Finite Group Databasebeta

← C3×#86001 #11904953

Subgroups — C3×#86001 #11904953

Order 1152.

2275 conjugacy classes of subgroups.

The subgroup lattice has 829 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#123C211yesmaximal, characteristic, complemented
2C3×#5804C211yesmaximal, characteristic
3C3×#5798C211yesmaximal, characteristic, complemented
4C2×C3×#929C211yesmaximal, characteristic, complemented
5C2×C3×#926C211yesmaximal, characteristic, complemented
6C3×#5665C214yesmaximal, complemented
7C3×#5658C214yesmaximal, complemented
8C3×#5650C214yesmaximal, complemented
9C3×#5649C214yesmaximal, complemented
10C3×#5513C214yesmaximal, complemented
11C3×#5495C214yesmaximal, complemented
12C3×#5486C211yesmaximal, characteristic, complemented
13C3×#5483C211yesmaximal, characteristic, complemented
14C3×#3491—31nomaximal
15#86001C311yesmaximal, characteristic, direct product factor
16C22×C32×D4C2211yescharacteristic
17C23×C32×C4C2211yescharacteristic
18C22×C3×#67C2211yescharacteristic
19C32×#123C2214yes—
20C32×#123C2212yescomplemented
21C32×#123C2212yescomplemented
22C2×C32×C4⋊C4C2212yescomplemented
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×C32×C22⋊C4C2212yescomplemented
25C3×#953C2212yes—
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2212yescomplemented
30C3×#939C2214yes—
31C3×#937C2212yes—
32C3×#935C2212yes—
33C3×D4×Dic3C2214yes—
34C3×D4×Dic3C2214yescomplemented
35C3×#929C2214yes—
36C3×#929C2212yes—
37C3×#929C2212yescomplemented
38C3×#929C2212yescomplemented
39C3×C4×#67C2214yes—
40C2×C3×(C2×D3)⋊C4C2212yescomplemented
41C3×#926C2214yescomplemented
42C3×#926C2212yescomplemented
43C3×#926C2214yescomplemented
44C2×C3×C4⋊Dic3C2212yescomplemented
45C3×#924C2214yescomplemented
46C2×C3×Dic3⋊C4C2212yescomplemented
47C2×C3×C4×Dic3C2212yescomplemented
48C3×#898C2214yescomplemented
49C3×#898C2214yescomplemented
50C3×#897C2214yescomplemented
51C3×#892C2214yescomplemented
52C3×#890C2214yescomplemented
53C3×#889C2214yescomplemented
54C3×#889C2214yescomplemented
55C3×#887C2214yescomplemented
56C3×#886C2214yescomplemented
57C3×#885C2214yescomplemented
58C3×#883C2214yescomplemented
59C3×#67⋊C4C2214yescomplemented
60C3×#67⋊C4C2214yescomplemented
61C3×D3×C22⋊C4C2212yescomplemented
62C3×#879C2214yescomplemented
63C3×#879C2214yescomplemented
64C3×#878C2214yescomplemented
65C3×#878C2214yescomplemented
66C3×#878C2214yescomplemented
67C3×#877C2214yescomplemented
68C3×#877C2212yescomplemented
69C3×#552—34no—
70C3×#552—34no—
71C3×#551—34no—
72C3×#551—34no—
73C3×#543—31no—
74C3×#539—34no—
75C3×#534—31no—
76C3×#529—34no—
77C2×C3×#123—21no—
78C2×C3×#123—31no—
79C2×C3×#123D311yescharacteristic, complemented
80C2×C3×#123C2×C311yescharacteristic, complemented
81C3×#518—31no—
