Finite Group Databasebeta

← C3×#10595217 #13174763

Subgroups — C3×#10595217 #13174763

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×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C32×#940C211yesmaximal, characteristic, complemented
3C32×#938C211yesmaximal, characteristic, complemented
4C3×#63980C212yesmaximal, complemented
5C3×#63970C212yesmaximal, complemented
6C3×#63969C212yesmaximal, complemented
7C3×#63962C212yesmaximal, complemented
8C3×#63908C211yesmaximal, characteristic, complemented
9C3×#63898C211yesmaximal, characteristic, complemented
10C3×#63869C211yesmaximal, characteristic, complemented
11C3×#63855C211yesmaximal, characteristic, complemented
12C3×#5719—31nomaximal
13C3×#5619—31nomaximal
14#10595217C311yesmaximal, characteristic, direct product factor
15C2×C33×D4C2211yescharacteristic
16C22×C3×C3⋊Dic3C2212yes—
17C2×C32×#67C2212yes—
18C2×C32×#67C2212yes—
19C2×C32×#67C2212yes—
20C2×C32×D12C2211yescharacteristic
21C2×C32×C4×D3C2211yescharacteristic
22C2×C3×#625C2212yes—
23C2×C3×D3×Dic3C2212yes—
24C3×#3757C2212yes—
25C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C3×C4×C3⋊Dic3C2211yescharacteristic
27C32×#217C2212yes—
28C32×C4⋊Dic3C2211yescharacteristic
29C32×C4×Dic3C2211yescharacteristic
30C3×#3724C2212yes—
31C3×Dic3⋊Dic3C2211yescharacteristic
32C3×Dic3⋊Dic3C2212yes—
33C3×Dic3⋊Dic3C2211yescharacteristic
34C3×(C2×D3)⋊Dic3C2212yes—
35C3×(C2×D3)⋊Dic3C2212yes—
36C3×(C2×D3)⋊Dic3C2211yescharacteristic
37C3×(C2×D3)⋊Dic3C2211yescharacteristic
38C32×#127—31no—
39C32×#121—31no—
40D4×C3⋊Dic3C2×C311yescharacteristic, complemented
41C3×#940—21no—
42C3×#940D311yescharacteristic, complemented
43C3×#940C2×C311yescharacteristic, complemented
44C3×#939—32no—
45C3×#939—32no—
46C3×#939—32no—
47C3×#938—21no—
48C3×#938—32no—
49C3×#938—31no—
50C3×#938D311yescharacteristic, complemented
51C3×#938C2×C311yescharacteristic, complemented
52C3×#935—32no—
53C3×#935—32no—
54C3×D4×Dic3—31no—
55C3×D4×Dic3—31no—
56C3×D4×Dic3—31no—
57C3×D4×Dic3—61no—
58C3×#930—31no—
59C3×#926—31no—
60C3×#893—31no—
61C3×#890—31no—
62C3×#886—32no—
63C3×#883—32no—
64C3×#872—31no—
65C3×#870—31no—
66#63980C2×C312yescomplemented
67#63970C2×C312yescomplemented
68#63969C2×C312yescomplemented
69#63962C2×C312yescomplemented
70#63908C2×C311yescharacteristic, complemented
71#63898C2×C311yescharacteristic, complemented
72#63869C2×C311yescharacteristic, complemented
73#63855C2×C311yescharacteristic, complemented
74C23×C33C2312yes—
75C22×C32×D3C2312yes—
76C22×C32×D3C2311yescharacteristic
77C33×D4—22no—
78C2×C33×C4C2311yescharacteristic
79C2×C3×C3⋊Dic3—42no—
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2312yes—
83C32×#67—42no—
84C32×#67—42no—
85C32×#67—42no—
86C2×C32×Dic3C2311yescharacteristic
87C2×C32×Dic3C2312yes—
88C2×C32×Dic3C2311yescharacteristic
89C2×C32×Dic3C2311yescharacteristic
