Finite Group Databasebeta

← C3×C22⋊C4×#67 #11804741

Subgroups — C3×C22⋊C4×#67 #11804741

Order 1152.

2841 conjugacy classes of subgroups.

The subgroup lattice has 875 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×#67C211yesmaximal, characteristic
2C22×C32×C22⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×C4×#67C212yesmaximal, complemented
4C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
5C3×#5247C211yesmaximal, characteristic, complemented
6C3×#5213C212yesmaximal, complemented
7C3×#4957C212yesmaximal, complemented
8C3×#4956C212yesmaximal, complemented
9C3×#4955C211yesmaximal, characteristic, complemented
10C3×#4942C211yesmaximal, characteristic, complemented
11C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
12C3×D4×C22⋊C4—31nomaximal
13C22⋊C4×#67C311yesmaximal, characteristic, direct product factor
14C25×C32C2211yescharacteristic
15C24×C3×D3C2211yescharacteristic
16C23×C32×C4C2212yescomplemented
17C22×C3×#67—28no—
18C22×C3×#67C418yescomplemented
19C22×C3×#67C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic
24C22×C3×C4×D3C2212yescomplemented
25C2×C32×C22⋊C4—24no—
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×C32×C22⋊C4C2211yescharacteristic
28C2×C32×C22⋊C4C2212yescomplemented
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2212yescomplemented
32C2×C3×#217C2212yescomplemented
33C3×C4×#67—28no—
34C2×C3×(C2×D3)⋊C4C2212yescomplemented
35C2×C3×(C2×D3)⋊C4C2212yescomplemented
36C2×C3×(C2×D3)⋊C4C2212yescomplemented
37C2×C3×Dic3⋊C4C2212yescomplemented
38C2×C3×C4×Dic3C2212yescomplemented
39C3×D3×C22⋊C4—24no—
40C3×C3⋊#95C2212yescomplemented
41C3×C3⋊#95C2212yescomplemented
42C23×C3×D4—31no—
43C23×#67C2×C311yescharacteristic
44C2×C3×C4×D4—32no—
45C22×C3×C22⋊C4—21no—
46C22×C3×C22⋊C4—31no—
47C22×C3×C22⋊C4D311yescharacteristic, complemented
48C22×C3×C22⋊C4C2×C311yescharacteristic, complemented
49C2×C4×#67C2×C312yescomplemented
50C2×D3×C22⋊C4C2×C311yescharacteristic, complemented
51C3×#390—32no—
52C3×#386—32no—
53C3×#386—32no—
54C3×#380—31no—
55C3×#379—31no—
56C3×#379—31no—
57C3×C4×C22⋊C4—31no—
58#5247C2×C311yescharacteristic, complemented
59#5213C2×C312yescomplemented
60#4957C2×C312yescomplemented
61#4956C2×C312yescomplemented
62#4955C2×C311yescharacteristic, complemented
63#4942C2×C311yescharacteristic, complemented
64Dic3×C22⋊C4C2×C311yescharacteristic, complemented
65C24×C32—22no—
66C24×C32—24no—
67C24×C32—22no—
68C24×C32—42no—
69C24×C32C2×C414yescomplemented
70C24×C32C2311yescharacteristic
71C24×C32C2311yescharacteristic
72C24×C32C2311yescharacteristic
73C23×C3×D3—22no—
74C23×C3×D3—22no—
75C23×C3×D3—24no—
76C23×C3×D3—42no—
77C23×C3×D3C2×C414yescomplemented
78C23×C3×D3C2311yescharacteristic
79C23×C3×D3C2311yescharacteristic
