Finite Group Databasebeta

← C67×#26408 #30705659

Subgroups — C67×#26408 #30705659

Order 17152.

902 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C67×#2440C211yesmaximal, characteristic, complemented
2C67×#2361C211yesmaximal, characteristic
3C67×#2099C211yesmaximal, characteristic, complemented
4C67×#2086C211yesmaximal, characteristic, complemented
5C67×#2067C211yesmaximal, characteristic, complemented
6C67×#2023C211yesmaximal, characteristic, complemented
7C67×#1988C211yesmaximal, characteristic, complemented
8C67×#1918C211yesmaximal, characteristic, complemented
9C67×#1893C211yesmaximal, characteristic
10C67×#1874C211yesmaximal, characteristic
11C67×#1862C211yesmaximal, characteristic, complemented
12C67×#1852C211yesmaximal, characteristic, complemented
13C67×#1850C211yesmaximal, characteristic, complemented
14C67×#1802C211yesmaximal, characteristic, complemented
15C2×#340×C67C211yesmaximal, characteristic, complemented
16C23×C8×C67C2211yescharacteristic
17C2×C4⋊Q8×C67C2211yescharacteristic
18C2×C22⋊Q8×C67—21no—
19C2×#121×C67C2211yescharacteristic
20C2×C4×D4×C67—21no—
21C2×C4×D4×C67C2211yescharacteristic
22C22×C4⋊C4×C67C2211yescharacteristic
23C22×C4⋊C4×C67C2211yescharacteristic
24C2×#107×C67C2211yescharacteristic
25C2×#107×C67C2211yescharacteristic
26C2×C4⋊C8×C67C2211yescharacteristic
27C2×C4⋊C8×C67C2211yescharacteristic
28C2×#102×C67C2211yescharacteristic
29C2×#102×C67C2211yescharacteristic
30C2×#102×C67C2211yescharacteristic
31C2×#102×C67C2211yescharacteristic
32C2×C22⋊C8×C67C2211yescharacteristic
33#398×C67—21no—
34#395×C67—21no—
35#390×C67C2211yescharacteristic
36#389×C67C2211yescharacteristic
37#389×C67C2211yescharacteristic
38#389×C67C2211yescharacteristic
39#388×C67—21no—
40#386×C67—21no—
41#385×C67—21no—
42#385×C67—21no—
43#384×C67C2211yescharacteristic
44#380×C67C2211yescharacteristic
45C4×C4⋊C4×C67C2211yescharacteristic
46C4×C22⋊C4×C67C2211yescharacteristic
47#340×C67C2211yescharacteristic
48#340×C67C2211yescharacteristic
49#340×C67C2211yescharacteristic
50#340×C67C2211yescharacteristic
51#340×C67C2211yescharacteristic
52#340×C67C2211yescharacteristic
53#340×C67C2211yescharacteristic
54#340×C67C2211yescharacteristic
55#340×C67C2211yescharacteristic
56#340×C67C2211yescharacteristic
57#336×C67C2211yescharacteristic
58#336×C67C2211yescharacteristic
59C22×Q8×C67—21no—
60C22×D4×C67—21no—
61C22×D4×C67C2311yescharacteristic
62C23×C4×C67—21no—
63C23×C4×C67—21no—
64C23×C4×C67—21no—
65C23×C4×C67C2311yescharacteristic
66C22×C8×C67—22no—
67C22×C8×C67—41no—
68C22×C8×C67—41no—
69C22×C8×C67C2311yescharacteristic
70C22×C8×C67C2311yescharacteristic
71C22×C8×C67C2311yescharacteristic
