Finite Group Databasebeta

← C3×#62962 #10681569

Subgroups — C3×#62962 #10681569

Order 768.

6566 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3561C214yesmaximal, complemented
2C3×#3557C218yesmaximal, complemented
3C3×#3554C214yesmaximal, complemented
4C3×#3554C218yesmaximal, complemented
5C3×#3550C214yesmaximal, complemented
6C3×#3535C218yesmaximal, complemented
7C3×#3522C214yesmaximal, complemented
8C3×#3520C214yesmaximal, complemented
9C3×#3510C214yesmaximal, complemented
10C3×#3508C212yesmaximal, complemented
11C3×#3507C214yesmaximal, complemented
12C3×#3502C211yesmaximal, characteristic, complemented
13C3×#3501C212yesmaximal, complemented
14C2×C3×#559C211yesmaximal, characteristic, complemented
15C3×Q8×#41C212yesmaximal, complemented
16C3×#3461C211yesmaximal, characteristic, complemented
17C3×#3460C212yesmaximal, complemented
18#62962C311yesmaximal, characteristic, direct product factor, Sylow
19C3×#563C22116yescomplemented
20C3×#563C2218yescomplemented
21C3×#562C22116yescomplemented
22C3×#562C2218yescomplemented
23C3×#559C2214yes—
24C3×#559C2214yes—
25C3×#559C2218yes—
26C3×#559C2214yes—
27C3×#559C2214yes—
28C3×#559C2218yescomplemented
29C3×#559C2218yescomplemented
30C3×Q82C2212yescomplemented
31C3×Q82C2214yescomplemented
32C3×#557C2212yescomplemented
33C3×#557C2214yescomplemented
34C3×#557C2214yescomplemented
35C3×#557C2218yescomplemented
36C3×#556C2214yescomplemented
37C3×#556C2218yescomplemented
38C3×#556C2218yescomplemented
39C3×#556C2218yescomplemented
40C3×#554C2214yes—
41C3×#554C2218yes—
42C3×#554C2212yescomplemented
43C3×#554C2214yescomplemented
44C3×#554C2218yescomplemented
45C3×#554C2218yescomplemented
46C3×#554C2218yescomplemented
47C3×#552C22116yescomplemented
48C3×#552C2218yescomplemented
49C3×#551C22116yes—
50C3×#551C22116yes—
51C3×#550C2214yes—
52C3×#550C2214yes—
53C3×D4×Q8C2214yes—
54C3×D4×Q8C2212yescomplemented
55C3×D4×Q8C2218yescomplemented
56C3×D4×Q8C2214yescomplemented
57C3×#548C2218yescomplemented
58C3×#548C2218yescomplemented
59C3×#547C2214yescomplemented
60C3×#547C2214yescomplemented
61C3×#547C22116yescomplemented
62C3×#546C2218yes—
63C3×#546C2218yes—
64C3×#544C2212yes—
65C3×#544C2211yescharacteristic
66C3×#544C2214yes—
67C3×#543C2218yes—
68C3×#542C2218yescomplemented
69C3×#542C2214yescomplemented
70C3×#542C2218yescomplemented
71C3×#542C2218yescomplemented
72C3×#542C2218yescomplemented
73C3×#542C22116yescomplemented
74C3×#542C2218yescomplemented
75C3×#542C22116yescomplemented
76C3×#541C2214yescomplemented
77C3×#540C2218yes—
78C3×#540C2218yescomplemented
79C3×#539C2214yes—
80C3×#539C22116yescomplemented
81C3×#539C22116yescomplemented
82C3×#539C22116yescomplemented
83C3×#538C2218yes—
84C3×#537C2211yescharacteristic
85C3×#536C2212yes—
86C3×#536C2218yescomplemented
87C3×#536C22116yescomplemented
88C3×#535C2214yes—
89C3×#533C2214yes—
90C3×#533C2212yes—
91C3×#533C2214yes—
92C3×#533C2214yescomplemented
93C3×#533C2214yescomplemented
94C3×#533C2218yescomplemented
95C3×#532C2214yes—
96C3×#532C2214yes—
97C3×#532C2218yescomplemented
98C2×C3×#127C2211yescharacteristic
99C3×#529C2214yes—
100C3×#529C2218yescomplemented
101C3×#529C2214yescomplemented
102C3×#529C2218yescomplemented
103C3×#529C2218yescomplemented
104C2×C3×#124C2212yes—
105C2×C3×#124C2212yes—
106C3×#525C2218yes—
107C2×C3×#123C2214yes—
108C2×C3×C22⋊Q8C2218yes—
109C3×#520C2218yescomplemented
