Finite Group Databasebeta

← C2×C3×#5663 #11901470

Subgroups — C2×C3×#5663 #11901470

Order 1152.

2691 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#123C211yesmaximal, characteristic, complemented
2C2×C3×#940C211yesmaximal, characteristic, complemented
3C2×C3×#939C211yesmaximal, characteristic, complemented
4C2×C3×#930C211yesmaximal, characteristic, complemented
5C2×C3×C4×#67C211yesmaximal, characteristic, complemented
6C3×#5663C2116yesmaximal, direct product factor
7C2×C3×#895C211yesmaximal, characteristic, complemented
8C2×C3×#894C211yesmaximal, characteristic, complemented
9C2×C3×#892C211yesmaximal, characteristic, complemented
10C2×C3×#889C211yesmaximal, characteristic, complemented
11C2×C3×#886C211yesmaximal, characteristic, complemented
12C2×C3×#884C211yesmaximal, characteristic, complemented
13C2×C3×#884C211yesmaximal, characteristic, complemented
14C2×C3×#884C211yesmaximal, characteristic, complemented
15C2×C3×#883C211yesmaximal, characteristic, complemented
16C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
17C2×C3×#540—31nomaximal
18C2×#5663C311yesmaximal, characteristic, direct product factor
19C22×C32×D4C2211yescharacteristic
20C23×C32×C4C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic
26C22×C3×#67C2211yescharacteristic
27C23×C3×Dic3C2211yescharacteristic
28C22×C3×D12C2211yescharacteristic
29C22×C3×D12C2211yescharacteristic
30C22×C3×D12C2211yescharacteristic
31C22×C3×C4×D3C2211yescharacteristic
32C22×C3×C4×D3C2211yescharacteristic
33C22×C3×C4×D3C2211yescharacteristic
34C32×#123C2218yescomplemented
35C2×C32×C4⋊C4C2211yescharacteristic
36C2×C32×C4⋊C4C2211yescharacteristic
37C2×C32×C22⋊C4C2211yescharacteristic
38C2×C32×C22⋊C4C2211yescharacteristic
39C2×C32×C22⋊C4C2211yescharacteristic
40C2×C3×#217C2211yescharacteristic
41C3×#940C2218yescomplemented
42C3×#939C2218yescomplemented
43C3×#930C2218yescomplemented
44C3×C4×#67C2218yescomplemented
45C2×C3×(C2×D3)⋊C4C2211yescharacteristic
46C2×C3×(C2×D3)⋊C4C2211yescharacteristic
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic
50C2×C3×(C2×D3)⋊C4C2211yescharacteristic
51C2×C3×C4⋊Dic3C2211yescharacteristic
52C2×C3×C4⋊Dic3C2211yescharacteristic
53C2×C3×Dic3⋊C4C2211yescharacteristic
54C2×C3×Dic3⋊C4C2211yescharacteristic
55C2×C3×Dic3⋊C4C2211yescharacteristic
56C2×C3×Dic3⋊C4C2211yescharacteristic
57C2×C3×C4×Dic3C2211yescharacteristic
58C2×C3×C4×Dic3C2211yescharacteristic
59C3×#895C2218yescomplemented
60C3×#894C2218yescomplemented
61C3×#892C2218yescomplemented
62C3×#889C2218yescomplemented
63C3×#886C2218yescomplemented
64C3×#884C2218yescomplemented
65C3×#884C2218yescomplemented
66C3×#884C2218yescomplemented
67C3×#883C2218yescomplemented
68C3×#67⋊C4C2218yescomplemented
69C3×#540—316no—
70C2×C3×#127—31no—
71C2×C3×#125—31no—
72C2×C3×#123—21no—
73C2×C3×#123—31no—
74C2×C3×#123—31no—
75C2×C3×#123—31no—
76C2×C3×#123D311yescharacteristic, complemented
77C2×C3×#123C2×C311yescharacteristic, complemented
78C2×C3×#121—31no—
79C2×C3×#121—31no—
80C2×C3×#121—31no—
81C2×C3×#121—31no—
82C2×C3×#121—31no—
83C2×C3×#121—31no—
84C2×C3×C4×D4—31no—
85C2×C3×C4×D4—31no—
