Finite Group Databasebeta

← C2×C3×#5558 #11903114

Subgroups — C2×C3×#5558 #11903114

Order 1152.

2717 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic, complemented
2C2×C3×#938C211yesmaximal, characteristic, complemented
3C2×C3×#938C211yesmaximal, characteristic, complemented
4C2×C3×#929C212yesmaximal, complemented
5C2×C3×C4×#67C212yesmaximal, complemented
6C3×#5558C2116yesmaximal, direct product factor
7C2×C3×#892C211yesmaximal, characteristic, complemented
8C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
9C2×C3×#884C212yesmaximal, complemented
10C2×C3×#879C212yesmaximal, complemented
11C2×C3×C4×D12C211yesmaximal, characteristic, complemented
12C2×C3×#870C211yesmaximal, characteristic, complemented
13C2×C3×#553—31nomaximal
14C2×#5558C311yesmaximal, characteristic, direct product factor
15C22×C32×D4C2211yescharacteristic
16C23×C32×C4C2212yes—
17C22×C3×#67C2212yes—
18C22×C3×#67C2212yes—
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2212yes—
23C32×C4×D4C2218yescomplemented
24C2×C32×C4⋊C4C2211yescharacteristic
25C2×C32×C22⋊C4C2212yes—
26C2×C32×C42C2211yescharacteristic
27C2×C3×#217C2212yes—
28C2×C3×#217C2212yes—
29C3×#938C2218yescomplemented
30C3×#938C2218yescomplemented
31C3×#929C22116yescomplemented
32C3×C4×#67C22116yescomplemented
33C2×C3×(C2×D3)⋊C4C2212yes—
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C2×C3×C4⋊Dic3C2211yescharacteristic
38C2×C3×C4⋊Dic3C2211yescharacteristic
39C2×C3×Dic3⋊C4C2212yes—
40C2×C3×Dic3⋊C4C2212yes—
41C2×C3×Dic3⋊C4C2212yes—
42C2×C3×C4×Dic3C2212yes—
43C3×#892C2218yescomplemented
44C3×D3×C4⋊C4C2218yescomplemented
45C3×#884C22116yescomplemented
46C3×#879C22116yescomplemented
47C3×C4×D12C2218yescomplemented
48C3×#870C2218yescomplemented
49C3×#553—316no—
50C2×C3×#126—32no—
51C2×C3×#125—31no—
52C2×C3×#123—32no—
53C2×C3×#121—31no—
54C2×C3×#121—31no—
55C2×C3×#121—32no—
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×#938C2×C311yescharacteristic, complemented
64C2×#938C2×C311yescharacteristic, complemented
65C2×#929C2×C312yescomplemented
66C2×C4×#67C2×C312yescomplemented
67#5558C2×C3116yesdirect product factor
68C2×#892C2×C311yescharacteristic, complemented
69C2×D3×C4⋊C4C2×C311yescharacteristic, complemented
70C2×#884C2×C312yescomplemented
71C2×#879C2×C312yescomplemented
72C2×C4×D12C2×C311yescharacteristic, complemented
73C2×#870C2×C311yescharacteristic, complemented
74C24×C32C2312yes—
75C23×C3×D3C2311yescharacteristic
76C23×C3×D3C2311yescharacteristic
77C2×C32×D4—24no—
78C2×C32×D4C2314yes—
79C22×C32×C4—44no—
80C22×C32×C4C2312yes—
81C22×C32×C4C2311yescharacteristic
82C22×C32×C4C2311yescharacteristic
83C22×C32×C4C2318yes—
84C22×C32×C4C2311yescharacteristic
85C2×C3×#67—28no—
86C2×C3×#67—44no—
87C2×C3×#67C2318yes—
88C2×C3×#67C2318yes—
89C22×C3×Dic3C2311yescharacteristic
