Finite Group Databasebeta

← C3×#10594448 #13173995

Subgroups — C3×#10594448 #13173995

Order 1728.

1114 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64101C211yesmaximal, characteristic
2C32×#890C211yesmaximal, characteristic, complemented
3C32×#888C211yesmaximal, characteristic, complemented
4C3×#63918C211yesmaximal, characteristic, complemented
5C3×#63895C212yesmaximal
6C3×#63888C212yesmaximal
7C3×C4×#624C211yesmaximal, characteristic
8C3×#63869C211yesmaximal, characteristic, complemented
9C3×#63849C211yesmaximal, characteristic
10C3×#63843C212yesmaximal, complemented
11C3×#63838C212yesmaximal, complemented
12C3×#5728—31nomaximal
13C3×#5688—31nomaximal
14#10594448C311yesmaximal, characteristic, direct product factor
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C32×Dic6C2212yes—
17C2×C3×#627C2212yes—
18C2×C3×#624C2211yescharacteristic
19C2×C3×#624C2211yescharacteristic
20C33×C4⋊C4C2211yescharacteristic
21C3×#3752C2212yes—
22C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C3×C4×C3⋊Dic3C2212yes—
24C32×C4⋊Dic3C2212yes—
25C32×C4⋊Dic3C2211yescharacteristic
26C32×C4⋊Dic3C2211yescharacteristic
27C32×Dic3⋊C4C2212yes—
28C32×Dic3⋊C4C2212yes—
29C32×C4×Dic3C2211yescharacteristic
30C32×C4×Dic3C2211yescharacteristic
31C3×#3724C2212yes—
32C3×Dic3⋊Dic3C2212yes—
33C3×Dic3⋊Dic3C2212yes—
34C3×#3722C2212yes—
35C3×Dic32C2211yescharacteristic
36C3×Dic32C2212yes—
37C3×Dic32C2211yescharacteristic
38C32×C4⋊Q8—31no—
39C32×#125—31no—
40#64101C2×C311yescharacteristic
41C3×#946—32no—
42C3×Q8×Dic3—32no—
43C3×#897—32no—
44C3×#896—32no—
45C3×#896—32no—
46C3×#892—31no—
47C3×#892—31no—
48C3×#892—31no—
49C3×#892—31no—
50C3×#892—61no—
51C3×#890—21no—
52C3×#890—31no—
53C3×#890D311yescharacteristic, complemented
54C3×#890C2×C311yescharacteristic, complemented
55C3×#888—21no—
56C3×#888—31no—
57C3×#888D311yescharacteristic, complemented
58C3×#888C2×C311yescharacteristic, complemented
59C3×#887—32no—
60C3×#887—32no—
61C3×#887—32no—
62C3×C42×D3—31no—
63C3×C42×D3—31no—
64C3×#870—31no—
65C3×#869—31no—
66#63918C2×C311yescharacteristic, complemented
67#63895C2×C312yes—
68#63888C2×C312yes—
69C4×#624C2×C311yescharacteristic
70#63869C2×C311yescharacteristic, complemented
71#63849C2×C311yescharacteristic
72#63843C2×C312yescomplemented
73#63838C2×C312yescomplemented
74C22×C3×C3⋊D3C2311yescharacteristic
75C2×C33×C4C2312yes—
76C2×C33×C4C2311yescharacteristic
77C2×C3×C3⋊Dic3C2312yes—
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C3×C4×C3⋊D3Q814yescomplemented
80C2×C32×Dic3C2311yescharacteristic
81C2×C32×Dic3C2311yescharacteristic
82C2×C32×Dic3C2312yes—
83C2×C32×Dic3C2312yes—
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2311yescharacteristic
86C32×Dic6—24no—
87C3×#627—24no—
88C3×#624—22no—
89C3×#624—22no—
