Finite Group Databasebeta

← C67×#14118 #30693369

Subgroups — C67×#14118 #30693369

Order 17152.

1746 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#388×C67C211yesmaximal, characteristic
2C2×#388×C67C211yesmaximal, characteristic
3C2×#385×C67C211yesmaximal, characteristic
4C2×C4×C4⋊C4×C67C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊C4×C67C211yesmaximal, characteristic
6C67×#1444C211yesmaximal, characteristic, complemented
7C67×#1441C211yesmaximal, characteristic, complemented
8C67×#1439C211yesmaximal, characteristic
9C67×#1439C211yesmaximal, characteristic
10C67×#1436C211yesmaximal, characteristic, complemented
11C67×#1436C211yesmaximal, characteristic, complemented
12C67×#1436C211yesmaximal, characteristic, complemented
13C67×C4⋊#95C211yesmaximal, characteristic, complemented
14C67×#1434C211yesmaximal, characteristic, complemented
15C67×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C67C2211yescharacteristic
17C22×C4⋊C4×C67C2211yescharacteristic
18C22×C4⋊C4×C67C2211yescharacteristic
19C22×C4⋊C4×C67C2211yescharacteristic
20C22×C4⋊C4×C67C2211yescharacteristic
21C22×C4⋊C4×C67C2211yescharacteristic
22C22×C4⋊C4×C67C2211yescharacteristic
23C22×C22⋊C4×C67C2211yescharacteristic
24C22×C22⋊C4×C67C2211yescharacteristic
25C22×C22⋊C4×C67C2211yescharacteristic
26C22×C22⋊C4×C67C2211yescharacteristic
27C22×C22⋊C4×C67C2211yescharacteristic
28C22×C22⋊C4×C67C2211yescharacteristic
29C22×C42×C67C2211yescharacteristic
30C22×C42×C67C2211yescharacteristic
31C22×C42×C67C2211yescharacteristic
32C22×C42×C67C2211yescharacteristic
33#388×C67—24no—
34#388×C67C418yescomplemented
35#385×C67—24no—
36C4×C4⋊C4×C67—24no—
37C4×C22⋊C4×C67—24no—
38C2×#95×C67C2211yescharacteristic
39C2×#95×C67C2211yescharacteristic
40C2×#95×C67C2211yescharacteristic
41C2×#95×C67C2211yescharacteristic
42C2×#95×C67C2211yescharacteristic
43C2×#95×C67C2211yescharacteristic
44C2×#95×C67C2211yescharacteristic
45C2×#95×C67C2211yescharacteristic
46C2×#95×C67C2211yescharacteristic
47C2×#95×C67C2211yescharacteristic
48C2×#95×C67C2211yescharacteristic
49C2×#95×C67C2211yescharacteristic
50C2×#95×C67C2211yescharacteristic
51C2×#95×C67C2211yescharacteristic
52C2×#95×C67C2211yescharacteristic
53C2×#95×C67C2211yescharacteristic
54C2×#95×C67C2211yescharacteristic
55C2×#95×C67C2211yescharacteristic
56C25×C67C2311yescharacteristic
57C23×C4×C67—22no—
58C23×C4×C67—22no—
59C23×C4×C67—22no—
60C23×C4×C67—22no—
61C23×C4×C67—22no—
62C23×C4×C67—41no—
63C23×C4×C67—41no—
64C23×C4×C67C2311yescharacteristic
65C23×C4×C67C2311yescharacteristic
66C23×C4×C67C2311yescharacteristic
67C23×C4×C67C2311yescharacteristic
68C23×C4×C67C2311yescharacteristic
69C23×C4×C67C2311yescharacteristic
70C23×C4×C67C2311yescharacteristic
71C23×C4×C67C2311yescharacteristic
72C23×C4×C67C2311yescharacteristic
73C23×C4×C67C2311yescharacteristic
74C23×C4×C67C2311yescharacteristic
75C23×C4×C67C2311yescharacteristic
76C23×C4×C67C2311yescharacteristic
77C23×C4×C67C2311yescharacteristic
