Finite Group Databasebeta

← C3×#10595125 #13174769

Subgroups — C3×#10595125 #13174769

Order 1728.

1310 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64149C211yesmaximal, characteristic, complemented
2C32×#938C211yesmaximal, characteristic, complemented
3C32×D4×Dic3C211yesmaximal, characteristic, complemented
4C3×#63978C212yesmaximal, complemented
5C3×#63975C212yesmaximal, complemented
6C3×#63966C212yesmaximal, complemented
7C3×#63958C212yesmaximal, complemented
8C3×#63909C211yesmaximal, characteristic, complemented
9C3×#63894C211yesmaximal, characteristic, complemented
10C3×#63872C211yesmaximal, characteristic, complemented
11C3×#63855C211yesmaximal, characteristic, complemented
12C3×#5619—31nomaximal
13C3×#5562—31nomaximal
14#10595125C311yesmaximal, characteristic, direct product factor
15C2×C33×D4C2211yescharacteristic
16C2×C3×#638C2212yes—
17C2×C3×#638C2212yes—
18C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×C32×#67C2212yes—
20C22×C32×Dic3C2212yes—
21C2×C32×C4×D3C2211yescharacteristic
22C2×C3×#626C2212yes—
23C2×C3×#624C2212yes—
24C3×C4×C3⋊Dic3C2211yescharacteristic
25C32×#217C2212yes—
26C32×#217C2212yes—
27C32×C4⋊Dic3C2211yescharacteristic
28C32×C4⋊Dic3C2211yescharacteristic
29C32×C4×Dic3C2211yescharacteristic
30C3×Dic3⋊Dic3C2212yes—
31C3×Dic3⋊Dic3C2211yescharacteristic
32C3×Dic3⋊Dic3C2211yescharacteristic
33C3×Dic3⋊Dic3C2212yes—
34C3×#3722C2212yes—
35C3×#3722C2212yes—
36C3×(C2×D3)⋊Dic3C2211yescharacteristic
37C3×(C2×D3)⋊Dic3C2211yescharacteristic
38C32×#121—31no—
39C32×C4×D4—31no—
40#64149C2×C311yescharacteristic, complemented
41C3×#940—31no—
42C3×#940—31no—
43C3×#940—61no—
44C3×#939—32no—
45C3×#938—21no—
46C3×#938—32no—
47C3×#938D311yescharacteristic, complemented
48C3×#938C2×C311yescharacteristic, complemented
49C3×D4×Dic3—21no—
50C3×D4×Dic3D311yescharacteristic, complemented
51C3×D4×Dic3C2×C311yescharacteristic, complemented
52C3×#930—32no—
53C3×#930—31no—
54C3×#929—32no—
55C3×#926—31no—
56C3×#895—31no—
57C3×#893—31no—
58C3×#890—31no—
59C3×#890—31no—
60C3×#886—32no—
61C3×#884—32no—
62C3×#883—32no—
63C3×#883—32no—
64C3×C4×D12—31no—
65C3×#872—31no—
66#63978C2×C312yescomplemented
67#63975C2×C312yescomplemented
68#63966C2×C312yescomplemented
69#63958C2×C312yescomplemented
70#63909C2×C311yescharacteristic, complemented
71#63894C2×C311yescharacteristic, complemented
72#63872C2×C311yescharacteristic, complemented
73#63855C2×C311yescharacteristic, complemented
74C23×C33C2312yes—
75C22×C3×C3⋊D3C2312yes—
76C22×C32×D3C2311yescharacteristic
77C33×D4—22no—
78C2×C33×C4C2311yescharacteristic
79C3×#638—42no—
80C3×#638—42no—
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C3×C4⋊(C3⋊D3)—22no—
84C32×#67—42no—
