Finite Group Databasebeta

← C3×#10591392 #13158402

Subgroups — C3×#10591392 #13158402

Order 1728.

1362 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#626C211yesmaximal, characteristic
2C2×C3×#3752C211yesmaximal, characteristic, complemented
3C2×C32×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C2×C32×C4⋊Dic3C211yesmaximal, characteristic, complemented
5C2×C3×#3722C211yesmaximal, characteristic, complemented
6C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
7C3×#63579C211yesmaximal, characteristic, complemented
8C3×#4991—31nomaximal
9C3×#4961—31nomaximal
10#10591392C311yesmaximal, characteristic, direct product factor
11C23×C3×C3⋊D3C2211yescharacteristic
12C23×C32×D3C2211yescharacteristic
13C22×C33×C4C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C32×Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C2×C3×#626—22no—
19C2×C3×#626—22no—
20C2×C3×#626—22no—
21C3×#3752—22no—
22C32×(C2×D3)⋊C4—22no—
23C32×C4⋊Dic3—22no—
24C3×#3722—22no—
25C3×(C2×D3)⋊Dic3—22no—
26C22×C3×#67—31no—
27C22×C3×D12—31no—
28C22×#626C2×C311yescharacteristic
29C2×C32×C4⋊C4—31no—
30C2×C32×C22⋊C4—31no—
31C2×#3752C2×C311yescharacteristic, complemented
32C2×C3×#217—31no—
33C2×C3×(C2×D3)⋊C4—21no—
34C2×C3×(C2×D3)⋊C4—31no—
35C2×C3×(C2×D3)⋊C4—31no—
36C2×C3×(C2×D3)⋊C4—31no—
37C2×C3×(C2×D3)⋊C4—31no—
38C2×C3×(C2×D3)⋊C4—31no—
39C2×C3×(C2×D3)⋊C4—61no—
40C2×C3×(C2×D3)⋊C4D311yescharacteristic, complemented
41C2×C3×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
42C2×C3×C4⋊Dic3—21no—
43C2×C3×C4⋊Dic3D311yescharacteristic, complemented
44C2×C3×C4⋊Dic3C2×C311yescharacteristic, complemented
45C2×#3722C2×C311yescharacteristic, complemented
46C2×(C2×D3)⋊Dic3C2×C311yescharacteristic, complemented
47C3×C3⋊#95—31no—
48C3×C3⋊#95—31no—
49#63579C2×C311yescharacteristic, complemented
50C23×C33C2311yescharacteristic
51C22×C3×C3⋊D3—21no—
52C22×C3×C3⋊D3—21no—
53C22×C3×C3⋊D3—21no—
54C22×C3×C3⋊D3—21no—
55C22×C3×C3⋊D3—21no—
56C22×C3×C3⋊D3—21no—
57C22×C3×C3⋊D3D412yes—
58C22×C32×D3—21no—
59C22×C32×D3—21no—
60C22×C32×D3—21no—
61C22×C32×D3—21no—
62C22×C32×D3—21no—
63C22×C32×D3—21no—
64C22×C32×D3D412yes—
65C2×C33×C4—21no—
66C2×C33×C4—21no—
67C2×C33×C4D412yescomplemented
68C2×C3×C3⋊Dic3—21no—
69C2×C3×C3⋊Dic3—21no—
70C2×C3×C3⋊Dic3—21no—
71C2×C32×Dic3—21no—
72C2×C32×Dic3—21no—
73C2×C32×Dic3—21no—
74C2×C32×Dic3—21no—
75C2×C32×Dic3—21no—
76C2×C32×Dic3—21no—
77C2×C32×Dic3—21no—
78C2×C32×Dic3—21no—
79C2×C32×Dic3D412yes—
80C3×#626—28no—
81C3×#394—91no—
82#4991—31no—
83#4961—31no—
84C24×C32—31no—
85C23×C3⋊D3C22×C311yescharacteristic
86C23×C3×D3—21no—
87C23×C3×D3—31no—
88C23×C3×D3—31no—
89C23×C3×D3—61no—
90C23×C3×D3C2×D311yescharacteristic
91C23×C3×D3C22×C311yescharacteristic
92C22×C32×C4—21no—