90C22×C3×Dic3C2312yes—
91C22×C3×Dic3C2312yes—
92C22×C3×Dic3C2311yescharacteristic
93C2×C3×D12—24no—
94C2×C3×D12C2314yes—
95C2×C3×C4×D3—24no—
96C2×C3×C4×D3—24no—
97C2×C3×C4×D3—44no—
98C2×C3×C4×D3C2314yes—
99C2×C3×C4×D3C2314yes—
100C2×C3×C4×D3C2318yes—
101C32×C4⋊C4C2314yes—
102C32×C22⋊C4C2318yes—
103C32×C42C2314yes—
104C3×#217C2318yes—
105C3×#217C2318yes—
106C3×(C2×D3)⋊C4C2318yes—
107C3×(C2×D3)⋊C4C2314yes—
108C3×(C2×D3)⋊C4C2314yes—
109C3×C4⋊Dic3C2314yes—
110C3×C4⋊Dic3C2314yes—
111C3×C4⋊Dic3C2314yes—
112C3×Dic3⋊C4C2318yes—
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—22no—
124C23×C3×C4—31no—
125C23×C3×C4—31no—
126C23×C3×C4—32no—
127C23×C3×C4C2×D312yes—
128C23×C3×C4C22×C312yes—
129C22×#67C22×C312yes—
130C22×#67C22×C312yes—
131C22×D12C22×C311yescharacteristic
132C22×C4×D3C22×C311yescharacteristic
133C22×C4×D3C22×C311yescharacteristic
134C22×C4×D3C22×C312yes—
135C3×#126—316no—
136C3×#125—38no—
137C3×#123—316no—
138C3×#121—38no—
139C3×#121—38no—
140C3×#121—316no—
141C3×C4×D4—28no—
142C3×C4×D4—316no—
143C3×C4×D4—38no—
144C3×C4×D4C2×D318yescomplemented
145C3×C4×D4C22×C318yescomplemented
146C3×#117—38no—
147C2×C3×C4⋊C4—21no—
148C2×C3×C4⋊C4—32no—
149C2×C3×C4⋊C4—32no—
150C2×C3×C4⋊C4—32no—
151C2×C3×C4⋊C4—31no—
152C2×C3×C4⋊C4—31no—
153C2×C3×C4⋊C4—31no—
154C2×C3×C4⋊C4—38no—
155C2×C3×C4⋊C4C2×D311yescharacteristic
156C2×C3×C4⋊C4C22×C311yescharacteristic
157C2×C3×C22⋊C4—22no—
158C2×C3×C22⋊C4—32no—
159C2×C3×C22⋊C4—32no—
160C2×C3×C22⋊C4—32no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4C2×D312yes—
164C2×C3×C22⋊C4C22×C312yes—
165C2×C3×C42—21no—
166C2×C3×C42—32no—
167C2×C3×C42C2×D311yescharacteristic
168C2×C3×C42C22×C311yescharacteristic
169C2×#217C22×C312yes—
170C2×#217C22×C312yes—
171#938C22×C318yescomplemented
172#938C22×C318yescomplemented
173#929C22×C3116yescomplemented
174C4×#67C22×C3116yescomplemented
175C2×(C2×D3)⋊C4C22×C311yescharacteristic
176C2×(C2×D3)⋊C4C22×C311yescharacteristic
177C2×(C2×D3)⋊C4C22×C312yes—
178C2×C4⋊Dic3C22×C311yescharacteristic
179C2×C4⋊Dic3C22×C311yescharacteristic
180C2×C4⋊Dic3C22×C311yescharacteristic
181C2×Dic3⋊C4C22×C312yes—
182C2×Dic3⋊C4C22×C312yes—
183C2×Dic3⋊C4C22×C312yes—
184C2×C4×Dic3C22×C312yes—
185#892C22×C318yescomplemented
186D3×C4⋊C4C22×C318yescomplemented
187#884C22×C3116yescomplemented
188#879C22×C3116yescomplemented
189C4×D12C22×C318yescomplemented
190#870C22×C318yescomplemented
191C23×C32—24no—
192C23×C32—24no—
193C23×C32—24no—
194C23×C32C2414yes—
195C23×C32C2411yescharacteristic
196C22×C3×D3—22no—
197C22×C3×D3—22no—
198C22×C3×D3—22no—
199C22×C3×D3—22no—
200C22×C3×D3—22no—
201C22×C3×D3#4114yes—
202C22×C3×D3C2412yes—
203C22×C3×D3C2412yes—
204C32×D4—28no—
205C2×C32×C4—22no—
206C2×C32×C4—22no—
207C2×C32×C4—24no—
208C2×C32×C4—48no—
209C2×C32×C4#4114yes—
210C2×C32×C4C2414yes—
