Finite Group Databasebeta

← C3×#40605 #10659212

Subgroups — C3×#40605 #10659212

Order 768.

2548 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#553C211yesmaximal, characteristic, complemented
2C2×C3×#550C211yesmaximal, characteristic, complemented
3C3×#2818C211yesmaximal, characteristic, complemented
4C3×#2815C211yesmaximal, characteristic, complemented
5C3×#2691C212yesmaximal, complemented
6C3×#2675C212yesmaximal, complemented
7C3×#2673C212yesmaximal, complemented
8C3×#2673C212yesmaximal, complemented
9C3×#2661C211yesmaximal, characteristic, complemented
10C3×#2637C211yesmaximal, characteristic, complemented
11C3×#2619C211yesmaximal, characteristic, complemented
12C3×#2618C211yesmaximal, characteristic, complemented
13C3×#2615C211yesmaximal, characteristic, complemented
14C3×#2599C211yesmaximal, characteristic, complemented
15C3×#2543C211yesmaximal, characteristic, complemented
16C3×#2464C212yesmaximal, complemented
17C3×#2460C212yesmaximal, complemented
18C3×#2456C212yesmaximal, complemented
19C3×#2456C212yesmaximal, complemented
20C3×#2430C211yesmaximal, characteristic, complemented
21C3×#2406C211yesmaximal, characteristic, complemented
22C3×#2388C211yesmaximal, characteristic, complemented
23C3×#2318C211yesmaximal, characteristic, complemented
24#40605C311yesmaximal, characteristic, direct product factor, Sylow
25C22×C3×#41C2211yescharacteristic
26C22×C3×#41C2211yescharacteristic
27C3×#553—28no—
28C3×#550—28no—
29C2×C3×#127C2211yescharacteristic
30C2×C3×#127C2212yes—
31C2×C3×#126C2211yescharacteristic
32C2×C3×#126C2211yescharacteristic
33C2×C3×#125C2211yescharacteristic
34C2×C3×#123C2211yescharacteristic
35C2×C3×#123C2211yescharacteristic
36C2×C3×#123C2212yes—
37C2×C3×#123C2212yes—
38C2×C3×#121C2211yescharacteristic
39C2×C3×#121C2211yescharacteristic
40C2×C3×#121C2212yes—
41C2×C3×#121C2212yes—
42C2×C3×#121C2211yescharacteristic
43C2×C3×#121C2211yescharacteristic
44C2×C3×#121C2211yescharacteristic
45C2×C3×#121C2211yescharacteristic
46C2×C3×#121C2212yes—
47C2×C3×#121C2212yes—
48C2×C3×#121C2212yes—
49C2×C3×#121C2212yes—
50C2×C3×C4×Q8C2211yescharacteristic
51C2×C3×C4×D4C2211yescharacteristic
52C2×C3×C4×D4C2212yes—
53C2×C3×C4×D4C2211yescharacteristic
54C2×C3×C4×D4C2211yescharacteristic
55C2×C3×C4×D4C2212yes—
56C2×C3×C4×D4C2211yescharacteristic
57C2×C3×#117C2211yescharacteristic
58C22×C3×C4⋊C4C2211yescharacteristic
59C3×#398C2211yescharacteristic
60C3×#398C2211yescharacteristic
61C3×#398C2212yes—
62C3×#397C2211yescharacteristic
63C3×#397C2211yescharacteristic
64C3×#397C2212yes—
65C3×#396C2212yes—
66C3×#396C2212yes—
67C3×#396C2212yes—
68C3×#395C2211yescharacteristic
69C3×#395C2211yescharacteristic
70C3×#394C2211yescharacteristic
71C3×#394C2211yescharacteristic
72C3×#394C2211yescharacteristic
73C3×#394C2212yes—
74C3×#394C2212yes—
75C3×#394C2211yescharacteristic
76C3×#394C2212yes—
77C3×#394C2212yes—
78C3×#394C2212yes—
79C3×#393C2211yescharacteristic
80C3×#393C2211yescharacteristic
81C3×#392C2211yescharacteristic
82C3×#392C2212yes—
83C3×#392C2211yescharacteristic
84C3×#392C2212yes—
85C3×#392C2211yescharacteristic
86C3×#392C2212yes—
87C3×#392C2212yes—
88C3×#392C2212yes—
89C3×#392C2212yes—
90C3×#392C2212yes—
91C3×#392C2212yes—
92C3×#392C2212yes—
93C3×#392C2212yes—
94C3×#392C2211yescharacteristic
95C3×#390C2212yes—
96C3×#390C2212yes—
97C3×#388C2212yes—
98C3×#388C2212yes—
99C3×#388C2212yes—
100C3×#388C2212yes—