93C22×C32×C4—21no—
94C22×C32×C4—21no—
95C22×C32×C4—31no—
96C22×C32×C4—31no—
97C22×C32×C4—31no—
98C22×C32×C4—41no—
99C22×C32×C4C2×D311yescharacteristic
100C22×C32×C4C2×D311yescharacteristic
101C22×C32×C4C22×C311yescharacteristic
102C22×C3⋊Dic3C22×C311yescharacteristic
103C2×C3×#67—62no—
104C2×C3×#67—62no—
105C2×C3×#67—62no—
106C22×C3×Dic3—21no—
107C22×C3×Dic3—21no—
108C22×C3×Dic3—21no—
109C22×C3×Dic3—31no—
110C22×C3×Dic3—31no—
111C22×C3×Dic3—61no—
112C22×C3×Dic3C2×D311yescharacteristic
113C22×C3×Dic3C2×D311yescharacteristic
114C22×C3×Dic3C2×D311yescharacteristic
115C22×C3×Dic3C22×C311yescharacteristic
116C22×C3×Dic3C22×C311yescharacteristic
117C22×C3×Dic3C22×C311yescharacteristic
118C2×C3×D12—62no—
119C2×C3×D12—62no—
120C2×C3×D12—62no—
121C2×#626—22no—
122C2×#626—22no—
123C2×#626—22no—
124C32×C4⋊C4—62no—
125C32×C22⋊C4—62no—
126#3752—22no—
127C3×#217—62no—
128C3×(C2×D3)⋊C4—24no—
129C3×(C2×D3)⋊C4—22no—
130C3×(C2×D3)⋊C4—22no—
131C3×(C2×D3)⋊C4—62no—
132C3×(C2×D3)⋊C4—62no—
133C3×(C2×D3)⋊C4—64no—
134C3×(C2×D3)⋊C4—62no—
135C3×(C2×D3)⋊C4—62no—
136C3×(C2×D3)⋊C4—62no—
137C3×C4⋊Dic3—24no—
138C3×C4⋊Dic3—22no—
139C3×C4⋊Dic3—22no—
140#3722—22no—
141(C2×D3)⋊Dic3—22no—
142C22×C33C2×D411yescharacteristic
143C22×C33C2×D411yescharacteristic
144C22×C33C2×D411yescharacteristic
145C22×C33C2×D411yescharacteristic
146C22×C33#4111yescharacteristic
147C22×C33#4111yescharacteristic
148C22×C33#4111yescharacteristic
149C2×C3×C3⋊D3—22no—
150C2×C3×C3⋊D3—22no—
151C2×C3×C3⋊D3—22no—
152C2×C3×C3⋊D3—41no—
153C2×C3×C3⋊D3—41no—
154C2×C3×C3⋊D3—41no—
155C2×C3×C3⋊D3—41no—
156C2×C32×D3—22no—
157C2×C32×D3—22no—
158C2×C32×D3—22no—
159C2×C32×D3—41no—
160C2×C32×D3—41no—
161C2×C32×D3—41no—
162C2×C32×D3—41no—
163C33×C4—22no—
164C3×C3⋊Dic3—41no—
165C32×Dic3—22no—
166C32×Dic3—41no—
167C32×Dic3—41no—
168C22×C3×D4—91no—
169C22×#67—31no—
170C22×D12—31no—
171C2×C3×C4⋊C4—31no—
172C2×C3×C4⋊C4—31no—
173C2×C3×C4⋊C4—61no—
174C2×C3×C22⋊C4—31no—
175C2×C3×C22⋊C4—31no—
176C2×C3×C22⋊C4—61no—
177C2×C3×C22⋊C4—91no—
178C2×C3×C22⋊C4—91no—
179C2×C3×C22⋊C4—91no—
180C2×#217—31no—
181C2×(C2×D3)⋊C4—31no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—61no—
187C2×(C2×D3)⋊C4C3×D311yescharacteristic, complemented
188C2×C4⋊Dic3C3×D311yescharacteristic, complemented
189C3×#95—91no—
190C3⋊#95—31no—
191C3⋊#95—31no—
192C23×C32—21no—
193C23×C32—21no—
194C23×C32—21no—
195C23×C32—32no—
196C23×C32—41no—
197C23×C32—61no—
198C23×C32—61no—
199C23×C32—61no—
200C23×C32—61no—
201C23×C32—61no—
202C23×C32—61no—
203C23×C32C22×D311yescharacteristic
204C23×C32C22×D311yescharacteristic
205C23×C32C23×C311yescharacteristic
206C22×C3⋊D3—21no—
207C22×C3⋊D3—21no—
208C22×C3⋊D3—21no—
209C22×C3⋊D3—21no—
210C22×C3⋊D3—21no—
211C22×C3⋊D3—21no—