211C2×C32×C4C2412yes—
212C2×C32×C4C2412yes—
213C2×C32×C4C2412yes—
214C3×#67—216no—
215C3×#67—48no—
216C2×C3×Dic3—22no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3—24no—
219C2×C3×Dic3—24no—
220C2×C3×Dic3C2412yes—
221C2×C3×Dic3C2414yes—
222C2×C3×Dic3C2414yes—
223C2×C3×Dic3C2412yes—
224C3×D12—28no—
225C3×C4×D3—28no—
226C3×C4×D3—28no—
227C3×C4×D3—48no—
228#553—316no—
229C2×#126—32no—
230C2×#125—31no—
231C2×#123—32no—
232C2×#121—31no—
233C2×#121—31no—
234C2×#121—32no—
235C2×C4×D4—32no—
236C2×C4×D4—31no—
237C2×C4×D4C3×D311yescharacteristic, complemented
238C2×#117—31no—
239C22×C4⋊C4—31no—
240C24×C3—22no—
241C24×C3—31no—
242C24×C3—31no—
243C24×C3C22×D312yes—
244C24×C3C23×C312yes—
245C23×D3C23×C311yescharacteristic
246C23×D3C23×C311yescharacteristic
247C2×C3×D4—28no—
248C2×C3×D4—24no—
249C2×C3×D4—24no—
250C2×C3×D4—24no—
251C2×C3×D4—38no—
252C2×C3×D4—38no—
253C2×C3×D4—34no—
254C2×C3×D4—64no—
255C2×C3×D4—68no—
256C2×C3×D4—124no—
257C2×C3×D4C22×D314yes—
258C2×C3×D4C23×C314yes—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—22no—
263C22×C3×C4—28no—
264C22×C3×C4—31no—
265C22×C3×C4—32no—
266C22×C3×C4—31no—
267C22×C3×C4—32no—
268C22×C3×C4—34no—
269C22×C3×C4—34no—
270C22×C3×C4—38no—
271C22×C3×C4—44no—
272C22×C3×C4—44no—
273C22×C3×C4—48no—
274C22×C3×C4—64no—
275C22×C3×C4—64no—
276C22×C3×C4—124no—
277C22×C3×C4C22×D312yes—
278C22×C3×C4C22×D311yescharacteristic
279C22×C3×C4C22×D311yescharacteristic
280C22×C3×C4C22×D318yes—
281C22×C3×C4C22×D311yescharacteristic
282C22×C3×C4C23×C312yes—
283C22×C3×C4C23×C311yescharacteristic
284C22×C3×C4C23×C311yescharacteristic
285C22×C3×C4C23×C318yes—
286C22×C3×C4C23×C311yescharacteristic
287C2×#67—28no—
288C2×#67—44no—
289C2×#67C23×C318yes—
290C2×#67C23×C318yes—
291C22×Dic3C23×C311yescharacteristic
292C22×Dic3C23×C312yes—
293C22×Dic3C23×C312yes—
294C22×Dic3C23×C311yescharacteristic
295C2×D12—24no—
296C2×D12C23×C314yes—
297C2×C4×D3—24no—
298C2×C4×D3—24no—
299C2×C4×D3—44no—
300C2×C4×D3C23×C314yes—
301C2×C4×D3C23×C314yes—
302C2×C4×D3C23×C318yes—
303C3×C4⋊C4—24no—
304C3×C4⋊C4—38no—
305C3×C4⋊C4—38no—
306C3×C4⋊C4—38no—
307C3×C4⋊C4—34no—
308C3×C4⋊C4—34no—
309C3×C4⋊C4—34no—
310C3×C4⋊C4C22×D314yes—
311C3×C4⋊C4C23×C314yes—
312C3×C22⋊C4—28no—
313C3×C22⋊C4—38no—
314C3×C22⋊C4—38no—
315C3×C22⋊C4—38no—
316C3×C22⋊C4—34no—
317C3×C22⋊C4—34no—
318C3×C22⋊C4C22×D318yes—
319C3×C22⋊C4C23×C318yes—
320C3×C42—24no—
321C3×C42—38no—
322C3×C42C22×D314yes—
323C3×C42C23×C314yes—
324#217C23×C318yes—
325#217C23×C318yes—
326(C2×D3)⋊C4C23×C314yes—
327(C2×D3)⋊C4C23×C314yes—
328(C2×D3)⋊C4C23×C318yes—
329C4⋊Dic3C23×C314yes—
330C4⋊Dic3C23×C314yes—
331C4⋊Dic3C23×C314yes—
332Dic3⋊C4C23×C318yes—
333Dic3⋊C4C23×C318yes—
334Dic3⋊C4C23×C318yes—
335C4×Dic3C23×C318yes—
336C22×C32—24no—
337C22×C32—24no—
338C22×C32—24no—
339C22×C32—48no—