101C3×#388C2212yes—
102C3×#387C2212yes—
103C3×#387C2212yes—
104C3×#387C2212yes—
105C3×#387C2212yes—
106C3×#386C2212yes—
107C3×#386C2212yes—
108C3×#386C2212yes—
109C3×#386C2212yes—
110C3×#386C2212yes—
111C3×#386C2212yes—
112C3×#386C2212yes—
113C3×#385C2212yes—
114C3×#385C2212yes—
115C3×#385C2212yes—
116C3×#385C2212yes—
117C3×#385C2212yes—
118C3×#383C2211yescharacteristic
119C3×#382C2211yescharacteristic
120C3×#381C2211yescharacteristic
121C3×#380C2211yescharacteristic
122C3×#380C2212yes—
123C3×C4×C22⋊C4C2211yescharacteristic
124C3×C4×C22⋊C4C2212yes—
125C2×C3×#95C2211yescharacteristic
126C2×#553C2×C311yescharacteristic, complemented
127C2×#550C2×C311yescharacteristic, complemented
128#2818C2×C311yescharacteristic, complemented
129#2815C2×C311yescharacteristic, complemented
130#2691C2×C312yescomplemented
131#2675C2×C312yescomplemented
132#2673C2×C312yescomplemented
133#2673C2×C312yescomplemented
134#2661C2×C311yescharacteristic, complemented
135#2637C2×C311yescharacteristic, complemented
136#2619C2×C311yescharacteristic, complemented
137#2618C2×C311yescharacteristic, complemented
138#2615C2×C311yescharacteristic, complemented
139#2599C2×C311yescharacteristic, complemented
140#2543C2×C311yescharacteristic, complemented
141#2464C2×C312yescomplemented
142#2460C2×C312yescomplemented
143#2456C2×C312yescomplemented
144#2456C2×C312yescomplemented
145#2430C2×C311yescharacteristic, complemented
146#2406C2×C311yescharacteristic, complemented
147#2388C2×C311yescharacteristic, complemented
148#2318C2×C311yescharacteristic, complemented
149C2×C3×#41—24no—
150C2×C3×#41—24no—
151C2×C3×#41—44no—
152C2×C3×#41—44no—
153C22×C3×Q8C2311yescharacteristic
154C22×C3×D4C2312yes—
155C22×C3×D4C2312yes—
156C22×C3×D4C2311yescharacteristic
157C22×C3×D4C2311yescharacteristic
158C22×C3×D4C2311yescharacteristic
159C22×C3×D4C2312yes—
160C22×C3×D4C2312yes—
161C22×C3×D4C2312yes—
162C22×C3×D4C2311yescharacteristic
163C22×C3×D4C2311yescharacteristic
164C22×C3×D4C2312yes—
165C22×C3×D4C2311yescharacteristic
166C22×C3×D4C2311yescharacteristic
167C22×C3×D4C2312yes—
168C22×C3×D4C2312yes—
169C22×C3×D4C2312yes—
170C22×C3×D4C2312yes—
171C22×C3×D4C2311yescharacteristic
172C23×C3×C4C2312yes—
173C23×C3×C4C2312yes—
174C23×C3×C4C2311yescharacteristic
175C23×C3×C4C2311yescharacteristic
176C23×C3×C4C2311yescharacteristic
177C23×C3×C4C2311yescharacteristic
178C23×C3×C4C2312yes—
179C23×C3×C4C2311yescharacteristic
180C23×C3×C4C2311yescharacteristic
181C3×#127—28no—
182C3×#127—24no—
183C3×#126—24no—
184C3×#126—24no—
185C3×#125—24no—
186C3×#123—24no—
187C3×#123—24no—
188C3×#123—44no—
189C3×#123—44no—
190C3×#121—24no—
191C3×#121—24no—
192C3×#121—24no—
193C3×#121—24no—
194C3×#121—24no—
195C3×#121—28no—
196C3×#121—28no—
197C3×#121—24no—
198C3×#121—44no—
199C3×#121—44no—
200C3×#121—44no—
201C3×#121—44no—
202C3×C4×Q8—24no—
203C3×C4×D4—24no—
204C3×C4×D4—28no—
205C3×C4×D4—24no—
206C3×C4×D4—24no—
207C3×C4×D4—44no—
208C3×C4×D4D418yescomplemented
209C3×#117—24no—
210C2×C3×C4⋊C4—24no—
211C2×C3×C4⋊C4C2311yescharacteristic
212C2×C3×C4⋊C4C2312yes—
213C2×C3×C4⋊C4C2311yescharacteristic
214C2×C3×C4⋊C4C2311yescharacteristic
215C2×C3×C4⋊C4C2311yescharacteristic
216C2×C3×C4⋊C4C2312yes—
217C2×C3×C4⋊C4C2312yes—
218C2×C3×C4⋊C4C2312yes—
219C2×C3×C4⋊C4C2311yescharacteristic
220C2×C3×C4⋊C4C2311yescharacteristic
221C2×C3×C4⋊C4C2311yescharacteristic
222C2×C3×C4⋊C4C2311yescharacteristic
