Finite Group Databasebeta

← C3×#10594946 #13174603

Subgroups — C3×#10594946 #13174603

Order 1728.

1270 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64139C211yesmaximal, characteristic, complemented
2C32×C4×#67C211yesmaximal, characteristic, complemented
3C32×#926C211yesmaximal, characteristic, complemented
4C3×#63975C212yesmaximal, complemented
5C3×#63971C212yesmaximal, complemented
6C3×#63909C211yesmaximal, characteristic, complemented
7C3×#63894C211yesmaximal, characteristic, complemented
8C3×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
9C3×#63880C212yesmaximal, complemented
10C3×#63869C211yesmaximal, characteristic, complemented
11C3×#63868C212yesmaximal, complemented
12C3×#5565—31nomaximal
13C3×#5530—31nomaximal
14#10594946C311yesmaximal, characteristic, direct product factor
15C22×C33×C4C2211yescharacteristic
16C2×C3×#638C2212yes—
17C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
18C2×C32×#67C2211yescharacteristic
19C2×C32×C4×D3C2211yescharacteristic
20C2×C3×#626C2212yes—
21C2×C3×#624C2212yes—
22C2×C3×D3×Dic3C2212yes—
23C3×#3752C2212yes—
24C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C32×#217C2212yes—
26C32×#217C2211yescharacteristic
27C32×(C2×D3)⋊C4C2211yescharacteristic
28C32×C4⋊Dic3C2211yescharacteristic
29C32×C4⋊Dic3C2211yescharacteristic
30C32×Dic3⋊C4C2211yescharacteristic
31C32×C4×Dic3C2212yes—
32C32×C4×Dic3C2211yescharacteristic
33C3×#3724C2212yes—
34C3×Dic3⋊Dic3C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×#3722C2212yes—
37C3×#3722C2212yes—
38C32×C4×D4—31no—
39C32×#117—31no—
40#64139C2×C311yescharacteristic, complemented
41C3×#939—32no—
42C3×#930—31no—
43C3×#930—31no—
44C3×#930—31no—
45C3×#930—61no—
46C3×C4×#67—21no—
47C3×C4×#67D311yescharacteristic, complemented
48C3×C4×#67C2×C311yescharacteristic, complemented
49C3×#926—21no—
50C3×#926D311yescharacteristic, complemented
51C3×#926C2×C311yescharacteristic, complemented
52C2×C3×C4⋊Dic3—31no—
53C3×#898—32no—
54C3×#895—31no—
55C3×#893—31no—
56C3×D3×C4⋊C4—31no—
57C3×#890—31no—
58C3×#884—32no—
59C3×#883—32no—
60C3×#883—32no—
61C3×#67⋊C4—32no—
62C3×#876—32no—
63C3×C4×D12—32no—
64C3×C4×D12—31no—
65C3×#870—31no—
66#63975C2×C312yescomplemented
67#63971C2×C312yescomplemented
68#63909C2×C311yescharacteristic, complemented
69#63894C2×C311yescharacteristic, complemented
70D3×C4⋊Dic3C2×C311yescharacteristic, complemented
71#63880C2×C312yescomplemented
72#63869C2×C311yescharacteristic, complemented
73#63868C2×C312yescomplemented
74C23×C33C2311yescharacteristic
75C22×C3×C3⋊D3C2312yes—
76C22×C32×D3C2311yescharacteristic
77C2×C33×C4—22no—
78C2×C33×C4C2311yescharacteristic
79C2×C33×C4C2311yescharacteristic
80C3×#638—42no—
81C2×C3×C3⋊Dic3C2312yes—
