Finite Group Databasebeta

← C2×C3×#5636 #11903216

Subgroups — C2×C3×#5636 #11903216

Order 1152.

2561 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C3×#946C211yesmaximal, characteristic, complemented
3C2×C3×#944C211yesmaximal, characteristic, complemented
4C2×C3×C4×#67C211yesmaximal, characteristic
5C22×C3×Dic3⋊C4C211yesmaximal, characteristic, complemented
6C3×#5636C2116yesmaximal, direct product factor
7C2×C3×#896C211yesmaximal, characteristic, complemented
8C2×C3×#896C211yesmaximal, characteristic, complemented
9C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
10C2×C3×#889C211yesmaximal, characteristic, complemented
11C2×C3×#889C211yesmaximal, characteristic, complemented
12C2×C3×#887C211yesmaximal, characteristic, complemented
13C2×C3×#67⋊C4C211yesmaximal, characteristic
14C2×C3×#67⋊C4C211yesmaximal, characteristic
15C2×C3×#878C211yesmaximal, characteristic, complemented
16C2×C3×#878C211yesmaximal, characteristic, complemented
17C2×C3×#554—31nomaximal
18C2×#5636C311yesmaximal, characteristic, direct product factor
19C22×C32×Q8C2211yescharacteristic
20C23×C32×C4C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic
27C22×C3×Dic6C2211yescharacteristic
28C22×C3×Dic6C2211yescharacteristic
29C32×C22⋊Q8C2218yescomplemented
30C2×C32×C4⋊C4C2211yescharacteristic
31C2×C32×C4⋊C4C2211yescharacteristic
32C2×C32×C4⋊C4C2211yescharacteristic
33C2×C32×C22⋊C4C2211yescharacteristic
34C2×C32×C22⋊C4C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic
36C3×#946C2218yescomplemented
37C3×#944C2218yescomplemented
38C3×C4×#67C2218yes—
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×C4⋊Dic3C2211yescharacteristic
43C2×C3×C4⋊Dic3C2211yescharacteristic
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×Dic3⋊C4C2211yescharacteristic
52C2×C3×Dic3⋊C4C2211yescharacteristic
53C2×C3×Dic3⋊C4C2211yescharacteristic
54C2×C3×Dic3⋊C4C2211yescharacteristic
55C2×C3×Dic3⋊C4C2218yescomplemented
56C2×C3×C4×Dic3C2211yescharacteristic
57C2×C3×C4×Dic3C2211yescharacteristic
58C2×C3×C4×Dic3C2211yescharacteristic
59C3×#896C2218yescomplemented
60C3×#896C2218yescomplemented
61C3×D3×C4⋊C4C2218yescomplemented
62C3×#889C2218yescomplemented
63C3×#889C2218yescomplemented
64C3×#887C2218yescomplemented
65C3×#67⋊C4C2218yes—
66C3×#67⋊C4C2218yes—
67C3×#878C2218yescomplemented
68C3×#878C2218yescomplemented
69C3×#554—316no—
70C2×C3×C4⋊Q8—31no—
71C2×C3×#125—31no—
72C2×C3×#125—31no—
73C2×C3×C22⋊Q8—21no—
74C2×C3×C22⋊Q8—31no—
75C2×C3×C22⋊Q8—31no—
76C2×C3×C22⋊Q8—31no—
77C2×C3×C22⋊Q8—31no—
78C2×C3×C22⋊Q8—31no—
79C2×C3×C22⋊Q8D311yescharacteristic, complemented
80C2×C3×C22⋊Q8C2×C311yescharacteristic, complemented
81C2×C3×C4×Q8—31no—
82C2×C3×C4×D4—31no—
83C2×C3×C4×D4—31no—
84C2×C3×C4×D4—31no—
85C22×C3×C4⋊C4—31no—
86C22×C3×C4⋊C4—31no—
