Finite Group Databasebeta

← C67×#13995 #30693246

Subgroups — C67×#13995 #30693246

Order 17152.

4210 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C67C211yesmaximal, characteristic
2C23×C22⋊C4×C67C211yesmaximal, characteristic, complemented
3C2×#390×C67C212yesmaximal, complemented
4C2×#386×C67C211yesmaximal, characteristic, complemented
5C2×#386×C67C211yesmaximal, characteristic, complemented
6C2×#385×C67C211yesmaximal, characteristic, complemented
7C2×#379×C67C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊C4×C67C211yesmaximal, characteristic, complemented
9C67×#1439C212yesmaximal, complemented
10C67×#1438C212yesmaximal, complemented
11C67×#1437C212yesmaximal, complemented
12C26×C67C2211yescharacteristic
13C23×D4×C67C2211yescharacteristic
14C23×D4×C67C2212yes—
15C24×C4×C67C2211yescharacteristic
16C24×C4×C67C2211yescharacteristic
17C2×#120×C67—24no—
18C2×#120×C67—24no—
19C2×#120×C67C418yescomplemented
20C22×C4⋊C4×C67C2212yescomplemented
21C22×C22⋊C4×C67—24no—
22C22×C22⋊C4×C67—28no—
23C22×C22⋊C4×C67C2211yescharacteristic
24C22×C22⋊C4×C67C2212yes—
25C22×C22⋊C4×C67C2212yes—
26C22×C22⋊C4×C67C2212yes—
27C22×C22⋊C4×C67C2212yes—
28C22×C22⋊C4×C67C2211yescharacteristic
29C22×C22⋊C4×C67C2212yes—
30C22×C22⋊C4×C67C2211yescharacteristic
31C22×C22⋊C4×C67C2211yescharacteristic, complemented
32C22×C22⋊C4×C67C2212yescomplemented
33C22×C22⋊C4×C67C2211yescharacteristic, complemented
34C22×C42×C67C2212yescomplemented
35#390×C67—28no—
36#386×C67—24no—
37#386×C67—24no—
38#385×C67—24no—
39#379×C67—24no—
40C4×C22⋊C4×C67—24no—
41C2×#95×C67C2212yescomplemented
42C2×#95×C67C2212yescomplemented
43C2×#95×C67C2211yescharacteristic, complemented
44C2×#95×C67C2212yescomplemented
45C2×#95×C67C2211yescharacteristic, complemented
46C25×C67—24no—
47C25×C67—22no—
48C25×C67—24no—
49C25×C67—22no—
50C25×C67—22no—
51C25×C67—22no—
52C25×C67—22no—
53C25×C67—22no—
54C25×C67—42no—
55C25×C67—42no—
56C25×C67C2×C414yes—
57C25×C67C2311yescharacteristic
58C25×C67C2312yes—
59C25×C67C2311yescharacteristic
60C22×D4×C67—22no—
61C22×D4×C67—22no—
62C22×D4×C67—22no—
63C22×D4×C67—22no—
64C22×D4×C67—24no—
65C22×D4×C67—24no—
66C22×D4×C67—22no—
67C22×D4×C67—22no—
68C22×D4×C67—24no—
69C22×D4×C67—24no—
70C22×D4×C67—42no—
71C22×D4×C67—42no—
72C22×D4×C67C2×C414yes—
73C22×D4×C67C2×C418yescomplemented
74C23×C4×C67—22no—
75C23×C4×C67—22no—
76C23×C4×C67—22no—
77C23×C4×C67—24no—
78C23×C4×C67—24no—
79C23×C4×C67—22no—
80C23×C4×C67—22no—
81C23×C4×C67—42no—
82C23×C4×C67—42no—
83C23×C4×C67D414yescomplemented
84C23×C4×C67C2311yescharacteristic
85C23×C4×C67C2311yescharacteristic
86C23×C4×C67C2311yescharacteristic
87C23×C4×C67C2312yes—
88C23×C4×C67C2312yes—
89C23×C4×C67C2311yescharacteristic
