Finite Group Databasebeta

← C2×C3×#5511 #11903219

Subgroups — C2×C3×#5511 #11903219

Order 1152.

2609 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
1C22×C32×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C211yesmaximal, characteristic
3C2×C3×C4×#67C212yesmaximal
4C2×C3×#924C212yesmaximal, complemented
5C2×C3×#924C211yesmaximal, characteristic, complemented
6C3×#5511C2116yesmaximal, direct product factor
7C2×C3×#897C211yesmaximal, characteristic, complemented
8C2×C3×#896C212yesmaximal, complemented
9C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
10C2×C3×#889C212yesmaximal, complemented
11C2×C3×#888C211yesmaximal, characteristic, complemented
12C2×C3×#887C211yesmaximal, characteristic, complemented
13C2×C3×#554—31nomaximal
14C2×#5511C311yesmaximal, characteristic, direct product factor
15C23×C32×C4C2211yescharacteristic
16C23×C32×C4C2212yes—
17C22×C3×#67C2211yescharacteristic
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×C4×D3C2212yes—
20C22×C3×Dic6C2211yescharacteristic
21C22×C3×Dic6C2212yes—
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×C32×C4⋊C4C2212yes—
25C2×C32×C4⋊C4C2218yescomplemented
26C2×C3×#217C2212yes—
27C2×C3×#217C2211yescharacteristic
28C3×C4×#67C2218yes—
29C3×C4×#67C22116yes—
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2212yes—
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×C4⋊Dic3C2212yes—
34C3×#924C22116yescomplemented
35C3×#924C2218yescomplemented
36C2×C3×Dic3⋊C4C2212yes—
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×#897C2218yescomplemented
44C3×#896C22116yescomplemented
45C3×D3×C4⋊C4C2218yescomplemented
46C3×#889C22116yescomplemented
47C3×#888C2218yescomplemented
48C3×#887C2218yescomplemented
49C3×#554—316no—
50C2×C3×C4⋊Q8—31no—
51C2×C3×#125—32no—
52C2×C3×C22⋊Q8—32no—
53C2×C3×C22⋊Q8—31no—
54C2×C3×C22⋊Q8—32no—
55C2×C3×C22⋊Q8—31no—
56C2×C3×C4×Q8—31no—
57C2×C3×C4×D4—32no—
58C2×C3×C4×D4—31no—
59C22×C3×C4⋊C4—21no—
60C22×C3×C4⋊C4—31no—
61C22×C3×C4⋊C4D311yescharacteristic, complemented
62C22×C3×C4⋊C4C2×C311yescharacteristic, complemented
63C2×C4×#67C2×C311yescharacteristic
64C2×C4×#67C2×C312yes—
65C2×#924C2×C312yescomplemented
66C2×#924C2×C311yescharacteristic, complemented
67#5511C2×C3116yesdirect product factor
68C2×#897C2×C311yescharacteristic, complemented
69C2×#896C2×C312yescomplemented
70C2×D3×C4⋊C4C2×C311yescharacteristic, complemented
71C2×#889C2×C312yescomplemented
72C2×#888C2×C311yescharacteristic, complemented
73C2×#887C2×C311yescharacteristic, complemented
74C24×C32C2311yescharacteristic
75C23×C3×D3C2311yescharacteristic
