Finite Group Databasebeta

← C2×C3×#5693 #11902970

Subgroups — C2×C3×#5693 #11902970

Order 1152.

2361 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#125C211yesmaximal, characteristic, complemented
2C3×#5693C2116yesmaximal, direct product factor
3C2×C3×#898C211yesmaximal, characteristic, complemented
4C2×C3×#898C211yesmaximal, characteristic, complemented
5C2×C3×#896C211yesmaximal, characteristic, complemented
6C2×C3×#896C211yesmaximal, characteristic, complemented
7C2×C3×#894C211yesmaximal, characteristic
8C2×C3×#894C211yesmaximal, characteristic
9C2×C3×#893C211yesmaximal, characteristic
10C2×C3×#892C211yesmaximal, characteristic, complemented
11C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
12C2×C3×#889C211yesmaximal, characteristic, complemented
13C2×C3×#889C211yesmaximal, characteristic, complemented
14C2×C3×#887C211yesmaximal, characteristic, complemented
15C2×C3×#872C211yesmaximal, characteristic, complemented
16C2×C3×#872C211yesmaximal, characteristic, complemented
17C2×C3×#552—31nomaximal
18C2×#5693C311yesmaximal, characteristic, direct product factor
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×Dic6C2211yescharacteristic
25C32×#125C2218yescomplemented
26C2×C32×C4⋊C4C2211yescharacteristic
27C2×C32×C4⋊C4C2211yescharacteristic
28C2×C32×C4⋊C4C2211yescharacteristic
29C2×C32×C4⋊C4C2211yescharacteristic
30C2×C32×C4⋊C4C2211yescharacteristic
31C2×C32×C4⋊C4C2211yescharacteristic
32C2×C32×C42C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×C4⋊Dic3C2211yescharacteristic
42C2×C3×C4⋊Dic3C2211yescharacteristic
43C2×C3×Dic3⋊C4C2211yescharacteristic
44C2×C3×Dic3⋊C4C2211yescharacteristic
45C2×C3×Dic3⋊C4C2211yescharacteristic
46C2×C3×Dic3⋊C4C2211yescharacteristic
47C2×C3×Dic3⋊C4C2211yescharacteristic
48C2×C3×Dic3⋊C4C2211yescharacteristic
49C2×C3×Dic3⋊C4C2211yescharacteristic
50C2×C3×Dic3⋊C4C2211yescharacteristic
51C2×C3×C4×Dic3C2211yescharacteristic
52C2×C3×C4×Dic3C2211yescharacteristic
53C2×C3×C4×Dic3C2211yescharacteristic
54C2×C3×C4×Dic3C2211yescharacteristic
55C3×#898C2218yescomplemented
56C3×#898C2218yescomplemented
57C3×#896C2218yescomplemented
58C3×#896C2218yescomplemented
59C3×#894C2218yes—
60C3×#894C2218yes—
61C3×#893C2218yes—
62C3×#892C2218yescomplemented
63C3×D3×C4⋊C4C2218yescomplemented
64C3×#889C2218yescomplemented
65C3×#889C2218yescomplemented
66C3×#887C2218yescomplemented
67C3×#872C2218yescomplemented
68C3×#872C2218yescomplemented
69C3×#552—316no—
70C2×C3×#126—31no—
71C2×C3×#126—31no—
72C2×C3×#125—21no—
73C2×C3×#125—31no—
74C2×C3×#125—31no—
75C2×C3×#125D311yescharacteristic, complemented
76C2×C3×#125C2×C311yescharacteristic, complemented