78C2×C4⋊C4×C67—22no—
79C2×C4⋊C4×C67—22no—
80C2×C4⋊C4×C67—22no—
81C2×C4⋊C4×C67—22no—
82C2×C4⋊C4×C67—22no—
83C2×C4⋊C4×C67—22no—
84C2×C4⋊C4×C67—22no—
85C2×C4⋊C4×C67—22no—
86C2×C4⋊C4×C67—22no—
87C2×C4⋊C4×C67—22no—
88C2×C4⋊C4×C67—41no—
89C2×C4⋊C4×C67—41no—
90C2×C4⋊C4×C67—41no—
91C2×C4⋊C4×C67—41no—
92C2×C4⋊C4×C67—41no—
93C2×C4⋊C4×C67—41no—
94C2×C4⋊C4×C67C2×C414yescomplemented
95C2×C4⋊C4×C67D414yes—
96C2×C22⋊C4×C67—22no—
97C2×C22⋊C4×C67—22no—
98C2×C22⋊C4×C67—22no—
99C2×C22⋊C4×C67—22no—
100C2×C22⋊C4×C67—22no—
101C2×C22⋊C4×C67—22no—
102C2×C22⋊C4×C67—22no—
103C2×C22⋊C4×C67—22no—
104C2×C22⋊C4×C67—22no—
105C2×C22⋊C4×C67—41no—
106C2×C22⋊C4×C67—41no—
107C2×C22⋊C4×C67—41no—
108C2×C22⋊C4×C67—41no—
109C2×C22⋊C4×C67C2×C414yes—
110C2×C22⋊C4×C67C2×C414yes—
111C2×C22⋊C4×C67C2×C414yes—
112C2×C22⋊C4×C67D414yes—
113C2×C22⋊C4×C67Q814yes—
114C2×C42×C67—22no—
115C2×C42×C67—22no—
116C2×C42×C67—22no—
117C2×C42×C67—22no—
118C2×C42×C67—22no—
119C2×C42×C67—22no—
120C2×C42×C67—22no—
121C2×C42×C67—22no—
122C2×C42×C67—41no—
123C2×C42×C67—41no—
124C2×C42×C67—41no—
125C2×C42×C67C2×C414yescomplemented
126#95×C67—22no—
127#95×C67—22no—
128#95×C67—22no—
129#95×C67—22no—
130#95×C67—22no—
131#95×C67—22no—
132#95×C67—22no—
133#95×C67—22no—
134#95×C67—22no—
135#95×C67—22no—
136#95×C67—22no—
137#95×C67—22no—
138#95×C67—22no—
139#95×C67—41no—
140#95×C67—41no—
141#95×C67—41no—
142#95×C67C2×C414yescomplemented
143#95×C67C2×C414yescomplemented
144C24×C67—21no—
145C24×C67—21no—
146C24×C67—21no—
147C24×C67—21no—
148C24×C67—21no—
149C24×C67—21no—
150C24×C67—21no—
151C24×C67—21no—
152C24×C67—21no—
153C24×C67—21no—
154C24×C67—21no—
155C24×C67—21no—
156C24×C67C22×C412yes—
157C24×C67C2×D412yes—
158C24×C67C2×Q812yes—
159C24×C67C2411yescharacteristic
160C22×C4×C67—21no—
161C22×C4×C67—21no—
162C22×C4×C67—21no—
163C22×C4×C67—21no—
164C22×C4×C67—21no—
165C22×C4×C67—21no—
166C22×C4×C67—21no—
167C22×C4×C67—21no—
168C22×C4×C67—21no—
169C22×C4×C67—21no—
170C22×C4×C67—21no—
171C22×C4×C67—21no—
172C22×C4×C67—21no—
173C22×C4×C67—21no—
174C22×C4×C67—21no—
175C22×C4×C67—21no—
176C22×C4×C67—28no—
177C22×C4×C67—21no—
178C22×C4×C67—21no—
179C22×C4×C67—21no—
180C22×C4×C67—21no—
181C22×C4×C67—21no—
182C22×C4×C67—21no—
183C22×C4×C67—21no—
184C22×C4×C67—21no—
185C22×C4×C67—21no—
186C22×C4×C67—21no—
187C22×C4×C67—21no—
188C22×C4×C67—21no—
189C22×C4×C67—21no—
190C22×C4×C67—21no—
191C22×C4×C67—21no—
192C22×C4×C67—21no—
193C22×C4×C67—21no—
194C22×C4×C67—21no—
195C22×C4×C67—21no—
196C22×C4×C67—21no—
197C22×C4×C67—21no—
198C22×C4×C67—21no—
199C22×C4×C67—21no—
200C22×C4×C67—21no—
201C22×C4×C67—21no—
202C22×C4×C67—21no—
203C22×C4×C67—21no—
204C22×C4×C67—21no—
205C22×C4×C67—21no—
206C22×C4×C67—21no—
207C22×C4×C67—21no—
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—21no—
220C22×C4×C67—21no—
221C22×C4×C67—21no—
222C22×C4×C67—21no—
223C22×C4×C67—21no—
224C22×C4×C67—21no—
225C22×C4×C67—21no—
226C22×C4×C67—21no—
227C22×C4×C67—21no—
228C22×C4×C67—21no—
229C22×C4×C67—21no—
230C22×C4×C67—21no—
