Finite Group Databasebeta

← C3×#10594809 #13174644

Subgroups — C3×#10594809 #13174644

Order 1728.

1146 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#638C211yesmaximal, characteristic
2C32×#926C211yesmaximal, characteristic, complemented
3C32×#924C211yesmaximal, characteristic, complemented
4C3×#63956C212yesmaximal, complemented
5C3×#63953C212yesmaximal
6C3×#63919C211yesmaximal, characteristic, complemented
7C3×#63871C211yesmaximal, characteristic, complemented
8C3×#63868C212yesmaximal, complemented
9C3×#63849C211yesmaximal, characteristic, complemented
10C3×#63843C211yesmaximal, characteristic, complemented
11C3×#63837C212yesmaximal, complemented
12C3×#5641—31nomaximal
13C3×#5533—31nomaximal
14#10594809C311yesmaximal, characteristic, direct product factor
15C22×C33×C4C2211yescharacteristic
16C2×C3×#638C2211yescharacteristic
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×C32×Dic6C2211yescharacteristic
19C2×C3×#627C2212yes—
20C3×#3757C2211yescharacteristic
21C3×#3752C2211yescharacteristic
22C3×#3750C2211yescharacteristic
23C3×C4×C3⋊Dic3C2211yescharacteristic
24C32×#217C2212yes—
25C32×#217C2212yes—
26C32×C4⋊Dic3C2211yescharacteristic
27C32×C4⋊Dic3C2211yescharacteristic
28C32×C4⋊Dic3C2211yescharacteristic
29C32×Dic3⋊C4C2212yes—
30C32×C4×Dic3C2212yes—
31C3×#3724C2212yes—
32C3×Dic3⋊Dic3C2212yes—
33C3×Dic3⋊Dic3C2212yes—
34C3×#3722C2212yes—
35C3×#3722C2212yes—
36C3×Dic32C2212yes—
37C3×Dic32C2212yes—
38C32×C22⋊Q8—31no—
39C32×#117—31no—
40C4×#638C2×C311yescharacteristic
41C3×#946—31no—
42C3×Q8×Dic3—31no—
43C3×C4×#67—31no—
44C3×C4×#67—31no—
45C3×C4×#67—61no—
46C3×#926—21no—
47C3×#926D311yescharacteristic, complemented
48C3×#926C2×C311yescharacteristic, complemented
49C3×#924—21no—
50C3×#924D311yescharacteristic, complemented
51C3×#924C2×C311yescharacteristic, complemented
52C3×#898—32no—
53C3×#897—31no—
54C3×#892—31no—
55C3×#892—31no—
56C3×#888—31no—
57C3×#888—31no—
58C3×#887—31no—
59C3×#887—32no—
60C3×#885—32no—
61C3×#885—32no—
62C3×#879—32no—
63C3×#879—32no—
64C3×#876—32no—
65C3×C4×Dic6—32no—
66#63956C2×C312yescomplemented
67#63953C2×C312yes—
68#63919C2×C311yescharacteristic, complemented
69#63871C2×C311yescharacteristic, complemented
70#63868C2×C312yescomplemented
71#63849C2×C311yescharacteristic, complemented
72#63843C2×C311yescharacteristic, complemented
73#63837C2×C312yescomplemented
74C23×C33C2311yescharacteristic
75C22×C3×C3⋊D3C2311yescharacteristic
76C2×C33×C4—22no—
77C2×C33×C4C2311yescharacteristic
78C2×C33×C4C2311yescharacteristic
79C3×#638—22no—
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C3×C4×C3⋊D3—22no—
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2312yes—
87C2×C32×Dic3C2312yes—
88C32×Dic6—22no—
89C3×#627—24no—
90C3×#556—91no—
91#5641—31no—
92#5533—31no—
93C2×C32×Q8—31no—
94C22×C32×C4—21no—
95C22×C32×C4—21no—
96C22×C32×C4—21no—
97C22×C32×C4—41no—