85C2×C32×Dic3—42no—
86C2×C32×Dic3C2311yescharacteristic
87C2×C32×Dic3C2311yescharacteristic
88C2×C32×Dic3C2312yes—
89C2×C32×Dic3C2312yes—
90C2×C32×Dic3C2311yescharacteristic
91C32×C4×D3—22no—
92C3×#626—42no—
93C3×#624—42no—
94C3×#540—91no—
95#5619—31no—
96#5562—31no—
97C2×C32×D4—21no—
98C2×C32×D4—21no—
99C2×C32×D4—21no—
100C2×C32×D4—32no—
101C2×C32×D4—41no—
102C2×C32×D4C2×D311yescharacteristic
103C2×C32×D4C2×D311yescharacteristic
104C2×C32×D4C22×C311yescharacteristic
105C22×C32×C4—32no—
106C22×C32×C4—31no—
107C2×#638C22×C312yes—
108C2×#638C22×C312yes—
109C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
110C2×C3×#67—22no—
111C2×C3×#67—32no—
112C2×C3×#67—32no—
113C2×C3×#67—32no—
114C2×C3×#67—32no—
115C2×C3×#67—32no—
116C2×C3×#67—62no—
117C2×C3×#67—62no—
118C2×C3×#67C2×D312yes—
119C2×C3×#67C22×C312yes—
120C22×C3×Dic3—22no—
121C22×C3×Dic3C2×D312yes—
122C22×C3×Dic3C22×C312yes—
123C2×C3×D12—31no—
124C2×C3×D12—31no—
125C2×C3×D12—32no—
126C2×C3×D12—61no—
127C2×C3×C4×D3—21no—
128C2×C3×C4×D3—32no—
129C2×C3×C4×D3—32no—
130C2×C3×C4×D3C2×D311yescharacteristic
131C2×C3×C4×D3C22×C311yescharacteristic
132C2×#626C22×C312yes—
133C2×#624C22×C312yes—
134C32×C4⋊C4—31no—
135C32×C4⋊C4—31no—
136C32×C22⋊C4—32no—
137C32×C22⋊C4—32no—
138C32×C42—31no—
139C4×C3⋊Dic3C22×C311yescharacteristic
140C3×#217—22no—
141C3×#217—22no—
142C3×#217—31no—
143C3×#217—31no—
144C3×#217C2×D312yes—
145C3×#217C2×D312yes—
146C3×#217C22×C312yes—
147C3×#217C22×C312yes—
148C3×(C2×D3)⋊C4—31no—
149C3×(C2×D3)⋊C4—31no—
150C3×(C2×D3)⋊C4—32no—
151C3×(C2×D3)⋊C4—32no—
152C3×(C2×D3)⋊C4—32no—
153C3×(C2×D3)⋊C4—32no—
154C3×C4⋊Dic3—21no—
155C3×C4⋊Dic3—21no—
156C3×C4⋊Dic3—31no—
157C3×C4⋊Dic3—32no—
158C3×C4⋊Dic3—31no—
159C3×C4⋊Dic3—32no—
160C3×C4⋊Dic3C2×D311yescharacteristic
161C3×C4⋊Dic3C2×D311yescharacteristic
162C3×C4⋊Dic3C22×C311yescharacteristic
163C3×C4⋊Dic3C22×C311yescharacteristic
164C3×Dic3⋊C4—31no—
165C3×Dic3⋊C4—32no—
166C3×Dic3⋊C4—32no—
167C3×Dic3⋊C4—31no—
168C3×C4×Dic3—21no—
169C3×C4×Dic3—31no—
170C3×C4×Dic3—31no—
171C3×C4×Dic3—61no—
172C3×C4×Dic3C2×D311yescharacteristic
173C3×C4×Dic3C22×C311yescharacteristic
174Dic3⋊Dic3C22×C311yescharacteristic
175Dic3⋊Dic3C22×C311yescharacteristic
176Dic3⋊Dic3C22×C312yes—
177Dic3⋊Dic3C22×C312yes—
178#3722C22×C312yes—
179#3722C22×C312yes—
180(C2×D3)⋊Dic3C22×C311yescharacteristic
181(C2×D3)⋊Dic3C22×C311yescharacteristic
182C22×C33—22no—
183C22×C33—22no—
184C22×C33—22no—
185C22×C33C2411yescharacteristic
186C2×C3×C3⋊D3—22no—
187C2×C3×C3⋊D3—22no—
188C2×C3×C3⋊D3—22no—
189C2×C32×D3—21no—
190C2×C32×D3—21no—
191C2×C32×D3—21no—
192C33×C4#4112yes—
193C3×C3⋊Dic3—21no—
194C3×C3⋊Dic3—21no—
195C32×Dic3—21no—
196C32×Dic3—21no—
197C32×Dic3—21no—