77C2×C3×#123—31no—
78C2×C3×#123—31no—
79C2×C3×C22⋊Q8—31no—
80C2×C3×C22⋊Q8—31no—
81C2×C3×C4×Q8—31no—
82C2×C3×C4×D4—31no—
83C2×C3×#117—31no—
84C2×C3×#117—31no—
85C2×C3×#117—31no—
86C22×C3×C4⋊C4—31no—
87#5693C2×C3116yesdirect product factor
88C2×#898C2×C311yescharacteristic, complemented
89C2×#898C2×C311yescharacteristic, complemented
90C2×#896C2×C311yescharacteristic, complemented
91C2×#896C2×C311yescharacteristic, complemented
92C2×#894C2×C311yescharacteristic
93C2×#894C2×C311yescharacteristic
94C2×#893C2×C311yescharacteristic
95C2×#892C2×C311yescharacteristic, complemented
96C2×D3×C4⋊C4C2×C311yescharacteristic, complemented
97C2×#889C2×C311yescharacteristic, complemented
98C2×#889C2×C311yescharacteristic, complemented
99C2×#887C2×C311yescharacteristic, complemented
100C2×#872C2×C311yescharacteristic, complemented
101C2×#872C2×C311yescharacteristic, complemented
102C23×C3×D3C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C2×C3×D12—24no—
118C2×C3×D12C2314yes—
119C2×C3×C4×D3—24no—
120C2×C3×C4×D3—24no—
121C2×C3×C4×D3—24no—
122C2×C3×C4×D3—24no—
123C2×C3×C4×D3C2314yes—
124C2×C3×C4×D3C2314yes—
125C2×C3×C4×D3C2314yes—
126C2×C3×C4×D3C2314yes—
127C2×C3×Dic6—24no—
128C2×C3×Dic6C2314yes—
129C32×C4⋊C4C2314yes—
130C32×C4⋊C4C2314yes—
131C32×C4⋊C4C2314yes—
132C32×C4⋊C4C2314yes—
133C32×C4⋊C4C2314yes—
134C32×C4⋊C4C2314yes—
135C32×C42C2314yes—
136C3×(C2×D3)⋊C4C2314yes—
137C3×(C2×D3)⋊C4C2314yes—
138C3×(C2×D3)⋊C4C2314yes—
139C3×(C2×D3)⋊C4C2314yes—
140C3×(C2×D3)⋊C4C2314yes—
141C3×(C2×D3)⋊C4C2314yes—
142C3×(C2×D3)⋊C4C2314yes—
143C3×(C2×D3)⋊C4C2314yes—
144C3×C4⋊Dic3C2314yes—
145C3×C4⋊Dic3C2314yes—
146C3×Dic3⋊C4C2314yes—
147C3×Dic3⋊C4C2314yes—
148C3×Dic3⋊C4C2314yes—
149C3×Dic3⋊C4C2314yes—
150C3×Dic3⋊C4C2314yes—
151C3×Dic3⋊C4C2314yes—
152C3×Dic3⋊C4C2314yes—
153C3×Dic3⋊C4C2314yes—
154C3×C4×Dic3C2314yes—
155C3×C4×Dic3C2314yes—
156C3×C4×Dic3C2314yes—
157C3×C4×Dic3C2314yes—
158C2×#552—31noSylow
159C22×C3×Q8—31no—
160C22×C3×D4—31no—
161C23×C3×C4—31no—
162C23×C3×C4—31no—
163C23×C3×C4—31no—
164C23×C3×C4—31no—
165C22×D12C22×C311yescharacteristic
166C22×C4×D3C22×C311yescharacteristic
167C22×C4×D3C22×C311yescharacteristic
168C22×C4×D3C22×C311yescharacteristic
169C22×C4×D3C22×C311yescharacteristic
170C22×Dic6C22×C311yescharacteristic
171C3×#126—38no—
172C3×#126—38no—
173C3×#125—28no—
174C3×#125—38no—
175C3×#125—38no—
176C3×#125C2×D318yescomplemented
177C3×#125C22×C318yescomplemented
178C3×#123—38no—
179C3×#123—38no—
180C3×C22⋊Q8—38no—
181C3×C22⋊Q8—38no—
182C3×C4×Q8—38no—
183C3×C4×D4—38no—
184C3×#117—38no—
185C3×#117—38no—
186C3×#117—38no—
187C2×C3×C4⋊C4—21no—
188C2×C3×C4⋊C4—21no—
