Finite Group Databasebeta

← C67×#24034 #30703285

Subgroups — C67×#24034 #30703285

Order 17152.

1380 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C67C211yesmaximal, characteristic
2C2×#482×C67C211yesmaximal, characteristic, complemented
3C2×#416×C67C211yesmaximal, characteristic, complemented
4C67×#2485C211yesmaximal, characteristic, complemented
5C67×#2041C211yesmaximal, characteristic, complemented
6C67×#2041C211yesmaximal, characteristic, complemented
7C67×#2034C211yesmaximal, characteristic, complemented
8C67×#2033C211yesmaximal, characteristic, complemented
9C67×#1893C211yesmaximal, characteristic, complemented
10C67×#1869C211yesmaximal, characteristic, complemented
11C67×#1865C211yesmaximal, characteristic, complemented
12C67×#1863C211yesmaximal, characteristic, complemented
13C67×#1788C211yesmaximal, characteristic, complemented
14C67×#1788C211yesmaximal, characteristic, complemented
15C67×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C67C2211yescharacteristic
17C22×#41×C67C2211yescharacteristic
18C23×C8×C67C2211yescharacteristic
19#550×C67—24no—
20#550×C67—24no—
21C2×#127×C67—21no—
22C2×#127×C67C2211yescharacteristic
23C2×#121×C67—21no—
24C2×#121×C67—21no—
25C2×#121×C67C2211yescharacteristic
26C2×#121×C67C2211yescharacteristic
27C2×C4×Q8×C67C2211yescharacteristic
28C2×C4×D4×C67—21no—
29C2×C4×D4×C67C2211yescharacteristic
30C2×#117×C67C2211yescharacteristic
31#482×C67—24no—
32C2×#107×C67C2211yescharacteristic
33C2×#106×C67C2211yescharacteristic
34#416×C67—24no—
35C2×#103×C67C2211yescharacteristic
36C2×#103×C67C2211yescharacteristic
37C2×#103×C67C2211yescharacteristic
38C2×#103×C67C2211yescharacteristic
39C2×#102×C67C2211yescharacteristic
40C2×#102×C67C2211yescharacteristic
41C2×#102×C67C2211yescharacteristic
42C2×#102×C67C2211yescharacteristic
43C2×#102×C67C2211yescharacteristic
44C2×#102×C67C2211yescharacteristic
45C2×#102×C67C2211yescharacteristic
46C2×#102×C67C2211yescharacteristic
47C2×C22⋊C8×C67C2211yescharacteristic
48C2×C22⋊C8×C67C2211yescharacteristic
49C2×C22⋊C8×C67C2211yescharacteristic
50#397×C67—21no—
51#394×C67—21no—
52#389×C67C2211yescharacteristic
53#389×C67C2211yescharacteristic
54#388×C67—21no—
55#387×C67—21no—
56#380×C67C2211yescharacteristic
57#380×C67C2211yescharacteristic
58#380×C67C2211yescharacteristic
59#340×C67C2211yescharacteristic
60#340×C67C2211yescharacteristic
61#336×C67C2211yescharacteristic
62#336×C67C2211yescharacteristic
63C2×#41×C67—22no—
64C2×#41×C67—22no—
65C2×#41×C67—22no—
66C2×#41×C67—22no—
67C2×#41×C67—22no—
68C2×#41×C67—22no—
69C2×#41×C67—22no—
70C2×#41×C67—41no—
71C2×#41×C67—41no—
72C2×#41×C67—41no—
73C2×#41×C67—41no—
74C2×#41×C67D414yes—
75C22×Q8×C67C2311yescharacteristic
76C22×D4×C67—21no—
77C22×D4×C67—21no—
78C22×D4×C67—21no—
79C22×D4×C67—21no—
80C22×D4×C67—21no—
81C22×D4×C67—21no—
82C22×D4×C67D411yescharacteristic
83C22×D4×C67C2311yescharacteristic
84C22×D4×C67C2311yescharacteristic
85C23×C4×C67—21no—
86C23×C4×C67—21no—