87C2×#946C2×C311yescharacteristic, complemented
88C2×#944C2×C311yescharacteristic, complemented
89C2×C4×#67C2×C311yescharacteristic
90C22×Dic3⋊C4C2×C311yescharacteristic, complemented
91#5636C2×C3116yesdirect product factor
92C2×#896C2×C311yescharacteristic, complemented
93C2×#896C2×C311yescharacteristic, complemented
94C2×D3×C4⋊C4C2×C311yescharacteristic, complemented
95C2×#889C2×C311yescharacteristic, complemented
96C2×#889C2×C311yescharacteristic, complemented
97C2×#887C2×C311yescharacteristic, complemented
98C2×#67⋊C4C2×C311yescharacteristic
99C2×#67⋊C4C2×C311yescharacteristic
100C2×#878C2×C311yescharacteristic, complemented
101C2×#878C2×C311yescharacteristic, complemented
102C24×C32C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C2×C32×Q8—42no—
105C2×C32×Q8C2314yes—
106C22×C32×C4—42no—
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C22×C32×C4C2311yescharacteristic
112C22×C32×C4C2311yescharacteristic
113C22×C32×C4C2314yes—
114C2×C3×#67Q818yescomplemented
115C2×C3×#67C2314yes—
116C22×C3×Dic3—24no—
117C22×C3×Dic3—42no—
118C22×C3×Dic3C2314yes—
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2314yes—
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C2×C3×C4×D3—24no—
128C2×C3×C4×D3—42no—
129C2×C3×C4×D3—42no—
130C2×C3×C4×D3C2314yes—
131C2×C3×C4×D3C2314yes—
132C2×C3×C4×D3C2314yes—
133C2×C3×Dic6—24no—
134C2×C3×Dic6—42no—
135C2×C3×Dic6C2314yes—
136C2×C3×Dic6C2314yes—
137C32×C4⋊C4C2314yes—
138C32×C4⋊C4C2314yes—
139C32×C4⋊C4C2314yes—
140C32×C22⋊C4C2314yes—
141C32×C22⋊C4C2314yes—
142C3×#217C2314yes—
143C3×(C2×D3)⋊C4C2314yes—
144C3×(C2×D3)⋊C4C2314yes—
145C3×(C2×D3)⋊C4C2314yes—
146C3×C4⋊Dic3C2314yes—
147C3×C4⋊Dic3C2314yes—
148C3×Dic3⋊C4C2314yes—
149C3×Dic3⋊C4C2314yes—
150C3×Dic3⋊C4C2314yes—
151C3×Dic3⋊C4C2314yes—
152C3×Dic3⋊C4C2314yes—
153C3×Dic3⋊C4C2314yes—
154C3×Dic3⋊C4C2314yes—
155C3×Dic3⋊C4C2314yes—
156C3×Dic3⋊C4C2314yes—
157C3×Dic3⋊C4C2314yes—
158C3×Dic3⋊C4C2314yes—
159C3×C4×Dic3C2314yes—
160C3×C4×Dic3C2314yes—
161C3×C4×Dic3C2314yes—
162C2×#554—31noSylow
163C22×C3×Q8—21no—
164C22×C3×Q8—31no—
165C22×C3×Q8—31no—
166C22×C3×Q8C2×D311yescharacteristic
167C22×C3×Q8C22×C311yescharacteristic
168C22×C3×D4—31no—
169C23×C3×C4—21no—
170C23×C3×C4—31no—
171C23×C3×C4—31no—
172C23×C3×C4—31no—
173C23×C3×C4—31no—
174C23×C3×C4—31no—
175C23×C3×C4C2×D311yescharacteristic
176C23×C3×C4C22×C311yescharacteristic
177C22×#67C22×C311yescharacteristic
178C23×Dic3C22×C311yescharacteristic
179C23×Dic3C22×C311yescharacteristic
180C22×C4×D3C22×C311yescharacteristic
181C22×C4×D3C22×C311yescharacteristic
182C22×C4×D3C22×C311yescharacteristic
183C22×Dic6C22×C311yescharacteristic
184C22×Dic6C22×C311yescharacteristic
185C3×C4⋊Q8—38no—
186C3×#125—38no—
187C3×#125—38no—
188C3×C22⋊Q8—28no—
189C3×C22⋊Q8—38no—
190C3×C22⋊Q8—38no—
