Finite Group Databasebeta

← C3×C4×#1004 #11900162

Subgroups — C3×C4×#1004 #11900162

Order 1152.

3533 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1004C211yesmaximal, characteristic
2C2×C32×C4×D4C211yesmaximal, characteristic, complemented
3C3×#5798C211yesmaximal, characteristic, complemented
4C2×C3×C4×#67C214yesmaximal, complemented
5C3×#5546C214yesmaximal, complemented
6C3×#5545C214yesmaximal, complemented
7C3×C4×D3×D4C214yesmaximal, complemented
8C3×C4×#237C214yesmaximal, complemented
9C3×#5504C212yesmaximal, complemented
10C3×#5486C214yesmaximal, complemented
11C3×C4×#235C212yesmaximal, complemented
12C3×C4×H(5,𝔽2)—31nomaximal
13C4×#1004C311yesmaximal, characteristic, direct product factor
14C22×C32×D4C2211yescharacteristic
15C23×C32×C4C2212yescomplemented
16C22×C3×#67C2214yes—
17C3×#1004C4116yesdirect product factor
18C2×C3×#237C2214yes—
19C2×C3×D3×D4C2214yes—
20C2×C3×#235C2212yes—
21C22×C3×C4×D3C2214yescomplemented
22C32×C4×D4C2214yescomplemented
23C32×C4×D4C2214yescomplemented
24C2×C32×C4⋊C4C2211yescharacteristic, complemented
25C2×C32×C22⋊C4C2212yescomplemented
26C2×C32×C42C2211yescharacteristic, complemented
27C2×C3×#217C2214yescomplemented
28C3×D4×Dic3C2214yescomplemented
29C3×D4×Dic3C2214yescomplemented
30C3×C4×#67C2218yescomplemented
31C3×C4×#67C2214yescomplemented
32C3×C4×#67C2218yescomplemented
33C3×C4×#67C2218yescomplemented
34C3×C4×#67C2214yescomplemented
35C2×C3×(C2×D3)⋊C4C2214yescomplemented
36C3×#926C2212yescomplemented
37C2×C3×Dic3⋊C4C2214yescomplemented
38C2×C3×C4×Dic3C2214yescomplemented
39C3×#893C2214yescomplemented
40C3×#892C2214yescomplemented
41C3×D3×C4⋊C4C2214yescomplemented
42C3×#887C2214yescomplemented
43C3×#67⋊C4C2218yescomplemented
44C3×#67⋊C4C2218yescomplemented
45C3×D3×C22⋊C4C2218yescomplemented
46C3×#877C2218yescomplemented
47C3×C4×D12C2212yescomplemented
48C3×C4×D12C2212yescomplemented
49C3×#872C2214yescomplemented
50C3×C42×D3C2214yescomplemented
51C3×C4×Dic6C2212yescomplemented
52C3×C4×Dic6C2212yescomplemented
53C2×C3×H(5,𝔽2)—31no—
54C2×#1004C2×C311yescharacteristic
55C3×#520—34no—
56C3×#520—32no—
57C3×#518—31no—
58C3×#518—34no—
59C3×#518—34no—
60C3×C4×#41—34no—
61C3×C4×#41—32no—
62C2×C3×C4×D4—21no—
63C2×C3×C4×D4—34no—
64C2×C3×C4×D4—34no—
65C2×C3×C4×D4D311yescharacteristic, complemented
66C2×C3×C4×D4C2×C311yescharacteristic, complemented
67#5798C2×C311yescharacteristic, complemented
68C2×C4×#67C2×C314yescomplemented
69#5546C2×C314yescomplemented
70#5545C2×C314yescomplemented
71C4×D3×D4C2×C314yescomplemented
72C4×#237C2×C314yescomplemented
73#5504C2×C312yescomplemented
74#5486C2×C314yescomplemented
75C4×#235C2×C312yescomplemented