72C22×C8×C67C2311yescharacteristic
73C4⋊Q8×C67—22no—
74C4⋊Q8×C67—41no—
75C22⋊Q8×C67—44no—
76#121×C67—22no—
77#121×C67Q814yescomplemented
78C4×D4×C67—22no—
79C4×D4×C67—41no—
80C4×D4×C67—44no—
81C2×C4⋊C4×C67—22no—
82C2×C4⋊C4×C67—22no—
83C2×C4⋊C4×C67—21no—
84C2×C4⋊C4×C67—21no—
85C2×C4⋊C4×C67—21no—
86C2×C4⋊C4×C67—21no—
87C2×C4⋊C4×C67—21no—
88C2×C4⋊C4×C67—21no—
89C2×C4⋊C4×C67—21no—
90C2×C4⋊C4×C67—21no—
91C2×C4⋊C4×C67—41no—
92C2×C4⋊C4×C67—41no—
93C2×C4⋊C4×C67C2311yescharacteristic
94C2×C4⋊C4×C67C2311yescharacteristic
95C2×C4⋊C4×C67C2311yescharacteristic
96C2×C4⋊C4×C67C2311yescharacteristic
97C2×C4⋊C4×C67C2311yescharacteristic
98C2×C4⋊C4×C67C2311yescharacteristic
99C2×C4⋊C4×C67C2311yescharacteristic
100C2×C22⋊C4×C67—21no—
101C2×C22⋊C4×C67—21no—
102C2×C22⋊C4×C67—21no—
103C2×C22⋊C4×C67—21no—
104C2×C22⋊C4×C67—21no—
105C2×C22⋊C4×C67D411yescharacteristic
106C2×C22⋊C4×C67D411yescharacteristic
107C2×C42×C67—21no—
108C2×C42×C67C2311yescharacteristic
109C2×C42×C67C2311yescharacteristic
110#107×C67—22no—
111#107×C67—41no—
112C4⋊C8×C67—41no—
113C4⋊C8×C67—41no—
114#102×C67—22no—
115#102×C67—41no—
116#102×C67—41no—
117#102×C67—41no—
118C22⋊C8×C67—22no—
119#95×C67—21no—
120#95×C67—21no—
121#95×C67—21no—
122#95×C67—21no—
123#95×C67—21no—
124#95×C67D411yescharacteristic
125#95×C67D411yescharacteristic
126C24×C67—21no—
127C24×C67C2×D411yescharacteristic
128C2×Q8×C67—42no—
129C2×Q8×C67—42no—
130C2×Q8×C67—81no—
131C2×D4×C67—24no—
132C2×D4×C67—21no—
133C2×D4×C67—21no—
134C2×D4×C67—21no—
135C2×D4×C67—21no—
136C2×D4×C67—21no—
137C2×D4×C67—42no—
138C2×D4×C67—42no—
139C2×D4×C67C2×Q812yes—
140C22×C4×C67—21no—
141C22×C4×C67—21no—
142C22×C4×C67—21no—
143C22×C4×C67—21no—
144C22×C4×C67—21no—
145C22×C4×C67—21no—
146C22×C4×C67—21no—
147C22×C4×C67—21no—
148C22×C4×C67—21no—
149C22×C4×C67—21no—
150C22×C4×C67—21no—
151C22×C4×C67—42no—
152C22×C4×C67—42no—
153C22×C4×C67—42no—
154C22×C4×C67—42no—
155C22×C4×C67—42no—
156C22×C4×C67—42no—
157C22×C4×C67—81no—
158C22×C4×C67—81no—
159C22×C4×C67—81no—
160C22×C4×C67C2×D411yescharacteristic
161C22×C4×C67C2×D411yescharacteristic
162C22×C4×C67C2×D411yescharacteristic
163C22×C4×C67C2×D411yescharacteristic
164C22×C4×C67C2×D411yescharacteristic
165C22×C4×C67C2×Q812yes—
166C22×C4×C67#4112yes—
167C22×C4×C67C2411yescharacteristic
168C2×C8×C67—21no—
169C2×C8×C67—21no—
170C2×C8×C67—21no—
171C2×C8×C67—21no—
172C2×C8×C67—21no—
173C2×C8×C67—21no—
174C2×C8×C67—21no—
175C2×C8×C67—21no—
176C2×C8×C67—21no—
177C2×C8×C67—21no—
178C2×C8×C67—21no—
179C2×C8×C67—21no—
180C2×C8×C67—44no—
181C4⋊C4×C67—21no—
182C4⋊C4×C67—21no—
183C4⋊C4×C67—21no—
184C4⋊C4×C67—21no—
185C4⋊C4×C67—21no—
186C4⋊C4×C67—21no—
