Finite Group Databasebeta

← C67×#22424 #30701675

Subgroups — C67×#22424 #30701675

Order 17152.

1598 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C67C211yesmaximal, characteristic
2C2×#435×C67C211yesmaximal, characteristic, complemented
3C2×#418×C67C211yesmaximal, characteristic, complemented
4C2×#416×C67C211yesmaximal, characteristic, complemented
5C67×#2354C211yesmaximal, characteristic, complemented
6C67×#1983C211yesmaximal, characteristic, complemented
7C67×#1959C211yesmaximal, characteristic, complemented
8C67×#1894C211yesmaximal, characteristic, complemented
9C67×#1893C211yesmaximal, characteristic, complemented
10C67×#1875C211yesmaximal, characteristic, complemented
11C67×#1873C211yesmaximal, characteristic, complemented
12C67×#1802C211yesmaximal, characteristic, complemented
13C67×#1788C211yesmaximal, characteristic, complemented
14C67×#1786C211yesmaximal, characteristic, complemented
15C67×#1762C211yesmaximal, characteristic, complemented
16C22×#41×C67C2211yescharacteristic
17C23×D4×C67C2211yescharacteristic
18C22×M16×C67C2211yescharacteristic
19C23×C8×C67C2211yescharacteristic, complemented
20#546×C67—24no—
21#546×C67C418yescomplemented
22C2×#124×C67C2211yescharacteristic
23C2×#123×C67—21no—
24C2×C22⋊Q8×C67C2211yescharacteristic
25C2×#121×C67—21no—
26C2×#121×C67C2211yescharacteristic
27C2×#120×C67—21no—
28C2×C4×D4×C67C2211yescharacteristic
29C2×C4×D4×C67C2211yescharacteristic
30C2×#117×C67C2211yescharacteristic
31C2×#117×C67C2211yescharacteristic, complemented
32C22×C22⋊C4×C67—21no—
33#435×C67—24no—
34C2×C4⋊C8×C67C2211yescharacteristic, complemented
35#418×C67—24no—
36#416×C67—24no—
37C2×#103×C67C2211yescharacteristic, complemented
38C2×#103×C67C2211yescharacteristic, complemented
39C2×#103×C67C2211yescharacteristic, complemented
40C2×#103×C67C2211yescharacteristic, complemented
41C2×#102×C67C2211yescharacteristic
42C2×#102×C67C2211yescharacteristic
43C2×#102×C67C2211yescharacteristic
44C2×#102×C67C2211yescharacteristic
45C2×#102×C67C2211yescharacteristic
46C2×#102×C67C2211yescharacteristic
47C2×#102×C67C2211yescharacteristic
48C2×#102×C67C2211yescharacteristic
49C2×C22⋊C8×C67C2211yescharacteristic
50C2×C22⋊C8×C67C2211yescharacteristic, complemented
51C2×#97×C67C2211yescharacteristic, complemented
52#390×C67—21no—
53#388×C67—21no—
54#388×C67—21no—
55#384×C67C2211yescharacteristic, complemented
56#380×C67C2211yescharacteristic
57#380×C67C2211yescharacteristic, complemented
58C4×C4⋊C4×C67—21no—
59C4×C4⋊C4×C67C2211yescharacteristic, complemented
60#340×C67C2211yescharacteristic, complemented
61#340×C67C2211yescharacteristic, complemented
62#340×C67C2211yescharacteristic, complemented
63#340×C67C2211yescharacteristic, complemented
64C25×C67—21no—
65C2×#41×C67—22no—
66C2×#41×C67—22no—
67C2×#41×C67—22no—
68C2×#41×C67—41no—
69C2×#41×C67—41no—
70C2×#41×C67C2×C414yes—
71C22×Q8×C67C2311yescharacteristic
72C22×D4×C67—22no—
73C22×D4×C67—22no—
74C22×D4×C67—21no—
75C22×D4×C67—21no—
76C22×D4×C67—21no—
77C22×D4×C67—22no—