90C32×D12—22no—
91C32×C4×D3—22no—
92C3×#625—42no—
93C3×D3×Dic3—42no—
94C3×#540—91no—
95#5719—31no—
96#5619—31no—
97C2×C32×D4—21no—
98C2×C32×D4—21no—
99C2×C32×D4—21no—
100C2×C32×D4—32no—
101C2×C32×D4—32no—
102C2×C32×D4—32no—
103C2×C32×D4—31no—
104C2×C32×D4—41no—
105C2×C32×D4C2×D311yescharacteristic
106C2×C32×D4C2×D311yescharacteristic
107C2×C32×D4C22×C311yescharacteristic
108C22×C32×C4—31no—
109C22×C3⋊Dic3C22×C312yes—
110C2×C3×#67—22no—
111C2×C3×#67—22no—
112C2×C3×#67—22no—
113C2×C3×#67—32no—
114C2×C3×#67—32no—
115C2×C3×#67C2×D312yes—
116C2×C3×#67C2×D312yes—
117C2×C3×#67C2×D312yes—
118C2×C3×#67C22×C312yes—
119C2×C3×#67C22×C312yes—
120C2×C3×#67C22×C312yes—
121C22×C3×Dic3—32no—
122C22×C3×Dic3—32no—
123C22×C3×Dic3—32no—
124C22×C3×Dic3—62no—
125C2×C3×D12—21no—
126C2×C3×D12C2×D311yescharacteristic
127C2×C3×D12C22×C311yescharacteristic
128C2×C3×C4×D3—21no—
129C2×C3×C4×D3—32no—
130C2×C3×C4×D3C2×D311yescharacteristic
131C2×C3×C4×D3C22×C311yescharacteristic
132C2×#625C22×C312yes—
133C2×D3×Dic3C22×C312yes—
134C32×C4⋊C4—31no—
135C32×C22⋊C4—32no—
136C32×C42—31no—
137#3757C22×C312yes—
138C4⋊(C3⋊Dic3)C22×C311yescharacteristic
139C4×C3⋊Dic3C22×C311yescharacteristic
140C3×#217—22no—
141C3×#217—32no—
142C3×#217—32no—
143C3×#217—31no—
144C3×#217—31no—
145C3×#217—32no—
146C3×#217—32no—
147C3×#217—62no—
148C3×#217C2×D312yes—
149C3×#217C22×C312yes—
150C3×(C2×D3)⋊C4—32no—
151C3×(C2×D3)⋊C4—32no—
152C3×(C2×D3)⋊C4—31no—
153C3×(C2×D3)⋊C4—31no—
154C3×C4⋊Dic3—21no—
155C3×C4⋊Dic3—31no—
156C3×C4⋊Dic3—31no—
157C3×C4⋊Dic3—31no—
158C3×C4⋊Dic3—31no—
159C3×C4⋊Dic3—32no—
160C3×C4⋊Dic3—61no—
161C3×C4⋊Dic3C2×D311yescharacteristic
162C3×C4⋊Dic3C22×C311yescharacteristic
163C3×Dic3⋊C4—32no—
164C3×Dic3⋊C4—31no—
165C3×Dic3⋊C4—31no—
166C3×Dic3⋊C4—32no—
167C3×Dic3⋊C4—32no—
168C3×C4×Dic3—21no—
169C3×C4×Dic3—31no—
170C3×C4×Dic3—31no—
171C3×C4×Dic3—61no—
172C3×C4×Dic3C2×D311yescharacteristic
173C3×C4×Dic3C22×C311yescharacteristic
174#3724C22×C312yes—
175Dic3⋊Dic3C22×C311yescharacteristic
176Dic3⋊Dic3C22×C311yescharacteristic
177Dic3⋊Dic3C22×C312yes—
178(C2×D3)⋊Dic3C22×C311yescharacteristic
179(C2×D3)⋊Dic3C22×C311yescharacteristic
180(C2×D3)⋊Dic3C22×C312yes—
181(C2×D3)⋊Dic3C22×C312yes—
182C22×C33—22no—
183C22×C33—22no—
184C22×C33—22no—
185C22×C33C2411yescharacteristic
186C2×C32×D3—21no—
187C2×C32×D3—22no—
188C2×C32×D3—21no—
189C2×C32×D3—22no—
190C2×C32×D3—21no—
191C2×C32×D3—22no—
192C33×C4#4112yes—
193C3×C3⋊Dic3—21no—
194C3×C3⋊Dic3—21no—
195C3×C3⋊Dic3—22no—
196C32×Dic3—21no—
197C32×Dic3—21no—
198C32×Dic3—21no—
199C32×Dic3—22no—
200C3×#127—31no—
201C3×#127—31no—
202C3×#127—61no—
203C3×#125—91no—
204C3×#123—92no—
205C3×#123—92no—
206C3×#121—31no—
207C3×#121—31no—
208C3×#121—61no—
209C3×#121—91no—
210C3×#121—92no—
211C3×#121—92no—
212C3×C4×D4—91no—
213C3×C4×D4—91no—
214C3×#117—91no—
