Finite Group Databasebeta

← C2×C3×#5635 #11903228

Subgroups — C2×C3×#5635 #11903228

Order 1152.

2561 conjugacy classes of subgroups.

The subgroup lattice has 652 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×Q8×Dic3C211yesmaximal, characteristic, complemented
4C2×C3×C4×#67C211yesmaximal, characteristic
5C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
6C3×#5635C2116yesmaximal, direct product factor
7C2×C3×#897C212yesmaximal, complemented
8C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
9C2×C3×#889C212yesmaximal, complemented
10C2×C3×#888C211yesmaximal, characteristic, complemented
11C2×C3×#67⋊C4C212yesmaximal
12C2×C3×#878C212yesmaximal, complemented
13C2×C3×#554—31nomaximal
14C2×#5635C311yesmaximal, characteristic, direct product factor
15C22×C32×Q8C2211yescharacteristic
16C23×C32×C4C2211yescharacteristic
17C22×C3×#67C2211yescharacteristic
18C23×C3×Dic3C2212yes—
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2212yes—
21C22×C3×Dic6C2212yes—
22C32×C22⋊Q8C2218yescomplemented
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×C32×C4⋊C4C2212yes—
25C2×C32×C22⋊C4C2212yes—
26C2×C3×#217C2211yescharacteristic
27C3×#946C2218yescomplemented
28C3×Q8×Dic3C2218yescomplemented
29C3×C4×#67C2218yes—
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2212yes—
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×C4⋊Dic3C2212yes—
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C2×C3×C4⋊Dic3C2212yes—
36C2×C3×C4⋊Dic3C2218yescomplemented
37C2×C3×Dic3⋊C4C2212yes—
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2212yes—
40C2×C3×Dic3⋊C4C2212yes—
41C2×C3×C4×Dic3C2211yescharacteristic
42C2×C3×C4×Dic3C2212yes—
43C3×#897C22116yescomplemented
44C3×D3×C4⋊C4C2218yescomplemented
45C3×#889C22116yescomplemented
46C3×#888C2218yescomplemented
47C3×#67⋊C4C22116yes—
48C3×#878C22116yescomplemented
49C3×#554—316no—
50C2×C3×C4⋊Q8—31no—
51C2×C3×#125—32no—
52C2×C3×C22⋊Q8—21no—
53C2×C3×C22⋊Q8—31no—
54C2×C3×C22⋊Q8—32no—
55C2×C3×C22⋊Q8—32no—
56C2×C3×C22⋊Q8D311yescharacteristic, complemented
57C2×C3×C22⋊Q8C2×C311yescharacteristic, complemented
58C2×C3×C4×Q8—31no—
59C2×C3×C4×D4—31no—
60C2×C3×C4×D4—32no—
61C22×C3×C4⋊C4—31no—
62C22×C3×C4⋊C4—31no—
63C2×#946C2×C311yescharacteristic, complemented
64C2×Q8×Dic3C2×C311yescharacteristic, complemented
65C2×C4×#67C2×C311yescharacteristic
66C22×C4⋊Dic3C2×C311yescharacteristic, complemented
67#5635C2×C3116yesdirect product factor