76C22×C32×C4—24no—
77C22×C32×C4—44no—
78C22×C32×C4C2312yes—
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2312yes—
81C22×C32×C4C2314yes—
82C22×C32×C4C2318yes—
83C22×C32×C4C2311yescharacteristic
84C2×C3×#67Q818yescomplemented
85C2×C3×#67C2314yes—
86C22×C3×Dic3C2312yes—
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2312yes—
90C22×C3×Dic3C2311yescharacteristic
91C2×C3×C4×D3—24no—
92C2×C3×C4×D3—44no—
93C2×C3×C4×D3C2314yes—
94C2×C3×C4×D3C2318yes—
95C2×C3×Dic6—24no—
96C2×C3×Dic6—44no—
97C2×C3×Dic6C2314yes—
98C2×C3×Dic6C2318yes—
99C32×C4⋊C4C2314yes—
100C32×C4⋊C4C2314yes—
101C32×C4⋊C4C2318yes—
102C3×#217C2318yes—
103C3×#217C2314yes—
104C3×(C2×D3)⋊C4C2314yes—
105C3×(C2×D3)⋊C4C2318yes—
106C3×C4⋊Dic3C2314yes—
107C3×C4⋊Dic3C2318yes—
108C3×Dic3⋊C4C2318yes—
109C3×Dic3⋊C4C2318yes—
110C3×Dic3⋊C4C2314yes—
111C3×Dic3⋊C4C2318yes—
112C3×Dic3⋊C4C2318yes—
113C3×C4×Dic3C2314yes—
114C3×C4×Dic3C2318yes—
115C2×#554—31noSylow
116C22×C3×Q8—31no—
117C22×C3×Q8—32no—
118C22×C3×D4—31no—
119C23×C3×C4—21no—
120C23×C3×C4—22no—
121C23×C3×C4—31no—
122C23×C3×C4—32no—
123C23×C3×C4C2×D311yescharacteristic
124C23×C3×C4C2×D312yes—
125C23×C3×C4C22×C311yescharacteristic
126C23×C3×C4C22×C312yes—
127C22×#67C22×C311yescharacteristic
128C22×C4×D3C22×C311yescharacteristic
129C22×C4×D3C22×C312yes—
130C22×Dic6C22×C311yescharacteristic
131C22×Dic6C22×C312yes—
132C3×C4⋊Q8—38no—
133C3×#125—316no—
134C3×C22⋊Q8—316no—
135C3×C22⋊Q8—38no—
136C3×C22⋊Q8—316no—
137C3×C22⋊Q8—38no—
138C3×C4×Q8—38no—
139C3×C4×D4—316no—
140C3×C4×D4—38no—
141C2×C3×C4⋊C4—21no—
142C2×C3×C4⋊C4—22no—
143C2×C3×C4⋊C4—21no—
144C2×C3×C4⋊C4—28no—
145C2×C3×C4⋊C4—32no—
146C2×C3×C4⋊C4—31no—
147C2×C3×C4⋊C4—32no—
148C2×C3×C4⋊C4—32no—
149C2×C3×C4⋊C4—32no—
150C2×C3×C4⋊C4—31no—
151C2×C3×C4⋊C4—32no—
152C2×C3×C4⋊C4—38no—
153C2×C3×C4⋊C4C2×D311yescharacteristic
154C2×C3×C4⋊C4C2×D312yes—
155C2×C3×C4⋊C4C2×D311yescharacteristic
156C2×C3×C4⋊C4C2×D318yescomplemented
157C2×C3×C4⋊C4C22×C311yescharacteristic
158C2×C3×C4⋊C4C22×C311yescharacteristic
159C2×C3×C4⋊C4C22×C312yes—
160C2×C3×C4⋊C4C22×C318yescomplemented
161C2×C3×C22⋊C4—32no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—32no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C42—32no—
166C2×C3×C42—31no—
167C2×#217C22×C312yes—
168C2×#217C22×C311yescharacteristic
169C4×#67C22×C318yes—
170C4×#67C22×C3116yes—
171C2×(C2×D3)⋊C4C22×C311yescharacteristic
172C2×(C2×D3)⋊C4C22×C312yes—
173C2×C4⋊Dic3C22×C311yescharacteristic
174C2×C4⋊Dic3C22×C312yes—
175#924C22×C3116yescomplemented
176#924C22×C318yescomplemented