191C3×C22⋊Q8—38no—
192C3×C22⋊Q8—38no—
193C3×C22⋊Q8—38no—
194C3×C22⋊Q8C2×D318yescomplemented
195C3×C22⋊Q8C22×C318yescomplemented
196C3×C4×Q8—38no—
197C3×C4×D4—38no—
198C3×C4×D4—38no—
199C3×C4×D4—38no—
200C2×C3×C4⋊C4—21no—
201C2×C3×C4⋊C4—21no—
202C2×C3×C4⋊C4—21no—
203C2×C3×C4⋊C4—31no—
204C2×C3×C4⋊C4—31no—
205C2×C3×C4⋊C4—31no—
206C2×C3×C4⋊C4—31no—
207C2×C3×C4⋊C4—31no—
208C2×C3×C4⋊C4—31no—
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—38no—
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⋊C4C2×D311yescharacteristic
221C2×C3×C4⋊C4C22×C311yescharacteristic
222C2×C3×C4⋊C4C22×C311yescharacteristic
223C2×C3×C4⋊C4C22×C311yescharacteristic
224C2×C3×C22⋊C4—21no—
225C2×C3×C22⋊C4—21no—
226C2×C3×C22⋊C4—31no—
227C2×C3×C22⋊C4—31no—
228C2×C3×C22⋊C4—31no—
229C2×C3×C22⋊C4—31no—
230C2×C3×C22⋊C4C2×D311yescharacteristic
231C2×C3×C22⋊C4C2×D311yescharacteristic
232C2×C3×C22⋊C4C22×C311yescharacteristic
233C2×C3×C22⋊C4C22×C311yescharacteristic
234C2×C3×C42—31no—
235C2×C3×C42—31no—
236C2×C3×C42—31no—
237C2×#217C22×C311yescharacteristic
238#946C22×C318yescomplemented
239#944C22×C318yescomplemented
240C4×#67C22×C318yes—
241C2×(C2×D3)⋊C4C22×C311yescharacteristic
242C2×(C2×D3)⋊C4C22×C311yescharacteristic
243C2×(C2×D3)⋊C4C22×C311yescharacteristic
244C2×C4⋊Dic3C22×C311yescharacteristic
245C2×C4⋊Dic3C22×C311yescharacteristic
246C2×Dic3⋊C4C22×C311yescharacteristic
247C2×Dic3⋊C4C22×C311yescharacteristic
248C2×Dic3⋊C4C22×C311yescharacteristic
249C2×Dic3⋊C4C22×C311yescharacteristic
250C2×Dic3⋊C4C22×C311yescharacteristic
251C2×Dic3⋊C4C22×C311yescharacteristic
252C2×Dic3⋊C4C22×C311yescharacteristic
253C2×Dic3⋊C4C22×C311yescharacteristic
254C2×Dic3⋊C4C22×C311yescharacteristic
255C2×Dic3⋊C4C22×C311yescharacteristic
256C2×Dic3⋊C4C22×C311yescharacteristic
257C2×Dic3⋊C4C22×C318yescomplemented
258C2×C4×Dic3C22×C311yescharacteristic
259C2×C4×Dic3C22×C311yescharacteristic
260C2×C4×Dic3C22×C311yescharacteristic
261#896C22×C318yescomplemented
262#896C22×C318yescomplemented
263D3×C4⋊C4C22×C318yescomplemented
264#889C22×C318yescomplemented
265#889C22×C318yescomplemented
266#887C22×C318yescomplemented
267#67⋊C4C22×C318yes—
268#67⋊C4C22×C318yes—
269#878C22×C318yescomplemented
270#878C22×C318yescomplemented
271C23×C32—22no—
272C23×C32—22no—
273C23×C32C2×Q814yes—
274C23×C32C2412yes—
275C23×C32C2411yescharacteristic
276C22×C3×D3—22no—
277C22×C3×D3—22no—
278C22×C3×D3C2×Q814yes—
279C22×C3×D3C2412yes—
280C32×Q8—44no—
281C2×C32×C4—22no—
282C2×C32×C4—22no—
283C2×C32×C4—22no—
284C2×C32×C4—22no—
285C2×C32×C4—22no—
286C2×C32×C4—22no—
287C2×C32×C4—44no—
288C2×C32×C4C2412yes—
289C2×C32×C4C2412yes—
290C2×C32×C4C2412yes—
291C2×C32×C4C2412yes—
292C2×C32×C4C2412yes—
293C2×C32×C4C2412yes—
294C3×#67C2×Q8116yescomplemented
295C2×C3×Dic3—22no—
296C2×C3×Dic3—22no—