82C3×#518—31no—
83C2×C3×#117—31no—
84#5804C2×C311yescharacteristic
85#5798C2×C311yescharacteristic, complemented
86C2×#929C2×C311yescharacteristic, complemented
87C2×#926C2×C311yescharacteristic, complemented
88#5665C2×C314yescomplemented
89#5658C2×C314yescomplemented
90#5650C2×C314yescomplemented
91#5649C2×C314yescomplemented
92#5513C2×C314yescomplemented
93#5495C2×C314yescomplemented
94#5486C2×C311yescharacteristic, complemented
95#5483C2×C311yescharacteristic, complemented
96C24×C32C2311yescharacteristic
97C24×C32C2311yescharacteristic
98C23×C3×D3C2311yescharacteristic
99C2×C32×D4—24no—
100C2×C32×D4C2312yes—
101C2×C32×D4C2312yes—
102C22×C32×C4—24no—
103C22×C32×C4C2311yescharacteristic
104C22×C32×C4C2312yes—
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2312yes—
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2312yes—
109C2×C3×#67—24no—
110C2×C3×#67C2312yes—
111C2×C3×#67C2312yes—
112C2×C3×#67C2314yes—
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2314yes—
115C22×C3×Dic3C2312yes—
116C22×C3×Dic3C2312yes—
117C22×C3×Dic3C2312yes—
118C2×C3×C4×D3C2314yes—
119C2×C3×Dic6C2314yes—
120C32×C4⋊C4C2314yes—
121C32×C4⋊C4C2314yes—
122C32×C22⋊C4C2312yes—
123C32×C22⋊C4C2314yes—
124C32×C22⋊C4C2312yes—
125C32×C22⋊C4C2314yes—
126C3×#217C2314yes—
127C3×#217C2312yes—
128C3×#217C2312yes—
129C3×#217C2312yes—
130C3×#217C2314yes—
131C3×#217C2312yes—
132C3×#217C2312yes—
133C3×#217C2312yes—
134C3×(C2×D3)⋊C4C2314yes—
135C3×(C2×D3)⋊C4C2314yes—
136C3×(C2×D3)⋊C4C2314yes—
137C3×(C2×D3)⋊C4C2314yes—
138C3×C4⋊Dic3C2314yes—
139C3×C4⋊Dic3C2314yes—
140C3×C4⋊Dic3C2314yes—
141C3×C4⋊Dic3C2314yes—
142C3×Dic3⋊C4C2314yes—
143C3×Dic3⋊C4C2314yes—
144C3×Dic3⋊C4C2314yes—
145C3×Dic3⋊C4C2314yes—
146C3×Dic3⋊C4C2314yes—
147C3×Dic3⋊C4C2314yes—
148C3×C4×Dic3C2314yes—
149C3×C4×Dic3C2314yes—
150C3×C4×Dic3C2314yes—
151C3×C4×Dic3C2314yes—
152#3491—31noSylow
153C22×C3×D4—21no—
154C22×C3×D4—31no—
155C22×C3×D4C2×D311yescharacteristic
156C22×C3×D4C22×C311yescharacteristic
157C23×C3×C4—21no—
158C23×C3×C4C2×D311yescharacteristic
159C23×C3×C4C22×C311yescharacteristic
160C22×#67C22×C311yescharacteristic
161C3×#126—34no—
162C3×#126—34no—
163C3×#126—34no—
164C3×#126—34no—
165C3×#125—34no—
166C3×#125—34no—
167C3×#125—34no—
168C3×#124—34no—
169C3×#123—24no—
170C3×#123—22no—
171C3×#123—22no—
172C3×#123—32no—
173C3×#123—34no—
174C3×#123—32no—
175C3×#123—32no—
176C3×#123—32no—
177C3×#123—34no—
178C3×#123—34no—
179C3×#123C2×D314yes—
180C3×#123C2×D312yescomplemented
181C3×#123C2×D312yescomplemented
182C3×#123C22×C314yes—
183C3×#123C22×C312yescomplemented
184C3×#123C22×C312yescomplemented
185C3×C22⋊Q8—34no—
186C3×C22⋊Q8—34no—
187C3×C22⋊Q8—34no—
188C3×C22⋊Q8—34no—
189C3×C22⋊Q8—34no—
190C3×#121—34no—
191C3×#120—32no—