82C3×C4⋊(C3⋊D3)—22no—
83C32×#67—22no—
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2312yes—
87C2×C32×Dic3C2311yescharacteristic
88C2×C32×Dic3C2311yescharacteristic
89C32×C4×D3—22no—
90C3×#626—24no—
91C3×#624—42no—
92C3×D3×Dic3—42no—
93C3×#553—91no—
94#5565—31no—
95#5530—31no—
96C2×C32×D4—31no—
97C22×C32×C4—21no—
98C22×C32×C4—21no—
99C22×C32×C4—21no—
100C22×C32×C4—31no—
101C22×C32×C4—41no—
102C22×C32×C4C2×D311yescharacteristic
103C22×C32×C4C2×D311yescharacteristic
104C22×C32×C4C22×C311yescharacteristic
105C2×#638C22×C312yes—
106C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
107C2×C3×#67—21no—
108C2×C3×#67—32no—
109C2×C3×#67—32no—
110C2×C3×#67—32no—
111C2×C3×#67—62no—
112C2×C3×#67C2×D311yescharacteristic
113C2×C3×#67C22×C311yescharacteristic
114C22×C3×Dic3—32no—
115C2×C3×D12—32no—
116C2×C3×D12—31no—
117C2×C3×D12—31no—
118C2×C3×D12—61no—
119C2×C3×C4×D3—21no—
120C2×C3×C4×D3—32no—
121C2×C3×C4×D3—32no—
122C2×C3×C4×D3—32no—
123C2×C3×C4×D3C2×D311yescharacteristic
124C2×C3×C4×D3C22×C311yescharacteristic
125C2×#626C22×C312yes—
126C2×#624C22×C312yes—
127C2×D3×Dic3C22×C312yes—
128C32×C4⋊C4—31no—
129C32×C4⋊C4—31no—
130C32×C4⋊C4—31no—
131C32×C22⋊C4—31no—
132C32×C22⋊C4—32no—
133C32×C22⋊C4—31no—
134C32×C42—32no—
135C32×C42—31no—
136#3752C22×C312yes—
137C4⋊(C3⋊Dic3)C22×C311yescharacteristic
138C3×#217—22no—
139C3×#217—21no—
140C3×#217C2×D311yescharacteristic
141C3×#217C2×D312yes—
142C3×#217C22×C312yes—
143C3×#217C22×C311yescharacteristic
144C3×(C2×D3)⋊C4—21no—
145C3×(C2×D3)⋊C4—32no—
146C3×(C2×D3)⋊C4—32no—
147C3×(C2×D3)⋊C4—32no—
148C3×(C2×D3)⋊C4—32no—
149C3×(C2×D3)⋊C4—32no—
150C3×(C2×D3)⋊C4—32no—
151C3×(C2×D3)⋊C4—62no—
152C3×(C2×D3)⋊C4C2×D311yescharacteristic
153C3×(C2×D3)⋊C4C22×C311yescharacteristic
154C3×C4⋊Dic3—21no—
155C3×C4⋊Dic3—21no—
156C3×C4⋊Dic3—31no—
157C3×C4⋊Dic3—31no—
158C3×C4⋊Dic3—32no—
159C3×C4⋊Dic3—32no—
160C3×C4⋊Dic3—61no—
161C3×C4⋊Dic3C2×D311yescharacteristic
162C3×C4⋊Dic3C2×D311yescharacteristic
163C3×C4⋊Dic3C22×C311yescharacteristic
164C3×C4⋊Dic3C22×C311yescharacteristic
165C3×Dic3⋊C4—21no—
166C3×Dic3⋊C4—32no—
167C3×Dic3⋊C4—32no—
168C3×Dic3⋊C4—32no—
169C3×Dic3⋊C4—32no—
170C3×Dic3⋊C4C2×D311yescharacteristic
171C3×Dic3⋊C4C22×C311yescharacteristic
172C3×C4×Dic3—22no—
173C3×C4×Dic3—21no—
174C3×C4×Dic3C2×D312yes—
175C3×C4×Dic3C2×D311yescharacteristic
176C3×C4×Dic3C22×C312yes—
177C3×C4×Dic3C22×C311yescharacteristic
178#3724C22×C312yes—
179Dic3⋊Dic3C22×C312yes—
180Dic3⋊Dic3C22×C312yes—
181#3722C22×C312yes—
182#3722C22×C312yes—
183C22×C33—21no—
184C22×C33—21no—
185C22×C33—21no—
186C22×C33C2411yescharacteristic
187C2×C3×C3⋊D3—22no—
188C2×C3×C3⋊D3—22no—
189C2×C3×C3⋊D3—22no—
190C2×C32×D3—21no—
191C2×C32×D3—21no—
