Finite Group Databasebeta

← C2×C3×#5565 #11903102

Subgroups — C2×C3×#5565 #11903102

Order 1152.

2717 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic, complemented
2C2×C3×#939C212yesmaximal, complemented
3C2×C3×#930C211yesmaximal, characteristic, complemented
4C2×C3×#930C211yesmaximal, characteristic, complemented
5C2×C3×#926C211yesmaximal, characteristic, complemented
6C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
7C3×#5565C2116yesmaximal, direct product factor
8C2×C3×#898C212yesmaximal, complemented
9C2×C3×#883C212yesmaximal, complemented
10C2×C3×#67⋊C4C212yesmaximal, complemented
11C2×C3×C4×D12C211yesmaximal, characteristic, complemented
12C2×C3×#870C211yesmaximal, characteristic, complemented
13C2×C3×#553—31nomaximal
14C2×#5565C311yesmaximal, characteristic, direct product factor
15C22×C32×D4C2211yescharacteristic
16C23×C32×C4C2211yescharacteristic
17C23×C32×C4C2211yescharacteristic
18C22×C3×#67C2212yes—
19C22×C3×#67C2212yes—
20C23×C3×Dic3C2212yes—
21C22×C3×D12C2211yescharacteristic
22C22×C3×C4×D3C2212yes—
23C32×C4×D4C2218yescomplemented
24C2×C32×C4⋊C4C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×C32×C42C2211yescharacteristic
28C2×C3×#217C2212yes—
29C3×#939C22116yescomplemented
30C3×#930C2218yescomplemented
31C3×#930C2218yescomplemented
32C2×C3×(C2×D3)⋊C4C2212yes—
33C2×C3×(C2×D3)⋊C4C2212yes—
34C2×C3×(C2×D3)⋊C4C2212yes—
35C3×#926C2218yescomplemented
36C2×C3×C4⋊Dic3C2212yes—
37C2×C3×C4⋊Dic3C2211yescharacteristic
38C2×C3×C4⋊Dic3C2211yescharacteristic
39C2×C3×C4⋊Dic3C2211yescharacteristic
40C2×C3×C4⋊Dic3C2218yescomplemented
41C2×C3×Dic3⋊C4C2212yes—
42C2×C3×Dic3⋊C4C2212yes—
43C2×C3×C4×Dic3C2212yes—
44C3×#898C22116yescomplemented
45C3×#883C22116yescomplemented
46C3×#67⋊C4C22116yescomplemented
47C3×C4×D12C2218yescomplemented
48C3×#870C2218yescomplemented
49C3×#553—316no—
50C2×C3×#126—32no—
51C2×C3×#125—31no—
52C2×C3×#123—32no—
53C2×C3×#121—32no—
54C2×C3×#121—31no—
55C2×C3×#121—31no—
56C2×C3×C4×D4—21no—
57C2×C3×C4×D4—32no—
58C2×C3×C4×D4—31no—
59C2×C3×C4×D4D311yescharacteristic, complemented
60C2×C3×C4×D4C2×C311yescharacteristic, complemented
61C2×C3×#117—31no—
62C22×C3×C4⋊C4—31no—
63C2×#939C2×C312yescomplemented
64C2×#930C2×C311yescharacteristic, complemented
65C2×#930C2×C311yescharacteristic, complemented
66C2×#926C2×C311yescharacteristic, complemented
67C22×C4⋊Dic3C2×C311yescharacteristic, complemented
68#5565C2×C3116yesdirect product factor
69C2×#898C2×C312yescomplemented
70C2×#883C2×C312yescomplemented
71C2×#67⋊C4C2×C312yescomplemented