110C3×#519C2212yes—
111C3×#518C2214yes—
112C3×C4×#41C2214yes—
113C3×C4×#41C2212yes—
114C2×C3×C4×Q8C2211yescharacteristic
115C2×C3×C4×Q8C2211yescharacteristic
116C2×C3×C4×Q8C2214yescomplemented
117C2×C3×C4×D4C2212yes—
118C2×C3×C4×D4C2212yes—
119#3561C2×C314yescomplemented
120#3557C2×C318yescomplemented
121#3554C2×C314yescomplemented
122#3554C2×C318yescomplemented
123#3550C2×C314yescomplemented
124#3535C2×C318yescomplemented
125#3522C2×C314yescomplemented
126#3520C2×C314yescomplemented
127#3510C2×C314yescomplemented
128#3508C2×C312yescomplemented
129#3507C2×C314yescomplemented
130#3502C2×C311yescharacteristic, complemented
131#3501C2×C312yescomplemented
132C2×#559C2×C311yescharacteristic, complemented
133Q8×#41C2×C312yescomplemented
134#3461C2×C311yescharacteristic, complemented
135#3460C2×C312yescomplemented
136C2×C3×#41C2312yes—
137C2×C3×#41C2318yes—
138C2×C3×#41C2318yes—
139C2×C3×#41C2318yes—
140C22×C3×Q8C2311yescharacteristic
141C22×C3×Q8C2311yescharacteristic
142C22×C3×Q8C2314yes—
143C22×C3×Q8C2318yes—
144C22×C3×D4C2312yes—
145C22×C3×D4C2312yes—
146C22×C3×D4C2312yes—
147C23×C3×C4C2314yes—
148C3×C4⋊Q8C2312yes—
149C3×C4⋊Q8C2314yes—
150C3×C4⋊Q8C2318yes—
151C3×C4⋊Q8C23116yes—
152C3×C4⋊Q8C2318yes—
153C3×C4⋊Q8C2314yes—
154C3×C4⋊Q8C2314yes—
155C3×C4⋊Q8C2318yes—
156C3×C4⋊Q8C2312yes—
157C3×C4⋊Q8C2314yes—
158C3×C4⋊Q8C2314yes—
159C3×C4⋊Q8C2314yes—
160C3×C4⋊Q8C2314yes—
161C3×C4⋊Q8C2314yes—
162C3×#127C2314yes—
163C3×#127C2314yes—
164C3×#127C2318yes—
165C3×#126C23116yes—
166C3×#126C23116yes—
167C3×#126C23116yes—
168C3×#126C23116yes—
169C3×#126C2318yes—
170C3×#126C2318yes—
171C3×#126C23116yes—
172C3×#125C2318yes—
173C3×#125C23116yes—
174C3×#125C2314yes—
175C3×#125C2318yes—
176C3×#125C2318yes—
177C3×#125C2314yes—
178C3×#125C2314yes—
179C3×#125C2318yes—
180C3×#125C2314yes—
181C3×#125C2314yes—
182C3×#125C2318yes—
183C3×#125C2318yes—
184C3×#124C2318yes—
185C3×#124C2318yes—
186C3×#124C2318yes—
187C3×#124C2318yes—
188C3×#124C2318yes—
189C3×#124C2318yes—
190C3×#124C2318yes—
191C3×#124C2314yes—
192C3×#124C23116yes—
193C3×#124C23116yes—
194C3×#124C2314yes—
195C3×#124C23116yes—
196C3×#123C23116yes—
197C3×#123C23116yes—
198C3×#123C23116yes—
199C3×#123C23116yes—
200C3×#123C23116yes—
201C3×#123C23116yes—
202C3×#123C23116yes—
203C3×#123C23116yes—
204C3×#123C2318yes—
205C3×#123C23116yes—
206C3×#123C2318yes—
207C3×#123C23116yes—
208C3×C22⋊Q8C2318yes—
209C3×C22⋊Q8C2318yes—
210C3×C22⋊Q8C2318yes—
211C3×C22⋊Q8C23116yes—
212C3×C22⋊Q8C23116yes—
213C3×C22⋊Q8C23116yes—
214C3×C22⋊Q8C2318yes—
215C3×C22⋊Q8C23116yes—
216C3×C22⋊Q8C23116yes—
217C3×C22⋊Q8C23116yes—
218C3×C22⋊Q8C23116yes—
219C3×C22⋊Q8C2314yes—
220C3×C22⋊Q8C2318yes—
221C3×C22⋊Q8C2318yes—
222C3×C22⋊Q8C2318yes—
223C3×C22⋊Q8C2318yes—
224C3×C22⋊Q8C2314yes—
225C3×C22⋊Q8C2314yes—
226C3×C22⋊Q8C2314yes—
227C3×C22⋊Q8C2314yes—
228C3×C22⋊Q8C2318yes—
229C3×C22⋊Q8C2314yes—
230C3×C22⋊Q8C2318yes—
231C3×C22⋊Q8C2318yes—
232C3×C22⋊Q8C2314yes—
233C3×C22⋊Q8C2318yes—
234C3×C22⋊Q8C2314yes—
235C3×#121C2318yes—
236C3×#121C2318yes—
237C3×#121C23116yes—
238C3×#121C23116yes—
239C3×#121C23116yes—
240C3×#121C2314yes—
241C3×#121C2318yes—
242C3×#121C2318yes—
243C3×#121C2314yes—
244C3×#121C2318yes—
245C3×#120C23116yes—
246C3×C4×Q8C2314yes—
247C3×C4×Q8C2312yes—
248C3×C4×Q8C2312yes—
249C3×C4×Q8C2314yes—
250C3×C4×Q8C2318yes—
251C3×C4×Q8C2314yes—
252C3×C4×Q8C2314yes—