231C22×C4×C67—21no—
232C22×C4×C67—21no—
233C22×C4×C67—21no—
234C22×C4×C67—21no—
235C22×C4×C67—21no—
236C22×C4×C67—21no—
237C22×C4×C67—21no—
238C22×C4×C67—21no—
239C22×C4×C67—44no—
240C22×C4×C67—44no—
241C22×C4×C67—44no—
242C22×C4×C67—44no—
243C22×C4×C67—44no—
244C22×C4×C67—44no—
245C22×C4×C67C22×C412yes—
246C22×C4×C67C22×C412yes—
247C22×C4×C67C22×C412yes—
248C22×C4×C67C22×C412yes—
249C22×C4×C67C22×C412yes—
250C22×C4×C67C22×C412yes—
251C22×C4×C67C2×D412yes—
252C22×C4×C67C2×D412yes—
253C22×C4×C67C2×D412yes—
254C22×C4×C67C2×D412yes—
255C22×C4×C67C2×D412yes—
256C22×C4×C67C2×Q812yes—
257C22×C4×C67C2×Q812yes—
258C22×C4×C67#4112yes—
259C22×C4×C67#4112yes—
260C22×C4×C67#4112yes—
261C22×C4×C67#4112yes—
262C22×C4×C67#4112yes—
263C22×C4×C67#4112yes—
264C22×C4×C67#4112yes—
265C4⋊C4×C67—28no—
266C4⋊C4×C67—28no—
267C4⋊C4×C67—44no—
268C4⋊C4×C67—44no—
269C4⋊C4×C67—44no—
270C4⋊C4×C67—44no—
271C22⋊C4×C67—28no—
272C22⋊C4×C67—28no—
273C22⋊C4×C67—44no—
274C22⋊C4×C67—44no—
275C22⋊C4×C67—44no—
276C22⋊C4×C67C4⋊C4116yescomplemented
277C42×C67—28no—
278C42×C67—44no—
279C42×C67—44no—
280C42×C67—44no—
281C23×C67—22no—
282C23×C67—22no—
283C23×C67—22no—
284C23×C67—22no—
285C23×C67—22no—
286C23×C67—22no—
287C23×C67—22no—
288C23×C67—22no—
289C23×C67—22no—
290C23×C67—22no—
291C23×C67—22no—
292C23×C67—22no—
293C23×C67—22no—
294C23×C67—22no—
295C23×C67—22no—
296C23×C67—22no—
297C23×C67—22no—
298C23×C67—22no—
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—41no—
310C23×C67—41no—
311C23×C67—41no—
312C23×C67—41no—
313C23×C67—41no—
314C23×C67—41no—
315C23×C67C2×C4⋊C414yes—
316C23×C67C23×C411yescharacteristic
317C23×C67C22×D411yescharacteristic
318C23×C67C22×D411yescharacteristic
319C23×C67C22×Q811yescharacteristic
320C23×C67C2×#4111yescharacteristic
321C23×C67C2×#4111yescharacteristic
322C23×C67C2×#4111yescharacteristic
323C23×C67C2×#4111yescharacteristic
324C23×C67C2×#4111yescharacteristic
325C23×C67C2×#4111yescharacteristic
326C23×C67C2×#4111yescharacteristic
327C23×C67H(5,𝔽2)11yescharacteristic
328C23×C67H(5,𝔽2)11yescharacteristic
329C23×C67H(5,𝔽2)11yescharacteristic
330C23×C672−1+411yescharacteristic
331C2×C4×C67—22no—
332C2×C4×C67—22no—
333C2×C4×C67—22no—
334C2×C4×C67—22no—
335C2×C4×C67—22no—
336C2×C4×C67—22no—
337C2×C4×C67—22no—
338C2×C4×C67—22no—
339C2×C4×C67—22no—
340C2×C4×C67—22no—
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—22no—
353C2×C4×C67—22no—
354C2×C4×C67—22no—
355C2×C4×C67—22no—
356C2×C4×C67—22no—
357C2×C4×C67—22no—
358C2×C4×C67—22no—
359C2×C4×C67—22no—
360C2×C4×C67—22no—
361C2×C4×C67—22no—
362C2×C4×C67—22no—
363C2×C4×C67—22no—
364C2×C4×C67—22no—
365C2×C4×C67—22no—
366C2×C4×C67—22no—
367C2×C4×C67—22no—
368C2×C4×C67—22no—
369C2×C4×C67—22no—
370C2×C4×C67—22no—
371C2×C4×C67—22no—
372C2×C4×C67—22no—
373C2×C4×C67—22no—
374C2×C4×C67—22no—
375C2×C4×C67—22no—
376C2×C4×C67—22no—
377C2×C4×C67—22no—
378C2×C4×C67—22no—
379C2×C4×C67—416no—
380C2×C4×C67—41no—
381C2×C4×C67—41no—
382C2×C4×C67—41no—
383C2×C4×C67—41no—
