Finite Group Databasebeta

← C67×#13873 #30693124

Subgroups — C67×#13873 #30693124

Order 17152.

3526 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C67C211yesmaximal, characteristic
2C2×#388×C67C212yesmaximal, complemented
3C2×#380×C67C211yesmaximal, characteristic, complemented
4C2×#379×C67C211yesmaximal, characteristic
5C2×#379×C67C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C67C211yesmaximal, characteristic, complemented
7C67×#1440C212yesmaximal, complemented
8C67×#1439C212yesmaximal, complemented
9C67×#1437C212yesmaximal, complemented
10C67×C22⋊#95C211yesmaximal, characteristic, complemented
11C67×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C67C2211yescharacteristic
13C24×C4×C67C2211yescharacteristic
14C24×C4×C67C2211yescharacteristic
15C22×C4⋊C4×C67C2212yescomplemented
16C22×C22⋊C4×C67—28no—
17C22×C22⋊C4×C67C418yescomplemented
18C22×C22⋊C4×C67C2211yescharacteristic
19C22×C22⋊C4×C67C2211yescharacteristic
20C22×C22⋊C4×C67C2212yes—
21C22×C22⋊C4×C67C2212yes—
22C22×C22⋊C4×C67C2212yes—
23C22×C22⋊C4×C67C2212yes—
24C22×C22⋊C4×C67C2211yescharacteristic
25C22×C22⋊C4×C67C2211yescharacteristic
26C22×C22⋊C4×C67C2211yescharacteristic
27C22×C22⋊C4×C67C2211yescharacteristic
28C22×C22⋊C4×C67C2211yescharacteristic
29C22×C22⋊C4×C67C2211yescharacteristic
30C22×C42×C67C2212yescomplemented
31#388×C67—28no—
32#380×C67—24no—
33#379×C67—24no—
34#379×C67—24no—
35C4×C22⋊C4×C67—24no—
36C2×#95×C67C2212yescomplemented
37C2×#95×C67C2212yescomplemented
38C2×#95×C67C2212yescomplemented
39C2×#95×C67C2212yescomplemented
40C2×#95×C67C2212yescomplemented
41C2×#95×C67C2212yescomplemented
42C25×C67—24no—
43C25×C67—24no—
44C25×C67—22no—
45C25×C67—22no—
46C25×C67—22no—
47C25×C67—22no—
48C25×C67—22no—
49C25×C67—22no—
50C25×C67—42no—
51C25×C67—42no—
52C25×C67C2×C414yes—
53C25×C67C2311yescharacteristic
54C25×C67C2311yescharacteristic
55C25×C67C2311yescharacteristic
56C23×C4×C67—22no—
57C23×C4×C67—22no—
58C23×C4×C67—22no—
59C23×C4×C67—22no—
60C23×C4×C67—24no—
61C23×C4×C67—24no—
62C23×C4×C67—42no—
63C23×C4×C67—42no—
64C23×C4×C67C2×C414yes—
65C23×C4×C67C2×C414yes—
66C23×C4×C67C2312yes—
67C23×C4×C67C2312yes—
68C23×C4×C67C2311yescharacteristic
69C23×C4×C67C2311yescharacteristic
70C23×C4×C67C2312yes—
71C23×C4×C67C2312yes—
72C23×C4×C67C2311yescharacteristic
73C23×C4×C67C2311yescharacteristic
74C2×C4⋊C4×C67—24no—
75C2×C4⋊C4×C67—24no—
76C2×C4⋊C4×C67—42no—
77C2×C22⋊C4×C67—24no—
78C2×C22⋊C4×C67—22no—
79C2×C22⋊C4×C67—22no—
80C2×C22⋊C4×C67—22no—
81C2×C22⋊C4×C67—22no—
82C2×C22⋊C4×C67—24no—
83C2×C22⋊C4×C67—24no—
84C2×C22⋊C4×C67—232no—
85C2×C22⋊C4×C67—22no—
86C2×C22⋊C4×C67—22no—
87C2×C22⋊C4×C67—22no—
88C2×C22⋊C4×C67—24no—