253C3×C4×Q8C2318yes—
254C3×C4×Q8C2312yes—
255C3×C4×Q8C2314yes—
256C3×C4×Q8C2314yes—
257C3×C4×Q8C2312yes—
258C3×C4×Q8C2314yes—
259C3×C4×Q8C2318yes—
260C3×C4×Q8C2318yes—
261C3×C4×Q8C2318yes—
262C3×C4×Q8C2314yes—
263C3×C4×Q8C2318yes—
264C3×C4×Q8C2314yes—
265C3×C4×Q8C2314yes—
266C3×C4×Q8C2318yes—
267C3×C4×D4C2314yes—
268C3×C4×D4C2318yes—
269C3×C4×D4C2318yes—
270C3×C4×D4C2318yes—
271C3×C4×D4C2314yes—
272C3×C4×D4C2318yes—
273C3×C4×D4C2318yes—
274C3×C4×D4C2318yes—
275C3×C4×D4C2318yes—
276C3×C4×D4C2314yes—
277C3×C4×D4C2314yes—
278C3×C4×D4C2318yes—
279C3×C4×D4C2318yes—
280C3×C4×D4C23116yes—
281C3×C4×D4C23116yes—
282C3×C4×D4C2318yes—
283C3×C4×D4C2314yes—
284C3×C4×D4C2312yes—
285C3×C4×D4C2318yes—
286C3×C4×D4C2314yes—
287C3×C4×D4C2312yes—
288C3×C4×D4C23116yes—
289C3×C4×D4C2314yes—
290C3×#117C2312yes—
291C3×#117C2314yes—
292C3×#117C2314yes—
293C3×#117C2318yes—
294C3×#117C2318yes—
295C3×#117C2318yes—
296C3×#117C23116yes—
297C3×#117C2318yes—
298C3×#117C23116yes—
299C2×C3×C4⋊C4C2311yescharacteristic
300C2×C3×C4⋊C4C2311yescharacteristic
301C2×C3×C4⋊C4C2312yes—
302C2×C3×C4⋊C4C2312yes—
303C2×C3×C4⋊C4C2314yes—
304C2×C3×C4⋊C4C2318yes—
305C2×C3×C4⋊C4C23116yes—
306C2×C3×C4⋊C4C2318yes—
307C2×C3×C22⋊C4C2314yes—
308C2×C3×C22⋊C4C2314yes—
309C2×C3×C22⋊C4C23116yes—
310C2×C3×C22⋊C4C2314yes—
311C2×C3×C42C2312yes—
312C2×C3×C42C2312yes—
313C2×C3×C42C2311yescharacteristic
314C2×C3×C42C2318yes—
315C2×C3×C42C2314yes—
316#563C22×C3116yescomplemented
317#563C22×C318yescomplemented
318#562C22×C3116yescomplemented
319#562C22×C318yescomplemented
320#559C22×C314yes—
321#559C22×C314yes—
322#559C22×C318yes—
323#559C22×C314yes—
324#559C22×C314yes—
325#559C22×C318yescomplemented
326#559C22×C318yescomplemented
327Q82C22×C312yescomplemented
328Q82C22×C314yescomplemented
329#557C22×C312yescomplemented
330#557C22×C314yescomplemented
331#557C22×C314yescomplemented
332#557C22×C318yescomplemented
333#556C22×C314yescomplemented
334#556C22×C318yescomplemented
335#556C22×C318yescomplemented
336#556C22×C318yescomplemented
337#554C22×C314yes—
338#554C22×C318yes—
339#554C22×C312yescomplemented
340#554C22×C314yescomplemented
341#554C22×C318yescomplemented
342#554C22×C318yescomplemented
343#554C22×C318yescomplemented
344#552C22×C3116yescomplemented
345#552C22×C318yescomplemented
346#551C22×C3116yes—
347#551C22×C3116yes—
348#550C22×C314yes—
349#550C22×C314yes—
350D4×Q8C22×C314yes—
351D4×Q8C22×C312yescomplemented
352D4×Q8C22×C318yescomplemented
353D4×Q8C22×C314yescomplemented
354#548C22×C318yescomplemented
355#548C22×C318yescomplemented
356#547C22×C314yescomplemented
357#547C22×C314yescomplemented
358#547C22×C3116yescomplemented
359#546C22×C318yes—
360#546C22×C318yes—
361#544C22×C312yes—
362#544C22×C311yescharacteristic
363#544C22×C314yes—
364#543C22×C318yes—
365#542C22×C318yescomplemented
366#542C22×C314yescomplemented
367#542C22×C318yescomplemented
368#542C22×C318yescomplemented
369#542C22×C318yescomplemented
370#542C22×C3116yescomplemented
371#542C22×C318yescomplemented
372#542C22×C3116yescomplemented
373#541C22×C314yescomplemented
374#540C22×C318yes—
375#540C22×C318yescomplemented
376#539C22×C314yes—
377#539C22×C3116yescomplemented
378#539C22×C3116yescomplemented
379#539C22×C3116yescomplemented
380#538C22×C318yes—
381#537C22×C311yescharacteristic
382#536C22×C312yes—
383#536C22×C318yescomplemented
384#536C22×C3116yescomplemented
