Finite Group Databasebeta

← C2×C3×#5696 #11901543

Subgroups — C2×C3×#5696 #11901543

Order 1152.

2121 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#125C211yesmaximal, characteristic, complemented
2C3×#5696C2116yesmaximal, direct product factor
3C2×C3×#898C211yesmaximal, characteristic
4C2×C3×#898C211yesmaximal, characteristic
5C2×C3×#898C211yesmaximal, characteristic
6C2×C3×#896C211yesmaximal, characteristic
7C2×C3×#896C211yesmaximal, characteristic
8C2×C3×#892C211yesmaximal, characteristic
9C2×C3×#890C211yesmaximal, characteristic, complemented
10C2×C3×#889C211yesmaximal, characteristic, complemented
11C2×C3×#889C211yesmaximal, characteristic, complemented
12C2×C3×#889C211yesmaximal, characteristic, complemented
13C2×C3×#888C211yesmaximal, characteristic, complemented
14C2×C3×#887C211yesmaximal, characteristic, complemented
15C2×C3×#876C211yesmaximal, characteristic
16C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
17C2×C3×#541—31nomaximal
18C2×#5696C311yesmaximal, characteristic, direct product factor
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic
22C32×#125C2218yescomplemented
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×C32×C4⋊C4C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×C32×C4⋊C4C2211yescharacteristic
27C2×C32×C4⋊C4C2211yescharacteristic
28C2×C32×C4⋊C4C2211yescharacteristic
29C2×C32×C42C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C2×C3×C4⋊Dic3C2211yescharacteristic
38C2×C3×C4⋊Dic3C2211yescharacteristic
39C2×C3×C4⋊Dic3C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
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×C4×Dic3C2211yescharacteristic
51C2×C3×C4×Dic3C2211yescharacteristic
52C2×C3×C4×Dic3C2211yescharacteristic
53C2×C3×C4×Dic3C2211yescharacteristic
54C2×C3×C4×Dic3C2211yescharacteristic
55C3×#898C2218yes—
56C3×#898C2218yes—
57C3×#898C2218yes—
58C3×#896C2218yes—
59C3×#896C2218yes—
60C3×#892C2218yes—
61C3×#890C2218yescomplemented
62C3×#889C2218yescomplemented
63C3×#889C2218yescomplemented
64C3×#889C2218yescomplemented
65C3×#888C2218yescomplemented
66C3×#887C2218yescomplemented
67C3×#876C2218yes—
68C3×C4×Dic6C2218yescomplemented
69C3×#541—316no—
70C2×C3×C4⋊Q8—31no—
71C2×C3×#126—31no—
72C2×C3×#126—31no—
73C2×C3×#126—31no—
74C2×C3×#126—31no—
75C2×C3×#125—21no—
76C2×C3×#125—31no—
77C2×C3×#125—31no—
78C2×C3×#125—31no—
79C2×C3×#125—31no—
80C2×C3×#125D311yescharacteristic, complemented
81C2×C3×#125C2×C311yescharacteristic, complemented
82C2×C3×C22⋊Q8—31no—
83C2×C3×C22⋊Q8—31no—
84C2×C3×C4×Q8—31no—
85C2×C3×C4×Q8—31no—
86C2×C3×#117—31no—
87#5696C2×C3116yesdirect product factor
88C2×#898C2×C311yescharacteristic
89C2×#898C2×C311yescharacteristic
90C2×#898C2×C311yescharacteristic