187C4⋊C4×C67—21no—
188C4⋊C4×C67—21no—
189C4⋊C4×C67—21no—
190C4⋊C4×C67—21no—
191C4⋊C4×C67—21no—
192C4⋊C4×C67—42no—
193C4⋊C4×C67—42no—
194C4⋊C4×C67—42no—
195C4⋊C4×C67—42no—
196C4⋊C4×C67—42no—
197C4⋊C4×C67—42no—
198C4⋊C4×C67—42no—
199C4⋊C4×C67—81no—
200C4⋊C4×C67C2×Q812yes—
201C4⋊C4×C67#4112yes—
202C4⋊C4×C67#4112yes—
203C22⋊C4×C67—22no—
204C22⋊C4×C67—24no—
205C22⋊C4×C67—42no—
206C22⋊C4×C67—42no—
207C22⋊C4×C67—42no—
208C22⋊C4×C67—81no—
209C22⋊C4×C67D814yes—
210C42×C67—21no—
211C42×C67—21no—
212C42×C67—21no—
213C42×C67—21no—
214C42×C67—42no—
215C23×C67—21no—
216C23×C67—21no—
217C23×C67—21no—
218C23×C67—21no—
219C23×C67—22no—
220C23×C67—41no—
221C23×C67—41no—
222C23×C67—41no—
223C23×C67—41no—
224C23×C67—41no—
225C23×C67—41no—
226C23×C67C22⋊Q812yes—
227C23×C67C2×D812yes—
228C23×C67#13712yes—
229C23×C67C22×D411yescharacteristic
230Q8×C67—84no—
231D4×C67—22no—
232D4×C67—22no—
233D4×C67—48no—
234D4×C67—41no—
235D4×C67—41no—
236C2×C4×C67—21no—
237C2×C4×C67—21no—
238C2×C4×C67—21no—
239C2×C4×C67—21no—
240C2×C4×C67—21no—
241C2×C4×C67—21no—
242C2×C4×C67—22no—
243C2×C4×C67—22no—
244C2×C4×C67—22no—
245C2×C4×C67—22no—
246C2×C4×C67—22no—
247C2×C4×C67—21no—
248C2×C4×C67—21no—
249C2×C4×C67—22no—
250C2×C4×C67—22no—
251C2×C4×C67—21no—
252C2×C4×C67—21no—
253C2×C4×C67—21no—
254C2×C4×C67—21no—
255C2×C4×C67—41no—
256C2×C4×C67—41no—
257C2×C4×C67—41no—
258C2×C4×C67—41no—
259C2×C4×C67—41no—
260C2×C4×C67—41no—
261C2×C4×C67—41no—
262C2×C4×C67—41no—
263C2×C4×C67—41no—
264C2×C4×C67—41no—
265C2×C4×C67—41no—
266C2×C4×C67—41no—
267C2×C4×C67—41no—
268C2×C4×C67—41no—
269C2×C4×C67—41no—
270C2×C4×C67—41no—
271C2×C4×C67—41no—
272C2×C4×C67—41no—
273C2×C4×C67—84no—
274C2×C4×C67—84no—
275C2×C4×C67—84no—
276C2×C4×C67C22⋊Q812yes—
277C2×C4×C67C2×D812yes—
278C2×C4×C67C2×D812yes—
279C2×C4×C67C22×Q811yescharacteristic
280C2×C4×C67C2×#4111yescharacteristic
281C2×C4×C67C2×#4111yescharacteristic
282C2×C4×C67C2×#4111yescharacteristic
283C2×C4×C67H(5,𝔽2)11yescharacteristic
284C2×C4×C67H(5,𝔽2)11yescharacteristic
285C8×C67—41no—
286C8×C67—41no—
287C8×C67—41no—
288C8×C67—41no—
289C22×C67—22no—
290C22×C67—22no—
291C22×C67—22no—
292C22×C67—22no—
293C22×C67—22no—
294C22×C67—22no—
295C22×C67—42no—
296C22×C67—42no—
297C22×C67—42no—
298C22×C67—81no—
299C22×C67—81no—
300C22×C67—81no—
301C22×C67—81no—
302C22×C67#47414yes—
303C22×C67C2×C22⋊Q811yescharacteristic
304C22×C67#54611yescharacteristic
305C22×C67#54611yescharacteristic
306C22×C67C22×D811yescharacteristic
307C22×C67C2×#13711yescharacteristic
308C22×C67#57711yescharacteristic
309C22×C67#57711yescharacteristic
310C4×C67—22no—
311C4×C67—22no—
312C4×C67—22no—
313C4×C67—42no—
314C4×C67—42no—
315C4×C67—41no—