89C2×C22⋊C4×C67—24no—
90C2×C22⋊C4×C67—24no—
91C2×C22⋊C4×C67—24no—
92C2×C22⋊C4×C67—22no—
93C2×C22⋊C4×C67—22no—
94C2×C22⋊C4×C67—22no—
95C2×C22⋊C4×C67—24no—
96C2×C22⋊C4×C67—24no—
97C2×C22⋊C4×C67—24no—
98C2×C22⋊C4×C67—24no—
99C2×C22⋊C4×C67—42no—
100C2×C22⋊C4×C67—42no—
101C2×C22⋊C4×C67—42no—
102C2×C22⋊C4×C67—42no—
103C2×C22⋊C4×C67C2×C414yes—
104C2×C22⋊C4×C67C2×C414yes—
105C2×C22⋊C4×C67C2×C414yes—
106C2×C22⋊C4×C67C2×C414yes—
107C2×C22⋊C4×C67D414yes—
108C2×C22⋊C4×C67D414yes—
109C2×C22⋊C4×C67D418yes—
110C2×C42×C67—24no—
111C2×C42×C67—24no—
112C2×C42×C67—42no—
113#95×C67—24no—
114#95×C67—24no—
115#95×C67—24no—
116#95×C67—24no—
117#95×C67—42no—
118#95×C67—42no—
119C24×C67—22no—
120C24×C67—22no—
121C24×C67—22no—
122C24×C67—22no—
123C24×C67—216no—
124C24×C67—216no—
125C24×C67—28no—
126C24×C67—28no—
127C24×C67—28no—
128C24×C67—22no—
129C24×C67—21no—
130C24×C67—21no—
131C24×C67—21no—
132C24×C67—21no—
133C24×C67—21no—
134C24×C67—21no—
135C24×C67—22no—
136C24×C67—21no—
137C24×C67—21no—
138C24×C67—21no—
139C24×C67—21no—
140C24×C67—21no—
141C24×C67—21no—
142C24×C67—22no—
143C24×C67—22no—
144C24×C67—22no—
145C24×C67—22no—
146C24×C67—28no—
147C24×C67—28no—
148C24×C67—44no—
149C24×C67—44no—
150C24×C67—48no—
151C24×C67—48no—
152C24×C67—48no—
153C24×C67—48no—
154C24×C67—48no—
155C24×C67—48no—
156C24×C67—48no—
157C24×C67—48no—
158C24×C67—48no—
159C24×C67—48no—
160C24×C67—44no—
161C24×C67—44no—
162C24×C67—44no—
163C24×C67—44no—
164C24×C67C22×C412yes—
165C24×C67C22×C412yes—
166C24×C67C22×C412yes—
167C24×C67C2×D414yes—
168C24×C67C2×D412yes—
169C24×C67C2×D412yes—
170C24×C67#4114yes—
171C24×C67#4112yes—
172C24×C67#4112yes—
173C24×C67#4112yes—
174C24×C67#4112yes—
175C24×C67C2411yescharacteristic
176C22×C4×C67—21no—
177C22×C4×C67—21no—
178C22×C4×C67—21no—
179C22×C4×C67—21no—
180C22×C4×C67—22no—
181C22×C4×C67—22no—
182C22×C4×C67—28no—
183C22×C4×C67—28no—
184C22×C4×C67—22no—
185C22×C4×C67—22no—
186C22×C4×C67—22no—
187C22×C4×C67—22no—
188C22×C4×C67—22no—
189C22×C4×C67—21no—
190C22×C4×C67—21no—
191C22×C4×C67—22no—
192C22×C4×C67—22no—
193C22×C4×C67—22no—
194C22×C4×C67—22no—
195C22×C4×C67—22no—
196C22×C4×C67—21no—
197C22×C4×C67—21no—
198C22×C4×C67—22no—
199C22×C4×C67—22no—
200C22×C4×C67—22no—
201C22×C4×C67—22no—
202C22×C4×C67—22no—
203C22×C4×C67—22no—
204C22×C4×C67—28no—
205C22×C4×C67—28no—
206C22×C4×C67—22no—
207C22×C4×C67—22no—
208C22×C4×C67—22no—
209C22×C4×C67—22no—
210C22×C4×C67—22no—
211C22×C4×C67—22no—
212C22×C4×C67—22no—
213C22×C4×C67—22no—
214C22×C4×C67—22no—
215C22×C4×C67—22no—
216C22×C4×C67—22no—
217C22×C4×C67—22no—
218C22×C4×C67—22no—
219C22×C4×C67—22no—
220C22×C4×C67—44no—
221C22×C4×C67—44no—