80C22×C32×C4—24no—
81C22×C32×C4—24no—
82C22×C32×C4—42no—
83C22×C32×C4C2312yes—
84C22×C32×C4C2312yes—
85C2×C3×#67—24no—
86C2×C3×#67—24no—
87C2×C3×#67—232no—
88C2×C3×#67—24no—
89C2×C3×#67C2×C414yes—
90C2×C3×#67C2×C414yescomplemented
91C2×C3×#67C2×C414yescomplemented
92C2×C3×#67C2×C414yescomplemented
93C2×C3×#67D418yes—
94C22×C3×Dic3—24no—
95C22×C3×Dic3C2×C414yescomplemented
96C22×C3×Dic3C2312yes—
97C22×C3×Dic3C2312yes—
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C2×C3×C4×D3—24no—
101C2×C3×C4×D3—24no—
102C2×C3×C4×D3—42no—
103C32×C22⋊C4—22no—
104C32×C22⋊C4—24no—
105C32×C22⋊C4D414yescomplemented
106C3×#217—22no—
107C3×#217—24no—
108C3×#217—22no—
109C3×#217—42no—
110C3×(C2×D3)⋊C4—24no—
111C3×(C2×D3)⋊C4—24no—
112C3×(C2×D3)⋊C4—42no—
113C3×Dic3⋊C4—24no—
114C3×C4×Dic3—24no—
115D4×C22⋊C4—31noSylow
116C25×C3—21no—
117C25×C3—31no—
118C25×C3C2×D311yescharacteristic
119C25×C3C22×C311yescharacteristic
120C24×D3C22×C311yescharacteristic
121C22×C3×D4—31no—
122C22×C3×D4—38no—
123C22×C3×D4—31no—
124C22×C3×D4—31no—
125C22×C3×D4—31no—
126C22×C3×D4—68no—
127C23×C3×C4—22no—
128C23×C3×C4—31no—
129C23×C3×C4—32no—
130C23×C3×C4C2×D312yescomplemented
131C23×C3×C4C22×C312yescomplemented
132C22×#67—28no—
133C22×#67C3×C418yescomplemented
134C22×#67C22×C311yescharacteristic
135C22×#67C22×C311yescharacteristic
136C22×#67C22×C311yescharacteristic
137C22×#67C22×C311yescharacteristic
138C23×Dic3C22×C311yescharacteristic
139C22×C4×D3C22×C312yescomplemented
140C3×C4×D4—68no—
141C2×C3×C4⋊C4—32no—
142C2×C3×C22⋊C4—28no—
143C2×C3×C22⋊C4—24no—
144C2×C3×C22⋊C4—24no—
145C2×C3×C22⋊C4—21no—
146C2×C3×C22⋊C4—21no—
147C2×C3×C22⋊C4—22no—
148C2×C3×C22⋊C4—31no—
149C2×C3×C22⋊C4—31no—
150C2×C3×C22⋊C4—32no—
151C2×C3×C22⋊C4—32no—
152C2×C3×C22⋊C4—32no—
153C2×C3×C22⋊C4—32no—
154C2×C3×C22⋊C4—32no—
155C2×C3×C22⋊C4—64no—
156C2×C3×C22⋊C4C2×D311yescharacteristic
157C2×C3×C22⋊C4C2×D311yescharacteristic
158C2×C3×C22⋊C4C2×D312yescomplemented
159C2×C3×C22⋊C4C22×C311yescharacteristic
160C2×C3×C22⋊C4C22×C311yescharacteristic
161C2×C3×C22⋊C4C22×C312yescomplemented
162C2×C3×C42—32no—
163C2×#217C22×C311yescharacteristic
164C2×#217C22×C311yescharacteristic
165C2×#217C22×C312yescomplemented
166C2×#217C22×C312yescomplemented
167C4×#67—28no—
168C2×(C2×D3)⋊C4C22×C312yescomplemented
169C2×(C2×D3)⋊C4C22×C312yescomplemented
170C2×(C2×D3)⋊C4C22×C312yescomplemented
171C2×Dic3⋊C4C22×C312yescomplemented
172C2×C4×Dic3C22×C312yescomplemented
173D3×C22⋊C4—24no—
174C3×#95—32no—
175C3×#95—32no—
176C3⋊#95C22×C312yescomplemented
177C3⋊#95C22×C312yescomplemented
178C23×C32—21no—
179C23×C32—21no—
180C23×C32—22no—
181C23×C32—28no—
182C23×C32—21no—
183C23×C32—21no—
184C23×C32—22no—
185C23×C32—22no—
186C23×C32—28no—
187C23×C32—22no—