90C3×#533—91no—
91#5728—31no—
92#5688—31no—
93C2×C32×Q8—32no—
94C2×C4×C3⋊D3C22×C311yescharacteristic
95C2×C3×C4×D3—31no—
96C2×C3×C4×D3—31no—
97C2×C3×C4×D3—31no—
98C2×C3×C4×D3—31no—
99C2×C3×C4×D3—31no—
100C2×C3×C4×D3—31no—
101C2×C3×C4×D3—61no—
102C2×C3×Dic6—22no—
103C2×C3×Dic6—32no—
104C2×C3×Dic6—32no—
105C2×C3×Dic6C2×D312yes—
106C2×C3×Dic6C22×C312yes—
107C2×#627C22×C312yes—
108C2×#624C22×C311yescharacteristic
109C2×#624C22×C311yescharacteristic
110C32×C4⋊C4—21no—
111C32×C4⋊C4—21no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4—32no—
114C32×C4⋊C4—32no—
115C32×C4⋊C4—32no—
116C32×C4⋊C4—31no—
117C32×C4⋊C4—31no—
118C32×C4⋊C4—41no—
119C32×C4⋊C4C2×D311yescharacteristic
120C32×C4⋊C4C2×D311yescharacteristic
121C32×C4⋊C4C22×C311yescharacteristic
122C32×C42—31no—
123C32×C42—31no—
124#3752C22×C312yes—
125C4⋊(C3⋊Dic3)C22×C311yescharacteristic
126C4×C3⋊Dic3C22×C312yes—
127C3×(C2×D3)⋊C4—32no—
128C3×(C2×D3)⋊C4—32no—
129C3×(C2×D3)⋊C4—32no—
130C3×(C2×D3)⋊C4—32no—
131C3×(C2×D3)⋊C4—62no—
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3—22no—
134C3×C4⋊Dic3—21no—
135C3×C4⋊Dic3—31no—
136C3×C4⋊Dic3—31no—
137C3×C4⋊Dic3—32no—
138C3×C4⋊Dic3—32no—
139C3×C4⋊Dic3—61no—
140C3×C4⋊Dic3C2×D311yescharacteristic
141C3×C4⋊Dic3C2×D311yescharacteristic
142C3×C4⋊Dic3C2×D312yes—
143C3×C4⋊Dic3C22×C311yescharacteristic
144C3×C4⋊Dic3C22×C312yes—
145C3×C4⋊Dic3C22×C311yescharacteristic
146C3×Dic3⋊C4—22no—
147C3×Dic3⋊C4—22no—
148C3×Dic3⋊C4—32no—
149C3×Dic3⋊C4—32no—
150C3×Dic3⋊C4—32no—
151C3×Dic3⋊C4—32no—
152C3×Dic3⋊C4C2×D312yes—
153C3×Dic3⋊C4C2×D312yes—
154C3×Dic3⋊C4C22×C312yes—
155C3×Dic3⋊C4C22×C312yes—
156C3×C4×Dic3—21no—
157C3×C4×Dic3—21no—
158C3×C4×Dic3—32no—
159C3×C4×Dic3—32no—
160C3×C4×Dic3—32no—
161C3×C4×Dic3—31no—
162C3×C4×Dic3—31no—
163C3×C4×Dic3—31no—
164C3×C4×Dic3—32no—
165C3×C4×Dic3—31no—
166C3×C4×Dic3—62no—
167C3×C4×Dic3C2×D311yescharacteristic
168C3×C4×Dic3C2×D311yescharacteristic
169C3×C4×Dic3C22×C311yescharacteristic
170C3×C4×Dic3C22×C311yescharacteristic
171#3724C22×C312yes—
172Dic3⋊Dic3C22×C312yes—
173Dic3⋊Dic3C22×C312yes—
174#3722C22×C312yes—
175Dic32C22×C311yescharacteristic
176Dic32C22×C312yes—
177Dic32C22×C311yescharacteristic
178C22×C33C2411yescharacteristic
179C2×C3×C3⋊D3—21no—
180C2×C3×C3⋊D3—21no—
181C2×C3×C3⋊D3C2×Q812yes—
182C33×C4—22no—
183C33×C4C2×Q812yes—
184C3×C3⋊Dic3—22no—
185C3×C3⋊Dic3C2×Q812yes—
186C32×Dic3—21no—
187C32×Dic3—21no—
188C32×Dic3—22no—
189C32×Dic3—22no—
190C32×Dic3#4112yes—
191C32×Dic3#4112yes—
192C3×C4⋊Q8—31no—
193C3×C4⋊Q8—31no—
194C3×C4⋊Q8—61no—
195C3×C4⋊Q8—91no—
196C3×#125—31no—
197C3×#125—31no—
198C3×#125—61no—
199C3×#125—91no—
200C3×C22⋊Q8—92no—
201C3×C22⋊Q8—92no—
202C3×C4×Q8—92no—
203C3×C4×Q8—92no—
204C3×#117—91no—
205C3×#117—91no—
206C2×C3×C42—91no—
207#946—32no—