384C2×C4×C67—41no—
385C2×C4×C67—41no—
386C2×C4×C67—41no—
387C2×C4×C67—41no—
388C2×C4×C67—41no—
389C2×C4×C67—41no—
390C2×C4×C67—41no—
391C2×C4×C67—41no—
392C2×C4×C67—41no—
393C2×C4×C67—41no—
394C2×C4×C67—41no—
395C2×C4×C67—41no—
396C2×C4×C67—41no—
397C2×C4×C67—41no—
398C2×C4×C67—41no—
399C2×C4×C67—41no—
400C2×C4×C67—41no—
401C2×C4×C67—41no—
402C2×C4×C67—41no—
403C2×C4×C67—41no—
404C2×C4×C67—41no—
405C2×C4×C67—41no—
406C2×C4×C67—41no—
407C2×C4×C67—41no—
408C2×C4×C67—41no—
409C2×C4×C67—41no—
410C2×C4×C67—41no—
411C2×C4×C67—41no—
412C2×C4×C67—41no—
413C2×C4×C67—41no—
414C2×C4×C67—41no—
415C2×C4×C67—41no—
416C2×C4×C67—41no—
417C2×C4×C67—41no—
418C2×C4×C67—41no—
419C2×C4×C67—41no—
420C2×C4×C67—41no—
421C2×C4×C67—41no—
422C2×C4×C67—41no—
423C2×C4×C67—41no—
424C2×C4×C67—41no—
425C2×C4×C67—41no—
426C2×C4×C67C2×C4⋊C414yes—
427C2×C4×C67C2×C4⋊C414yes—
428C2×C4×C67C4×D414yes—
429C2×C4×C67#12314yes—
430C22×C67—24no—
431C22×C67—24no—
432C22×C67—24no—
433C22×C67—42no—
434C22×C67—42no—
435C22×C67—42no—
436C22×C67—42no—
437C22×C67—42no—
438C22×C67—42no—
439C22×C67—42no—
440C22×C67—42no—
441C22×C67—42no—
442C22×C67—42no—
443C22×C67—42no—
444C22×C67—42no—
445C22×C67C22×C4⋊C411yescharacteristic
446C22×C67C2×C4×D411yescharacteristic
447C22×C67C4×#4111yescharacteristic
448C22×C67C4×#4111yescharacteristic
449C22×C67C4×#4111yescharacteristic
450C22×C67#51811yescharacteristic
451C22×C67#52011yescharacteristic
452C22×C67C2×#12311yescharacteristic
453C22×C67#52511yescharacteristic
454C22×C67#52511yescharacteristic
455C22×C67#52511yescharacteristic
456C22×C67#52911yescharacteristic
457C22×C67#52911yescharacteristic
458C22×C67#53311yescharacteristic
459C22×C67#53311yescharacteristic
460C22×C67#53811yescharacteristic
461C22×C67#53811yescharacteristic
462C22×C67#54211yescharacteristic
463C22×C67#54211yescharacteristic
464C22×C67D4211yescharacteristic
465C22×C67#54611yescharacteristic
466C22×C67#54611yescharacteristic
467C22×C67#54611yescharacteristic
468C22×C67#54711yescharacteristic
469C22×C67D4×Q811yescharacteristic
470C22×C67#55011yescharacteristic
471C22×C67#55111yescharacteristic
472C22×C67#55211yescharacteristic
473C22×C67#55311yescharacteristic
474C22×C67#55311yescharacteristic
475C22×C67#55411yescharacteristic
476C22×C67#55411yescharacteristic
477C22×C67#55411yescharacteristic
478C22×C67#55511yescharacteristic
479C22×C67#55611yescharacteristic
480C4×C67—24no—
481C4×C67—24no—
482C4×C67—24no—
483C4×C67—24no—
484C4×C67—42no—
485C4×C67—42no—
486C4×C67—42no—
487C4×C67—42no—
488C4×C67—42no—
489C4×C67—42no—
490C4×C67—42no—
491C4×C67—42no—
492C4×C67—81no—
493C4×C67—81no—
494#14118C6711yesmaximal, characteristic, direct product factor, Sylow
495C2×C67—44no—
496C2×C67#229611yescharacteristic
497C2×C67C4×#12311yescharacteristic
498C2×C67#233711yescharacteristic
499C2×C67D4×C4⋊C411yescharacteristic
500C2×C67#234911yescharacteristic
501C2×C67#236311yescharacteristic
502C2×C67#237311yescharacteristic
503C2×C67#241811yescharacteristic