212C22×C3⋊D3C3×D412yes—
213C22×C3×D3—22no—
214C22×C3×D3—22no—
215C22×C3×D3—21no—
216C22×C3×D3—21no—
217C22×C3×D3—21no—
218C22×C3×D3—21no—
219C22×C3×D3—21no—
220C22×C3×D3—21no—
221C22×C3×D3—21no—
222C22×C3×D3—21no—
223C22×C3×D3—21no—
224C22×C3×D3—21no—
225C22×C3×D3—21no—
226C22×C3×D3—21no—
227C22×C3×D3—22no—
228C22×C3×D3—32no—
229C22×C3×D3—32no—
230C22×C3×D3—41no—
231C22×C3×D3—41no—
232C22×C3×D3—41no—
233C22×C3×D3—41no—
234C22×C3×D3—62no—
235C22×C3×D3—62no—
236C22×C3×D3—62no—
237C22×C3×D3—61no—
238C22×C3×D3—61no—
239C22×C3×D3—61no—
240C22×C3×D3—61no—
241C22×C3×D3—61no—
242C22×C3×D3—61no—
243C22×C3×D3—61no—
244C22×C3×D3—61no—
245C22×C3×D3—61no—
246C22×C3×D3—61no—
247C22×C3×D3—61no—
248C22×C3×D3—61no—
249C22×C3×D3—121no—
250C22×C3×D3—121no—
251C22×C3×D3—121no—
252C22×C3×D3—121no—
253C22×C3×D3D1212yes—
254C22×C3×D3C3×D412yes—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—22no—
258C2×C32×C4—22no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—22no—
264C2×C32×C4—22no—
265C2×C32×C4—22no—
266C2×C32×C4—32no—
267C2×C32×C4—42no—
268C2×C32×C4—41no—
269C2×C32×C4—41no—
270C2×C32×C4—41no—
271C2×C32×C4—41no—
272C2×C32×C4—42no—
273C2×C32×C4—42no—
274C2×C32×C4—61no—
275C2×C32×C4—61no—
276C2×C32×C4—61no—
277C2×C32×C4—61no—
278C2×C32×C4—61no—
279C2×C32×C4—61no—
280C2×C32×C4—61no—
281C2×C32×C4—61no—
282C2×C32×C4D1212yescomplemented
283C2×C32×C4#6712yescomplemented
284C2×C32×C4C3×D412yescomplemented
285C2×C3⋊Dic3—21no—
286C2×C3⋊Dic3—21no—
287C2×C3⋊Dic3—21no—
288C3×#67—68no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—22no—
294C2×C3×Dic3—22no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—22no—
308C2×C3×Dic3—41no—
309C2×C3×Dic3—41no—
310C2×C3×Dic3—41no—
311C2×C3×Dic3—41no—
312C2×C3×Dic3—41no—
313C2×C3×Dic3—41no—
314C2×C3×Dic3—62no—
315C2×C3×Dic3—61no—
316C2×C3×Dic3—61no—
317C2×C3×Dic3—61no—
318C2×C3×Dic3—61no—
319C2×C3×Dic3—61no—
320C2×C3×Dic3—61no—
321C2×C3×Dic3—121no—
322C2×C3×Dic3—121no—
323C2×C3×Dic3#6712yes—
324C2×C3×Dic3C3×D412yes—
325C3×D12—68no—
326#626—28no—
327#394—91noSylow
328C2×C33#12011yescharacteristic
329C2×C33#12111yescharacteristic
330C2×C33#12111yescharacteristic
331C2×C33#12111yescharacteristic
332C2×C33#12311yescharacteristic
333C2×C33#12311yescharacteristic
334C2×C33#12411yescharacteristic
335C3×C3⋊D3—42no—
336C32×D3—42no—
337C24×C3—31no—
338C24×C3—31no—
339C24×C3—61no—
340C24×C3—91no—
341C23×D3—31no—
342C23×D3—31no—
343C23×D3—61no—
344C23×D3C2×C3×D311yescharacteristic
345C2×C3×D4—182no—
346C2×C3×D4—182no—
347C2×C3×D4—182no—
348C22×C3×C4—21no—
349C22×C3×C4—21no—
350C22×C3×C4—21no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—41no—
358C22×C3×C4—61no—
359C22×C3×C4—61no—
360C22×C3×C4—61no—
361C22×C3×C4—91no—