72C2×C4×D12C2×C311yescharacteristic, complemented
73C2×#870C2×C311yescharacteristic, complemented
74C24×C32C2311yescharacteristic
75C24×C32C2311yescharacteristic
76C23×C3×D3C2312yes—
77C2×C32×D4—24no—
78C2×C32×D4C2314yes—
79C22×C32×C4—24no—
80C22×C32×C4—24no—
81C22×C32×C4C2311yescharacteristic
82C22×C32×C4C2311yescharacteristic
83C22×C32×C4C2311yescharacteristic
84C22×C32×C4C2311yescharacteristic
85C22×C32×C4C2314yes—
86C22×C32×C4C2314yes—
87C22×C32×C4C2311yescharacteristic
88C2×C3×#67—28no—
89C2×C3×#67—44no—
90C2×C3×#67C2318yes—
91C2×C3×#67C2318yes—
92C22×C3×Dic3—44no—
93C22×C3×Dic3C2312yes—
94C22×C3×Dic3C2312yes—
95C22×C3×Dic3C2312yes—
96C22×C3×Dic3C2318yes—
97C2×C3×D12—24no—
98C2×C3×D12C2314yes—
99C2×C3×C4×D3—44no—
100C2×C3×C4×D3C2318yes—
101C32×C4⋊C4C2314yes—
102C32×C22⋊C4C2314yes—
103C32×C22⋊C4C2314yes—
104C32×C42C2314yes—
105C3×#217C2318yes—
106C3×(C2×D3)⋊C4C2318yes—
107C3×(C2×D3)⋊C4C2318yes—
108C3×(C2×D3)⋊C4C2318yes—
109C3×C4⋊Dic3C2318yes—
110C3×C4⋊Dic3C2314yes—
111C3×C4⋊Dic3C2314yes—
112C3×C4⋊Dic3C2314yes—
113C3×Dic3⋊C4C2318yes—
114C3×Dic3⋊C4C2318yes—
115C3×C4×Dic3C2318yes—
116C2×#553—31noSylow
117C22×C3×D4—21no—
118C22×C3×D4—32no—
119C22×C3×D4—32no—
120C22×C3×D4—31no—
121C22×C3×D4C2×D311yescharacteristic
122C22×C3×D4C22×C311yescharacteristic
123C23×C3×C4—21no—
124C23×C3×C4—21no—
125C23×C3×C4—32no—
126C23×C3×C4—32no—
127C23×C3×C4C2×D311yescharacteristic
128C23×C3×C4C2×D311yescharacteristic
129C23×C3×C4C22×C311yescharacteristic
130C23×C3×C4C22×C311yescharacteristic
131C22×#67C22×C312yes—
132C22×#67C22×C312yes—
133C23×Dic3C22×C312yes—
134C22×D12C22×C311yescharacteristic
135C22×C4×D3C22×C312yes—
136C3×#126—316no—
137C3×#125—38no—
138C3×#123—316no—
139C3×#121—316no—
140C3×#121—38no—
141C3×#121—38no—
142C3×C4×D4—28no—
143C3×C4×D4—316no—
144C3×C4×D4—38no—
145C3×C4×D4C2×D318yescomplemented
146C3×C4×D4C22×C318yescomplemented
147C3×#117—38no—
148C2×C3×C4⋊C4—21no—
149C2×C3×C4⋊C4—32no—
150C2×C3×C4⋊C4—32no—
151C2×C3×C4⋊C4—31no—
152C2×C3×C4⋊C4—31no—
153C2×C3×C4⋊C4—32no—
154C2×C3×C4⋊C4—31no—
155C2×C3×C4⋊C4—38no—
156C2×C3×C4⋊C4C2×D311yescharacteristic
157C2×C3×C4⋊C4C22×C311yescharacteristic
158C2×C3×C22⋊C4—21no—
159C2×C3×C22⋊C4—21no—
160C2×C3×C22⋊C4—32no—
161C2×C3×C22⋊C4—32no—
162C2×C3×C22⋊C4—32no—
163C2×C3×C22⋊C4—32no—
164C2×C3×C22⋊C4C2×D311yescharacteristic
165C2×C3×C22⋊C4C2×D311yescharacteristic
166C2×C3×C22⋊C4C22×C311yescharacteristic
167C2×C3×C22⋊C4C22×C311yescharacteristic
168C2×C3×C42—21no—
169C2×C3×C42—32no—
170C2×C3×C42C2×D311yescharacteristic
171C2×C3×C42C22×C311yescharacteristic
172C2×#217C22×C312yes—