223C2×C3×C4⋊C4C2311yescharacteristic
224C2×C3×C4⋊C4C2311yescharacteristic
225C2×C3×C4⋊C4C2312yes—
226C2×C3×C4⋊C4C2312yes—
227C2×C3×C4⋊C4C2312yes—
228C2×C3×C4⋊C4C2311yescharacteristic
229C2×C3×C22⋊C4C2312yes—
230C2×C3×C22⋊C4C2312yes—
231C2×C3×C22⋊C4C2312yes—
232C2×C3×C22⋊C4C2311yescharacteristic
233C2×C3×C22⋊C4C2311yescharacteristic
234C2×C3×C22⋊C4C2311yescharacteristic
235C2×C3×C22⋊C4C2312yes—
236C2×C3×C22⋊C4C2311yescharacteristic
237C2×C3×C22⋊C4C2311yescharacteristic
238C2×C3×C22⋊C4C2312yes—
239C2×C3×C22⋊C4C2311yescharacteristic
240C2×C3×C22⋊C4C2311yescharacteristic
241C2×C3×C22⋊C4C2311yescharacteristic
242C2×C3×C22⋊C4C2312yes—
243C2×C3×C22⋊C4C2312yes—
244C2×C3×C22⋊C4C2312yes—
245C2×C3×C22⋊C4C2312yes—
246C2×C3×C22⋊C4C2312yes—
247C2×C3×C22⋊C4C2312yes—
248C2×C3×C22⋊C4C2312yes—
249C2×C3×C22⋊C4C2312yes—
250C2×C3×C22⋊C4C2312yes—
251C2×C3×C22⋊C4C2312yes—
252C2×C3×C22⋊C4C2312yes—
253C2×C3×C22⋊C4C2312yes—
254C2×C3×C22⋊C4C2312yes—
255C2×C3×C22⋊C4C2312yes—
256C2×C3×C22⋊C4C2312yes—
257C2×C3×C22⋊C4C2312yes—
258C2×C3×C22⋊C4C2311yescharacteristic
259C2×C3×C22⋊C4C2311yescharacteristic
260C2×C3×C42C2311yescharacteristic
261C2×C3×C42C2312yes—
262C2×C3×C42C2311yescharacteristic
263C2×C3×C42C2312yes—
264C2×C3×C42C2311yescharacteristic
265C3×#95C2311yescharacteristic
266C3×#95C2311yescharacteristic
267C3×#95C2312yes—
268C3×#95C2311yescharacteristic
269C3×#95C2312yes—
270C3×#95C2311yescharacteristic
271C3×#95C2312yes—
272C3×#95C2312yes—
273C3×#95C2312yes—
274C3×#95C2312yes—
275C3×#95C2312yes—
276C3×#95C2312yes—
277C3×#95C2312yes—
278C3×#95C2312yes—
279C3×#95C2312yes—
280C3×#95C2312yes—
281C3×#95C2312yes—
282C22×#41C22×C311yescharacteristic
283C22×#41C22×C311yescharacteristic
284#553—28no—
285#550—28no—
286C2×#127C22×C311yescharacteristic
287C2×#127C22×C312yes—
288C2×#126C22×C311yescharacteristic
289C2×#126C22×C311yescharacteristic
290C2×#125C22×C311yescharacteristic
291C2×#123C22×C311yescharacteristic
292C2×#123C22×C311yescharacteristic
293C2×#123C22×C312yes—
294C2×#123C22×C312yes—
295C2×#121C22×C311yescharacteristic
296C2×#121C22×C311yescharacteristic
297C2×#121C22×C311yescharacteristic
298C2×#121C22×C311yescharacteristic
299C2×#121C22×C311yescharacteristic
300C2×#121C22×C311yescharacteristic
301C2×#121C22×C312yes—
302C2×#121C22×C312yes—
303C2×#121C22×C312yes—
304C2×#121C22×C312yes—
305C2×#121C22×C312yes—
306C2×#121C22×C312yes—
307C2×C4×Q8C22×C311yescharacteristic
308C2×C4×D4C22×C311yescharacteristic
309C2×C4×D4C22×C312yes—
310C2×C4×D4C22×C311yescharacteristic
311C2×C4×D4C22×C311yescharacteristic
312C2×C4×D4C22×C312yes—
313C2×C4×D4C22×C311yescharacteristic
314C2×#117C22×C311yescharacteristic
315C22×C4⋊C4C22×C311yescharacteristic
316#398C22×C311yescharacteristic
317#398C22×C311yescharacteristic
318#398C22×C312yes—
319#397C22×C311yescharacteristic
320#397C22×C311yescharacteristic
321#397C22×C312yes—
322#396C22×C312yes—
323#396C22×C312yes—
324#396C22×C312yes—
325#395C22×C311yescharacteristic
326#395C22×C311yescharacteristic
327#394C22×C311yescharacteristic
328#394C22×C311yescharacteristic
329#394C22×C312yes—
330#394C22×C312yes—
331#394C22×C311yescharacteristic
332#394C22×C311yescharacteristic
333#394C22×C312yes—
334#394C22×C312yes—
335#394C22×C312yes—
336#393C22×C311yescharacteristic
337#393C22×C311yescharacteristic
338#392C22×C311yescharacteristic
339#392C22×C311yescharacteristic
340#392C22×C312yes—
341#392C22×C312yes—