189C2×C3×C4⋊C4—21no—
190C2×C3×C4⋊C4—21no—
191C2×C3×C4⋊C4—21no—
192C2×C3×C4⋊C4—21no—
193C2×C3×C4⋊C4—31no—
194C2×C3×C4⋊C4—31no—
195C2×C3×C4⋊C4—31no—
196C2×C3×C4⋊C4—31no—
197C2×C3×C4⋊C4—31no—
198C2×C3×C4⋊C4—31no—
199C2×C3×C4⋊C4—31no—
200C2×C3×C4⋊C4—31no—
201C2×C3×C4⋊C4—31no—
202C2×C3×C4⋊C4—31no—
203C2×C3×C4⋊C4—38no—
204C2×C3×C4⋊C4C2×D311yescharacteristic
205C2×C3×C4⋊C4C2×D311yescharacteristic
206C2×C3×C4⋊C4C2×D311yescharacteristic
207C2×C3×C4⋊C4C2×D311yescharacteristic
208C2×C3×C4⋊C4C2×D311yescharacteristic
209C2×C3×C4⋊C4C2×D311yescharacteristic
210C2×C3×C4⋊C4C22×C311yescharacteristic
211C2×C3×C4⋊C4C22×C311yescharacteristic
212C2×C3×C4⋊C4C22×C311yescharacteristic
213C2×C3×C4⋊C4C22×C311yescharacteristic
214C2×C3×C4⋊C4C22×C311yescharacteristic
215C2×C3×C4⋊C4C22×C311yescharacteristic
216C2×C3×C22⋊C4—31no—
217C2×C3×C22⋊C4—31no—
218C2×C3×C22⋊C4—31no—
219C2×C3×C22⋊C4—31no—
220C2×C3×C22⋊C4—31no—
221C2×C3×C22⋊C4—31no—
222C2×C3×C22⋊C4—31no—
223C2×C3×C22⋊C4—31no—
224C2×C3×C42—21no—
225C2×C3×C42—31no—
226C2×C3×C42—31no—
227C2×C3×C42—31no—
228C2×C3×C42—31no—
229C2×C3×C42C2×D311yescharacteristic
230C2×C3×C42C22×C311yescharacteristic
231C2×(C2×D3)⋊C4C22×C311yescharacteristic
232C2×(C2×D3)⋊C4C22×C311yescharacteristic
233C2×(C2×D3)⋊C4C22×C311yescharacteristic
234C2×(C2×D3)⋊C4C22×C311yescharacteristic
235C2×(C2×D3)⋊C4C22×C311yescharacteristic
236C2×(C2×D3)⋊C4C22×C311yescharacteristic
237C2×(C2×D3)⋊C4C22×C311yescharacteristic
238C2×(C2×D3)⋊C4C22×C311yescharacteristic
239C2×C4⋊Dic3C22×C311yescharacteristic
240C2×C4⋊Dic3C22×C311yescharacteristic
241C2×Dic3⋊C4C22×C311yescharacteristic
242C2×Dic3⋊C4C22×C311yescharacteristic
243C2×Dic3⋊C4C22×C311yescharacteristic
244C2×Dic3⋊C4C22×C311yescharacteristic
245C2×Dic3⋊C4C22×C311yescharacteristic
246C2×Dic3⋊C4C22×C311yescharacteristic
247C2×Dic3⋊C4C22×C311yescharacteristic
248C2×Dic3⋊C4C22×C311yescharacteristic
249C2×C4×Dic3C22×C311yescharacteristic
250C2×C4×Dic3C22×C311yescharacteristic
251C2×C4×Dic3C22×C311yescharacteristic
252C2×C4×Dic3C22×C311yescharacteristic
253#898C22×C318yescomplemented
254#898C22×C318yescomplemented
255#896C22×C318yescomplemented
256#896C22×C318yescomplemented
257#894C22×C318yes—
258#894C22×C318yes—
259#893C22×C318yes—
260#892C22×C318yescomplemented
261D3×C4⋊C4C22×C318yescomplemented
262#889C22×C318yescomplemented
263#889C22×C318yescomplemented
264#887C22×C318yescomplemented
265#872C22×C318yescomplemented
266#872C22×C318yescomplemented
267C23×C32C2411yescharacteristic
268C22×C3×D3—22no—
269C22×C3×D3—22no—
270C22×C3×D3—22no—
271C22×C3×D3—22no—
272C22×C3×D3—22no—
273C22×C3×D3#4114yes—
274C22×C3×D3C2412yes—