173#939C22×C3116yescomplemented
174#930C22×C318yescomplemented
175#930C22×C318yescomplemented
176C2×(C2×D3)⋊C4C22×C312yes—
177C2×(C2×D3)⋊C4C22×C312yes—
178C2×(C2×D3)⋊C4C22×C312yes—
179#926C22×C318yescomplemented
180C2×C4⋊Dic3C22×C311yescharacteristic
181C2×C4⋊Dic3C22×C311yescharacteristic
182C2×C4⋊Dic3C22×C311yescharacteristic
183C2×C4⋊Dic3C22×C312yes—
184C2×C4⋊Dic3C22×C318yescomplemented
185C2×Dic3⋊C4C22×C312yes—
186C2×Dic3⋊C4C22×C312yes—
187C2×C4×Dic3C22×C312yes—
188#898C22×C3116yescomplemented
189#883C22×C3116yescomplemented
190#67⋊C4C22×C3116yescomplemented
191C4×D12C22×C318yescomplemented
192#870C22×C318yescomplemented
193C23×C32—22no—
194C23×C32—22no—
195C23×C32—22no—
196C23×C32—22no—
197C23×C32—22no—
198C23×C32#4114yes—
199C23×C32C2412yes—
200C23×C32C2412yes—
201C23×C32C2411yescharacteristic
202C22×C3×D3—24no—
203C22×C3×D3—24no—
204C22×C3×D3—24no—
205C22×C3×D3C2414yes—
206C32×D4—28no—
207C2×C32×C4—22no—
208C2×C32×C4—22no—
209C2×C32×C4—22no—
210C2×C32×C4—22no—
211C2×C32×C4—28no—
212C2×C32×C4—28no—
213C2×C32×C4#4114yes—
214C2×C32×C4C2412yes—
215C2×C32×C4C2412yes—
216C2×C32×C4C2412yes—
217C2×C32×C4C2412yes—
218C2×C32×C4C2412yes—
219C3×#67—216no—
220C3×#67—48no—
221C2×C3×Dic3—24no—
222C2×C3×Dic3—24no—
223C2×C3×Dic3—24no—
224C2×C3×Dic3—48no—
225C2×C3×Dic3C2414yes—
226C2×C3×Dic3C2414yes—
227C2×C3×Dic3C2414yes—
228C3×D12—28no—
229C3×C4×D3—48no—
230#553—316no—
231C2×#126—32no—
232C2×#125—31no—
233C2×#123—32no—
234C2×#121—32no—
235C2×#121—31no—
236C2×#121—31no—
237C2×C4×D4—32no—
238C2×C4×D4—31no—
239C2×C4×D4C3×D311yescharacteristic, complemented
240C2×#117—31no—
241C22×C4⋊C4—31no—
242C24×C3—21no—
243C24×C3—21no—
244C24×C3—32no—
245C24×C3C22×D311yescharacteristic
246C24×C3C22×D311yescharacteristic
247C24×C3C23×C311yescharacteristic
248C24×C3C23×C311yescharacteristic
249C23×D3C23×C312yes—
250C2×C3×D4—28no—
251C2×C3×D4—24no—
252C2×C3×D4—24no—
253C2×C3×D4—24no—
254C2×C3×D4—38no—
255C2×C3×D4—38no—
256C2×C3×D4—34no—
257C2×C3×D4—68no—
258C2×C3×D4—64no—
259C2×C3×D4—124no—
260C2×C3×D4C22×D314yes—
261C2×C3×D4C23×C314yes—
262C22×C3×C4—24no—
263C22×C3×C4—24no—
264C22×C3×C4—24no—
265C22×C3×C4—24no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—24no—
272C22×C3×C4—24no—
273C22×C3×C4—32no—
274C22×C3×C4—32no—
275C22×C3×C4—32no—
276C22×C3×C4—38no—
277C22×C3×C4—38no—
278C22×C3×C4—44no—
279C22×C3×C4—44no—
280C22×C3×C4—124no—
281C22×C3×C4—124no—
282C22×C3×C4C22×D314yes—
283C22×C3×C4C22×D314yes—
284C22×C3×C4C22×D311yescharacteristic
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C22×D311yescharacteristic