362C22×C3×C4D3211yescharacteristic
363C22×C3×C4C2×C3×D311yescharacteristic
364C22×C3×C4C2×C3×D311yescharacteristic
365C2×#67—62no—
366C2×#67—62no—
367C2×#67—62no—
368C22×Dic3—31no—
369C22×Dic3—31no—
370C22×Dic3—61no—
371C22×Dic3C2×C3×D311yescharacteristic
372C22×Dic3C2×C3×D311yescharacteristic
373C22×Dic3C2×C3×D311yescharacteristic
374C2×D12—62no—
375C2×D12—62no—
376C2×D12—62no—
377C3×C4⋊C4—62no—
378C3×C4⋊C4—62no—
379C3×C4⋊C4—64no—
380C3×C22⋊C4—64no—
381C3×C22⋊C4—62no—
382C3×C22⋊C4—62no—
383C3×C22⋊C4—182no—
384C3×C22⋊C4—182no—
385C3×C22⋊C4—182no—
386#217—62no—
387(C2×D3)⋊C4—22no—
388(C2×D3)⋊C4—62no—
389(C2×D3)⋊C4—62no—
390(C2×D3)⋊C4—64no—
391(C2×D3)⋊C4—62no—
392(C2×D3)⋊C4—62no—
393(C2×D3)⋊C4—62no—
394C4⋊Dic3—22no—
395C22×C32—21no—
396C22×C32—21no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—21no—
403C22×C32—21no—
404C22×C32—21no—
405C22×C32—21no—
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—21no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32—41no—
423C22×C32—62no—
424C22×C32—62no—
425C22×C32—62no—
426C22×C32—121no—
427C22×C32—121no—
428C22×C32—121no—
429C22×C32—121no—
430C22×C32C2×D1211yescharacteristic
431C22×C32C2×D1211yescharacteristic
432C22×C32#23511yescharacteristic
433C22×C32#23511yescharacteristic
434C22×C32D3×D411yescharacteristic
435C22×C32D3×D411yescharacteristic
436C22×C32D3×D411yescharacteristic
437C22×C32D3×D411yescharacteristic
438C22×C32#23711yescharacteristic
439C22×C32#23711yescharacteristic
440C22×C32#23911yescharacteristic
441C22×C32#23911yescharacteristic
442C22×C32C2×#6711yescharacteristic
443C22×C32C2×#6711yescharacteristic
444C22×C32C2×C3×D411yescharacteristic
445C22×C32C2×C3×D411yescharacteristic
446C22×C32C2×C3×D411yescharacteristic
447C22×C32C2×C3×D411yescharacteristic
448C22×C32C3×#4111yescharacteristic
449C22×C32C3×#4111yescharacteristic
450C22×C32C3×#4111yescharacteristic
451C2×C3⋊D3—22no—
452C2×C3⋊D3—22no—
453C2×C3⋊D3—22no—
454C2×C3⋊D3—41no—
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
458C2×C3×D3—24no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—22no—
462C2×C3×D3—22no—
463C2×C3×D3—22no—
464C2×C3×D3—22no—
465C2×C3×D3—42no—
466C2×C3×D3—42no—
467C2×C3×D3—42no—
468C2×C3×D3—42no—
469C2×C3×D3—42no—
470C2×C3×D3—42no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—64no—
480C2×C3×D3—62no—
481C2×C3×D3—62no—
482C2×C3×D3—62no—
483C2×C3×D3—62no—
484C2×C3×D3—62no—
485C2×C3×D3—62no—
486C2×C3×D3—122no—
487C2×C3×D3—122no—
488C2×C3×D3—122no—
489C2×C3×D3—122no—
490C2×C3×D3—122no—
491C2×C3×D3—122no—
492C2×C3×D3—121no—
493C2×C3×D3—121no—
494C2×C3×D3—121no—
495C2×C3×D3—121no—
496C2×C3×D3—121no—
497C2×C3×D3—121no—
498C2×C3×D3—121no—
499C2×C3×D3—121no—
500C32×C4—22no—
501C32×C4—24no—
502C32×C4—22no—