68C2×#897C2×C312yescomplemented
69C2×D3×C4⋊C4C2×C311yescharacteristic, complemented
70C2×#889C2×C312yescomplemented
71C2×#888C2×C311yescharacteristic, complemented
72C2×#67⋊C4C2×C312yes—
73C2×#878C2×C312yescomplemented
74C24×C32C2311yescharacteristic
75C23×C3×D3C2311yescharacteristic
76C2×C32×Q8—24no—
77C2×C32×Q8C2314yes—
78C22×C32×C4—24no—
79C22×C32×C4C2312yes—
80C22×C32×C4C2312yes—
81C22×C32×C4C2311yescharacteristic
82C22×C32×C4C2314yes—
83C22×C32×C4C2311yescharacteristic
84C2×C3×#67Q818yescomplemented
85C2×C3×#67C2314yes—
86C22×C3×Dic3—44no—
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2311yescharacteristic
90C22×C3×Dic3C2312yes—
91C22×C3×Dic3C2318yes—
92C22×C3×Dic3C2311yescharacteristic
93C2×C3×C4×D3—24no—
94C2×C3×C4×D3—44no—
95C2×C3×C4×D3C2314yes—
96C2×C3×C4×D3C2318yes—
97C2×C3×Dic6—44no—
98C2×C3×Dic6C2318yes—
99C32×C4⋊C4C2314yes—
100C32×C4⋊C4C2318yes—
101C32×C22⋊C4C2318yes—
102C3×#217C2314yes—
103C3×(C2×D3)⋊C4C2318yes—
104C3×(C2×D3)⋊C4C2314yes—
105C3×C4⋊Dic3C2318yes—
106C3×C4⋊Dic3C2314yes—
107C3×C4⋊Dic3C2318yes—
108C3×C4⋊Dic3C2314yes—
109C3×Dic3⋊C4C2318yes—
110C3×Dic3⋊C4C2318yes—
111C3×Dic3⋊C4C2318yes—
112C3×Dic3⋊C4C2314yes—
113C3×C4×Dic3C2318yes—
114C3×C4×Dic3C2314yes—
115C2×#554—31noSylow
116C22×C3×Q8—21no—
117C22×C3×Q8—32no—
118C22×C3×Q8C2×D311yescharacteristic
119C22×C3×Q8C22×C311yescharacteristic
120C22×C3×D4—31no—
121C23×C3×C4—21no—
122C23×C3×C4—32no—
123C23×C3×C4—31no—
124C23×C3×C4—32no—
125C23×C3×C4C2×D311yescharacteristic
126C23×C3×C4C22×C311yescharacteristic
127C22×#67C22×C311yescharacteristic
128C23×Dic3C22×C312yes—
129C22×C4×D3C22×C311yescharacteristic
130C22×C4×D3C22×C312yes—
131C22×Dic6C22×C312yes—
132C3×C4⋊Q8—38no—
133C3×#125—316no—
134C3×C22⋊Q8—28no—
135C3×C22⋊Q8—38no—
136C3×C22⋊Q8—316no—
137C3×C22⋊Q8—316no—
138C3×C22⋊Q8C2×D318yescomplemented
139C3×C22⋊Q8C22×C318yescomplemented
140C3×C4×Q8—38no—
141C3×C4×D4—38no—
142C3×C4×D4—316no—
143C2×C3×C4⋊C4—21no—
144C2×C3×C4⋊C4—22no—
145C2×C3×C4⋊C4—32no—
146C2×C3×C4⋊C4—31no—
147C2×C3×C4⋊C4—32no—
148C2×C3×C4⋊C4—32no—
149C2×C3×C4⋊C4—31no—
150C2×C3×C4⋊C4—32no—
151C2×C3×C4⋊C4—31no—
152C2×C3×C4⋊C4—32no—
153C2×C3×C4⋊C4—38no—
154C2×C3×C4⋊C4—38no—
155C2×C3×C4⋊C4C2×D311yescharacteristic
156C2×C3×C4⋊C4C2×D312yes—
157C2×C3×C4⋊C4C22×C311yescharacteristic
158C2×C3×C4⋊C4C22×C312yes—
159C2×C3×C22⋊C4—22no—
160C2×C3×C22⋊C4—31no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—32no—