91C2×#896C2×C311yescharacteristic
92C2×#896C2×C311yescharacteristic
93C2×#892C2×C311yescharacteristic
94C2×#890C2×C311yescharacteristic, complemented
95C2×#889C2×C311yescharacteristic, complemented
96C2×#889C2×C311yescharacteristic, complemented
97C2×#889C2×C311yescharacteristic, complemented
98C2×#888C2×C311yescharacteristic, complemented
99C2×#887C2×C311yescharacteristic, complemented
100C2×#876C2×C311yescharacteristic
101C2×C4×Dic6C2×C311yescharacteristic, complemented
102C23×C3×D3C2311yescharacteristic
103C22×C32×C4C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C2×C3×C4×D3—24no—
118C2×C3×C4×D3C2314yes—
119C2×C3×Dic6—24no—
120C2×C3×Dic6—24no—
121C2×C3×Dic6C2314yes—
122C2×C3×Dic6C2314yes—
123C32×C4⋊C4C2314yes—
124C32×C4⋊C4C2314yes—
125C32×C4⋊C4C2314yes—
126C32×C4⋊C4C2314yes—
127C32×C4⋊C4C2314yes—
128C32×C4⋊C4C2314yes—
129C32×C42C2314yes—
130C3×(C2×D3)⋊C4C2314yes—
131C3×(C2×D3)⋊C4C2314yes—
132C3×(C2×D3)⋊C4C2314yes—
133C3×(C2×D3)⋊C4C2314yes—
134C3×(C2×D3)⋊C4C2314yes—
135C3×(C2×D3)⋊C4C2314yes—
136C3×C4⋊Dic3C2314yes—
137C3×C4⋊Dic3C2314yes—
138C3×C4⋊Dic3C2314yes—
139C3×C4⋊Dic3C2314yes—
140C3×Dic3⋊C4C2314yes—
141C3×Dic3⋊C4C2314yes—
142C3×Dic3⋊C4C2314yes—
143C3×Dic3⋊C4C2314yes—
144C3×Dic3⋊C4C2314yes—
145C3×Dic3⋊C4C2314yes—
146C3×Dic3⋊C4C2314yes—
147C3×Dic3⋊C4C2314yes—
148C3×Dic3⋊C4C2314yes—
149C3×Dic3⋊C4C2314yes—
150C3×C4×Dic3C2314yes—
151C3×C4×Dic3C2314yes—
152C3×C4×Dic3C2314yes—
153C3×C4×Dic3C2314yes—
154C3×C4×Dic3C2314yes—
155C2×#541—31noSylow
156C22×C3×Q8—31no—
157C22×C3×Q8—31no—
158C23×C3×C4—31no—
159C22×C4×D3C22×C311yescharacteristic
160C22×Dic6C22×C311yescharacteristic
161C22×Dic6C22×C311yescharacteristic
162C3×C4⋊Q8—38no—
163C3×#126—38no—
164C3×#126—38no—
165C3×#126—38no—
166C3×#126—38no—
167C3×#125—28no—
168C3×#125—38no—
169C3×#125—38no—
170C3×#125—38no—
171C3×#125—38no—
172C3×#125C2×D318yescomplemented
173C3×#125C22×C318yescomplemented
174C3×C22⋊Q8—38no—
175C3×C22⋊Q8—38no—
176C3×C4×Q8—38no—
177C3×C4×Q8—38no—
178C3×#117—38no—
179C2×C3×C4⋊C4—21no—
180C2×C3×C4⋊C4—21no—
181C2×C3×C4⋊C4—21no—
182C2×C3×C4⋊C4—21no—
183C2×C3×C4⋊C4—21no—
184C2×C3×C4⋊C4—21no—
185C2×C3×C4⋊C4—31no—
186C2×C3×C4⋊C4—31no—
187C2×C3×C4⋊C4—31no—
188C2×C3×C4⋊C4—31no—
189C2×C3×C4⋊C4—31no—
190C2×C3×C4⋊C4—31no—
191C2×C3×C4⋊C4—31no—
192C2×C3×C4⋊C4—31no—
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⋊C4C2×D311yescharacteristic
200C2×C3×C4⋊C4C2×D311yescharacteristic
201C2×C3×C4⋊C4C2×D311yescharacteristic
202C2×C3×C4⋊C4C2×D311yescharacteristic
203C2×C3×C4⋊C4C2×D311yescharacteristic
204C2×C3×C4⋊C4C2×D311yescharacteristic
205C2×C3×C4⋊C4C22×C311yescharacteristic
206C2×C3×C4⋊C4C22×C311yescharacteristic
207C2×C3×C4⋊C4C22×C311yescharacteristic
208C2×C3×C4⋊C4C22×C311yescharacteristic