215#940C3×D311yescharacteristic, complemented
216#939—32no—
217#939—32no—
218#939—32no—
219#938—32no—
220#938—31no—
221#938C3×D311yescharacteristic, complemented
222#935—32no—
223#935—32no—
224D4×Dic3—31no—
225D4×Dic3—31no—
226D4×Dic3—31no—
227D4×Dic3—61no—
228#930—31no—
229#926—31no—
230#893—31no—
231#890—31no—
232#886—32no—
233#883—32no—
234#872—31no—
235#870—31no—
236C23×C32—22no—
237C23×C32—22no—
238C23×C32—22no—
239C23×C32—32no—
240C23×C32—31no—
241C23×C32—42no—
242C23×C32C22×D312yes—
243C23×C32C22×D312yes—
244C23×C32C23×C312yes—
245C22×C3×D3—21no—
246C22×C3×D3—22no—
247C22×C3×D3C22×D312yes—
248C22×C3×D3C22×D311yescharacteristic
249C22×C3×D3C23×C312yes—
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—62no—
259C32×D4—122no—
260C32×D4—122no—
261C32×D4—122no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—31no—
266C2×C32×C4—31no—
267C2×C32×C4—32no—
268C2×C32×C4—31no—
269C2×C32×C4—41no—
270C2×C32×C4—62no—
271C2×C32×C4C22×D311yescharacteristic
272C2×C32×C4C22×D311yescharacteristic
273C2×C32×C4C23×C311yescharacteristic
274C2×C3⋊Dic3—42no—
275C2×C3⋊Dic3C23×C311yescharacteristic
276C2×C3⋊Dic3C23×C312yes—
277C2×C3⋊Dic3C23×C311yescharacteristic
278C3×#67—42no—
279C3×#67—42no—
280C3×#67—42no—
281C3×#67—42no—
282C3×#67—42no—
283C3×#67—42no—
284C3×#67—44no—
285C3×#67—44no—
286C3×#67—44no—
287C3×#67—122no—
288C3×#67—122no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
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—32no—
298C2×C3×Dic3—32no—
299C2×C3×Dic3—61no—
300C2×C3×Dic3—61no—
301C2×C3×Dic3—62no—
302C2×C3×Dic3—122no—
303C2×C3×Dic3—122no—
304C2×C3×Dic3—122no—
305C2×C3×Dic3—124no—
306C2×C3×Dic3C22×D311yescharacteristic
307C2×C3×Dic3C22×D311yescharacteristic
308C2×C3×Dic3C22×D312yes—
309C2×C3×Dic3C22×D311yescharacteristic
310C2×C3×Dic3C23×C311yescharacteristic
311C2×C3×Dic3C23×C311yescharacteristic
312C2×C3×Dic3C23×C311yescharacteristic
313C2×C3×Dic3C23×C312yes—
314C3×D12—22no—
315C3×D12—22no—
316C3×D12—42no—
317C3×C4×D3—22no—
318C3×C4×D3—22no—
319C3×C4×D3—42no—
320C3×C4×D3—122no—
321#625—42no—
322D3×Dic3—42no—
323#540—91noSylow
324C2×C33—42no—
325C2×C33C2×#4111yescharacteristic
326C2×C33H(5,𝔽2)11yescharacteristic
327C2×C33H(5,𝔽2)11yescharacteristic
328C32×D3—41no—
329C32×D3—42no—
330C2×C3×D4—21no—
331C2×C3×D4—21no—
332C2×C3×D4—21no—
333C2×C3×D4—32no—
334C2×C3×D4—32no—
335C2×C3×D4—32no—
336C2×C3×D4—32no—
337C2×C3×D4—32no—
338C2×C3×D4—32no—
339C2×C3×D4—31no—
340C2×C3×D4—31no—
341C2×C3×D4—41no—
342C2×C3×D4—61no—
343C2×C3×D4—62no—
344C2×C3×D4—62no—
345C2×C3×D4—62no—
346C2×C3×D4—92no—
347C2×C3×D4D3211yescharacteristic
348C2×C3×D4C2×C3×D311yescharacteristic
349C2×C3×D4C2×C3×D311yescharacteristic
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—61no—
353C22×C3×C4—92no—
354C22×C3×C4—92no—
355C2×#67—32no—
356C2×#67—32no—
357C2×#67C2×C3×D312yes—