87C23×C4×C67C2311yescharacteristic
88C23×C4×C67C2311yescharacteristic
89C22×C8×C67—22no—
90C22×C8×C67—41no—
91C22×C8×C67—41no—
92C22×C8×C67C2311yescharacteristic
93C22×C8×C67C2311yescharacteristic
94C22×C8×C67C2311yescharacteristic
95C22×C8×C67C2311yescharacteristic
96#127×C67—28no—
97#127×C67—22no—
98#127×C67—22no—
99#121×C67—28no—
100#121×C67—28no—
101#121×C67—22no—
102#121×C67—22no—
103#121×C67—22no—
104#121×C67D414yes—
105C4×Q8×C67—22no—
106C4×Q8×C67—22no—
107C4×D4×C67—28no—
108C4×D4×C67—22no—
109C4×D4×C67—22no—
110#117×C67—22no—
111#117×C67—22no—
112C2×C4⋊C4×C67—21no—
113C2×C4⋊C4×C67—21no—
114C2×C4⋊C4×C67—21no—
115C2×C4⋊C4×C67D411yescharacteristic
116C2×C4⋊C4×C67C2311yescharacteristic
117C2×C4⋊C4×C67C2311yescharacteristic
118C2×C4⋊C4×C67C2311yescharacteristic
119C2×C4⋊C4×C67C2311yescharacteristic
120C2×C4⋊C4×C67C2311yescharacteristic
121C2×C22⋊C4×C67—21no—
122C2×C22⋊C4×C67—21no—
123C2×C22⋊C4×C67—21no—
124C2×C22⋊C4×C67—21no—
125C2×C22⋊C4×C67—21no—
126C2×C22⋊C4×C67—21no—
127C2×C22⋊C4×C67D411yescharacteristic
128C2×C22⋊C4×C67D411yescharacteristic
129C2×C42×C67—21no—
130C2×C42×C67—21no—
131C2×C42×C67C2311yescharacteristic
132#107×C67—22no—
133#106×C67—22no—
134#103×C67—22no—
135#103×C67—22no—
136#103×C67—22no—
137#103×C67—22no—
138#102×C67—22no—
139#102×C67—22no—
140#102×C67—22no—
141#102×C67—22no—
142#102×C67—41no—
143#102×C67—41no—
144#102×C67—41no—
145#102×C67—41no—
146C22⋊C8×C67—22no—
147C22⋊C8×C67—41no—
148C22⋊C8×C67—41no—
149#95×C67—21no—
150#95×C67—21no—
151#95×C67—21no—
152#95×C67—21no—
153#95×C67—21no—
154C24×C67—21no—
155C24×C67—21no—
156C24×C67C2×D411yescharacteristic
157C24×C67C2×D411yescharacteristic
158#41×C67—28no—
159#41×C67—44no—
160#41×C67—44no—
161#41×C67—44no—
162#41×C67—44no—
163#41×C67—44no—
164#41×C67—44no—
165#41×C67—44no—
166C2×Q8×C67—21no—
167C2×Q8×C67—21no—
168C2×Q8×C67—21no—
169C2×Q8×C67C2×D412yes—
170C2×Q8×C67#4112yes—
171C2×Q8×C67#4112yes—
172C2×D4×C67—24no—
173C2×D4×C67—24no—
174C2×D4×C67—22no—
175C2×D4×C67—24no—
176C2×D4×C67—24no—
177C2×D4×C67—24no—
178C2×D4×C67—24no—
179C2×D4×C67—22no—
180C2×D4×C67—21no—
181C2×D4×C67—21no—
182C2×D4×C67—21no—
183C2×D4×C67—21no—
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—41no—
191C2×D4×C67—42no—
192C2×D4×C67—42no—
193C2×D4×C67—42no—
194C2×D4×C67—42no—
195C2×D4×C67—42no—
196C2×D4×C67—42no—
197C2×D4×C67—81no—
198C2×D4×C67—81no—
199C2×D4×C67—81no—
200C2×D4×C67—81no—
201C2×D4×C67—81no—
202C2×D4×C67—81no—
203C2×D4×C67C2×D412yes—
204C2×D4×C67C2×D412yes—
205C22×C4×C67—21no—
206C22×C4×C67—21no—
207C22×C4×C67—21no—
208C22×C4×C67—21no—
209C22×C4×C67—21no—
210C22×C4×C67—24no—
211C22×C4×C67—21no—
212C22×C4×C67—24no—
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—42no—
224C22×C4×C67—42no—
225C22×C4×C67—42no—
226C22×C4×C67—42no—
227C22×C4×C67C2×D411yescharacteristic
228C22×C4×C67C2×D411yescharacteristic
229C22×C4×C67C2×D411yescharacteristic
230C22×C4×C67C2×D412yes—
231C22×C4×C67C2×D412yes—