177C2×Dic3⋊C4C22×C312yes—
178C2×Dic3⋊C4C22×C312yes—
179C2×Dic3⋊C4C22×C311yescharacteristic
180C2×Dic3⋊C4C22×C312yes—
181C2×Dic3⋊C4C22×C312yes—
182C2×C4×Dic3C22×C311yescharacteristic
183C2×C4×Dic3C22×C312yes—
184#897C22×C318yescomplemented
185#896C22×C3116yescomplemented
186D3×C4⋊C4C22×C318yescomplemented
187#889C22×C3116yescomplemented
188#888C22×C318yescomplemented
189#887C22×C318yescomplemented
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—
199C2×C32×C4—22no—
200C2×C32×C4—28no—
201C2×C32×C4—24no—
202C2×C32×C4—24no—
203C2×C32×C4—48no—
204C2×C32×C4#4114yes—
205C2×C32×C4C2414yes—
206C2×C32×C4C2412yes—
207C2×C32×C4C2414yes—
208C2×C32×C4C2412yes—
209C3×#67C2×Q8116yescomplemented
210C2×C3×Dic3—24no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—24no—
214C2×C3×Dic3C2×Q814yes—
215C2×C3×Dic3C2414yes—
216C2×C3×Dic3C2412yes—
217C2×C3×Dic3C2412yes—
218C2×C3×Dic3C2414yes—
219C2×C3×Dic3C2412yes—
220C3×C4×D3—28no—
221C3×C4×D3—48no—
222C3×Dic6—28no—
223C3×Dic6—48no—
224#554—316no—
225C2×C4⋊Q8—31no—
226C2×#125—32no—
227C2×C22⋊Q8—32no—
228C2×C22⋊Q8—31no—
229C2×C22⋊Q8—32no—
230C2×C22⋊Q8—31no—
231C2×C4×Q8—31no—
232C2×C4×D4—32no—
233C2×C4×D4—31no—
234C22×C4⋊C4—31no—
235C22×C4⋊C4C3×D311yescharacteristic, complemented
236C24×C3—21no—
237C24×C3—31no—
238C24×C3C22×D311yescharacteristic
239C24×C3C23×C311yescharacteristic
240C23×D3C23×C311yescharacteristic
241C2×C3×Q8—34no—
242C2×C3×Q8—38no—
243C2×C3×Q8—64no—
244C2×C3×Q8—124no—
245C2×C3×D4—38no—
246C2×C3×D4—34no—
247C22×C3×C4—28no—
248C22×C3×C4—24no—
249C22×C3×C4—24no—
250C22×C3×C4—21no—
251C22×C3×C4—24no—
252C22×C3×C4—21no—
253C22×C3×C4—22no—
254C22×C3×C4—22no—
255C22×C3×C4—28no—
256C22×C3×C4—31no—
257C22×C3×C4—32no—
258C22×C3×C4—31no—
259C22×C3×C4—31no—
260C22×C3×C4—32no—
261C22×C3×C4—34no—
262C22×C3×C4—38no—
263C22×C3×C4—44no—
264C22×C3×C4—44no—
265C22×C3×C4—48no—
266C22×C3×C4—64no—
267C22×C3×C4—124no—
268C22×C3×C4C22×D314yes—
269C22×C3×C4C22×D312yes—
270C22×C3×C4C22×D311yescharacteristic
271C22×C3×C4C22×D312yes—
272C22×C3×C4C22×D318yes—
273C22×C3×C4C22×D311yescharacteristic
274C22×C3×C4C23×C312yes—
275C22×C3×C4C23×C311yescharacteristic
276C22×C3×C4C23×C312yes—
277C22×C3×C4C23×C314yes—
278C22×C3×C4C23×C318yes—
279C22×C3×C4C23×C311yescharacteristic
280C2×#67C3×Q818yescomplemented
281C2×#67C23×C314yes—
282C22×Dic3C23×C312yes—
283C22×Dic3C23×C311yescharacteristic
284C22×Dic3C23×C311yescharacteristic
285C22×Dic3C23×C312yes—
286C22×Dic3C23×C311yescharacteristic
287C2×C4×D3—24no—
288C2×C4×D3—44no—
289C2×C4×D3C23×C314yes—
290C2×C4×D3C23×C318yes—
291C2×Dic6—24no—