163C2×C3×C22⋊C4C2×D312yes—
164C2×C3×C22⋊C4C22×C312yes—
165C2×C3×C42—32no—
166C2×C3×C42—31no—
167C2×#217C22×C311yescharacteristic
168#946C22×C318yescomplemented
169Q8×Dic3C22×C318yescomplemented
170C4×#67C22×C318yes—
171C2×(C2×D3)⋊C4C22×C312yes—
172C2×(C2×D3)⋊C4C22×C311yescharacteristic
173C2×C4⋊Dic3C22×C312yes—
174C2×C4⋊Dic3C22×C311yescharacteristic
175C2×C4⋊Dic3C22×C312yes—
176C2×C4⋊Dic3C22×C311yescharacteristic
177C2×C4⋊Dic3C22×C318yescomplemented
178C2×Dic3⋊C4C22×C312yes—
179C2×Dic3⋊C4C22×C312yes—
180C2×Dic3⋊C4C22×C312yes—
181C2×Dic3⋊C4C22×C311yescharacteristic
182C2×C4×Dic3C22×C312yes—
183C2×C4×Dic3C22×C311yescharacteristic
184#897C22×C3116yescomplemented
185D3×C4⋊C4C22×C318yescomplemented
186#889C22×C3116yescomplemented
187#888C22×C318yescomplemented
188#67⋊C4C22×C3116yes—
189#878C22×C3116yescomplemented
190C23×C32—22no—
191C23×C32—22no—
192C23×C32C2×Q814yes—
193C23×C32C2412yes—
194C23×C32C2411yescharacteristic
195C22×C3×D3—22no—
196C22×C3×D3—22no—
197C22×C3×D3C2×Q814yes—
198C22×C3×D3C2412yes—
199C32×Q8—28no—
200C2×C32×C4—22no—
201C2×C32×C4—24no—
202C2×C32×C4—24no—
203C2×C32×C4—28no—
204C2×C32×C4#4114yes—
205C2×C32×C4C2414yes—
206C2×C32×C4C2414yes—
207C2×C32×C4C2412yes—
208C2×C32×C4C2412yes—
209C3×#67C2×Q8116yescomplemented
210C2×C3×Dic3—22no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—24no—
213C2×C3×Dic3—24no—
214C2×C3×Dic3—48no—
215C2×C3×Dic3C2×Q814yes—
216C2×C3×Dic3C2414yes—
217C2×C3×Dic3C2412yes—
218C2×C3×Dic3C2412yes—
219C2×C3×Dic3C2414yes—
220C2×C3×Dic3C2412yes—
221C3×C4×D3—28no—
222C3×C4×D3—48no—
223C3×Dic6—48no—
224#554—316no—
225C2×C4⋊Q8—31no—
226C2×#125—32no—
227C2×C22⋊Q8—31no—
228C2×C22⋊Q8—32no—
229C2×C22⋊Q8—32no—
230C2×C22⋊Q8C3×D311yescharacteristic, complemented
231C2×C4×Q8—31no—
232C2×C4×D4—31no—
233C2×C4×D4—32no—
234C22×C4⋊C4—31no—
235C22×C4⋊C4—31no—
236C24×C3—21no—
237C24×C3—31no—
238C24×C3C22×D311yescharacteristic
239C24×C3C23×C311yescharacteristic
240C23×D3C23×C311yescharacteristic
241C2×C3×Q8—24no—
242C2×C3×Q8—24no—
243C2×C3×Q8—24no—
244C2×C3×Q8—38no—
245C2×C3×Q8—44no—
246C2×C3×Q8—124no—
247C2×C3×Q8C22×D314yes—
248C2×C3×Q8C23×C314yes—
249C2×C3×D4—38no—
250C2×C3×D4—34no—
251C22×C3×C4—24no—
252C22×C3×C4—24no—
253C22×C3×C4—21no—
254C22×C3×C4—22no—
255C22×C3×C4—22no—
256C22×C3×C4—21no—
257C22×C3×C4—24no—
258C22×C3×C4—31no—
259C22×C3×C4—31no—
260C22×C3×C4—32no—
261C22×C3×C4—31no—
262C22×C3×C4—32no—
263C22×C3×C4—38no—