275C22×C3×D3C2412yes—
276C2×C32×C4—22no—
277C2×C32×C4—22no—
278C2×C32×C4—22no—
279C2×C32×C4—22no—
280C2×C32×C4—22no—
281C2×C32×C4—22no—
282C2×C32×C4—22no—
283C2×C32×C4C2412yes—
284C2×C32×C4C2412yes—
285C2×C32×C4C2412yes—
286C2×C32×C4C2412yes—
287C2×C32×C4C2412yes—
288C2×C32×C4C2412yes—
289C2×C32×C4C2412yes—
290C2×C3×Dic3—22no—
291C2×C3×Dic3—22no—
292C2×C3×Dic3—22no—
293C2×C3×Dic3—22no—
294C2×C3×Dic3—22no—
295C2×C3×Dic3#4114yes—
296C2×C3×Dic3C2412yes—
297C2×C3×Dic3C2412yes—
298C2×C3×Dic3C2412yes—
299C2×C3×Dic3C2412yes—
300C2×C3×Dic3C2412yes—
301C2×C3×Dic3C2412yes—
302C3×D12—28no—
303C3×C4×D3—28no—
304C3×C4×D3—28no—
305C3×C4×D3—28no—
306C3×C4×D3—28no—
307C3×Dic6—28no—
308#552—316no—
309C2×#126—31no—
310C2×#126—31no—
311C2×#125—31no—
312C2×#125—31no—
313C2×#125C3×D311yescharacteristic, complemented
314C2×#123—31no—
315C2×#123—31no—
316C2×C22⋊Q8—31no—
317C2×C22⋊Q8—31no—
318C2×C4×Q8—31no—
319C2×C4×D4—31no—
320C2×#117—31no—
321C2×#117—31no—
322C2×#117—31no—
323C22×C4⋊C4—31no—
324C24×C3—31no—
325C24×C3—31no—
326C23×D3C23×C311yescharacteristic
327C23×D3C23×C311yescharacteristic
328C2×C3×Q8—34no—
329C2×C3×Q8—64no—
330C2×C3×D4—34no—
331C2×C3×D4—64no—
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—21no—
337C22×C3×C4—21no—
338C22×C3×C4—21no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4—31no—
345C22×C3×C4—34no—
346C22×C3×C4—34no—
347C22×C3×C4—34no—
348C22×C3×C4—34no—
349C22×C3×C4—64no—
350C22×C3×C4—64no—
351C22×C3×C4—64no—
352C22×C3×C4—64no—
353C22×C3×C4C22×D311yescharacteristic
354C22×C3×C4C22×D311yescharacteristic
355C22×C3×C4C22×D311yescharacteristic
356C22×C3×C4C22×D311yescharacteristic
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C22×D311yescharacteristic
359C22×C3×C4C22×D311yescharacteristic
360C22×C3×C4C23×C311yescharacteristic
361C22×C3×C4C23×C311yescharacteristic
362C22×C3×C4C23×C311yescharacteristic
363C22×C3×C4C23×C311yescharacteristic
364C22×C3×C4C23×C311yescharacteristic
365C22×C3×C4C23×C311yescharacteristic
366C22×C3×C4C23×C311yescharacteristic
367C22×Dic3C23×C311yescharacteristic
368C22×Dic3C23×C311yescharacteristic
369C22×Dic3C23×C311yescharacteristic
370C22×Dic3C23×C311yescharacteristic
371C22×Dic3C23×C311yescharacteristic
372C22×Dic3C23×C311yescharacteristic
373C2×D12—24no—
374C2×D12C23×C314yes—
375C2×C4×D3—24no—
376C2×C4×D3—24no—
377C2×C4×D3—24no—
378C2×C4×D3—24no—
379C2×C4×D3C23×C314yes—
380C2×C4×D3C23×C314yes—
381C2×C4×D3C23×C314yes—
382C2×C4×D3C23×C314yes—
383C2×Dic6—24no—
384C2×Dic6C23×C314yes—
385C3×C4⋊C4—24no—
386C3×C4⋊C4—24no—
387C3×C4⋊C4—24no—
388C3×C4⋊C4—24no—
389C3×C4⋊C4—24no—
390C3×C4⋊C4—24no—
391C3×C4⋊C4—34no—