222C22×C4×C67—48no—
223C22×C4×C67—48no—
224C22×C4×C67—48no—
225C22×C4×C67—48no—
226C22×C4×C67C22×C412yes—
227C22×C4×C67C22×C412yes—
228C22×C4×C67C22×C412yes—
229C22×C4×C67C22×C412yes—
230C22×C4×C67C2×D414yes—
231C22×C4×C67C2×D414yes—
232C22×C4×C67C2×D414yes—
233C22×C4×C67C2×D414yes—
234C4⋊C4×C67—48no—
235C22⋊C4×C67—28no—
236C22⋊C4×C67—28no—
237C22⋊C4×C67—28no—
238C22⋊C4×C67—28no—
239C22⋊C4×C67—28no—
240C22⋊C4×C67—48no—
241C22⋊C4×C67—48no—
242C22⋊C4×C67—48no—
243C22⋊C4×C67—48no—
244C22⋊C4×C67—44no—
245C22⋊C4×C67—44no—
246C22⋊C4×C67C22⋊C4116yescomplemented
247C42×C67—48no—
248C23×C67—22no—
249C23×C67—22no—
250C23×C67—22no—
251C23×C67—22no—
252C23×C67—24no—
253C23×C67—24no—
254C23×C67—24no—
255C23×C67—24no—
256C23×C67—24no—
257C23×C67—24no—
258C23×C67—24no—
259C23×C67—24no—
260C23×C67—24no—
261C23×C67—24no—
262C23×C67—24no—
263C23×C67—24no—
264C23×C67—232no—
265C23×C67—22no—
266C23×C67—22no—
267C23×C67—22no—
268C23×C67—22no—
269C23×C67—22no—
270C23×C67—22no—
271C23×C67—22no—
272C23×C67—22no—
273C23×C67—22no—
274C23×C67—22no—
275C23×C67—22no—
276C23×C67—22no—
277C23×C67—24no—
278C23×C67—24no—
279C23×C67—24no—
280C23×C67—24no—
281C23×C67—24no—
282C23×C67—24no—
283C23×C67—24no—
284C23×C67—24no—
285C23×C67—24no—
286C23×C67—24no—
287C23×C67—24no—
288C23×C67—24no—
289C23×C67—416no—
290C23×C67—416no—
291C23×C67—416no—
292C23×C67—416no—
293C23×C67—416no—
294C23×C67—432no—
295C23×C67—432no—
296C23×C67—432no—
297C23×C67—432no—
298C23×C67—41no—
299C23×C67—41no—
300C23×C67—41no—
301C23×C67—41no—
302C23×C67—41no—
303C23×C67—41no—
304C23×C67—41no—
305C23×C67—41no—
306C23×C67—42no—
307C23×C67—42no—
308C23×C67—42no—
309C23×C67—42no—
310C23×C67—42no—
311C23×C67—42no—
312C23×C67—42no—
313C23×C67—42no—
314C23×C67—42no—
315C23×C67—42no—
316C23×C67—42no—
317C23×C67—42no—
318C23×C67—416no—
319C23×C67C2×C22⋊C414yes—
320C23×C67#11714yes—
321C23×C67#11714yes—
322C23×C67C4×D414yes—
323C23×C67C4×D414yes—
324C23×C67#12114yes—
325C23×C67#12314yes—
326C23×C67#12414yes—
327C23×C67#12614yes—
328C23×C67C23×C411yescharacteristic
329C23×C67C22×D412yes—
330C23×C67C22×D411yescharacteristic
331C23×C67C22×D411yescharacteristic
332C23×C67C2×#4111yescharacteristic
333C23×C67C2×#4111yescharacteristic
334C23×C67C2×#4112yes—
335C23×C67C2×#4111yescharacteristic
336C23×C67C2×#4111yescharacteristic
337C23×C67H(5,𝔽2)12yes—
338C23×C67H(5,𝔽2)12yes—
339C2×C4×C67—22no—
340C2×C4×C67—22no—
341C2×C4×C67—22no—
342C2×C4×C67—22no—
343C2×C4×C67—24no—
344C2×C4×C67—24no—
345C2×C4×C67—24no—
346C2×C4×C67—24no—
347C2×C4×C67—22no—
348C2×C4×C67—22no—
349C2×C4×C67—22no—
350C2×C4×C67—22no—
351C2×C4×C67—22no—
352C2×C4×C67—22no—
353C2×C4×C67—24no—
354C2×C4×C67—24no—