188C23×C32—22no—
189C23×C32—44no—
190C23×C32—48no—
191C23×C32—48no—
192C23×C32C22×C412yes—
193C23×C32C22×C412yes—
194C23×C32C22×C412yes—
195C23×C32C2×D414yes—
196C23×C32C2×D412yes—
197C23×C32#4112yes—
198C23×C32C2411yescharacteristic
199C22×C3×D3—21no—
200C22×C3×D3—21no—
201C22×C3×D3—22no—
202C22×C3×D3—28no—
203C22×C3×D3—21no—
204C22×C3×D3—22no—
205C22×C3×D3—21no—
206C22×C3×D3—22no—
207C22×C3×D3—28no—
208C22×C3×D3—44no—
209C22×C3×D3—48no—
210C22×C3×D3—48no—
211C22×C3×D3C22×C412yes—
212C22×C3×D3C22×C412yes—
213C22×C3×D3C2×D414yes—
214C2×C32×C4—22no—
215C2×C32×C4—22no—
216C2×C32×C4—22no—
217C2×C32×C4—22no—
218C2×C32×C4—22no—
219C2×C32×C4—48no—
220C2×C32×C4C2×D414yescomplemented
221C3×#67—28no—
222C3×#67—28no—
223C3×#67—28no—
224C3×#67C22⋊C4116yesdirect product factor
225C2×C3×Dic3—22no—
226C2×C3×Dic3—28no—
227C2×C3×Dic3—22no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3—22no—
230C2×C3×Dic3—22no—
231C2×C3×Dic3—22no—
232C2×C3×Dic3—22no—
233C2×C3×Dic3C22×C412yes—
234C2×C3×Dic3C22×C412yes—
235C2×C3×Dic3C2×D414yes—
236C3×C4×D3—48no—
237C23×D4—31no—
238C2×C4×D4—32no—
239C22×C22⋊C4—31no—
240C22×C22⋊C4C3×D311yescharacteristic, complemented
241#390—32no—
242#386—32no—
243#386—32no—
244#380—31no—
245#379—31no—
246#379—31no—
247C4×C22⋊C4—31no—
248C24×C3—24no—
249C24×C3—24no—
250C24×C3—22no—
251C24×C3—24no—
252C24×C3—22no—
253C24×C3—22no—
254C24×C3—24no—
255C24×C3—22no—
256C24×C3—24no—
257C24×C3—21no—
258C24×C3—21no—
259C24×C3—21no—
260C24×C3—31no—
261C24×C3—31no—
262C24×C3—34no—
263C24×C3—44no—
264C24×C3—42no—
265C24×C3—42no—
266C24×C3—44no—
267C24×C3—64no—
268C24×C3—62no—
269C24×C3—62no—
270C24×C3—122no—
271C24×C3C4×D314yescomplemented
272C24×C3C2×C3×C414yescomplemented
273C24×C3C22×D311yescharacteristic
274C24×C3C22×D311yescharacteristic
275C24×C3C22×D311yescharacteristic
276C24×C3C23×C311yescharacteristic
277C24×C3C23×C311yescharacteristic
278C24×C3C23×C311yescharacteristic
279C23×D3—22no—
280C23×D3—22no—
281C23×D3—24no—
282C23×D3—42no—
283C23×D3C2×C3×C414yescomplemented
284C23×D3C23×C311yescharacteristic
285C23×D3C23×C311yescharacteristic
286C2×C3×D4—34no—
287C2×C3×D4—38no—
288C2×C3×D4—34no—
289C2×C3×D4—34no—
290C2×C3×D4—34no—
291C2×C3×D4—64no—
292C2×C3×D4—632no—
293C2×C3×D4—64no—
294C2×C3×D4—64no—
295C22×C3×C4—28no—
296C22×C3×C4—24no—
297C22×C3×C4—24no—
298C22×C3×C4—24no—
299C22×C3×C4—24no—
300C22×C3×C4—22no—
301C22×C3×C4—22no—
302C22×C3×C4—31no—
303C22×C3×C4—34no—
304C22×C3×C4—31no—
305C22×C3×C4—32no—
306C22×C3×C4—32no—
307C22×C3×C4—44no—
308C22×C3×C4—42no—
309C22×C3×C4—42no—
310C22×C3×C4—44no—
311C22×C3×C4—64no—
312C22×C3×C4—64no—
313C22×C3×C4—64no—
314C22×C3×C4—122no—
315C22×C3×C4C22×D312yes—
316C22×C3×C4C22×D312yes—
317C22×C3×C4C23×C312yes—