76C24×C32C2312yes—
77C23×C3×D3C2314yes—
78C2×C32×D4C2×C418yescomplemented
79C2×C32×D4C2314yes—
80C22×C32×C4—44no—
81C22×C32×C4C2314yes—
82C22×C32×C4C2311yescharacteristic
83C22×C32×C4C2314yes—
84C22×C32×C4C2312yes—
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C2×C3×#67C2×C4132yescomplemented
88C2×C3×#67C2318yes—
89C2×C3×#67C2314yes—
90C22×C3×Dic3C2314yes—
91C22×C3×Dic3C2314yes—
92C22×C3×Dic3C2314yes—
93C3×#237C2×C4132yescomplemented
94C3×D3×D4C2×C4132yescomplemented
95C3×#235C2×C4116yescomplemented
96C2×C3×D12C2312yes—
97C2×C3×C4×D3—48no—
98C2×C3×C4×D3C2314yes—
99C2×C3×C4×D3C2314yes—
100C2×C3×C4×D3C2318yes—
101C2×C3×C4×D3C2314yes—
102C2×C3×Dic6C2312yes—
103C32×C4⋊C4C2314yes—
104C32×C22⋊C4C2318yes—
105C32×C42C2312yes—
106C32×C42C2312yes—
107C3×#217C2318yes—
108C3×#217C2314yes—
109C3×(C2×D3)⋊C4C2314yes—
110C3×(C2×D3)⋊C4C2318yes—
111C3×(C2×D3)⋊C4C2314yes—
112C3×C4⋊Dic3C2312yes—
113C3×C4⋊Dic3C2312yes—
114C3×Dic3⋊C4C2314yes—
115C3×Dic3⋊C4C2318yes—
116C3×Dic3⋊C4C2314yes—
117C3×C4×Dic3C2314yes—
118C3×C4×Dic3C2318yes—
119C3×C4×Dic3C2314yes—
120C3×C4×Dic3C2314yes—
121C4×H(5,𝔽2)—31noSylow
122C3×H(5,𝔽2)—316no—
123C2×C3×#41—34no—
124C2×C3×#41—32no—
125C22×C3×D4—21no—
126C22×C3×D4—34no—
127C22×C3×D4—34no—
128C22×C3×D4C2×D311yescharacteristic
129C22×C3×D4C22×C311yescharacteristic
130C23×C3×C4—22no—
131C23×C3×C4—34no—
132C23×C3×C4C2×D312yescomplemented
133C23×C3×C4C22×C312yescomplemented
134C22×#67C22×C314yes—
135#1004C3×C4116yesdirect product factor
136C2×#237C22×C314yes—
137C2×D3×D4C22×C314yes—
138C2×#235C22×C312yes—
139C22×C4×D3C22×C314yescomplemented
140C3×C4×Q8—34no—
141C3×C4×Q8—32no—
142C3×C4×Q8—32no—
143C3×C4×D4—24no—
144C3×C4×D4—24no—
145C3×C4×D4—34no—
146C3×C4×D4—34no—
147C3×C4×D4—38no—
148C3×C4×D4—34no—
149C3×C4×D4—38no—
150C3×C4×D4—38no—
151C3×C4×D4—34no—
152C3×C4×D4—34no—
153C3×C4×D4—38no—
154C3×C4×D4—38no—
155C3×C4×D4—32no—
156C3×C4×D4—32no—
157C3×C4×D4C2×D314yescomplemented
158C3×C4×D4C2×D314yescomplemented
159C3×C4×D4C22×C314yescomplemented
160C3×C4×D4C22×C314yescomplemented
161C3×#117—32no—
162C3×#117—34no—
163C3×#117—38no—
164C3×#117—34no—
165C2×C3×C4⋊C4—21no—
166C2×C3×C4⋊C4—34no—
167C2×C3×C4⋊C4—34no—
168C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
169C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
170C2×C3×C22⋊C4—22no—
171C2×C3×C22⋊C4—34no—
172C2×C3×C22⋊C4—34no—
173C2×C3×C22⋊C4—38no—
174C2×C3×C22⋊C4C2×D312yescomplemented
175C2×C3×C22⋊C4C22×C312yescomplemented
176C2×C3×C42—21no—
177C2×C3×C42—34no—
178C2×C3×C42—34no—
179C2×C3×C42C2×D311yescharacteristic, complemented
180C2×C3×C42C22×C311yescharacteristic, complemented
181C2×#217C22×C314yescomplemented