198C32×Dic3—22no—
199C32×Dic3—22no—
200C3×#127—91no—
201C3×#125—91no—
202C3×#123—92no—
203C3×#123—92no—
204C3×#121—31no—
205C3×#121—31no—
206C3×#121—61no—
207C3×#121—92no—
208C3×#121—91no—
209C3×#121—92no—
210C3×C4×D4—31no—
211C3×C4×D4—31no—
212C3×C4×D4—61no—
213C3×C4×D4—91no—
214C3×#117—91no—
215#940—31no—
216#940—31no—
217#940—61no—
218#939—32no—
219#938—32no—
220#938C3×D311yescharacteristic, complemented
221D4×Dic3C3×D311yescharacteristic, complemented
222#930—32no—
223#930—31no—
224#929—32no—
225#926—31no—
226#895—31no—
227#893—31no—
228#890—31no—
229#890—31no—
230#886—32no—
231#884—32no—
232#883—32no—
233#883—32no—
234C4×D12—31no—
235#872—31no—
236C23×C32—22no—
237C23×C32—22no—
238C23×C32—22no—
239C23×C32—31no—
240C23×C32—42no—
241C23×C32C22×D312yes—
242C23×C32C22×D312yes—
243C23×C32C23×C312yes—
244C22×C3⋊D3C23×C312yes—
245C22×C3×D3—21no—
246C22×C3×D3—32no—
247C22×C3×D3—32no—
248C22×C3×D3—62no—
249C22×C3×D3C22×D311yescharacteristic
250C22×C3×D3C23×C311yescharacteristic
251C32×D4—22no—
252C32×D4—24no—
253C32×D4—22no—
254C32×D4—22no—
255C32×D4—42no—
256C32×D4—42no—
257C32×D4—44no—
258C32×D4—122no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—32no—
263C2×C32×C4—32no—
264C2×C32×C4—31no—
265C2×C32×C4—31no—
266C2×C32×C4—31no—
267C2×C32×C4—41no—
268C2×C32×C4—62no—
269C2×C32×C4—122no—
270C2×C32×C4C22×D311yescharacteristic
271C2×C32×C4C22×D311yescharacteristic
272C2×C32×C4C23×C311yescharacteristic
273#638—42no—
274#638—42no—
275C2×C3⋊Dic3C23×C311yescharacteristic
276C2×C3⋊Dic3C23×C311yescharacteristic
277C4⋊(C3⋊D3)—22no—
278C3×#67—42no—
279C3×#67—42no—
280C3×#67—44no—
281C3×#67—122no—
282C3×#67—122no—
283C3×#67—122no—
284C3×#67—122no—
285C3×#67—122no—
286C3×#67—124no—
287C3×#67—124no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—22no—
291C2×C3×Dic3—22no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—31no—
294C2×C3×Dic3—31no—
295C2×C3×Dic3—31no—
296C2×C3×Dic3—31no—
297C2×C3×Dic3—42no—
298C2×C3×Dic3—42no—
299C2×C3×Dic3—44no—
300C2×C3×Dic3—61no—
301C2×C3×Dic3—61no—
302C2×C3×Dic3C22×D311yescharacteristic
303C2×C3×Dic3C22×D311yescharacteristic
304C2×C3×Dic3C22×D311yescharacteristic
305C2×C3×Dic3C22×D312yes—
306C2×C3×Dic3C22×D312yes—
307C2×C3×Dic3C23×C311yescharacteristic
308C2×C3×Dic3C23×C311yescharacteristic
309C2×C3×Dic3C23×C311yescharacteristic
310C2×C3×Dic3C23×C312yes—
311C2×C3×Dic3C23×C312yes—
312C3×D12—62no—
313C3×D12—62no—
314C3×D12—122no—
315C3×D12—122no—
316C3×C4×D3—22no—
317C3×C4×D3—22no—
318C3×C4×D3—42no—
319C3×C4×D3—122no—
320C3×C4×D3—122no—
321#626—42no—
322#624—42no—
323#540—91noSylow
324C2×C33—42no—
325C2×C33C2×#4111yescharacteristic
326C2×C33H(5,𝔽2)11yescharacteristic
327C2×C33H(5,𝔽2)11yescharacteristic