358C2×#67C2×C3×D312yes—
359C2×#67C2×C3×D312yes—
360C22×Dic3—32no—
361C22×Dic3—32no—
362C22×Dic3—32no—
363C22×Dic3—62no—
364C2×D12C2×C3×D311yescharacteristic
365C2×C4×D3—32no—
366C2×C4×D3C2×C3×D311yescharacteristic
367C3×C4⋊C4—31no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4—92no—
371C3×C4⋊C4—91no—
372C3×C4⋊C4—91no—
373C3×C4⋊C4—92no—
374C3×C4⋊C4—91no—
375C3×C22⋊C4—32no—
376C3×C22⋊C4—32no—
377C3×C22⋊C4—62no—
378C3×C22⋊C4—91no—
379C3×C22⋊C4—91no—
380C3×C22⋊C4—92no—
381C3×C22⋊C4—92no—
382C3×C22⋊C4—92no—
383C3×C42—31no—
384C3×C42—31no—
385C3×C42—61no—
386C3×C42—91no—
387#217—32no—
388#217—32no—
389#217—31no—
390#217—31no—
391#217—32no—
392#217—32no—
393#217—62no—
394#217C2×C3×D312yes—
395(C2×D3)⋊C4—31no—
396(C2×D3)⋊C4—31no—
397(C2×D3)⋊C4—32no—
398(C2×D3)⋊C4—32no—
399C4⋊Dic3—31no—
400C4⋊Dic3—31no—
401C4⋊Dic3—31no—
402C4⋊Dic3—31no—
403C4⋊Dic3—32no—
404C4⋊Dic3—61no—
405C4⋊Dic3C2×C3×D311yescharacteristic
406Dic3⋊C4—32no—
407Dic3⋊C4—32no—
408Dic3⋊C4—31no—
409Dic3⋊C4—31no—
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—62no—
441C22×C32—62no—
442C22×C32—61no—
443C22×C32—62no—
444C22×C32—82no—
445C22×C32—82no—
446C22×C32C23×D311yescharacteristic
447C22×C32C23×D311yescharacteristic
448C22×C32C24×C311yescharacteristic
449C2×C3×D3—22no—
450C2×C3×D3—21no—
451C2×C3×D3—22no—
452C2×C3×D3—22no—
453C2×C3×D3—21no—
454C2×C3×D3—22no—
455C2×C3×D3—21no—
456C2×C3×D3—21no—
457C2×C3×D3—22no—
458C2×C3×D3—22no—
459C2×C3×D3—21no—
460C2×C3×D3—22no—
461C2×C3×D3—21no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—42no—
465C2×C3×D3—42no—
466C2×C3×D3—42no—
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#23712yes—
476C32×C4#23712yes—
477C32×C4C3×#4112yes—
478C3⋊Dic3—21no—
479C3⋊Dic3—21no—
480C3⋊Dic3—22no—
481C3×Dic3—22no—
482C3×Dic3—22no—
483C3×Dic3—21no—
484C3×Dic3—22no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—22no—
489C3×Dic3—21no—
490C3×Dic3—21no—
491C3×Dic3—41no—
492C3×Dic3—42no—
493C3×Dic3—62no—
494C3×Dic3—61no—
495C3×Dic3—61no—
496C3×Dic3—61no—
497C3×Dic3—62no—
498C3×Dic3—61no—
499C3×Dic3—62no—
500C3×Dic3—121no—
501C3×Dic3—122no—
502#127—31no—
503#125—91no—
504#123—92no—
505#123—92no—
506#121—31no—
507#121—91no—
508#121—92no—
509#121—92no—
510C4×D4—91no—
511C4×D4—91no—
512#117—91no—
513C33#54011yescharacteristic, complemented, Sylow
514C23×C3—22no—
515C23×C3—22no—
516C23×C3—22no—
517C23×C3—31no—
518C23×C3—32no—
519C23×C3—32no—
520C23×C3—31no—
521C23×C3—42no—
522C23×C3—61no—
523C23×C3—62no—
524C23×C3C2×D3212yes—
525C23×C3C22×C3×D312yes—
526C23×C3C22×C3×D312yes—
527C22×D3C22×C3×D312yes—
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—62no—
537C3×D4—62no—
538C3×D4—122no—
539C3×D4—122no—
540C3×D4—122no—
541C3×D4—122no—
542C3×D4—122no—
543C3×D4—122no—
544C3×D4—122no—
545C3×D4—124no—
546C3×D4—124no—
547C3×D4—124no—