90C23×C4×C67C2312yes—
91C23×C4×C67C2311yescharacteristic
92#120×C67—232no—
93C2×C4⋊C4×C67—24no—
94C2×C4⋊C4×C67—24no—
95C2×C4⋊C4×C67—42no—
96C2×C22⋊C4×C67—232no—
97C2×C22⋊C4×C67—24no—
98C2×C22⋊C4×C67—22no—
99C2×C22⋊C4×C67—22no—
100C2×C22⋊C4×C67—24no—
101C2×C22⋊C4×C67—24no—
102C2×C22⋊C4×C67—24no—
103C2×C22⋊C4×C67—24no—
104C2×C22⋊C4×C67—24no—
105C2×C22⋊C4×C67—24no—
106C2×C22⋊C4×C67—22no—
107C2×C22⋊C4×C67—22no—
108C2×C22⋊C4×C67—22no—
109C2×C22⋊C4×C67—24no—
110C2×C22⋊C4×C67—24no—
111C2×C22⋊C4×C67—24no—
112C2×C22⋊C4×C67—24no—
113C2×C22⋊C4×C67—24no—
114C2×C22⋊C4×C67—22no—
115C2×C22⋊C4×C67—22no—
116C2×C22⋊C4×C67—24no—
117C2×C22⋊C4×C67—24no—
118C2×C22⋊C4×C67—42no—
119C2×C22⋊C4×C67—42no—
120C2×C22⋊C4×C67—42no—
121C2×C22⋊C4×C67—42no—
122C2×C22⋊C4×C67C2×C414yes—
123C2×C22⋊C4×C67C2×C418yescomplemented
124C2×C22⋊C4×C67D414yes—
125C2×C22⋊C4×C67D414yes—
126C2×C22⋊C4×C67D418yescomplemented
127C2×C22⋊C4×C67D414yescomplemented
128C2×C42×C67—24no—
129C2×C42×C67—24no—
130C2×C42×C67—42no—
131#95×C67—24no—
132#95×C67—24no—
133#95×C67—24no—
134#95×C67—22no—
135#95×C67—22no—
136C24×C67—22no—
137C24×C67—22no—
138C24×C67—22no—
139C24×C67—22no—
140C24×C67—28no—
141C24×C67—28no—
142C24×C67—216no—
143C24×C67—216no—
144C24×C67—28no—
145C24×C67—22no—
146C24×C67—22no—
147C24×C67—22no—
148C24×C67—22no—
149C24×C67—22no—
150C24×C67—22no—
151C24×C67—22no—
152C24×C67—22no—
153C24×C67—22no—
154C24×C67—22no—
155C24×C67—22no—
156C24×C67—22no—
157C24×C67—28no—
158C24×C67—28no—
159C24×C67—21no—
160C24×C67—22no—
161C24×C67—21no—
162C24×C67—21no—
163C24×C67—21no—
164C24×C67—21no—
165C24×C67—21no—
166C24×C67—22no—
167C24×C67—22no—
168C24×C67—22no—
169C24×C67—48no—
170C24×C67—48no—
171C24×C67—48no—
172C24×C67—48no—
173C24×C67—48no—
174C24×C67—48no—
175C24×C67—48no—
176C24×C67—48no—
177C24×C67—48no—
178C24×C67—44no—
179C24×C67—44no—
180C24×C67—48no—
181C24×C67—44no—
182C24×C67—44no—
183C24×C67—44no—
184C24×C67—44no—
185C24×C67C22×C412yes—
186C24×C67C22×C414yes—
187C24×C67C22×C412yes—
188C24×C67C2×D414yes—
189C24×C67C2×D412yes—
190C24×C67C2×D412yes—
191C24×C67C2×D412yes—
192C24×C67C2×D412yes—
193C24×C67#4114yes—
194C24×C67#4112yes—
195C24×C67#4112yes—
196C24×C67C2411yescharacteristic
197C2×D4×C67—28no—
198C2×D4×C67—28no—
199C2×D4×C67—28no—
200C2×D4×C67—216no—
201C2×D4×C67—216no—
202C2×D4×C67—48no—
203C2×D4×C67—48no—
204C2×D4×C67—48no—
205C2×D4×C67—48no—
206C2×D4×C67—48no—
207C2×D4×C67—44no—
208C2×D4×C67—44no—
209C2×D4×C67—44no—
210C2×D4×C67—44no—
211C22×C4×C67—21no—
212C22×C4×C67—22no—
213C22×C4×C67—21no—
214C22×C4×C67—22no—
215C22×C4×C67—22no—
216C22×C4×C67—22no—
217C22×C4×C67—22no—
218C22×C4×C67—28no—
219C22×C4×C67—28no—
220C22×C4×C67—22no—
221C22×C4×C67—22no—
222C22×C4×C67—22no—
223C22×C4×C67—22no—