192C3×#120—32no—
193C3×C4×Q8—34no—
194C3×C4×D4—34no—
195C3×C4×D4—34no—
196C3×C4×D4—34no—
197C3×C4×D4—34no—
198C3×C4×D4—34no—
199C3×#117—34no—
200C3×#117—34no—
201C3×#117—32no—
202C3×#117—34no—
203C3×#117—32no—
204C3×#117—34no—
205C2×C3×C4⋊C4—22no—
206C2×C3×C4⋊C4—32no—
207C2×C3×C4⋊C4—32no—
208C2×C3×C4⋊C4C2×D312yescomplemented
209C2×C3×C4⋊C4C22×C312yescomplemented
210C2×C3×C22⋊C4—21no—
211C2×C3×C22⋊C4—22no—
212C2×C3×C22⋊C4—31no—
213C2×C3×C22⋊C4—31no—
214C2×C3×C22⋊C4—31no—
215C2×C3×C22⋊C4—32no—
216C2×C3×C22⋊C4—32no—
217C2×C3×C22⋊C4—32no—
218C2×C3×C22⋊C4C2×D311yescharacteristic
219C2×C3×C22⋊C4C2×D312yescomplemented
220C2×C3×C22⋊C4C22×C311yescharacteristic
221C2×C3×C22⋊C4C22×C312yescomplemented
222C2×C3×C42—32no—
223#953C22×C312yes—
224C2×#217C22×C311yescharacteristic
225C2×#217C22×C311yescharacteristic
226C2×#217C22×C311yescharacteristic
227C2×#217C22×C312yescomplemented
228#939C22×C314yes—
229#937C22×C312yes—
230#935C22×C312yes—
231D4×Dic3C22×C314yes—
232D4×Dic3C22×C314yescomplemented
233#929C22×C314yes—
234#929C22×C312yes—
235#929C22×C312yescomplemented
236#929C22×C312yescomplemented
237C4×#67C22×C314yes—
238C2×(C2×D3)⋊C4C22×C312yescomplemented
239#926C22×C314yescomplemented
240#926C22×C314yescomplemented
241#926C22×C312yescomplemented
242C2×C4⋊Dic3C22×C312yescomplemented
243#924C22×C314yescomplemented
244C2×Dic3⋊C4C22×C312yescomplemented
245C2×C4×Dic3C22×C312yescomplemented
246#898C22×C314yescomplemented
247#898C22×C314yescomplemented
248#897C22×C314yescomplemented
249#892C22×C314yescomplemented
250#890C22×C314yescomplemented
251#889C22×C314yescomplemented
252#889C22×C314yescomplemented
253#887C22×C314yescomplemented
254#886C22×C314yescomplemented
255#885C22×C314yescomplemented
256#883C22×C314yescomplemented
257#67⋊C4C22×C314yescomplemented
258#67⋊C4C22×C314yescomplemented
259D3×C22⋊C4C22×C312yescomplemented
260#879C22×C314yescomplemented
261#879C22×C314yescomplemented
262#878C22×C314yescomplemented
263#878C22×C314yescomplemented
264#878C22×C314yescomplemented
265#877C22×C314yescomplemented
266#877C22×C312yescomplemented
267C23×C32—22no—
268C23×C32—42no—
269C23×C32—42no—
270C23×C32#4114yes—
271C23×C32C2412yes—
272C23×C32C2411yescharacteristic
273C23×C32C2411yescharacteristic
274C23×C32C2411yescharacteristic
275C22×C3×D3—22no—
276C22×C3×D3—42no—
277C22×C3×D3C2412yes—
278C32×D4—24no—
279C32×D4—24no—
280C2×C32×C4—24no—
281C2×C32×C4—24no—
282C2×C32×C4—22no—
283C2×C32×C4—22no—
284C2×C32×C4—22no—
285C2×C32×C4—42no—
286C2×C32×C4C2412yes—
287C2×C32×C4C2412yes—
288C2×C32×C4C2414yes—
289C2×C32×C4C2412yes—
290C3×#67—24no—
291C3×#67—24no—
292C3×#67—44no—
293C2×C3×Dic3—22no—
294C2×C3×Dic3—42no—
295C2×C3×Dic3—44no—
296C2×C3×Dic3—42no—
297C2×C3×Dic3—42no—
298C2×C3×Dic3C2414yes—