264C22×C3×C4—34no—
265C22×C3×C4—38no—
266C22×C3×C4—44no—
267C22×C3×C4—64no—
268C22×C3×C4—124no—
269C22×C3×C4—124no—
270C22×C3×C4C22×D314yes—
271C22×C3×C4C22×D312yes—
272C22×C3×C4C22×D311yescharacteristic
273C22×C3×C4C22×D312yes—
274C22×C3×C4C22×D311yescharacteristic
275C22×C3×C4C23×C312yes—
276C22×C3×C4C23×C312yes—
277C22×C3×C4C23×C311yescharacteristic
278C22×C3×C4C23×C314yes—
279C22×C3×C4C23×C311yescharacteristic
280C2×#67C3×Q818yescomplemented
281C2×#67C23×C314yes—
282C22×Dic3—44no—
283C22×Dic3C23×C312yes—
284C22×Dic3C23×C311yescharacteristic
285C22×Dic3C23×C311yescharacteristic
286C22×Dic3C23×C312yes—
287C22×Dic3C23×C318yes—
288C22×Dic3C23×C311yescharacteristic
289C2×C4×D3—24no—
290C2×C4×D3—44no—
291C2×C4×D3C23×C314yes—
292C2×C4×D3C23×C318yes—
293C2×Dic6—44no—
294C2×Dic6C23×C318yes—
295C3×C4⋊C4—24no—
296C3×C4⋊C4—28no—
297C3×C4⋊C4—38no—
298C3×C4⋊C4—34no—
299C3×C4⋊C4—38no—
300C3×C4⋊C4—38no—
301C3×C4⋊C4—34no—
302C3×C4⋊C4—38no—
303C3×C4⋊C4—34no—
304C3×C4⋊C4—38no—
305C3×C4⋊C4C22×D314yes—
306C3×C4⋊C4C22×D318yes—
307C3×C4⋊C4C23×C314yes—
308C3×C4⋊C4C23×C318yes—
309C3×C22⋊C4—28no—
310C3×C22⋊C4—34no—
311C3×C22⋊C4—34no—
312C3×C22⋊C4—38no—
313C3×C22⋊C4C22×D318yes—
314C3×C22⋊C4C23×C318yes—
315C3×C42—38no—
316C3×C42—34no—
317#217C23×C314yes—
318(C2×D3)⋊C4C23×C318yes—
319(C2×D3)⋊C4C23×C314yes—
320C4⋊Dic3C23×C318yes—
321C4⋊Dic3C23×C314yes—
322C4⋊Dic3C23×C318yes—
323C4⋊Dic3C23×C314yes—
324Dic3⋊C4C23×C318yes—
325Dic3⋊C4C23×C318yes—
326Dic3⋊C4C23×C318yes—
327Dic3⋊C4C23×C314yes—
328C4×Dic3C23×C318yes—
329C4×Dic3C23×C314yes—
330C22×C32—28no—
331C22×C32—22no—
332C22×C32—22no—
333C22×C32C22×Q814yes—
334C22×C32C22×Q812yes—
335C22×C32C2×#4112yes—
336C22×C32H(5,𝔽2)12yes—
337C22×C32C2511yescharacteristic
338C2×C3×D3—28no—
339C2×C3×D3—22no—
340C2×C3×D3—22no—
341C2×C3×D3C22×Q814yes—
342C32×C4—22no—
343C32×C4—24no—
344C32×C4—24no—
345C32×C4C2×#4114yes—
346C3×Dic3—22no—
347C3×Dic3—22no—
348C3×Dic3—24no—
349C3×Dic3—24no—
350C3×Dic3C22×Q814yes—
351C22×Q8—32no—
352C22×Q8C2×C3×D311yescharacteristic
353C22×D4—31no—
354C23×C4—32no—
355C23×C4—31no—
356C23×C4—32no—
357C23×C4C2×C3×D311yescharacteristic
358C4⋊Q8—38no—
359#125—316no—
360C22⋊Q8—38no—
361C22⋊Q8—316no—
362C22⋊Q8—316no—
363C22⋊Q8C2×C3×D318yescomplemented
364C4×Q8—38no—
365C4×D4—38no—
366C4×D4—316no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—32no—
369C2×C4⋊C4—32no—
370C2×C4⋊C4—31no—