342#392C22×C311yescharacteristic
343#392C22×C312yes—
344#392C22×C312yes—
345#392C22×C312yes—
346#392C22×C311yescharacteristic
347#392C22×C312yes—
348#392C22×C312yes—
349#392C22×C312yes—
350#392C22×C312yes—
351#392C22×C312yes—
352#390C22×C312yes—
353#390C22×C312yes—
354#388C22×C312yes—
355#388C22×C312yes—
356#388C22×C312yes—
357#388C22×C312yes—
358#388C22×C312yes—
359#387C22×C312yes—
360#387C22×C312yes—
361#387C22×C312yes—
362#387C22×C312yes—
363#386C22×C312yes—
364#386C22×C312yes—
365#386C22×C312yes—
366#386C22×C312yes—
367#386C22×C312yes—
368#386C22×C312yes—
369#386C22×C312yes—
370#385C22×C312yes—
371#385C22×C312yes—
372#385C22×C312yes—
373#385C22×C312yes—
374#385C22×C312yes—
375#383C22×C311yescharacteristic
376#382C22×C311yescharacteristic
377#381C22×C311yescharacteristic
378#380C22×C311yescharacteristic
379#380C22×C312yes—
380C4×C22⋊C4C22×C311yescharacteristic
381C4×C22⋊C4C22×C312yes—
382C2×#95C22×C311yescharacteristic
383C24×C3C2411yescharacteristic
384C24×C3C2411yescharacteristic
385C24×C3C2412yes—
386C24×C3C2412yes—
387C24×C3C2411yescharacteristic
388C24×C3C2411yescharacteristic
389C3×#41—416no—
390C3×#41—416no—
391C2×C3×Q8—22no—
392C2×C3×Q8—24no—
393C2×C3×D4—22no—
394C2×C3×D4—22no—
395C2×C3×D4—22no—
396C2×C3×D4—24no—
397C2×C3×D4—24no—
398C2×C3×D4—22no—
399C2×C3×D4—24no—
400C2×C3×D4—24no—
401C2×C3×D4—24no—
402C2×C3×D4—22no—
403C2×C3×D4—22no—
404C2×C3×D4—22no—
405C2×C3×D4—24no—
406C2×C3×D4—22no—
407C2×C3×D4—24no—
408C2×C3×D4—24no—
409C2×C3×D4—42no—
410C2×C3×D4—41no—
411C2×C3×D4—42no—
412C2×C3×D4—42no—
413C2×C3×D4—42no—
414C2×C3×D4—42no—
415C2×C3×D4—42no—
416C2×C3×D4—42no—
417C2×C3×D4—42no—
418C2×C3×D4—42no—
419C2×C3×D4—42no—
420C2×C3×D4—42no—
421C2×C3×D4—42no—
422C2×C3×D4—42no—
423C2×C3×D4—42no—
424C2×C3×D4—42no—
425C2×C3×D4—42no—
426C2×C3×D4—42no—
427C2×C3×D4—42no—
428C2×C3×D4—42no—
429C2×C3×D4—42no—
430C2×C3×D4—42no—
431C2×C3×D4—42no—
432C2×C3×D4—42no—
433C2×C3×D4—42no—
434C2×C3×D4—42no—
435C2×C3×D4—42no—
436C2×C3×D4—42no—
437C2×C3×D4—42no—
438C2×C3×D4—42no—
439C2×C3×D4C2×D414yes—
440C22×C3×C4—22no—
441C22×C3×C4—22no—
442C22×C3×C4—22no—
443C22×C3×C4—24no—
444C22×C3×C4—24no—
445C22×C3×C4—24no—
446C22×C3×C4—22no—
447C22×C3×C4—24no—
448C22×C3×C4—22no—
449C22×C3×C4—22no—
450C22×C3×C4—41no—
451C22×C3×C4—41no—
452C22×C3×C4—42no—
453C22×C3×C4—42no—
454C22×C3×C4—42no—
455C22×C3×C4—42no—
456C22×C3×C4—42no—
457C22×C3×C4—42no—
458C22×C3×C4—42no—
459C22×C3×C4—42no—
460C22×C3×C4—42no—
461C22×C3×C4C2×D414yes—
462C22×C3×C4C2×D414yes—
463C22×C3×C4C2412yes—
464C22×C3×C4C2412yes—
465C22×C3×C4C2412yes—
466C22×C3×C4C2411yescharacteristic
467C22×C3×C4C2411yescharacteristic
468C22×C3×C4C2412yes—
469C22×C3×C4C2412yes—
470C22×C3×C4C2411yescharacteristic
471C22×C3×C4C2411yescharacteristic
472C22×C3×C4C2411yescharacteristic
473C22×C3×C4C2411yescharacteristic
474C22×C3×C4C2411yescharacteristic
475C22×C3×C4C2411yescharacteristic
476C22×C3×C4C2411yescharacteristic
477C22×C3×C4C2411yescharacteristic
478C22×C3×C4C2412yes—
479C22×C3×C4C2411yescharacteristic
480C3×C4⋊C4—22no—
481C3×C4⋊C4—22no—
482C3×C4⋊C4—22no—
483C3×C4⋊C4—22no—
484C3×C4⋊C4—22no—
485C3×C4⋊C4—22no—
486C3×C4⋊C4—22no—
487C3×C4⋊C4—24no—
488C3×C4⋊C4—22no—
489C3×C4⋊C4—22no—
490C3×C4⋊C4—22no—
491C3×C4⋊C4—24no—
492C3×C4⋊C4—24no—
493C3×C4⋊C4—24no—
494C3×C4⋊C4—42no—
495C3×C4⋊C4—42no—
496C3×C4⋊C4—42no—
497C3×C4⋊C4C2×D414yes—
498C3×C22⋊C4—22no—
499C3×C22⋊C4—22no—
