Finite Group Databasebeta

← C2×C3×#2714 #10670743

Subgroups — C2×C3×#2714 #10670743

Order 768.

3434 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#126C211yesmaximal, characteristic, complemented
2C22×C3×#121C211yesmaximal, characteristic, complemented
3C3×#2714C2116yesmaximal, direct product factor
4C2×C3×#397C211yesmaximal, characteristic, complemented
5C2×C3×#394C211yesmaximal, characteristic, complemented
6C2×C3×#394C211yesmaximal, characteristic, complemented
7C2×C3×#392C211yesmaximal, characteristic, complemented
8C2×C3×#392C211yesmaximal, characteristic, complemented
9C2×C3×#392C211yesmaximal, characteristic, complemented
10C2×C3×#390C211yesmaximal, characteristic, complemented
11C2×C3×#390C211yesmaximal, characteristic, complemented
12C2×C3×#390C211yesmaximal, characteristic, complemented
13C2×C3×#388C211yesmaximal, characteristic, complemented
14C2×C3×#387C211yesmaximal, characteristic, complemented
15C2×C3×#386C211yesmaximal, characteristic, complemented
16C2×C3×#385C211yesmaximal, characteristic, complemented
17C2×#2714C311yesmaximal, characteristic, direct product factor, Sylow
18C23×C3×D4C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C23×C3×D4C2211yescharacteristic
21C23×C3×D4C2211yescharacteristic
22C23×C3×D4C2211yescharacteristic
23C23×C3×D4C2211yescharacteristic
24C24×C3×C4C2211yescharacteristic
25C2×C3×#126—28no—
26C2×C3×#126C2218yescomplemented
27C2×C3×#121—28no—
28C2×C3×#121C2218yescomplemented
29C22×C3×C4⋊C4C2211yescharacteristic
30C22×C3×C4⋊C4C2211yescharacteristic
31C22×C3×C4⋊C4C2211yescharacteristic
32C22×C3×C4⋊C4C2211yescharacteristic
33C22×C3×C4⋊C4C2211yescharacteristic
34C22×C3×C22⋊C4C2211yescharacteristic
35C22×C3×C22⋊C4C2211yescharacteristic
36C22×C3×C22⋊C4C2211yescharacteristic
37C22×C3×C22⋊C4C2211yescharacteristic
38C22×C3×C22⋊C4C2211yescharacteristic
39C22×C3×C22⋊C4C2211yescharacteristic
40C22×C3×C22⋊C4C2211yescharacteristic
41C22×C3×C22⋊C4C2211yescharacteristic
42C22×C3×C22⋊C4C2211yescharacteristic
43C22×C3×C22⋊C4C2211yescharacteristic
44C22×C3×C22⋊C4C2211yescharacteristic
45C22×C3×C22⋊C4C2211yescharacteristic
46C22×C3×C22⋊C4C2211yescharacteristic
47C22×C3×C22⋊C4C2211yescharacteristic
48C22×C3×C22⋊C4C2211yescharacteristic
49C22×C3×C42C2211yescharacteristic
50C22×C3×C42C2211yescharacteristic
51C3×#397C2218yescomplemented
52C3×#394C2218yescomplemented
53C3×#394C2218yescomplemented
54C3×#392C2218yescomplemented
55C3×#392C2218yescomplemented
56C3×#392C2218yescomplemented
57C3×#390C2218yescomplemented
58C3×#390C2218yescomplemented
59C3×#390C2218yescomplemented
60C3×#388C2218yescomplemented