371C2×C4⋊C4—38no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—32no—
374C2×C4⋊C4—32no—
375C2×C4⋊C4—32no—
376C2×C4⋊C4—38no—
377C2×C4⋊C4C2×C3×D311yescharacteristic
378C2×C4⋊C4C2×C3×D312yes—
379C2×C22⋊C4—31no—
380C2×C22⋊C4—31no—
381C2×C22⋊C4—32no—
382C2×C22⋊C4C2×C3×D312yes—
383C2×C42—32no—
384C2×C42—31no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—21no—
390C23×C3—22no—
391C23×C3—24no—
392C23×C3—34no—
393C23×C3—32no—
394C23×C3—42no—
395C23×C3—42no—
396C23×C3—62no—
397C23×C3—62no—
398C23×C3D3×Q814yes—
399C23×C3C2×C3×Q814yes—
400C23×C3C23×D312yes—
401C23×C3C23×D311yescharacteristic
402C23×C3C24×C312yes—
403C23×C3C24×C311yescharacteristic
404C22×D3—22no—
405C22×D3—22no—
406C22×D3C2×C3×Q814yes—
407C22×D3C24×C312yes—
408C3×Q8—28no—
409C3×Q8—28no—
410C3×Q8—48no—
411C3×Q8—128no—
412C3×D4—316no—
413C2×C3×C4—22no—
414C2×C3×C4—24no—
415C2×C3×C4—24no—
416C2×C3×C4—22no—
417C2×C3×C4—24no—
418C2×C3×C4—24no—
419C2×C3×C4—28no—
420C2×C3×C4—28no—
421C2×C3×C4—22no—
422C2×C3×C4—24no—
423C2×C3×C4—24no—
424C2×C3×C4—22no—
425C2×C3×C4—24no—
426C2×C3×C4—34no—
427C2×C3×C4—32no—
428C2×C3×C4—32no—
429C2×C3×C4—34no—
430C2×C3×C4—32no—
431C2×C3×C4—34no—
432C2×C3×C4—48no—
433C2×C3×C4—44no—
434C2×C3×C4—42no—
435C2×C3×C4—44no—
436C2×C3×C4—62no—
437C2×C3×C4—64no—
438C2×C3×C4—64no—
439C2×C3×C4—62no—
440C2×C3×C4—68no—
441C2×C3×C4—128no—
442C2×C3×C4—128no—
443C2×C3×C4#23714yes—
444C2×C3×C4C3×#4114yes—
445C2×C3×C4C23×D314yes—
446C2×C3×C4C23×D312yes—
447C2×C3×C4C23×D314yes—
448C2×C3×C4C23×D312yes—
449C2×C3×C4C24×C314yes—
450C2×C3×C4C24×C314yes—
451C2×C3×C4C24×C312yes—
452C2×C3×C4C24×C312yes—
453#67C2×C3×Q8116yescomplemented
454C2×Dic3—22no—
455C2×Dic3—22no—
456C2×Dic3—24no—
457C2×Dic3—24no—
458C2×Dic3—48no—
459C2×Dic3C2×C3×Q814yes—
460C2×Dic3C24×C314yes—
461C2×Dic3C24×C312yes—
462C2×Dic3C24×C312yes—
463C2×Dic3C24×C314yes—
464C2×Dic3C24×C312yes—
465C4×D3—28no—
466C4×D3—48no—
467Dic6—48no—
468C2×C32—24no—
469C2×C32#55414yescomplemented
470C2×C32C23×Q811yescharacteristic
471C2×C32C22×#4111yescharacteristic
472C2×C32C2×H(5,𝔽2)11yescharacteristic
473C3×D3—24no—
474C24—31no—
475C24C22×C3×D311yescharacteristic
476C2×Q8—24no—
477C2×Q8—38no—
478C2×Q8—124no—
479C2×Q8C22×C3×D314yes—
480C2×D4—34no—
481C2×D4—38no—
482C22×C4—24no—
483C22×C4—31no—
484C22×C4—31no—
485C22×C4—32no—
486C22×C4—31no—
487C22×C4—32no—
488C22×C4—38no—
489C22×C4—34no—
490C22×C4—38no—
491C22×C4—64no—
492C22×C4—124no—
493C22×C4—124no—