392C3×C4⋊C4—34no—
393C3×C4⋊C4—34no—
394C3×C4⋊C4—34no—
395C3×C4⋊C4—34no—
396C3×C4⋊C4—34no—
397C3×C4⋊C4—34no—
398C3×C4⋊C4—34no—
399C3×C4⋊C4—34no—
400C3×C4⋊C4—34no—
401C3×C4⋊C4C22×D314yes—
402C3×C4⋊C4C22×D314yes—
403C3×C4⋊C4C22×D314yes—
404C3×C4⋊C4C22×D314yes—
405C3×C4⋊C4C22×D314yes—
406C3×C4⋊C4C22×D314yes—
407C3×C4⋊C4C23×C314yes—
408C3×C4⋊C4C23×C314yes—
409C3×C4⋊C4C23×C314yes—
410C3×C4⋊C4C23×C314yes—
411C3×C4⋊C4C23×C314yes—
412C3×C4⋊C4C23×C314yes—
413C3×C22⋊C4—34no—
414C3×C22⋊C4—34no—
415C3×C22⋊C4—34no—
416C3×C22⋊C4—34no—
417C3×C22⋊C4—34no—
418C3×C22⋊C4—34no—
419C3×C22⋊C4—34no—
420C3×C22⋊C4—34no—
421C3×C42—24no—
422C3×C42—34no—
423C3×C42—34no—
424C3×C42—34no—
425C3×C42—34no—
426C3×C42C22×D314yes—
427C3×C42C23×C314yes—
428(C2×D3)⋊C4C23×C314yes—
429(C2×D3)⋊C4C23×C314yes—
430(C2×D3)⋊C4C23×C314yes—
431(C2×D3)⋊C4C23×C314yes—
432(C2×D3)⋊C4C23×C314yes—
433(C2×D3)⋊C4C23×C314yes—
434(C2×D3)⋊C4C23×C314yes—
435(C2×D3)⋊C4C23×C314yes—
436C4⋊Dic3C23×C314yes—
437C4⋊Dic3C23×C314yes—
438Dic3⋊C4C23×C314yes—
439Dic3⋊C4C23×C314yes—
440Dic3⋊C4C23×C314yes—
441Dic3⋊C4C23×C314yes—
442Dic3⋊C4C23×C314yes—
443Dic3⋊C4C23×C314yes—
444Dic3⋊C4C23×C314yes—
445Dic3⋊C4C23×C314yes—
446C4×Dic3C23×C314yes—
447C4×Dic3C23×C314yes—
448C4×Dic3C23×C314yes—
449C4×Dic3C23×C314yes—
450C22×C32C2×#4112yes—
451C22×C32C2×#4112yes—
452C22×C322−1+412yes—
453C22×C32C2511yescharacteristic
454C2×C3×D3—28no—
455C2×C3×D3—22no—
456C2×C3×D3—22no—
457C2×C3×D3—22no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—44no—
461C2×C3×D3C2×#4114yes—
462C32×C4—22no—
463C32×C4—22no—
464C32×C4—22no—
465C32×C4—22no—
466C32×C4—22no—
467C32×C4—22no—
468C32×C4—22no—
469C3×Dic3—22no—
470C3×Dic3—22no—
471C3×Dic3—22no—
472C3×Dic3—22no—
473C3×Dic3—22no—
474C3×Dic3C2×#4114yes—
475C22×Q8—31no—
476C22×D4—31no—
477C23×C4—31no—
478C23×C4—31no—
479C23×C4—31no—
480C23×C4—31no—
481#126—38no—
482#126—38no—
483#125—38no—
484#125—38no—
485#125C2×C3×D318yescomplemented
486#123—38no—
487#123—38no—
488C22⋊Q8—38no—
489C22⋊Q8—38no—
490C4×Q8—38no—
491C4×D4—38no—
492#117—38no—
493#117—38no—
494#117—38no—
495C2×C4⋊C4—31no—
496C2×C4⋊C4—31no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—31no—
499C2×C4⋊C4—31no—
500C2×C4⋊C4—31no—
501C2×C4⋊C4—31no—
502C2×C4⋊C4—31no—
503C2×C4⋊C4—31no—
504C2×C4⋊C4—31no—
505C2×C4⋊C4—38no—
506C2×C4⋊C4C2×C3×D311yescharacteristic
507C2×C4⋊C4C2×C3×D311yescharacteristic
508C2×C4⋊C4C2×C3×D311yescharacteristic
509C2×C4⋊C4C2×C3×D311yescharacteristic
510C2×C4⋊C4C2×C3×D311yescharacteristic
511C2×C4⋊C4C2×C3×D311yescharacteristic
512C2×C22⋊C4—31no—
513C2×C22⋊C4—31no—
514C2×C22⋊C4—31no—
515C2×C22⋊C4—31no—
516C2×C22⋊C4—31no—
517C2×C22⋊C4—31no—
