Finite Group Databasebeta

← C2×C3×#5661 #11903099

Subgroups — C2×C3×#5661 #11903099

Order 1152.

2675 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#123C211yesmaximal, characteristic, complemented
2C2×C3×#939C211yesmaximal, characteristic, complemented
3C2×C3×#938C211yesmaximal, characteristic, complemented
4C2×C3×C4×#67C211yesmaximal, characteristic, complemented
5C2×C3×C4×#67C211yesmaximal, characteristic, complemented
6C3×#5661C2116yesmaximal, direct product factor
7C2×C3×#898C211yesmaximal, characteristic, complemented
8C2×C3×#893C211yesmaximal, characteristic, complemented
9C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
10C2×C3×#889C211yesmaximal, characteristic, complemented
11C2×C3×#884C211yesmaximal, characteristic, complemented
12C2×C3×#884C211yesmaximal, characteristic, complemented
13C2×C3×#883C211yesmaximal, characteristic, complemented
14C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
15C2×C3×#879C211yesmaximal, characteristic, complemented
16C2×C3×#877C211yesmaximal, characteristic, complemented
17C2×C3×#553—31nomaximal
18C2×#5661C311yesmaximal, characteristic, direct product factor
19C22×C32×D4C2211yescharacteristic
20C23×C32×C4C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C23×C3×Dic3C2211yescharacteristic
26C22×C3×D12C2211yescharacteristic
27C22×C3×C4×D3C2211yescharacteristic
28C22×C3×C4×D3C2211yescharacteristic
29C22×C3×C4×D3C2211yescharacteristic
30C22×C3×C4×D3C2211yescharacteristic
31C32×#123C2218yescomplemented
32C2×C32×C4⋊C4C2211yescharacteristic
33C2×C32×C4⋊C4C2211yescharacteristic
34C2×C32×C22⋊C4C2211yescharacteristic
35C2×C32×C22⋊C4C2211yescharacteristic
36C2×C32×C22⋊C4C2211yescharacteristic
37C2×C3×#217C2211yescharacteristic
38C2×C3×#217C2211yescharacteristic
39C2×C3×#217C2211yescharacteristic
40C3×#939C2218yescomplemented
41C3×#938C2218yescomplemented
42C3×C4×#67C2218yescomplemented
43C3×C4×#67C2218yescomplemented
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic
45C2×C3×(C2×D3)⋊C4C2211yescharacteristic
46C2×C3×(C2×D3)⋊C4C2211yescharacteristic
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic
48C2×C3×C4⋊Dic3C2211yescharacteristic
49C2×C3×C4⋊Dic3C2211yescharacteristic
50C2×C3×Dic3⋊C4C2211yescharacteristic
51C2×C3×Dic3⋊C4C2211yescharacteristic
52C2×C3×Dic3⋊C4C2211yescharacteristic
53C2×C3×Dic3⋊C4C2211yescharacteristic
54C2×C3×Dic3⋊C4C2211yescharacteristic
55C2×C3×Dic3⋊C4C2211yescharacteristic
56C2×C3×C4×Dic3C2211yescharacteristic
57C2×C3×C4×Dic3C2211yescharacteristic
58C2×C3×C4×Dic3C2211yescharacteristic
59C3×#898C2218yescomplemented
60C3×#893C2218yescomplemented
61C3×D3×C4⋊C4C2218yescomplemented
62C3×#889C2218yescomplemented
63C3×#884C2218yescomplemented
64C3×#884C2218yescomplemented
65C3×#883C2218yescomplemented
66C3×#67⋊C4C2218yescomplemented
67C3×#879C2218yescomplemented
68C3×#877C2218yescomplemented
69C3×#553—316no—
70C2×C3×#126—31no—
71C2×C3×#126—31no—
72C2×C3×#125—31no—
73C2×C3×#123—21no—
74C2×C3×#123—31no—
75C2×C3×#123D311yescharacteristic, complemented