297C2×C3×Dic3—22no—
298C2×C3×Dic3—22no—
299C2×C3×Dic3—22no—
300C2×C3×Dic3—28no—
301C2×C3×Dic3—44no—
302C2×C3×Dic3C2×Q814yes—
303C2×C3×Dic3#4114yes—
304C2×C3×Dic3C2412yes—
305C2×C3×Dic3C2412yes—
306C2×C3×Dic3C2412yes—
307C2×C3×Dic3C2412yes—
308C2×C3×Dic3C2412yes—
309C2×C3×Dic3C2412yes—
310C2×C3×Dic3C2412yes—
311C3×C4×D3—28no—
312C3×C4×D3—44no—
313C3×C4×D3—44no—
314C3×Dic6—28no—
315C3×Dic6—44no—
316#554—316no—
317C2×C4⋊Q8—31no—
318C2×#125—31no—
319C2×#125—31no—
320C2×C22⋊Q8—31no—
321C2×C22⋊Q8—31no—
322C2×C22⋊Q8—31no—
323C2×C22⋊Q8—31no—
324C2×C22⋊Q8—31no—
325C2×C22⋊Q8C3×D311yescharacteristic, complemented
326C2×C4×Q8—31no—
327C2×C4×D4—31no—
328C2×C4×D4—31no—
329C2×C4×D4—31no—
330C22×C4⋊C4—31no—
331C22×C4⋊C4—31no—
332C24×C3—21no—
333C24×C3—31no—
334C24×C3C22×D311yescharacteristic
335C24×C3C23×C311yescharacteristic
336C23×D3C23×C311yescharacteristic
337C2×C3×Q8—24no—
338C2×C3×Q8—34no—
339C2×C3×Q8—34no—
340C2×C3×Q8—42no—
341C2×C3×Q8—42no—
342C2×C3×Q8—44no—
343C2×C3×Q8—64no—
344C2×C3×Q8—122no—
345C2×C3×Q8C22×D314yes—
346C2×C3×Q8C23×C314yes—
347C2×C3×D4—38no—
348C2×C3×D4—34no—
349C22×C3×C4—21no—
350C22×C3×C4—21no—
351C22×C3×C4—21no—
352C22×C3×C4—21no—
353C22×C3×C4—21no—
354C22×C3×C4—21no—
355C22×C3×C4—24no—
356C22×C3×C4—31no—
357C22×C3×C4—31no—
358C22×C3×C4—34no—
359C22×C3×C4—31no—
360C22×C3×C4—31no—
361C22×C3×C4—31no—
362C22×C3×C4—31no—
363C22×C3×C4—31no—
364C22×C3×C4—34no—
365C22×C3×C4—34no—
366C22×C3×C4—34no—
367C22×C3×C4—34no—
368C22×C3×C4—42no—
369C22×C3×C4—42no—
370C22×C3×C4—44no—
371C22×C3×C4—64no—
372C22×C3×C4—64no—
373C22×C3×C4—122no—
374C22×C3×C4—122no—
375C22×C3×C4—122no—
376C22×C3×C4C22×D311yescharacteristic
377C22×C3×C4C22×D311yescharacteristic
378C22×C3×C4C22×D311yescharacteristic
379C22×C3×C4C22×D311yescharacteristic
380C22×C3×C4C22×D311yescharacteristic
381C22×C3×C4C22×D311yescharacteristic
382C22×C3×C4C22×D314yes—
383C22×C3×C4C23×C311yescharacteristic
384C22×C3×C4C23×C311yescharacteristic
385C22×C3×C4C23×C311yescharacteristic
386C22×C3×C4C23×C311yescharacteristic
387C22×C3×C4C23×C311yescharacteristic
388C22×C3×C4C23×C311yescharacteristic
389C22×C3×C4C23×C314yes—
390C2×#67C3×Q818yescomplemented
391C2×#67C23×C314yes—
392C22×Dic3—24no—
393C22×Dic3—42no—
394C22×Dic3C23×C314yes—
395C22×Dic3C23×C311yescharacteristic
396C22×Dic3C23×C311yescharacteristic
397C22×Dic3C23×C311yescharacteristic
398C22×Dic3C23×C311yescharacteristic
399C22×Dic3C23×C311yescharacteristic
400C22×Dic3C23×C314yes—
401C22×Dic3C23×C311yescharacteristic
402C22×Dic3C23×C311yescharacteristic
403C2×C4×D3—24no—
404C2×C4×D3—42no—
405C2×C4×D3—42no—
406C2×C4×D3C23×C314yes—
407C2×C4×D3C23×C314yes—
408C2×C4×D3C23×C314yes—
409C2×Dic6—24no—
410C2×Dic6—42no—
411C2×Dic6C23×C314yes—
412C2×Dic6C23×C314yes—
413C3×C4⋊C4—24no—
414C3×C4⋊C4—24no—
415C3×C4⋊C4—24no—