316C4×C67—41no—
317C4×C67—42no—
318C4×C67—81no—
319C4×C67—81no—
320C4×C67—81no—
321C4×C67—81no—
322C4×C67#52911yescharacteristic
323C4×C67#53811yescharacteristic
324C4×C67#55411yescharacteristic
325C4×C67#55411yescharacteristic
326#26408C6711yesmaximal, characteristic, direct product factor, Sylow
327C2×C67—24no—
328C2×C67—82no—
329C2×C67#245011yescharacteristic
330C2×C67C2×#47411yescharacteristic
331C2×C67#308411yescharacteristic
332C2×C67#329411yescharacteristic
333C2×C67#329411yescharacteristic
334C2×C67#331611yescharacteristic
335C2×C67#332011yescharacteristic
336#2440C2×C6711yescharacteristic, complemented
337#2361C2×C6711yescharacteristic
338#2099C2×C6711yescharacteristic, complemented
339#2086C2×C6711yescharacteristic, complemented
340#2067C2×C6711yescharacteristic, complemented
341#2023C2×C6711yescharacteristic, complemented
342#1988C2×C6711yescharacteristic, complemented
343#1918C2×C6711yescharacteristic, complemented
344#1893C2×C6711yescharacteristic
345#1874C2×C6711yescharacteristic
346#1862C2×C6711yescharacteristic, complemented
347#1852C2×C6711yescharacteristic, complemented
348#1850C2×C6711yescharacteristic, complemented
349#1802C2×C6711yescharacteristic, complemented
350C2×#340C2×C6711yescharacteristic, complemented
351C67#2640811yescharacteristic, direct product factor, Sylow
352C23×C8C22×C6711yescharacteristic
353C2×C4⋊Q8C22×C6711yescharacteristic
354C2×C22⋊Q8—21no—
355C2×#121C22×C6711yescharacteristic
356C2×C4×D4—21no—
357C2×C4×D4C22×C6711yescharacteristic
358C22×C4⋊C4C22×C6711yescharacteristic
359C22×C4⋊C4C22×C6711yescharacteristic
360C2×#107C22×C6711yescharacteristic
361C2×#107C22×C6711yescharacteristic
362C2×C4⋊C8C22×C6711yescharacteristic
363C2×C4⋊C8C22×C6711yescharacteristic
364C2×#102C22×C6711yescharacteristic
365C2×#102C22×C6711yescharacteristic
366C2×#102C22×C6711yescharacteristic
367C2×#102C22×C6711yescharacteristic
368C2×C22⋊C8C22×C6711yescharacteristic
369#398—21no—
370#395—21no—
371#390C22×C6711yescharacteristic
372#389C22×C6711yescharacteristic
373#389C22×C6711yescharacteristic
374#389C22×C6711yescharacteristic
375#388—21no—
376#386—21no—
377#385—21no—
378#385—21no—
379#384C22×C6711yescharacteristic
380#380C22×C6711yescharacteristic
381C4×C4⋊C4C22×C6711yescharacteristic
382C4×C22⋊C4C22×C6711yescharacteristic
383#340C22×C6711yescharacteristic
384#340C22×C6711yescharacteristic
385#340C22×C6711yescharacteristic
386#340C22×C6711yescharacteristic
387#340C22×C6711yescharacteristic
388#340C22×C6711yescharacteristic
389#340C22×C6711yescharacteristic
390#340C22×C6711yescharacteristic
391#340C22×C6711yescharacteristic
392#340C22×C6711yescharacteristic