76C2×C3×#123C2×C311yescharacteristic, complemented
77C2×C3×#121—31no—
78C2×C3×#121—31no—
79C2×C3×#121—31no—
80C2×C3×#121—31no—
81C2×C3×C4×D4—31no—
82C2×C3×C4×D4—31no—
83C2×C3×C4×D4—31no—
84C2×C3×C4×D4—31no—
85C2×C3×#117—31no—
86C22×C3×C4⋊C4—31no—
87C2×#939C2×C311yescharacteristic, complemented
88C2×#938C2×C311yescharacteristic, complemented
89C2×C4×#67C2×C311yescharacteristic, complemented
90C2×C4×#67C2×C311yescharacteristic, complemented
91#5661C2×C3116yesdirect product factor
92C2×#898C2×C311yescharacteristic, complemented
93C2×#893C2×C311yescharacteristic, complemented
94C2×D3×C4⋊C4C2×C311yescharacteristic, complemented
95C2×#889C2×C311yescharacteristic, complemented
96C2×#884C2×C311yescharacteristic, complemented
97C2×#884C2×C311yescharacteristic, complemented
98C2×#883C2×C311yescharacteristic, complemented
99C2×#67⋊C4C2×C311yescharacteristic, complemented
100C2×#879C2×C311yescharacteristic, complemented
101C2×#877C2×C311yescharacteristic, complemented
102C24×C32C2311yescharacteristic
103C24×C32C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C2×C32×D4—42no—
107C2×C32×D4C2314yes—
108C22×C32×C4—42no—
109C22×C32×C4C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C22×C32×C4C2311yescharacteristic
112C22×C32×C4C2311yescharacteristic
113C22×C32×C4C2311yescharacteristic
114C22×C32×C4C2314yes—
115C2×C3×#67—24no—
116C2×C3×#67—24no—
117C2×C3×#67—24no—
118C2×C3×#67—42no—
119C2×C3×#67C2314yes—
120C2×C3×#67C2314yes—
121C2×C3×#67C2314yes—
122C2×C3×#67C2314yes—
123C22×C3×Dic3—24no—
124C22×C3×Dic3C2314yes—
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C2×C3×D12—24no—
132C2×C3×D12C2314yes—
133C2×C3×C4×D3—24no—
134C2×C3×C4×D3—42no—
135C2×C3×C4×D3—42no—
136C2×C3×C4×D3—42no—
137C2×C3×C4×D3C2314yes—
138C2×C3×C4×D3C2314yes—
139C2×C3×C4×D3C2314yes—
140C2×C3×C4×D3C2314yes—
141C32×C4⋊C4C2314yes—
142C32×C4⋊C4C2314yes—
143C32×C22⋊C4C2314yes—
144C32×C22⋊C4C2314yes—
145C32×C22⋊C4C2314yes—
146C3×#217C2314yes—
147C3×#217C2314yes—
148C3×#217C2314yes—
149C3×(C2×D3)⋊C4C2314yes—
150C3×(C2×D3)⋊C4C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×C4⋊Dic3C2314yes—
154C3×C4⋊Dic3C2314yes—
155C3×Dic3⋊C4C2314yes—
156C3×Dic3⋊C4C2314yes—
157C3×Dic3⋊C4C2314yes—
158C3×Dic3⋊C4C2314yes—
159C3×Dic3⋊C4C2314yes—
160C3×Dic3⋊C4C2314yes—
161C3×C4×Dic3C2314yes—
162C3×C4×Dic3C2314yes—
163C3×C4×Dic3C2314yes—
164C2×#553—31noSylow
165C22×C3×D4—21no—
166C22×C3×D4—31no—
167C22×C3×D4—31no—
168C22×C3×D4—31no—
169C22×C3×D4—31no—
170C22×C3×D4—31no—
171C22×C3×D4C2×D311yescharacteristic
172C22×C3×D4C22×C311yescharacteristic
173C23×C3×C4—21no—
174C23×C3×C4—31no—
175C23×C3×C4—31no—
176C23×C3×C4—31no—
177C23×C3×C4—31no—
178C23×C3×C4—31no—
179C23×C3×C4C2×D311yescharacteristic
180C23×C3×C4C22×C311yescharacteristic
181C22×#67C22×C311yescharacteristic
182C22×#67C22×C311yescharacteristic
183C22×#67C22×C311yescharacteristic
184C22×#67C22×C311yescharacteristic
185C23×Dic3C22×C311yescharacteristic
186C22×D12C22×C311yescharacteristic
187C22×C4×D3C22×C311yescharacteristic
188C22×C4×D3C22×C311yescharacteristic