209C2×C3×C4⋊C4C22×C311yescharacteristic
210C2×C3×C4⋊C4C22×C311yescharacteristic
211C2×C3×C22⋊C4—31no—
212C2×C3×C22⋊C4—31no—
213C2×C3×C22⋊C4—31no—
214C2×C3×C22⋊C4—31no—
215C2×C3×C22⋊C4—31no—
216C2×C3×C22⋊C4—31no—
217C2×C3×C42—21no—
218C2×C3×C42—31no—
219C2×C3×C42—31no—
220C2×C3×C42—31no—
221C2×C3×C42—31no—
222C2×C3×C42—31no—
223C2×C3×C42C2×D311yescharacteristic
224C2×C3×C42C22×C311yescharacteristic
225C2×(C2×D3)⋊C4C22×C311yescharacteristic
226C2×(C2×D3)⋊C4C22×C311yescharacteristic
227C2×(C2×D3)⋊C4C22×C311yescharacteristic
228C2×(C2×D3)⋊C4C22×C311yescharacteristic
229C2×(C2×D3)⋊C4C22×C311yescharacteristic
230C2×(C2×D3)⋊C4C22×C311yescharacteristic
231C2×C4⋊Dic3C22×C311yescharacteristic
232C2×C4⋊Dic3C22×C311yescharacteristic
233C2×C4⋊Dic3C22×C311yescharacteristic
234C2×C4⋊Dic3C22×C311yescharacteristic
235C2×Dic3⋊C4C22×C311yescharacteristic
236C2×Dic3⋊C4C22×C311yescharacteristic
237C2×Dic3⋊C4C22×C311yescharacteristic
238C2×Dic3⋊C4C22×C311yescharacteristic
239C2×Dic3⋊C4C22×C311yescharacteristic
240C2×Dic3⋊C4C22×C311yescharacteristic
241C2×Dic3⋊C4C22×C311yescharacteristic
242C2×Dic3⋊C4C22×C311yescharacteristic
243C2×Dic3⋊C4C22×C311yescharacteristic
244C2×Dic3⋊C4C22×C311yescharacteristic
245C2×C4×Dic3C22×C311yescharacteristic
246C2×C4×Dic3C22×C311yescharacteristic
247C2×C4×Dic3C22×C311yescharacteristic
248C2×C4×Dic3C22×C311yescharacteristic
249C2×C4×Dic3C22×C311yescharacteristic
250#898C22×C318yes—
251#898C22×C318yes—
252#898C22×C318yes—
253#896C22×C318yes—
254#896C22×C318yes—
255#892C22×C318yes—
256#890C22×C318yescomplemented
257#889C22×C318yescomplemented
258#889C22×C318yescomplemented
259#889C22×C318yescomplemented
260#888C22×C318yescomplemented
261#887C22×C318yescomplemented
262#876C22×C318yes—
263C4×Dic6C22×C318yescomplemented
264C23×C32C2411yescharacteristic
265C22×C3×D3—22no—
266C22×C3×D3—22no—
267C22×C3×D3—22no—
268C22×C3×D3C2412yes—
269C2×C32×C4—22no—
270C2×C32×C4—22no—
271C2×C32×C4—22no—
272C2×C32×C4—22no—
273C2×C32×C4—22no—
274C2×C32×C4—22no—
275C2×C32×C4—22no—
276C2×C32×C4C2412yes—
277C2×C32×C4C2412yes—
278C2×C32×C4C2412yes—
279C2×C32×C4C2412yes—
280C2×C32×C4C2412yes—
281C2×C32×C4C2412yes—
282C2×C32×C4C2412yes—
283C2×C3×Dic3—22no—
284C2×C3×Dic3—22no—
285C2×C3×Dic3—22no—
286C2×C3×Dic3—22no—
287C2×C3×Dic3—22no—
288C2×C3×Dic3—22no—
289C2×C3×Dic3#4114yes—
290C2×C3×Dic3C2412yes—
291C2×C3×Dic3C2412yes—
292C2×C3×Dic3C2412yes—
293C2×C3×Dic3C2412yes—
294C2×C3×Dic3C2412yes—
295C2×C3×Dic3C2412yes—
296C2×C3×Dic3C2412yes—
297C3×C4×D3—28no—
298C3×Dic6—28no—
299C3×Dic6—28no—
300#541—316no—
301C2×C4⋊Q8—31no—
302C2×#126—31no—
303C2×#126—31no—
304C2×#126—31no—
305C2×#126—31no—
306C2×#125—31no—
307C2×#125—31no—
308C2×#125—31no—
309C2×#125—31no—