208Q8×Dic3—32no—
209#897—32no—
210#896—32no—
211#896—32no—
212#892—31no—
213#892—31no—
214#892—31no—
215#892—31no—
216#892—61no—
217#890—31no—
218#890C3×D311yescharacteristic, complemented
219#888—31no—
220#888C3×D311yescharacteristic, complemented
221#887—32no—
222#887—32no—
223#887—32no—
224C42×D3—31no—
225C42×D3—31no—
226#870—31no—
227#869—31no—
228C22×C3⋊D3C23×C311yescharacteristic
229C22×C3×D3—31no—
230C22×C3×D3—31no—
231C22×C3×D3—61no—
232C32×Q8—64no—
233C2×C32×C4—21no—
234C2×C32×C4—22no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4—22no—
238C2×C32×C4—22no—
239C2×C32×C4—31no—
240C2×C32×C4—31no—
241C2×C32×C4—31no—
242C2×C32×C4—31no—
243C2×C32×C4—32no—
244C2×C32×C4—32no—
245C2×C32×C4—41no—
246C2×C32×C4—42no—
247C2×C32×C4C22×D312yes—
248C2×C32×C4C22×D312yes—
249C2×C32×C4C22×D311yescharacteristic
250C2×C32×C4C22×D311yescharacteristic
251C2×C32×C4C23×C312yes—
252C2×C32×C4C23×C311yescharacteristic
253C2×C3⋊Dic3C23×C312yes—
254C2×C3⋊Dic3C23×C311yescharacteristic
255C4×C3⋊D3C3×Q814yescomplemented
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—22no—
261C2×C3×Dic3—22no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3—32no—
265C2×C3×Dic3—32no—
266C2×C3×Dic3—61no—
267C2×C3×Dic3—62no—
268C2×C3×Dic3C22×D311yescharacteristic
269C2×C3×Dic3C22×D311yescharacteristic
270C2×C3×Dic3C22×D312yes—
271C2×C3×Dic3C22×D312yes—
272C2×C3×Dic3C22×D311yescharacteristic
273C2×C3×Dic3C22×D311yescharacteristic
274C2×C3×Dic3C23×C312yes—
275C2×C3×Dic3C23×C312yes—
276C2×C3×Dic3C23×C311yescharacteristic
277C2×C3×Dic3C23×C311yescharacteristic
278C2×C3×Dic3C23×C311yescharacteristic
279C2×C3×Dic3C23×C311yescharacteristic
280C3×C4×D3—34no—
281C3×C4×D3—34no—
282C3×C4×D3—64no—
283C3×C4×D3—62no—
284C3×C4×D3—62no—
285C3×C4×D3—62no—
286C3×C4×D3—62no—
287C3×Dic6—24no—
288C3×Dic6—24no—
289C3×Dic6—44no—
290C3×Dic6—64no—
291C3×Dic6—64no—
292#627—24no—
293#624—22no—
294#624—22no—
295#533—91noSylow
296C2×C33C22×Q811yescharacteristic
297C2×C33C2×#4111yescharacteristic
298C2×C33C2×#4111yescharacteristic
299C3×C3⋊D3—22no—
300C2×C3×Q8—32no—
301C2×C3×Q8—32no—
302C2×C3×Q8—62no—
303C2×C3×Q8—92no—
304C22×C3×C4—91no—
305C22×C3×C4—91no—
306C22×C3×C4—91no—
307C2×C4×D3—31no—
308C2×C4×D3—31no—
309C2×C4×D3—31no—
310C2×C4×D3—31no—
311C2×C4×D3—31no—
312C2×C4×D3—31no—
313C2×C4×D3—61no—
314C2×Dic6—32no—
315C2×Dic6—32no—
316C2×Dic6C2×C3×D312yes—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—32no—
321C3×C4⋊C4—32no—
322C3×C4⋊C4—31no—
323C3×C4⋊C4—31no—
324C3×C4⋊C4—32no—
325C3×C4⋊C4—32no—
326C3×C4⋊C4—32no—
327C3×C4⋊C4—32no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—41no—
331C3×C4⋊C4—62no—
332C3×C4⋊C4—62no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4—62no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—92no—
337C3×C4⋊C4—92no—