189C22×C4×D3C22×C311yescharacteristic
190C22×C4×D3C22×C311yescharacteristic
191C3×#126—38no—
192C3×#126—38no—
193C3×#125—38no—
194C3×#123—28no—
195C3×#123—38no—
196C3×#123C2×D318yescomplemented
197C3×#123C22×C318yescomplemented
198C3×#121—38no—
199C3×#121—38no—
200C3×#121—38no—
201C3×#121—38no—
202C3×C4×D4—38no—
203C3×C4×D4—38no—
204C3×C4×D4—38no—
205C3×C4×D4—38no—
206C3×#117—38no—
207C2×C3×C4⋊C4—21no—
208C2×C3×C4⋊C4—21no—
209C2×C3×C4⋊C4—31no—
210C2×C3×C4⋊C4—31no—
211C2×C3×C4⋊C4—31no—
212C2×C3×C4⋊C4—31no—
213C2×C3×C4⋊C4—31no—
214C2×C3×C4⋊C4—31no—
215C2×C3×C4⋊C4—31no—
216C2×C3×C4⋊C4—31no—
217C2×C3×C4⋊C4—38no—
218C2×C3×C4⋊C4C2×D311yescharacteristic
219C2×C3×C4⋊C4C2×D311yescharacteristic
220C2×C3×C4⋊C4C22×C311yescharacteristic
221C2×C3×C4⋊C4C22×C311yescharacteristic
222C2×C3×C22⋊C4—21no—
223C2×C3×C22⋊C4—21no—
224C2×C3×C22⋊C4—21no—
225C2×C3×C22⋊C4—31no—
226C2×C3×C22⋊C4—31no—
227C2×C3×C22⋊C4—31no—
228C2×C3×C22⋊C4—31no—
229C2×C3×C22⋊C4—31no—
230C2×C3×C22⋊C4—31no—
231C2×C3×C22⋊C4—31no—
232C2×C3×C22⋊C4C2×D311yescharacteristic
233C2×C3×C22⋊C4C2×D311yescharacteristic
234C2×C3×C22⋊C4C2×D311yescharacteristic
235C2×C3×C22⋊C4C22×C311yescharacteristic
236C2×C3×C22⋊C4C22×C311yescharacteristic
237C2×C3×C22⋊C4C22×C311yescharacteristic
238C2×C3×C42—31no—
239C2×C3×C42—31no—
240C2×C3×C42—31no—
241C2×#217C22×C311yescharacteristic
242C2×#217C22×C311yescharacteristic
243C2×#217C22×C311yescharacteristic
244#939C22×C318yescomplemented
245#938C22×C318yescomplemented
246C4×#67C22×C318yescomplemented
247C4×#67C22×C318yescomplemented
248C2×(C2×D3)⋊C4C22×C311yescharacteristic
249C2×(C2×D3)⋊C4C22×C311yescharacteristic
250C2×(C2×D3)⋊C4C22×C311yescharacteristic
251C2×(C2×D3)⋊C4C22×C311yescharacteristic
252C2×C4⋊Dic3C22×C311yescharacteristic
253C2×C4⋊Dic3C22×C311yescharacteristic
254C2×Dic3⋊C4C22×C311yescharacteristic
255C2×Dic3⋊C4C22×C311yescharacteristic
256C2×Dic3⋊C4C22×C311yescharacteristic
257C2×Dic3⋊C4C22×C311yescharacteristic
258C2×Dic3⋊C4C22×C311yescharacteristic
259C2×Dic3⋊C4C22×C311yescharacteristic
260C2×C4×Dic3C22×C311yescharacteristic
261C2×C4×Dic3C22×C311yescharacteristic
262C2×C4×Dic3C22×C311yescharacteristic
263#898C22×C318yescomplemented
264#893C22×C318yescomplemented
265D3×C4⋊C4C22×C318yescomplemented
266#889C22×C318yescomplemented
267#884C22×C318yescomplemented
268#884C22×C318yescomplemented
269#883C22×C318yescomplemented
270#67⋊C4C22×C318yescomplemented
271#879C22×C318yescomplemented
272#877C22×C318yescomplemented
273C23×C32—22no—
274C23×C32—22no—
275C23×C32—22no—
276C23×C32—22no—
277C23×C32—22no—
278C23×C32—22no—
279C23×C32C2412yes—
280C23×C32C2412yes—
281C23×C32C2411yescharacteristic
282C22×C3×D3—22no—
283C22×C3×D3—22no—
284C22×C3×D3—22no—
285C22×C3×D3—22no—
286C22×C3×D3—22no—
287C22×C3×D3#4114yes—
288C22×C3×D3C2412yes—
289C22×C3×D3C2412yes—
290C32×D4—44no—
291C2×C32×C4—22no—
292C2×C32×C4—22no—
293C2×C32×C4—22no—
294C2×C32×C4—22no—
295C2×C32×C4—22no—
296C2×C32×C4—44no—
297C2×C32×C4C2412yes—
298C2×C32×C4C2412yes—
299C2×C32×C4C2412yes—
300C2×C32×C4C2412yes—