224C22×C4×C67—22no—
225C22×C4×C67—21no—
226C22×C4×C67—21no—
227C22×C4×C67—22no—
228C22×C4×C67—22no—
229C22×C4×C67—21no—
230C22×C4×C67—21no—
231C22×C4×C67—21no—
232C22×C4×C67—22no—
233C22×C4×C67—22no—
234C22×C4×C67—21no—
235C22×C4×C67—21no—
236C22×C4×C67—21no—
237C22×C4×C67—22no—
238C22×C4×C67—22no—
239C22×C4×C67—22no—
240C22×C4×C67—22no—
241C22×C4×C67—22no—
242C22×C4×C67—28no—
243C22×C4×C67—21no—
244C22×C4×C67—21no—
245C22×C4×C67—22no—
246C22×C4×C67—21no—
247C22×C4×C67—21no—
248C22×C4×C67—21no—
249C22×C4×C67—21no—
250C22×C4×C67—22no—
251C22×C4×C67—22no—
252C22×C4×C67—22no—
253C22×C4×C67—44no—
254C22×C4×C67—48no—
255C22×C4×C67—48no—
256C22×C4×C67—48no—
257C22×C4×C67—48no—
258C22×C4×C67—44no—
259C22×C4×C67—44no—
260C22×C4×C67C22×C412yes—
261C22×C4×C67C22×C414yes—
262C22×C4×C67C2×D414yes—
263C22×C4×C67C2×D412yes—
264C22×C4×C67C2×D414yes—
265C22×C4×C67C2×D414yes—
266C22×C4×C67C2×D414yes—
267C22×C4×C67C2×D414yes—
268C22×C4×C67C2×D412yes—
269C4⋊C4×C67—48no—
270C22⋊C4×C67—216no—
271C22⋊C4×C67—28no—
272C22⋊C4×C67—216no—
273C22⋊C4×C67—216no—
274C22⋊C4×C67—48no—
275C22⋊C4×C67—48no—
276C22⋊C4×C67—48no—
277C22⋊C4×C67—44no—
278C22⋊C4×C67—44no—
279C22⋊C4×C67—44no—
280C22⋊C4×C67C22⋊C4116yescomplemented
281C42×C67—48no—
282C23×C67—24no—
283C23×C67—24no—
284C23×C67—22no—
285C23×C67—22no—
286C23×C67—24no—
287C23×C67—22no—
288C23×C67—22no—
289C23×C67—24no—
290C23×C67—24no—
291C23×C67—24no—
292C23×C67—24no—
293C23×C67—24no—
294C23×C67—24no—
295C23×C67—24no—
296C23×C67—24no—
297C23×C67—24no—
298C23×C67—232no—
299C23×C67—24no—
300C23×C67—24no—
301C23×C67—24no—
302C23×C67—24no—
303C23×C67—24no—
304C23×C67—24no—
305C23×C67—24no—
306C23×C67—24no—
307C23×C67—24no—
308C23×C67—24no—
309C23×C67—24no—
310C23×C67—24no—
311C23×C67—24no—
312C23×C67—24no—
313C23×C67—24no—
314C23×C67—24no—
315C23×C67—24no—
316C23×C67—24no—
317C23×C67—22no—
318C23×C67—22no—
319C23×C67—24no—
320C23×C67—22no—
321C23×C67—24no—
322C23×C67—432no—
323C23×C67—432no—
324C23×C67—416no—
325C23×C67—416no—
326C23×C67—416no—
327C23×C67—432no—
328C23×C67—416no—
329C23×C67—432no—
330C23×C67—416no—
331C23×C67—42no—
332C23×C67—42no—
333C23×C67—42no—
334C23×C67—42no—
335C23×C67—42no—
336C23×C67—42no—
337C23×C67—42no—
338C23×C67—42no—
339C23×C67—42no—
340C23×C67—42no—
341C23×C67—42no—
342C23×C67—42no—
343C23×C67—42no—
344C23×C67—42no—
345C23×C67—42no—
346C23×C67—42no—
347C23×C67—416no—
348C23×C67—41no—
349C23×C67—41no—
350C23×C67—41no—
351C23×C67—41no—
352C23×C67—42no—
353C23×C67—41no—
354C23×C67—41no—
355C23×C67—41no—
356C23×C67—41no—
357C23×C67—42no—
358C23×C67—42no—
359C23×C67—42no—
360C23×C67—42no—
361C23×C67—42no—
362C23×C67—42no—
363C23×C67—42no—
364C23×C67—42no—
365C23×C67—42no—
366C23×C67C2×C22⋊C414yes—