287C22×C3×C4C22×D311yescharacteristic
288C22×C3×C4C22×D311yescharacteristic
289C22×C3×C4C23×C311yescharacteristic
290C22×C3×C4C23×C311yescharacteristic
291C22×C3×C4C23×C311yescharacteristic
292C22×C3×C4C23×C311yescharacteristic
293C22×C3×C4C23×C314yes—
294C22×C3×C4C23×C314yes—
295C22×C3×C4C23×C311yescharacteristic
296C2×#67—28no—
297C2×#67—44no—
298C2×#67C23×C318yes—
299C2×#67C23×C318yes—
300C22×Dic3—44no—
301C22×Dic3C23×C312yes—
302C22×Dic3C23×C312yes—
303C22×Dic3C23×C312yes—
304C22×Dic3C23×C318yes—
305C2×D12—24no—
306C2×D12C23×C314yes—
307C2×C4×D3—44no—
308C2×C4×D3C23×C318yes—
309C3×C4⋊C4—24no—
310C3×C4⋊C4—38no—
311C3×C4⋊C4—38no—
312C3×C4⋊C4—34no—
313C3×C4⋊C4—34no—
314C3×C4⋊C4—38no—
315C3×C4⋊C4—34no—
316C3×C4⋊C4C22×D314yes—
317C3×C4⋊C4C23×C314yes—
318C3×C22⋊C4—24no—
319C3×C22⋊C4—24no—
320C3×C22⋊C4—38no—
321C3×C22⋊C4—38no—
322C3×C22⋊C4—38no—
323C3×C22⋊C4—38no—
324C3×C22⋊C4C22×D314yes—
325C3×C22⋊C4C22×D314yes—
326C3×C22⋊C4C23×C314yes—
327C3×C22⋊C4C23×C314yes—
328C3×C42—24no—
329C3×C42—38no—
330C3×C42C22×D314yes—
331C3×C42C23×C314yes—
332#217C23×C318yes—
333(C2×D3)⋊C4C23×C318yes—
334(C2×D3)⋊C4C23×C318yes—
335(C2×D3)⋊C4C23×C318yes—
336C4⋊Dic3C23×C314yes—
337C4⋊Dic3C23×C314yes—
338C4⋊Dic3C23×C314yes—
339C4⋊Dic3C23×C318yes—
340Dic3⋊C4C23×C318yes—
341Dic3⋊C4C23×C318yes—
342C4×Dic3C23×C318yes—
343C22×C32—22no—
344C22×C32—28no—
345C22×C32—22no—
346C22×C32—22no—
347C22×C32—22no—
348C22×C32—22no—
349C22×C32—44no—
350C22×C32C2×#4114yes—
351C22×C32C2×#4112yes—
352C22×C32C2×#4112yes—
353C22×C32H(5,𝔽2)12yes—
354C22×C32C2511yescharacteristic
355C2×C3×D3—24no—
356C2×C3×D3—24no—
357C2×C3×D3—24no—
358C2×C3×D3—48no—
359C32×C4—22no—
360C32×C4—22no—
361C32×C4—22no—
362C32×C4—22no—
363C32×C4C2×#4114yes—
364C3×Dic3—24no—
365C3×Dic3—24no—
366C3×Dic3—24no—
367C22×D4—32no—
368C22×D4—32no—
369C22×D4—31no—
370C22×D4C2×C3×D311yescharacteristic
371C23×C4—32no—
372C23×C4—32no—
373C23×C4C2×C3×D311yescharacteristic
374C23×C4C2×C3×D311yescharacteristic
375#126—316no—
376#125—38no—
377#123—316no—
378#121—316no—
379#121—38no—
380#121—38no—
381C4×D4—316no—
382C4×D4—38no—
383C4×D4C2×C3×D318yescomplemented
384#117—38no—
385C2×C4⋊C4—31no—
386C2×C4⋊C4—31no—
387C2×C4⋊C4—32no—
388C2×C4⋊C4—38no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—32no—
391C2×C4⋊C4—32no—
392C2×C4⋊C4C2×C3×D311yescharacteristic
393C2×C22⋊C4—32no—
394C2×C22⋊C4—32no—
395C2×C22⋊C4—32no—
396C2×C22⋊C4—32no—
397C2×C22⋊C4C2×C3×D311yescharacteristic
398C2×C22⋊C4C2×C3×D311yescharacteristic
399C2×C42—32no—
400C2×C42C2×C3×D311yescharacteristic