355C2×C4×C67—24no—
356C2×C4×C67—24no—
357C2×C4×C67—24no—
358C2×C4×C67—24no—
359C2×C4×C67—416no—
360C2×C4×C67—416no—
361C2×C4×C67—42no—
362C2×C4×C67—42no—
363C2×C4×C67—42no—
364C2×C4×C67—42no—
365C2×C4×C67—42no—
366C2×C4×C67—42no—
367C2×C4×C67—42no—
368C2×C4×C67—42no—
369C2×C4×C67—42no—
370C2×C4×C67—42no—
371C2×C4×C67—42no—
372C2×C4×C67—42no—
373C2×C4×C67—42no—
374C2×C4×C67—42no—
375C2×C4×C67—42no—
376C2×C4×C67—42no—
377C2×C4×C67—42no—
378C2×C4×C67—42no—
379C2×C4×C67—42no—
380C2×C4×C67—42no—
381C2×C4×C67—42no—
382C2×C4×C67—42no—
383C2×C4×C67—42no—
384C2×C4×C67—42no—
385C2×C4×C67—42no—
386C2×C4×C67—42no—
387C2×C4×C67C2×C22⋊C414yes—
388C2×C4×C67C2×C22⋊C414yes—
389C22×C67—24no—
390C22×C67—24no—
391C22×C67—24no—
392C22×C67—24no—
393C22×C67—24no—
394C22×C67—28no—
395C22×C67—28no—
396C22×C67—28no—
397C22×C67—28no—
398C22×C67—24no—
399C22×C67—24no—
400C22×C67—24no—
401C22×C67—24no—
402C22×C67—24no—
403C22×C67—24no—
404C22×C67—24no—
405C22×C67—464no—
406C22×C67—42no—
407C22×C67—42no—
408C22×C67—42no—
409C22×C67—42no—
410C22×C67—42no—
411C22×C67—42no—
412C22×C67—44no—
413C22×C67—44no—
414C22×C67—44no—
415C22×C67—44no—
416C22×C67—44no—
417C22×C67—44no—
418C22×C67—44no—
419C22×C67—44no—
420C22×C67—42no—
421C22×C67—42no—
422C22×C67#38818yescomplemented
423C22×C67C22×C22⋊C411yescharacteristic
424C22×C67C2×#11711yescharacteristic
425C22×C67C2×#11711yescharacteristic
426C22×C67C2×C4×D411yescharacteristic
427C22×C67C2×C4×D411yescharacteristic
428C22×C67#51811yescharacteristic
429C22×C67#51811yescharacteristic
430C22×C67C2×#12111yescharacteristic
431C22×C67C2×#12311yescharacteristic
432C22×C67#52512yes—
433C22×C67#52512yes—
434C22×C67C2×#12411yescharacteristic
435C22×C67C2×#12611yescharacteristic
436C22×C67#53812yes—
437C22×C67#53812yes—
438C22×C67D4212yes—
439C22×C67D4212yes—
440C22×C67#54612yes—
441C22×C67#54612yes—
442C22×C67#54612yes—
443C22×C67#54612yes—
444C22×C67#55112yes—
445C22×C67#55112yes—
446C4×C67—24no—
447C4×C67—24no—
448C4×C67—42no—
449C4×C67—42no—
450C4×C67—44no—
451C4×C67—44no—
452C4×C67—82no—
453C4×C67—82no—
454#13873C6711yesmaximal, characteristic, direct product factor, Sylow
455C2×C67—28no—
456C2×C67—44no—
457C2×C67—44no—
458C2×C67#228011yescharacteristic
459C2×C67C2×#38811yescharacteristic
460C2×C67#231211yescharacteristic
461C2×C67D4×C22⋊C411yescharacteristic
462C2×C67D4×C22⋊C411yescharacteristic
463C2×C67#234211yescharacteristic
464C2×C67#234211yescharacteristic
465C2×C67#241812yes—
466C2×C67#242412yes—
467C2×C67#247212yes—
468C2×C67#248012yes—
469C23×C22⋊C4C2×C6711yescharacteristic
470C2×#388C2×C6712yescomplemented
471C2×#380C2×C6711yescharacteristic, complemented