86C2×C3×#117—31no—
87C2×#940C2×C311yescharacteristic, complemented
88C2×#939C2×C311yescharacteristic, complemented
89C2×#930C2×C311yescharacteristic, complemented
90C2×C4×#67C2×C311yescharacteristic, complemented
91#5663C2×C3116yesdirect product factor
92C2×#895C2×C311yescharacteristic, complemented
93C2×#894C2×C311yescharacteristic, complemented
94C2×#892C2×C311yescharacteristic, complemented
95C2×#889C2×C311yescharacteristic, complemented
96C2×#886C2×C311yescharacteristic, complemented
97C2×#884C2×C311yescharacteristic, complemented
98C2×#884C2×C311yescharacteristic, complemented
99C2×#884C2×C311yescharacteristic, complemented
100C2×#883C2×C311yescharacteristic, complemented
101C2×#67⋊C4C2×C311yescharacteristic, complemented
102C24×C32C2311yescharacteristic
103C24×C32C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C2×C32×D4—42no—
108C2×C32×D4C2314yes—
109C22×C32×C4—42no—
110C22×C32×C4C2311yescharacteristic
111C22×C32×C4C2311yescharacteristic
112C22×C32×C4C2311yescharacteristic
113C22×C32×C4C2311yescharacteristic
114C22×C32×C4C2311yescharacteristic
115C22×C32×C4C2314yes—
116C2×C3×#67—24no—
117C2×C3×#67—24no—
118C2×C3×#67—42no—
119C2×C3×#67—42no—
120C2×C3×#67—42no—
121C2×C3×#67—42no—
122C2×C3×#67C2314yes—
123C2×C3×#67C2314yes—
124C2×C3×#67C2314yes—
125C2×C3×#67C2314yes—
126C2×C3×#67C2314yes—
127C2×C3×#67C2314yes—
128C22×C3×Dic3—42no—
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2314yes—
134C22×C3×Dic3C2311yescharacteristic
135C2×C3×D12—42no—
136C2×C3×D12—42no—
137C2×C3×D12—42no—
138C2×C3×D12C2314yes—
139C2×C3×D12C2314yes—
140C2×C3×D12C2314yes—
141C2×C3×C4×D3—24no—
142C2×C3×C4×D3—42no—
143C2×C3×C4×D3—42no—
144C2×C3×C4×D3C2314yes—
145C2×C3×C4×D3C2314yes—
146C2×C3×C4×D3C2314yes—
147C32×C4⋊C4C2314yes—
148C32×C4⋊C4C2314yes—
149C32×C22⋊C4C2314yes—
150C32×C22⋊C4C2314yes—
151C32×C22⋊C4C2314yes—
152C3×#217C2314yes—
153C3×(C2×D3)⋊C4C2314yes—
154C3×(C2×D3)⋊C4C2314yes—
155C3×(C2×D3)⋊C4C2314yes—
156C3×(C2×D3)⋊C4C2314yes—
157C3×(C2×D3)⋊C4C2314yes—
158C3×(C2×D3)⋊C4C2314yes—
159C3×C4⋊Dic3C2314yes—
160C3×C4⋊Dic3C2314yes—
161C3×Dic3⋊C4C2314yes—
162C3×Dic3⋊C4C2314yes—
163C3×Dic3⋊C4C2314yes—
164C3×Dic3⋊C4C2314yes—
165C3×C4×Dic3C2314yes—
166C3×C4×Dic3C2314yes—
167C2×#540—31noSylow
168C22×C3×D4—21no—
169C22×C3×D4—31no—
170C22×C3×D4—31no—
171C22×C3×D4—31no—
172C22×C3×D4—31no—
173C22×C3×D4—31no—
174C22×C3×D4—31no—
175C22×C3×D4—31no—
176C22×C3×D4—31no—
177C22×C3×D4—31no—
178C22×C3×D4C2×D311yescharacteristic
179C22×C3×D4C22×C311yescharacteristic
180C23×C3×C4—21no—
181C23×C3×C4—31no—
182C23×C3×C4—31no—
183C23×C3×C4—31no—
184C23×C3×C4—31no—
185C23×C3×C4C2×D311yescharacteristic
186C23×C3×C4C22×C311yescharacteristic
187C22×#67C22×C311yescharacteristic
188C22×#67C22×C311yescharacteristic
189C22×#67C22×C311yescharacteristic
190C22×#67C22×C311yescharacteristic
191C22×#67C22×C311yescharacteristic
192C22×#67C22×C311yescharacteristic
193C23×Dic3C22×C311yescharacteristic
194C22×D12C22×C311yescharacteristic
195C22×D12C22×C311yescharacteristic
196C22×D12C22×C311yescharacteristic
197C22×C4×D3C22×C311yescharacteristic