416C3×C4⋊C4—34no—
417C3×C4⋊C4—34no—
418C3×C4⋊C4—34no—
419C3×C4⋊C4—34no—
420C3×C4⋊C4—34no—
421C3×C4⋊C4—34no—
422C3×C4⋊C4—34no—
423C3×C4⋊C4—34no—
424C3×C4⋊C4—34no—
425C3×C4⋊C4—34no—
426C3×C4⋊C4—34no—
427C3×C4⋊C4—34no—
428C3×C4⋊C4—34no—
429C3×C4⋊C4C22×D314yes—
430C3×C4⋊C4C22×D314yes—
431C3×C4⋊C4C22×D314yes—
432C3×C4⋊C4C23×C314yes—
433C3×C4⋊C4C23×C314yes—
434C3×C4⋊C4C23×C314yes—
435C3×C22⋊C4—24no—
436C3×C22⋊C4—24no—
437C3×C22⋊C4—34no—
438C3×C22⋊C4—34no—
439C3×C22⋊C4—34no—
440C3×C22⋊C4—34no—
441C3×C22⋊C4C22×D314yes—
442C3×C22⋊C4C22×D314yes—
443C3×C22⋊C4C23×C314yes—
444C3×C22⋊C4C23×C314yes—
445C3×C42—34no—
446C3×C42—34no—
447C3×C42—34no—
448#217C23×C314yes—
449(C2×D3)⋊C4C23×C314yes—
450(C2×D3)⋊C4C23×C314yes—
451(C2×D3)⋊C4C23×C314yes—
452C4⋊Dic3C23×C314yes—
453C4⋊Dic3C23×C314yes—
454Dic3⋊C4C23×C314yes—
455Dic3⋊C4C23×C314yes—
456Dic3⋊C4C23×C314yes—
457Dic3⋊C4C23×C314yes—
458Dic3⋊C4C23×C314yes—
459Dic3⋊C4C23×C314yes—
460Dic3⋊C4C23×C314yes—
461Dic3⋊C4C23×C314yes—
462Dic3⋊C4C23×C314yes—
463Dic3⋊C4C23×C314yes—
464Dic3⋊C4C23×C314yes—
465C4×Dic3C23×C314yes—
466C4×Dic3C23×C314yes—
467C4×Dic3C23×C314yes—
468C22×C32—28no—
469C22×C32—22no—
470C22×C32—22no—
471C22×C32C22×Q814yes—
472C22×C32C22×Q812yes—
473C22×C32C2×#4112yes—
474C22×C32H(5,𝔽2)12yes—
475C22×C32C2511yescharacteristic
476C2×C3×D3—28no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3C22×Q814yes—
480C32×C4—22no—
481C32×C4—22no—
482C32×C4—22no—
483C32×C4—22no—
484C32×C4—22no—
485C32×C4—22no—
486C3×Dic3—22no—
487C3×Dic3—22no—
488C3×Dic3—22no—
489C3×Dic3—22no—
490C3×Dic3—22no—
491C3×Dic3C22×Q814yes—
492C3×Dic3C2×#4114yes—
493C22×Q8—31no—
494C22×Q8—31no—
495C22×Q8C2×C3×D311yescharacteristic
496C22×D4—31no—
497C23×C4—31no—
498C23×C4—31no—
499C23×C4—31no—
500C23×C4—31no—
501C23×C4—31no—
502C23×C4C2×C3×D311yescharacteristic
503C4⋊Q8—38no—
504#125—38no—
505#125—38no—
506C22⋊Q8—38no—
507C22⋊Q8—38no—
508C22⋊Q8—38no—
509C22⋊Q8—38no—
510C22⋊Q8—38no—
511C22⋊Q8C2×C3×D318yescomplemented
512C4×Q8—38no—
513C4×D4—38no—
514C4×D4—38no—
515C4×D4—38no—
516C2×C4⋊C4—31no—
517C2×C4⋊C4—31no—
518C2×C4⋊C4—31no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—31no—
521C2×C4⋊C4—31no—
522C2×C4⋊C4—38no—
523C2×C4⋊C4—31no—
524C2×C4⋊C4—31no—
525C2×C4⋊C4—31no—
526C2×C4⋊C4—31no—
527C2×C4⋊C4—31no—
528C2×C4⋊C4—31no—
529C2×C4⋊C4—31no—
530C2×C4⋊C4—38no—
531C2×C4⋊C4C2×C3×D311yescharacteristic
532C2×C4⋊C4C2×C3×D311yescharacteristic
533C2×C4⋊C4C2×C3×D311yescharacteristic
534C2×C22⋊C4—31no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—31no—
537C2×C22⋊C4—31no—
538C2×C22⋊C4C2×C3×D311yescharacteristic
539C2×C22⋊C4C2×C3×D311yescharacteristic
540C2×C42—31no—
541C2×C42—31no—
542C2×C42—31no—
543C23×C3—22no—
544C23×C3—22no—
545C23×C3—22no—
546C23×C3—22no—
547C23×C3—21no—
548C23×C3—22no—