385#535C22×C314yes—
386#533C22×C314yes—
387#533C22×C312yes—
388#533C22×C314yes—
389#533C22×C314yescomplemented
390#533C22×C314yescomplemented
391#533C22×C318yescomplemented
392#532C22×C314yes—
393#532C22×C314yes—
394#532C22×C318yescomplemented
395C2×#127C22×C311yescharacteristic
396#529C22×C314yes—
397#529C22×C318yescomplemented
398#529C22×C314yescomplemented
399#529C22×C318yescomplemented
400#529C22×C318yescomplemented
401C2×#124C22×C312yes—
402C2×#124C22×C312yes—
403#525C22×C318yes—
404C2×#123C22×C314yes—
405C2×C22⋊Q8C22×C318yes—
406#520C22×C318yescomplemented
407#519C22×C312yes—
408#518C22×C314yes—
409C4×#41C22×C314yes—
410C4×#41C22×C312yes—
411C2×C4×Q8C22×C311yescharacteristic
412C2×C4×Q8C22×C311yescharacteristic
413C2×C4×Q8C22×C314yescomplemented
414C2×C4×D4C22×C312yes—
415C2×C4×D4C22×C312yes—
416C24×C3C2414yes—
417C3×#41—28no—
418C3×#41—416no—
419C3×#41—88no—
420C3×#41—88no—
421C2×C3×Q8—24no—
422C2×C3×Q8—42no—
423C2×C3×Q8—48no—
424C2×C3×Q8—88no—
425C2×C3×Q8C2414yes—
426C2×C3×Q8C2412yes—
427C2×C3×Q8C2412yes—
428C2×C3×Q8C2414yes—
429C2×C3×Q8C2418yes—
430C2×C3×Q8C2412yes—
431C2×C3×Q8C2414yes—
432C2×C3×Q8C2418yes—
433C2×C3×Q8C2418yes—
434C2×C3×Q8C2414yes—
435C2×C3×D4—28no—
436C2×C3×D4—44no—
437C2×C3×D4—82no—
438C2×C3×D4C2414yes—
439C2×C3×D4C2418yes—
440C2×C3×D4C2412yes—
441C2×C3×D4C2414yes—
442C2×C3×D4C24116yes—
443C2×C3×D4C2414yes—
444C2×C3×D4C24116yes—
445C2×C3×D4C2414yes—
446C2×C3×D4C2418yes—
447C22×C3×C4—84no—
448C22×C3×C4C2411yescharacteristic
449C22×C3×C4C2414yes—
450C22×C3×C4C2412yes—
451C22×C3×C4C2414yes—
452C22×C3×C4C2412yes—
453C22×C3×C4C2412yes—
454C22×C3×C4C2412yes—
455C22×C3×C4C2411yescharacteristic
456C22×C3×C4C2418yes—
457C22×C3×C4C2414yes—
458C22×C3×C4C2418yes—
459C22×C3×C4C24116yes—
460C22×C3×C4C24116yes—
461C22×C3×C4C2418yes—
462C22×C3×C4C2418yes—
463C22×C3×C4C2411yescharacteristic
464C3×C4⋊C4C2411yescharacteristic
465C3×C4⋊C4C2418yes—
466C3×C4⋊C4C2418yes—
467C3×C4⋊C4C2414yes—
468C3×C4⋊C4C2418yes—
469C3×C4⋊C4C2414yes—
470C3×C4⋊C4C2418yes—
471C3×C4⋊C4C2418yes—
472C3×C4⋊C4C2414yes—
473C3×C4⋊C4C2412yes—
474C3×C4⋊C4C2411yescharacteristic
475C3×C4⋊C4C2414yes—
476C3×C4⋊C4C24116yes—
477C3×C4⋊C4C2418yes—
478C3×C4⋊C4C2418yes—
479C3×C4⋊C4C2414yes—
480C3×C4⋊C4C2418yes—
481C3×C4⋊C4C2418yes—
482C3×C4⋊C4C2414yes—
483C3×C4⋊C4C2418yes—
484C3×C4⋊C4C2418yes—
485C3×C4⋊C4C2412yes—
486C3×C4⋊C4C2412yes—
487C3×C4⋊C4C2414yes—
488C3×C4⋊C4C2414yes—
489C3×C4⋊C4C2418yes—
490C3×C4⋊C4C2414yes—
491C3×C4⋊C4C2418yes—
492C3×C4⋊C4C2414yes—
493C3×C4⋊C4C2418yes—
494C3×C4⋊C4C2418yes—
495C3×C4⋊C4C2414yes—
496C3×C4⋊C4C2418yes—
497C3×C4⋊C4C2418yes—
498C3×C22⋊C4C2414yes—
499C3×C22⋊C4C2418yes—
500C3×C22⋊C4C2418yes—
501C3×C22⋊C4C24116yes—
502C3×C22⋊C4C24116yes—
503C3×C22⋊C4C24116yes—
504C3×C22⋊C4C24116yes—
505C3×C22⋊C4C2418yes—
506C3×C22⋊C4C24116yes—
507C3×C22⋊C4C24116yes—
508C3×C22⋊C4C2414yes—
509C3×C22⋊C4C2414yes—
510C3×C22⋊C4C2418yes—
511C3×C22⋊C4C2418yes—
512C3×C22⋊C4C2418yes—
513C3×C22⋊C4C2418yes—
514C3×C22⋊C4C2418yes—
515C3×C42C2414yes—
516C3×C42C2412yes—
517C3×C42C2418yes—
518C3×C42C2414yes—
519C3×C42C2414yes—
520C3×C42C2414yes—
521C3×C42C2414yes—
522C3×C42C2418yes—
523C3×C42C2412yes—
524C3×C42C2418yes—
525C3×C42C2414yes—
526C3×C42C2414yes—
527C3×C42C24116yes—
528C2×#41C23×C312yes—
529C2×#41C23×C318yes—
530C2×#41C23×C318yes—
531C2×#41C23×C318yes—
532C22×Q8C23×C311yescharacteristic