182D4×Dic3C22×C314yescomplemented
183D4×Dic3C22×C314yescomplemented
184C4×#67C22×C314yescomplemented
185C4×#67C22×C314yescomplemented
186C4×#67C22×C318yescomplemented
187C4×#67C22×C318yescomplemented
188C4×#67C22×C318yescomplemented
189C2×(C2×D3)⋊C4C22×C314yescomplemented
190#926C22×C312yescomplemented
191C2×Dic3⋊C4C22×C314yescomplemented
192C2×C4×Dic3C22×C314yescomplemented
193#893C22×C314yescomplemented
194#892C22×C314yescomplemented
195D3×C4⋊C4C22×C314yescomplemented
196#887C22×C314yescomplemented
197#67⋊C4C22×C318yescomplemented
198#67⋊C4C22×C318yescomplemented
199D3×C22⋊C4C22×C318yescomplemented
200#877C22×C318yescomplemented
201C4×D12C22×C312yescomplemented
202C4×D12C22×C312yescomplemented
203#872C22×C314yescomplemented
204C42×D3C22×C314yescomplemented
205C4×Dic6C22×C312yescomplemented
206C4×Dic6C22×C312yescomplemented
207C23×C32—42no—
208C23×C32—42no—
209C23×C32C22×C418yescomplemented
210C23×C32C2414yes—
211C23×C32C2411yescharacteristic
212C22×C3×D3—44no—
213C22×C3×D3—44no—
214C22×C3×D3C22×C4116yescomplemented
215C22×C3×D3C2414yes—
216C32×D4C22×C4116yescomplemented
217C2×C32×C4—22no—
218C2×C32×C4—28no—
219C2×C32×C4—44no—
220C2×C32×C4—42no—
221C2×C32×C4—41no—
222C2×C32×C4C22×C414yescomplemented
223C2×C32×C4C2412yes—
224C2×C32×C4C2414yes—
225C2×C32×C4C2411yescharacteristic
226C2×C32×C4C2412yes—
227C2×C32×C4C2411yescharacteristic
228C3×#67C22×C4116yescomplemented
229C3×#67C22×C4132yescomplemented
230C2×C3×Dic3—44no—
231C2×C3×Dic3—44no—
232C2×C3×Dic3C22×C4116yescomplemented
233C2×C3×Dic3C2414yes—
234C2×C3×Dic3C2414yes—
235C2×C3×Dic3C2414yes—
236C3×D12C22×C418yescomplemented
237C3×C4×D3—28no—
238C3×C4×D3—48no—
239C3×C4×D3—44no—
240C3×C4×D3C22×C4116yescomplemented
241C3×Dic6C22×C418yescomplemented
242C2×H(5,𝔽2)—31no—
243#520—34no—
244#520—32no—
245#518—31no—
246#518—34no—
247#518—34no—
248C4×#41—34no—
249C4×#41—32no—
250C2×C4×D4—34no—
251C2×C4×D4—34no—
252C2×C4×D4C3×D311yescharacteristic, complemented
253C24×C3—22no—
254C24×C3—34no—
255C24×C3C22×D312yes—
256C24×C3C23×C312yes—
257C23×D3C23×C314yes—
258C3×#41—332no—
259C3×#41—316no—
260C2×C3×Q8—32no—
261C2×C3×D4—28no—
262C2×C3×D4—24no—
263C2×C3×D4—332no—
264C2×C3×D4—34no—
265C2×C3×D4—38no—
266C2×C3×D4—332no—
267C2×C3×D4—32no—
268C2×C3×D4C4×D318yescomplemented
269C2×C3×D4C2×C3×C418yescomplemented
270C2×C3×D4C22×D314yes—
271C2×C3×D4C23×C314yes—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—22no—
276C22×C3×C4—24no—
277C22×C3×C4—24no—
278C22×C3×C4—34no—
279C22×C3×C4—34no—
280C22×C3×C4—34no—
281C22×C3×C4—34no—
282C22×C3×C4—34no—
283C22×C3×C4—34no—
284C22×C3×C4—38no—
285C22×C3×C4—44no—
286C22×C3×C4—44no—
287C22×C3×C4—48no—