78C22×D4×C67—41no—
79C22×D4×C67—41no—
80C22×D4×C67C2×C414yes—
81C22×D4×C67D411yescharacteristic
82C22×D4×C67C2311yescharacteristic
83C22×D4×C67C2311yescharacteristic
84C23×C4×C67—21no—
85C23×C4×C67—21no—
86C23×C4×C67C2311yescharacteristic
87C23×C4×C67C2311yescharacteristic
88C2×M16×C67—22no—
89C2×M16×C67—22no—
90C2×M16×C67—41no—
91C22×C8×C67—22no—
92C22×C8×C67—22no—
93C22×C8×C67—41no—
94C22×C8×C67C2311yescharacteristic
95C22×C8×C67C2311yescharacteristic
96C22×C8×C67C2311yescharacteristic
97C22×C8×C67C2311yescharacteristic
98#124×C67—22no—
99#124×C67C2×C414yes—
100#123×C67—28no—
101C22⋊Q8×C67—22no—
102C22⋊Q8×C67C2×C414yes—
103#121×C67—22no—
104#121×C67—28no—
105#121×C67C2×C414yes—
106#120×C67—28no—
107C4×D4×C67—22no—
108C4×D4×C67C2×C414yes—
109C4×D4×C67C2×C414yes—
110C4×D4×C67D414yes—
111#117×C67—22no—
112#117×C67—22no—
113#117×C67—41no—
114#117×C67—41no—
115C2×C4⋊C4×C67—21no—
116C2×C4⋊C4×C67—21no—
117C2×C4⋊C4×C67—21no—
118C2×C4⋊C4×C67D411yescharacteristic
119C2×C4⋊C4×C67C2311yescharacteristic
120C2×C4⋊C4×C67C2311yescharacteristic
121C2×C4⋊C4×C67C2311yescharacteristic
122C2×C4⋊C4×C67C2311yescharacteristic
123C2×C4⋊C4×C67C2311yescharacteristic
124C2×C22⋊C4×C67—21no—
125C2×C22⋊C4×C67—21no—
126C2×C22⋊C4×C67—21no—
127C2×C22⋊C4×C67—21no—
128C2×C22⋊C4×C67—21no—
129C2×C22⋊C4×C67—28no—
130C2×C22⋊C4×C67—21no—
131C2×C22⋊C4×C67—21no—
132C2×C22⋊C4×C67—21no—
133C2×C22⋊C4×C67—21no—
134C2×C22⋊C4×C67D411yescharacteristic
135C2×C22⋊C4×C67D411yescharacteristic
136C2×C42×C67—21no—
137C2×C42×C67—21no—
138C2×C42×C67—21no—
139C2×C42×C67C2311yescharacteristic
140C4⋊C8×C67—22no—
141#103×C67—22no—
142#103×C67—22no—
143#103×C67—41no—
144#103×C67—41no—
145#102×C67—22no—
146#102×C67—22no—
147#102×C67—22no—
148#102×C67—22no—
149#102×C67—22no—
150#102×C67—41no—
151#102×C67—41no—
152#102×C67D414yescomplemented
153C22⋊C8×C67—22no—
154C22⋊C8×C67—22no—
155#97×C67—22no—
156#95×C67—21no—
157#95×C67—21no—
158#95×C67—21no—
159C24×C67—21no—
160C24×C67—21no—
161C24×C67—24no—
162C24×C67—42no—
163C24×C67—42no—
164C24×C67—42no—
165C24×C67—42no—
166C24×C67—81no—
167C24×C67—81no—
168C24×C67C2×D411yescharacteristic
169C24×C67C2×D411yescharacteristic
170#41×C67—28no—
171#41×C67—44no—
172#41×C67—44no—
173#41×C67—44no—
174C2×Q8×C67—21no—
175C2×Q8×C67—21no—
176C2×Q8×C67—21no—
177C2×Q8×C67—21no—
178C2×Q8×C67—21no—
179C2×Q8×C67C22×C412yes—
180C2×D4×C67—28no—
181C2×D4×C67—24no—
182C2×D4×C67—24no—
183C2×D4×C67—24no—
184C2×D4×C67—21no—
185C2×D4×C67—21no—
186C2×D4×C67—21no—
187C2×D4×C67—21no—
188C2×D4×C67—21no—
189C2×D4×C67—21no—
190C2×D4×C67—21no—
191C2×D4×C67—21no—
192C2×D4×C67—44no—
193C2×D4×C67—44no—
194C2×D4×C67—44no—
195C2×D4×C67—41no—
196C2×D4×C67—41no—
197C2×D4×C67—42no—
198C2×D4×C67—42no—
199C2×D4×C67—42no—
200C2×D4×C67—42no—
201C2×D4×C67—81no—
202C2×D4×C67—81no—
203C2×D4×C67C22⋊C414yes—
204C2×D4×C67C22×C412yes—
205C2×D4×C67C22×C412yes—
206C2×D4×C67C2×D412yes—
207C2×D4×C67#4112yes—
208C22×C4×C67—21no—
209C22×C4×C67—21no—
210C22×C4×C67—21no—
211C22×C4×C67—21no—
212C22×C4×C67—21no—