533C22×Q8C23×C311yescharacteristic
534C22×Q8C23×C314yes—
535C22×Q8C23×C318yes—
536C22×D4C23×C312yes—
537C22×D4C23×C312yes—
538C22×D4C23×C312yes—
539C23×C4C23×C314yes—
540C4⋊Q8C23×C312yes—
541C4⋊Q8C23×C312yes—
542C4⋊Q8C23×C318yes—
543C4⋊Q8C23×C314yes—
544C4⋊Q8C23×C314yes—
545C4⋊Q8C23×C314yes—
546C4⋊Q8C23×C314yes—
547C4⋊Q8C23×C314yes—
548C4⋊Q8C23×C314yes—
549C4⋊Q8C23×C318yes—
550C4⋊Q8C23×C318yes—
551C4⋊Q8C23×C314yes—
552C4⋊Q8C23×C314yes—
553C4⋊Q8C23×C3116yes—
554#127C23×C314yes—
555#127C23×C314yes—
556#127C23×C318yes—
557#126C23×C318yes—
558#126C23×C3116yes—
559#126C23×C318yes—
560#126C23×C3116yes—
561#126C23×C3116yes—
562#126C23×C3116yes—
563#126C23×C3116yes—
564#125C23×C314yes—
565#125C23×C314yes—
566#125C23×C314yes—
567#125C23×C318yes—
568#125C23×C314yes—
569#125C23×C318yes—
570#125C23×C314yes—
571#125C23×C318yes—
572#125C23×C318yes—
573#125C23×C318yes—
574#125C23×C318yes—
575#125C23×C3116yes—
576#124C23×C318yes—
577#124C23×C318yes—
578#124C23×C318yes—
579#124C23×C318yes—
580#124C23×C314yes—
581#124C23×C318yes—
582#124C23×C314yes—
583#124C23×C318yes—
584#124C23×C318yes—
585#124C23×C3116yes—
586#124C23×C3116yes—
587#124C23×C3116yes—
588#123C23×C3116yes—
589#123C23×C3116yes—
590#123C23×C3116yes—
591#123C23×C318yes—
592#123C23×C3116yes—
593#123C23×C3116yes—
594#123C23×C318yes—
595#123C23×C3116yes—
596#123C23×C3116yes—
597#123C23×C3116yes—
598#123C23×C3116yes—
599#123C23×C3116yes—
600C22⋊Q8C23×C314yes—
601C22⋊Q8C23×C318yes—
602C22⋊Q8C23×C318yes—
603C22⋊Q8C23×C318yes—
604C22⋊Q8C23×C3116yes—
605C22⋊Q8C23×C318yes—
606C22⋊Q8C23×C318yes—
607C22⋊Q8C23×C314yes—
608C22⋊Q8C23×C314yes—
609C22⋊Q8C23×C314yes—
610C22⋊Q8C23×C314yes—
611C22⋊Q8C23×C318yes—
612C22⋊Q8C23×C314yes—
613C22⋊Q8C23×C318yes—
614C22⋊Q8C23×C318yes—
615C22⋊Q8C23×C318yes—
616C22⋊Q8C23×C318yes—
617C22⋊Q8C23×C314yes—
618C22⋊Q8C23×C318yes—
619C22⋊Q8C23×C314yes—
620C22⋊Q8C23×C318yes—
621C22⋊Q8C23×C3116yes—
622C22⋊Q8C23×C3116yes—
623C22⋊Q8C23×C3116yes—
624C22⋊Q8C23×C3116yes—
625C22⋊Q8C23×C3116yes—
626C22⋊Q8C23×C3116yes—
627#121C23×C314yes—
628#121C23×C318yes—
629#121C23×C318yes—
630#121C23×C318yes—
631#121C23×C314yes—
632#121C23×C318yes—
633#121C23×C318yes—
634#121C23×C3116yes—
635#121C23×C3116yes—
636#121C23×C3116yes—
637#120C23×C3116yes—
638C4×Q8C23×C312yes—
639C4×Q8C23×C314yes—
640C4×Q8C23×C312yes—
641C4×Q8C23×C314yes—
642C4×Q8C23×C314yes—
643C4×Q8C23×C314yes—
644C4×Q8C23×C314yes—
645C4×Q8C23×C318yes—
646C4×Q8C23×C314yes—
647C4×Q8C23×C318yes—
648C4×Q8C23×C314yes—
649C4×Q8C23×C312yes—
650C4×Q8C23×C312yes—
651C4×Q8C23×C314yes—
652C4×Q8C23×C318yes—
653C4×Q8C23×C318yes—
654C4×Q8C23×C318yes—
655C4×Q8C23×C314yes—
656C4×Q8C23×C318yes—
657C4×Q8C23×C314yes—
658C4×Q8C23×C318yes—
659C4×D4C23×C314yes—
660C4×D4C23×C318yes—
661C4×D4C23×C318yes—
662C4×D4C23×C318yes—
663C4×D4C23×C314yes—
664C4×D4C23×C318yes—
665C4×D4C23×C314yes—
666C4×D4C23×C312yes—
667C4×D4C23×C314yes—
668C4×D4C23×C318yes—
669C4×D4C23×C314yes—
670C4×D4C23×C314yes—
671C4×D4C23×C312yes—
672C4×D4C23×C318yes—
673C4×D4C23×C318yes—
674C4×D4C23×C318yes—
675C4×D4C23×C318yes—
676C4×D4C23×C3116yes—
677C4×D4C23×C3116yes—
678C4×D4C23×C318yes—
679C4×D4C23×C314yes—
680C4×D4C23×C3116yes—
681C4×D4C23×C318yes—
682#117C23×C312yes—
683#117C23×C314yes—
684#117C23×C314yes—
685#117C23×C318yes—
686#117C23×C318yes—
687#117C23×C318yes—
688#117C23×C3116yes—
689#117C23×C318yes—
690#117C23×C3116yes—