518C2×C22⋊C4—31no—
519C2×C22⋊C4—31no—
520C2×C42—31no—
521C2×C42—31no—
522C2×C42—31no—
523C2×C42—31no—
524C2×C42C2×C3×D311yescharacteristic
525C23×C3—21no—
526C23×C3—34no—
527C23×C3—32no—
528C23×C3—32no—
529C23×C3—62no—
530C23×C3—62no—
531C23×C3—62no—
532C23×C3—62no—
533C23×C3—62no—
534C23×C3C23×D311yescharacteristic
535C23×C3C24×C311yescharacteristic
536C22×D3—22no—
537C22×D3—22no—
538C22×D3—22no—
539C22×D3—22no—
540C22×D3—22no—
541C22×D3C3×#4114yes—
542C22×D3C24×C312yes—
543C22×D3C24×C312yes—
544C3×Q8—68no—
545C3×D4—68no—
546C2×C3×C4—24no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—34no—
569C2×C3×C4—32no—
570C2×C3×C4—32no—
571C2×C3×C4—32no—
572C2×C3×C4—32no—
573C2×C3×C4—32no—
574C2×C3×C4—32no—
575C2×C3×C4—42no—
576C2×C3×C4—42no—
577C2×C3×C4—42no—
578C2×C3×C4—42no—
579C2×C3×C4—42no—
580C2×C3×C4—42no—
581C2×C3×C4—68no—
582C2×C3×C4—68no—
583C2×C3×C4—68no—
584C2×C3×C4—68no—
585C2×C3×C4—62no—
586C2×C3×C4—62no—
587C2×C3×C4—62no—
588C2×C3×C4—62no—
589C2×C3×C4—62no—
590C2×C3×C4C23×D312yes—
591C2×C3×C4C23×D312yes—
592C2×C3×C4C23×D312yes—
593C2×C3×C4C23×D312yes—
594C2×C3×C4C23×D312yes—
595C2×C3×C4C23×D312yes—
596C2×C3×C4C23×D312yes—
597C2×C3×C4C24×C312yes—
598C2×C3×C4C24×C312yes—
599C2×C3×C4C24×C312yes—
600C2×C3×C4C24×C312yes—
601C2×C3×C4C24×C312yes—
602C2×C3×C4C24×C312yes—
603C2×C3×C4C24×C312yes—
604C2×Dic3—22no—
605C2×Dic3—22no—
606C2×Dic3—22no—
607C2×Dic3—22no—
608C2×Dic3—22no—
609C2×Dic3C3×#4114yes—
610C2×Dic3C24×C312yes—
611C2×Dic3C24×C312yes—
612C2×Dic3C24×C312yes—
613C2×Dic3C24×C312yes—
614C2×Dic3C24×C312yes—
615C2×Dic3C24×C312yes—
616D12—28no—
617C4×D3—28no—
618C4×D3—28no—
619C4×D3—28no—
620C4×D3—28no—
621Dic6—28no—
622C2×C32#55214yescomplemented
623C2×C32C22×#4111yescharacteristic
624C2×C32C22×#4111yescharacteristic
625C2×C32C2×2−1+411yescharacteristic
626C3×D3—24no—
627C3×D3—42no—
628C24—31no—
629C24—31no—
630C2×Q8—34no—
631C2×Q8—64no—
632C2×D4—34no—
633C2×D4—64no—
634C22×C4—31no—
635C22×C4—31no—
636C22×C4—31no—
637C22×C4—31no—
638C22×C4—31no—
639C22×C4—31no—
640C22×C4—34no—
641C22×C4—34no—
642C22×C4—34no—
643C22×C4—34no—
644C22×C4—64no—
645C22×C4—64no—
646C22×C4—64no—
647C22×C4—64no—
648C22×C4C22×C3×D311yescharacteristic
649C22×C4C22×C3×D311yescharacteristic
650C22×C4C22×C3×D311yescharacteristic
651C22×C4C22×C3×D311yescharacteristic
652C22×C4C22×C3×D311yescharacteristic
653C22×C4C22×C3×D311yescharacteristic
654C22×C4C22×C3×D311yescharacteristic
655C4⋊C4—34no—
656C4⋊C4—34no—
657C4⋊C4—34no—
658C4⋊C4—34no—
659C4⋊C4—34no—
660C4⋊C4—34no—
661C4⋊C4—34no—
662C4⋊C4—34no—
663C4⋊C4—34no—
664C4⋊C4—34no—
665C4⋊C4C22×C3×D314yes—
666C4⋊C4C22×C3×D314yes—