213C22×C4×C67—21no—
214C22×C4×C67—21no—
215C22×C4×C67—21no—
216C22×C4×C67—21no—
217C22×C4×C67—21no—
218C22×C4×C67—21no—
219C22×C4×C67—24no—
220C22×C4×C67—24no—
221C22×C4×C67—21no—
222C22×C4×C67—21no—
223C22×C4×C67—21no—
224C22×C4×C67—42no—
225C22×C4×C67—42no—
226C22×C4×C67—81no—
227C22×C4×C67—81no—
228C22×C4×C67C22×C412yes—
229C22×C4×C67C22×C412yes—
230C22×C4×C67C2×D411yescharacteristic
231C22×C4×C67C2×D411yescharacteristic
232C22×C4×C67C2×D411yescharacteristic
233C22×C4×C67C2×D411yescharacteristic
234C22×C4×C67C2×D412yes—
235C22×C4×C67C2×D412yes—
236C22×C4×C67C2411yescharacteristic
237M16×C67—44no—
238C2×C8×C67—21no—
239C2×C8×C67—21no—
240C2×C8×C67—21no—
241C2×C8×C67—21no—
242C2×C8×C67—21no—
243C2×C8×C67—21no—
244C2×C8×C67—21no—
245C2×C8×C67—21no—
246C2×C8×C67—21no—
247C2×C8×C67—21no—
248C2×C8×C67—21no—
249C2×C8×C67—44no—
250C2×C8×C67C2×D412yes—
251C4⋊C4×C67—24no—
252C4⋊C4×C67—21no—
253C4⋊C4×C67—21no—
254C4⋊C4×C67—21no—
255C4⋊C4×C67—21no—
256C4⋊C4×C67—21no—
257C4⋊C4×C67—21no—
258C4⋊C4×C67—21no—
259C4⋊C4×C67—21no—
260C4⋊C4×C67—42no—
261C4⋊C4×C67—81no—
262C4⋊C4×C67C22⋊C414yes—
263C4⋊C4×C67C22×C412yes—
264C4⋊C4×C67C2×D412yes—
265C22⋊C4×C67—24no—
266C22⋊C4×C67—24no—
267C22⋊C4×C67—24no—
268C22⋊C4×C67—24no—
269C22⋊C4×C67—24no—
270C22⋊C4×C67—42no—
271C22⋊C4×C67—42no—
272C22⋊C4×C67—81no—
273C22⋊C4×C67—81no—
274C22⋊C4×C67C22⋊C414yes—
275C22⋊C4×C67C22⋊C414yes—
276C42×C67—42no—
277C42×C67—42no—
278C42×C67—42no—
279C42×C67C22×C412yes—
280C42×C67C2×D412yes—
281C23×C67—22no—
282C23×C67—21no—
283C23×C67—21no—
284C23×C67—22no—
285C23×C67—21no—
286C23×C67—21no—
287C23×C67—22no—
288C23×C67—21no—
289C23×C67—21no—
290C23×C67—21no—
291C23×C67—21no—
292C23×C67—21no—
293C23×C67—21no—
294C23×C67—21no—
295C23×C67—21no—
296C23×C67—22no—
297C23×C67—48no—
298C23×C67—48no—
299C23×C67—41no—
300C23×C67—41no—
301C23×C67—41no—
302C23×C67—41no—
303C23×C67—41no—
304C23×C67—41no—
305C23×C67—41no—
306C23×C67—41no—
307C23×C67—41no—
308C23×C67—41no—
309C23×C67—84no—
310C23×C67—84no—
311C23×C67—84no—
312C23×C67—84no—
313C23×C67—84no—
314C23×C67C2×C22⋊C412yes—
315C23×C67C2×C22⋊C412yes—
316C23×C67C22×D411yescharacteristic
317Q8×C67—22no—
318Q8×C67—22no—
319Q8×C67—41no—
320Q8×C67—41no—
321D4×C67—22no—
322D4×C67—22no—
323D4×C67—22no—
324D4×C67—22no—
325D4×C67—22no—
326D4×C67—44no—
327D4×C67—48no—
328D4×C67—48no—
329D4×C67—41no—
330D4×C67—41no—
331D4×C67—84no—
332D4×C67C4×D414yes—
333C2×C4×C67—21no—
334C2×C4×C67—21no—
335C2×C4×C67—21no—
336C2×C4×C67—21no—
337C2×C4×C67—21no—
338C2×C4×C67—21no—
339C2×C4×C67—21no—
340C2×C4×C67—21no—
341C2×C4×C67—22no—
342C2×C4×C67—22no—
343C2×C4×C67—22no—
344C2×C4×C67—22no—
345C2×C4×C67—22no—
346C2×C4×C67—22no—
347C2×C4×C67—22no—
348C2×C4×C67—22no—
349C2×C4×C67—22no—
350C2×C4×C67—22no—
351C2×C4×C67—22no—
352C2×C4×C67—48no—
353C2×C4×C67—41no—
354C2×C4×C67—41no—
355C2×C4×C67—41no—
356C2×C4×C67—41no—
357C2×C4×C67—41no—
358C2×C4×C67—41no—
359C2×C4×C67—41no—
360C2×C4×C67—41no—
361C2×C4×C67—41no—
362C2×C4×C67—41no—
363C2×C4×C67—41no—
364C2×C4×C67—41no—