292C2×Dic6—44no—
293C2×Dic6C23×C314yes—
294C2×Dic6C23×C318yes—
295C3×C4⋊C4—24no—
296C3×C4⋊C4—28no—
297C3×C4⋊C4—24no—
298C3×C4⋊C4—38no—
299C3×C4⋊C4—34no—
300C3×C4⋊C4—38no—
301C3×C4⋊C4—38no—
302C3×C4⋊C4—38no—
303C3×C4⋊C4—34no—
304C3×C4⋊C4—38no—
305C3×C4⋊C4C22×D314yes—
306C3×C4⋊C4C22×D318yes—
307C3×C4⋊C4C22×D314yes—
308C3×C4⋊C4C23×C314yes—
309C3×C4⋊C4C23×C314yes—
310C3×C4⋊C4C23×C318yes—
311C3×C22⋊C4—38no—
312C3×C22⋊C4—34no—
313C3×C22⋊C4—38no—
314C3×C22⋊C4—34no—
315C3×C42—38no—
316C3×C42—34no—
317#217C23×C318yes—
318#217C23×C314yes—
319(C2×D3)⋊C4C23×C314yes—
320(C2×D3)⋊C4C23×C318yes—
321C4⋊Dic3C23×C314yes—
322C4⋊Dic3C23×C318yes—
323Dic3⋊C4C23×C318yes—
324Dic3⋊C4C23×C318yes—
325Dic3⋊C4C23×C314yes—
326Dic3⋊C4C23×C318yes—
327Dic3⋊C4C23×C318yes—
328C4×Dic3C23×C314yes—
329C4×Dic3C23×C318yes—
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—24no—
347C3×Dic3—22no—
348C3×Dic3—22no—
349C3×Dic3—24no—
350C3×Dic3C22×Q814yes—
351C22×Q8—31no—
352C22×Q8—32no—
353C22×D4—31no—
354C23×C4—31no—
355C23×C4—32no—
356C23×C4C2×C3×D311yescharacteristic
357C23×C4C2×C3×D312yes—
358C4⋊Q8—38no—
359#125—316no—
360C22⋊Q8—316no—
361C22⋊Q8—38no—
362C22⋊Q8—316no—
363C22⋊Q8—38no—
364C4×Q8—38no—
365C4×D4—316no—
366C4×D4—38no—
367C2×C4⋊C4—32no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—31no—
370C2×C4⋊C4—32no—
371C2×C4⋊C4—32no—
372C2×C4⋊C4—32no—
373C2×C4⋊C4—32no—
374C2×C4⋊C4—38no—
375C2×C4⋊C4C2×C3×D311yescharacteristic
376C2×C4⋊C4C2×C3×D312yes—
377C2×C4⋊C4C2×C3×D311yescharacteristic
378C2×C4⋊C4C2×C3×D318yescomplemented
379C2×C22⋊C4—32no—
380C2×C22⋊C4—31no—
381C2×C22⋊C4—32no—
382C2×C22⋊C4—31no—
383C2×C42—32no—
384C2×C42—31no—
385C23×C3—24no—
386C23×C3—24no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—21no—
393C23×C3—24no—
394C23×C3—34no—
395C23×C3—32no—
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—68no—
409C3×Q8—128no—
410C3×D4—316no—
411C2×C3×C4—24no—
412C2×C3×C4—216no—
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—22no—
423C2×C3×C4—24no—
424C2×C3×C4—24no—
425C2×C3×C4—24no—
426C2×C3×C4—34no—
427C2×C3×C4—32no—
428C2×C3×C4—34no—
429C2×C3×C4—32no—
430C2×C3×C4—32no—
431C2×C3×C4—34no—
432C2×C3×C4—44no—
433C2×C3×C4—44no—
434C2×C3×C4—48no—
435C2×C3×C4—48no—
436C2×C3×C4—416no—
437C2×C3×C4—62no—
438C2×C3×C4—64no—
439C2×C3×C4—64no—
440C2×C3×C4—62no—
441C2×C3×C4—68no—
442C2×C3×C4—128no—
443C2×C3×C4#23514yes—
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×C312yes—
451C2×C3×C4C24×C314yes—
452C2×C3×C4C24×C312yes—
453#67C2×C3×Q8116yescomplemented
454C2×Dic3—24no—
455C2×Dic3—22no—
456C2×Dic3—22no—
457C2×Dic3—24no—