367C23×C67C4×D418yes—
368C23×C67C4×D414yes—
369C23×C67C4×D414yes—
370C23×C67#12114yes—
371C23×C67#12114yes—
372C23×C67#12414yes—
373C23×C67#12714yes—
374C23×C67C23×C411yescharacteristic
375C23×C67C22×D411yescharacteristic
376C23×C67C22×D411yescharacteristic
377C23×C67C22×D411yescharacteristic
378C23×C67C22×D412yes—
379C23×C67C22×D411yescharacteristic
380C23×C67C2×#4111yescharacteristic
381C23×C67C2×#4111yescharacteristic
382C23×C67C2×#4112yes—
383C23×C67H(5,𝔽2)12yes—
384C23×C67H(5,𝔽2)12yes—
385D4×C67—432no—
386D4×C67—416no—
387C2×C4×C67—24no—
388C2×C4×C67—24no—
389C2×C4×C67—22no—
390C2×C4×C67—22no—
391C2×C4×C67—24no—
392C2×C4×C67—24no—
393C2×C4×C67—24no—
394C2×C4×C67—24no—
395C2×C4×C67—24no—
396C2×C4×C67—24no—
397C2×C4×C67—22no—
398C2×C4×C67—22no—
399C2×C4×C67—22no—
400C2×C4×C67—22no—
401C2×C4×C67—24no—
402C2×C4×C67—24no—
403C2×C4×C67—22no—
404C2×C4×C67—22no—
405C2×C4×C67—24no—
406C2×C4×C67—24no—
407C2×C4×C67—24no—
408C2×C4×C67—24no—
409C2×C4×C67—416no—
410C2×C4×C67—416no—
411C2×C4×C67—41no—
412C2×C4×C67—41no—
413C2×C4×C67—42no—
414C2×C4×C67—41no—
415C2×C4×C67—42no—
416C2×C4×C67—41no—
417C2×C4×C67—42no—
418C2×C4×C67—42no—
419C2×C4×C67—42no—
420C2×C4×C67—42no—
421C2×C4×C67—42no—
422C2×C4×C67—42no—
423C2×C4×C67—42no—
424C2×C4×C67—42no—
425C2×C4×C67—41no—
426C2×C4×C67—41no—
427C2×C4×C67—41no—
428C2×C4×C67—41no—
429C2×C4×C67—41no—
430C2×C4×C67—41no—
431C2×C4×C67—42no—
432C2×C4×C67—42no—
433C2×C4×C67—42no—
434C2×C4×C67—42no—
435C2×C4×C67C2×C22⋊C418yescomplemented
436C2×C4×C67#12014yescomplemented
437C22×C67—24no—
438C22×C67—28no—
439C22×C67—28no—
440C22×C67—24no—
441C22×C67—24no—
442C22×C67—28no—
443C22×C67—24no—
444C22×C67—28no—
445C22×C67—24no—
446C22×C67—24no—
447C22×C67—28no—
448C22×C67—28no—
449C22×C67—28no—
450C22×C67—464no—
451C22×C67—44no—
452C22×C67—44no—
453C22×C67—44no—
454C22×C67—44no—
455C22×C67—44no—
456C22×C67—44no—
457C22×C67—44no—
458C22×C67—44no—
459C22×C67—44no—
460C22×C67—44no—
461C22×C67—44no—
462C22×C67—44no—
463C22×C67—42no—
464C22×C67—44no—
465C22×C67—44no—
466C22×C67—42no—
467C22×C67—42no—
468C22×C67—81no—
469C22×C67—81no—
470C22×C67—82no—
471C22×C67—81no—
472C22×C67—82no—
473C22×C67—81no—
474C22×C67#39018yescomplemented
475C22×C67C22×C22⋊C411yescharacteristic
476C22×C67C2×C4×D411yescharacteristic
477C22×C67C2×C4×D412yes—
478C22×C67C2×C4×D411yescharacteristic
479C22×C67#51812yes—
480C22×C67C2×#12011yescharacteristic
481C22×C67C2×#12111yescharacteristic
482C22×C67C2×#12111yescharacteristic
483C22×C67#52511yescharacteristic
484C22×C67#52512yes—
485C22×C67C2×#12411yescharacteristic
486C22×C67C2×#12711yescharacteristic
487C22×C67#53411yescharacteristic
488C22×C67#53511yescharacteristic
489C22×C67#53812yes—
490C22×C67D4212yes—