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—22no—
405C23×C3—24no—
406C23×C3—22no—
407C23×C3—22no—
408C23×C3—22no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—22no—
412C23×C3—21no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—24no—
416C23×C3—34no—
417C23×C3—42no—
418C23×C3—42no—
419C23×C3—42no—
420C23×C3—42no—
421C23×C3—64no—
422C23×C3—64no—
423C23×C3—64no—
424C23×C3#23514yes—
425C23×C3C3×#4114yes—
426C23×C3C23×D312yes—
427C23×C3C23×D312yes—
428C23×C3C23×D311yescharacteristic
429C23×C3C24×C312yes—
430C23×C3C24×C312yes—
431C23×C3C24×C311yescharacteristic
432C22×D3—24no—
433C22×D3—24no—
434C22×D3—24no—
435C22×D3C24×C314yes—
436C3×D4—216no—
437C3×D4—28no—
438C3×D4—28no—
439C3×D4—616no—
440C3×D4—68no—
441C3×D4—128no—
442C2×C3×C4—24no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—28no—
452C2×C3×C4—28no—
453C2×C3×C4—28no—
454C2×C3×C4—28no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—24no—
461C2×C3×C4—34no—
462C2×C3×C4—34no—
463C2×C3×C4—34no—
464C2×C3×C4—48no—
465C2×C3×C4—48no—
466C2×C3×C4—42no—
467C2×C3×C4—42no—
468C2×C3×C4—42no—
469C2×C3×C4—64no—
470C2×C3×C4—64no—
471C2×C3×C4—64no—
472C2×C3×C4—128no—
473C2×C3×C4—128no—
474C2×C3×C4#23714yes—
475C2×C3×C4C3×#4114yes—
476C2×C3×C4C23×D312yes—
477C2×C3×C4C23×D312yes—
478C2×C3×C4C23×D312yes—
479C2×C3×C4C23×D312yes—
480C2×C3×C4C23×D312yes—
481C2×C3×C4C24×C312yes—
482C2×C3×C4C24×C312yes—
483C2×C3×C4C24×C312yes—
484C2×C3×C4C24×C312yes—
485C2×C3×C4C24×C312yes—
486#67—216no—
487#67—48no—
488C2×Dic3—24no—
489C2×Dic3—24no—
490C2×Dic3—24no—
491C2×Dic3—48no—
492C2×Dic3C24×C314yes—
493C2×Dic3C24×C314yes—
494C2×Dic3C24×C314yes—
495D12—28no—
496C4×D3—48no—
497C2×C32—24no—
498C2×C32—42no—
499C2×C32#55314yescomplemented
500C2×C32C22×#4111yescharacteristic
501C2×C32C22×#4111yescharacteristic
502C2×C32C2×H(5,𝔽2)11yescharacteristic
503C3×D3—44no—
504C24—32no—
505C24C22×C3×D311yescharacteristic
506C24C22×C3×D311yescharacteristic
507C2×D4—24no—
508C2×D4—38no—
509C2×D4—38no—
510C2×D4—34no—
511C2×D4—68no—
512C2×D4—64no—
513C2×D4—124no—
514C2×D4C22×C3×D314yes—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—32no—
518C22×C4—32no—
519C22×C4—32no—
520C22×C4—38no—
521C22×C4—38no—
522C22×C4—124no—
523C22×C4—124no—
524C22×C4C22×C3×D311yescharacteristic
525C22×C4C22×C3×D311yescharacteristic
526C22×C4C22×C3×D311yescharacteristic
527C22×C4C22×C3×D311yescharacteristic
528C22×C4C22×C3×D314yes—
529C22×C4C22×C3×D314yes—
530C22×C4C22×C3×D311yescharacteristic
531C4⋊C4—34no—
532C4⋊C4—34no—
533C4⋊C4—38no—
534C4⋊C4—34no—
535C4⋊C4—38no—