232C22×C4×C67C2×D411yescharacteristic
233C22×C4×C67C2411yescharacteristic
234C2×C8×C67—21no—
235C2×C8×C67—21no—
236C2×C8×C67—21no—
237C2×C8×C67—21no—
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—44no—
247C4⋊C4×C67—24no—
248C4⋊C4×C67—22no—
249C4⋊C4×C67—21no—
250C4⋊C4×C67—21no—
251C4⋊C4×C67—21no—
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—42no—
259C4⋊C4×C67—81no—
260C4⋊C4×C67C2×D412yes—
261C22⋊C4×C67—24no—
262C22⋊C4×C67—22no—
263C22⋊C4×C67—24no—
264C22⋊C4×C67—22no—
265C22⋊C4×C67—42no—
266C22⋊C4×C67—42no—
267C22⋊C4×C67—81no—
268C22⋊C4×C67—81no—
269C42×C67—24no—
270C42×C67—21no—
271C42×C67—21no—
272C42×C67—42no—
273C23×C67—21no—
274C23×C67—21no—
275C23×C67—21no—
276C23×C67—21no—
277C23×C67—21no—
278C23×C67—21no—
279C23×C67—21no—
280C23×C67—22no—
281C23×C67—22no—
282C23×C67—21no—
283C23×C67—21no—
284C23×C67—21no—
285C23×C67—21no—
286C23×C67—21no—
287C23×C67—21no—
288C23×C67—41no—
289C23×C67—41no—
290C23×C67—41no—
291C23×C67—41no—
292C23×C67—41no—
293C23×C67—41no—
294C23×C67—41no—
295C23×C67—41no—
296C23×C67—41no—
297C23×C67—41no—
298C23×C67—41no—
299C23×C67—41no—
300C23×C67#12012yes—
301C23×C67C22×D411yescharacteristic
302Q8×C67—22no—
303Q8×C67—22no—
304Q8×C67—22no—
305Q8×C67#12314yes—
306D4×C67—22no—
307D4×C67—22no—
308D4×C67—22no—
309D4×C67—22no—
310D4×C67—44no—
311D4×C67—48no—
312D4×C67—48no—
313D4×C67—48no—
314D4×C67—41no—
315D4×C67—41no—
316D4×C67—41no—
317D4×C67—41no—
318D4×C67—84no—
319D4×C67—84no—
320D4×C67—84no—
321C2×C4×C67—21no—
322C2×C4×C67—22no—
323C2×C4×C67—21no—
324C2×C4×C67—21no—
325C2×C4×C67—22no—
326C2×C4×C67—22no—
327C2×C4×C67—21no—
328C2×C4×C67—22no—
329C2×C4×C67—22no—
330C2×C4×C67—22no—
331C2×C4×C67—22no—
332C2×C4×C67—21no—
333C2×C4×C67—22no—
334C2×C4×C67—21no—
335C2×C4×C67—21no—
336C2×C4×C67—21no—
337C2×C4×C67—21no—
338C2×C4×C67—21no—
339C2×C4×C67—48no—
340C2×C4×C67—48no—
341C2×C4×C67—41no—
342C2×C4×C67—41no—
343C2×C4×C67—41no—
344C2×C4×C67—41no—
345C2×C4×C67—41no—
346C2×C4×C67—41no—
347C2×C4×C67—41no—
348C2×C4×C67—41no—
349C2×C4×C67—41no—
350C2×C4×C67—41no—
351C2×C4×C67—41no—
352C2×C4×C67—41no—
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#12012yes—
360C2×C4×C67#13512yes—
361C2×C4×C67C22×D411yescharacteristic
362C2×C4×C67C22×D411yescharacteristic
363C2×C4×C67C2×#4111yescharacteristic
364C2×C4×C67C2×#4111yescharacteristic
365C2×C4×C67H(5,𝔽2)11yescharacteristic
366C2×C4×C67H(5,𝔽2)11yescharacteristic
367C8×C67—41no—
368C8×C67—41no—
369C8×C67—41no—
370C8×C67—41no—
371C22×C67—22no—
372C22×C67—22no—
373C22×C67—22no—
374C22×C67—41no—
375C22×C67—41no—
376C22×C67—41no—
377C22×C67—41no—
378C22×C67—42no—
379C22×C67—42no—
380C22×C67—41no—
381C22×C67—41no—
382C22×C67—42no—
383C22×C67—42no—
384C22×C67—41no—
385C22×C67—42no—
386C22×C67—42no—
387C22×C67—41no—
388C22×C67—41no—
389C22×C67—41no—
390C22×C67—41no—
391C22×C67—81no—
392C22×C67—81no—
393C22×C67—81no—
394C22×C67—81no—
395C22×C67—81no—
396C22×C67—81no—
397C22×C67—81no—
398C22×C67—81no—
399C22×C67C2×#12011yescharacteristic