500C3×C22⋊C4—22no—
501C3×C22⋊C4—22no—
502C3×C22⋊C4—24no—
503C3×C22⋊C4—24no—
504C3×C22⋊C4—22no—
505C3×C22⋊C4—22no—
506C3×C22⋊C4—22no—
507C3×C22⋊C4—22no—
508C3×C22⋊C4—24no—
509C3×C22⋊C4—24no—
510C3×C22⋊C4—24no—
511C3×C22⋊C4—24no—
512C3×C22⋊C4—42no—
513C3×C22⋊C4—42no—
514C3×C22⋊C4—42no—
515C3×C22⋊C4—42no—
516C3×C22⋊C4—42no—
517C3×C22⋊C4—42no—
518C3×C22⋊C4—42no—
519C3×C22⋊C4—42no—
520C3×C22⋊C4—42no—
521C3×C22⋊C4—42no—
522C3×C22⋊C4—42no—
523C3×C22⋊C4—42no—
524C3×C22⋊C4—42no—
525C3×C22⋊C4—42no—
526C3×C22⋊C4—42no—
527C3×C22⋊C4C2×D414yes—
528C3×C22⋊C4C2×D414yes—
529C3×C42—22no—
530C3×C42—22no—
531C3×C42—24no—
532C3×C42—42no—
533C3×C42C2×D414yes—
534C2×#41—24no—
535C2×#41—24no—
536C2×#41—44no—
537C2×#41—44no—
538C22×Q8C23×C311yescharacteristic
539C22×D4C23×C311yescharacteristic
540C22×D4C23×C312yes—
541C22×D4C23×C312yes—
542C22×D4C23×C311yescharacteristic
543C22×D4C23×C311yescharacteristic
544C22×D4C23×C312yes—
545C22×D4C23×C311yescharacteristic
546C22×D4C23×C311yescharacteristic
547C22×D4C23×C312yes—
548C22×D4C23×C312yes—
549C22×D4C23×C312yes—
550C22×D4C23×C311yescharacteristic
551C22×D4C23×C311yescharacteristic
552C22×D4C23×C312yes—
553C22×D4C23×C312yes—
554C22×D4C23×C312yes—
555C22×D4C23×C312yes—
556C22×D4C23×C311yescharacteristic
557C23×C4C23×C311yescharacteristic
558C23×C4C23×C311yescharacteristic
559C23×C4C23×C312yes—
560C23×C4C23×C312yes—
561C23×C4C23×C311yescharacteristic
562C23×C4C23×C311yescharacteristic
563C23×C4C23×C312yes—
564C23×C4C23×C311yescharacteristic
565C23×C4C23×C311yescharacteristic
566#127—28no—
567#127—24no—
568#126—24no—
569#126—24no—
570#125—24no—
571#123—24no—
572#123—24no—
573#123—44no—
574#123—44no—
575#121—24no—
576#121—24no—
577#121—24no—
578#121—24no—
579#121—24no—
580#121—28no—
581#121—28no—
582#121—24no—
583#121—44no—
584#121—44no—
585#121—44no—
586#121—44no—
587C4×Q8—24no—
588C4×D4—24no—
589C4×D4—28no—
590C4×D4—24no—
591C4×D4—24no—
592C4×D4—44no—
593C4×D4C3×D418yescomplemented
594#117—24no—
595C2×C4⋊C4—24no—
596C2×C4⋊C4C23×C311yescharacteristic
597C2×C4⋊C4C23×C311yescharacteristic
598C2×C4⋊C4C23×C311yescharacteristic
599C2×C4⋊C4C23×C311yescharacteristic
600C2×C4⋊C4C23×C311yescharacteristic
601C2×C4⋊C4C23×C311yescharacteristic
602C2×C4⋊C4C23×C312yes—
603C2×C4⋊C4C23×C311yescharacteristic
604C2×C4⋊C4C23×C312yes—
605C2×C4⋊C4C23×C311yescharacteristic
606C2×C4⋊C4C23×C312yes—
607C2×C4⋊C4C23×C312yes—
608C2×C4⋊C4C23×C311yescharacteristic
609C2×C4⋊C4C23×C311yescharacteristic
610C2×C4⋊C4C23×C312yes—
611C2×C4⋊C4C23×C312yes—
612C2×C4⋊C4C23×C312yes—
613C2×C4⋊C4C23×C311yescharacteristic
614C2×C22⋊C4C23×C311yescharacteristic
615C2×C22⋊C4C23×C311yescharacteristic
616C2×C22⋊C4C23×C312yes—
617C2×C22⋊C4C23×C312yes—
618C2×C22⋊C4C23×C311yescharacteristic
619C2×C22⋊C4C23×C311yescharacteristic
620C2×C22⋊C4C23×C311yescharacteristic
621C2×C22⋊C4C23×C312yes—
622C2×C22⋊C4C23×C311yescharacteristic
623C2×C22⋊C4C23×C312yes—
624C2×C22⋊C4C23×C312yes—
625C2×C22⋊C4C23×C311yescharacteristic
626C2×C22⋊C4C23×C311yescharacteristic
627C2×C22⋊C4C23×C312yes—
628C2×C22⋊C4C23×C312yes—
629C2×C22⋊C4C23×C312yes—
630C2×C22⋊C4C23×C312yes—
631C2×C22⋊C4C23×C312yes—
632C2×C22⋊C4C23×C312yes—
633C2×C22⋊C4C23×C312yes—
634C2×C22⋊C4C23×C312yes—
635C2×C22⋊C4C23×C312yes—
636C2×C22⋊C4C23×C312yes—
637C2×C22⋊C4C23×C312yes—
638C2×C22⋊C4C23×C312yes—
639C2×C22⋊C4C23×C312yes—
640C2×C22⋊C4C23×C312yes—
641C2×C22⋊C4C23×C312yes—
642C2×C22⋊C4C23×C312yes—