458C2×Dic3C2×C3×Q814yes—
459C2×Dic3C24×C314yes—
460C2×Dic3C24×C312yes—
461C2×Dic3C24×C312yes—
462C2×Dic3C24×C314yes—
463C2×Dic3C24×C312yes—
464C4×D3—28no—
465C4×D3—48no—
466Dic6—28no—
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—34no—
477C2×Q8—38no—
478C2×Q8—64no—
479C2×Q8—124no—
480C2×D4—34no—
481C2×D4—38no—
482C22×C4—24no—
483C22×C4—31no—
484C22×C4—32no—
485C22×C4—31no—
486C22×C4—31no—
487C22×C4—32no—
488C22×C4—34no—
489C22×C4—38no—
490C22×C4—44no—
491C22×C4—64no—
492C22×C4—124no—
493C22×C4C22×C3×D312yes—
494C22×C4C22×C3×D311yescharacteristic
495C22×C4C22×C3×D312yes—
496C22×C4C22×C3×D314yes—
497C22×C4C22×C3×D318yes—
498C22×C4C22×C3×D311yescharacteristic
499C4⋊C4—38no—
500C4⋊C4—34no—
501C4⋊C4—34no—
502C4⋊C4—38no—
503C4⋊C4—38no—
504C4⋊C4—38no—
505C4⋊C4—38no—
506C4⋊C4C22×C3×D314yes—
507C4⋊C4C22×C3×D318yes—
508C4⋊C4C22×C3×D314yes—
509C22⋊C4—38no—
510C22⋊C4—34no—
511C22⋊C4—38no—
512C22⋊C4—34no—
513C42—38no—
514C42—34no—
515C22×C3—24no—
516C22×C3—24no—
517C22×C3—216no—
518C22×C3—22no—
519C22×C3—22no—
520C22×C3—22no—
521C22×C3—22no—
522C22×C3—28no—
523C22×C3—28no—
524C22×C3—22no—
525C22×C3—22no—
526C22×C3—24no—
527C22×C3—22no—
528C22×C3—21no—
529C22×C3—34no—
530C22×C3—62no—
531C22×C3—62no—
532C22×C3—68no—
533C22×C3C2×#23512yes—
534C22×C3#100412yes—
535C22×C3C2×D3×Q814yes—
536C22×C3C2×D3×Q812yes—
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—24no—
548C3×C4—22no—
549C3×C4—24no—
550C3×C4—24no—
551C3×C4—22no—
552C3×C4—24no—
553C3×C4—24no—
554C3×C4—24no—
555C3×C4—34no—
556C3×C4—44no—
557C3×C4—44no—
558C3×C4—62no—
559C3×C4—64no—
560C3×C4—64no—
561C3×C4—62no—
562C3×C4C2×#23514yes—
563C3×C4C2×C3×#4114yes—
564Dic3—24no—
565Dic3—22no—
566Dic3—22no—
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—68no—
580Q8—128no—
581D4—316no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—28no—
586C2×C4—34no—
587C2×C4—32no—
588C2×C4—34no—
589C2×C4—32no—
590C2×C4—32no—
591C2×C4—34no—
592C2×C4—48no—
593C2×C4—62no—
594C2×C4—64no—
595C2×C4—64no—
596C2×C4—62no—
597C2×C4—68no—
598C2×C4—128no—
599C2×C4C3×#23514yes—
600C2×C4C23×C3×D314yes—
601C2×C4C23×C3×D312yes—
602C2×C4C23×C3×D314yes—
603C2×C4C23×C3×D312yes—
604C2×C3—28no—
605C2×C3—24no—
606C2×C3—24no—
607C2×C3—24no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—64no—
612C2×C3#551114yesdirect product factor
613C2×C3C3×#55414yescomplemented
614C2×C3C22×#23511yescharacteristic
615C2×C3C2×#100411yescharacteristic
616C2×C3C22×D3×Q811yescharacteristic
617C2×C3C23×C3×Q811yescharacteristic
618C2×C3C22×C3×#4111yescharacteristic