288C22×C3×C4—128no—
289C22×C3×C4C22×D314yes—
290C22×C3×C4C22×D311yescharacteristic
291C22×C3×C4C22×D311yescharacteristic
292C22×C3×C4C22×D314yes—
293C22×C3×C4C22×D312yes—
294C22×C3×C4C22×D311yescharacteristic
295C22×C3×C4C23×C314yes—
296C22×C3×C4C23×C311yescharacteristic
297C22×C3×C4C23×C314yes—
298C22×C3×C4C23×C311yescharacteristic
299C22×C3×C4C23×C312yes—
300C22×C3×C4C23×C311yescharacteristic
301C2×#67C2×C3×C4132yescomplemented
302C2×#67C23×C318yes—
303C2×#67C23×C314yes—
304C22×Dic3C23×C314yes—
305C22×Dic3C23×C314yes—
306C22×Dic3C23×C314yes—
307#237C2×C3×C4132yescomplemented
308D3×D4C2×C3×C4132yescomplemented
309#235C2×C3×C4116yescomplemented
310C2×D12C23×C312yes—
311C2×C4×D3—48no—
312C2×C4×D3C23×C314yes—
313C2×C4×D3C23×C314yes—
314C2×C4×D3C23×C318yes—
315C2×C4×D3C23×C314yes—
316C2×Dic6C23×C312yes—
317C3×C4⋊C4—24no—
318C3×C4⋊C4—38no—
319C3×C4⋊C4—34no—
320C3×C4⋊C4—34no—
321C3×C4⋊C4—32no—
322C3×C4⋊C4—32no—
323C3×C4⋊C4C22×D314yes—
324C3×C4⋊C4C23×C314yes—
325C3×C22⋊C4—28no—
326C3×C22⋊C4—34no—
327C3×C22⋊C4—38no—
328C3×C22⋊C4—38no—
329C3×C22⋊C4—34no—
330C3×C22⋊C4—34no—
331C3×C22⋊C4C22×D318yes—
332C3×C22⋊C4C23×C318yes—
333C3×C42—22no—
334C3×C42—22no—
335C3×C42—38no—
336C3×C42—34no—
337C3×C42—34no—
338C3×C42—34no—
339C3×C42C22×D312yes—
340C3×C42C22×D312yes—
341C3×C42C23×C312yes—
342C3×C42C23×C312yes—
343#217C23×C318yes—
344#217C23×C314yes—
345(C2×D3)⋊C4C23×C314yes—
346(C2×D3)⋊C4C23×C314yes—
347(C2×D3)⋊C4C23×C318yes—
348C4⋊Dic3C23×C312yes—
349C4⋊Dic3C23×C312yes—
350Dic3⋊C4C23×C314yes—
351Dic3⋊C4C23×C314yes—
352Dic3⋊C4C23×C318yes—
353C4×Dic3C23×C314yes—
354C4×Dic3C23×C314yes—
355C4×Dic3C23×C314yes—
356C4×Dic3C23×C318yes—
357C22×C32—21no—
358C22×C32—21no—
359C22×C32—24no—
360C22×C32—24no—
361C22×C32—48no—
362C22×C32C23×C418yes—
363C22×C32C23×C412yes—
364C22×C32C2511yescharacteristic
365C2×C3×D3—24no—
366C2×C3×D3—24no—
367C2×C3×D3—416no—
368C2×C3×D3C23×C418yes—
369C32×C4—21no—
370C32×C4—24no—
371C32×C4—22no—
372C32×C4C23×C414yes—
373C32×C4H(5,𝔽2)12yescomplemented
374C3×Dic3—24no—
375C3×Dic3—24no—
376C3×Dic3C23×C418yes—
377H(5,𝔽2)—316no—
378C2×#41—34no—
379C2×#41—32no—
380C22×D4—34no—
381C22×D4—34no—
382C22×D4C2×C3×D311yescharacteristic
383C23×C4—34no—
384C23×C4C2×C3×D312yescomplemented
385C4×Q8—34no—
386C4×Q8—32no—
387C4×Q8—32no—
388C4×D4—34no—
389C4×D4—34no—
390C4×D4—38no—
391C4×D4—34no—
392C4×D4—38no—
393C4×D4—38no—
394C4×D4—34no—
395C4×D4—34no—
396C4×D4—38no—
397C4×D4—38no—
398C4×D4—32no—
399C4×D4—32no—
400C4×D4C2×C3×D314yescomplemented
401C4×D4C2×C3×D314yescomplemented
402#117—32no—
403#117—34no—
404#117—38no—
405#117—34no—
406C2×C4⋊C4—34no—
407C2×C4⋊C4—34no—
408C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