667C4⋊C4C22×C3×D314yes—
668C4⋊C4C22×C3×D314yes—
669C4⋊C4C22×C3×D314yes—
670C4⋊C4C22×C3×D314yes—
671C22⋊C4—34no—
672C22⋊C4—34no—
673C22⋊C4—34no—
674C22⋊C4—34no—
675C22⋊C4—34no—
676C22⋊C4—34no—
677C22⋊C4—34no—
678C22⋊C4—34no—
679C42—34no—
680C42—34no—
681C42—34no—
682C42—34no—
683C42C22×C3×D314yes—
684C22×C3—22no—
685C22×C3—22no—
686C22×C3—22no—
687C22×C3—21no—
688C22×C3—34no—
689C22×C3—68no—
690C22×C3—62no—
691C22×C3—62no—
692C22×C3—62no—
693C22×C3—62no—
694C22×C3—62no—
695C22×C3—124no—
696C22×C3#100712yes—
697C22×C3D3×#4112yes—
698C22×C3D3×#4112yes—
699C22×C3C2×C3×#4112yes—
700C22×C3C2×C3×#4112yes—
701C22×C3C3×2−1+412yes—
702C22×C3C24×D311yescharacteristic
703C22×C3C25×C311yescharacteristic
704C2×D3—22no—
705C2×D3—22no—
706C2×D3—28no—
707C2×D3—22no—
708C2×D3—22no—
709C2×D3—22no—
710C2×D3—44no—
711C2×D3C2×C3×#4114yes—
712C3×C4—24no—
713C3×C4—22no—
714C3×C4—22no—
715C3×C4—22no—
716C3×C4—22no—
717C3×C4—22no—
718C3×C4—22no—
719C3×C4—22no—
720C3×C4—22no—
721C3×C4—22no—
722C3×C4—22no—
723C3×C4—22no—
724C3×C4—22no—
725C3×C4—22no—
726C3×C4—22no—
727C3×C4—34no—
728C3×C4—42no—
729C3×C4—42no—
730C3×C4—42no—
731C3×C4—42no—
732C3×C4—42no—
733C3×C4—42no—
734C3×C4—62no—
735C3×C4—62no—
736C3×C4—62no—
737C3×C4—62no—
738C3×C4—62no—
739Dic3—22no—
740Dic3—22no—
741Dic3—22no—
742Dic3—22no—
743Dic3—22no—
744Dic3C2×C3×#4114yes—
745C32C2×#55211yescharacteristic, complemented, Sylow
746C23—34no—
747C23—32no—
748C23—32no—
749C23—62no—
750C23—62no—
751C23—62no—
752C23—62no—
753C23—62no—
754C23C23×C3×D311yescharacteristic
755Q8—68no—
756D4—68no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—34no—
765C2×C4—32no—
766C2×C4—32no—
767C2×C4—32no—
768C2×C4—32no—
769C2×C4—32no—
770C2×C4—32no—
771C2×C4—68no—
772C2×C4—68no—
773C2×C4—68no—
774C2×C4—68no—
775C2×C4—62no—
776C2×C4—62no—
777C2×C4—62no—
778C2×C4—62no—
779C2×C4—62no—
780C2×C4C23×C3×D312yes—
781C2×C4C23×C3×D312yes—
782C2×C4C23×C3×D312yes—
783C2×C4C23×C3×D312yes—
784C2×C4C23×C3×D312yes—
785C2×C4C23×C3×D312yes—
786C2×C4C23×C3×D312yes—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—24no—
791C2×C3—64no—
792C2×C3—122no—
793C2×C3#569314yesdirect product factor
794C2×C3C3×#55214yescomplemented
795C2×C3C2×#100711yescharacteristic
796C2×C3C2×D3×#4111yescharacteristic
797C2×C3C2×D3×#4111yescharacteristic
798C2×C3C22×C3×#4111yescharacteristic
799C2×C3C22×C3×#4111yescharacteristic
800C2×C3C2×C3×2−1+411yescharacteristic
801D3—24no—
802D3—42no—
803C22—34no—
804C22—62no—
805C22—62no—
806C22—68no—
807C22—62no—
808C22—62no—
809C22—62no—
810C22—124no—
811C22C3×#100712yes—
812C22C3×D3×#4112yes—
813C22C3×D3×#4112yes—
814C22C24×C3×D311yescharacteristic