365C2×C4×C67—41no—
366C2×C4×C67—41no—
367C2×C4×C67—41no—
368C2×C4×C67—84no—
369C2×C4×C67C2×C22⋊C412yes—
370C2×C4×C67C2×C22⋊C412yes—
371C2×C4×C67C2×C22⋊C412yes—
372C2×C4×C67C2×C22⋊C412yes—
373C2×C4×C67C23×C411yescharacteristic
374C2×C4×C67C22×D411yescharacteristic
375C2×C4×C67C22×D411yescharacteristic
376C2×C4×C67C2×#4111yescharacteristic
377C2×C4×C67H(5,𝔽2)11yescharacteristic
378C2×C4×C67H(5,𝔽2)11yescharacteristic
379C8×C67—22no—
380C8×C67—41no—
381C8×C67—41no—
382C8×C67—41no—
383C22×C67—22no—
384C22×C67—22no—
385C22×C67—24no—
386C22×C67—22no—
387C22×C67—22no—
388C22×C67—22no—
389C22×C67—22no—
390C22×C67—42no—
391C22×C67—42no—
392C22×C67—41no—
393C22×C67—41no—
394C22×C67—42no—
395C22×C67—41no—
396C22×C67—41no—
397C22×C67—42no—
398C22×C67—41no—
399C22×C67—41no—
400C22×C67—42no—
401C22×C67—41no—
402C22×C67—41no—
403C22×C67—42no—
404C22×C67—42no—
405C22×C67—42no—
406C22×C67—42no—
407C22×C67—816no—
408C22×C67—81no—
409C22×C67—81no—
410C22×C67—81no—
411C22×C67—81no—
412C22×C67C22×C22⋊C411yescharacteristic
413C22×C67D4211yescharacteristic
414C22×C67#54611yescharacteristic
415C22×C67#57511yescharacteristic
416C22×C67#57511yescharacteristic
417C22×C67#57611yescharacteristic
418C22×C67#57711yescharacteristic
419C4×C67—22no—
420C4×C67—22no—
421C4×C67—22no—
422C4×C67—22no—
423C4×C67—42no—
424C4×C67—42no—
425C4×C67—42no—
426C4×C67—81no—
427C4×C67—81no—
428C4×C67—81no—
429C4×C67C2×C4×D411yescharacteristic
430C4×C67#51811yescharacteristic
431C4×C67D4211yescharacteristic
432C4×C67#54611yescharacteristic
433#22424C6711yesmaximal, characteristic, direct product factor, Sylow
434C2×C67—42no—
435C2×C67—42no—
436C2×C67—44no—
437C2×C67—82no—
438C2×C67D4×C22⋊C411yescharacteristic
439C2×C67#289611yescharacteristic
440C2×C67#289711yescharacteristic
441C2×C67#326711yescharacteristic
442C2×C67#326811yescharacteristic
443C2×C67#331111yescharacteristic
444C2×C67#331911yescharacteristic
445C2×#546C2×C6711yescharacteristic
446C2×#435C2×C6711yescharacteristic, complemented
447C2×#418C2×C6711yescharacteristic, complemented
448C2×#416C2×C6711yescharacteristic, complemented
449#2354C2×C6711yescharacteristic, complemented
450#1983C2×C6711yescharacteristic, complemented
451#1959C2×C6711yescharacteristic, complemented
452#1894C2×C6711yescharacteristic, complemented
453#1893C2×C6711yescharacteristic, complemented
454#1875C2×C6711yescharacteristic, complemented
455#1873C2×C6711yescharacteristic, complemented
456#1802C2×C6711yescharacteristic, complemented
457#1788C2×C6711yescharacteristic, complemented
458#1786C2×C6711yescharacteristic, complemented
459#1762C2×C6711yescharacteristic, complemented
460C67#2242411yescharacteristic, direct product factor, Sylow
461C22×#41C22×C6711yescharacteristic
462C23×D4C22×C6711yescharacteristic
463C22×M16C22×C6711yescharacteristic
464C23×C8C22×C6711yescharacteristic, complemented
465#546—24no—
466#546C4×C6718yescomplemented
467C2×#124C22×C6711yescharacteristic
468C2×#123—21no—
469C2×C22⋊Q8C22×C6711yescharacteristic
470C2×#121—21no—