192C2×C32×D3#4112yes—
193C33×C4—21no—
194C33×C4#4112yes—
195C3×C3⋊Dic3—22no—
196C32×Dic3—21no—
197C32×Dic3—22no—
198C32×Dic3—21no—
199C32×Dic3—22no—
200C32×Dic3—21no—
201C3×#126—92no—
202C3×#125—91no—
203C3×#123—92no—
204C3×#121—92no—
205C3×#121—91no—
206C3×#121—91no—
207C3×C4×D4—31no—
208C3×C4×D4—31no—
209C3×C4×D4—61no—
210C3×C4×D4—92no—
211C3×C4×D4—91no—
212C3×#117—31no—
213C3×#117—31no—
214C3×#117—61no—
215C2×C3×C4⋊C4—91no—
216#939—32no—
217#930—31no—
218#930—31no—
219#930—31no—
220#930—61no—
221C4×#67C3×D311yescharacteristic, complemented
222#926C3×D311yescharacteristic, complemented
223C2×C4⋊Dic3—31no—
224#898—32no—
225#895—31no—
226#893—31no—
227D3×C4⋊C4—31no—
228#890—31no—
229#884—32no—
230#883—32no—
231#883—32no—
232#67⋊C4—32no—
233#876—32no—
234C4×D12—32no—
235C4×D12—31no—
236#870—31no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—31no—
241C23×C32—41no—
242C23×C32C22×D311yescharacteristic
243C23×C32C22×D311yescharacteristic
244C23×C32C23×C311yescharacteristic
245C22×C3⋊D3C23×C312yes—
246C22×C3×D3—21no—
247C22×C3×D3—32no—
248C22×C3×D3—32no—
249C22×C3×D3—62no—
250C22×C3×D3C22×D311yescharacteristic
251C22×C3×D3C23×C311yescharacteristic
252C32×D4—62no—
253C2×C32×C4—22no—
254C2×C32×C4—24no—
255C2×C32×C4—22no—
256C2×C32×C4—22no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—31no—
264C2×C32×C4—31no—
265C2×C32×C4—32no—
266C2×C32×C4—32no—
267C2×C32×C4—31no—
268C2×C32×C4—41no—
269C2×C32×C4—41no—
270C2×C32×C4—42no—
271C2×C32×C4—42no—
272C2×C32×C4—44no—
273C2×C32×C4—62no—
274C2×C32×C4C22×D311yescharacteristic
275C2×C32×C4C22×D311yescharacteristic
276C2×C32×C4C22×D311yescharacteristic
277C2×C32×C4C22×D311yescharacteristic
278C2×C32×C4C23×C311yescharacteristic
279C2×C32×C4C23×C311yescharacteristic
280#638—42no—
281C2×C3⋊Dic3C23×C312yes—
282C4⋊(C3⋊D3)—22no—
283C3×#67—24no—
284C3×#67—22no—
285C3×#67—22no—
286C3×#67—64no—
287C3×#67—122no—
288C3×#67—122no—
289C3×#67—124no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—22no—
292C2×C3×Dic3—22no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—32no—
296C2×C3×Dic3—32no—
297C2×C3×Dic3—62no—
298C2×C3×Dic3—122no—
299C2×C3×Dic3C22×D311yescharacteristic
300C2×C3×Dic3C22×D312yes—
301C2×C3×Dic3C22×D311yescharacteristic
302C2×C3×Dic3C22×D312yes—
303C2×C3×Dic3C22×D311yescharacteristic
304C2×C3×Dic3C23×C311yescharacteristic
305C2×C3×Dic3C23×C311yescharacteristic
306C2×C3×Dic3C23×C312yes—
307C2×C3×Dic3C23×C312yes—
308C2×C3×Dic3C23×C311yescharacteristic
309C3×D12—64no—
310C3×D12—62no—
311C3×D12—62no—
312C3×D12—122no—
313C3×C4×D3—22no—
314C3×C4×D3—22no—
315C3×C4×D3—42no—
316C3×C4×D3—122no—
317C3×C4×D3—122no—
318C3×C4×D3—122no—
319#626—24no—
320#624—42no—
321D3×Dic3—42no—
322#553—91noSylow