310C2×#125C3×D311yescharacteristic, complemented
311C2×C22⋊Q8—31no—
312C2×C22⋊Q8—31no—
313C2×C4×Q8—31no—
314C2×C4×Q8—31no—
315C2×#117—31no—
316C24×C3—31no—
317C23×D3C23×C311yescharacteristic
318C2×C3×Q8—34no—
319C2×C3×Q8—34no—
320C2×C3×Q8—64no—
321C2×C3×Q8—64no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—34no—
337C22×C3×C4—64no—
338C22×C3×C4C22×D311yescharacteristic
339C22×C3×C4C22×D311yescharacteristic
340C22×C3×C4C22×D311yescharacteristic
341C22×C3×C4C22×D311yescharacteristic
342C22×C3×C4C22×D311yescharacteristic
343C22×C3×C4C22×D311yescharacteristic
344C22×C3×C4C22×D311yescharacteristic
345C22×C3×C4C23×C311yescharacteristic
346C22×C3×C4C23×C311yescharacteristic
347C22×C3×C4C23×C311yescharacteristic
348C22×C3×C4C23×C311yescharacteristic
349C22×C3×C4C23×C311yescharacteristic
350C22×C3×C4C23×C311yescharacteristic
351C22×C3×C4C23×C311yescharacteristic
352C22×Dic3C23×C311yescharacteristic
353C22×Dic3C23×C311yescharacteristic
354C22×Dic3C23×C311yescharacteristic
355C22×Dic3C23×C311yescharacteristic
356C22×Dic3C23×C311yescharacteristic
357C22×Dic3C23×C311yescharacteristic
358C22×Dic3C23×C311yescharacteristic
359C2×C4×D3—24no—
360C2×C4×D3C23×C314yes—
361C2×Dic6—24no—
362C2×Dic6—24no—
363C2×Dic6C23×C314yes—
364C2×Dic6C23×C314yes—
365C3×C4⋊C4—24no—
366C3×C4⋊C4—24no—
367C3×C4⋊C4—24no—
368C3×C4⋊C4—24no—
369C3×C4⋊C4—24no—
370C3×C4⋊C4—24no—
371C3×C4⋊C4—34no—
372C3×C4⋊C4—34no—
373C3×C4⋊C4—34no—
374C3×C4⋊C4—34no—
375C3×C4⋊C4—34no—
376C3×C4⋊C4—34no—
377C3×C4⋊C4—34no—
378C3×C4⋊C4—34no—
379C3×C4⋊C4—34no—
380C3×C4⋊C4—34no—
381C3×C4⋊C4—34no—
382C3×C4⋊C4—34no—
383C3×C4⋊C4—34no—
384C3×C4⋊C4—34no—
385C3×C4⋊C4C22×D314yes—
386C3×C4⋊C4C22×D314yes—
387C3×C4⋊C4C22×D314yes—
388C3×C4⋊C4C22×D314yes—
389C3×C4⋊C4C22×D314yes—
390C3×C4⋊C4C22×D314yes—
391C3×C4⋊C4C23×C314yes—
392C3×C4⋊C4C23×C314yes—
393C3×C4⋊C4C23×C314yes—
394C3×C4⋊C4C23×C314yes—
395C3×C4⋊C4C23×C314yes—
396C3×C4⋊C4C23×C314yes—
397C3×C22⋊C4—34no—
398C3×C22⋊C4—34no—
399C3×C22⋊C4—34no—
400C3×C22⋊C4—34no—
401C3×C22⋊C4—34no—
402C3×C22⋊C4—34no—
403C3×C42—24no—
404C3×C42—34no—
405C3×C42—34no—
406C3×C42—34no—
407C3×C42—34no—
408C3×C42—34no—
409C3×C42C22×D314yes—
410C3×C42C23×C314yes—
411(C2×D3)⋊C4C23×C314yes—
412(C2×D3)⋊C4C23×C314yes—
413(C2×D3)⋊C4C23×C314yes—
414(C2×D3)⋊C4C23×C314yes—
415(C2×D3)⋊C4C23×C314yes—
416(C2×D3)⋊C4C23×C314yes—
417C4⋊Dic3C23×C314yes—
418C4⋊Dic3C23×C314yes—
419C4⋊Dic3C23×C314yes—
420C4⋊Dic3C23×C314yes—
421Dic3⋊C4C23×C314yes—
422Dic3⋊C4C23×C314yes—
423Dic3⋊C4C23×C314yes—
424Dic3⋊C4C23×C314yes—
425Dic3⋊C4C23×C314yes—
426Dic3⋊C4C23×C314yes—
427Dic3⋊C4C23×C314yes—
428Dic3⋊C4C23×C314yes—
429Dic3⋊C4C23×C314yes—
430Dic3⋊C4C23×C314yes—
431C4×Dic3C23×C314yes—
432C4×Dic3C23×C314yes—