198C22×C4×D3C22×C311yescharacteristic
199C22×C4×D3C22×C311yescharacteristic
200C3×#127—38no—
201C3×#125—38no—
202C3×#123—28no—
203C3×#123—38no—
204C3×#123—38no—
205C3×#123—38no—
206C3×#123C2×D318yescomplemented
207C3×#123C22×C318yescomplemented
208C3×#121—38no—
209C3×#121—38no—
210C3×#121—38no—
211C3×#121—38no—
212C3×#121—38no—
213C3×#121—38no—
214C3×C4×D4—38no—
215C3×C4×D4—38no—
216C3×#117—38no—
217C2×C3×C4⋊C4—21no—
218C2×C3×C4⋊C4—21no—
219C2×C3×C4⋊C4—31no—
220C2×C3×C4⋊C4—31no—
221C2×C3×C4⋊C4—31no—
222C2×C3×C4⋊C4—31no—
223C2×C3×C4⋊C4—31no—
224C2×C3×C4⋊C4—31no—
225C2×C3×C4⋊C4C2×D311yescharacteristic
226C2×C3×C4⋊C4C2×D311yescharacteristic
227C2×C3×C4⋊C4C22×C311yescharacteristic
228C2×C3×C4⋊C4C22×C311yescharacteristic
229C2×C3×C22⋊C4—21no—
230C2×C3×C22⋊C4—21no—
231C2×C3×C22⋊C4—21no—
232C2×C3×C22⋊C4—31no—
233C2×C3×C22⋊C4—31no—
234C2×C3×C22⋊C4—31no—
235C2×C3×C22⋊C4—31no—
236C2×C3×C22⋊C4—31no—
237C2×C3×C22⋊C4—31no—
238C2×C3×C22⋊C4—31no—
239C2×C3×C22⋊C4C2×D311yescharacteristic
240C2×C3×C22⋊C4C2×D311yescharacteristic
241C2×C3×C22⋊C4C2×D311yescharacteristic
242C2×C3×C22⋊C4C22×C311yescharacteristic
243C2×C3×C22⋊C4C22×C311yescharacteristic
244C2×C3×C22⋊C4C22×C311yescharacteristic
245C2×C3×C42—31no—
246C2×C3×C42—31no—
247C2×#217C22×C311yescharacteristic
248#940C22×C318yescomplemented
249#939C22×C318yescomplemented
250#930C22×C318yescomplemented
251C4×#67C22×C318yescomplemented
252C2×(C2×D3)⋊C4C22×C311yescharacteristic
253C2×(C2×D3)⋊C4C22×C311yescharacteristic
254C2×(C2×D3)⋊C4C22×C311yescharacteristic
255C2×(C2×D3)⋊C4C22×C311yescharacteristic
256C2×(C2×D3)⋊C4C22×C311yescharacteristic
257C2×(C2×D3)⋊C4C22×C311yescharacteristic
258C2×C4⋊Dic3C22×C311yescharacteristic
259C2×C4⋊Dic3C22×C311yescharacteristic
260C2×Dic3⋊C4C22×C311yescharacteristic
261C2×Dic3⋊C4C22×C311yescharacteristic
262C2×Dic3⋊C4C22×C311yescharacteristic
263C2×Dic3⋊C4C22×C311yescharacteristic
264C2×C4×Dic3C22×C311yescharacteristic
265C2×C4×Dic3C22×C311yescharacteristic
266#895C22×C318yescomplemented
267#894C22×C318yescomplemented
268#892C22×C318yescomplemented
269#889C22×C318yescomplemented
270#886C22×C318yescomplemented
271#884C22×C318yescomplemented
272#884C22×C318yescomplemented
273#884C22×C318yescomplemented
274#883C22×C318yescomplemented
275#67⋊C4C22×C318yescomplemented
276C23×C32—22no—
277C23×C32—22no—
278C23×C32—22no—
279C23×C32—22no—
280C23×C32—22no—
281C23×C32—22no—
282C23×C32C2412yes—
283C23×C32C2412yes—
284C23×C32C2411yescharacteristic
285C22×C3×D3—22no—
286C22×C3×D3—22no—
287C22×C3×D3—22no—
288C22×C3×D3—22no—
289C22×C3×D3—22no—
290C22×C3×D3—22no—
291C22×C3×D3—22no—
292C22×C3×D3—22no—
293C22×C3×D3—22no—
294C22×C3×D3C2412yes—
295C22×C3×D3C2412yes—
296C22×C3×D3C2412yes—
297C32×D4—44no—
298C2×C32×C4—22no—
299C2×C32×C4—22no—
300C2×C32×C4—22no—
301C2×C32×C4—22no—
302C2×C32×C4—22no—
303C2×C32×C4—44no—
304C2×C32×C4C2412yes—
305C2×C32×C4C2412yes—
306C2×C32×C4C2412yes—
307C2×C32×C4C2412yes—
308C2×C32×C4C2412yes—
309C3×#67—28no—
310C3×#67—28no—
311C3×#67—44no—
312C3×#67—44no—
313C3×#67—44no—
314C3×#67—44no—
315C2×C3×Dic3—22no—
316C2×C3×Dic3—22no—
317C2×C3×Dic3—22no—