318C22×C3×C4C23×C312yes—
319C2×#67—24no—
320C2×#67—24no—
321C2×#67—232no—
322C2×#67—24no—
323C2×#67C2×C3×C414yes—
324C2×#67C2×C3×C414yescomplemented
325C2×#67C2×C3×C414yescomplemented
326C2×#67C2×C3×C414yescomplemented
327C2×#67C3×D418yes—
328C22×Dic3—24no—
329C22×Dic3C2×C3×C414yescomplemented
330C22×Dic3C23×C312yes—
331C22×Dic3C23×C312yes—
332C22×Dic3C23×C311yescharacteristic
333C22×Dic3C23×C311yescharacteristic
334C2×C4×D3—24no—
335C2×C4×D3—24no—
336C2×C4×D3—42no—
337C3×C4⋊C4—64no—
338C3×C22⋊C4—24no—
339C3×C22⋊C4—28no—
340C3×C22⋊C4—22no—
341C3×C22⋊C4—22no—
342C3×C22⋊C4—24no—
343C3×C22⋊C4—24no—
344C3×C22⋊C4—24no—
345C3×C22⋊C4—64no—
346C3×C22⋊C4—62no—
347C3×C22⋊C4—64no—
348C3×C22⋊C4—62no—
349C3×C22⋊C4—64no—
350C3×C22⋊C4—122no—
351C3×C22⋊C4—122no—
352C3×C22⋊C4#6714yesdirect product factor
353C3×C22⋊C4C3×D414yescomplemented
354C3×C42—64no—
355#217—22no—
356#217—24no—
357#217—22no—
358#217—42no—
359(C2×D3)⋊C4—24no—
360(C2×D3)⋊C4—24no—
361(C2×D3)⋊C4—42no—
362Dic3⋊C4—24no—
363C4×Dic3—24no—
364C22×C32—22no—
365C22×C32—22no—
366C22×C32—24no—
367C22×C32—24no—
368C22×C32—22no—
369C22×C32—22no—
370C22×C32—22no—
371C22×C32—24no—
372C22×C32—24no—
373C22×C32—22no—
374C22×C32—22no—
375C22×C32—416no—
376C22×C32—42no—
377C22×C32—42no—
378C22×C32C2×C22⋊C414yescomplemented
379C22×C32C4×D414yescomplemented
380C22×C32C23×C411yescharacteristic
381C22×C32C22×D412yes—
382C22×C32C22×D411yescharacteristic
383C22×C32C2×#4111yescharacteristic
384C22×C32H(5,𝔽2)12yes—
385C2×C3×D3—22no—
386C2×C3×D3—22no—
387C2×C3×D3—24no—
388C2×C3×D3—24no—
389C2×C3×D3—22no—
390C2×C3×D3—22no—
391C2×C3×D3—22no—
392C2×C3×D3—416no—
393C2×C3×D3—42no—
394C2×C3×D3—42no—
395C2×C3×D3C2×C22⋊C414yescomplemented
396C32×C4—24no—
397C32×C4—42no—
398C3×Dic3—22no—
399C3×Dic3—42no—
400C3×Dic3—42no—
401C3×Dic3C2×C22⋊C414yescomplemented
402C25—31no—
403C25C2×C3×D311yescharacteristic
404C22×D4—31no—
405C22×D4—38no—
406C22×D4—31no—
407C22×D4—31no—
408C22×D4—31no—
409C22×D4—68no—
410C23×C4—31no—
411C23×C4—32no—
412C23×C4C2×C3×D312yescomplemented
413C4×D4—68no—
414C2×C4⋊C4—32no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—31no—
417C2×C22⋊C4—32no—
418C2×C22⋊C4—31no—
419C2×C22⋊C4—32no—
420C2×C22⋊C4—32no—
421C2×C22⋊C4—32no—
422C2×C22⋊C4—32no—
423C2×C22⋊C4—64no—
424C2×C22⋊C4C2×C3×D311yescharacteristic
425C2×C22⋊C4C2×C3×D311yescharacteristic
426C2×C22⋊C4C2×C3×D312yescomplemented
427C2×C42—32no—
428#95—32no—
429#95—32no—
430C23×C3—22no—
431C23×C3—24no—
432C23×C3—22no—
433C23×C3—21no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—21no—
438C23×C3—22no—
439C23×C3—21no—
440C23×C3—21no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—216no—
445C23×C3—22no—
446C23×C3—28no—
447C23×C3—28no—
448C23×C3—28no—
449C23×C3—28no—