472C2×#379C2×C6711yescharacteristic
473C2×#379C2×C6711yescharacteristic
474C2×C4×C22⋊C4C2×C6711yescharacteristic, complemented
475#1440C2×C6712yescomplemented
476#1439C2×C6712yescomplemented
477#1437C2×C6712yescomplemented
478C22⋊#95C2×C6711yescharacteristic, complemented
479C22⋊#95C2×C6711yescharacteristic, complemented
480C67#1387311yescharacteristic, direct product factor, Sylow
481C26C22×C6711yescharacteristic
482C24×C4C22×C6711yescharacteristic
483C24×C4C22×C6711yescharacteristic
484C22×C4⋊C4C22×C6712yescomplemented
485C22×C22⋊C4—28no—
486C22×C22⋊C4C4×C6718yescomplemented
487C22×C22⋊C4C22×C6711yescharacteristic
488C22×C22⋊C4C22×C6711yescharacteristic
489C22×C22⋊C4C22×C6712yes—
490C22×C22⋊C4C22×C6712yes—
491C22×C22⋊C4C22×C6712yes—
492C22×C22⋊C4C22×C6712yes—
493C22×C22⋊C4C22×C6711yescharacteristic
494C22×C22⋊C4C22×C6711yescharacteristic
495C22×C22⋊C4C22×C6711yescharacteristic
496C22×C22⋊C4C22×C6711yescharacteristic
497C22×C22⋊C4C22×C6711yescharacteristic
498C22×C22⋊C4C22×C6711yescharacteristic
499C22×C42C22×C6712yescomplemented
500#388—28no—
501#380—24no—
502#379—24no—
503#379—24no—
504C4×C22⋊C4—24no—
505C2×#95C22×C6712yescomplemented
506C2×#95C22×C6712yescomplemented
507C2×#95C22×C6712yescomplemented
508C2×#95C22×C6712yescomplemented
509C2×#95C22×C6712yescomplemented
510C2×#95C22×C6712yescomplemented
511C25—24no—
512C25—24no—
513C25—22no—
514C25—22no—
515C25—22no—
516C25—22no—
517C25—22no—
518C25—22no—
519C25—42no—
520C25—42no—
521C25C2×C4×C6714yes—
522C25C23×C6711yescharacteristic
523C25C23×C6711yescharacteristic
524C25C23×C6711yescharacteristic
525C23×C4—22no—
526C23×C4—22no—
527C23×C4—22no—
528C23×C4—22no—
529C23×C4—24no—
530C23×C4—24no—
531C23×C4—42no—
532C23×C4—42no—
533C23×C4C2×C4×C6714yes—
534C23×C4C2×C4×C6714yes—
535C23×C4C23×C6712yes—
536C23×C4C23×C6712yes—
537C23×C4C23×C6711yescharacteristic
538C23×C4C23×C6711yescharacteristic
539C23×C4C23×C6712yes—
540C23×C4C23×C6712yes—
541C23×C4C23×C6711yescharacteristic
542C23×C4C23×C6711yescharacteristic
543C2×C4⋊C4—24no—
544C2×C4⋊C4—24no—
545C2×C4⋊C4—42no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—232no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4C2×C4×C6714yes—
573C2×C22⋊C4C2×C4×C6714yes—
574C2×C22⋊C4C2×C4×C6714yes—
575C2×C22⋊C4C2×C4×C6714yes—
576C2×C22⋊C4D4×C6714yes—
577C2×C22⋊C4D4×C6714yes—
578C2×C22⋊C4D4×C6718yes—
579C2×C42—24no—
580C2×C42—24no—
581C2×C42—42no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—42no—
587#95—42no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—216no—
593C24—216no—
594C24—28no—
595C24—28no—
596C24—28no—
597C24—22no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—22no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—28no—