61C3×#387C2218yescomplemented
62C3×#386C2218yescomplemented
63C3×#385C2218yescomplemented
64C2×C3×#95C2211yescharacteristic
65C2×C3×#95C2211yescharacteristic
66C2×C3×#95C2211yescharacteristic
67C2×C3×#95C2211yescharacteristic
68C2×C3×#95C2211yescharacteristic
69C2×C3×#95C2211yescharacteristic
70C22×#126C2×C311yescharacteristic, complemented
71C22×#121C2×C311yescharacteristic, complemented
72#2714C2×C3116yesdirect product factor
73C2×#397C2×C311yescharacteristic, complemented
74C2×#394C2×C311yescharacteristic, complemented
75C2×#394C2×C311yescharacteristic, complemented
76C2×#392C2×C311yescharacteristic, complemented
77C2×#392C2×C311yescharacteristic, complemented
78C2×#392C2×C311yescharacteristic, complemented
79C2×#390C2×C311yescharacteristic, complemented
80C2×#390C2×C311yescharacteristic, complemented
81C2×#390C2×C311yescharacteristic, complemented
82C2×#388C2×C311yescharacteristic, complemented
83C2×#387C2×C311yescharacteristic, complemented
84C2×#386C2×C311yescharacteristic, complemented
85C2×#385C2×C311yescharacteristic, complemented
86C25×C3C2311yescharacteristic
87C25×C3C2311yescharacteristic
88C25×C3C2311yescharacteristic
89C25×C3C2311yescharacteristic
90C22×C3×D4—24no—
91C22×C3×D4—24no—
92C22×C3×D4—24no—
93C22×C3×D4—24no—
94C22×C3×D4—24no—
95C22×C3×D4—24no—
96C22×C3×D4—24no—
97C22×C3×D4—42no—
98C22×C3×D4—42no—
99C22×C3×D4—42no—
100C22×C3×D4—42no—
101C22×C3×D4—42no—
102C22×C3×D4—42no—
103C22×C3×D4—42no—
104C22×C3×D4—42no—
105C22×C3×D4—42no—
106C22×C3×D4—42no—
107C22×C3×D4—42no—
108C22×C3×D4C2314yes—
109C22×C3×D4C2314yes—
110C22×C3×D4C2314yes—
111C22×C3×D4C2314yes—
112C22×C3×D4C2314yes—
113C22×C3×D4C2314yes—
114C23×C3×C4—24no—
115C23×C3×C4—42no—
116C23×C3×C4—42no—
117C23×C3×C4C2311yescharacteristic
118C23×C3×C4C2311yescharacteristic
119C23×C3×C4C2311yescharacteristic
120C23×C3×C4C2311yescharacteristic
121C23×C3×C4C2311yescharacteristic
122C23×C3×C4C2311yescharacteristic
123C23×C3×C4C2311yescharacteristic
124C23×C3×C4C2311yescharacteristic
125C23×C3×C4C2311yescharacteristic
126C23×C3×C4C2311yescharacteristic
127C23×C3×C4C2311yescharacteristic
128C23×C3×C4C2314yes—
129C3×#126—232no—
130C3×#121—232no—
131C2×C3×C4⋊C4—24no—
132C2×C3×C4⋊C4—24no—
133C2×C3×C4⋊C4—42no—
134C2×C3×C4⋊C4—42no—
135C2×C3×C4⋊C4D418yescomplemented
136C2×C3×C4⋊C4C2314yes—
137C2×C3×C4⋊C4C2314yes—
138C2×C3×C4⋊C4C2314yes—
139C2×C3×C4⋊C4C2314yes—
140C2×C3×C4⋊C4C2314yes—
141C2×C3×C22⋊C4—24no—
142C2×C3×C22⋊C4—24no—
143C2×C3×C22⋊C4—24no—
144C2×C3×C22⋊C4—24no—
145C2×C3×C22⋊C4—24no—
146C2×C3×C22⋊C4—24no—
147C2×C3×C22⋊C4—24no—
148C2×C3×C22⋊C4—42no—