450C23×C3—21no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—21no—
454C23×C3—21no—
455C23×C3—22no—
456C23×C3—21no—
457C23×C3—22no—
458C23×C3—21no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—24no—
464C23×C3—22no—
465C23×C3—32no—
466C23×C3—34no—
467C23×C3—32no—
468C23×C3—42no—
469C23×C3—42no—
470C23×C3—48no—
471C23×C3—42no—
472C23×C3—42no—
473C23×C3—44no—
474C23×C3—44no—
475C23×C3—48no—
476C23×C3—48no—
477C23×C3—48no—
478C23×C3—48no—
479C23×C3—48no—
480C23×C3—416no—
481C23×C3—416no—
482C23×C3—68no—
483C23×C3—61no—
484C23×C3—62no—
485C23×C3—61no—
486C23×C3—68no—
487C23×C3—61no—
488C23×C3—62no—
489C23×C3—62no—
490C23×C3—61no—
491C23×C3—124no—
492C23×C3—128no—
493C23×C3—128no—
494C23×C3C2×C4×D312yes—
495C23×C3C2×C4×D312yes—
496C23×C3C2×C4×D312yes—
497C23×C3#23512yes—
498C23×C3D3×D414yes—
499C23×C3C2×#6712yes—
500C23×C3C22×C3×C412yes—
501C23×C3C22×C3×C412yes—
502C23×C3C22×C3×C412yes—
503C23×C3C2×C3×D414yes—
504C23×C3C2×C3×D412yes—
505C23×C3C3×#4112yes—
506C23×C3C23×D311yescharacteristic
507C23×C3C24×C311yescharacteristic
508C22×D3—21no—
509C22×D3—21no—
510C22×D3—22no—
511C22×D3—28no—
512C22×D3—21no—
513C22×D3—22no—
514C22×D3—21no—
515C22×D3—22no—
516C22×D3—28no—
517C22×D3—44no—
518C22×D3—48no—
519C22×D3—48no—
520C22×D3C22×C3×C412yes—
521C22×D3C22×C3×C412yes—
522C22×D3C2×C3×D414yes—
523C3×D4—316no—
524C3×D4—68no—
525C3×D4—68no—
526C3×D4—68no—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—24no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—24no—
539C2×C3×C4—32no—
540C2×C3×C4—34no—
541C2×C3×C4—32no—
542C2×C3×C4—42no—
543C2×C3×C4—42no—
544C2×C3×C4—42no—
545C2×C3×C4—42no—
546C2×C3×C4—48no—
547C2×C3×C4—48no—
548C2×C3×C4—416no—
549C2×C3×C4—68no—
550C2×C3×C4—62no—
551C2×C3×C4—62no—
552C2×C3×C4—62no—
553C2×C3×C4—62no—
554C2×C3×C4—62no—
555C2×C3×C4—62no—
556C2×C3×C4—62no—
557C2×C3×C4—128no—
558C2×C3×C4C2×#6714yescomplemented
559C2×C3×C4C2×C3×D414yescomplemented
560#67—28no—
561#67—28no—
562#67—28no—
563#67C3×C22⋊C4116yesdirect product factor
564C2×Dic3—22no—
565C2×Dic3—28no—
566C2×Dic3—22no—
567C2×Dic3—22no—
568C2×Dic3—22no—
569C2×Dic3—22no—
570C2×Dic3—22no—
571C2×Dic3—22no—
572C2×Dic3C22×C3×C412yes—
573C2×Dic3C22×C3×C412yes—
574C2×Dic3C2×C3×D414yes—
575C4×D3—48no—
576C2×C32—24no—
577C2×C32—24no—
578C2×C32—42no—
579C2×C32C22×C22⋊C411yescharacteristic
580C2×C32C2×C4×D411yescharacteristic
581C2×C32#51811yescharacteristic
582C2×C32D4212yes—
583C2×C32#54612yes—
584C3×D3—24no—
585C3×D3—42no—
586C24—22no—
587C24—24no—
588C24—22no—
589C24—31no—
590C24—31no—
591C24—34no—
592C24—42no—
593C24—64no—
594C24—62no—
595C24—62no—
596C24—122no—
597C24C3×C4×D314yescomplemented
598C24C22×C3×D311yescharacteristic
599C24C22×C3×D311yescharacteristic
600C24C22×C3×D311yescharacteristic