98C22×C32×C4C2×D311yescharacteristic
99C22×C32×C4C2×D311yescharacteristic
100C22×C32×C4C22×C311yescharacteristic
101C2×#638C22×C311yescharacteristic
102C2×C4×C3⋊D3C22×C311yescharacteristic
103C2×C3×#67—31no—
104C2×C3×#67—31no—
105C2×C3×#67—61no—
106C2×C3×C4×D3—31no—
107C2×C3×C4×D3—31no—
108C2×C3×C4×D3—61no—
109C2×C3×Dic6—21no—
110C2×C3×Dic6—32no—
111C2×C3×Dic6—32no—
112C2×C3×Dic6C2×D311yescharacteristic
113C2×C3×Dic6C22×C311yescharacteristic
114C2×#627C22×C312yes—
115C32×C4⋊C4—31no—
116C32×C4⋊C4—32no—
117C32×C4⋊C4—31no—
118C32×C4⋊C4—31no—
119C32×C22⋊C4—32no—
120C32×C22⋊C4—32no—
121C32×C42—32no—
122#3757C22×C311yescharacteristic
123#3752C22×C311yescharacteristic
124#3750C22×C311yescharacteristic
125C4×C3⋊Dic3C22×C311yescharacteristic
126C3×#217—22no—
127C3×#217—22no—
128C3×#217—31no—
129C3×#217—31no—
130C3×#217—61no—
131C3×#217C2×D312yes—
132C3×#217C2×D312yes—
133C3×#217C22×C312yes—
134C3×#217C22×C312yes—
135C3×(C2×D3)⋊C4—31no—
136C3×(C2×D3)⋊C4—31no—
137C3×(C2×D3)⋊C4—32no—
138C3×(C2×D3)⋊C4—32no—
139C3×(C2×D3)⋊C4—32no—
140C3×(C2×D3)⋊C4—32no—
141C3×(C2×D3)⋊C4—61no—
142C3×C4⋊Dic3—21no—
143C3×C4⋊Dic3—21no—
144C3×C4⋊Dic3—21no—
145C3×C4⋊Dic3—32no—
146C3×C4⋊Dic3—32no—
147C3×C4⋊Dic3C2×D311yescharacteristic
148C3×C4⋊Dic3C2×D311yescharacteristic
149C3×C4⋊Dic3C2×D311yescharacteristic
150C3×C4⋊Dic3C22×C311yescharacteristic
151C3×C4⋊Dic3C22×C311yescharacteristic
152C3×C4⋊Dic3C22×C311yescharacteristic
153C3×Dic3⋊C4—22no—
154C3×Dic3⋊C4—31no—
155C3×Dic3⋊C4—31no—
156C3×Dic3⋊C4—32no—
157C3×Dic3⋊C4—32no—
158C3×Dic3⋊C4—32no—
159C3×Dic3⋊C4—32no—
160C3×Dic3⋊C4—61no—
161C3×Dic3⋊C4C2×D312yes—
162C3×Dic3⋊C4C22×C312yes—
163C3×C4×Dic3—22no—
164C3×C4×Dic3—31no—
165C3×C4×Dic3—31no—
166C3×C4×Dic3—32no—
167C3×C4×Dic3—32no—
168C3×C4×Dic3—32no—
169C3×C4×Dic3—32no—
170C3×C4×Dic3—61no—
171C3×C4×Dic3C2×D312yes—
172C3×C4×Dic3C22×C312yes—
173#3724C22×C312yes—
174Dic3⋊Dic3C22×C312yes—
175Dic3⋊Dic3C22×C312yes—
176#3722C22×C312yes—
177#3722C22×C312yes—
178Dic32C22×C312yes—
179Dic32C22×C312yes—
180C22×C33—21no—
181C22×C33—21no—
182C22×C33—21no—
183C22×C33C2411yescharacteristic
184C2×C3×C3⋊D3—21no—
185C2×C3×C3⋊D3—21no—
186C2×C3×C3⋊D3—21no—
187C33×C4—21no—
188C33×C4#4112yes—
189C3×C3⋊Dic3—21no—
190C3×C3⋊Dic3—21no—
191C3×C3⋊Dic3#4112yes—
192C32×Dic3—22no—
193C32×Dic3—22no—
194C32×Dic3—22no—
195C32×Dic3—22no—
196C3×C4⋊Q8—91no—
197C3×#126—92no—
198C3×#126—92no—
199C3×#124—92no—
200C3×C22⋊Q8—31no—
201C3×C22⋊Q8—31no—
202C3×C22⋊Q8—61no—
203C3×C22⋊Q8—91no—
204C3×C4×Q8—92no—
205C3×C4×Q8—91no—
206C3×C4×D4—91no—
207C3×#117—31no—
208C3×#117—31no—
209C3×#117—61no—
210C3×#117—91no—
211#946—31no—
212Q8×Dic3—31no—
213C4×#67—31no—
214C4×#67—31no—
215C4×#67—61no—
216#926C3×D311yescharacteristic, complemented
217#924C3×D311yescharacteristic, complemented
218#898—32no—
219#897—31no—
220#892—31no—
221#892—31no—
222#888—31no—
223#888—31no—