400C22×C67#54611yescharacteristic
401C22×C67#54611yescharacteristic
402C22×C67C2×#13511yescharacteristic
403C22×C67#57511yescharacteristic
404C22×C67#57611yescharacteristic
405C22×C67#57711yescharacteristic
406C4×C67—22no—
407C4×C67—24no—
408C4×C67—22no—
409C4×C67—41no—
410C4×C67—41no—
411C4×C67—42no—
412C4×C67—81no—
413C4×C67—81no—
414C4×C67—81no—
415C4×C67—81no—
416C4×C67C2×#12311yescharacteristic
417C4×C67#53411yescharacteristic
418C4×C67#54611yescharacteristic
419C4×C67#54611yescharacteristic
420#24034C6711yesmaximal, characteristic, direct product factor, Sylow
421C2×C67—42no—
422C2×C67—81no—
423C2×C67—82no—
424C2×C67—82no—
425C2×C67#240511yescharacteristic
426C2×C67#300211yescharacteristic
427C2×C67#301211yescharacteristic
428C2×C67#330411yescharacteristic
429C2×C67#330511yescharacteristic
430C2×C67#330911yescharacteristic
431C2×C67#331711yescharacteristic
432C2×#550C2×C6711yescharacteristic
433C2×#482C2×C6711yescharacteristic, complemented
434C2×#416C2×C6711yescharacteristic, complemented
435#2485C2×C6711yescharacteristic, complemented
436#2041C2×C6711yescharacteristic, complemented
437#2041C2×C6711yescharacteristic, complemented
438#2034C2×C6711yescharacteristic, complemented
439#2033C2×C6711yescharacteristic, complemented
440#1893C2×C6711yescharacteristic, complemented
441#1869C2×C6711yescharacteristic, complemented
442#1865C2×C6711yescharacteristic, complemented
443#1863C2×C6711yescharacteristic, complemented
444#1788C2×C6711yescharacteristic, complemented
445#1788C2×C6711yescharacteristic, complemented
446#1788C2×C6711yescharacteristic, complemented
447C67#2403411yescharacteristic, direct product factor, Sylow
448C22×#41C22×C6711yescharacteristic
449C22×#41C22×C6711yescharacteristic
450C23×C8C22×C6711yescharacteristic
451#550—24no—
452#550—24no—
453C2×#127—21no—
454C2×#127C22×C6711yescharacteristic
455C2×#121—21no—
456C2×#121—21no—
457C2×#121C22×C6711yescharacteristic
458C2×#121C22×C6711yescharacteristic
459C2×C4×Q8C22×C6711yescharacteristic
460C2×C4×D4—21no—
461C2×C4×D4C22×C6711yescharacteristic
462C2×#117C22×C6711yescharacteristic
463#482—24no—
464C2×#107C22×C6711yescharacteristic
465C2×#106C22×C6711yescharacteristic
466#416—24no—
467C2×#103C22×C6711yescharacteristic
468C2×#103C22×C6711yescharacteristic
469C2×#103C22×C6711yescharacteristic
470C2×#103C22×C6711yescharacteristic
471C2×#102C22×C6711yescharacteristic
472C2×#102C22×C6711yescharacteristic
473C2×#102C22×C6711yescharacteristic
474C2×#102C22×C6711yescharacteristic
475C2×#102C22×C6711yescharacteristic
476C2×#102C22×C6711yescharacteristic
477C2×#102C22×C6711yescharacteristic
478C2×#102C22×C6711yescharacteristic
479C2×C22⋊C8C22×C6711yescharacteristic
480C2×C22⋊C8C22×C6711yescharacteristic
481C2×C22⋊C8C22×C6711yescharacteristic
482#397—21no—
483#394—21no—
484#389C22×C6711yescharacteristic
485#389C22×C6711yescharacteristic
486#388—21no—
487#387—21no—
488#380C22×C6711yescharacteristic
489#380C22×C6711yescharacteristic