409C2×C22⋊C4—34no—
410C2×C22⋊C4—34no—
411C2×C22⋊C4—38no—
412C2×C22⋊C4C2×C3×D312yescomplemented
413C2×C42—34no—
414C2×C42—34no—
415C2×C42C2×C3×D311yescharacteristic, complemented
416C23×C3—21no—
417C23×C3—24no—
418C23×C3—28no—
419C23×C3—34no—
420C23×C3—316no—
421C23×C3—42no—
422C23×C3—42no—
423C23×C3—42no—
424C23×C3—42no—
425C23×C3—44no—
426C23×C3—44no—
427C23×C3—124no—
428C23×C3—124no—
429C23×C3C2×C4×D318yescomplemented
430C23×C3C22×C3×C418yescomplemented
431C23×C3C23×D311yescharacteristic
432C23×C3C23×D314yes—
433C23×C3C24×C311yescharacteristic
434C23×C3C24×C314yes—
435C22×D3—44no—
436C22×D3—44no—
437C22×D3C22×C3×C4116yescomplemented
438C22×D3C24×C314yes—
439C3×Q8—38no—
440C3×D4—216no—
441C3×D4—332no—
442C3×D4—316no—
443C3×D4—38no—
444C3×D4C2×C4×D3116yescomplemented
445C3×D4C22×C3×C4116yescomplemented
446C2×C3×C4—24no—
447C2×C3×C4—22no—
448C2×C3×C4—28no—
449C2×C3×C4—28no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—22no—
455C2×C3×C4—24no—
456C2×C3×C4—24no—
457C2×C3×C4—316no—
458C2×C3×C4—34no—
459C2×C3×C4—316no—
460C2×C3×C4—34no—
461C2×C3×C4—34no—
462C2×C3×C4—48no—
463C2×C3×C4—44no—
464C2×C3×C4—42no—
465C2×C3×C4—42no—
466C2×C3×C4—44no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—48no—
470C2×C3×C4—42no—
471C2×C3×C4—44no—
472C2×C3×C4—68no—
473C2×C3×C4—124no—
474C2×C3×C4—128no—
475C2×C3×C4—124no—
476C2×C3×C4—124no—
477C2×C3×C4C2×C4×D314yescomplemented
478C2×C3×C4C22×C3×C414yescomplemented
479C2×C3×C4C23×D312yes—
480C2×C3×C4C23×D314yes—
481C2×C3×C4C23×D311yescharacteristic
482C2×C3×C4C23×D312yes—
483C2×C3×C4C23×D311yescharacteristic
484C2×C3×C4C24×C312yes—
485C2×C3×C4C24×C314yes—
486C2×C3×C4C24×C311yescharacteristic
487C2×C3×C4C24×C312yes—
488C2×C3×C4C24×C311yescharacteristic
489#67C22×C3×C4116yescomplemented
490#67C22×C3×C4132yescomplemented
491C2×Dic3—44no—
492C2×Dic3—44no—
493C2×Dic3C22×C3×C4116yescomplemented
494C2×Dic3C24×C314yes—
495C2×Dic3C24×C314yes—
496C2×Dic3C24×C314yes—
497D12C22×C3×C418yescomplemented
498C4×D3—28no—
499C4×D3—48no—
500C4×D3—44no—
501C4×D3C22×C3×C4116yescomplemented
502Dic6C22×C3×C418yescomplemented
503C2×C32—22no—
504C2×C32—28no—
505C2×C32C24×C411yescharacteristic
506C2×C32C2×H(5,𝔽2)11yescharacteristic
507C2×C32#58511yescharacteristic
508C3×D3—28no—
509C24—34no—
510C24C22×C3×D312yes—
511#41—332no—
512#41—316no—
513C2×Q8—32no—
514C2×D4—34no—
515C2×D4—38no—
516C2×D4—332no—
517C2×D4—332no—
518C2×D4—32no—
519C2×D4C3×C4×D318yescomplemented
520C2×D4C22×C3×D314yes—
521C22×C4—34no—
522C22×C4—34no—
523C22×C4—34no—
524C22×C4—34no—
525C22×C4—34no—
526C22×C4—34no—
527C22×C4—38no—
528C22×C4—44no—
529C22×C4—128no—
530C22×C4C22×C3×D314yes—