301C2×C32×C4C2412yes—
302C3×#67—28no—
303C3×#67—28no—
304C3×#67—28no—
305C3×#67—44no—
306C2×C3×Dic3—22no—
307C2×C3×Dic3—22no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—22no—
310C2×C3×Dic3—22no—
311C2×C3×Dic3—28no—
312C2×C3×Dic3#4114yes—
313C2×C3×Dic3C2412yes—
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2412yes—
316C2×C3×Dic3C2412yes—
317C2×C3×Dic3C2412yes—
318C2×C3×Dic3C2412yes—
319C3×D12—28no—
320C3×C4×D3—28no—
321C3×C4×D3—44no—
322C3×C4×D3—44no—
323C3×C4×D3—44no—
324#553—316no—
325C2×#126—31no—
326C2×#126—31no—
327C2×#125—31no—
328C2×#123—31no—
329C2×#123C3×D311yescharacteristic, complemented
330C2×#121—31no—
331C2×#121—31no—
332C2×#121—31no—
333C2×#121—31no—
334C2×C4×D4—31no—
335C2×C4×D4—31no—
336C2×C4×D4—31no—
337C2×C4×D4—31no—
338C2×#117—31no—
339C22×C4⋊C4—31no—
340C24×C3—21no—
341C24×C3—21no—
342C24×C3—31no—
343C24×C3—31no—
344C24×C3C22×D311yescharacteristic
345C24×C3C22×D311yescharacteristic
346C24×C3C23×C311yescharacteristic
347C24×C3C23×C311yescharacteristic
348C23×D3C23×C311yescharacteristic
349C23×D3C23×C311yescharacteristic
350C2×C3×D4—24no—
351C2×C3×D4—34no—
352C2×C3×D4—34no—
353C2×C3×D4—34no—
354C2×C3×D4—34no—
355C2×C3×D4—34no—
356C2×C3×D4—42no—
357C2×C3×D4—42no—
358C2×C3×D4—44no—
359C2×C3×D4—64no—
360C2×C3×D4—64no—
361C2×C3×D4—64no—
362C2×C3×D4—64no—
363C2×C3×D4—122no—
364C2×C3×D4C22×D314yes—
365C2×C3×D4C23×C314yes—
366C22×C3×C4—21no—
367C22×C3×C4—21no—
368C22×C3×C4—21no—
369C22×C3×C4—21no—
370C22×C3×C4—21no—
371C22×C3×C4—24no—
372C22×C3×C4—31no—
373C22×C3×C4—34no—
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—31no—
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—34no—
380C22×C3×C4—34no—
381C22×C3×C4—34no—
382C22×C3×C4—34no—
383C22×C3×C4—42no—
384C22×C3×C4—42no—
385C22×C3×C4—44no—
386C22×C3×C4—64no—
387C22×C3×C4—64no—
388C22×C3×C4—122no—
389C22×C3×C4—122no—
390C22×C3×C4—122no—
391C22×C3×C4C22×D311yescharacteristic
392C22×C3×C4C22×D311yescharacteristic
393C22×C3×C4C22×D311yescharacteristic
394C22×C3×C4C22×D311yescharacteristic
395C22×C3×C4C22×D311yescharacteristic
396C22×C3×C4C22×D314yes—
397C22×C3×C4C23×C311yescharacteristic
398C22×C3×C4C23×C311yescharacteristic
399C22×C3×C4C23×C311yescharacteristic
400C22×C3×C4C23×C311yescharacteristic
401C22×C3×C4C23×C311yescharacteristic
402C22×C3×C4C23×C314yes—
403C2×#67—24no—
404C2×#67—24no—
405C2×#67—24no—
406C2×#67—42no—
407C2×#67C23×C314yes—
408C2×#67C23×C314yes—
409C2×#67C23×C314yes—
410C2×#67C23×C314yes—
411C22×Dic3—24no—
412C22×Dic3C23×C314yes—
413C22×Dic3C23×C311yescharacteristic
414C22×Dic3C23×C311yescharacteristic
415C22×Dic3C23×C311yescharacteristic
416C22×Dic3C23×C311yescharacteristic
417C22×Dic3C23×C311yescharacteristic
418C22×Dic3C23×C311yescharacteristic
419C2×D12—24no—
420C2×D12C23×C314yes—
421C2×C4×D3—24no—
422C2×C4×D3—42no—
423C2×C4×D3—42no—
424C2×C4×D3—42no—
425C2×C4×D3C23×C314yes—
426C2×C4×D3C23×C314yes—
427C2×C4×D3C23×C314yes—
428C2×C4×D3C23×C314yes—
429C3×C4⋊C4—24no—
430C3×C4⋊C4—24no—
431C3×C4⋊C4—34no—
432C3×C4⋊C4—34no—