224#887—31no—
225#887—32no—
226#885—32no—
227#885—32no—
228#879—32no—
229#879—32no—
230#876—32no—
231C4×Dic6—32no—
232C23×C32—21no—
233C23×C32—21no—
234C23×C32—21no—
235C23×C32—41no—
236C23×C32C22×D311yescharacteristic
237C23×C32C22×D311yescharacteristic
238C23×C32C23×C311yescharacteristic
239C22×C3⋊D3C23×C311yescharacteristic
240C22×C3×D3—31no—
241C22×C3×D3—31no—
242C22×C3×D3—61no—
243C32×Q8—62no—
244C2×C32×C4—22no—
245C2×C32×C4—24no—
246C2×C32×C4—22no—
247C2×C32×C4—22no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—32no—
255C2×C32×C4—32no—
256C2×C32×C4—32no—
257C2×C32×C4—32no—
258C2×C32×C4—41no—
259C2×C32×C4—41no—
260C2×C32×C4—42no—
261C2×C32×C4—42no—
262C2×C32×C4—44no—
263C2×C32×C4C22×D311yescharacteristic
264C2×C32×C4C22×D311yescharacteristic
265C2×C32×C4C22×D311yescharacteristic
266C2×C32×C4C22×D311yescharacteristic
267C2×C32×C4C23×C311yescharacteristic
268C2×C32×C4C23×C311yescharacteristic
269#638—22no—
270C2×C3⋊Dic3C23×C311yescharacteristic
271C2×C3⋊Dic3C23×C311yescharacteristic
272C2×C3⋊Dic3C23×C311yescharacteristic
273C4×C3⋊D3—22no—
274C3×#67—62no—
275C3×#67—62no—
276C3×#67—64no—
277C2×C3×Dic3—22no—
278C2×C3×Dic3—22no—
279C2×C3×Dic3—22no—
280C2×C3×Dic3—22no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3—31no—
284C2×C3×Dic3—31no—
285C2×C3×Dic3—31no—
286C2×C3×Dic3—31no—
287C2×C3×Dic3—61no—
288C2×C3×Dic3—61no—
289C2×C3×Dic3—61no—
290C2×C3×Dic3C22×D312yes—
291C2×C3×Dic3C22×D312yes—
292C2×C3×Dic3C22×D312yes—
293C2×C3×Dic3C22×D312yes—
294C2×C3×Dic3C23×C312yes—
295C2×C3×Dic3C23×C312yes—
296C2×C3×Dic3C23×C312yes—
297C2×C3×Dic3C23×C312yes—
298C3×C4×D3—62no—
299C3×C4×D3—62no—
300C3×C4×D3—122no—
301C3×Dic6—22no—
302C3×Dic6—22no—
303C3×Dic6—42no—
304C3×Dic6—64no—
305C3×Dic6—64no—
306#627—24no—
307#556—91noSylow
308C2×C33—41no—
309C2×C33C2×#4111yescharacteristic
310C2×C33C2×#4111yescharacteristic
311C2×C332−1+411yescharacteristic
312C3×C3⋊D3—41no—
313C2×C3×Q8—31no—
314C2×C3×Q8—31no—
315C2×C3×Q8—61no—
316C2×C3×Q8—92no—
317C2×C3×D4—91no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—41no—
322C22×C3×C4—91no—
323C22×C3×C4D3211yescharacteristic
324C22×C3×C4C2×C3×D311yescharacteristic
325C22×C3×C4C2×C3×D311yescharacteristic
326C2×#67—31no—
327C2×#67—31no—
328C2×#67—61no—
329C2×C4×D3—31no—
330C2×C4×D3—31no—
331C2×C4×D3—61no—
332C2×Dic6—32no—
333C2×Dic6—32no—
334C2×Dic6C2×C3×D311yescharacteristic
335C3×C4⋊C4—32no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—32no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—62no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—92no—
348C3×C4⋊C4—92no—
349C3×C4⋊C4—92no—
350C3×C4⋊C4—91no—
351C3×C22⋊C4—32no—
352C3×C22⋊C4—32no—
353C3×C22⋊C4—32no—
354C3×C22⋊C4—32no—
355C3×C22⋊C4—62no—
356C3×C22⋊C4—62no—
357C3×C22⋊C4—92no—
358C3×C22⋊C4—92no—
359C3×C22⋊C4—91no—
360C3×C22⋊C4—91no—
361C3×C42—32no—
362C3×C42—32no—
363C3×C42—62no—