490#380C22×C6711yescharacteristic
491#340C22×C6711yescharacteristic
492#340C22×C6711yescharacteristic
493#336C22×C6711yescharacteristic
494#336C22×C6711yescharacteristic
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41D4×C6714yes—
507C22×Q8C23×C6711yescharacteristic
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4D4×C6711yescharacteristic
515C22×D4C23×C6711yescharacteristic
516C22×D4C23×C6711yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C23×C6711yescharacteristic
520C23×C4C23×C6711yescharacteristic
521C22×C8—22no—
522C22×C8—41no—
523C22×C8—41no—
524C22×C8C23×C6711yescharacteristic
525C22×C8C23×C6711yescharacteristic
526C22×C8C23×C6711yescharacteristic
527C22×C8C23×C6711yescharacteristic
528#127—28no—
529#127—22no—
530#127—22no—
531#121—28no—
532#121—28no—
533#121—22no—
534#121—22no—
535#121—22no—
536#121D4×C6714yes—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×D4—28no—
540C4×D4—22no—
541C4×D4—22no—
542#117—22no—
543#117—22no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4D4×C6711yescharacteristic
548C2×C4⋊C4C23×C6711yescharacteristic
549C2×C4⋊C4C23×C6711yescharacteristic
550C2×C4⋊C4C23×C6711yescharacteristic
551C2×C4⋊C4C23×C6711yescharacteristic
552C2×C4⋊C4C23×C6711yescharacteristic
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4D4×C6711yescharacteristic
560C2×C22⋊C4D4×C6711yescharacteristic
561C2×C42—21no—
562C2×C42—21no—
563C2×C42C23×C6711yescharacteristic
564#107—22no—
565#106—22no—
566#103—22no—
567#103—22no—
568#103—22no—
569#103—22no—
570#102—22no—
571#102—22no—
572#102—22no—
573#102—22no—
574#102—41no—
575#102—41no—
576#102—41no—
577#102—41no—
578C22⋊C8—22no—
579C22⋊C8—41no—
580C22⋊C8—41no—
581#95—21no—
582#95—21no—
583#95—21no—
584#95—21no—
585#95—21no—
586C24—21no—
587C24—21no—
588C24C2×D4×C6711yescharacteristic
589C24C2×D4×C6711yescharacteristic
590#41—28no—
591#41—44no—
592#41—44no—
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8C2×D4×C6712yes—
602C2×Q8#41×C6712yes—
603C2×Q8#41×C6712yes—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—22no—
607C2×D4—24no—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—41no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4C2×D4×C6712yes—
636C2×D4C2×D4×C6712yes—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—24no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4C2×D4×C6711yescharacteristic
660C22×C4C2×D4×C6711yescharacteristic
661C22×C4C2×D4×C6711yescharacteristic
662C22×C4C2×D4×C6712yes—
663C22×C4C2×D4×C6712yes—
664C22×C4C2×D4×C6711yescharacteristic
665C22×C4C24×C6711yescharacteristic
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—44no—
679C4⋊C4—24no—
680C4⋊C4—22no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—42no—
691C4⋊C4—81no—
692C4⋊C4C2×D4×C6712yes—
693C22⋊C4—24no—
694C22⋊C4—22no—
695C22⋊C4—24no—
696C22⋊C4—22no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—81no—
700C22⋊C4—81no—
701C42—24no—
702C42—21no—
703C42—21no—