318C2×C3×Dic3—22no—
319C2×C3×Dic3—44no—
320C2×C3×Dic3#4114yes—
321C2×C3×Dic3C2412yes—
322C2×C3×Dic3C2412yes—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2412yes—
325C2×C3×Dic3C2412yes—
326C3×D12—44no—
327C3×D12—44no—
328C3×D12—44no—
329C3×C4×D3—28no—
330C3×C4×D3—44no—
331C3×C4×D3—44no—
332#540—316no—
333C2×#127—31no—
334C2×#125—31no—
335C2×#123—31no—
336C2×#123—31no—
337C2×#123—31no—
338C2×#123C3×D311yescharacteristic, complemented
339C2×#121—31no—
340C2×#121—31no—
341C2×#121—31no—
342C2×#121—31no—
343C2×#121—31no—
344C2×#121—31no—
345C2×C4×D4—31no—
346C2×C4×D4—31no—
347C2×#117—31no—
348C24×C3—21no—
349C24×C3—21no—
350C24×C3—31no—
351C24×C3—31no—
352C24×C3—31no—
353C24×C3C22×D311yescharacteristic
354C24×C3C22×D311yescharacteristic
355C24×C3C23×C311yescharacteristic
356C24×C3C23×C311yescharacteristic
357C23×D3C23×C311yescharacteristic
358C23×D3C23×C311yescharacteristic
359C23×D3C23×C311yescharacteristic
360C2×C3×D4—24no—
361C2×C3×D4—34no—
362C2×C3×D4—34no—
363C2×C3×D4—34no—
364C2×C3×D4—34no—
365C2×C3×D4—34no—
366C2×C3×D4—34no—
367C2×C3×D4—34no—
368C2×C3×D4—34no—
369C2×C3×D4—34no—
370C2×C3×D4—42no—
371C2×C3×D4—42no—
372C2×C3×D4—44no—
373C2×C3×D4—64no—
374C2×C3×D4—64no—
375C2×C3×D4—122no—
376C2×C3×D4—122no—
377C2×C3×D4—122no—
378C2×C3×D4—122no—
379C2×C3×D4—122no—
380C2×C3×D4—122no—
381C2×C3×D4—122no—
382C2×C3×D4C22×D314yes—
383C2×C3×D4C23×C314yes—
384C22×C3×C4—21no—
385C22×C3×C4—21no—
386C22×C3×C4—21no—
387C22×C3×C4—21no—
388C22×C3×C4—21no—
389C22×C3×C4—24no—
390C22×C3×C4—31no—
391C22×C3×C4—31no—
392C22×C3×C4—31no—
393C22×C3×C4—31no—
394C22×C3×C4—31no—
395C22×C3×C4—34no—
396C22×C3×C4—34no—
397C22×C3×C4—34no—
398C22×C3×C4—34no—
399C22×C3×C4—42no—
400C22×C3×C4—42no—
401C22×C3×C4—44no—
402C22×C3×C4—64no—
403C22×C3×C4—122no—
404C22×C3×C4—122no—
405C22×C3×C4—122no—
406C22×C3×C4C22×D311yescharacteristic
407C22×C3×C4C22×D311yescharacteristic
408C22×C3×C4C22×D311yescharacteristic
409C22×C3×C4C22×D311yescharacteristic
410C22×C3×C4C22×D311yescharacteristic
411C22×C3×C4C22×D314yes—
412C22×C3×C4C23×C311yescharacteristic
413C22×C3×C4C23×C311yescharacteristic
414C22×C3×C4C23×C311yescharacteristic
415C22×C3×C4C23×C311yescharacteristic
416C22×C3×C4C23×C311yescharacteristic
417C22×C3×C4C23×C314yes—
418C2×#67—24no—
419C2×#67—24no—
420C2×#67—42no—
421C2×#67—42no—
422C2×#67—42no—
423C2×#67—42no—
424C2×#67C23×C314yes—
425C2×#67C23×C314yes—
426C2×#67C23×C314yes—
427C2×#67C23×C314yes—
428C2×#67C23×C314yes—
429C2×#67C23×C314yes—
430C22×Dic3—42no—
431C22×Dic3C23×C311yescharacteristic
432C22×Dic3C23×C311yescharacteristic
433C22×Dic3C23×C311yescharacteristic
434C22×Dic3C23×C311yescharacteristic
435C22×Dic3C23×C314yes—
436C22×Dic3C23×C311yescharacteristic
437C2×D12—42no—
438C2×D12—42no—
439C2×D12—42no—
440C2×D12C23×C314yes—
441C2×D12C23×C314yes—
442C2×D12C23×C314yes—
443C2×C4×D3—24no—
444C2×C4×D3—42no—
445C2×C4×D3—42no—
446C2×C4×D3C23×C314yes—
447C2×C4×D3C23×C314yes—
448C2×C4×D3C23×C314yes—
449C3×C4⋊C4—24no—
450C3×C4⋊C4—24no—
451C3×C4⋊C4—34no—
452C3×C4⋊C4—34no—
453C3×C4⋊C4—34no—
454C3×C4⋊C4—34no—
455C3×C4⋊C4—34no—
456C3×C4⋊C4—34no—