323C2×C33—41no—
324C2×C33C2×#4111yescharacteristic
325C2×C33C2×#4111yescharacteristic
326C2×C33H(5,𝔽2)11yescharacteristic
327C3×C3⋊D3—42no—
328C32×D3—22no—
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—61no—
332C2×C3×D4—92no—
333C2×C3×D4—92no—
334C2×C3×D4—91no—
335C22×C3×C4—21no—
336C22×C3×C4—21no—
337C22×C3×C4—21no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—41no—
341C22×C3×C4—61no—
342C22×C3×C4—92no—
343C22×C3×C4—92no—
344C22×C3×C4D3211yescharacteristic
345C22×C3×C4C2×C3×D311yescharacteristic
346C22×C3×C4C2×C3×D311yescharacteristic
347C2×#67—32no—
348C2×#67—32no—
349C2×#67—32no—
350C2×#67—62no—
351C2×#67C2×C3×D311yescharacteristic
352C22×Dic3—32no—
353C2×D12—32no—
354C2×D12—31no—
355C2×D12—31no—
356C2×D12—61no—
357C2×C4×D3—32no—
358C2×C4×D3—32no—
359C2×C4×D3—32no—
360C2×C4×D3C2×C3×D311yescharacteristic
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4—31no—
365C3×C4⋊C4—31no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—61no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4—92no—
371C3×C4⋊C4—92no—
372C3×C4⋊C4—92no—
373C3×C4⋊C4—91no—
374C3×C22⋊C4—32no—
375C3×C22⋊C4—31no—
376C3×C22⋊C4—31no—
377C3×C22⋊C4—32no—
378C3×C22⋊C4—31no—
379C3×C22⋊C4—31no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—62no—
382C3×C22⋊C4—61no—
383C3×C22⋊C4—92no—
384C3×C22⋊C4—92no—
385C3×C22⋊C4—92no—
386C3×C42—32no—
387C3×C42—31no—
388C3×C42—31no—
389C3×C42—32no—
390C3×C42—62no—
391C3×C42—61no—
392#217C2×C3×D311yescharacteristic
393#217C2×C3×D312yes—
394(C2×D3)⋊C4—32no—
395(C2×D3)⋊C4—32no—
396(C2×D3)⋊C4—32no—
397(C2×D3)⋊C4—32no—
398(C2×D3)⋊C4—32no—
399(C2×D3)⋊C4—32no—
400(C2×D3)⋊C4—62no—
401(C2×D3)⋊C4C2×C3×D311yescharacteristic
402C4⋊Dic3—31no—
403C4⋊Dic3—31no—
404C4⋊Dic3—32no—
405C4⋊Dic3—32no—
406C4⋊Dic3—61no—
407C4⋊Dic3C2×C3×D311yescharacteristic
408C4⋊Dic3C2×C3×D311yescharacteristic
409Dic3⋊C4—32no—
410Dic3⋊C4—32no—
411Dic3⋊C4—32no—
412Dic3⋊C4—32no—
413Dic3⋊C4C2×C3×D311yescharacteristic
414C4×Dic3C2×C3×D312yes—
415C4×Dic3C2×C3×D311yescharacteristic
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32—22no—
420C22×C32—22no—
421C22×C32—22no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—32no—
432C22×C32—41no—
433C22×C32—41no—
434C22×C32—41no—
435C22×C32—41no—
436C22×C32—41no—
437C22×C32—41no—
438C22×C32—41no—
439C22×C32—42no—
440C22×C32—42no—
441C22×C32—42no—
442C22×C32—61no—
443C22×C32—61no—
444C22×C32C23×D311yescharacteristic
445C22×C32C23×D311yescharacteristic
446C22×C32C24×C311yescharacteristic
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—22no—
455C2×C3×D3—41no—
456C2×C3×D3—41no—
457C2×C3×D3—62no—
458C2×C3×D3—62no—
459C2×C3×D3—62no—
460C2×C3×D3—62no—
461C2×C3×D3—62no—
462C2×C3×D3—62no—