433C3×C4⋊C4—34no—
434C3×C4⋊C4—34no—
435C3×C4⋊C4—34no—
436C3×C4⋊C4—34no—
437C3×C4⋊C4—34no—
438C3×C4⋊C4—34no—
439C3×C4⋊C4C22×D314yes—
440C3×C4⋊C4C22×D314yes—
441C3×C4⋊C4C23×C314yes—
442C3×C4⋊C4C23×C314yes—
443C3×C22⋊C4—24no—
444C3×C22⋊C4—24no—
445C3×C22⋊C4—24no—
446C3×C22⋊C4—34no—
447C3×C22⋊C4—34no—
448C3×C22⋊C4—34no—
449C3×C22⋊C4—34no—
450C3×C22⋊C4—34no—
451C3×C22⋊C4—34no—
452C3×C22⋊C4—34no—
453C3×C22⋊C4C22×D314yes—
454C3×C22⋊C4C22×D314yes—
455C3×C22⋊C4C22×D314yes—
456C3×C22⋊C4C23×C314yes—
457C3×C22⋊C4C23×C314yes—
458C3×C22⋊C4C23×C314yes—
459C3×C42—34no—
460C3×C42—34no—
461C3×C42—34no—
462#217C23×C314yes—
463#217C23×C314yes—
464#217C23×C314yes—
465(C2×D3)⋊C4C23×C314yes—
466(C2×D3)⋊C4C23×C314yes—
467(C2×D3)⋊C4C23×C314yes—
468(C2×D3)⋊C4C23×C314yes—
469C4⋊Dic3C23×C314yes—
470C4⋊Dic3C23×C314yes—
471Dic3⋊C4C23×C314yes—
472Dic3⋊C4C23×C314yes—
473Dic3⋊C4C23×C314yes—
474Dic3⋊C4C23×C314yes—
475Dic3⋊C4C23×C314yes—
476Dic3⋊C4C23×C314yes—
477C4×Dic3C23×C314yes—
478C4×Dic3C23×C314yes—
479C4×Dic3C23×C314yes—
480C22×C32—22no—
481C22×C32—22no—
482C22×C32—22no—
483C22×C32—22no—
484C22×C32—22no—
485C22×C32—22no—
486C22×C32—44no—
487C22×C32—44no—
488C22×C32C2×#4112yes—
489C22×C32C2×#4112yes—
490C22×C32H(5,𝔽2)12yes—
491C22×C32C2511yescharacteristic
492C2×C3×D3—28no—
493C2×C3×D3—22no—
494C2×C3×D3—22no—
495C2×C3×D3—22no—
496C2×C3×D3—22no—
497C2×C3×D3—22no—
498C2×C3×D3—44no—
499C2×C3×D3C2×#4114yes—
500C32×C4—22no—
501C32×C4—22no—
502C32×C4—22no—
503C32×C4—22no—
504C32×C4—22no—
505C3×Dic3—22no—
506C3×Dic3—22no—
507C3×Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—22no—
510C3×Dic3C2×#4114yes—
511C22×D4—31no—
512C22×D4—31no—
513C22×D4—31no—
514C22×D4—31no—
515C22×D4—31no—
516C22×D4C2×C3×D311yescharacteristic
517C23×C4—31no—
518C23×C4—31no—
519C23×C4—31no—
520C23×C4—31no—
521C23×C4—31no—
522C23×C4C2×C3×D311yescharacteristic
523#126—38no—
524#126—38no—
525#125—38no—
526#123—38no—
527#123C2×C3×D318yescomplemented
528#121—38no—
529#121—38no—
530#121—38no—
531#121—38no—
532C4×D4—38no—
533C4×D4—38no—
534C4×D4—38no—
535C4×D4—38no—
536#117—38no—
537C2×C4⋊C4—31no—
538C2×C4⋊C4—31no—
539C2×C4⋊C4—31no—
540C2×C4⋊C4—31no—
541C2×C4⋊C4—31no—
542C2×C4⋊C4—31no—
543C2×C4⋊C4—31no—
544C2×C4⋊C4—31no—
545C2×C4⋊C4—38no—
546C2×C4⋊C4C2×C3×D311yescharacteristic
547C2×C4⋊C4C2×C3×D311yescharacteristic
548C2×C22⋊C4—31no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—31no—
552C2×C22⋊C4—31no—
553C2×C22⋊C4—31no—
554C2×C22⋊C4—31no—
555C2×C22⋊C4C2×C3×D311yescharacteristic
556C2×C22⋊C4C2×C3×D311yescharacteristic
557C2×C22⋊C4C2×C3×D311yescharacteristic
558C2×C42—31no—
559C2×C42—31no—
560C2×C42—31no—
561C23×C3—24no—
562C23×C3—22no—
563C23×C3—22no—
564C23×C3—22no—
565C23×C3—22no—
566C23×C3—22no—
567C23×C3—22no—
568C23×C3—22no—
569C23×C3—22no—
570C23×C3—22no—
571C23×C3—22no—
572C23×C3—22no—
573C23×C3—22no—
574C23×C3—21no—
575C23×C3—22no—
576C23×C3—22no—
577C23×C3—34no—
578C23×C3—32no—
579C23×C3—32no—
580C23×C3—42no—
581C23×C3—42no—
582C23×C3—42no—
583C23×C3—42no—
584C23×C3—42no—
585C23×C3—62no—