491C22×C67D4212yes—
492C22×C67D4212yes—
493C22×C67#54612yes—
494C22×C67#54612yes—
495C22×C67#54612yes—
496C22×C67#54612yes—
497C22×C67#55112yes—
498C4×C67—28no—
499C4×C67—24no—
500C4×C67—42no—
501C4×C67—44no—
502C4×C67—44no—
503C4×C67—42no—
504C4×C67—81no—
505C4×C67—81no—
506#13995C6711yesmaximal, characteristic, direct product factor, Sylow
507C2×C67—28no—
508C2×C67—48no—
509C2×C67—82no—
510C2×C67C2×#39011yescharacteristic
511C2×C67C4×#12011yescharacteristic
512C2×C67#232111yescharacteristic
513C2×C67D4×C22⋊C412yes—
514C2×C67#235812yes—
515C2×C67#241011yescharacteristic
516C2×C67#241111yescharacteristic
517C2×C67#242412yes—
518C2×C67#243311yescharacteristic
519C2×C67#247212yes—
520C2×C67#253911yescharacteristic
521C22×#120C2×C6711yescharacteristic
522C23×C22⋊C4C2×C6711yescharacteristic, complemented
523C2×#390C2×C6712yescomplemented
524C2×#386C2×C6711yescharacteristic, complemented
525C2×#386C2×C6711yescharacteristic, complemented
526C2×#385C2×C6711yescharacteristic, complemented
527C2×#379C2×C6711yescharacteristic, complemented
528C2×C4×C22⋊C4C2×C6711yescharacteristic, complemented
529#1439C2×C6712yescomplemented
530#1438C2×C6712yescomplemented
531#1437C2×C6712yescomplemented
532C67#1399511yescharacteristic, direct product factor, Sylow
533C26C22×C6711yescharacteristic
534C23×D4C22×C6711yescharacteristic
535C23×D4C22×C6712yes—
536C24×C4C22×C6711yescharacteristic
537C24×C4C22×C6711yescharacteristic
538C2×#120—24no—
539C2×#120—24no—
540C2×#120C4×C6718yescomplemented
541C22×C4⋊C4C22×C6712yescomplemented
542C22×C22⋊C4—24no—
543C22×C22⋊C4—28no—
544C22×C22⋊C4C22×C6712yes—
545C22×C22⋊C4C22×C6711yescharacteristic
546C22×C22⋊C4C22×C6712yes—
547C22×C22⋊C4C22×C6712yes—
548C22×C22⋊C4C22×C6712yes—
549C22×C22⋊C4C22×C6712yes—
550C22×C22⋊C4C22×C6711yescharacteristic
551C22×C22⋊C4C22×C6711yescharacteristic
552C22×C22⋊C4C22×C6711yescharacteristic, complemented
553C22×C22⋊C4C22×C6712yescomplemented
554C22×C22⋊C4C22×C6711yescharacteristic, complemented
555C22×C42C22×C6712yescomplemented
556#390—28no—
557#386—24no—
558#386—24no—
559#385—24no—
560#379—24no—
561C4×C22⋊C4—24no—
562C2×#95C22×C6711yescharacteristic, complemented
563C2×#95C22×C6712yescomplemented
564C2×#95C22×C6712yescomplemented
565C2×#95C22×C6712yescomplemented
566C2×#95C22×C6711yescharacteristic, complemented
567C25—24no—
568C25—22no—
569C25—24no—
570C25—22no—
571C25—22no—
572C25—22no—
573C25—22no—
574C25—22no—
575C25—42no—
576C25—42no—
577C25C2×C4×C6714yes—
578C25C23×C6711yescharacteristic
579C25C23×C6712yes—
580C25C23×C6711yescharacteristic
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—22no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—24no—
590C22×D4—24no—
591C22×D4—42no—