299C2×C3×Dic3C2412yes—
300C2×C3×Dic3C2414yes—
301C2×C3×Dic3C2414yes—
302C3×C4×D3—44no—
303C3×Dic6—44no—
304#552—34no—
305#552—34no—
306#551—34no—
307#551—34no—
308#543—31no—
309#539—34no—
310#534—31no—
311#529—34no—
312C2×#123—31no—
313C2×#123C3×D311yescharacteristic, complemented
314#518—31no—
315#518—31no—
316C2×#117—31no—
317C24×C3—21no—
318C24×C3—21no—
319C24×C3—31no—
320C24×C3C22×D311yescharacteristic
321C24×C3C22×D311yescharacteristic
322C24×C3C23×C311yescharacteristic
323C24×C3C23×C311yescharacteristic
324C23×D3C23×C311yescharacteristic
325C2×C3×Q8—34no—
326C2×C3×D4—24no—
327C2×C3×D4—24no—
328C2×C3×D4—22no—
329C2×C3×D4—22no—
330C2×C3×D4—32no—
331C2×C3×D4—32no—
332C2×C3×D4—34no—
333C2×C3×D4—44no—
334C2×C3×D4—64no—
335C2×C3×D4C22×D312yes—
336C2×C3×D4C22×D312yes—
337C2×C3×D4C23×C312yes—
338C2×C3×D4C23×C312yes—
339C22×C3×C4—24no—
340C22×C3×C4—24no—
341C22×C3×C4—22no—
342C22×C3×C4—22no—
343C22×C3×C4—21no—
344C22×C3×C4—21no—
345C22×C3×C4—22no—
346C22×C3×C4—21no—
347C22×C3×C4—31no—
348C22×C3×C4—32no—
349C22×C3×C4—32no—
350C22×C3×C4—32no—
351C22×C3×C4—34no—
352C22×C3×C4—34no—
353C22×C3×C4—44no—
354C22×C3×C4C22×D311yescharacteristic
355C22×C3×C4C22×D312yes—
356C22×C3×C4C22×D312yes—
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C22×D311yescharacteristic
359C22×C3×C4C22×D312yes—
360C22×C3×C4C23×C311yescharacteristic
361C22×C3×C4C23×C312yes—
362C22×C3×C4C23×C311yescharacteristic
363C22×C3×C4C23×C312yes—
364C22×C3×C4C23×C311yescharacteristic
365C22×C3×C4C23×C312yes—
366C2×#67—24no—
367C2×#67C23×C312yes—
368C2×#67C23×C312yes—
369C2×#67C23×C314yes—
370C22×Dic3C23×C311yescharacteristic
371C22×Dic3C23×C314yes—
372C22×Dic3C23×C312yes—
373C22×Dic3C23×C312yes—
374C22×Dic3C23×C312yes—
375C2×C4×D3C23×C314yes—
376C2×Dic6C23×C314yes—
377C3×C4⋊C4—24no—
378C3×C4⋊C4—24no—
379C3×C4⋊C4—34no—
380C3×C4⋊C4—34no—
381C3×C4⋊C4—34no—
382C3×C4⋊C4—34no—
383C3×C4⋊C4—34no—
384C3×C4⋊C4—34no—
385C3×C4⋊C4—34no—
386C3×C4⋊C4—34no—
387C3×C4⋊C4—34no—
388C3×C4⋊C4—34no—
389C3×C4⋊C4C22×D314yes—
390C3×C4⋊C4C22×D314yes—
391C3×C4⋊C4C23×C314yes—
392C3×C4⋊C4C23×C314yes—
393C3×C22⋊C4—22no—
394C3×C22⋊C4—22no—
395C3×C22⋊C4—24no—
396C3×C22⋊C4—24no—
397C3×C22⋊C4—32no—
398C3×C22⋊C4—32no—
399C3×C22⋊C4—32no—
400C3×C22⋊C4—32no—
401C3×C22⋊C4—32no—
402C3×C22⋊C4—32no—
403C3×C22⋊C4—34no—
404C3×C22⋊C4—34no—
405C3×C22⋊C4—34no—
406C3×C22⋊C4—34no—
407C3×C22⋊C4—34no—
408C3×C22⋊C4—34no—
409C3×C22⋊C4C22×D312yes—
410C3×C22⋊C4C22×D312yes—
411C3×C22⋊C4C22×D314yes—
412C3×C22⋊C4C22×D314yes—
413C3×C22⋊C4C23×C312yes—
414C3×C22⋊C4C23×C314yes—
415C3×C22⋊C4C23×C312yes—
416C3×C22⋊C4C23×C314yes—
417C3×C42—34no—
418C3×C42—34no—
419C3×C42—34no—
420C3×C42—34no—
421#217C23×C314yes—
422#217C23×C312yes—
423#217C23×C312yes—
424#217C23×C312yes—