338C3×C4⋊C4—92no—
339C3×C4⋊C4—91no—
340C3×C4⋊C4D3211yescharacteristic
341C3×C4⋊C4C2×C3×D311yescharacteristic
342C3×C4⋊C4C2×C3×D311yescharacteristic
343C3×C22⋊C4—92no—
344C3×C22⋊C4—92no—
345C3×C42—31no—
346C3×C42—31no—
347C3×C42—31no—
348C3×C42—31no—
349C3×C42—61no—
350C3×C42—61no—
351C3×C42—91no—
352C3×C42—91no—
353C3×C42—92no—
354C3×C42—92no—
355(C2×D3)⋊C4—32no—
356(C2×D3)⋊C4—32no—
357(C2×D3)⋊C4—32no—
358(C2×D3)⋊C4—32no—
359(C2×D3)⋊C4—62no—
360C4⋊Dic3—31no—
361C4⋊Dic3—31no—
362C4⋊Dic3—32no—
363C4⋊Dic3—32no—
364C4⋊Dic3—61no—
365C4⋊Dic3C2×C3×D311yescharacteristic
366C4⋊Dic3C2×C3×D311yescharacteristic
367C4⋊Dic3C2×C3×D312yes—
368Dic3⋊C4—32no—
369Dic3⋊C4—32no—
370Dic3⋊C4—32no—
371Dic3⋊C4—32no—
372Dic3⋊C4C2×C3×D312yes—
373Dic3⋊C4C2×C3×D312yes—
374C4×Dic3—32no—
375C4×Dic3—32no—
376C4×Dic3—31no—
377C4×Dic3—31no—
378C4×Dic3—31no—
379C4×Dic3—31no—
380C4×Dic3—32no—
381C4×Dic3—32no—
382C4×Dic3—62no—
383C4×Dic3C2×C3×D311yescharacteristic
384C4×Dic3C2×C3×D311yescharacteristic
385C22×C32—21no—
386C22×C32—21no—
387C22×C32—21no—
388C22×C32—41no—
389C22×C32C23×D311yescharacteristic
390C22×C32C23×D311yescharacteristic
391C22×C32C24×C311yescharacteristic
392C2×C3⋊D3—21no—
393C2×C3⋊D3—21no—
394C2×C3⋊D3C2×C3×Q812yes—
395C2×C3×D3—32no—
396C2×C3×D3—32no—
397C2×C3×D3—62no—
398C2×C3×D3—61no—
399C2×C3×D3—61no—
400C2×C3×D3—61no—
401C2×C3×D3—61no—
402C2×C3×D3—121no—
403C2×C3×D3—121no—
404C32×C4—22no—
405C32×C4—22no—
406C32×C4—22no—
407C32×C4—22no—
408C32×C4—22no—
409C32×C4—22no—
410C32×C4—32no—
411C32×C4—32no—
412C32×C4—42no—
413C32×C4—42no—
414C32×C4—42no—
415C32×C4—42no—
416C32×C4—61no—
417C32×C4—62no—
418C32×C4—61no—
419C32×C4—62no—
420C32×C4—82no—
421C32×C4D3×Q812yes—
422C32×C4D3×Q812yes—
423C32×C4C2×C3×Q812yes—
424C3⋊Dic3—22no—
425C3⋊Dic3C2×C3×Q812yes—
426C3×Dic3—22no—
427C3×Dic3—22no—
428C3×Dic3—21no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—22no—
433C3×Dic3—22no—
434C3×Dic3—22no—
435C3×Dic3—22no—
436C3×Dic3—32no—
437C3×Dic3—32no—
438C3×Dic3—42no—
439C3×Dic3—42no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3—62no—
443C3×Dic3—62no—
444C3×Dic3—62no—
445C3×Dic3—122no—
446C3×Dic3#23712yes—
447C3×Dic3#23912yes—
448C3×Dic3C3×#4112yes—
449C3×Dic3C3×#4112yes—
450C4⋊Q8—31no—
451C4⋊Q8—91no—
452#125—31no—
453#125—91no—
454C22⋊Q8—92no—
455C22⋊Q8—92no—
456C4×Q8—92no—
457C4×Q8—92no—
458#117—91no—
459#117—91no—
460C2×C42—91no—
461C33#53311yescharacteristic, complemented, Sylow
462C23×C3—91no—
463C22×D3—31no—
464C22×D3—31no—
465C22×D3—61no—
466C3×Q8—64no—
467C3×Q8—64no—
468C3×Q8—124no—
469C3×Q8—184no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—31no—
477C2×C3×C4—31no—
478C2×C3×C4—31no—
479C2×C3×C4—31no—
480C2×C3×C4—31no—
481C2×C3×C4—31no—
482C2×C3×C4—32no—