601C2×D4—34no—
602C2×D4—38no—
603C2×D4—34no—
604C2×D4—34no—
605C2×D4—34no—
606C2×D4—64no—
607C2×D4—632no—
608C2×D4—64no—
609C2×D4—64no—
610C22×C4—24no—
611C22×C4—24no—
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—34no—
615C22×C4—32no—
616C22×C4—32no—
617C22×C4—42no—
618C22×C4—64no—
619C22×C4—64no—
620C22×C4—64no—
621C22×C4—122no—
622C22×C4C22×C3×D312yes—
623C22×C4C22×C3×D312yes—
624C4⋊C4—64no—
625C22⋊C4—22no—
626C22⋊C4—24no—
627C22⋊C4—64no—
628C22⋊C4—62no—
629C22⋊C4—64no—
630C22⋊C4—62no—
631C22⋊C4—64no—
632C22⋊C4—122no—
633C22⋊C4—122no—
634C22⋊C4C3×#6714yesdirect product factor
635C42—64no—
636C22×C3—28no—
637C22×C3—24no—
638C22×C3—28no—
639C22×C3—24no—
640C22×C3—22no—
641C22×C3—22no—
642C22×C3—22no—
643C22×C3—24no—
644C22×C3—24no—
645C22×C3—22no—
646C22×C3—24no—
647C22×C3—24no—
648C22×C3—22no—
649C22×C3—22no—
650C22×C3—22no—
651C22×C3—22no—
652C22×C3—24no—
653C22×C3—24no—
654C22×C3—24no—
655C22×C3—24no—
656C22×C3—24no—
657C22×C3—22no—
658C22×C3—22no—
659C22×C3—22no—
660C22×C3—22no—
661C22×C3—22no—
662C22×C3—22no—
663C22×C3—24no—
664C22×C3—24no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—22no—
668C22×C3—22no—
669C22×C3—21no—
670C22×C3—34no—
671C22×C3—44no—
672C22×C3—44no—
673C22×C3—42no—
674C22×C3—42no—
675C22×C3—42no—
676C22×C3—42no—
677C22×C3—416no—
678C22×C3—416no—
679C22×C3—432no—
680C22×C3—44no—
681C22×C3—44no—
682C22×C3—42no—
683C22×C3—42no—
684C22×C3—42no—
685C22×C3—42no—
686C22×C3—62no—
687C22×C3—64no—
688C22×C3—62no—
689C22×C3—64no—
690C22×C3—62no—
691C22×C3—62no—
692C22×C3—62no—
693C22×C3—1216no—
694C22×C3—122no—
695C22×C3—122no—
696C22×C3D3×C22⋊C414yescomplemented
697C22×C3C4×#6714yescomplemented
698C22×C3C2×C3×C22⋊C414yescomplemented
699C22×C3C3×C4×D414yescomplemented
700C22×C3C22×C4×D311yescharacteristic
701C22×C3C2×#23511yescharacteristic
702C22×C3C2×D3×D412yes—
703C22×C3#100412yes—
704C22×C3C22×#6711yescharacteristic
705C22×C3C23×C3×C411yescharacteristic
706C22×C3C22×C3×D412yes—
707C22×C3C22×C3×D411yescharacteristic
708C22×C3C2×C3×#4111yescharacteristic
709C22×C3C3×H(5,𝔽2)12yes—
710C2×D3—22no—
711C2×D3—22no—
712C2×D3—24no—
713C2×D3—24no—
714C2×D3—22no—
715C2×D3—22no—
716C2×D3—22no—
717C2×D3—416no—
718C2×D3—42no—
719C2×D3—42no—
720C2×D3C2×C3×C22⋊C414yescomplemented
721C3×C4—24no—
722C3×C4—24no—
723C3×C4—34no—
724C3×C4—44no—
725C3×C4—44no—
726C3×C4—42no—
727C3×C4—42no—
728C3×C4—62no—
729C3×C4—122no—
730C3×C4—122no—
731Dic3—22no—
732Dic3—42no—
733Dic3—42no—
734Dic3C2×C3×C22⋊C414yescomplemented
735C32D4×C22⋊C411yescharacteristic, complemented, Sylow
736C23—21no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—21no—
741C23—28no—
742C23—28no—
743C23—21no—
744C23—22no—
745C23—22no—
746C23—21no—
747C23—32no—