691C2×C4⋊C4C23×C311yescharacteristic
692C2×C4⋊C4C23×C311yescharacteristic
693C2×C4⋊C4C23×C312yes—
694C2×C4⋊C4C23×C312yes—
695C2×C4⋊C4C23×C314yes—
696C2×C4⋊C4C23×C318yes—
697C2×C4⋊C4C23×C3116yes—
698C2×C4⋊C4C23×C318yes—
699C2×C22⋊C4C23×C314yes—
700C2×C22⋊C4C23×C314yes—
701C2×C22⋊C4C23×C3116yes—
702C2×C22⋊C4C23×C314yes—
703C2×C42C23×C312yes—
704C2×C42C23×C312yes—
705C2×C42C23×C311yescharacteristic
706C2×C42C23×C318yes—
707C2×C42C23×C314yes—
708C23×C3—28no—
709C23×C3—44no—
710C23×C3—44no—
711C23×C3C2518yes—
712C23×C3C2514yes—
713C23×C3C2511yescharacteristic
714C3×Q8—28no—
715C3×Q8—24no—
716C3×Q8—24no—
717C3×Q8—28no—
718C3×Q8—48no—
719C3×Q8—42no—
720C3×Q8—44no—
721C3×Q8—48no—
722C3×Q8—48no—
723C3×Q8—44no—
724C3×D4—28no—
725C3×D4—216no—
726C3×D4—24no—
727C3×D4—28no—
728C3×D4—44no—
729C3×D4—48no—
730C3×D4—416no—
731C3×D4—44no—
732C3×D4—416no—
733C2×C3×C4—24no—
734C2×C3×C4—28no—
735C2×C3×C4—22no—
736C2×C3×C4—28no—
737C2×C3×C4—42no—
738C2×C3×C4—42no—
739C2×C3×C4—48no—
740C2×C3×C4—48no—
741C2×C3×C4—41no—
742C2×C3×C4—48no—
743C2×C3×C4—42no—
744C2×C3×C4—416no—
745C2×C3×C4—416no—
746C2×C3×C4—48no—
747C2×C3×C4—44no—
748C2×C3×C42−1+414yes—
749C2×C3×C4C2514yes—
750C2×C3×C4C2514yes—
751C2×C3×C4C2511yescharacteristic
752C2×C3×C4C2512yes—
753C2×C3×C4C2514yes—
754C2×C3×C4C2518yes—
755C2×C3×C4C2518yes—
756C2×C3×C4C2512yes—
757C2×C3×C4C2514yes—
758C2×C3×C4C2514yes—
759C2×C3×C4C2512yes—
760C2×C3×C4C2514yes—
761C2×C3×C4C2512yes—
762C2×C3×C4C2511yescharacteristic
763C24C24×C314yes—
764#41—28no—
765#41—416no—
766#41—88no—
767#41—88no—
768C2×Q8—24no—
769C2×Q8—42no—
770C2×Q8—48no—
771C2×Q8—88no—
772C2×Q8C24×C314yes—
773C2×Q8C24×C312yes—
774C2×Q8C24×C312yes—
775C2×Q8C24×C314yes—
776C2×Q8C24×C318yes—
777C2×Q8C24×C312yes—
778C2×Q8C24×C314yes—
779C2×Q8C24×C318yes—
780C2×Q8C24×C318yes—
781C2×Q8C24×C314yes—
782C2×D4—28no—
783C2×D4—44no—
784C2×D4—82no—
785C2×D4C24×C314yes—
786C2×D4C24×C318yes—
787C2×D4C24×C312yes—
788C2×D4C24×C314yes—
789C2×D4C24×C3116yes—
790C2×D4C24×C314yes—
791C2×D4C24×C3116yes—
792C2×D4C24×C314yes—
793C2×D4C24×C318yes—
794C22×C4—84no—
795C22×C4C24×C311yescharacteristic
796C22×C4C24×C314yes—
797C22×C4C24×C312yes—
798C22×C4C24×C314yes—
799C22×C4C24×C312yes—
800C22×C4C24×C312yes—
801C22×C4C24×C312yes—
802C22×C4C24×C311yescharacteristic
803C22×C4C24×C318yes—
804C22×C4C24×C314yes—
805C22×C4C24×C318yes—
806C22×C4C24×C3116yes—
807C22×C4C24×C3116yes—
808C22×C4C24×C318yes—
809C22×C4C24×C318yes—
810C22×C4C24×C311yescharacteristic
811C4⋊C4C24×C311yescharacteristic
812C4⋊C4C24×C318yes—
813C4⋊C4C24×C318yes—
814C4⋊C4C24×C314yes—
815C4⋊C4C24×C318yes—
816C4⋊C4C24×C314yes—
817C4⋊C4C24×C318yes—
818C4⋊C4C24×C318yes—
819C4⋊C4C24×C314yes—
820C4⋊C4C24×C312yes—
821C4⋊C4C24×C311yescharacteristic
822C4⋊C4C24×C314yes—
823C4⋊C4C24×C3116yes—
824C4⋊C4C24×C318yes—
825C4⋊C4C24×C318yes—
826C4⋊C4C24×C314yes—
827C4⋊C4C24×C318yes—
828C4⋊C4C24×C318yes—
829C4⋊C4C24×C314yes—
830C4⋊C4C24×C318yes—
831C4⋊C4C24×C318yes—
832C4⋊C4C24×C312yes—
833C4⋊C4C24×C312yes—
834C4⋊C4C24×C314yes—
835C4⋊C4C24×C314yes—
836C4⋊C4C24×C318yes—
837C4⋊C4C24×C314yes—
838C4⋊C4C24×C318yes—
839C4⋊C4C24×C314yes—
840C4⋊C4C24×C318yes—
841C4⋊C4C24×C318yes—
842C4⋊C4C24×C314yes—
843C4⋊C4C24×C318yes—
844C4⋊C4C24×C318yes—
845C22⋊C4C24×C314yes—
846C22⋊C4C24×C318yes—
847C22⋊C4C24×C318yes—
848C22⋊C4C24×C3116yes—
849C22⋊C4C24×C3116yes—
850C22⋊C4C24×C3116yes—
851C22⋊C4C24×C3116yes—