503C32×C4—22no—
504C32×C4—42no—
505C32×C4—42no—
506C32×C4—44no—
507C32×C4—62no—
508C32×C4—121no—
509C32×C4—121no—
510C3⋊Dic3—41no—
511C3×Dic3—22no—
512C3×Dic3—22no—
513C3×Dic3—42no—
514C3×Dic3—42no—
515C3×Dic3—42no—
516C3×Dic3—41no—
517C3×Dic3—41no—
518C3×Dic3—41no—
519C3×Dic3—41no—
520C3×Dic3—122no—
521C3×Dic3—121no—
522C3×Dic3—121no—
523C22×D4—91no—
524C2×C4⋊C4—31no—
525C2×C22⋊C4—31no—
526C2×C22⋊C4—91no—
527C2×C22⋊C4—91no—
528C2×C22⋊C4—91no—
529#95—91no—
530C33#39411yescharacteristic, complemented, Sylow
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—21no—
534C23×C3—32no—
535C23×C3—32no—
536C23×C3—41no—
537C23×C3—62no—
538C23×C3—62no—
539C23×C3—62no—
540C23×C3—61no—
541C23×C3—61no—
542C23×C3—61no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—61no—
547C23×C3—61no—
548C23×C3—61no—
549C23×C3—61no—
550C23×C3—61no—
551C23×C3—61no—
552C23×C3—92no—
553C23×C3—121no—
554C23×C3—121no—
555C23×C3—121no—
556C23×C3—121no—
557C23×C3—181no—
558C23×C3—181no—
559C23×C3—181no—
560C23×C3—181no—
561C23×C3—181no—
562C23×C3—181no—
563C23×C3C2×D3211yescharacteristic
564C23×C3C22×C3×D311yescharacteristic
565C23×C3C22×C3×D311yescharacteristic
566C22×D3—21no—
567C22×D3—21no—
568C22×D3—21no—
569C22×D3—21no—
570C22×D3—21no—
571C22×D3—21no—
572C22×D3—32no—
573C22×D3—32no—
574C22×D3—62no—
575C22×D3—62no—
576C22×D3—62no—
577C22×D3—61no—
578C22×D3—61no—
579C22×D3—61no—
580C22×D3—61no—
581C22×D3—61no—
582C22×D3—61no—
583C22×D3—61no—
584C22×D3—61no—
585C22×D3—61no—
586C22×D3—61no—
587C22×D3—61no—
588C22×D3—61no—
589C22×D3—121no—
590C22×D3—121no—
591C22×D3—121no—
592C22×D3—121no—
593C22×D3C3×D1212yes—
594C3×D4—188no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
605C2×C3×C4—22no—
606C2×C3×C4—32no—
607C2×C3×C4—32no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—42no—
613C2×C3×C4—42no—
614C2×C3×C4—42no—
615C2×C3×C4—62no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
618C2×C3×C4—61no—
619C2×C3×C4—61no—
620C2×C3×C4—62no—
621C2×C3×C4—62no—
622C2×C3×C4—61no—
623C2×C3×C4—61no—
624C2×C3×C4—61no—
625C2×C3×C4—61no—
626C2×C3×C4—61no—
627C2×C3×C4—61no—
628C2×C3×C4—61no—
629C2×C3×C4—61no—
630C2×C3×C4—61no—
631C2×C3×C4—61no—
632C2×C3×C4—61no—
633C2×C3×C4—61no—
634C2×C3×C4—121no—
635C2×C3×C4—121no—
636C2×C3×C4—121no—
637C2×C3×C4—121no—
638C2×C3×C4—121no—
639C2×C3×C4—121no—
640C2×C3×C4—181no—
641C2×C3×C4—181no—
642C2×C3×C4—181no—
643C2×C3×C4#62612yescomplemented
644C2×C3×C4C3×D1212yescomplemented
645C2×C3×C4C3×#6712yescomplemented
646#67—68no—
647C2×Dic3—21no—
648C2×Dic3—21no—
649C2×Dic3—21no—
650C2×Dic3—21no—
651C2×Dic3—21no—
652C2×Dic3—21no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—62no—
656C2×Dic3—61no—
657C2×Dic3—61no—
658C2×Dic3—61no—