463C2×C3×D3—122no—
464C2×C3×D3—122no—
465C2×C3×D3—122no—
466C2×C3×D3#23512yes—
467C2×C3×D3C3×#4112yes—
468C32×C4—21no—
469C32×C4—22no—
470C32×C4—21no—
471C32×C4—21no—
472C32×C4—22no—
473C32×C4—22no—
474C32×C4—22no—
475C32×C4—42no—
476C32×C4—41no—
477C32×C4—41no—
478C32×C4—42no—
479C32×C4—61no—
480C32×C4—62no—
481C32×C4—61no—
482C32×C4—61no—
483C32×C4—62no—
484C32×C4#23512yes—
485C32×C4#23712yes—
486C32×C4C3×#4112yes—
487C3⋊Dic3—22no—
488C3×Dic3—22no—
489C3×Dic3—21no—
490C3×Dic3—21no—
491C3×Dic3—22no—
492C3×Dic3—21no—
493C3×Dic3—22no—
494C3×Dic3—22no—
495C3×Dic3—21no—
496C3×Dic3—21no—
497C3×Dic3—22no—
498C3×Dic3—21no—
499C3×Dic3—41no—
500C3×Dic3—42no—
501C3×Dic3—41no—
502C3×Dic3—42no—
503C3×Dic3—62no—
504C3×Dic3—62no—
505C3×Dic3—122no—
506#126—92no—
507#125—91no—
508#123—92no—
509#121—92no—
510#121—91no—
511#121—91no—
512C4×D4—31no—
513C4×D4—92no—
514C4×D4—91no—
515#117—31no—
516C2×C4⋊C4—91no—
517C33#55311yescharacteristic, complemented, Sylow
518C23×C3—21no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—31no—
522C23×C3—31no—
523C23×C3—41no—
524C23×C3—61no—
525C23×C3—92no—
526C23×C3C2×D3211yescharacteristic
527C23×C3C22×C3×D311yescharacteristic
528C23×C3C22×C3×D311yescharacteristic
529C22×D3—32no—
530C22×D3—32no—
531C22×D3—62no—
532C22×D3C22×C3×D311yescharacteristic
533C3×D4—62no—
534C3×D4—62no—
535C3×D4—64no—
536C3×D4—184no—
537C3×D4—182no—
538C3×D4—362no—
539C2×C3×C4—24no—
540C2×C3×C4—22no—
541C2×C3×C4—22no—
542C2×C3×C4—22no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—31no—
550C2×C3×C4—32no—
551C2×C3×C4—32no—
552C2×C3×C4—31no—
553C2×C3×C4—31no—
554C2×C3×C4—31no—
555C2×C3×C4—31no—
556C2×C3×C4—32no—
557C2×C3×C4—32no—
558C2×C3×C4—31no—
559C2×C3×C4—42no—
560C2×C3×C4—42no—
561C2×C3×C4—44no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—62no—
567C2×C3×C4—62no—
568C2×C3×C4—61no—
569C2×C3×C4—62no—
570C2×C3×C4—62no—
571C2×C3×C4—92no—
572C2×C3×C4—122no—
573C2×C3×C4—362no—
574C2×C3×C4—362no—
575C2×C3×C4C2×D3211yescharacteristic
576C2×C3×C4C2×D3211yescharacteristic
577C2×C3×C4C22×C3×D311yescharacteristic
578C2×C3×C4C22×C3×D311yescharacteristic
579C2×C3×C4C22×C3×D311yescharacteristic
580C2×C3×C4C22×C3×D311yescharacteristic
581#67—22no—
582#67—64no—
583#67—122no—
584#67—122no—
585#67—124no—
586C2×Dic3—32no—
587C2×Dic3—32no—
588C2×Dic3—62no—
589C2×Dic3—122no—
590C2×Dic3C22×C3×D311yescharacteristic
591C2×Dic3C22×C3×D312yes—
592C2×Dic3C22×C3×D311yescharacteristic
593C2×Dic3C22×C3×D312yes—
594C2×Dic3C22×C3×D311yescharacteristic
595D12—64no—
596D12—62no—
597D12—62no—
598D12—122no—
599C4×D3—22no—
600C4×D3—122no—
601C4×D3—122no—
602C4×D3—122no—
603C2×C32—21no—
604C2×C32—21no—
605C2×C32—21no—
606C2×C32—21no—
607C2×C32—21no—