616C24—28no—
617C24—44no—
618C24—44no—
619C24—48no—
620C24—48no—
621C24—48no—
622C24—48no—
623C24—48no—
624C24—48no—
625C24—48no—
626C24—48no—
627C24—48no—
628C24—48no—
629C24—44no—
630C24—44no—
631C24—44no—
632C24—44no—
633C24C22×C4×C6712yes—
634C24C22×C4×C6712yes—
635C24C22×C4×C6712yes—
636C24C2×D4×C6714yes—
637C24C2×D4×C6712yes—
638C24C2×D4×C6712yes—
639C24#41×C6714yes—
640C24#41×C6712yes—
641C24#41×C6712yes—
642C24#41×C6712yes—
643C24#41×C6712yes—
644C24C24×C6711yescharacteristic
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—28no—
652C22×C4—28no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—28no—
674C22×C4—28no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—48no—
692C22×C4—48no—
693C22×C4—48no—
694C22×C4—48no—
695C22×C4C22×C4×C6712yes—
696C22×C4C22×C4×C6712yes—
697C22×C4C22×C4×C6712yes—
698C22×C4C22×C4×C6712yes—
699C22×C4C2×D4×C6714yes—
700C22×C4C2×D4×C6714yes—
701C22×C4C2×D4×C6714yes—
702C22×C4C2×D4×C6714yes—
703C4⋊C4—48no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—48no—
710C22⋊C4—48no—
711C22⋊C4—48no—
712C22⋊C4—48no—
713C22⋊C4—44no—
714C22⋊C4—44no—
715C22⋊C4C22⋊C4×C67116yescomplemented
716C42—48no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—232no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—416no—
759C23—416no—
760C23—416no—
761C23—416no—
762C23—416no—
763C23—432no—
764C23—432no—
765C23—432no—
766C23—432no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—416no—
788C23C2×C22⋊C4×C6714yes—
789C23#117×C6714yes—
790C23#117×C6714yes—
791C23C4×D4×C6714yes—
792C23C4×D4×C6714yes—
793C23#121×C6714yes—
794C23#123×C6714yes—
795C23#124×C6714yes—
796C23#126×C6714yes—
797C23C23×C4×C6711yescharacteristic
798C23C22×D4×C6712yes—
799C23C22×D4×C6711yescharacteristic
800C23C22×D4×C6711yescharacteristic
801C23C2×#41×C6711yescharacteristic
802C23C2×#41×C6711yescharacteristic
803C23C2×#41×C6712yes—
804C23C2×#41×C6711yescharacteristic
805C23C2×#41×C6711yescharacteristic
806C23H(5,𝔽2)×C6712yes—
807C23H(5,𝔽2)×C6712yes—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—416no—
829C2×C4—416no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4C2×C22⋊C4×C6714yes—
857C2×C4C2×C22⋊C4×C6714yes—
858C22—24no—
859C22—24no—
860C22—24no—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—28no—
865C22—28no—
866C22—28no—
867C22—28no—
868C22—24no—
869C22—24no—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—24no—
874C22—464no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—44no—
884C22—44no—
885C22—44no—
886C22—44no—
887C22—44no—
888C22—44no—
889C22—44no—
890C22—44no—
891C22#388×C6718yescomplemented