748C23—34no—
749C23—32no—
750C23—44no—
751C23—48no—
752C23—48no—
753C23—68no—
754C23—61no—
755C23—62no—
756C23—61no—
757C23—68no—
758C23—61no—
759C23—62no—
760C23—62no—
761C23—61no—
762C23—124no—
763C23—128no—
764C23—128no—
765C23C2×C3×C4×D312yes—
766C23C2×C3×C4×D312yes—
767C23C2×C3×C4×D312yes—
768C23C3×#23512yes—
769C23C3×D3×D414yes—
770C23C2×C3×#6712yes—
771C23C23×C3×D311yescharacteristic
772D4—316no—
773D4—68no—
774D4—68no—
775D4—68no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—32no—
782C2×C4—34no—
783C2×C4—32no—
784C2×C4—48no—
785C2×C4—68no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—62no—
789C2×C4—62no—
790C2×C4—62no—
791C2×C4—62no—
792C2×C4—62no—
793C2×C4—128no—
794C2×C4C2×C3×#6714yescomplemented
795C2×C3—28no—
796C2×C3—24no—
797C2×C3—24no—
798C2×C3—24no—
799C2×C3—24no—
800C2×C3—22no—
801C2×C3—21no—
802C2×C3—22no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—44no—
806C2×C3—44no—
807C2×C3—42no—
808C2×C3—42no—
809C2×C3—64no—
810C2×C3—122no—
811C2×C3C2×D3×C22⋊C411yescharacteristic
812C2×C3#548611yescharacteristic
813C2×C3#549012yes—
814C2×C3C2×C4×#6711yescharacteristic
815C2×C3D4×#6712yes—
816C2×C3C22×C3×C22⋊C411yescharacteristic
817C2×C3C2×C3×C4×D411yescharacteristic
818C2×C3C3×#51811yescharacteristic
819C2×C3C3×D4212yes—
820C2×C3C3×#54612yes—
821D3—24no—
822D3—42no—
823C22—24no—
824C22—24no—
825C22—22no—
826C22—24no—
827C22—24no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—34no—
835C22—416no—
836C22—42no—
837C22—42no—
838C22—64no—
839C22—62no—
840C22—64no—
841C22—62no—
842C22—62no—
843C22—62no—
844C22—62no—
845C22—1216no—
846C22—122no—
847C22—122no—
848C22C3×D3×C22⋊C414yescomplemented
849C22C3×C4×#6714yescomplemented
850C22C22×C3×C4×D311yescharacteristic
851C22C2×C3×#23511yescharacteristic
852C22C2×C3×D3×D412yes—
853C22C3×#100412yes—
854C22C22×C3×#6711yescharacteristic
855C4—24no—
856C4—34no—
857C4—42no—
858C4—62no—
859C4—122no—
860C4—122no—
861C3—21no—
862C3C22⋊C4×#6711yescharacteristic, direct product factor
863C3C3×D4×C22⋊C411yescharacteristic, complemented
864C2—24no—
865C2—24no—
866C2—42no—
867C2—64no—
868C2—122no—
869C2C2×C3×D3×C22⋊C411yescharacteristic
870C2C3×#548611yescharacteristic
871C2C3×#549012yes—
872C2C2×C3×C4×#6711yescharacteristic
873C2C3×D4×#6712yes—
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC22×C32×C22⋊C4C2
socleC23×C32C24
prime radicalC23×C3×#67C2
cosocleC23×C3C24×C3
hypercenterC22×C3×C22⋊C4D3
hypocenterC3C3×D4×C22⋊C4
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C32×C22⋊C4C2semidirect
3. C2×C3×C4×#67C2semidirect
4. C2×C3×D3×C22⋊C4C2semidirect
5. C3×#5247C2semidirect
6. C3×#5213C2semidirect
7. C3×#4957C2semidirect
8. C3×#4956C2semidirect
9. C3×#4955C2semidirect
10. C3×#4942C2semidirect