483C2×C3×C4—32no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—32no—
487C2×C3×C4—32no—
488C2×C3×C4—41no—
489C2×C3×C4—42no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—62no—
495C2×C3×C4—62no—
496C2×C3×C4—91no—
497C2×C3×C4—94no—
498C2×C3×C4—92no—
499C2×C3×C4—182no—
500C2×C3×C4—182no—
501C2×C3×C4C2×D3212yes—
502C2×C3×C4C2×D3211yescharacteristic
503C2×C3×C4C22×C3×D312yes—
504C2×C3×C4C22×C3×D312yes—
505C2×C3×C4C22×C3×D311yescharacteristic
506C2×C3×C4C22×C3×D311yescharacteristic
507C2×Dic3—31no—
508C2×Dic3—31no—
509C2×Dic3—32no—
510C2×Dic3—32no—
511C2×Dic3—61no—
512C2×Dic3—62no—
513C2×Dic3C22×C3×D311yescharacteristic
514C2×Dic3C22×C3×D311yescharacteristic
515C2×Dic3C22×C3×D312yes—
516C2×Dic3C22×C3×D312yes—
517C2×Dic3C22×C3×D311yescharacteristic
518C2×Dic3C22×C3×D311yescharacteristic
519C4×D3—34no—
520C4×D3—34no—
521C4×D3—64no—
522C4×D3—62no—
523C4×D3—62no—
524C4×D3—62no—
525C4×D3—62no—
526Dic6—24no—
527Dic6—64no—
528Dic6—64no—
529C2×C32—21no—
530C2×C32—21no—
531C2×C32—21no—
532C2×C32—21no—
533C2×C32—21no—
534C2×C32—21no—
535C2×C32—21no—
536C2×C32—21no—
537C2×C32—21no—
538C2×C32—41no—
539C2×C32—41no—
540C2×C32—41no—
541C2×C32C2×#23711yescharacteristic
542C2×C32C2×D3×Q811yescharacteristic
543C2×C32C2×D3×Q811yescharacteristic
544C2×C32C2×#23911yescharacteristic
545C2×C32D3×#4111yescharacteristic
546C2×C32D3×#4111yescharacteristic
547C2×C32C22×C3×Q811yescharacteristic
548C2×C32C2×C3×#4111yescharacteristic
549C2×C32C2×C3×#4111yescharacteristic
550C3⋊D3—22no—
551C3×D3—62no—
552C3×D3—62no—
553C3×D3—122no—
554C2×Q8—32no—
555C2×Q8—92no—
556C22×C4—91no—
557C22×C4—91no—
558C22×C4—91no—
559C4⋊C4—31no—
560C4⋊C4—31no—
561C4⋊C4—32no—
562C4⋊C4—32no—
563C4⋊C4—32no—
564C4⋊C4—92no—
565C4⋊C4—92no—
566C4⋊C4—92no—
567C4⋊C4—91no—
568C4⋊C4C3×D3211yescharacteristic
569C22⋊C4—92no—
570C22⋊C4—92no—
571C42—31no—
572C42—31no—
573C42—91no—
574C42—91no—
575C42—92no—
576C42—92no—
577C22×C3—21no—
578C22×C3—21no—
579C22×C3—21no—
580C22×C3—41no—
581C22×C3—92no—
582C22×C3—181no—
583C22×C3—181no—
584C22×C3C22×D3211yescharacteristic
585C22×C3C23×C3×D311yescharacteristic
586C22×C3C23×C3×D311yescharacteristic
587C2×D3—32no—
588C2×D3—32no—
589C2×D3—62no—
590C2×D3—61no—
591C2×D3—61no—
592C2×D3—61no—
593C2×D3—61no—
594C2×D3—121no—
595C2×D3—121no—
596C3×C4—22no—
597C3×C4—22no—
598C3×C4—22no—
599C3×C4—22no—
600C3×C4—22no—
601C3×C4—22no—
602C3×C4—32no—
603C3×C4—32no—
604C3×C4—32no—
605C3×C4—32no—
606C3×C4—42no—
607C3×C4—42no—
608C3×C4—42no—
609C3×C4—42no—
610C3×C4—62no—
611C3×C4—62no—
612C3×C4—61no—
613C3×C4—62no—
614C3×C4—61no—
615C3×C4—62no—
616C3×C4—61no—
617C3×C4—62no—
618C3×C4—61no—
619C3×C4—62no—
620C3×C4—82no—
621C3×C4—92no—
622C3×C4—122no—
623C3×C4—121no—
624C3×C4—122no—
625C3×C4—121no—
626C3×C4—182no—
627C3×C4#379712yes—
628C3×C4C3×D3×Q812yes—