457C3×C4⋊C4C22×D314yes—
458C3×C4⋊C4C22×D314yes—
459C3×C4⋊C4C23×C314yes—
460C3×C4⋊C4C23×C314yes—
461C3×C22⋊C4—24no—
462C3×C22⋊C4—24no—
463C3×C22⋊C4—24no—
464C3×C22⋊C4—34no—
465C3×C22⋊C4—34no—
466C3×C22⋊C4—34no—
467C3×C22⋊C4—34no—
468C3×C22⋊C4—34no—
469C3×C22⋊C4—34no—
470C3×C22⋊C4—34no—
471C3×C22⋊C4C22×D314yes—
472C3×C22⋊C4C22×D314yes—
473C3×C22⋊C4C22×D314yes—
474C3×C22⋊C4C23×C314yes—
475C3×C22⋊C4C23×C314yes—
476C3×C22⋊C4C23×C314yes—
477C3×C42—34no—
478C3×C42—34no—
479#217C23×C314yes—
480(C2×D3)⋊C4C23×C314yes—
481(C2×D3)⋊C4C23×C314yes—
482(C2×D3)⋊C4C23×C314yes—
483(C2×D3)⋊C4C23×C314yes—
484(C2×D3)⋊C4C23×C314yes—
485(C2×D3)⋊C4C23×C314yes—
486C4⋊Dic3C23×C314yes—
487C4⋊Dic3C23×C314yes—
488Dic3⋊C4C23×C314yes—
489Dic3⋊C4C23×C314yes—
490Dic3⋊C4C23×C314yes—
491Dic3⋊C4C23×C314yes—
492C4×Dic3C23×C314yes—
493C4×Dic3C23×C314yes—
494C22×C32—22no—
495C22×C32—22no—
496C22×C32—22no—
497C22×C32—22no—
498C22×C32—22no—
499C22×C32—22no—
500C22×C32—44no—
501C22×C32—44no—
502C22×C32C2×#4112yes—
503C22×C32H(5,𝔽2)12yes—
504C22×C32H(5,𝔽2)12yes—
505C22×C32C2511yescharacteristic
506C2×C3×D3—22no—
507C2×C3×D3—22no—
508C2×C3×D3—22no—
509C2×C3×D3—22no—
510C2×C3×D3—22no—
511C2×C3×D3—22no—
512C2×C3×D3—22no—
513C2×C3×D3—22no—
514C2×C3×D3—22no—
515C2×C3×D3—44no—
516C2×C3×D3—44no—
517C2×C3×D3—44no—
518C32×C4—22no—
519C32×C4—22no—
520C32×C4—22no—
521C32×C4—22no—
522C32×C4—22no—
523C3×Dic3—22no—
524C3×Dic3—22no—
525C3×Dic3—22no—
526C3×Dic3—22no—
527C3×Dic3C2×#4114yes—
528C22×D4—31no—
529C22×D4—31no—
530C22×D4—31no—
531C22×D4—31no—
532C22×D4—31no—
533C22×D4—31no—
534C22×D4—31no—
535C22×D4—31no—
536C22×D4—31no—
537C22×D4C2×C3×D311yescharacteristic
538C23×C4—31no—
539C23×C4—31no—
540C23×C4—31no—
541C23×C4—31no—
542C23×C4C2×C3×D311yescharacteristic
543#127—38no—
544#125—38no—
545#123—38no—
546#123—38no—
547#123—38no—
548#123C2×C3×D318yescomplemented
549#121—38no—
550#121—38no—
551#121—38no—
552#121—38no—
553#121—38no—
554#121—38no—
555C4×D4—38no—
556C4×D4—38no—
557#117—38no—
558C2×C4⋊C4—31no—
559C2×C4⋊C4—31no—
560C2×C4⋊C4—31no—
561C2×C4⋊C4—31no—
562C2×C4⋊C4—31no—
563C2×C4⋊C4—31no—
564C2×C4⋊C4C2×C3×D311yescharacteristic
565C2×C4⋊C4C2×C3×D311yescharacteristic
566C2×C22⋊C4—31no—
567C2×C22⋊C4—31no—
568C2×C22⋊C4—31no—
569C2×C22⋊C4—31no—
570C2×C22⋊C4—31no—
571C2×C22⋊C4—31no—
572C2×C22⋊C4—31no—
573C2×C22⋊C4C2×C3×D311yescharacteristic
574C2×C22⋊C4C2×C3×D311yescharacteristic
575C2×C22⋊C4C2×C3×D311yescharacteristic
576C2×C42—31no—
577C2×C42—31no—
578C23×C3—24no—
579C23×C3—22no—
580C23×C3—22no—
581C23×C3—22no—
582C23×C3—22no—
583C23×C3—22no—
584C23×C3—22no—
585C23×C3—22no—
586C23×C3—22no—
587C23×C3—22no—
588C23×C3—22no—
589C23×C3—22no—
590C23×C3—22no—
591C23×C3—21no—
592C23×C3—22no—
593C23×C3—22no—
594C23×C3—32no—
595C23×C3—32no—
596C23×C3—32no—
597C23×C3—42no—
598C23×C3—42no—
599C23×C3—42no—
600C23×C3—42no—
601C23×C3—42no—
602C23×C3—62no—
603C23×C3—62no—
604C23×C3—62no—
605C23×C3—62no—
606C23×C3—62no—
607C23×C3—62no—
608C23×C3—62no—
609C23×C3—62no—
610C23×C3—62no—
611C23×C3C23×D312yes—
612C23×C3C23×D312yes—
613C23×C3C23×D311yescharacteristic
614C23×C3C24×C312yes—