531C22×C4C22×C3×D311yescharacteristic
532C22×C4C22×C3×D311yescharacteristic
533C22×C4C22×C3×D314yes—
534C22×C4C22×C3×D312yes—
535C22×C4C22×C3×D311yescharacteristic
536C4⋊C4—38no—
537C4⋊C4—34no—
538C4⋊C4—32no—
539C4⋊C4—34no—
540C4⋊C4—32no—
541C4⋊C4C22×C3×D314yes—
542C22⋊C4—34no—
543C22⋊C4—38no—
544C22⋊C4—38no—
545C22⋊C4—34no—
546C22⋊C4—34no—
547C22⋊C4C22×C3×D318yes—
548C42—34no—
549C42—38no—
550C42—34no—
551C42—34no—
552C42C22×C3×D312yes—
553C42C22×C3×D312yes—
554C22×C3—22no—
555C22×C3—22no—
556C22×C3—21no—
557C22×C3—24no—
558C22×C3—21no—
559C22×C3—24no—
560C22×C3—24no—
561C22×C3—21no—
562C22×C3—24no—
563C22×C3—21no—
564C22×C3—22no—
565C22×C3—28no—
566C22×C3—21no—
567C22×C3—38no—
568C22×C3—44no—
569C22×C3—44no—
570C22×C3—48no—
571C22×C3—48no—
572C22×C3—416no—
573C22×C3—64no—
574C22×C3—64no—
575C22×C3—1216no—
576C22×C3C22×C4×D318yes—
577C22×C3C22×C4×D312yes—
578C22×C3C23×C3×C418yes—
579C22×C3C23×C3×C412yes—
580C22×C3C24×D311yescharacteristic
581C22×C3C25×C311yescharacteristic
582C2×D3—24no—
583C2×D3—24no—
584C2×D3—416no—
585C2×D3C23×C3×C418yes—
586C3×C4—22no—
587C3×C4—21no—
588C3×C4—24no—
589C3×C4—22no—
590C3×C4—24no—
591C3×C4—21no—
592C3×C4—22no—
593C3×C4—24no—
594C3×C4—22no—
595C3×C4—38no—
596C3×C4—44no—
597C3×C4—42no—
598C3×C4—64no—
599C3×C4—64no—
600C3×C4C22×C4×D314yes—
601C3×C4#100412yesdirect product factor
602C3×C4C23×C3×C414yes—
603C3×C4C3×H(5,𝔽2)12yescomplemented
604Dic3—24no—
605Dic3—24no—
606Dic3C23×C3×C418yes—
607C32C4×H(5,𝔽2)11yescharacteristic, complemented, Sylow
608C23—34no—
609C23—316no—
610C23—42no—
611C23—42no—
612C23—124no—
613C23—124no—
614C23C2×C3×C4×D318yescomplemented
615C23C23×C3×D311yescharacteristic
616C23C23×C3×D314yes—
617Q8—38no—
618D4—332no—
619D4—316no—
620D4—38no—
621D4C2×C3×C4×D3116yescomplemented
622C2×C4—22no—
623C2×C4—28no—
624C2×C4—316no—
625C2×C4—34no—
626C2×C4—316no—
627C2×C4—34no—
628C2×C4—34no—
629C2×C4—44no—
630C2×C4—42no—
631C2×C4—41no—
632C2×C4—68no—
633C2×C4—128no—
634C2×C4—124no—
635C2×C4—124no—
636C2×C4—124no—
637C2×C4C2×C3×C4×D314yescomplemented
638C2×C4C23×C3×D312yes—
639C2×C4C23×C3×D314yes—
640C2×C4C23×C3×D311yescharacteristic
641C2×C4C23×C3×D312yes—
642C2×C4C23×C3×D311yescharacteristic
643C2×C3—24no—
644C2×C3—28no—
645C2×C3—22no—
646C2×C3—22no—
647C2×C3—28no—
648C2×C3—21no—
649C2×C3—21no—
650C2×C3—21no—
651C2×C3—48no—
652C2×C3—68no—
653C2×C3C23×C4×D311yescharacteristic
654C2×C3C2×#100411yescharacteristic
655C2×C3#596411yescharacteristic
656C2×C3C24×C3×C411yescharacteristic
657C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
658C2×C3C3×#58511yescharacteristic
659D3—28no—
660C22—21no—
661C22—24no—
662C22—21no—