425#217C23×C314yes—
426#217C23×C312yes—
427#217C23×C312yes—
428#217C23×C312yes—
429(C2×D3)⋊C4C23×C314yes—
430(C2×D3)⋊C4C23×C314yes—
431(C2×D3)⋊C4C23×C314yes—
432(C2×D3)⋊C4C23×C314yes—
433C4⋊Dic3C23×C314yes—
434C4⋊Dic3C23×C314yes—
435C4⋊Dic3C23×C314yes—
436C4⋊Dic3C23×C314yes—
437Dic3⋊C4C23×C314yes—
438Dic3⋊C4C23×C314yes—
439Dic3⋊C4C23×C314yes—
440Dic3⋊C4C23×C314yes—
441Dic3⋊C4C23×C314yes—
442Dic3⋊C4C23×C314yes—
443C4×Dic3C23×C314yes—
444C4×Dic3C23×C314yes—
445C4×Dic3C23×C314yes—
446C4×Dic3C23×C314yes—
447C22×C32—22no—
448C22×C32—22no—
449C22×C32—22no—
450C22×C32—22no—
451C22×C32—24no—
452C22×C32—44no—
453C22×C32—82no—
454C22×C32C2×#4112yes—
455C22×C32C2×#4112yes—
456C22×C32C2×#4112yes—
457C22×C32C2511yescharacteristic
458C2×C3×D3—22no—
459C2×C3×D3—24no—
460C2×C3×D3—82no—
461C32×C4—22no—
462C32×C4—22no—
463C32×C4—22no—
464C32×C4—24no—
465C3×Dic3—22no—
466C3×Dic3—24no—
467C3×Dic3—24no—
468C3×Dic3—24no—
469C22×D4—31no—
470C22×D4C2×C3×D311yescharacteristic
471C23×C4C2×C3×D311yescharacteristic
472#126—34no—
473#126—34no—
474#126—34no—
475#126—34no—
476#125—34no—
477#125—34no—
478#125—34no—
479#124—34no—
480#123—32no—
481#123—32no—
482#123—32no—
483#123—34no—
484#123—32no—
485#123—34no—
486#123—34no—
487#123C2×C3×D314yes—
488#123C2×C3×D312yescomplemented
489#123C2×C3×D312yescomplemented
490C22⋊Q8—34no—
491C22⋊Q8—34no—
492C22⋊Q8—34no—
493C22⋊Q8—34no—
494C22⋊Q8—34no—
495#121—34no—
496#120—32no—
497#120—32no—
498C4×Q8—34no—
499C4×D4—34no—
500C4×D4—34no—
501C4×D4—34no—
502C4×D4—34no—
503C4×D4—34no—
504#117—34no—
505#117—34no—
506#117—32no—
507#117—34no—
508#117—32no—
509#117—34no—
510C2×C4⋊C4—32no—
511C2×C4⋊C4—32no—
512C2×C4⋊C4C2×C3×D312yescomplemented
513C2×C22⋊C4—31no—
514C2×C22⋊C4—31no—
515C2×C22⋊C4—31no—
516C2×C22⋊C4—32no—
517C2×C22⋊C4—32no—
518C2×C22⋊C4—32no—
519C2×C22⋊C4C2×C3×D311yescharacteristic
520C2×C22⋊C4C2×C3×D312yescomplemented
521C2×C42—32no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—22no—
528C23×C3—24no—
529C23×C3—32no—
530C23×C3—42no—
531C23×C3—42no—
532C23×C3—42no—
533C23×C3—42no—
534C23×C3—42no—
535C23×C3—44no—
536C23×C3—44no—
537C23×C3—62no—
538C23×C3—122no—
539C23×C3#23714yes—
540C23×C3C3×#4114yes—
541C23×C3C23×D312yes—
542C23×C3C23×D311yescharacteristic
543C23×C3C23×D311yescharacteristic
544C23×C3C23×D311yescharacteristic
545C23×C3C24×C312yes—
546C23×C3C24×C311yescharacteristic
547C23×C3C24×C311yescharacteristic
548C23×C3C24×C311yescharacteristic
549C22×D3—22no—
550C22×D3—42no—
551C22×D3C24×C312yes—
552C3×Q8—124no—
553C3×D4—24no—
554C3×D4—24no—
555C3×D4—24no—
556C3×D4—24no—
557C3×D4—44no—
558C3×D4—44no—
559C3×D4—64no—
560C3×D4—64no—
561C3×D4—124no—
562C2×C3×C4—24no—
563C2×C3×C4—24no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—24no—