615C23×C3C24×C312yes—
616C23×C3C24×C311yescharacteristic
617C22×D3—22no—
618C22×D3—22no—
619C22×D3—22no—
620C22×D3—22no—
621C22×D3—22no—
622C22×D3—22no—
623C22×D3—22no—
624C22×D3—22no—
625C22×D3—22no—
626C22×D3C24×C312yes—
627C22×D3C24×C312yes—
628C22×D3C24×C312yes—
629C3×D4—44no—
630C3×D4—44no—
631C3×D4—48no—
632C3×D4—68no—
633C3×D4—68no—
634C3×D4—124no—
635C3×D4—124no—
636C3×D4—124no—
637C3×D4—124no—
638C3×D4—124no—
639C3×D4—124no—
640C3×D4—124no—
641C2×C3×C4—22no—
642C2×C3×C4—22no—
643C2×C3×C4—22no—
644C2×C3×C4—22no—
645C2×C3×C4—22no—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—22no—
652C2×C3×C4—22no—
653C2×C3×C4—22no—
654C2×C3×C4—22no—
655C2×C3×C4—22no—
656C2×C3×C4—34no—
657C2×C3×C4—32no—
658C2×C3×C4—32no—
659C2×C3×C4—32no—
660C2×C3×C4—32no—
661C2×C3×C4—32no—
662C2×C3×C4—42no—
663C2×C3×C4—42no—
664C2×C3×C4—42no—
665C2×C3×C4—42no—
666C2×C3×C4—42no—
667C2×C3×C4—44no—
668C2×C3×C4—44no—
669C2×C3×C4—48no—
670C2×C3×C4—68no—
671C2×C3×C4—62no—
672C2×C3×C4—62no—
673C2×C3×C4—62no—
674C2×C3×C4—62no—
675C2×C3×C4—124no—
676C2×C3×C4—124no—
677C2×C3×C4—124no—
678C2×C3×C4C23×D312yes—
679C2×C3×C4C23×D312yes—
680C2×C3×C4C23×D312yes—
681C2×C3×C4C23×D312yes—
682C2×C3×C4C23×D312yes—
683C2×C3×C4C24×C312yes—
684C2×C3×C4C24×C312yes—
685C2×C3×C4C24×C312yes—
686C2×C3×C4C24×C312yes—
687C2×C3×C4C24×C312yes—
688#67—28no—
689#67—28no—
690#67—44no—
691#67—44no—
692#67—44no—
693#67—44no—
694C2×Dic3—22no—
695C2×Dic3—22no—
696C2×Dic3—22no—
697C2×Dic3—22no—
698C2×Dic3—44no—
699C2×Dic3C3×#4114yes—
700C2×Dic3C24×C312yes—
701C2×Dic3C24×C312yes—
702C2×Dic3C24×C312yes—
703C2×Dic3C24×C312yes—
704C2×Dic3C24×C312yes—
705D12—44no—
706D12—44no—
707D12—44no—
708C4×D3—28no—
709C4×D3—44no—
710C4×D3—44no—
711C2×C32—42no—
712C2×C32—42no—
713C2×C32#54014yescomplemented
714C2×C32C22×#4111yescharacteristic
715C2×C32C2×H(5,𝔽2)11yescharacteristic
716C2×C32C2×H(5,𝔽2)11yescharacteristic
717C3×D3—42no—
718C3×D3—42no—
719C3×D3—42no—
720C24—31no—
721C24—31no—
722C24—31no—
723C24C22×C3×D311yescharacteristic
724C24C22×C3×D311yescharacteristic
725C2×D4—34no—
726C2×D4—34no—
727C2×D4—34no—
728C2×D4—34no—
729C2×D4—34no—
730C2×D4—34no—
731C2×D4—34no—
732C2×D4—34no—
733C2×D4—34no—
734C2×D4—42no—
735C2×D4—64no—
736C2×D4—64no—
737C2×D4—122no—
738C2×D4—122no—
739C2×D4—122no—
740C2×D4—122no—
741C2×D4—122no—
742C2×D4—122no—
743C2×D4—122no—
744C2×D4C22×C3×D314yes—
745C22×C4—31no—
746C22×C4—31no—
747C22×C4—31no—
748C22×C4—31no—
749C22×C4—31no—
750C22×C4—34no—
751C22×C4—34no—
752C22×C4—34no—
753C22×C4—34no—
754C22×C4—42no—
755C22×C4—64no—
756C22×C4—122no—
757C22×C4—122no—
758C22×C4—122no—
759C22×C4C22×C3×D311yescharacteristic
760C22×C4C22×C3×D311yescharacteristic
761C22×C4C22×C3×D311yescharacteristic
762C22×C4C22×C3×D311yescharacteristic
763C22×C4C22×C3×D311yescharacteristic
764C22×C4C22×C3×D314yes—
765C4⋊C4—34no—
766C4⋊C4—34no—
767C4⋊C4—34no—
768C4⋊C4—34no—
769C4⋊C4—34no—
770C4⋊C4—34no—
771C4⋊C4C22×C3×D314yes—
772C4⋊C4C22×C3×D314yes—
773C22⋊C4—34no—
774C22⋊C4—34no—
775C22⋊C4—34no—
776C22⋊C4—34no—
777C22⋊C4—34no—
778C22⋊C4—34no—
779C22⋊C4—34no—
780C22⋊C4C22×C3×D314yes—