548C3×D4—362no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—31no—
553C2×C3×C4—31no—
554C2×C3×C4—31no—
555C2×C3×C4—32no—
556C2×C3×C4—31no—
557C2×C3×C4—31no—
558C2×C3×C4—32no—
559C2×C3×C4—31no—
560C2×C3×C4—41no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—62no—
565C2×C3×C4—62no—
566C2×C3×C4—62no—
567C2×C3×C4—91no—
568C2×C3×C4—91no—
569C2×C3×C4—92no—
570C2×C3×C4—122no—
571C2×C3×C4—362no—
572C2×C3×C4—362no—
573C2×C3×C4C2×D3211yescharacteristic
574C2×C3×C4C22×C3×D311yescharacteristic
575C2×C3×C4C22×C3×D311yescharacteristic
576#67—42no—
577#67—42no—
578#67—42no—
579#67—122no—
580#67—122no—
581C2×Dic3—31no—
582C2×Dic3—31no—
583C2×Dic3—31no—
584C2×Dic3—31no—
585C2×Dic3—32no—
586C2×Dic3—32no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—62no—
590C2×Dic3—122no—
591C2×Dic3—122no—
592C2×Dic3—122no—
593C2×Dic3—124no—
594C2×Dic3C22×C3×D311yescharacteristic
595C2×Dic3C22×C3×D311yescharacteristic
596C2×Dic3C22×C3×D312yes—
597C2×Dic3C22×C3×D311yescharacteristic
598D12—22no—
599C4×D3—22no—
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×C32—122no—
622C2×C32C2×#23711yescharacteristic
623C2×C32C2×#23711yescharacteristic
624C2×C32#100411yescharacteristic
625C2×C32#100411yescharacteristic
626C2×C32#100411yescharacteristic
627C2×C32#100911yescharacteristic
628C2×C32C2×C3×#4111yescharacteristic
629C2×C32C3×H(5,𝔽2)11yescharacteristic
630C2×C32C3×H(5,𝔽2)11yescharacteristic
631C3×D3—42no—
632C3×D3—42no—
633C3×D3—41no—
634C3×D3—42no—
635C3×D3—41no—
636C3×D3—82no—
637C2×D4—32no—
638C2×D4—32no—
639C2×D4—32no—
640C2×D4—31no—
641C2×D4—92no—
642C2×D4C3×D3211yescharacteristic
643C22×C4—31no—
644C22×C4—92no—
645C22×C4—92no—
646C4⋊C4—31no—
647C4⋊C4—91no—
648C4⋊C4—91no—
649C4⋊C4—92no—
650C4⋊C4—92no—
651C4⋊C4—91no—
652C22⋊C4—32no—
653C22⋊C4—91no—
654C22⋊C4—91no—
655C22⋊C4—92no—
656C22⋊C4—92no—
657C22⋊C4—92no—
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—62no—
685C22×C3—61no—
686C22×C3—62no—
687C22×C3—61no—
688C22×C3—61no—
689C22×C3—62no—
690C22×C3—61no—
691C22×C3—62no—
692C22×C3—62no—
693C22×C3—61no—
694C22×C3—61no—
695C22×C3—62no—
696C22×C3—82no—
697C22×C3—82no—
698C22×C3—121no—
699C22×C3—121no—
700C22×C3—122no—
701C22×C3—122no—
702C22×C3—122no—
703C22×C3C22×D3211yescharacteristic
704C22×C3C23×C3×D311yescharacteristic
705C22×C3C23×C3×D311yescharacteristic
706C2×D3—21no—
707C2×D3—22no—
708C2×D3—22no—
709C2×D3—21no—
710C2×D3—22no—
711C2×D3—21no—
712C3×C4—22no—
713C3×C4—22no—
714C3×C4—22no—
715C3×C4—42no—
716C3×C4—62no—
717C3×C4—62no—
718C3×C4—62no—
719C3×C4—61no—
720C3×C4—61no—
721C3×C4—61no—
722C3×C4—61no—
723C3×C4—62no—
724C3×C4—61no—
725C3×C4—61no—
726C3×C4—121no—
727C3×C4—122no—
728C3×C4—181no—
729C3×C4—181no—
730C3×C4—182no—
731C3×C4#380512yes—
732C3×C4C3×#23712yes—
733C3×C4C3×#23712yes—
734Dic3—21no—
735Dic3—22no—
736Dic3—21no—
737Dic3—21no—
738Dic3—62no—
739Dic3—61no—