852C22⋊C4C24×C318yes—
853C22⋊C4C24×C3116yes—
854C22⋊C4C24×C3116yes—
855C22⋊C4C24×C314yes—
856C22⋊C4C24×C314yes—
857C22⋊C4C24×C318yes—
858C22⋊C4C24×C318yes—
859C22⋊C4C24×C318yes—
860C22⋊C4C24×C318yes—
861C22⋊C4C24×C318yes—
862C42C24×C314yes—
863C42C24×C312yes—
864C42C24×C318yes—
865C42C24×C314yes—
866C42C24×C314yes—
867C42C24×C314yes—
868C42C24×C314yes—
869C42C24×C318yes—
870C42C24×C312yes—
871C42C24×C318yes—
872C42C24×C314yes—
873C42C24×C314yes—
874C42C24×C3116yes—
875C22×C3—21no—
876C22×C3—21no—
877C22×C3—24no—
878C22×C3—28no—
879C22×C3—24no—
880C22×C3—28no—
881C22×C3—28no—
882C22×C3—24no—
883C22×C3—88no—
884C22×C3C2×2−1+412yes—
885C22×C3C2611yescharacteristic
886C3×C4—24no—
887C3×C4—24no—
888C3×C4—24no—
889C3×C4—21no—
890C3×C4—28no—
891C3×C4—24no—
892C3×C4—22no—
893C3×C4—24no—
894C3×C4—22no—
895C3×C4—24no—
896C3×C4—22no—
897C3×C4—28no—
898C3×C4C2×2−1+414yes—
899C3×C4#58512yes—
900C23—28no—
901C23—44no—
902C23—44no—
903C23C25×C318yes—
904C23C25×C314yes—
905C23C25×C311yescharacteristic
906Q8—28no—
907Q8—24no—
908Q8—24no—
909Q8—28no—
910Q8—48no—
911Q8—42no—
912Q8—44no—
913Q8—48no—
914Q8—48no—
915Q8—44no—
916D4—28no—
917D4—216no—
918D4—24no—
919D4—28no—
920D4—44no—
921D4—48no—
922D4—416no—
923D4—44no—
924D4—416no—
925C2×C4—24no—
926C2×C4—28no—
927C2×C4—22no—
928C2×C4—28no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—48no—
932C2×C4—48no—
933C2×C4—41no—
934C2×C4—48no—
935C2×C4—42no—
936C2×C4—416no—
937C2×C4—416no—
938C2×C4—48no—
939C2×C4—44no—
940C2×C4C3×2−1+414yes—
941C2×C4C25×C314yes—
942C2×C4C25×C314yes—
943C2×C4C25×C311yescharacteristic
944C2×C4C25×C312yes—
945C2×C4C25×C314yes—
946C2×C4C25×C318yes—
947C2×C4C25×C318yes—
948C2×C4C25×C312yes—
949C2×C4C25×C314yes—
950C2×C4C25×C314yes—
951C2×C4C25×C312yes—
952C2×C4C25×C314yes—
953C2×C4C25×C312yes—
954C2×C4C25×C311yescharacteristic
955C2×C3—22no—
956C2×C3—44no—
957C2×C3—48no—
958C2×C3C22×2−1+411yescharacteristic
959C2×C3C2×#58511yescharacteristic
960C2×C3H(7,𝔽2)11yescharacteristic
961C22—21no—
962C22—21no—
963C22—24no—
964C22—28no—
965C22—24no—
966C22—28no—
967C22—28no—
968C22—24no—
969C22—88no—
970C22C2×C3×2−1+412yes—
971C22C26×C311yescharacteristic
972C4—24no—
973C4—24no—
974C4—24no—
975C4—21no—
976C4—28no—
977C4—24no—
978C4—22no—
979C4—24no—
980C4—22no—
981C4—24no—
982C4—22no—
983C4—28no—
984C4C2×C3×2−1+414yes—
985C4C3×#58512yes—
986C3#6296211yescharacteristic, direct product factor, Sylow
987C2—22no—
988C2—48no—
989C2—44no—
990C2C22×C3×2−1+411yescharacteristic
991C2C2×C3×#58511yescharacteristic
992C2C3×H(7,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C3C26
commutator, Frattini, cosocleC22C26×C3
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#3561C2semidirect
2. C3×#3557C2semidirect
3. C3×#3554C2semidirect
4. C3×#3554C2semidirect
5. C3×#3550C2semidirect
6. C3×#3535C2semidirect
7. C3×#3522C2semidirect
8. C3×#3520C2semidirect
9. C3×#3510C2semidirect
10. C3×#3508C2semidirect
11. C3×#3507C2semidirect
12. C3×#3502C2semidirect
13. C3×#3501C2semidirect
14. C2×C3×#559C2semidirect
15. C3×Q8×#41C2semidirect
16. C3×#3461C2semidirect
17. C3×#3460C2semidirect
18. #62962C3direct (N × H)
19. C3×#563C22semidirect
20. C3×#563C22semidirect
21. C3×#562C22semidirect
22. C3×#562C22semidirect
28. C3×#559C22semidirect
29. C3×#559C22semidirect
30. C3×Q82C22semidirect
31. C3×Q82C22semidirect
32. C3×#557C22semidirect