149C2×C3×C22⋊C4—42no—
150C2×C3×C22⋊C4—42no—
151C2×C3×C22⋊C4—42no—
152C2×C3×C22⋊C4—42no—
153C2×C3×C22⋊C4—42no—
154C2×C3×C22⋊C4—42no—
155C2×C3×C22⋊C4—42no—
156C2×C3×C22⋊C4C2314yes—
157C2×C3×C22⋊C4C2314yes—
158C2×C3×C22⋊C4C2314yes—
159C2×C3×C22⋊C4C2314yes—
160C2×C3×C22⋊C4C2314yes—
161C2×C3×C22⋊C4C2314yes—
162C2×C3×C22⋊C4C2314yes—
163C2×C3×C22⋊C4C2314yes—
164C2×C3×C22⋊C4C2314yes—
165C2×C3×C22⋊C4C2314yes—
166C2×C3×C22⋊C4C2314yes—
167C2×C3×C22⋊C4C2314yes—
168C2×C3×C22⋊C4C2314yes—
169C2×C3×C22⋊C4C2314yes—
170C2×C3×C22⋊C4C2314yes—
171C2×C3×C42—24no—
172C2×C3×C42—42no—
173C2×C3×C42C2314yes—
174C2×C3×C42C2314yes—
175C3×#95C2314yes—
176C3×#95C2314yes—
177C3×#95C2314yes—
178C3×#95C2314yes—
179C3×#95C2314yes—
180C3×#95C2314yes—
181C23×D4C22×C311yescharacteristic
182C23×D4C22×C311yescharacteristic
183C23×D4C22×C311yescharacteristic
184C23×D4C22×C311yescharacteristic
185C23×D4C22×C311yescharacteristic
186C23×D4C22×C311yescharacteristic
187C24×C4C22×C311yescharacteristic
188C2×#126—28no—
189C2×#126C22×C318yescomplemented
190C2×#121—28no—
191C2×#121C22×C318yescomplemented
192C22×C4⋊C4C22×C311yescharacteristic
193C22×C4⋊C4C22×C311yescharacteristic
194C22×C4⋊C4C22×C311yescharacteristic
195C22×C4⋊C4C22×C311yescharacteristic
196C22×C4⋊C4C22×C311yescharacteristic
197C22×C22⋊C4C22×C311yescharacteristic
198C22×C22⋊C4C22×C311yescharacteristic
199C22×C22⋊C4C22×C311yescharacteristic
200C22×C22⋊C4C22×C311yescharacteristic
201C22×C22⋊C4C22×C311yescharacteristic
202C22×C22⋊C4C22×C311yescharacteristic
203C22×C22⋊C4C22×C311yescharacteristic
204C22×C22⋊C4C22×C311yescharacteristic
205C22×C22⋊C4C22×C311yescharacteristic
206C22×C22⋊C4C22×C311yescharacteristic
207C22×C22⋊C4C22×C311yescharacteristic
208C22×C22⋊C4C22×C311yescharacteristic
209C22×C22⋊C4C22×C311yescharacteristic
210C22×C22⋊C4C22×C311yescharacteristic
211C22×C22⋊C4C22×C311yescharacteristic
212C22×C42C22×C311yescharacteristic
213C22×C42C22×C311yescharacteristic
214#397C22×C318yescomplemented
215#394C22×C318yescomplemented
216#394C22×C318yescomplemented
217#392C22×C318yescomplemented
218#392C22×C318yescomplemented
219#392C22×C318yescomplemented
220#390C22×C318yescomplemented
221#390C22×C318yescomplemented
222#390C22×C318yescomplemented
223#388C22×C318yescomplemented
224#387C22×C318yescomplemented
225#386C22×C318yescomplemented
226#385C22×C318yescomplemented
227C2×#95C22×C311yescharacteristic
228C2×#95C22×C311yescharacteristic
229C2×#95C22×C311yescharacteristic
230C2×#95C22×C311yescharacteristic
231C2×#95C22×C311yescharacteristic
232C2×#95C22×C311yescharacteristic
233C24×C3—22no—
234C24×C3—22no—