549C23×C3—24no—
550C23×C3—34no—
551C23×C3—32no—
552C23×C3—42no—
553C23×C3—42no—
554C23×C3—62no—
555C23×C3—62no—
556C23×C3D3×Q814yes—
557C23×C3C2×C3×Q814yes—
558C23×C3C23×D312yes—
559C23×C3C23×D311yescharacteristic
560C23×C3C24×C312yes—
561C23×C3C24×C311yescharacteristic
562C22×D3—22no—
563C22×D3—22no—
564C22×D3C2×C3×Q814yes—
565C22×D3C24×C312yes—
566C3×Q8—44no—
567C3×Q8—44no—
568C3×Q8—48no—
569C3×Q8—68no—
570C3×Q8—124no—
571C3×D4—316no—
572C2×C3×C4—24no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—34no—
592C2×C3×C4—34no—
593C2×C3×C4—32no—
594C2×C3×C4—32no—
595C2×C3×C4—32no—
596C2×C3×C4—32no—
597C2×C3×C4—32no—
598C2×C3×C4—32no—
599C2×C3×C4—32no—
600C2×C3×C4—42no—
601C2×C3×C4—42no—
602C2×C3×C4—42no—
603C2×C3×C4—42no—
604C2×C3×C4—42no—
605C2×C3×C4—44no—
606C2×C3×C4—44no—
607C2×C3×C4—48no—
608C2×C3×C4—68no—
609C2×C3×C4—68no—
610C2×C3×C4—62no—
611C2×C3×C4—62no—
612C2×C3×C4—62no—
613C2×C3×C4—62no—
614C2×C3×C4—62no—
615C2×C3×C4—124no—
616C2×C3×C4—124no—
617C2×C3×C4—124no—
618C2×C3×C4C23×D312yes—
619C2×C3×C4C23×D312yes—
620C2×C3×C4C23×D312yes—
621C2×C3×C4C23×D312yes—
622C2×C3×C4C23×D312yes—
623C2×C3×C4C23×D312yes—
624C2×C3×C4C24×C312yes—
625C2×C3×C4C24×C312yes—
626C2×C3×C4C24×C312yes—
627C2×C3×C4C24×C312yes—
628C2×C3×C4C24×C312yes—
629C2×C3×C4C24×C312yes—
630#67C2×C3×Q8116yescomplemented
631C2×Dic3—22no—
632C2×Dic3—22no—
633C2×Dic3—22no—
634C2×Dic3—22no—
635C2×Dic3—22no—
636C2×Dic3—28no—
637C2×Dic3—44no—
638C2×Dic3C2×C3×Q814yes—
639C2×Dic3C3×#4114yes—
640C2×Dic3C24×C312yes—
641C2×Dic3C24×C312yes—
642C2×Dic3C24×C312yes—
643C2×Dic3C24×C312yes—
644C2×Dic3C24×C312yes—
645C2×Dic3C24×C312yes—
646C2×Dic3C24×C312yes—
647C4×D3—28no—
648C4×D3—44no—
649C4×D3—44no—
650Dic6—28no—
651Dic6—44no—
652C2×C32—24no—
653C2×C32#55414yescomplemented
654C2×C32C23×Q811yescharacteristic
655C2×C32C22×#4111yescharacteristic
656C2×C32C2×H(5,𝔽2)11yescharacteristic
657C3×D3—24no—
658C24—31no—
659C24C22×C3×D311yescharacteristic
660C2×Q8—34no—
661C2×Q8—34no—
662C2×Q8—42no—
663C2×Q8—64no—
664C2×Q8—122no—
665C2×Q8C22×C3×D314yes—
666C2×D4—34no—
667C2×D4—38no—
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—31no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—31no—
674C22×C4—31no—
675C22×C4—34no—
676C22×C4—34no—
677C22×C4—34no—
678C22×C4—34no—
679C22×C4—34no—
680C22×C4—42no—
681C22×C4—64no—
682C22×C4—64no—
683C22×C4—122no—
684C22×C4—122no—
685C22×C4—122no—
686C22×C4C22×C3×D311yescharacteristic
687C22×C4C22×C3×D311yescharacteristic
688C22×C4C22×C3×D311yescharacteristic
689C22×C4C22×C3×D311yescharacteristic
690C22×C4C22×C3×D311yescharacteristic
691C22×C4C22×C3×D311yescharacteristic
692C22×C4C22×C3×D314yes—
693C4⋊C4—34no—
694C4⋊C4—34no—
695C4⋊C4—34no—
696C4⋊C4—34no—
697C4⋊C4—34no—
698C4⋊C4—34no—
699C4⋊C4—34no—
700C4⋊C4—34no—
701C4⋊C4—34no—