328C3×C3⋊D3—42no—
329C32×D3—41no—
330C2×C3×D4—21no—
331C2×C3×D4—21no—
332C2×C3×D4—21no—
333C2×C3×D4—32no—
334C2×C3×D4—32no—
335C2×C3×D4—41no—
336C2×C3×D4—62no—
337C2×C3×D4—92no—
338C2×C3×D4—92no—
339C2×C3×D4—92no—
340C2×C3×D4—91no—
341C2×C3×D4D3211yescharacteristic
342C2×C3×D4C2×C3×D311yescharacteristic
343C2×C3×D4C2×C3×D311yescharacteristic
344C22×C3×C4—32no—
345C22×C3×C4—32no—
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—61no—
349C22×C3×C4—62no—
350C22×C3×C4—92no—
351C2×#67—32no—
352C2×#67—32no—
353C2×#67—32no—
354C2×#67—32no—
355C2×#67—32no—
356C2×#67—62no—
357C2×#67—62no—
358C2×#67C2×C3×D312yes—
359C22×Dic3C2×C3×D312yes—
360C2×D12—31no—
361C2×D12—31no—
362C2×D12—32no—
363C2×D12—61no—
364C2×C4×D3—32no—
365C2×C4×D3—32no—
366C2×C4×D3C2×C3×D311yescharacteristic
367C3×C4⋊C4—31no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4—31no—
370C3×C4⋊C4—31no—
371C3×C4⋊C4—61no—
372C3×C4⋊C4—61no—
373C3×C4⋊C4—91no—
374C3×C4⋊C4—91no—
375C3×C4⋊C4—92no—
376C3×C4⋊C4—92no—
377C3×C22⋊C4—32no—
378C3×C22⋊C4—32no—
379C3×C22⋊C4—32no—
380C3×C22⋊C4—32no—
381C3×C22⋊C4—62no—
382C3×C22⋊C4—62no—
383C3×C22⋊C4—92no—
384C3×C22⋊C4—92no—
385C3×C22⋊C4—91no—
386C3×C22⋊C4—91no—
387C3×C42—31no—
388C3×C42—31no—
389C3×C42—61no—
390C3×C42—91no—
391#217—31no—
392#217—31no—
393#217C2×C3×D312yes—
394#217C2×C3×D312yes—
395(C2×D3)⋊C4—31no—
396(C2×D3)⋊C4—31no—
397(C2×D3)⋊C4—32no—
398(C2×D3)⋊C4—32no—
399(C2×D3)⋊C4—32no—
400(C2×D3)⋊C4—32no—
401C4⋊Dic3—31no—
402C4⋊Dic3—32no—
403C4⋊Dic3—31no—
404C4⋊Dic3—32no—
405C4⋊Dic3C2×C3×D311yescharacteristic
406C4⋊Dic3C2×C3×D311yescharacteristic
407Dic3⋊C4—31no—
408Dic3⋊C4—31no—
409Dic3⋊C4—32no—
410Dic3⋊C4—32no—
411C4×Dic3—31no—
412C4×Dic3—31no—
413C4×Dic3—61no—
414C4×Dic3C2×C3×D311yescharacteristic
415C22×C32—22no—
416C22×C32—24no—
417C22×C32—22no—
418C22×C32—22no—
419C22×C32—22no—
420C22×C32—22no—
421C22×C32—22no—
422C22×C32—22no—
423C22×C32—22no—
424C22×C32—22no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32—41no—
429C22×C32—42no—
430C22×C32—42no—
431C22×C32—44no—
432C22×C32—42no—
433C22×C32—42no—
434C22×C32—42no—
435C22×C32—42no—
436C22×C32—42no—
437C22×C32—42no—
438C22×C32—61no—
439C22×C32—61no—
440C22×C32—61no—
441C22×C32—82no—
442C22×C32—82no—
443C22×C32C23×D311yescharacteristic
444C22×C32C23×D311yescharacteristic
445C22×C32C24×C311yescharacteristic
446C2×C3⋊D3—22no—
447C2×C3⋊D3—22no—
448C2×C3⋊D3—22no—
449C2×C3×D3—22no—
450C2×C3×D3—21no—
451C2×C3×D3—21no—
452C2×C3×D3—21no—
453C2×C3×D3—21no—
454C2×C3×D3—21no—
455C2×C3×D3—21no—
456C2×C3×D3—41no—
457C2×C3×D3—41no—
458C2×C3×D3—62no—
459C2×C3×D3—62no—
460C2×C3×D3—62no—
461C2×C3×D3—62no—
462C2×C3×D3—62no—
463C2×C3×D3—62no—
464C2×C3×D3—122no—
465C2×C3×D3—122no—