663C22—24no—
664C22—38no—
665C22—48no—
666C22—64no—
667C22—64no—
668C22—1216no—
669C22C22×C3×C4×D318yes—
670C22C22×C3×C4×D312yes—
671C22C24×C3×D311yescharacteristic
672C4—21no—
673C4—24no—
674C4—22no—
675C4—38no—
676C4—64no—
677C4—64no—
678C4C22×C3×C4×D314yes—
679C4C3×#100412yesdirect product factor
680C3—21no—
681C3C4×#100411yescharacteristic, direct product factor
682C3C3×C4×H(5,𝔽2)11yescharacteristic, complemented
683C2—22no—
684C2—28no—
685C2—68no—
686C2C23×C3×C4×D311yescharacteristic
687C2C2×C3×#100411yescharacteristic
688C2C3×#596411yescharacteristic
subgroupG/H
centerC2×C3×C4C23×D3
commutatorC2×C3C24×C3×C4
FrattiniC22C24×C3×D3
FittingC2×C32×C4×D4C2
socleC22×C32C25
prime radicalC2×C3×#1004C2
cosocleC22×C3C25×C3
hypercenterC2×C3×C4×D4D3
hypocenterC3C3×C4×H(5,𝔽2)
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C32×C4×D4C2semidirect
3. C3×#5798C2semidirect
4. C2×C3×C4×#67C2semidirect
5. C3×#5546C2semidirect
6. C3×#5545C2semidirect
7. C3×C4×D3×D4C2semidirect
8. C3×C4×#237C2semidirect
9. C3×#5504C2semidirect
10. C3×#5486C2semidirect
11. C3×C4×#235C2semidirect
13. C4×#1004C3direct (N × H)
15. C23×C32×C4C22semidirect
17. C3×#1004C4direct (N × H)
21. C22×C3×C4×D3C22semidirect
22. C32×C4×D4C22semidirect
23. C32×C4×D4C22semidirect
24. C2×C32×C4⋊C4C22semidirect
25. C2×C32×C22⋊C4C22semidirect
26. C2×C32×C42C22semidirect
27. C2×C3×#217C22semidirect
28. C3×D4×Dic3C22semidirect
29. C3×D4×Dic3C22semidirect
30. C3×C4×#67C22semidirect
31. C3×C4×#67C22semidirect
32. C3×C4×#67C22semidirect
33. C3×C4×#67C22semidirect
34. C3×C4×#67C22semidirect
35. C2×C3×(C2×D3)⋊C4C22semidirect
36. C3×#926C22semidirect
37. C2×C3×Dic3⋊C4C22semidirect
38. C2×C3×C4×Dic3C22semidirect
39. C3×#893C22semidirect
40. C3×#892C22semidirect
41. C3×D3×C4⋊C4C22semidirect
42. C3×#887C22semidirect
43. C3×#67⋊C4C22semidirect
44. C3×#67⋊C4C22semidirect
45. C3×D3×C22⋊C4C22semidirect
46. C3×#877C22semidirect
47. C3×C4×D12C22semidirect
48. C3×C4×D12C22semidirect
49. C3×#872C22semidirect
50. C3×C42×D3C22semidirect
51. C3×C4×Dic6C22semidirect
52. C3×C4×Dic6C22semidirect
65. C2×C3×C4×D4D3semidirect
66. C2×C3×C4×D4C2×C3semidirect
67. #5798C2×C3semidirect
68. C2×C4×#67C2×C3semidirect
69. #5546C2×C3semidirect
70. #5545C2×C3semidirect
71. C4×D3×D4C2×C3semidirect
72. C4×#237C2×C3semidirect
73. #5504C2×C3semidirect
74. #5486C2×C3semidirect
75. C4×#235C2×C3semidirect
78. C2×C32×D4C2×C4semidirect
87. C2×C3×#67C2×C4semidirect
93. C3×#237C2×C4semidirect
94. C3×D3×D4C2×C4semidirect
95. C3×#235C2×C4semidirect
132. C23×C3×C4C2×D3semidirect
133. C23×C3×C4C22×C3semidirect
135. #1004C3×C4direct (N × H)
139. C22×C4×D3C22×C3semidirect