494C22×C4C22×C3×D312yes—
495C22×C4C22×C3×D311yescharacteristic
496C22×C4C22×C3×D312yes—
497C22×C4C22×C3×D314yes—
498C22×C4C22×C3×D311yescharacteristic
499C4⋊C4—34no—
500C4⋊C4—38no—
501C4⋊C4—38no—
502C4⋊C4—34no—
503C4⋊C4—34no—
504C4⋊C4—38no—
505C4⋊C4—38no—
506C4⋊C4—38no—
507C4⋊C4C22×C3×D314yes—
508C4⋊C4C22×C3×D318yes—
509C22⋊C4—34no—
510C22⋊C4—34no—
511C22⋊C4—38no—
512C22⋊C4C22×C3×D318yes—
513C42—38no—
514C42—34no—
515C22×C3—28no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—22no—
519C22×C3—22no—
520C22×C3—28no—
521C22×C3—22no—
522C22×C3—22no—
523C22×C3—24no—
524C22×C3—22no—
525C22×C3—21no—
526C22×C3—34no—
527C22×C3—42no—
528C22×C3—42no—
529C22×C3—48no—
530C22×C3—68no—
531C22×C3—62no—
532C22×C3—62no—
533C22×C3C2×#23712yes—
534C22×C3C2×D3×Q814yes—
535C22×C3C2×D3×Q812yes—
536C22×C3#100912yes—
537C22×C3C22×C3×Q814yes—
538C22×C3C22×C3×Q812yes—
539C22×C3C2×C3×#4112yes—
540C22×C3C3×H(5,𝔽2)12yes—
541C22×C3C24×D311yescharacteristic
542C22×C3C25×C311yescharacteristic
543C2×D3—22no—
544C2×D3—22no—
545C2×D3—28no—
546C2×D3C22×C3×Q814yes—
547C3×C4—22no—
548C3×C4—24no—
549C3×C4—24no—
550C3×C4—22no—
551C3×C4—24no—
552C3×C4—24no—
553C3×C4—24no—
554C3×C4—34no—
555C3×C4—42no—
556C3×C4—44no—
557C3×C4—44no—
558C3×C4—62no—
559C3×C4—64no—
560C3×C4—64no—
561C3×C4—62no—
562C3×C4C2×#23714yes—
563C3×C4C2×C3×#4114yes—
564Dic3—22no—
565Dic3—22no—
566Dic3—24no—
567Dic3—24no—
568Dic3C22×C3×Q814yes—
569C32C2×#55411yescharacteristic, complemented, Sylow
570C23—22no—
571C23—22no—
572C23—34no—
573C23—32no—
574C23—62no—
575C23—62no—
576C23C3×D3×Q814yes—
577C23C23×C3×D312yes—
578C23C23×C3×D311yescharacteristic
579Q8—28no—
580Q8—128no—
581D4—316no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—28no—
586C2×C4—34no—
587C2×C4—32no—
588C2×C4—32no—
589C2×C4—34no—
590C2×C4—32no—
591C2×C4—34no—
592C2×C4—62no—
593C2×C4—64no—
594C2×C4—64no—
595C2×C4—62no—
596C2×C4—68no—
597C2×C4—128no—
598C2×C4—128no—
599C2×C4C3×#23714yes—
600C2×C4C23×C3×D314yes—
601C2×C4C23×C3×D312yes—
602C2×C4C23×C3×D314yes—
603C2×C4C23×C3×D312yes—
604C2×C3—24no—
605C2×C3—24no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—24no—
610C2×C3—44no—
611C2×C3—64no—
612C2×C3#563514yesdirect product factor
613C2×C3C3×#55414yescomplemented
614C2×C3C22×#23711yescharacteristic
615C2×C3C22×D3×Q811yescharacteristic
616C2×C3C2×#100911yescharacteristic
617C2×C3C23×C3×Q811yescharacteristic
618C2×C3C22×C3×#4111yescharacteristic