586C23×C3—62no—
587C23×C3—62no—
588C23×C3—62no—
589C23×C3—62no—
590C23×C3C23×D312yes—
591C23×C3C23×D312yes—
592C23×C3C23×D311yescharacteristic
593C23×C3C24×C312yes—
594C23×C3C24×C312yes—
595C23×C3C24×C311yescharacteristic
596C22×D3—22no—
597C22×D3—22no—
598C22×D3—22no—
599C22×D3—22no—
600C22×D3—22no—
601C22×D3C3×#4114yes—
602C22×D3C24×C312yes—
603C22×D3C24×C312yes—
604C3×D4—44no—
605C3×D4—44no—
606C3×D4—48no—
607C3×D4—68no—
608C3×D4—68no—
609C3×D4—68no—
610C3×D4—68no—
611C3×D4—124no—
612C2×C3×C4—22no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—22no—
617C2×C3×C4—22no—
618C2×C3×C4—22no—
619C2×C3×C4—22no—
620C2×C3×C4—22no—
621C2×C3×C4—22no—
622C2×C3×C4—22no—
623C2×C3×C4—22no—
624C2×C3×C4—22no—
625C2×C3×C4—22no—
626C2×C3×C4—22no—
627C2×C3×C4—34no—
628C2×C3×C4—32no—
629C2×C3×C4—32no—
630C2×C3×C4—32no—
631C2×C3×C4—32no—
632C2×C3×C4—32no—
633C2×C3×C4—32no—
634C2×C3×C4—42no—
635C2×C3×C4—42no—
636C2×C3×C4—42no—
637C2×C3×C4—42no—
638C2×C3×C4—42no—
639C2×C3×C4—44no—
640C2×C3×C4—44no—
641C2×C3×C4—48no—
642C2×C3×C4—68no—
643C2×C3×C4—68no—
644C2×C3×C4—62no—
645C2×C3×C4—62no—
646C2×C3×C4—62no—
647C2×C3×C4—62no—
648C2×C3×C4—62no—
649C2×C3×C4—124no—
650C2×C3×C4—124no—
651C2×C3×C4—124no—
652C2×C3×C4C23×D312yes—
653C2×C3×C4C23×D312yes—
654C2×C3×C4C23×D312yes—
655C2×C3×C4C23×D312yes—
656C2×C3×C4C23×D312yes—
657C2×C3×C4C24×C312yes—
658C2×C3×C4C24×C312yes—
659C2×C3×C4C24×C312yes—
660C2×C3×C4C24×C312yes—
661C2×C3×C4C24×C312yes—
662#67—28no—
663#67—28no—
664#67—28no—
665#67—44no—
666C2×Dic3—22no—
667C2×Dic3—22no—
668C2×Dic3—22no—
669C2×Dic3—22no—
670C2×Dic3—22no—
671C2×Dic3—28no—
672C2×Dic3C3×#4114yes—
673C2×Dic3C24×C312yes—
674C2×Dic3C24×C312yes—
675C2×Dic3C24×C312yes—
676C2×Dic3C24×C312yes—
677C2×Dic3C24×C312yes—
678C2×Dic3C24×C312yes—
679D12—28no—
680C4×D3—28no—
681C4×D3—44no—
682C4×D3—44no—
683C4×D3—44no—
684C2×C32—42no—
685C2×C32—42no—
686C2×C32#55314yescomplemented
687C2×C32C22×#4111yescharacteristic
688C2×C32C22×#4111yescharacteristic
689C2×C32C2×H(5,𝔽2)11yescharacteristic
690C3×D3—24no—
691C3×D3—42no—
692C24—31no—
693C24—31no—
694C24C22×C3×D311yescharacteristic
695C24C22×C3×D311yescharacteristic
696C2×D4—34no—
697C2×D4—34no—
698C2×D4—34no—
699C2×D4—34no—
700C2×D4—34no—
701C2×D4—42no—
702C2×D4—64no—
703C2×D4—64no—
704C2×D4—64no—
705C2×D4—64no—
706C2×D4—122no—
707C2×D4C22×C3×D314yes—
708C22×C4—31no—
709C22×C4—31no—
710C22×C4—31no—
711C22×C4—31no—
712C22×C4—31no—
713C22×C4—31no—
714C22×C4—34no—
715C22×C4—34no—
716C22×C4—34no—
717C22×C4—34no—
718C22×C4—34no—
719C22×C4—42no—
720C22×C4—64no—
721C22×C4—64no—
722C22×C4—122no—
723C22×C4—122no—
724C22×C4—122no—
725C22×C4C22×C3×D311yescharacteristic
726C22×C4C22×C3×D311yescharacteristic
727C22×C4C22×C3×D311yescharacteristic
728C22×C4C22×C3×D311yescharacteristic
729C22×C4C22×C3×D311yescharacteristic
730C22×C4C22×C3×D314yes—
731C4⋊C4—34no—
732C4⋊C4—34no—
733C4⋊C4—34no—
734C4⋊C4—34no—
735C4⋊C4—34no—
736C4⋊C4—34no—
737C4⋊C4—34no—
738C4⋊C4—34no—
739C4⋊C4C22×C3×D314yes—
740C4⋊C4C22×C3×D314yes—
741C22⋊C4—34no—
742C22⋊C4—34no—