536C4⋊C4—38no—
537C4⋊C4C22×C3×D314yes—
538C22⋊C4—38no—
539C22⋊C4—38no—
540C22⋊C4—38no—
541C22⋊C4—38no—
542C22⋊C4C22×C3×D314yes—
543C22⋊C4C22×C3×D314yes—
544C42—38no—
545C42C22×C3×D314yes—
546C22×C3—22no—
547C22×C3—22no—
548C22×C3—22no—
549C22×C3—22no—
550C22×C3—28no—
551C22×C3—28no—
552C22×C3—24no—
553C22×C3—22no—
554C22×C3—22no—
555C22×C3—22no—
556C22×C3—22no—
557C22×C3—22no—
558C22×C3—22no—
559C22×C3—22no—
560C22×C3—24no—
561C22×C3—22no—
562C22×C3—22no—
563C22×C3—21no—
564C22×C3—42no—
565C22×C3—42no—
566C22×C3—48no—
567C22×C3—42no—
568C22×C3—42no—
569C22×C3—48no—
570C22×C3—44no—
571C22×C3—44no—
572C22×C3—64no—
573C22×C3—64no—
574C22×C3—64no—
575C22×C3—128no—
576C22×C3C2×#23514yes—
577C22×C3C2×#23512yes—
578C22×C3C2×#23712yes—
579C22×C3#100912yes—
580C22×C3C2×C3×#4114yes—
581C22×C3C2×C3×#4112yes—
582C22×C3C2×C3×#4112yes—
583C22×C3C3×H(5,𝔽2)12yes—
584C22×C3C24×D311yescharacteristic
585C22×C3C25×C311yescharacteristic
586C2×D3—24no—
587C2×D3—24no—
588C2×D3—24no—
589C2×D3—48no—
590C3×C4—24no—
591C3×C4—22no—
592C3×C4—22no—
593C3×C4—22no—
594C3×C4—22no—
595C3×C4—22no—
596C3×C4—22no—
597C3×C4—22no—
598C3×C4—22no—
599C3×C4—24no—
600C3×C4—42no—
601C3×C4—42no—
602C3×C4—42no—
603C3×C4—64no—
604C3×C4—64no—
605C3×C4—64no—
606C3×C4C2×#23714yes—
607C3×C4C2×C3×#4114yes—
608Dic3—24no—
609Dic3—24no—
610Dic3—24no—
611C32C2×#55311yescharacteristic, complemented, Sylow
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—34no—
618C23—64no—
619C23—64no—
620C23—64no—
621C23C3×#23514yes—
622C23C23×C3×D312yes—
623C23C23×C3×D312yes—
624C23C23×C3×D311yescharacteristic
625D4—28no—
626D4—616no—
627D4—68no—
628D4—128no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—28no—
634C2×C4—28no—
635C2×C4—34no—
636C2×C4—34no—
637C2×C4—34no—
638C2×C4—64no—
639C2×C4—64no—
640C2×C4—64no—
641C2×C4—128no—
642C2×C4—128no—
643C2×C4C3×#23714yes—
644C2×C4C23×C3×D312yes—
645C2×C4C23×C3×D312yes—
646C2×C4C23×C3×D312yes—
647C2×C4C23×C3×D312yes—
648C2×C4C23×C3×D312yes—
649C2×C3—24no—
650C2×C3—24no—
651C2×C3—24no—
652C2×C3—21no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—44no—
656C2×C3—44no—
657C2×C3—42no—
658C2×C3—42no—
659C2×C3—124no—
660C2×C3#556514yesdirect product factor
661C2×C3C3×#55314yescomplemented
662C2×C3C22×#23511yescharacteristic
663C2×C3C22×#23711yescharacteristic
664C2×C3C2×#100911yescharacteristic
665C2×C3C22×C3×#4111yescharacteristic
666C2×C3C22×C3×#4111yescharacteristic
667C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
668D3—44no—
669C22—28no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—44no—