393#336C22×C6711yescharacteristic
394#336C22×C6711yescharacteristic
395C22×Q8—21no—
396C22×D4—21no—
397C22×D4C23×C6711yescharacteristic
398C23×C4—21no—
399C23×C4—21no—
400C23×C4—21no—
401C23×C4C23×C6711yescharacteristic
402C22×C8—22no—
403C22×C8—41no—
404C22×C8—41no—
405C22×C8C23×C6711yescharacteristic
406C22×C8C23×C6711yescharacteristic
407C22×C8C23×C6711yescharacteristic
408C22×C8C23×C6711yescharacteristic
409C4⋊Q8—22no—
410C4⋊Q8—41no—
411C22⋊Q8—44no—
412#121—22no—
413#121Q8×C6714yescomplemented
414C4×D4—22no—
415C4×D4—41no—
416C4×D4—44no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—41no—
428C2×C4⋊C4—41no—
429C2×C4⋊C4C23×C6711yescharacteristic
430C2×C4⋊C4C23×C6711yescharacteristic
431C2×C4⋊C4C23×C6711yescharacteristic
432C2×C4⋊C4C23×C6711yescharacteristic
433C2×C4⋊C4C23×C6711yescharacteristic
434C2×C4⋊C4C23×C6711yescharacteristic
435C2×C4⋊C4C23×C6711yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4D4×C6711yescharacteristic
442C2×C22⋊C4D4×C6711yescharacteristic
443C2×C42—21no—
444C2×C42C23×C6711yescharacteristic
445C2×C42C23×C6711yescharacteristic
446#107—22no—
447#107—41no—
448C4⋊C8—41no—
449C4⋊C8—41no—
450#102—22no—
451#102—41no—
452#102—41no—
453#102—41no—
454C22⋊C8—22no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95D4×C6711yescharacteristic
461#95D4×C6711yescharacteristic
462C24—21no—
463C24C2×D4×C6711yescharacteristic
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—81no—
467C2×D4—24no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4C2×Q8×C6712yes—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—81no—
494C22×C4—81no—
495C22×C4—81no—
496C22×C4C2×D4×C6711yescharacteristic
497C22×C4C2×D4×C6711yescharacteristic
498C22×C4C2×D4×C6711yescharacteristic
499C22×C4C2×D4×C6711yescharacteristic
500C22×C4C2×D4×C6711yescharacteristic
501C22×C4C2×Q8×C6712yes—
502C22×C4#41×C6712yes—
503C22×C4C24×C6711yescharacteristic
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—44no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—42no—
529C4⋊C4—42no—
530C4⋊C4—42no—
531C4⋊C4—42no—
532C4⋊C4—42no—
533C4⋊C4—42no—
534C4⋊C4—42no—
535C4⋊C4—81no—
536C4⋊C4C2×Q8×C6712yes—
537C4⋊C4#41×C6712yes—
538C4⋊C4#41×C6712yes—
539C22⋊C4—22no—
540C22⋊C4—24no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—81no—
545C22⋊C4D8×C6714yes—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—42no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—22no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23C22⋊Q8×C6712yes—
563C23C2×D8×C6712yes—
564C23#137×C6712yes—
565C23C22×D4×C6711yescharacteristic
566Q8—84no—
567D4—22no—
568D4—22no—
569D4—48no—
570D4—41no—
571D4—41no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—84no—