235C24×C3—22no—
236C24×C3—22no—
237C24×C3—22no—
238C24×C3—22no—
239C24×C3—22no—
240C24×C3—22no—
241C24×C3—22no—
242C24×C3—22no—
243C24×C3—22no—
244C24×C3—22no—
245C24×C3—22no—
246C24×C3—22no—
247C24×C3—22no—
248C24×C3—22no—
249C24×C3—22no—
250C24×C3—22no—
251C24×C3—22no—
252C24×C3—22no—
253C24×C3—22no—
254C24×C3—22no—
255C24×C3—22no—
256C24×C3—22no—
257C24×C3—22no—
258C24×C3—22no—
259C24×C3—22no—
260C24×C3#4114yes—
261C24×C3C2412yes—
262C24×C3C2412yes—
263C24×C3C2412yes—
264C24×C3C2412yes—
265C24×C3C2411yescharacteristic
266C2×C3×D4—28no—
267C2×C3×D4—28no—
268C2×C3×D4—28no—
269C2×C3×D4—28no—
270C2×C3×D4—28no—
271C2×C3×D4—28no—
272C2×C3×D4—28no—
273C2×C3×D4—44no—
274C2×C3×D4—44no—
275C2×C3×D4—44no—
276C2×C3×D4—44no—
277C2×C3×D4—44no—
278C2×C3×D4—44no—
279C2×C3×D4—44no—
280C2×C3×D4—44no—
281C2×C3×D4—44no—
282C2×C3×D4—44no—
283C2×C3×D4—44no—
284C2×C3×D4—416no—
285C2×C3×D4—416no—
286C2×C3×D4—416no—
287C2×C3×D4—416no—
288C2×C3×D4—416no—
289C2×C3×D4—416no—
290C22×C3×C4—22no—
291C22×C3×C4—22no—
292C22×C3×C4—22no—
293C22×C3×C4—22no—
294C22×C3×C4—22no—
295C22×C3×C4—22no—
296C22×C3×C4—22no—
297C22×C3×C4—22no—
298C22×C3×C4—22no—
299C22×C3×C4—22no—
300C22×C3×C4—22no—
301C22×C3×C4—22no—
302C22×C3×C4—22no—
303C22×C3×C4—22no—
304C22×C3×C4—22no—
305C22×C3×C4—22no—
306C22×C3×C4—22no—
307C22×C3×C4—22no—
308C22×C3×C4—22no—
309C22×C3×C4—22no—
310C22×C3×C4—22no—
311C22×C3×C4—22no—
312C22×C3×C4—22no—
313C22×C3×C4—22no—
314C22×C3×C4—22no—
315C22×C3×C4—22no—
316C22×C3×C4—22no—
317C22×C3×C4—22no—
318C22×C3×C4—22no—
319C22×C3×C4—28no—
320C22×C3×C4—44no—
321C22×C3×C4—44no—
322C22×C3×C4—416no—
323C22×C3×C4C2×D414yes—
324C22×C3×C4C2×D414yes—
325C22×C3×C4C2×D414yes—
326C22×C3×C4#4114yes—
327C22×C3×C4C2412yes—
328C22×C3×C4C2412yes—
329C22×C3×C4C2412yes—
330C22×C3×C4C2412yes—
331C22×C3×C4C2412yes—
332C22×C3×C4C2412yes—
333C22×C3×C4C2412yes—
334C22×C3×C4C2412yes—
335C22×C3×C4C2412yes—
336C22×C3×C4C2412yes—
337C22×C3×C4C2412yes—
338C3×C4⋊C4—28no—
339C3×C4⋊C4—28no—
340C3×C4⋊C4—44no—
341C3×C4⋊C4—44no—
342C3×C4⋊C4C2×D4116yescomplemented
343C3×C22⋊C4—28no—
344C3×C22⋊C4—28no—
345C3×C22⋊C4—28no—
346C3×C22⋊C4—28no—
347C3×C22⋊C4—28no—
348C3×C22⋊C4—28no—
349C3×C22⋊C4—28no—
350C3×C22⋊C4—44no—
351C3×C22⋊C4—44no—
352C3×C22⋊C4—44no—
353C3×C22⋊C4—44no—
354C3×C22⋊C4—44no—
355C3×C22⋊C4—44no—
356C3×C22⋊C4—44no—
357C3×C22⋊C4—44no—
358C3×C42—28no—
359C3×C42—44no—
360C25C23×C311yescharacteristic
361C25C23×C311yescharacteristic
362C25C23×C311yescharacteristic
363C25C23×C311yescharacteristic
364C22×D4—24no—
365C22×D4—24no—
366C22×D4—24no—
367C22×D4—24no—
368C22×D4—24no—