592C22×D4—42no—
593C22×D4C2×C4×C6714yes—
594C22×D4C2×C4×C6718yescomplemented
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—24no—
599C23×C4—24no—
600C23×C4—22no—
601C23×C4—22no—
602C23×C4—42no—
603C23×C4—42no—
604C23×C4D4×C6714yescomplemented
605C23×C4C23×C6711yescharacteristic
606C23×C4C23×C6711yescharacteristic
607C23×C4C23×C6711yescharacteristic
608C23×C4C23×C6712yes—
609C23×C4C23×C6712yes—
610C23×C4C23×C6711yescharacteristic
611C23×C4C23×C6712yes—
612C23×C4C23×C6711yescharacteristic
613#120—232no—
614C2×C4⋊C4—24no—
615C2×C4⋊C4—24no—
616C2×C4⋊C4—42no—
617C2×C22⋊C4—232no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—24no—
623C2×C22⋊C4—24no—
624C2×C22⋊C4—24no—
625C2×C22⋊C4—24no—
626C2×C22⋊C4—24no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—24no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—24no—
639C2×C22⋊C4—42no—
640C2×C22⋊C4—42no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4—42no—
643C2×C22⋊C4C2×C4×C6714yes—
644C2×C22⋊C4C2×C4×C6718yescomplemented
645C2×C22⋊C4D4×C6714yes—
646C2×C22⋊C4D4×C6714yes—
647C2×C22⋊C4D4×C6718yescomplemented
648C2×C22⋊C4D4×C6714yescomplemented
649C2×C42—24no—
650C2×C42—24no—
651C2×C42—42no—
652#95—24no—
653#95—24no—
654#95—24no—
655#95—22no—
656#95—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—28no—
662C24—28no—
663C24—216no—
664C24—216no—
665C24—28no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—28no—
679C24—28no—
680C24—21no—
681C24—22no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—48no—
691C24—48no—
692C24—48no—
693C24—48no—
694C24—48no—
695C24—48no—
696C24—48no—
697C24—48no—
698C24—48no—
699C24—44no—
700C24—44no—
701C24—48no—
702C24—44no—
703C24—44no—
704C24—44no—
705C24—44no—
706C24C22×C4×C6712yes—
707C24C22×C4×C6714yes—
708C24C22×C4×C6712yes—
709C24C2×D4×C6714yes—
710C24C2×D4×C6712yes—
711C24C2×D4×C6712yes—
712C24C2×D4×C6712yes—
713C24C2×D4×C6712yes—
714C24#41×C6714yes—
715C24#41×C6712yes—
716C24#41×C6712yes—
717C24C24×C6711yescharacteristic
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—216no—
722C2×D4—216no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—44no—
732C22×C4—21no—
733C22×C4—22no—
734C22×C4—21no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—28no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—44no—
775C22×C4—48no—
776C22×C4—48no—
777C22×C4—48no—
778C22×C4—48no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4C22×C4×C6712yes—
782C22×C4C22×C4×C6714yes—
783C22×C4C2×D4×C6714yes—
784C22×C4C2×D4×C6712yes—
785C22×C4C2×D4×C6714yes—
786C22×C4C2×D4×C6714yes—
787C22×C4C2×D4×C6714yes—
788C22×C4C2×D4×C6712yes—
789C22×C4C2×D4×C6714yes—
790C4⋊C4—48no—
791C22⋊C4—216no—
792C22⋊C4—28no—
793C22⋊C4—216no—
794C22⋊C4—216no—
795C22⋊C4—48no—
