×C4—121no—
665C3×C4—182no—
666C3×C4—181no—
667C3×C4#379612yes—
668C3×C4C3×#23712yes—
669C3×C4C3×#23912yes—
670Dic3—21no—
671Dic3—21no—
672Dic3—22no—
673Dic3—21no—
674Dic3—32no—
675Dic3—32no—
676Dic3—62no—
677Dic3—64no—
678Dic3—62no—
679Dic3—61no—
680Dic3—62no—
681Dic3—61no—
682Dic3—121no—
683C32—21no—
684C32—21no—
685C32—21no—
686C32—41no—
687C32#560011yescharacteristic, complemented
688C32#569111yescharacteristic, complemented
689C32C3×#52911yescharacteristic, complemented
690C23—31no—
691C23—32no—
692Q8—182no—
693D4—64no—
694D4—62no—
695C2×C4—31no—
696C2×C4—31no—
697C2×C4—31no—
698C2×C4—32no—
699C2×C4—62no—
700C2×C4—91no—
701C2×C4—91no—
702C2×C4—92no—
703C2×C4—182no—
704C2×C4—184no—
705C2×C4—182no—
706C2×C4C2×C3×D3212yes—
707C2×C4C2×C3×D3211yescharacteristic
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—41no—
718C2×C3—41no—
719C2×C3—41no—
720C2×C3—62no—
721C2×C3—62no—
722C2×C3—122no—
723C2×C3—122no—
724C2×C3—122no—
725C2×C3—242no—
726C2×C3C2×#379611yescharacteristic
727C2×C3D3×#23711yescharacteristic
728C2×C3#6431911yescharacteristic
729C2×C3C2×C3×#23711yescharacteristic
730C2×C3C2×C3×#23711yescharacteristic
731C2×C3C2×C3×#23911yescharacteristic
732C2×C3C3×D3×#4111yescharacteristic
733C2×C3C3×D3×#4111yescharacteristic
734C2×C3C3×D3×#4111yescharacteristic
735D3—22no—
736D3—42no—
737C22—32no—
738C22—61no—
739C22—61no—
740C22—62no—
741C22—62no—
742C22—62no—
743C22C22×C3×D3211yescharacteristic
744C4—22no—
745C4—61no—
746C4—62no—
747C4—61no—
748C4—61no—
749C4—92no—
750C4—182no—
751C4—181no—
752C4C3×#379612yes—
753C3—21no—
754C3—21no—
755C3—21no—
756C3—41no—
757C3#1059442711yescharacteristic, direct product factor
758C3C3×#560011yescharacteristic, complemented
759C3C3×#569111yescharacteristic, complemented
760C2—62no—
761C2—122no—
762C2C2×C3×#379611yescharacteristic
763C2C3×D3×#23711yescharacteristic
764C2C3×#6431911yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C24
prime radicalC32×#895C2
hypercenterC3×C4⋊C4D32
hypocenterC32C3×#529
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#64096C2semidirect
3. C32×#890C2semidirect
4. C3×#63898C2semidirect
5. C3×#63898C2semidirect
6. C3×#63884C2semidirect
7. C3×#63878C2semidirect
8. C3×C4×D3×Dic3C2semidirect
9. C3×#63860C2semidirect
10. C3×#63858C2semidirect
11. C3×#63857C2semidirect
14. #10594427C3direct (N × H)
40. #64096C2×C3semidirect
57. C3×#890D3semidirect
58. C3×#890C2×C3semidirect
66. #63898C2×C3semidirect
67. #63898C2×C3semidirect
68. #63884C2×C3semidirect
69. #63878C2×C3semidirect
70. C4×D3×Dic3C2×C3semidirect
71. #63860C2×C3semidirect
72. #63858C2×C3semidirect
73. #63857C2×C3semidirect
224. #890C3×D3semidirect
482. C33#529semidirect
687. C32#5600semidirect
688. C32#5691semidirect
689. C32C3×#529semidirect
757. C3#10594427direct (N × H)
758. C3C3×#5600semidirect
759. C3C3×#5691semidirect

Maximal subgroups

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

subgroupindex
C3×#640962
C32×#8952
C32×#8902
C3×#638982
C3×#638842
C3×#638782
C3×C4×D3×Dic32
C3×#638602
C3×#638582
C3×#638572
C3×#56913
C3×#56003
#105944273