568C2×C3×C4—24no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—24no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—34no—
577C2×C3×C4—34no—
578C2×C3×C4—32no—
579C2×C3×C4—34no—
580C2×C3×C4—44no—
581C2×C3×C4—44no—
582C2×C3×C4—42no—
583C2×C3×C4—42no—
584C2×C3×C4—42no—
585C2×C3×C4—42no—
586C2×C3×C4—42no—
587C2×C3×C4—44no—
588C2×C3×C4—62no—
589C2×C3×C4—124no—
590C2×C3×C4—122no—
591C2×C3×C4—124no—
592C2×C3×C4—122no—
593C2×C3×C4—122no—
594C2×C3×C4C23×D312yes—
595C2×C3×C4C23×D312yes—
596C2×C3×C4C23×D314yes—
597C2×C3×C4C23×D312yes—
598C2×C3×C4C24×C312yes—
599C2×C3×C4C24×C312yes—
600C2×C3×C4C24×C314yes—
601C2×C3×C4C24×C312yes—
602#67—24no—
603#67—24no—
604#67—44no—
605C2×Dic3—22no—
606C2×Dic3—42no—
607C2×Dic3—44no—
608C2×Dic3—42no—
609C2×Dic3—42no—
610C2×Dic3C24×C314yes—
611C2×Dic3C24×C312yes—
612C2×Dic3C24×C314yes—
613C2×Dic3C24×C314yes—
614C4×D3—44no—
615Dic6—44no—
616C2×C32—22no—
617C2×C32—22no—
618C2×C32—22no—
619C2×C32—42no—
620C2×C32C22×#4111yescharacteristic
621C2×C32#58512yes—
622C3×D3—42no—
623C24—31no—
624C24C22×C3×D311yescharacteristic
625C24C22×C3×D311yescharacteristic
626C2×Q8—34no—
627C2×D4—24no—
628C2×D4—32no—
629C2×D4—32no—
630C2×D4—34no—
631C2×D4—64no—
632C2×D4C22×C3×D312yes—
633C2×D4C22×C3×D312yes—
634C22×C4—24no—
635C22×C4—31no—
636C22×C4—32no—
637C22×C4—32no—
638C22×C4—32no—
639C22×C4—34no—
640C22×C4—34no—
641C22×C4C22×C3×D311yescharacteristic
642C22×C4C22×C3×D312yes—
643C22×C4C22×C3×D312yes—
644C22×C4C22×C3×D311yescharacteristic
645C22×C4C22×C3×D311yescharacteristic
646C22×C4C22×C3×D312yes—
647C4⋊C4—34no—
648C4⋊C4—34no—
649C4⋊C4—34no—
650C4⋊C4—34no—
651C4⋊C4—34no—
652C4⋊C4—34no—
653C4⋊C4—34no—
654C4⋊C4—34no—
655C4⋊C4—34no—
656C4⋊C4—34no—
657C4⋊C4C22×C3×D314yes—
658C4⋊C4C22×C3×D314yes—
659C22⋊C4—32no—
660C22⋊C4—32no—
661C22⋊C4—32no—
662C22⋊C4—32no—
663C22⋊C4—32no—
664C22⋊C4—32no—
665C22⋊C4—34no—
666C22⋊C4—34no—
667C22⋊C4—34no—
668C22⋊C4—34no—
669C22⋊C4—34no—
670C22⋊C4—34no—
671C22⋊C4C22×C3×D312yes—
672C22⋊C4C22×C3×D312yes—
673C22⋊C4C22×C3×D314yes—
674C22⋊C4C22×C3×D314yes—
675C42—34no—
676C42—34no—
677C42—34no—
678C42—34no—
679C22×C3—24no—
680C22×C3—22no—
681C22×C3—22no—
682C22×C3—22no—
683C22×C3—22no—
684C22×C3—22no—
685C22×C3—22no—
686C22×C3—22no—
687C22×C3—24no—
688C22×C3—22no—
689C22×C3—24no—
690C22×C3—22no—
691C22×C3—22no—
692C22×C3—22no—
693C22×C3—21no—
694C22×C3—42no—
695C22×C3—42no—
696C22×C3—42no—
697C22×C3—44no—
698C22×C3—44no—
699C22×C3—44no—
700C22×C3—48no—
701C22×C3—62no—
702C22×C3—64no—
703C22×C3—82no—
704C22×C3—82no—
705C22×C3—84no—
706C22×C3—242no—
707C22×C3C2×#23712yes—
708C22×C3C2×#23712yes—
709C22×C3C2×#23712yes—
710C22×C3C2×C3×#4112yes—
711C22×C3C2×C3×#4112yes—
712C22×C3C2×C3×#4112yes—
713C22×C3C24×D311yescharacteristic