815C4—22no—
816C4—22no—
817C4—22no—
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—34no—
823C4—62no—
824C4—62no—
825C4—62no—
826C4—62no—
827C4—62no—
828C3—21no—
829C3C2×#569311yescharacteristic, direct product factor
830C3C2×C3×#55211yescharacteristic, complemented
831C2—64no—
832C2—122no—
833C2C3×#569314yesdirect product factor
834C2C2×C3×#100711yescharacteristic
835C2C2×C3×D3×#4111yescharacteristic
836C2C2×C3×D3×#4111yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×#125C2
socleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC2×C3×#125D3
hypocenterC3C2×C3×#552
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#125

Complements

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

NH ≅ G/Ntype
1. C2×C32×#125C2semidirect
2. C3×#5693C2direct (N × H)
3. C2×C3×#898C2semidirect
4. C2×C3×#898C2semidirect
5. C2×C3×#896C2semidirect
6. C2×C3×#896C2semidirect
10. C2×C3×#892C2semidirect
11. C2×C3×D3×C4⋊C4C2semidirect
12. C2×C3×#889C2semidirect
13. C2×C3×#889C2semidirect
14. C2×C3×#887C2semidirect
15. C2×C3×#872C2semidirect
16. C2×C3×#872C2semidirect
18. C2×#5693C3direct (N × H)
25. C32×#125C22semidirect
55. C3×#898C22semidirect
56. C3×#898C22semidirect
57. C3×#896C22semidirect
58. C3×#896C22semidirect
62. C3×#892C22semidirect
63. C3×D3×C4⋊C4C22semidirect
64. C3×#889C22semidirect
65. C3×#889C22semidirect
66. C3×#887C22semidirect
67. C3×#872C22semidirect
68. C3×#872C22semidirect
75. C2×C3×#125D3semidirect
76. C2×C3×#125C2×C3semidirect
87. #5693C2×C3direct (N × H)
88. C2×#898C2×C3semidirect
89. C2×#898C2×C3semidirect
90. C2×#896C2×C3semidirect
91. C2×#896C2×C3semidirect
95. C2×#892C2×C3semidirect
96. C2×D3×C4⋊C4C2×C3semidirect
97. C2×#889C2×C3semidirect
98. C2×#889C2×C3semidirect
99. C2×#887C2×C3semidirect
100. C2×#872C2×C3semidirect
101. C2×#872C2×C3semidirect
176. C3×#125C2×D3semidirect
177. C3×#125C22×C3semidirect
253. #898C22×C3semidirect
254. #898C22×C3semidirect
255. #896C22×C3semidirect
256. #896C22×C3semidirect
260. #892C22×C3semidirect
261. D3×C4⋊C4C22×C3semidirect
262. #889C22×C3semidirect
263. #889C22×C3semidirect
264. #887C22×C3semidirect
265. #872C22×C3semidirect
266. #872C22×C3semidirect
313. C2×#125C3×D3semidirect
485. #125C2×C3×D3semidirect
622. C2×C32#552semidirect
745. C32C2×#552semidirect
793. C2×C3#5693direct (N × H)
794. C2×C3C3×#552semidirect
829. C3C2×#5693direct (N × H)
830. C3C2×C3×#552semidirect
833. C2C3×#5693direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1252
C3×#56932
C2×C3×#8982
C2×C3×#8962
C2×C3×#8942
C2×C3×#8932
C2×C3×#8922
C2×C3×D3×C4⋊C42
C2×C3×#8892
C2×C3×#8872
C2×C3×#8722
C2×C3×#5523
C2×#56933