704C42—42no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—22no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23#120×C6712yes—
733C23C22×D4×C6711yescharacteristic
734Q8—22no—
735Q8—22no—
736Q8—22no—
737Q8#123×C6714yes—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—44no—
743D4—48no—
744D4—48no—
745D4—48no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—84no—
751D4—84no—
752D4—84no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—48no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4#120×C6712yes—
792C2×C4#135×C6712yes—
793C2×C4C22×D4×C6711yescharacteristic
794C2×C4C22×D4×C6711yescharacteristic
795C2×C4C2×#41×C6711yescharacteristic
796C2×C4C2×#41×C6711yescharacteristic
797C2×C4H(5,𝔽2)×C6711yescharacteristic
798C2×C4H(5,𝔽2)×C6711yescharacteristic
799C8—41no—
800C8—41no—
801C8—41no—
802C8—41no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—42no—
818C22—42no—
819C22—41no—
820C22—41no—
821C22—42no—
822C22—42no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22C2×#120×C6711yescharacteristic
832C22#546×C6711yescharacteristic
833C22#546×C6711yescharacteristic
834C22C2×#135×C6711yescharacteristic
835C22#575×C6711yescharacteristic
836C22#576×C6711yescharacteristic
837C22#577×C6711yescharacteristic
838C4—22no—
839C4—24no—
840C4—22no—
841C4—41no—
842C4—42no—
843C4—41no—
844C4—81no—
845C4—81no—
846C4—81no—
847C4—81no—
848C4C2×#123×C6711yescharacteristic
849C4#534×C6711yescharacteristic
850C4#546×C6711yescharacteristic
851C4#546×C6711yescharacteristic
852C2—42no—
853C2—81no—
854C2—82no—
855C2—82no—
856C2C67×#240511yescharacteristic
857C2C67×#300211yescharacteristic
858C2C67×#301211yescharacteristic
859C2C67×#330411yescharacteristic
860C2C67×#330511yescharacteristic
861C2C67×#330911yescharacteristic
862C2C67×#331711yescharacteristic
subgroupG/H
center, socleC23×C67C22×D4
commutator, Frattini, cosocleC22×C4C24×C67
prime radicalC2×#550×C67C2
LCSG ▷ C22×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×#482×C67C2semidirect
3. C2×#416×C67C2semidirect
4. C67×#2485C2semidirect
5. C67×#2041C2semidirect
6. C67×#2041C2semidirect
7. C67×#2034C2semidirect
8. C67×#2033C2semidirect
9. C67×#1893C2semidirect
10. C67×#1869C2semidirect
11. C67×#1865C2semidirect
12. C67×#1863C2semidirect
13. C67×#1788C2semidirect
14. C67×#1788C2semidirect
15. C67×#1788C2semidirect
420. #24034C67direct (N × H)
433. C2×#482C2×C67semidirect
434. C2×#416C2×C67semidirect
435. #2485C2×C67semidirect
436. #2041C2×C67semidirect
437. #2041C2×C67semidirect
438. #2034C2×C67semidirect
439. #2033C2×C67semidirect
440. #1893C2×C67semidirect
441. #1869C2×C67semidirect
442. #1865C2×C67semidirect
443. #1863C2×C67semidirect
444. #1788C2×C67semidirect
445. #1788C2×C67semidirect
446. #1788C2×C67semidirect
447. C67#24034direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#550×C672
C2×#482×C672
C2×#416×C672
C67×#24852
C67×#20412
C67×#20342
C67×#20332
C67×#18932
C67×#18692
C67×#18652
C67×#18632
C67×#17882
#2403467