781C22⋊C4C22×C3×D314yes—
782C22⋊C4C22×C3×D314yes—
783C42—34no—
784C42—34no—
785C22×C3—24no—
786C22×C3—22no—
787C22×C3—22no—
788C22×C3—22no—
789C22×C3—22no—
790C22×C3—22no—
791C22×C3—22no—
792C22×C3—22no—
793C22×C3—22no—
794C22×C3—22no—
795C22×C3—22no—
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—21no—
802C22×C3—42no—
803C22×C3—42no—
804C22×C3—42no—
805C22×C3—42no—
806C22×C3—42no—
807C22×C3—48no—
808C22×C3—44no—
809C22×C3—44no—
810C22×C3—44no—
811C22×C3—44no—
812C22×C3—62no—
813C22×C3—62no—
814C22×C3—62no—
815C22×C3—62no—
816C22×C3—62no—
817C22×C3—62no—
818C22×C3—62no—
819C22×C3—62no—
820C22×C3—62no—
821C22×C3—84no—
822C22×C3—124no—
823C22×C3—124no—
824C22×C3—124no—
825C22×C3#100412yes—
826C22×C3D3×#4112yes—
827C22×C3#100912yes—
828C22×C3C2×C3×#4112yes—
829C22×C3C3×H(5,𝔽2)12yes—
830C22×C3C3×H(5,𝔽2)12yes—
831C22×C3C24×D311yescharacteristic
832C22×C3C25×C311yescharacteristic
833C2×D3—22no—
834C2×D3—22no—
835C2×D3—22no—
836C2×D3—22no—
837C2×D3—22no—
838C2×D3—22no—
839C2×D3—22no—
840C2×D3—22no—
841C2×D3—22no—
842C2×D3—44no—
843C2×D3—44no—
844C2×D3—44no—
845C3×C4—22no—
846C3×C4—22no—
847C3×C4—22no—
848C3×C4—22no—
849C3×C4—22no—
850C3×C4—22no—
851C3×C4—22no—
852C3×C4—22no—
853C3×C4—22no—
854C3×C4—22no—
855C3×C4—34no—
856C3×C4—42no—
857C3×C4—42no—
858C3×C4—42no—
859C3×C4—42no—
860C3×C4—42no—
861C3×C4—62no—
862C3×C4—62no—
863C3×C4—62no—
864C3×C4—62no—
865Dic3—22no—
866Dic3—22no—
867Dic3—22no—
868Dic3—22no—
869Dic3C2×C3×#4114yes—
870C32C2×#54011yescharacteristic, complemented, Sylow
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—32no—
878C23—32no—
879C23—32no—
880C23—62no—
881C23—62no—
882C23—62no—
883C23—62no—
884C23—62no—
885C23—62no—
886C23—62no—
887C23—62no—
888C23—62no—
889C23C23×C3×D312yes—
890C23C23×C3×D312yes—
891C23C23×C3×D311yescharacteristic
892D4—44no—
893D4—68no—
894D4—68no—
895D4—124no—
896D4—124no—
897D4—124no—
898D4—124no—
899D4—124no—
900D4—124no—
901D4—124no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—34no—
908C2×C4—32no—
909C2×C4—32no—
910C2×C4—32no—
911C2×C4—32no—
912C2×C4—32no—
913C2×C4—44no—
914C2×C4—68no—
915C2×C4—62no—
916C2×C4—62no—
917C2×C4—62no—
918C2×C4—62no—
919C2×C4—124no—
920C2×C4—124no—
921C2×C4—124no—
922C2×C4C23×C3×D312yes—
923C2×C4C23×C3×D312yes—
924C2×C4C23×C3×D312yes—
925C2×C4C23×C3×D312yes—
926C2×C4C23×C3×D312yes—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—24no—
931C2×C3—44no—
932C2×C3—42no—
933C2×C3—42no—
934C2×C3—42no—
935C2×C3—42no—
936C2×C3—82no—
937C2×C3—122no—
938C2×C3—122no—
939C2×C3—122no—
940C2×C3#566314yesdirect product factor
941C2×C3C3×#54014yescomplemented
942C2×C3C2×#100411yescharacteristic
943C2×C3C2×D3×#4111yescharacteristic
944C2×C3C2×#100911yescharacteristic
945C2×C3C22×C3×#4111yescharacteristic
946C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
947C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
948D3—42no—
949D3—42no—
950D3—42no—
951C22—22no—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—44no—
958C22—44no—
959C22—62no—
960C22—62no—
961C22—62no—
962C22—62no—
963C22—62no—
964C22—62no—
965C22—62no—
966C22—62no—