466C2×C3×D3—122no—
467C32×C4—22no—
468C32×C4—22no—
469C32×C4—22no—
470C32×C4—42no—
471C32×C4—61no—
472C32×C4—61no—
473C32×C4—61no—
474C32×C4—62no—
475C32×C4—62no—
476C32×C4#23512yes—
477C32×C4#23712yes—
478C32×C4C3×#4112yes—
479C3⋊Dic3—21no—
480C3⋊Dic3—21no—
481C3×Dic3—22no—
482C3×Dic3—21no—
483C3×Dic3—22no—
484C3×Dic3—21no—
485C3×Dic3—22no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—21no—
489C3×Dic3—22no—
490C3×Dic3—22no—
491C3×Dic3—21no—
492C3×Dic3—41no—
493C3×Dic3—41no—
494C3×Dic3—42no—
495C3×Dic3—42no—
496C3×Dic3—62no—
497C3×Dic3—62no—
498C3×Dic3—61no—
499C3×Dic3—61no—
500C3×Dic3—61no—
501C3×Dic3—61no—
502#127—91no—
503#125—91no—
504#123—92no—
505#123—92no—
506#121—31no—
507#121—92no—
508#121—91no—
509#121—92no—
510C4×D4—31no—
511C4×D4—91no—
512#117—91no—
513C33#54011yescharacteristic, complemented, Sylow
514C23×C3—22no—
515C23×C3—22no—
516C23×C3—22no—
517C23×C3—31no—
518C23×C3—31no—
519C23×C3—42no—
520C23×C3—61no—
521C23×C3—92no—
522C23×C3C2×D3212yes—
523C23×C3C22×C3×D312yes—
524C23×C3C22×C3×D312yes—
525C22×D3—32no—
526C22×D3—32no—
527C22×D3—62no—
528C22×D3C22×C3×D311yescharacteristic
529C3×D4—24no—
530C3×D4—22no—
531C3×D4—22no—
532C3×D4—22no—
533C3×D4—42no—
534C3×D4—42no—
535C3×D4—44no—
536C3×D4—122no—
537C3×D4—122no—
538C3×D4—124no—
539C3×D4—182no—
540C3×D4—362no—
541C3×D4—362no—
542C3×D4—362no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—31no—
547C2×C3×C4—31no—
548C2×C3×C4—31no—
549C2×C3×C4—32no—
550C2×C3×C4—32no—
551C2×C3×C4—32no—
552C2×C3×C4—32no—
553C2×C3×C4—31no—
554C2×C3×C4—31no—
555C2×C3×C4—31no—
556C2×C3×C4—41no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—62no—
561C2×C3×C4—62no—
562C2×C3×C4—62no—
563C2×C3×C4—62no—
564C2×C3×C4—91no—
565C2×C3×C4—91no—
566C2×C3×C4—122no—
567C2×C3×C4—122no—
568C2×C3×C4—122no—
569C2×C3×C4—124no—
570C2×C3×C4—362no—
571C2×C3×C4C2×D3211yescharacteristic
572C2×C3×C4C22×C3×D311yescharacteristic
573C2×C3×C4C22×C3×D311yescharacteristic
574#67—42no—
575#67—122no—
576#67—122no—
577#67—122no—
578#67—122no—
579#67—122no—
580#67—124no—
581#67—124no—
582C2×Dic3—31no—
583C2×Dic3—31no—
584C2×Dic3—31no—
585C2×Dic3—31no—
586C2×Dic3—42no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3C22×C3×D311yescharacteristic
590C2×Dic3C22×C3×D311yescharacteristic
591C2×Dic3C22×C3×D311yescharacteristic
592C2×Dic3C22×C3×D312yes—
593C2×Dic3C22×C3×D312yes—
594D12—62no—
595D12—62no—
596D12—122no—
597D12—122no—
598C4×D3—22no—
599C4×D3—122no—
600C4×D3—122no—
601C2×C32—21no—
602C2×C32—21no—
603C2×C32—21no—
604C2×C32—21no—
605C2×C32—21no—
606C2×C32—21no—
607C2×C32—21no—
608C2×C32—21no—
609C2×C32—21no—
610C2×C32—41no—
611C2×C32—41no—
612C2×C32—41no—
613C2×C32—42no—
614C2×C32—44no—
615C2×C32—42no—