340C22×C32C2×#4112yes—
341C22×C32C2×#4112yes—
342C22×C32H(5,𝔽2)12yes—
343C22×C32C2511yescharacteristic
344C2×C3×D3—28no—
345C2×C3×D3—22no—
346C2×C3×D3—22no—
347C2×C3×D3—22no—
348C2×C3×D3—22no—
349C2×C3×D3—22no—
350C2×C3×D3—44no—
351C2×C3×D3C2×#4114yes—
352C32×C4—22no—
353C32×C4—22no—
354C32×C4—24no—
355C32×C4C2×#4114yes—
356C3×Dic3—22no—
357C3×Dic3—22no—
358C3×Dic3—24no—
359C3×Dic3—24no—
360C22×D4—32no—
361C22×D4—32no—
362C22×D4—31no—
363C22×D4C2×C3×D311yescharacteristic
364C23×C4—31no—
365C23×C4—31no—
366C23×C4—32no—
367C23×C4C2×C3×D312yes—
368#126—316no—
369#125—38no—
370#123—316no—
371#121—38no—
372#121—38no—
373#121—316no—
374C4×D4—316no—
375C4×D4—38no—
376C4×D4C2×C3×D318yescomplemented
377#117—38no—
378C2×C4⋊C4—31no—
379C2×C4⋊C4—32no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—32no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—32no—
384C2×C4⋊C4—38no—
385C2×C4⋊C4C2×C3×D311yescharacteristic
386C2×C22⋊C4—32no—
387C2×C22⋊C4—32no—
388C2×C22⋊C4—32no—
389C2×C22⋊C4—31no—
390C2×C22⋊C4—31no—
391C2×C22⋊C4C2×C3×D312yes—
392C2×C42—32no—
393C2×C42C2×C3×D311yescharacteristic
394C23×C3—28no—
395C23×C3—24no—
396C23×C3—24no—
397C23×C3—24no—
398C23×C3—24no—
399C23×C3—24no—
400C23×C3—24no—
401C23×C3—21no—
402C23×C3—24no—
403C23×C3—34no—
404C23×C3—32no—
405C23×C3—32no—
406C23×C3—44no—
407C23×C3—44no—
408C23×C3—62no—
409C23×C3—62no—
410C23×C3—62no—
411C23×C3—62no—
412C23×C3—62no—
413C23×C3C23×D314yes—
414C23×C3C23×D311yescharacteristic
415C23×C3C24×C314yes—
416C23×C3C24×C311yescharacteristic
417C22×D3—22no—
418C22×D3—22no—
419C22×D3—22no—
420C22×D3—22no—
421C22×D3—22no—
422C22×D3C3×#4114yes—
423C22×D3C24×C312yes—
424C22×D3C24×C312yes—
425C3×D4—216no—
426C3×D4—28no—
427C3×D4—28no—
428C3×D4—68no—
429C3×D4—616no—
430C3×D4—128no—
431C2×C3×C4—24no—
432C2×C3×C4—22no—
433C2×C3×C4—24no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—24no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—24no—
442C2×C3×C4—24no—
443C2×C3×C4—32no—
444C2×C3×C4—34no—
445C2×C3×C4—32no—
446C2×C3×C4—34no—
447C2×C3×C4—42no—
448C2×C3×C4—44no—
449C2×C3×C4—48no—
450C2×C3×C4—48no—
451C2×C3×C4—416no—
452C2×C3×C4—62no—
453C2×C3×C4—62no—
454C2×C3×C4—64no—
455C2×C3×C4—64no—
456C2×C3×C4—68no—
457C2×C3×C4—68no—
458C2×C3×C4—128no—
459C2×C3×C4#23514yes—
460C2×C3×C4C3×#4114yes—
461C2×C3×C4C23×D314yes—
462C2×C3×C4C23×D312yes—
463C2×C3×C4C23×D312yes—
464C2×C3×C4C23×D312yes—
465C2×C3×C4C24×C314yes—
466C2×C3×C4C24×C312yes—
467C2×C3×C4C24×C312yes—
468C2×C3×C4C24×C312yes—
469#67—216no—
470#67—48no—
471C2×Dic3—22no—
472C2×Dic3—22no—
473C2×Dic3—24no—
474C2×Dic3—24no—
475C2×Dic3C24×C312yes—
476C2×Dic3C24×C314yes—
477C2×Dic3C24×C314yes—
478C2×Dic3C24×C312yes—
479D12—28no—
480C4×D3—28no—
481C4×D3—28no—
482C4×D3—48no—
483C2×C32—44no—
484C2×C32#55314yescomplemented