676C22—64no—
677C22—64no—
678C22—64no—
679C22—128no—
680C22C2×C3×#23514yes—
681C22C2×C3×#23512yes—
682C22C2×C3×#23712yes—
683C22C3×#100912yes—
684C22C24×C3×D311yescharacteristic
685C4—22no—
686C4—22no—
687C4—22no—
688C4—22no—
689C4—64no—
690C4—64no—
691C4—64no—
692C4C2×C3×#23714yes—
693C3—21no—
694C3C2×#556511yescharacteristic, direct product factor
695C3C2×C3×#55311yescharacteristic, complemented
696C2—24no—
697C2—42no—
698C2—124no—
699C2C3×#556514yesdirect product factor
700C2C22×C3×#23511yescharacteristic
701C2C22×C3×#23711yescharacteristic
702C2C2×C3×#100911yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×C4×D4C2
socleC23×C32C24
hypercenterC2×C3×C4×D4D3
hypocenterC3C2×C3×#553
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×D4C2semidirect
2. C2×C3×#939C2semidirect
3. C2×C3×#930C2semidirect
4. C2×C3×#930C2semidirect
5. C2×C3×#926C2semidirect
6. C22×C3×C4⋊Dic3C2semidirect
7. C3×#5565C2direct (N × H)
8. C2×C3×#898C2semidirect
9. C2×C3×#883C2semidirect
10. C2×C3×#67⋊C4C2semidirect
11. C2×C3×C4×D12C2semidirect
12. C2×C3×#870C2semidirect
14. C2×#5565C3direct (N × H)
23. C32×C4×D4C22semidirect
29. C3×#939C22semidirect
30. C3×#930C22semidirect
31. C3×#930C22semidirect
35. C3×#926C22semidirect
40. C2×C3×C4⋊Dic3C22semidirect
44. C3×#898C22semidirect
45. C3×#883C22semidirect
46. C3×#67⋊C4C22semidirect
47. C3×C4×D12C22semidirect
48. C3×#870C22semidirect
59. C2×C3×C4×D4D3semidirect
60. C2×C3×C4×D4C2×C3semidirect
63. C2×#939C2×C3semidirect
64. C2×#930C2×C3semidirect
65. C2×#930C2×C3semidirect
66. C2×#926C2×C3semidirect
67. C22×C4⋊Dic3C2×C3semidirect
68. #5565C2×C3direct (N × H)
69. C2×#898C2×C3semidirect
70. C2×#883C2×C3semidirect
71. C2×#67⋊C4C2×C3semidirect
72. C2×C4×D12C2×C3semidirect
73. C2×#870C2×C3semidirect
145. C3×C4×D4C2×D3semidirect
146. C3×C4×D4C22×C3semidirect
173. #939C22×C3semidirect
174. #930C22×C3semidirect
175. #930C22×C3semidirect
179. #926C22×C3semidirect
184. C2×C4⋊Dic3C22×C3semidirect
188. #898C22×C3semidirect
189. #883C22×C3semidirect
190. #67⋊C4C22×C3semidirect
191. C4×D12C22×C3semidirect
192. #870C22×C3semidirect
239. C2×C4×D4C3×D3semidirect
383. C4×D4C2×C3×D3semidirect
499. C2×C32#553semidirect
611. C32C2×#553semidirect
660. C2×C3#5565direct (N × H)
661. C2×C3C3×#553semidirect
694. C3C2×#5565direct (N × H)
695. C3C2×C3×#553semidirect
699. C2C3×#5565direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×C3×#9392
C2×C3×#9302
C2×C3×#9262
C22×C3×C4⋊Dic32
C3×#55652
C2×C3×#8982
C2×C3×#8832
C2×C3×#67⋊C42
C2×C3×C4×D122
C2×C3×#8702
C2×C3×#5533
C2×#55653