364C3×C42—92no—
365C3×C42—92no—
366C3×C42—91no—
367#217—31no—
368#217—31no—
369#217—61no—
370#217C2×C3×D312yes—
371#217C2×C3×D312yes—
372(C2×D3)⋊C4—31no—
373(C2×D3)⋊C4—31no—
374(C2×D3)⋊C4—32no—
375(C2×D3)⋊C4—32no—
376(C2×D3)⋊C4—32no—
377(C2×D3)⋊C4—32no—
378(C2×D3)⋊C4—61no—
379C4⋊Dic3—32no—
380C4⋊Dic3—32no—
381C4⋊Dic3C2×C3×D311yescharacteristic
382C4⋊Dic3C2×C3×D311yescharacteristic
383C4⋊Dic3C2×C3×D311yescharacteristic
384Dic3⋊C4—31no—
385Dic3⋊C4—31no—
386Dic3⋊C4—32no—
387Dic3⋊C4—32no—
388Dic3⋊C4—32no—
389Dic3⋊C4—32no—
390Dic3⋊C4—61no—
391Dic3⋊C4C2×C3×D312yes—
392C4×Dic3—31no—
393C4×Dic3—31no—
394C4×Dic3—32no—
395C4×Dic3—32no—
396C4×Dic3—32no—
397C4×Dic3—32no—
398C4×Dic3—61no—
399C4×Dic3C2×C3×D312yes—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—21no—
403C22×C32—22no—
404C22×C32—22no—
405C22×C32—22no—
406C22×C32—21no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32—42no—
423C22×C32—42no—
424C22×C32—42no—
425C22×C32C23×D311yescharacteristic
426C22×C32C23×D311yescharacteristic
427C22×C32C24×C311yescharacteristic
428C2×C3⋊D3—21no—
429C2×C3⋊D3—21no—
430C2×C3⋊D3—21no—
431C2×C3×D3—62no—
432C2×C3×D3—61no—
433C2×C3×D3—61no—
434C2×C3×D3—61no—
435C2×C3×D3—61no—
436C2×C3×D3—61no—
437C2×C3×D3—61no—
438C2×C3×D3—121no—
439C2×C3×D3—121no—
440C32×C4—21no—
441C32×C4—22no—
442C32×C4—21no—
443C32×C4—21no—
444C32×C4—22no—
445C32×C4—22no—
446C32×C4—22no—
447C32×C4—42no—
448C32×C4—41no—
449C32×C4—41no—
450C32×C4—42no—
451C32×C4—62no—
452C32×C4—62no—
453C32×C4—62no—
454C32×C4—62no—
455C32×C4#23512yes—
456C32×C4#23712yes—
457C32×C4C3×#4112yes—
458C3⋊Dic3—21no—
459C3⋊Dic3—21no—
460C3⋊Dic3C3×#4112yes—
461C3×Dic3—22no—
462C3×Dic3—22no—
463C3×Dic3—22no—
464C3×Dic3—22no—
465C3×Dic3—22no—
466C3×Dic3—22no—
467C3×Dic3—22no—
468C3×Dic3—22no—
469C3×Dic3—32no—
470C3×Dic3—32no—
471C3×Dic3—42no—
472C3×Dic3—42no—
473C3×Dic3—42no—
474C3×Dic3—42no—
475C3×Dic3—62no—
476C3×Dic3—61no—
477C3×Dic3—61no—
478C3×Dic3—61no—
479C3×Dic3—61no—
480C3×Dic3—121no—
481C3×Dic3—121no—
482C4⋊Q8—91no—
483#126—92no—
484#126—92no—
485#124—92no—
486C22⋊Q8—31no—
487C22⋊Q8—91no—
488C4×Q8—92no—
489C4×Q8—91no—
490C4×D4—91no—
491#117—31no—
492#117—91no—
493C33#55611yescharacteristic, complemented, Sylow
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—41no—
498C23×C3—91no—
499C23×C3C2×D3211yescharacteristic
500C23×C3C22×C3×D311yescharacteristic
501C23×C3C22×C3×D311yescharacteristic
502C22×D3—31no—
503C22×D3—31no—
504C22×D3—61no—
505C3×Q8—62no—
506C3×Q8—62no—
507C3×Q8—122no—
508C3×Q8—184no—
509C3×D4—182no—
510C2×C3×C4—24no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—32no—
521C2×C3×C4—32no—
522C2×C3×C4—32no—
523C2×C3×C4—32no—
524C2×C3×C4—32no—
525C2×C3×C4—32no—
526C2×C3×C4—32no—
527C2×C3×C4—32no—
528C2×C3×C4—42no—
529C2×C3×C4—42no—
530C2×C3×C4—44no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—62no—