471C2×#121C22×C6711yescharacteristic
472C2×#120—21no—
473C2×C4×D4C22×C6711yescharacteristic
474C2×C4×D4C22×C6711yescharacteristic
475C2×#117C22×C6711yescharacteristic
476C2×#117C22×C6711yescharacteristic, complemented
477C22×C22⋊C4—21no—
478#435—24no—
479C2×C4⋊C8C22×C6711yescharacteristic, complemented
480#418—24no—
481#416—24no—
482C2×#103C22×C6711yescharacteristic, complemented
483C2×#103C22×C6711yescharacteristic, complemented
484C2×#103C22×C6711yescharacteristic, complemented
485C2×#103C22×C6711yescharacteristic, complemented
486C2×#102C22×C6711yescharacteristic
487C2×#102C22×C6711yescharacteristic
488C2×#102C22×C6711yescharacteristic
489C2×#102C22×C6711yescharacteristic
490C2×#102C22×C6711yescharacteristic
491C2×#102C22×C6711yescharacteristic
492C2×#102C22×C6711yescharacteristic
493C2×#102C22×C6711yescharacteristic
494C2×C22⋊C8C22×C6711yescharacteristic
495C2×C22⋊C8C22×C6711yescharacteristic, complemented
496C2×#97C22×C6711yescharacteristic, complemented
497#390—21no—
498#388—21no—
499#388—21no—
500#384C22×C6711yescharacteristic, complemented
501#380C22×C6711yescharacteristic
502#380C22×C6711yescharacteristic, complemented
503C4×C4⋊C4—21no—
504C4×C4⋊C4C22×C6711yescharacteristic, complemented
505#340C22×C6711yescharacteristic, complemented
506#340C22×C6711yescharacteristic, complemented
507#340C22×C6711yescharacteristic, complemented
508#340C22×C6711yescharacteristic, complemented
509C25—21no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C2×C4×C6714yes—
516C22×Q8C23×C6711yescharacteristic
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4C2×C4×C6714yes—
526C22×D4D4×C6711yescharacteristic
527C22×D4C23×C6711yescharacteristic
528C22×D4C23×C6711yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C23×C6711yescharacteristic
532C23×C4C23×C6711yescharacteristic
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—41no—
536C22×C8—22no—
537C22×C8—22no—
538C22×C8—41no—
539C22×C8C23×C6711yescharacteristic
540C22×C8C23×C6711yescharacteristic
541C22×C8C23×C6711yescharacteristic
542C22×C8C23×C6711yescharacteristic
543#124—22no—
544#124C2×C4×C6714yes—
545#123—28no—
546C22⋊Q8—22no—
547C22⋊Q8C2×C4×C6714yes—
548#121—22no—
549#121—28no—
550#121C2×C4×C6714yes—
551#120—28no—
552C4×D4—22no—
553C4×D4C2×C4×C6714yes—
554C4×D4C2×C4×C6714yes—
555C4×D4D4×C6714yes—
556#117—22no—
557#117—22no—
558#117—41no—
559#117—41no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4D4×C6711yescharacteristic
564C2×C4⋊C4C23×C6711yescharacteristic
565C2×C4⋊C4C23×C6711yescharacteristic
566C2×C4⋊C4C23×C6711yescharacteristic
567C2×C4⋊C4C23×C6711yescharacteristic
568C2×C4⋊C4C23×C6711yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—28no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4D4×C6711yescharacteristic
580C2×C22⋊C4D4×C6711yescharacteristic
581C2×C42—21no—
582C2×C42—21no—
583C2×C42—21no—
584C2×C42C23×C6711yescharacteristic
585C4⋊C8—22no—
586#103—22no—
587#103—22no—
588#103—41no—
589#103—41no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—22no—