619C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
620D3—24no—
621C22—22no—
622C22—22no—
623C22—28no—
624C22—34no—
625C22—62no—
626C22—62no—
627C22—68no—
628C22C2×C3×#23712yes—
629C22C2×C3×D3×Q814yes—
630C22C2×C3×D3×Q812yes—
631C22C3×#100912yes—
632C22C24×C3×D311yescharacteristic
633C4—22no—
634C4—24no—
635C4—24no—
636C4—34no—
637C4—62no—
638C4—64no—
639C4—64no—
640C4—62no—
641C4C2×C3×#23714yes—
642C3—21no—
643C3C2×#563511yescharacteristic, direct product factor
644C3C2×C3×#55411yescharacteristic, complemented
645C2—24no—
646C2—64no—
647C2C3×#563514yesdirect product factor
648C2C22×C3×#23711yescharacteristic
649C2C22×C3×D3×Q811yescharacteristic
650C2C2×C3×#100911yescharacteristic
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×Q8×Dic3C2semidirect
5. C22×C3×C4⋊Dic3C2semidirect
6. C3×#5635C2direct (N × H)
7. C2×C3×#897C2semidirect
8. C2×C3×D3×C4⋊C4C2semidirect
9. C2×C3×#889C2semidirect
10. C2×C3×#888C2semidirect
12. C2×C3×#878C2semidirect
14. C2×#5635C3direct (N × H)
22. C32×C22⋊Q8C22semidirect
27. C3×#946C22semidirect
28. C3×Q8×Dic3C22semidirect
36. C2×C3×C4⋊Dic3C22semidirect
43. C3×#897C22semidirect
44. C3×D3×C4⋊C4C22semidirect
45. C3×#889C22semidirect
46. C3×#888C22semidirect
48. C3×#878C22semidirect
56. C2×C3×C22⋊Q8D3semidirect
57. C2×C3×C22⋊Q8C2×C3semidirect
63. C2×#946C2×C3semidirect
64. C2×Q8×Dic3C2×C3semidirect
66. C22×C4⋊Dic3C2×C3semidirect
67. #5635C2×C3direct (N × H)
68. C2×#897C2×C3semidirect
69. C2×D3×C4⋊C4C2×C3semidirect
70. C2×#889C2×C3semidirect
71. C2×#888C2×C3semidirect
73. C2×#878C2×C3semidirect
84. C2×C3×#67Q8semidirect
138. C3×C22⋊Q8C2×D3semidirect
139. C3×C22⋊Q8C22×C3semidirect
168. #946C22×C3semidirect
169. Q8×Dic3C22×C3semidirect
177. C2×C4⋊Dic3C22×C3semidirect
184. #897C22×C3semidirect
185. D3×C4⋊C4C22×C3semidirect
186. #889C22×C3semidirect
187. #888C22×C3semidirect
189. #878C22×C3semidirect
209. C3×#67C2×Q8semidirect
230. C2×C22⋊Q8C3×D3semidirect
280. C2×#67C3×Q8semidirect
363. C22⋊Q8C2×C3×D3semidirect
453. #67C2×C3×Q8semidirect
469. C2×C32#554semidirect
569. C32C2×#554semidirect
612. C2×C3#5635direct (N × H)
613. C2×C3C3×#554semidirect
643. C3C2×#5635direct (N × H)
644. C3C2×C3×#554semidirect
647. C2C3×#5635direct (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×Q8×Dic32
C2×C3×C4×#672
C22×C3×C4⋊Dic32
C3×#56352
C2×C3×#8972
C2×C3×D3×C4⋊C42
C2×C3×#8892
C2×C3×#8882
C2×C3×#67⋊C42
C2×C3×#8782
C2×C3×#5543
C2×#56353