967C22—62no—
968C22—124no—
969C22—124no—
970C22—124no—
971C22C3×#100412yes—
972C22C3×D3×#4112yes—
973C22C3×#100912yes—
974C22C24×C3×D311yescharacteristic
975C4—22no—
976C4—22no—
977C4—22no—
978C4—22no—
979C4—22no—
980C4—34no—
981C4—62no—
982C4—62no—
983C4—62no—
984C4—62no—
985C3—21no—
986C3C2×#566311yescharacteristic, direct product factor
987C3C2×C3×#54011yescharacteristic, complemented
988C2—42no—
989C2—42no—
990C2—122no—
991C2—122no—
992C2—122no—
993C2C3×#566314yesdirect product factor
994C2C2×C3×#100411yescharacteristic
995C2C2×C3×D3×#4111yescharacteristic
996C2C2×C3×#100911yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×#123C2
socleC23×C32C24
hypercenterC2×C3×#123D3
hypocenterC3C2×C3×#540
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#123

Complements

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

NH ≅ G/Ntype
1. C2×C32×#123C2semidirect
2. C2×C3×#940C2semidirect
3. C2×C3×#939C2semidirect
4. C2×C3×#930C2semidirect
5. C2×C3×C4×#67C2semidirect
6. C3×#5663C2direct (N × H)
7. C2×C3×#895C2semidirect
8. C2×C3×#894C2semidirect
9. C2×C3×#892C2semidirect
10. C2×C3×#889C2semidirect
11. C2×C3×#886C2semidirect
12. C2×C3×#884C2semidirect
13. C2×C3×#884C2semidirect
14. C2×C3×#884C2semidirect
15. C2×C3×#883C2semidirect
16. C2×C3×#67⋊C4C2semidirect
18. C2×#5663C3direct (N × H)
34. C32×#123C22semidirect
41. C3×#940C22semidirect
42. C3×#939C22semidirect
43. C3×#930C22semidirect
44. C3×C4×#67C22semidirect
59. C3×#895C22semidirect
60. C3×#894C22semidirect
61. C3×#892C22semidirect
62. C3×#889C22semidirect
63. C3×#886C22semidirect
64. C3×#884C22semidirect
65. C3×#884C22semidirect
66. C3×#884C22semidirect
67. C3×#883C22semidirect
68. C3×#67⋊C4C22semidirect
76. C2×C3×#123D3semidirect
77. C2×C3×#123C2×C3semidirect
87. C2×#940C2×C3semidirect
88. C2×#939C2×C3semidirect
89. C2×#930C2×C3semidirect
90. C2×C4×#67C2×C3semidirect
91. #5663C2×C3direct (N × H)
92. C2×#895C2×C3semidirect
93. C2×#894C2×C3semidirect
94. C2×#892C2×C3semidirect
95. C2×#889C2×C3semidirect
96. C2×#886C2×C3semidirect
97. C2×#884C2×C3semidirect
98. C2×#884C2×C3semidirect
99. C2×#884C2×C3semidirect
100. C2×#883C2×C3semidirect
101. C2×#67⋊C4C2×C3semidirect
206. C3×#123C2×D3semidirect
207. C3×#123C22×C3semidirect
248. #940C22×C3semidirect
249. #939C22×C3semidirect
250. #930C22×C3semidirect
251. C4×#67C22×C3semidirect
266. #895C22×C3semidirect
267. #894C22×C3semidirect
268. #892C22×C3semidirect
269. #889C22×C3semidirect
270. #886C22×C3semidirect
271. #884C22×C3semidirect
272. #884C22×C3semidirect
273. #884C22×C3semidirect
274. #883C22×C3semidirect
275. #67⋊C4C22×C3semidirect
338. C2×#123C3×D3semidirect
548. #123C2×C3×D3semidirect
713. C2×C32#540semidirect
870. C32C2×#540semidirect
940. C2×C3#5663direct (N × H)
941. C2×C3C3×#540semidirect
986. C3C2×#5663direct (N × H)
987. C3C2×C3×#540semidirect
993. C2C3×#5663direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1232
C2×C3×#9402
C2×C3×#9392
C2×C3×#9302
C2×C3×C4×#672
C3×#56632
C2×C3×#8952
C2×C3×#8942
C2×C3×#8922
C2×C3×#8892
C2×C3×#8862
C2×C3×#8842
C2×C3×#8832
C2×C3×#67⋊C42
C2×C3×#5403
C2×#56633