11. C3×Dic3×C22⋊C4C2semidirect
13. C22⋊C4×#67C3direct (N × H)
16. C23×C32×C4C22semidirect
18. C22×C3×#67C4semidirect
24. C22×C3×C4×D3C22semidirect
28. C2×C32×C22⋊C4C22semidirect
31. C2×C3×#217C22semidirect
32. C2×C3×#217C22semidirect
34. C2×C3×(C2×D3)⋊C4C22semidirect
35. C2×C3×(C2×D3)⋊C4C22semidirect
36. C2×C3×(C2×D3)⋊C4C22semidirect
37. C2×C3×Dic3⋊C4C22semidirect
38. C2×C3×C4×Dic3C22semidirect
40. C3×C3⋊#95C22semidirect
41. C3×C3⋊#95C22semidirect
47. C22×C3×C22⋊C4D3semidirect
48. C22×C3×C22⋊C4C2×C3semidirect
49. C2×C4×#67C2×C3semidirect
50. C2×D3×C22⋊C4C2×C3semidirect
58. #5247C2×C3semidirect
59. #5213C2×C3semidirect
60. #4957C2×C3semidirect
61. #4956C2×C3semidirect
62. #4955C2×C3semidirect
63. #4942C2×C3semidirect
64. Dic3×C22⋊C4C2×C3semidirect
69. C24×C32C2×C4semidirect
77. C23×C3×D3C2×C4semidirect
90. C2×C3×#67C2×C4semidirect
91. C2×C3×#67C2×C4semidirect
92. C2×C3×#67C2×C4semidirect
95. C22×C3×Dic3C2×C4semidirect
105. C32×C22⋊C4D4semidirect
130. C23×C3×C4C2×D3semidirect
131. C23×C3×C4C22×C3semidirect
133. C22×#67C3×C4semidirect
139. C22×C4×D3C22×C3semidirect
158. C2×C3×C22⋊C4C2×D3semidirect
161. C2×C3×C22⋊C4C22×C3semidirect
165. C2×#217C22×C3semidirect
166. C2×#217C22×C3semidirect
168. C2×(C2×D3)⋊C4C22×C3semidirect
169. C2×(C2×D3)⋊C4C22×C3semidirect
170. C2×(C2×D3)⋊C4C22×C3semidirect
171. C2×Dic3⋊C4C22×C3semidirect
172. C2×C4×Dic3C22×C3semidirect
176. C3⋊#95C22×C3semidirect
177. C3⋊#95C22×C3semidirect
220. C2×C32×C4C2×D4semidirect
224. C3×#67C22⋊C4direct (N × H)
240. C22×C22⋊C4C3×D3semidirect
271. C24×C3C4×D3semidirect
272. C24×C3C2×C3×C4semidirect
283. C23×D3C2×C3×C4semidirect
324. C2×#67C2×C3×C4semidirect
325. C2×#67C2×C3×C4semidirect
326. C2×#67C2×C3×C4semidirect
329. C22×Dic3C2×C3×C4semidirect
352. C3×C22⋊C4#67direct (N × H)
353. C3×C22⋊C4C3×D4semidirect
378. C22×C32C2×C22⋊C4semidirect
379. C22×C32C4×D4semidirect
395. C2×C3×D3C2×C22⋊C4semidirect
401. C3×Dic3C2×C22⋊C4semidirect
412. C23×C4C2×C3×D3semidirect
426. C2×C22⋊C4C2×C3×D3semidirect
558. C2×C3×C4C2×#67semidirect
559. C2×C3×C4C2×C3×D4semidirect
563. #67C3×C22⋊C4direct (N × H)
597. C24C3×C4×D3semidirect
634. C22⋊C4C3×#67direct (N × H)
696. C22×C3D3×C22⋊C4semidirect
697. C22×C3C4×#67semidirect
698. C22×C3C2×C3×C22⋊C4semidirect
699. C22×C3C3×C4×D4semidirect
720. C2×D3C2×C3×C22⋊C4semidirect
734. Dic3C2×C3×C22⋊C4semidirect
735. C32D4×C22⋊C4semidirect
794. C2×C4C2×C3×#67semidirect
848. C22C3×D3×C22⋊C4semidirect
849. C22C3×C4×#67semidirect
862. C3C22⋊C4×#67direct (N × H)
863. C3C3×D4×C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C23×C3×#672
C22×C32×C22⋊C42
C2×C3×C4×#672
C2×C3×D3×C22⋊C42
C3×#52472
C3×#52132
C3×#49572
C3×#49562
C3×#49552
C3×#49422
C3×Dic3×C22⋊C42
C3×D4×C22⋊C43
C22⋊C4×#673