702C4⋊C4—34no—
703C4⋊C4—34no—
704C4⋊C4—34no—
705C4⋊C4—34no—
706C4⋊C4C22×C3×D314yes—
707C4⋊C4C22×C3×D314yes—
708C4⋊C4C22×C3×D314yes—
709C22⋊C4—34no—
710C22⋊C4—34no—
711C22⋊C4—34no—
712C22⋊C4—34no—
713C22⋊C4C22×C3×D314yes—
714C22⋊C4C22×C3×D314yes—
715C42—34no—
716C42—34no—
717C42—34no—
718C22×C3—28no—
719C22×C3—22no—
720C22×C3—22no—
721C22×C3—22no—
722C22×C3—22no—
723C22×C3—28no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—24no—
727C22×C3—22no—
728C22×C3—21no—
729C22×C3—34no—
730C22×C3—42no—
731C22×C3—42no—
732C22×C3—48no—
733C22×C3—68no—
734C22×C3—62no—
735C22×C3—62no—
736C22×C3#100412yes—
737C22×C3C2×D3×Q814yes—
738C22×C3C2×D3×Q812yes—
739C22×C3D3×#4112yes—
740C22×C3C22×C3×Q814yes—
741C22×C3C22×C3×Q812yes—
742C22×C3C2×C3×#4112yes—
743C22×C3C3×H(5,𝔽2)12yes—
744C22×C3C24×D311yescharacteristic
745C22×C3C25×C311yescharacteristic
746C2×D3—22no—
747C2×D3—22no—
748C2×D3—28no—
749C2×D3C22×C3×Q814yes—
750C3×C4—24no—
751C3×C4—22no—
752C3×C4—22no—
753C3×C4—22no—
754C3×C4—22no—
755C3×C4—22no—
756C3×C4—22no—
757C3×C4—22no—
758C3×C4—22no—
759C3×C4—22no—
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—22no—
763C3×C4—34no—
764C3×C4—34no—
765C3×C4—42no—
766C3×C4—42no—
767C3×C4—42no—
768C3×C4—42no—
769C3×C4—42no—
770C3×C4—62no—
771C3×C4—62no—
772C3×C4—62no—
773C3×C4—62no—
774C3×C4—62no—
775Dic3—22no—
776Dic3—22no—
777Dic3—22no—
778Dic3—22no—
779Dic3—22no—
780Dic3C22×C3×Q814yes—
781Dic3C2×C3×#4114yes—
782C32C2×#55411yescharacteristic, complemented, Sylow
783C23—22no—
784C23—22no—
785C23—34no—
786C23—32no—
787C23—62no—
788C23—62no—
789C23C3×D3×Q814yes—
790C23C23×C3×D312yes—
791C23C23×C3×D311yescharacteristic
792Q8—44no—
793Q8—68no—
794Q8—124no—
795D4—316no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—34no—
803C2×C4—34no—
804C2×C4—32no—
805C2×C4—32no—
806C2×C4—32no—
807C2×C4—32no—
808C2×C4—32no—
809C2×C4—32no—
810C2×C4—32no—
811C2×C4—44no—
812C2×C4—68no—
813C2×C4—68no—
814C2×C4—62no—
815C2×C4—62no—
816C2×C4—62no—
817C2×C4—62no—
818C2×C4—62no—
819C2×C4—124no—
820C2×C4—124no—
821C2×C4—124no—
822C2×C4C23×C3×D312yes—
823C2×C4C23×C3×D312yes—
824C2×C4C23×C3×D312yes—
825C2×C4C23×C3×D312yes—
826C2×C4C23×C3×D312yes—
827C2×C4C23×C3×D312yes—
828C2×C3—24no—
829C2×C3—24no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—24no—
834C2×C3—44no—
835C2×C3—64no—
836C2×C3#563614yesdirect product factor
837C2×C3C3×#55414yescomplemented
838C2×C3C2×#100411yescharacteristic
839C2×C3C22×D3×Q811yescharacteristic
840C2×C3C2×D3×#4111yescharacteristic
841C2×C3C23×C3×Q811yescharacteristic
842C2×C3C22×C3×#4111yescharacteristic
843C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
844D3—24no—
845C22—22no—
846C22—22no—
847C22—28no—
848C22—34no—
849C22—62no—
850C22—62no—
851C22—68no—
852C22C3×#100412yes—
853C22C2×C3×D3×Q814yes—