608C2×C32—21no—
609C2×C32—21no—
610C2×C32—21no—
611C2×C32—21no—
612C2×C32—41no—
613C2×C32—41no—
614C2×C32—41no—
615C2×C32—42no—
616C2×C32—42no—
617C2×C32—42no—
618C2×C32—44no—
619C2×C32—41no—
620C2×C32—41no—
621C2×C32—41no—
622C2×C32—62no—
623C2×C32C2×#23511yescharacteristic
624C2×C32C2×#23511yescharacteristic
625C2×C32C2×#23711yescharacteristic
626C2×C32D3×#4111yescharacteristic
627C2×C32#100911yescharacteristic
628C2×C32#100911yescharacteristic
629C2×C32C2×C3×#4111yescharacteristic
630C2×C32C2×C3×#4111yescharacteristic
631C2×C32C3×H(5,𝔽2)11yescharacteristic
632C3⋊D3—42no—
633C3×D3—22no—
634C3×D3—22no—
635C3×D3—42no—
636C3×D3—122no—
637C3×D3—122no—
638C3×D3—242no—
639C2×D4—31no—
640C2×D4—92no—
641C2×D4—92no—
642C2×D4—91no—
643C22×C4—31no—
644C22×C4—92no—
645C22×C4—92no—
646C22×C4C3×D3211yescharacteristic
647C4⋊C4—31no—
648C4⋊C4—31no—
649C4⋊C4—31no—
650C4⋊C4—92no—
651C4⋊C4—92no—
652C4⋊C4—92no—
653C4⋊C4—91no—
654C22⋊C4—32no—
655C22⋊C4—31no—
656C22⋊C4—31no—
657C22⋊C4—92no—
658C22⋊C4—92no—
659C22⋊C4—92no—
660C42—32no—
661C42—31no—
662C22×C3—22no—
663C22×C3—22no—
664C22×C3—22no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—32no—
678C22×C3—32no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—42no—
686C22×C3—42no—
687C22×C3—42no—
688C22×C3—41no—
689C22×C3—62no—
690C22×C3—61no—
691C22×C3—61no—
692C22×C3—61no—
693C22×C3—61no—
694C22×C3—121no—
695C22×C3—121no—
696C22×C3—182no—
697C22×C3—182no—
698C22×C3—182no—
699C22×C3C22×D3211yescharacteristic
700C22×C3C23×C3×D311yescharacteristic
701C22×C3C23×C3×D311yescharacteristic
702C2×D3—21no—
703C2×D3—21no—
704C2×D3—62no—
705C2×D3—62no—
706C2×D3—62no—
707C2×D3—62no—
708C2×D3—62no—
709C2×D3—62no—
710C2×D3—122no—
711C2×D3—122no—
712C2×D3—122no—
713C2×D3C3×#23512yes—
714C3×C4—22no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—22no—
719C3×C4—22no—
720C3×C4—22no—
721C3×C4—41no—
722C3×C4—41no—
723C3×C4—42no—
724C3×C4—42no—
725C3×C4—62no—
726C3×C4—61no—
727C3×C4—62no—
728C3×C4—61no—
729C3×C4—62no—
730C3×C4—61no—
731C3×C4—62no—
732C3×C4—61no—
733C3×C4—61no—
734C3×C4—61no—
735C3×C4—62no—
736C3×C4—121no—
737C3×C4—122no—
738C3×C4—122no—
739C3×C4—121no—
740C3×C4—182no—
741C3×C4#380412yes—
742C3×C4C3×#23512yes—
743C3×C4C3×#23712yes—
744Dic3—21no—
745Dic3—21no—
746Dic3—22no—
747Dic3—21no—
748Dic3—22no—
749Dic3—62no—
750Dic3—62no—
751Dic3—122no—
752C32—21no—
753C32—21no—
754C32—21no—
755C32—41no—
756C32#553011yescharacteristic, complemented
757C32#556511yescharacteristic, complemented
758C32C3×#55311yescharacteristic, complemented
759C23—31no—
760C23—92no—
761C23C2×C3×D3211yescharacteristic
762D4—62no—
763D4—184no—
764D4—182no—
765D4—362no—
766C2×C4—22no—
767C2×C4—31no—
768C2×C4—32no—
769C2×C4—32no—