433C4×Dic3C23×C314yes—
434C4×Dic3C23×C314yes—
435C4×Dic3C23×C314yes—
436C22×C32C2×#4112yes—
437C22×C322−1+412yes—
438C22×C322−1+412yes—
439C22×C32C2511yescharacteristic
440C2×C3×D3—22no—
441C2×C3×D3—22no—
442C2×C3×D3—22no—
443C2×C3×D3—44no—
444C32×C4—22no—
445C32×C4—22no—
446C32×C4—22no—
447C32×C4—22no—
448C32×C4—22no—
449C32×C4—22no—
450C32×C4—22no—
451C3×Dic3—22no—
452C3×Dic3—22no—
453C3×Dic3—22no—
454C3×Dic3—22no—
455C3×Dic3—22no—
456C3×Dic3—22no—
457C3×Dic3C2×#4114yes—
458C22×Q8—31no—
459C22×Q8—31no—
460C23×C4—31no—
461C4⋊Q8—38no—
462#126—38no—
463#126—38no—
464#126—38no—
465#126—38no—
466#125—38no—
467#125—38no—
468#125—38no—
469#125—38no—
470#125C2×C3×D318yescomplemented
471C22⋊Q8—38no—
472C22⋊Q8—38no—
473C4×Q8—38no—
474C4×Q8—38no—
475#117—38no—
476C2×C4⋊C4—31no—
477C2×C4⋊C4—31no—
478C2×C4⋊C4—31no—
479C2×C4⋊C4—31no—
480C2×C4⋊C4—31no—
481C2×C4⋊C4—31no—
482C2×C4⋊C4—31no—
483C2×C4⋊C4—31no—
484C2×C4⋊C4—31no—
485C2×C4⋊C4—31no—
486C2×C4⋊C4—31no—
487C2×C4⋊C4—31no—
488C2×C4⋊C4—31no—
489C2×C4⋊C4—31no—
490C2×C4⋊C4C2×C3×D311yescharacteristic
491C2×C4⋊C4C2×C3×D311yescharacteristic
492C2×C4⋊C4C2×C3×D311yescharacteristic
493C2×C4⋊C4C2×C3×D311yescharacteristic
494C2×C4⋊C4C2×C3×D311yescharacteristic
495C2×C4⋊C4C2×C3×D311yescharacteristic
496C2×C22⋊C4—31no—
497C2×C22⋊C4—31no—
498C2×C22⋊C4—31no—
499C2×C22⋊C4—31no—
500C2×C22⋊C4—31no—
501C2×C22⋊C4—31no—
502C2×C42—31no—
503C2×C42—31no—
504C2×C42—31no—
505C2×C42—31no—
506C2×C42—31no—
507C2×C42C2×C3×D311yescharacteristic
508C23×C3—21no—
509C23×C3—32no—
510C23×C3—62no—
511C23×C3—62no—
512C23×C3—62no—
513C23×C3C23×D311yescharacteristic
514C23×C3C24×C311yescharacteristic
515C22×D3—22no—
516C22×D3—22no—
517C22×D3—22no—
518C22×D3C24×C312yes—
519C3×Q8—68no—
520C3×Q8—68no—
521C2×C3×C4—24no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—22no—
542C2×C3×C4—22no—
543C2×C3×C4—34no—
544C2×C3×C4—32no—
545C2×C3×C4—32no—
546C2×C3×C4—32no—
547C2×C3×C4—32no—
548C2×C3×C4—32no—
549C2×C3×C4—32no—
550C2×C3×C4—32no—
551C2×C3×C4—42no—
552C2×C3×C4—42no—
553C2×C3×C4—42no—
554C2×C3×C4—42no—
555C2×C3×C4—42no—
556C2×C3×C4—42no—
557C2×C3×C4—68no—
558C2×C3×C4—62no—
559C2×C3×C4—62no—
560C2×C3×C4—62no—
561C2×C3×C4—62no—
562C2×C3×C4—62no—
563C2×C3×C4—62no—
564C2×C3×C4C23×D312yes—
565C2×C3×C4C23×D312yes—
566C2×C3×C4C23×D312yes—
567C2×C3×C4C23×D312yes—
568C2×C3×C4C23×D312yes—
569C2×C3×C4C23×D312yes—
570C2×C3×C4C23×D312yes—
571C2×C3×C4C24×C312yes—
572C2×C3×C4C24×C312yes—
573C2×C3×C4C24×C312yes—
574C2×C3×C4C24×C312yes—
575C2×C3×C4C24×C312yes—
576C2×C3×C4C24×C312yes—
577C2×C3×C4C24×C312yes—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3C3×#4114yes—
585C2×Dic3C24×C312yes—
586C2×Dic3C24×C312yes—
587C2×Dic3C24×C312yes—
588C2×Dic3C24×C312yes—