504C2×C67#242311yescharacteristic
505C2×C67#245611yescharacteristic
506C2×C67#246511yescharacteristic
507C2×C67#246811yescharacteristic
508C2×C67#247411yescharacteristic
509C2×C67#257411yescharacteristic
510C2×C67#258711yescharacteristic
511C2×#388C2×C6711yescharacteristic
512C2×#388C2×C6711yescharacteristic
513C2×#385C2×C6711yescharacteristic
514C2×C4×C4⋊C4C2×C6711yescharacteristic, complemented
515C2×C4×C22⋊C4C2×C6711yescharacteristic
516#1444C2×C6711yescharacteristic, complemented
517#1441C2×C6711yescharacteristic, complemented
518#1439C2×C6711yescharacteristic
519#1439C2×C6711yescharacteristic
520#1436C2×C6711yescharacteristic, complemented
521#1436C2×C6711yescharacteristic, complemented
522#1436C2×C6711yescharacteristic, complemented
523C4⋊#95C2×C6711yescharacteristic, complemented
524#1434C2×C6711yescharacteristic, complemented
525C22⋊#95C2×C6711yescharacteristic
526C67#1411811yescharacteristic, direct product factor, Sylow
527C24×C4C22×C6711yescharacteristic
528C22×C4⋊C4C22×C6711yescharacteristic
529C22×C4⋊C4C22×C6711yescharacteristic
530C22×C4⋊C4C22×C6711yescharacteristic
531C22×C4⋊C4C22×C6711yescharacteristic
532C22×C4⋊C4C22×C6711yescharacteristic
533C22×C4⋊C4C22×C6711yescharacteristic
534C22×C22⋊C4C22×C6711yescharacteristic
535C22×C22⋊C4C22×C6711yescharacteristic
536C22×C22⋊C4C22×C6711yescharacteristic
537C22×C22⋊C4C22×C6711yescharacteristic
538C22×C22⋊C4C22×C6711yescharacteristic
539C22×C22⋊C4C22×C6711yescharacteristic
540C22×C42C22×C6711yescharacteristic
541C22×C42C22×C6711yescharacteristic
542C22×C42C22×C6711yescharacteristic
543C22×C42C22×C6711yescharacteristic
544#388—24no—
545#388C4×C6718yescomplemented
546#385—24no—
547C4×C4⋊C4—24no—
548C4×C22⋊C4—24no—
549C2×#95C22×C6711yescharacteristic
550C2×#95C22×C6711yescharacteristic
551C2×#95C22×C6711yescharacteristic
552C2×#95C22×C6711yescharacteristic
553C2×#95C22×C6711yescharacteristic
554C2×#95C22×C6711yescharacteristic
555C2×#95C22×C6711yescharacteristic
556C2×#95C22×C6711yescharacteristic
557C2×#95C22×C6711yescharacteristic
558C2×#95C22×C6711yescharacteristic
559C2×#95C22×C6711yescharacteristic
560C2×#95C22×C6711yescharacteristic
561C2×#95C22×C6711yescharacteristic
562C2×#95C22×C6711yescharacteristic
563C2×#95C22×C6711yescharacteristic
564C2×#95C22×C6711yescharacteristic
565C2×#95C22×C6711yescharacteristic
566C2×#95C22×C6711yescharacteristic
567C25C23×C6711yescharacteristic
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—22no—
573C23×C4—41no—
574C23×C4—41no—
575C23×C4C23×C6711yescharacteristic
576C23×C4C23×C6711yescharacteristic
577C23×C4C23×C6711yescharacteristic
578C23×C4C23×C6711yescharacteristic
579C23×C4C23×C6711yescharacteristic
580C23×C4C23×C6711yescharacteristic
581C23×C4C23×C6711yescharacteristic
582C23×C4C23×C6711yescharacteristic
583C23×C4C23×C6711yescharacteristic
584C23×C4C23×C6711yescharacteristic
585C23×C4C23×C6711yescharacteristic
586C23×C4C23×C6711yescharacteristic
587C23×C4C23×C6711yescharacteristic