854C22C2×C3×D3×Q812yes—
855C22C3×D3×#4112yes—
856C22C24×C3×D311yescharacteristic
857C4—22no—
858C4—22no—
859C4—22no—
860C4—22no—
861C4—22no—
862C4—22no—
863C4—34no—
864C4—34no—
865C4—62no—
866C4—62no—
867C4—62no—
868C4—62no—
869C4—62no—
870C3—21no—
871C3C2×#563611yescharacteristic, direct product factor
872C3C2×C3×#55411yescharacteristic, complemented
873C2—24no—
874C2—64no—
875C2C3×#563614yesdirect product factor
876C2C2×C3×#100411yescharacteristic
877C2C22×C3×D3×Q811yescharacteristic
878C2C2×C3×D3×#4111yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×C22⋊Q8C2
socleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC2×C3×C22⋊Q8D3
hypocenterC3C2×C3×#554
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C22⋊Q8C2semidirect
2. C2×C3×#946C2semidirect
3. C2×C3×#944C2semidirect
5. C22×C3×Dic3⋊C4C2semidirect
6. C3×#5636C2direct (N × H)
7. C2×C3×#896C2semidirect
8. C2×C3×#896C2semidirect
9. C2×C3×D3×C4⋊C4C2semidirect
10. C2×C3×#889C2semidirect
11. C2×C3×#889C2semidirect
12. C2×C3×#887C2semidirect
15. C2×C3×#878C2semidirect
16. C2×C3×#878C2semidirect
18. C2×#5636C3direct (N × H)
29. C32×C22⋊Q8C22semidirect
36. C3×#946C22semidirect
37. C3×#944C22semidirect
55. C2×C3×Dic3⋊C4C22semidirect
59. C3×#896C22semidirect
60. C3×#896C22semidirect
61. C3×D3×C4⋊C4C22semidirect
62. C3×#889C22semidirect
63. C3×#889C22semidirect
64. C3×#887C22semidirect
67. C3×#878C22semidirect
68. C3×#878C22semidirect
79. C2×C3×C22⋊Q8D3semidirect
80. C2×C3×C22⋊Q8C2×C3semidirect
87. C2×#946C2×C3semidirect
88. C2×#944C2×C3semidirect
90. C22×Dic3⋊C4C2×C3semidirect
91. #5636C2×C3direct (N × H)
92. C2×#896C2×C3semidirect
93. C2×#896C2×C3semidirect
94. C2×D3×C4⋊C4C2×C3semidirect
95. C2×#889C2×C3semidirect
96. C2×#889C2×C3semidirect
97. C2×#887C2×C3semidirect
100. C2×#878C2×C3semidirect
101. C2×#878C2×C3semidirect
114. C2×C3×#67Q8semidirect
194. C3×C22⋊Q8C2×D3semidirect
195. C3×C22⋊Q8C22×C3semidirect
238. #946C22×C3semidirect
239. #944C22×C3semidirect
257. C2×Dic3⋊C4C22×C3semidirect
261. #896C22×C3semidirect
262. #896C22×C3semidirect
263. D3×C4⋊C4C22×C3semidirect
264. #889C22×C3semidirect
265. #889C22×C3semidirect
266. #887C22×C3semidirect
269. #878C22×C3semidirect
270. #878C22×C3semidirect
294. C3×#67C2×Q8semidirect
325. C2×C22⋊Q8C3×D3semidirect
390. C2×#67C3×Q8semidirect
511. C22⋊Q8C2×C3×D3semidirect
630. #67C2×C3×Q8semidirect
653. C2×C32#554semidirect
782. C32C2×#554semidirect
836. C2×C3#5636direct (N × H)
837. C2×C3C3×#554semidirect
871. C3C2×#5636direct (N × H)
872. C3C2×C3×#554semidirect
875. C2C3×#5636direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C22⋊Q82
C2×C3×#9462
C2×C3×#9442
C2×C3×C4×#672
C22×C3×Dic3⋊C42
C3×#56362
C2×C3×#8962
C2×C3×D3×C4⋊C42
C2×C3×#8892
C2×C3×#8872
C2×C3×#67⋊C42
C2×C3×#8782
C2×C3×#5543
C2×#56363