369C22×D4—24no—
370C22×D4—24no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—42no—
376C22×D4—42no—
377C22×D4—42no—
378C22×D4—42no—
379C22×D4—42no—
380C22×D4—42no—
381C22×D4—42no—
382C22×D4C23×C314yes—
383C22×D4C23×C314yes—
384C22×D4C23×C314yes—
385C22×D4C23×C314yes—
386C22×D4C23×C314yes—
387C22×D4C23×C314yes—
388C23×C4—24no—
389C23×C4—42no—
390C23×C4—42no—
391C23×C4C23×C311yescharacteristic
392C23×C4C23×C311yescharacteristic
393C23×C4C23×C311yescharacteristic
394C23×C4C23×C311yescharacteristic
395C23×C4C23×C311yescharacteristic
396C23×C4C23×C311yescharacteristic
397C23×C4C23×C311yescharacteristic
398C23×C4C23×C311yescharacteristic
399C23×C4C23×C311yescharacteristic
400C23×C4C23×C311yescharacteristic
401C23×C4C23×C311yescharacteristic
402C23×C4C23×C314yes—
403#126—232no—
404#121—232no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—42no—
408C2×C4⋊C4—42no—
409C2×C4⋊C4C3×D418yescomplemented
410C2×C4⋊C4C23×C314yes—
411C2×C4⋊C4C23×C314yes—
412C2×C4⋊C4C23×C314yes—
413C2×C4⋊C4C23×C314yes—
414C2×C4⋊C4C23×C314yes—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4—24no—
418C2×C22⋊C4—24no—
419C2×C22⋊C4—24no—
420C2×C22⋊C4—24no—
421C2×C22⋊C4—24no—
422C2×C22⋊C4—42no—
423C2×C22⋊C4—42no—
424C2×C22⋊C4—42no—
425C2×C22⋊C4—42no—
426C2×C22⋊C4—42no—
427C2×C22⋊C4—42no—
428C2×C22⋊C4—42no—
429C2×C22⋊C4—42no—
430C2×C22⋊C4C23×C314yes—
431C2×C22⋊C4C23×C314yes—
432C2×C22⋊C4C23×C314yes—
433C2×C22⋊C4C23×C314yes—
434C2×C22⋊C4C23×C314yes—
435C2×C22⋊C4C23×C314yes—
436C2×C22⋊C4C23×C314yes—
437C2×C22⋊C4C23×C314yes—
438C2×C22⋊C4C23×C314yes—
439C2×C22⋊C4C23×C314yes—
440C2×C22⋊C4C23×C314yes—
441C2×C22⋊C4C23×C314yes—
442C2×C22⋊C4C23×C314yes—
443C2×C22⋊C4C23×C314yes—
444C2×C22⋊C4C23×C314yes—
445C2×C42—24no—
446C2×C42—42no—
447C2×C42C23×C314yes—
448C2×C42C23×C314yes—
449#95C23×C314yes—
450#95C23×C314yes—
451#95C23×C314yes—
452#95C23×C314yes—
453#95C23×C314yes—
454#95C23×C314yes—
455C23×C3—28no—
456C23×C3—28no—
457C23×C3—28no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
475C23×C3—22no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—44no—
486C23×C3—44no—
487C23×C3—44no—
488C23×C3—44no—
489C23×C3—44no—
490C23×C3—44no—
491C23×C3—44no—
492C23×C3—44no—
493C23×C3—44no—
494C23×C3—44no—
495C23×C3—44no—
496C23×C3—44no—
497C23×C3—44no—
498C23×C3—44no—
499C23×C3—44no—
500C23×C3—44no—
501C23×C3—44no—
502C23×C3—44no—
503C23×C3—44no—
504C23×C3—44no—
505C23×C3—44no—
506C23×C3—44no—
507C23×C3—44no—
508C23×C3—44no—
509C23×C3—44no—
510C23×C3C22×D412yes—
511C23×C3C2×#4114yes—
512C23×C3C2×#4112yes—
513C23×C3C2×#4112yes—
514C23×C3H(5,𝔽2)12yes—
515C23×C3H(5,𝔽2)12yes—