643C2×C22⋊C4C23×C311yescharacteristic
644C2×C22⋊C4C23×C311yescharacteristic
645C2×C42C23×C311yescharacteristic
646C2×C42C23×C311yescharacteristic
647C2×C42C23×C312yes—
648C2×C42C23×C312yes—
649C2×C42C23×C311yescharacteristic
650#95C23×C311yescharacteristic
651#95C23×C311yescharacteristic
652#95C23×C312yes—
653#95C23×C311yescharacteristic
654#95C23×C312yes—
655#95C23×C311yescharacteristic
656#95C23×C312yes—
657#95C23×C312yes—
658#95C23×C312yes—
659#95C23×C312yes—
660#95C23×C312yes—
661#95C23×C312yes—
662#95C23×C312yes—
663#95C23×C312yes—
664#95C23×C312yes—
665#95C23×C312yes—
666#95C23×C312yes—
667C23×C3—21no—
668C23×C3—22no—
669C23×C3—22no—
670C23×C3—21no—
671C23×C3—22no—
672C23×C3—21no—
673C23×C3—22no—
674C23×C3—21no—
675C23×C3—21no—
676C23×C3—21no—
677C23×C3—22no—
678C23×C3—22no—
679C23×C3—22no—
680C23×C3—22no—
681C23×C3—22no—
682C23×C3—22no—
683C23×C3—22no—
684C23×C3—21no—
685C23×C3—22no—
686C23×C3—22no—
687C23×C3—22no—
688C23×C3—21no—
689C23×C3—21no—
690C23×C3—22no—
691C23×C3—22no—
692C23×C3—22no—
693C23×C3—22no—
694C23×C3—22no—
695C23×C3—22no—
696C23×C3—22no—
697C23×C3—21no—
698C23×C3—22no—
699C23×C3C22×D412yes—
700C23×C3C22×D412yes—
701C23×C3C2511yescharacteristic
702C3×Q8—28no—
703C3×D4—44no—
704C3×D4—44no—
705C3×D4—48no—
706C3×D4—48no—
707C3×D4—48no—
708C3×D4—44no—
709C3×D4—44no—
710C3×D4—44no—
711C3×D4—44no—
712C3×D4—48no—
713C3×D4—82no—
714C3×D4—84no—
715C3×D4—82no—
716C3×D4—84no—
717C3×D4—84no—
718C3×D4—84no—
719C3×D4—84no—
720C3×D4—84no—
721C2×C3×C4—21no—
722C2×C3×C4—22no—
723C2×C3×C4—22no—
724C2×C3×C4—21no—
725C2×C3×C4—22no—
726C2×C3×C4—22no—
727C2×C3×C4—22no—
728C2×C3×C4—21no—
729C2×C3×C4—21no—
730C2×C3×C4—22no—
731C2×C3×C4—21no—
732C2×C3×C4—21no—
733C2×C3×C4—21no—
734C2×C3×C4—22no—
735C2×C3×C4—21no—
736C2×C3×C4—21no—
737C2×C3×C4—22no—
738C2×C3×C4—22no—
739C2×C3×C4—22no—
740C2×C3×C4—22no—
741C2×C3×C4—22no—
742C2×C3×C4—22no—
743C2×C3×C4—22no—
744C2×C3×C4—22no—
745C2×C3×C4—22no—
746C2×C3×C4—21no—
747C2×C3×C4—22no—
748C2×C3×C4—21no—
749C2×C3×C4—22no—
750C2×C3×C4—22no—
751C2×C3×C4—22no—
752C2×C3×C4—22no—
753C2×C3×C4—22no—
754C2×C3×C4—22no—
755C2×C3×C4—22no—
756C2×C3×C4—22no—
757C2×C3×C4—44no—
758C2×C3×C4—44no—
759C2×C3×C4—44no—
760C2×C3×C4—48no—
761C2×C3×C4—48no—
762C2×C3×C4—44no—
763C2×C3×C4—82no—
764C2×C3×C4—82no—
765C2×C3×C4—84no—
766C2×C3×C4C22×D412yes—
767C2×C3×C4C22×D412yes—
768C2×C3×C4C22×D412yes—
769C2×C3×C4C22×D412yes—
770C2×C3×C4C22×D412yes—
771C2×C3×C4H(5,𝔽2)12yes—
772C2×C3×C4H(5,𝔽2)14yes—
773C24C24×C311yescharacteristic
774C24C24×C311yescharacteristic
775C24C24×C312yes—
776C24C24×C312yes—
777C24C24×C311yescharacteristic
778C24C24×C311yescharacteristic
779#41—416no—
780#41—416no—
781C2×Q8—22no—
782C2×Q8—24no—
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—22no—
786C2×D4—24no—
787C2×D4—24no—
788C2×D4—22no—
789C2×D4—24no—
790C2×D4—24no—
791C2×D4—24no—
792C2×D4—22no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—24no—
796C2×D4—22no—
797C2×D4—24no—
798C2×D4—24no—
799C2×D4—42no—
800C2×D4—42no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—41no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—42no—
812C2×D4—42no—
813C2×D4—42no—
814C2×D4—42no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—42no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—42no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—42no—
829C2×D4C2×C3×D414yes—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—22no—