588C23×C4C23×C6711yescharacteristic
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—41no—
600C2×C4⋊C4—41no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4C2×C4×C6714yescomplemented
606C2×C4⋊C4D4×C6714yes—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—41no—
617C2×C22⋊C4—41no—
618C2×C22⋊C4—41no—
619C2×C22⋊C4—41no—
620C2×C22⋊C4C2×C4×C6714yes—
621C2×C22⋊C4C2×C4×C6714yes—
622C2×C22⋊C4C2×C4×C6714yes—
623C2×C22⋊C4D4×C6714yes—
624C2×C22⋊C4Q8×C6714yes—
625C2×C42—22no—
626C2×C42—22no—
627C2×C42—22no—
628C2×C42—22no—
629C2×C42—22no—
630C2×C42—22no—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—41no—
634C2×C42—41no—
635C2×C42—41no—
636C2×C42C2×C4×C6714yescomplemented
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—22no—
648#95—22no—
649#95—22no—
650#95—41no—
651#95—41no—
652#95—41no—
653#95C2×C4×C6714yescomplemented
654#95C2×C4×C6714yescomplemented
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C22×C4×C6712yes—
668C24C2×D4×C6712yes—
669C24C2×Q8×C6712yes—
670C24C24×C6711yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—28no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4C22×C4×C6712yes—
757C22×C4C22×C4×C6712yes—
758C22×C4C22×C4×C6712yes—
759C22×C4C22×C4×C6712yes—
760C22×C4C22×C4×C6712yes—
761C22×C4C22×C4×C6712yes—
762C22×C4C2×D4×C6712yes—
763C22×C4C2×D4×C6712yes—
764C22×C4C2×D4×C6712yes—
765C22×C4C2×D4×C6712yes—
766C22×C4C2×D4×C6712yes—
767C22×C4C2×Q8×C6712yes—
768C22×C4C2×Q8×C6712yes—
769C22×C4#41×C6712yes—
770C22×C4#41×C6712yes—
771C22×C4#41×C6712yes—
772C22×C4#41×C6712yes—
773C22×C4#41×C6712yes—
774C22×C4#41×C6712yes—
775C22×C4#41×C6712yes—
776C4⋊C4—28no—
777C4⋊C4—28no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C22⋊C4—28no—
783C22⋊C4—28no—
784C22⋊C4—44no—
785C22⋊C4—44no—
786C22⋊C4—44no—
787C22⋊C4C4⋊C4×C67116yescomplemented
788C42—28no—
789C42—44no—
790C42—44no—
791C42—44no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C4⋊C4×C6714yes—
827C23C23×C4×C6711yescharacteristic
828C23C22×D4×C6711yescharacteristic
829C23C22×D4×C6711yescharacteristic
830C23C22×Q8×C6711yescharacteristic
831C23C2×#41×C6711yescharacteristic
832C23C2×#41×C6711yescharacteristic
833C23C2×#41×C6711yescharacteristic
834C23C2×#41×C6711yescharacteristic
835C23C2×#41×C6711yescharacteristic
836C23C2×#41×C6711yescharacteristic
837C23C2×#41×C6711yescharacteristic
838C23H(5,𝔽2)×C6711yescharacteristic
839C23H(5,𝔽2)×C6711yescharacteristic
840C23H(5,𝔽2)×C6711yescharacteristic
841C232−1+4×C6711yescharacteristic
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—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—416no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4C2×C4⋊C4×C6714yes—
938C2×C4C2×C4⋊C4×C6714yes—
939C2×C4C4×D4×C6714yes—
940C2×C4#123×C6714yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C4⋊C4×C6711yescharacteristic
957C22C2×C4×D4×C6711yescharacteristic
958C22C4×#41×C6711yescharacteristic
959C22C4×#41×C6711yescharacteristic
960C22C4×#41×C6711yescharacteristic
961C22#518×C6711yescharacteristic