659C2×Dic3—61no—
660C2×Dic3—61no—
661C2×Dic3—61no—
662C2×Dic3—121no—
663C2×Dic3—121no—
664C2×Dic3C3×#6712yes—
665D12—68no—
666C2×C32—21no—
667C2×C32—21no—
668C2×C32—21no—
669C2×C32—21no—
670C2×C32—21no—
671C2×C32—21no—
672C2×C32—21no—
673C2×C32—21no—
674C2×C32—21no—
675C2×C32—21no—
676C2×C32—21no—
677C2×C32—21no—
678C2×C32—21no—
679C2×C32—21no—
680C2×C32—21no—
681C2×C32—21no—
682C2×C32—21no—
683C2×C32—21no—
684C2×C32—21no—
685C2×C32—21no—
686C2×C32—21no—
687C2×C32—41no—
688C2×C32—41no—
689C2×C32—41no—
690C2×C32—41no—
691C2×C32—41no—
692C2×C32—41no—
693C2×C32—41no—
694C2×C32—122no—
695C2×C32#88211yescharacteristic
696C2×C32#88311yescharacteristic
697C2×C32#88511yescharacteristic
698C2×C32#88611yescharacteristic
699C2×C32#89411yescharacteristic
700C2×C32#89411yescharacteristic
701C2×C32#89511yescharacteristic
702C2×C32#89511yescharacteristic
703C2×C32#93011yescharacteristic
704C2×C32#93011yescharacteristic
705C2×C32#93711yescharacteristic
706C2×C32#93811yescharacteristic
707C2×C32#93911yescharacteristic
708C2×C32#94711yescharacteristic
709C2×C32C3×#12011yescharacteristic
710C2×C32C3×#12111yescharacteristic
711C2×C32C3×#12111yescharacteristic
712C2×C32C3×#12111yescharacteristic
713C2×C32C3×#12311yescharacteristic
714C2×C32C3×#12311yescharacteristic
715C2×C32C3×#12411yescharacteristic
716C3⋊D3—42no—
717C3×D3—44no—
718C3×D3—42no—
719C3×D3—42no—
720C3×D3—124no—
721C3×D3—122no—
722C3×D3—122no—
723C24—31no—
724C24—91no—
725C2×D4—182no—
726C2×D4—182no—
727C2×D4—182no—
728C22×C4—31no—
729C22×C4—31no—
730C22×C4—31no—
731C22×C4—91no—
732C22×C4C3×D3211yescharacteristic
733C4⋊C4—62no—
734C22⋊C4—62no—
735C22⋊C4—182no—
736C22⋊C4—182no—
737C22⋊C4—182no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—21no—
751C22×C3—21no—
752C22×C3—21no—
753C22×C3—21no—
754C22×C3—21no—
755C22×C3—21no—
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—41no—
760C22×C3—41no—
761C22×C3—41no—
762C22×C3—41no—
763C22×C3—41no—
764C22×C3—41no—
765C22×C3—41no—
766C22×C3—64no—
767C22×C3—62no—
768C22×C3—62no—
769C22×C3—62no—
770C22×C3—62no—
771C22×C3—62no—
772C22×C3—62no—
773C22×C3—122no—
774C22×C3—122no—
775C22×C3—122no—
776C22×C3—122no—
777C22×C3—122no—
778C22×C3—122no—
779C22×C3—121no—
780C22×C3—121no—
781C22×C3—121no—
782C22×C3—121no—
783C22×C3—121no—
784C22×C3—121no—
785C22×C3—121no—
786C22×C3—121no—
787C22×C3—182no—
788C22×C3—182no—
789C22×C3—182no—
790C22×C3—361no—
791C22×C3—361no—
792C22×C3—361no—
793C22×C3—361no—
794C22×C3#379611yescharacteristic
795C22×C3#379911yescharacteristic
796C22×C3D3×D1211yescharacteristic
797C22×C3#380211yescharacteristic
798C22×C3#380411yescharacteristic
799C22×C3C2×#62611yescharacteristic
800C22×C3D3×#6711yescharacteristic
801C22×C3C2×C3×D1211yescharacteristic