714C22×C3C25×C311yescharacteristic
715C2×D3—22no—
716C2×D3—24no—
717C2×D3—82no—
718C3×C4—22no—
719C3×C4—22no—
720C3×C4—22no—
721C3×C4—24no—
722C3×C4—22no—
723C3×C4—22no—
724C3×C4—22no—
725C3×C4—24no—
726C3×C4—42no—
727C3×C4—42no—
728C3×C4—42no—
729C3×C4—44no—
730C3×C4—62no—
731C3×C4—64no—
732C3×C4—64no—
733C3×C4—64no—
734Dic3—22no—
735Dic3—24no—
736Dic3—24no—
737Dic3—24no—
738C32#349111yescharacteristic, complemented, Sylow
739C23—22no—
740C23—32no—
741C23—42no—
742C23—42no—
743C23—62no—
744C23—122no—
745C23C3×#23714yes—
746C23C23×C3×D312yes—
747C23C23×C3×D311yescharacteristic
748C23C23×C3×D311yescharacteristic
749C23C23×C3×D311yescharacteristic
750Q8—124no—
751D4—24no—
752D4—24no—
753D4—64no—
754D4—64no—
755D4—124no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—34no—
762C2×C4—34no—
763C2×C4—32no—
764C2×C4—34no—
765C2×C4—42no—
766C2×C4—62no—
767C2×C4—124no—
768C2×C4—122no—
769C2×C4—124no—
770C2×C4—122no—
771C2×C4—122no—
772C2×C4C23×C3×D312yes—
773C2×C4C23×C3×D312yes—
774C2×C4C23×C3×D314yes—
775C2×C4C23×C3×D312yes—
776C2×C3—24no—
777C2×C3—22no—
778C2×C3—22no—
779C2×C3—22no—
780C2×C3—22no—
781C2×C3—22no—
782C2×C3—22no—
783C2×C3—21no—
784C2×C3—22no—
785C2×C3—42no—
786C2×C3—42no—
787C2×C3—42no—
788C2×C3—42no—
789C2×C3—82no—
790C2×C3—122no—
791C2×C3C22×#23711yescharacteristic
792C2×C3#596412yes—
793C2×C3C22×C3×#4111yescharacteristic
794C2×C3C3×#58512yes—
795D3—42no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—24no—
801C22—44no—
802C22—62no—
803C22—64no—
804C22—82no—
805C22—242no—
806C22C2×C3×#23712yes—
807C22C2×C3×#23712yes—
808C22C2×C3×#23712yes—
809C22C24×C3×D311yescharacteristic
810C4—22no—
811C4—22no—
812C4—22no—
813C4—24no—
814C4—62no—
815C4—64no—
816C4—64no—
817C4—64no—
818C3—21no—
819C3#8600111yescharacteristic, direct product factor
820C3C3×#349111yescharacteristic, complemented
821C2—22no—
822C2—22no—
823C2—22no—
824C2—42no—
825C2—122no—
826C2C22×C3×#23711yescharacteristic
827C2C3×#596412yes—
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×#123C2
socleC22×C32C25
prime radicalC3×#5804C2
hypercenterC2×C3×#123D3
hypocenterC3C3×#3491
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×#123

Complements

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

NH ≅ G/Ntype
1. C2×C32×#123C2semidirect
3. C3×#5798C2semidirect
4. C2×C3×#929C2semidirect
5. C2×C3×#926C2semidirect
6. C3×#5665C2semidirect
7. C3×#5658C2semidirect
8. C3×#5650C2semidirect
9. C3×#5649C2semidirect
10. C3×#5513C2semidirect
11. C3×#5495C2semidirect
12. C3×#5486C2semidirect
13. C3×#5483C2semidirect
15. #86001C3direct (N × H)
20. C32×#123C22semidirect
21. C32×#123C22semidirect
22. C2×C32×C4⋊C4C22semidirect
24. C2×C32×C22⋊C4C22semidirect
29. C2×C3×#217C22semidirect
34. C3×D4×Dic3C22semidirect