516C23×C3H(5,𝔽2)12yes—
517C23×C3H(5,𝔽2)12yes—
518C23×C3C2511yescharacteristic
519C3×D4—416no—
520C3×D4—416no—
521C3×D4—416no—
522C3×D4—416no—
523C3×D4—416no—
524C3×D4—416no—
525C2×C3×C4—28no—
526C2×C3×C4—28no—
527C2×C3×C4—28no—
528C2×C3×C4—28no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
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—22no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—22no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—416no—
559C2×C3×C4—44no—
560C2×C3×C4—44no—
561C2×C3×C4—44no—
562C2×C3×C4—44no—
563C2×C3×C4—44no—
564C2×C3×C4—44no—
565C2×C3×C4—44no—
566C2×C3×C4C22×D414yes—
567C2×C3×C4C22×D414yes—
568C2×C3×C4C22×D414yes—
569C2×C3×C4C2×#4114yes—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24C3×#4114yes—
598C24C24×C312yes—
599C24C24×C312yes—
600C24C24×C312yes—
601C24C24×C312yes—
602C24C24×C311yescharacteristic
603C2×D4—28no—
604C2×D4—28no—
605C2×D4—28no—
606C2×D4—28no—
607C2×D4—28no—
608C2×D4—28no—
609C2×D4—28no—
610C2×D4—44no—
611C2×D4—44no—
612C2×D4—44no—
613C2×D4—44no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—44no—
618C2×D4—44no—
619C2×D4—44no—
620C2×D4—44no—
621C2×D4—416no—
622C2×D4—416no—
623C2×D4—416no—
624C2×D4—416no—
625C2×D4—416no—
626C2×D4—416no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—28no—
657C22×C4—44no—
658C22×C4—44no—
659C22×C4—416no—
660C22×C4C2×C3×D414yes—
661C22×C4C2×C3×D414yes—
662C22×C4C2×C3×D414yes—
663C22×C4C3×#4114yes—
664C22×C4C24×C312yes—
665C22×C4C24×C312yes—
666C22×C4C24×C312yes—
667C22×C4C24×C312yes—
668C22×C4C24×C312yes—
669C22×C4C24×C312yes—
670C22×C4C24×C312yes—
671C22×C4C24×C312yes—
672C22×C4C24×C312yes—
673C22×C4C24×C312yes—
674C22×C4C24×C312yes—
675C4⋊C4—28no—
676C4⋊C4—28no—
677C4⋊C4—44no—
678C4⋊C4—44no—
679C4⋊C4C2×C3×D4116yescomplemented
680C22⋊C4—28no—
681C22⋊C4—28no—
682C22⋊C4—28no—
683C22⋊C4—28no—
684C22⋊C4—28no—
685C22⋊C4—28no—
686C22⋊C4—28no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—44no—
694C22⋊C4—44no—
695C42—28no—
696C42—44no—
697C22×C3—24no—
698C22×C3—24no—
699C22×C3—24no—
700C22×C3—42no—
701C22×C3—42no—
702C22×C3—42no—
703C22×C3—416no—
704C22×C3—42no—
705C22×C3—42no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3—42no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3—42no—
713C22×C3—42no—
714C22×C3—42no—
715C22×C3—42no—
716C22×C3—42no—
717C22×C3—42no—
718C22×C3—42no—
719C22×C3—42no—
720C22×C3—42no—
721C22×C3—42no—
722C22×C3—42no—
723C22×C3—42no—
724C22×C3—42no—
725C22×C3—42no—
726C22×C3—88no—
727C22×C3—88no—
728C22×C3—88no—
729C22×C3#53514yes—
730C22×C3#53814yes—
731C22×C3#53814yes—