157. C3×C4×D4C2×D3semidirect
158. C3×C4×D4C2×D3semidirect
159. C3×C4×D4C22×C3semidirect
160. C3×C4×D4C22×C3semidirect
168. C2×C3×C4⋊C4C2×D3semidirect
169. C2×C3×C4⋊C4C22×C3semidirect
174. C2×C3×C22⋊C4C2×D3semidirect
175. C2×C3×C22⋊C4C22×C3semidirect
179. C2×C3×C42C2×D3semidirect
180. C2×C3×C42C22×C3semidirect
181. C2×#217C22×C3semidirect
182. D4×Dic3C22×C3semidirect
183. D4×Dic3C22×C3semidirect
184. C4×#67C22×C3semidirect
185. C4×#67C22×C3semidirect
186. C4×#67C22×C3semidirect
187. C4×#67C22×C3semidirect
188. C4×#67C22×C3semidirect
189. C2×(C2×D3)⋊C4C22×C3semidirect
190. #926C22×C3semidirect
191. C2×Dic3⋊C4C22×C3semidirect
192. C2×C4×Dic3C22×C3semidirect
193. #893C22×C3semidirect
194. #892C22×C3semidirect
195. D3×C4⋊C4C22×C3semidirect
196. #887C22×C3semidirect
197. #67⋊C4C22×C3semidirect
198. #67⋊C4C22×C3semidirect
199. D3×C22⋊C4C22×C3semidirect
200. #877C22×C3semidirect
201. C4×D12C22×C3semidirect
202. C4×D12C22×C3semidirect
203. #872C22×C3semidirect
204. C42×D3C22×C3semidirect
205. C4×Dic6C22×C3semidirect
206. C4×Dic6C22×C3semidirect
209. C23×C32C22×C4semidirect
214. C22×C3×D3C22×C4semidirect
216. C32×D4C22×C4semidirect
222. C2×C32×C4C22×C4semidirect
228. C3×#67C22×C4semidirect
229. C3×#67C22×C4semidirect
232. C2×C3×Dic3C22×C4semidirect
236. C3×D12C22×C4semidirect
240. C3×C4×D3C22×C4semidirect
241. C3×Dic6C22×C4semidirect
252. C2×C4×D4C3×D3semidirect
268. C2×C3×D4C4×D3semidirect
269. C2×C3×D4C2×C3×C4semidirect
301. C2×#67C2×C3×C4semidirect
307. #237C2×C3×C4semidirect
308. D3×D4C2×C3×C4semidirect
309. #235C2×C3×C4semidirect
373. C32×C4H(5,𝔽2)semidirect
384. C23×C4C2×C3×D3semidirect
400. C4×D4C2×C3×D3semidirect
401. C4×D4C2×C3×D3semidirect
408. C2×C4⋊C4C2×C3×D3semidirect
412. C2×C22⋊C4C2×C3×D3semidirect
415. C2×C42C2×C3×D3semidirect
429. C23×C3C2×C4×D3semidirect
430. C23×C3C22×C3×C4semidirect
437. C22×D3C22×C3×C4semidirect
444. C3×D4C2×C4×D3semidirect
445. C3×D4C22×C3×C4semidirect
477. C2×C3×C4C2×C4×D3semidirect
478. C2×C3×C4C22×C3×C4semidirect
489. #67C22×C3×C4semidirect
490. #67C22×C3×C4semidirect
493. C2×Dic3C22×C3×C4semidirect
497. D12C22×C3×C4semidirect
501. C4×D3C22×C3×C4semidirect
502. Dic6C22×C3×C4semidirect
519. C2×D4C3×C4×D3semidirect
601. C3×C4#1004direct (N × H)
603. C3×C4C3×H(5,𝔽2)semidirect
607. C32C4×H(5,𝔽2)semidirect
614. C23C2×C3×C4×D3semidirect
621. D4C2×C3×C4×D3semidirect
637. C2×C4C2×C3×C4×D3semidirect
679. C4C3×#1004direct (N × H)
681. C3C4×#1004direct (N × H)
682. C3C3×C4×H(5,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10042
C2×C32×C4×D42
C3×#57982
C2×C3×C4×#672
C3×#55462
C3×#55452
C3×C4×D3×D42
C3×C4×#2372
C3×#55042
C3×#54862
C3×C4×#2352
C3×C4×H(5,𝔽2)3
C4×#10043