796C22⋊C4—48no—
797C22⋊C4—48no—
798C22⋊C4—44no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C22⋊C4C22⋊C4×C67116yescomplemented
802C42—48no—
803C23—24no—
804C23—24no—
805C23—22no—
806C23—22no—
807C23—24no—
808C23—22no—
809C23—22no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—232no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—24no—
842C23—24no—
843C23—432no—
844C23—432no—
845C23—416no—
846C23—416no—
847C23—416no—
848C23—416no—
849C23—432no—
850C23—416no—
851C23—432no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—416no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—42no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23—42no—
887C23C2×C22⋊C4×C6714yes—
888C23C4×D4×C6718yes—
889C23C4×D4×C6714yes—
890C23C4×D4×C6714yes—
891C23#121×C6714yes—
892C23#121×C6714yes—
893C23#124×C6714yes—
894C23#127×C6714yes—
895C23C23×C4×C6711yescharacteristic
896C23C22×D4×C6711yescharacteristic
897C23C22×D4×C6711yescharacteristic
898C23C22×D4×C6711yescharacteristic
899C23C22×D4×C6712yes—
900C23C22×D4×C6711yescharacteristic
901C23C2×#41×C6711yescharacteristic
902C23C2×#41×C6711yescharacteristic
903C23C2×#41×C6712yes—
904C23H(5,𝔽2)×C6712yes—
905C23H(5,𝔽2)×C6712yes—
906D4—432no—
907D4—416no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—416no—
931C2×C4—416no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—42no—
937C2×C4—41no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4C2×C22⋊C4×C6718yescomplemented
957C2×C4#120×C6714yescomplemented
958C22—24no—
959C22—24no—
960C22—24no—
961C22—28no—
962C22—28no—
963C22—24no—
964C22—24no—
965C22—28no—
966C22—24no—
967C22—28no—
968C22—28no—
969C22—28no—
970C22—28no—
971C22—464no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—44no—
977C22—44no—
978C22—44no—
979C22—44no—
980C22—44no—
981C22—44no—
982C22—44no—
983C22—44no—
984C22—42no—
985C22—42no—
986C22—42no—
987C22—44no—
988C22—44no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—82no—
993C22—81no—
994C22—82no—
995C22#390×C6718yescomplemented
996C22C22×C22⋊C4×C6711yescharacteristic
997C22C2×C4×D4×C6711yescharacteristic
998C22C2×C4×D4×C6711yescharacteristic
999C22C2×C4×D4×C6712yes—
1000C22#518×C6712yes—
1001C22C2×#120×C6711yescharacteristic
1002C22C2×#121×C6711yescharacteristic
1003C22C2×#121×C6711yescharacteristic
1004C22#525×C6711yescharacteristic
1005C22#525×C6712yes—
1006C22C2×#124×C6711yescharacteristic
1007C22C2×#127×C6711yescharacteristic
1008C22#534×C6711yescharacteristic
1009C22#535×C6711yescharacteristic
1010C22#538×C6712yes—
1011C22D42×C6712yes—
1012C22D42×C6712yes—
1013C22D42×C6712yes—
1014C22#546×C6712yes—
1015C22#546×C6712yes—
1016C22#546×C6712yes—
1017C22#546×C6712yes—
1018C22#551×C6712yes—
1019C4—28no—