802C22×C3C2×C3×D1211yescharacteristic
803C22×C3C3×#23511yescharacteristic
804C22×C3C3×#23511yescharacteristic
805C22×C3C3×D3×D411yescharacteristic
806C22×C3C3×D3×D411yescharacteristic
807C22×C3C3×D3×D411yescharacteristic
808C22×C3C3×D3×D411yescharacteristic
809C22×C3C3×#23711yescharacteristic
810C22×C3C3×#23711yescharacteristic
811C22×C3C3×#23911yescharacteristic
812C22×C3C3×#23911yescharacteristic
813C22×C3C2×C3×#6711yescharacteristic
814C22×C3C2×C3×#6711yescharacteristic
815C2×D3—22no—
816C2×D3—22no—
817C2×D3—22no—
818C2×D3—41no—
819C2×D3—41no—
820C2×D3—41no—
821C2×D3—41no—
822C2×D3—64no—
823C2×D3—62no—
824C2×D3—62no—
825C2×D3—62no—
826C2×D3—62no—
827C2×D3—62no—
828C2×D3—62no—
829C2×D3—122no—
830C2×D3—122no—
831C2×D3—122no—
832C2×D3—122no—
833C2×D3—122no—
834C2×D3—122no—
835C2×D3—121no—
836C2×D3—121no—
837C2×D3—121no—
838C2×D3—121no—
839C2×D3—121no—
840C2×D3—121no—
841C2×D3—121no—
842C2×D3—121no—
843C3×C4—24no—
844C3×C4—22no—
845C3×C4—22no—
846C3×C4—22no—
847C3×C4—42no—
848C3×C4—42no—
849C3×C4—44no—
850C3×C4—62no—
851C3×C4—62no—
852C3×C4—122no—
853C3×C4—122no—
854C3×C4—122no—
855C3×C4—121no—
856C3×C4—121no—
857C3×C4—121no—
858C3×C4—121no—
859C3×C4—361no—
860Dic3—22no—
861Dic3—41no—
862Dic3—41no—
863Dic3—122no—
864Dic3—121no—
865Dic3—121no—
866C32—21no—
867C32—21no—
868C32—21no—
869C32—41no—
870C32#496111yescharacteristic, complemented
871C32#499111yescharacteristic, complemented
872C32C3×#39411yescharacteristic, complemented
873C23—32no—
874C23—61no—
875C23—61no—
876C23—61no—
877C23—61no—
878C23—61no—
879C23—61no—
880C23—92no—
881C23—181no—
882C23—181no—
883C23—181no—
884C23—181no—
885C23—181no—
886C23—181no—
887C23C2×C3×D3211yescharacteristic
888D4—188no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—32no—
892C2×C4—61no—
893C2×C4—61no—
894C2×C4—61no—
895C2×C4—61no—
896C2×C4—61no—
897C2×C4—61no—
898C2×C4—61no—
899C2×C4—61no—
900C2×C4—181no—
901C2×C4—181no—
902C2×C4—181no—
903C2×C4C3×#62612yescomplemented
904C2×C3—21no—
905C2×C3—21no—
906C2×C3—21no—
907C2×C3—21no—
908C2×C3—21no—
909C2×C3—21no—
910C2×C3—21no—
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—21no—
923C2×C3—21no—
924C2×C3—21no—
925C2×C3—41no—
926C2×C3—41no—
927C2×C3—41no—
928C2×C3—41no—
929C2×C3—41no—
930C2×C3—41no—
931C2×C3—41no—
932C2×C3—124no—
933C2×C3—122no—
934C2×C3—122no—
935C2×C3—362no—
936C2×C3#6385411yescharacteristic
937C2×C3#6389011yescharacteristic
938C2×C3#6390711yescharacteristic
939C2×C3#6390911yescharacteristic
940C2×C3#6391611yescharacteristic
941C2×C3#6392211yescharacteristic
942C2×C3#6397811yescharacteristic
943C2×C3C3×#88211yescharacteristic
944C2×C3C3×#88311yescharacteristic
945C2×C3C3×#88511yescharacteristic
946C2×C3C3×#88611yescharacteristic