534C2×C3×C4—62no—
535C2×C3×C4—62no—
536C2×C3×C4—62no—
537C2×C3×C4—91no—
538C2×C3×C4—91no—
539C2×C3×C4—91no—
540C2×C3×C4—182no—
541C2×C3×C4C2×D3211yescharacteristic
542C2×C3×C4C2×D3211yescharacteristic
543C2×C3×C4C22×C3×D311yescharacteristic
544C2×C3×C4C22×C3×D311yescharacteristic
545C2×C3×C4C22×C3×D311yescharacteristic
546C2×C3×C4C22×C3×D311yescharacteristic
547#67—62no—
548#67—62no—
549#67—64no—
550C2×Dic3—31no—
551C2×Dic3—31no—
552C2×Dic3—31no—
553C2×Dic3—31no—
554C2×Dic3—31no—
555C2×Dic3—31no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3C22×C3×D312yes—
560C2×Dic3C22×C3×D312yes—
561C2×Dic3C22×C3×D312yes—
562C2×Dic3C22×C3×D312yes—
563C4×D3—62no—
564C4×D3—62no—
565C4×D3—122no—
566Dic6—22no—
567Dic6—64no—
568Dic6—64no—
569C2×C32—21no—
570C2×C32—21no—
571C2×C32—21no—
572C2×C32—21no—
573C2×C32—21no—
574C2×C32—21no—
575C2×C32—21no—
576C2×C32—21no—
577C2×C32—21no—
578C2×C32—41no—
579C2×C32—41no—
580C2×C32—41no—
581C2×C32—42no—
582C2×C32—42no—
583C2×C32—42no—
584C2×C32—44no—
585C2×C32—41no—
586C2×C32—41no—
587C2×C32—41no—
588C2×C32C2×#23511yescharacteristic
589C2×C32C2×#23711yescharacteristic
590C2×C32#100711yescharacteristic
591C2×C32D3×#4111yescharacteristic
592C2×C32D3×#4111yescharacteristic
593C2×C32#101011yescharacteristic
594C2×C32C2×C3×#4111yescharacteristic
595C2×C32C2×C3×#4111yescharacteristic
596C2×C32C3×2−1+411yescharacteristic
597C3⋊D3—41no—
598C3×D3—122no—
599C3×D3—121no—
600C3×D3—121no—
601C2×Q8—31no—
602C2×Q8—92no—
603C2×D4—91no—
604C22×C4—91no—
605C22×C4C3×D3211yescharacteristic
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—32no—
610C4⋊C4—92no—
611C4⋊C4—92no—
612C4⋊C4—92no—
613C4⋊C4—91no—
614C22⋊C4—32no—
615C22⋊C4—32no—
616C22⋊C4—92no—
617C22⋊C4—92no—
618C22⋊C4—91no—
619C22⋊C4—91no—
620C42—32no—
621C42—92no—
622C42—92no—
623C42—91no—
624C22×C3—22no—
625C22×C3—22no—
626C22×C3—22no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—42no—
646C22×C3—42no—
647C22×C3—42no—
648C22×C3—41no—
649C22×C3—181no—
650C22×C3—181no—
651C22×C3—181no—
652C22×C3C22×D3211yescharacteristic
653C22×C3C23×C3×D311yescharacteristic
654C22×C3C23×C3×D311yescharacteristic
655C2×D3—62no—
656C2×D3—61no—
657C2×D3—61no—
658C2×D3—61no—
659C2×D3—61no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—121no—
663C2×D3—121no—
664C3×C4—22no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—22no—
669C3×C4—22no—
670C3×C4—22no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—42no—
674C3×C4—42no—
675C3×C4—62no—
676C3×C4—62no—
677C3×C4—62no—
678C3×C4—62no—
679C3×C4—62no—
680C3×C4—62no—
681C3×C4—62no—
682C3×C4—62no—
683C3×C4—92no—
684C3×C4—122no—
685C3×C4—122no—
686C3×C4—122no—
687C3×C4—122no—
688C3×C4—181no—
689C3×C4—181no—
690C3×C4#380412yes—
691C3×C4C3×#23512yes—
692C3×C4C3×#23712yes—
693Dic3—22no—
694Dic3—22no—
695Dic3—22no—
696Dic3—22no—
697Dic3—32no—
698Dic3—32no—
699Dic3—62no—
700Dic3—61no—