732C22×C3#54614yes—
733C22×C3#55014yes—
734C22×C3#55314yes—
735C22×C3#56014yes—
736C22×C3C23×D411yescharacteristic
737C22×C3C22×#4111yescharacteristic
738C22×C3C22×#4111yescharacteristic
739C22×C3C2×H(5,𝔽2)11yescharacteristic
740C22×C3C2×H(5,𝔽2)11yescharacteristic
741C22×C3C2×H(5,𝔽2)11yescharacteristic
742C22×C3C2×H(5,𝔽2)11yescharacteristic
743C3×C4—24no—
744C3×C4—24no—
745C3×C4—24no—
746C3×C4—24no—
747C3×C4—42no—
748C3×C4—42no—
749C3×C4—42no—
750C3×C4—42no—
751C3×C4—42no—
752C3×C4—42no—
753C3×C4—42no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—28no—
761C23—28no—
762C23—28no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—44no—
789C23—44no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23—44no—
798C23—44no—
799C23—44no—
800C23—44no—
801C23—44no—
802C23—44no—
803C23—44no—
804C23—44no—
805C23—44no—
806C23—44no—
807C23—44no—
808C23—44no—
809C23C22×C3×D412yes—
810C23C2×C3×#4114yes—
811C23C2×C3×#4112yes—
812C23C2×C3×#4112yes—
813C23C3×H(5,𝔽2)12yes—
814C23C3×H(5,𝔽2)12yes—
815C23C3×H(5,𝔽2)12yes—
816C23C3×H(5,𝔽2)12yes—
817C23C25×C311yescharacteristic
818D4—416no—
819D4—416no—
820D4—416no—
821D4—416no—
822D4—416no—
823D4—416no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—28no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—28no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—416no—
858C2×C4—44no—
859C2×C4—44no—
860C2×C4—44no—
861C2×C4—44no—
862C2×C4—44no—
863C2×C4—44no—
864C2×C4—44no—
865C2×C4C22×C3×D414yes—
866C2×C4C22×C3×D414yes—
867C2×C4C22×C3×D414yes—
868C2×C4C2×C3×#4114yes—
869C2×C3—44no—
870C2×C3—82no—
871C2×C3—82no—
872C2×C3—82no—
873C2×C3#271418yesdirect product factor
874C2×C3C2×#53511yescharacteristic
875C2×C3C2×#53811yescharacteristic
876C2×C3C2×#53811yescharacteristic
877C2×C3C2×#54611yescharacteristic
878C2×C3C2×#55011yescharacteristic
879C2×C3C2×#55311yescharacteristic
880C2×C3C2×#56011yescharacteristic
881C22—24no—
882C22—24no—
883C22—24no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—416no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—88no—
911C22—88no—
912C22—88no—
913C22C3×#53514yes—
914C22C3×#53814yes—
915C22C3×#53814yes—
916C22C3×#54614yes—
917C22C3×#55014yes—
918C22C3×#55314yes—
919C22C3×#56014yes—
920C22C23×C3×D411yescharacteristic
921C22C22×C3×#4111yescharacteristic
922C22C22×C3×#4111yescharacteristic
923C22C2×C3×H(5,𝔽2)11yescharacteristic
924C22C2×C3×H(5,𝔽2)11yescharacteristic
925C22C2×C3×H(5,𝔽2)11yescharacteristic
926C22C2×C3×H(5,𝔽2)11yescharacteristic
927C4—24no—
928C4—24no—
929C4—24no—
930C4—24no—
931C4—42no—
932C4—42no—
933C4—42no—
934C4—42no—