485C2×C32C22×#4111yescharacteristic
486C2×C32C22×#4111yescharacteristic
487C2×C32C2×H(5,𝔽2)11yescharacteristic
488C3×D3—24no—
489C3×D3—42no—
490C24—31no—
491C24—31no—
492C24C22×C3×D312yes—
493C2×D4—24no—
494C2×D4—38no—
495C2×D4—38no—
496C2×D4—34no—
497C2×D4—64no—
498C2×D4—68no—
499C2×D4—124no—
500C2×D4C22×C3×D314yes—
501C22×C4—31no—
502C22×C4—32no—
503C22×C4—31no—
504C22×C4—32no—
505C22×C4—34no—
506C22×C4—34no—
507C22×C4—38no—
508C22×C4—44no—
509C22×C4—64no—
510C22×C4—64no—
511C22×C4—124no—
512C22×C4C22×C3×D312yes—
513C22×C4C22×C3×D311yescharacteristic
514C22×C4C22×C3×D311yescharacteristic
515C22×C4C22×C3×D318yes—
516C22×C4C22×C3×D311yescharacteristic
517C4⋊C4—34no—
518C4⋊C4—38no—
519C4⋊C4—34no—
520C4⋊C4—38no—
521C4⋊C4—34no—
522C4⋊C4—38no—
523C4⋊C4C22×C3×D314yes—
524C22⋊C4—38no—
525C22⋊C4—38no—
526C22⋊C4—38no—
527C22⋊C4—34no—
528C22⋊C4—34no—
529C22⋊C4C22×C3×D318yes—
530C42—38no—
531C42C22×C3×D314yes—
532C22×C3—28no—
533C22×C3—24no—
534C22×C3—24no—
535C22×C3—24no—
536C22×C3—24no—
537C22×C3—24no—
538C22×C3—24no—
539C22×C3—22no—
540C22×C3—22no—
541C22×C3—22no—
542C22×C3—21no—
543C22×C3—34no—
544C22×C3—44no—
545C22×C3—44no—
546C22×C3—416no—
547C22×C3—48no—
548C22×C3—48no—
549C22×C3—62no—
550C22×C3—62no—
551C22×C3—68no—
552C22×C3—62no—
553C22×C3—62no—
554C22×C3—62no—
555C22×C3—124no—
556C22×C3C2×#23512yes—
557C22×C3#100412yes—
558C22×C3D3×#4112yes—
559C22×C3C2×C3×#4112yes—
560C22×C3C2×C3×#4112yes—
561C22×C3C3×H(5,𝔽2)12yes—
562C22×C3C24×D311yescharacteristic
563C22×C3C25×C311yescharacteristic
564C2×D3—22no—
565C2×D3—22no—
566C2×D3—28no—
567C2×D3—22no—
568C2×D3—22no—
569C2×D3—22no—
570C2×D3—44no—
571C2×D3C2×C3×#4114yes—
572C3×C4—24no—
573C3×C4—22no—
574C3×C4—24no—
575C3×C4—22no—
576C3×C4—22no—
577C3×C4—24no—
578C3×C4—22no—
579C3×C4—24no—
580C3×C4—44no—
581C3×C4—42no—
582C3×C4—62no—
583C3×C4—62no—
584C3×C4—64no—
585C3×C4—64no—
586C3×C4C2×#23514yes—
587C3×C4C2×C3×#4114yes—
588Dic3—22no—
589Dic3—22no—
590Dic3—24no—
591Dic3—24no—
592C32C2×#55311yescharacteristic, complemented, Sylow
593C23—24no—
594C23—24no—
595C23—24no—
596C23—34no—
597C23—32no—
598C23—32no—
599C23—62no—
600C23—62no—
601C23—62no—
602C23—62no—
603C23—62no—
604C23C23×C3×D314yes—
605C23C23×C3×D311yescharacteristic
606D4—28no—
607D4—68no—
608D4—616no—
609D4—128no—
610C2×C4—22no—
611C2×C4—24no—
612C2×C4—22no—
613C2×C4—32no—
614C2×C4—34no—
615C2×C4—32no—
616C2×C4—34no—
617C2×C4—48no—
618C2×C4—62no—
619C2×C4—62no—
620C2×C4—64no—
621C2×C4—64no—
622C2×C4—68no—
623C2×C4—68no—
624C2×C4—128no—
625C2×C4C3×#23514yes—
626C2×C4C23×C3×D314yes—
627C2×C4C23×C3×D312yes—
628C2×C4C23×C3×D312yes—
629C2×C4C23×C3×D312yes—
630C2×C3—24no—
631C2×C3—21no—
632C2×C3—21no—
633C2×C3—21no—
634C2×C3—48no—
635C2×C3—44no—
636C2×C3—44no—
637C2×C3—64no—
638C2×C3—122no—
639C2×C3#555814yesdirect product factor