616C2×C32—42no—
617C2×C32—82no—
618C2×C32—82no—
619C2×C32—84no—
620C2×C32—121no—
621C2×C32C2×#23511yescharacteristic
622C2×C32C2×#23711yescharacteristic
623C2×C32#100411yescharacteristic
624C2×C32#100411yescharacteristic
625C2×C32#100911yescharacteristic
626C2×C32#100911yescharacteristic
627C2×C32C2×C3×#4111yescharacteristic
628C2×C32C3×H(5,𝔽2)11yescharacteristic
629C2×C32C3×H(5,𝔽2)11yescharacteristic
630C3⋊D3—42no—
631C3×D3—42no—
632C3×D3—41no—
633C3×D3—41no—
634C3×D3—122no—
635C3×D3—122no—
636C3×D3—242no—
637C2×D4—32no—
638C2×D4—92no—
639C2×D4—92no—
640C2×D4—92no—
641C2×D4—91no—
642C2×D4C3×D3211yescharacteristic
643C22×C4—32no—
644C22×C4—31no—
645C22×C4—92no—
646C4⋊C4—31no—
647C4⋊C4—31no—
648C4⋊C4—91no—
649C4⋊C4—91no—
650C4⋊C4—92no—
651C4⋊C4—92no—
652C22⋊C4—32no—
653C22⋊C4—32no—
654C22⋊C4—92no—
655C22⋊C4—92no—
656C22⋊C4—91no—
657C22⋊C4—91no—
658C42—31no—
659C42—91no—
660C22×C3—24no—
661C22×C3—22no—
662C22×C3—22no—
663C22×C3—22no—
664C22×C3—22no—
665C22×C3—22no—
666C22×C3—22no—
667C22×C3—22no—
668C22×C3—22no—
669C22×C3—22no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—42no—
674C22×C3—42no—
675C22×C3—42no—
676C22×C3—42no—
677C22×C3—42no—
678C22×C3—42no—
679C22×C3—42no—
680C22×C3—42no—
681C22×C3—44no—
682C22×C3—41no—
683C22×C3—62no—
684C22×C3—61no—
685C22×C3—61no—
686C22×C3—61no—
687C22×C3—61no—
688C22×C3—61no—
689C22×C3—61no—
690C22×C3—82no—
691C22×C3—82no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3—182no—
695C22×C3—182no—
696C22×C3—182no—
697C22×C3C22×D3211yescharacteristic
698C22×C3C23×C3×D311yescharacteristic
699C22×C3C23×C3×D311yescharacteristic
700C2×D3—21no—
701C2×D3—21no—
702C2×D3—21no—
703C2×D3—62no—
704C2×D3—62no—
705C2×D3—62no—
706C2×D3—62no—
707C2×D3—62no—
708C2×D3—62no—
709C2×D3—122no—
710C2×D3—122no—
711C2×D3—122no—
712C3×C4—22no—
713C3×C4—22no—
714C3×C4—22no—
715C3×C4—42no—
716C3×C4—62no—
717C3×C4—61no—
718C3×C4—62no—
719C3×C4—61no—
720C3×C4—62no—
721C3×C4—61no—
722C3×C4—61no—
723C3×C4—61no—
724C3×C4—62no—
725C3×C4—62no—
726C3×C4—61no—
727C3×C4—121no—
728C3×C4—122no—
729C3×C4—122no—
730C3×C4—121no—
731C3×C4—181no—
732C3×C4—181no—
733C3×C4#380412yes—
734C3×C4C3×#23512yes—
735C3×C4C3×#23712yes—
736Dic3—21no—
737Dic3—22no—
738Dic3—21no—
739Dic3—22no—
740Dic3—21no—
741Dic3—62no—
742Dic3—62no—
743Dic3—61no—
744Dic3—61no—
745Dic3—61no—
746Dic3—61no—
747C32—21no—
748C32—21no—
749C32—21no—
750C32—41no—
751C32#556211yescharacteristic, complemented
752C32#561911yescharacteristic, complemented
753C32C3×#54011yescharacteristic, complemented
754C23—31no—
755C23—92no—
756C23C2×C3×D3212yes—
757D4—22no—
758D4—122no—
759D4—182no—
760D4—362no—
761D4—362no—
762D4—362no—
763C2×C4—31no—
764C2×C4—31no—