740Dic3—61no—
741Dic3—61no—
742Dic3—62no—
743Dic3—61no—
744Dic3—62no—
745Dic3—122no—
746Dic3—121no—
747C32—21no—
748C32—21no—
749C32—21no—
750C32—41no—
751C32#561911yescharacteristic, complemented
752C32#571911yescharacteristic, complemented
753C32C3×#54011yescharacteristic, complemented
754C23—31no—
755C23—32no—
756C23C2×C3×D3212yes—
757D4—22no—
758D4—62no—
759D4—122no—
760D4—122no—
761D4—122no—
762D4—362no—
763C2×C4—31no—
764C2×C4—31no—
765C2×C4—31no—
766C2×C4—32no—
767C2×C4—62no—
768C2×C4—91no—
769C2×C4—91no—
770C2×C4—92no—
771C2×C4—362no—
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—122no—
795C2×C3—121no—
796C2×C3—122no—
797C2×C3—121no—
798C2×C3—242no—
799C2×C3#6431311yescharacteristic
800C2×C3#6431411yescharacteristic
801C2×C3C2×#380511yescharacteristic
802C2×C3C2×C3×#23711yescharacteristic
803C2×C3C2×C3×#23711yescharacteristic
804C2×C3C3×#100411yescharacteristic
805C2×C3C3×#100411yescharacteristic
806C2×C3C3×#100411yescharacteristic
807C2×C3C3×#100911yescharacteristic
808D3—41no—
809D3—42no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—61no—
814C22—62no—
815C22—62no—
816C22—61no—
817C22—62no—
818C22—61no—
819C22C22×C3×D3211yescharacteristic
820C4—61no—
821C4—62no—
822C4—61no—
823C4—61no—
824C4—181no—
825C4—181no—
826C4—182no—
827C4C3×#380512yes—
828C3—21no—
829C3—21no—
830C3—21no—
831C3—41no—
832C3#1059521711yescharacteristic, direct product factor
833C3C3×#561911yescharacteristic, complemented
834C3C3×#571911yescharacteristic, complemented
835C2—42no—
836C2—121no—
837C2—122no—
838C2C3×#6431311yescharacteristic
839C2C3×#6431411yescharacteristic
840C2C2×C3×#380511yescharacteristic
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×D4×C3⋊Dic3C2semidirect
2. C32×#940C2semidirect
3. C32×#938C2semidirect
4. C3×#63980C2semidirect
5. C3×#63970C2semidirect
6. C3×#63969C2semidirect
7. C3×#63962C2semidirect
8. C3×#63908C2semidirect
9. C3×#63898C2semidirect
10. C3×#63869C2semidirect
11. C3×#63855C2semidirect
14. #10595217C3direct (N × H)
40. D4×C3⋊Dic3C2×C3semidirect
42. C3×#940D3semidirect
43. C3×#940C2×C3semidirect
50. C3×#938D3semidirect
51. C3×#938C2×C3semidirect
66. #63980C2×C3semidirect
67. #63970C2×C3semidirect
68. #63969C2×C3semidirect
69. #63962C2×C3semidirect
70. #63908C2×C3semidirect
71. #63898C2×C3semidirect
72. #63869C2×C3semidirect
73. #63855C2×C3semidirect
215. #940C3×D3semidirect
221. #938C3×D3semidirect
513. C33#540semidirect
751. C32#5619semidirect
752. C32#5719semidirect
753. C32C3×#540semidirect
832. C3#10595217direct (N × H)
833. C3C3×#5619semidirect
834. C3C3×#5719semidirect

Maximal subgroups

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

subgroupindex
C3×D4×C3⋊Dic32
C32×#9402
C32×#9382
C3×#639802
C3×#639702
C3×#639692
C3×#639622
C3×#639082
C3×#638982
C3×#638692
C3×#638552
C3×#57193
C3×#56193
#105952173