37. C3×#929C22semidirect
38. C3×#929C22semidirect
40. C2×C3×(C2×D3)⋊C4C22semidirect
41. C3×#926C22semidirect
42. C3×#926C22semidirect
43. C3×#926C22semidirect
44. C2×C3×C4⋊Dic3C22semidirect
45. C3×#924C22semidirect
46. C2×C3×Dic3⋊C4C22semidirect
47. C2×C3×C4×Dic3C22semidirect
48. C3×#898C22semidirect
49. C3×#898C22semidirect
50. C3×#897C22semidirect
51. C3×#892C22semidirect
52. C3×#890C22semidirect
53. C3×#889C22semidirect
54. C3×#889C22semidirect
55. C3×#887C22semidirect
56. C3×#886C22semidirect
57. C3×#885C22semidirect
58. C3×#883C22semidirect
59. C3×#67⋊C4C22semidirect
60. C3×#67⋊C4C22semidirect
61. C3×D3×C22⋊C4C22semidirect
62. C3×#879C22semidirect
63. C3×#879C22semidirect
64. C3×#878C22semidirect
65. C3×#878C22semidirect
66. C3×#878C22semidirect
67. C3×#877C22semidirect
68. C3×#877C22semidirect
79. C2×C3×#123D3semidirect
80. C2×C3×#123C2×C3semidirect
85. #5798C2×C3semidirect
86. C2×#929C2×C3semidirect
87. C2×#926C2×C3semidirect
88. #5665C2×C3semidirect
89. #5658C2×C3semidirect
90. #5650C2×C3semidirect
91. #5649C2×C3semidirect
92. #5513C2×C3semidirect
93. #5495C2×C3semidirect
94. #5486C2×C3semidirect
95. #5483C2×C3semidirect
180. C3×#123C2×D3semidirect
181. C3×#123C2×D3semidirect
183. C3×#123C22×C3semidirect
184. C3×#123C22×C3semidirect
208. C2×C3×C4⋊C4C2×D3semidirect
209. C2×C3×C4⋊C4C22×C3semidirect
219. C2×C3×C22⋊C4C2×D3semidirect
221. C2×C3×C22⋊C4C22×C3semidirect
227. C2×#217C22×C3semidirect
232. D4×Dic3C22×C3semidirect
235. #929C22×C3semidirect
236. #929C22×C3semidirect
238. C2×(C2×D3)⋊C4C22×C3semidirect
239. #926C22×C3semidirect
240. #926C22×C3semidirect
241. #926C22×C3semidirect
242. C2×C4⋊Dic3C22×C3semidirect
243. #924C22×C3semidirect
244. C2×Dic3⋊C4C22×C3semidirect
245. C2×C4×Dic3C22×C3semidirect
246. #898C22×C3semidirect
247. #898C22×C3semidirect
248. #897C22×C3semidirect
249. #892C22×C3semidirect
250. #890C22×C3semidirect
251. #889C22×C3semidirect
252. #889C22×C3semidirect
253. #887C22×C3semidirect
254. #886C22×C3semidirect
255. #885C22×C3semidirect
256. #883C22×C3semidirect
257. #67⋊C4C22×C3semidirect
258. #67⋊C4C22×C3semidirect
259. D3×C22⋊C4C22×C3semidirect
260. #879C22×C3semidirect
261. #879C22×C3semidirect
262. #878C22×C3semidirect
263. #878C22×C3semidirect
264. #878C22×C3semidirect
265. #877C22×C3semidirect
266. #877C22×C3semidirect
313. C2×#123C3×D3semidirect
488. #123C2×C3×D3semidirect
489. #123C2×C3×D3semidirect
512. C2×C4⋊C4C2×C3×D3semidirect
520. C2×C22⋊C4C2×C3×D3semidirect
738. C32#3491semidirect
819. C3#86001direct (N × H)
820. C3C3×#3491semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1232
C3×#58042
C3×#57982
C2×C3×#9292
C2×C3×#9262
C3×#56652
C3×#56582
C3×#56502
C3×#56492
C3×#55132
C3×#54952
C3×#54862
C3×#54832
C3×#34913
#860013