701Dic3—61no—
702Dic3—61no—
703Dic3—61no—
704Dic3—121no—
705Dic3—121no—
706C32—21no—
707C32—21no—
708C32—21no—
709C32—41no—
710C32#553311yescharacteristic, complemented
711C32#564111yescharacteristic, complemented
712C32C3×#55611yescharacteristic, complemented
713C23—91no—
714C23C2×C3×D3211yescharacteristic
715Q8—62no—
716Q8—184no—
717D4—182no—
718C2×C4—22no—
719C2×C4—32no—
720C2×C4—32no—
721C2×C4—32no—
722C2×C4—32no—
723C2×C4—91no—
724C2×C4—91no—
725C2×C4—91no—
726C2×C4—182no—
727C2×C4C2×C3×D3211yescharacteristic
728C2×C4C2×C3×D3211yescharacteristic
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—42no—
739C2×C3—42no—
740C2×C3—42no—
741C2×C3—44no—
742C2×C3—41no—
743C2×C3—41no—
744C2×C3—41no—
745C2×C3—41no—
746C2×C3—41no—
747C2×C3—41no—
748C2×C3—361no—
749C2×C3#6429711yescharacteristic
750C2×C3#6430611yescharacteristic
751C2×C3C2×#380411yescharacteristic
752C2×C3C2×C3×#23511yescharacteristic
753C2×C3C2×C3×#23711yescharacteristic
754C2×C3C3×#100711yescharacteristic
755C2×C3C3×D3×#4111yescharacteristic
756C2×C3C3×D3×#4111yescharacteristic
757C2×C3C3×#101011yescharacteristic
758D3—122no—
759D3—121no—
760D3—121no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—181no—
765C22—181no—
766C22—181no—
767C22C22×C3×D3211yescharacteristic
768C4—21no—
769C4—62no—
770C4—62no—
771C4—62no—
772C4—62no—
773C4—92no—
774C4—181no—
775C4—181no—
776C4C3×#380412yes—
777C3—21no—
778C3—21no—
779C3—21no—
780C3—41no—
781C3#1059480911yescharacteristic, direct product factor
782C3C3×#553311yescharacteristic, complemented
783C3C3×#564111yescharacteristic, complemented
784C2—41no—
785C2—361no—
786C2C3×#6429711yescharacteristic
787C2C3×#6430611yescharacteristic
788C2C2×C3×#380411yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
prime radicalC2×C3×#638C22
hypercenterC22×C3×C4D32
hypocenterC32C3×#556
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
2. C32×#926C2semidirect
3. C32×#924C2semidirect
4. C3×#63956C2semidirect
6. C3×#63919C2semidirect
7. C3×#63871C2semidirect
8. C3×#63868C2semidirect
9. C3×#63849C2semidirect
10. C3×#63843C2semidirect
11. C3×#63837C2semidirect
14. #10594809C3direct (N × H)
47. C3×#926D3semidirect
48. C3×#926C2×C3semidirect
50. C3×#924D3semidirect
51. C3×#924C2×C3semidirect
66. #63956C2×C3semidirect
68. #63919C2×C3semidirect
69. #63871C2×C3semidirect
70. #63868C2×C3semidirect
71. #63849C2×C3semidirect
72. #63843C2×C3semidirect
73. #63837C2×C3semidirect
216. #926C3×D3semidirect
217. #924C3×D3semidirect
493. C33#556semidirect
710. C32#5533semidirect
711. C32#5641semidirect
712. C32C3×#556semidirect
781. C3#10594809direct (N × H)
782. C3C3×#5533semidirect
783. C3C3×#5641semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#6382
C32×#9262
C32×#9242
C3×#639562
C3×#639532
C3×#639192
C3×#638712
C3×#638682
C3×#638492
C3×#638432
C3×#638372
C3×#56413
C3×#55333
#105948093