619C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
620D3—24no—
621C22—28no—
622C22—22no—
623C22—22no—
624C22—34no—
625C22—68no—
626C22—62no—
627C22—62no—
628C22C2×C3×#23512yes—
629C22C3×#100412yes—
630C22C2×C3×D3×Q814yes—
631C22C2×C3×D3×Q812yes—
632C22C24×C3×D311yescharacteristic
633C4—22no—
634C4—24no—
635C4—24no—
636C4—34no—
637C4—62no—
638C4—64no—
639C4—64no—
640C4—62no—
641C4C2×C3×#23514yes—
642C3—21no—
643C3C2×#551111yescharacteristic, direct product factor
644C3C2×C3×#55411yescharacteristic, complemented
645C2—24no—
646C2—64no—
647C2C3×#551114yesdirect product factor
648C2C22×C3×#23511yescharacteristic
649C2C2×C3×#100411yescharacteristic
650C2C22×C3×D3×Q811yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC22×C32×C4⋊C4C2
socleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC22×C3×C4⋊C4D3
hypocenterC3C2×C3×#554
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C32×C4⋊C4C2semidirect
4. C2×C3×#924C2semidirect
5. C2×C3×#924C2semidirect
6. C3×#5511C2direct (N × H)
7. C2×C3×#897C2semidirect
8. C2×C3×#896C2semidirect
9. C2×C3×D3×C4⋊C4C2semidirect
10. C2×C3×#889C2semidirect
11. C2×C3×#888C2semidirect
12. C2×C3×#887C2semidirect
14. C2×#5511C3direct (N × H)
25. C2×C32×C4⋊C4C22semidirect
34. C3×#924C22semidirect
35. C3×#924C22semidirect
43. C3×#897C22semidirect
44. C3×#896C22semidirect
45. C3×D3×C4⋊C4C22semidirect
46. C3×#889C22semidirect
47. C3×#888C22semidirect
48. C3×#887C22semidirect
61. C22×C3×C4⋊C4D3semidirect
62. C22×C3×C4⋊C4C2×C3semidirect
65. C2×#924C2×C3semidirect
66. C2×#924C2×C3semidirect
67. #5511C2×C3direct (N × H)
68. C2×#897C2×C3semidirect
69. C2×#896C2×C3semidirect
70. C2×D3×C4⋊C4C2×C3semidirect
71. C2×#889C2×C3semidirect
72. C2×#888C2×C3semidirect
73. C2×#887C2×C3semidirect
84. C2×C3×#67Q8semidirect
156. C2×C3×C4⋊C4C2×D3semidirect
160. C2×C3×C4⋊C4C22×C3semidirect
175. #924C22×C3semidirect
176. #924C22×C3semidirect
184. #897C22×C3semidirect
185. #896C22×C3semidirect
186. D3×C4⋊C4C22×C3semidirect
187. #889C22×C3semidirect
188. #888C22×C3semidirect
189. #887C22×C3semidirect
209. C3×#67C2×Q8semidirect
235. C22×C4⋊C4C3×D3semidirect
280. C2×#67C3×Q8semidirect
378. C2×C4⋊C4C2×C3×D3semidirect
453. #67C2×C3×Q8semidirect
469. C2×C32#554semidirect
569. C32C2×#554semidirect
612. C2×C3#5511direct (N × H)
613. C2×C3C3×#554semidirect
643. C3C2×#5511direct (N × H)
644. C3C2×C3×#554semidirect
647. C2C3×#5511direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×C4⋊C42
C2×C3×C4×#672
C2×C3×#9242
C3×#55112
C2×C3×#8972
C2×C3×#8962
C2×C3×D3×C4⋊C42
C2×C3×#8892
C2×C3×#8882
C2×C3×#8872
C2×C3×#5543
C2×#55113