743C22⋊C4—34no—
744C22⋊C4—34no—
745C22⋊C4—34no—
746C22⋊C4—34no—
747C22⋊C4—34no—
748C22⋊C4C22×C3×D314yes—
749C22⋊C4C22×C3×D314yes—
750C22⋊C4C22×C3×D314yes—
751C42—34no—
752C42—34no—
753C42—34no—
754C22×C3—24no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—22no—
758C22×C3—22no—
759C22×C3—22no—
760C22×C3—22no—
761C22×C3—22no—
762C22×C3—22no—
763C22×C3—22no—
764C22×C3—22no—
765C22×C3—22no—
766C22×C3—22no—
767C22×C3—22no—
768C22×C3—22no—
769C22×C3—22no—
770C22×C3—21no—
771C22×C3—34no—
772C22×C3—42no—
773C22×C3—42no—
774C22×C3—42no—
775C22×C3—42no—
776C22×C3—42no—
777C22×C3—48no—
778C22×C3—44no—
779C22×C3—44no—
780C22×C3—44no—
781C22×C3—44no—
782C22×C3—68no—
783C22×C3—62no—
784C22×C3—62no—
785C22×C3—62no—
786C22×C3—62no—
787C22×C3—62no—
788C22×C3—84no—
789C22×C3—124no—
790C22×C3#100412yes—
791C22×C3D3×#4112yes—
792C22×C3D3×#4112yes—
793C22×C3C2×C3×#4112yes—
794C22×C3C2×C3×#4112yes—
795C22×C3C3×H(5,𝔽2)12yes—
796C22×C3C24×D311yescharacteristic
797C22×C3C25×C311yescharacteristic
798C2×D3—22no—
799C2×D3—22no—
800C2×D3—28no—
801C2×D3—22no—
802C2×D3—22no—
803C2×D3—22no—
804C2×D3—44no—
805C2×D3C2×C3×#4114yes—
806C3×C4—22no—
807C3×C4—22no—
808C3×C4—22no—
809C3×C4—22no—
810C3×C4—22no—
811C3×C4—22no—
812C3×C4—22no—
813C3×C4—22no—
814C3×C4—22no—
815C3×C4—22no—
816C3×C4—34no—
817C3×C4—42no—
818C3×C4—42no—
819C3×C4—42no—
820C3×C4—42no—
821C3×C4—42no—
822C3×C4—62no—
823C3×C4—62no—
824C3×C4—62no—
825C3×C4—62no—
826C3×C4—62no—
827Dic3—22no—
828Dic3—22no—
829Dic3—22no—
830Dic3—22no—
831Dic3—22no—
832Dic3C2×C3×#4114yes—
833C32C2×#55311yescharacteristic, complemented, Sylow
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—34no—
841C23—32no—
842C23—32no—
843C23—62no—
844C23—62no—
845C23—62no—
846C23—62no—
847C23—62no—
848C23C23×C3×D312yes—
849C23C23×C3×D312yes—
850C23C23×C3×D311yescharacteristic
851D4—44no—
852D4—68no—
853D4—68no—
854D4—68no—
855D4—68no—
856D4—124no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—34no—
863C2×C4—32no—
864C2×C4—32no—
865C2×C4—32no—
866C2×C4—32no—
867C2×C4—32no—
868C2×C4—32no—
869C2×C4—44no—
870C2×C4—68no—
871C2×C4—68no—
872C2×C4—62no—
873C2×C4—62no—
874C2×C4—62no—
875C2×C4—62no—
876C2×C4—62no—
877C2×C4—124no—
878C2×C4—124no—
879C2×C4—124no—
880C2×C4C23×C3×D312yes—
881C2×C4C23×C3×D312yes—
882C2×C4C23×C3×D312yes—
883C2×C4C23×C3×D312yes—
884C2×C4C23×C3×D312yes—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—21no—
888C2×C3—24no—
889C2×C3—44no—
890C2×C3—42no—
891C2×C3—42no—
892C2×C3—42no—
893C2×C3—42no—
894C2×C3—64no—
895C2×C3—82no—
896C2×C3—122no—
897C2×C3#566114yesdirect product factor
898C2×C3C3×#55314yescomplemented
899C2×C3C2×#100411yescharacteristic
900C2×C3C2×D3×#4111yescharacteristic
901C2×C3C2×D3×#4111yescharacteristic
902C2×C3C22×C3×#4111yescharacteristic
903C2×C3C22×C3×#4111yescharacteristic
904C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
905D3—24no—
906D3—42no—
907C22—22no—
908C22—22no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—22no—
913C22—34no—
914C22—44no—
915C22—44no—
916C22—62no—