962C22#520×C6711yescharacteristic
963C22C2×#123×C6711yescharacteristic
964C22#525×C6711yescharacteristic
965C22#525×C6711yescharacteristic
966C22#525×C6711yescharacteristic
967C22#529×C6711yescharacteristic
968C22#529×C6711yescharacteristic
969C22#533×C6711yescharacteristic
970C22#533×C6711yescharacteristic
971C22#538×C6711yescharacteristic
972C22#538×C6711yescharacteristic
973C22#542×C6711yescharacteristic
974C22#542×C6711yescharacteristic
975C22D42×C6711yescharacteristic
976C22#546×C6711yescharacteristic
977C22#546×C6711yescharacteristic
978C22#546×C6711yescharacteristic
979C22#547×C6711yescharacteristic
980C22D4×Q8×C6711yescharacteristic
981C22#550×C6711yescharacteristic
982C22#551×C6711yescharacteristic
983C22#552×C6711yescharacteristic
984C22#553×C6711yescharacteristic
985C22#553×C6711yescharacteristic
986C22#554×C6711yescharacteristic
987C22#554×C6711yescharacteristic
988C22#554×C6711yescharacteristic
989C22#555×C6711yescharacteristic
990C22#556×C6711yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—24no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—81no—
1004C4—81no—
1005C2—44no—
1006C2C67×#229611yescharacteristic
1007C2C4×#123×C6711yescharacteristic
1008C2C67×#233711yescharacteristic
1009C2D4×C4⋊C4×C6711yescharacteristic
1010C2C67×#234911yescharacteristic
1011C2C67×#236311yescharacteristic
1012C2C67×#237311yescharacteristic
1013C2C67×#241811yescharacteristic
1014C2C67×#242311yescharacteristic
1015C2C67×#245611yescharacteristic
1016C2C67×#246511yescharacteristic
1017C2C67×#246811yescharacteristic
1018C2C67×#247411yescharacteristic
1019C2C67×#257411yescharacteristic
1020C2C67×#258711yescharacteristic
subgroupG/H
center, socleC24×C67C24
commutatorC23C23×C4×C67
Frattini, cosocleC24C24×C67
prime radicalC25×C67C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C67 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C4×C4⋊C4×C67C2semidirect
6. C67×#1444C2semidirect
7. C67×#1441C2semidirect
10. C67×#1436C2semidirect
11. C67×#1436C2semidirect
12. C67×#1436C2semidirect
13. C67×C4⋊#95C2semidirect
14. C67×#1434C2semidirect
34. #388×C67C4semidirect
94. C2×C4⋊C4×C67C2×C4semidirect
125. C2×C42×C67C2×C4semidirect
142. #95×C67C2×C4semidirect
143. #95×C67C2×C4semidirect
276. C22⋊C4×C67C4⋊C4semidirect
494. #14118C67direct (N × H)
514. C2×C4×C4⋊C4C2×C67semidirect
516. #1444C2×C67semidirect
517. #1441C2×C67semidirect
520. #1436C2×C67semidirect
521. #1436C2×C67semidirect
522. #1436C2×C67semidirect
523. C4⋊#95C2×C67semidirect
524. #1434C2×C67semidirect
526. C67#14118direct (N × H)
545. #388C4×C67semidirect
605. C2×C4⋊C4C2×C4×C67semidirect
636. C2×C42C2×C4×C67semidirect
653. #95C2×C4×C67semidirect
654. #95C2×C4×C67semidirect
787. C22⋊C4C4⋊C4×C67semidirect

Maximal subgroups

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

subgroupindex
C2×#388×C672
C2×#385×C672
C2×C4×C4⋊C4×C672
C2×C4×C22⋊C4×C672
C67×#14442
C67×#14412
C67×#14392
C67×#14362
C67×C4⋊#952
C67×#14342
C67×C22⋊#952
#1411867