765C2×C4—31no—
766C2×C4—32no—
767C2×C4—32no—
768C2×C4—62no—
769C2×C4—91no—
770C2×C4—91no—
771C2×C4—122no—
772C2×C4—362no—
773C2×C4C2×C3×D3211yescharacteristic
774C2×C3—21no—
775C2×C3—21no—
776C2×C3—21no—
777C2×C3—21no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—44no—
784C2×C3—42no—
785C2×C3—42no—
786C2×C3—42no—
787C2×C3—41no—
788C2×C3—41no—
789C2×C3—41no—
790C2×C3—82no—
791C2×C3—82no—
792C2×C3—84no—
793C2×C3—122no—
794C2×C3—121no—
795C2×C3—121no—
796C2×C3—362no—
797C2×C3#6431411yescharacteristic
798C2×C3#6431411yescharacteristic
799C2×C3C2×#380411yescharacteristic
800C2×C3C2×C3×#23511yescharacteristic
801C2×C3C2×C3×#23711yescharacteristic
802C2×C3C3×#100411yescharacteristic
803C2×C3C3×#100411yescharacteristic
804C2×C3C3×#100911yescharacteristic
805C2×C3C3×#100911yescharacteristic
806D3—41no—
807D3—122no—
808D3—122no—
809D3—242no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—61no—
814C22—61no—
815C22—61no—
816C22—182no—
817C22—182no—
818C22—182no—
819C22C22×C3×D3211yescharacteristic
820C4—61no—
821C4—61no—
822C4—62no—
823C4—61no—
824C4—62no—
825C4—181no—
826C4—181no—
827C4C3×#380412yes—
828C3—21no—
829C3—21no—
830C3—21no—
831C3—41no—
832C3#1059512511yescharacteristic, direct product factor
833C3C3×#556211yescharacteristic, complemented
834C3C3×#561911yescharacteristic, complemented
835C2—42no—
836C2—121no—
837C2—362no—
838C2C3×#6431411yescharacteristic
839C2C3×#6431411yescharacteristic
840C2C2×C3×#380411yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C3×#540
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C3×#64149C2semidirect
2. C32×#938C2semidirect
3. C32×D4×Dic3C2semidirect
4. C3×#63978C2semidirect
5. C3×#63975C2semidirect
6. C3×#63966C2semidirect
7. C3×#63958C2semidirect
8. C3×#63909C2semidirect
9. C3×#63894C2semidirect
10. C3×#63872C2semidirect
11. C3×#63855C2semidirect
14. #10595125C3direct (N × H)
40. #64149C2×C3semidirect
47. C3×#938D3semidirect
48. C3×#938C2×C3semidirect
50. C3×D4×Dic3D3semidirect
51. C3×D4×Dic3C2×C3semidirect
66. #63978C2×C3semidirect
67. #63975C2×C3semidirect
68. #63966C2×C3semidirect
69. #63958C2×C3semidirect
70. #63909C2×C3semidirect
71. #63894C2×C3semidirect
72. #63872C2×C3semidirect
73. #63855C2×C3semidirect
220. #938C3×D3semidirect
221. D4×Dic3C3×D3semidirect
513. C33#540semidirect
751. C32#5562semidirect
752. C32#5619semidirect
753. C32C3×#540semidirect
832. C3#10595125direct (N × H)
833. C3C3×#5562semidirect
834. C3C3×#5619semidirect

Maximal subgroups

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

subgroupindex
C3×#641492
C32×#9382
C32×D4×Dic32
C3×#639782
C3×#639752
C3×#639662
C3×#639582
C3×#639092
C3×#638942
C3×#638722
C3×#638552
C3×#56193
C3×#55623
#105951253