917C22—62no—
918C22—68no—
919C22—62no—
920C22—62no—
921C22—62no—
922C22—124no—
923C22C3×#100412yes—
924C22C3×D3×#4112yes—
925C22C3×D3×#4112yes—
926C22C24×C3×D311yescharacteristic
927C4—22no—
928C4—22no—
929C4—22no—
930C4—22no—
931C4—22no—
932C4—34no—
933C4—62no—
934C4—62no—
935C4—62no—
936C4—62no—
937C4—62no—
938C3—21no—
939C3C2×#566111yescharacteristic, direct product factor
940C3C2×C3×#55311yescharacteristic, complemented
941C2—42no—
942C2—42no—
943C2—64no—
944C2—122no—
945C2C3×#566114yesdirect product factor
946C2C2×C3×#100411yescharacteristic
947C2C2×C3×D3×#4111yescharacteristic
948C2C2×C3×D3×#4111yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×#123C2
socleC23×C32C24
hypercenterC2×C3×#123D3
hypocenterC3C2×C3×#553
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×#939C2semidirect
3. C2×C3×#938C2semidirect
4. C2×C3×C4×#67C2semidirect
5. C2×C3×C4×#67C2semidirect
6. C3×#5661C2direct (N × H)
7. C2×C3×#898C2semidirect
8. C2×C3×#893C2semidirect
9. C2×C3×D3×C4⋊C4C2semidirect
10. C2×C3×#889C2semidirect
11. C2×C3×#884C2semidirect
12. C2×C3×#884C2semidirect
13. C2×C3×#883C2semidirect
14. C2×C3×#67⋊C4C2semidirect
15. C2×C3×#879C2semidirect
16. C2×C3×#877C2semidirect
18. C2×#5661C3direct (N × H)
31. C32×#123C22semidirect
40. C3×#939C22semidirect
41. C3×#938C22semidirect
42. C3×C4×#67C22semidirect
43. C3×C4×#67C22semidirect
59. C3×#898C22semidirect
60. C3×#893C22semidirect
61. C3×D3×C4⋊C4C22semidirect
62. C3×#889C22semidirect
63. C3×#884C22semidirect
64. C3×#884C22semidirect
65. C3×#883C22semidirect
66. C3×#67⋊C4C22semidirect
67. C3×#879C22semidirect
68. C3×#877C22semidirect
75. C2×C3×#123D3semidirect
76. C2×C3×#123C2×C3semidirect
87. C2×#939C2×C3semidirect
88. C2×#938C2×C3semidirect
89. C2×C4×#67C2×C3semidirect
90. C2×C4×#67C2×C3semidirect
91. #5661C2×C3direct (N × H)
92. C2×#898C2×C3semidirect
93. C2×#893C2×C3semidirect
94. C2×D3×C4⋊C4C2×C3semidirect
95. C2×#889C2×C3semidirect
96. C2×#884C2×C3semidirect
97. C2×#884C2×C3semidirect
98. C2×#883C2×C3semidirect
99. C2×#67⋊C4C2×C3semidirect
100. C2×#879C2×C3semidirect
101. C2×#877C2×C3semidirect
196. C3×#123C2×D3semidirect
197. C3×#123C22×C3semidirect
244. #939C22×C3semidirect
245. #938C22×C3semidirect
246. C4×#67C22×C3semidirect
247. C4×#67C22×C3semidirect
263. #898C22×C3semidirect
264. #893C22×C3semidirect
265. D3×C4⋊C4C22×C3semidirect
266. #889C22×C3semidirect
267. #884C22×C3semidirect
268. #884C22×C3semidirect
269. #883C22×C3semidirect
270. #67⋊C4C22×C3semidirect
271. #879C22×C3semidirect
272. #877C22×C3semidirect
329. C2×#123C3×D3semidirect
527. #123C2×C3×D3semidirect
686. C2×C32#553semidirect
833. C32C2×#553semidirect
897. C2×C3#5661direct (N × H)
898. C2×C3C3×#553semidirect
939. C3C2×#5661direct (N × H)
940. C3C2×C3×#553semidirect
945. C2C3×#5661direct (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×#9392
C2×C3×#9382
C2×C3×C4×#672
C3×#56612
C2×C3×#8982
C2×C3×#8932
C2×C3×D3×C4⋊C42
C2×C3×#8892
C2×C3×#8842
C2×C3×#8832
C2×C3×#67⋊C42
C2×C3×#8792
C2×C3×#8772
C2×C3×#5533
C2×#56613