589C2×Dic3C24×C312yes—
590C2×Dic3C24×C312yes—
591C2×Dic3C24×C312yes—
592C4×D3—28no—
593Dic6—28no—
594Dic6—28no—
595C2×C32#54114yescomplemented
596C2×C32C22×#4111yescharacteristic
597C2×C32C2×2−1+411yescharacteristic
598C2×C32C2×2−1+411yescharacteristic
599C3×D3—42no—
600C24—31no—
601C2×Q8—34no—
602C2×Q8—34no—
603C2×Q8—64no—
604C2×Q8—64no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—31no—
610C22×C4—31no—
611C22×C4—31no—
612C22×C4—34no—
613C22×C4—64no—
614C22×C4C22×C3×D311yescharacteristic
615C22×C4C22×C3×D311yescharacteristic
616C22×C4C22×C3×D311yescharacteristic
617C22×C4C22×C3×D311yescharacteristic
618C22×C4C22×C3×D311yescharacteristic
619C22×C4C22×C3×D311yescharacteristic
620C22×C4C22×C3×D311yescharacteristic
621C4⋊C4—34no—
622C4⋊C4—34no—
623C4⋊C4—34no—
624C4⋊C4—34no—
625C4⋊C4—34no—
626C4⋊C4—34no—
627C4⋊C4—34no—
628C4⋊C4—34no—
629C4⋊C4—34no—
630C4⋊C4—34no—
631C4⋊C4—34no—
632C4⋊C4—34no—
633C4⋊C4—34no—
634C4⋊C4—34no—
635C4⋊C4C22×C3×D314yes—
636C4⋊C4C22×C3×D314yes—
637C4⋊C4C22×C3×D314yes—
638C4⋊C4C22×C3×D314yes—
639C4⋊C4C22×C3×D314yes—
640C4⋊C4C22×C3×D314yes—
641C22⋊C4—34no—
642C22⋊C4—34no—
643C22⋊C4—34no—
644C22⋊C4—34no—
645C22⋊C4—34no—
646C22⋊C4—34no—
647C42—34no—
648C42—34no—
649C42—34no—
650C42—34no—
651C42—34no—
652C42C22×C3×D314yes—
653C22×C3—22no—
654C22×C3—22no—
655C22×C3—22no—
656C22×C3—21no—
657C22×C3—62no—
658C22×C3—62no—
659C22×C3—62no—
660C22×C3—124no—
661C22×C3#100712yes—
662C22×C3D3×#4112yes—
663C22×C3#101012yes—
664C22×C3C2×C3×#4112yes—
665C22×C3C3×2−1+412yes—
666C22×C3C3×2−1+412yes—
667C22×C3C24×D311yescharacteristic
668C22×C3C25×C311yescharacteristic
669C2×D3—22no—
670C2×D3—22no—
671C2×D3—22no—
672C2×D3—44no—
673C3×C4—24no—
674C3×C4—22no—
675C3×C4—22no—
676C3×C4—22no—
677C3×C4—22no—
678C3×C4—22no—
679C3×C4—22no—
680C3×C4—22no—
681C3×C4—22no—
682C3×C4—22no—
683C3×C4—22no—
684C3×C4—22no—
685C3×C4—22no—
686C3×C4—22no—
687C3×C4—22no—
688C3×C4—34no—
689C3×C4—42no—
690C3×C4—42no—
691C3×C4—42no—
692C3×C4—42no—
693C3×C4—42no—
694C3×C4—42no—
695C3×C4—62no—
696C3×C4—62no—
697C3×C4—62no—
698C3×C4—62no—
699C3×C4—62no—
700C3×C4—62no—
701Dic3—22no—
702Dic3—22no—
703Dic3—22no—
704Dic3—22no—
705Dic3—22no—
706Dic3—22no—
707Dic3C2×C3×#4114yes—
708C32C2×#54111yescharacteristic, complemented, Sylow
709C23—32no—
710C23—62no—
711C23—62no—
712C23—62no—
713C23C23×C3×D311yescharacteristic
714Q8—68no—
715Q8—68no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—34no—
724C2×C4—32no—
725C2×C4—32no—
726C2×C4—32no—
727C2×C4—32no—
728C2×C4—32no—
729C2×C4—32no—
730C2×C4—32no—
731C2×C4—68no—
732C2×C4—62no—
733C2×C4—62no—
734C2×C4—62no—
735C2×C4—62no—
736C2×C4—62no—
737C2×C4—62no—
738C2×C4C23×C3×D312yes—
739C2×C4C23×C3×D312yes—
740C2×C4C23×C3×D312yes—