640C2×C3C3×#55314yescomplemented
641C2×C3C22×#23511yescharacteristic
642C2×C3C2×#100411yescharacteristic
643C2×C3C2×D3×#4111yescharacteristic
644C2×C3C22×C3×#4111yescharacteristic
645C2×C3C22×C3×#4111yescharacteristic
646C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
647D3—24no—
648D3—42no—
649C22—24no—
650C22—24no—
651C22—24no—
652C22—34no—
653C22—48no—
654C22—68no—
655C22—62no—
656C22—62no—
657C22—62no—
658C22—62no—
659C22—62no—
660C22—124no—
661C22C2×C3×#23512yes—
662C22C3×#100412yes—
663C22C3×D3×#4112yes—
664C22C24×C3×D311yescharacteristic
665C4—22no—
666C4—24no—
667C4—22no—
668C4—62no—
669C4—62no—
670C4—64no—
671C4—64no—
672C4C2×C3×#23514yes—
673C3—21no—
674C3C2×#555811yescharacteristic, direct product factor
675C3C2×C3×#55311yescharacteristic, complemented
676C2—44no—
677C2—64no—
678C2—122no—
679C2C3×#555814yesdirect product factor
680C2C22×C3×#23511yescharacteristic
681C2C2×C3×#100411yescharacteristic
682C2C2×C3×D3×#4111yescharacteristic
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×#938C2semidirect
3. C2×C3×#938C2semidirect
4. C2×C3×#929C2semidirect
5. C2×C3×C4×#67C2semidirect
6. C3×#5558C2direct (N × H)
7. C2×C3×#892C2semidirect
8. C2×C3×D3×C4⋊C4C2semidirect
9. C2×C3×#884C2semidirect
10. C2×C3×#879C2semidirect
11. C2×C3×C4×D12C2semidirect
12. C2×C3×#870C2semidirect
14. C2×#5558C3direct (N × H)
23. C32×C4×D4C22semidirect
29. C3×#938C22semidirect
30. C3×#938C22semidirect
31. C3×#929C22semidirect
32. C3×C4×#67C22semidirect
43. C3×#892C22semidirect
44. C3×D3×C4⋊C4C22semidirect
45. C3×#884C22semidirect
46. C3×#879C22semidirect
47. C3×C4×D12C22semidirect
48. C3×#870C22semidirect
59. C2×C3×C4×D4D3semidirect
60. C2×C3×C4×D4C2×C3semidirect
63. C2×#938C2×C3semidirect
64. C2×#938C2×C3semidirect
65. C2×#929C2×C3semidirect
66. C2×C4×#67C2×C3semidirect
67. #5558C2×C3direct (N × H)
68. C2×#892C2×C3semidirect
69. C2×D3×C4⋊C4C2×C3semidirect
70. C2×#884C2×C3semidirect
71. C2×#879C2×C3semidirect
72. C2×C4×D12C2×C3semidirect
73. C2×#870C2×C3semidirect
144. C3×C4×D4C2×D3semidirect
145. C3×C4×D4C22×C3semidirect
171. #938C22×C3semidirect
172. #938C22×C3semidirect
173. #929C22×C3semidirect
174. C4×#67C22×C3semidirect
185. #892C22×C3semidirect
186. D3×C4⋊C4C22×C3semidirect
187. #884C22×C3semidirect
188. #879C22×C3semidirect
189. C4×D12C22×C3semidirect
190. #870C22×C3semidirect
237. C2×C4×D4C3×D3semidirect
376. C4×D4C2×C3×D3semidirect
484. C2×C32#553semidirect
592. C32C2×#553semidirect
639. C2×C3#5558direct (N × H)
640. C2×C3C3×#553semidirect
674. C3C2×#5558direct (N × H)
675. C3C2×C3×#553semidirect
679. C2C3×#5558direct (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×#9382
C2×C3×#9292
C2×C3×C4×#672
C3×#55582
C2×C3×#8922
C2×C3×D3×C4⋊C42
C2×C3×#8842
C2×C3×#8792
C2×C3×C4×D122
C2×C3×#8702
C2×C3×#5533
C2×#55583