837C22×C4—24no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—42no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—41no—
845C22×C4—41no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4C2×C3×D414yes—
852C22×C4C2×C3×D414yes—
853C22×C4C24×C312yes—
854C22×C4C24×C312yes—
855C22×C4C24×C312yes—
856C22×C4C24×C311yescharacteristic
857C22×C4C24×C311yescharacteristic
858C22×C4C24×C312yes—
859C22×C4C24×C312yes—
860C22×C4C24×C311yescharacteristic
861C22×C4C24×C311yescharacteristic
862C22×C4C24×C311yescharacteristic
863C22×C4C24×C311yescharacteristic
864C22×C4C24×C311yescharacteristic
865C22×C4C24×C311yescharacteristic
866C22×C4C24×C311yescharacteristic
867C22×C4C24×C311yescharacteristic
868C22×C4C24×C312yes—
869C22×C4C24×C311yescharacteristic
870C4⋊C4—22no—
871C4⋊C4—22no—
872C4⋊C4—22no—
873C4⋊C4—22no—
874C4⋊C4—22no—
875C4⋊C4—22no—
876C4⋊C4—22no—
877C4⋊C4—24no—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—22no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—42no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4C2×C3×D414yes—
888C22⋊C4—22no—
889C22⋊C4—22no—
890C22⋊C4—22no—
891C22⋊C4—22no—
892C22⋊C4—24no—
893C22⋊C4—24no—
894C22⋊C4—22no—
895C22⋊C4—22no—
896C22⋊C4—22no—
897C22⋊C4—22no—
898C22⋊C4—24no—
899C22⋊C4—24no—
900C22⋊C4—24no—
901C22⋊C4—24no—
902C22⋊C4—42no—
903C22⋊C4—42no—
904C22⋊C4—42no—
905C22⋊C4—42no—
906C22⋊C4—42no—
907C22⋊C4—42no—
908C22⋊C4—42no—
909C22⋊C4—42no—
910C22⋊C4—42no—
911C22⋊C4—42no—
912C22⋊C4—42no—
913C22⋊C4—42no—
914C22⋊C4—42no—
915C22⋊C4—42no—
916C22⋊C4—42no—
917C22⋊C4C2×C3×D414yes—
918C22⋊C4C2×C3×D414yes—
919C42—22no—
920C42—22no—
921C42—24no—
922C42—42no—
923C42C2×C3×D414yes—
924C22×C3—22no—
925C22×C3—22no—
926C22×C3—22no—
927C22×C3—22no—
928C22×C3—22no—
929C22×C3—22no—
930C22×C3—42no—
931C22×C3—42no—
932C22×C3—42no—
933C22×C3—42no—
934C22×C3—42no—
935C22×C3—42no—
936C22×C3—41no—
937C22×C3—41no—
938C22×C3—42no—
939C22×C3—42no—
940C22×C3—41no—
941C22×C3—41no—
942C22×C3—41no—
943C22×C3—41no—
944C22×C3—42no—
945C22×C3—42no—
946C22×C3—42no—
947C22×C3—42no—
948C22×C3—42no—
949C22×C3—42no—
950C22×C3—42no—
951C22×C3—42no—
952C22×C3—42no—
953C22×C3—42no—
954C22×C3—42no—
955C22×C3—42no—
956C22×C3—42no—
957C22×C3—42no—
958C22×C3C23×D411yescharacteristic
959C22×C3C2×H(5,𝔽2)12yes—
960C22×C3C2×H(5,𝔽2)11yescharacteristic
961C22×C3#58512yes—
962C22×C3#58511yescharacteristic
963C3×C4—22no—
964C3×C4—22no—
965C3×C4—22no—
966C3×C4—22no—
967C3×C4—24no—
968C3×C4—22no—
969C3×C4—22no—
970C3×C4—41no—
971C3×C4—41no—
972C3×C4—41no—
973C3×C4—41no—
974C3×C4—41no—
975C3×C4—42no—
976C3×C4—42no—
977C3×C4—42no—
978C3×C4—42no—
979C3×C4—42no—
980C23—21no—
981C23—22no—
982C23—22no—
983C23—21no—
984C23—22no—
985C23—21no—
986C23—22no—
987C23—21no—
988C23—21no—
989C23—21no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—21no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—21no—
1002C23—21no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—21no—
1011C23—22no—
1012C23C22×C3×D412yes—
1013C23C22×C3×D412yes—
1014C23C25×C311yescharacteristic
1015Q8—28no—
1016D4—44no—
1017D4—48no—
1018D4—48no—
1019D4—44no—
1020D4—44no—
1021D4—44no—
1022D4—48no—
1023D4—44no—
1024D4—44no—
1025D4—48no—
1026D4—82no—
1027D4—84no—
1028D4—82no—
1029D4—84no—
1030D4—84no—
1031D4—84no—
1032D4—84no—
1033D4—84no—