595#102—41no—
596#102—41no—
597#102D4×C6714yescomplemented
598C22⋊C8—22no—
599C22⋊C8—22no—
600#97—22no—
601#95—21no—
602#95—21no—
603#95—21no—
604C24—21no—
605C24—21no—
606C24—24no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—81no—
612C24—81no—
613C24C2×D4×C6711yescharacteristic
614C24C2×D4×C6711yescharacteristic
615#41—28no—
616#41—44no—
617#41—44no—
618#41—44no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8C22×C4×C6712yes—
625C2×D4—28no—
626C2×D4—24no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—41no—
641C2×D4—41no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4C22⋊C4×C6714yes—
649C2×D4C22×C4×C6712yes—
650C2×D4C22×C4×C6712yes—
651C2×D4C2×D4×C6712yes—
652C2×D4#41×C6712yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—81no—
672C22×C4—81no—
673C22×C4C22×C4×C6712yes—
674C22×C4C22×C4×C6712yes—
675C22×C4C2×D4×C6711yescharacteristic
676C22×C4C2×D4×C6711yescharacteristic
677C22×C4C2×D4×C6711yescharacteristic
678C22×C4C2×D4×C6711yescharacteristic
679C22×C4C2×D4×C6712yes—
680C22×C4C2×D4×C6712yes—
681C22×C4C24×C6711yescharacteristic
682M16—44no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—44no—
695C2×C8C2×D4×C6712yes—
696C4⋊C4—24no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—42no—
706C4⋊C4—81no—
707C4⋊C4C22⋊C4×C6714yes—
708C4⋊C4C22×C4×C6712yes—
709C4⋊C4C2×D4×C6712yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—81no—
718C22⋊C4—81no—
719C22⋊C4C22⋊C4×C6714yes—
720C22⋊C4C22⋊C4×C6714yes—
721C42—42no—
722C42—42no—
723C42—42no—
724C42C22×C4×C6712yes—
725C42C2×D4×C6712yes—
726C23—22no—
727C23—21no—
728C23—21no—
729C23—22no—
730C23—21no—
731C23—21no—
732C23—22no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—22no—
742C23—48no—
743C23—48no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23C2×C22⋊C4×C6712yes—
760C23C2×C22⋊C4×C6712yes—
761C23C22×D4×C6711yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—41no—
765Q8—41no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—44no—
772D4—48no—
773D4—48no—
774D4—41no—
775D4—41no—
776D4—84no—
777D4C4×D4×C6714yes—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—48no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—84no—
814C2×C4C2×C22⋊C4×C6712yes—
815C2×C4C2×C22⋊C4×C6712yes—
816C2×C4C2×C22⋊C4×C6712yes—
817C2×C4C2×C22⋊C4×C6712yes—
818C2×C4C23×C4×C6711yescharacteristic
819C2×C4C22×D4×C6711yescharacteristic
820C2×C4C22×D4×C6711yescharacteristic
821C2×C4C2×#41×C6711yescharacteristic
822C2×C4H(5,𝔽2)×C6711yescharacteristic
823C2×C4H(5,𝔽2)×C6711yescharacteristic
824C8—22no—
825C8—41no—
826C8—41no—
827C8—41no—
828C22—22no—
829C22—22no—
830C22—24no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—41no—
836C22—41no—
837C22—42no—
838C22—41no—
839C22—41no—
840C22—42no—
841C22—41no—
842C22—41no—
843C22—42no—
844C22—41no—
845C22—41no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—816no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22C22×C22⋊C4×C6711yescharacteristic
858C22D42×C6711yescharacteristic
859C22#546×C6711yescharacteristic