892C22C22×C22⋊C4×C6711yescharacteristic
893C22C2×#117×C6711yescharacteristic
894C22C2×#117×C6711yescharacteristic
895C22C2×C4×D4×C6711yescharacteristic
896C22C2×C4×D4×C6711yescharacteristic
897C22#518×C6711yescharacteristic
898C22#518×C6711yescharacteristic
899C22C2×#121×C6711yescharacteristic
900C22C2×#123×C6711yescharacteristic
901C22#525×C6712yes—
902C22#525×C6712yes—
903C22C2×#124×C6711yescharacteristic
904C22C2×#126×C6711yescharacteristic
905C22#538×C6712yes—
906C22#538×C6712yes—
907C22D42×C6712yes—
908C22D42×C6712yes—
909C22#546×C6712yes—
910C22#546×C6712yes—
911C22#546×C6712yes—
912C22#546×C6712yes—
913C22#551×C6712yes—
914C22#551×C6712yes—
915C4—24no—
916C4—24no—
917C4—42no—
918C4—42no—
919C4—44no—
920C4—44no—
921C4—82no—
922C4—82no—
923C2—28no—
924C2—44no—
925C2—44no—
926C2C67×#228011yescharacteristic
927C2C2×#388×C6711yescharacteristic
928C2C67×#231211yescharacteristic
929C2D4×C22⋊C4×C6711yescharacteristic
930C2D4×C22⋊C4×C6711yescharacteristic
931C2C67×#234211yescharacteristic
932C2C67×#234211yescharacteristic
933C2C67×#241812yes—
934C2C67×#242412yes—
935C2C67×#247212yes—
936C2C67×#248012yes—
subgroupG/H
center, socleC24×C67C24
commutatorC23C23×C4×C67
Frattini, cosocleC24C24×C67
prime radicalC26×C67C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C67 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#388×C67C2semidirect
3. C2×#380×C67C2semidirect
6. C2×C4×C22⋊C4×C67C2semidirect
7. C67×#1440C2semidirect
8. C67×#1439C2semidirect
9. C67×#1437C2semidirect
10. C67×C22⋊#95C2semidirect
11. C67×C22⋊#95C2semidirect
15. C22×C4⋊C4×C67C22semidirect
17. C22×C22⋊C4×C67C4semidirect
30. C22×C42×C67C22semidirect
36. C2×#95×C67C22semidirect
37. C2×#95×C67C22semidirect
38. C2×#95×C67C22semidirect
39. C2×#95×C67C22semidirect
40. C2×#95×C67C22semidirect
41. C2×#95×C67C22semidirect
246. C22⋊C4×C67C22⋊C4semidirect
422. C22×C67#388semidirect
454. #13873C67direct (N × H)
470. C2×#388C2×C67semidirect
471. C2×#380C2×C67semidirect
474. C2×C4×C22⋊C4C2×C67semidirect
475. #1440C2×C67semidirect
476. #1439C2×C67semidirect
477. #1437C2×C67semidirect
478. C22⋊#95C2×C67semidirect
479. C22⋊#95C2×C67semidirect
480. C67#13873direct (N × H)
484. C22×C4⋊C4C22×C67semidirect
486. C22×C22⋊C4C4×C67semidirect
499. C22×C42C22×C67semidirect
505. C2×#95C22×C67semidirect
506. C2×#95C22×C67semidirect
507. C2×#95C22×C67semidirect
508. C2×#95C22×C67semidirect
509. C2×#95C22×C67semidirect
510. C2×#95C22×C67semidirect
715. C22⋊C4C22⋊C4×C67semidirect
891. C22#388×C67semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C672
C2×#388×C672
C2×#380×C672
C2×#379×C672
C2×C4×C22⋊C4×C672
C67×#14402
C67×#14392
C67×#14372
C67×C22⋊#952
#1387367