33. C3×#557C22semidirect
34. C3×#557C22semidirect
35. C3×#557C22semidirect
36. C3×#556C22semidirect
37. C3×#556C22semidirect
38. C3×#556C22semidirect
39. C3×#556C22semidirect
42. C3×#554C22semidirect
43. C3×#554C22semidirect
44. C3×#554C22semidirect
45. C3×#554C22semidirect
46. C3×#554C22semidirect
47. C3×#552C22semidirect
48. C3×#552C22semidirect
54. C3×D4×Q8C22semidirect
55. C3×D4×Q8C22semidirect
56. C3×D4×Q8C22semidirect
57. C3×#548C22semidirect
58. C3×#548C22semidirect
59. C3×#547C22semidirect
60. C3×#547C22semidirect
61. C3×#547C22semidirect
68. C3×#542C22semidirect
69. C3×#542C22semidirect
70. C3×#542C22semidirect
71. C3×#542C22semidirect
72. C3×#542C22semidirect
73. C3×#542C22semidirect
74. C3×#542C22semidirect
75. C3×#542C22semidirect
76. C3×#541C22semidirect
78. C3×#540C22semidirect
80. C3×#539C22semidirect
81. C3×#539C22semidirect
82. C3×#539C22semidirect
86. C3×#536C22semidirect
87. C3×#536C22semidirect
92. C3×#533C22semidirect
93. C3×#533C22semidirect
94. C3×#533C22semidirect
97. C3×#532C22semidirect
100. C3×#529C22semidirect
101. C3×#529C22semidirect
102. C3×#529C22semidirect
103. C3×#529C22semidirect
109. C3×#520C22semidirect
116. C2×C3×C4×Q8C22semidirect
119. #3561C2×C3semidirect
120. #3557C2×C3semidirect
121. #3554C2×C3semidirect
122. #3554C2×C3semidirect
123. #3550C2×C3semidirect
124. #3535C2×C3semidirect
125. #3522C2×C3semidirect
126. #3520C2×C3semidirect
127. #3510C2×C3semidirect
128. #3508C2×C3semidirect
129. #3507C2×C3semidirect
130. #3502C2×C3semidirect
131. #3501C2×C3semidirect
132. C2×#559C2×C3semidirect
133. Q8×#41C2×C3semidirect
134. #3461C2×C3semidirect
135. #3460C2×C3semidirect
316. #563C22×C3semidirect
317. #563C22×C3semidirect
318. #562C22×C3semidirect
319. #562C22×C3semidirect
325. #559C22×C3semidirect
326. #559C22×C3semidirect
327. Q82C22×C3semidirect
328. Q82C22×C3semidirect
329. #557C22×C3semidirect
330. #557C22×C3semidirect
331. #557C22×C3semidirect
332. #557C22×C3semidirect
333. #556C22×C3semidirect
334. #556C22×C3semidirect
335. #556C22×C3semidirect
336. #556C22×C3semidirect
339. #554C22×C3semidirect
340. #554C22×C3semidirect
341. #554C22×C3semidirect
342. #554C22×C3semidirect
343. #554C22×C3semidirect
344. #552C22×C3semidirect
345. #552C22×C3semidirect
351. D4×Q8C22×C3semidirect
352. D4×Q8C22×C3semidirect
353. D4×Q8C22×C3semidirect
354. #548C22×C3semidirect
355. #548C22×C3semidirect
356. #547C22×C3semidirect
357. #547C22×C3semidirect
358. #547C22×C3semidirect
365. #542C22×C3semidirect
366. #542C22×C3semidirect
367. #542C22×C3semidirect
368. #542C22×C3semidirect
369. #542C22×C3semidirect
370. #542C22×C3semidirect
371. #542C22×C3semidirect
372. #542C22×C3semidirect
373. #541C22×C3semidirect
375. #540C22×C3semidirect
377. #539C22×C3semidirect
378. #539C22×C3semidirect
379. #539C22×C3semidirect
383. #536C22×C3semidirect
384. #536C22×C3semidirect
389. #533C22×C3semidirect
390. #533C22×C3semidirect
391. #533C22×C3semidirect
394. #532C22×C3semidirect
397. #529C22×C3semidirect
398. #529C22×C3semidirect
399. #529C22×C3semidirect
400. #529C22×C3semidirect
406. #520C22×C3semidirect
413. C2×C4×Q8C22×C3semidirect
986. C3#62962direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35612
C3×#35572
C3×#35542
C3×#35502
C3×#35352
C3×#35222
C3×#35202
C3×#35102
C3×#35082
C3×#35072
C3×#35022
C3×#35012
C2×C3×#5592
C3×Q8×#412
C3×#34612
C3×#34602
#629623