860C22#575×C6711yescharacteristic
861C22#575×C6711yescharacteristic
862C22#576×C6711yescharacteristic
863C22#577×C6711yescharacteristic
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—42no—
869C4—42no—
870C4—42no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4C2×C4×D4×C6711yescharacteristic
875C4#518×C6711yescharacteristic
876C4D42×C6711yescharacteristic
877C4#546×C6711yescharacteristic
878C2—42no—
879C2—42no—
880C2—44no—
881C2—82no—
882C2D4×C22⋊C4×C6711yescharacteristic
883C2C67×#289611yescharacteristic
884C2C67×#289711yescharacteristic
885C2C67×#326711yescharacteristic
886C2C67×#326811yescharacteristic
887C2C67×#331111yescharacteristic
888C2C67×#331911yescharacteristic
subgroupG/H
center, socleC23×C67C22×D4
commutatorC2×C4C23×C4×C67
Frattini, cosocleC22×C4C24×C67
prime radicalC2×#546×C67C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C67 ◁ C2×C4×D4×C67 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#435×C67C2semidirect
3. C2×#418×C67C2semidirect
4. C2×#416×C67C2semidirect
5. C67×#2354C2semidirect
6. C67×#1983C2semidirect
7. C67×#1959C2semidirect
8. C67×#1894C2semidirect
9. C67×#1893C2semidirect
10. C67×#1875C2semidirect
11. C67×#1873C2semidirect
12. C67×#1802C2semidirect
13. C67×#1788C2semidirect
14. C67×#1786C2semidirect
15. C67×#1762C2semidirect
19. C23×C8×C67C22semidirect
21. #546×C67C4semidirect
31. C2×#117×C67C22semidirect
34. C2×C4⋊C8×C67C22semidirect
37. C2×#103×C67C22semidirect
38. C2×#103×C67C22semidirect
39. C2×#103×C67C22semidirect
40. C2×#103×C67C22semidirect
50. C2×C22⋊C8×C67C22semidirect
51. C2×#97×C67C22semidirect
55. #384×C67C22semidirect
57. #380×C67C22semidirect
59. C4×C4⋊C4×C67C22semidirect
60. #340×C67C22semidirect
61. #340×C67C22semidirect
62. #340×C67C22semidirect
63. #340×C67C22semidirect
152. #102×C67D4semidirect
433. #22424C67direct (N × H)
446. C2×#435C2×C67semidirect
447. C2×#418C2×C67semidirect
448. C2×#416C2×C67semidirect
449. #2354C2×C67semidirect
450. #1983C2×C67semidirect
451. #1959C2×C67semidirect
452. #1894C2×C67semidirect
453. #1893C2×C67semidirect
454. #1875C2×C67semidirect
455. #1873C2×C67semidirect
456. #1802C2×C67semidirect
457. #1788C2×C67semidirect
458. #1786C2×C67semidirect
459. #1762C2×C67semidirect
460. C67#22424direct (N × H)
464. C23×C8C22×C67semidirect
466. #546C4×C67semidirect
476. C2×#117C22×C67semidirect
479. C2×C4⋊C8C22×C67semidirect
482. C2×#103C22×C67semidirect
483. C2×#103C22×C67semidirect
484. C2×#103C22×C67semidirect
485. C2×#103C22×C67semidirect
495. C2×C22⋊C8C22×C67semidirect
496. C2×#97C22×C67semidirect
500. #384C22×C67semidirect
502. #380C22×C67semidirect
504. C4×C4⋊C4C22×C67semidirect
505. #340C22×C67semidirect
506. #340C22×C67semidirect
507. #340C22×C67semidirect
508. #340C22×C67semidirect
597. #102D4×C67semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C672
C2×#435×C672
C2×#418×C672
C2×#416×C672
C67×#23542
C67×#19832
C67×#19592
C67×#18942
C67×#18932
C67×#18752
C67×#18732
C67×#18022
C67×#17882
C67×#17862
C67×#17622
#2242467