1020C4—24no—
1021C4—42no—
1022C4—42no—
1023C4—44no—
1024C4—44no—
1025C4—81no—
1026C4—81no—
1027C2—28no—
1028C2—48no—
1029C2—82no—
1030C2C2×#390×C6711yescharacteristic
1031C2C4×#120×C6711yescharacteristic
1032C2C67×#232111yescharacteristic
1033C2D4×C22⋊C4×C6712yes—
1034C2C67×#235812yes—
1035C2C67×#241011yescharacteristic
1036C2C67×#241111yescharacteristic
1037C2C67×#242412yes—
1038C2C67×#243311yescharacteristic
1039C2C67×#247212yes—
1040C2C67×#253911yescharacteristic
subgroupG/H
center, socleC24×C67C24
commutatorC23C23×C4×C67
Frattini, cosocleC24C24×C67
prime radicalC22×#120×C67C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C67 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C67C2semidirect
3. C2×#390×C67C2semidirect
4. C2×#386×C67C2semidirect
5. C2×#386×C67C2semidirect
6. C2×#385×C67C2semidirect
7. C2×#379×C67C2semidirect
8. C2×C4×C22⋊C4×C67C2semidirect
9. C67×#1439C2semidirect
10. C67×#1438C2semidirect
11. C67×#1437C2semidirect
19. C2×#120×C67C4semidirect
20. C22×C4⋊C4×C67C22semidirect
31. C22×C22⋊C4×C67C22semidirect
32. C22×C22⋊C4×C67C22semidirect
33. C22×C22⋊C4×C67C22semidirect
34. C22×C42×C67C22semidirect
41. C2×#95×C67C22semidirect
42. C2×#95×C67C22semidirect
43. C2×#95×C67C22semidirect
44. C2×#95×C67C22semidirect
45. C2×#95×C67C22semidirect
73. C22×D4×C67C2×C4semidirect
83. C23×C4×C67D4semidirect
123. C2×C22⋊C4×C67C2×C4semidirect
126. C2×C22⋊C4×C67D4semidirect
127. C2×C22⋊C4×C67D4semidirect
280. C22⋊C4×C67C22⋊C4semidirect
435. C2×C4×C67C2×C22⋊C4semidirect
436. C2×C4×C67#120semidirect
474. C22×C67#390semidirect
506. #13995C67direct (N × H)
522. C23×C22⋊C4C2×C67semidirect
523. C2×#390C2×C67semidirect
524. C2×#386C2×C67semidirect
525. C2×#386C2×C67semidirect
526. C2×#385C2×C67semidirect
527. C2×#379C2×C67semidirect
528. C2×C4×C22⋊C4C2×C67semidirect
529. #1439C2×C67semidirect
530. #1438C2×C67semidirect
531. #1437C2×C67semidirect
532. C67#13995direct (N × H)
540. C2×#120C4×C67semidirect
541. C22×C4⋊C4C22×C67semidirect
552. C22×C22⋊C4C22×C67semidirect
553. C22×C22⋊C4C22×C67semidirect
554. C22×C22⋊C4C22×C67semidirect
555. C22×C42C22×C67semidirect
562. C2×#95C22×C67semidirect
563. C2×#95C22×C67semidirect
564. C2×#95C22×C67semidirect
565. C2×#95C22×C67semidirect
566. C2×#95C22×C67semidirect
594. C22×D4C2×C4×C67semidirect
604. C23×C4D4×C67semidirect
644. C2×C22⋊C4C2×C4×C67semidirect
647. C2×C22⋊C4D4×C67semidirect
648. C2×C22⋊C4D4×C67semidirect
801. C22⋊C4C22⋊C4×C67semidirect
956. C2×C4C2×C22⋊C4×C67semidirect
957. C2×C4#120×C67semidirect
995. C22#390×C67semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C672
C23×C22⋊C4×C672
C2×#390×C672
C2×#386×C672
C2×#385×C672
C2×#379×C672
C2×C4×C22⋊C4×C672
C67×#14392
C67×#14382
C67×#14372
#1399567