935C4—42no—
936C4—42no—
937C4—42no—
938C3C2×#271411yescharacteristic, direct product factor, Sylow
939C2—44no—
940C2—82no—
941C2—82no—
942C2—82no—
943C2C3×#271418yesdirect product factor
944C2C2×C3×#53511yescharacteristic
945C2C2×C3×#53811yescharacteristic
946C2C2×C3×#53811yescharacteristic
947C2C2×C3×#54611yescharacteristic
948C2C2×C3×#55011yescharacteristic
949C2C2×C3×#55311yescharacteristic
950C2C2×C3×#56011yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC23C25×C3
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×#126C2semidirect
2. C22×C3×#121C2semidirect
3. C3×#2714C2direct (N × H)
4. C2×C3×#397C2semidirect
5. C2×C3×#394C2semidirect
6. C2×C3×#394C2semidirect
7. C2×C3×#392C2semidirect
8. C2×C3×#392C2semidirect
9. C2×C3×#392C2semidirect
10. C2×C3×#390C2semidirect
11. C2×C3×#390C2semidirect
12. C2×C3×#390C2semidirect
13. C2×C3×#388C2semidirect
14. C2×C3×#387C2semidirect
15. C2×C3×#386C2semidirect
16. C2×C3×#385C2semidirect
17. C2×#2714C3direct (N × H)
26. C2×C3×#126C22semidirect
28. C2×C3×#121C22semidirect
51. C3×#397C22semidirect
52. C3×#394C22semidirect
53. C3×#394C22semidirect
54. C3×#392C22semidirect
55. C3×#392C22semidirect
56. C3×#392C22semidirect
57. C3×#390C22semidirect
58. C3×#390C22semidirect
59. C3×#390C22semidirect
60. C3×#388C22semidirect
61. C3×#387C22semidirect
62. C3×#386C22semidirect
63. C3×#385C22semidirect
70. C22×#126C2×C3semidirect
71. C22×#121C2×C3semidirect
72. #2714C2×C3direct (N × H)
73. C2×#397C2×C3semidirect
74. C2×#394C2×C3semidirect
75. C2×#394C2×C3semidirect
76. C2×#392C2×C3semidirect
77. C2×#392C2×C3semidirect
78. C2×#392C2×C3semidirect
79. C2×#390C2×C3semidirect
80. C2×#390C2×C3semidirect
81. C2×#390C2×C3semidirect
82. C2×#388C2×C3semidirect
83. C2×#387C2×C3semidirect
84. C2×#386C2×C3semidirect
85. C2×#385C2×C3semidirect
135. C2×C3×C4⋊C4D4semidirect
189. C2×#126C22×C3semidirect
191. C2×#121C22×C3semidirect
214. #397C22×C3semidirect
215. #394C22×C3semidirect
216. #394C22×C3semidirect
217. #392C22×C3semidirect
218. #392C22×C3semidirect
219. #392C22×C3semidirect
220. #390C22×C3semidirect
221. #390C22×C3semidirect
222. #390C22×C3semidirect
223. #388C22×C3semidirect
224. #387C22×C3semidirect
225. #386C22×C3semidirect
226. #385C22×C3semidirect
342. C3×C4⋊C4C2×D4semidirect
409. C2×C4⋊C4C3×D4semidirect
679. C4⋊C4C2×C3×D4semidirect
873. C2×C3#2714direct (N × H)
938. C3C2×#2714direct (N × H)
943. C2C3×#2714direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1262
C22×C3×#1212
C3×#27142
C2×C3×#3972
C2×C3×#3942
C2×C3×#3922
C2×C3×#3902
C2×C3×#3882
C2×C3×#3872
C2×C3×#3862
C2×C3×#3852
C2×#27143