629C3×C4C3×D3×Q812yes—
630Dic3—22no—
631Dic3—22no—
632Dic3—21no—
633Dic3—21no—
634Dic3—32no—
635Dic3—32no—
636Dic3—62no—
637Dic3—62no—
638Dic3—62no—
639Dic3—122no—
640Dic3C3×#23712yes—
641Dic3C3×#23912yes—
642C32—21no—
643C32—21no—
644C32—21no—
645C32—41no—
646C32#568811yescharacteristic, complemented
647C32#572811yescharacteristic, complemented
648C32C3×#53311yescharacteristic, complemented
649C23—91no—
650Q8—64no—
651Q8—184no—
652C2×C4—31no—
653C2×C4—31no—
654C2×C4—31no—
655C2×C4—31no—
656C2×C4—32no—
657C2×C4—32no—
658C2×C4—91no—
659C2×C4—94no—
660C2×C4—92no—
661C2×C4—182no—
662C2×C4—182no—
663C2×C4C2×C3×D3212yes—
664C2×C4C2×C3×D3211yescharacteristic
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—21no—
674C2×C3—41no—
675C2×C3—41no—
676C2×C3—41no—
677C2×C3—182no—
678C2×C3C2×#379711yescharacteristic
679C2×C3D3×#23711yescharacteristic
680C2×C3D3×#23911yescharacteristic
681C2×C3C2×C3×#23711yescharacteristic
682C2×C3C2×C3×D3×Q811yescharacteristic
683C2×C3C2×C3×D3×Q811yescharacteristic
684C2×C3C2×C3×#23911yescharacteristic
685C2×C3C3×D3×#4111yescharacteristic
686C2×C3C3×D3×#4111yescharacteristic
687D3—62no—
688D3—62no—
689D3—122no—
690C22—92no—
691C22—181no—
692C22—181no—
693C22C22×C3×D3211yescharacteristic
694C4—22no—
695C4—32no—
696C4—32no—
697C4—61no—
698C4—62no—
699C4—61no—
700C4—62no—
701C4—92no—
702C4—182no—
703C4C3×#379712yes—
704C3—21no—
705C3—21no—
706C3—21no—
707C3—41no—
708C3#1059444811yescharacteristic, direct product factor
709C3C3×#568811yescharacteristic, complemented
710C3C3×#572811yescharacteristic, complemented
711C2—182no—
712C2C2×C3×#379711yescharacteristic
713C2C3×D3×#23711yescharacteristic
714C2C3×D3×#23911yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C24
prime radicalC22×C3×C3⋊D3C23
hypercenterC3×C4⋊C4D32
hypocenterC32C3×#533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C32×#890C2semidirect
3. C32×#888C2semidirect
4. C3×#63918C2semidirect
8. C3×#63869C2semidirect
10. C3×#63843C2semidirect
11. C3×#63838C2semidirect
14. #10594448C3direct (N × H)
53. C3×#890D3semidirect
54. C3×#890C2×C3semidirect
57. C3×#888D3semidirect
58. C3×#888C2×C3semidirect
66. #63918C2×C3semidirect
70. #63869C2×C3semidirect
72. #63843C2×C3semidirect
73. #63838C2×C3semidirect
79. C3×C4×C3⋊D3Q8semidirect
218. #890C3×D3semidirect
220. #888C3×D3semidirect
255. C4×C3⋊D3C3×Q8semidirect
461. C33#533semidirect
646. C32#5688semidirect
647. C32#5728semidirect
648. C32C3×#533semidirect
708. C3#10594448direct (N × H)
709. C3C3×#5688semidirect
710. C3C3×#5728semidirect

Maximal subgroups

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

subgroupindex
C3×#641012
C32×#8902
C32×#8882
C3×#639182
C3×#638952
C3×#638882
C3×C4×#6242
C3×#638692
C3×#638492
C3×#638432
C3×#638382
C3×#57283
C3×#56883
#105944483