1034C2×C4—21no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—21no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—22no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—22no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—21no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—44no—
1071C2×C4—44no—
1072C2×C4—48no—
1073C2×C4—48no—
1074C2×C4—44no—
1075C2×C4—44no—
1076C2×C4—82no—
1077C2×C4—82no—
1078C2×C4—84no—
1079C2×C4C22×C3×D412yes—
1080C2×C4C22×C3×D412yes—
1081C2×C4C22×C3×D412yes—
1082C2×C4C22×C3×D412yes—
1083C2×C4C22×C3×D412yes—
1084C2×C4C3×H(5,𝔽2)12yes—
1085C2×C4C3×H(5,𝔽2)14yes—
1086C2×C3—42no—
1087C2×C3—42no—
1088C2×C3—82no—
1089C2×C3—82no—
1090C2×C3—81no—
1091C2×C3—81no—
1092C2×C3#344911yescharacteristic
1093C2×C3#348411yescharacteristic
1094C2×C3#348811yescharacteristic
1095C2×C3#353912yes—
1096C2×C3#354612yes—
1097C22—22no—
1098C22—22no—
1099C22—22no—
1100C22—22no—
1101C22—22no—
1102C22—22no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—41no—
1110C22—41no—
1111C22—42no—
1112C22—42no—
1113C22—41no—
1114C22—41no—
1115C22—41no—
1116C22—41no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22C23×C3×D411yescharacteristic
1132C22C2×C3×H(5,𝔽2)12yes—
1133C22C2×C3×H(5,𝔽2)11yescharacteristic
1134C22C3×#58512yes—
1135C22C3×#58511yescharacteristic
1136C4—22no—
1137C4—22no—
1138C4—22no—
1139C4—22no—
1140C4—24no—
1141C4—22no—
1142C4—22no—
1143C4—41no—
1144C4—41no—
1145C4—41no—
1146C4—41no—
1147C4—41no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C3#4060511yescharacteristic, direct product factor, Sylow
1154C2—42no—
1155C2—42no—
1156C2—82no—
1157C2—82no—
1158C2—81no—
1159C2—81no—
1160C2C3×#344911yescharacteristic
1161C2C3×#348411yescharacteristic
1162C2C3×#348811yescharacteristic
1163C2C3×#353912yes—
1164C2C3×#354612yes—
subgroupG/H
center, socleC23×C3C25
commutator, Frattini, cosocleC23C25×C3
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#553C2semidirect
2. C2×C3×#550C2semidirect
3. C3×#2818C2semidirect
4. C3×#2815C2semidirect
5. C3×#2691C2semidirect
6. C3×#2675C2semidirect
7. C3×#2673C2semidirect
8. C3×#2673C2semidirect
9. C3×#2661C2semidirect
10. C3×#2637C2semidirect
11. C3×#2619C2semidirect
12. C3×#2618C2semidirect
13. C3×#2615C2semidirect
14. C3×#2599C2semidirect
15. C3×#2543C2semidirect
16. C3×#2464C2semidirect
17. C3×#2460C2semidirect
18. C3×#2456C2semidirect
19. C3×#2456C2semidirect
20. C3×#2430C2semidirect
21. C3×#2406C2semidirect
22. C3×#2388C2semidirect
23. C3×#2318C2semidirect
24. #40605C3direct (N × H)
126. C2×#553C2×C3semidirect
127. C2×#550C2×C3semidirect
128. #2818C2×C3semidirect
129. #2815C2×C3semidirect
130. #2691C2×C3semidirect
131. #2675C2×C3semidirect
132. #2673C2×C3semidirect
133. #2673C2×C3semidirect
134. #2661C2×C3semidirect
135. #2637C2×C3semidirect
136. #2619C2×C3semidirect
137. #2618C2×C3semidirect
138. #2615C2×C3semidirect
139. #2599C2×C3semidirect
140. #2543C2×C3semidirect
141. #2464C2×C3semidirect
142. #2460C2×C3semidirect
143. #2456C2×C3semidirect
144. #2456C2×C3semidirect
145. #2430C2×C3semidirect
146. #2406C2×C3semidirect
147. #2388C2×C3semidirect
148. #2318C2×C3semidirect
208. C3×C4×D4D4semidirect
593. C4×D4C3×D4semidirect
1153. C3#40605direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5532
C2×C3×#5502
C3×#28182
C3×#28152
C3×#26912
C3×#26752
C3×#26732
C3×#26612
C3×#26372
C3×#26192
C3×#26182
C3×#26152
C3×#25992
C3×#25432
C3×#24642
C3×#24602
C3×#24562
C3×#24302
C3×#24062
C3×#23882
C3×#23182
#406053