741C2×C4C23×C3×D312yes—
742C2×C4C23×C3×D312yes—
743C2×C4C23×C3×D312yes—
744C2×C4C23×C3×D312yes—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—24no—
749C2×C3—122no—
750C2×C3#569614yesdirect product factor
751C2×C3C3×#54114yescomplemented
752C2×C3C2×#100711yescharacteristic
753C2×C3C2×D3×#4111yescharacteristic
754C2×C3C2×#101011yescharacteristic
755C2×C3C22×C3×#4111yescharacteristic
756C2×C3C2×C3×2−1+411yescharacteristic
757C2×C3C2×C3×2−1+411yescharacteristic
758D3—42no—
759C22—62no—
760C22—62no—
761C22—62no—
762C22—124no—
763C22C3×#100712yes—
764C22C3×D3×#4112yes—
765C22C3×#101012yes—
766C22C24×C3×D311yescharacteristic
767C4—22no—
768C4—22no—
769C4—22no—
770C4—22no—
771C4—22no—
772C4—22no—
773C4—22no—
774C4—34no—
775C4—62no—
776C4—62no—
777C4—62no—
778C4—62no—
779C4—62no—
780C4—62no—
781C3—21no—
782C3C2×#569611yescharacteristic, direct product factor
783C3C2×C3×#54111yescharacteristic, complemented
784C2—122no—
785C2C3×#569614yesdirect product factor
786C2C2×C3×#100711yescharacteristic
787C2C2×C3×D3×#4111yescharacteristic
788C2C2×C3×#101011yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×#125C2
socleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C3×#125D3
hypocenterC3C2×C3×#541
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×#5696C2direct (N × H)
9. C2×C3×#890C2semidirect
10. C2×C3×#889C2semidirect
11. C2×C3×#889C2semidirect
12. C2×C3×#889C2semidirect
13. C2×C3×#888C2semidirect
14. C2×C3×#887C2semidirect
16. C2×C3×C4×Dic6C2semidirect
18. C2×#5696C3direct (N × H)
22. C32×#125C22semidirect
61. C3×#890C22semidirect
62. C3×#889C22semidirect
63. C3×#889C22semidirect
64. C3×#889C22semidirect
65. C3×#888C22semidirect
66. C3×#887C22semidirect
68. C3×C4×Dic6C22semidirect
80. C2×C3×#125D3semidirect
81. C2×C3×#125C2×C3semidirect
87. #5696C2×C3direct (N × H)
94. C2×#890C2×C3semidirect
95. C2×#889C2×C3semidirect
96. C2×#889C2×C3semidirect
97. C2×#889C2×C3semidirect
98. C2×#888C2×C3semidirect
99. C2×#887C2×C3semidirect
101. C2×C4×Dic6C2×C3semidirect
172. C3×#125C2×D3semidirect
173. C3×#125C22×C3semidirect
256. #890C22×C3semidirect
257. #889C22×C3semidirect
258. #889C22×C3semidirect
259. #889C22×C3semidirect
260. #888C22×C3semidirect
261. #887C22×C3semidirect
263. C4×Dic6C22×C3semidirect
310. C2×#125C3×D3semidirect
470. #125C2×C3×D3semidirect
595. C2×C32#541semidirect
708. C32C2×#541semidirect
750. C2×C3#5696direct (N × H)
751. C2×C3C3×#541semidirect
782. C3C2×#5696direct (N × H)
783. C3C2×C3×#541semidirect
785. C2C3×#5696direct (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×#56962
C2×C3×#8982
C2×C3×#8962
C2×C3×#8922
C2×C3×#8902
C2×C3×#8892
C2×C3×#8882
C2×C3×#8872
C2×C3×#8762
C2×C3×C4×Dic62
C2×C3×#5413
C2×#56963