947C2×C3C3×#89411yescharacteristic
948C2×C3C3×#89411yescharacteristic
949C2×C3C3×#89511yescharacteristic
950C2×C3C3×#89511yescharacteristic
951C2×C3C3×#93011yescharacteristic
952C2×C3C3×#93011yescharacteristic
953C2×C3C3×#93711yescharacteristic
954C2×C3C3×#93811yescharacteristic
955C2×C3C3×#93911yescharacteristic
956C2×C3C3×#94711yescharacteristic
957D3—42no—
958D3—124no—
959D3—122no—
960D3—122no—
961C22—62no—
962C22—62no—
963C22—62no—
964C22—121no—
965C22—121no—
966C22—121no—
967C22—121no—
968C22—182no—
969C22—182no—
970C22—182no—
971C22—361no—
972C22—361no—
973C22—361no—
974C22—361no—
975C22C3×#379611yescharacteristic
976C22C3×#379911yescharacteristic
977C22C3×D3×D1211yescharacteristic
978C22C3×#380211yescharacteristic
979C22C3×#380411yescharacteristic
980C22C2×C3×#62611yescharacteristic
981C22C3×D3×#6711yescharacteristic
982C4—22no—
983C4—62no—
984C4—121no—
985C4—121no—
986C4—361no—
987C3—21no—
988C3—21no—
989C3—21no—
990C3—41no—
991C3#1059139211yescharacteristic, direct product factor
992C3C3×#496111yescharacteristic, complemented
993C3C3×#499111yescharacteristic, complemented
994C2—122no—
995C2—362no—
996C2C3×#6385411yescharacteristic
997C2C3×#6389011yescharacteristic
998C2C3×#6390711yescharacteristic
999C2C3×#6390911yescharacteristic
1000C2C3×#6391611yescharacteristic
1001C2C3×#6392211yescharacteristic
1002C2C3×#6397811yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutator, cosocleC23×C32C23×C3
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC22×C3×#626C2
hypercenterC22×C3×C4D32
hypocenterC32C3×#394
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#3752C2semidirect
3. C2×C32×(C2×D3)⋊C4C2semidirect
4. C2×C32×C4⋊Dic3C2semidirect
5. C2×C3×#3722C2semidirect
6. C2×C3×(C2×D3)⋊Dic3C2semidirect
7. C3×#63579C2semidirect
10. #10591392C3direct (N × H)
31. C2×#3752C2×C3semidirect
40. C2×C3×(C2×D3)⋊C4D3semidirect
41. C2×C3×(C2×D3)⋊C4C2×C3semidirect
43. C2×C3×C4⋊Dic3D3semidirect
44. C2×C3×C4⋊Dic3C2×C3semidirect
45. C2×#3722C2×C3semidirect
46. C2×(C2×D3)⋊Dic3C2×C3semidirect
49. #63579C2×C3semidirect
67. C2×C33×C4D4semidirect
187. C2×(C2×D3)⋊C4C3×D3semidirect
188. C2×C4⋊Dic3C3×D3semidirect
282. C2×C32×C4D12semidirect
283. C2×C32×C4#67semidirect
284. C2×C32×C4C3×D4semidirect
530. C33#394semidirect
643. C2×C3×C4#626semidirect
644. C2×C3×C4C3×D12semidirect
645. C2×C3×C4C3×#67semidirect
870. C32#4961semidirect
871. C32#4991semidirect
872. C32C3×#394semidirect
903. C2×C4C3×#626semidirect
991. C3#10591392direct (N × H)
992. C3C3×#4961semidirect
993. C3C3×#4991semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#6262
C2×C3×#37522
C2×C32×(C2×D3)⋊C42
C2×C32×C4⋊Dic32
C2×C3×#37222
C2×C3×(C2×D3)⋊Dic32
C3×#635792
C3×#49913
C3×#49613
#105913923