770C2×C4—31no—
771C2×C4—31no—
772C2×C4—62no—
773C2×C4—92no—
774C2×C4—362no—
775C2×C4—362no—
776C2×C4C2×C3×D3211yescharacteristic
777C2×C4C2×C3×D3211yescharacteristic
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—42no—
788C2×C3—42no—
789C2×C3—42no—
790C2×C3—44no—
791C2×C3—41no—
792C2×C3—41no—
793C2×C3—41no—
794C2×C3—41no—
795C2×C3—41no—
796C2×C3—41no—
797C2×C3—62no—
798C2×C3—62no—
799C2×C3—122no—
800C2×C3—362no—
801C2×C3D3×#23511yescharacteristic
802C2×C3#6430811yescharacteristic
803C2×C3C2×#380411yescharacteristic
804C2×C3C2×C3×#23511yescharacteristic
805C2×C3C2×C3×#23511yescharacteristic
806C2×C3C2×C3×#23711yescharacteristic
807C2×C3C3×D3×#4111yescharacteristic
808C2×C3C3×#100911yescharacteristic
809C2×C3C3×#100911yescharacteristic
810D3—22no—
811D3—122no—
812D3—122no—
813D3—242no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—32no—
818C22—61no—
819C22—61no—
820C22—182no—
821C22—182no—
822C22—182no—
823C22C22×C3×D3211yescharacteristic
824C4—21no—
825C4—61no—
826C4—61no—
827C4—62no—
828C4—61no—
829C4—62no—
830C4—182no—
831C4C3×#380412yes—
832C3—21no—
833C3—21no—
834C3—21no—
835C3—41no—
836C3#1059494611yescharacteristic, direct product factor
837C3C3×#553011yescharacteristic, complemented
838C3C3×#556511yescharacteristic, complemented
839C2—41no—
840C2—62no—
841C2—362no—
842C2C3×D3×#23511yescharacteristic
843C2C3×#6430811yescharacteristic
844C2C2×C3×#380411yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
hypercenterC22×C3×C4D32
hypocenterC32C3×#553
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C3×#64139C2semidirect
2. C32×C4×#67C2semidirect
3. C32×#926C2semidirect
4. C3×#63975C2semidirect
5. C3×#63971C2semidirect
6. C3×#63909C2semidirect
7. C3×#63894C2semidirect
8. C3×D3×C4⋊Dic3C2semidirect
9. C3×#63880C2semidirect
10. C3×#63869C2semidirect
11. C3×#63868C2semidirect
14. #10594946C3direct (N × H)
40. #64139C2×C3semidirect
47. C3×C4×#67D3semidirect
48. C3×C4×#67C2×C3semidirect
50. C3×#926D3semidirect
51. C3×#926C2×C3semidirect
66. #63975C2×C3semidirect
67. #63971C2×C3semidirect
68. #63909C2×C3semidirect
69. #63894C2×C3semidirect
70. D3×C4⋊Dic3C2×C3semidirect
71. #63880C2×C3semidirect
72. #63869C2×C3semidirect
73. #63868C2×C3semidirect
221. C4×#67C3×D3semidirect
222. #926C3×D3semidirect
517. C33#553semidirect
756. C32#5530semidirect
757. C32#5565semidirect
758. C32C3×#553semidirect
836. C3#10594946direct (N × H)
837. C3C3×#5530semidirect
838. C3C3×#5565semidirect

Maximal subgroups

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

subgroupindex
C3×#641392
C32×C4×#672
C32×#9262
C3×#639752
C3×#639712
C3×#639092
C3×#638942
C3×D3×C4⋊Dic32
C3×#638802
C3×#638692
C3×#638682
C3×#55653
C3×#55303
#105949463