610C2×C4—84no—
611C2×C4—84no—
612C2×C4C22⋊Q8×C6712yes—
613C2×C4C2×D8×C6712yes—
614C2×C4C2×D8×C6712yes—
615C2×C4C22×Q8×C6711yescharacteristic
616C2×C4C2×#41×C6711yescharacteristic
617C2×C4C2×#41×C6711yescharacteristic
618C2×C4C2×#41×C6711yescharacteristic
619C2×C4H(5,𝔽2)×C6711yescharacteristic
620C2×C4H(5,𝔽2)×C6711yescharacteristic
621C8—41no—
622C8—41no—
623C8—41no—
624C8—41no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—42no—
632C22—42no—
633C22—42no—
634C22—81no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22#474×C6714yes—
639C22C2×C22⋊Q8×C6711yescharacteristic
640C22#546×C6711yescharacteristic
641C22#546×C6711yescharacteristic
642C22C22×D8×C6711yescharacteristic
643C22C2×#137×C6711yescharacteristic
644C22#577×C6711yescharacteristic
645C22#577×C6711yescharacteristic
646C4—22no—
647C4—22no—
648C4—22no—
649C4—42no—
650C4—42no—
651C4—41no—
652C4—41no—
653C4—42no—
654C4—81no—
655C4—81no—
656C4—81no—
657C4—81no—
658C4#529×C6711yescharacteristic
659C4#538×C6711yescharacteristic
660C4#554×C6711yescharacteristic
661C4#554×C6711yescharacteristic
662C2—24no—
663C2—82no—
664C2C67×#245011yescharacteristic
665C2C2×#474×C6711yescharacteristic
666C2C67×#308411yescharacteristic
667C2C67×#329411yescharacteristic
668C2C67×#329411yescharacteristic
669C2C67×#331611yescharacteristic
670C2C67×#332011yescharacteristic
subgroupG/H
center, socleC23×C67C22×D4
commutator, Frattini, cosocleC22×C4C24×C67
prime radicalC2×#121×C67C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C67 ◁ C4×C22⋊C4×C67 ◁ G

Complements

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

NH ≅ G/Ntype
1. C67×#2440C2semidirect
3. C67×#2099C2semidirect
4. C67×#2086C2semidirect
5. C67×#2067C2semidirect
6. C67×#2023C2semidirect
7. C67×#1988C2semidirect
8. C67×#1918C2semidirect
11. C67×#1862C2semidirect
12. C67×#1852C2semidirect
13. C67×#1850C2semidirect
14. C67×#1802C2semidirect
15. C2×#340×C67C2semidirect
77. #121×C67Q8semidirect
326. #26408C67direct (N × H)
336. #2440C2×C67semidirect
338. #2099C2×C67semidirect
339. #2086C2×C67semidirect
340. #2067C2×C67semidirect
341. #2023C2×C67semidirect
342. #1988C2×C67semidirect
343. #1918C2×C67semidirect
346. #1862C2×C67semidirect
347. #1852C2×C67semidirect
348. #1850C2×C67semidirect
349. #1802C2×C67semidirect
350. C2×#340C2×C67semidirect
351. C67#26408direct (N × H)
413. #121Q8×C67semidirect

Maximal subgroups

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

subgroupindex
C67×#24402
C67×#23612
C67×#20992
C67×#20862
C67×#20672
C67×#20232
C67×#19882
C67×#19182
C67×#18932
C67×#18742
C67×#18622
C67×#18522
C67×#18502
C67×#18022
C2×#340×C672
#2640867